Finite Group Databasebeta

← C3×#15320 #10633927

Subgroups — C3×#15320 #10633927

Order 768.

2830 conjugacy classes of subgroups.

The subgroup lattice has 1520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#121C211yesmaximal, characteristic, complemented
2C2×C3×#394C211yesmaximal, characteristic, complemented
3C2×C3×#392C211yesmaximal, characteristic, complemented
4C2×C3×#392C211yesmaximal, characteristic, complemented
5C2×C3×#392C211yesmaximal, characteristic, complemented
6C2×C3×#390C211yesmaximal, characteristic, complemented
7C2×C3×#388C211yesmaximal, characteristic, complemented
8C2×C3×#386C211yesmaximal, characteristic, complemented
9C3×#1441C211yesmaximal, characteristic, complemented
10C3×#1440C211yesmaximal, characteristic, complemented
11C3×#1438C211yesmaximal, characteristic, complemented
12C3×#1438C211yesmaximal, characteristic, complemented
13C3×#1438C211yesmaximal, characteristic, complemented
14C3×#1437C211yesmaximal, characteristic, complemented
15C3×C22⋊#95C211yesmaximal, characteristic, complemented
16#15320C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×D4C2211yescharacteristic
18C23×C3×D4C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C23×C3×D4C2211yescharacteristic
21C23×C3×D4C2211yescharacteristic
22C23×C3×D4C2211yescharacteristic
23C24×C3×C4C2211yescharacteristic
24C2×C3×#121—24no—
25C2×C3×#121—24no—
26C2×C3×#121—24no—
27C22×C3×C4⋊C4C2211yescharacteristic
28C22×C3×C4⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×C3×C22⋊C4C2211yescharacteristic
32C22×C3×C22⋊C4C2211yescharacteristic
33C22×C3×C22⋊C4C2211yescharacteristic
34C22×C3×C22⋊C4C2211yescharacteristic
35C22×C3×C22⋊C4C2211yescharacteristic
36C22×C3×C22⋊C4C2211yescharacteristic
37C22×C3×C22⋊C4C2211yescharacteristic
38C22×C3×C22⋊C4C2211yescharacteristic
39C22×C3×C22⋊C4C2211yescharacteristic
40C22×C3×C22⋊C4C2211yescharacteristic
41C22×C3×C22⋊C4C2211yescharacteristic
42C22×C3×C22⋊C4C2211yescharacteristic
43C22×C3×C22⋊C4C2211yescharacteristic
44C22×C3×C42C2211yescharacteristic
45C3×#394—24no—
46C3×#392—24no—
47C3×#392—24no—
48C3×#392—24no—
49C3×#390—24no—
50C3×#388—24no—
51C3×#386—24no—
52C2×C3×#95C2211yescharacteristic
53C2×C3×#95C2211yescharacteristic
54C2×C3×#95C2211yescharacteristic
55C2×C3×#95C2211yescharacteristic
56C2×C3×#95C2211yescharacteristic
57C2×C3×#95C2211yescharacteristic
58C2×C3×#95C2211yescharacteristic
59C2×C3×#95C2211yescharacteristic
60C2×C3×#95C2211yescharacteristic
61C2×C3×#95C2211yescharacteristic
62C22×#121C2×C311yescharacteristic, complemented
63C2×#394C2×C311yescharacteristic, complemented
64C2×#392C2×C311yescharacteristic, complemented
65C2×#392C2×C311yescharacteristic, complemented
66C2×#392C2×C311yescharacteristic, complemented
67C2×#390C2×C311yescharacteristic, complemented
68C2×#388C2×C311yescharacteristic, complemented
69C2×#386C2×C311yescharacteristic, complemented
70#1441C2×C311yescharacteristic, complemented
71#1440C2×C311yescharacteristic, complemented
72#1438C2×C311yescharacteristic, complemented
73#1438C2×C311yescharacteristic, complemented
74#1438C2×C311yescharacteristic, complemented
75#1437C2×C311yescharacteristic, complemented
76C22⋊#95C2×C311yescharacteristic, complemented
77C25×C3C2311yescharacteristic
78C25×C3C2311yescharacteristic
79C25×C3C2311yescharacteristic
80C25×C3C2311yescharacteristic
81C22×C3×D4—22no—
82C22×C3×D4—22no—
83C22×C3×D4—22no—
84C22×C3×D4—22no—
85C22×C3×D4—22no—
86C22×C3×D4—22no—
87C22×C3×D4—22no—
88C22×C3×D4—22no—
89C22×C3×D4—22no—
90C22×C3×D4—22no—
91C22×C3×D4—22no—
92C22×C3×D4—22no—
93C22×C3×D4—22no—
94C22×C3×D4—22no—
95C22×C3×D4—22no—
96C22×C3×D4—22no—
97C22×C3×D4—22no—
98C22×C3×D4—22no—
99C22×C3×D4—22no—
100C22×C3×D4—22no—
101C22×C3×D4—22no—
102C22×C3×D4—22no—
103C22×C3×D4—22no—
104C22×C3×D4—22no—
105C22×C3×D4—22no—
106C22×C3×D4—41no—
107C22×C3×D4—41no—
108C22×C3×D4—41no—
109C22×C3×D4—41no—
110C22×C3×D4—41no—
111C22×C3×D4—41no—
112C22×C3×D4—41no—
113C22×C3×D4—41no—
114C22×C3×D4—41no—
115C22×C3×D4—41no—
116C22×C3×D4—41no—
117C22×C3×D4—41no—
118C22×C3×D4—41no—
119C22×C3×D4—41no—
120C22×C3×D4—41no—
121C22×C3×D4—41no—
122C22×C3×D4D414yescomplemented
123C23×C3×C4—22no—
124C23×C3×C4—22no—
125C23×C3×C4—22no—
126C23×C3×C4—22no—
127C23×C3×C4—22no—
128C23×C3×C4—41no—
129C23×C3×C4—41no—
130C23×C3×C4C2311yescharacteristic
131C23×C3×C4C2311yescharacteristic
132C23×C3×C4C2311yescharacteristic
133C23×C3×C4C2311yescharacteristic
134C23×C3×C4C2311yescharacteristic
135C23×C3×C4C2311yescharacteristic
136C23×C3×C4C2311yescharacteristic
137C23×C3×C4C2311yescharacteristic
138C23×C3×C4C2311yescharacteristic
139C23×C3×C4C2311yescharacteristic
140C23×C3×C4C2311yescharacteristic
141C3×#121—232no—
142C2×C3×C4⋊C4—22no—
143C2×C3×C4⋊C4—22no—
144C2×C3×C4⋊C4—22no—
145C2×C3×C4⋊C4—22no—
146C2×C3×C4⋊C4—41no—
147C2×C3×C4⋊C4D414yescomplemented
148C2×C3×C22⋊C4—22no—
149C2×C3×C22⋊C4—22no—
150C2×C3×C22⋊C4—22no—
151C2×C3×C22⋊C4—22no—
152C2×C3×C22⋊C4—22no—
153C2×C3×C22⋊C4—22no—
154C2×C3×C22⋊C4—22no—
155C2×C3×C22⋊C4—22no—
156C2×C3×C22⋊C4—22no—
157C2×C3×C22⋊C4—22no—
158C2×C3×C22⋊C4—22no—
159C2×C3×C22⋊C4—22no—
160C2×C3×C22⋊C4—22no—
161C2×C3×C22⋊C4—22no—
162C2×C3×C22⋊C4—22no—
163C2×C3×C22⋊C4—22no—
164C2×C3×C22⋊C4—22no—
165C2×C3×C22⋊C4—22no—
166C2×C3×C22⋊C4—22no—
167C2×C3×C22⋊C4—22no—
168C2×C3×C22⋊C4—22no—
169C2×C3×C22⋊C4—22no—
170C2×C3×C22⋊C4—22no—
171C2×C3×C22⋊C4—22no—
172C2×C3×C22⋊C4—22no—
173C2×C3×C22⋊C4—22no—
174C2×C3×C22⋊C4—22no—
175C2×C3×C22⋊C4—22no—
176C2×C3×C22⋊C4—41no—
177C2×C3×C22⋊C4—41no—
178C2×C3×C22⋊C4—41no—
179C2×C3×C22⋊C4—41no—
180C2×C3×C22⋊C4—41no—
181C2×C3×C22⋊C4—41no—
182C2×C3×C22⋊C4—41no—
183C2×C3×C22⋊C4—41no—
184C2×C3×C22⋊C4—41no—
185C2×C3×C22⋊C4—41no—
186C2×C3×C22⋊C4—41no—
187C2×C3×C22⋊C4—41no—
188C2×C3×C22⋊C4—41no—
189C2×C3×C22⋊C4—41no—
190C2×C3×C22⋊C4D414yescomplemented
191C2×C3×C22⋊C4D414yescomplemented
192C2×C3×C22⋊C4D414yescomplemented
193C2×C3×C42—22no—
194C2×C3×C42—22no—
195C2×C3×C42—41no—
196C3×#95—22no—
197C3×#95—22no—
198C3×#95—22no—
199C3×#95—22no—
200C3×#95—22no—
201C3×#95—22no—
202C3×#95—22no—
203C3×#95—22no—
204C3×#95—41no—
205C3×#95—41no—
206C23×D4C22×C311yescharacteristic
207C23×D4C22×C311yescharacteristic
208C23×D4C22×C311yescharacteristic
209C23×D4C22×C311yescharacteristic
210C23×D4C22×C311yescharacteristic
211C23×D4C22×C311yescharacteristic
212C24×C4C22×C311yescharacteristic
213C2×#121—24no—
214C2×#121—24no—
215C2×#121—24no—
216C22×C4⋊C4C22×C311yescharacteristic
217C22×C4⋊C4C22×C311yescharacteristic
218C22×C22⋊C4C22×C311yescharacteristic
219C22×C22⋊C4C22×C311yescharacteristic
220C22×C22⋊C4C22×C311yescharacteristic
221C22×C22⋊C4C22×C311yescharacteristic
222C22×C22⋊C4C22×C311yescharacteristic
223C22×C22⋊C4C22×C311yescharacteristic
224C22×C22⋊C4C22×C311yescharacteristic
225C22×C22⋊C4C22×C311yescharacteristic
226C22×C22⋊C4C22×C311yescharacteristic
227C22×C22⋊C4C22×C311yescharacteristic
228C22×C22⋊C4C22×C311yescharacteristic
229C22×C22⋊C4C22×C311yescharacteristic
230C22×C22⋊C4C22×C311yescharacteristic
231C22×C22⋊C4C22×C311yescharacteristic
232C22×C22⋊C4C22×C311yescharacteristic
233C22×C42C22×C311yescharacteristic
234#394—24no—
235#392—24no—
236#392—24no—
237#392—24no—
238#390—24no—
239#388—24no—
240#386—24no—
241C2×#95C22×C311yescharacteristic
242C2×#95C22×C311yescharacteristic
243C2×#95C22×C311yescharacteristic
244C2×#95C22×C311yescharacteristic
245C2×#95C22×C311yescharacteristic
246C2×#95C22×C311yescharacteristic
247C2×#95C22×C311yescharacteristic
248C2×#95C22×C311yescharacteristic
249C2×#95C22×C311yescharacteristic
250C2×#95C22×C311yescharacteristic
251C24×C3—21no—
252C24×C3—21no—
253C24×C3—21no—
254C24×C3—21no—
255C24×C3—21no—
256C24×C3—21no—
257C24×C3—21no—
258C24×C3—21no—
259C24×C3—21no—
260C24×C3—21no—
261C24×C3—21no—
262C24×C3—21no—
263C24×C3—21no—
264C24×C3—21no—
265C24×C3—21no—
266C24×C3—21no—
267C24×C3—21no—
268C24×C3—21no—
269C24×C3—21no—
270C24×C3—21no—
271C24×C3—21no—
272C24×C3—21no—
273C24×C3—21no—
274C24×C3—21no—
275C24×C3—21no—
276C24×C3—21no—
277C24×C3—21no—
278C24×C3—21no—
279C24×C3—21no—
280C24×C3—21no—
281C24×C3—21no—
282C24×C3—21no—
283C24×C3—21no—
284C24×C3—21no—
285C24×C3—21no—
286C24×C3—21no—
287C24×C3—21no—
288C24×C3—21no—
289C24×C3—21no—
290C24×C3—21no—
291C24×C3—21no—
292C24×C3—21no—
293C24×C3—21no—
294C24×C3—21no—
295C24×C3—21no—
296C24×C3—21no—
297C24×C3—21no—
298C24×C3—21no—
299C24×C3—21no—
300C24×C3—21no—
301C24×C3—21no—
302C24×C3—21no—
303C24×C3—21no—
304C24×C3—21no—
305C24×C3C2×D412yes—
306C24×C3C2×D412yes—
307C24×C3C2×D412yes—
308C24×C3C2×D412yes—
309C24×C3C2×D412yes—
310C24×C3#4112yes—
311C24×C3C2411yescharacteristic
312C2×C3×D4—28no—
313C2×C3×D4—28no—
314C2×C3×D4—28no—
315C2×C3×D4—28no—
316C2×C3×D4—28no—
317C2×C3×D4—44no—
318C2×C3×D4—44no—
319C2×C3×D4—44no—
320C2×C3×D4—44no—
321C2×C3×D4—44no—
322C2×C3×D4—44no—
323C2×C3×D4—44no—
324C2×C3×D4—44no—
325C2×C3×D4—44no—
326C2×C3×D4—44no—
327C2×C3×D4—44no—
328C2×C3×D4—44no—
329C2×C3×D4—44no—
330C2×C3×D4—44no—
331C2×C3×D4—44no—
332C2×C3×D4—44no—
333C2×C3×D4—44no—
334C2×C3×D4—44no—
335C2×C3×D4—44no—
336C2×C3×D4—44no—
337C2×C3×D4—44no—
338C2×C3×D4—44no—
339C2×C3×D4—44no—
340C2×C3×D4—44no—
341C2×C3×D4—44no—
342C2×C3×D4—44no—
343C2×C3×D4—44no—
344C2×C3×D4—44no—
345C2×C3×D4—44no—
346C2×C3×D4—44no—
347C2×C3×D4—44no—
348C2×C3×D4—44no—
349C2×C3×D4—44no—
350C2×C3×D4—44no—
351C2×C3×D4—44no—
352C2×C3×D4—44no—
353C2×C3×D4—44no—
354C22×C3×C4—21no—
355C22×C3×C4—21no—
356C22×C3×C4—21no—
357C22×C3×C4—21no—
358C22×C3×C4—21no—
359C22×C3×C4—21no—
360C22×C3×C4—21no—
361C22×C3×C4—21no—
362C22×C3×C4—28no—
363C22×C3×C4—21no—
364C22×C3×C4—21no—
365C22×C3×C4—21no—
366C22×C3×C4—21no—
367C22×C3×C4—21no—
368C22×C3×C4—21no—
369C22×C3×C4—21no—
370C22×C3×C4—21no—
371C22×C3×C4—21no—
372C22×C3×C4—21no—
373C22×C3×C4—21no—
374C22×C3×C4—21no—
375C22×C3×C4—21no—
376C22×C3×C4—21no—
377C22×C3×C4—21no—
378C22×C3×C4—21no—
379C22×C3×C4—21no—
380C22×C3×C4—21no—
381C22×C3×C4—21no—
382C22×C3×C4—21no—
383C22×C3×C4—21no—
384C22×C3×C4—21no—
385C22×C3×C4—21no—
386C22×C3×C4—21no—
387C22×C3×C4—21no—
388C22×C3×C4—21no—
389C22×C3×C4—21no—
390C22×C3×C4—21no—
391C22×C3×C4—21no—
392C22×C3×C4—21no—
393C22×C3×C4—21no—
394C22×C3×C4—21no—
395C22×C3×C4—21no—
396C22×C3×C4—21no—
397C22×C3×C4—21no—
398C22×C3×C4—21no—
399C22×C3×C4—21no—
400C22×C3×C4—21no—
401C22×C3×C4—21no—
402C22×C3×C4—21no—
403C22×C3×C4—21no—
404C22×C3×C4—21no—
405C22×C3×C4—21no—
406C22×C3×C4—21no—
407C22×C3×C4—21no—
408C22×C3×C4—21no—
409C22×C3×C4—21no—
410C22×C3×C4—21no—
411C22×C3×C4—21no—
412C22×C3×C4—21no—
413C22×C3×C4—21no—
414C22×C3×C4—21no—
415C22×C3×C4—21no—
416C22×C3×C4—21no—
417C22×C3×C4—21no—
418C22×C3×C4—21no—
419C22×C3×C4—44no—
420C22×C3×C4—44no—
421C22×C3×C4—44no—
422C22×C3×C4—44no—
423C22×C3×C4—44no—
424C22×C3×C4—44no—
425C22×C3×C4C2×D412yes—
426C22×C3×C4C2×D412yes—
427C22×C3×C4C2×D412yes—
428C22×C3×C4C2×D412yes—
429C22×C3×C4C2×D412yes—
430C22×C3×C4C2×D412yes—
431C22×C3×C4C2×D412yes—
432C22×C3×C4C2×D412yes—
433C22×C3×C4C2×D412yes—
434C22×C3×C4C2×D412yes—
435C22×C3×C4#4112yes—
436C22×C3×C4#4112yes—
437C22×C3×C4#4112yes—
438C3×C4⋊C4—28no—
439C3×C4⋊C4—44no—
440C3×C22⋊C4—28no—
441C3×C22⋊C4—28no—
442C3×C22⋊C4—28no—
443C3×C22⋊C4—44no—
444C3×C22⋊C4—44no—
445C3×C22⋊C4—44no—
446C3×C22⋊C4—44no—
447C3×C22⋊C4—44no—
448C3×C22⋊C4—44no—
449C3×C22⋊C4—44no—
450C3×C22⋊C4—44no—
451C3×C22⋊C4—44no—
452C3×C22⋊C4—44no—
453C3×C22⋊C4—44no—
454C3×C22⋊C4—44no—
455C3×C42—44no—
456C25C23×C311yescharacteristic
457C25C23×C311yescharacteristic
458C25C23×C311yescharacteristic
459C25C23×C311yescharacteristic
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4—22no—
466C22×D4—22no—
467C22×D4—22no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4—22no—
476C22×D4—22no—
477C22×D4—22no—
478C22×D4—22no—
479C22×D4—22no—
480C22×D4—22no—
481C22×D4—22no—
482C22×D4—22no—
483C22×D4—22no—
484C22×D4—22no—
485C22×D4—41no—
486C22×D4—41no—
487C22×D4—41no—
488C22×D4—41no—
489C22×D4—41no—
490C22×D4—41no—
491C22×D4—41no—
492C22×D4—41no—
493C22×D4—41no—
494C22×D4—41no—
495C22×D4—41no—
496C22×D4—41no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C3×D414yescomplemented
502C23×C4—22no—
503C23×C4—22no—
504C23×C4—22no—
505C23×C4—22no—
506C23×C4—22no—
507C23×C4—41no—
508C23×C4—41no—
509C23×C4C23×C311yescharacteristic
510C23×C4C23×C311yescharacteristic
511C23×C4C23×C311yescharacteristic
512C23×C4C23×C311yescharacteristic
513C23×C4C23×C311yescharacteristic
514C23×C4C23×C311yescharacteristic
515C23×C4C23×C311yescharacteristic
516C23×C4C23×C311yescharacteristic
517C23×C4C23×C311yescharacteristic
518C23×C4C23×C311yescharacteristic
519C23×C4C23×C311yescharacteristic
520#121—232no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—41no—
526C2×C4⋊C4C3×D414yescomplemented
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—22no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—41no—
556C2×C22⋊C4—41no—
557C2×C22⋊C4—41no—
558C2×C22⋊C4—41no—
559C2×C22⋊C4—41no—
560C2×C22⋊C4—41no—
561C2×C22⋊C4—41no—
562C2×C22⋊C4—41no—
563C2×C22⋊C4—41no—
564C2×C22⋊C4—41no—
565C2×C22⋊C4—41no—
566C2×C22⋊C4—41no—
567C2×C22⋊C4—41no—
568C2×C22⋊C4—41no—
569C2×C22⋊C4C3×D414yescomplemented
570C2×C22⋊C4C3×D414yescomplemented
571C2×C22⋊C4C3×D414yescomplemented
572C2×C42—22no—
573C2×C42—22no—
574C2×C42—41no—
575#95—22no—
576#95—22no—
577#95—22no—
578#95—22no—
579#95—22no—
580#95—22no—
581#95—22no—
582#95—22no—
583#95—41no—
584#95—41no—
585C23×C3—22no—
586C23×C3—22no—
587C23×C3—22no—
588C23×C3—22no—
589C23×C3—22no—
590C23×C3—22no—
591C23×C3—22no—
592C23×C3—22no—
593C23×C3—22no—
594C23×C3—22no—
595C23×C3—22no—
596C23×C3—22no—
597C23×C3—22no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—22no—
603C23×C3—22no—
604C23×C3—22no—
605C23×C3—22no—
606C23×C3—22no—
607C23×C3—22no—
608C23×C3—22no—
609C23×C3—22no—
610C23×C3—22no—
611C23×C3—22no—
612C23×C3—22no—
613C23×C3—22no—
614C23×C3—22no—
615C23×C3—22no—
616C23×C3—22no—
617C23×C3—22no—
618C23×C3—22no—
619C23×C3—22no—
620C23×C3—22no—
621C23×C3—22no—
622C23×C3—22no—
623C23×C3—22no—
624C23×C3—41no—
625C23×C3—41no—
626C23×C3—41no—
627C23×C3—41no—
628C23×C3—41no—
629C23×C3—41no—
630C23×C3—41no—
631C23×C3—41no—
632C23×C3—41no—
633C23×C3—41no—
634C23×C3—41no—
635C23×C3—41no—
636C23×C3—41no—
637C23×C3—41no—
638C23×C3—41no—
639C23×C3—41no—
640C23×C3—41no—
641C23×C3—41no—
642C23×C3—41no—
643C23×C3—41no—
644C23×C3—41no—
645C23×C3—41no—
646C23×C3—41no—
647C23×C3—41no—
648C23×C3—41no—
649C23×C3—41no—
650C23×C3—41no—
651C23×C3—41no—
652C23×C3—41no—
653C23×C3—41no—
654C23×C3—41no—
655C23×C3—41no—
656C23×C3—41no—
657C23×C3—41no—
658C23×C3—41no—
659C23×C3—41no—
660C23×C3—41no—
661C23×C3—41no—
662C23×C3—41no—
663C23×C3—41no—
664C23×C3—41no—
665C23×C3—41no—
666C23×C3—41no—
667C23×C3—41no—
668C23×C3—41no—
669C23×C3—41no—
670C23×C3—41no—
671C23×C3—41no—
672C23×C3—41no—
673C23×C3—41no—
674C23×C3—41no—
675C23×C3—41no—
676C23×C3—41no—
677C23×C3—41no—
678C23×C3—41no—
679C23×C3—41no—
680C23×C3—41no—
681C23×C3—41no—
682C23×C3—41no—
683C23×C3—41no—
684C23×C3—41no—
685C23×C3—41no—
686C23×C3—41no—
687C23×C3—41no—
688C23×C3—41no—
689C23×C3—41no—
690C23×C3—41no—
691C23×C3—41no—
692C23×C3—41no—
693C23×C3—41no—
694C23×C3—41no—
695C23×C3—41no—
696C23×C3—41no—
697C23×C3—41no—
698C23×C3—41no—
699C23×C3—41no—
700C23×C3—41no—
701C23×C3—41no—
702C23×C3—41no—
703C23×C3—41no—
704C23×C3—41no—
705C23×C3—41no—
706C23×C3—41no—
707C23×C3—41no—
708C23×C3—41no—
709C23×C3—41no—
710C23×C3—41no—
711C23×C3—41no—
712C23×C3—41no—
713C23×C3—41no—
714C23×C3—41no—
715C23×C3—41no—
716C23×C3—41no—
717C23×C3—41no—
718C23×C3—41no—
719C23×C3—41no—
720C23×C3—41no—
721C23×C3—41no—
722C23×C3—41no—
723C23×C3—41no—
724C23×C3#12114yes—
725C23×C3C22×D411yescharacteristic
726C23×C3C22×D411yescharacteristic
727C23×C3C22×D411yescharacteristic
728C23×C3C22×D411yescharacteristic
729C23×C3C22×D411yescharacteristic
730C23×C3C2×#4111yescharacteristic
731C23×C3C2×#4111yescharacteristic
732C23×C3C2×#4111yescharacteristic
733C23×C3C2×#4111yescharacteristic
734C23×C3H(5,𝔽2)11yescharacteristic
735C23×C3H(5,𝔽2)11yescharacteristic
736C23×C3H(5,𝔽2)11yescharacteristic
737C23×C3H(5,𝔽2)11yescharacteristic
738C23×C3H(5,𝔽2)11yescharacteristic
739C23×C3H(5,𝔽2)11yescharacteristic
740C3×D4—416no—
741C3×D4—416no—
742C3×D4—416no—
743C3×D4—416no—
744C3×D4—416no—
745C3×D4—416no—
746C2×C3×C4—22no—
747C2×C3×C4—22no—
748C2×C3×C4—22no—
749C2×C3×C4—22no—
750C2×C3×C4—22no—
751C2×C3×C4—22no—
752C2×C3×C4—22no—
753C2×C3×C4—22no—
754C2×C3×C4—22no—
755C2×C3×C4—22no—
756C2×C3×C4—22no—
757C2×C3×C4—22no—
758C2×C3×C4—22no—
759C2×C3×C4—22no—
760C2×C3×C4—22no—
761C2×C3×C4—22no—
762C2×C3×C4—22no—
763C2×C3×C4—22no—
764C2×C3×C4—22no—
765C2×C3×C4—22no—
766C2×C3×C4—22no—
767C2×C3×C4—22no—
768C2×C3×C4—22no—
769C2×C3×C4—22no—
770C2×C3×C4—22no—
771C2×C3×C4—22no—
772C2×C3×C4—22no—
773C2×C3×C4—22no—
774C2×C3×C4—22no—
775C2×C3×C4—22no—
776C2×C3×C4—22no—
777C2×C3×C4—22no—
778C2×C3×C4—22no—
779C2×C3×C4—416no—
780C2×C3×C4—41no—
781C2×C3×C4—41no—
782C2×C3×C4—41no—
783C2×C3×C4—41no—
784C2×C3×C4—41no—
785C2×C3×C4—41no—
786C2×C3×C4—41no—
787C2×C3×C4—41no—
788C2×C3×C4—41no—
789C2×C3×C4—41no—
790C2×C3×C4—41no—
791C2×C3×C4—41no—
792C2×C3×C4—41no—
793C2×C3×C4—41no—
794C2×C3×C4—41no—
795C2×C3×C4—41no—
796C2×C3×C4—41no—
797C2×C3×C4—41no—
798C2×C3×C4—41no—
799C2×C3×C4—41no—
800C2×C3×C4—41no—
801C2×C3×C4—41no—
802C2×C3×C4—41no—
803C2×C3×C4—41no—
804C2×C3×C4—41no—
805C2×C3×C4—41no—
806C2×C3×C4—41no—
807C2×C3×C4—41no—
808C2×C3×C4—41no—
809C2×C3×C4—41no—
810C2×C3×C4—41no—
811C2×C3×C4—41no—
812C2×C3×C4—41no—
813C2×C3×C4—41no—
814C2×C3×C4—41no—
815C2×C3×C4—41no—
816C2×C3×C4—41no—
817C2×C3×C4—41no—
818C2×C3×C4—41no—
819C2×C3×C4—41no—
820C2×C3×C4—41no—
821C2×C3×C4—41no—
822C2×C3×C4#12014yes—
823C2×C3×C4#12114yes—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24C2×C3×D412yes—
879C24C2×C3×D412yes—
880C24C2×C3×D412yes—
881C24C2×C3×D412yes—
882C24C2×C3×D412yes—
883C24C3×#4112yes—
884C24C24×C311yescharacteristic
885C2×D4—28no—
886C2×D4—28no—
887C2×D4—28no—
888C2×D4—28no—
889C2×D4—28no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—44no—
926C2×D4—44no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—28no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4C2×C3×D412yes—
999C22×C4C2×C3×D412yes—
1000C22×C4C2×C3×D412yes—
1001C22×C4C2×C3×D412yes—
1002C22×C4C2×C3×D412yes—
1003C22×C4C2×C3×D412yes—
1004C22×C4C2×C3×D412yes—
1005C22×C4C2×C3×D412yes—
1006C22×C4C2×C3×D412yes—
1007C22×C4C2×C3×D412yes—
1008C22×C4C3×#4112yes—
1009C22×C4C3×#4112yes—
1010C22×C4C3×#4112yes—
1011C4⋊C4—28no—
1012C4⋊C4—44no—
1013C22⋊C4—28no—
1014C22⋊C4—28no—
1015C22⋊C4—28no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C42—44no—
1029C22×C3—24no—
1030C22×C3—24no—
1031C22×C3—24no—
1032C22×C3—42no—
1033C22×C3—42no—
1034C22×C3—42no—
1035C22×C3—42no—
1036C22×C3—42no—
1037C22×C3—42no—
1038C22×C3—42no—
1039C22×C3—42no—
1040C22×C3—42no—
1041C22×C3—42no—
1042C22×C3—42no—
1043C22×C3—42no—
1044C22×C3—42no—
1045C22×C3—42no—
1046C22×C3—42no—
1047C22×C3—42no—
1048C22×C3—42no—
1049C22×C3—42no—
1050C22×C3—42no—
1051C22×C3—42no—
1052C22×C3—42no—
1053C22×C3—42no—
1054C22×C3—42no—
1055C22×C3—42no—
1056C22×C3—42no—
1057C22×C3—42no—
1058C22×C3—42no—
1059C22×C3—42no—
1060C22×C3—42no—
1061C22×C3—42no—
1062C22×C3—42no—
1063C22×C3—42no—
1064C22×C3—42no—
1065C22×C3—81no—
1066C22×C3—81no—
1067C22×C3—81no—
1068C22×C3—81no—
1069C22×C3—81no—
1070C22×C3—81no—
1071C22×C3—81no—
1072C22×C3—81no—
1073C22×C3—81no—
1074C22×C3—81no—
1075C22×C3—81no—
1076C22×C3—81no—
1077C22×C3—81no—
1078C22×C3—81no—
1079C22×C3—81no—
1080C22×C3—81no—
1081C22×C3—81no—
1082C22×C3—81no—
1083C22×C3—81no—
1084C22×C3—81no—
1085C22×C3—81no—
1086C22×C3—81no—
1087C22×C3—81no—
1088C22×C3—81no—
1089C22×C3C2×#12011yescharacteristic
1090C22×C3C2×#12111yescharacteristic
1091C22×C3C2×#12111yescharacteristic
1092C22×C3#52511yescharacteristic
1093C22×C3#53211yescharacteristic
1094C22×C3#53211yescharacteristic
1095C22×C3#53411yescharacteristic
1096C22×C3#53411yescharacteristic
1097C22×C3#53511yescharacteristic
1098C22×C3#53511yescharacteristic
1099C22×C3#53511yescharacteristic
1100C22×C3#53811yescharacteristic
1101C22×C3#53811yescharacteristic
1102C22×C3#54011yescharacteristic
1103C22×C3#54011yescharacteristic
1104C22×C3D4211yescharacteristic
1105C22×C3D4211yescharacteristic
1106C22×C3D4211yescharacteristic
1107C22×C3D4211yescharacteristic
1108C22×C3D4211yescharacteristic
1109C22×C3#54611yescharacteristic
1110C22×C3#54611yescharacteristic
1111C22×C3#54611yescharacteristic
1112C22×C3#54611yescharacteristic
1113C22×C3#54611yescharacteristic
1114C22×C3#54611yescharacteristic
1115C22×C3#54611yescharacteristic
1116C22×C3#54611yescharacteristic
1117C22×C3#55011yescharacteristic
1118C22×C3#55011yescharacteristic
1119C22×C3#55311yescharacteristic
1120C22×C3#55311yescharacteristic
1121C22×C3#55511yescharacteristic
1122C22×C3#56011yescharacteristic
1123C22×C3#56011yescharacteristic
1124C3×C4—24no—
1125C3×C4—24no—
1126C3×C4—42no—
1127C3×C4—42no—
1128C3×C4—42no—
1129C3×C4—42no—
1130C3×C4—42no—
1131C3×C4—42no—
1132C3×C4—42no—
1133C3×C4—81no—
1134C3×C4—81no—
1135C23—22no—
1136C23—22no—
1137C23—22no—
1138C23—22no—
1139C23—22no—
1140C23—22no—
1141C23—22no—
1142C23—22no—
1143C23—22no—
1144C23—22no—
1145C23—22no—
1146C23—22no—
1147C23—22no—
1148C23—22no—
1149C23—22no—
1150C23—22no—
1151C23—22no—
1152C23—22no—
1153C23—22no—
1154C23—22no—
1155C23—22no—
1156C23—22no—
1157C23—22no—
1158C23—22no—
1159C23—22no—
1160C23—22no—
1161C23—22no—
1162C23—22no—
1163C23—22no—
1164C23—22no—
1165C23—22no—
1166C23—22no—
1167C23—22no—
1168C23—22no—
1169C23—22no—
1170C23—22no—
1171C23—22no—
1172C23—22no—
1173C23—22no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23—41no—
1192C23—41no—
1193C23—41no—
1194C23—41no—
1195C23—41no—
1196C23—41no—
1197C23—41no—
1198C23—41no—
1199C23—41no—
1200C23—41no—
1201C23—41no—
1202C23—41no—
1203C23—41no—
1204C23—41no—
1205C23—41no—
1206C23—41no—
1207C23—41no—
1208C23—41no—
1209C23—41no—
1210C23—41no—
1211C23—41no—
1212C23—41no—
1213C23—41no—
1214C23—41no—
1215C23—41no—
1216C23—41no—
1217C23—41no—
1218C23—41no—
1219C23—41no—
1220C23—41no—
1221C23—41no—
1222C23—41no—
1223C23—41no—
1224C23—41no—
1225C23—41no—
1226C23—41no—
1227C23—41no—
1228C23—41no—
1229C23—41no—
1230C23—41no—
1231C23—41no—
1232C23—41no—
1233C23—41no—
1234C23—41no—
1235C23—41no—
1236C23—41no—
1237C23—41no—
1238C23—41no—
1239C23—41no—
1240C23—41no—
1241C23—41no—
1242C23—41no—
1243C23—41no—
1244C23—41no—
1245C23—41no—
1246C23—41no—
1247C23—41no—
1248C23—41no—
1249C23—41no—
1250C23—41no—
1251C23—41no—
1252C23—41no—
1253C23—41no—
1254C23—41no—
1255C23—41no—
1256C23—41no—
1257C23—41no—
1258C23—41no—
1259C23—41no—
1260C23—41no—
1261C23—41no—
1262C23—41no—
1263C23—41no—
1264C23—41no—
1265C23—41no—
1266C23—41no—
1267C23—41no—
1268C23—41no—
1269C23—41no—
1270C23—41no—
1271C23—41no—
1272C23—41no—
1273C23—41no—
1274C23C3×#12114yes—
1275C23C22×C3×D411yescharacteristic
1276C23C22×C3×D411yescharacteristic
1277C23C22×C3×D411yescharacteristic
1278C23C22×C3×D411yescharacteristic
1279C23C22×C3×D411yescharacteristic
1280C23C2×C3×#4111yescharacteristic
1281C23C2×C3×#4111yescharacteristic
1282C23C2×C3×#4111yescharacteristic
1283C23C2×C3×#4111yescharacteristic
1284C23C3×H(5,𝔽2)11yescharacteristic
1285C23C3×H(5,𝔽2)11yescharacteristic
1286C23C3×H(5,𝔽2)11yescharacteristic
1287C23C3×H(5,𝔽2)11yescharacteristic
1288C23C3×H(5,𝔽2)11yescharacteristic
1289C23C3×H(5,𝔽2)11yescharacteristic
1290D4—416no—
1291D4—416no—
1292D4—416no—
1293D4—416no—
1294D4—416no—
1295D4—416no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—416no—
1330C2×C4—41no—
1331C2×C4—41no—
1332C2×C4—41no—
1333C2×C4—41no—
1334C2×C4—41no—
1335C2×C4—41no—
1336C2×C4—41no—
1337C2×C4—41no—
1338C2×C4—41no—
1339C2×C4—41no—
1340C2×C4—41no—
1341C2×C4—41no—
1342C2×C4—41no—
1343C2×C4—41no—
1344C2×C4—41no—
1345C2×C4—41no—
1346C2×C4—41no—
1347C2×C4—41no—
1348C2×C4—41no—
1349C2×C4—41no—
1350C2×C4—41no—
1351C2×C4—41no—
1352C2×C4—41no—
1353C2×C4—41no—
1354C2×C4—41no—
1355C2×C4—41no—
1356C2×C4—41no—
1357C2×C4—41no—
1358C2×C4—41no—
1359C2×C4—41no—
1360C2×C4—41no—
1361C2×C4—41no—
1362C2×C4—41no—
1363C2×C4—41no—
1364C2×C4—41no—
1365C2×C4—41no—
1366C2×C4—41no—
1367C2×C4—41no—
1368C2×C4—41no—
1369C2×C4—41no—
1370C2×C4—41no—
1371C2×C4—41no—
1372C2×C4C3×#12014yes—
1373C2×C4C3×#12114yes—
1374C2×C3—44no—
1375C2×C3—82no—
1376C2×C3—82no—
1377C2×C3—82no—
1378C2×C3#240811yescharacteristic
1379C2×C3#241011yescharacteristic
1380C2×C3#241411yescharacteristic
1381C2×C3#242411yescharacteristic
1382C2×C3#242811yescharacteristic
1383C2×C3#243111yescharacteristic
1384C2×C3#246411yescharacteristic
1385C2×C3#254311yescharacteristic
1386C2×C3#255511yescharacteristic
1387C2×C3#266911yescharacteristic
1388C2×C3#267311yescharacteristic
1389C2×C3#267811yescharacteristic
1390C2×C3#269911yescharacteristic
1391C2×C3#270311yescharacteristic
1392C2×C3#271411yescharacteristic
1393C22—24no—
1394C22—24no—
1395C22—24no—
1396C22—42no—
1397C22—42no—
1398C22—42no—
1399C22—42no—
1400C22—42no—
1401C22—42no—
1402C22—42no—
1403C22—42no—
1404C22—42no—
1405C22—42no—
1406C22—42no—
1407C22—42no—
1408C22—42no—
1409C22—42no—
1410C22—42no—
1411C22—42no—
1412C22—42no—
1413C22—42no—
1414C22—42no—
1415C22—42no—
1416C22—42no—
1417C22—42no—
1418C22—42no—
1419C22—42no—
1420C22—42no—
1421C22—42no—
1422C22—42no—
1423C22—42no—
1424C22—42no—
1425C22—42no—
1426C22—42no—
1427C22—42no—
1428C22—42no—
1429C22—81no—
1430C22—81no—
1431C22—81no—
1432C22—81no—
1433C22—81no—
1434C22—81no—
1435C22—81no—
1436C22—81no—
1437C22—81no—
1438C22—81no—
1439C22—81no—
1440C22—81no—
1441C22—81no—
1442C22—81no—
1443C22—81no—
1444C22—81no—
1445C22—81no—
1446C22—81no—
1447C22—81no—
1448C22—81no—
1449C22—81no—
1450C22—81no—
1451C22—81no—
1452C22—81no—
1453C22C2×C3×#12011yescharacteristic
1454C22C2×C3×#12111yescharacteristic
1455C22C2×C3×#12111yescharacteristic
1456C22C3×#52511yescharacteristic
1457C22C3×#53211yescharacteristic
1458C22C3×#53211yescharacteristic
1459C22C3×#53411yescharacteristic
1460C22C3×#53411yescharacteristic
1461C22C3×#53511yescharacteristic
1462C22C3×#53511yescharacteristic
1463C22C3×#53511yescharacteristic
1464C22C3×#53811yescharacteristic
1465C22C3×#53811yescharacteristic
1466C22C3×#54011yescharacteristic
1467C22C3×#54011yescharacteristic
1468C22C3×D4211yescharacteristic
1469C22C3×D4211yescharacteristic
1470C22C3×D4211yescharacteristic
1471C22C3×D4211yescharacteristic
1472C22C3×D4211yescharacteristic
1473C22C3×#54611yescharacteristic
1474C22C3×#54611yescharacteristic
1475C22C3×#54611yescharacteristic
1476C22C3×#54611yescharacteristic
1477C22C3×#54611yescharacteristic
1478C22C3×#54611yescharacteristic
1479C22C3×#54611yescharacteristic
1480C22C3×#54611yescharacteristic
1481C22C3×#55011yescharacteristic
1482C22C3×#55011yescharacteristic
1483C22C3×#55311yescharacteristic
1484C22C3×#55311yescharacteristic
1485C22C3×#55511yescharacteristic
1486C22C3×#56011yescharacteristic
1487C22C3×#56011yescharacteristic
1488C4—24no—
1489C4—24no—
1490C4—42no—
1491C4—42no—
1492C4—42no—
1493C4—42no—
1494C4—42no—
1495C4—42no—
1496C4—42no—
1497C4—81no—
1498C4—81no—
1499C3#1532011yescharacteristic, direct product factor, Sylow
1500C2—44no—
1501C2—82no—
1502C2—82no—
1503C2—82no—
1504C2C3×#240811yescharacteristic
1505C2C3×#241011yescharacteristic
1506C2C3×#241411yescharacteristic
1507C2C3×#242411yescharacteristic
1508C2C3×#242811yescharacteristic
1509C2C3×#243111yescharacteristic
1510C2C3×#246411yescharacteristic
1511C2C3×#254311yescharacteristic
1512C2C3×#255511yescharacteristic
1513C2C3×#266911yescharacteristic
1514C2C3×#267311yescharacteristic
1515C2C3×#267811yescharacteristic
1516C2C3×#269911yescharacteristic
1517C2C3×#270311yescharacteristic
1518C2C3×#271411yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×C3×#121C2semidirect
2. C2×C3×#394C2semidirect
3. C2×C3×#392C2semidirect
4. C2×C3×#392C2semidirect
5. C2×C3×#392C2semidirect
6. C2×C3×#390C2semidirect
7. C2×C3×#388C2semidirect
8. C2×C3×#386C2semidirect
9. C3×#1441C2semidirect
10. C3×#1440C2semidirect
11. C3×#1438C2semidirect
12. C3×#1438C2semidirect
13. C3×#1438C2semidirect
14. C3×#1437C2semidirect
15. C3×C22⋊#95C2semidirect
16. #15320C3direct (N × H)
62. C22×#121C2×C3semidirect
63. C2×#394C2×C3semidirect
64. C2×#392C2×C3semidirect
65. C2×#392C2×C3semidirect
66. C2×#392C2×C3semidirect
67. C2×#390C2×C3semidirect
68. C2×#388C2×C3semidirect
69. C2×#386C2×C3semidirect
70. #1441C2×C3semidirect
71. #1440C2×C3semidirect
72. #1438C2×C3semidirect
73. #1438C2×C3semidirect
74. #1438C2×C3semidirect
75. #1437C2×C3semidirect
76. C22⋊#95C2×C3semidirect
122. C22×C3×D4D4semidirect
147. C2×C3×C4⋊C4D4semidirect
190. C2×C3×C22⋊C4D4semidirect
191. C2×C3×C22⋊C4D4semidirect
192. C2×C3×C22⋊C4D4semidirect
501. C22×D4C3×D4semidirect
526. C2×C4⋊C4C3×D4semidirect
569. C2×C22⋊C4C3×D4semidirect
570. C2×C22⋊C4C3×D4semidirect
571. C2×C22⋊C4C3×D4semidirect
1499. C3#15320direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C3×#1212
C2×C3×#3942
C2×C3×#3922
C2×C3×#3902
C2×C3×#3882
C2×C3×#3862
C3×#14412
C3×#14402
C3×#14382
C3×#14372
C3×C22⋊#952
#153203