Finite Group Databasebeta

← C3×#15316 #10633923

Subgroups — C3×#15316 #10633923

Order 768.

2442 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#121C211yesmaximal, characteristic
2C2×C3×#396C211yesmaximal, characteristic, complemented
3C2×C3×#394C211yesmaximal, characteristic, complemented
4C2×C3×#394C211yesmaximal, characteristic, complemented
5C2×C3×#394C211yesmaximal, characteristic, complemented
6C2×C3×#390C211yesmaximal, characteristic, complemented
7C2×C3×#389C211yesmaximal, characteristic, complemented
8C2×C3×#385C211yesmaximal, characteristic, complemented
9C3×#1441C211yesmaximal, characteristic, complemented
10C3×#1439C211yesmaximal, characteristic, complemented
11C3×#1439C211yesmaximal, characteristic, complemented
12C3×#1438C211yesmaximal, characteristic, complemented
13C3×#1438C211yesmaximal, characteristic, complemented
14C3×#1437C211yesmaximal, characteristic, complemented
15C3×C22⋊#95C211yesmaximal, characteristic, complemented
16#15316C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×D4C2211yescharacteristic
18C23×C3×D4C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C24×C3×C4C2211yescharacteristic
21C2×C3×#121—24no—
22C2×C3×#121—24no—
23C2×C3×#121—24no—
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C4⋊C4C2211yescharacteristic
28C22×C3×C4⋊C4C2211yescharacteristic
29C22×C3×C4⋊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×#396—24no—
46C3×#394—24no—
47C3×#394—24no—
48C3×#394—24no—
49C3×#390—24no—
50C3×#389—24no—
51C3×#385—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
63C2×#396C2×C311yescharacteristic, complemented
64C2×#394C2×C311yescharacteristic, complemented
65C2×#394C2×C311yescharacteristic, complemented
66C2×#394C2×C311yescharacteristic, complemented
67C2×#390C2×C311yescharacteristic, complemented
68C2×#389C2×C311yescharacteristic, complemented
69C2×#385C2×C311yescharacteristic, complemented
70#1441C2×C311yescharacteristic, complemented
71#1439C2×C311yescharacteristic, complemented
72#1439C2×C311yescharacteristic, complemented
73#1438C2×C311yescharacteristic, complemented
74#1438C2×C311yescharacteristic, complemented
75#1437C2×C311yescharacteristic, complemented
76C22⋊#95C2×C311yescharacteristic, complemented
77C25×C3C2311yescharacteristic
78C25×C3C2311yescharacteristic
79C25×C3C2311yescharacteristic
80C22×C3×D4—22no—
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—41no—
95C22×C3×D4—41no—
96C22×C3×D4—41no—
97C22×C3×D4—41no—
98C22×C3×D4—41no—
99C22×C3×D4—41no—
100C22×C3×D4D414yes—
101C23×C3×C4—22no—
102C23×C3×C4—22no—
103C23×C3×C4—22no—
104C23×C3×C4—22no—
105C23×C3×C4—22no—
106C23×C3×C4—41no—
107C23×C3×C4—41no—
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C23×C3×C4C2311yescharacteristic
111C23×C3×C4C2311yescharacteristic
112C23×C3×C4C2311yescharacteristic
113C23×C3×C4C2311yescharacteristic
114C23×C3×C4C2311yescharacteristic
115C23×C3×C4C2311yescharacteristic
116C23×C3×C4C2311yescharacteristic
117C23×C3×C4C2311yescharacteristic
118C23×C3×C4C2311yescharacteristic
119C23×C3×C4C2311yescharacteristic
120C3×#121—232no—
121C2×C3×C4⋊C4—22no—
122C2×C3×C4⋊C4—22no—
123C2×C3×C4⋊C4—22no—
124C2×C3×C4⋊C4—22no—
125C2×C3×C4⋊C4—22no—
126C2×C3×C4⋊C4—22no—
127C2×C3×C4⋊C4—22no—
128C2×C3×C4⋊C4—22no—
129C2×C3×C4⋊C4—22no—
130C2×C3×C4⋊C4—22no—
131C2×C3×C4⋊C4—22no—
132C2×C3×C4⋊C4—22no—
133C2×C3×C4⋊C4—22no—
134C2×C3×C4⋊C4—41no—
135C2×C3×C4⋊C4—41no—
136C2×C3×C4⋊C4—41no—
137C2×C3×C4⋊C4D414yes—
138C2×C3×C4⋊C4D414yescomplemented
139C2×C3×C22⋊C4—22no—
140C2×C3×C22⋊C4—22no—
141C2×C3×C22⋊C4—22no—
142C2×C3×C22⋊C4—22no—
143C2×C3×C22⋊C4—22no—
144C2×C3×C22⋊C4—22no—
145C2×C3×C22⋊C4—22no—
146C2×C3×C22⋊C4—22no—
147C2×C3×C22⋊C4—22no—
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—41no—
170C2×C3×C22⋊C4—41no—
171C2×C3×C22⋊C4—41no—
172C2×C3×C22⋊C4—41no—
173C2×C3×C22⋊C4—41no—
174C2×C3×C22⋊C4—41no—
175C2×C3×C22⋊C4—41no—
176C2×C3×C22⋊C4—41no—
177C2×C3×C22⋊C4—41no—
178C2×C3×C22⋊C4—41no—
179C2×C3×C22⋊C4D414yes—
180C2×C3×C22⋊C4D414yescomplemented
181C2×C3×C42—22no—
182C2×C3×C42—22no—
183C2×C3×C42—41no—
184C3×#95—22no—
185C3×#95—22no—
186C3×#95—22no—
187C3×#95—22no—
188C3×#95—22no—
189C3×#95—22no—
190C3×#95—22no—
191C3×#95—22no—
192C3×#95—41no—
193C3×#95—41no—
194C23×D4C22×C311yescharacteristic
195C23×D4C22×C311yescharacteristic
196C23×D4C22×C311yescharacteristic
197C24×C4C22×C311yescharacteristic
198C2×#121—24no—
199C2×#121—24no—
200C2×#121—24no—
201C22×C4⋊C4C22×C311yescharacteristic
202C22×C4⋊C4C22×C311yescharacteristic
203C22×C4⋊C4C22×C311yescharacteristic
204C22×C4⋊C4C22×C311yescharacteristic
205C22×C4⋊C4C22×C311yescharacteristic
206C22×C4⋊C4C22×C311yescharacteristic
207C22×C22⋊C4C22×C311yescharacteristic
208C22×C22⋊C4C22×C311yescharacteristic
209C22×C22⋊C4C22×C311yescharacteristic
210C22×C22⋊C4C22×C311yescharacteristic
211C22×C22⋊C4C22×C311yescharacteristic
212C22×C22⋊C4C22×C311yescharacteristic
213C22×C22⋊C4C22×C311yescharacteristic
214C22×C22⋊C4C22×C311yescharacteristic
215C22×C22⋊C4C22×C311yescharacteristic
216C22×C22⋊C4C22×C311yescharacteristic
217C22×C22⋊C4C22×C311yescharacteristic
218C22×C22⋊C4C22×C311yescharacteristic
219C22×C22⋊C4C22×C311yescharacteristic
220C22×C22⋊C4C22×C311yescharacteristic
221C22×C42C22×C311yescharacteristic
222#396—24no—
223#394—24no—
224#394—24no—
225#394—24no—
226#390—24no—
227#389—24no—
228#385—24no—
229C2×#95C22×C311yescharacteristic
230C2×#95C22×C311yescharacteristic
231C2×#95C22×C311yescharacteristic
232C2×#95C22×C311yescharacteristic
233C2×#95C22×C311yescharacteristic
234C2×#95C22×C311yescharacteristic
235C2×#95C22×C311yescharacteristic
236C2×#95C22×C311yescharacteristic
237C2×#95C22×C311yescharacteristic
238C2×#95C22×C311yescharacteristic
239C24×C3—21no—
240C24×C3—21no—
241C24×C3—21no—
242C24×C3—21no—
243C24×C3—21no—
244C24×C3—21no—
245C24×C3—21no—
246C24×C3—21no—
247C24×C3—21no—
248C24×C3—21no—
249C24×C3—21no—
250C24×C3—21no—
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×C3C2×D412yes—
280C24×C3C2×D412yes—
281C24×C3C2×D412yes—
282C24×C3C2×D412yes—
283C24×C3#4112yes—
284C24×C3C2411yescharacteristic
285C2×C3×D4—28no—
286C2×C3×D4—28no—
287C2×C3×D4—28no—
288C2×C3×D4—28no—
289C2×C3×D4—44no—
290C2×C3×D4—44no—
291C2×C3×D4—44no—
292C2×C3×D4—44no—
293C2×C3×D4—44no—
294C2×C3×D4—44no—
295C2×C3×D4—44no—
296C2×C3×D4—44no—
297C2×C3×D4—44no—
298C2×C3×D4—44no—
299C2×C3×D4—44no—
300C2×C3×D4—44no—
301C2×C3×D4—44no—
302C2×C3×D4—44no—
303C2×C3×D4—44no—
304C2×C3×D4—44no—
305C2×C3×D4—44no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—28no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—21no—
340C22×C3×C4—21no—
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4—21no—
345C22×C3×C4—21no—
346C22×C3×C4—21no—
347C22×C3×C4—21no—
348C22×C3×C4—21no—
349C22×C3×C4—21no—
350C22×C3×C4—21no—
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
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—21no—
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—44no—
378C22×C3×C4—44no—
379C22×C3×C4—44no—
380C22×C3×C4—44no—
381C22×C3×C4—44no—
382C22×C3×C4—44no—
383C22×C3×C4C2×D412yes—
384C22×C3×C4C2×D412yes—
385C22×C3×C4C2×D412yes—
386C22×C3×C4C2×D412yes—
387C22×C3×C4C2×D412yes—
388C22×C3×C4C2×D412yes—
389C22×C3×C4C2×D412yes—
390C22×C3×C4C2×D412yes—
391C22×C3×C4C2×D412yes—
392C22×C3×C4C2×D412yes—
393C22×C3×C4C2×D412yes—
394C22×C3×C4#4112yes—
395C22×C3×C4#4112yes—
396C22×C3×C4#4112yes—
397C3×C4⋊C4—28no—
398C3×C4⋊C4—28no—
399C3×C4⋊C4—44no—
400C3×C4⋊C4—44no—
401C3×C4⋊C4—44no—
402C3×C4⋊C4—44no—
403C3×C22⋊C4—28no—
404C3×C22⋊C4—28no—
405C3×C22⋊C4—28no—
406C3×C22⋊C4—44no—
407C3×C22⋊C4—44no—
408C3×C22⋊C4—44no—
409C3×C22⋊C4—44no—
410C3×C22⋊C4—44no—
411C3×C22⋊C4—44no—
412C3×C22⋊C4—44no—
413C3×C22⋊C4—44no—
414C3×C22⋊C4—44no—
415C3×C22⋊C4—44no—
416C3×C22⋊C4—44no—
417C3×C42—44no—
418C25C23×C311yescharacteristic
419C25C23×C311yescharacteristic
420C25C23×C311yescharacteristic
421C22×D4—22no—
422C22×D4—22no—
423C22×D4—22no—
424C22×D4—22no—
425C22×D4—22no—
426C22×D4—22no—
427C22×D4—22no—
428C22×D4—22no—
429C22×D4—22no—
430C22×D4—22no—
431C22×D4—22no—
432C22×D4—22no—
433C22×D4—22no—
434C22×D4—22no—
435C22×D4—41no—
436C22×D4—41no—
437C22×D4—41no—
438C22×D4—41no—
439C22×D4—41no—
440C22×D4—41no—
441C22×D4C3×D414yes—
442C23×C4—22no—
443C23×C4—22no—
444C23×C4—22no—
445C23×C4—22no—
446C23×C4—22no—
447C23×C4—41no—
448C23×C4—41no—
449C23×C4C23×C311yescharacteristic
450C23×C4C23×C311yescharacteristic
451C23×C4C23×C311yescharacteristic
452C23×C4C23×C311yescharacteristic
453C23×C4C23×C311yescharacteristic
454C23×C4C23×C311yescharacteristic
455C23×C4C23×C311yescharacteristic
456C23×C4C23×C311yescharacteristic
457C23×C4C23×C311yescharacteristic
458C23×C4C23×C311yescharacteristic
459C23×C4C23×C311yescharacteristic
460C23×C4C23×C311yescharacteristic
461#121—232no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—41no—
476C2×C4⋊C4—41no—
477C2×C4⋊C4—41no—
478C2×C4⋊C4C3×D414yes—
479C2×C4⋊C4C3×D414yescomplemented
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—41no—
511C2×C22⋊C4—41no—
512C2×C22⋊C4—41no—
513C2×C22⋊C4—41no—
514C2×C22⋊C4—41no—
515C2×C22⋊C4—41no—
516C2×C22⋊C4—41no—
517C2×C22⋊C4—41no—
518C2×C22⋊C4—41no—
519C2×C22⋊C4—41no—
520C2×C22⋊C4C3×D414yes—
521C2×C22⋊C4C3×D414yescomplemented
522C2×C42—22no—
523C2×C42—22no—
524C2×C42—41no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—41no—
534#95—41no—
535C23×C3—22no—
536C23×C3—22no—
537C23×C3—22no—
538C23×C3—22no—
539C23×C3—22no—
540C23×C3—22no—
541C23×C3—22no—
542C23×C3—22no—
543C23×C3—22no—
544C23×C3—22no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—22no—
550C23×C3—22no—
551C23×C3—22no—
552C23×C3—22no—
553C23×C3—22no—
554C23×C3—22no—
555C23×C3—22no—
556C23×C3—22no—
557C23×C3—22no—
558C23×C3—22no—
559C23×C3—22no—
560C23×C3—22no—
561C23×C3—22no—
562C23×C3—22no—
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—41no—
568C23×C3—41no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3—41no—
573C23×C3—41no—
574C23×C3—41no—
575C23×C3—41no—
576C23×C3—41no—
577C23×C3—41no—
578C23×C3—41no—
579C23×C3—41no—
580C23×C3—41no—
581C23×C3—41no—
582C23×C3—41no—
583C23×C3—41no—
584C23×C3—41no—
585C23×C3—41no—
586C23×C3—41no—
587C23×C3—41no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3—41no—
594C23×C3—41no—
595C23×C3—41no—
596C23×C3—41no—
597C23×C3—41no—
598C23×C3—41no—
599C23×C3—41no—
600C23×C3—41no—
601C23×C3—41no—
602C23×C3—41no—
603C23×C3—41no—
604C23×C3—41no—
605C23×C3—41no—
606C23×C3—41no—
607C23×C3—41no—
608C23×C3—41no—
609C23×C3—41no—
610C23×C3—41no—
611C23×C3—41no—
612C23×C3—41no—
613C23×C3—41no—
614C23×C3—41no—
615C23×C3—41no—
616C23×C3—41no—
617C23×C3—41no—
618C23×C3—41no—
619C23×C3—41no—
620C23×C3—41no—
621C23×C3—41no—
622C23×C3—41no—
623C23×C3—41no—
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#12114yes—
640C23×C3C22×D411yescharacteristic
641C23×C3C22×D411yescharacteristic
642C23×C3C22×D411yescharacteristic
643C23×C3C22×D411yescharacteristic
644C23×C3C22×D411yescharacteristic
645C23×C3C2×#4111yescharacteristic
646C23×C3C2×#4111yescharacteristic
647C23×C3C2×#4111yescharacteristic
648C23×C3C2×#4111yescharacteristic
649C23×C3H(5,𝔽2)11yescharacteristic
650C23×C3H(5,𝔽2)11yescharacteristic
651C23×C3H(5,𝔽2)11yescharacteristic
652C23×C3H(5,𝔽2)11yescharacteristic
653C23×C32−1+411yescharacteristic
654C23×C32−1+411yescharacteristic
655C3×D4—416no—
656C3×D4—416no—
657C3×D4—416no—
658C2×C3×C4—22no—
659C2×C3×C4—22no—
660C2×C3×C4—22no—
661C2×C3×C4—22no—
662C2×C3×C4—22no—
663C2×C3×C4—22no—
664C2×C3×C4—22no—
665C2×C3×C4—22no—
666C2×C3×C4—22no—
667C2×C3×C4—22no—
668C2×C3×C4—22no—
669C2×C3×C4—22no—
670C2×C3×C4—22no—
671C2×C3×C4—22no—
672C2×C3×C4—22no—
673C2×C3×C4—22no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
676C2×C3×C4—22no—
677C2×C3×C4—22no—
678C2×C3×C4—22no—
679C2×C3×C4—22no—
680C2×C3×C4—22no—
681C2×C3×C4—22no—
682C2×C3×C4—22no—
683C2×C3×C4—22no—
684C2×C3×C4—22no—
685C2×C3×C4—22no—
686C2×C3×C4—22no—
687C2×C3×C4—22no—
688C2×C3×C4—22no—
689C2×C3×C4—22no—
690C2×C3×C4—22no—
691C2×C3×C4—416no—
692C2×C3×C4—41no—
693C2×C3×C4—41no—
694C2×C3×C4—41no—
695C2×C3×C4—41no—
696C2×C3×C4—41no—
697C2×C3×C4—41no—
698C2×C3×C4—41no—
699C2×C3×C4—41no—
700C2×C3×C4—41no—
701C2×C3×C4—41no—
702C2×C3×C4—41no—
703C2×C3×C4—41no—
704C2×C3×C4—41no—
705C2×C3×C4—41no—
706C2×C3×C4—41no—
707C2×C3×C4—41no—
708C2×C3×C4—41no—
709C2×C3×C4—41no—
710C2×C3×C4—41no—
711C2×C3×C4—41no—
712C2×C3×C4—41no—
713C2×C3×C4—41no—
714C2×C3×C4—41no—
715C2×C3×C4—41no—
716C2×C3×C4—41no—
717C2×C3×C4—41no—
718C2×C3×C4—41no—
719C2×C3×C4—41no—
720C2×C3×C4—41no—
721C2×C3×C4—41no—
722C2×C3×C4—41no—
723C2×C3×C4—41no—
724C2×C3×C4—41no—
725C2×C3×C4—41no—
726C2×C3×C4—41no—
727C2×C3×C4—41no—
728C2×C3×C4—41no—
729C2×C3×C4—41no—
730C2×C3×C4—41no—
731C2×C3×C4—41no—
732C2×C3×C4—41no—
733C2×C3×C4—41no—
734C2×C3×C4—41no—
735C2×C3×C4—41no—
736C2×C3×C4—41no—
737C2×C3×C4—41no—
738C2×C3×C4—41no—
739C2×C3×C4—41no—
740C2×C3×C4#12014yes—
741C2×C3×C4#12114yes—
742C2×C3×C4#12114yescomplemented
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24C2×C3×D412yes—
784C24C2×C3×D412yes—
785C24C2×C3×D412yes—
786C24C2×C3×D412yes—
787C24C3×#4112yes—
788C24C24×C311yescharacteristic
789C2×D4—28no—
790C2×D4—28no—
791C2×D4—28no—
792C2×D4—28no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
797C2×D4—44no—
798C2×D4—44no—
799C2×D4—44no—
800C2×D4—44no—
801C2×D4—44no—
802C2×D4—44no—
803C2×D4—44no—
804C2×D4—44no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—44no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—28no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4C2×C3×D412yes—
888C22×C4C2×C3×D412yes—
889C22×C4C2×C3×D412yes—
890C22×C4C2×C3×D412yes—
891C22×C4C2×C3×D412yes—
892C22×C4C2×C3×D412yes—
893C22×C4C2×C3×D412yes—
894C22×C4C2×C3×D412yes—
895C22×C4C2×C3×D412yes—
896C22×C4C2×C3×D412yes—
897C22×C4C2×C3×D412yes—
898C22×C4C3×#4112yes—
899C22×C4C3×#4112yes—
900C22×C4C3×#4112yes—
901C4⋊C4—28no—
902C4⋊C4—28no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C22⋊C4—28no—
908C22⋊C4—28no—
909C22⋊C4—28no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C42—44no—
922C22×C3—24no—
923C22×C3—24no—
924C22×C3—24no—
925C22×C3—42no—
926C22×C3—42no—
927C22×C3—42no—
928C22×C3—42no—
929C22×C3—42no—
930C22×C3—42no—
931C22×C3—42no—
932C22×C3—42no—
933C22×C3—42no—
934C22×C3—42no—
935C22×C3—42no—
936C22×C3—42no—
937C22×C3—42no—
938C22×C3—42no—
939C22×C3—42no—
940C22×C3—42no—
941C22×C3—42no—
942C22×C3—42no—
943C22×C3—42no—
944C22×C3—42no—
945C22×C3—42no—
946C22×C3—42no—
947C22×C3—42no—
948C22×C3—42no—
949C22×C3—42no—
950C22×C3—42no—
951C22×C3—81no—
952C22×C3—81no—
953C22×C3—81no—
954C22×C3—81no—
955C22×C3—81no—
956C22×C3—81no—
957C22×C3—81no—
958C22×C3—81no—
959C22×C3—81no—
960C22×C3—81no—
961C22×C3—81no—
962C22×C3—81no—
963C22×C3—81no—
964C22×C3—81no—
965C22×C3—81no—
966C22×C3—81no—
967C22×C3C2×#12011yescharacteristic
968C22×C3C2×#12111yescharacteristic
969C22×C3C2×#12111yescharacteristic
970C22×C3C2×#12111yescharacteristic
971C22×C3#52911yescharacteristic
972C22×C3#53211yescharacteristic
973C22×C3#53411yescharacteristic
974C22×C3#53511yescharacteristic
975C22×C3#53611yescharacteristic
976C22×C3#53711yescharacteristic
977C22×C3#53711yescharacteristic
978C22×C3#53811yescharacteristic
979C22×C3#53911yescharacteristic
980C22×C3#54011yescharacteristic
981C22×C3#54211yescharacteristic
982C22×C3D4211yescharacteristic
983C22×C3D4211yescharacteristic
984C22×C3D4211yescharacteristic
985C22×C3D4211yescharacteristic
986C22×C3#54611yescharacteristic
987C22×C3#54611yescharacteristic
988C22×C3#54611yescharacteristic
989C22×C3#54611yescharacteristic
990C22×C3#54611yescharacteristic
991C22×C3#54711yescharacteristic
992C22×C3#54711yescharacteristic
993C22×C3#54711yescharacteristic
994C22×C3#54811yescharacteristic
995C22×C3#54811yescharacteristic
996C22×C3#54811yescharacteristic
997C22×C3#55011yescharacteristic
998C22×C3#55311yescharacteristic
999C22×C3#55311yescharacteristic
1000C22×C3#56211yescharacteristic
1001C22×C3#56211yescharacteristic
1002C3×C4—24no—
1003C3×C4—24no—
1004C3×C4—24no—
1005C3×C4—42no—
1006C3×C4—42no—
1007C3×C4—42no—
1008C3×C4—42no—
1009C3×C4—42no—
1010C3×C4—81no—
1011C3×C4—81no—
1012C3×C4—81no—
1013C3×C4—81no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23C3×#12114yes—
1119C23C22×C3×D411yescharacteristic
1120C23C22×C3×D411yescharacteristic
1121C23C22×C3×D411yescharacteristic
1122C23C22×C3×D411yescharacteristic
1123C23C22×C3×D411yescharacteristic
1124C23C2×C3×#4111yescharacteristic
1125C23C2×C3×#4111yescharacteristic
1126C23C2×C3×#4111yescharacteristic
1127C23C2×C3×#4111yescharacteristic
1128C23C3×H(5,𝔽2)11yescharacteristic
1129C23C3×H(5,𝔽2)11yescharacteristic
1130C23C3×H(5,𝔽2)11yescharacteristic
1131C23C3×H(5,𝔽2)11yescharacteristic
1132C23C3×2−1+411yescharacteristic
1133C23C3×2−1+411yescharacteristic
1134D4—416no—
1135D4—416no—
1136D4—416no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—416no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4C3×#12014yes—
1220C2×C4C3×#12114yes—
1221C2×C4C3×#12114yescomplemented
1222C2×C3—44no—
1223C2×C3—82no—
1224C2×C3—82no—
1225C2×C3#240811yescharacteristic
1226C2×C3#241011yescharacteristic
1227C2×C3#241611yescharacteristic
1228C2×C3#241611yescharacteristic
1229C2×C3#242511yescharacteristic
1230C2×C3#242611yescharacteristic
1231C2×C3#242811yescharacteristic
1232C2×C3#243211yescharacteristic
1233C2×C3#255911yescharacteristic
1234C2×C3#267211yescharacteristic
1235C2×C3#267611yescharacteristic
1236C2×C3#268111yescharacteristic
1237C2×C3#268211yescharacteristic
1238C2×C3#270111yescharacteristic
1239C2×C3#271111yescharacteristic
1240C22—24no—
1241C22—24no—
1242C22—24no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22C2×C3×#12011yescharacteristic
1286C22C2×C3×#12111yescharacteristic
1287C22C2×C3×#12111yescharacteristic
1288C22C2×C3×#12111yescharacteristic
1289C22C3×#52911yescharacteristic
1290C22C3×#53211yescharacteristic
1291C22C3×#53411yescharacteristic
1292C22C3×#53511yescharacteristic
1293C22C3×#53611yescharacteristic
1294C22C3×#53711yescharacteristic
1295C22C3×#53711yescharacteristic
1296C22C3×#53811yescharacteristic
1297C22C3×#53911yescharacteristic
1298C22C3×#54011yescharacteristic
1299C22C3×#54211yescharacteristic
1300C22C3×D4211yescharacteristic
1301C22C3×D4211yescharacteristic
1302C22C3×D4211yescharacteristic
1303C22C3×D4211yescharacteristic
1304C22C3×#54611yescharacteristic
1305C22C3×#54611yescharacteristic
1306C22C3×#54611yescharacteristic
1307C22C3×#54611yescharacteristic
1308C22C3×#54611yescharacteristic
1309C22C3×#54711yescharacteristic
1310C22C3×#54711yescharacteristic
1311C22C3×#54711yescharacteristic
1312C22C3×#54811yescharacteristic
1313C22C3×#54811yescharacteristic
1314C22C3×#54811yescharacteristic
1315C22C3×#55011yescharacteristic
1316C22C3×#55311yescharacteristic
1317C22C3×#55311yescharacteristic
1318C22C3×#56211yescharacteristic
1319C22C3×#56211yescharacteristic
1320C4—24no—
1321C4—24no—
1322C4—24no—
1323C4—42no—
1324C4—42no—
1325C4—42no—
1326C4—42no—
1327C4—42no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C3#1531611yescharacteristic, direct product factor, Sylow
1333C2—44no—
1334C2—82no—
1335C2—82no—
1336C2C3×#240811yescharacteristic
1337C2C3×#241011yescharacteristic
1338C2C3×#241611yescharacteristic
1339C2C3×#241611yescharacteristic
1340C2C3×#242511yescharacteristic
1341C2C3×#242611yescharacteristic
1342C2C3×#242811yescharacteristic
1343C2C3×#243211yescharacteristic
1344C2C3×#255911yescharacteristic
1345C2C3×#267211yescharacteristic
1346C2C3×#267611yescharacteristic
1347C2C3×#268111yescharacteristic
1348C2C3×#268211yescharacteristic
1349C2C3×#270111yescharacteristic
1350C2C3×#271111yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC22×C3×#121C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#396C2semidirect
3. C2×C3×#394C2semidirect
4. C2×C3×#394C2semidirect
5. C2×C3×#394C2semidirect
6. C2×C3×#390C2semidirect
7. C2×C3×#389C2semidirect
8. C2×C3×#385C2semidirect
9. C3×#1441C2semidirect
10. C3×#1439C2semidirect
11. C3×#1439C2semidirect
12. C3×#1438C2semidirect
13. C3×#1438C2semidirect
14. C3×#1437C2semidirect
15. C3×C22⋊#95C2semidirect
16. #15316C3direct (N × H)
63. C2×#396C2×C3semidirect
64. C2×#394C2×C3semidirect
65. C2×#394C2×C3semidirect
66. C2×#394C2×C3semidirect
67. C2×#390C2×C3semidirect
68. C2×#389C2×C3semidirect
69. C2×#385C2×C3semidirect
70. #1441C2×C3semidirect
71. #1439C2×C3semidirect
72. #1439C2×C3semidirect
73. #1438C2×C3semidirect
74. #1438C2×C3semidirect
75. #1437C2×C3semidirect
76. C22⋊#95C2×C3semidirect
138. C2×C3×C4⋊C4D4semidirect
180. C2×C3×C22⋊C4D4semidirect
479. C2×C4⋊C4C3×D4semidirect
521. C2×C22⋊C4C3×D4semidirect
742. C2×C3×C4#121semidirect
1221. C2×C4C3×#121semidirect
1332. C3#15316direct (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×#3962
C2×C3×#3942
C2×C3×#3902
C2×C3×#3892
C2×C3×#3852
C3×#14412
C3×#14392
C3×#14382
C3×#14372
C3×C22⋊#952
#153163