Finite Group Databasebeta

← C3×#14760 #10633367

Subgroups — C3×#14760 #10633367

Order 768.

2414 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#123C211yesmaximal, characteristic, complemented
2C2×C3×#392C211yesmaximal, characteristic
3C2×C3×#390C211yesmaximal, characteristic, complemented
4C2×C3×#388C211yesmaximal, characteristic, complemented
5C2×C3×#386C211yesmaximal, characteristic, complemented
6C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
7C3×#1441C211yesmaximal, characteristic, complemented
8C3×#1440C211yesmaximal, characteristic, complemented
9C3×#1439C211yesmaximal, characteristic, complemented
10C3×#1439C211yesmaximal, characteristic, complemented
11C3×#1438C211yesmaximal, characteristic, complemented
12C3×#1438C211yesmaximal, characteristic, complemented
13C3×#1438C211yesmaximal, characteristic, complemented
14C3×#1437C211yesmaximal, characteristic, complemented
15C3×#1436C211yesmaximal, characteristic, complemented
16#14760C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×D4C2211yescharacteristic
18C23×C3×D4C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C24×C3×C4C2211yescharacteristic
21C2×C3×#123—24no—
22C2×C3×#123—24no—
23C2×C3×#123—24no—
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊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×C42C2211yescharacteristic
42C22×C3×C42C2211yescharacteristic
43C3×#392—24no—
44C3×#390—24no—
45C3×#388—24no—
46C3×#386—24no—
47C3×C4×C22⋊C4—24no—
48C2×C3×#95C2211yescharacteristic
49C2×C3×#95C2211yescharacteristic
50C2×C3×#95C2211yescharacteristic
51C2×C3×#95C2211yescharacteristic
52C2×C3×#95C2211yescharacteristic
53C2×C3×#95C2211yescharacteristic
54C2×C3×#95C2211yescharacteristic
55C2×C3×#95C2211yescharacteristic
56C2×C3×#95C2211yescharacteristic
57C2×C3×#95C2211yescharacteristic
58C2×C3×#95C2211yescharacteristic
59C2×C3×#95C2211yescharacteristic
60C22×#123C2×C311yescharacteristic, complemented
61C2×#392C2×C311yescharacteristic
62C2×#390C2×C311yescharacteristic, complemented
63C2×#388C2×C311yescharacteristic, complemented
64C2×#386C2×C311yescharacteristic, complemented
65C2×C4×C22⋊C4C2×C311yescharacteristic, complemented
66#1441C2×C311yescharacteristic, complemented
67#1440C2×C311yescharacteristic, complemented
68#1439C2×C311yescharacteristic, complemented
69#1439C2×C311yescharacteristic, complemented
70#1438C2×C311yescharacteristic, complemented
71#1438C2×C311yescharacteristic, complemented
72#1438C2×C311yescharacteristic, complemented
73#1437C2×C311yescharacteristic, complemented
74#1436C2×C311yescharacteristic, complemented
75C25×C3C2311yescharacteristic
76C25×C3C2311yescharacteristic
77C25×C3C2311yescharacteristic
78C22×C3×D4—22no—
79C22×C3×D4—22no—
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—41no—
94C22×C3×D4—41no—
95C22×C3×D4—41no—
96C22×C3×D4—41no—
97C22×C3×D4—41no—
98C22×C3×D4—41no—
99C23×C3×C4—22no—
100C23×C3×C4—22no—
101C23×C3×C4—22no—
102C23×C3×C4—22no—
103C23×C3×C4—41no—
104C23×C3×C4—41no—
105C23×C3×C4D414yescomplemented
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
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
118C3×#123—232no—
119C2×C3×C4⋊C4—22no—
120C2×C3×C4⋊C4—22no—
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—41no—
127C2×C3×C4⋊C4D414yescomplemented
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4—22no—
130C2×C3×C22⋊C4—22no—
131C2×C3×C22⋊C4—22no—
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—22no—
134C2×C3×C22⋊C4—22no—
135C2×C3×C22⋊C4—22no—
136C2×C3×C22⋊C4—22no—
137C2×C3×C22⋊C4—22no—
138C2×C3×C22⋊C4—22no—
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—41no—
159C2×C3×C22⋊C4—41no—
160C2×C3×C22⋊C4—41no—
161C2×C3×C22⋊C4—41no—
162C2×C3×C22⋊C4—41no—
163C2×C3×C22⋊C4—41no—
164C2×C3×C22⋊C4—41no—
165C2×C3×C22⋊C4—41no—
166C2×C3×C22⋊C4—41no—
167C2×C3×C22⋊C4—41no—
168C2×C3×C22⋊C4D414yes—
169C2×C3×C22⋊C4D414yescomplemented
170C2×C3×C42—22no—
171C2×C3×C42—22no—
172C2×C3×C42—22no—
173C2×C3×C42—22no—
174C2×C3×C42—41no—
175C2×C3×C42—41no—
176C3×#95—22no—
177C3×#95—22no—
178C3×#95—22no—
179C3×#95—22no—
180C3×#95—22no—
181C3×#95—22no—
182C3×#95—22no—
183C3×#95—22no—
184C3×#95—22no—
185C3×#95—41no—
186C3×#95—41no—
187C3×#95—41no—
188C23×D4C22×C311yescharacteristic
189C23×D4C22×C311yescharacteristic
190C23×D4C22×C311yescharacteristic
191C24×C4C22×C311yescharacteristic
192C2×#123—24no—
193C2×#123—24no—
194C2×#123—24no—
195C22×C4⋊C4C22×C311yescharacteristic
196C22×C4⋊C4C22×C311yescharacteristic
197C22×C4⋊C4C22×C311yescharacteristic
198C22×C22⋊C4C22×C311yescharacteristic
199C22×C22⋊C4C22×C311yescharacteristic
200C22×C22⋊C4C22×C311yescharacteristic
201C22×C22⋊C4C22×C311yescharacteristic
202C22×C22⋊C4C22×C311yescharacteristic
203C22×C22⋊C4C22×C311yescharacteristic
204C22×C22⋊C4C22×C311yescharacteristic
205C22×C22⋊C4C22×C311yescharacteristic
206C22×C22⋊C4C22×C311yescharacteristic
207C22×C22⋊C4C22×C311yescharacteristic
208C22×C22⋊C4C22×C311yescharacteristic
209C22×C22⋊C4C22×C311yescharacteristic
210C22×C22⋊C4C22×C311yescharacteristic
211C22×C22⋊C4C22×C311yescharacteristic
212C22×C42C22×C311yescharacteristic
213C22×C42C22×C311yescharacteristic
214#392—24no—
215#390—24no—
216#388—24no—
217#386—24no—
218C4×C22⋊C4—24no—
219C2×#95C22×C311yescharacteristic
220C2×#95C22×C311yescharacteristic
221C2×#95C22×C311yescharacteristic
222C2×#95C22×C311yescharacteristic
223C2×#95C22×C311yescharacteristic
224C2×#95C22×C311yescharacteristic
225C2×#95C22×C311yescharacteristic
226C2×#95C22×C311yescharacteristic
227C2×#95C22×C311yescharacteristic
228C2×#95C22×C311yescharacteristic
229C2×#95C22×C311yescharacteristic
230C2×#95C22×C311yescharacteristic
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3—21no—
237C24×C3—21no—
238C24×C3—21no—
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×C3C2×D412yes—
272C24×C3C2×D412yes—
273C24×C3C2×D412yes—
274C24×C3#4112yes—
275C24×C3#4112yes—
276C24×C3C2411yescharacteristic
277C2×C3×D4—28no—
278C2×C3×D4—28no—
279C2×C3×D4—28no—
280C2×C3×D4—44no—
281C2×C3×D4—44no—
282C2×C3×D4—44no—
283C2×C3×D4—44no—
284C2×C3×D4—44no—
285C2×C3×D4—44no—
286C2×C3×D4—44no—
287C2×C3×D4—44no—
288C2×C3×D4—44no—
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—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—28no—
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—21no—
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—28no—
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—44no—
371C22×C3×C4—44no—
372C22×C3×C4—44no—
373C22×C3×C4—44no—
374C22×C3×C4—44no—
375C22×C3×C4C2×D412yes—
376C22×C3×C4C2×D412yes—
377C22×C3×C4C2×D412yes—
378C22×C3×C4C2×D412yes—
379C22×C3×C4C2×D412yes—
380C22×C3×C4C2×D412yes—
381C22×C3×C4C2×D412yes—
382C22×C3×C4C2×D412yes—
383C22×C3×C4C2×D412yes—
384C22×C3×C4#4112yes—
385C22×C3×C4#4112yes—
386C22×C3×C4#4112yes—
387C22×C3×C4#4112yes—
388C22×C3×C4#4112yes—
389C3×C4⋊C4—28no—
390C3×C4⋊C4—28no—
391C3×C4⋊C4—44no—
392C3×C22⋊C4—28no—
393C3×C22⋊C4—28no—
394C3×C22⋊C4—28no—
395C3×C22⋊C4—28no—
396C3×C22⋊C4—28no—
397C3×C22⋊C4—28no—
398C3×C22⋊C4—44no—
399C3×C22⋊C4—44no—
400C3×C22⋊C4—44no—
401C3×C22⋊C4—44no—
402C3×C22⋊C4—44no—
403C3×C22⋊C4—44no—
404C3×C22⋊C4—44no—
405C3×C22⋊C4—44no—
406C3×C42—44no—
407C3×C42—44no—
408C25C23×C311yescharacteristic
409C25C23×C311yescharacteristic
410C25C23×C311yescharacteristic
411C22×D4—22no—
412C22×D4—22no—
413C22×D4—22no—
414C22×D4—22no—
415C22×D4—22no—
416C22×D4—22no—
417C22×D4—22no—
418C22×D4—22no—
419C22×D4—22no—
420C22×D4—22no—
421C22×D4—22no—
422C22×D4—22no—
423C22×D4—22no—
424C22×D4—22no—
425C22×D4—22no—
426C22×D4—41no—
427C22×D4—41no—
428C22×D4—41no—
429C22×D4—41no—
430C22×D4—41no—
431C22×D4—41no—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—41no—
437C23×C4—41no—
438C23×C4C3×D414yescomplemented
439C23×C4C23×C311yescharacteristic
440C23×C4C23×C311yescharacteristic
441C23×C4C23×C311yescharacteristic
442C23×C4C23×C311yescharacteristic
443C23×C4C23×C311yescharacteristic
444C23×C4C23×C311yescharacteristic
445C23×C4C23×C311yescharacteristic
446C23×C4C23×C311yescharacteristic
447C23×C4C23×C311yescharacteristic
448C23×C4C23×C311yescharacteristic
449C23×C4C23×C311yescharacteristic
450C23×C4C23×C311yescharacteristic
451#123—232no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—41no—
460C2×C4⋊C4C3×D414yescomplemented
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
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—41no—
492C2×C22⋊C4—41no—
493C2×C22⋊C4—41no—
494C2×C22⋊C4—41no—
495C2×C22⋊C4—41no—
496C2×C22⋊C4—41no—
497C2×C22⋊C4—41no—
498C2×C22⋊C4—41no—
499C2×C22⋊C4—41no—
500C2×C22⋊C4—41no—
501C2×C22⋊C4C3×D414yes—
502C2×C22⋊C4C3×D414yescomplemented
503C2×C42—22no—
504C2×C42—22no—
505C2×C42—22no—
506C2×C42—22no—
507C2×C42—41no—
508C2×C42—41no—
509#95—22no—
510#95—22no—
511#95—22no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95—22no—
516#95—22no—
517#95—22no—
518#95—41no—
519#95—41no—
520#95—41no—
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—22no—
534C23×C3—22no—
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—41no—
554C23×C3—41no—
555C23×C3—41no—
556C23×C3—41no—
557C23×C3—41no—
558C23×C3—41no—
559C23×C3—41no—
560C23×C3—41no—
561C23×C3—41no—
562C23×C3—41no—
563C23×C3—41no—
564C23×C3—41no—
565C23×C3—41no—
566C23×C3—41no—
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#12114yes—
626C23×C3C22×D411yescharacteristic
627C23×C3C22×D411yescharacteristic
628C23×C3C22×D411yescharacteristic
629C23×C3C22×D411yescharacteristic
630C23×C3C2×#4111yescharacteristic
631C23×C3C2×#4111yescharacteristic
632C23×C3C2×#4111yescharacteristic
633C23×C3C2×#4111yescharacteristic
634C23×C3C2×#4111yescharacteristic
635C23×C3C2×#4111yescharacteristic
636C23×C3C2×#4111yescharacteristic
637C23×C3H(5,𝔽2)11yescharacteristic
638C23×C3H(5,𝔽2)11yescharacteristic
639C23×C3H(5,𝔽2)11yescharacteristic
640C23×C3H(5,𝔽2)11yescharacteristic
641C3×D4—416no—
642C3×D4—416no—
643C3×D4—416no—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—22no—
654C2×C3×C4—22no—
655C2×C3×C4—22no—
656C2×C3×C4—22no—
657C2×C3×C4—22no—
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—416no—
681C2×C3×C4—41no—
682C2×C3×C4—41no—
683C2×C3×C4—41no—
684C2×C3×C4—41no—
685C2×C3×C4—41no—
686C2×C3×C4—41no—
687C2×C3×C4—41no—
688C2×C3×C4—41no—
689C2×C3×C4—41no—
690C2×C3×C4—41no—
691C2×C3×C4—41no—
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#12014yes—
728C2×C3×C4#12314yescomplemented
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
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—
769C24C2×C3×D412yes—
770C24C2×C3×D412yes—
771C24C2×C3×D412yes—
772C24C3×#4112yes—
773C24C3×#4112yes—
774C24C24×C311yescharacteristic
775C2×D4—28no—
776C2×D4—28no—
777C2×D4—28no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
790C2×D4—44no—
791C2×D4—44no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—28no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
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—21no—
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—28no—
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—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4C2×C3×D412yes—
874C22×C4C2×C3×D412yes—
875C22×C4C2×C3×D412yes—
876C22×C4C2×C3×D412yes—
877C22×C4C2×C3×D412yes—
878C22×C4C2×C3×D412yes—
879C22×C4C2×C3×D412yes—
880C22×C4C2×C3×D412yes—
881C22×C4C2×C3×D412yes—
882C22×C4C3×#4112yes—
883C22×C4C3×#4112yes—
884C22×C4C3×#4112yes—
885C22×C4C3×#4112yes—
886C22×C4C3×#4112yes—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—44no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—28no—
894C22⋊C4—28no—
895C22⋊C4—28no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C42—44no—
905C42—44no—
906C22×C3—24no—
907C22×C3—24no—
908C22×C3—24no—
909C22×C3—42no—
910C22×C3—42no—
911C22×C3—42no—
912C22×C3—42no—
913C22×C3—42no—
914C22×C3—42no—
915C22×C3—42no—
916C22×C3—42no—
917C22×C3—42no—
918C22×C3—42no—
919C22×C3—42no—
920C22×C3—42no—
921C22×C3—42no—
922C22×C3—42no—
923C22×C3—42no—
924C22×C3—42no—
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—81no—
936C22×C3—81no—
937C22×C3—81no—
938C22×C3—81no—
939C22×C3—81no—
940C22×C3—81no—
941C22×C3—81no—
942C22×C3—81no—
943C22×C3—81no—
944C22×C3—81no—
945C22×C3—81no—
946C22×C3—81no—
947C22×C3—81no—
948C22×C3—81no—
949C22×C3—81no—
950C22×C3—81no—
951C22×C3C2×#12011yescharacteristic
952C22×C3C2×#12111yescharacteristic
953C22×C3C2×#12311yescharacteristic
954C22×C3#52511yescharacteristic
955C22×C3#52511yescharacteristic
956C22×C3#52511yescharacteristic
957C22×C3#52511yescharacteristic
958C22×C3#52911yescharacteristic
959C22×C3#52911yescharacteristic
960C22×C3#53211yescharacteristic
961C22×C3#53211yescharacteristic
962C22×C3#53211yescharacteristic
963C22×C3#53211yescharacteristic
964C22×C3#53411yescharacteristic
965C22×C3#53511yescharacteristic
966C22×C3#53811yescharacteristic
967C22×C3#53811yescharacteristic
968C22×C3#54011yescharacteristic
969C22×C3#54011yescharacteristic
970C22×C3D4211yescharacteristic
971C22×C3D4211yescharacteristic
972C22×C3#54611yescharacteristic
973C22×C3#54611yescharacteristic
974C22×C3#54611yescharacteristic
975C22×C3#54611yescharacteristic
976C22×C3#54611yescharacteristic
977C22×C3#54611yescharacteristic
978C22×C3#55011yescharacteristic
979C22×C3#55011yescharacteristic
980C22×C3#55111yescharacteristic
981C22×C3#55111yescharacteristic
982C22×C3#55111yescharacteristic
983C22×C3#55311yescharacteristic
984C22×C3#55311yescharacteristic
985C22×C3#55911yescharacteristic
986C3×C4—24no—
987C3×C4—24no—
988C3×C4—42no—
989C3×C4—42no—
990C3×C4—42no—
991C3×C4—42no—
992C3×C4—42no—
993C3×C4—42no—
994C3×C4—42no—
995C3×C4—42no—
996C3×C4—81no—
997C3×C4—81no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
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—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
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—
1102C23C3×#12114yes—
1103C23C22×C3×D411yescharacteristic
1104C23C22×C3×D411yescharacteristic
1105C23C22×C3×D411yescharacteristic
1106C23C22×C3×D411yescharacteristic
1107C23C2×C3×#4111yescharacteristic
1108C23C2×C3×#4111yescharacteristic
1109C23C2×C3×#4111yescharacteristic
1110C23C2×C3×#4111yescharacteristic
1111C23C2×C3×#4111yescharacteristic
1112C23C2×C3×#4111yescharacteristic
1113C23C2×C3×#4111yescharacteristic
1114C23C3×H(5,𝔽2)11yescharacteristic
1115C23C3×H(5,𝔽2)11yescharacteristic
1116C23C3×H(5,𝔽2)11yescharacteristic
1117C23C3×H(5,𝔽2)11yescharacteristic
1118D4—416no—
1119D4—416no—
1120D4—416no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
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—416no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
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×C4C3×#12014yes—
1205C2×C4C3×#12314yescomplemented
1206C2×C3—44no—
1207C2×C3—82no—
1208C2×C3—82no—
1209C2×C3#238811yescharacteristic
1210C2×C3#241011yescharacteristic
1211C2×C3#241111yescharacteristic
1212C2×C3#241811yescharacteristic
1213C2×C3#243111yescharacteristic
1214C2×C3#244511yescharacteristic
1215C2×C3#245611yescharacteristic
1216C2×C3#245711yescharacteristic
1217C2×C3#246411yescharacteristic
1218C2×C3#247111yescharacteristic
1219C2×C3#255411yescharacteristic
1220C2×C3#255711yescharacteristic
1221C2×C3#260211yescharacteristic
1222C2×C3#266111yescharacteristic
1223C2×C3#285411yescharacteristic
1224C22—24no—
1225C22—24no—
1226C22—24no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22C2×C3×#12011yescharacteristic
1270C22C2×C3×#12111yescharacteristic
1271C22C2×C3×#12311yescharacteristic
1272C22C3×#52511yescharacteristic
1273C22C3×#52511yescharacteristic
1274C22C3×#52511yescharacteristic
1275C22C3×#52511yescharacteristic
1276C22C3×#52911yescharacteristic
1277C22C3×#52911yescharacteristic
1278C22C3×#53211yescharacteristic
1279C22C3×#53211yescharacteristic
1280C22C3×#53211yescharacteristic
1281C22C3×#53211yescharacteristic
1282C22C3×#53411yescharacteristic
1283C22C3×#53511yescharacteristic
1284C22C3×#53811yescharacteristic
1285C22C3×#53811yescharacteristic
1286C22C3×#54011yescharacteristic
1287C22C3×#54011yescharacteristic
1288C22C3×D4211yescharacteristic
1289C22C3×D4211yescharacteristic
1290C22C3×#54611yescharacteristic
1291C22C3×#54611yescharacteristic
1292C22C3×#54611yescharacteristic
1293C22C3×#54611yescharacteristic
1294C22C3×#54611yescharacteristic
1295C22C3×#54611yescharacteristic
1296C22C3×#55011yescharacteristic
1297C22C3×#55011yescharacteristic
1298C22C3×#55111yescharacteristic
1299C22C3×#55111yescharacteristic
1300C22C3×#55111yescharacteristic
1301C22C3×#55311yescharacteristic
1302C22C3×#55311yescharacteristic
1303C22C3×#55911yescharacteristic
1304C4—24no—
1305C4—24no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—42no—
1314C4—81no—
1315C4—81no—
1316C3#1476011yescharacteristic, direct product factor, Sylow
1317C2—44no—
1318C2—82no—
1319C2—82no—
1320C2C3×#238811yescharacteristic
1321C2C3×#241011yescharacteristic
1322C2C3×#241111yescharacteristic
1323C2C3×#241811yescharacteristic
1324C2C3×#243111yescharacteristic
1325C2C3×#244511yescharacteristic
1326C2C3×#245611yescharacteristic
1327C2C3×#245711yescharacteristic
1328C2C3×#246411yescharacteristic
1329C2C3×#247111yescharacteristic
1330C2C3×#255411yescharacteristic
1331C2C3×#255711yescharacteristic
1332C2C3×#260211yescharacteristic
1333C2C3×#266111yescharacteristic
1334C2C3×#285411yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC2×C3×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×#123C2semidirect
3. C2×C3×#390C2semidirect
4. C2×C3×#388C2semidirect
5. C2×C3×#386C2semidirect
6. C2×C3×C4×C22⋊C4C2semidirect
7. C3×#1441C2semidirect
8. C3×#1440C2semidirect
9. C3×#1439C2semidirect
10. C3×#1439C2semidirect
11. C3×#1438C2semidirect
12. C3×#1438C2semidirect
13. C3×#1438C2semidirect
14. C3×#1437C2semidirect
15. C3×#1436C2semidirect
16. #14760C3direct (N × H)
60. C22×#123C2×C3semidirect
62. C2×#390C2×C3semidirect
63. C2×#388C2×C3semidirect
64. C2×#386C2×C3semidirect
65. C2×C4×C22⋊C4C2×C3semidirect
66. #1441C2×C3semidirect
67. #1440C2×C3semidirect
68. #1439C2×C3semidirect
69. #1439C2×C3semidirect
70. #1438C2×C3semidirect
71. #1438C2×C3semidirect
72. #1438C2×C3semidirect
73. #1437C2×C3semidirect
74. #1436C2×C3semidirect
105. C23×C3×C4D4semidirect
127. C2×C3×C4⋊C4D4semidirect
169. C2×C3×C22⋊C4D4semidirect
438. C23×C4C3×D4semidirect
460. C2×C4⋊C4C3×D4semidirect
502. C2×C22⋊C4C3×D4semidirect
728. C2×C3×C4#123semidirect
1205. C2×C4C3×#123semidirect
1316. C3#14760direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1232
C2×C3×#3922
C2×C3×#3902
C2×C3×#3882
C2×C3×#3862
C2×C3×C4×C22⋊C42
C3×#14412
C3×#14402
C3×#14392
C3×#14382
C3×#14372
C3×#14362
#147603