Finite Group Databasebeta

← #11807829

Subgroups — #11807829

Order 1152.

1089 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64087C211yesmaximal, characteristic
2C3×#4951C211yesmaximal, characteristic
3C3×#4951C211yesmaximal, characteristic
4#10591720C211yesmaximal, characteristic
5#10591703C211yesmaximal, characteristic
6#10591703C211yesmaximal, characteristic
7#10591697C211yesmaximal, characteristic
8#10591273C211yesmaximal, characteristic, complemented
9#10591271C211yesmaximal, characteristic, complemented
10#10591264C211yesmaximal, characteristic, complemented
11#10591263C211yesmaximal, characteristic, complemented
12#10591213C211yesmaximal, characteristic, complemented
13#10591212C211yesmaximal, characteristic, complemented
14#10591197C211yesmaximal, characteristic, complemented
15#10591197C211yesmaximal, characteristic, complemented
16#75492—31nomaximal
17#75491—31nomaximal
18C23×C3⋊Dic3C2211yescharacteristic
19C22×#634C2211yescharacteristic
20C2×C32×C22⋊C4C2211yescharacteristic
21C2×#3757C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25#64087C418yescomplemented
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×#3724C2211yescharacteristic
37C2×#3724C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40C3×C3⋊#95C2211yescharacteristic
41C3×C3⋊#95C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44#63579C2211yescharacteristic
45#63579C2211yescharacteristic
46#63579C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×#878—31no—
55C2×#878—31no—
56C2×#878—61no—
57C3×#388—31no—
58C3×#388—31no—
59#4978—31no—
60#4976—31no—
61#4973—31no—
62#4972—31no—
63#4951D311yescharacteristic
64#4951D311yescharacteristic
65#4945—31no—
66#4945—31no—
67#4944—31no—
68#4944—31no—
69#4943—31no—
70#4943—31no—
71#4942—31no—
72#4942—31no—
73#4933—31no—
74#4933—31no—
75#4929—31no—
76#4928—31no—
77#4655—31no—
78#4654—31no—
79#4653—31no—
80#4652—31no—
81#4652—31no—
82#4647—31no—
83#4646—31no—
84#4646—31no—
85C24×C32C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C3⋊Dic3—41no—
89C22×C3⋊Dic3—41no—
90C22×C3⋊Dic3C2×C414yes—
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C2×#634—41no—
96C2×#634—41no—
97C2×#634C2×C414yes—
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C32×C22⋊C4C2×C414yes—
107#3757C2×C414yes—
108C4⋊(C3⋊Dic3)C2×C414yes—
109#3750C2×C414yes—
110#3750C2×C414yes—
111C3×#217—41no—
112C3×#217—41no—
113C3×#217—41no—
114C3×#217—41no—
115C3×C4⋊Dic3—41no—
116C3×C4⋊Dic3—41no—
117C3×C4×Dic3—41no—
118C3×C4×Dic3—41no—
119#3724—41no—
120#3724—41no—
121#3724—41no—
122#3724—41no—
123Dic32—41no—
124Dic32—41no—
125#2378—91noSylow
126C23×Dic3—31no—
127C23×Dic3—31no—
128C23×Dic3—61no—
129C22×Dic6—31no—
130C22×Dic6—31no—
131C22×Dic6—61no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4—31no—
136C2×C3×C22⋊C4—31no—
137C2×C3×C22⋊C4—31no—
138C2×C3×C22⋊C4—31no—
139C2×C3×C22⋊C4C2×D311yescharacteristic
140C2×C3×C22⋊C4C2×D311yescharacteristic
141C2×C3×C42—31no—
142C2×C3×C42—31no—
143C2×#217—31no—
144C2×#217—31no—
145C2×#217—61no—
146C2×#217C2×D311yescharacteristic
147C2×#217C2×D311yescharacteristic
148C2×#217C2×D311yescharacteristic
149C2×#217C2×D311yescharacteristic
150C2×C4⋊Dic3—31no—
151C2×C4⋊Dic3—31no—
152C2×C4⋊Dic3—61no—
153C2×C4⋊Dic3C2×D311yescharacteristic
154C2×C4⋊Dic3C2×D311yescharacteristic
155C2×Dic3⋊C4—31no—
156C2×Dic3⋊C4—31no—
157C2×Dic3⋊C4—31no—
158C2×Dic3⋊C4—31no—
159C2×Dic3⋊C4—31no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—61no—
168C2×Dic3⋊C4—61no—
169C2×C4×Dic3—31no—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—31no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3C2×D311yescharacteristic
174C2×C4×Dic3C2×D311yescharacteristic
175#878—38no—
176#878—38no—
177#878—68no—
178C3×#95—31no—
179C3×#95—31no—
180C3×#95—31no—
181C3×#95—31no—
182C3⋊#95—31no—
183C3⋊#95—31no—
184C3⋊#95—31no—
185C3⋊#95—31no—
186C3⋊#95—31no—
187C3⋊#95—31no—
188C3⋊#95—31no—
189C3⋊#95—31no—
190C3⋊#95—31no—
191C3⋊#95—31no—
192C3⋊#95—31no—
193C3⋊#95—31no—
194C3⋊#95—31no—
195C3⋊#95—31no—
196C3⋊#95—31no—
197C3⋊#95—31no—
198C3⋊#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—31no—
202C3⋊#95C2×D311yescharacteristic
203C3⋊#95C2×D311yescharacteristic
204C3⋊#95C2×D311yescharacteristic
205C3⋊#95C2×D311yescharacteristic
206C23×C32—21no—
207C23×C32—21no—
208C23×C32—21no—
209C23×C32—21no—
210C23×C32—21no—
211C23×C32—21no—
212C23×C32C22×C412yes—
213C23×C32C2411yescharacteristic
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4C22×C412yes—
219C2×C32×C4C22×C412yes—
220C2×C3⋊Dic3—21no—
221C2×C3⋊Dic3—21no—
222C2×C3⋊Dic3—21no—
223C2×C3⋊Dic3—21no—
224C2×C3⋊Dic3—21no—
225C2×C3⋊Dic3—21no—
226C2×C3⋊Dic3—21no—
227C2×C3⋊Dic3—21no—
228C2×C3⋊Dic3—44no—
229C2×C3⋊Dic3C22×C412yes—
230C2×C3⋊Dic3C22×C412yes—
231C2×C3⋊Dic3C22×C412yes—
232C2×C3⋊Dic3C22×C412yes—
233#634—44no—
234C2×C3×Dic3—21no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—21no—
237C2×C3×Dic3—21no—
238C2×C3×Dic3—21no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C22⋊Q8—91no—
259#391—91no—
260#391—91no—
261#389—91no—
262#389—91no—
263#388—31no—
264#388—31no—
265#388—91no—
266#388—91no—
267#387—91no—
268#387—91no—
269#387—91no—
270#387—91no—
271#381—91no—
272#380—91no—
273C24×C3—21no—
274C24×C3C22×D311yescharacteristic
275C24×C3C22×D311yescharacteristic
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—31no—
279C22×C3×C4—31no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C22×D311yescharacteristic
289C22×C3×C4C22×D311yescharacteristic
290C22×Dic3—31no—
291C22×Dic3—31no—
292C22×Dic3—31no—
293C22×Dic3—31no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—31no—
298C22×Dic3—34no—
299C22×Dic3—34no—
300C22×Dic3—61no—
301C22×Dic3—64no—
302C22×Dic3—61no—
303C22×Dic3—61no—
304C22×Dic3—61no—
305C22×Dic3—121no—
306C22×Dic3—121no—
307C22×Dic3—121no—
308C22×Dic3—121no—
309C22×Dic3—122no—
310C22×Dic3—122no—
311C22×Dic3C22×D311yescharacteristic
312C22×Dic3C22×D311yescharacteristic
313C22×Dic3C22×D311yescharacteristic
314C22×Dic3C22×D311yescharacteristic
315C22×Dic3C22×D311yescharacteristic
316C22×Dic3C22×D311yescharacteristic
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D311yescharacteristic
319C2×Dic6—34no—
320C2×Dic6—34no—
321C2×Dic6—64no—
322C2×Dic6—121no—
323C2×Dic6—121no—
324C2×Dic6—121no—
325C2×Dic6—121no—
326C2×Dic6—122no—
327C2×Dic6—122no—
328C3×C4⋊C4—121no—
329C3×C4⋊C4—121no—
330C3×C22⋊C4—24no—
331C3×C22⋊C4—121no—
332C3×C22⋊C4—121no—
333C3×C22⋊C4—121no—
334C3×C22⋊C4—121no—
335C3×C22⋊C4C4×D314yes—
336C3×C22⋊C4C4×D314yes—
337C3×C42—121no—
338C3×C42—121no—
339#217—34no—
340#217—34no—
341#217—41no—
342#217—41no—
343#217—41no—
344#217—41no—
345#217—64no—
346C4⋊Dic3—34no—
347C4⋊Dic3—34no—
348C4⋊Dic3—41no—
349C4⋊Dic3—41no—
350C4⋊Dic3—64no—
351Dic3⋊C4—34no—
352Dic3⋊C4—34no—
353Dic3⋊C4—34no—
354Dic3⋊C4—34no—
355Dic3⋊C4—64no—
356Dic3⋊C4—64no—
357Dic3⋊C4—121no—
358Dic3⋊C4—121no—
359Dic3⋊C4—121no—
360Dic3⋊C4—121no—
361Dic3⋊C4—121no—
362Dic3⋊C4—121no—
363Dic3⋊C4—121no—
364Dic3⋊C4—121no—
365C4×Dic3—41no—
366C4×Dic3—41no—
367C4×Dic3—121no—
368C4×Dic3—121no—
369C4×Dic3—121no—
370C4×Dic3—121no—
371C22×C32—22no—
372C22×C32—22no—
373C22×C32—22no—
374C22×C32—41no—
375C22×C32—41no—
376C22×C32—41no—
377C22×C32—41no—
378C22×C32C23×C411yescharacteristic
379C22×C32H(5,𝔽2)11yescharacteristic
380C22×C32H(5,𝔽2)11yescharacteristic
381C22×C32H(5,𝔽2)11yescharacteristic
382C22×C322−1+411yescharacteristic
383C22×C322−1+411yescharacteristic
384C22×C322−1+411yescharacteristic
385C32×C4—22no—
386C32×C4—22no—
387C3⋊Dic3—22no—
388C3⋊Dic3—22no—
389C3⋊Dic3—22no—
390C3⋊Dic3—22no—
391C3×Dic3—41no—
392C3×Dic3—41no—
393C3×Dic3—41no—
394C3×Dic3—41no—
395C3×Dic3—41no—
396C3×Dic3—41no—
397C3×Dic3—41no—
398C3×Dic3—41no—
399C22×Q8—91no—
400C23×C4—91no—
401C22⋊Q8—98no—
402C2×C4⋊C4—31no—
403C2×C4⋊C4—31no—
404C2×C4⋊C4—91no—
405C2×C4⋊C4—91no—
406C2×C4⋊C4—91no—
407C2×C4⋊C4—91no—
408C2×C4⋊C4—91no—
409C2×C4⋊C4—91no—
410C2×C4⋊C4—91no—
411C2×C22⋊C4—31no—
412C2×C22⋊C4—31no—
413C2×C22⋊C4—31no—
414C2×C22⋊C4—31no—
415C2×C22⋊C4—91no—
416C2×C22⋊C4D3211yescharacteristic
417C2×C42—31no—
418C2×C42—31no—
419C2×C42—91no—
420C2×C42—91no—
421#95—31no—
422#95—31no—
423#95—31no—
424#95—31no—
425#95—91no—
426#95—91no—
427#95—91no—
428#95—91no—
429#95—91no—
430#95—91no—
431#95—91no—
432#95—91no—
433#95—91no—
434#95—91no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3—21no—
442C23×C3—21no—
443C23×C3—21no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—21no—
450C23×C3—22no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3C2×C4×D312yes—
456C23×C3C2×C4×D312yes—
457C23×C3C23×D311yescharacteristic
458C23×C3C23×D311yescharacteristic
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4C2×C4×D312yes—
498C2×C3×C4C2×C4×D312yes—
499C2×C3×C4C2×C4×D312yes—
500C2×C3×C4C2×C4×D312yes—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—32no—
526C2×Dic3—32no—
527C2×Dic3—32no—
528C2×Dic3—32no—
529C2×Dic3—32no—
530C2×Dic3—32no—
531C2×Dic3—32no—
532C2×Dic3—32no—
533C2×Dic3—62no—
534C2×Dic3—62no—
535C2×Dic3—62no—
536C2×Dic3—62no—
537C2×Dic3—62no—
538C2×Dic3—62no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—121no—
556C2×Dic3—121no—
557C2×Dic3—121no—
558C2×Dic3—121no—
559C2×Dic3—121no—
560C2×Dic3—121no—
561C2×Dic3—124no—
562C2×Dic3—124no—
563C2×Dic3—128no—
564Dic6—124no—
565Dic6—124no—
566Dic6—128no—
567C2×C32—42no—
568C2×C32#51811yescharacteristic
569C2×C32#51911yescharacteristic
570C2×C32#52011yescharacteristic
571C2×C32#56211yescharacteristic
572C2×C32#56211yescharacteristic
573C2×C32#56311yescharacteristic
574C2×C32#56311yescharacteristic
575C24C2×D3211yescharacteristic
576C2×Q8—94no—
577C2×Q8—361no—
578C2×Q8—361no—
579C22×C4—31no—
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—31no—
587C22×C4—91no—
588C22×C4—91no—
589C22×C4—91no—
590C22×C4—91no—
591C22×C4—94no—
592C22×C4—361no—
593C22×C4—361no—
594C22×C4C2×D3211yescharacteristic
595C22×C4C2×D3211yescharacteristic
596C4⋊C4—94no—
597C4⋊C4—94no—
598C4⋊C4—94no—
599C4⋊C4—121no—
600C4⋊C4—121no—
601C4⋊C4—361no—
602C4⋊C4—361no—
603C4⋊C4—361no—
604C4⋊C4—361no—
605C22⋊C4—94no—
606C22⋊C4—121no—
607C22⋊C4—121no—
608C22⋊C4—121no—
609C22⋊C4—121no—
610C22⋊C4#62414yes—
611C42—121no—
612C42—121no—
613C42—361no—
614C42—361no—
615C22×C3—24no—
616C22×C3—22no—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—42no—
630C22×C3—42no—
631C22×C3—42no—
632C22×C3—42no—
633C22×C3—42no—
634C22×C3—42no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3C22×C4×D311yescharacteristic
644C22×C3C22×C4×D311yescharacteristic
645C22×C3#100411yescharacteristic
646C22×C3#100411yescharacteristic
647C22×C3#100411yescharacteristic
648C22×C3#100411yescharacteristic
649C22×C3#100911yescharacteristic
650C22×C3#100911yescharacteristic
651C22×C3#101011yescharacteristic
652C22×C3#101011yescharacteristic
653C22×C3#101011yescharacteristic
654C22×C3#101011yescharacteristic
655C22×C3#101011yescharacteristic
656C22×C3#101011yescharacteristic
657C3×C4—22no—
658C3×C4—22no—
659C3×C4—22no—
660C3×C4—22no—
661C3×C4—42no—
662C3×C4—42no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4—121no—
671Dic3—41no—
672Dic3—41no—
673Dic3—41no—
674Dic3—41no—
675Dic3—41no—
676Dic3—41no—
677Dic3—41no—
678Dic3—41no—
679Dic3—64no—
680Dic3—62no—
681Dic3—62no—
682Dic3—62no—
683Dic3—62no—
684Dic3—62no—
685Dic3—62no—
686Dic3—62no—
687Dic3—62no—
688Dic3—122no—
689Dic3—122no—
690Dic3—122no—
691C32#237811yescharacteristic, complemented, Sylow
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23C2×#62412yes—
699C23C22×D3211yescharacteristic
700Q8—364no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—92no—
730C2×C4—92no—
731C2×C4—92no—
732C2×C4—92no—
733C2×C4—181no—
734C2×C4—181no—
735C2×C4—181no—
736C2×C4—181no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—181no—
741C2×C4—364no—
742C2×C4C2×#62412yes—
743C2×C4C2×#62412yes—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—44no—
752C2×C3—42no—
753C2×C3—42no—
754C2×C3#551611yescharacteristic
755C2×C3#551611yescharacteristic
756C2×C3#554511yescharacteristic
757C2×C3#554511yescharacteristic
758C2×C3#554611yescharacteristic
759C2×C3#554611yescharacteristic
760C2×C3#562111yescharacteristic
761C2×C3#562111yescharacteristic
762C2×C3#565111yescharacteristic
763C2×C3#566711yescharacteristic
764C2×C3#567211yescharacteristic
765C2×C3#568411yescharacteristic
766C2×C3#571211yescharacteristic
767C2×C3#571211yescharacteristic
768C22—22no—
769C22—22no—
770C22—22no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22#6429811yescharacteristic
776C22#6429811yescharacteristic
777C22#6430911yescharacteristic
778C22#6431311yescharacteristic
779C22#6431411yescharacteristic
780C22#6431411yescharacteristic
781C22C22×#62411yescharacteristic
782C4—22no—
783C4—22no—
784C4—121no—
785C4—121no—
786C4—121no—
787C4—121no—
788C4—121no—
789C4—121no—
790C4—121no—
791C4—121no—
792C4—182no—
793C4—182no—
794C4—182no—
795C4—182no—
796C3—21no—
797C3#7549111yescharacteristic, complemented
798C3#7549211yescharacteristic, complemented
799C2—42no—
800C2#1059404411yescharacteristic
801C2#1059417211yescharacteristic
802C2#1059417611yescharacteristic
803C2#1059423911yescharacteristic
804C2#1059482811yescharacteristic
805C2#1059521911yescharacteristic
806C2#1059522311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2378
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. #10591273C2semidirect
9. #10591271C2semidirect
10. #10591264C2semidirect
11. #10591263C2semidirect
12. #10591213C2semidirect
13. #10591212C2semidirect
14. #10591197C2semidirect
15. #10591197C2semidirect
25. #64087C4semidirect
691. C32#2378semidirect
797. C3#75491semidirect
798. C3#75492semidirect

Maximal subgroups

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

subgroupindex
C2×#640872
C3×#49512
#105917202
#105917032
#105916972
#105912732
#105912712
#105912642
#105912632
#105912132
#105912122
#105911972
#754923
#754913