Finite Group Databasebeta

← #10762829

Subgroups — #10762829

Order 768.

990 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86240C211yesmaximal, characteristic
2#79333C211yesmaximal, characteristic, complemented
3#74263C211yesmaximal, characteristic, complemented
4C3×#1514C211yesmaximal, characteristic, complemented
5#71811C211yesmaximal, characteristic, complemented
6#70833C211yesmaximal, characteristic, complemented
7#69565C211yesmaximal, characteristic, complemented
8#68307C211yesmaximal, characteristic, complemented
9#68305C211yesmaximal, characteristic, complemented
10#68303C211yesmaximal, characteristic, complemented
11#68301C211yesmaximal, characteristic, complemented
12#68283C211yesmaximal, characteristic, complemented
13#68281C211yesmaximal, characteristic, complemented
14#68279C211yesmaximal, characteristic, complemented
15#68277C211yesmaximal, characteristic, complemented
16#17607—31nomaximal, Sylow
17C3×#532C2211yescharacteristic
18#5829—21no—
19#5824—21no—
20#5733C411yescharacteristic, complemented
21#5729C411yescharacteristic, complemented
22#5719C411yescharacteristic, complemented
23#5715C411yescharacteristic, complemented
24#5679—21no—
25#5670—21no—
26#5610—21no—
27#5606C2211yescharacteristic
28D3×#121C2211yescharacteristic
29#5601—21no—
30#5600C2211yescharacteristic
31#5596C2211yescharacteristic
32#5562C411yescharacteristic, complemented
33#5561C411yescharacteristic, complemented
34#5556—21no—
35#5546C411yescharacteristic, complemented
36#5545C411yescharacteristic, complemented
37#5540—21no—
38#5479C2211yescharacteristic
39C2×#872C2211yescharacteristic
40C3×#432C2211yescharacteristic, complemented
41C3×#383C2211yescharacteristic, complemented
42C4×C4⋊Dic3C2211yescharacteristic, complemented
43#4925C2211yescharacteristic, complemented
44#4840—21no—
45#4839—21no—
46#4726C2211yescharacteristic
47D3×C22⋊C8C2211yescharacteristic
48#4719C2211yescharacteristic, complemented
49#4718C2211yescharacteristic, complemented
50#4709—21no—
51#4708—21no—
52#4670—21no—
53#4669—21no—
54#4667C2211yescharacteristic
55#4666C2211yescharacteristic
56#4651C2211yescharacteristic, complemented
57#4649—21no—
58#4649C2211yescharacteristic, complemented
59#4647—21no—
60C3×#327C2211yescharacteristic
61C3×#327C2211yescharacteristic
62C3×#327C2211yescharacteristic, complemented
63C3×#327C2211yescharacteristic, complemented
64#4537C2211yescharacteristic
65#4537C2211yescharacteristic
66#4537C2211yescharacteristic, complemented
67#4537C2211yescharacteristic, complemented
68#4470C2211yescharacteristic
69#4470C2211yescharacteristic
70#4467C2211yescharacteristic, complemented
71#4467C2211yescharacteristic, complemented
72#4452C2211yescharacteristic, complemented
73#4452C2211yescharacteristic, complemented
74#4451C2211yescharacteristic
75#4451C2211yescharacteristic
76#3494—31no—
77#2924—31no—
78#2347—31no—
79#1521—31no—
80#1521—31no—
81#1519—31no—
82#1514—31no—
83#1514D311yescharacteristic, complemented
84#1513—31no—
85#1509—31no—
86#1509—31no—
87#1507—31no—
88#1502—31no—
89#1502—31no—
90#1501—31no—
91C2×C3×#41—21no—
92C2×#237—21no—
93C2×#237C2×C411yescharacteristic
94C2×D3×D4—21no—
95C2×D3×D4C2×C411yescharacteristic
96C22×C4×D3C2311yescharacteristic
97C3×C4⋊Q8C2×C411yescharacteristic
98C3×#127C2×C411yescharacteristic
99C3×#124—21no—
100C3×#121—21no—
101C3×#121C2311yescharacteristic
102C3×#121C2311yescharacteristic
103C3×C4×D4—21no—
104C3×C4×D4C2×C411yescharacteristic
105C3×C4×D4C2×C411yescharacteristic
106C2×C3×C42C2311yescharacteristic
107#947—21no—
108#946—21no—
109#946—21no—
110#944—21no—
111#940C2×C411yescharacteristic
112#939—21no—
113#939—21no—
114#939—21no—
115#939—21no—
116#939—21no—
117#939—21no—
118#938C2×C411yescharacteristic
119#938C2×C411yescharacteristic
120#937—21no—
121#937—21no—
122#937—21no—
123#936C2×C411yescharacteristic
124#935—21no—
125#935—21no—
126#935—21no—
127D4×Dic3—21no—
128D4×Dic3—21no—
129D4×Dic3C2×C411yescharacteristic
130D4×Dic3C2×C411yescharacteristic
131#930—21no—
132#930C2311yescharacteristic
133#929—21no—
134#929—21no—
135#929—21no—
136C4×#67—21no—
137C4×#67—21no—
138C4×#67—21no—
139C2×(C2×D3)⋊C4—21no—
140C2×(C2×D3)⋊C4—21no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4D411yescharacteristic
143C2×(C2×D3)⋊C4D411yescharacteristic
144C2×C4⋊Dic3—21no—
145#924—21no—
146#924C2311yescharacteristic
147C2×Dic3⋊C4—21no—
148C2×Dic3⋊C4—21no—
149C2×Dic3⋊C4—21no—
150C2×Dic3⋊C4D411yescharacteristic
151C2×Dic3⋊C4D411yescharacteristic
152C2×C4×Dic3—21no—
153C2×C4×Dic3—21no—
154C2×C4×Dic3—21no—
155C2×C4×Dic3C2311yescharacteristic
156C2×ΓL(1,𝔽25)—21no—
157C2×D3×C8—21no—
158#898—21no—
159#897C2×C411yescharacteristic
160#896—21no—
161#895C2×C411yescharacteristic
162#894—21no—
163#893C2×C411yescharacteristic
164#892C2×C411yescharacteristic
165D3×C4⋊C4C2×C411yescharacteristic
166#890C2×C411yescharacteristic
167#889—21no—
168#888C2×C411yescharacteristic
169#887C2×C411yescharacteristic
170#885—21no—
171#885—21no—
172#884—21no—
173#884—21no—
174#883—21no—
175#883—21no—
176#67⋊C4—21no—
177#67⋊C4—21no—
178#67⋊C4—21no—
179#67⋊C4—21no—
180D3×C22⋊C4—21no—
181D3×C22⋊C4—21no—
182#879—21no—
183#879—21no—
184#877—21no—
185#877—21no—
186#876—21no—
187#875C2×C411yescharacteristic
188C4×D12C2×C411yescharacteristic
189#872—21no—
190#872C2×C411yescharacteristic
191#872C2×C411yescharacteristic
192#872C2×C411yescharacteristic
193#872C2×C411yescharacteristic
194#872D411yescharacteristic
195#872D411yescharacteristic
196#872D411yescharacteristic
197#872D411yescharacteristic
198#870C2×C411yescharacteristic
199C4×Dic6C2×C411yescharacteristic
200C3×C4⋊C8—21no—
201C3×C22⋊C8C2311yescharacteristic
202C3×C22⋊C8C2311yescharacteristic
203C3×#97—21no—
204C3×#95—21no—
205C3×#95—21no—
206C3×#95C2311yescharacteristic
207C3×#95C2311yescharacteristic
208C3⋊#95—21no—
209C3⋊#95—21no—
210C3⋊#95C2311yescharacteristic
211C3⋊#95C2311yescharacteristic
212#830C2311yescharacteristic
213#830C2311yescharacteristic
214(C2×D3)⋊C8—21no—
215(C2×D3)⋊C8—21no—
216#815—21no—
217Dic3⋊C8—21no—
218Dic3⋊C8—21no—
219C8×Dic3—21no—
220C4⋊(C3⋊C8)—21no—
221C4×C3⋊C8—21no—
222#555—61no—
223#553—61no—
224#553—61no—
225#551—61no—
226#551—61no—
227#547—61no—
228#546—61no—
229#546—61no—
230#544—31no—
231#542—31no—
232#542—31no—
233#540—31no—
234#540—31no—
235#535—31no—
236#532—31no—
237#532C2×D311yescharacteristic
238#529—31no—
239#529—31no—
240#525—31no—
241C2×#121—31no—
242#520—31no—
243#518—31no—
244C2×#117—31no—
245#433—61no—
246#433—61no—
247#432—31no—
248#432C2×D311yescharacteristic, complemented
249#431—31no—
250#431—31no—
251#424—61no—
252#407—31no—
253C2×C22⋊C8—31no—
254#405—61no—
255#389—61no—
256#388—61no—
257#388—61no—
258#383—31no—
259#383C2×D311yescharacteristic, complemented
260#380—31no—
261C4×C4⋊C4—31no—
262C4×C4⋊C4—31no—
263C4×C4⋊C4—61no—
264C4×C22⋊C4—31no—
265#328—31no—
266#328—31no—
267#328—31no—
268#328—31no—
269#327—31no—
270#327—31no—
271#327—31no—
272#327—31no—
273#327—31no—
274#327—31no—
275#327—31no—
276#327—31no—
277#327C2×D311yescharacteristic
278#327C2×D311yescharacteristic
279#327C2×D311yescharacteristic, complemented
280#327C2×D311yescharacteristic, complemented
281C23×D3—21no—
282C23×D3C2×D411yescharacteristic
283C3×#41—81no—
284C3×#41—81no—
285C2×C3×Q8—21no—
286C2×C3×D4—21no—
287C2×C3×D4—21no—
288C2×C3×D4—21no—
289C2×C3×D4—21no—
290C2×C3×D4C22×C411yescharacteristic
291C2×C3×D4C22×C411yescharacteristic
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4C2×D411yescharacteristic
297C22×C3×C4C2×D411yescharacteristic
298C22×C3×C4C2411yescharacteristic
299C2×#67—21no—
300C2×#67—21no—
301C2×#67—21no—
302C2×#67—21no—
303C2×#67—21no—
304C2×#67—21no—
305C2×#67—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3C2×D411yescharacteristic
312C22×Dic3C2×D411yescharacteristic
313C22×Dic3C2×D411yescharacteristic
314#237—42no—
315#237—81no—
316#237—81no—
317D3×D4—42no—
318D3×D4—81no—
319D3×D4—81no—
320C2×D12—21no—
321C2×D12C22×C411yescharacteristic
322C2×C4×D3—21no—
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—42no—
326C2×C4×D3C22×C411yescharacteristic
327C2×C4×D3C22×C411yescharacteristic
328C2×C4×D3C2×D411yescharacteristic
329C2×C4×D3C2×D411yescharacteristic
330C2×Dic6—21no—
331C2×Dic6C22×C411yescharacteristic
332C2×C3×C8—21no—
333C2×C3×C8—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4C22×C411yescharacteristic
336C3×C4⋊C4C22×C411yescharacteristic
337C3×C22⋊C4—21no—
338C3×C22⋊C4—21no—
339C3×C22⋊C4—21no—
340C3×C22⋊C4—21no—
341C3×C42C22×C411yescharacteristic
342C3×C42C22×C411yescharacteristic
343C3×C42C2×D411yescharacteristic
344C3×C42C2×D411yescharacteristic
345#217—21no—
346#217—21no—
347#217—21no—
348#217—21no—
349#217—21no—
350#217—21no—
351#217—21no—
352(C2×D3)⋊C4—21no—
353(C2×D3)⋊C4—21no—
354(C2×D3)⋊C4—21no—
355(C2×D3)⋊C4—21no—
356(C2×D3)⋊C4—21no—
357(C2×D3)⋊C4—21no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—42no—
361(C2×D3)⋊C4—81no—
362(C2×D3)⋊C4C22⋊C411yescharacteristic
363(C2×D3)⋊C4C22⋊C411yescharacteristic
364(C2×D3)⋊C4C22⋊C411yescharacteristic
365(C2×D3)⋊C4C22⋊C411yescharacteristic
366(C2×D3)⋊C4C22⋊C411yescharacteristic
367(C2×D3)⋊C4C22⋊C411yescharacteristic
368(C2×D3)⋊C4C22⋊C411yescharacteristic
369(C2×D3)⋊C4C22⋊C411yescharacteristic
370C4⋊Dic3—21no—
371C4⋊Dic3—21no—
372C4⋊Dic3—42no—
373C4⋊Dic3C22×C411yescharacteristic
374C4⋊Dic3C22×C411yescharacteristic
375Dic3⋊C4—21no—
376Dic3⋊C4—21no—
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—42no—
384Dic3⋊C4—42no—
385Dic3⋊C4C22⋊C411yescharacteristic
386Dic3⋊C4C22⋊C411yescharacteristic
387Dic3⋊C4C22⋊C411yescharacteristic
388Dic3⋊C4C22⋊C411yescharacteristic
389Dic3⋊C4C22⋊C411yescharacteristic
390Dic3⋊C4C22⋊C411yescharacteristic
391Dic3⋊C4C22⋊C411yescharacteristic
392Dic3⋊C4C22⋊C411yescharacteristic
393C4×Dic3—21no—
394C4×Dic3—21no—
395C4×Dic3—21no—
396C4×Dic3—42no—
397C4×Dic3—81no—
398C4×Dic3—81no—
399C4×Dic3C22×C411yescharacteristic
400C4×Dic3C22×C411yescharacteristic
401C4×Dic3C2×D411yescharacteristic
402C4×Dic3C2×D411yescharacteristic
403C2×C3⋊C8—21no—
404C2×C3⋊C8—21no—
405ΓL(1,𝔽25)—42no—
406D3×C8—42no—
407C2×#41—21no—
408C2×#41—31no—
409C2×#41—61no—
410C22×D4—31no—
411C22×D4—61no—
412C23×C4—31no—
413C2×M16—61no—
414C22×C8—61no—
415C4⋊Q8—31no—
416C4⋊Q8—61no—
417C4⋊Q8C4×D311yescharacteristic
418#127—31no—
419#127C4×D311yescharacteristic
420#126—61no—
421#126—61no—
422#126—61no—
423#126—61no—
424#125—31no—
425#125—31no—
426#125—61no—
427#124—21no—
428#124—31no—
429#124—31no—
430#124—61no—
431#124—61no—
432#124—61no—
433#123—61no—
434#123—61no—
435#123—61no—
436#123—61no—
437#123—61no—
438#123—61no—
439#123—61no—
440#123—61no—
441#123—61no—
442C22⋊Q8—31no—
443C22⋊Q8—31no—
444C22⋊Q8—61no—
445C22⋊Q8—61no—
446C22⋊Q8—61no—
447C22⋊Q8—61no—
448#121—21no—
449#121—31no—
450#121—31no—
451#121—31no—
452#121—31no—
453#121—61no—
454#121—61no—
455#121—61no—
456#121—61no—
457#121—61no—
458#121—61no—
459#121—61no—
460#121—61no—
461#121—61no—
462#121C22×D311yescharacteristic
463#121C22×D311yescharacteristic
464#120—61no—
465#120—61no—
466#120—61no—
467C4×Q8—31no—
468C4×Q8—31no—
469C4×D4—21no—
470C4×D4—31no—
471C4×D4—31no—
472C4×D4—31no—
473C4×D4—31no—
474C4×D4—61no—
475C4×D4—61no—
476C4×D4—61no—
477C4×D4—61no—
478C4×D4—61no—
479C4×D4—61no—
480C4×D4—61no—
481C4×D4—61no—
482C4×D4—61no—
483C4×D4C4×D311yescharacteristic
484C4×D4C4×D311yescharacteristic
485#117—31no—
486#117—31no—
487#117—31no—
488#117—31no—
489#117—31no—
490#117—31no—
491#117—31no—
492#117—31no—
493#117—31no—
494#117—61no—
495#117—61no—
496#117—61no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—31no—
499C2×C4⋊C4—31no—
500C2×C4⋊C4—61no—
501C2×C4⋊C4—61no—
502C2×C4⋊C4—61no—
503C2×C4⋊C4—61no—
504C2×C22⋊C4—31no—
505C2×C22⋊C4—31no—
506C2×C22⋊C4—61no—
507C2×C22⋊C4—61no—
508C2×C22⋊C4—61no—
509C2×C22⋊C4—61no—
510C2×C22⋊C4—61no—
511C2×C42—31no—
512C2×C42—61no—
513C2×C42—61no—
514C2×C42—61no—
515C2×C42C22×D311yescharacteristic
516C4⋊C8—21no—
517C4⋊C8—61no—
518C4⋊C8—61no—
519C4⋊C8—61no—
520C22⋊C8—31no—
521C22⋊C8—31no—
522C22⋊C8—61no—
523C22⋊C8—61no—
524C22⋊C8C22×D311yescharacteristic
525C22⋊C8C22×D311yescharacteristic
526#97—21no—
527#97—61no—
528C4×C8—61no—
529C4×C8—61no—
530#95—21no—
531#95—21no—
532#95—31no—
533#95—31no—
534#95—61no—
535#95—61no—
536#95C22×D311yescharacteristic
537#95C22×D311yescharacteristic
538C23×C3—21no—
539C23×C3—21no—
540C23×C3C22×D411yescharacteristic
541C22×D3—21no—
542C22×D3—21no—
543C22×D3—21no—
544C22×D3—41no—
545C22×D3—41no—
546C22×D3—42no—
547C22×D3—81no—
548C22×D3—81no—
549C22×D3C2×C22⋊C411yescharacteristic
550C22×D3C2×C22⋊C411yescharacteristic
551C3×Q8—81no—
552C3×D4—41no—
553C3×D4—41no—
554C3×D4—41no—
555C3×D4—41no—
556C3×D4—41no—
557C3×D4—41no—
558C3×D4—81no—
559C3×D4—81no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—81no—
573C2×C3×C4—81no—
574C2×C3×C4C2×C22⋊C411yescharacteristic
575C2×C3×C4C2×C22⋊C411yescharacteristic
576C2×C3×C4C2×C22⋊C411yescharacteristic
577C2×C3×C4C2×C22⋊C411yescharacteristic
578C2×C3×C4C23×C411yescharacteristic
579C2×C3×C4C22×D411yescharacteristic
580#67—42no—
581#67—41no—
582#67—41no—
583#67—42no—
584#67—81no—
585#67—81no—
586#67—81no—
587#67—81no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—41no—
596C2×Dic3—41no—
597C2×Dic3—41no—
598C2×Dic3—42no—
599C2×Dic3—41no—
600C2×Dic3—41no—
601C2×Dic3—41no—
602C2×Dic3—81no—
603C2×Dic3—81no—
604C2×Dic3C2×C22⋊C411yescharacteristic
605C2×Dic3C2×C22⋊C411yescharacteristic
606C2×Dic3C2×C22⋊C411yescharacteristic
607C2×Dic3C2×C22⋊C411yescharacteristic
608C2×Dic3C2×C22⋊C411yescharacteristic
609C2×Dic3C2×C22⋊C411yescharacteristic
610D12—41no—
611D12—81no—
612C4×D3—22no—
613C4×D3—22no—
614C4×D3—41no—
615C4×D3—41no—
616C4×D3—81no—
617C4×D3—81no—
618C4×D3—81no—
619Dic6—41no—
620Dic6—81no—
621C3×C8—41no—
622C3×C8—41no—
623C3⋊C8—41no—
624C3⋊C8—41no—
625C24—31no—
626C24—61no—
627#41—81no—
628#41—81no—
629#41—122no—
630#41—241no—
631#41—241no—
632C2×Q8—21no—
633C2×Q8—31no—
634C2×Q8—61no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—31no—
640C2×D4—61no—
641C2×D4—61no—
642C2×D4—61no—
643C2×D4—61no—
644C2×D4—61no—
645C2×D4—61no—
646C2×D4—61no—
647C2×D4—61no—
648C2×D4—122no—
649C2×D4—241no—
650C2×D4—241no—
651C2×D4C2×C4×D311yescharacteristic
652C2×D4C2×C4×D311yescharacteristic
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—31no—
658C22×C4—31no—
659C22×C4—31no—
660C22×C4—31no—
661C22×C4—31no—
662C22×C4—31no—
663C22×C4—31no—
664C22×C4—61no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4—61no—
670C22×C4—61no—
671C22×C4—61no—
672C22×C4—122no—
673C22×C4D3×D411yescharacteristic
674C22×C4D3×D411yescharacteristic
675C22×C4C23×D311yescharacteristic
676M16—122no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—61no—
680C2×C8—61no—
681C2×C8—122no—
682C4⋊C4—21no—
683C4⋊C4—31no—
684C4⋊C4—31no—
685C4⋊C4—31no—
686C4⋊C4—31no—
687C4⋊C4—31no—
688C4⋊C4—31no—
689C4⋊C4—31no—
690C4⋊C4—31no—
691C4⋊C4—31no—
692C4⋊C4—31no—
693C4⋊C4—61no—
694C4⋊C4—61no—
695C4⋊C4—61no—
696C4⋊C4—61no—
697C4⋊C4—61no—
698C4⋊C4—61no—
699C4⋊C4—61no—
700C4⋊C4—61no—
701C4⋊C4—61no—
702C4⋊C4—61no—
703C4⋊C4—122no—
704C4⋊C4—122no—
705C4⋊C4—122no—
706C4⋊C4C2×C4×D311yescharacteristic
707C4⋊C4C2×C4×D311yescharacteristic
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—31no—
713C22⋊C4—31no—
714C22⋊C4—31no—
715C22⋊C4—31no—
716C22⋊C4—31no—
717C22⋊C4—31no—
718C22⋊C4—31no—
719C22⋊C4—31no—
720C22⋊C4—61no—
721C22⋊C4—61no—
722C22⋊C4—61no—
723C22⋊C4—61no—
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—61no—
727C22⋊C4—61no—
728C22⋊C4—61no—
729C22⋊C4—61no—
730C22⋊C4—61no—
731C22⋊C4—61no—
732C22⋊C4—61no—
733C22⋊C4—61no—
734C22⋊C4—61no—
735C22⋊C4—122no—
736C22⋊C4—241no—
737C42—31no—
738C42—31no—
739C42—31no—
740C42—31no—
741C42—61no—
742C42—61no—
743C42—61no—
744C42—122no—
745C42—241no—
746C42—241no—
747C42C2×C4×D311yescharacteristic
748C42C2×C4×D311yescharacteristic
749C42D3×D411yescharacteristic
750C42D3×D411yescharacteristic
751C22×C3—21no—
752C22×C3—21no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3C22×C22⋊C411yescharacteristic
760C22×C3#57611yescharacteristic
761C22×C3#57711yescharacteristic
762C2×D3—21no—
763C2×D3—21no—
764C2×D3—21no—
765C2×D3—21no—
766C2×D3—21no—
767C2×D3—21no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—81no—
772C2×D3—81no—
773C2×D3—162no—
774C3×C4—21no—
775C3×C4—21no—
776C3×C4—21no—
777C3×C4—21no—
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—41no—
781C3×C4—41no—
782C3×C4—81no—
783C3×C4—81no—
784Dic3—21no—
785Dic3—21no—
786Dic3—21no—
787Dic3—21no—
788Dic3—21no—
789Dic3—42no—
790Dic3—41no—
791Dic3—41no—
792Dic3—41no—
793Dic3—81no—
794Dic3#41012yes—
795C23—21no—
796C23—21no—
797C23—31no—
798C23—31no—
799C23—61no—
800C23—61no—
801C23—61no—
802C23—121no—
803C23—121no—
804C23—122no—
805C23—241no—
806C23—241no—
807C23C2×D3×D411yescharacteristic
808Q8—81no—
809Q8—121no—
810Q8—241no—
811D4—41no—
812D4—41no—
813D4—41no—
814D4—41no—
815D4—41no—
816D4—41no—
817D4—81no—
818D4—81no—
819D4—121no—
820D4—122no—
821D4—122no—
822D4—121no—
823D4—121no—
824D4—241no—
825D4—241no—
826D4—241no—
827D4—241no—
828D4—241no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—31no—
834C2×C4—31no—
835C2×C4—31no—
836C2×C4—31no—
837C2×C4—31no—
838C2×C4—31no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—62no—
848C2×C4—62no—
849C2×C4—62no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—62no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—121no—
859C2×C4—121no—
860C2×C4—122no—
861C2×C4—121no—
862C2×C4—121no—
863C2×C4—121no—
864C2×C4—121no—
865C2×C4—121no—
866C2×C4—121no—
867C2×C4—241no—
868C2×C4—241no—
869C2×C4—241no—
870C2×C4—241no—
871C2×C4—241no—
872C2×C4D3×C22⋊C411yescharacteristic
873C2×C4D3×C22⋊C411yescharacteristic
874C2×C4D3×C22⋊C411yescharacteristic
875C2×C4D3×C22⋊C411yescharacteristic
876C2×C4C22×C4×D311yescharacteristic
877C2×C4C2×D3×D411yescharacteristic
878C8—41no—
879C8—41no—
880C8—121no—
881C8—121no—
882C2×C3—21no—
883C2×C3—21no—
884C2×C3—81no—
885C2×C3—81no—
886C2×C3C2×#41011yescharacteristic
887C2×C3#289711yescharacteristic
888C2×C3#290111yescharacteristic
889D3—41no—
890D3—41no—
891D3—81no—
892C22—21no—
893C22—21no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—61no—
901C22—61no—
902C22—61no—
903C22—61no—
904C22—61no—
905C22—61no—
906C22—121no—
907C22—121no—
908C22—121no—
909C22—241no—
910C22—241no—
911C22—482no—
912C22C2×D3×C22⋊C411yescharacteristic
913C22#577411yescharacteristic
914C22#577511yescharacteristic
915C4—21no—
916C4—21no—
917C4—21no—
918C4—21no—
919C4—21no—
920C4—21no—
921C4—32no—
922C4—41no—
923C4—41no—
924C4—61no—
925C4—61no—
926C4—61no—
927C4—61no—
928C4—61no—
929C4—81no—
930C4—81no—
931C4—122no—
932C4—121no—
933C4—121no—
934C4—121no—
935C4—241no—
936C3#1760711yescharacteristic, complemented, Sylow
937C2—21no—
938C2—21no—
939C2—81no—
940C2—81no—
941C2—121no—
942C2—121no—
943C2—241no—
944C2D3×#41011yescharacteristic
945C2#7892511yescharacteristic
946C2#7899211yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊C4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1514C2
socleC22×C3C22×C22⋊C4
prime radical#86240C2
cosocleC22×C3×C4C24
hypercenter#1514D3
hypocenterC3#17607
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1514

Complements

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

NH ≅ G/Ntype
2. #79333C2semidirect
3. #74263C2semidirect
4. C3×#1514C2semidirect
5. #71811C2semidirect
6. #70833C2semidirect
7. #69565C2semidirect
8. #68307C2semidirect
9. #68305C2semidirect
10. #68303C2semidirect
11. #68301C2semidirect
12. #68283C2semidirect
13. #68281C2semidirect
14. #68279C2semidirect
15. #68277C2semidirect
20. #5733C4semidirect
21. #5729C4semidirect
22. #5719C4semidirect
23. #5715C4semidirect
32. #5562C4semidirect
33. #5561C4semidirect
35. #5546C4semidirect
36. #5545C4semidirect
40. C3×#432C22semidirect
41. C3×#383C22semidirect
42. C4×C4⋊Dic3C22semidirect
43. #4925C22semidirect
48. #4719C22semidirect
49. #4718C22semidirect
56. #4651C22semidirect
58. #4649C22semidirect
62. C3×#327C22semidirect
63. C3×#327C22semidirect
66. #4537C22semidirect
67. #4537C22semidirect
70. #4467C22semidirect
71. #4467C22semidirect
72. #4452C22semidirect
73. #4452C22semidirect
83. #1514D3semidirect
248. #432C2×D3semidirect
259. #383C2×D3semidirect
279. #327C2×D3semidirect
280. #327C2×D3semidirect
936. C3#17607semidirect

Maximal subgroups

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

subgroupindex
#862402
#793332
#742632
C3×#15142
#718112
#708332
#695652
#683072
#683052
#683032
#683012
#682832
#682812
#682792
#682772
#176073