Finite Group Databasebeta

← #11884190

Subgroups — #11884190

Order 1152.

1064 conjugacy classes of subgroups.

The subgroup lattice has 881 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595078C211yesmaximal, characteristic
2Dic6×#67C211yesmaximal, characteristic, complemented
3C2×#63833C211yesmaximal, characteristic, complemented
4C2×D3×#204C211yesmaximal, characteristic, complemented
5#10592432C211yesmaximal, characteristic, complemented
6C3×#4738C211yesmaximal, characteristic, complemented
7C3×#4728C211yesmaximal, characteristic, complemented
8#10591176C211yesmaximal, characteristic, complemented
9#10590952C211yesmaximal, characteristic, complemented
10#10590942C211yesmaximal, characteristic, complemented
11#10590897C211yesmaximal, characteristic, complemented
12#10590859C211yesmaximal, characteristic, complemented
13#10590848C211yesmaximal, characteristic, complemented
14#10590795C211yesmaximal, characteristic, complemented
15#10590760C211yesmaximal, characteristic, complemented
16#80061—31nomaximal
17#79495—31nomaximal
18C2×#3828C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic, complemented
20C2×D3×D12C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic
22#64133C2211yescharacteristic, complemented
23C2×#3746C2211yescharacteristic, complemented
24C2×#3744C2211yescharacteristic
25C3×#930C2211yescharacteristic
26C3×C4×#67C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic, complemented
28C2×C3×#204C2211yescharacteristic
29C2×C3×#204C2211yescharacteristic
30C2×C3×D3×C8C2211yescharacteristic
31#63983—21no—
32Dic3×#67—21no—
33#63964—21no—
34#63958—21no—
35#63921—21no—
36#63894C2211yescharacteristic
37#63887—21no—
38#63866C2211yescharacteristic, complemented
39#63860C2211yescharacteristic
40#63857C2211yescharacteristic
41#63856C2211yescharacteristic
42#63853—21no—
43Dic3×Dic6C2211yescharacteristic, complemented
44#63839—21no—
45C2×#3719C2211yescharacteristic, complemented
46C2×#3719C2211yescharacteristic, complemented
47#63833—24no—
48C2×#3717C2211yescharacteristic
49C2×#3717C2211yescharacteristic
50C2×#3716C2211yescharacteristic
51D3×#204—24no—
52C32×C22⋊C8C2211yescharacteristic, complemented
53#63648C2211yescharacteristic
54#63643C2211yescharacteristic, complemented
55C3×(C2×D3)⋊C8C2211yescharacteristic
56C3×#816C2211yescharacteristic, complemented
57C3×#816C2211yescharacteristic, complemented
58C3×#815C2211yescharacteristic, complemented
59C3×Dic3⋊C8C2211yescharacteristic, complemented
60#63575C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63563C2211yescharacteristic
63Q8×#67—31no—
64C2×#942—31no—
65C2×D3×SD16—31no—
66C2×#909—31no—
67C22×#204—31no—
68#5612—31no—
69#5550—31no—
70D4×Dic6—31no—
71C3×#448—31no—
72C3×#435—31no—
73#5169—31no—
74#5167—31no—
75#5166—31no—
76#5134—31no—
77#5116—31no—
78#5042—31no—
79#4845—31no—
80#4841—31no—
81#4818—31no—
82#4817—31no—
83#4813—31no—
84#4809—31no—
85#4739—31no—
86#4738D311yescharacteristic, complemented
87#4733—31no—
88#4733—31no—
89#4733—61no—
90#4731—31no—
91#4728D311yescharacteristic, complemented
92#4715—31no—
93#4710—31no—
94C22×D32—21no—
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97#3828—22no—
98#3828—41no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3—21no—
101C2×#634C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67D411yescharacteristic
105C22×C3×Dic3—21no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6—22no—
109C2×C3×Dic6—21no—
110C2×C3×Dic6—41no—
111C2×C3×Dic6C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#627—21no—
114C2×#626—21no—
115C2×#624—21no—
116C2×D3×Dic3—21no—
117D3×D12—22no—
118D3×D12—41no—
119D3×Dic6—22no—
120D3×Dic6—41no—
121C2×C32×C8C2311yescharacteristic
122C2×C32×C8C2311yescharacteristic
123#3757—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3750—21no—
126#3746—41no—
127#3744—22no—
128C3×#217D411yescharacteristic
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4D411yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3C2311yescharacteristic
134C3×#208—22no—
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×#204—22no—
138C3×#204—41no—
139C3×D3×C8—22no—
140#3724—21no—
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145#3722—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150Dic32—21no—
151#3719—22no—
152#3719—22no—
153#3717—22no—
154#3717D414yescomplemented
155#3716—22no—
156#3266—91noSylow
157C22×C3×Q8—31no—
158C2×D3×Q8—31no—
159C2×D3×D4—31no—
160C2×#235—31no—
161C2×#235—31no—
162C2×#235—61no—
163C22×D12—31no—
164C22×Dic6—31no—
165C22×Dic6C2×D311yescharacteristic, complemented
166C2×C3×SD16—31no—
167C2×C3×SD16—31no—
168C2×C3×M16—31no—
169C22×C3×C8—31no—
170C3×#121—31no—
171C3×C4×D4—31no—
172#946—31no—
173#946—61no—
174Q8×Dic3—31no—
175#944—31no—
176#944—61no—
177C2×#216—31no—
178C2×#216—31no—
179#942—64no—
180C2×#215—31no—
181C2×#215—31no—
182#938—61no—
183#937—61no—
184#937—61no—
185#936—31no—
186D4×Dic3—61no—
187C2×#214—31no—
188#930C2×D311yescharacteristic
189C4×#67—61no—
190C4×#67C2×D311yescharacteristic
191#924—31no—
192#924—31no—
193#924—31no—
194#924—31no—
195#924—61no—
196#924—61no—
197C2×#208C2×D311yescharacteristic, complemented
198D3×SD16—64no—
199#909—64no—
200C2×Dic12—31no—
201C2×Dic12—31no—
202C2×Dic12—31no—
203C2×Dic12—31no—
204C2×Dic12—61no—
205C2×#204—31no—
206C2×#204—31no—
207C2×#204—31no—
208C2×#204—31no—
209C2×#204—31no—
210C2×#204—61no—
211C2×#204—64no—
212C2×#204C2×D311yescharacteristic
213C2×#204C2×D311yescharacteristic
214C2×D3×C8C2×D311yescharacteristic
215#897—31no—
216#894—61no—
217#893—31no—
218#888—61no—
219#884—61no—
220#883—61no—
221D3×C22⋊C4—61no—
222D3×C22⋊C4—61no—
223#878—61no—
224#878—61no—
225#875—31no—
226C4×D12—31no—
227#869—31no—
228C4×Dic6—31no—
229C3×C4⋊C8—31no—
230C3×#103—31no—
231C3×#103—31no—
232C3×C22⋊C8—21no—
233C3×C22⋊C8—31no—
234C3×C22⋊C8C2×D311yescharacteristic, complemented
235C3×C22⋊C8C2×D311yescharacteristic, complemented
236C3×#97—31no—
237#832—31no—
238#821—31no—
239#821—31no—
240#821—31no—
241#821—61no—
242(C2×D3)⋊C8C2×D311yescharacteristic
243#818—31no—
244#816—31no—
245#816—31no—
246#816—31no—
247#816—61no—
248#816C2×D311yescharacteristic, complemented
249#816C2×D311yescharacteristic, complemented
250#815C2×D311yescharacteristic, complemented
251Dic3⋊C8C2×D311yescharacteristic, complemented
252#810—31no—
253#807—31no—
254C23×C32C2×D411yescharacteristic
255C22×C3⋊D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3C2×D411yescharacteristic
258C2×D32—42no—
259C2×D32—42no—
260C2×D32—81no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2411yescharacteristic
265#638—42no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)C2×D412yes—
271C4×C3⋊D3—42no—
272#634—21no—
273#634—21no—
274#634—21no—
275#634—21no—
276C3×#67—22no—
277C3×#67—81no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—42no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C3×D12—21no—
286C3×D12—21no—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—42no—
293C3×Dic6C2×D412yes—
294#627—42no—
295#626—42no—
296#624—81no—
297D3×Dic3—42no—
298C32×C8—21no—
299C32×C8—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8C2×D412yes—
302C2×#137—91no—
303C22×SD16—91no—
304D4×Q8—91no—
305#546—91no—
306#497—91no—
307#468—91no—
308#467—91no—
309#464—91no—
310#461—91no—
311#452—91no—
312#451—91no—
313#450—91no—
314#448—31no—
315#440—91no—
316#435—31no—
317C23×D3—61no—
318C23×D3—61no—
319C2×C3×Q8—31no—
320C2×C3×Q8—31no—
321C2×C3×Q8—62no—
322C2×C3×Q8—61no—
323C2×C3×Q8—121no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—61no—
327C22×C3×C4—21no—
328C22×C3×C4—31no—
329C22×C3×C4—61no—
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C2×#67—21no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—121no—
337C2×#67D1211yescharacteristic
338C22×Dic3—21no—
339C22×Dic3—61no—
340D3×Q8—62no—
341D3×Q8—121no—
342D3×D4—62no—
343D3×D4—121no—
344#235—62no—
345#235—62no—
346#235—122no—
347#235—121no—
348#235—121no—
349#235—122no—
350C2×D12—31no—
351C2×D12—31no—
352C2×D12—61no—
353C2×D12—62no—
354C2×D12—61no—
355C2×D12—121no—
356C2×D12C22×D311yescharacteristic
357C2×C4×D3—61no—
358C2×C4×D3—61no—
359C2×C4×D3—61no—
360C2×C4×D3—61no—
361C2×C4×D3—61no—
362C2×C4×D3—121no—
363C2×C4×D3C22×D311yescharacteristic
364C2×Dic6—22no—
365C2×Dic6—21no—
366C2×Dic6—31no—
367C2×Dic6—31no—
368C2×Dic6—31no—
369C2×Dic6—31no—
370C2×Dic6—41no—
371C2×Dic6—61no—
372C2×Dic6—61no—
373C2×Dic6—62no—
374C2×Dic6—61no—
375C2×Dic6—61no—
376C2×Dic6—121no—
377C2×Dic6C22×D311yescharacteristic
378C2×Dic6C22×D311yescharacteristic
379C3×SD16—62no—
380C3×SD16—121no—
381C3×M16—62no—
382C2×C3×C8—21no—
383C2×C3×C8—21no—
384C2×C3×C8—31no—
385C2×C3×C8—31no—
386C2×C3×C8—62no—
387C2×C3×C8C22×D311yescharacteristic
388C2×C3×C8C22×D311yescharacteristic
389C2×C3×C8C22×D311yescharacteristic
390C2×C3×C8C22×D311yescharacteristic
391C3×C4⋊C4—31no—
392C3×C4⋊C4—31no—
393C3×C22⋊C4—31no—
394C3×C22⋊C4—31no—
395C3×C22⋊C4—61no—
396C3×C42—31no—
397#217—61no—
398#217—61no—
399#217—61no—
400#217—61no—
401#217—61no—
402#217—61no—
403#217—121no—
404#217D1211yescharacteristic
405#216—62no—
406#216—62no—
407#215—34no—
408#215—62no—
409#214—62no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4D1211yescharacteristic
418C4⋊Dic3—31no—
419C4⋊Dic3—31no—
420C4⋊Dic3—61no—
421C4⋊Dic3—61no—
422C4⋊Dic3—61no—
423C4⋊Dic3—61no—
424C4⋊Dic3—61no—
425C4⋊Dic3C22×D311yescharacteristic
426Dic3⋊C4—61no—
427Dic3⋊C4—61no—
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—121no—
435Dic3⋊C4D1211yescharacteristic
436C4×Dic3—61no—
437C4×Dic3—61no—
438C4×Dic3C22×D311yescharacteristic
439#208—22no—
440C2×C3⋊C8C22×D311yescharacteristic
441C2×C3⋊C8C22×D311yescharacteristic
442Dic12—62no—
443Dic12—62no—
444Dic12—121no—
445Dic12—121no—
446Dic12—122no—
447#204—22no—
448#204—34no—
449#204—41no—
450#204—62no—
451#204—62no—
452#204—62no—
453#204—62no—
454#204—122no—
455D3×C8—22no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32C22×D411yescharacteristic
460C2×C3⋊D3—22no—
461C2×C3⋊D3—41no—
462C2×C3⋊D3—41no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3#13712yescomplemented
469D32—84no—
470C32×C4—21no—
471C32×C4C22×D411yescharacteristic
472C32×C4H(5,𝔽2)11yescharacteristic
473C3⋊Dic3—41no—
474C3⋊Dic3—41no—
475C3⋊Dic3—41no—
476C3×Dic3—22no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—21no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C2×#41—91no—
483C22×Q8—31no—
484C22×Q8—91no—
485C22×D4—91no—
486#137—184no—
487C2×Q16—91no—
488C2×Q16—91no—
489C2×Q16—91no—
490C2×SD16—31no—
491C2×SD16—31no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×SD16—184no—
497C2×M16—31no—
498C22×C8—31no—
499C4⋊Q8—91no—
500C4⋊Q8—181no—
501#124—91no—
502#123—181no—
503C22⋊Q8—91no—
504C22⋊Q8—91no—
505C22⋊Q8—91no—
506C22⋊Q8—181no—
507C22⋊Q8—181no—
508#121—31no—
509#121—181no—
510#120—181no—
511C4×Q8—91no—
512C4×D4—31no—
513C4×D4—91no—
514C4×D4—181no—
515C2×C22⋊C4—181no—
516#107—91no—
517C4⋊C8—31no—
518#103—31no—
519#103—31no—
520#103—91no—
521#103—91no—
522#102—91no—
523#102—91no—
524C22⋊C8—31no—
525C22⋊C8D3211yescharacteristic, complemented
526#97—31no—
527C23×C3—21no—
528C23×C3—31no—
529C23×C3—61no—
530C23×C3C2×D1211yescharacteristic
531C23×C3D3×D411yescharacteristic
532C22×D3—21no—
533C22×D3—61no—
534C22×D3—61no—
535C22×D3—121no—
536C22×D3—122no—
537C22×D3—122no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3—241no—
541C22×D3—241no—
542C22×D3C2×D1211yescharacteristic
543C3×Q8—32no—
544C3×Q8—61no—
545C3×Q8—61no—
546C3×Q8—61no—
547C3×Q8—122no—
548C3×D4—62no—
549C3×D4—61no—
550C3×D4—61no—
551C3×D4—241no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—31no—
559C2×C3×C4—31no—
560C2×C3×C4—31no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—122no—
569C2×C3×C4C2×D1211yescharacteristic
570C2×C3×C4D3×D411yescharacteristic
571C2×C3×C4C23×D311yescharacteristic
572C2×C3×C4C23×D311yescharacteristic
573#67—22no—
574#67—81no—
575#67—122no—
576#67—122no—
577#67—122no—
578#67—124no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—42no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—121no—
590C2×Dic3—121no—
591C2×Dic3—121no—
592C2×Dic3—122no—
593C2×Dic3C2×D1211yescharacteristic
594C2×Dic3C2×D1211yescharacteristic
595C2×Dic3C2×D1211yescharacteristic
596D12—21no—
597D12—21no—
598D12—32no—
599D12—32no—
600D12—62no—
601D12—61no—
602D12—61no—
603D12—121no—
604D12—122no—
605C4×D3—21no—
606C4×D3—21no—
607C4×D3—122no—
608C4×D3—122no—
609C4×D3—124no—
610C4×D3—122no—
611C4×D3—241no—
612C4×D3—241no—
613Dic6—21no—
614Dic6—21no—
615Dic6—21no—
616Dic6—42no—
617Dic6—62no—
618Dic6—61no—
619Dic6—61no—
620Dic6—61no—
621Dic6—61no—
622Dic6—61no—
623Dic6—61no—
624Dic6—61no—
625Dic6—61no—
626Dic6—121no—
627Dic6—121no—
628Dic6—121no—
629Dic6—122no—
630Dic6—122no—
631Dic6D3×D412yes—
632C3×C8—21no—
633C3×C8—21no—
634C3×C8—21no—
635C3×C8—21no—
636C3×C8—32no—
637C3×C8—41no—
638C3×C8—41no—
639C3×C8—61no—
640C3⋊C8—21no—
641C3⋊C8D3×D412yes—
642C2×C32—41no—
643C2×C32D4211yescharacteristic
644C2×C32C2×#13711yescharacteristic
645C2×C32#57711yescharacteristic
646C3⋊D3—42no—
647C3×D3—22no—
648C3×D3—81no—
649C24—181no—
650#41—182no—
651#41—361no—
652C2×Q8—31no—
653C2×Q8—31no—
654C2×Q8—62no—
655C2×Q8—61no—
656C2×Q8—91no—
657C2×Q8—91no—
658C2×Q8—121no—
659C2×Q8—181no—
660C2×Q8—182no—
661C2×Q8—361no—
662C2×D4—31no—
663C2×D4—31no—
664C2×D4—61no—
665C2×D4—91no—
666C2×D4—181no—
667C2×D4—182no—
668C2×D4—181no—
669C2×D4—361no—
670C22×C4—31no—
671C22×C4—61no—
672C22×C4—181no—
673C22×C4—181no—
674C22×C4—181no—
675C22×C4C2×D3211yescharacteristic
676Q16—182no—
677Q16—182no—
678Q16—361no—
679SD16—62no—
680SD16—94no—
681SD16—121no—
682SD16—182no—
683SD16—182no—
684SD16—182no—
685M16—62no—
686C2×C8—31no—
687C2×C8—31no—
688C2×C8—62no—
689C2×C8C2×D3211yescharacteristic
690C2×C8C2×D3211yescharacteristic
691C4⋊C4—31no—
692C4⋊C4—31no—
693C4⋊C4—91no—
694C4⋊C4—181no—
695C4⋊C4—181no—
696C4⋊C4—181no—
697C4⋊C4—181no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C22⋊C4—31no—
701C22⋊C4—31no—
702C22⋊C4—61no—
703C22⋊C4—181no—
704C22⋊C4—181no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C42—31no—
710C42—181no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—32no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3C22×D1211yescharacteristic
728C22×C3C2×D3×D411yescharacteristic
729C2×D3—21no—
730C2×D3—21no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—41no—
734C2×D3—62no—
735C2×D3—62no—
736C2×D3—122no—
737C2×D3—121no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—241no—
742C2×D3—241no—
743C2×D3—244no—
744C2×D3—244no—
745C2×D3#90912yescomplemented
746C3×C4—21no—
747C3×C4—21no—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—41no—
751C3×C4—61no—
752C3×C4—61no—
753C3×C4—62no—
754C3×C4—61no—
755C3×C4—121no—
756C3×C4—121no—
757C3×C4C2×D3×D411yescharacteristic
758C3×C4C2×D3×D411yescharacteristic
759C3×C4#100411yescharacteristic
760C3×C4#100911yescharacteristic
761Dic3—21no—
762Dic3—21no—
763Dic3—21no—
764Dic3—22no—
765Dic3—41no—
766Dic3—41no—
767Dic3—122no—
768Dic3—121no—
769Dic3—121no—
770Dic3—121no—
771Dic3—121no—
772Dic3—121no—
773Dic3—121no—
774Dic3—241no—
775Dic3—241no—
776C32#326611yescharacteristic, complemented, Sylow
777C23—31no—
778C23—61no—
779C23—181no—
780C23—362no—
781C23—362no—
782C23—721no—
783C23D3×D1211yescharacteristic
784Q8—32no—
785Q8—61no—
786Q8—61no—
787Q8—61no—
788Q8—122no—
789Q8—181no—
790Q8—181no—
791Q8—181no—
792Q8—181no—
793Q8—362no—
794D4—62no—
795D4—61no—
796D4—61no—
797D4—92no—
798D4—181no—
799D4—241no—
800D4—362no—
801D4—362no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—31no—
805C2×C4—31no—
806C2×C4—31no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—122no—
813C2×C4—181no—
814C2×C4—181no—
815C2×C4—181no—
816C2×C4—362no—
817C2×C4—362no—
818C2×C4—721no—
819C2×C4D3×D1211yescharacteristic
820C2×C4C22×D3211yescharacteristic
821C8—21no—
822C8—21no—
823C8—32no—
824C8—61no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—41no—
829C2×C3—41no—
830C2×C3—62no—
831C2×C3—81no—
832C2×C3—241no—
833C2×C3D4×D1211yescharacteristic
834C2×C3#559011yescharacteristic
835C2×C3C2×#90911yescharacteristic
836C2×C3#575111yescharacteristic
837C2×C3#576211yescharacteristic
838C2×C3D3×#13711yescharacteristic
839D3—22no—
840D3—81no—
841D3—122no—
842D3—122no—
843D3—242no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—32no—
848C22—61no—
849C22—61no—
850C22—121no—
851C22—121no—
852C22—121no—
853C22—182no—
854C22—361no—
855C22—361no—
856C22—724no—
857C22C2×D3×D1211yescharacteristic
858C4—21no—
859C4—61no—
860C4—61no—
861C4—61no—
862C4—62no—
863C4—121no—
864C4—121no—
865C4—361no—
866C4—361no—
867C4—361no—
868C4D32×D411yescharacteristic
869C4#6431411yescharacteristic
870C3—21no—
871C3#7949511yescharacteristic, complemented
872C3#8006111yescharacteristic, complemented
873C2—41no—
874C2—62no—
875C2—241no—
876C2—362no—
877C2#1059427711yescharacteristic
878C2#1059467711yescharacteristic
879C2D3×#90911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10595078C2
hypercenterC22⋊C8D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. Dic6×#67C2semidirect
3. C2×#63833C2semidirect
4. C2×D3×#204C2semidirect
5. #10592432C2semidirect
6. C3×#4738C2semidirect
7. C3×#4728C2semidirect
8. #10591176C2semidirect
9. #10590952C2semidirect
10. #10590942C2semidirect
11. #10590897C2semidirect
12. #10590859C2semidirect
13. #10590848C2semidirect
14. #10590795C2semidirect
15. #10590760C2semidirect
19. C22×C3×Dic6C22semidirect
22. #64133C22semidirect
23. C2×#3746C22semidirect
27. C2×C3×#208C22semidirect
38. #63866C22semidirect
43. Dic3×Dic6C22semidirect
45. C2×#3719C22semidirect
46. C2×#3719C22semidirect
52. C32×C22⋊C8C22semidirect
54. #63643C22semidirect
56. C3×#816C22semidirect
57. C3×#816C22semidirect
58. C3×#815C22semidirect
59. C3×Dic3⋊C8C22semidirect
60. #63575C22semidirect
61. #63567C22semidirect
86. #4738D3semidirect
91. #4728D3semidirect
154. #3717D4semidirect
165. C22×Dic6C2×D3semidirect
197. C2×#208C2×D3semidirect
234. C3×C22⋊C8C2×D3semidirect
235. C3×C22⋊C8C2×D3semidirect
248. #816C2×D3semidirect
249. #816C2×D3semidirect
250. #815C2×D3semidirect
251. Dic3⋊C8C2×D3semidirect
468. C2×C3×D3#137semidirect
525. C22⋊C8D32semidirect
745. C2×D3#909semidirect
776. C32#3266semidirect
871. C3#79495semidirect
872. C3#80061semidirect

Maximal subgroups

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

subgroupindex
#105950782
Dic6×#672
C2×#638332
C2×D3×#2042
#105924322
C3×#47382
C3×#47282
#105911762
#105909522
#105909422
#105908972
#105908592
#105908482
#105907952
#105907602
#800613
#794953