Finite Group Databasebeta

← #11884140

Subgroups — #11884140

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#10595246C211yesmaximal, characteristic
2C2×#63931C211yesmaximal, characteristic, complemented
3C2×D3×#214C211yesmaximal, characteristic, complemented
4#10594383C211yesmaximal, characteristic, complemented
5#10592482C211yesmaximal, characteristic, complemented
6C3×#4776C211yesmaximal, characteristic, complemented
7C3×#4757C211yesmaximal, characteristic, complemented
8#10591489C211yesmaximal, characteristic, complemented
9#10590952C211yesmaximal, characteristic, complemented
10#10590897C211yesmaximal, characteristic, complemented
11#10590824C211yesmaximal, characteristic, complemented
12#10590728C211yesmaximal, characteristic, complemented
13#10590579C211yesmaximal, characteristic, complemented
14#10590532C211yesmaximal, characteristic, complemented
15#10590506C211yesmaximal, characteristic, complemented
16#80169—31nomaximal
17#79795—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×#3797C2211yescharacteristic, complemented
21C2×D3×Dic6C2211yescharacteristic
22C2×#3754C2211yescharacteristic
23C2×#3746C2211yescharacteristic, complemented
24#64106C2211yescharacteristic, complemented
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27C2×C3×#214C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic
29C3×#897C2211yescharacteristic
30C3×#887C2211yescharacteristic, complemented
31#63978—21no—
32#63977—21no—
33#63962—21no—
34C2×(C2×D3)⋊Dic3—21no—
35#63931—24no—
36D3×#214—24no—
37#63918—21no—
38#63916C2211yescharacteristic
39C4×#626C2211yescharacteristic
40#63895—21no—
41#63893—21no—
42#63880—21no—
43#63866C2211yescharacteristic, complemented
44#63860C2211yescharacteristic
45#63857C2211yescharacteristic
46C2×#3719C2211yescharacteristic, complemented
47C2×#3719C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3712C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic
52C32×#102C2211yescharacteristic
53#63647C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55C3×(C2×D3)⋊C8C2211yescharacteristic
56C3×#816C2211yescharacteristic, complemented
57C3×#815C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic
59C3×#807C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63565C2211yescharacteristic, complemented
63#5806—31no—
64C22×#214—31no—
65C2×#915—31no—
66C2×#915—31no—
67C2×D3×SD16—31no—
68#5632—31no—
69Q8×D12—31no—
70#5554—31no—
71C3×#450—31no—
72C3×#440—31no—
73#5170—31no—
74#5167—31no—
75#5162—31no—
76#5051—31no—
77#5028—31no—
78#5019—31no—
79#4887—31no—
80#4886—31no—
81#4809—31no—
82#4806—31no—
83#4783—31no—
84#4783—31no—
85#4783—61no—
86#4780—31no—
87#4776D311yescharacteristic, complemented
88#4767—31no—
89#4757D311yescharacteristic, complemented
90#4739—31no—
91#4730—31no—
92#4715—31no—
93#4706—31no—
94C23×C3×D3—21no—
95C2×C32×D4C2311yescharacteristic
96C2×#638—21no—
97C22×C3⋊Dic3—21no—
98#3830—22no—
99#3830—41no—
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×#634C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C2×C3×#67—21no—
104C22×C3×Dic3—21no—
105C3×D3×D4—22no—
106C3×D3×D4—41no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×#627—21no—
112C2×#627—21no—
113C2×#626—21no—
114C2×#626D411yescharacteristic
115C2×#624—21no—
116C2×D3×Dic3—21no—
117#3797—22no—
118#3797—41no—
119D3×Dic6—22no—
120D3×Dic6—41no—
121C2×C32×C8C2311yescharacteristic
122C32×C4⋊C4C2311yescharacteristic
123#3754—22no—
124#3752—21no—
125C4⋊(C3⋊Dic3)—21no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127#3746—41no—
128C3×#217—21no—
129C3×#214—22no—
130C3×#214D414yescomplemented
131C3×(C2×D3)⋊C4—21no—
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×#204—41no—
140Dic3⋊Dic3—21no—
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3D411yescharacteristic
144#3722D411yescharacteristic
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3D411yescharacteristic
150#3719—22no—
151#3719—22no—
152#3716—22no—
153#3715—22no—
154#3712—22no—
155D3×C3⋊C8—22no—
156#3266—91noSylow
157C22×C3×D4—31no—
158C2×D3×Q8—31no—
159C2×D3×Q8—31no—
160C2×D3×Q8—31no—
161C2×#237—31no—
162C2×#237—31no—
163C2×#237—61no—
164C2×D3×D4C2×D311yescharacteristic
165C22×Dic6—31no—
166C2×C3×SD16—31no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C3×C22⋊Q8—31no—
170C3×C4×Q8—31no—
171C3×C4×D4—31no—
172#953—61no—
173C2×#217—61no—
174#944—31no—
175C2×#216—31no—
176C2×#216—31no—
177C2×#215—31no—
178#939—61no—
179#938—31no—
180#936—31no—
181#935—61no—
182D4×Dic3C2×D311yescharacteristic
183C2×#214—31no—
184C2×#214—31no—
185C2×#214—31no—
186C2×#214—31no—
187C2×#214—61no—
188C2×#214—64no—
189C2×#214C2×D311yescharacteristic
190C2×#214C2×D311yescharacteristic
191#930—61no—
192C4×#67—31no—
193C2×(C2×D3)⋊C4—61no—
194#924—31no—
195C22×C3⋊C8—31no—
196#915—64no—
197#915—64no—
198D3×SD16—64no—
199C2×Dic12—31no—
200C2×Dic12—31no—
201C2×Dic12—31no—
202C2×Dic12—31no—
203C2×Dic12—61no—
204C2×#204—31no—
205C2×#204C2×D311yescharacteristic
206C2×ΓL(1,𝔽25)—31no—
207C2×ΓL(1,𝔽25)—31no—
208C2×D3×C8—31no—
209#897—31no—
210#897—31no—
211#897—31no—
212#897—61no—
213#897—61no—
214#897—61no—
215#897C2×D311yescharacteristic
216#896—61no—
217#895—31no—
218#888—61no—
219#887C2×D311yescharacteristic, complemented
220#886—61no—
221#882—61no—
222#67⋊C4—61no—
223#878—61no—
224#875—31no—
225C4×D12—31no—
226C4×D12—61no—
227#869—31no—
228#869—61no—
229C3×#107—31no—
230C3×#103—31no—
231C3×#102—21no—
232C3×#102—31no—
233C3×#102C2×D311yescharacteristic
234C3×#102C2×D311yescharacteristic
235C3×C22⋊C8—31no—
236C3×#97—31no—
237#835—31no—
238(C2×D3)⋊C8—31no—
239(C2×D3)⋊C8—31no—
240(C2×D3)⋊C8—61no—
241(C2×D3)⋊C8C2×D311yescharacteristic
242#816—31no—
243#816C2×D311yescharacteristic, complemented
244#815C2×D311yescharacteristic, complemented
245Dic3⋊C8—31no—
246#810—31no—
247#810—31no—
248#810—31no—
249#810—31no—
250#810—61no—
251#809C2×D311yescharacteristic
252#807C2×D311yescharacteristic, complemented
253C4⋊(C3⋊C8)—31no—
254C23×C32—21no—
255C22×C3⋊D3C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3—42no—
258C22×C3×D3—42no—
259C22×C3×D3—81no—
260C22×C3×D3C2×D411yescharacteristic
261C32×D4—21no—
262C32×D4C2×D412yes—
263C2×C32×C4—21no—
264C2×C32×C4C2411yescharacteristic
265#638—42no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—42no—
269C2×C3⋊Dic3C2×D411yescharacteristic
270C4×C3⋊D3—21no—
271C4×C3⋊D3—21no—
272#634—21no—
273#634—21no—
274#634—21no—
275#634—21no—
276C3×#67—42no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—81no—
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C3×D12—21no—
285C3×D12—21no—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6C2×D412yes—
292#627—42no—
293#627—42no—
294#626—22no—
295#626—81no—
296#624—42no—
297D3×Dic3—42no—
298C32×C8—21no—
299C3⋊(C3⋊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—31no—
314#448—91no—
315#440—31no—
316#435—91no—
317C24×C3—61no—
318C23×D3—21no—
319C2×C3×Q8—31no—
320C2×C3×Q8—31no—
321C2×C3×D4—21no—
322C2×C3×D4—31no—
323C2×C3×D4—61no—
324C2×C3×D4—62no—
325C2×C3×D4—121no—
326C2×C3×D4C22×D311yescharacteristic
327C2×C3×D4C22×D311yescharacteristic
328C22×C3×C4—31no—
329C22×C3×C4—61no—
330C2×#67—21no—
331C2×#67—31no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—121no—
336C22×Dic3—21no—
337C22×Dic3—61no—
338C22×Dic3—61no—
339C22×Dic3—61no—
340C22×Dic3—121no—
341D3×Q8—62no—
342D3×Q8—62no—
343D3×Q8—62no—
344D3×Q8—121no—
345D3×Q8—121no—
346D3×Q8—121no—
347#237—62no—
348#237—62no—
349#237—122no—
350#237—121no—
351#237—121no—
352#237—122no—
353D3×D4—22no—
354D3×D4—41no—
355C2×D12—31no—
356C2×D12—61no—
357C2×D12C22×D311yescharacteristic
358C2×C4×D3—31no—
359C2×C4×D3—31no—
360C2×C4×D3—61no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3—61no—
364C2×C4×D3C22×D311yescharacteristic
365C2×Dic6—31no—
366C2×Dic6—31no—
367C2×Dic6—31no—
368C2×Dic6—31no—
369C2×Dic6—61no—
370C2×Dic6—61no—
371C2×Dic6—62no—
372C2×Dic6—61no—
373C2×Dic6—61no—
374C2×Dic6—61no—
375C2×Dic6—61no—
376C2×Dic6—121no—
377C2×Dic6C22×D311yescharacteristic
378C2×Dic6C22×D311yescharacteristic
379C3×SD16—34no—
380C3×SD16—62no—
381C3×SD16—121no—
382C2×C3×C8—21no—
383C2×C3×C8—31no—
384C2×C3×C8—31no—
385C2×C3×C8C22×D311yescharacteristic
386C2×C3×C8C22×D311yescharacteristic
387C3×C4⋊C4—21no—
388C3×C4⋊C4—31no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4C22×D311yescharacteristic
392C3×C4⋊C4C22×D311yescharacteristic
393C3×C22⋊C4—61no—
394C3×C22⋊C4—61no—
395C3×C42—31no—
396C3×C42—61no—
397#217—21no—
398#217—31no—
399#217—61no—
400#217—61no—
401#217—61no—
402#217—61no—
403#216—62no—
404#216—62no—
405#215—62no—
406#214—22no—
407#214—62no—
408#214—62no—
409#214—62no—
410#214—62no—
411#214—122no—
412#214D1214yescomplemented
413(C2×D3)⋊C4—21no—
414(C2×D3)⋊C4—31no—
415(C2×D3)⋊C4—31no—
416(C2×D3)⋊C4—31no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—121no—
424C4⋊Dic3—21no—
425C4⋊Dic3—31no—
426C4⋊Dic3—61no—
427C4⋊Dic3—61no—
428C4⋊Dic3—61no—
429C4⋊Dic3—61no—
430C4⋊Dic3—61no—
431C4⋊Dic3—121no—
432C4⋊Dic3C22×D311yescharacteristic
433Dic3⋊C4—21no—
434Dic3⋊C4—31no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438C4×Dic3—21no—
439C4×Dic3C22×D311yescharacteristic
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—61no—
443C2×C3⋊C8—62no—
444C2×C3⋊C8C22×D311yescharacteristic
445C2×C3⋊C8C22×D311yescharacteristic
446Dic12—62no—
447Dic12—62no—
448Dic12—121no—
449Dic12—121no—
450Dic12—122no—
451#204—41no—
452#204—62no—
453ΓL(1,𝔽25)—62no—
454ΓL(1,𝔽25)—62no—
455D3×C8—62no—
456C22×C32—22no—
457C22×C32—41no—
458C22×C32—41no—
459C22×C32C22×D411yescharacteristic
460C2×C3⋊D3—21no—
461C2×C3⋊D3—21no—
462C2×C3⋊D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—84no—
469C2×C3×D3#13712yescomplemented
470C32×C4—41no—
471C32×C4C22×D411yescharacteristic
472C32×C4H(5,𝔽2)11yescharacteristic
473C3⋊Dic3—21no—
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—91no—
484C22×Q8—91no—
485C22×D4—31no—
486#137—184no—
487C2×Q16—91no—
488C2×Q16—91no—
489C2×Q16—91no—
490C2×SD16—31no—
491C2×SD16—31no—
492C2×SD16—31no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×SD16—184no—
497C2×M16—91no—
498C22×C8—91no—
499C4⋊Q8—91no—
500C4⋊Q8—181no—
501#124—91no—
502#123—181no—
503C22⋊Q8—31no—
504C22⋊Q8—91no—
505C22⋊Q8—91no—
506C22⋊Q8—181no—
507C22⋊Q8—181no—
508#121—91no—
509#121—181no—
510#120—181no—
511C4×Q8—31no—
512C4×D4—31no—
513C4×D4—91no—
514C4×D4—181no—
515C2×C22⋊C4—181no—
516#107—31no—
517C4⋊C8—91no—
518#103—31no—
519#103—91no—
520#103—91no—
521#103—91no—
522#102—31no—
523#102D3211yescharacteristic
524C22⋊C8—31no—
525C22⋊C8—91no—
526#97—31no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—31no—
530C23×C3—41no—
531C23×C3—61no—
532C23×C3—122no—
533C23×C3—122no—
534C23×C3—241no—
535C22×D3—21no—
536C22×D3—31no—
537C22×D3—31no—
538C22×D3—42no—
539C22×D3—42no—
540C22×D3—61no—
541C22×D3—81no—
542C22×D3D3×D411yescharacteristic
543C3×Q8—32no—
544C3×Q8—61no—
545C3×Q8—61no—
546C3×Q8—61no—
547C3×D4—21no—
548C3×D4—21no—
549C3×D4—22no—
550C3×D4—41no—
551C3×D4—61no—
552C3×D4—61no—
553C3×D4—122no—
554C3×D4C2×D1212yes—
555C3×D4D3×D412yes—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—31no—
560C2×C3×C4—31no—
561C2×C3×C4—31no—
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—241no—
569C2×C3×C4C23×D311yescharacteristic
570C2×C3×C4C23×D311yescharacteristic
571#67—42no—
572#67—62no—
573#67—122no—
574#67—122no—
575#67—124no—
576#67—241no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—31no—
581C2×Dic3—31no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—81no—
588C2×Dic3—121no—
589C2×Dic3—121no—
590C2×Dic3—122no—
591C2×Dic3—122no—
592C2×Dic3—122no—
593C2×Dic3—124no—
594C2×Dic3D3×D411yescharacteristic
595C2×Dic3D3×D411yescharacteristic
596C2×Dic3D3×D411yescharacteristic
597D12—21no—
598D12—21no—
599D12—62no—
600D12—241no—
601C4×D3—21no—
602C4×D3—21no—
603C4×D3—61no—
604C4×D3—61no—
605C4×D3—61no—
606C4×D3—61no—
607C4×D3—121no—
608C4×D3—121no—
609C4×D3—122no—
610C4×D3—122no—
611C4×D3—122no—
612Dic6—21no—
613Dic6—21no—
614Dic6—21no—
615Dic6—62no—
616Dic6—61no—
617Dic6—61no—
618Dic6—61no—
619Dic6—61no—
620Dic6—61no—
621Dic6—61no—
622Dic6—61no—
623Dic6—61no—
624Dic6—121no—
625Dic6—121no—
626Dic6—121no—
627Dic6—122no—
628Dic6—122no—
629Dic6—122no—
630Dic6—122no—
631Dic6C2×D1212yes—
632C3×C8—21no—
633C3×C8—21no—
634C3×C8—32no—
635C3×C8—41no—
636C3×C8—61no—
637C3⋊C8—21no—
638C3⋊C8—61no—
639C3⋊C8—61no—
640C3⋊C8—121no—
641C3⋊C8C2×D1212yes—
642C2×C32—42no—
643C2×C32D4211yescharacteristic
644C2×C32C2×#13711yescharacteristic
645C2×C32#57711yescharacteristic
646C3⋊D3—41no—
647C3×D3—22no—
648C3×D3—81no—
649C24—61no—
650#41—182no—
651#41—361no—
652C2×Q8—31no—
653C2×Q8—31no—
654C2×Q8—91no—
655C2×Q8—91no—
656C2×Q8—181no—
657C2×Q8—181no—
658C2×Q8—182no—
659C2×Q8—182no—
660C2×Q8—361no—
661C2×Q8—361no—
662C2×D4—31no—
663C2×D4—61no—
664C2×D4—62no—
665C2×D4—91no—
666C2×D4—121no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4C2×D3211yescharacteristic
670C22×C4—31no—
671C22×C4—61no—
672C22×C4—91no—
673C22×C4—181no—
674C22×C4—181no—
675C22×C4—181no—
676Q16—182no—
677Q16—182no—
678Q16—361no—
679SD16—34no—
680SD16—62no—
681SD16—121no—
682SD16—182no—
683SD16—182no—
684SD16—182no—
685M16—182no—
686C2×C8—31no—
687C2×C8—31no—
688C2×C8—91no—
689C2×C8—182no—
690C2×C8C2×D3211yescharacteristic
691C4⋊C4—31no—
692C4⋊C4—61no—
693C4⋊C4—61no—
694C4⋊C4—91no—
695C4⋊C4—181no—
696C4⋊C4—181no—
697C4⋊C4—181no—
698C4⋊C4—181no—
699C4⋊C4C2×D3211yescharacteristic
700C22⋊C4—61no—
701C22⋊C4—61no—
702C22⋊C4—91no—
703C22⋊C4—91no—
704C22⋊C4—181no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C42—31no—
710C42—61no—
711C22×C3—22no—
712C22×C3—22no—
713C22×C3—21no—
714C22×C3—32no—
715C22×C3—42no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—61no—
721C22×C3—61no—
722C22×C3—81no—
723C22×C3—81no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—244no—
728C22×C3C2×D3×D411yescharacteristic
729C22×C3C2×D3×D411yescharacteristic
730C2×D3—21no—
731C2×D3—21no—
732C2×D3—41no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—61no—
736C2×D3—61no—
737C2×D3—61no—
738C2×D3—61no—
739C2×D3—61no—
740C2×D3—61no—
741C2×D3—84no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3#91512yescomplemented
746C3×C4—21no—
747C3×C4—21no—
748C3×C4—41no—
749C3×C4—41no—
750C3×C4—61no—
751C3×C4—61no—
752C3×C4—61no—
753C3×C4—62no—
754C3×C4—81no—
755C3×C4—121no—
756C3×C4—121no—
757C3×C4C22×D1211yescharacteristic
758C3×C4C2×D3×D411yescharacteristic
759C3×C4#100411yescharacteristic
760C3×C4#100911yescharacteristic
761Dic3—21no—
762Dic3—21no—
763Dic3—22no—
764Dic3—21no—
765Dic3—41no—
766Dic3—41no—
767Dic3—61no—
768Dic3—61no—
769Dic3—121no—
770Dic3—122no—
771Dic3—121no—
772Dic3—121no—
773Dic3—121no—
774Dic3—121no—
775Dic3—241no—
776C32#326611yescharacteristic, complemented, Sylow
777C23—21no—
778C23—31no—
779C23—61no—
780C23—91no—
781C23—122no—
782C23—122no—
783C23—241no—
784Q8—32no—
785Q8—61no—
786Q8—61no—
787Q8—61no—
788Q8—181no—
789Q8—181no—
790Q8—181no—
791Q8—181no—
792Q8—362no—
793Q8—362no—
794D4—21no—
795D4—61no—
796D4—61no—
797D4—122no—
798D4—182no—
799D4—362no—
800D4—721no—
801D4D3×D1212yes—
802C2×C4—21no—
803C2×C4—31no—
804C2×C4—31no—
805C2×C4—31no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—91no—
812C2×C4—181no—
813C2×C4—181no—
814C2×C4—181no—
815C2×C4—181no—
816C2×C4—241no—
817C2×C4—362no—
818C2×C4—362no—
819C2×C4—362no—
820C2×C4C22×D3211yescharacteristic
821C8—21no—
822C8—32no—
823C8—61no—
824C8—181no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—42no—
829C2×C3—42no—
830C2×C3—62no—
831C2×C3—82no—
832C2×C3—241no—
833C2×C3D4×D1211yescharacteristic
834C2×C3#559011yescharacteristic
835C2×C3C2×#91511yescharacteristic
836C2×C3#577511yescharacteristic
837C2×C3#577511yescharacteristic
838C2×C3D3×#13711yescharacteristic
839D3—22no—
840D3—81no—
841D3—121no—
842D3—121no—
843D3—241no—
844C22—22no—
845C22—32no—
846C22—41no—
847C22—41no—
848C22—61no—
849C22—61no—
850C22—121no—
851C22—121no—
852C22—121no—
853C22—181no—
854C22—181no—
855C22—181no—
856C22—244no—
857C22D32×D411yescharacteristic
858C4—41no—
859C4—61no—
860C4—61no—
861C4—61no—
862C4—62no—
863C4—121no—
864C4—121no—
865C4—181no—
866C4—361no—
867C4—361no—
868C4C2×D3×D1211yescharacteristic
869C4#6431411yescharacteristic
870C3—21no—
871C3#7979511yescharacteristic, complemented
872C3#8016911yescharacteristic, complemented
873C2—42no—
874C2—62no—
875C2—241no—
876C2—361no—
877C2#1059427711yescharacteristic
878C2#1059473311yescharacteristic
879C2D3×#91511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595246C2
hypercenter#102D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. C2×#63931C2semidirect
3. C2×D3×#214C2semidirect
4. #10594383C2semidirect
5. #10592482C2semidirect
6. C3×#4776C2semidirect
7. C3×#4757C2semidirect
8. #10591489C2semidirect
9. #10590952C2semidirect
10. #10590897C2semidirect
11. #10590824C2semidirect
12. #10590728C2semidirect
13. #10590579C2semidirect
14. #10590532C2semidirect
15. #10590506C2semidirect
20. C2×#3797C22semidirect
23. C2×#3746C22semidirect
24. #64106C22semidirect
30. C3×#887C22semidirect
43. #63866C22semidirect
46. C2×#3719C22semidirect
47. C2×#3719C22semidirect
50. C2×#3712C22semidirect
53. #63647C22semidirect
54. #63637C22semidirect
56. C3×#816C22semidirect
57. C3×#815C22semidirect
59. C3×#807C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63567C22semidirect
62. #63565C22semidirect
87. #4776D3semidirect
89. #4757D3semidirect
130. C3×#214D4semidirect
219. #887C2×D3semidirect
243. #816C2×D3semidirect
244. #815C2×D3semidirect
252. #807C2×D3semidirect
412. #214D12semidirect
469. C2×C3×D3#137semidirect
745. C2×D3#915semidirect
776. C32#3266semidirect
871. C3#79795semidirect
872. C3#80169semidirect

Maximal subgroups

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

subgroupindex
#105952462
C2×#639312
C2×D3×#2142
#105943832
#105924822
C3×#47762
C3×#47572
#105914892
#105909522
#105908972
#105908242
#105907282
#105905792
#105905322
#105905062
#801693
#797953