Finite Group Databasebeta

← #11884122

Subgroups — #11884122

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
1C3×#5829C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic, complemented
3C2×D3×#214C211yesmaximal, characteristic, complemented
4Dic6×#67C211yesmaximal, characteristic, complemented
5#10592938C211yesmaximal, characteristic, complemented
6#10591653C211yesmaximal, characteristic, complemented
7#10591635C211yesmaximal, characteristic, complemented
8#10591627C211yesmaximal, characteristic, complemented
9#10591578C211yesmaximal, characteristic, complemented
10#10591489C211yesmaximal, characteristic, complemented
11#10591458C211yesmaximal, characteristic, complemented
12#10591440C211yesmaximal, characteristic, complemented
13#10591176C211yesmaximal, characteristic, complemented
14#10591171C211yesmaximal, characteristic, complemented
15#10591147C211yesmaximal, characteristic, complemented
16#83987—31nomaximal
17#83506—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic, complemented
21C2×D3×Dic6C2211yescharacteristic
22C2×#3756C2211yescharacteristic, complemented
23C2×#3754C2211yescharacteristic
24#64133C2211yescharacteristic, complemented
25C3×#951—24no—
26C3×#947C2211yescharacteristic
27C3×#946C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic, complemented
29C2×C3×#216C2211yescharacteristic, complemented
30C3×#939—21no—
31C3×#937—21no—
32C3×D4×Dic3C2211yescharacteristic
33C2×C3×#214C2211yescharacteristic
34C2×C3×#214C2211yescharacteristic
35C3×#930C2211yescharacteristic
36C3×#929—21no—
37C3×C4×#67C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4—21no—
39C2×C3×#208C2211yescharacteristic, complemented
40Dic3×#67—21no—
41#63964—21no—
42D3×#214—24no—
43#63887—21no—
44#63866C2211yescharacteristic, complemented
45#63856C2211yescharacteristic
46Dic3×Dic6C2211yescharacteristic, complemented
47#63839—21no—
48C2×#3716C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3715C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic
52#63662C2211yescharacteristic, complemented
53#63659C2211yescharacteristic
54#63657C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63563C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic, complemented
63C2×C3×#137—31no—
64C3×#546—31no—
65#5829D311yescharacteristic
66C2×#951D311yescharacteristic, complemented
67Q8×#67—31no—
68C22×#214—31no—
69C2×D3×SD16—31no—
70D4×Dic6—31no—
71#5239—31no—
72#5239—31no—
73#5239—61no—
74#5227—31no—
75#5218—31no—
76#5190—31no—
77#5188—31no—
78#5186—31no—
79#5185—31no—
80#5169—31no—
81#5164—31no—
82#5162—31no—
83#5134—31no—
84#5127—31no—
85#5060—31no—
86#5054—31no—
87#5051—31no—
88#5050—31no—
89#5042—31no—
90#5040—31no—
91#5019—31no—
92#5018—31no—
93#5011—31no—
94C23×C3×D3—21no—
95C32×#41—22no—
96C32×#41—41no—
97C2×C32×Q8C2311yescharacteristic
98C2×C32×D4—21no—
99C2×C32×D4C2311yescharacteristic
100C22×C32×C4—21no—
101C22×C32×C4C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67D411yescharacteristic
106C22×C3×Dic3—21no—
107C22×C3×Dic3—21no—
108C3×D3×D4—22no—
109C3×D3×D4—41no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6—22no—
113C2×C3×Dic6—21no—
114C2×C3×Dic6—41no—
115C2×C3×Dic6C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#627—21no—
118C2×D3×Dic3—21no—
119D3×Dic6—22no—
120D3×Dic6—41no—
121#3757—21no—
122#3756—41no—
123#3754—22no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3750—21no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#217—21no—
129C3×#217D411yescharacteristic
130C3×#216—22no—
131C3×#216—22no—
132C3×#214—22no—
133C3×#214D414yescomplemented
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4D411yescharacteristic
139C3×C4⋊Dic3C2311yescharacteristic
140C3×Dic3⋊C4—21no—
141C3×Dic3⋊C4D411yescharacteristic
142C3×C4×Dic3C2311yescharacteristic
143C3×#208—22no—
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146#3724—21no—
147Dic3⋊Dic3—21no—
148Dic3⋊Dic3—21no—
149Dic3⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151Dic32—21no—
152#3716—22no—
153#3715—22no—
154#3715—41no—
155D3×C3⋊C8—22no—
156#3266—91noSylow
157C2×C3×#41—21no—
158C2×C3×#41C2×D311yescharacteristic
159C2×C3×#41C2×D311yescharacteristic
160C22×C3×Q8—31no—
161C22×C3×D4—31no—
162C2×D3×Q8—31no—
163C2×D3×D4C2×D311yescharacteristic
164C22×Dic6—31no—
165C22×Dic6C2×D311yescharacteristic, complemented
166C3×#137—64no—
167C2×C3×Q16—31no—
168C2×C3×Q16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×M16—31no—
172C3×#124—31no—
173C3×#123—61no—
174C3×C22⋊Q8—31no—
175C3×#121—31no—
176C3×#121—61no—
177C3×#120—61no—
178C3×C4×D4—31no—
179C3×C4×D4—31no—
180C2×C3×C22⋊C4—61no—
181#951—24no—
182#947C2×D311yescharacteristic
183#946—31no—
184#946—61no—
185#946C2×D311yescharacteristic
186Q8×Dic3—31no—
187#944—31no—
188#944—61no—
189C2×#216—31no—
190C2×#216—31no—
191C2×#216—61no—
192C2×#216C2×D311yescharacteristic, complemented
193C2×#216C2×D311yescharacteristic, complemented
194C2×#215—31no—
195C2×#215—31no—
196#939—21no—
197#937—21no—
198D4×Dic3—61no—
199D4×Dic3C2×D311yescharacteristic
200C2×#214—31no—
201C2×#214—31no—
202C2×#214—31no—
203C2×#214—31no—
204C2×#214—31no—
205C2×#214—61no—
206C2×#214—64no—
207C2×#214C2×D311yescharacteristic
208C2×#214C2×D311yescharacteristic
209#930C2×D311yescharacteristic
210#929—21no—
211C4×#67—61no—
212C4×#67C2×D311yescharacteristic
213C2×(C2×D3)⋊C4—21no—
214#924—31no—
215#924—31no—
216#924—31no—
217#924—61no—
218#924—61no—
219C2×#208C2×D311yescharacteristic, complemented
220C22×C3⋊C8—31no—
221D3×SD16—64no—
222C2×#204—31no—
223C2×D3×C8—31no—
224#888—61no—
225#878—61no—
226#878—61no—
227#869—31no—
228C4×Dic6—31no—
229#835—31no—
230#835—31no—
231#835—31no—
232#835—31no—
233#835—61no—
234#832—31no—
235#832—31no—
236#832—31no—
237#832—61no—
238#830—31no—
239#830—31no—
240#830—31no—
241#830—61no—
242#821—31no—
243(C2×D3)⋊C8—31no—
244#818—31no—
245#816—31no—
246#815—31no—
247Dic3⋊C8—31no—
248#810—31no—
249#810—31no—
250#810—31no—
251#807—31no—
252C4⋊(C3⋊C8)—31no—
253#803—31no—
254C23×C32—21no—
255C23×C32C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3—42no—
258C22×C3×D3—42no—
259C22×C3×D3—81no—
260C22×C3×D3C2×D411yescharacteristic
261C32×Q8—21no—
262C32×Q8—21no—
263C32×D4—21no—
264C32×D4—42no—
265C32×D4C2×D412yes—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—42no—
270C2×C32×C4C2×D411yescharacteristic
271C2×C32×C4C2411yescharacteristic
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—21no—
274#634—21no—
275#634—21no—
276C3×#67—22no—
277C3×#67—42no—
278C3×#67—81no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—42no—
283C2×C3×Dic3—81no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×D12—21no—
288C3×D12—21no—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—42no—
295C3×Dic6C2×D412yes—
296#627—42no—
297D3×Dic3—42no—
298C3⋊(C3⋊C8)—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8C2×D412yes—
302C2×#137—31no—
303C22×SD16—91no—
304D4×Q8—91no—
305#546—31no—
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—91no—
315#440—91no—
316#435—91no—
317C24×C3—61no—
318C23×D3—21no—
319C3×#41—22no—
320C3×#41—22no—
321C3×#41—42no—
322C3×#41—41no—
323C3×#41—41no—
324C3×#41—42no—
325C2×C3×Q8—21no—
326C2×C3×Q8—31no—
327C2×C3×Q8—31no—
328C2×C3×Q8—62no—
329C2×C3×Q8—61no—
330C2×C3×Q8—121no—
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×Q8C22×D311yescharacteristic
333C2×C3×D4—21no—
334C2×C3×D4—21no—
335C2×C3×D4—21no—
336C2×C3×D4—31no—
337C2×C3×D4—31no—
338C2×C3×D4—41no—
339C2×C3×D4—61no—
340C2×C3×D4—62no—
341C2×C3×D4—61no—
342C2×C3×D4—121no—
343C2×C3×D4C22×D311yescharacteristic
344C2×C3×D4C22×D311yescharacteristic
345C22×C3×C4—21no—
346C22×C3×C4—21no—
347C22×C3×C4—21no—
348C22×C3×C4—31no—
349C22×C3×C4—41no—
350C22×C3×C4—61no—
351C22×C3×C4—61no—
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C2×#67—21no—
355C2×#67—21no—
356C2×#67#6711yescharacteristic
357C22×Dic3—21no—
358C22×Dic3—21no—
359C22×Dic3—61no—
360D3×Q8—62no—
361D3×Q8—121no—
362D3×D4—22no—
363D3×D4—41no—
364C2×D12C22×D311yescharacteristic
365C2×C4×D3—61no—
366C2×C4×D3C22×D311yescharacteristic
367C2×Dic6—22no—
368C2×Dic6—21no—
369C2×Dic6—31no—
370C2×Dic6—31no—
371C2×Dic6—41no—
372C2×Dic6—61no—
373C2×Dic6—62no—
374C2×Dic6—61no—
375C2×Dic6—61no—
376C2×Dic6—121no—
377C2×Dic6C22×D311yescharacteristic
378C2×Dic6C22×D311yescharacteristic
379C3×Q16—62no—
380C3×Q16—62no—
381C3×SD16—34no—
382C3×SD16—62no—
383C3×M16—62no—
384C2×C3×C8—31no—
385C2×C3×C8—31no—
386C3×C4⋊C4—31no—
387C3×C4⋊C4—31no—
388C3×C4⋊C4—61no—
389C3×C22⋊C4—31no—
390C3×C22⋊C4—31no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C42—31no—
397#217—21no—
398#217—61no—
399#217—61no—
400#217—61no—
401#217—121no—
402#217#6711yescharacteristic
403#216—22no—
404#216—22no—
405#216—121no—
406#216—121no—
407#216—122no—
408#215—62no—
409#215—121no—
410#214—22no—
411#214—62no—
412#214—62no—
413#214—62no—
414#214—62no—
415#214—122no—
416#214—121no—
417#214#6714yescomplemented
418(C2×D3)⋊C4—21no—
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4#6711yescharacteristic
424C4⋊Dic3—31no—
425C4⋊Dic3—31no—
426C4⋊Dic3—61no—
427C4⋊Dic3—61no—
428C4⋊Dic3—61no—
429C4⋊Dic3—61no—
430C4⋊Dic3C22×D311yescharacteristic
431Dic3⋊C4—21no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439Dic3⋊C4—121no—
440Dic3⋊C4#6711yescharacteristic
441C4×Dic3—61no—
442C4×Dic3—61no—
443C4×Dic3C22×D311yescharacteristic
444#208—22no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—61no—
450C2×C3⋊C8—61no—
451C2×C3⋊C8—62no—
452C2×C3⋊C8C22×D311yescharacteristic
453C2×C3⋊C8C22×D311yescharacteristic
454#204—62no—
455D3×C8—62no—
456C22×C32—21no—
457C22×C32—22no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—41no—
461C22×C32—41no—
462C22×C32C22×D411yescharacteristic
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—21no—
471C32×C4—41no—
472C32×C4C22×D411yescharacteristic
473C32×C4H(5,𝔽2)11yescharacteristic
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×#41D3211yescharacteristic
483C22×Q8—31no—
484C22×Q8—91no—
485C22×D4—31no—
486#137—64no—
487C2×Q16—31no—
488C2×Q16—31no—
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—91no—
499C4⋊Q8—91no—
500C4⋊Q8—181no—
501#124—31no—
502#123—61no—
503C22⋊Q8—31no—
504C22⋊Q8—91no—
505C22⋊Q8—91no—
506C22⋊Q8—181no—
507C22⋊Q8—181no—
508#121—31no—
509#121—61no—
510#120—61no—
511C4×Q8—91no—
512C4×D4—31no—
513C4×D4—31no—
514C4×D4—181no—
515C2×C22⋊C4—61no—
516#107—91no—
517C4⋊C8—91no—
518#103—91no—
519#103—91no—
520#103—91no—
521#103—91no—
522#102—91no—
523#102—91no—
524C22⋊C8—91no—
525C22⋊C8—91no—
526#97—91no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—31no—
531C23×C3—41no—
532C23×C3—61no—
533C23×C3—122no—
534C23×C3—122no—
535C23×C3—241no—
536C23×C3D3×D411yescharacteristic
537C23×C3C2×#6711yescharacteristic
538C22×D3—21no—
539C22×D3—42no—
540C22×D3—42no—
541C22×D3—81no—
542C22×D3C2×#6711yescharacteristic
543C3×Q8—22no—
544C3×Q8—21no—
545C3×Q8—21no—
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8—32no—
549C3×Q8—41no—
550C3×Q8—61no—
551C3×Q8—61no—
552C3×Q8—61no—
553C3×Q8—122no—
554C3×D4—21no—
555C3×D4—21no—
556C3×D4—22no—
557C3×D4—41no—
558C3×D4—42no—
559C3×D4—42no—
560C3×D4—44no—
561C3×D4—62no—
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—122no—
565C3×D4—241no—
566C3×D4D3×D412yes—
567C3×D4C2×#6712yes—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—31no—
577C2×C3×C4—31no—
578C2×C3×C4—31no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—42no—
583C2×C3×C4—42no—
584C2×C3×C4—44no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—122no—
591C2×C3×C4—241no—
592C2×C3×C4D3×D411yescharacteristic
593C2×C3×C4C2×#6711yescharacteristic
594C2×C3×C4C23×D311yescharacteristic
595C2×C3×C4C23×D311yescharacteristic
596#67—22no—
597#67—42no—
598#67—81no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—42no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—81no—
608C2×Dic3—121no—
609C2×Dic3—121no—
610C2×Dic3—122no—
611C2×Dic3C2×#6711yescharacteristic
612C2×Dic3C2×#6711yescharacteristic
613C2×Dic3C2×#6711yescharacteristic
614D12—21no—
615D12—21no—
616C4×D3—21no—
617C4×D3—21no—
618C4×D3—122no—
619Dic6—21no—
620Dic6—21no—
621Dic6—21no—
622Dic6—42no—
623Dic6—61no—
624Dic6—61no—
625Dic6—61no—
626Dic6—61no—
627Dic6—121no—
628Dic6—121no—
629Dic6—122no—
630Dic6—122no—
631Dic6C2×#6712yes—
632C3×C8—32no—
633C3×C8—61no—
634C3⋊C8—21no—
635C3⋊C8—61no—
636C3⋊C8—61no—
637C3⋊C8—61no—
638C3⋊C8—61no—
639C3⋊C8—121no—
640C3⋊C8—121no—
641C3⋊C8C2×#6712yes—
642C2×C32—42no—
643C2×C32—41no—
644C2×C32D4211yescharacteristic
645C2×C32C2×#13711yescharacteristic
646C2×C32#57711yescharacteristic
647C3×D3—22no—
648C3×D3—81no—
649C24—61no—
650#41—22no—
651#41—41no—
652C2×Q8—31no—
653C2×Q8—31no—
654C2×Q8—62no—
655C2×Q8—61no—
656C2×Q8—91no—
657C2×Q8—121no—
658C2×Q8—181no—
659C2×Q8—182no—
660C2×Q8—361no—
661C2×Q8C2×D3211yescharacteristic
662C2×D4—21no—
663C2×D4—31no—
664C2×D4—31no—
665C2×D4—61no—
666C2×D4—62no—
667C2×D4—61no—
668C2×D4—121no—
669C2×D4C2×D3211yescharacteristic
670C22×C4—21no—
671C22×C4—31no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—181no—
675C22×C4C2×D3211yescharacteristic
676Q16—62no—
677Q16—62no—
678Q16—361no—
679SD16—34no—
680SD16—62no—
681SD16—182no—
682SD16—182no—
683SD16—182no—
684SD16—361no—
685M16—62no—
686C2×C8—31no—
687C2×C8—31no—
688C2×C8—91no—
689C2×C8—91no—
690C2×C8—182no—
691C4⋊C4—31no—
692C4⋊C4—31no—
693C4⋊C4—61no—
694C4⋊C4—91no—
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—61no—
704C22⋊C4—61no—
705C22⋊C4—61no—
706C22⋊C4—61no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C42—31no—
710C42—181no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—22no—
715C22×C3—21no—
716C22×C3—22no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—32no—
721C22×C3—42no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—61no—
730C22×C3—61no—
731C22×C3—81no—
732C22×C3—81no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—244no—
737C22×C3C2×D3×D411yescharacteristic
738C22×C3C22×#6711yescharacteristic
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—84no—
745C2×D3#95112yescomplemented
746C3×C4—21no—
747C3×C4—21no—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—41no—
751C3×C4—42no—
752C3×C4—41no—
753C3×C4—41no—
754C3×C4—61no—
755C3×C4—61no—
756C3×C4—61no—
757C3×C4—62no—
758C3×C4—121no—
759C3×C4—121no—
760C3×C4C2×D3×D411yescharacteristic
761C3×C4#100411yescharacteristic
762C3×C4#100411yescharacteristic
763C3×C4C22×#6711yescharacteristic
764Dic3—22no—
765Dic3—21no—
766Dic3—21no—
767Dic3—21no—
768Dic3—41no—
769Dic3—41no—
770Dic3—121no—
771Dic3—121no—
772Dic3—121no—
773Dic3—121no—
774Dic3—241no—
775Dic3—241no—
776C32#326611yescharacteristic, complemented, Sylow
777C23—21no—
778C23—31no—
779C23—61no—
780C23—122no—
781C23—122no—
782C23—241no—
783C23D3×#6711yescharacteristic
784Q8—21no—
785Q8—21no—
786Q8—32no—
787Q8—61no—
788Q8—61no—
789Q8—61no—
790Q8—122no—
791Q8—181no—
792Q8—181no—
793Q8—362no—
794D4—21no—
795D4—42no—
796D4—62no—
797D4—61no—
798D4—61no—
799D4—122no—
800D4—241no—
801D4D3×#6712yes—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—31no—
806C2×C4—31no—
807C2×C4—31no—
808C2×C4—42no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—122no—
815C2×C4—181no—
816C2×C4—181no—
817C2×C4—241no—
818C2×C4—362no—
819C2×C4D3×#6711yescharacteristic
820C2×C4C22×D3211yescharacteristic
821C8—32no—
822C8—61no—
823C8—181no—
824C8—181no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—41no—
829C2×C3—42no—
830C2×C3—42no—
831C2×C3—41no—
832C2×C3—62no—
833C2×C3—81no—
834C2×C3—82no—
835C2×C3—241no—
836C2×C3D3×#13711yescharacteristic
837C2×C3#577811yescharacteristic
838C2×C3D4×#6711yescharacteristic
839C2×C3D4×#6711yescharacteristic
840C2×C3C2×#95111yescharacteristic
841C2×C3#583611yescharacteristic
842D3—22no—
843D3—81no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—22no—
848C22—32no—
849C22—41no—
850C22—41no—
851C22—61no—
852C22—61no—
853C22—121no—
854C22—121no—
855C22—121no—
856C22—244no—
857C22C2×D3×#6711yescharacteristic
858C4—21no—
859C4—41no—
860C4—61no—
861C4—61no—
862C4—61no—
863C4—62no—
864C4—121no—
865C4—121no—
866C4—361no—
867C4—361no—
868C4C2×D3×#6711yescharacteristic
869C4#6433011yescharacteristic
870C3—21no—
871C3#8350611yescharacteristic, complemented
872C3#8398711yescharacteristic, complemented
873C2—41no—
874C2—42no—
875C2—62no—
876C2—241no—
877C2D3×#95111yescharacteristic
878C2#1059546411yescharacteristic
879C2#67211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC3×#5829C2
hypercenterC2×#41D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×C3×#951C2semidirect
3. C2×D3×#214C2semidirect
4. Dic6×#67C2semidirect
5. #10592938C2semidirect
6. #10591653C2semidirect
7. #10591635C2semidirect
8. #10591627C2semidirect
9. #10591578C2semidirect
10. #10591489C2semidirect
11. #10591458C2semidirect
12. #10591440C2semidirect
13. #10591176C2semidirect
14. #10591171C2semidirect
15. #10591147C2semidirect
20. C22×C3×Dic6C22semidirect
22. C2×#3756C22semidirect
24. #64133C22semidirect
28. C2×C3×#216C22semidirect
29. C2×C3×#216C22semidirect
39. C2×C3×#208C22semidirect
44. #63866C22semidirect
46. Dic3×Dic6C22semidirect
52. #63662C22semidirect
54. #63657C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63565C22semidirect
59. #63565C22semidirect
62. #63554C22semidirect
66. C2×#951D3semidirect
133. C3×#214D4semidirect
165. C22×Dic6C2×D3semidirect
192. C2×#216C2×D3semidirect
193. C2×#216C2×D3semidirect
219. C2×#208C2×D3semidirect
417. #214#67semidirect
469. C2×C3×D3#137semidirect
745. C2×D3#951semidirect
776. C32#3266semidirect
871. C3#83506semidirect
872. C3#83987semidirect

Maximal subgroups

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

subgroupindex
C3×#58292
C2×C3×#9512
C2×D3×#2142
Dic6×#672
#105929382
#105916532
#105916352
#105916272
#105915782
#105914892
#105914582
#105914402
#105911762
#105911712
#105911472
#839873
#835063