Finite Group Databasebeta

← #11884143

Subgroups — #11884143

Order 1152.

1050 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595427C211yesmaximal, characteristic
2#10595400C211yesmaximal, characteristic, complemented
3C2×#63943C211yesmaximal, characteristic, complemented
4C2×D3×#215C211yesmaximal, characteristic, complemented
5#10592889C211yesmaximal, characteristic, complemented
6C3×#5187C211yesmaximal, characteristic, complemented
7C3×#5186C211yesmaximal, characteristic, complemented
8#10591596C211yesmaximal, characteristic, complemented
9#10591589C211yesmaximal, characteristic, complemented
10#10591579C211yesmaximal, characteristic, complemented
11#10591569C211yesmaximal, characteristic, complemented
12#10590951C211yesmaximal, characteristic, complemented
13#10590946C211yesmaximal, characteristic, complemented
14#10590743C211yesmaximal, characteristic, complemented
15#10590725C211yesmaximal, characteristic, complemented
16#80241—31nomaximal
17#80204—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic, complemented
22C2×C32×Q16C2211yescharacteristic, complemented
23#64156C2211yescharacteristic
24#64153C2211yescharacteristic, complemented
25C2×#3756C2211yescharacteristic, complemented
26C2×#3755C2211yescharacteristic
27C2×#3744C2211yescharacteristic
28C3×#946C2211yescharacteristic
29C3×#946C2211yescharacteristic, complemented
30C2×C3×#216C2211yescharacteristic, complemented
31C2×C3×#215C2211yescharacteristic
32#63943—24no—
33D3×#215—24no—
34#63922—21no—
35D3×(C2×D3)⋊C4—21no—
36#63909C2211yescharacteristic
37C4×#625C2211yescharacteristic
38#63898C2211yescharacteristic
39#63887—21no—
40#63886—21no—
41#63879—21no—
42#63857C2211yescharacteristic
43#63851—21no—
44#63850—21no—
45#63843C2211yescharacteristic, complemented
46#63839—21no—
47C2×#3717C2211yescharacteristic
48C2×#3716C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3711C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic
52#63642C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59#63576C2211yescharacteristic, complemented
60#63572C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63564C2211yescharacteristic
63#5829—31no—
64C2×#951—31no—
65Q8×#67—31no—
66C22×#215—31no—
67C2×#918—31no—
68C2×D3×SD16—31no—
69#5632—31no—
70#5630—31no—
71C3×#452—31no—
72C3×#451—31no—
73#5190—31no—
74#5190—31no—
75#5190—61no—
76#5187D311yescharacteristic, complemented
77#5186D311yescharacteristic, complemented
78#5185—31no—
79#5162—31no—
80#5051—31no—
81#5049—31no—
82#4818—31no—
83#4817—31no—
84#4813—31no—
85#4812—31no—
86#4806—31no—
87#4798—31no—
88#4776—31no—
89#4757—31no—
90#4738—31no—
91#4731—31no—
92#4730—31no—
93#4728—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C3×#239—22no—
100C3×#239—41no—
101C3×D3×Q8—22no—
102C3×D3×Q8—41no—
103C2×C3×D12—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6—21no—
110C2×C3×Dic6C2311yescharacteristic
111C2×#627—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#625D411yescharacteristic
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117D3×D12—22no—
118D3×D12—41no—
119D3×Dic6—22no—
120D3×Dic6—41no—
121C32×Q16—41no—
122C2×C32×C8C2311yescharacteristic
123#3756—22no—
124#3755—22no—
125#3752—21no—
126#3752—21no—
127#3750—21no—
128#3750—21no—
129C4×C3⋊Dic3C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131#3744—41no—
132C3×#216—22no—
133C3×#215—22no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×C4⋊Dic3C2311yescharacteristic
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142#3724D411yescharacteristic
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145#3722—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3D411yescharacteristic
149(C2×D3)⋊Dic3D411yescharacteristic
150Dic32—21no—
151#3717—22no—
152#3716—22no—
153#3715D414yescomplemented
154#3711—22no—
155D3×C3⋊C8—22no—
156#3266—91noSylow
157C2×C3×#41—31no—
158C22×C3×Q8—31no—
159C2×#239C2×D311yescharacteristic
160C2×D3×Q8—31no—
161C2×D3×Q8C2×D311yescharacteristic
162C2×D3×D4—31no—
163C22×D12—31no—
164C22×Dic6—31no—
165C2×C3×Q16—21no—
166C2×C3×Q16—31no—
167C2×C3×Q16C2×D311yescharacteristic, complemented
168C2×C3×Q16C2×D311yescharacteristic, complemented
169C2×C3×SD16—31no—
170C3×C22⋊Q8—31no—
171C3×C22⋊Q8—31no—
172#951—64no—
173#947—31no—
174#947—31no—
175#947—61no—
176#946—61no—
177#946C2×D311yescharacteristic
178#946C2×D311yescharacteristic, complemented
179Q8×Dic3—31no—
180#944—31no—
181#944—31no—
182#944—61no—
183#944—61no—
184C2×#216—31no—
185C2×#216—31no—
186C2×#216—61no—
187C2×#216C2×D311yescharacteristic, complemented
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—61no—
193C2×#215—64no—
194C2×#215C2×D311yescharacteristic
195#939—61no—
196#937—61no—
197D4×Dic3—31no—
198C2×#214—31no—
199C2×#214—31no—
200#930—31no—
201#929—61no—
202C4×#67—31no—
203C4×#67—31no—
204C4×#67—61no—
205C2×(C2×D3)⋊C4—61no—
206#924—31no—
207#924—61no—
208C2×#208—31no—
209C22×C3⋊C8—31no—
210#918—64no—
211D3×SD16—64no—
212C2×#204—31no—
213C2×#204—31no—
214C2×#204—31no—
215C2×#204—31no—
216C2×#204—61no—
217C2×ΓL(1,𝔽25)—31no—
218C2×D3×C8—31no—
219#897—31no—
220#896—61no—
221#895—31no—
222#895—61no—
223#894—61no—
224#893—31no—
225#888—61no—
226#887—31no—
227#882—61no—
228#67⋊C4—61no—
229D3×C22⋊C4—61no—
230#878—61no—
231C3×#103—31no—
232C3×#103—31no—
233C3×#103—31no—
234C3×#102—31no—
235C3×C22⋊C8—31no—
236C3×C22⋊C8—31no—
237#835C2×D311yescharacteristic, complemented
238#835C2×D311yescharacteristic, complemented
239#821—31no—
240#821C2×D311yescharacteristic
241(C2×D3)⋊C8C2×D311yescharacteristic
242(C2×D3)⋊C8C2×D311yescharacteristic, complemented
243#816—31no—
244#816C2×D311yescharacteristic, complemented
245#815—31no—
246#815—31no—
247#815—61no—
248Dic3⋊C8—31no—
249Dic3⋊C8—31no—
250#810—31no—
251#809—31no—
252#807—31no—
253#807—31no—
254C22×C3⋊D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3C2×D411yescharacteristic
257C22×C3×D3C2×D411yescharacteristic
258C2×D32—42no—
259C2×D32—42no—
260C2×D32—81no—
261C32×Q8—21no—
262C32×Q8—21no—
263C32×Q8—21no—
264C32×Q8—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2411yescharacteristic
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3C2×D411yescharacteristic
270C2×C3⋊Dic3C2×D411yescharacteristic
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273#634—21no—
274#634—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C3×D12—21no—
281C3×D12—42no—
282C3×D12C2×D412yes—
283C3×C4×D3—21no—
284C3×C4×D3—21no—
285C3×C4×D3—21no—
286C3×C4×D3—21no—
287C3×C4×D3—42no—
288C3×C4×D3—42no—
289C3×Dic6—21no—
290C3×Dic6—42no—
291C3×Dic6C2×D412yes—
292#627—42no—
293#626—42no—
294#626—81no—
295#625—22no—
296D3×Dic3—42no—
297D3×Dic3—81no—
298C32×C8—21no—
299C3⋊(C3⋊C8)C2×D412yes—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
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—31no—
312#451—31no—
313#450—91no—
314#448—91no—
315#440—91no—
316#435—91no—
317C23×D3—61no—
318C23×D3—61no—
319C3×#41—62no—
320C3×#41—121no—
321C2×C3×Q8—21no—
322C2×C3×Q8—21no—
323C2×C3×Q8—31no—
324C2×C3×Q8—61no—
325C2×C3×Q8—62no—
326C2×C3×Q8—121no—
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×D4—31no—
332C2×C3×D4—61no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—61no—
336C22×C3×C4—61no—
337C2×#67—31no—
338C2×#67—31no—
339C2×#67—61no—
340C2×#67—61no—
341C22×Dic3—61no—
342C22×Dic3—61no—
343#239—22no—
344#239—41no—
345D3×Q8—22no—
346D3×Q8—41no—
347D3×Q8—62no—
348D3×Q8—121no—
349D3×D4—62no—
350D3×D4—121no—
351C2×D12—21no—
352C2×D12—31no—
353C2×D12—31no—
354C2×D12—61no—
355C2×D12—62no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—121no—
359C2×D12C22×D311yescharacteristic
360C2×C4×D3—21no—
361C2×C4×D3—21no—
362C2×C4×D3—61no—
363C2×C4×D3—61no—
364C2×C4×D3C22×D311yescharacteristic
365C2×C4×D3C22×D311yescharacteristic
366C2×Dic6—21no—
367C2×Dic6—31no—
368C2×Dic6—31no—
369C2×Dic6—61no—
370C2×Dic6—62no—
371C2×Dic6—61no—
372C2×Dic6—61no—
373C2×Dic6—121no—
374C2×Dic6C22×D311yescharacteristic
375C3×Q16—41no—
376C3×Q16—41no—
377C3×Q16—42no—
378C3×Q16—62no—
379C3×SD16—62no—
380C2×C3×C8—21no—
381C2×C3×C8—31no—
382C2×C3×C8—31no—
383C2×C3×C8C22×D311yescharacteristic
384C2×C3×C8C22×D311yescharacteristic
385C3×C4⋊C4—31no—
386C3×C4⋊C4—31no—
387C3×C4⋊C4—61no—
388C3×C4⋊C4—61no—
389C3×C22⋊C4—61no—
390C3×C22⋊C4—61no—
391#217—31no—
392#217—31no—
393#217—61no—
394#217—61no—
395#216—22no—
396#216—62no—
397#216—62no—
398#216—122no—
399#215—22no—
400#215—34no—
401#215—62no—
402#215—62no—
403#215—62no—
404#215—122no—
405#214—34no—
406#214—62no—
407(C2×D3)⋊C4—21no—
408(C2×D3)⋊C4—21no—
409(C2×D3)⋊C4—31no—
410(C2×D3)⋊C4—31no—
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)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—121no—
420(C2×D3)⋊C4—121no—
421C4⋊Dic3—61no—
422C4⋊Dic3—61no—
423C4⋊Dic3C22×D311yescharacteristic
424C4⋊Dic3C22×D311yescharacteristic
425Dic3⋊C4—21no—
426Dic3⋊C4—21no—
427Dic3⋊C4—31no—
428Dic3⋊C4—31no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4—121no—
436Dic3⋊C4—121no—
437C4×Dic3—31no—
438C4×Dic3—31no—
439C4×Dic3—61no—
440C4×Dic3—61no—
441C4×Dic3—61no—
442#208—62no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—61no—
446C2×C3⋊C8—62no—
447C2×C3⋊C8C22×D311yescharacteristic
448C2×C3⋊C8C22×D311yescharacteristic
449#204—62no—
450#204—62no—
451#204—121no—
452#204—121no—
453#204—122no—
454ΓL(1,𝔽25)—62no—
455D3×C8—62no—
456C22×C32C22×D411yescharacteristic
457C2×C3⋊D3—41no—
458C2×C3⋊D3—41no—
459C2×C3⋊D3—41no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—22no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3#13712yescomplemented
469D32—84no—
470C32×C4—41no—
471C32×C4—41no—
472C32×C4C22×D411yescharacteristic
473C32×C4H(5,𝔽2)11yescharacteristic
474C3⋊Dic3—21no—
475C3⋊Dic3—21no—
476C3⋊Dic3—41no—
477C3×Dic3—22no—
478C3×Dic3—21no—
479C3×Dic3—21no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C2×#41—31no—
483C22×Q8—31no—
484C22×Q8—91no—
485C22×D4—91no—
486#137—184no—
487C2×Q16—31no—
488C2×Q16—91no—
489C2×Q16D3211yescharacteristic, complemented
490C2×SD16—31no—
491C2×SD16—91no—
492C2×SD16—91no—
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—31no—
505C22⋊Q8—91no—
506C22⋊Q8—181no—
507C22⋊Q8—181no—
508#121—91no—
509#121—181no—
510#120—181no—
511C4×Q8—91no—
512C4×D4—91no—
513C4×D4—91no—
514C4×D4—181no—
515C2×C22⋊C4—181no—
516#107—91no—
517C4⋊C8—91no—
518#103—31no—
519#103—31no—
520#103—31no—
521#103—91no—
522#102—31no—
523#102—91no—
524C22⋊C8—31no—
525C22⋊C8—31no—
526#97—91no—
527C23×C3—31no—
528C23×C3—31no—
529C23×C3—61no—
530C22×D3—21no—
531C22×D3—61no—
532C22×D3—61no—
533C22×D3—121no—
534C22×D3—122no—
535C22×D3—122no—
536C22×D3—122no—
537C22×D3—122no—
538C22×D3—241no—
539C22×D3—241no—
540C22×D3D3×D411yescharacteristic
541C22×D3D3×D411yescharacteristic
542C3×Q8—21no—
543C3×Q8—21no—
544C3×Q8—21no—
545C3×Q8—21no—
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8—32no—
551C3×Q8—41no—
552C3×Q8—41no—
553C3×Q8—41no—
554C3×Q8—41no—
555C3×Q8—61no—
556C3×Q8—122no—
557C3×D4—32no—
558C3×D4—61no—
559C3×D4—122no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—31no—
566C2×C3×C4—31no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—122no—
577C2×C3×C4—122no—
578C2×C3×C4C23×D311yescharacteristic
579C2×C3×C4C23×D311yescharacteristic
580#67—62no—
581#67—62no—
582#67—122no—
583#67—241no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—31no—
588C2×Dic3—31no—
589C2×Dic3—31no—
590C2×Dic3—31no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—121no—
596C2×Dic3—122no—
597C2×Dic3—241no—
598C2×Dic3D3×D411yescharacteristic
599C2×Dic3D3×D411yescharacteristic
600D12—21no—
601D12—42no—
602D12—61no—
603D12—61no—
604D12—61no—
605D12—61no—
606D12—121no—
607D12—121no—
608D12—122no—
609D12—241no—
610D12D3×D412yes—
611C4×D3—21no—
612C4×D3—21no—
613C4×D3—21no—
614C4×D3—21no—
615C4×D3—42no—
616C4×D3—42no—
617C4×D3—122no—
618C4×D3—241no—
619Dic6—21no—
620Dic6—42no—
621Dic6—61no—
622Dic6—61no—
623Dic6—61no—
624Dic6—61no—
625Dic6—121no—
626Dic6—121no—
627Dic6—122no—
628Dic6—122no—
629Dic6D3×D412yes—
630C3×C8—22no—
631C3×C8—21no—
632C3×C8—21no—
633C3×C8—61no—
634C3×C8—61no—
635C3⋊C8—21no—
636C3⋊C8—21no—
637C3⋊C8—32no—
638C3⋊C8—32no—
639C3⋊C8—62no—
640C2×C32D4211yescharacteristic
641C2×C32C2×#13711yescharacteristic
642C2×C32#57711yescharacteristic
643C3⋊D3—81no—
644C3×D3—22no—
645C3×D3—42no—
646C3×D3—41no—
647C24—181no—
648#41—62no—
649#41—121no—
650C2×Q8—31no—
651C2×Q8—61no—
652C2×Q8—62no—
653C2×Q8—91no—
654C2×Q8—121no—
655C2×Q8—181no—
656C2×Q8—182no—
657C2×Q8—361no—
658C2×Q8C2×D3211yescharacteristic
659C2×Q8C2×D3211yescharacteristic
660C2×D4—31no—
661C2×D4—61no—
662C2×D4—91no—
663C2×D4—91no—
664C2×D4—181no—
665C2×D4—182no—
666C2×D4—181no—
667C2×D4—361no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—61no—
671C22×C4—61no—
672C22×C4—181no—
673C22×C4—181no—
674Q16—41no—
675Q16—62no—
676Q16—182no—
677SD16—62no—
678SD16—94no—
679SD16—182no—
680SD16—182no—
681SD16—182no—
682SD16—361no—
683M16—182no—
684C2×C8—31no—
685C2×C8—31no—
686C2×C8—91no—
687C2×C8—182no—
688C2×C8C2×D3211yescharacteristic
689C4⋊C4—31no—
690C4⋊C4—31no—
691C4⋊C4—61no—
692C4⋊C4—61no—
693C4⋊C4—91no—
694C4⋊C4—181no—
695C4⋊C4—181no—
696C4⋊C4—181no—
697C4⋊C4—181no—
698C22⋊C4—61no—
699C22⋊C4—61no—
700C22⋊C4—91no—
701C22⋊C4—91no—
702C22⋊C4—181no—
703C22⋊C4—181no—
704C22⋊C4—181no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C42—91no—
708C42—181no—
709C22×C3—21no—
710C22×C3—32no—
711C22×C3—61no—
712C22×C3—61no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—62no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3C2×D3×D411yescharacteristic
720C22×C3C2×D3×D411yescharacteristic
721C2×D3—21no—
722C2×D3—21no—
723C2×D3—21no—
724C2×D3—21no—
725C2×D3—21no—
726C2×D3—22no—
727C2×D3—41no—
728C2×D3—41no—
729C2×D3—121no—
730C2×D3—121no—
731C2×D3—121no—
732C2×D3—121no—
733C2×D3—121no—
734C2×D3—121no—
735C2×D3—241no—
736C2×D3—241no—
737C2×D3—241no—
738C2×D3—244no—
739C2×D3—244no—
740C2×D3#91812yescomplemented
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—41no—
744C3×C4—41no—
745C3×C4—41no—
746C3×C4—41no—
747C3×C4—61no—
748C3×C4—62no—
749C3×C4—61no—
750C3×C4—81no—
751C3×C4—81no—
752C3×C4—121no—
753C3×C4—121no—
754C3×C4C2×D3×D411yescharacteristic
755C3×C4C2×D3×D411yescharacteristic
756C3×C4#100411yescharacteristic
757C3×C4#100411yescharacteristic
758Dic3—22no—
759Dic3—21no—
760Dic3—21no—
761Dic3—41no—
762Dic3—41no—
763Dic3—61no—
764Dic3—61no—
765Dic3—61no—
766Dic3—61no—
767Dic3—121no—
768Dic3—121no—
769Dic3—121no—
770Dic3—121no—
771Dic3—241no—
772C32#326611yescharacteristic, complemented, Sylow
773C23—31no—
774C23—31no—
775C23—61no—
776C23—181no—
777C23—362no—
778C23—362no—
779C23—721no—
780Q8—21no—
781Q8—21no—
782Q8—21no—
783Q8—21no—
784Q8—32no—
785Q8—61no—
786Q8—122no—
787Q8—181no—
788Q8—181no—
789Q8—362no—
790D4—32no—
791D4—61no—
792D4—122no—
793D4—182no—
794D4—181no—
795D4—181no—
796D4—362no—
797D4—721no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—31no—
801C2×C4—31no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—91no—
810C2×C4—91no—
811C2×C4—122no—
812C2×C4—122no—
813C2×C4—181no—
814C2×C4—362no—
815C2×C4—721no—
816C2×C4C22×D3211yescharacteristic
817C8—21no—
818C8—61no—
819C8—61no—
820C8—92no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—62no—
825C2×C3—122no—
826C2×C3—121no—
827C2×C3#559011yescharacteristic
828C2×C3#559011yescharacteristic
829C2×C3C2×#91811yescharacteristic
830C2×C3#577011yescharacteristic
831C2×C3D3×#13711yescharacteristic
832C2×C3#577811yescharacteristic
833D3—22no—
834D3—41no—
835D3—42no—
836D3—241no—
837D3—241no—
838D3—481no—
839C22—32no—
840C22—61no—
841C22—61no—
842C22—61no—
843C22—61no—
844C22—61no—
845C22—62no—
846C22—121no—
847C22—121no—
848C22—361no—
849C22—361no—
850C22—361no—
851C22—724no—
852C22D32×D411yescharacteristic
853C4—41no—
854C4—41no—
855C4—61no—
856C4—61no—
857C4—62no—
858C4—121no—
859C4—121no—
860C4—181no—
861C4—181no—
862C4—361no—
863C4D32×D411yescharacteristic
864C4#6433011yescharacteristic
865C3—21no—
866C3#8020411yescharacteristic, complemented
867C3#8024111yescharacteristic, complemented
868C2—62no—
869C2—121no—
870C2—122no—
871C2—721no—
872C2D3×#91811yescharacteristic
873C2#1059477011yescharacteristic
874C2#1059528911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radical#10595427C2
hypercenterC2×Q16D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. #10595400C2semidirect
3. C2×#63943C2semidirect
4. C2×D3×#215C2semidirect
5. #10592889C2semidirect
6. C3×#5187C2semidirect
7. C3×#5186C2semidirect
8. #10591596C2semidirect
9. #10591589C2semidirect
10. #10591579C2semidirect
11. #10591569C2semidirect
12. #10590951C2semidirect
13. #10590946C2semidirect
14. #10590743C2semidirect
15. #10590725C2semidirect
21. C2×D3×Dic6C22semidirect
22. C2×C32×Q16C22semidirect
24. #64153C22semidirect
25. C2×#3756C22semidirect
29. C3×#946C22semidirect
30. C2×C3×#216C22semidirect
45. #63843C22semidirect
50. C2×#3711C22semidirect
52. #63642C22semidirect
53. C3×#835C22semidirect
54. C3×#835C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. #63576C22semidirect
60. #63572C22semidirect
61. #63567C22semidirect
76. #5187D3semidirect
77. #5186D3semidirect
153. #3715D4semidirect
167. C2×C3×Q16C2×D3semidirect
168. C2×C3×Q16C2×D3semidirect
178. #946C2×D3semidirect
187. C2×#216C2×D3semidirect
237. #835C2×D3semidirect
238. #835C2×D3semidirect
242. (C2×D3)⋊C8C2×D3semidirect
244. #816C2×D3semidirect
468. C2×C3×D3#137semidirect
489. C2×Q16D32semidirect
740. C2×D3#918semidirect
772. C32#3266semidirect
866. C3#80204semidirect
867. C3#80241semidirect

Maximal subgroups

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

subgroupindex
#105954272
#105954002
C2×#639432
C2×D3×#2152
#105928892
C3×#51872
C3×#51862
#105915962
#105915892
#105915792
#105915692
#105909512
#105909462
#105907432
#105907252
#802413
#802043