Finite Group Databasebeta

← #11884426

Subgroups — #11884426

Order 1152.

1082 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#904C211yesmaximal, characteristic, complemented
2#10595070C211yesmaximal, characteristic, complemented
3#10595006C211yesmaximal, characteristic, complemented
4C2×#63798C211yesmaximal, characteristic, complemented
5#10592810C211yesmaximal, characteristic, complemented
6C3×#5115C211yesmaximal, characteristic, complemented
7#10591161C211yesmaximal, characteristic, complemented
8#10591161C211yesmaximal, characteristic, complemented
9#10590965C211yesmaximal, characteristic, complemented
10#10590945C211yesmaximal, characteristic, complemented
11#10590887C211yesmaximal, characteristic, complemented
12#10590845C211yesmaximal, characteristic, complemented
13#10590797C211yesmaximal, characteristic, complemented
14#10590779C211yesmaximal, characteristic, complemented
15#10590749C211yesmaximal, characteristic, complemented
16#83922—31nomaximal
17#80728—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic, complemented
20C2×#3802C2211yescharacteristic
21C2×#3796C2211yescharacteristic
22C22×C32×C8C2211yescharacteristic, complemented
23C4×#638C2211yescharacteristic
24C2×#3743C2211yescharacteristic
25C3×#930C2211yescharacteristic
26C3×#930C2211yescharacteristic, complemented
27C2×C3×Dic12C2211yescharacteristic, complemented
28C3×#904—24no—
29C2×C3×D24C2211yescharacteristic
30C2×C3×D24C2211yescharacteristic
31C2×C3×#204C2211yescharacteristic
32C2×C3×#204C2211yescharacteristic, complemented
33#63983—21no—
34#63979—21no—
35#63970—21no—
36#63970—21no—
37D3×(C2×D3)⋊C4—21no—
38#63916C2211yescharacteristic
39#63914C2211yescharacteristic, complemented
40#63906—21no—
41#63905—21no—
42#63898C2211yescharacteristic
43#63879—21no—
44#63871C2211yescharacteristic
45#63863C2211yescharacteristic
46#63843C2211yescharacteristic, complemented
47C2×#3715C2211yescharacteristic
48C2×#3715C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic
50C2×#3713C2211yescharacteristic
51#63798—24no—
52#63657C2211yescharacteristic, complemented
53#63647C2211yescharacteristic
54#63642C2211yescharacteristic, complemented
55#63641C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic
57C3×#821C2211yescharacteristic, complemented
58C3×#818C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63562C2211yescharacteristic
62#63562C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64#5834—31no—
65#5829—31no—
66C2×#914—31no—
67C2×#911—31no—
68C2×#904D311yescharacteristic, complemented
69#5612—31no—
70#5599—31no—
71C3×#466—31no—
72#5238—31no—
73#5238—31no—
74#5187—31no—
75#5185—31no—
76#5176—31no—
77#5174—31no—
78#5164—31no—
79#5156—31no—
80#5154—31no—
81#5150—31no—
82#5115D311yescharacteristic, complemented
83#5111—31no—
84#5111—31no—
85#5111—61no—
86#5037—31no—
87#5037—31no—
88#4889—31no—
89#4886—31no—
90#4786—31no—
91#4783—31no—
92#4773—31no—
93#4767—31no—
94C22×D32—21no—
95C22×C32×C4C2311yescharacteristic
96C2×#638D411yescharacteristic
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C3×#235—22no—
103C3×#235—22no—
104C3×#235—41no—
105C3×#235—41no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×Dic6C2311yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114C2×#626—21no—
115C2×#626—21no—
116C2×#625—21no—
117C2×#625—21no—
118C2×#625—21no—
119C2×D3×Dic3—21no—
120C2×D3×Dic3—21no—
121#3802—22no—
122#3802—41no—
123#3796—22no—
124#3796—41no—
125C2×C32×C8—22no—
126C2×C32×C8C2311yescharacteristic
127C2×C32×C8C2311yescharacteristic
128#3757D411yescharacteristic
129#3752D411yescharacteristic
130#3750D411yescharacteristic
131C4×C3⋊Dic3C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134#3743—22no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic12—22no—
140C3×D24—22no—
141C3×D24—22no—
142C3×#204—22no—
143C3×#204D414yescomplemented
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3—21no—
146#3722—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151Dic32—21no—
152#3715—22no—
153#3715—41no—
154#3713—22no—
155#3713—41no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#239—31no—
160C2×#237—31no—
161C2×D3×D4—31no—
162C2×D3×D4—31no—
163C2×#235C2×D311yescharacteristic
164C2×#235C2×D311yescharacteristic, complemented
165C3×#135—64no—
166C2×C3×Q16—31no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C2×C3×D8—31no—
170C2×C3×D8—31no—
171C22×C3×C8—21no—
172C22×C3×C8C2×D311yescharacteristic, complemented
173C22×C3×C8C2×D311yescharacteristic, complemented
174C3×#121—31no—
175C3×#121—31no—
176#947—31no—
177#946—31no—
178Q8×Dic3—31no—
179C2×#215—31no—
180C2×#215—31no—
181#940—31no—
182#940—31no—
183#940—61no—
184#940—61no—
185#939—61no—
186#939—61no—
187#938—31no—
188#938—61no—
189#938—61no—
190#937—61no—
191#937—61no—
192#936—31no—
193D4×Dic3—31no—
194C2×#214—31no—
195C2×#214—31no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213—31no—
199C2×#213—31no—
200#930—61no—
201#930C2×D311yescharacteristic
202#930C2×D311yescharacteristic, complemented
203#929—61no—
204C4×#67—31no—
205C4×#67—31no—
206C4×#67—61no—
207C4×#67—61no—
208C2×(C2×D3)⋊C4—61no—
209#914—64no—
210#911—64no—
211C2×Dic12C2×D311yescharacteristic, complemented
212#904—24no—
213C2×D24C2×D311yescharacteristic
214C2×D24C2×D311yescharacteristic
215C2×#204C2×D311yescharacteristic
216C2×#204C2×D311yescharacteristic, complemented
217C2×ΓL(1,𝔽25)—31no—
218C2×ΓL(1,𝔽25)—31no—
219C2×ΓL(1,𝔽25)—61no—
220#897—31no—
221#895—31no—
222#893—31no—
223#887—31no—
224#884—61no—
225#883—61no—
226#67⋊C4—61no—
227D3×C22⋊C4—61no—
228C3×#107—31no—
229C3×#102—31no—
230C3×#102—31no—
231#835—31no—
232#835—31no—
233#832—31no—
234#832—31no—
235#830—31no—
236#830—31no—
237#830—61no—
238#821C2×D311yescharacteristic
239#821C2×D311yescharacteristic, complemented
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8—61no—
243#818C2×D311yescharacteristic, complemented
244#815—31no—
245#815—31no—
246#815—61no—
247Dic3⋊C8—31no—
248Dic3⋊C8—31no—
249Dic3⋊C8—61no—
250#810—31no—
251#810—31no—
252#809—31no—
253#809—31no—
254C23×C32C2×D411yescharacteristic
255C22×C3⋊D3C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—81no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4C2×D411yescharacteristic
266C2×C32×C4C2411yescharacteristic
267#638—41no—
268C2×C3⋊Dic3C2×D411yescharacteristic
269C2×C3⋊Dic3C2×D411yescharacteristic
270C2×C3⋊Dic3C2×D411yescharacteristic
271C4×C3⋊D3—21no—
272C4×C3⋊D3—21no—
273C3×#67—42no—
274C3×#67—42no—
275C3×#67—81no—
276C3×#67—81no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12C2×D412yes—
289C3×C4×D3—42no—
290C3×C4×D3—42no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6C2×D412yes—
295#626—42no—
296#626—81no—
297#625—42no—
298#625—42no—
299#625—81no—
300D3×Dic3—42no—
301D3×Dic3—81no—
302C32×C8—21no—
303C32×C8C2×D412yes—
304C3⋊(C3⋊C8)—21no—
305C3⋊(C3⋊C8)—21no—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—31no—
308#550—91no—
309#546—91no—
310#496—91no—
311#468—91no—
312#466—31no—
313#464—91no—
314#459—91no—
315#452—91no—
316#449—91no—
317#449—91no—
318#447—91no—
319#440—91no—
320#435—91no—
321C23×D3—61no—
322C23×D3—61no—
323C3×#41—62no—
324C3×#41—62no—
325C3×#41—121no—
326C3×#41—121no—
327C2×C3×Q8—31no—
328C2×C3×Q8—31no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C22×C3×C4—21no—
338C22×C3×C4—61no—
339C22×C3×C4—61no—
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C2×#67—21no—
343C2×#67—21no—
344C2×#67—21no—
345C2×#67—21no—
346C2×#67—31no—
347C2×#67—31no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C22×Dic3—61no—
358C22×Dic3—61no—
359#239—62no—
360#239—121no—
361#237—62no—
362#237—121no—
363D3×D4—62no—
364D3×D4—62no—
365D3×D4—121no—
366D3×D4—121no—
367#235—22no—
368#235—22no—
369#235—41no—
370#235—41no—
371C2×D12—61no—
372C2×D12—61no—
373C2×D12C22×D311yescharacteristic
374C2×D12C22×D311yescharacteristic
375C2×D12C22×D311yescharacteristic
376C2×D12C22×D311yescharacteristic
377C2×C4×D3—21no—
378C2×C4×D3—21no—
379C2×C4×D3—31no—
380C2×C4×D3—31no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×Dic6C22×D311yescharacteristic
385C2×Dic6C22×D311yescharacteristic
386C3×Q16—62no—
387C3×SD16—34no—
388C3×SD16—62no—
389C3×D8—62no—
390C3×D8—62no—
391C2×C3×C8—22no—
392C2×C3×C8—22no—
393C2×C3×C8—21no—
394C2×C3×C8—21no—
395C2×C3×C8—42no—
396C2×C3×C8C22×D311yescharacteristic
397C2×C3×C8C22×D311yescharacteristic
398C2×C3×C8C22×D311yescharacteristic
399C2×C3×C8C22×D311yescharacteristic
400C3×C4⋊C4—31no—
401C3×C4⋊C4—31no—
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404#217—31no—
405#217—31no—
406#217—61no—
407#217—61no—
408#217—61no—
409#217—61no—
410#217—61no—
411#215—62no—
412#215—121no—
413#214—62no—
414#214—121no—
415#213—62no—
416#213—62no—
417#213—121no—
418#213—121no—
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—31no—
422(C2×D3)⋊C4—31no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430C4⋊Dic3—61no—
431C4⋊Dic3—61no—
432C4⋊Dic3C22×D311yescharacteristic
433C4⋊Dic3C22×D311yescharacteristic
434Dic3⋊C4—31no—
435Dic3⋊C4—31no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439C4×Dic3—31no—
440C4×Dic3—31no—
441C4×Dic3—61no—
442C4×Dic3—61no—
443C4×Dic3—61no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—61no—
449C2×C3⋊C8—61no—
450Dic12—22no—
451D24—22no—
452D24—22no—
453#204—22no—
454#204#6714yescomplemented
455ΓL(1,𝔽25)—62no—
456ΓL(1,𝔽25)—62no—
457ΓL(1,𝔽25)—122no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32C22×D411yescharacteristic
462C2×C3⋊D3—21no—
463C2×C3⋊D3—21no—
464C2×C3⋊D3—21no—
465C2×C3×D3—22no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477D32—84no—
478C32×C4—21no—
479C32×C4C22×D411yescharacteristic
480C32×C4H(5,𝔽2)11yescharacteristic
481C3⋊Dic3—21no—
482C3⋊Dic3—21no—
483C3⋊Dic3—21no—
484C3×Dic3—22no—
485C3×Dic3—41no—
486C3×Dic3—41no—
487C3×Dic3—41no—
488C2×#41—31no—
489C2×#41—31no—
490C2×#41—91no—
491C22×D4—91no—
492AGL(1,ℤ/8)—184no—
493#135—64no—
494C2×Q16—31no—
495C2×SD16—31no—
496C2×SD16—31no—
497C2×SD16—91no—
498C2×SD16—91no—
499C2×D8—31no—
500C2×D8—31no—
501C2×D8—91no—
502C2×D8—91no—
503C2×M16—91no—
504C22×C8D3211yescharacteristic, complemented
505#127—91no—
506#127—181no—
507#124—91no—
508#123—181no—
509C22⋊Q8—91no—
510#121—31no—
511#121—31no—
512#121—91no—
513#121—181no—
514#121—181no—
515#121—181no—
516#120—181no—
517C4×Q8—91no—
518C4×D4—91no—
519C4×D4—91no—
520C4×D4—181no—
521C2×C22⋊C4—181no—
522#107—31no—
523C4⋊C8—91no—
524#103—91no—
525#103—91no—
526#102—31no—
527#102—31no—
528#102—91no—
529#102—91no—
530C22⋊C8—91no—
531C22⋊C8—91no—
532#97—91no—
533C23×C3—21no—
534C23×C3—61no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3D3×D411yescharacteristic
539C23×C3D3×D411yescharacteristic
540C22×D3—21no—
541C22×D3—21no—
542C22×D3—21no—
543C22×D3—21no—
544C22×D3—31no—
545C22×D3—31no—
546C22×D3—61no—
547C22×D3—122no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—241no—
552C22×D3—241no—
553C3×Q8—32no—
554C3×Q8—61no—
555C3×Q8—61no—
556C3×Q8—61no—
557C3×D4—32no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—61no—
561C3×D4—61no—
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—61no—
565C3×D4—122no—
566C3×D4—122no—
567C3×D4—241no—
568C3×D4—241no—
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—41no—
576C2×C3×C4—41no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—122no—
582C2×C3×C4—122no—
583C2×C3×C4D3×D411yescharacteristic
584C2×C3×C4D3×D411yescharacteristic
585C2×C3×C4C23×D311yescharacteristic
586C2×C3×C4C23×D311yescharacteristic
587#67—42no—
588#67—42no—
589#67—81no—
590#67—81no—
591#67—122no—
592#67—122no—
593#67—122no—
594#67—122no—
595#67—122no—
596#67—121no—
597#67—121no—
598#67—122no—
599#67—241no—
600#67—241no—
601#67—241no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—31no—
607C2×Dic3—31no—
608C2×Dic3—31no—
609C2×Dic3—31no—
610C2×Dic3—31no—
611C2×Dic3—31no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—122no—
616C2×Dic3—241no—
617D12—21no—
618D12—21no—
619D12—21no—
620D12—21no—
621D12—21no—
622D12—21no—
623D12—21no—
624D12—122no—
625D12—241no—
626D12C2×#6712yes—
627C4×D3—42no—
628C4×D3—42no—
629C4×D3—61no—
630C4×D3—61no—
631C4×D3—61no—
632C4×D3—61no—
633C4×D3—121no—
634C4×D3—121no—
635C4×D3—122no—
636C4×D3—241no—
637Dic6—21no—
638Dic6—21no—
639Dic6—21no—
640Dic6C2×#6712yes—
641C3×C8—21no—
642C3×C8—21no—
643C3×C8—22no—
644C3×C8—41no—
645C3×C8D3×D412yes—
646C3×C8C2×#6712yes—
647C3⋊C8—61no—
648C3⋊C8—61no—
649C3⋊C8—61no—
650C3⋊C8—61no—
651C3⋊C8—121no—
652C3⋊C8—121no—
653C2×C32—41no—
654C2×C32D4211yescharacteristic
655C2×C32#57511yescharacteristic
656C2×C32#57611yescharacteristic
657C3⋊D3—41no—
658C3×D3—42no—
659C3×D3—81no—
660C3×D3—81no—
661C3×D3—81no—
662C24—181no—
663#41—62no—
664#41—62no—
665#41—121no—
666#41—121no—
667#41—182no—
668#41—361no—
669C2×Q8—31no—
670C2×Q8—31no—
671C2×D4—31no—
672C2×D4—31no—
673C2×D4—31no—
674C2×D4—31no—
675C2×D4—61no—
676C2×D4—61no—
677C2×D4—61no—
678C2×D4—61no—
679C2×D4—91no—
680C2×D4—181no—
681C2×D4—181no—
682C2×D4—181no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—182no—
686C2×D4—361no—
687C22×C4—61no—
688C22×C4—61no—
689C22×C4—91no—
690C22×C4—181no—
691C22×C4—181no—
692C22×C4C2×D3211yescharacteristic
693Q16—62no—
694SD16—34no—
695SD16—62no—
696SD16—182no—
697SD16—361no—
698D8—62no—
699D8—62no—
700D8—182no—
701D8—361no—
702M16—182no—
703C2×C8—22no—
704C2×C8—91no—
705C2×C8—91no—
706C2×C8C2×D3211yescharacteristic
707C2×C8C2×D3211yescharacteristic
708C4⋊C4—31no—
709C4⋊C4—31no—
710C4⋊C4—91no—
711C4⋊C4—181no—
712C4⋊C4—181no—
713C22⋊C4—61no—
714C22⋊C4—61no—
715C22⋊C4—91no—
716C22⋊C4—91no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C22⋊C4—181no—
720C22⋊C4—181no—
721C22⋊C4—181no—
722C42—91no—
723C42—181no—
724C22×C3—22no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—62no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3C2×D3×D411yescharacteristic
747C22×C3C2×D3×D411yescharacteristic
748C2×D3—22no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—61no—
761C2×D3—61no—
762C2×D3—61no—
763C2×D3—61no—
764C2×D3—61no—
765C2×D3—61no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—244no—
770C2×D3—244no—
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—21no—
775C3×C4—41no—
776C3×C4—62no—
777C3×C4—121no—
778C3×C4—121no—
779C3×C4—121no—
780C3×C4C2×D3×D411yescharacteristic
781C3×C4#100411yescharacteristic
782C3×C4#100911yescharacteristic
783C3×C4C22×#6711yescharacteristic
784Dic3—22no—
785Dic3—41no—
786Dic3—41no—
787Dic3—41no—
788Dic3—61no—
789Dic3—61no—
790Dic3—61no—
791Dic3—61no—
792Dic3—61no—
793Dic3—61no—
794Dic3—121no—
795Dic3—121no—
796Dic3—121no—
797C32#326811yescharacteristic, complemented, Sylow
798C23—61no—
799C23—61no—
800C23—61no—
801C23—61no—
802C23—91no—
803C23—362no—
804C23—362no—
805C23—721no—
806C23#380211yescharacteristic
807Q8—32no—
808Q8—61no—
809Q8—61no—
810Q8—61no—
811D4—32no—
812D4—61no—
813D4—61no—
814D4—61no—
815D4—61no—
816D4—61no—
817D4—61no—
818D4—61no—
819D4—122no—
820D4—122no—
821D4—241no—
822D4—241no—
823D4—362no—
824D4—361no—
825D4—362no—
826D4—362no—
827D4—721no—
828D4—721no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—91no—
836C2×C4—91no—
837C2×C4—91no—
838C2×C4—122no—
839C2×C4—122no—
840C2×C4—181no—
841C2×C4—181no—
842C2×C4—362no—
843C2×C4—721no—
844C2×C4#380211yescharacteristic
845C2×C4C22×D3211yescharacteristic
846C8—21no—
847C8—181no—
848C8—181no—
849C8D3×#6712yes—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—42no—
854C2×C3—41no—
855C2×C3—41no—
856C2×C3—122no—
857C2×C3—241no—
858C2×C3—241no—
859C2×C3—241no—
860C2×C3#560911yescharacteristic
861C2×C3#575711yescharacteristic
862C2×C3#576811yescharacteristic
863C2×C3#576811yescharacteristic
864C2×C3#576911yescharacteristic
865C2×C3D4×#6711yescharacteristic
866D3—42no—
867D3—81no—
868D3—81no—
869D3—81no—
870D3—121no—
871D3—121no—
872D3—241no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—62no—
877C22—121no—
878C22—121no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—121no—
885C22—121no—
886C22—121no—
887C22—121no—
888C22—181no—
889C22—181no—
890C22—181no—
891C22—724no—
892C22C2×#380211yescharacteristic
893C4—21no—
894C4—62no—
895C4—121no—
896C4—121no—
897C4—121no—
898C4—181no—
899C4—181no—
900C4—181no—
901C4#6430711yescharacteristic
902C4C2×D3×#6711yescharacteristic
903C3—21no—
904C3#8072811yescharacteristic, complemented
905C3#8392211yescharacteristic, complemented
906C2—41no—
907C2—122no—
908C2—241no—
909C2—241no—
910C2—241no—
911C2—361no—
912C2#1059468511yescharacteristic
913C2#1059468711yescharacteristic
914C2#1059506911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32#3268
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
1. C2×C3×#904C2semidirect
2. #10595070C2semidirect
3. #10595006C2semidirect
4. C2×#63798C2semidirect
5. #10592810C2semidirect
6. C3×#5115C2semidirect
7. #10591161C2semidirect
8. #10591161C2semidirect
9. #10590965C2semidirect
10. #10590945C2semidirect
11. #10590887C2semidirect
12. #10590845C2semidirect
13. #10590797C2semidirect
14. #10590779C2semidirect
15. #10590749C2semidirect
19. C2×C3×#235C22semidirect
22. C22×C32×C8C22semidirect
26. C3×#930C22semidirect
27. C2×C3×Dic12C22semidirect
32. C2×C3×#204C22semidirect
39. #63914C22semidirect
46. #63843C22semidirect
48. C2×#3715C22semidirect
52. #63657C22semidirect
54. #63642C22semidirect
55. #63641C22semidirect
57. C3×#821C22semidirect
58. C3×#818C22semidirect
59. #63565C22semidirect
60. #63565C22semidirect
62. #63562C22semidirect
68. C2×#904D3semidirect
82. #5115D3semidirect
143. C3×#204D4semidirect
164. C2×#235C2×D3semidirect
172. C22×C3×C8C2×D3semidirect
173. C22×C3×C8C2×D3semidirect
202. #930C2×D3semidirect
211. C2×Dic12C2×D3semidirect
216. C2×#204C2×D3semidirect
239. #821C2×D3semidirect
243. #818C2×D3semidirect
454. #204#67semidirect
504. C22×C8D32semidirect
797. C32#3268semidirect
904. C3#80728semidirect
905. C3#83922semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9042
#105950702
#105950062
C2×#637982
#105928102
C3×#51152
#105911612
#105909652
#105909452
#105908872
#105908452
#105907972
#105907792
#105907492
#839223
#807283