Finite Group Databasebeta

← #11872136

Subgroups — #11872136

Order 1152.

911 conjugacy classes of subgroups.

The subgroup lattice has 799 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595223C211yesmaximal, characteristic, complemented
2#10595121C211yesmaximal, characteristic, complemented
3#10592855C211yesmaximal, characteristic
4C3×#5153C211yesmaximal, characteristic, complemented
5C3×Dic3×D8C211yesmaximal, characteristic, complemented
6#10591467C211yesmaximal, characteristic, complemented
7#10591440C211yesmaximal, characteristic, complemented
8#10591432C211yesmaximal, characteristic, complemented
9#10591425C211yesmaximal, characteristic, complemented
10#10591408C211yesmaximal, characteristic, complemented
11#10591404C211yesmaximal, characteristic, complemented
12#10590792C211yesmaximal, characteristic, complemented
13#10590764C211yesmaximal, characteristic, complemented
14#10590715C211yesmaximal, characteristic, complemented
15#10590648C211yesmaximal, characteristic, complemented
16#80508—31nomaximal
17#79594—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C32×D8C2211yescharacteristic
20#64147C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22C3×#936C2211yescharacteristic, complemented
23C3×D4×Dic3C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic, complemented
26C2×C3×#214C2211yescharacteristic
27#63974—21no—
28#63966—21no—
29#63964—21no—
30C2×#3722—21no—
31#63956—21no—
32#63953—21no—
33#63952—21no—
34#63952—21no—
35#63918C2211yescharacteristic, complemented
36#63894C2211yescharacteristic
37#63894C2211yescharacteristic
38#63874C2211yescharacteristic
39#63871C2211yescharacteristic
40#63849C2211yescharacteristic
41Dic3×Dic6C2211yescharacteristic, complemented
42C2×#3717C2211yescharacteristic
43#63659C2211yescharacteristic
44#63648C2211yescharacteristic
45#63647C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49C3×#818C2211yescharacteristic, complemented
50C3×#816C2211yescharacteristic, complemented
51C3×Dic3⋊C8C2211yescharacteristic, complemented
52C3×C8×Dic3C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63557C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61#5682—31no—
62#5561—31no—
63#5545—31no—
64#5545—31no—
65C3×#463—31no—
66C3×C4×D8—31no—
67#5169—31no—
68#5164—31no—
69#5156—31no—
70#5156—31no—
71#5156—61no—
72#5153D311yescharacteristic, complemented
73Dic3×D8D311yescharacteristic, complemented
74#5057—31no—
75#5018—31no—
76#5014—31no—
77#5008—31no—
78#4890—31no—
79#4888—31no—
80#4846—31no—
81#4840—31no—
82#4814—31no—
83#4788—31no—
84#4787—31no—
85#4785—31no—
86#4784—31no—
87#4779—31no—
88#4776—31no—
89#4761—31no—
90C4×#204—31no—
91#4690—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×#638—21no—
97D4×C3⋊D3—22no—
98D4×C3⋊D3—22no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×#624—21no—
107C2×#624—21no—
108C32×D8—22no—
109C2×C32×C8C2311yescharacteristic
110#3757—21no—
111#3753—22no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×#217—21no—
115C3×#217—21no—
116C3×#217—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#214—22no—
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4×Dic3C2311yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127#3724D411yescharacteristic
128#3724D411yescharacteristic
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132#3722—21no—
133#3722—21no—
134#3722—21no—
135#3722—21no—
136#3722D411yescharacteristic
137#3722D411yescharacteristic
138Dic32—21no—
139Dic32—21no—
140#3717—22no—
141#3118—91noSylow
142C2×D3×D4—31no—
143C2×D3×D4—31no—
144C2×D3×D4—61no—
145C2×C3×SD16—31no—
146C2×C3×D8—21no—
147C2×C3×D8C2×D311yescharacteristic
148C2×C3×D8C2×D311yescharacteristic
149C3×#124—31no—
150C3×C4×D4—31no—
151C3×C4×D4—31no—
152C3×C4×D4—31no—
153#946—31no—
154Q8×Dic3—31no—
155C2×#215—31no—
156#938—31no—
157#938—31no—
158#938—61no—
159#936C2×D311yescharacteristic, complemented
160D4×Dic3C2×D311yescharacteristic
161D4×Dic3C2×D311yescharacteristic
162D4×Dic3C2×D311yescharacteristic, complemented
163C2×#214C2×D311yescharacteristic
164C2×#213—31no—
165C2×#213—31no—
166C2×#213—61no—
167#929—61no—
168C4×#67—61no—
169C4×#67—61no—
170C2×(C2×D3)⋊C4—61no—
171C2×(C2×D3)⋊C4—61no—
172#924—61no—
173C2×#204—31no—
174#897—31no—
175#893—31no—
176#893—31no—
177#892—31no—
178#892—31no—
179#888—31no—
180#886—61no—
181#885—61no—
182#885—61no—
183#67⋊C4—61no—
184#67⋊C4—61no—
185D3×C22⋊C4—61no—
186D3×C22⋊C4—61no—
187#879—61no—
188#879—61no—
189#878—61no—
190C4×D12—31no—
191C4×D12—31no—
192#872—31no—
193#872—31no—
194#869—31no—
195C4×Dic6—31no—
196C3×#107—31no—
197C3×C4⋊C8—31no—
198C3×#103—31no—
199C3×#102—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×C4×C8—31no—
203#835—31no—
204#832—31no—
205#832—31no—
206#832—61no—
207#832C2×D311yescharacteristic
208#832C2×D311yescharacteristic, complemented
209#832C2×D311yescharacteristic, complemented
210#821—31no—
211#821—31no—
212#821—31no—
213#821—61no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—61no—
219#818—31no—
220#818C2×D311yescharacteristic, complemented
221#817—31no—
222#816C2×D311yescharacteristic, complemented
223#815—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8C2×D311yescharacteristic, complemented
226C8×Dic3C2×D311yescharacteristic, complemented
227#810—31no—
228#809—31no—
229#808—31no—
230#808—31no—
231#808—31no—
232#807—31no—
233C4⋊(C3⋊C8)—31no—
234#803—31no—
235C23×C32—21no—
236C23×C32—21no—
237C22×C3⋊D3—21no—
238C22×C3⋊D3—24no—
239C22×C3⋊D3—81no—
240C22×C3⋊D3—81no—
241C22×C3⋊D3C2×D411yescharacteristic
242C32×D4—21no—
243C32×D4—21no—
244C32×D4—21no—
245C32×D4#4112yes—
246C2×C32×C4C2411yescharacteristic
247#638—24no—
248#638—81no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3C2×D411yescharacteristic
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)#4112yes—
253C4×C3⋊D3—21no—
254C4×C3⋊D3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—81no—
260C2×C3×Dic3—81no—
261C2×C3×Dic3—81no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×Dic6—21no—
267C3×Dic6—21no—
268#627—81no—
269#624—81no—
270#624—81no—
271C32×C8—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#542—91no—
276#518—91no—
277#485—91no—
278#482—91no—
279#476—91no—
280#474—91no—
281#463—31no—
282#463—91no—
283#450—91no—
284#447—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—31no—
289#433—91no—
290C23×D3—61no—
291C23×D3—61no—
292C23×D3—121no—
293C2×C3×Q8—31no—
294C2×C3×D4—21no—
295C2×C3×D4—21no—
296C2×C3×D4C22×D311yescharacteristic
297C2×C3×D4C22×D311yescharacteristic
298C2×C3×D4C22×D311yescharacteristic
299C2×C3×D4C22×D311yescharacteristic
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—121no—
308C2×#67—121no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312D3×D4—62no—
313D3×D4—62no—
314D3×D4—62no—
315D3×D4—62no—
316D3×D4—122no—
317D3×D4—122no—
318C2×D12—31no—
319C2×D12—31no—
320C2×D12—61no—
321C2×C4×D3—31no—
322C2×C4×D3—31no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×Dic6—61no—
329C2×Dic6—61no—
330C2×Dic6C22×D311yescharacteristic
331C3×SD16—62no—
332C3×D8—22no—
333C3×D8—22no—
334C3×D8—42no—
335C2×C3×C8—21no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C22⋊C4—61no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—31no—
349C3×C42—31no—
350#217—21no—
351#217—21no—
352#217—21no—
353#217—21no—
354#217—21no—
355#217—61no—
356#217—61no—
357#217—121no—
358#215—62no—
359#214—22no—
360#213—62no—
361#213—62no—
362#213—122no—
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—31no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—31no—
385Dic3⋊C4—31no—
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3C22×D311yescharacteristic
396C4×Dic3C22×D311yescharacteristic
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8C22×D311yescharacteristic
401C2×C3⋊C8C22×D311yescharacteristic
402#204—62no—
403C22×C32—22no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32—41no—
409C22×C32C22×D411yescharacteristic
410C2×C3⋊D3—21no—
411C2×C3⋊D3—21no—
412C2×C3⋊D3—22no—
413C2×C3⋊D3—21no—
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—84no—
417C32×C4C2×#4111yescharacteristic
418C32×C4C2×#4111yescharacteristic
419C3⋊Dic3—21no—
420C3⋊Dic3—41no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C22×D4—91no—
430C2×SD16—31no—
431C2×SD16—91no—
432C2×D8—91no—
433C2×D8D3211yescharacteristic
434C4⋊Q8—91no—
435#126—181no—
436#124—31no—
437#124—181no—
438#123—181no—
439C22⋊Q8—91no—
440C22⋊Q8—181no—
441#121—91no—
442C4×Q8—91no—
443C4×D4—31no—
444C4×D4—31no—
445C4×D4—31no—
446C4×D4—91no—
447C4×D4—91no—
448C4×D4—181no—
449C4×D4—181no—
450#117—91no—
451#117—91no—
452C2×C22⋊C4—181no—
453C2×C22⋊C4—181no—
454#107—31no—
455#107—91no—
456#106—91no—
457#106—91no—
458C4⋊C8—31no—
459C4⋊C8—91no—
460#103—31no—
461#103—91no—
462#102—31no—
463#102—31no—
464#102—31no—
465#102—91no—
466#102—91no—
467#102—91no—
468C22⋊C8—91no—
469C22⋊C8—91no—
470#97—91no—
471C4×C8—31no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—41no—
477C23×C3—41no—
478C22×D3—31no—
479C22×D3—31no—
480C22×D3—61no—
481C22×D3—61no—
482C22×D3—61no—
483C22×D3—64no—
484C22×D3—64no—
485C22×D3—121no—
486C22×D3—124no—
487C22×D3—241no—
488C22×D3—241no—
489C22×D3—241no—
490C22×D3—241no—
491C22×D3—242no—
492C22×D3—242no—
493C3×Q8—61no—
494C3×Q8—61no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—21no—
500C3×D4—21no—
501C3×D4—22no—
502C3×D4—41no—
503C3×D4—41no—
504C3×D4—41no—
505C3×D4#23512yes—
506C3×D4#23712yes—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—241no—
517C2×C3×C4—241no—
518C2×C3×C4—241no—
519C2×C3×C4C23×D311yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521#67—64no—
522#67—64no—
523#67—124no—
524#67—241no—
525#67—241no—
526#67—242no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—81no—
537C2×Dic3—81no—
538C2×Dic3—81no—
539C2×Dic3—121no—
540C2×Dic3D3×D411yescharacteristic
541C2×Dic3D3×D411yescharacteristic
542C2×Dic3D3×D411yescharacteristic
543C2×Dic3D3×D411yescharacteristic
544D12—32no—
545D12—32no—
546D12—62no—
547D12—61no—
548D12—61no—
549D12—121no—
550C4×D3—61no—
551C4×D3—61no—
552C4×D3—61no—
553C4×D3—61no—
554C4×D3—121no—
555C4×D3—121no—
556C4×D3—241no—
557C4×D3—241no—
558C4×D3—241no—
559C4×D3—241no—
560Dic6—21no—
561Dic6—21no—
562Dic6—241no—
563Dic6—241no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—41no—
567C3×C8—61no—
568C3×C8—61no—
569C3⋊C8—21no—
570C3⋊C8—21no—
571C3⋊C8—61no—
572C3⋊C8—61no—
573C3⋊C8—121no—
574C2×C32—42no—
575C2×C32—81no—
576C2×C32#52511yescharacteristic
577C2×C32#57611yescharacteristic
578C2×C32#57711yescharacteristic
579C3⋊D3—41no—
580C3⋊D3—42no—
581C24—181no—
582C2×Q8—31no—
583C2×Q8—181no—
584C2×D4—91no—
585C2×D4—181no—
586C2×D4—182no—
587C2×D4—182no—
588C2×D4—181no—
589C2×D4C2×D3211yescharacteristic
590C2×D4C2×D3211yescharacteristic
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—91no—
595C22×C4—181no—
596C22×C4—181no—
597SD16—62no—
598SD16—182no—
599D8—22no—
600D8—182no—
601C2×C8—31no—
602C2×C8—31no—
603C2×C8—91no—
604C2×C8C2×D3211yescharacteristic
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—91no—
609C4⋊C4—91no—
610C4⋊C4—91no—
611C4⋊C4—181no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—91no—
620C22⋊C4—91no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C42—31no—
627C42—31no—
628C42—181no—
629C42—181no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—21no—
633C22×C3—42no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—81no—
647C22×C3—81no—
648C22×C3—81no—
649C22×C3C2×D3×D411yescharacteristic
650C22×C3C2×D3×D411yescharacteristic
651C2×D3—62no—
652C2×D3—61no—
653C2×D3—61no—
654C2×D3—61no—
655C2×D3—61no—
656C2×D3—61no—
657C2×D3—62no—
658C2×D3—61no—
659C2×D3—62no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—122no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—241no—
668C2×D3—241no—
669C2×D3—244no—
670C2×D3—244no—
671C2×D3—248no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—61no—
678C3×C4—121no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4C2×#23511yescharacteristic
683C3×C4C2×#23711yescharacteristic
684C3×C4D3×#4111yescharacteristic
685C3×C4D3×#4111yescharacteristic
686Dic3—21no—
687Dic3—21no—
688Dic3—21no—
689Dic3—21no—
690Dic3—41no—
691Dic3—41no—
692Dic3—41no—
693Dic3—41no—
694Dic3—61no—
695Dic3—61no—
696Dic3—121no—
697Dic3—121no—
698Dic3—121no—
699Dic3—241no—
700C32#311811yescharacteristic, complemented, Sylow
701C23—21no—
702C23—21no—
703C23—91no—
704C23—184no—
705C23—181no—
706C23—721no—
707C23—721no—
708Q8—61no—
709Q8—61no—
710Q8—721no—
711D4—21no—
712D4—21no—
713D4—21no—
714D4—92no—
715D4—184no—
716D4—181no—
717D4—721no—
718D4#380412yes—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—91no—
728C2×C4—181no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—241no—
732C2×C4—241no—
733C2×C4—241no—
734C2×C4—721no—
735C2×C4—721no—
736C2×C4C22×D3211yescharacteristic
737C8—21no—
738C8—61no—
739C8—61no—
740C8—181no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—42no—
745C2×C3—42no—
746C2×C3—82no—
747C2×C3—81no—
748C2×C3—81no—
749C2×C3—161no—
750C2×C3#554711yescharacteristic
751C2×C3#560611yescharacteristic
752C2×C3#575711yescharacteristic
753C2×C3#576911yescharacteristic
754C2×C3#577011yescharacteristic
755C2×C3#577511yescharacteristic
756D3—122no—
757D3—121no—
758D3—122no—
759D3—121no—
760D3—122no—
761D3—242no—
762C22—22no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—181no—
769C22—182no—
770C22—181no—
771C22—181no—
772C22—361no—
773C22—361no—
774C22—724no—
775C22D32×D411yescharacteristic
776C4—61no—
777C4—61no—
778C4—61no—
779C4—61no—
780C4—121no—
781C4—121no—
782C4—121no—
783C4—121no—
784C4—181no—
785C4—361no—
786C4#6431211yescharacteristic
787C4C2×#380411yescharacteristic
788C3—21no—
789C3#7959411yescharacteristic, complemented
790C3#8050811yescharacteristic, complemented
791C2—42no—
792C2—81no—
793C2—361no—
794C2—362no—
795C2#1059473411yescharacteristic
796C2#1059473611yescharacteristic
797C2#1059513811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
prime radical#10592855C2
hypercenterC2×D8D32
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10595223C2semidirect
2. #10595121C2semidirect
4. C3×#5153C2semidirect
5. C3×Dic3×D8C2semidirect
6. #10591467C2semidirect
7. #10591440C2semidirect
8. #10591432C2semidirect
9. #10591425C2semidirect
10. #10591408C2semidirect
11. #10591404C2semidirect
12. #10590792C2semidirect
13. #10590764C2semidirect
14. #10590715C2semidirect
15. #10590648C2semidirect
22. C3×#936C22semidirect
25. C3×D4×Dic3C22semidirect
35. #63918C22semidirect
41. Dic3×Dic6C22semidirect
47. C3×#832C22semidirect
48. C3×#832C22semidirect
49. C3×#818C22semidirect
50. C3×#816C22semidirect
51. C3×Dic3⋊C8C22semidirect
52. C3×C8×Dic3C22semidirect
53. #63575C22semidirect
54. #63574C22semidirect
55. #63573C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63565C22semidirect
60. #63554C22semidirect
72. #5153D3semidirect
73. Dic3×D8D3semidirect
159. #936C2×D3semidirect
162. D4×Dic3C2×D3semidirect
208. #832C2×D3semidirect
209. #832C2×D3semidirect
220. #818C2×D3semidirect
222. #816C2×D3semidirect
225. Dic3⋊C8C2×D3semidirect
226. C8×Dic3C2×D3semidirect
700. C32#3118semidirect
789. C3#79594semidirect
790. C3#80508semidirect

Maximal subgroups

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

subgroupindex
#105952232
#105951212
#105928552
C3×#51532
C3×Dic3×D82
#105914672
#105914402
#105914322
#105914252
#105914082
#105914042
#105907922
#105907642
#105907152
#105906482
#805083
#795943