Finite Group Databasebeta

← #11872744

Subgroups — #11872744

Order 1152.

906 conjugacy classes of subgroups.

The subgroup lattice has 813 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595215C211yesmaximal, characteristic, complemented
2#10595125C211yesmaximal, characteristic, complemented
3#10592849C211yesmaximal, characteristic, complemented
4C3×#5156C211yesmaximal, characteristic, complemented
5C3×#5152C211yesmaximal, characteristic, complemented
6#10591479C211yesmaximal, characteristic, complemented
7#10591448C211yesmaximal, characteristic, complemented
8#10591433C211yesmaximal, characteristic, complemented
9Dic3×#213C211yesmaximal, characteristic, complemented
10#10591422C211yesmaximal, characteristic, complemented
11#10591400C211yesmaximal, characteristic, complemented
12#10590782C211yesmaximal, characteristic, complemented
13#10590746C211yesmaximal, characteristic, complemented
14#10590704C211yesmaximal, characteristic, complemented
15#10590697C211yesmaximal, characteristic, complemented
16#79993—31nomaximal
17#79874—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×C32×D8C2211yescharacteristic
20#64149C2211yescharacteristic, complemented
21D4×C3⋊Dic3C2211yescharacteristic
22C2×#3753C2211yescharacteristic
23C3×#938C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic, complemented
26C2×C3×#213C2211yescharacteristic
27#63978—21no—
28#63975—21no—
29#67⋊Dic3—21no—
30Dic3×#67—21no—
31D3×#217—21no—
32#63966—21no—
33C2×(C2×D3)⋊Dic3—21no—
34#63958—21no—
35#63909C2211yescharacteristic
36#63898C2211yescharacteristic
37#63894C2211yescharacteristic, complemented
38Dic3×D12C2211yescharacteristic
39#63872C2211yescharacteristic, complemented
40#63855C2211yescharacteristic
41#63841C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43#63659C2211yescharacteristic, complemented
44#63648C2211yescharacteristic, complemented
45#63641C2211yescharacteristic, complemented
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#817C2211yescharacteristic, complemented
52C3×#815C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5798—31no—
62#5619—31no—
63#5562—31no—
64#5545—31no—
65C3×#447—31no—
66C3×#442—31no—
67#5217—31no—
68#5156D311yescharacteristic, complemented
69#5152D311yescharacteristic, complemented
70#5150—31no—
71#5150—31no—
72#5150—31no—
73#5150—61no—
74Dic3×D8—31no—
75#5035—31no—
76C4×#213—31no—
77C4×#213—31no—
78#4871—31no—
79#4866—31no—
80#4786—31no—
81#4785—31no—
82#4779—31no—
83#4773—31no—
84#4766—31no—
85#4763—31no—
86#4763—31no—
87#4756—31no—
88#4737—31no—
89#4720—31no—
90#4711—31no—
91#4709—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×#638—21no—
97C22×C3⋊Dic3—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C3×D3×D4—22no—
104C3×D3×D4—22no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×#626—21no—
108C2×#624—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C32×D8—22no—
112C2×C32×C8C2311yescharacteristic
113#3757—21no—
114#3753—22no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4×C3⋊Dic3C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#213—22no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3D411yescharacteristic
131Dic3⋊Dic3D411yescharacteristic
132#3722—21no—
133#3722—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3D411yescharacteristic
138(C2×D3)⋊Dic3D411yescharacteristic
139Dic32—21no—
140#3714—22no—
141#3122—91noSylow
142C22×C3×D4—31no—
143C2×D3×D4C2×D311yescharacteristic
144C2×C3×D8—21no—
145C2×C3×D8—31no—
146C2×C3×D8C2×D311yescharacteristic
147C2×C3×D8C2×D311yescharacteristic
148C3×#121—31no—
149C3×C4×D4—31no—
150C3×C4×D4—31no—
151C2×#217—61no—
152C2×#217—61no—
153#940—31no—
154#940—31no—
155#940—61no—
156#939—61no—
157#938—61no—
158#938C2×D311yescharacteristic
159D4×Dic3—31no—
160D4×Dic3—31no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163D4×Dic3—61no—
164D4×Dic3—61no—
165D4×Dic3—61no—
166D4×Dic3C2×D311yescharacteristic
167D4×Dic3C2×D311yescharacteristic, complemented
168C2×#213—31no—
169C2×#213—31no—
170C2×#213—31no—
171C2×#213—61no—
172C2×#213C2×D311yescharacteristic
173#930—31no—
174#930—61no—
175#929—61no—
176C4×#67—61no—
177C2×(C2×D3)⋊C4—61no—
178#926—31no—
179#926—31no—
180C2×D24—31no—
181#895—31no—
182#893—31no—
183#893—31no—
184#892—31no—
185#890—31no—
186#890—31no—
187#886—61no—
188#884—61no—
189#883—61no—
190#883—61no—
191#67⋊C4—61no—
192D3×C22⋊C4—61no—
193C4×D12—31no—
194C4×D12—31no—
195#872—31no—
196C3×#106—31no—
197C3×#102—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×#102—31no—
201C3×C22⋊C8—31no—
202C3×#97—31no—
203#832—31no—
204#832—31no—
205#832—31no—
206#832—61no—
207#832C2×D311yescharacteristic
208#832C2×D311yescharacteristic
209#832C2×D311yescharacteristic, complemented
210#830—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—61no—
215#821C2×D311yescharacteristic
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8C2×D311yescharacteristic
218#818—31no—
219#817—31no—
220#817C2×D311yescharacteristic, complemented
221#815C2×D311yescharacteristic, complemented
222Dic3⋊C8—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—61no—
227C8×Dic3—31no—
228#809—31no—
229#809—31no—
230#808—31no—
231#807—31no—
232#807—31no—
233#807—31no—
234C4×C3⋊C8—31no—
235C23×C32—21no—
236C23×C32—21no—
237C22×C3⋊D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—24no—
240C22×C3×D3—81no—
241C22×C3×D3—81no—
242C22×C3×D3C2×D411yescharacteristic
243C32×D4—21no—
244C32×D4—21no—
245C32×D4—21no—
246C32×D4#4112yes—
247C2×C32×C4C2411yescharacteristic
248#638—81no—
249#638—81no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—81no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C2×C3⋊Dic3C2×D411yescharacteristic
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256C3×#67—24no—
257C3×#67—81no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—81no—
262C2×C3×Dic3—81no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12#4112yes—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270#626—81no—
271#624—81no—
272D3×Dic3—81no—
273D3×Dic3—81no—
274C32×C8—21no—
275C3⋊(C3⋊C8)—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278#540—91no—
279#518—91no—
280#482—91no—
281#482—91no—
282#478—91no—
283#478—91no—
284#459—91no—
285#459—91no—
286#447—31no—
287#447—91no—
288#442—31no—
289#442—91no—
290C4×D8—91no—
291C4×D8—91no—
292#433—91no—
293C24×C3—61no—
294C23×D3—21no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C2×C3×D4—62no—
300C2×C3×D4—62no—
301C2×C3×D4—61no—
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C22×D311yescharacteristic
306C22×C3×C4—31no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C2×#67—21no—
310C2×#67—21no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—121no—
317C2×#67—121no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—121no—
325D3×D4—22no—
326D3×D4—22no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—61no—
330C2×D12—61no—
331C2×D12C22×D311yescharacteristic
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3C22×D311yescharacteristic
337C3×D8—22no—
338C3×D8—22no—
339C3×D8—42no—
340C3×D8—62no—
341C2×C3×C8—21no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C42—31no—
353#217—21no—
354#217—21no—
355#217—21no—
356#217—31no—
357#217—31no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—121no—
364#213—22no—
365#213—62no—
366#213—62no—
367#213—62no—
368#213—122no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3C22×D311yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388Dic3⋊C4—31no—
389Dic3⋊C4—31no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3C22×D311yescharacteristic
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403D24—62no—
404C22×C32—22no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32—41no—
409C22×C32—41no—
410C22×C32C22×D411yescharacteristic
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3⋊D3—41no—
414C2×C3×D3—21no—
415C2×C3×D3—22no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—84no—
421C32×C4C2×#4111yescharacteristic
422C32×C4C2×#4111yescharacteristic
423C3⋊Dic3—21no—
424C3⋊Dic3—21no—
425C3⋊Dic3—41no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C22×D4—31no—
433C2×D8—31no—
434C2×D8—91no—
435C2×D8—91no—
436C2×D8D3211yescharacteristic
437#127—91no—
438#125—91no—
439#123—181no—
440#123—181no—
441#121—31no—
442#121—91no—
443#121—181no—
444#121—181no—
445C4×D4—31no—
446C4×D4—31no—
447C4×D4—91no—
448C4×D4—91no—
449C4×D4—91no—
450C4×D4—91no—
451C4×D4—181no—
452C4×D4—181no—
453#117—91no—
454#117—91no—
455C2×C22⋊C4—181no—
456C2×C22⋊C4—181no—
457#107—91no—
458#107—91no—
459#106—31no—
460#106—91no—
461C4⋊C8—91no—
462C4⋊C8—91no—
463#102—31no—
464#102—31no—
465#102—31no—
466#102—31no—
467#102—91no—
468#102—91no—
469#102—91no—
470#102—91no—
471C22⋊C8—31no—
472C22⋊C8—91no—
473#97—31no—
474C4×C8—91no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—31no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—64no—
483C23×C3—61no—
484C23×C3—241no—
485C23×C3—241no—
486C22×D3—21no—
487C22×D3—24no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—81no—
491C22×D3—81no—
492C22×D3—121no—
493C22×D3D3×D411yescharacteristic
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—21no—
500C3×D4—22no—
501C3×D4—32no—
502C3×D4—41no—
503C3×D4—41no—
504C3×D4—41no—
505C3×D4—64no—
506C3×D4—61no—
507C3×D4—241no—
508C3×D4#23512yes—
509C3×D4#23712yes—
510C2×C3×C4—21no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—241no—
520C2×C3×C4—241no—
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523#67—24no—
524#67—81no—
525#67—241no—
526#67—241no—
527#67—241no—
528#67—241no—
529#67—241no—
530#67—242no—
531#67—242no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—81no—
544C2×Dic3—81no—
545C2×Dic3—121no—
546C2×Dic3—241no—
547C2×Dic3—241no—
548C2×Dic3—241no—
549C2×Dic3—241no—
550C2×Dic3—242no—
551C2×Dic3D3×D411yescharacteristic
552C2×Dic3D3×D411yescharacteristic
553C2×Dic3D3×D411yescharacteristic
554D12—21no—
555D12—61no—
556D12—61no—
557D12—61no—
558D12—61no—
559D12—121no—
560D12—121no—
561D12—241no—
562D12#23712yes—
563C4×D3—21no—
564C4×D3—21no—
565C4×D3—241no—
566C4×D3—241no—
567C4×D3—241no—
568C4×D3—241no—
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—41no—
572C3×C8—61no—
573C3×C8—61no—
574C3⋊C8—21no—
575C3⋊C8—21no—
576C3⋊C8—61no—
577C3⋊C8—61no—
578C3⋊C8—121no—
579C2×C32—42no—
580C2×C32—81no—
581C2×C32#52511yescharacteristic
582C2×C32#57611yescharacteristic
583C2×C32#57611yescharacteristic
584C3⋊D3—81no—
585C3×D3—41no—
586C3×D3—42no—
587C24—61no—
588C2×D4—31no—
589C2×D4—61no—
590C2×D4—62no—
591C2×D4—62no—
592C2×D4—61no—
593C2×D4—91no—
594C2×D4—181no—
595C2×D4—181no—
596C2×D4—181no—
597C2×D4C2×D3211yescharacteristic
598C2×D4C2×D3211yescharacteristic
599C22×C4—31no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—181no—
603C22×C4—181no—
604C22×C4—181no—
605C22×C4—181no—
606D8—22no—
607D8—62no—
608D8—182no—
609D8—182no—
610C2×C8—31no—
611C2×C8—31no—
612C2×C8—91no—
613C2×C8C2×D3211yescharacteristic
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—31no—
617C4⋊C4—91no—
618C4⋊C4—91no—
619C4⋊C4—91no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—91no—
626C22⋊C4—91no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C42—31no—
634C42—91no—
635C42—181no—
636C22×C3—22no—
637C22×C3—22no—
638C22×C3—21no—
639C22×C3—42no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—62no—
654C22×C3—81no—
655C22×C3—81no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—244no—
662C22×C3C2×D3×D411yescharacteristic
663C22×C3C2×D3×D411yescharacteristic
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—22no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—84no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3—241no—
678C2×D3—241no—
679C2×D3—241no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—61no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4C2×#23511yescharacteristic
689C3×C4C2×#23711yescharacteristic
690C3×C4C2×#23711yescharacteristic
691C3×C4D3×#4111yescharacteristic
692Dic3—21no—
693Dic3—21no—
694Dic3—21no—
695Dic3—41no—
696Dic3—41no—
697Dic3—41no—
698Dic3—62no—
699Dic3—61no—
700Dic3—61no—
701Dic3—61no—
702Dic3—61no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—241no—
707C32#312211yescharacteristic, complemented, Sylow
708C23—21no—
709C23—21no—
710C23—31no—
711C23—64no—
712C23—61no—
713C23—181no—
714C23—241no—
715C23—241no—
716D4—21no—
717D4—21no—
718D4—21no—
719D4—32no—
720D4—64no—
721D4—61no—
722D4—181no—
723D4—181no—
724D4—241no—
725D4—721no—
726D4—721no—
727D4—721no—
728D4#380412yes—
729C2×C4—31no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—91no—
738C2×C4—91no—
739C2×C4—181no—
740C2×C4—241no—
741C2×C4—241no—
742C2×C4—721no—
743C2×C4—721no—
744C2×C4—721no—
745C2×C4—721no—
746C2×C4C22×D3211yescharacteristic
747C8—21no—
748C8—61no—
749C8—61no—
750C8—181no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—42no—
755C2×C3—42no—
756C2×C3—82no—
757C2×C3—81no—
758C2×C3—81no—
759C2×C3—121no—
760C2×C3—122no—
761C2×C3—161no—
762C2×C3#554711yescharacteristic
763C2×C3#558611yescharacteristic
764C2×C3#575711yescharacteristic
765C2×C3#577411yescharacteristic
766C2×C3#577411yescharacteristic
767C2×C3#577411yescharacteristic
768D3—41no—
769D3—42no—
770D3—241no—
771D3—241no—
772D3—481no—
773C22—22no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—61no—
780C22—62no—
781C22—61no—
782C22—61no—
783C22—121no—
784C22—121no—
785C22—244no—
786C22—361no—
787C22—361no—
788C22—361no—
789C22D32×D411yescharacteristic
790C4—61no—
791C4—61no—
792C4—61no—
793C4—121no—
794C4—121no—
795C4—121no—
796C4—181no—
797C4—181no—
798C4—361no—
799C4D3×#23711yescharacteristic
800C4C2×#380411yescharacteristic
801C3—21no—
802C3#7987411yescharacteristic, complemented
803C3#7999311yescharacteristic, complemented
804C2—42no—
805C2—81no—
806C2—121no—
807C2—122no—
808C2—721no—
809C2#1059473211yescharacteristic
810C2#1059473511yescharacteristic
811C2#1059512911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3122
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. #10595215C2semidirect
2. #10595125C2semidirect
3. #10592849C2semidirect
4. C3×#5156C2semidirect
5. C3×#5152C2semidirect
6. #10591479C2semidirect
7. #10591448C2semidirect
8. #10591433C2semidirect
9. Dic3×#213C2semidirect
10. #10591422C2semidirect
11. #10591400C2semidirect
12. #10590782C2semidirect
13. #10590746C2semidirect
14. #10590704C2semidirect
15. #10590697C2semidirect
20. #64149C22semidirect
25. C3×D4×Dic3C22semidirect
37. #63894C22semidirect
39. #63872C22semidirect
43. #63659C22semidirect
44. #63648C22semidirect
45. #63641C22semidirect
48. C3×#832C22semidirect
51. C3×#817C22semidirect
52. C3×#815C22semidirect
53. #63576C22semidirect
54. #63575C22semidirect
55. #63573C22semidirect
56. #63572C22semidirect
57. #63564C22semidirect
60. Dic3×C3⋊C8C22semidirect
68. #5156D3semidirect
69. #5152D3semidirect
167. D4×Dic3C2×D3semidirect
209. #832C2×D3semidirect
220. #817C2×D3semidirect
221. #815C2×D3semidirect
707. C32#3122semidirect
802. C3#79874semidirect
803. C3#79993semidirect

Maximal subgroups

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

subgroupindex
#105952152
#105951252
#105928492
C3×#51562
C3×#51522
#105914792
#105914482
#105914332
Dic3×#2132
#105914222
#105914002
#105907822
#105907462
#105907042
#105906972
#799933
#798743