Finite Group Databasebeta

← #11872778

Subgroups — #11872778

Order 1152.

889 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595218C211yesmaximal, characteristic, complemented
2#10594606C211yesmaximal, characteristic, complemented
3#10592478C211yesmaximal, characteristic, complemented
4C3×#4786C211yesmaximal, characteristic, complemented
5C3×#4785C211yesmaximal, characteristic, complemented
6#10591516C211yesmaximal, characteristic, complemented
7#10591428C211yesmaximal, characteristic, complemented
8Dic3×#213C211yesmaximal, characteristic, complemented
9#10590945C211yesmaximal, characteristic, complemented
10#10590772C211yesmaximal, characteristic, complemented
11#10590771C211yesmaximal, characteristic, complemented
12#10590647C211yesmaximal, characteristic, complemented
13#10590545C211yesmaximal, characteristic, complemented
14#10590513C211yesmaximal, characteristic, complemented
15#10590452C211yesmaximal, characteristic, complemented
16#80317—31nomaximal
17#79874—31nomaximal
18C2×#3802C2211yescharacteristic
19#64147C2211yescharacteristic
20#64101C2211yescharacteristic
21C3×#940C2211yescharacteristic, complemented
22C3×D4×Dic3C2211yescharacteristic, complemented
23C2×C3×#213C2211yescharacteristic
24C2×C3×#213C2211yescharacteristic
25C2×C3×D24C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#893C2211yescharacteristic
28#63978—21no—
29#63971—21no—
30#63969—21no—
31#63961—21no—
32D3×(C2×D3)⋊C4—21no—
33D3×(C2×D3)⋊C4—21no—
34#63916C2211yescharacteristic
35#63902—21no—
36C4×#625—21no—
37Dic3×D12C2211yescharacteristic
38Dic3×D12C2211yescharacteristic
39Dic3×D12C2211yescharacteristic, complemented
40#63874C2211yescharacteristic
41#63869C2211yescharacteristic, complemented
42C2×#3713C2211yescharacteristic
43C32×#102C2211yescharacteristic, complemented
44#63659C2211yescharacteristic, complemented
45#63647C2211yescharacteristic
46#63644C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#815C2211yescharacteristic, complemented
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic, complemented
52C3×#808C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5719—31no—
62#5562—31no—
63#5545—31no—
64#5545—31no—
65C3×#459—31no—
66C3×#442—31no—
67#5156—31no—
68#5156—31no—
69#5156—31no—
70#5152—31no—
71#5150—31no—
72Dic3×D8—31no—
73#5072—31no—
74C4×#213—31no—
75C4×#213—31no—
76#5009—31no—
77#4871—31no—
78#4866—31no—
79#4847—31no—
80#4840—31no—
81#4786D311yescharacteristic, complemented
82#4785D311yescharacteristic, complemented
83#4784—31no—
84#4779—31no—
85#4779—31no—
86#4779—61no—
87#4773—31no—
88#4763—31no—
89#4756—31no—
90#4711—31no—
91#4709—31no—
92C22×D32—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×#626—21no—
105C2×#625—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109#3802—22no—
110#3802—22no—
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3757—21no—
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4×C3⋊Dic3—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#213—22no—
121C3×#213—22no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4×Dic3C2311yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×D24—22no—
130#3724—21no—
131#3724D411yescharacteristic
132#3724D411yescharacteristic
133Dic3⋊Dic3—21no—
134#3722D411yescharacteristic
135#3722D411yescharacteristic
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140#3713—22no—
141#3122—91noSylow
142C2×D3×D4—31no—
143C2×D3×D4—31no—
144C2×C3×D8—31no—
145C2×C3×D8—31no—
146C2×C3×D8—31no—
147C3×#127—31no—
148C3×C4×D4—31no—
149C3×C4×D4—31no—
150C3×C4×D4—31no—
151#940C2×D311yescharacteristic, complemented
152#939—61no—
153#939—61no—
154#938—31no—
155#938—31no—
156#938—31no—
157#938—61no—
158#935—61no—
159#935—61no—
160D4×Dic3—31no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163D4×Dic3C2×D311yescharacteristic, complemented
164C2×#213—31no—
165C2×#213—31no—
166C2×#213C2×D311yescharacteristic
167C2×#213C2×D311yescharacteristic
168#930—61no—
169#929—61no—
170C4×#67—61no—
171C4×#67—61no—
172C2×(C2×D3)⋊C4—61no—
173C2×(C2×D3)⋊C4—61no—
174C2×D24C2×D311yescharacteristic
175#895—31no—
176#893C2×D311yescharacteristic
177#893C2×D311yescharacteristic
178#892—31no—
179#892—31no—
180#892—61no—
181#890—31no—
182#884—61no—
183#883—61no—
184#67⋊C4—61no—
185#67⋊C4—61no—
186D3×C22⋊C4—61no—
187D3×C22⋊C4—61no—
188C4×D12—31no—
189C4×D12—31no—
190C4×D12—31no—
191#872—31no—
192#872—31no—
193#870—31no—
194C3×#106—31no—
195C3×C4⋊C8—31no—
196C3×#102—21no—
197C3×#102—31no—
198C3×#102—31no—
199C3×#102C2×D311yescharacteristic, complemented
200C3×#102C2×D311yescharacteristic, complemented
201C3×#97—31no—
202#832—31no—
203#832—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—61no—
209#821—31no—
210#821—31no—
211#821—31no—
212#821C2×D311yescharacteristic
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—61no—
218#818—31no—
219#817—31no—
220#817—31no—
221#817—61no—
222#815C2×D311yescharacteristic, complemented
223Dic3⋊C8—31no—
224Dic3⋊C8C2×D311yescharacteristic, complemented
225C8×Dic3—31no—
226#809—31no—
227#809C2×D311yescharacteristic, complemented
228#808C2×D311yescharacteristic, complemented
229#807—31no—
230#807—31no—
231#807—31no—
232#807—61no—
233C4⋊(C3⋊C8)—31no—
234C4×C3⋊C8—31no—
235C23×C32—21no—
236C22×C3⋊D3C2×D411yescharacteristic
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C2×D32—24no—
241C2×D32—81no—
242C2×D32—81no—
243C32×D4—21no—
244C32×D4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247#638—81no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3C2×D411yescharacteristic
251C4×C3⋊D3—21no—
252C4×C3⋊D3—21no—
253C3×#67—81no—
254C3×#67—81no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—81no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12#4112yes—
266C3×D12#4112yes—
267C3×C4×D3—81no—
268C3×C4×D3—81no—
269#626—81no—
270#625—24no—
271D3×Dic3—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—31no—
285#459—91no—
286#447—91no—
287#447—91no—
288#442—31no—
289#442—91no—
290C4×D8—91no—
291C4×D8—91no—
292#433—91no—
293C23×D3—61no—
294C23×D3—61no—
295C2×C3×D4—21no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—31no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C22×D311yescharacteristic
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C2×#67—21no—
307C2×#67—21no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—121no—
314C22×Dic3—21no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318D3×D4—62no—
319D3×D4—62no—
320D3×D4—62no—
321D3×D4—62no—
322C2×D12—61no—
323C2×D12C22×D311yescharacteristic
324C2×D12C22×D311yescharacteristic
325C2×D12C22×D311yescharacteristic
326C2×C4×D3—21no—
327C2×C4×D3—21no—
328C2×C4×D3—31no—
329C2×C4×D3—31no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C3×D8—62no—
335C3×D8—62no—
336C3×D8—62no—
337C2×C3×C8—21no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C3×C4⋊C4—21no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C42—31no—
350C3×C42—31no—
351#217—21no—
352#217—61no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—121no—
359#213—22no—
360#213—22no—
361#213—62no—
362#213—62no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
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—
375(C2×D3)⋊C4—121no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
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—121no—
394C4×Dic3C22×D311yescharacteristic
395C4×Dic3C22×D311yescharacteristic
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—61no—
399C2×C3⋊C8C22×D311yescharacteristic
400C2×C3⋊C8C22×D311yescharacteristic
401D24—22no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32C22×D411yescharacteristic
406C2×C3⋊D3—21no—
407C2×C3⋊D3—21no—
408C2×C3⋊D3—21no—
409C2×C3×D3—22no—
410C2×C3×D3—22no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418D32—84no—
419C32×C4—41no—
420C32×C4C2×#4111yescharacteristic
421C32×C4C2×#4111yescharacteristic
422C3⋊Dic3—21no—
423C3⋊Dic3—41no—
424C3⋊Dic3—41no—
425C3×Dic3—21no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C22×D4—91no—
431C2×D8—31no—
432C2×D8—31no—
433C2×D8—31no—
434C2×D8—91no—
435#127—31no—
436#125—91no—
437#123—181no—
438#123—181no—
439#121—91no—
440#121—91no—
441#121—181no—
442#121—181no—
443C4×D4—31no—
444C4×D4—31no—
445C4×D4—31no—
446C4×D4—91no—
447C4×D4—91no—
448C4×D4—91no—
449C4×D4—181no—
450C4×D4—181no—
451#117—91no—
452#117—91no—
453C2×C22⋊C4—181no—
454C2×C22⋊C4—181no—
455#107—91no—
456#107—91no—
457#106—31no—
458#106—91no—
459C4⋊C8—31no—
460C4⋊C8—91no—
461#102—31no—
462#102—31no—
463#102—91no—
464#102—91no—
465#102—91no—
466#102—91no—
467#102—91no—
468#102D3211yescharacteristic, complemented
469C22⋊C8—91no—
470C22⋊C8—91no—
471#97—31no—
472C4×C8—91no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—41no—
476C23×C3—61no—
477C23×C3—61no—
478C23×C3—61no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—31no—
483C22×D3—31no—
484C22×D3—61no—
485C22×D3—64no—
486C22×D3—64no—
487C22×D3—241no—
488C22×D3—241no—
489C22×D3—241no—
490C22×D3—241no—
491C3×D4—21no—
492C3×D4—21no—
493C3×D4—21no—
494C3×D4—21no—
495C3×D4—32no—
496C3×D4—32no—
497C3×D4—41no—
498C3×D4—41no—
499C3×D4—61no—
500C3×D4—61no—
501C3×D4—61no—
502C3×D4—61no—
503C3×D4—241no—
504C3×D4—241no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—41no—
513C2×C3×C4—61no—
514C2×C3×C4—241no—
515C2×C3×C4—241no—
516C2×C3×C4—241no—
517C2×C3×C4C23×D311yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519#67—64no—
520#67—64no—
521#67—81no—
522#67—81no—
523#67—241no—
524#67—241no—
525#67—241no—
526#67—242no—
527C2×Dic3—21no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—81no—
536C2×Dic3—121no—
537C2×Dic3—121no—
538C2×Dic3—241no—
539C2×Dic3—241no—
540C2×Dic3—241no—
541C2×Dic3D3×D411yescharacteristic
542C2×Dic3D3×D411yescharacteristic
543C2×Dic3D3×D411yescharacteristic
544C2×Dic3D3×D411yescharacteristic
545D12—21no—
546D12—21no—
547D12—21no—
548D12—21no—
549D12—241no—
550D12#23512yes—
551D12#23712yes—
552C4×D3—61no—
553C4×D3—61no—
554C4×D3—61no—
555C4×D3—61no—
556C4×D3—81no—
557C4×D3—81no—
558C4×D3—121no—
559C4×D3—121no—
560C4×D3—241no—
561C4×D3—241no—
562C4×D3—241no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—41no—
566C3×C8—61no—
567C3×C8—61no—
568C3⋊C8—21no—
569C3⋊C8—21no—
570C3⋊C8—61no—
571C3⋊C8—61no—
572C3⋊C8—121no—
573C2×C32—81no—
574C2×C32#52511yescharacteristic
575C2×C32#57611yescharacteristic
576C2×C32#57611yescharacteristic
577C3⋊D3—41no—
578C3×D3—42no—
579C3×D3—42no—
580C3×D3—81no—
581C24—181no—
582C2×D4—31no—
583C2×D4—31no—
584C2×D4—31no—
585C2×D4—61no—
586C2×D4—61no—
587C2×D4—181no—
588C2×D4—181no—
589C2×D4—182no—
590C2×D4—182no—
591C2×D4—181no—
592C2×D4C2×D3211yescharacteristic
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—91no—
597C22×C4—181no—
598C22×C4—181no—
599C22×C4—181no—
600D8—62no—
601D8—62no—
602D8—62no—
603D8—182no—
604C2×C8—31no—
605C2×C8—31no—
606C2×C8—91no—
607C2×C8C2×D3211yescharacteristic
608C4⋊C4—31no—
609C4⋊C4—91no—
610C4⋊C4—91no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4C2×D3211yescharacteristic
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—
626C22⋊C4—181no—
627C42—31no—
628C42—31no—
629C42—181no—
630C22×C3—21no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—62no—
638C22×C3—62no—
639C22×C3—81no—
640C22×C3—81no—
641C22×C3—81no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3C2×D3×D411yescharacteristic
650C22×C3C2×D3×D411yescharacteristic
651C2×D3—22no—
652C2×D3—22no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—244no—
670C2×D3—244no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—81no—
680C3×C4—121no—
681C3×C4C2×#23511yescharacteristic
682C3×C4C2×#23711yescharacteristic
683C3×C4D3×#4111yescharacteristic
684C3×C4D3×#4111yescharacteristic
685Dic3—21no—
686Dic3—21no—
687Dic3—21no—
688Dic3—21no—
689Dic3—41no—
690Dic3—61no—
691Dic3—61no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—121no—
697Dic3—241no—
698Dic3—241no—
699C32#312211yescharacteristic, complemented, Sylow
700C23—21no—
701C23—61no—
702C23—61no—
703C23—61no—
704C23—91no—
705C23—184no—
706C23—721no—
707C23—721no—
708D4—21no—
709D4—21no—
710D4—32no—
711D4—32no—
712D4—61no—
713D4—61no—
714D4—61no—
715D4—61no—
716D4—184no—
717D4—241no—
718D4—241no—
719D4—721no—
720D4—721no—
721C2×C4—21no—
722C2×C4—31no—
723C2×C4—31no—
724C2×C4—31no—
725C2×C4—31no—
726C2×C4—61no—
727C2×C4—91no—
728C2×C4—181no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—241no—
733C2×C4—241no—
734C2×C4—241no—
735C2×C4—721no—
736C2×C4—721no—
737C2×C4—721no—
738C2×C4C22×D3211yescharacteristic
739C8—21no—
740C8—61no—
741C8—61no—
742C8—181no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—81no—
747C2×C3—81no—
748C2×C3—122no—
749C2×C3—122no—
750C2×C3—161no—
751C2×C3—241no—
752C2×C3#554711yescharacteristic
753C2×C3#560611yescharacteristic
754C2×C3#575711yescharacteristic
755C2×C3#577411yescharacteristic
756C2×C3#577411yescharacteristic
757C2×C3#577411yescharacteristic
758D3—42no—
759D3—42no—
760D3—81no—
761D3—121no—
762D3—121no—
763D3—241no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—62no—
768C22—62no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22—181no—
777C22—181no—
778C22—181no—
779C22—724no—
780C22D32×D411yescharacteristic
781C4—41no—
782C4—61no—
783C4—61no—
784C4—61no—
785C4—61no—
786C4—121no—
787C4—181no—
788C4—361no—
789C4—361no—
790C4D3×#23511yescharacteristic
791C4D3×#23711yescharacteristic
792C3—21no—
793C3#7987411yescharacteristic, complemented
794C3#8031711yescharacteristic, complemented
795C2—81no—
796C2—122no—
797C2—122no—
798C2—241no—
799C2—361no—
800C2#1059428611yescharacteristic
801C2#1059473211yescharacteristic
802C2#1059475011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3122
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595218C2semidirect
2. #10594606C2semidirect
3. #10592478C2semidirect
4. C3×#4786C2semidirect
5. C3×#4785C2semidirect
6. #10591516C2semidirect
7. #10591428C2semidirect
8. Dic3×#213C2semidirect
9. #10590945C2semidirect
10. #10590772C2semidirect
11. #10590771C2semidirect
12. #10590647C2semidirect
13. #10590545C2semidirect
14. #10590513C2semidirect
15. #10590452C2semidirect
21. C3×#940C22semidirect
22. C3×D4×Dic3C22semidirect
39. Dic3×D12C22semidirect
41. #63869C22semidirect
43. C32×#102C22semidirect
44. #63659C22semidirect
46. #63644C22semidirect
47. #63634C22semidirect
49. C3×#815C22semidirect
50. C3×Dic3⋊C8C22semidirect
51. C3×#809C22semidirect
52. C3×#808C22semidirect
53. #63575C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
57. #63563C22semidirect
60. Dic3×C3⋊C8C22semidirect
81. #4786D3semidirect
82. #4785D3semidirect
151. #940C2×D3semidirect
163. D4×Dic3C2×D3semidirect
199. C3×#102C2×D3semidirect
200. C3×#102C2×D3semidirect
222. #815C2×D3semidirect
224. Dic3⋊C8C2×D3semidirect
227. #809C2×D3semidirect
228. #808C2×D3semidirect
468. #102D32semidirect
699. C32#3122semidirect
793. C3#79874semidirect
794. C3#80317semidirect

Maximal subgroups

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

subgroupindex
#105952182
#105946062
#105924782
C3×#47862
C3×#47852
#105915162
#105914282
Dic3×#2132
#105909452
#105907722
#105907712
#105906472
#105905452
#105905132
#105904522
#803173
#798743