Finite Group Databasebeta

← #11872183

Subgroups — #11872183

Order 1152.

866 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595215C211yesmaximal, characteristic, complemented
2#10594592C211yesmaximal, characteristic, complemented
3#10592458C211yesmaximal, characteristic, complemented
4C3×#4785C211yesmaximal, characteristic, complemented
5C3×#4776C211yesmaximal, characteristic, complemented
6#10591476C211yesmaximal, characteristic, complemented
7#10591447C211yesmaximal, characteristic
8Dic3×#214C211yesmaximal, characteristic, complemented
9#10590834C211yesmaximal, characteristic, complemented
10#10590766C211yesmaximal, characteristic, complemented
11#10590750C211yesmaximal, characteristic, complemented
12#10590697C211yesmaximal, characteristic, complemented
13#10590472C211yesmaximal, characteristic, complemented
14#10590452C211yesmaximal, characteristic, complemented
15#10590447C211yesmaximal, characteristic, complemented
16#80136—31nomaximal
17#79886—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19D4×C3⋊Dic3C2211yescharacteristic
20#64097C2211yescharacteristic, complemented
21C3×D4×Dic3C2211yescharacteristic
22C2×C3×#214C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25C3×#897C2211yescharacteristic
26C3×#893C2211yescharacteristic, complemented
27#67⋊Dic3—21no—
28Dic3×#67—21no—
29D3×#217—21no—
30C2×(C2×D3)⋊Dic3—21no—
31#63913—21no—
32#63908C2211yescharacteristic
33#63905—21no—
34#63898C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36#63863C2211yescharacteristic, complemented
37#63858—21no—
38#63857—21no—
39#63855C2211yescharacteristic
40Dic3×Dic6C2211yescharacteristic, complemented
41#63841C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43C32×#102C2211yescharacteristic
44#63659C2211yescharacteristic
45#63645C2211yescharacteristic, complemented
46#63641C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic, complemented
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#815C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#808C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5798—31no—
62#5643—31no—
63#5561—31no—
64#5545—31no—
65C3×#450—31no—
66C3×#442—31no—
67#5217—31no—
68#5165—31no—
69#5165—31no—
70#5164—31no—
71Dic3×SD16—31no—
72#5156—31no—
73#5153—31no—
74#5045—31no—
75C4×#214—31no—
76C4×#213—31no—
77#4870—31no—
78#4868—31no—
79#4787—31no—
80#4785D311yescharacteristic, complemented
81#4784—31no—
82#4776D311yescharacteristic, complemented
83#4761—31no—
84#4759—31no—
85#4759—31no—
86#4759—61no—
87#4756—31no—
88#4737—31no—
89#4720—31no—
90#4710—31no—
91#4709—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×#634—21no—
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C3×D3×D4—22no—
99C3×D3×D4—22no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#625—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×C32×C8C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110#3757—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113#3750—21no—
114C4×C3⋊Dic3C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C3×#217—21no—
117C3×#214—22no—
118C3×#213—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4×Dic3C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C3×#204—22no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3D411yescharacteristic
129Dic3⋊Dic3D411yescharacteristic
130(C2×D3)⋊Dic3—21no—
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3D411yescharacteristic
137(C2×D3)⋊Dic3D411yescharacteristic
138Dic32—21no—
139Dic32—21no—
140#3713—22no—
141#3118—91noSylow
142C22×C3×D4—31no—
143C2×D3×D4C2×D311yescharacteristic
144C2×C3×SD16—31no—
145C2×C3×SD16—31no—
146C2×C3×D8—31no—
147C3×C22⋊Q8—31no—
148C3×C4×D4—31no—
149C3×C4×D4—31no—
150C2×#217—61no—
151C2×#217—61no—
152#947—31no—
153Q8×Dic3—31no—
154#938—31no—
155#936—31no—
156D4×Dic3—31no—
157D4×Dic3—31no—
158D4×Dic3—31no—
159D4×Dic3—31no—
160D4×Dic3—61no—
161D4×Dic3—61no—
162D4×Dic3—61no—
163D4×Dic3C2×D311yescharacteristic
164C2×#214C2×D311yescharacteristic
165C2×#213—31no—
166C2×#213—31no—
167C2×#213C2×D311yescharacteristic
168#930—31no—
169#929—61no—
170C4×#67—61no—
171C2×(C2×D3)⋊C4—61no—
172#926—31no—
173#926—31no—
174#924—61no—
175C2×#204C2×D311yescharacteristic
176#898—61no—
177#897—61no—
178#897C2×D311yescharacteristic
179#893—31no—
180#893C2×D311yescharacteristic, complemented
181#892—31no—
182#888—31no—
183#888—31no—
184#888—61no—
185#885—61no—
186#885—61no—
187#883—61no—
188#67⋊C4—61no—
189D3×C22⋊C4—61no—
190#879—61no—
191C4×D12—31no—
192#872—31no—
193C4×Dic6—31no—
194C3×#106—31no—
195C3×#102—21no—
196C3×#102—31no—
197C3×#102—31no—
198C3×#102C2×D311yescharacteristic
199C3×#102C2×D311yescharacteristic
200C3×C22⋊C8—31no—
201C3×#97—31no—
202#835—31no—
203#835—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—61no—
209#830—31no—
210#821—31no—
211#821—31no—
212#821C2×D311yescharacteristic, complemented
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8C2×D311yescharacteristic
215#818—31no—
216#818—31no—
217#818—61no—
218#817—31no—
219#816—31no—
220#815C2×D311yescharacteristic, complemented
221Dic3⋊C8—31no—
222Dic3⋊C8—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8—61no—
226C8×Dic3—31no—
227#810—31no—
228#809C2×D311yescharacteristic
229#808—31no—
230#808C2×D311yescharacteristic, complemented
231#807—31no—
232#807—31no—
233#807—61no—
234C4×C3⋊C8—31no—
235C23×C32—21no—
236C22×C3×D3—21no—
237C22×C3×D3—24no—
238C22×C3×D3—21no—
239C22×C3×D3—81no—
240C22×C3×D3—81no—
241C22×C3×D3C2×D411yescharacteristic
242C32×D4—21no—
243C32×D4#4112yes—
244C2×C32×C4—21no—
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—81no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C2×C3⋊Dic3C2×D411yescharacteristic
251#634—81no—
252C3×#67—24no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—81no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—21no—
262C3×D12#4112yes—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—81no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268#625—81no—
269D3×Dic3—81no—
270D3×Dic3—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—91no—
282#463—91no—
283#450—31no—
284#447—91no—
285#442—31no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C24×C3—61no—
291C23×D3—21no—
292C2×C3×Q8—31no—
293C2×C3×D4—21no—
294C2×C3×D4—31no—
295C2×C3×D4—31no—
296C2×C3×D4—61no—
297C2×C3×D4—62no—
298C2×C3×D4—62no—
299C2×C3×D4C22×D311yescharacteristic
300C2×C3×D4C22×D311yescharacteristic
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C2×#67—21no—
305C2×#67—61no—
306C2×#67—61no—
307C22×Dic3—21no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—121no—
313D3×D4—22no—
314D3×D4—22no—
315C2×D12C22×D311yescharacteristic
316C2×D12C22×D311yescharacteristic
317C2×C4×D3—21no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3C22×D311yescharacteristic
321C2×Dic6—61no—
322C2×Dic6—61no—
323C2×Dic6—121no—
324C2×Dic6C22×D311yescharacteristic
325C3×SD16—62no—
326C3×SD16—62no—
327C3×D8—62no—
328C2×C3×C8—21no—
329C2×C3×C8—31no—
330C2×C3×C8—31no—
331C2×C3×C8C22×D311yescharacteristic
332C2×C3×C8C22×D311yescharacteristic
333C3×C4⋊C4—21no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4C22×D311yescharacteristic
337C3×C4⋊C4C22×D311yescharacteristic
338C3×C22⋊C4—61no—
339C3×C22⋊C4—61no—
340C3×C22⋊C4—61no—
341C3×C42—31no—
342#217—21no—
343#217—31no—
344#217—31no—
345#217—61no—
346#217—61no—
347#217—61no—
348#217—61no—
349#217—61no—
350#217—61no—
351#217—61no—
352#217—61no—
353#217—121no—
354#214—22no—
355#213—22no—
356#213—62no—
357#213—62no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—31no—
361(C2×D3)⋊C4—31no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368C4⋊Dic3—21no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—31no—
380Dic3⋊C4—31no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—121no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3C22×D311yescharacteristic
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398#204—22no—
399C22×C32—22no—
400C22×C32—41no—
401C22×C32—41no—
402C22×C32C22×D411yescharacteristic
403C2×C3×D3—21no—
404C2×C3×D3—22no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—41no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—84no—
413C32×C4—41no—
414C32×C4C2×#4111yescharacteristic
415C32×C4C2×#4111yescharacteristic
416C3⋊Dic3—21no—
417C3⋊Dic3—21no—
418C3⋊Dic3—41no—
419C3⋊Dic3—41no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C22×D4—31no—
426C2×SD16—31no—
427C2×SD16—31no—
428C2×D8—31no—
429C2×D8—91no—
430C4⋊Q8—91no—
431#126—181no—
432#124—91no—
433#124—181no—
434#123—181no—
435C22⋊Q8—31no—
436C22⋊Q8—181no—
437#121—91no—
438C4×Q8—91no—
439C4×D4—31no—
440C4×D4—31no—
441C4×D4—91no—
442C4×D4—91no—
443C4×D4—91no—
444C4×D4—181no—
445C4×D4—181no—
446#117—91no—
447#117—91no—
448C2×C22⋊C4—181no—
449C2×C22⋊C4—181no—
450#107—91no—
451#107—91no—
452#106—31no—
453#106—91no—
454C4⋊C8—91no—
455C4⋊C8—91no—
456#103—91no—
457#103—91no—
458#102—31no—
459#102—31no—
460#102—91no—
461#102—91no—
462#102—91no—
463#102D3211yescharacteristic
464C22⋊C8—31no—
465C22⋊C8—91no—
466#97—31no—
467C4×C8—91no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—31no—
471C23×C3—41no—
472C23×C3—64no—
473C23×C3—61no—
474C23×C3—61no—
475C23×C3—241no—
476C23×C3—241no—
477C22×D3—21no—
478C22×D3—24no—
479C22×D3—21no—
480C22×D3—81no—
481C22×D3—81no—
482C22×D3D3×D411yescharacteristic
483C3×Q8—61no—
484C3×Q8—61no—
485C3×D4—21no—
486C3×D4—21no—
487C3×D4—22no—
488C3×D4—32no—
489C3×D4—41no—
490C3×D4—64no—
491C3×D4—61no—
492C3×D4—61no—
493C3×D4—61no—
494C3×D4#23512yes—
495C3×D4#23712yes—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—41no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—241no—
508C2×C3×C4—241no—
509C2×C3×C4C23×D311yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511#67—24no—
512#67—241no—
513#67—241no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—81no—
527C2×Dic3—121no—
528C2×Dic3—121no—
529C2×Dic3—241no—
530C2×Dic3—241no—
531C2×Dic3—241no—
532C2×Dic3—241no—
533C2×Dic3—242no—
534C2×Dic3D3×D411yescharacteristic
535C2×Dic3D3×D411yescharacteristic
536C2×Dic3D3×D411yescharacteristic
537D12—21no—
538D12—21no—
539D12—21no—
540D12#23712yes—
541C4×D3—21no—
542C4×D3—21no—
543C4×D3—81no—
544C4×D3—241no—
545C4×D3—241no—
546Dic6—21no—
547Dic6—21no—
548Dic6—241no—
549Dic6—241no—
550Dic6—242no—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—41no—
554C3×C8—61no—
555C3×C8—61no—
556C3⋊C8—21no—
557C3⋊C8—21no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—121no—
561C2×C32—42no—
562C2×C32#52511yescharacteristic
563C2×C32#57611yescharacteristic
564C2×C32#57711yescharacteristic
565C3×D3—41no—
566C3×D3—42no—
567C3×D3—81no—
568C24—61no—
569C2×Q8—31no—
570C2×Q8—181no—
571C2×D4—31no—
572C2×D4—31no—
573C2×D4—61no—
574C2×D4—62no—
575C2×D4—62no—
576C2×D4—181no—
577C2×D4C2×D3211yescharacteristic
578C22×C4—31no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—181no—
582C22×C4—181no—
583C22×C4—181no—
584SD16—62no—
585SD16—62no—
586D8—62no—
587D8—182no—
588C2×C8—31no—
589C2×C8—31no—
590C2×C8—91no—
591C2×C8C2×D3211yescharacteristic
592C4⋊C4—31no—
593C4⋊C4—61no—
594C4⋊C4—91no—
595C4⋊C4—91no—
596C4⋊C4—91no—
597C4⋊C4—91no—
598C4⋊C4—181no—
599C4⋊C4—181no—
600C4⋊C4C2×D3211yescharacteristic
601C22⋊C4—61no—
602C22⋊C4—61no—
603C22⋊C4—61no—
604C22⋊C4—91no—
605C22⋊C4—91no—
606C22⋊C4—181no—
607C22⋊C4—181no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C42—31no—
614C42—91no—
615C42—181no—
616C42—181no—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—21no—
620C22×C3—42no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3—61no—
628C22×C3—62no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3—121no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—244no—
637C22×C3C2×D3×D411yescharacteristic
638C22×C3C2×D3×D411yescharacteristic
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—22no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—84no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—61no—
654C3×C4—61no—
655C3×C4—61no—
656C3×C4—81no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4C2×#23511yescharacteristic
660C3×C4C2×#23711yescharacteristic
661C3×C4C2×#23711yescharacteristic
662C3×C4D3×#4111yescharacteristic
663Dic3—21no—
664Dic3—21no—
665Dic3—21no—
666Dic3—41no—
667Dic3—41no—
668Dic3—62no—
669Dic3—61no—
670Dic3—61no—
671Dic3—61no—
672Dic3—61no—
673Dic3—121no—
674Dic3—121no—
675Dic3—121no—
676Dic3—121no—
677Dic3—121no—
678Dic3—241no—
679Dic3—241no—
680C32#311811yescharacteristic, complemented, Sylow
681C23—21no—
682C23—31no—
683C23—64no—
684C23—61no—
685C23—61no—
686C23—241no—
687C23—241no—
688Q8—61no—
689Q8—61no—
690Q8—721no—
691D4—21no—
692D4—32no—
693D4—64no—
694D4—61no—
695D4—61no—
696D4—61no—
697D4—721no—
698D4#379512yes—
699C2×C4—21no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—91no—
708C2×C4—91no—
709C2×C4—181no—
710C2×C4—181no—
711C2×C4—241no—
712C2×C4—241no—
713C2×C4—721no—
714C2×C4—721no—
715C2×C4—721no—
716C2×C4C22×D3211yescharacteristic
717C8—21no—
718C8—61no—
719C8—61no—
720C8—181no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—42no—
725C2×C3—42no—
726C2×C3—82no—
727C2×C3—121no—
728C2×C3—122no—
729C2×C3—241no—
730C2×C3#554711yescharacteristic
731C2×C3#558611yescharacteristic
732C2×C3#576211yescharacteristic
733C2×C3#577411yescharacteristic
734C2×C3#577411yescharacteristic
735C2×C3#577511yescharacteristic
736D3—41no—
737D3—42no—
738D3—81no—
739C22—22no—
740C22—41no—
741C22—41no—
742C22—61no—
743C22—62no—
744C22—61no—
745C22—61no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22—244no—
752C22D32×D411yescharacteristic
753C4—41no—
754C4—61no—
755C4—61no—
756C4—61no—
757C4—121no—
758C4—121no—
759C4—181no—
760C4—181no—
761C4—361no—
762C4—361no—
763C4C2×#379511yescharacteristic
764C4D3×#23711yescharacteristic
765C3—21no—
766C3#7988611yescharacteristic, complemented
767C3#8013611yescharacteristic, complemented
768C2—42no—
769C2—121no—
770C2—122no—
771C2—241no—
772C2#1059405411yescharacteristic
773C2#1059473511yescharacteristic
774C2#1059474911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10591447C2
hypercenter#102D32
hypocenterC32#3118
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. #10595215C2semidirect
2. #10594592C2semidirect
3. #10592458C2semidirect
4. C3×#4785C2semidirect
5. C3×#4776C2semidirect
6. #10591476C2semidirect
8. Dic3×#214C2semidirect
9. #10590834C2semidirect
10. #10590766C2semidirect
11. #10590750C2semidirect
12. #10590697C2semidirect
13. #10590472C2semidirect
14. #10590452C2semidirect
15. #10590447C2semidirect
20. #64097C22semidirect
26. C3×#893C22semidirect
36. #63863C22semidirect
40. Dic3×Dic6C22semidirect
45. #63645C22semidirect
46. #63641C22semidirect
47. #63634C22semidirect
48. C3×#821C22semidirect
50. C3×#815C22semidirect
52. C3×#808C22semidirect
53. #63573C22semidirect
54. #63572C22semidirect
55. #63566C22semidirect
56. #63565C22semidirect
58. #63563C22semidirect
60. Dic3×C3⋊C8C22semidirect
80. #4785D3semidirect
82. #4776D3semidirect
180. #893C2×D3semidirect
212. #821C2×D3semidirect
220. #815C2×D3semidirect
230. #808C2×D3semidirect
680. C32#3118semidirect
766. C3#79886semidirect
767. C3#80136semidirect

Maximal subgroups

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

subgroupindex
#105952152
#105945922
#105924582
C3×#47852
C3×#47762
#105914762
#105914472
Dic3×#2142
#105908342
#105907662
#105907502
#105906972
#105904722
#105904522
#105904472
#801363
#798863