Finite Group Databasebeta

← #11872166

Subgroups — #11872166

Order 1152.

860 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#10593996C211yesmaximal, characteristic, complemented
2#10593876C211yesmaximal, characteristic, complemented
3#10592389C211yesmaximal, characteristic, complemented
4C3×C4×D24C211yesmaximal, characteristic, complemented
5C3×C4×#204C211yesmaximal, characteristic, complemented
6#10590945C211yesmaximal, characteristic
7#10590943C211yesmaximal, characteristic, complemented
8#10590778C211yesmaximal, characteristic, complemented
9#10590776C211yesmaximal, characteristic, complemented
10#10590751C211yesmaximal, characteristic, complemented
11#10590750C211yesmaximal, characteristic, complemented
12#10590715C211yesmaximal, characteristic, complemented
13#10590652C211yesmaximal, characteristic, complemented
14#10590358C211yesmaximal, characteristic, complemented
15#10590344C211yesmaximal, characteristic, complemented
16#79696—31nomaximal
17#79594—31nomaximal
18C2×#3802C2211yescharacteristic
19#64081C2211yescharacteristic
20C2×C3×D24C2211yescharacteristic
21C2×C3×#204C2211yescharacteristic
22C3×C4×D12C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×C4×D12C2211yescharacteristic, complemented
25C3×C4×Dic6C2211yescharacteristic, complemented
26D3×(C2×D3)⋊C4—21no—
27D3×(C2×D3)⋊C4—21no—
28#63919C2211yescharacteristic, complemented
29#63916C2211yescharacteristic
30#63898C2211yescharacteristic
31#63898C2211yescharacteristic
32#63879—21no—
33#63879—21no—
34#63871C2211yescharacteristic
35#63863C2211yescharacteristic, complemented
36#63859—21no—
37#63852—21no—
38#63851—21no—
39#63850—21no—
40#63849C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43C32×C4×C8C2211yescharacteristic, complemented
44#63647C2211yescharacteristic
45#63647C2211yescharacteristic
46#63641C2211yescharacteristic, complemented
47#63641C2211yescharacteristic, complemented
48#63630C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic, complemented
52C3×#818C2211yescharacteristic, complemented
53C3×#817C2211yescharacteristic, complemented
54C3×#816C2211yescharacteristic, complemented
55#63576C2211yescharacteristic, complemented
56#63574C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic, complemented
61#5582—31no—
62#5561—31no—
63#5545—31no—
64#5545—31no—
65C3×C4×SD16—31no—
66C3×C4×D8—31no—
67#5169—31no—
68#5165—31no—
69#5156—31no—
70#5153—31no—
71#5026—31no—
72#5018—31no—
73#5014—31no—
74#5014—31no—
75#4890—31no—
76#4888—31no—
77#4870—31no—
78#4866—31no—
79#4819—31no—
80#4814—31no—
81#4787—31no—
82#4779—31no—
83#4776—31no—
84#4773—31no—
85#4761—31no—
86#4759—31no—
87C4×D24D311yescharacteristic, complemented
88C4×#204D311yescharacteristic, complemented
89#4690—31no—
90#4690—31no—
91#4690—61no—
92C22×D32—21no—
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×C3×D12C2311yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×Dic6C2311yescharacteristic
101C2×#627—21no—
102C2×#626—21no—
103C2×#625—21no—
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106#3802—22no—
107#3802—22no—
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C42C2311yescharacteristic
111#3752D411yescharacteristic
112#3752D411yescharacteristic
113#3750D411yescharacteristic
114#3750D411yescharacteristic
115C4×C3⋊Dic3C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3—21no—
127C3×D24—22no—
128C3×#204—22no—
129#3724—21no—
130Dic3⋊Dic3—21no—
131#3722—21no—
132#3722—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139#3715—22no—
140#3713—22no—
141#3118—91noSylow
142C2×D3×D4—31no—
143C2×D3×D4—31no—
144C2×C3×SD16—31no—
145C2×C3×D8—31no—
146C3×C4×Q8—31no—
147C3×C4×D4—31no—
148C3×C4×D4—31no—
149C3×C4×D4—31no—
150#947—31no—
151#946—31no—
152C2×#215—31no—
153#938—31no—
154#936—31no—
155D4×Dic3—31no—
156D4×Dic3—31no—
157C2×#214—31no—
158C2×#213—31no—
159C2×#213—31no—
160#929—61no—
161C4×#67—61no—
162C4×#67—61no—
163C2×(C2×D3)⋊C4—61no—
164C2×(C2×D3)⋊C4—61no—
165#924—61no—
166C2×D24C2×D311yescharacteristic
167C2×#204C2×D311yescharacteristic
168#897—31no—
169#896—61no—
170#895—31no—
171#894—61no—
172#893—31no—
173#893—31no—
174#892—31no—
175#892—31no—
176#888—31no—
177#888—31no—
178#885—61no—
179#67⋊C4—61no—
180#67⋊C4—61no—
181D3×C22⋊C4—61no—
182D3×C22⋊C4—61no—
183#879—61no—
184#876—61no—
185#875—61no—
186C4×D12C2×D311yescharacteristic
187C4×D12C2×D311yescharacteristic
188C4×D12C2×D311yescharacteristic, complemented
189#872—31no—
190#872—31no—
191#872—61no—
192C4×Dic6C2×D311yescharacteristic, complemented
193C3×#107—31no—
194C3×#106—31no—
195C3×#103—31no—
196C3×#102—31no—
197C3×#102—31no—
198C3×#102—31no—
199C3×C4×C8—21no—
200C3×C4×C8C2×D311yescharacteristic, complemented
201C3×C4×C8C2×D311yescharacteristic, complemented
202#835—31no—
203#832—31no—
204#832—31no—
205#832—31no—
206#821C2×D311yescharacteristic
207#821C2×D311yescharacteristic
208#821C2×D311yescharacteristic, complemented
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—61no—
214(C2×D3)⋊C8—61no—
215#818C2×D311yescharacteristic, complemented
216#817C2×D311yescharacteristic, complemented
217#816C2×D311yescharacteristic, complemented
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—31no—
221Dic3⋊C8—31no—
222Dic3⋊C8—61no—
223Dic3⋊C8—61no—
224#810—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#808—31no—
229#808—31no—
230#807—31no—
231#807—31no—
232#803—31no—
233#803—31no—
234#803—61no—
235C22×C3⋊D3C2×D411yescharacteristic
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C2×D32—24no—
240C2×D32—81no—
241C2×D32—81no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3C2×D411yescharacteristic
246C2×C3⋊Dic3C2×D411yescharacteristic
247C2×C3⋊Dic3C2×D411yescharacteristic
248C4×C3⋊D3—21no—
249C4×C3⋊D3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C3×D12—21no—
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—21no—
259C3×D12#4112yes—
260C3×D12#4112yes—
261C3×C4×D3—81no—
262C3×C4×D3—81no—
263C3×C4×D3—81no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266#627—81no—
267#626—81no—
268#625—24no—
269D3×Dic3—81no—
270D3×Dic3—81no—
271C32×C8—21no—
272C32×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—91no—
284#447—91no—
285#442—91no—
286#440—91no—
287C4×SD16—31no—
288C4×D8—31no—
289#433—91no—
290C23×D3—61no—
291C23×D3—61no—
292C2×C3×Q8—31no—
293C2×C3×D4—31no—
294C2×C3×D4—31no—
295C2×C3×D4—31no—
296C22×C3×C4—61no—
297C22×C3×C4—61no—
298C22×C3×C4—61no—
299C2×#67—61no—
300C2×#67—61no—
301C2×#67—61no—
302C22×Dic3—61no—
303C22×Dic3—61no—
304D3×D4—62no—
305D3×D4—62no—
306D3×D4—62no—
307D3×D4—62no—
308C2×D12—61no—
309C2×D12C22×D311yescharacteristic
310C2×D12C22×D311yescharacteristic
311C2×D12C22×D311yescharacteristic
312C2×C4×D3—21no—
313C2×C4×D3—21no—
314C2×C4×D3—21no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×Dic6—61no—
321C2×Dic6—61no—
322C2×Dic6C22×D311yescharacteristic
323C3×SD16—62no—
324C3×D8—62no—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C2×C3×C8C22×D311yescharacteristic
328C2×C3×C8C22×D311yescharacteristic
329C2×C3×C8C22×D311yescharacteristic
330C2×C3×C8C22×D311yescharacteristic
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—61no—
336C3×C22⋊C4—61no—
337C3×C22⋊C4—61no—
338C3×C22⋊C4—61no—
339C3×C42—21no—
340C3×C42—61no—
341C3×C42C22×D311yescharacteristic
342C3×C42C22×D311yescharacteristic
343#217—61no—
344#217—61no—
345#217—61no—
346#217—61no—
347#217—61no—
348#215—62no—
349#214—62no—
350#213—62no—
351#213—62no—
352(C2×D3)⋊C4—21no—
353(C2×D3)⋊C4—21no—
354(C2×D3)⋊C4—21no—
355(C2×D3)⋊C4—31no—
356(C2×D3)⋊C4—31no—
357(C2×D3)⋊C4—31no—
358(C2×D3)⋊C4—31no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
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—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3C22×D311yescharacteristic
372C4⋊Dic3C22×D311yescharacteristic
373C4⋊Dic3C22×D311yescharacteristic
374C4⋊Dic3C22×D311yescharacteristic
375Dic3⋊C4—21no—
376Dic3⋊C4—31no—
377Dic3⋊C4—31no—
378Dic3⋊C4—31no—
379Dic3⋊C4—31no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385C4×Dic3—21no—
386C4×Dic3—31no—
387C4×Dic3—31no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8—61no—
397D24—22no—
398#204—22no—
399C22×C32C22×D411yescharacteristic
400C2×C3⋊D3—21no—
401C2×C3⋊D3—21no—
402C2×C3⋊D3—21no—
403C2×C3×D3—22no—
404C2×C3×D3—22no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412D32—84no—
413C32×C4—21no—
414C32×C4—21no—
415C32×C4C2×#4111yescharacteristic
416C32×C4C2×#4111yescharacteristic
417C3⋊Dic3—21no—
418C3⋊Dic3—21no—
419C3⋊Dic3—21no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C22×D4—91no—
426C2×SD16—31no—
427C2×SD16—91no—
428C2×D8—31no—
429C2×D8—91no—
430C4⋊Q8—91no—
431#126—181no—
432#124—91no—
433#124—181no—
434#123—181no—
435C22⋊Q8—91no—
436C22⋊Q8—181no—
437#121—91no—
438C4×Q8—31no—
439C4×D4—31no—
440C4×D4—31no—
441C4×D4—31no—
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—31no—
451#107—91no—
452#106—31no—
453#106—91no—
454C4⋊C8—91no—
455C4⋊C8—91no—
456#103—31no—
457#103—91no—
458#102—31no—
459#102—31no—
460#102—31no—
461#102—91no—
462#102—91no—
463#102—91no—
464C22⋊C8—91no—
465C22⋊C8—91no—
466#97—91no—
467C4×C8D3211yescharacteristic, complemented
468C23×C3—61no—
469C23×C3—61no—
470C23×C3—61no—
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—31no—
475C22×D3—31no—
476C22×D3—61no—
477C22×D3—64no—
478C22×D3—64no—
479C22×D3—241no—
480C22×D3—241no—
481C22×D3—241no—
482C22×D3—241no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×D4—32no—
486C3×D4—32no—
487C3×D4—61no—
488C3×D4—61no—
489C3×D4—61no—
490C3×D4—61no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—241no—
500C2×C3×C4—241no—
501C2×C3×C4—241no—
502C2×C3×C4D3×D411yescharacteristic
503C2×C3×C4D3×D411yescharacteristic
504C2×C3×C4D3×D411yescharacteristic
505C2×C3×C4D3×D411yescharacteristic
506C2×C3×C4C23×D311yescharacteristic
507C2×C3×C4C23×D311yescharacteristic
508#67—64no—
509#67—64no—
510#67—241no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—241no—
526C2×Dic3—241no—
527D12—21no—
528D12—21no—
529D12—21no—
530D12—21no—
531D12—241no—
532D12#23512yes—
533D12#23512yes—
534C4×D3—61no—
535C4×D3—61no—
536C4×D3—61no—
537C4×D3—61no—
538C4×D3—81no—
539C4×D3—81no—
540C4×D3—81no—
541C4×D3—121no—
542C4×D3—121no—
543C4×D3—241no—
544C4×D3—241no—
545Dic6—21no—
546Dic6—21no—
547Dic6—241no—
548Dic6—241no—
549C3×C8—21no—
550C3×C8—21no—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—41no—
554C3×C8—41no—
555C3⋊C8—61no—
556C3⋊C8—61no—
557C3⋊C8—61no—
558C3⋊C8—61no—
559C3⋊C8—121no—
560C3⋊C8—121no—
561C2×C32#52511yescharacteristic
562C2×C32#57611yescharacteristic
563C2×C32#57711yescharacteristic
564C3⋊D3—41no—
565C3×D3—42no—
566C3×D3—42no—
567C3×D3—81no—
568C24—181no—
569C2×Q8—31no—
570C2×Q8—181no—
571C2×D4—31no—
572C2×D4—31no—
573C2×D4—31no—
574C2×D4—181no—
575C2×D4—181no—
576C2×D4—182no—
577C2×D4—182no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—91no—
582C22×C4—181no—
583C22×C4—181no—
584SD16—62no—
585SD16—182no—
586D8—62no—
587D8—182no—
588C2×C8—91no—
589C2×C8—91no—
590C2×C8C2×D3211yescharacteristic
591C2×C8C2×D3211yescharacteristic
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—61no—
597C4⋊C4—91no—
598C4⋊C4—91no—
599C4⋊C4—181no—
600C4⋊C4—181no—
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—61no—
614C42—91no—
615C42—181no—
616C42C2×D3211yescharacteristic
617C22×C3—21no—
618C22×C3—62no—
619C22×C3—62no—
620C22×C3—121no—
621C22×C3—121no—
622C22×C3—121no—
623C22×C3—121no—
624C22×C3—121no—
625C22×C3—121no—
626C22×C3—121no—
627C22×C3C2×D3×D411yescharacteristic
628C22×C3C2×D3×D411yescharacteristic
629C2×D3—22no—
630C2×D3—22no—
631C2×D3—41no—
632C2×D3—41no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—61no—
639C2×D3—61no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—244no—
648C2×D3—244no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4—121no—
662C3×C4C2×#23511yescharacteristic
663C3×C4C2×#23511yescharacteristic
664C3×C4D3×#4111yescharacteristic
665C3×C4D3×#4111yescharacteristic
666Dic3—41no—
667Dic3—41no—
668Dic3—41no—
669Dic3—41no—
670Dic3—41no—
671Dic3—61no—
672Dic3—61no—
673Dic3—61no—
674Dic3—61no—
675Dic3—61no—
676Dic3—61no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680C32#311811yescharacteristic, complemented, Sylow
681C23—61no—
682C23—61no—
683C23—61no—
684C23—91no—
685C23—184no—
686C23—721no—
687C23—721no—
688Q8—61no—
689Q8—61no—
690Q8—721no—
691D4—32no—
692D4—32no—
693D4—61no—
694D4—61no—
695D4—61no—
696D4—61no—
697D4—184no—
698D4—721no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—91no—
705C2×C4—91no—
706C2×C4—91no—
707C2×C4—181no—
708C2×C4—181no—
709C2×C4—241no—
710C2×C4—241no—
711C2×C4—241no—
712C2×C4—721no—
713C2×C4—721no—
714C2×C4#380211yescharacteristic
715C2×C4#380211yescharacteristic
716C2×C4C22×D3211yescharacteristic
717C8—21no—
718C8—21no—
719C8—181no—
720C8—181no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—122no—
725C2×C3—122no—
726C2×C3—241no—
727C2×C3#554711yescharacteristic
728C2×C3#554711yescharacteristic
729C2×C3#575711yescharacteristic
730C2×C3#576211yescharacteristic
731C2×C3#576911yescharacteristic
732C2×C3#577011yescharacteristic
733D3—42no—
734D3—42no—
735D3—81no—
736D3—121no—
737D3—121no—
738D3—241no—
739C22—62no—
740C22—62no—
741C22—121no—
742C22—121no—
743C22—121no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—181no—
749C22—181no—
750C22—181no—
751C22—724no—
752C22C2×#380211yescharacteristic
753C4—21no—
754C4—21no—
755C4—121no—
756C4—121no—
757C4—121no—
758C4—121no—
759C4—121no—
760C4—181no—
761C4—181no—
762C4—181no—
763C4D3×#23511yescharacteristic
764C4D3×#23511yescharacteristic
765C3—21no—
766C3#7959411yescharacteristic, complemented
767C3#7969611yescharacteristic, complemented
768C2—122no—
769C2—122no—
770C2—241no—
771C2—361no—
772C2#1059400611yescharacteristic
773C2#1059468611yescharacteristic
774C2#1059468711yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10590945C2
hypercenterC4×C8D32
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #10593996C2semidirect
2. #10593876C2semidirect
3. #10592389C2semidirect
4. C3×C4×D24C2semidirect
5. C3×C4×#204C2semidirect
7. #10590943C2semidirect
8. #10590778C2semidirect
9. #10590776C2semidirect
10. #10590751C2semidirect
11. #10590750C2semidirect
12. #10590715C2semidirect
13. #10590652C2semidirect
14. #10590358C2semidirect
15. #10590344C2semidirect
24. C3×C4×D12C22semidirect
25. C3×C4×Dic6C22semidirect
28. #63919C22semidirect
35. #63863C22semidirect
43. C32×C4×C8C22semidirect
46. #63641C22semidirect
47. #63641C22semidirect
48. #63630C22semidirect
51. C3×#821C22semidirect
52. C3×#818C22semidirect
53. C3×#817C22semidirect
54. C3×#816C22semidirect
55. #63576C22semidirect
56. #63574C22semidirect
57. #63565C22semidirect
60. #63562C22semidirect
87. C4×D24D3semidirect
88. C4×#204D3semidirect
188. C4×D12C2×D3semidirect
192. C4×Dic6C2×D3semidirect
200. C3×C4×C8C2×D3semidirect
201. C3×C4×C8C2×D3semidirect
208. #821C2×D3semidirect
215. #818C2×D3semidirect
216. #817C2×D3semidirect
217. #816C2×D3semidirect
467. C4×C8D32semidirect
680. C32#3118semidirect
766. C3#79594semidirect
767. C3#79696semidirect

Maximal subgroups

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

subgroupindex
#105939962
#105938762
#105923892
C3×C4×D242
C3×C4×#2042
#105909452
#105909432
#105907782
#105907762
#105907512
#105907502
#105907152
#105906522
#105903582
#105903442
#796963
#795943