Finite Group Databasebeta

← #11870395

Subgroups — #11870395

Order 1152.

849 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594523C211yesmaximal, characteristic
2#10594511C211yesmaximal, characteristic, complemented
3#10592584C211yesmaximal, characteristic, complemented
4C3×#4888C211yesmaximal, characteristic, complemented
5C3×#4881C211yesmaximal, characteristic, complemented
6#10590955C211yesmaximal, characteristic, complemented
7#10590686C211yesmaximal, characteristic, complemented
8#10590677C211yesmaximal, characteristic, complemented
9#10590671C211yesmaximal, characteristic, complemented
10#10590610C211yesmaximal, characteristic, complemented
11D3×#808C211yesmaximal, characteristic, complemented
12#10590526C211yesmaximal, characteristic, complemented
13#10590445C211yesmaximal, characteristic, complemented
14#10590439C211yesmaximal, characteristic, complemented
15#10590424C211yesmaximal, characteristic, complemented
16#81521—31nomaximal
17#79222—31nomaximal
18C2×#3799C2211yescharacteristic
19C2×#3798C2211yescharacteristic
20#64104C2211yescharacteristic
21#64101C2211yescharacteristic
22C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
23C3×#897C2211yescharacteristic
24C3×#892C2211yescharacteristic
25C3×#892C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C4×#627—21no—
28#63910—21no—
29#63909—21no—
30#63909C2211yescharacteristic
31#63906—21no—
32#63902—21no—
33#63900C2211yescharacteristic
34#63895—21no—
35D3×C4⋊Dic3C2211yescharacteristic
36D3×C4⋊Dic3C2211yescharacteristic
37#63880—21no—
38#63880—21no—
39#63871C2211yescharacteristic
40C2×D3×C3⋊C8C2211yescharacteristic
41C32×#107C2211yescharacteristic
42#63648C2211yescharacteristic
43#63647C2211yescharacteristic
44#63636C2211yescharacteristic
45#63635C2211yescharacteristic
46C3×(C2×D3)⋊C8C2211yescharacteristic
47C3×#817C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#808C2211yescharacteristic
51C3×#808C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63574C2211yescharacteristic
54#63573C2211yescharacteristic
55#63566C2211yescharacteristic
56#63565C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63557C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61#5629—31no—
62#5523—31no—
63#5523—31no—
64#5510—31no—
65C3×#485—31no—
66C3×#428—31no—
67#5133—31no—
68#5129—31no—
69#5043—31no—
70#5003—31no—
71#5002—31no—
72C2×#808—31no—
73#4888—31no—
74#4888D311yescharacteristic, complemented
75#4885—31no—
76#4885—31no—
77#4885—31no—
78#4885—61no—
79#4881D311yescharacteristic, complemented
80#4863—31no—
81#4863—31no—
82#4863—31no—
83#4862—31no—
84#4862—31no—
85D3×#106—31no—
86#4815—31no—
87#4805—31no—
88#4804—31no—
89#4803—31no—
90#4735—31no—
91#4727—31no—
92C2×C4⋊(C3⋊D3)—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×C3×C4×D3—21no—
96C2×C3×C4×D3C2311yescharacteristic
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#627D411yescharacteristic
100C2×#626—21no—
101C2×#626—21no—
102C2×#626D411yescharacteristic
103C2×#626D411yescharacteristic
104C2×#625D411yescharacteristic
105C2×#624—21no—
106C2×#624—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109#3799—22no—
110#3799—22no—
111#3798—22no—
112#3798—22no—
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116#3752—21no—
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4×C3⋊Dic3—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3—21no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C3×ΓL(1,𝔽25)—22no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138#3722—21no—
139#3722—21no—
140D3×C3⋊C8—22no—
141#3099—91noSylow
142C2×#239—31no—
143C2×#235—31no—
144C2×#235—31no—
145C2×#235—31no—
146C2×C3×M16—31no—
147C3×C22⋊Q8—31no—
148C3×#117—31no—
149C3×#117—31no—
150C2×C3×C4⋊C4—31no—
151#946—31no—
152#930—31no—
153#930—61no—
154#930—61no—
155C2×C4⋊Dic3—31no—
156C2×C4⋊Dic3—31no—
157C22×C3⋊C8—31no—
158C2×ΓL(1,𝔽25)C2×D311yescharacteristic
159C2×D3×C8—31no—
160#897—31no—
161#897—61no—
162#897C2×D311yescharacteristic
163#896—61no—
164#895—31no—
165#895—31no—
166#895—31no—
167#895—61no—
168#895—61no—
169#895—61no—
170#892—31no—
171#892—31no—
172#892—61no—
173#892C2×D311yescharacteristic
174#892C2×D311yescharacteristic
175D3×C4⋊C4—31no—
176D3×C4⋊C4—31no—
177D3×C4⋊C4—31no—
178D3×C4⋊C4—31no—
179D3×C4⋊C4C2×D311yescharacteristic
180#884—61no—
181#884—61no—
182#67⋊C4—61no—
183#67⋊C4—61no—
184#67⋊C4—61no—
185#67⋊C4—61no—
186C4×D12—61no—
187C4×D12—61no—
188C4×Dic6—61no—
189C4×Dic6—61no—
190C3×#107—21no—
191C3×#107—31no—
192C3×#107C2×D311yescharacteristic
193C3×#107C2×D311yescharacteristic
194C3×#106—31no—
195C3×#106—31no—
196C3×#106—31no—
197C3×#103—31no—
198C3×#103—31no—
199C3×C22⋊C8—31no—
200#835—31no—
201#835—31no—
202#830—31no—
203#821—31no—
204#821—31no—
205#821—31no—
206#821—31no—
207#821—61no—
208(C2×D3)⋊C8—31no—
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)⋊C8C2×D311yescharacteristic
215#817—31no—
216#817C2×D311yescharacteristic
217#816—31no—
218#816C2×D311yescharacteristic
219#810—31no—
220#810C2×D311yescharacteristic
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—61no—
226#808—31no—
227#808—31no—
228#808—31no—
229#808—31no—
230#808—31no—
231#808—61no—
232#808C2×D311yescharacteristic
233#808C2×D311yescharacteristic
234#807C2×D311yescharacteristic
235C22×C3⋊D3—21no—
236C22×C3⋊D3C2×D411yescharacteristic
237C22×C3×D3C2×D411yescharacteristic
238C22×C3×D3C2×D411yescharacteristic
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4C2411yescharacteristic
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3C2×D411yescharacteristic
244C4⋊(C3⋊D3)—21no—
245C4⋊(C3⋊D3)—21no—
246C4⋊(C3⋊D3)—81no—
247C4×C3⋊D3—21no—
248C4×C3⋊D3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×C4×D3—21no—
256C3×C4×D3—21no—
257C3×C4×D3—81no—
258C3×C4×D3#4112yes—
259C3×C4×D3#4112yes—
260C3×Dic6—21no—
261C3×Dic6—21no—
262#627—22no—
263#626—22no—
264#626—22no—
265#626—42no—
266#626—81no—
267#625—22no—
268#624—42no—
269#624—81no—
270D3×Dic3—81no—
271D3×Dic3—81no—
272C32×C8—21no—
273C3⋊(C3⋊C8)—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#537—91no—
277#520—91no—
278#485—31no—
279#485—91no—
280#483—91no—
281#483—91no—
282#482—91no—
283#482—91no—
284#481—91no—
285#481—91no—
286#428—31no—
287C2×#106—91no—
288#417—91no—
289#416—91no—
290#408—91no—
291C2×C3×Q8—31no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—61no—
295C2×#67—31no—
296C2×#67—31no—
297C2×#67—31no—
298C2×#67—31no—
299C2×#67—61no—
300C2×#67—61no—
301C22×Dic3—61no—
302C22×Dic3—61no—
303#239—62no—
304#239—62no—
305#235—62no—
306#235—62no—
307#235—62no—
308#235—62no—
309#235—62no—
310#235—62no—
311C2×D12—31no—
312C2×D12—31no—
313C2×D12—31no—
314C2×D12—31no—
315C2×D12—61no—
316C2×D12—61no—
317C2×D12—61no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12—121no—
321C2×C4×D3—21no—
322C2×C4×D3—31no—
323C2×C4×D3—31no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3C22×D311yescharacteristic
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6C22×D311yescharacteristic
336C3×M16—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—21no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C42—61no—
357C3×C42—61no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—21no—
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—121no—
370(C2×D3)⋊C4—121no—
371C4⋊Dic3—21no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381Dic3⋊C4—21no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387C4×Dic3—21no—
388C4×Dic3—21no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—121no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—61no—
395C2×C3⋊C8—62no—
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398ΓL(1,𝔽25)—22no—
399D3×C8—62no—
400C22×C32C22×D411yescharacteristic
401C2×C3⋊D3—21no—
402C2×C3⋊D3—21no—
403C2×C3⋊D3—21no—
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3#12312yes—
413C32×C4—41no—
414C32×C4—41no—
415C32×C4C2×#4111yescharacteristic
416C32×C4C2×#4111yescharacteristic
417C3⋊Dic3—21no—
418C3⋊Dic3—41no—
419C3×Dic3—21no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3#12312yes—
425C2×#41—91no—
426C2×#41—91no—
427C2×M16—31no—
428C22×C8—91no—
429C22⋊Q8—31no—
430C22⋊Q8—91no—
431C22⋊Q8—181no—
432#121—91no—
433#121—91no—
434#121—181no—
435#121—181no—
436#121—181no—
437C4×Q8—181no—
438C4×D4—181no—
439C4×D4—181no—
440C4×D4—181no—
441#117—31no—
442#117—31no—
443#117—91no—
444C2×C4⋊C4—31no—
445C2×C4⋊C4—91no—
446C2×C4⋊C4—91no—
447C2×C4⋊C4—91no—
448#107—31no—
449#107D3211yescharacteristic
450#106—31no—
451#106—31no—
452#106—31no—
453#106—91no—
454#106—91no—
455#106—91no—
456#103—31no—
457#103—31no—
458#103—91no—
459#103—91no—
460#102—91no—
461#102—91no—
462#102—91no—
463#102—91no—
464C22⋊C8—31no—
465C22⋊C8—91no—
466C22⋊C8—91no—
467C22⋊C8—91no—
468C23×C3—31no—
469C23×C3—31no—
470C22×D3—31no—
471C22×D3—31no—
472C22×D3—61no—
473C22×D3—61no—
474C22×D3—61no—
475C22×D3—121no—
476C22×D3D3×D411yescharacteristic
477C22×D3D3×D411yescharacteristic
478C3×Q8—61no—
479C3×Q8—61no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—31no—
486C2×C3×C4—32no—
487C2×C3×C4—32no—
488C2×C3×C4—31no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—241no—
498C2×C3×C4C23×D311yescharacteristic
499C2×C3×C4C23×D311yescharacteristic
500#67—62no—
501#67—62no—
502#67—62no—
503#67—62no—
504#67—122no—
505#67—241no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—31no—
511C2×Dic3—31no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—121no—
516C2×Dic3—241no—
517C2×Dic3—241no—
518C2×Dic3D3×D411yescharacteristic
519C2×Dic3D3×D411yescharacteristic
520D12—62no—
521D12—62no—
522D12—61no—
523D12—61no—
524D12—61no—
525D12—61no—
526D12—121no—
527D12—121no—
528D12—122no—
529D12—241no—
530D12—241no—
531D12—242no—
532D12—241no—
533C4×D3—21no—
534C4×D3—21no—
535C4×D3—61no—
536C4×D3—61no—
537C4×D3—61no—
538C4×D3—61no—
539C4×D3—81no—
540C4×D3—121no—
541C4×D3—121no—
542C4×D3—122no—
543C4×D3—122no—
544C4×D3—241no—
545C4×D3—241no—
546C4×D3—241no—
547C4×D3—241no—
548C4×D3#23512yes—
549C4×D3#23912yes—
550Dic6—21no—
551Dic6—21no—
552Dic6—62no—
553Dic6—62no—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—41no—
557C3×C8—61no—
558C3×C8—61no—
559C3⋊C8—21no—
560C3⋊C8—21no—
561C3⋊C8—61no—
562C3⋊C8—61no—
563C3⋊C8—121no—
564C2×C32C2×#12311yescharacteristic
565C2×C32#57711yescharacteristic
566C2×C32#57711yescharacteristic
567C3⋊D3—41no—
568C3⋊D3—81no—
569C3×D3—22no—
570C3×D3—41no—
571#41—182no—
572#41—182no—
573#41—182no—
574#41—182no—
575C2×Q8—31no—
576C2×Q8—91no—
577C2×D4—91no—
578C2×D4—91no—
579C2×D4—91no—
580C2×D4—91no—
581C2×D4—181no—
582C2×D4—181no—
583C2×D4—181no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—61no—
587C22×C4—91no—
588C22×C4—181no—
589C22×C4—181no—
590C22×C4—181no—
591C22×C4—181no—
592M16—62no—
593C2×C8—31no—
594C2×C8—31no—
595C2×C8—91no—
596C2×C8—182no—
597C2×C8C2×D3211yescharacteristic
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—91no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4C2×D3211yescharacteristic
609C4⋊C4C2×D3211yescharacteristic
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C42—61no—
618C42—61no—
619C42—181no—
620C22×C3—21no—
621C22×C3—32no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3C2×D3×D411yescharacteristic
628C22×C3C2×D3×D411yescharacteristic
629C2×D3—21no—
630C2×D3—21no—
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—61no—
635C2×D3—61no—
636C2×D3—61no—
637C2×D3—61no—
638C2×D3—61no—
639C2×D3—61no—
640C2×D3—121no—
641C2×D3—121no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—121no—
649C2×D3—241no—
650C2×D3—241no—
651C2×D3—241no—
652C2×D3#89412yes—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—32no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—61no—
661C3×C4—81no—
662C3×C4—81no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4C2×#23511yescharacteristic
668C3×C4C2×#23911yescharacteristic
669C3×C4D3×#4111yescharacteristic
670C3×C4D3×#4111yescharacteristic
671Dic3—21no—
672Dic3—41no—
673Dic3—41no—
674Dic3—41no—
675Dic3—41no—
676Dic3—61no—
677Dic3—61no—
678Dic3—121no—
679Dic3—121no—
680Dic3—121no—
681Dic3—241no—
682Dic3#89412yes—
683C32#309911yescharacteristic, complemented, Sylow
684C23—31no—
685C23—31no—
686C23—91no—
687C23—181no—
688Q8—61no—
689Q8—61no—
690Q8—182no—
691D4—182no—
692D4—182no—
693D4—182no—
694D4—181no—
695D4—181no—
696D4—362no—
697D4—721no—
698D4—721no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—31no—
702C2×C4—32no—
703C2×C4—32no—
704C2×C4—31no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—91no—
712C2×C4—181no—
713C2×C4—181no—
714C2×C4—181no—
715C2×C4—241no—
716C2×C4—362no—
717C2×C4—721no—
718C2×C4—721no—
719C2×C4—721no—
720C2×C4C22×D3211yescharacteristic
721C8—21no—
722C8—61no—
723C8—61no—
724C8—181no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—62no—
729C2×C3—121no—
730C2×C3C2×#89411yescharacteristic
731C2×C3D3×#12311yescharacteristic
732C2×C3#577011yescharacteristic
733C2×C3#577511yescharacteristic
734C2×C3#577811yescharacteristic
735C2×C3#577811yescharacteristic
736D3—22no—
737D3—41no—
738D3—121no—
739D3—121no—
740D3—241no—
741D3—241no—
742D3—241no—
743D3—481no—
744C22—32no—
745C22—61no—
746C22—61no—
747C22—61no—
748C22—61no—
749C22—61no—
750C22—181no—
751C22—181no—
752C22—181no—
753C22—361no—
754C22—361no—
755C22—361no—
756C22D32×D411yescharacteristic
757C4—32no—
758C4—41no—
759C4—41no—
760C4—61no—
761C4—121no—
762C4—121no—
763C4—121no—
764C4—121no—
765C4—181no—
766C4—361no—
767C4D3×#23511yescharacteristic
768C4D3×#23911yescharacteristic
769C3—21no—
770C3#7922211yescharacteristic, complemented
771C3#8152111yescharacteristic, complemented
772C2—62no—
773C2—121no—
774C2—361no—
775C2—721no—
776C2D3×#89411yescharacteristic
777C2#1059473611yescharacteristic
778C2#1059476711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radical#10594523C2
hypercenter#107D32
hypocenterC32#3099
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10594511C2semidirect
3. #10592584C2semidirect
4. C3×#4888C2semidirect
5. C3×#4881C2semidirect
6. #10590955C2semidirect
7. #10590686C2semidirect
8. #10590677C2semidirect
9. #10590671C2semidirect
10. #10590610C2semidirect
11. D3×#808C2semidirect
12. #10590526C2semidirect
13. #10590445C2semidirect
14. #10590439C2semidirect
15. #10590424C2semidirect
74. #4888D3semidirect
79. #4881D3semidirect
683. C32#3099semidirect
770. C3#79222semidirect
771. C3#81521semidirect

Maximal subgroups

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

subgroupindex
#105945232
#105945112
#105925842
C3×#48882
C3×#48812
#105909552
#105906862
#105906772
#105906712
#105906102
D3×#8082
#105905262
#105904452
#105904392
#105904242
#815213
#792223