Finite Group Databasebeta

← #11872138

Subgroups — #11872138

Order 1152.

874 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595215C211yesmaximal, characteristic, complemented
2#10595124C211yesmaximal, characteristic, complemented
3#10592852C211yesmaximal, characteristic, complemented
4C3×#5156C211yesmaximal, characteristic
5C3×Dic3×D8C211yesmaximal, characteristic, complemented
6#10591495C211yesmaximal, characteristic, complemented
7#10591459C211yesmaximal, characteristic, complemented
8#10591434C211yesmaximal, characteristic, complemented
9#10591430C211yesmaximal, characteristic, complemented
10#10591422C211yesmaximal, characteristic, complemented
11#10591405C211yesmaximal, characteristic, complemented
12#10590778C211yesmaximal, characteristic, complemented
13#10590744C211yesmaximal, characteristic, complemented
14#10590708C211yesmaximal, characteristic, complemented
15#10590696C211yesmaximal, characteristic, complemented
16#79992—31nomaximal
17#79594—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×C32×D8C2211yescharacteristic
20#64145C2211yescharacteristic, complemented
21D4×C3⋊Dic3C2211yescharacteristic
22C2×#3754C2211yescharacteristic
23C3×#938C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic, complemented
26C2×C3×#213C2211yescharacteristic
27#67⋊Dic3—21no—
28Dic3×#67—21no—
29D3×#217—21no—
30#63964—21no—
31#63961—21no—
32C2×(C2×D3)⋊Dic3—21no—
33#63959—21no—
34#63956—21no—
35#63919C2211yescharacteristic, complemented
36#63898C2211yescharacteristic
37Dic3×D12C2211yescharacteristic
38#63857C2211yescharacteristic
39#63855C2211yescharacteristic
40#63844C2211yescharacteristic, complemented
41#63841C2211yescharacteristic
42C2×#3716C2211yescharacteristic
43#63659C2211yescharacteristic, complemented
44#63643C2211yescharacteristic, complemented
45#63641C2211yescharacteristic, complemented
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#818C2211yescharacteristic, complemented
52C3×C8×Dic3C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61#5798—31no—
62#5603—31no—
63#5561—31no—
64#5545—31no—
65C3×#447—31no—
66C3×C4×D8—31no—
67#5218—31no—
68#5156D311yescharacteristic
69#5153—31no—
70#5153—31no—
71#5153—31no—
72#5153—61no—
73#5152—31no—
74Dic3×D8D311yescharacteristic, complemented
75#5035—31no—
76#5018—31no—
77#5014—31no—
78#4890—31no—
79#4888—31no—
80#4787—31no—
81#4779—31no—
82#4776—31no—
83#4761—31no—
84#4761—31no—
85#4759—31no—
86#4758—31no—
87#4757—31no—
88#4723—31no—
89#4720—31no—
90C4×#204—31no—
91#4690—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C22×C3×Dic3—21no—
101C3×D3×D4—22no—
102C3×D3×D4—22no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×#627—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C32×D8—22no—
109C2×C32×C8C2311yescharacteristic
110#3757—21no—
111#3757—21no—
112#3757—21no—
113#3754—22no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4×C3⋊Dic3C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#213—22no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127#3724—21no—
128#3724—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3D411yescharacteristic
131Dic3⋊Dic3D411yescharacteristic
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#3716—22no—
141#3118—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#938C2×D311yescharacteristic
154#936—31no—
155#936—31no—
156#936—61no—
157#936—61no—
158#935—61no—
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×#214—31no—
169C2×#214—31no—
170C2×#214—31no—
171C2×#214—61no—
172C2×#213C2×D311yescharacteristic
173#929—61no—
174C4×#67—61no—
175C2×(C2×D3)⋊C4—61no—
176#926—31no—
177#926—31no—
178#924—31no—
179#924—61no—
180C2×#204—31no—
181#897—31no—
182#893—31no—
183#892—31no—
184#888—31no—
185#888—31no—
186#887—31no—
187#885—61no—
188#67⋊C4—61no—
189D3×C22⋊C4—61no—
190#879—61no—
191#879—61no—
192#878—61no—
193C4×D12—31no—
194#872—31no—
195C4×Dic6—31no—
196C3×#107—31no—
197C3×#102—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×#102—31no—
201C3×C22⋊C8—31no—
202C3×C4×C8—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#821C2×D311yescharacteristic
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8C2×D311yescharacteristic
214#818C2×D311yescharacteristic, complemented
215#817—31no—
216#817—31no—
217#816—31no—
218#816—31no—
219#816—31no—
220#816—61no—
221#815—31no—
222Dic3⋊C8—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—61no—
227C8×Dic3C2×D311yescharacteristic, complemented
228#810—31no—
229#809—31no—
230#808—31no—
231#808—31no—
232#807—31no—
233#807—31no—
234#803—31no—
235C23×C32—21no—
236C23×C32—21no—
237C22×C3×D3—21no—
238C22×C3×D3—24no—
239C22×C3×D3—81no—
240C22×C3×D3—81no—
241C22×C3×D3C2×D411yescharacteristic
242C32×D4—21no—
243C32×D4—21no—
244C32×D4—21no—
245C32×D4#4112yes—
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—81no—
250C2×C3⋊Dic3C2×D411yescharacteristic
251C2×C3⋊Dic3C2×D411yescharacteristic
252#634—21no—
253#634—21no—
254C3×#67—24no—
255C3×#67—81no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—81no—
260C2×C3×Dic3—81no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268#627—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—91no—
284#447—31no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—31no—
289#433—91no—
290C24×C3—61no—
291C23×D3—21no—
292C2×C3×D4—21no—
293C2×C3×D4—21no—
294C2×C3×D4—31no—
295C2×C3×D4—61no—
296C2×C3×D4—62no—
297C2×C3×D4—62no—
298C2×C3×D4—61no—
299C2×C3×D4C22×D311yescharacteristic
300C2×C3×D4C22×D311yescharacteristic
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C22×D311yescharacteristic
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C2×#67—21no—
307C2×#67—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—121no—
315D3×D4—22no—
316D3×D4—22no—
317C2×D12C22×D311yescharacteristic
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3C22×D311yescharacteristic
321C2×Dic6—31no—
322C2×Dic6—31no—
323C2×Dic6—61no—
324C2×Dic6—61no—
325C2×Dic6—61no—
326C3×D8—22no—
327C3×D8—22no—
328C3×D8—42no—
329C3×D8—62no—
330C2×C3×C8—21no—
331C2×C3×C8—31no—
332C2×C3×C8—31no—
333C2×C3×C8C22×D311yescharacteristic
334C2×C3×C8C22×D311yescharacteristic
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C22⋊C4—61no—
339C3×C22⋊C4—61no—
340C3×C22⋊C4—61no—
341C3×C42—31no—
342#217—21no—
343#217—21no—
344#217—21no—
345#217—31no—
346#217—31no—
347#217—61no—
348#217—61no—
349#217—61no—
350#217—61no—
351#217—61no—
352#217—61no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—121no—
358#217—121no—
359#217—121no—
360#214—62no—
361#214—62no—
362#214—62no—
363#214—122no—
364#213—22no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—31no—
381Dic3⋊C4—31no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387C4×Dic3—31no—
388C4×Dic3—31no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3C22×D311yescharacteristic
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—61no—
398C2×C3⋊C8C22×D311yescharacteristic
399C2×C3⋊C8C22×D311yescharacteristic
400#204—62no—
401C22×C32—22no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32C22×D411yescharacteristic
408C2×C3×D3—21no—
409C2×C3×D3—22no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—84no—
415C32×C4C2×#4111yescharacteristic
416C32×C4C2×#4111yescharacteristic
417C3⋊Dic3—21no—
418C3⋊Dic3—21no—
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C22×D4—31no—
428C2×SD16—91no—
429C2×SD16—91no—
430C2×D8—31no—
431C2×D8D3211yescharacteristic
432C4⋊Q8—91no—
433#126—181no—
434#124—91no—
435#124—181no—
436#123—181no—
437C22⋊Q8—91no—
438C22⋊Q8—181no—
439#121—31no—
440C4×Q8—91no—
441C4×D4—31no—
442C4×D4—31no—
443C4×D4—91no—
444C4×D4—91no—
445C4×D4—91no—
446C4×D4—181no—
447C4×D4—181no—
448#117—91no—
449#117—91no—
450C2×C22⋊C4—181no—
451C2×C22⋊C4—181no—
452#107—31no—
453#107—91no—
454#106—91no—
455#106—91no—
456C4⋊C8—91no—
457C4⋊C8—91no—
458#103—91no—
459#103—91no—
460#102—31no—
461#102—31no—
462#102—31no—
463#102—31no—
464#102—91no—
465#102—91no—
466C22⋊C8—31no—
467C22⋊C8—91no—
468#97—91no—
469C4×C8—31no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—31no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—64no—
478C23×C3—61no—
479C23×C3—241no—
480C23×C3—241no—
481C22×D3—21no—
482C22×D3—24no—
483C22×D3—81no—
484C22×D3—81no—
485C22×D3D3×D411yescharacteristic
486C3×D4—21no—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—22no—
493C3×D4—32no—
494C3×D4—41no—
495C3×D4—41no—
496C3×D4—41no—
497C3×D4—64no—
498C3×D4—61no—
499C3×D4—241no—
500C3×D4#23512yes—
501C3×D4#23712yes—
502C2×C3×C4—21no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—241no—
512C2×C3×C4—241no—
513C2×C3×C4C23×D311yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515#67—24no—
516#67—81no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—81no—
531C2×Dic3—81no—
532C2×Dic3—121no—
533C2×Dic3—121no—
534C2×Dic3—241no—
535C2×Dic3—241no—
536C2×Dic3—241no—
537C2×Dic3—241no—
538C2×Dic3—242no—
539C2×Dic3D3×D411yescharacteristic
540C2×Dic3D3×D411yescharacteristic
541C2×Dic3D3×D411yescharacteristic
542D12—21no—
543D12#23712yes—
544C4×D3—21no—
545C4×D3—21no—
546C4×D3—241no—
547C4×D3—241no—
548Dic6—61no—
549Dic6—61no—
550Dic6—61no—
551Dic6—61no—
552Dic6—121no—
553Dic6—121no—
554Dic6—241no—
555Dic6—241no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—41no—
559C3×C8—61no—
560C3×C8—61no—
561C3⋊C8—21no—
562C3⋊C8—21no—
563C3⋊C8—61no—
564C3⋊C8—61no—
565C3⋊C8—121no—
566C2×C32—42no—
567C2×C32—81no—
568C2×C32#52511yescharacteristic
569C2×C32#57611yescharacteristic
570C2×C32#57711yescharacteristic
571C3×D3—41no—
572C3×D3—42no—
573C24—61no—
574C2×Q8—91no—
575C2×Q8—181no—
576C2×D4—31no—
577C2×D4—61no—
578C2×D4—62no—
579C2×D4—62no—
580C2×D4—61no—
581C2×D4C2×D3211yescharacteristic
582C2×D4C2×D3211yescharacteristic
583C22×C4—31no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—181no—
587C22×C4—181no—
588C22×C4—181no—
589SD16—182no—
590SD16—182no—
591D8—22no—
592D8—62no—
593C2×C8—31no—
594C2×C8—31no—
595C2×C8—91no—
596C2×C8C2×D3211yescharacteristic
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—91no—
601C4⋊C4—91no—
602C4⋊C4—91no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—91no—
610C22⋊C4—91no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C42—31no—
619C42—91no—
620C42—181no—
621C42—181no—
622C22×C3—22no—
623C22×C3—22no—
624C22×C3—21no—
625C22×C3—42no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—62no—
640C22×C3—81no—
641C22×C3—81no—
642C22×C3—81no—
643C22×C3—81no—
644C22×C3—81no—
645C22×C3—121no—
646C22×C3—121no—
647C22×C3—244no—
648C22×C3C2×D3×D411yescharacteristic
649C22×C3C2×D3×D411yescharacteristic
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—21no—
653C2×D3—22no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—84no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4C2×#23511yescharacteristic
666C3×C4C2×#23711yescharacteristic
667C3×C4C2×#23711yescharacteristic
668C3×C4D3×#4111yescharacteristic
669Dic3—21no—
670Dic3—21no—
671Dic3—21no—
672Dic3—41no—
673Dic3—41no—
674Dic3—41no—
675Dic3—61no—
676Dic3—61no—
677Dic3—61no—
678Dic3—61no—
679Dic3—121no—
680Dic3—121no—
681Dic3—121no—
682Dic3—121no—
683Dic3—121no—
684Dic3—121no—
685Dic3—241no—
686Dic3—241no—
687C32#311811yescharacteristic, complemented, Sylow
688C23—21no—
689C23—21no—
690C23—31no—
691C23—64no—
692C23—61no—
693C23—241no—
694C23—241no—
695Q8—181no—
696Q8—181no—
697Q8—721no—
698D4—21no—
699D4—21no—
700D4—21no—
701D4—32no—
702D4—64no—
703D4—61no—
704D4—241no—
705D4#380412yes—
706C2×C4—31no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—91no—
715C2×C4—91no—
716C2×C4—181no—
717C2×C4—181no—
718C2×C4—241no—
719C2×C4—241no—
720C2×C4—721no—
721C2×C4—721no—
722C2×C4—721no—
723C2×C4C22×D3211yescharacteristic
724C8—21no—
725C8—61no—
726C8—61no—
727C8—181no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—42no—
732C2×C3—42no—
733C2×C3—82no—
734C2×C3—81no—
735C2×C3—81no—
736C2×C3—121no—
737C2×C3—122no—
738C2×C3—161no—
739C2×C3#554711yescharacteristic
740C2×C3#558611yescharacteristic
741C2×C3#575711yescharacteristic
742C2×C3#575711yescharacteristic
743C2×C3#577011yescharacteristic
744C2×C3#577511yescharacteristic
745D3—41no—
746D3—42no—
747C22—22no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—61no—
754C22—62no—
755C22—61no—
756C22—61no—
757C22—121no—
758C22—121no—
759C22—244no—
760C22D32×D411yescharacteristic
761C4—61no—
762C4—61no—
763C4—61no—
764C4—121no—
765C4—121no—
766C4—121no—
767C4—181no—
768C4—181no—
769C4—361no—
770C4—361no—
771C4D3×#23711yescharacteristic
772C4C2×#380411yescharacteristic
773C3—21no—
774C3#7959411yescharacteristic, complemented
775C3#7999211yescharacteristic, complemented
776C2—42no—
777C2—81no—
778C2—121no—
779C2—122no—
780C2#1059473111yescharacteristic
781C2#1059473611yescharacteristic
782C2#1059512911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
prime radicalC3×#5156C2
hypercenterC2×D8D32
hypocenterC32#3118
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. #10595124C2semidirect
3. #10592852C2semidirect
5. C3×Dic3×D8C2semidirect
6. #10591495C2semidirect
7. #10591459C2semidirect
8. #10591434C2semidirect
9. #10591430C2semidirect
10. #10591422C2semidirect
11. #10591405C2semidirect
12. #10590778C2semidirect
13. #10590744C2semidirect
14. #10590708C2semidirect
15. #10590696C2semidirect
20. #64145C22semidirect
25. C3×D4×Dic3C22semidirect
35. #63919C22semidirect
40. #63844C22semidirect
43. #63659C22semidirect
44. #63643C22semidirect
45. #63641C22semidirect
48. C3×#832C22semidirect
51. C3×#818C22semidirect
52. C3×C8×Dic3C22semidirect
53. #63576C22semidirect
54. #63573C22semidirect
55. #63573C22semidirect
56. #63572C22semidirect
57. #63567C22semidirect
60. #63554C22semidirect
74. Dic3×D8D3semidirect
167. D4×Dic3C2×D3semidirect
209. #832C2×D3semidirect
214. #818C2×D3semidirect
227. C8×Dic3C2×D3semidirect
687. C32#3118semidirect
774. C3#79594semidirect
775. C3#79992semidirect

Maximal subgroups

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

subgroupindex
#105952152
#105951242
#105928522
C3×#51562
C3×Dic3×D82
#105914952
#105914592
#105914342
#105914302
#105914222
#105914052
#105907782
#105907442
#105907082
#105906962
#799923
#795943