Finite Group Databasebeta

← #11872185

Subgroups — #11872185

Order 1152.

873 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595396C211yesmaximal, characteristic, complemented
2#10595215C211yesmaximal, characteristic, complemented
3SD16×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#5169C211yesmaximal, characteristic, complemented
5C3×#5165C211yesmaximal, characteristic, complemented
6#10591572C211yesmaximal, characteristic, complemented
7#10591567C211yesmaximal, characteristic, complemented
8#10591559C211yesmaximal, characteristic, complemented
9#10591447C211yesmaximal, characteristic
10#10591436C211yesmaximal, characteristic, complemented
11#10591410C211yesmaximal, characteristic, complemented
12#10590837C211yesmaximal, characteristic, complemented
13#10590757C211yesmaximal, characteristic, complemented
14#10590740C211yesmaximal, characteristic, complemented
15#10590698C211yesmaximal, characteristic, complemented
16#80509—31nomaximal
17#80136—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic, complemented
21D4×C3⋊Dic3C2211yescharacteristic
22C3×#947C2211yescharacteristic, complemented
23C3×#946C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27#67⋊Dic3—21no—
28Dic3×#67—21no—
29D3×#217—21no—
30C2×(C2×D3)⋊Dic3—21no—
31#63918C2211yescharacteristic, complemented
32#63915—21no—
33#63908C2211yescharacteristic
34#63898C2211yescharacteristic
35#63898C2211yescharacteristic, complemented
36#63893—21no—
37Dic3×D12C2211yescharacteristic
38#63891—21no—
39#63862—21no—
40#63855C2211yescharacteristic
41#63841C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43#63662C2211yescharacteristic, complemented
44#63659C2211yescharacteristic
45#63644C2211yescharacteristic, complemented
46C8×C3⋊Dic3C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic, complemented
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63555C2211yescharacteristic, complemented
61#5798—31no—
62#5682—31no—
63#5643—31no—
64#5545—31no—
65C3×#463—31no—
66C3×#450—31no—
67#5217—31no—
68#5169D311yescharacteristic, complemented
69#5165—31no—
70#5165D311yescharacteristic, complemented
71#5164—31no—
72Dic3×SD16—31no—
73Dic3×SD16—31no—
74Dic3×SD16—61no—
75#5156—31no—
76#5152—31no—
77#5057—31no—
78#5045—31no—
79#5007—31no—
80#4842—31no—
81#4840—31no—
82#4817—31no—
83#4815—31no—
84#4785—31no—
85#4779—31no—
86#4761—31no—
87#4759—31no—
88#4756—31no—
89#4756—31no—
90#4737—31no—
91#4720—31no—
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C3⋊Dic3—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×D3C2311yescharacteristic
103C2×#627—21no—
104C2×#625—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C32×SD16—22no—
109C2×C32×C8C2311yescharacteristic
110#3757—21no—
111C4⋊(C3⋊Dic3)—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4×C3⋊Dic3—21no—
115C4×C3⋊Dic3C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#215—22no—
119C3×#213—22no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
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)⋊Dic3—21no—
137(C2×D3)⋊Dic3D411yescharacteristic
138(C2×D3)⋊Dic3D411yescharacteristic
139Dic32—21no—
140#3713—22no—
141#3118—91noSylow
142C22×C3×D4—31no—
143C2×D3×D4C2×D311yescharacteristic
144C2×C3×SD16—21no—
145C2×C3×SD16—31no—
146C2×C3×SD16C2×D311yescharacteristic
147C2×C3×SD16C2×D311yescharacteristic
148C2×C3×D8—31no—
149C3×#124—31no—
150C3×C22⋊Q8—31no—
151C3×C4×D4—31no—
152C2×#217—61no—
153C2×#217—61no—
154#947C2×D311yescharacteristic, complemented
155#946C2×D311yescharacteristic
156Q8×Dic3—31no—
157Q8×Dic3—31no—
158Q8×Dic3—61no—
159C2×#215C2×D311yescharacteristic
160#938—31no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163D4×Dic3—31no—
164D4×Dic3—31no—
165D4×Dic3—31no—
166D4×Dic3—61no—
167D4×Dic3—61no—
168D4×Dic3—61no—
169D4×Dic3C2×D311yescharacteristic
170C2×#213—31no—
171C2×#213—31no—
172C2×#213C2×D311yescharacteristic
173#930—31no—
174C4×#67—61no—
175C2×(C2×D3)⋊C4—61no—
176#926—31no—
177#926—31no—
178#898—61no—
179#897—61no—
180#893—31no—
181#893—31no—
182#892—31no—
183#888—31no—
184#886—61no—
185#885—61no—
186#885—61no—
187#883—61no—
188#67⋊C4—61no—
189D3×C22⋊C4—61no—
190#879—61no—
191#878—61no—
192C4×D12—31no—
193#872—31no—
194#869—31no—
195C3×C4⋊C8—31no—
196C3×#103—31no—
197C3×#102—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×C22⋊C8—31no—
201#835—31no—
202#835—31no—
203#835—61no—
204#835C2×D311yescharacteristic, complemented
205#832—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—61no—
210#832C2×D311yescharacteristic
211#830—31no—
212#821—31no—
213#821—31no—
214#821C2×D311yescharacteristic
215#821C2×D311yescharacteristic, complemented
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8C2×D311yescharacteristic
218#818—31no—
219#817—31no—
220#817—31no—
221#817—31no—
222#817—61no—
223#815—31no—
224#815—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8C2×D311yescharacteristic, complemented
227C8×Dic3—31no—
228C8×Dic3—31no—
229C8×Dic3—61no—
230#808—31no—
231#807—31no—
232#807—31no—
233#807—31no—
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×Q8—21no—
243C32×Q8—21no—
244C32×D4—21no—
245C32×D4#4112yes—
246C2×C32×C4—21no—
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—81no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C3×#67—24no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—81no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—21no—
263C3×D12#4112yes—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266#627—81no—
267#625—81no—
268D3×Dic3—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—31no—
282#463—91no—
283#450—31no—
284#447—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C24×C3—61no—
291C23×D3—21no—
292C2×C3×Q8—21no—
293C2×C3×Q8C22×D311yescharacteristic
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×D4—21no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C2×C3×D4—62no—
300C2×C3×D4—62no—
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C22×D311yescharacteristic
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C2×#67—21no—
306C2×#67—61no—
307C2×#67—61no—
308C22×Dic3—21no—
309C22×Dic3—61no—
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×D12C22×D311yescharacteristic
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3C22×D311yescharacteristic
323C2×Dic6—61no—
324C2×Dic6—61no—
325C3×SD16—24no—
326C3×SD16—22no—
327C3×SD16—22no—
328C3×SD16—62no—
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—61no—
338C3×C22⋊C4—61no—
339C3×C22⋊C4—61no—
340C3×C22⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C42—31no—
343#217—21no—
344#217—31no—
345#217—31no—
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#215—22no—
355#213—22no—
356#213—62no—
357#213—62no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—31no—
362(C2×D3)⋊C4—31no—
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—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—121no—
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—31no—
384Dic3⋊C4—31no—
385Dic3⋊C4—61no—
386C4×Dic3—31no—
387C4×Dic3—31no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—121no—
394C4×Dic3C22×D311yescharacteristic
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—61no—
398C2×C3⋊C8C22×D311yescharacteristic
399C2×C3⋊C8C22×D311yescharacteristic
400C22×C32—22no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32C22×D411yescharacteristic
404C2×C3×D3—21no—
405C2×C3×D3—22no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—84no—
414C32×C4—41no—
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—
426C22×D4—31no—
427C2×SD16—31no—
428C2×SD16D3211yescharacteristic
429C2×D8—31no—
430C2×D8—91no—
431C4⋊Q8—91no—
432#126—181no—
433#124—31no—
434#124—181no—
435#123—181no—
436C22⋊Q8—31no—
437C22⋊Q8—181no—
438#121—91no—
439C4×Q8—91no—
440C4×D4—31no—
441C4×D4—91no—
442C4×D4—91no—
443C4×D4—91no—
444C4×D4—91no—
445C4×D4—181no—
446C4×D4—181no—
447#117—91no—
448#117—91no—
449C2×C22⋊C4—181no—
450C2×C22⋊C4—181no—
451#107—91no—
452#107—91no—
453#106—91no—
454#106—91no—
455C4⋊C8—31no—
456C4⋊C8—91no—
457#103—31no—
458#103—91no—
459#102—31no—
460#102—31no—
461#102—31no—
462#102—91no—
463#102—91no—
464#102—91no—
465C22⋊C8—31no—
466C22⋊C8—91no—
467#97—91no—
468C4×C8—91no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—31no—
472C23×C3—41no—
473C23×C3—64no—
474C23×C3—61no—
475C23×C3—61no—
476C23×C3—241no—
477C23×C3—241no—
478C22×D3—21no—
479C22×D3—24no—
480C22×D3—21no—
481C22×D3—81no—
482C22×D3—81no—
483C22×D3D3×D411yescharacteristic
484C3×Q8—22no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—41no—
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—22no—
493C3×D4—32no—
494C3×D4—41no—
495C3×D4—64no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—61no—
499C3×D4#23712yes—
500C3×D4#23712yes—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—41no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—241no—
513C2×C3×C4C23×D311yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515#67—24no—
516#67—241no—
517#67—241no—
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—121no—
532C2×Dic3—121no—
533C2×Dic3—241no—
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—21no—
544D12—21no—
545D12#23712yes—
546C4×D3—21no—
547C4×D3—21no—
548C4×D3—241no—
549C4×D3—241no—
550C4×D3—241no—
551Dic6—241no—
552Dic6—241no—
553C3×C8—22no—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—61no—
557C3×C8—61no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—121no—
563C2×C32—42no—
564C2×C32#52511yescharacteristic
565C2×C32#57611yescharacteristic
566C2×C32#57711yescharacteristic
567C3×D3—41no—
568C3×D3—42no—
569C3×D3—81no—
570C24—61no—
571C2×Q8—181no—
572C2×Q8C2×D3211yescharacteristic
573C2×D4—31no—
574C2×D4—31no—
575C2×D4—61no—
576C2×D4—62no—
577C2×D4—62no—
578C2×D4—181no—
579C2×D4C2×D3211yescharacteristic
580C22×C4—31no—
581C22×C4—61no—
582C22×C4—181no—
583C22×C4—181no—
584C22×C4—181no—
585C22×C4—181no—
586SD16—22no—
587SD16—62no—
588D8—62no—
589D8—182no—
590C2×C8—31no—
591C2×C8—31no—
592C2×C8—91no—
593C2×C8C2×D3211yescharacteristic
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—61no—
597C4⋊C4—91no—
598C4⋊C4—91no—
599C4⋊C4—91no—
600C4⋊C4—91no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C22⋊C4—61no—
604C22⋊C4—61no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—91no—
608C22⋊C4—91no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C42—31no—
616C42—91no—
617C42—181no—
618C42—181no—
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—21no—
622C22×C3—42no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—62no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3—244no—
639C22×C3C2×D3×D411yescharacteristic
640C22×C3C2×D3×D411yescharacteristic
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—22no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—84no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—42no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—61no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4C2×#23711yescharacteristic
662C3×C4C2×#23711yescharacteristic
663C3×C4C2×#23711yescharacteristic
664C3×C4D3×#4111yescharacteristic
665Dic3—21no—
666Dic3—21no—
667Dic3—21no—
668Dic3—41no—
669Dic3—41no—
670Dic3—62no—
671Dic3—61no—
672Dic3—61no—
673Dic3—61no—
674Dic3—61no—
675Dic3—121no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—241no—
681Dic3—241no—
682C32#311811yescharacteristic, complemented, Sylow
683C23—21no—
684C23—31no—
685C23—64no—
686C23—61no—
687C23—61no—
688C23—241no—
689C23—241no—
690Q8—21no—
691Q8—21no—
692Q8—721no—
693D4—21no—
694D4—32no—
695D4—64no—
696D4—61no—
697D4—61no—
698D4—61no—
699D4—721no—
700D4#380512yes—
701C2×C4—21no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—91no—
710C2×C4—91no—
711C2×C4—181no—
712C2×C4—181no—
713C2×C4—241no—
714C2×C4—721no—
715C2×C4—721no—
716C2×C4—721no—
717C2×C4—721no—
718C2×C4C22×D3211yescharacteristic
719C8—21no—
720C8—61no—
721C8—61no—
722C8—181no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—42no—
727C2×C3—42no—
728C2×C3—82no—
729C2×C3—121no—
730C2×C3—122no—
731C2×C3—241no—
732C2×C3#558611yescharacteristic
733C2×C3#560611yescharacteristic
734C2×C3#576211yescharacteristic
735C2×C3#577011yescharacteristic
736C2×C3#577411yescharacteristic
737C2×C3#577411yescharacteristic
738D3—41no—
739D3—42no—
740D3—81no—
741C22—22no—
742C22—41no—
743C22—41no—
744C22—61no—
745C22—62no—
746C22—61no—
747C22—61no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22—121no—
752C22—121no—
753C22—244no—
754C22D32×D411yescharacteristic
755C4—41no—
756C4—61no—
757C4—61no—
758C4—61no—
759C4—121no—
760C4—121no—
761C4—181no—
762C4—181no—
763C4—361no—
764C4—361no—
765C4D3×#23711yescharacteristic
766C4C2×#380511yescharacteristic
767C3—21no—
768C3#8013611yescharacteristic, complemented
769C3#8050911yescharacteristic, complemented
770C2—42no—
771C2—121no—
772C2—122no—
773C2—241no—
774C2#1059475011yescharacteristic
775C2#1059475311yescharacteristic
776C2#1059513011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radical#10591447C2
hypercenterC2×SD16D32
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #10595396C2semidirect
2. #10595215C2semidirect
3. SD16×C3⋊Dic3C2semidirect
4. C3×#5169C2semidirect
5. C3×#5165C2semidirect
6. #10591572C2semidirect
7. #10591567C2semidirect
8. #10591559C2semidirect
10. #10591436C2semidirect
11. #10591410C2semidirect
12. #10590837C2semidirect
13. #10590757C2semidirect
14. #10590740C2semidirect
15. #10590698C2semidirect
20. Q8×C3⋊Dic3C22semidirect
22. C3×#947C22semidirect
31. #63918C22semidirect
35. #63898C22semidirect
43. #63662C22semidirect
45. #63644C22semidirect
46. C8×C3⋊Dic3C22semidirect
47. C3×#835C22semidirect
50. C3×#821C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. #63576C22semidirect
54. #63575C22semidirect
55. #63573C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
58. #63563C22semidirect
60. #63555C22semidirect
68. #5169D3semidirect
70. #5165D3semidirect
154. #947C2×D3semidirect
204. #835C2×D3semidirect
215. #821C2×D3semidirect
226. Dic3⋊C8C2×D3semidirect
682. C32#3118semidirect
768. C3#80136semidirect
769. C3#80509semidirect

Maximal subgroups

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

subgroupindex
#105953962
#105952152
SD16×C3⋊Dic32
C3×#51692
C3×#51652
#105915722
#105915672
#105915592
#105914472
#105914362
#105914102
#105908372
#105907572
#105907402
#105906982
#805093
#801363