Finite Group Databasebeta

← #11888548

Subgroups — #11888548

Order 1152.

949 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595136C211yesmaximal, characteristic, complemented
2#10594629C211yesmaximal, characteristic, complemented
3#10592481C211yesmaximal, characteristic, complemented
4C3×#4785C211yesmaximal, characteristic, complemented
5C3×#4778C211yesmaximal, characteristic, complemented
6#10591520C211yesmaximal, characteristic, complemented
7#10591515C211yesmaximal, characteristic, complemented
8#10591471C211yesmaximal, characteristic, complemented
9#10590957C211yesmaximal, characteristic, complemented
10D3×#821C211yesmaximal, characteristic, complemented
11#10590893C211yesmaximal, characteristic, complemented
12#10590726C211yesmaximal, characteristic, complemented
13#10590558C211yesmaximal, characteristic, complemented
14#10590445C211yesmaximal, characteristic, complemented
15#10590439C211yesmaximal, characteristic, complemented
16#80683—31nomaximal
17#79880—31nomaximal
18C2×#3804—21no—
19C2×D3×D12C2211yescharacteristic
20C2×#3796C2211yescharacteristic
21#64147C2211yescharacteristic, complemented
22C2×#3753C2211yescharacteristic
23C2×#3743C2211yescharacteristic, complemented
24#64104C2211yescharacteristic
25C3×#938C2211yescharacteristic
26C3×D4×Dic3C2211yescharacteristic, complemented
27C2×C3×#214C2211yescharacteristic, complemented
28C2×C3×#213C2211yescharacteristic
29C2×C3×D3×C8C2211yescharacteristic
30C3×#897C2211yescharacteristic
31C3×#893C2211yescharacteristic
32#63975—21no—
33#63969—21no—
34#63964—21no—
35#63923—21no—
36D3×(C2×D3)⋊C4—21no—
37#63918C2211yescharacteristic, complemented
38#63909—21no—
39C4×#626C2211yescharacteristic
40#63900C2211yescharacteristic, complemented
41#63890—21no—
42D3×C4⋊Dic3C2211yescharacteristic
43#63864C2211yescharacteristic
44C32×#102C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63635C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×#816C2211yescharacteristic, complemented
49C3×#815C2211yescharacteristic, complemented
50C3×#808C2211yescharacteristic, complemented
51C3×#808C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63566C2211yescharacteristic, complemented
54#63565C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61#5630—31no—
62#5611—31no—
63#5554—31no—
64#5551—31no—
65C3×#465—31no—
66C3×#442—31no—
67#5172—31no—
68#5165—31no—
69#5158—31no—
70#5156—31no—
71C2×#821—31no—
72#5111—31no—
73#5043—31no—
74#5036—31no—
75#5016—31no—
76#5008—31no—
77#4870—31no—
78#4863—31no—
79#4863—31no—
80#4862—31no—
81#4803—31no—
82#4794—31no—
83#4785D311yescharacteristic, complemented
84#4782—31no—
85#4782—31no—
86#4782—61no—
87#4778D311yescharacteristic, complemented
88#4771—31no—
89D3×#102—31no—
90#4714—31no—
91#4706—31no—
92C22×D32—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×#626—21no—
106C2×#626—21no—
107C2×#626D411yescharacteristic
108C2×#624—21no—
109#3804—44no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112D3×D12—22no—
113D3×D12—41no—
114#3796—22no—
115#3796—41no—
116C2×C32×C8C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118#3757—21no—
119#3753—41no—
120#3752—21no—
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123#3743—41no—
124C3×#217—21no—
125C3×#217—21no—
126C3×#214—41no—
127C3×#213—22no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×D3×C8—41no—
137#3724—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3D411yescharacteristic
141#3722—21no—
142#3722—21no—
143#3722D411yescharacteristic
144(C2×D3)⋊Dic3D411yescharacteristic
145#3306—91noSylow
146C2×#239—31no—
147C2×#237—31no—
148C2×#237—61no—
149C2×D3×D4—31no—
150C2×#235—61no—
151C22×D12—31no—
152C2×C3×SD16—31no—
153C2×C3×D8—31no—
154C22×C3×C8—31no—
155C3×C22⋊Q8—31no—
156C3×#121—31no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159#947—31no—
160#938—31no—
161#938—31no—
162#938—61no—
163#938C2×D311yescharacteristic
164#935—61no—
165D4×Dic3C2×D311yescharacteristic, complemented
166C2×#214C2×D311yescharacteristic, complemented
167C2×#213—31no—
168C2×#213—31no—
169C2×#213—61no—
170C2×#213C2×D311yescharacteristic
171#930—61no—
172C4×#67—31no—
173C2×(C2×D3)⋊C4—61no—
174C2×C4⋊Dic3—31no—
175#924—61no—
176C2×ΓL(1,𝔽25)—31no—
177C2×ΓL(1,𝔽25)—31no—
178C2×ΓL(1,𝔽25)—61no—
179C2×D3×C8C2×D311yescharacteristic
180#897C2×D311yescharacteristic
181#895—31no—
182#895—31no—
183#895—61no—
184#895—61no—
185#894—61no—
186#893C2×D311yescharacteristic
187D3×C4⋊C4—31no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4—31no—
190#888—31no—
191#886—61no—
192#883—61no—
193#883—61no—
194#883—61no—
195#882—61no—
196#882—61no—
197D3×C22⋊C4—61no—
198#878—61no—
199#875—31no—
200C4×D12—31no—
201#869—31no—
202C3×#106—31no—
203C3×#106—31no—
204C3×#103—31no—
205C3×#102—21no—
206C3×#102—31no—
207C3×#102C2×D311yescharacteristic, complemented
208C3×#102C2×D311yescharacteristic, complemented
209C3×#97—31no—
210#835—31no—
211#835—31no—
212#832—31no—
213#832—31no—
214#830—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—61no—
221#821C2×D311yescharacteristic
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225#816—31no—
226#816C2×D311yescharacteristic, complemented
227#815C2×D311yescharacteristic, complemented
228Dic3⋊C8—31no—
229#810—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#808—31no—
234#808—31no—
235#808—61no—
236#808C2×D311yescharacteristic, complemented
237#808C2×D311yescharacteristic, complemented
238C4⋊(C3⋊C8)—31no—
239C23×C32—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3C2×D411yescharacteristic
242C22×C3×D3—21no—
243C22×C3×D3C2×D411yescharacteristic
244C2×D32—42no—
245C2×D32—42no—
246C2×D32—81no—
247C32×D4—21no—
248C32×D4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2411yescharacteristic
251#638—42no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3C2×D411yescharacteristic
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—81no—
257C4×C3⋊D3—21no—
258C4×C3⋊D3—21no—
259C3×#67—42no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—42no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12#4112yescomplemented
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—81no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274#627—42no—
275#626—22no—
276#626—42no—
277#626—42no—
278#624—42no—
279D3×Dic3—42no—
280D3×Dic3—42no—
281C32×C8—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#547—91no—
286#546—91no—
287#489—91no—
288#483—91no—
289#481—91no—
290#476—91no—
291#469—91no—
292#465—31no—
293#463—91no—
294#449—91no—
295#447—91no—
296#442—31no—
297#435—91no—
298#417—91no—
299C2×#102—91no—
300C23×D3—61no—
301C23×D3—61no—
302C2×C3×Q8—31no—
303C2×C3×D4—21no—
304C2×C3×D4—31no—
305C2×C3×D4—61no—
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C22×D311yescharacteristic
308C22×C3×C4—31no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C2×#67—21no—
312C2×#67—31no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—121no—
318C22×Dic3—21no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321#239—62no—
322#239—121no—
323#237—62no—
324#237—121no—
325#237—124no—
326D3×D4—62no—
327D3×D4—121no—
328#235—124no—
329C2×D12—31no—
330C2×D12—31no—
331C2×D12—31no—
332C2×D12—61no—
333C2×D12—62no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—61no—
337C2×D12—61no—
338C2×D12—121no—
339C2×D12—121no—
340C2×D12C22×D311yescharacteristic
341C2×C4×D3—21no—
342C2×C4×D3—31no—
343C2×C4×D3—31no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3C22×D311yescharacteristic
350C2×Dic6—61no—
351C2×Dic6—61no—
352C2×Dic6C22×D311yescharacteristic
353C3×SD16—121no—
354C3×D8—62no—
355C2×C3×C8—21no—
356C2×C3×C8—31no—
357C2×C3×C8—31no—
358C2×C3×C8—121no—
359C2×C3×C8C22×D311yescharacteristic
360C2×C3×C8C22×D311yescharacteristic
361C3×C4⋊C4—21no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C42—31no—
372#217—21no—
373#217—21no—
374#217—31no—
375#217—61no—
376#217—61no—
377#217—121no—
378#214—41no—
379#213—22no—
380#213—121no—
381#213—121no—
382#213—122no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—31no—
386(C2×D3)⋊C4—31no—
387(C2×D3)⋊C4—31no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—121no—
395C4⋊Dic3—21no—
396C4⋊Dic3—31no—
397C4⋊Dic3—31no—
398C4⋊Dic3—31no—
399C4⋊Dic3—61no—
400C4⋊Dic3—61no—
401C4⋊Dic3—61no—
402C4⋊Dic3C22×D311yescharacteristic
403C4⋊Dic3C22×D311yescharacteristic
404Dic3⋊C4—31no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409C4×Dic3C22×D311yescharacteristic
410C2×C3⋊C8—31no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—61no—
413C2×C3⋊C8C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415ΓL(1,𝔽25)—121no—
416ΓL(1,𝔽25)—121no—
417ΓL(1,𝔽25)—122no—
418D3×C8—41no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32C22×D411yescharacteristic
423C2×C3⋊D3—21no—
424C2×C3⋊D3—21no—
425C2×C3⋊D3—21no—
426C2×C3⋊D3—41no—
427C2×C3⋊D3—41no—
428C2×C3⋊D3—41no—
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—22no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3AGL(1,ℤ/8)12yes—
435D32—84no—
436C32×C4—41no—
437C32×C4C2×#4111yescharacteristic
438C32×C4H(5,𝔽2)11yescharacteristic
439C3⋊Dic3—21no—
440C3⋊Dic3—41no—
441C3×Dic3—21no—
442C3×Dic3—21no—
443C3×Dic3—21no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C2×#41—91no—
448C2×#41—181no—
449C22×D4—91no—
450C2×SD16—31no—
451C2×D8—31no—
452C2×D8—91no—
453C2×M16—91no—
454C22×C8—31no—
455C4⋊Q8—91no—
456#124—91no—
457#123—181no—
458#123—181no—
459#123—181no—
460C22⋊Q8—31no—
461C22⋊Q8—181no—
462#121—31no—
463#121—91no—
464#121—91no—
465#121—181no—
466#120—181no—
467C4×D4—31no—
468C4×D4—31no—
469C4×D4—91no—
470C2×C4⋊C4—91no—
471C2×C4⋊C4—91no—
472C2×C22⋊C4—181no—
473#106—31no—
474#106—31no—
475#106—91no—
476C4⋊C8—91no—
477#103—31no—
478#103—91no—
479#103—91no—
480#102—31no—
481#102—91no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102D3211yescharacteristic, complemented
487C22⋊C8—91no—
488C22⋊C8—91no—
489#97—31no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—31no—
493C23×C3—41no—
494C23×C3—61no—
495C22×D3—21no—
496C22×D3—31no—
497C22×D3—31no—
498C22×D3—61no—
499C22×D3—61no—
500C22×D3—61no—
501C22×D3—121no—
502C22×D3—122no—
503C22×D3—122no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—241no—
507C22×D3—241no—
508C22×D3D3×D411yescharacteristic
509C3×Q8—61no—
510C3×Q8—61no—
511C3×D4—21no—
512C3×D4—21no—
513C3×D4—21no—
514C3×D4—21no—
515C3×D4—32no—
516C3×D4—41no—
517C3×D4—41no—
518C3×D4—61no—
519C3×D4—122no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—41no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—122no—
533C2×C3×C4—241no—
534C2×C3×C4C23×D311yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536#67—42no—
537#67—62no—
538#67—122no—
539#67—122no—
540#67—122no—
541#67—122no—
542#67—242no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—42no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—121no—
553C2×Dic3—122no—
554C2×Dic3—122no—
555C2×Dic3D3×D411yescharacteristic
556C2×Dic3D3×D411yescharacteristic
557C2×Dic3D3×D411yescharacteristic
558D12—21no—
559D12—62no—
560D12—61no—
561D12—61no—
562D12—61no—
563D12—61no—
564D12—121no—
565D12—121no—
566D12—122no—
567D12—122no—
568D12—241no—
569D12—241no—
570D12—242no—
571D12#23512yescomplemented
572C4×D3—21no—
573C4×D3—21no—
574C4×D3—61no—
575C4×D3—61no—
576C4×D3—61no—
577C4×D3—61no—
578C4×D3—81no—
579C4×D3—121no—
580C4×D3—121no—
581C4×D3—122no—
582C4×D3—122no—
583C4×D3—122no—
584C4×D3—122no—
585Dic6—21no—
586Dic6—21no—
587Dic6—122no—
588Dic6—122no—
589C3×C8—21no—
590C3×C8—21no—
591C3×C8—41no—
592C3×C8—61no—
593C3×C8—61no—
594C3⋊C8—21no—
595C3⋊C8—21no—
596C3⋊C8—62no—
597C3⋊C8—61no—
598C3⋊C8—61no—
599C2×C32—81no—
600C2×C32#54611yescharacteristic
601C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
602C2×C32#57711yescharacteristic
603C3⋊D3—41no—
604C3⋊D3—81no—
605C3×D3—22no—
606C3×D3—42no—
607C24—181no—
608#41—182no—
609#41—364no—
610#41—361no—
611C2×Q8—31no—
612C2×Q8—181no—
613C2×D4—31no—
614C2×D4—61no—
615C2×D4—91no—
616C2×D4—91no—
617C2×D4—181no—
618C2×D4—181no—
619C2×D4—182no—
620C2×D4—181no—
621C2×D4—181no—
622C2×D4—361no—
623C2×D4C2×D3211yescharacteristic
624C22×C4—31no—
625C22×C4—61no—
626C22×C4—61no—
627C22×C4—91no—
628C22×C4—181no—
629C22×C4—181no—
630C22×C4—181no—
631SD16—121no—
632D8—62no—
633D8—361no—
634M16—361no—
635C2×C8—31no—
636C2×C8—31no—
637C2×C8—91no—
638C2×C8—121no—
639C2×C8C2×D3211yescharacteristic
640C4⋊C4—31no—
641C4⋊C4—31no—
642C4⋊C4—61no—
643C4⋊C4—91no—
644C4⋊C4—91no—
645C4⋊C4—181no—
646C4⋊C4—181no—
647C4⋊C4—181no—
648C4⋊C4C2×D3211yescharacteristic
649C22⋊C4—61no—
650C22⋊C4—61no—
651C22⋊C4—61no—
652C22⋊C4—61no—
653C22⋊C4—91no—
654C22⋊C4—91no—
655C22⋊C4—181no—
656C22⋊C4—181no—
657C22⋊C4—181no—
658C22⋊C4—181no—
659C42—31no—
660C22×C3—21no—
661C22×C3—32no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—61no—
669C22×C3—61no—
670C22×C3—62no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3—81no—
674C22×C3—121no—
675C22×C3—121no—
676C22×C3C2×D3×D411yescharacteristic
677C22×C3C2×D3×D411yescharacteristic
678C2×D3—21no—
679C2×D3—21no—
680C2×D3—22no—
681C2×D3—41no—
682C2×D3—41no—
683C2×D3—61no—
684C2×D3—61no—
685C2×D3—61no—
686C2×D3—61no—
687C2×D3—61no—
688C2×D3—61no—
689C2×D3—121no—
690C2×D3—121no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—241no—
699C2×D3—241no—
700C2×D3—241no—
701C2×D3—244no—
702C2×D3—244no—
703C2×D3#91412yes—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—41no—
707C3×C4—41no—
708C3×C4—61no—
709C3×C4—61no—
710C3×C4—61no—
711C3×C4—81no—
712C3×C4—121no—
713C3×C4—121no—
714C3×C4—121no—
715C3×C4C2×#23511yescharacteristic
716C3×C4#100411yescharacteristic
717C3×C4D3×#4111yescharacteristic
718C3×C4#100911yescharacteristic
719Dic3—21no—
720Dic3—21no—
721Dic3—21no—
722Dic3—41no—
723Dic3—41no—
724Dic3—41no—
725Dic3—61no—
726Dic3—61no—
727Dic3—121no—
728Dic3—121no—
729Dic3—121no—
730Dic3—241no—
731C32#330611yescharacteristic, complemented, Sylow
732C23—21no—
733C23—31no—
734C23—61no—
735C23—91no—
736C23—181no—
737C23—362no—
738C23—362no—
739C23—721no—
740Q8—61no—
741Q8—61no—
742Q8—362no—
743D4—21no—
744D4—21no—
745D4—32no—
746D4—61no—
747D4—122no—
748D4—182no—
749D4—181no—
750D4—181no—
751D4—362no—
752D4—362no—
753D4—362no—
754D4—721no—
755C2×C4—21no—
756C2×C4—31no—
757C2×C4—31no—
758C2×C4—31no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—91no—
765C2×C4—122no—
766C2×C4—181no—
767C2×C4—181no—
768C2×C4—181no—
769C2×C4—241no—
770C2×C4—362no—
771C2×C4—362no—
772C2×C4—362no—
773C2×C4C22×D3211yescharacteristic
774C8—21no—
775C8—61no—
776C8—61no—
777C8—181no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—62no—
782C2×C3—81no—
783C2×C3—81no—
784C2×C3—122no—
785C2×C3—161no—
786C2×C3#555011yescharacteristic
787C2×C3#561011yescharacteristic
788C2×C3C2×#91411yescharacteristic
789C2×C3#577011yescharacteristic
790C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
791C2×C3#577511yescharacteristic
792D3—22no—
793D3—42no—
794D3—121no—
795D3—121no—
796D3—241no—
797D3—241no—
798D3—241no—
799D3—481no—
800C22—32no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—61no—
805C22—61no—
806C22—62no—
807C22—121no—
808C22—121no—
809C22—181no—
810C22—181no—
811C22—181no—
812C22—361no—
813C22—361no—
814C22—361no—
815C22—724no—
816C22D32×D411yescharacteristic
817C4—41no—
818C4—61no—
819C4—61no—
820C4—61no—
821C4—121no—
822C4—121no—
823C4—121no—
824C4—181no—
825C4—361no—
826C4D3×#23511yescharacteristic
827C4#6431411yescharacteristic
828C3—21no—
829C3#7988011yescharacteristic, complemented
830C3#8068311yescharacteristic, complemented
831C2—62no—
832C2—81no—
833C2—122no—
834C2—361no—
835C2—721no—
836C2#1059428311yescharacteristic
837C2#1059473611yescharacteristic
838C2D3×#91411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3306
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. #10595136C2semidirect
2. #10594629C2semidirect
3. #10592481C2semidirect
4. C3×#4785C2semidirect
5. C3×#4778C2semidirect
6. #10591520C2semidirect
7. #10591515C2semidirect
8. #10591471C2semidirect
9. #10590957C2semidirect
10. D3×#821C2semidirect
11. #10590893C2semidirect
12. #10590726C2semidirect
13. #10590558C2semidirect
14. #10590445C2semidirect
15. #10590439C2semidirect
21. #64147C22semidirect
23. C2×#3743C22semidirect
26. C3×D4×Dic3C22semidirect
27. C2×C3×#214C22semidirect
37. #63918C22semidirect
40. #63900C22semidirect
44. C32×#102C22semidirect
46. #63635C22semidirect
48. C3×#816C22semidirect
49. C3×#815C22semidirect
50. C3×#808C22semidirect
51. C3×#808C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
53. #63566C22semidirect
54. #63565C22semidirect
59. #63557C22semidirect
83. #4785D3semidirect
87. #4778D3semidirect
165. D4×Dic3C2×D3semidirect
166. C2×#214C2×D3semidirect
207. C3×#102C2×D3semidirect
208. C3×#102C2×D3semidirect
226. #816C2×D3semidirect
227. #815C2×D3semidirect
236. #808C2×D3semidirect
237. #808C2×D3semidirect
268. C3×D12#41semidirect
486. #102D32semidirect
571. D12#235semidirect
731. C32#3306semidirect
829. C3#79880semidirect
830. C3#80683semidirect

Maximal subgroups

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

subgroupindex
#105951362
#105946292
#105924812
C3×#47852
C3×#47782
#105915202
#105915152
#105914712
#105909572
D3×#8212
#105908932
#105907262
#105905582
#105904452
#105904392
#806833
#798803