Finite Group Databasebeta

← #11889260

Subgroups — #11889260

Order 1152.

971 conjugacy classes of subgroups.

The subgroup lattice has 843 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596083C211yesmaximal, characteristic
2#10594809C211yesmaximal, characteristic, complemented
3C3×#5041C211yesmaximal, characteristic, complemented
4C3×#5035C211yesmaximal, characteristic, complemented
5#10591496C211yesmaximal, characteristic, complemented
6#10591467C211yesmaximal, characteristic, complemented
7#10591443C211yesmaximal, characteristic, complemented
8#10591426C211yesmaximal, characteristic, complemented
9#10591184C211yesmaximal, characteristic, complemented
10#10591157C211yesmaximal, characteristic, complemented
11#10591105C211yesmaximal, characteristic, complemented
12#10590524C211yesmaximal, characteristic, complemented
13#10590484C211yesmaximal, characteristic, complemented
14#10590450C211yesmaximal, characteristic, complemented
15#10590433C211yesmaximal, characteristic, complemented
16#81401—31nomaximal
17#80686—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3828C2211yescharacteristic
20C32×#121C2211yescharacteristic
21#64147—21no—
22#64146—21no—
23#64145C2211yescharacteristic
24C4×#638C2211yescharacteristic
25#64106C2211yescharacteristic
26#64102C2211yescharacteristic
27#64092—21no—
28C22⋊C4×C3⋊D3—21no—
29C2×C3×#214C2211yescharacteristic
30C3×#926C2211yescharacteristic, complemented
31C3×#924C2211yescharacteristic, complemented
32C22×C3×C3⋊C8C2211yescharacteristic, complemented
33#63956—21no—
34#63953—21no—
35#63919C2211yescharacteristic, complemented
36#63871C2211yescharacteristic
37#63868—21no—
38#63849C2211yescharacteristic
39#63843C2211yescharacteristic, complemented
40#63837—21no—
41C2×#3719C2211yescharacteristic, complemented
42C2×#3717C2211yescharacteristic
43C2×#3712C2211yescharacteristic
44C3×#832C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#830C2211yescharacteristic, complemented
48C3×#810C2211yescharacteristic, complemented
49C3×#808C2211yescharacteristic, complemented
50C3×#808C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52#63572C2211yescharacteristic, complemented
53#63567C2211yescharacteristic, complemented
54#63567C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63557C2211yescharacteristic
60#63555C2211yescharacteristic, complemented
61#5641—31no—
62#5612—31no—
63#5612—31no—
64#5612—61no—
65#5533—31no—
66C3×#482—31no—
67C3×#465—31no—
68#5169—31no—
69#5166—31no—
70#5113—31no—
71#5111—31no—
72#5047—31no—
73#5041D311yescharacteristic, complemented
74#5035D311yescharacteristic, complemented
75#5002—31no—
76#4889—31no—
77#4888—31no—
78#4870—31no—
79#4870—31no—
80#4868—31no—
81#4867—31no—
82#4817—31no—
83#4816—31no—
84#4776—31no—
85#4770—31no—
86#4770—31no—
87#4767—31no—
88#4765—31no—
89#4765—31no—
90#4733—31no—
91#4730—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97C2×#638—21no—
98C2×#638D411yescharacteristic
99D4×C3⋊D3—22no—
100D4×C3⋊D3—41no—
101#3828—22no—
102#3828—41no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4×C3⋊D3—21no—
105C2×C4×C3⋊D3—21no—
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×#634C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#627—21no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112#3757—21no—
113#3757—21no—
114#3757D411yescharacteristic
115#3752—21no—
116#3752—21no—
117#3752D411yescharacteristic
118C4⋊(C3⋊Dic3)—21no—
119#3750D411yescharacteristic
120C4×C3⋊Dic3C2311yescharacteristic
121C3×#217—21no—
122C3×#217—21no—
123C3×#214—41no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C2×C3×C3⋊C8—41no—
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138#3722—21no—
139Dic32—21no—
140Dic32—21no—
141#3719—41no—
142#3717—22no—
143#3712—41no—
144#3311—91noSylow
145C2×D3×D4—31no—
146C2×D3×D4—31no—
147C2×D3×D4—61no—
148C2×#235—31no—
149C2×#235—31no—
150C2×#235—61no—
151C2×C3×SD16—31no—
152C22×C3×C8—31no—
153C3×C22⋊Q8—31no—
154C3×#121—21no—
155C3×#121C2×D311yescharacteristic
156C3×#121C2×D311yescharacteristic
157C3×#117—31no—
158#946—31no—
159Q8×Dic3—31no—
160C2×#216—31no—
161C2×#215—31no—
162#938—61no—
163#938—61no—
164#938—62no—
165#937—61no—
166#937—61no—
167#937—62no—
168#936—31no—
169#936—31no—
170#936—61no—
171C2×#214C2×D311yescharacteristic
172C4×#67—31no—
173C4×#67—31no—
174C4×#67—61no—
175#926C2×D311yescharacteristic, complemented
176#924C2×D311yescharacteristic, complemented
177C22×C3⋊C8C2×D311yescharacteristic, complemented
178C2×Dic12—31no—
179C2×#204—31no—
180C2×ΓL(1,𝔽25)—31no—
181C2×ΓL(1,𝔽25)—31no—
182#898—61no—
183#897—31no—
184#897—31no—
185#897—31no—
186#897—61no—
187#893—31no—
188#893—31no—
189#893—61no—
190#892—31no—
191#892—31no—
192#888—31no—
193#888—31no—
194#887—31no—
195#887—61no—
196#885—61no—
197#885—61no—
198#883—61no—
199#883—61no—
200#883—62no—
201D3×C22⋊C4—61no—
202D3×C22⋊C4—61no—
203D3×C22⋊C4—62no—
204#879—61no—
205#879—61no—
206#876—61no—
207C4×Dic6—61no—
208C3×#107—31no—
209C3×#106—31no—
210C3×#106—31no—
211C3×#103—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×C22⋊C8—31no—
216#832C2×D311yescharacteristic
217#832C2×D311yescharacteristic
218#832C2×D311yescharacteristic
219#830C2×D311yescharacteristic, complemented
220#821—31no—
221#821—31no—
222#821—31no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225#816—31no—
226#816—31no—
227#816—31no—
228#815—31no—
229#815—31no—
230Dic3⋊C8—31no—
231Dic3⋊C8—31no—
232#810—31no—
233#810—31no—
234#810—31no—
235#810C2×D311yescharacteristic, complemented
236#809—31no—
237#809—31no—
238#809—31no—
239#808C2×D311yescharacteristic, complemented
240#808C2×D311yescharacteristic, complemented
241#807C2×D311yescharacteristic, complemented
242C23×C32—21no—
243C23×C32C2×D411yescharacteristic
244C22×C3⋊D3—21no—
245C22×C3⋊D3—42no—
246C22×C3⋊D3—42no—
247C22×C3⋊D3—81no—
248C22×C3⋊D3C2×D411yescharacteristic
249C32×D4—21no—
250C32×D4—21no—
251C32×D4—81no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257#638—41no—
258#638—42no—
259#638—42no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3C2×D411yescharacteristic
262C2×C3⋊Dic3C2×D411yescharacteristic
263C2×C3⋊Dic3C2×D411yescharacteristic
264C4⋊(C3⋊D3)—21no—
265C4⋊(C3⋊D3)#4112yes—
266C4×C3⋊D3—21no—
267C4×C3⋊D3—21no—
268C4×C3⋊D3—42no—
269C4×C3⋊D3—81no—
270#634—21no—
271#634—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C3×Dic6—21no—
277C3×Dic6—21no—
278#627—42no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283#556—91no—
284#546—91no—
285#489—91no—
286#485—91no—
287#482—31no—
288#476—91no—
289#470—91no—
290#465—31no—
291#464—91no—
292#452—91no—
293#450—91no—
294#440—91no—
295#435—91no—
296#418—91no—
297#416—91no—
298C23×D3—61no—
299C23×D3—61no—
300C23×D3—62no—
301C2×C3×Q8—31no—
302C2×C3×D4—22no—
303C2×C3×D4—21no—
304C2×C3×D4—21no—
305C2×C3×D4—21no—
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C22×D311yescharacteristic
308C22×C3×C4—21no—
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C2×#67—31no—
312C2×#67—31no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—62no—
317C2×#67—62no—
318C2×#67—61no—
319C2×#67—61no—
320D3×D4—62no—
321D3×D4—62no—
322D3×D4—122no—
323D3×D4—121no—
324D3×D4—121no—
325D3×D4—122no—
326#235—62no—
327#235—62no—
328#235—122no—
329#235—121no—
330#235—121no—
331#235—122no—
332C2×D12—31no—
333C2×D12—31no—
334C2×D12—61no—
335C2×C4×D3—31no—
336C2×C4×D3—31no—
337C2×C4×D3—61no—
338C2×C4×D3—62no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—62no—
344C2×Dic6—31no—
345C2×Dic6—31no—
346C2×Dic6—61no—
347C2×Dic6—61no—
348C2×Dic6—61no—
349C2×Dic6C22×D311yescharacteristic
350C3×SD16—121no—
351C2×C3×C8—31no—
352C2×C3×C8—31no—
353C2×C3×C8—31no—
354C2×C3×C8—31no—
355C2×C3×C8—121no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C22⋊C4—22no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C42—61no—
369#217—21no—
370#217—21no—
371#217—31no—
372#217—31no—
373#217—61no—
374#217—61no—
375#217—61no—
376#217—61no—
377#217—61no—
378#217—62no—
379#217—62no—
380#216—121no—
381#215—62no—
382#214—41no—
383(C2×D3)⋊C4—31no—
384(C2×D3)⋊C4—31no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
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—62no—
395(C2×D3)⋊C4—62no—
396C4⋊Dic3—61no—
397C4⋊Dic3—61no—
398C4⋊Dic3—61no—
399C4⋊Dic3—61no—
400C4⋊Dic3—62no—
401C4⋊Dic3C22×D311yescharacteristic
402C4⋊Dic3C22×D311yescharacteristic
403C4⋊Dic3C22×D311yescharacteristic
404Dic3⋊C4—21no—
405Dic3⋊C4—31no—
406Dic3⋊C4—31no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412C4×Dic3—21no—
413C4×Dic3—31no—
414C4×Dic3—31no—
415C4×Dic3—61no—
416C4×Dic3—61no—
417C4×Dic3—61no—
418C4×Dic3—61no—
419C4×Dic3—61no—
420C2×C3⋊C8—41no—
421C2×C3⋊C8C22×D311yescharacteristic
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424C2×C3⋊C8C22×D311yescharacteristic
425Dic12—121no—
426#204—62no—
427ΓL(1,𝔽25)—121no—
428ΓL(1,𝔽25)—121no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32—41no—
433C22×C32—41no—
434C22×C32—41no—
435C22×C32C22×D411yescharacteristic
436C2×C3⋊D3—22no—
437C2×C3⋊D3—21no—
438C2×C3⋊D3—21no—
439C2×C3⋊D3—21no—
440C2×C3⋊D3—41no—
441C2×C3⋊D3—41no—
442C2×C3⋊D3—84no—
443C32×C4—21no—
444C32×C4—41no—
445C32×C4C2×#4111yescharacteristic
446C32×C4H(5,𝔽2)11yescharacteristic
447C3⋊Dic3—21no—
448C3⋊Dic3—21no—
449C3⋊Dic3—21no—
450C3⋊Dic3—41no—
451C3×Dic3—41no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C2×#41—91no—
456C22×D4—91no—
457C2×Q16—91no—
458C2×SD16—31no—
459C2×SD16—91no—
460C2×M16—91no—
461C22×C8—31no—
462C4⋊Q8—91no—
463#126—181no—
464#126—181no—
465#124—91no—
466#124—181no—
467#123—181no—
468C22⋊Q8—31no—
469C22⋊Q8—91no—
470C22⋊Q8—91no—
471#121—181no—
472#121D3211yescharacteristic
473#120—181no—
474C4×Q8—91no—
475C4×Q8—181no—
476C4×D4—91no—
477C4×D4—91no—
478#117—31no—
479#117—91no—
480C2×C22⋊C4—181no—
481#107—31no—
482#106—31no—
483#106—31no—
484C4⋊C8—91no—
485#103—31no—
486#103—91no—
487#103—91no—
488#103—91no—
489#102—31no—
490#102—31no—
491#102—31no—
492#102—91no—
493#102—91no—
494#102—91no—
495C22⋊C8—31no—
496C22⋊C8—91no—
497#97—91no—
498C23×C3—22no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3D3×D411yescharacteristic
503C23×C3D3×D411yescharacteristic
504C22×D3—31no—
505C22×D3—31no—
506C22×D3—61no—
507C22×D3—62no—
508C22×D3—61no—
509C22×D3—61no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—124no—
513C22×D3—124no—
514C22×D3—122no—
515C22×D3—122no—
516C22×D3—241no—
517C22×D3—241no—
518C22×D3—242no—
519C3×Q8—61no—
520C3×Q8—61no—
521C3×D4—21no—
522C3×D4—21no—
523C3×D4—21no—
524C3×D4—21no—
525C3×D4—41no—
526C3×D4—41no—
527C3×D4—81no—
528C3×D4—81no—
529C3×D4—82no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—22no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4D3×D411yescharacteristic
546C2×C3×C4D3×D411yescharacteristic
547C2×C3×C4C23×D311yescharacteristic
548C2×C3×C4C23×D311yescharacteristic
549#67—121no—
550#67—121no—
551#67—122no—
552#67—122no—
553#67—122no—
554#67—122no—
555#67—124no—
556#67—124no—
557#67—122no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—31no—
565C2×Dic3—31no—
566C2×Dic3—31no—
567C2×Dic3—31no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—62no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574D12—32no—
575D12—32no—
576D12—62no—
577D12—62no—
578D12—61no—
579D12—61no—
580C4×D3—61no—
581C4×D3—61no—
582C4×D3—61no—
583C4×D3—61no—
584C4×D3—121no—
585C4×D3—121no—
586C4×D3—122no—
587C4×D3—122no—
588C4×D3—124no—
589C4×D3—241no—
590C4×D3—241no—
591C4×D3—242no—
592Dic6—21no—
593Dic6—21no—
594Dic6—61no—
595Dic6—61no—
596Dic6—61no—
597Dic6—61no—
598Dic6—121no—
599Dic6—121no—
600Dic6—122no—
601Dic6—122no—
602C3×C8—61no—
603C3×C8—61no—
604C3×C8—61no—
605C3×C8—61no—
606C3⋊C8—21no—
607C3⋊C8—21no—
608C3⋊C8—21no—
609C3⋊C8—21no—
610C2×C32—41no—
611C2×C32—81no—
612C2×C32#54611yescharacteristic
613C2×C32#57511yescharacteristic
614C2×C32#57711yescharacteristic
615C3⋊D3—41no—
616C3⋊D3—42no—
617C24—181no—
618#41—182no—
619#41—361no—
620C2×Q8—31no—
621C2×Q8—91no—
622C2×Q8—181no—
623C2×D4—21no—
624C2×D4—91no—
625C2×D4—91no—
626C2×D4—181no—
627C2×D4—182no—
628C2×D4—181no—
629C2×D4—361no—
630C2×D4C2×D3211yescharacteristic
631C22×C4—91no—
632C22×C4—181no—
633C22×C4—181no—
634C22×C4C2×D3211yescharacteristic
635Q16—361no—
636SD16—121no—
637SD16—182no—
638M16—361no—
639C2×C8—31no—
640C2×C8—31no—
641C2×C8—31no—
642C2×C8—31no—
643C2×C8—121no—
644C4⋊C4—31no—
645C4⋊C4—31no—
646C4⋊C4—31no—
647C4⋊C4—61no—
648C4⋊C4—91no—
649C4⋊C4—181no—
650C4⋊C4—181no—
651C4⋊C4—181no—
652C4⋊C4—181no—
653C4⋊C4C2×D3211yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—61no—
656C22⋊C4—61no—
657C22⋊C4—91no—
658C22⋊C4—91no—
659C22⋊C4—181no—
660C22⋊C4—181no—
661C22⋊C4—181no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C22⋊C4—181no—
665C42—61no—
666C42—91no—
667C42—181no—
668C42—181no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—42no—
680C22×C3—42no—
681C22×C3—42no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3C2×D3×D411yescharacteristic
689C22×C3C2×D3×D411yescharacteristic
690C2×D3—64no—
691C2×D3—62no—
692C2×D3—61no—
693C2×D3—62no—
694C2×D3—61no—
695C2×D3—61no—
696C2×D3—61no—
697C2×D3—61no—
698C2×D3—61no—
699C2×D3—62no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—122no—
703C2×D3—122no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—248no—
709C2×D3—244no—
710C2×D3—244no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—41no—
716C3×C4—42no—
717C3×C4—41no—
718C3×C4—41no—
719C3×C4—121no—
720C3×C4—121no—
721C3×C4—121no—
722C3×C4—121no—
723C3×C4#100411yescharacteristic
724C3×C4D3×#4111yescharacteristic
725C3×C4D3×#4111yescharacteristic
726C3×C4#100911yescharacteristic
727Dic3—41no—
728Dic3—41no—
729Dic3—41no—
730Dic3—41no—
731Dic3—61no—
732Dic3—61no—
733Dic3—61no—
734Dic3—61no—
735Dic3—61no—
736Dic3—61no—
737Dic3—121no—
738Dic3—121no—
739Dic3—121no—
740Dic3—122no—
741Dic3—121no—
742Dic3—121no—
743C32#331111yescharacteristic, complemented, Sylow
744C23—21no—
745C23—91no—
746C23—181no—
747C23—362no—
748C23—362no—
749C23—721no—
750C23#381111yescharacteristic
751Q8—61no—
752Q8—61no—
753Q8—181no—
754Q8—181no—
755Q8—362no—
756D4—21no—
757D4—21no—
758D4—81no—
759D4—92no—
760D4—181no—
761D4—361no—
762D4—362no—
763D4—362no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—91no—
772C2×C4—91no—
773C2×C4—91no—
774C2×C4—181no—
775C2×C4—181no—
776C2×C4—181no—
777C2×C4—362no—
778C2×C4—721no—
779C2×C4#381111yescharacteristic
780C2×C4C22×D3211yescharacteristic
781C8—61no—
782C8—61no—
783C8—61no—
784C8—61no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—41no—
789C2×C3—41no—
790C2×C3—81no—
791C2×C3—82no—
792C2×C3—81no—
793C2×C3—81no—
794C2×C3#561011yescharacteristic
795C2×C3#565411yescharacteristic
796C2×C3#576211yescharacteristic
797C2×C3#576811yescharacteristic
798C2×C3#576811yescharacteristic
799C2×C3#577511yescharacteristic
800D3—122no—
801D3—124no—
802D3—121no—
803D3—122no—
804D3—121no—
805D3—122no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—181no—
813C22—181no—
814C22—182no—
815C22—181no—
816C22—361no—
817C22—361no—
818C22—724no—
819C22C2×#381111yescharacteristic
820C4—21no—
821C4—41no—
822C4—121no—
823C4—121no—
824C4—121no—
825C4—121no—
826C4—181no—
827C4—181no—
828C4—181no—
829C4—361no—
830C4#6431211yescharacteristic
831C4#6431411yescharacteristic
832C3—21no—
833C3#8068611yescharacteristic, complemented
834C3#8140111yescharacteristic, complemented
835C2—41no—
836C2—81no—
837C2—361no—
838C2—362no—
839C2#1059511511yescharacteristic
840C2#1059516311yescharacteristic
841C2#1059546011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
prime radical#10596083C2
hypercenter#121D32
hypocenterC32#3311
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #10594809C2semidirect
3. C3×#5041C2semidirect
4. C3×#5035C2semidirect
5. #10591496C2semidirect
6. #10591467C2semidirect
7. #10591443C2semidirect
8. #10591426C2semidirect
9. #10591184C2semidirect
10. #10591157C2semidirect
11. #10591105C2semidirect
12. #10590524C2semidirect
13. #10590484C2semidirect
14. #10590450C2semidirect
15. #10590433C2semidirect
30. C3×#926C22semidirect
31. C3×#924C22semidirect
32. C22×C3×C3⋊C8C22semidirect
35. #63919C22semidirect
39. #63843C22semidirect
41. C2×#3719C22semidirect
47. C3×#830C22semidirect
48. C3×#810C22semidirect
49. C3×#808C22semidirect
50. C3×#808C22semidirect
51. C3×#807C22semidirect
52. #63572C22semidirect
53. #63567C22semidirect
54. #63567C22semidirect
55. #63567C22semidirect
60. #63555C22semidirect
73. #5041D3semidirect
74. #5035D3semidirect
175. #926C2×D3semidirect
176. #924C2×D3semidirect
177. C22×C3⋊C8C2×D3semidirect
219. #830C2×D3semidirect
235. #810C2×D3semidirect
239. #808C2×D3semidirect
240. #808C2×D3semidirect
241. #807C2×D3semidirect
743. C32#3311semidirect
833. C3#80686semidirect
834. C3#81401semidirect

Maximal subgroups

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

subgroupindex
#105960832
#105948092
C3×#50412
C3×#50352
#105914962
#105914672
#105914432
#105914262
#105911842
#105911572
#105911052
#105905242
#105904842
#105904502
#105904332
#814013
#806863