Finite Group Databasebeta

← #11872149

Subgroups — #11872149

Order 1152.

981 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596016C211yesmaximal, characteristic, complemented
2#10593955C211yesmaximal, characteristic, complemented
3C3×#5016C211yesmaximal, characteristic, complemented
4C3×#5008C211yesmaximal, characteristic, complemented
5#10591467C211yesmaximal, characteristic, complemented
6#10591456C211yesmaximal, characteristic
7#10591446C211yesmaximal, characteristic, complemented
8#10591435C211yesmaximal, characteristic, complemented
9#10590527C211yesmaximal, characteristic, complemented
10#10590513C211yesmaximal, characteristic, complemented
11#10590483C211yesmaximal, characteristic, complemented
12#10590462C211yesmaximal, characteristic, complemented
13#10590356C211yesmaximal, characteristic, complemented
14#10590313C211yesmaximal, characteristic, complemented
15#10590257C211yesmaximal, characteristic, complemented
16#81048—31nomaximal
17#80508—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21C4×#638—21no—
22C2×#3752—21no—
23#64102C2211yescharacteristic
24#64101C2211yescharacteristic
25#64090—21no—
26C22⋊C4×C3⋊D3—21no—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28#64081C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic
31C3×#875C2211yescharacteristic, complemented
32C3×#869C2211yescharacteristic, complemented
33#63916C2211yescharacteristic
34#63907—21no—
35#63898C2211yescharacteristic, complemented
36#63890—21no—
37#63887—21no—
38#63871C2211yescharacteristic
39#63858—21no—
40#63843C2211yescharacteristic, complemented
41C2×#3717C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C3×#832C2211yescharacteristic
44C3×#832C2211yescharacteristic
45C3×#810C2211yescharacteristic, complemented
46C3×#809C2211yescharacteristic, complemented
47C3×#808C2211yescharacteristic, complemented
48C3×#808C2211yescharacteristic, complemented
49C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
50C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53#63566C2211yescharacteristic, complemented
54#63564C2211yescharacteristic
55#63564C2211yescharacteristic
56#63563C2211yescharacteristic, complemented
57#63557C2211yescharacteristic
58#63557C2211yescharacteristic
59#63555C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61#5733—31no—
62#5682—31no—
63#5545—31no—
64#5545—31no—
65#5545—61no—
66C3×#476—31no—
67C3×#463—31no—
68#5169—31no—
69#5164—31no—
70#5156—31no—
71Dic3×D8—31no—
72#5087—31no—
73#5057—31no—
74#5016D311yescharacteristic, complemented
75#5008D311yescharacteristic, complemented
76#4869—31no—
77#4868—31no—
78#4866—31no—
79#4852—31no—
80#4846—31no—
81#4844—31no—
82#4840—31no—
83#4840—31no—
84#4814—31no—
85#4788—31no—
86#4785—31no—
87#4784—31no—
88#4776—31no—
89#4773—31no—
90#4757—31no—
91#4756—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×#638—21no—
96C22×C3⋊Dic3—21no—
97D4×C3⋊D3—22no—
98D4×C3⋊D3—22no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×Dic6—21no—
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×D3×Dic3—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C22⋊C4—21no—
110C32×C42C2311yescharacteristic
111#3757—21no—
112#3752—21no—
113#3752—21no—
114#3752—21no—
115#3752D411yescharacteristic
116#3752D411yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750D411yescharacteristic
119#3750D411yescharacteristic
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3C2311yescharacteristic
122C3×#214—22no—
123C3×#213—22no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139#3717—22no—
140#3714—22no—
141#3118—91noSylow
142C2×D3×D4—31no—
143C2×D3×D4—31no—
144C2×D3×D4—61no—
145C2×C3×SD16—31no—
146C2×C3×D8—31no—
147C3×C4⋊Q8—31no—
148C3×#124—31no—
149C3×C4×D4—21no—
150C3×C4×D4C2×D311yescharacteristic
151C3×C4×D4C2×D311yescharacteristic
152#947—61no—
153#946—31no—
154#946—61no—
155Q8×Dic3—31no—
156C2×#215—31no—
157#938—31no—
158D4×Dic3—31no—
159D4×Dic3—31no—
160D4×Dic3—31no—
161D4×Dic3—61no—
162C2×#214C2×D311yescharacteristic
163C2×#213—31no—
164C2×#213C2×D311yescharacteristic
165C4×#67—61no—
166C4×#67—61no—
167C4×#67—62no—
168C2×(C2×D3)⋊C4—61no—
169C2×(C2×D3)⋊C4—61no—
170C2×(C2×D3)⋊C4—62no—
171C2×D24—31no—
172C2×#204—31no—
173#898—61no—
174#897—31no—
175#895—31no—
176#894—61no—
177#893—31no—
178#893—31no—
179#893—31no—
180#893—61no—
181#892—31no—
182#892—31no—
183#892—61no—
184#887—31no—
185#886—61no—
186#885—61no—
187#67⋊C4—61no—
188#67⋊C4—61no—
189#67⋊C4—62no—
190D3×C22⋊C4—61no—
191D3×C22⋊C4—61no—
192D3×C22⋊C4—62no—
193#879—61no—
194#878—61no—
195#875C2×D311yescharacteristic, complemented
196C4×D12—31no—
197C4×D12—31no—
198C4×D12—61no—
199#872—31no—
200#872—31no—
201#872—61no—
202#869C2×D311yescharacteristic, complemented
203C3×#106—31no—
204C3×#106—31no—
205C3×C4⋊C8—31no—
206C3×C4⋊C8—31no—
207C3×#103—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211#835—31no—
212#832—31no—
213#832C2×D311yescharacteristic
214#832C2×D311yescharacteristic
215#821—31no—
216#821—31no—
217#821—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222#818—31no—
223#818—31no—
224#816—31no—
225#815—31no—
226#815—31no—
227C8×Dic3—31no—
228C8×Dic3—31no—
229#810C2×D311yescharacteristic, complemented
230#809—31no—
231#809—31no—
232#809C2×D311yescharacteristic, complemented
233#808C2×D311yescharacteristic, complemented
234#808C2×D311yescharacteristic, complemented
235#807—31no—
236#807—31no—
237C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
238C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
239C23×C32—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—24no—
242C22×C3⋊D3—81no—
243C22×C3⋊D3—81no—
244C22×C3⋊D3C2×D411yescharacteristic
245C22×C3×D3—21no—
246C32×D4—21no—
247C32×D4#4112yes—
248C2×C32×C4—21no—
249C2×C32×C4—81no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253#638—24no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—81no—
256C2×C3⋊Dic3C2×D411yescharacteristic
257C2×C3⋊Dic3C2×D411yescharacteristic
258C2×C3⋊Dic3C2×D411yescharacteristic
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)#4112yes—
261C4×C3⋊D3—21no—
262C4×C3⋊D3—21no—
263C4×C3⋊D3—81no—
264C4×C3⋊D3—81no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6—81no—
273#626—81no—
274D3×Dic3—81no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#542—91no—
280#518—91no—
281#485—91no—
282#482—91no—
283#476—31no—
284#474—91no—
285#463—31no—
286#463—91no—
287#450—91no—
288#447—91no—
289#442—91no—
290#440—91no—
291C4×SD16—91no—
292C4×D8—91no—
293#433—91no—
294C23×D3—61no—
295C23×D3—61no—
296C23×D3—62no—
297C2×C3×Q8—31no—
298C2×C3×Q8—61no—
299C2×C3×D4—21no—
300C2×C3×D4—31no—
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C22×D311yescharacteristic
303C22×C3×C4—22no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—62no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—62no—
314D3×D4—62no—
315D3×D4—62no—
316D3×D4—64no—
317D3×D4—64no—
318D3×D4—62no—
319D3×D4—62no—
320C2×D12—31no—
321C2×D12—31no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—31no—
326C2×C4×D3—31no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—62no—
332C2×C4×D3—62no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×Dic6—21no—
336C2×Dic6C22×D311yescharacteristic
337C3×SD16—62no—
338C3×D8—62no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C22⋊C4—22no—
350C3×C22⋊C4—21no—
351C3×C22⋊C4—21no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C42—21no—
355C3×C42C22×D311yescharacteristic
356C3×C42C22×D311yescharacteristic
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—62no—
362#215—62no—
363#214—22no—
364#213—22no—
365#213—62no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—62no—
383(C2×D3)⋊C4—62no—
384(C2×D3)⋊C4—62no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387C4⋊Dic3—21no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395Dic3⋊C4—31no—
396Dic3⋊C4—31no—
397Dic3⋊C4—31no—
398Dic3⋊C4—31no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403C4×Dic3—31no—
404C4×Dic3—31no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C4×Dic3—62no—
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413C2×C3⋊C8C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415D24—62no—
416#204—62no—
417C22×C32—22no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32C22×D411yescharacteristic
421C2×C3⋊D3—21no—
422C2×C3⋊D3—22no—
423C2×C3⋊D3—21no—
424C2×C3⋊D3—21no—
425C2×C3⋊D3—41no—
426C2×C3⋊D3—41no—
427C2×C3⋊D3—84no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C32×C4—21no—
432C32×C4—21no—
433C32×C4—41no—
434C32×C4C2×#4111yescharacteristic
435C32×C4C2×#4111yescharacteristic
436C3⋊Dic3—21no—
437C3⋊Dic3—21no—
438C3⋊Dic3—21no—
439C3⋊Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C22×D4—91no—
444C2×SD16—31no—
445C2×SD16—91no—
446C2×D8—31no—
447C2×D8—91no—
448C4⋊Q8—31no—
449#126—181no—
450#124—31no—
451#124—181no—
452#123—181no—
453C22⋊Q8—91no—
454C22⋊Q8—181no—
455#121—91no—
456C4×Q8—91no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—181no—
462C4×D4—181no—
463C4×D4D3211yescharacteristic
464#117—91no—
465#117—91no—
466C2×C22⋊C4—181no—
467C2×C22⋊C4—181no—
468#107—91no—
469#107—91no—
470#106—31no—
471#106—31no—
472C4⋊C8—31no—
473C4⋊C8—31no—
474#103—31no—
475#103—91no—
476#102—31no—
477#102—31no—
478#102—31no—
479#102—91no—
480#102—91no—
481#102—91no—
482C22⋊C8—91no—
483C22⋊C8—91no—
484#97—91no—
485C4×C8—91no—
486C23×C3—22no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—61no—
490C22×D3—21no—
491C22×D3—31no—
492C22×D3—31no—
493C22×D3—61no—
494C22×D3—62no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—68no—
498C22×D3—64no—
499C22×D3—64no—
500C22×D3—241no—
501C22×D3—241no—
502C22×D3—241no—
503C22×D3—241no—
504C22×D3—242no—
505C22×D3—242no—
506C3×Q8—61no—
507C3×Q8—61no—
508C3×Q8—241no—
509C3×D4—22no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—22no—
513C3×D4—61no—
514C3×D4—61no—
515C3×D4#23712yes—
516C3×D4#23912yes—
517C2×C3×C4—22no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—81no—
527C2×C3×C4—81no—
528C2×C3×C4—82no—
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4D3×D411yescharacteristic
531C2×C3×C4D3×D411yescharacteristic
532C2×C3×C4D3×D411yescharacteristic
533C2×C3×C4C23×D311yescharacteristic
534C2×C3×C4C23×D311yescharacteristic
535#67—68no—
536#67—64no—
537#67—64no—
538#67—241no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—31no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—62no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—241no—
555C2×Dic3—241no—
556C2×Dic3—241no—
557C2×Dic3—242no—
558D12—21no—
559D12—21no—
560D12—32no—
561D12—32no—
562D12—62no—
563D12—62no—
564D12—61no—
565D12—61no—
566D12—241no—
567C4×D3—62no—
568C4×D3—62no—
569C4×D3—61no—
570C4×D3—61no—
571C4×D3—61no—
572C4×D3—61no—
573C4×D3—241no—
574C4×D3—241no—
575C4×D3—241no—
576C4×D3—241no—
577C4×D3—241no—
578C4×D3—242no—
579C4×D3—242no—
580Dic6—21no—
581Dic6—21no—
582Dic6—81no—
583C3×C8—61no—
584C3×C8—61no—
585C3×C8—61no—
586C3×C8—61no—
587C3⋊C8—21no—
588C3⋊C8—21no—
589C3⋊C8—21no—
590C3⋊C8—21no—
591C2×C32—42no—
592C2×C32#52511yescharacteristic
593C2×C32#57611yescharacteristic
594C2×C32#57711yescharacteristic
595C3⋊D3—41no—
596C3⋊D3—42no—
597C3×D3—81no—
598C24—181no—
599C2×Q8—31no—
600C2×Q8—61no—
601C2×D4—31no—
602C2×D4—91no—
603C2×D4—181no—
604C2×D4—181no—
605C2×D4—182no—
606C2×D4—182no—
607C2×D4C2×D3211yescharacteristic
608C22×C4—21no—
609C22×C4—91no—
610C22×C4—181no—
611C22×C4—181no—
612C22×C4—181no—
613C22×C4—181no—
614SD16—62no—
615SD16—182no—
616D8—62no—
617D8—182no—
618C2×C8—31no—
619C2×C8—31no—
620C2×C8—31no—
621C2×C8—31no—
622C4⋊C4—31no—
623C4⋊C4—31no—
624C4⋊C4—61no—
625C4⋊C4—91no—
626C4⋊C4—91no—
627C4⋊C4—91no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—21no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—91no—
635C22⋊C4—91no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C42—91no—
644C42—181no—
645C42—181no—
646C42C2×D3211yescharacteristic
647C22×C3—24no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—21no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3C2×D3×D411yescharacteristic
661C22×C3C2×D3×D411yescharacteristic
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—62no—
666C2×D3—64no—
667C2×D3—61no—
668C2×D3—61no—
669C2×D3—61no—
670C2×D3—61no—
671C2×D3—61no—
672C2×D3—62no—
673C2×D3—61no—
674C2×D3—62no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3—122no—
678C2×D3—122no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—248no—
684C2×D3—244no—
685C2×D3—244no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—41no—
693C3×C4—41no—
694C3×C4—42no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—121no—
698C3×C4—121no—
699C3×C4—121no—
700C3×C4C2×#23711yescharacteristic
701C3×C4C2×#23911yescharacteristic
702C3×C4D3×#4111yescharacteristic
703C3×C4D3×#4111yescharacteristic
704Dic3—41no—
705Dic3—41no—
706Dic3—41no—
707Dic3—62no—
708Dic3—61no—
709Dic3—61no—
710Dic3—61no—
711Dic3—61no—
712Dic3—61no—
713Dic3—61no—
714Dic3—121no—
715Dic3—121no—
716Dic3—122no—
717Dic3—121no—
718Dic3—121no—
719C32#311811yescharacteristic, complemented, Sylow
720C23—21no—
721C23—61no—
722C23—91no—
723C23—184no—
724C23—181no—
725C23—721no—
726C23—721no—
727Q8—61no—
728Q8—61no—
729Q8—241no—
730D4—21no—
731D4—61no—
732D4—61no—
733D4—92no—
734D4—184no—
735D4—181no—
736D4—721no—
737D4#379612yes—
738C2×C4—21no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—81no—
743C2×C4—91no—
744C2×C4—91no—
745C2×C4—91no—
746C2×C4—181no—
747C2×C4—181no—
748C2×C4—181no—
749C2×C4—721no—
750C2×C4—721no—
751C2×C4—721no—
752C2×C4—721no—
753C2×C4#381111yescharacteristic
754C2×C4#381111yescharacteristic
755C2×C4C22×D3211yescharacteristic
756C8—61no—
757C8—61no—
758C8—61no—
759C8—61no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—44no—
764C2×C3—42no—
765C2×C3—42no—
766C2×C3—241no—
767C2×C3#560611yescharacteristic
768C2×C3#562711yescharacteristic
769C2×C3#576211yescharacteristic
770C2×C3#576911yescharacteristic
771C2×C3#577411yescharacteristic
772C2×C3#577511yescharacteristic
773D3—81no—
774D3—122no—
775D3—124no—
776D3—121no—
777D3—122no—
778D3—121no—
779D3—122no—
780C22—22no—
781C22—41no—
782C22—41no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—181no—
787C22—181no—
788C22—182no—
789C22—181no—
790C22—361no—
791C22—361no—
792C22—724no—
793C22C2×#381111yescharacteristic
794C4—21no—
795C4—21no—
796C4—41no—
797C4—121no—
798C4—121no—
799C4—121no—
800C4—181no—
801C4—181no—
802C4—181no—
803C4—361no—
804C4C2×#379611yescharacteristic
805C4#6430611yescharacteristic
806C3—21no—
807C3#8050811yescharacteristic, complemented
808C3#8104811yescharacteristic, complemented
809C2—42no—
810C2—241no—
811C2—361no—
812C2—362no—
813C2#1059492211yescharacteristic
814C2#1059511511yescharacteristic
815C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radical#10591456C2
hypercenterC4×D4D32
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596016C2semidirect
2. #10593955C2semidirect
3. C3×#5016C2semidirect
4. C3×#5008C2semidirect
5. #10591467C2semidirect
7. #10591446C2semidirect
8. #10591435C2semidirect
9. #10590527C2semidirect
10. #10590513C2semidirect
11. #10590483C2semidirect
12. #10590462C2semidirect
13. #10590356C2semidirect
14. #10590313C2semidirect
15. #10590257C2semidirect
31. C3×#875C22semidirect
32. C3×#869C22semidirect
35. #63898C22semidirect
40. #63843C22semidirect
45. C3×#810C22semidirect
46. C3×#809C22semidirect
47. C3×#808C22semidirect
48. C3×#808C22semidirect
49. C3×C4⋊(C3⋊C8)C22semidirect
50. C3×C4⋊(C3⋊C8)C22semidirect
51. #63575C22semidirect
52. #63575C22semidirect
53. #63566C22semidirect
56. #63563C22semidirect
59. #63555C22semidirect
60. #63553C22semidirect
74. #5016D3semidirect
75. #5008D3semidirect
195. #875C2×D3semidirect
202. #869C2×D3semidirect
229. #810C2×D3semidirect
232. #809C2×D3semidirect
233. #808C2×D3semidirect
234. #808C2×D3semidirect
237. C4⋊(C3⋊C8)C2×D3semidirect
238. C4⋊(C3⋊C8)C2×D3semidirect
719. C32#3118semidirect
807. C3#80508semidirect
808. C3#81048semidirect

Maximal subgroups

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

subgroupindex
#105960162
#105939552
C3×#50162
C3×#50082
#105914672
#105914562
#105914462
#105914352
#105905272
#105905132
#105904832
#105904622
#105903562
#105903132
#105902572
#810483
#805083