Finite Group Databasebeta

← #11887443

Subgroups — #11887443

Order 1152.

902 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594003C211yesmaximal, characteristic, complemented
2#10593925C211yesmaximal, characteristic, complemented
3#10592543C211yesmaximal, characteristic, complemented
4C3×#4847C211yesmaximal, characteristic, complemented
5C3×#4834C211yesmaximal, characteristic, complemented
6#10590968C211yesmaximal, characteristic, complemented
7#10590954C211yesmaximal, characteristic, complemented
8#10590947C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590832C211yesmaximal, characteristic, complemented
11#10590830C211yesmaximal, characteristic, complemented
12#10590704C211yesmaximal, characteristic, complemented
13#10590684C211yesmaximal, characteristic, complemented
14C4×#3714C211yesmaximal, characteristic, complemented
15#10590293C211yesmaximal, characteristic, complemented
16#81187—31nomaximal
17#79441—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C2×#3745C2211yescharacteristic
21C2×#3744C2211yescharacteristic, complemented
22#64084C2211yescharacteristic
23C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
24C2×C3×D3×C8C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic, complemented
26C3×C4×D12C2211yescharacteristic
27C3×C4×D12C2211yescharacteristic
28C3×#870C2211yescharacteristic, complemented
29#63922—21no—
30D3×(C2×D3)⋊C4—21no—
31#63909C2211yescharacteristic
32#63909C2211yescharacteristic
33#63909C2211yescharacteristic, complemented
34#63906—21no—
35#63890—21no—
36D3×C4⋊Dic3C2211yescharacteristic
37#63886—21no—
38#63881—21no—
39#63857C2211yescharacteristic
40#63853—21no—
41#63848—21no—
42#63841C2211yescharacteristic, complemented
43C2×#3714C2211yescharacteristic
44C32×C4⋊C8C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63643C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×#818C2211yescharacteristic, complemented
52C3×#817C2211yescharacteristic, complemented
53C3×C4×C3⋊C8C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic, complemented
60#63563C2211yescharacteristic
61#5695—31no—
62#5565—31no—
63#5554—31no—
64#5550—31no—
65C3×#478—31no—
66C3×C8×D4—31no—
67#5115—31no—
68#5114—31no—
69#5113—31no—
70C2×#821—31no—
71#5068—31no—
72C4×#213—31no—
73#4884—31no—
74#4883—31no—
75#4866—31no—
76#4864—31no—
77#4847D311yescharacteristic, complemented
78#4844—31no—
79#4844—31no—
80#4844—61no—
81#4834D311yescharacteristic, complemented
82#4781—31no—
83#4773—31no—
84#4772—31no—
85D3×#102—31no—
86#4737—31no—
87#4734—31no—
88#4732—31no—
89#4722—31no—
90#4697—31no—
91C4×D24—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×#634C2311yescharacteristic
97C2×C3×D12D411yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×#626—21no—
103C2×#626—21no—
104C2×#626—21no—
105C2×#626—21no—
106C2×#625—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109D3×D12—22no—
110D3×D12—41no—
111#3795—22no—
112#3795—41no—
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115C32×C42C2311yescharacteristic
116#3752—21no—
117#3752—21no—
118#3752—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3745—41no—
121#3744—41no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3D411yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C3×D3×C8—41no—
134C3×D3×C8—41no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138#3722—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143#3714—22no—
144#3297—91noSylow
145C2×#237—31no—
146C2×D3×D4—31no—
147C2×#235—31no—
148C22×D12—31no—
149C22×C3×C8—31no—
150C22×C3×C8—31no—
151C3×#125—31no—
152C3×C4×D4—31no—
153C3×C4×D4—31no—
154#939—61no—
155#937—61no—
156C2×#213—31no—
157#930—31no—
158#930—31no—
159#930—31no—
160#930—61no—
161C2×(C2×D3)⋊C4—61no—
162#926—31no—
163C2×C4⋊Dic3—31no—
164#924—31no—
165C2×D24—31no—
166C2×D24—31no—
167C2×D24—31no—
168C2×D24—61no—
169C2×#204—31no—
170C2×#204—31no—
171C2×#204—61no—
172C2×D3×C8C2×D311yescharacteristic
173C2×D3×C8C2×D311yescharacteristic, complemented
174#898—61no—
175#898—61no—
176#897—31no—
177#895—31no—
178#895—31no—
179#895—31no—
180#895—61no—
181#894—61no—
182#894—61no—
183#893—61no—
184#892—31no—
185D3×C4⋊C4—31no—
186#886—61no—
187#884—61no—
188#883—61no—
189#882—61no—
190#67⋊C4—61no—
191D3×C22⋊C4—61no—
192#875—31no—
193#875—31no—
194#875—61no—
195C4×D12—31no—
196C4×D12—31no—
197C4×D12—61no—
198C4×D12C2×D311yescharacteristic
199C4×D12C2×D311yescharacteristic
200#870C2×D311yescharacteristic, complemented
201C3×#107—31no—
202C3×#106—31no—
203C3×C4⋊C8—21no—
204C3×C4⋊C8C2×D311yescharacteristic, complemented
205C3×C4⋊C8C2×D311yescharacteristic, complemented
206C3×#102—31no—
207C3×#102—31no—
208C3×C22⋊C8—31no—
209C3×C22⋊C8—31no—
210C3×C4×C8—31no—
211#832—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—61no—
219#821C2×D311yescharacteristic
220#821C2×D311yescharacteristic
221(C2×D3)⋊C8C2×D311yescharacteristic
222(C2×D3)⋊C8C2×D311yescharacteristic, complemented
223#818—31no—
224#818C2×D311yescharacteristic, complemented
225#817C2×D311yescharacteristic, complemented
226#816—31no—
227#816—31no—
228#816—31no—
229#816—31no—
230#816—61no—
231#810—31no—
232#810—31no—
233#809—31no—
234#809—31no—
235#809—31no—
236#807—31no—
237C4×C3⋊C8C2×D311yescharacteristic, complemented
238C22×C3⋊D3—21no—
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C22×C3×D3C2×D411yescharacteristic
243C2×D32—42no—
244C2×D32—42no—
245C2×D32—81no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C4×C3⋊D3—81no—
256#634—21no—
257#634—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—22no—
264C3×D12—21no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—81no—
271#626—42no—
272#626—42no—
273#626—81no—
274#626—81no—
275#625—42no—
276D3×Dic3—42no—
277D3×Dic3—81no—
278C32×C8—21no—
279C32×C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—91no—
283#546—91no—
284#488—91no—
285#484—91no—
286#482—91no—
287#478—31no—
288#466—91no—
289#465—91no—
290#463—91no—
291#449—91no—
292#447—91no—
293C4×D8—91no—
294C8×D4—31no—
295#416—91no—
296C2×#102—91no—
297C23×D3—61no—
298C23×D3—61no—
299C2×C3×D4—31no—
300C2×C3×D4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312#237—62no—
313#237—121no—
314D3×D4—62no—
315D3×D4—121no—
316#235—62no—
317#235—121no—
318C2×D12—31no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—31no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12—62no—
325C2×D12—61no—
326C2×D12—61no—
327C2×D12—61no—
328C2×D12—61no—
329C2×D12—121no—
330C2×D12D1211yescharacteristic
331C2×D12C22×D311yescharacteristic
332C2×C4×D3—21no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—121no—
338C2×C4×D3C22×D311yescharacteristic
339C2×C4×D3C22×D311yescharacteristic
340C2×Dic6—31no—
341C2×Dic6—31no—
342C2×Dic6—61no—
343C2×C3×C8—21no—
344C2×C3×C8—21no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8—121no—
348C2×C3×C8—121no—
349C2×C3×C8C22×D311yescharacteristic
350C2×C3×C8C22×D311yescharacteristic
351C2×C3×C8C22×D311yescharacteristic
352C2×C3×C8C22×D311yescharacteristic
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C22⋊C4—31no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—61no—
362C3×C42—21no—
363C3×C42C22×D311yescharacteristic
364C3×C42C22×D311yescharacteristic
365#217—61no—
366#217—61no—
367#213—62no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
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—61no—
383(C2×D3)⋊C4—121no—
384(C2×D3)⋊C4—121no—
385(C2×D3)⋊C4—121no—
386(C2×D3)⋊C4D1211yescharacteristic
387(C2×D3)⋊C4D1211yescharacteristic
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3D1211yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396C4⋊Dic3C22×D311yescharacteristic
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405D24—62no—
406D24—121no—
407D24—121no—
408D24—122no—
409#204—121no—
410#204—121no—
411#204—122no—
412D3×C8—41no—
413D3×C8—41no—
414C22×C32C22×D411yescharacteristic
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—22no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3#13512yes—
430D32—84no—
431C32×C4—21no—
432C32×C4—21no—
433C32×C4C2×#4111yescharacteristic
434C32×C4H(5,𝔽2)11yescharacteristic
435C3⋊Dic3—41no—
436C3⋊Dic3—41no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C2×#41—91no—
443C22×D4—91no—
444C2×SD16—91no—
445C2×D8—91no—
446C2×D8—91no—
447C22×C8—31no—
448C22×C8—31no—
449#126—181no—
450#125—31no—
451#124—91no—
452#123—181no—
453#123—181no—
454C22⋊Q8—91no—
455#121—91no—
456#121—91no—
457#121—91no—
458#121—181no—
459#121—181no—
460#120—181no—
461C4×D4—31no—
462C4×D4—31no—
463C4×D4—91no—
464C4×D4—181no—
465#117—91no—
466C2×C4⋊C4—91no—
467C2×C22⋊C4—181no—
468#107—31no—
469#107—91no—
470#106—31no—
471C4⋊C8D3211yescharacteristic, complemented
472#103—91no—
473#103—91no—
474#103—91no—
475#102—31no—
476#102—31no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481#102—91no—
482C22⋊C8—31no—
483C22⋊C8—31no—
484C4×C8—31no—
485C23×C3—31no—
486C23×C3—31no—
487C23×C3—61no—
488C22×D3—21no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—61no—
492C22×D3—61no—
493C22×D3—121no—
494C22×D3—121no—
495C22×D3—122no—
496C22×D3—122no—
497C22×D3—122no—
498C22×D3—122no—
499C22×D3—241no—
500C22×D3—241no—
501C22×D3C2×D1211yescharacteristic
502C22×D3C2×D1211yescharacteristic
503C3×D4—32no—
504C3×D4—62no—
505C3×D4—61no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—241no—
519C2×C3×C4C2×D1211yescharacteristic
520C2×C3×C4C2×D1211yescharacteristic
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525#67—122no—
526#67—122no—
527#67—122no—
528#67—122no—
529#67—241no—
530#67—241no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—121no—
539C2×Dic3—121no—
540C2×Dic3—122no—
541C2×Dic3—241no—
542C2×Dic3C2×D1211yescharacteristic
543C2×Dic3C2×D1211yescharacteristic
544D12—22no—
545D12—21no—
546D12—62no—
547D12—61no—
548D12—61no—
549D12—61no—
550D12—61no—
551D12—61no—
552D12—61no—
553D12—61no—
554D12—61no—
555D12—121no—
556D12—121no—
557D12—121no—
558D12—122no—
559D12—122no—
560D12—241no—
561D12—241no—
562D12#23912yes—
563C4×D3—21no—
564C4×D3—21no—
565C4×D3—21no—
566C4×D3—21no—
567C4×D3—81no—
568C4×D3—122no—
569C4×D3—241no—
570C4×D3—241no—
571C4×D3—241no—
572C4×D3—242no—
573Dic6—61no—
574Dic6—61no—
575Dic6—61no—
576Dic6—61no—
577Dic6—121no—
578Dic6—121no—
579C3×C8—21no—
580C3×C8—21no—
581C3×C8—21no—
582C3×C8—21no—
583C3×C8—41no—
584C3×C8—41no—
585C3×C8—61no—
586C3×C8—61no—
587C3⋊C8—21no—
588C3⋊C8—21no—
589C2×C32#54611yescharacteristic
590C2×C32C2×#13511yescharacteristic
591C2×C32#57611yescharacteristic
592C3⋊D3—81no—
593C3⋊D3—81no—
594C3×D3—22no—
595C3×D3—42no—
596C3×D3—41no—
597C24—181no—
598#41—182no—
599#41—361no—
600C2×Q8—91no—
601C2×D4—31no—
602C2×D4—31no—
603C2×D4—91no—
604C2×D4—91no—
605C2×D4—181no—
606C2×D4—182no—
607C2×D4—181no—
608C2×D4—181no—
609C2×D4—181no—
610C2×D4—181no—
611C2×D4—361no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—61no—
615C22×C4—181no—
616C22×C4—181no—
617C22×C4—181no—
618SD16—361no—
619D8—182no—
620D8—361no—
621C2×C8—31no—
622C2×C8—31no—
623C2×C8—121no—
624C2×C8—121no—
625C2×C8C2×D3211yescharacteristic
626C2×C8C2×D3211yescharacteristic
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—91no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C22⋊C4—31no—
637C22⋊C4—31no—
638C22⋊C4—61no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C42—181no—
648C42C2×D3211yescharacteristic
649C22×C3—21no—
650C22×C3—32no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—62no—
656C22×C3—61no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3C22×D1211yescharacteristic
660C22×C3C2×D3×D411yescharacteristic
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—22no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—122no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—241no—
683C2×D3—241no—
684C2×D3—241no—
685C2×D3—241no—
686C2×D3—241no—
687C2×D3—244no—
688C2×D3—244no—
689C2×D3#90412yes—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—61no—
699C3×C4—61no—
700C3×C4—121no—
701C3×C4—121no—
702C3×C4—121no—
703C3×C4#100411yescharacteristic
704C3×C4C2×#23911yescharacteristic
705C3×C4D3×#4111yescharacteristic
706C3×C4#100911yescharacteristic
707Dic3—21no—
708Dic3—21no—
709Dic3—41no—
710Dic3—41no—
711Dic3—41no—
712Dic3—121no—
713Dic3—121no—
714Dic3—121no—
715Dic3—121no—
716Dic3—241no—
717Dic3—241no—
718C32#329711yescharacteristic, complemented, Sylow
719C23—31no—
720C23—31no—
721C23—61no—
722C23—181no—
723C23—181no—
724C23—362no—
725C23—362no—
726C23—721no—
727Q8—181no—
728Q8—181no—
729D4—32no—
730D4—62no—
731D4—61no—
732D4—181no—
733D4—181no—
734D4—181no—
735D4—181no—
736D4—362no—
737D4—362no—
738D4—362no—
739D4—721no—
740D4—721no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—181no—
751C2×C4—181no—
752C2×C4—241no—
753C2×C4—362no—
754C2×C4—721no—
755C2×C4—721no—
756C2×C4D3×D1211yescharacteristic
757C2×C4D3×D1211yescharacteristic
758C2×C4C22×D3211yescharacteristic
759C8—21no—
760C8—21no—
761C8—61no—
762C8—61no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—62no—
767C2×C3—121no—
768C2×C3—122no—
769C2×C3#555411yescharacteristic
770C2×C3#563011yescharacteristic
771C2×C3C2×#90411yescharacteristic
772C2×C3#575211yescharacteristic
773C2×C3D3×#13511yescharacteristic
774C2×C3#577411yescharacteristic
775D3—22no—
776D3—42no—
777D3—41no—
778D3—242no—
779D3—241no—
780D3—241no—
781D3—241no—
782D3—241no—
783D3—481no—
784C22—32no—
785C22—61no—
786C22—61no—
787C22—61no—
788C22—62no—
789C22—61no—
790C22—61no—
791C22—121no—
792C22—121no—
793C22—361no—
794C22—361no—
795C22—361no—
796C22—361no—
797C22—361no—
798C22—361no—
799C22—724no—
800C22C2×D3×D1211yescharacteristic
801C4—21no—
802C4—21no—
803C4—61no—
804C4—61no—
805C4—121no—
806C4—121no—
807C4—121no—
808C4—361no—
809C4—361no—
810C4#6431411yescharacteristic
811C4D3×#23911yescharacteristic
812C3—21no—
813C3#7944111yescharacteristic, complemented
814C3#8118711yescharacteristic, complemented
815C2—62no—
816C2—121no—
817C2—122no—
818C2—721no—
819C2—721no—
820C2#1059462911yescharacteristic
821C2D3×#90411yescharacteristic
822C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #10594003C2semidirect
2. #10593925C2semidirect
3. #10592543C2semidirect
4. C3×#4847C2semidirect
5. C3×#4834C2semidirect
6. #10590968C2semidirect
7. #10590954C2semidirect
8. #10590947C2semidirect
9. D3×#821C2semidirect
10. #10590832C2semidirect
11. #10590830C2semidirect
12. #10590704C2semidirect
13. #10590684C2semidirect
14. C4×#3714C2semidirect
15. #10590293C2semidirect
21. C2×#3744C22semidirect
23. C4×C4⋊(C3⋊D3)C22semidirect
25. C2×C3×D3×C8C22semidirect
28. C3×#870C22semidirect
33. #63909C22semidirect
42. #63841C22semidirect
44. C32×C4⋊C8C22semidirect
46. #63643C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×#818C22semidirect
52. C3×#817C22semidirect
53. C3×C4×C3⋊C8C22semidirect
54. #63575C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
59. #63564C22semidirect
77. #4847D3semidirect
81. #4834D3semidirect
173. C2×D3×C8C2×D3semidirect
200. #870C2×D3semidirect
204. C3×C4⋊C8C2×D3semidirect
205. C3×C4⋊C8C2×D3semidirect
222. (C2×D3)⋊C8C2×D3semidirect
224. #818C2×D3semidirect
225. #817C2×D3semidirect
237. C4×C3⋊C8C2×D3semidirect
471. C4⋊C8D32semidirect
718. C32#3297semidirect
813. C3#79441semidirect
814. C3#81187semidirect

Maximal subgroups

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

subgroupindex
#105940032
#105939252
#105925432
C3×#48472
C3×#48342
#105909682
#105909542
#105909472
D3×#8212
#105908322
#105908302
#105907042
#105906842
C4×#37142
#105902932
#811873
#794413