Finite Group Databasebeta

← #11857977

Subgroups — #11857977

Order 1152.

1623 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C211yesmaximal, characteristic
2C2×#63791C211yesmaximal, characteristic, complemented
3D3×#892C211yesmaximal, characteristic, complemented
4#10592503C211yesmaximal, characteristic, complemented
5C3×#4803C211yesmaximal, characteristic, complemented
6C3×#4802C211yesmaximal, characteristic, complemented
7#10591560C211yesmaximal, characteristic, complemented
8#10591557C211yesmaximal, characteristic, complemented
9#10591550C211yesmaximal, characteristic, complemented
10#10590956C211yesmaximal, characteristic, complemented
11#10590939C211yesmaximal, characteristic, complemented
12#10590671C211yesmaximal, characteristic, complemented
13#10590611C211yesmaximal, characteristic, complemented
14#10590609C211yesmaximal, characteristic, complemented
15#10590592C211yesmaximal, characteristic, complemented
16#78956—31nomaximal
17#78881—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21D3×#239—24no—
22D3×#239C418yescomplemented
23C2×D3×D12—21no—
24C2×D3×D12C2211yescharacteristic
25C2×C4×D32—21no—
26C2×C4×D32C2211yescharacteristic
27C2×#3799—21no—
28C2×#3799C2211yescharacteristic
29C2×#3796—21no—
30C2×#3796C2211yescharacteristic
31C2×C8×C3⋊D3C2211yescharacteristic, complemented
32#64101C2211yescharacteristic, complemented
33C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
34C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
35C3×#892C2211yescharacteristic
36C3×D3×C4⋊C4C2211yescharacteristic, complemented
37D3×(C2×D3)⋊C4—21no—
38D3×C4⋊Dic3C2211yescharacteristic, complemented
39#63878—21no—
40C4×D3×Dic3—21no—
41#63849C2211yescharacteristic, complemented
42#63841C2211yescharacteristic
43#63836—21no—
44C2×#3711C2211yescharacteristic
45C2×#3711C2211yescharacteristic, complemented
46C2×#3710C2211yescharacteristic, complemented
47#63791—24no—
48C32×#103C2211yescharacteristic, complemented
49#63662C2211yescharacteristic, complemented
50#63648C2211yescharacteristic, complemented
51#63636C2211yescharacteristic, complemented
52C3×#835C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#821C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63#63562C2211yescharacteristic, complemented
64C2×D3×#41—31no—
65C22×#239—31no—
66C2×D3×M16—31no—
67C2×D3×M16—31no—
68D3×#117—31no—
69C2×#892—31no—
70C3×#419—31no—
71C3×#417—31no—
72#5232—31no—
73#5225—31no—
74#5133—31no—
75#5131—31no—
76#5001—31no—
77#4966—31no—
78#4804—31no—
79#4804—31no—
80#4804—31no—
81#4804—31no—
82#4804—31no—
83#4804—31no—
84#4804—61no—
85#4803—31no—
86#4803—31no—
87#4803—31no—
88#4803D311yescharacteristic, complemented
89#4802—31no—
90#4802D311yescharacteristic, complemented
91#4772—31no—
92#4772—31no—
93#4770—31no—
94#4770—31no—
95C22×D32—21no—
96C22×D32D411yescharacteristic
97C2×C32×Q8C2311yescharacteristic
98#3832—22no—
99#3832C2×C414yescomplemented
100C2×C4⋊(C3⋊D3)—21no—
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3C2311yescharacteristic
104C3×#239—22no—
105C3×#239C2×C414yes—
106C3×D3×Q8—22no—
107C3×D3×Q8C2×C414yescomplemented
108C2×C3×D12—21no—
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6—21no—
116C2×C3×Dic6C2311yescharacteristic
117C2×#626—21no—
118C2×#626—21no—
119C2×#626—21no—
120C2×#624—21no—
121C2×#624D411yescharacteristic
122C2×D3×Dic3—21no—
123C2×D3×Dic3—21no—
124C2×D3×Dic3D411yescharacteristic
125C2×D3×Dic3D411yescharacteristic
126D3×D12—28no—
127D3×D12—22no—
128D3×D12C2×C414yescomplemented
129C4×D32—28no—
130C4×D32C2×C414yes—
131C4×D32D414yes—
132#3799—22no—
133#3799—28no—
134#3799C2×C414yes—
135#3796—22no—
136#3796—28no—
137#3796C2×C414yescomplemented
138C2×C32×C8C2311yescharacteristic
139C32×C4⋊C4C2311yescharacteristic
140#3752—21no—
141C4⋊(C3⋊Dic3)C2311yescharacteristic
142C4×C3⋊Dic3—21no—
143C2×C3⋊(C3⋊C8)C2311yescharacteristic
144C8×C3⋊D3—22no—
145C3×(C2×D3)⋊C4—21no—
146C3×C4⋊Dic3C2311yescharacteristic
147C3×C4⋊Dic3C2311yescharacteristic
148C3×Dic3⋊C4—21no—
149C3×C4×Dic3—21no—
150C2×C3×C3⋊C8C2311yescharacteristic
151C2×C3×C3⋊C8C2311yescharacteristic
152C3×ΓL(1,𝔽25)—22no—
153C3×ΓL(1,𝔽25)—22no—
154Dic3⋊Dic3—21no—
155#3722—21no—
156(C2×D3)⋊Dic3—21no—
157Dic32—21no—
158Dic32—21no—
159#3711—22no—
160#3711—22no—
161#3710—22no—
162#2896—91noSylow
163C2×C3×#41—31no—
164C22×C3×Q8—31no—
165D3×#41—38no—
166D3×#41—64no—
167C2×#239—31no—
168C2×#239—31no—
169C2×#239—38no—
170C2×#239—31no—
171C2×#239—31no—
172C2×#239—61no—
173C2×#239—61no—
174C2×#239—61no—
175C2×#239—64no—
176C2×#239C2×D311yescharacteristic
177C2×D3×Q8C2×D311yescharacteristic
178C2×#237—31no—
179C2×#237—61no—
180C2×D3×D4—31no—
181C2×D3×D4—61no—
182C2×#235—31no—
183C2×#235—61no—
184C22×D12—31no—
185C22×D12—61no—
186C22×C4×D3—31no—
187C22×C4×D3—31no—
188C22×C4×D3—61no—
189C22×C4×D3—61no—
190C2×C3×M16—31no—
191C2×C3×M16—31no—
192C3×#117—31no—
193C2×C3×C4⋊C4—31no—
194C2×(C2×D3)⋊C4—61no—
195#926—31no—
196C2×C4⋊Dic3—31no—
197C2×C4×Dic3—61no—
198C2×#208—31no—
199C2×#208—31no—
200D3×M16—64no—
201D3×M16—64no—
202C2×ΓL(1,𝔽25)—31no—
203C2×ΓL(1,𝔽25)—31no—
204C2×ΓL(1,𝔽25)C2×D311yescharacteristic
205C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
206C2×D3×C8—31no—
207C2×D3×C8—31no—
208C2×D3×C8—31no—
209C2×D3×C8—31no—
210C2×D3×C8—61no—
211#892—31no—
212#892—31no—
213#892—31no—
214#892—31no—
215#892—31no—
216#892—61no—
217#892—61no—
218#892—61no—
219#892C2×D311yescharacteristic
220D3×C4⋊C4—31no—
221D3×C4⋊C4C2×D311yescharacteristic, complemented
222D3×C22⋊C4—61no—
223#877—61no—
224#872—61no—
225C42×D3—61no—
226C3×#103—21no—
227C3×#103—31no—
228C3×#103—31no—
229C3×#103—31no—
230C3×#103—31no—
231C3×#103C2×D311yescharacteristic, complemented
232C3×#103C2×D311yescharacteristic, complemented
233C3×#102—31no—
234C3×#102—31no—
235#835—31no—
236#835—31no—
237#835—31no—
238#835—31no—
239#835—61no—
240#835C2×D311yescharacteristic, complemented
241#835C2×D311yescharacteristic, complemented
242#832—31no—
243#832—31no—
244#821—31no—
245#821—31no—
246#821—31no—
247#821—31no—
248#821—31no—
249#821—61no—
250#821C2×D311yescharacteristic, complemented
251#816—31no—
252#816C2×D311yescharacteristic, complemented
253#810—31no—
254#810C2×D311yescharacteristic, complemented
255#809—31no—
256#809—31no—
257#809—31no—
258#809—31no—
259#809—31no—
260#809—61no—
261#809C2×D311yescharacteristic, complemented
262C22×C3⋊D3—21no—
263C22×C3⋊D3C2×D411yescharacteristic
264C22×C3×D3—21no—
265C22×C3×D3C2×D411yescharacteristic
266C22×C3×D3C2×D411yescharacteristic
267C2×D32—24no—
268C2×D32—41no—
269C2×D32—41no—
270C2×D32—42no—
271C2×D32—42no—
272C2×D32C22⋊C414yes—
273C32×Q8—21no—
274C32×Q8C22×C412yes—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4C2411yescharacteristic
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3C2×D411yescharacteristic
280C4⋊(C3⋊D3)—24no—
281C4⋊(C3⋊D3)—21no—
282C4⋊(C3⋊D3)C22×C412yes—
283C4×C3⋊D3—24no—
284C4×C3⋊D3C22×C412yes—
285C4×C3⋊D3C2×D412yes—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C3×D12—24no—
292C3×D12—21no—
293C3×D12C22×C412yes—
294C3×C4×D3—24no—
295C3×C4×D3—24no—
296C3×C4×D3—42no—
297C3×C4×D3C22×C412yes—
298C3×C4×D3C22×C412yes—
299C3×C4×D3C2×D412yes—
300C3×C4×D3C2×D412yes—
301C3×Dic6—21no—
302C3×Dic6—24no—
303C3×Dic6C22×C412yes—
304#626—24no—
305#626—24no—
306#626—24no—
307#624—24no—
308#624C22⋊C414yes—
309D3×Dic3—24no—
310D3×Dic3—42no—
311D3×Dic3C22⋊C414yes—
312D3×Dic3C22⋊C414yes—
313C32×C8—21no—
314C3⋊(C3⋊C8)—21no—
315C3×C3⋊C8—21no—
316C3×C3⋊C8—21no—
317C22×#41—91no—
318C22×M16—91no—
319C2×#117—91no—
320#419—31no—
321#419—91no—
322#418—91no—
323#418—91no—
324#417—31no—
325#417—91no—
326#417—91no—
327#417—91no—
328#416—91no—
329#416—91no—
330#416—91no—
331#416—91no—
332C23×D3—31no—
333C23×D3—31no—
334C23×D3—61no—
335C23×D3—61no—
336C3×#41—34no—
337C3×#41—62no—
338C2×C3×Q8—21no—
339C2×C3×Q8—34no—
340C2×C3×Q8—31no—
341C2×C3×Q8—61no—
342C2×C3×Q8—62no—
343C2×C3×Q8C22×D311yescharacteristic
344C2×C3×Q8C22×D311yescharacteristic
345C2×C3×D4—31no—
346C2×C3×D4—61no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—61no—
350C22×C3×C4—61no—
351C22×C3×C4—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—61no—
358C22×Dic3—61no—
359#239—22no—
360#239—34no—
361#239—34no—
362#239—34no—
363#239—34no—
364#239—64no—
365#239—68no—
366#239—68no—
367#239—62no—
368#239—62no—
369#239—62no—
370#239—62no—
371#239—122no—
372#239C4×D314yes—
373D3×Q8—22no—
374D3×Q8C4×D314yescomplemented
375#237—34no—
376#237—62no—
377#237—68no—
378D3×D4—34no—
379D3×D4—68no—
380D3×D4—62no—
381#235—34no—
382#235—68no—
383#235—62no—
384C2×D12—21no—
385C2×D12—31no—
386C2×D12—31no—
387C2×D12—34no—
388C2×D12—61no—
389C2×D12—62no—
390C2×D12—68no—
391C2×D12—61no—
392C2×D12—61no—
393C2×D12—61no—
394C2×D12—61no—
395C2×D12—61no—
396C2×D12—121no—
397C2×D12C22×D311yescharacteristic
398C2×C4×D3—21no—
399C2×C4×D3—21no—
400C2×C4×D3—21no—
401C2×C4×D3—31no—
402C2×C4×D3—31no—
403C2×C4×D3—31no—
404C2×C4×D3—31no—
405C2×C4×D3—31no—
406C2×C4×D3—31no—
407C2×C4×D3—34no—
408C2×C4×D3—34no—
409C2×C4×D3—34no—
410C2×C4×D3—34no—
411C2×C4×D3—61no—
412C2×C4×D3—68no—
413C2×C4×D3—68no—
414C2×C4×D3—61no—
415C2×C4×D3—61no—
416C2×C4×D3—61no—
417C2×C4×D3—61no—
418C2×C4×D3—61no—
419C2×C4×D3—61no—
420C2×C4×D3—121no—
421C2×C4×D3C22×D311yescharacteristic
422C2×C4×D3C22×D311yescharacteristic
423C2×Dic6—21no—
424C2×Dic6C22×D311yescharacteristic
425C3×M16—62no—
426C3×M16—62no—
427C2×C3×C8—21no—
428C2×C3×C8—31no—
429C2×C3×C8—31no—
430C2×C3×C8C22×D311yescharacteristic
431C2×C3×C8C22×D311yescharacteristic
432C3×C4⋊C4—21no—
433C3×C4⋊C4—31no—
434C3×C4⋊C4—31no—
435C3×C4⋊C4—61no—
436C3×C4⋊C4C22×D311yescharacteristic
437C3×C4⋊C4C22×D311yescharacteristic
438C3×C22⋊C4—61no—
439C3×C42—61no—
440#217—61no—
441(C2×D3)⋊C4—21no—
442(C2×D3)⋊C4—61no—
443(C2×D3)⋊C4—61no—
444(C2×D3)⋊C4—61no—
445(C2×D3)⋊C4—61no—
446(C2×D3)⋊C4—61no—
447(C2×D3)⋊C4—121no—
448C4⋊Dic3—31no—
449C4⋊Dic3—31no—
450C4⋊Dic3—61no—
451C4⋊Dic3—61no—
452C4⋊Dic3C22×D311yescharacteristic
453C4⋊Dic3C22×D311yescharacteristic
454Dic3⋊C4—21no—
455Dic3⋊C4—61no—
456C4×Dic3—21no—
457C4×Dic3—61no—
458C4×Dic3—61no—
459C4×Dic3—61no—
460C4×Dic3—61no—
461C4×Dic3—61no—
462C4×Dic3—61no—
463C4×Dic3—121no—
464#208—62no—
465#208—62no—
466C2×C3⋊C8—31no—
467C2×C3⋊C8—31no—
468C2×C3⋊C8—61no—
469C2×C3⋊C8C22×D311yescharacteristic
470C2×C3⋊C8C22×D311yescharacteristic
471ΓL(1,𝔽25)—22no—
472ΓL(1,𝔽25)—22no—
473ΓL(1,𝔽25)—62no—
474ΓL(1,𝔽25)—62no—
475D3×C8—62no—
476D3×C8—62no—
477D3×C8—62no—
478D3×C8—62no—
479D3×C8—122no—
480C22×C32C22×D411yescharacteristic
481C2×C3⋊D3—21no—
482C2×C3⋊D3—21no—
483C2×C3⋊D3—22no—
484C2×C3⋊D3—41no—
485C2×C3⋊D3—41no—
486C2×C3⋊D3C2×C22⋊C412yes—
487C2×C3×D3—21no—
488C2×C3×D3—21no—
489C2×C3×D3—21no—
490C2×C3×D3—21no—
491C2×C3×D3—22no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3C2×C22⋊C412yes—
495C2×C3×D3C2×C22⋊C412yes—
496D32—44no—
497D32—48no—
498C32×C4—22no—
499C32×C4—41no—
500C32×C4C23×C411yescharacteristic
501C32×C4C22×D411yescharacteristic
502C3⋊Dic3—41no—
503C3⋊Dic3C2×C22⋊C412yes—
504C3×Dic3—22no—
505C3×Dic3—41no—
506C3×Dic3—41no—
507C3×Dic3C2×C22⋊C412yes—
508C3×Dic3C2×C22⋊C412yes—
509C2×#41—31no—
510C2×#41—91no—
511C2×#41—91no—
512C2×#41—98no—
513C2×#41—91no—
514C2×#41—181no—
515C2×#41—181no—
516C2×#41—184no—
517C22×Q8—31no—
518C22×D4—91no—
519C22×D4—181no—
520C23×C4—91no—
521C23×C4—181no—
522C2×M16—31no—
523C2×M16—31no—
524C2×M16—91no—
525C2×M16—91no—
526C2×M16—184no—
527C22×C8—91no—
528C22×C8—91no—
529#117—31no—
530#117—91no—
531#117—91no—
532#117—91no—
533#117—181no—
534#117—181no—
535C2×C4⋊C4—31no—
536C2×C4⋊C4—91no—
537C2×C22⋊C4—181no—
538C2×C42—181no—
539#103—31no—
540#103—31no—
541#103—31no—
542#103—31no—
543#103—91no—
544#103—91no—
545#103—91no—
546#103D3211yescharacteristic, complemented
547#102—31no—
548#102—31no—
549#102—91no—
550#102—91no—
551#102—91no—
552#102—91no—
553#102—91no—
554#102—91no—
555C23×C3—31no—
556C23×C3—31no—
557C23×C3—61no—
558C22×D3—21no—
559C22×D3—31no—
560C22×D3—31no—
561C22×D3—34no—
562C22×D3—34no—
563C22×D3—61no—
564C22×D3—64no—
565C22×D3—61no—
566C22×D3—61no—
567C22×D3—64no—
568C22×D3—121no—
569C22×D3—121no—
570C22×D3—121no—
571C22×D3—121no—
572C22×D3—121no—
573C22×D3—122no—
574C22×D3—122no—
575C22×D3—122no—
576C22×D3—122no—
577C22×D3D3×D411yescharacteristic
578C22×D3D3×D411yescharacteristic
579C3×Q8—21no—
580C3×Q8—21no—
581C3×Q8—22no—
582C3×Q8—32no—
583C3×Q8—41no—
584C3×Q8—64no—
585C3×Q8—61no—
586C3×Q8C2×C4×D312yes—
587C3×Q8C2×C4×D312yes—
588C3×D4—32no—
589C3×D4—64no—
590C3×D4—61no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—31no—
597C2×C3×C4—31no—
598C2×C3×C4—32no—
599C2×C3×C4—32no—
600C2×C3×C4—32no—
601C2×C3×C4—32no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—64no—
605C2×C3×C4—64no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—122no—
610C2×C3×C4C23×D311yescharacteristic
611C2×C3×C4C23×D311yescharacteristic
612#67—64no—
613#67—64no—
614#67—64no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—31no—
619C2×Dic3—31no—
620C2×Dic3—34no—
621C2×Dic3—34no—
622C2×Dic3—61no—
623C2×Dic3—64no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626C2×Dic3—121no—
627C2×Dic3—122no—
628C2×Dic3D3×D411yescharacteristic
629C2×Dic3D3×D411yescharacteristic
630D12—24no—
631D12—21no—
632D12—32no—
633D12—32no—
634D12—62no—
635D12—64no—
636D12—64no—
637D12—64no—
638D12—64no—
639D12—64no—
640D12—61no—
641D12—61no—
642D12—121no—
643D12—124no—
644D12C2×C4×D312yes—
645C4×D3—24no—
646C4×D3—24no—
647C4×D3—34no—
648C4×D3—34no—
649C4×D3—32no—
650C4×D3—32no—
651C4×D3—32no—
652C4×D3—32no—
653C4×D3—34no—
654C4×D3—34no—
655C4×D3—42no—
656C4×D3—62no—
657C4×D3—62no—
658C4×D3—64no—
659C4×D3—64no—
660C4×D3—64no—
661C4×D3—64no—
662C4×D3—64no—
663C4×D3—124no—
664C4×D3—122no—
665C4×D3C2×C4×D312yes—
666C4×D3C2×C4×D312yes—
667C4×D3D3×D412yes—
668C4×D3D3×D412yes—
669Dic6—21no—
670Dic6—24no—
671Dic6C2×C4×D312yes—
672C3×C8—21no—
673C3×C8—21no—
674C3×C8—41no—
675C3×C8—61no—
676C3×C8—61no—
677C3⋊C8—21no—
678C3⋊C8—21no—
679C3⋊C8—61no—
680C3⋊C8—61no—
681C3⋊C8—121no—
682C2×C32C22×C22⋊C411yescharacteristic
683C2×C32#57511yescharacteristic
684C2×C32#57511yescharacteristic
685C3⋊D3—22no—
686C3⋊D3—42no—
687C3×D3—22no—
688C3×D3—22no—
689C3×D3—42no—
690C24—91no—
691C24—181no—
692#41—34no—
693#41—62no—
694#41—94no—
695#41—94no—
696#41—94no—
697#41—182no—
698#41—188no—
699#41—188no—
700#41—182no—
701#41—182no—
702C2×Q8—34no—
703C2×Q8—31no—
704C2×Q8—61no—
705C2×Q8—62no—
706C2×Q8C2×D3211yescharacteristic
707C2×D4—31no—
708C2×D4—61no—
709C2×D4—94no—
710C2×D4—91no—
711C2×D4—181no—
712C2×D4—182no—
713C2×D4—181no—
714C2×D4—188no—
715C2×D4—181no—
716C2×D4—181no—
717C22×C4—31no—
718C22×C4—31no—
719C22×C4—61no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—91no—
723C22×C4—94no—
724C22×C4—94no—
725C22×C4—91no—
726C22×C4—91no—
727C22×C4—91no—
728C22×C4—181no—
729C22×C4—181no—
730C22×C4—188no—
731C22×C4—181no—
732C22×C4—181no—
733M16—62no—
734M16—62no—
735M16—182no—
736M16—182no—
737C2×C8—31no—
738C2×C8—31no—
739C2×C8—91no—
740C2×C8—182no—
741C2×C8—182no—
742C2×C8C2×D3211yescharacteristic
743C4⋊C4—31no—
744C4⋊C4—31no—
745C4⋊C4—61no—
746C4⋊C4—91no—
747C4⋊C4—181no—
748C4⋊C4C2×D3211yescharacteristic
749C22⋊C4—61no—
750C22⋊C4—181no—
751C22⋊C4—181no—
752C22⋊C4—181no—
753C42—61no—
754C42—181no—
755C42—181no—
756C42—181no—
757C22×C3—21no—
758C22×C3—32no—
759C22×C3—32no—
760C22×C3—61no—
761C22×C3—61no—
762C22×C3—61no—
763C22×C3—61no—
764C22×C3—62no—
765C22×C3—121no—
766C22×C3—121no—
767C22×C3C2×D3×D411yescharacteristic
768C22×C3C2×D3×D411yescharacteristic
769C2×D3—21no—
770C2×D3—21no—
771C2×D3—21no—
772C2×D3—21no—
773C2×D3—22no—
774C2×D3—32no—
775C2×D3—32no—
776C2×D3—41no—
777C2×D3—41no—
778C2×D3—62no—
779C2×D3—61no—
780C2×D3—61no—
781C2×D3—61no—
782C2×D3—61no—
783C2×D3—62no—
784C2×D3—62no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—122no—
788C2×D3—124no—
789C2×D3—124no—
790C2×D3—128no—
791C2×D3—128no—
792C2×D3—121no—
793C2×D3—121no—
794C2×D3—121no—
795C2×D3—121no—
796C2×D3—241no—
797C2×D3—241no—
798C2×D3D3×C22⋊C412yes—
799C2×D3D3×C22⋊C412yes—
800C3×C4—22no—
801C3×C4—22no—
802C3×C4—21no—
803C3×C4—21no—
804C3×C4—32no—
805C3×C4—32no—
806C3×C4—42no—
807C3×C4—41no—
808C3×C4—41no—
809C3×C4—62no—
810C3×C4—81no—
811C3×C4—121no—
812C3×C4—121no—
813C3×C4C22×C4×D311yescharacteristic
814C3×C4C22×C4×D311yescharacteristic
815C3×C4C2×D3×D411yescharacteristic
816C3×C4C2×D3×D411yescharacteristic
817Dic3—22no—
818Dic3—32no—
819Dic3—32no—
820Dic3—41no—
821Dic3—41no—
822Dic3—62no—
823Dic3—121no—
824Dic3—121no—
825Dic3—241no—
826Dic3D3×C22⋊C412yes—
827Dic3D3×C22⋊C412yes—
828C32#289611yescharacteristic, complemented, Sylow
829C23—31no—
830C23—31no—
831C23—61no—
832C23—94no—
833C23—91no—
834C23—184no—
835C23—181no—
836C23—361no—
837C23—361no—
838C23—362no—
839C23—362no—
840Q8—21no—
841Q8—32no—
842Q8—64no—
843Q8—61no—
844Q8C4×D3212yes—
845D4—32no—
846D4—64no—
847D4—61no—
848D4—92no—
849D4—184no—
850D4—184no—
851D4—184no—
852D4—184no—
853D4—181no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—31no—
857C2×C4—31no—
858C2×C4—32no—
859C2×C4—32no—
860C2×C4—32no—
861C2×C4—32no—
862C2×C4—64no—
863C2×C4—64no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—61no—
867C2×C4—94no—
868C2×C4—94no—
869C2×C4—94no—
870C2×C4—91no—
871C2×C4—92no—
872C2×C4—92no—
873C2×C4—122no—
874C2×C4—184no—
875C2×C4—184no—
876C2×C4—184no—
877C2×C4—181no—
878C2×C4—362no—
879C2×C4C22×D3211yescharacteristic
880C8—21no—
881C8—61no—
882C8—61no—
883C8—181no—
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—62no—
888C2×C3—62no—
889C2×C3—122no—
890C2×C3C2×D3×C22⋊C411yescharacteristic
891C2×C3C2×D3×C22⋊C411yescharacteristic
892C2×C3#577311yescharacteristic
893C2×C3#577711yescharacteristic
894C2×C3#577711yescharacteristic
895C2×C3#577711yescharacteristic
896D3—22no—
897D3—22no—
898D3—42no—
899D3—62no—
900D3—62no—
901D3—122no—
902D3—122no—
903D3—122no—
904D3—242no—
905C22—32no—
906C22—32no—
907C22—61no—
908C22—61no—
909C22—61no—
910C22—61no—
911C22—62no—
912C22—92no—
913C22—121no—
914C22—121no—
915C22—181no—
916C22—181no—
917C22—182no—
918C22—364no—
919C22—368no—
920C22—361no—
921C22—361no—
922C22D32×D411yescharacteristic
923C4—22no—
924C4—32no—
925C4—32no—
926C4—41no—
927C4—62no—
928C4—92no—
929C4—121no—
930C4—121no—
931C4—361no—
932C4C2×C4×D3211yescharacteristic
933C4D32×D411yescharacteristic
934C3—21no—
935C3#7888111yescharacteristic, complemented
936C3#7895611yescharacteristic, complemented
937C2—62no—
938C2—62no—
939C2—122no—
940C2—182no—
941C2—362no—
942C2D32×C22⋊C411yescharacteristic
943C2#1059474411yescharacteristic
944C2#1059476211yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×D3×#239C2
cosocleC2×C32×C4C24
hypercenter#103D32
hypocenterC32#2896
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. C2×#63791C2semidirect
3. D3×#892C2semidirect
4. #10592503C2semidirect
5. C3×#4803C2semidirect
6. C3×#4802C2semidirect
7. #10591560C2semidirect
8. #10591557C2semidirect
9. #10591550C2semidirect
10. #10590956C2semidirect
11. #10590939C2semidirect
12. #10590671C2semidirect
13. #10590611C2semidirect
14. #10590609C2semidirect
15. #10590592C2semidirect
22. D3×#239C4semidirect
31. C2×C8×C3⋊D3C22semidirect
32. #64101C22semidirect
34. C2×C3×ΓL(1,𝔽25)C22semidirect
36. C3×D3×C4⋊C4C22semidirect
38. D3×C4⋊Dic3C22semidirect
41. #63849C22semidirect
45. C2×#3711C22semidirect
46. C2×#3710C22semidirect
48. C32×#103C22semidirect
49. #63662C22semidirect
50. #63648C22semidirect
51. #63636C22semidirect
52. C3×#835C22semidirect
53. C3×#835C22semidirect
54. C3×#821C22semidirect
55. C3×#816C22semidirect
56. C3×#810C22semidirect
57. C3×#809C22semidirect
58. #63566C22semidirect
59. #63565C22semidirect
60. #63564C22semidirect
61. #63564C22semidirect
62. #63563C22semidirect
63. #63562C22semidirect
88. #4803D3semidirect
90. #4802D3semidirect
99. #3832C2×C4semidirect
107. C3×D3×Q8C2×C4semidirect
128. D3×D12C2×C4semidirect
137. #3796C2×C4semidirect
205. C2×ΓL(1,𝔽25)C2×D3semidirect
221. D3×C4⋊C4C2×D3semidirect
231. C3×#103C2×D3semidirect
232. C3×#103C2×D3semidirect
240. #835C2×D3semidirect
241. #835C2×D3semidirect
250. #821C2×D3semidirect
252. #816C2×D3semidirect
254. #810C2×D3semidirect
261. #809C2×D3semidirect
374. D3×Q8C4×D3semidirect
546. #103D32semidirect
828. C32#2896semidirect
935. C3#78881semidirect
936. C3#78956semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2392
C2×#637912
D3×#8922
#105925032
C3×#48032
C3×#48022
#105915602
#105915572
#105915502
#105909562
#105909392
#105906712
#105906112
#105906092
#105905922
#789563
#788813