Finite Group Databasebeta

← #11817825

Subgroups — #11817825

Order 1152.

1121 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63878C211yesmaximal, characteristic, complemented
2C2×#63859C211yesmaximal, characteristic, complemented
3#10592675C211yesmaximal, characteristic, complemented
4C3×#4993C211yesmaximal, characteristic, complemented
5C3×#4990C211yesmaximal, characteristic, complemented
6#10591388C211yesmaximal, characteristic
7#10591386C211yesmaximal, characteristic
8#10591373C211yesmaximal, characteristic, complemented
9#10591363C211yesmaximal, characteristic
10#10591303C211yesmaximal, characteristic, complemented
11#10591286C211yesmaximal, characteristic, complemented
12#10591284C211yesmaximal, characteristic, complemented
13#10591251C211yesmaximal, characteristic, complemented
14Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
15#10591198C211yesmaximal, characteristic, complemented
16#78027—31nomaximal
17#75536—31nomaximal
18C22×#625C2211yescharacteristic
19C22×D3×Dic3C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45#63878—24no—
46#63859—24no—
47#63658C2211yescharacteristic
48#63658C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#892—31no—
56C2×#879—31no—
57C2×#877—31no—
58C2×#876—31no—
59C3×#399—31no—
60C3×#388—31no—
61#4993—31no—
62#4993D311yescharacteristic, complemented
63#4990D311yescharacteristic, complemented
64#4983—31no—
65#4976—31no—
66#4976—31no—
67#4976—61no—
68Dic3×C4⋊C4—31no—
69#4959—31no—
70#4959—31no—
71#4958—31no—
72#4957—31no—
73#4957—31no—
74#4956—31no—
75#4951—31no—
76#4949—31no—
77#4946—31no—
78#4945—31no—
79C4×Dic3⋊C4—31no—
80#4670—31no—
81#4669—31no—
82#4668—31no—
83#4657—31no—
84#4654—31no—
85#4652—31no—
86C23×C3×D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C2×#625—22no—
102C2×#625—22no—
103C2×#625—41no—
104C2×D3×Dic3—22no—
105C2×D3×Dic3—22no—
106C2×D3×Dic3—22no—
107C32×C4⋊C4—41no—
108#3750—22no—
109#3750—22no—
110#3750—41no—
111C4×C3⋊Dic3—22no—
112C3×(C2×D3)⋊C4—22no—
113C3×(C2×D3)⋊C4—22no—
114C3×(C2×D3)⋊C4—22no—
115C3×(C2×D3)⋊C4—22no—
116C3×(C2×D3)⋊C4—41no—
117C3×(C2×D3)⋊C4—41no—
118C3×Dic3⋊C4—22no—
119C3×Dic3⋊C4—22no—
120C3×C4×Dic3—22no—
121#3724—22no—
122Dic3⋊Dic3—22no—
123Dic3⋊Dic3—41no—
124Dic3⋊Dic3D414yescomplemented
125(C2×D3)⋊Dic3—22no—
126(C2×D3)⋊Dic3—22no—
127(C2×D3)⋊Dic3—22no—
128(C2×D3)⋊Dic3—22no—
129(C2×D3)⋊Dic3—22no—
130Dic32—22no—
131Dic32—22no—
132#2479—91noSylow
133C22×#67—31no—
134C22×#67—31no—
135C23×Dic3—31no—
136C22×C4×D3—31no—
137C2×C3×C4⋊C4—21no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C4⋊C4C2×D311yescharacteristic
141C2×C3×C4⋊C4C2×D311yescharacteristic
142C2×C3×C22⋊C4—31no—
143C2×C3×C22⋊C4—31no—
144C2×C3×C22⋊C4—31no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4—31no—
148C2×C3×C42—31no—
149C2×#217—31no—
150C2×#217—31no—
151C2×#217—31no—
152C2×#217—31no—
153C2×#217—31no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4—31no—
157C2×(C2×D3)⋊C4—31no—
158C2×(C2×D3)⋊C4—31no—
159C2×(C2×D3)⋊C4C2×D311yescharacteristic
160C2×(C2×D3)⋊C4C2×D311yescharacteristic
161C2×(C2×D3)⋊C4C2×D311yescharacteristic
162C2×(C2×D3)⋊C4C2×D311yescharacteristic
163C2×(C2×D3)⋊C4C2×D311yescharacteristic
164C2×(C2×D3)⋊C4C2×D311yescharacteristic
165C2×C4⋊Dic3—31no—
166C2×C4⋊Dic3—31no—
167C2×C4⋊Dic3—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—31no—
170C2×Dic3⋊C4—31no—
171C2×Dic3⋊C4—31no—
172C2×Dic3⋊C4—31no—
173C2×Dic3⋊C4—31no—
174C2×Dic3⋊C4—31no—
175C2×Dic3⋊C4—31no—
176C2×Dic3⋊C4—31no—
177C2×Dic3⋊C4—31no—
178C2×Dic3⋊C4—31no—
179C2×Dic3⋊C4—61no—
180C2×Dic3⋊C4—61no—
181C2×Dic3⋊C4—61no—
182C2×Dic3⋊C4C2×D311yescharacteristic
183C2×Dic3⋊C4C2×D311yescharacteristic
184C2×C4×Dic3—31no—
185C2×C4×Dic3—31no—
186C2×C4×Dic3—31no—
187C2×C4×Dic3—31no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—31no—
190C2×C4×Dic3—61no—
191C2×C4×Dic3C2×D311yescharacteristic
192#892—64no—
193#879—64no—
194#877—64no—
195#876—64no—
196C3×#95—31no—
197C3×#95—31no—
198C3×#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—31no—
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—61no—
210C3⋊#95—61no—
211C3⋊#95C2×D311yescharacteristic
212C3⋊#95C2×D311yescharacteristic
213C3⋊#95C2×D311yescharacteristic
214C23×C32C2411yescharacteristic
215C22×C3×D3—21no—
216C22×C3×D3—21no—
217C22×C3×D3—21no—
218C22×C3×D3—21no—
219C22×C3×D3—21no—
220C22×C3×D3—21no—
221C22×C3×D3—21no—
222C22×C3×D3—21no—
223C22×C3×D3—21no—
224C22×C3×D3—21no—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—21no—
228C22×C3×D3#4112yes—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3C2×D412yes—
248C2×C3⋊Dic3#4112yes—
249C2×C3⋊Dic3#4112yes—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3C2×D412yes—
266C2×C3×Dic3C2×D412yes—
267C2×C3×Dic3#4112yes—
268#625—44no—
269D3×Dic3—28no—
270C2×#126—91no—
271C2×#117—91no—
272#399—31no—
273#399—91no—
274#398—91no—
275#394—91no—
276#390—91no—
277#389—91no—
278#388—31no—
279#388—91no—
280#388—91no—
281#387—91no—
282#386—91no—
283#385—91no—
284C4×C4⋊C4—91no—
285C24×C3—31no—
286C24×C3—31no—
287C23×D3C22×D311yescharacteristic
288C23×D3C22×D311yescharacteristic
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C2×#67—62no—
305C2×#67—62no—
306C2×#67—62no—
307C2×#67—62no—
308C2×#67—121no—
309C2×#67—121no—
310C22×Dic3—31no—
311C22×Dic3—31no—
312C22×Dic3—31no—
313C22×Dic3—31no—
314C22×Dic3—31no—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—62no—
323C22×Dic3—62no—
324C22×Dic3—62no—
325C22×Dic3C22×D311yescharacteristic
326C22×Dic3C22×D311yescharacteristic
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D311yescharacteristic
329C22×Dic3C22×D311yescharacteristic
330C22×Dic3C22×D311yescharacteristic
331C2×C4×D3—62no—
332C2×C4×D3—62no—
333C2×C4×D3—62no—
334C3×C4⋊C4—41no—
335C3×C4⋊C4—41no—
336C3×C4⋊C4—42no—
337C3×C4⋊C4—62no—
338C3×C4⋊C4—62no—
339C3×C22⋊C4—62no—
340C3×C22⋊C4—62no—
341C3×C22⋊C4—62no—
342C3×C22⋊C4—62no—
343C3×C22⋊C4—121no—
344C3×C22⋊C4—121no—
345C3×C42—62no—
346#217—62no—
347#217—62no—
348#217—62no—
349#217—62no—
350#217—62no—
351(C2×D3)⋊C4—22no—
352(C2×D3)⋊C4—22no—
353(C2×D3)⋊C4—22no—
354(C2×D3)⋊C4—22no—
355(C2×D3)⋊C4—41no—
356(C2×D3)⋊C4—41no—
357(C2×D3)⋊C4—62no—
358(C2×D3)⋊C4—62no—
359(C2×D3)⋊C4—62no—
360(C2×D3)⋊C4—62no—
361(C2×D3)⋊C4—62no—
362C4⋊Dic3—34no—
363C4⋊Dic3—62no—
364C4⋊Dic3—121no—
365Dic3⋊C4—22no—
366Dic3⋊C4—22no—
367Dic3⋊C4—34no—
368Dic3⋊C4—62no—
369Dic3⋊C4—62no—
370Dic3⋊C4—62no—
371Dic3⋊C4—62no—
372Dic3⋊C4—62no—
373Dic3⋊C4—62no—
374Dic3⋊C4—64no—
375Dic3⋊C4—62no—
376Dic3⋊C4—122no—
377Dic3⋊C4—121no—
378Dic3⋊C4—121no—
379Dic3⋊C4—121no—
380Dic3⋊C4—122no—
381C4×Dic3—22no—
382C4×Dic3—62no—
383C4×Dic3—62no—
384C4×Dic3—62no—
385C4×Dic3—62no—
386C4×Dic3—62no—
387C4×Dic3—62no—
388C4×Dic3—122no—
389C22×C32C22×D411yescharacteristic
390C22×C32C2×#4111yescharacteristic
391C22×C32C2×#4111yescharacteristic
392C22×C32C2×#4111yescharacteristic
393C22×C32C2×#4111yescharacteristic
394C22×C32H(5,𝔽2)11yescharacteristic
395C22×C322−1+411yescharacteristic
396C2×C3×D3—22no—
397C2×C3×D3—22no—
398C2×C3×D3—22no—
399C2×C3×D3—41no—
400C2×C3×D3—41no—
401C2×C3×D3—41no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C32×C4—41no—
411C32×C4—41no—
412C32×C4—41no—
413C3⋊Dic3—22no—
414C3⋊Dic3—22no—
415C3⋊Dic3—22no—
416C3⋊Dic3—41no—
417C3×Dic3—22no—
418C3×Dic3—22no—
419C3×Dic3—22no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C22×D4—91no—
424C23×C4—91no—
425#126—184no—
426#117—184no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—91no—
430C2×C4⋊C4—91no—
431C2×C4⋊C4—91no—
432C2×C4⋊C4—91no—
433C2×C4⋊C4—91no—
434C2×C4⋊C4—91no—
435C2×C4⋊C4—91no—
436C2×C4⋊C4D3211yescharacteristic
437C2×C22⋊C4—31no—
438C2×C22⋊C4—31no—
439C2×C22⋊C4—31no—
440C2×C22⋊C4—31no—
441C2×C22⋊C4—31no—
442C2×C22⋊C4—31no—
443C2×C22⋊C4—91no—
444C2×C22⋊C4—91no—
445C2×C22⋊C4—91no—
446C2×C22⋊C4—91no—
447C2×C22⋊C4—91no—
448C2×C42—31no—
449C2×C42—91no—
450C2×C42—91no—
451C2×C42—91no—
452#95—31no—
453#95—31no—
454#95—31no—
455#95—91no—
456#95—91no—
457#95—91no—
458#95—91no—
459#95—91no—
460C23×C3—21no—
461C23×C3—32no—
462C23×C3—61no—
463C23×C3—61no—
464C23×C3—61no—
465C23×C3—61no—
466C23×C3—61no—
467C23×C3—61no—
468C23×C3—61no—
469C23×C3—61no—
470C23×C3—61no—
471C23×C3—61no—
472C23×C3—61no—
473C23×C3—61no—
474C23×C3—61no—
475C23×C3C23×D311yescharacteristic
476C23×C3C23×D311yescharacteristic
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—21no—
483C22×D3—21no—
484C22×D3—21no—
485C22×D3—21no—
486C22×D3—21no—
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—21no—
490C22×D3#23512yes—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—32no—
512C2×C3×C4—32no—
513C2×C3×C4—32no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536#67—124no—
537#67—124no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—32no—
554C2×Dic3—32no—
555C2×Dic3—32no—
556C2×Dic3—32no—
557C2×Dic3—32no—
558C2×Dic3—32no—
559C2×Dic3—62no—
560C2×Dic3—62no—
561C2×Dic3—62no—
562C2×Dic3—68no—
563C2×Dic3—62no—
564C2×Dic3—62no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—121no—
584C2×Dic3—121no—
585C2×Dic3—121no—
586C2×Dic3—121no—
587C2×Dic3—121no—
588C2×Dic3—121no—
589C2×Dic3—121no—
590C2×Dic3D3×D412yes—
591C2×Dic3D3×D412yes—
592C2×Dic3#23712yes—
593C4×D3—68no—
594C2×C32#52511yescharacteristic
595C2×C32#52911yescharacteristic
596C2×C32#54211yescharacteristic
597C2×C32#54711yescharacteristic
598C2×C32#55011yescharacteristic
599C2×C32#55111yescharacteristic
600C2×C32#55211yescharacteristic
601C3×D3—42no—
602C3×D3—81no—
603C24—31no—
604C24—31no—
605C2×D4—182no—
606C2×D4—182no—
607C2×D4—361no—
608C22×C4—31no—
609C22×C4—31no—
610C22×C4—31no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—91no—
615C22×C4—91no—
616C22×C4—91no—
617C22×C4—91no—
618C22×C4—182no—
619C22×C4—182no—
620C22×C4—182no—
621C22×C4C2×D3211yescharacteristic
622C22×C4C2×D3211yescharacteristic
623C22×C4C2×D3211yescharacteristic
624C4⋊C4—41no—
625C4⋊C4—62no—
626C4⋊C4—62no—
627C4⋊C4—94no—
628C4⋊C4—182no—
629C4⋊C4—182no—
630C4⋊C4—182no—
631C4⋊C4—182no—
632C4⋊C4—361no—
633C4⋊C4—361no—
634C22⋊C4—62no—
635C22⋊C4—62no—
636C22⋊C4—62no—
637C22⋊C4—62no—
638C22⋊C4—121no—
639C22⋊C4—121no—
640C22⋊C4—182no—
641C22⋊C4—182no—
642C22⋊C4—182no—
643C22⋊C4—182no—
644C22⋊C4—182no—
645C42—62no—
646C42—182no—
647C42—182no—
648C42—182no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—62no—
657C22×C3—62no—
658C22×C3—62no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3C2×#23511yescharacteristic
671C22×C3C2×D3×D411yescharacteristic
672C22×C3C2×D3×D411yescharacteristic
673C22×C3C2×#23711yescharacteristic
674C22×C3#100411yescharacteristic
675C22×C3#100411yescharacteristic
676C22×C3#100711yescharacteristic
677C22×C3D3×#4111yescharacteristic
678C22×C3D3×#4111yescharacteristic
679C22×C3D3×#4111yescharacteristic
680C22×C3D3×#4111yescharacteristic
681C22×C3D3×#4111yescharacteristic
682C22×C3D3×#4111yescharacteristic
683C22×C3#101011yescharacteristic
684C2×D3—22no—
685C2×D3—22no—
686C2×D3—22no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—41no—
697C2×D3—41no—
698C3×C4—42no—
699C3×C4—42no—
700C3×C4—41no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—41no—
704C3×C4—41no—
705C3×C4—41no—
706C3×C4—62no—
707C3×C4—62no—
708C3×C4—62no—
709C3×C4—81no—
710C3×C4—121no—
711C3×C4—121no—
712C3×C4—121no—
713Dic3—22no—
714Dic3—22no—
715Dic3—22no—
716Dic3—41no—
717Dic3—41no—
718Dic3—41no—
719Dic3—64no—
720Dic3—62no—
721Dic3—62no—
722Dic3—62no—
723Dic3—62no—
724Dic3—62no—
725Dic3—62no—
726Dic3—122no—
727Dic3—122no—
728Dic3—121no—
729Dic3—121no—
730Dic3—241no—
731C32#247911yescharacteristic, complemented, Sylow
732C23—32no—
733C23—61no—
734C23—61no—
735C23—61no—
736C23—61no—
737C23—61no—
738C23—61no—
739C23—61no—
740C23—61no—
741C23—61no—
742C23—61no—
743C23—61no—
744C23—61no—
745C23—61no—
746C23C22×D3211yescharacteristic
747D4—364no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—32no—
758C2×C4—32no—
759C2×C4—32no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—92no—
776C2×C4—92no—
777C2×C4—92no—
778C2×C4—188no—
779C2×C4—181no—
780C2×C4—181no—
781C2×C4—181no—
782C2×C4—181no—
783C2×C4—181no—
784C2×C4—181no—
785C2×C4—181no—
786C2×C4—181no—
787C2×C4—181no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—21no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—122no—
796C2×C3—241no—
797C2×C3#553111yescharacteristic
798C2×C3#554711yescharacteristic
799C2×C3#555611yescharacteristic
800C2×C3#559911yescharacteristic
801C2×C3#563111yescharacteristic
802C2×C3#563911yescharacteristic
803C2×C3#564011yescharacteristic
804C2×C3#564911yescharacteristic
805C2×C3#565511yescharacteristic
806C2×C3#565611yescharacteristic
807C2×C3#565911yescharacteristic
808C2×C3#566911yescharacteristic
809C2×C3#570611yescharacteristic
810C2×C3#571811yescharacteristic
811D3—42no—
812D3—81no—
813C22—62no—
814C22—62no—
815C22—62no—
816C22—121no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—121no—
821C22—121no—
822C22—121no—
823C22—121no—
824C22—121no—
825C22—121no—
826C22—121no—
827C22D3×#23511yescharacteristic
828C22#6430611yescharacteristic
829C22D32×D411yescharacteristic
830C22D3×#23711yescharacteristic
831C22#6431511yescharacteristic
832C22#6431911yescharacteristic
833C22#6433011yescharacteristic
834C4—41no—
835C4—41no—
836C4—41no—
837C4—62no—
838C4—62no—
839C4—62no—
840C4—121no—
841C4—121no—
842C4—121no—
843C4—182no—
844C4—182no—
845C4—182no—
846C4—361no—
847C3—21no—
848C3#7553611yescharacteristic, complemented
849C3#7802711yescharacteristic, complemented
850C2—122no—
851C2—241no—
852C2#1059437111yescharacteristic
853C2#1059441111yescharacteristic
854C2#1059443511yescharacteristic
855C2#1059461411yescharacteristic
856C2#1059508811yescharacteristic
857C2#1059522711yescharacteristic
858C2#1059539111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC22×#625C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2479
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#63878C2semidirect
2. C2×#63859C2semidirect
3. #10592675C2semidirect
4. C3×#4993C2semidirect
5. C3×#4990C2semidirect
8. #10591373C2semidirect
10. #10591303C2semidirect
11. #10591286C2semidirect
12. #10591284C2semidirect
13. #10591251C2semidirect
14. Dic3×Dic3⋊C4C2semidirect
15. #10591198C2semidirect
62. #4993D3semidirect
63. #4990D3semidirect
124. Dic3⋊Dic3D4semidirect
731. C32#2479semidirect
848. C3#75536semidirect
849. C3#78027semidirect

Maximal subgroups

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

subgroupindex
C2×#638782
C2×#638592
#105926752
C3×#49932
C3×#49902
#105913882
#105913862
#105913732
#105913632
#105913032
#105912862
#105912842
#105912512
Dic3×Dic3⋊C42
#105911982
#780273
#755363