Finite Group Databasebeta

← #11887071

Subgroups — #11887071

Order 1152.

854 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 854 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595252C211yesmaximal, characteristic, complemented
2D4×#625C211yesmaximal, characteristic, complemented
3D4×#622C211yesmaximal, characteristic, complemented
4#10593520C212yesmaximal, complemented
5#10593519C212yesmaximal, complemented
6#10593492C212yesmaximal, complemented
7C2×#63739C212yesmaximal, complemented
8#10593417C211yesmaximal, characteristic, complemented
9C4×#3774C211yesmaximal, characteristic, complemented
10#10593348C211yesmaximal, characteristic, complemented
11#10593347C211yesmaximal, characteristic, complemented
12C2×C3×#237—21no—
13C2×C3×D3×D4—21no—
14C22×#625C2212yes—
15C22×#622C2212yescomplemented
16C2×#3774C2211yescharacteristic
17C2×#3774C2212yescomplemented
18D4×C3⋊Dic3C2211yescharacteristic
19#63980C2212yes—
20#63980C2212yescomplemented
21#63976—22no—
22C2×#3724C2212yescomplemented
23#63961—22no—
24#63914C2211yescharacteristic
25#63908—21no—
26C4×#625C2211yescharacteristic
27C4×#625C2211yescharacteristic, complemented
28#63873C2211yescharacteristic, complemented
29#63856—21no—
30C22⋊#622C2212yescomplemented
31C4⋊#622C2211yescharacteristic, complemented
32C4×#622C2211yescharacteristic, complemented
33#63743C2212yescomplemented
34#63743C2211yescharacteristic, complemented
35#63739C2212yes—
36#63739C2211yescharacteristic
37#63739C2212yescomplemented
38#63739C2212yescomplemented
39#63739C2211yescharacteristic, complemented
40#63739C2212yescomplemented
41#5824—61no—
42D4×#67—61no—
43C23×C3×D3—22no—
44C2×C32×D4D411yescharacteristic
45C22×C3⋊Dic3C2312yes—
46C2×C3×#67—22no—
47C2×C3×#67—22no—
48C22×C3×Dic3—22no—
49C3×#237—44no—
50C3×D3×D4—44no—
51C2×C3×D12—21no—
52C2×C3×C4×D3—21no—
53C2×C3×C4×D3—21no—
54C2×C3×Dic6—21no—
55C2×#625—24no—
56C2×#625—22no—
57C2×#625—21no—
58C2×#625—42no—
59C2×#625C2312yes—
60C2×#625C2311yescharacteristic
61C2×#625C2311yescharacteristic
62C2×#622—42no—
63C2×#622C2311yescharacteristic
64C2×#622C2311yescharacteristic
65C2×#622C2312yes—
66#3774—22no—
67#3774—42no—
68#3757D412yes—
69C4⋊(C3⋊Dic3)D411yescharacteristic
70C4×C3⋊Dic3C2311yescharacteristic
71#3724—22no—
72#3724—21no—
73#3724C2312yes—
74#3724C2311yescharacteristic
75#3724C2311yescharacteristic
76(C2×D3)⋊Dic3—22no—
77(C2×D3)⋊Dic3—21no—
78(C2×D3)⋊Dic3—21no—
79(C2×D3)⋊Dic3—22no—
80#3294—91nomaximal, Sylow
81C2×C3×#41—61no—
82C22×C3×D4—61no—
83C22×#67—62no—
84C2×#237—21no—
85C2×D3×D4—21no—
86#953—62no—
87#946—61no—
88#944—61no—
89#940—61no—
90#939—62no—
91#939—62no—
92#938—61no—
93#937—62no—
94#935—62no—
95D4×Dic3—61no—
96D4×Dic3—61no—
97#930—61no—
98#929—62no—
99C4×#67—61no—
100C4×#67—61no—
101#924—61no—
102C2×Dic3⋊C4—62no—
103C23×C32C2×D412yes—
104C22×C3×D3—21no—
105C22×C3×D3—22no—
106C22×C3×D3—21no—
107C22×C3×D3—44no—
108C22×C3×D3—44no—
109C22×C3×D3—82no—
110C32×D4D814yescomplemented
111C2×C32×C4C2×D411yescharacteristic
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3C2×D411yescharacteristic
115C2×C3⋊Dic3C2×D412yes—
116C2×C3⋊Dic3C2411yescharacteristic
117C3×#67—44no—
118C3×#67—44no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—44no—
123C3×D12—42no—
124C3×C4×D3—42no—
125C3×C4×D3—42no—
126C3×Dic6—42no—
127#625—21no—
128#625—21no—
129#625—22no—
130#625—21no—
131#625—22no—
132#625—44no—
133#625—81no—
134#625#4112yescomplemented
135#622—21no—
136#622—22no—
137#622—21no—
138#547—91no—
139D42—91no—
140#486—91no—
141#480—92no—
142#474—91no—
143#466—92no—
144#459—91no—
145#447—92no—
146C4×D8—91no—
147C8×D4—91no—
148C2×#102—92no—
149C24×C3—62no—
150C23×D3—22no—
151C3×#41—124no—
152C2×C3×Q8—61no—
153C2×C3×D4—21no—
154C2×C3×D4—21no—
155C2×C3×D4—61no—
156C2×C3×D4—62no—
157C2×C3×D4—62no—
158C2×C3×D4—124no—
159C22×C3×C4—61no—
160C22×C3×C4—61no—
161C22×C3×C4—62no—
162C2×#67—22no—
163C2×#67—22no—
164C2×#67—61no—
165C2×#67—61no—
166C2×#67—62no—
167C2×#67—62no—
168C2×#67—62no—
169C2×#67—62no—
170C2×#67—124no—
171C2×#67—124no—
172C22×Dic3—22no—
173C22×Dic3—62no—
174C22×Dic3—62no—
175#237—44no—
176D3×D4—44no—
177C2×D12—21no—
178C2×C4×D3—21no—
179C2×C4×D3—21no—
180C2×Dic6—21no—
181#217—62no—
182#217—62no—
183#217—62no—
184#217—61no—
185#217—61no—
186#217—62no—
187(C2×D3)⋊C4—61no—
188(C2×D3)⋊C4—61no—
189(C2×D3)⋊C4—62no—
190(C2×D3)⋊C4—62no—
191C4⋊Dic3—61no—
192C4⋊Dic3—61no—
193Dic3⋊C4—61no—
194Dic3⋊C4—62no—
195Dic3⋊C4—61no—
196Dic3⋊C4—62no—
197Dic3⋊C4—62no—
198Dic3⋊C4—62no—
199C4×Dic3—61no—
200C4×Dic3—61no—
201C22×C32—22no—
202C22×C32—22no—
203C22×C32C2×D814yes—
204C22×C32C22×D411yescharacteristic
205C2×C3×D3—22no—
206C2×C3×D3—41no—
207C2×C3×D3—41no—
208C2×C3×D3—42no—
209C2×C3×D3—41no—
210C2×C3×D3—41no—
211C2×C3×D3—42no—
212C2×C3×D3—42no—
213C2×C3×D3—41no—
214C2×C3×D3—88no—
215C32×C4C2×D812yes—
216C3⋊Dic3—22no—
217C3⋊Dic3—21no—
218C3⋊Dic3C2×#4111yescharacteristic
219C3⋊Dic3H(5,𝔽2)11yescharacteristic
220C3×Dic3—42no—
221C3×Dic3—41no—
222C3×Dic3—41no—
223C2×#41—61no—
224C22×D4—61no—
225C22×D4—92no—
226C2×D8—91no—
227C2×D8—92no—
228C22×C8—92no—
229C4⋊Q8—91no—
230#127—91no—
231#123—182no—
232C22⋊Q8—181no—
233#121—92no—
234#121—92no—
235#121—181no—
236#120—182no—
237C4×D4—91no—
238C4×D4—91no—
239C4×D4—91no—
240C2×C4⋊C4—92no—
241#107—91no—
242#107—92no—
243C4⋊C8—91no—
244#102—91no—
245#102—92no—
246#102—92no—
247#102—92no—
248#102—91no—
249#102—92no—
250C22⋊C8—92no—
251C4×C8—91no—
252C23×C3—22no—
253C23×C3—22no—
254C23×C3—61no—
255C23×C3—61no—
256C23×C3—62no—
257C23×C3—124no—
258C23×C3—124no—
259C23×C3—242no—
260C22×D3—21no—
261C22×D3—21no—
262C22×D3—22no—
263C22×D3—44no—
264C22×D3—44no—
265C22×D3—82no—
266C3×Q8—122no—
267C3×D4—24no—
268C3×D4—24no—
269C3×D4—122no—
270C3×D4—124no—
271C3×D4—124no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—61no—
275C2×C3×C4—62no—
276C2×C3×C4—61no—
277C2×C3×C4—122no—
278C2×C3×C4—122no—
279C2×C3×C4—124no—
280#67—44no—
281#67—44no—
282#67—62no—
283#67—62no—
284#67—121no—
285#67—121no—
286#67—122no—
287#67—122no—
288#67—124no—
289#67—124no—
290#67—242no—
291C2×Dic3—22no—
292C2×Dic3—21no—
293C2×Dic3—21no—
294C2×Dic3—44no—
295C2×Dic3—61no—
296C2×Dic3—61no—
297C2×Dic3—61no—
298C2×Dic3—61no—
299C2×Dic3—62no—
300C2×Dic3—62no—
301C2×Dic3—122no—
302C2×Dic3—122no—
303C2×Dic3—122no—
304C2×Dic3—122no—
305D12—42no—
306C4×D3—42no—
307C4×D3—42no—
308Dic6—42no—
309C2×C32—24no—
310C2×C32#54611yescharacteristic
311C2×C32C22×D811yescharacteristic
312C2×C32#57711yescharacteristic
313C3×D3—42no—
314C3×D3—81no—
315C3×D3—82no—
316C24—62no—
317#41—124no—
318C2×Q8—61no—
319C2×D4—62no—
320C2×D4—62no—
321C2×D4—61no—
322C2×D4—91no—
323C2×D4—92no—
324C2×D4—91no—
325C2×D4—124no—
326C2×D4—182no—
327C2×D4—181no—
328C2×D4—184no—
329C2×D4—362no—
330C2×D4GO+(4,𝔽2)11yescharacteristic
331C22×C4—62no—
332C22×C4—61no—
333C22×C4—61no—
334C22×C4—92no—
335D8—182no—
336D8—362no—
337C2×C8—91no—
338C2×C8—91no—
339C2×C8—92no—
340C2×C8—362no—
341C4⋊C4—91no—
342C4⋊C4—92no—
343C4⋊C4—91no—
344C4⋊C4—91no—
345C4⋊C4—182no—
346C4⋊C4—181no—
347C22⋊C4—92no—
348C22⋊C4—181no—
349C22⋊C4—181no—
350C22⋊C4—182no—
351C22⋊C4—182no—
352C42—91no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—24no—
356C22×C3—24no—
357C22×C3—42no—
358C22×C3—42no—
359C22×C3—42no—
360C22×C3—42no—
361C22×C3—62no—
362C22×C3—121no—
363C22×C3—121no—
364C22×C3—122no—
365C22×C3—121no—
366C22×C3—122no—
367C22×C3—121no—
368C22×C3—122no—
369C22×C3—121no—
370C22×C3—248no—
371C2×D3—22no—
372C2×D3—41no—
373C2×D3—41no—
374C2×D3—41no—
375C2×D3—42no—
376C2×D3—42no—
377C2×D3—41no—
378C2×D3—42no—
379C2×D3—41no—
380C2×D3—88no—
381C3×C4—22no—
382C3×C4—22no—
383C3×C4—121no—
384C3×C4—121no—
385C3×C4—122no—
386Dic3—42no—
387Dic3—41no—
388Dic3—41no—
389Dic3—61no—
390Dic3—61no—
391Dic3—61no—
392Dic3—61no—
393Dic3—122no—
394Dic3—122no—
395Dic3—121no—
396Dic3—121no—
397C32#329411yescharacteristic, complemented, Sylow
398C23—61no—
399C23—61no—
400C23—62no—
401C23—124no—
402C23—124no—
403C23—242no—
404C23C2×GO+(4,𝔽2)12yes—
405Q8—122no—
406D4—92no—
407D4—124no—
408D4—124no—
409D4—122no—
410D4—181no—
411D4—181no—
412D4—181no—
413D4—182no—
414D4—182no—
415D4—364no—
416D4—721no—
417D4#377414yescomplemented
418C2×C4—61no—
419C2×C4—61no—
420C2×C4—62no—
421C2×C4—91no—
422C2×C4—91no—
423C2×C4—92no—
424C2×C4—124no—
425C2×C4—122no—
426C2×C4—122no—
427C2×C4—182no—
428C2×C4—182no—
429C2×C4C2×GO+(4,𝔽2)11yescharacteristic
430C8—181no—
431C8—182no—
432C8—181no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—44no—
440C2×C3—44no—
441C2×C3—122no—
442C2×C3—242no—
443C2×C3—241no—
444D3—42no—
445D3—82no—
446D3—81no—
447C22—22no—
448C22—22no—
449C22—62no—
450C22—121no—
451C22—121no—
452C22—122no—
453C22—121no—
454C22—122no—
455C22—121no—
456C22—121no—
457C22—122no—
458C22—248no—
459C22C2×#377414yes—
460C22C22×GO+(4,𝔽2)11yescharacteristic
461C4—91no—
462C4—91no—
463C4—121no—
464C4—121no—
465C4—122no—
466C4—181no—
467C4—182no—
468C4C2×#377412yes—
469C3—21no—
470C3—21no—
471C2—24no—
472C2—122no—
473C2—242no—
474C2—241no—
475C2#1059651511yescharacteristic
476C2#1059651811yescharacteristic
477C2C22×#377411yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC2×C32×D4D4
socleC22×C32C22×D4
hypercenterC2×D4GO+(4,𝔽2)
hypocenterC32#3294
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #10595252C2semidirect
2. D4×#625C2semidirect
3. D4×#622C2semidirect
4. #10593520C2semidirect
5. #10593519C2semidirect
6. #10593492C2semidirect
7. C2×#63739C2semidirect
8. #10593417C2semidirect
9. C4×#3774C2semidirect
10. #10593348C2semidirect
11. #10593347C2semidirect
15. C22×#622C22semidirect
17. C2×#3774C22semidirect
20. #63980C22semidirect
22. C2×#3724C22semidirect
27. C4×#625C22semidirect
28. #63873C22semidirect
30. C22⋊#622C22semidirect
31. C4⋊#622C22semidirect
32. C4×#622C22semidirect
33. #63743C22semidirect
34. #63743C22semidirect
37. #63739C22semidirect
38. #63739C22semidirect
39. #63739C22semidirect
40. #63739C22semidirect
110. C32×D4D8semidirect
134. #625#41semidirect
397. C32#3294semidirect
417. D4#3774semidirect

Maximal subgroups

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

subgroupindex
#105952522
D4×#6252
D4×#6222
#105935202
#105935192
#105934922
C2×#637392
#105934172
C4×#37742
#105933482
#105933472
#32949