Finite Group Databasebeta

← #11860978

Subgroups — #11860978

Order 1152.

778 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 778 conjugacy classes of subgroups — too many to draw. Only its 151 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
1C2×#64223C211yesmaximal, characteristic
2#10594511C211yesmaximal, characteristic, complemented
3#10594509C211yesmaximal, characteristic, complemented
4#10593748C211yesmaximal, characteristic, complemented
5#10593433C212yesmaximal, complemented
6C4×#3775C212yesmaximal, complemented
7#10593419C212yesmaximal, complemented
8#10593387C211yesmaximal, characteristic, complemented
9#10593369C212yesmaximal, complemented
10#10593360C211yesmaximal, characteristic, complemented
11#10593360C211yesmaximal, characteristic, complemented
12C2×#3798C2211yescharacteristic
13C2×#3798C2211yescharacteristic
14C2×#3788C2211yescharacteristic
15C2×#3787C2211yescharacteristic
16C2×#3776C2211yescharacteristic
17C2×#3775C2211yescharacteristic
18C2×#3775C2211yescharacteristic
19C2×#3774C2211yescharacteristic
20#64223C418yescomplemented
21#64101C2211yescharacteristic
22C3×#892—21no—
23C3×D3×C4⋊C4—21no—
24C4×#627C2212yes—
25#63904—22no—
26#63902C2212yes—
27C4×#625C2212yes—
28#63900C2211yescharacteristic
29#63900C2211yescharacteristic
30D3×C4⋊Dic3—21no—
31#63880—22no—
32#63841—21no—
33#63838C2212yes—
34#63777C2212yes—
35C4×#622C2212yes—
36#63742C2212yes—
37#63742C2212yes—
38#63740C2212yes—
39#63740C2212yes—
40#63739C2212yes—
41#63739C2212yes—
42#5523—61no—
43#5504—61no—
44C2×C4×C3⋊D3C2311yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C3×C4×D3—21no—
47C2×C3×C4×D3—22no—
48C2×#627C2311yescharacteristic
49C2×#627C2311yescharacteristic
50C2×#626—21no—
51C2×#626—21no—
52C2×#625C2311yescharacteristic
53C2×#625C2311yescharacteristic
54C2×#624—21no—
55C2×#624—21no—
56C2×D3×Dic3—22no—
57#3798—22no—
58#3798—22no—
59#3798C2×C414yescomplemented
60#3798C2×C414yescomplemented
61C2×#622C2312yes—
62C2×#622C2311yescharacteristic
63C2×#622C2311yescharacteristic
64#3788—22no—
65#3787C2×C414yescomplemented
66#3776C2×C414yescomplemented
67#3775C2×C414yescomplemented
68#3775C2×C414yescomplemented
69#3774C2×C414yescomplemented
70C32×C4⋊C4D411yescharacteristic
71#3752D412yes—
72C4⋊(C3⋊Dic3)D411yescharacteristic
73C4×C3⋊Dic3C2312yes—
74C3×(C2×D3)⋊C4—22no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3—21no—
77C3×Dic3⋊C4—22no—
78C3×C4×Dic3—22no—
79#3724C2312yes—
80#3724C2312yes—
81Dic3⋊Dic3—22no—
82(C2×D3)⋊Dic3—22no—
83Dic32—22no—
84#2952—91nomaximal, Sylow
85C2×#235—61no—
86C2×#235—61no—
87C3×#117—61no—
88C2×C3×C4⋊C4—61no—
89C4×#67—62no—
90C4×#67—62no—
91#926—61no—
92C2×C4⋊Dic3—61no—
93#893—62no—
94#892—21no—
95#892—61no—
96#892—61no—
97#892—61no—
98D3×C4⋊C4—21no—
99D3×C4⋊C4—61no—
100D3×C4⋊C4—61no—
101D3×C4⋊C4—61no—
102#887—62no—
103#67⋊C4—62no—
104#67⋊C4—62no—
105C4×D12—62no—
106C4×Dic6—62no—
107C22×C3⋊D3C2×D411yescharacteristic
108C22×C3×D3—21no—
109C22×C3×D3—21no—
110C2×C32×C4C2×D412yes—
111C2×C32×C4C2×D411yescharacteristic
112C2×C3⋊Dic3C2×D412yes—
113C2×C3⋊Dic3C2411yescharacteristic
114C4×C3⋊D3C22×C412yes—
115C4×C3⋊D3#4112yes—
116C2×C3×Dic3—21no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—22no—
119C2×C3×Dic3—22no—
120C3×C4×D3—24no—
121C3×C4×D3—24no—
122C3×C4×D3—82no—
123#627—21no—
124#627—21no—
125#627C22×C412yes—
126#627C22×C412yes—
127#626—24no—
128#626—24no—
129#625—21no—
130#625—21no—
131#625C22×C412yes—
132#625C22×C412yes—
133#624—81no—
134#624—81no—
135D3×Dic3—82no—
136#622—22no—
137#622C22×C412yes—
138#622C22×C412yes—
139C2×#135—91no—
140#520—91no—
141#520—91no—
142#442—92no—
143#441—92no—
144C4×SD16—92no—
145C4×SD16—92no—
146C2×#106—91no—
147#417—91no—
148#417—91no—
149#405—91no—
150C22×C3×C4—61no—
151C22×C3×C4—61no—
152C22×C3×C4—62no—
153C2×#67—61no—
154C2×#67—61no—
155C2×#67—61no—
156C2×#67—61no—
157C22×Dic3—62no—
158#235—64no—
159#235—64no—
160#235—64no—
161#235—64no—
162C2×D12—61no—
163C2×D12—61no—
164C2×C4×D3—21no—
165C2×C4×D3—21no—
166C2×C4×D3—22no—
167C2×C4×D3—61no—
168C2×C4×D3—61no—
169C2×C4×D3—62no—
170C2×C4×D3—62no—
171C2×C4×D3—62no—
172C2×Dic6—61no—
173C2×Dic6—61no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—62no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C22⋊C4—62no—
180C3×C42—62no—
181#217—62no—
182(C2×D3)⋊C4—22no—
183(C2×D3)⋊C4—62no—
184(C2×D3)⋊C4—62no—
185(C2×D3)⋊C4—62no—
186C4⋊Dic3—21no—
187C4⋊Dic3—21no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—62no—
191Dic3⋊C4—22no—
192Dic3⋊C4—62no—
193Dic3⋊C4—62no—
194Dic3⋊C4—62no—
195C4×Dic3—22no—
196C4×Dic3—62no—
197C4×Dic3—62no—
198C4×Dic3—62no—
199C4×Dic3—62no—
200C22×C32C22×D411yescharacteristic
201C2×C3⋊D3—21no—
202C2×C3⋊D3—21no—
203C2×C3⋊D3C4×D412yes—
204C2×C3×D3—22no—
205C2×C3×D3—22no—
206C2×C3×D3—41no—
207C2×C3×D3—41no—
208C2×C3×D3—41no—
209C2×C3×D3—41no—
210C32×C4—22no—
211C32×C4C4×D412yes—
212C3⋊Dic3—22no—
213C3⋊Dic3C23×C411yescharacteristic
214C3⋊Dic3C2×#4111yescharacteristic
215C3×Dic3—22no—
216C3×Dic3—22no—
217C3×Dic3—42no—
218C3×Dic3—42no—
219C2×#41—91no—
220C2×#41—91no—
221#135—98no—
222C2×Q16—91no—
223C2×SD16—91no—
224C2×SD16—91no—
225C2×D8—91no—
226C2×M16—91no—
227C22×C8—91no—
228C4×Q8—92no—
229C4×Q8—92no—
230C4×D4—92no—
231C4×D4—92no—
232C4×D4—182no—
233C4×D4—182no—
234#117—61no—
235#117—91no—
236#117—181no—
237C2×C4⋊C4—61no—
238C2×C4⋊C4—91no—
239C2×C4⋊C4—91no—
240C2×C4⋊C4—181no—
241#106—92no—
242#106—92no—
243#103—92no—
244#103—92no—
245#102—92no—
246#102—92no—
247#97—92no—
248C4×C8—92no—
249C23×C3—61no—
250C23×C3—61no—
251C22×D3—21no—
252C22×D3—21no—
253C22×D3—61no—
254C22×D3—61no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—64no—
260C2×C3×C4—64no—
261C2×C3×C4—61no—
262C2×C3×C4—61no—
263C2×C3×C4—62no—
264C2×C3×C4—62no—
265C2×C3×C4—242no—
266#67—62no—
267#67—62no—
268#67—64no—
269#67—64no—
270#67—62no—
271#67—62no—
272C2×Dic3—21no—
273C2×Dic3—21no—
274C2×Dic3—22no—
275C2×Dic3—22no—
276C2×Dic3—61no—
277C2×Dic3—61no—
278C2×Dic3—62no—
279C2×Dic3—62no—
280C2×Dic3—242no—
281D12—64no—
282D12—64no—
283C4×D3—24no—
284C4×D3—24no—
285C4×D3—62no—
286C4×D3—62no—
287C4×D3—62no—
288C4×D3—62no—
289C4×D3—82no—
290C4×D3—242no—
291C4×D3—242no—
292C4×D3—242no—
293Dic6—62no—
294Dic6—62no—
295Dic6—62no—
296Dic6—62no—
297C2×C32C2×C4×D411yescharacteristic
298C2×C32#57711yescharacteristic
299C2×C32#57711yescharacteristic
300C3⋊D3—22no—
301C3×D3—42no—
302C3×D3—42no—
303#41—94no—
304#41—94no—
305#41—182no—
306#41—182no—
307C2×Q8—91no—
308C2×Q8—91no—
309C2×D4—91no—
310C2×D4—91no—
311C2×D4—181no—
312C2×D4—181no—
313C22×C4—61no—
314C22×C4—61no—
315C22×C4—62no—
316C22×C4—91no—
317C22×C4—181no—
318C22×C4—181no—
319C22×C4—182no—
320Q16—94no—
321SD16—94no—
322SD16—94no—
323D8—94no—
324M16—182no—
325C2×C8—91no—
326C2×C8—91no—
327C2×C8—94no—
328C2×C8—92no—
329C4⋊C4—61no—
330C4⋊C4—62no—
331C4⋊C4—61no—
332C4⋊C4—92no—
333C4⋊C4—92no—
334C4⋊C4—91no—
335C4⋊C4—182no—
336C4⋊C4GO+(4,𝔽2)11yescharacteristic
337C22⋊C4—62no—
338C22⋊C4—92no—
339C22⋊C4—182no—
340C42—62no—
341C42—92no—
342C42—182no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—62no—
346C22×C3—62no—
347C22×C3—121no—
348C22×C3—121no—
349C22×C3—121no—
350C22×C3—121no—
351C2×D3—22no—
352C2×D3—22no—
353C2×D3—41no—
354C2×D3—41no—
355C2×D3—41no—
356C2×D3—41no—
357C2×D3—62no—
358C2×D3—62no—
359C2×D3—121no—
360C2×D3—121no—
361C2×D3—121no—
362C2×D3—121no—
363C3×C4—22no—
364C3×C4—22no—
365C3×C4—42no—
366C3×C4—42no—
367C3×C4—62no—
368C3×C4—62no—
369C3×C4—122no—
370C3×C4—122no—
371Dic3—22no—
372Dic3—22no—
373Dic3—42no—
374Dic3—42no—
375Dic3—61no—
376Dic3—61no—
377Dic3—61no—
378Dic3—61no—
379Dic3—122no—
380Dic3—122no—
381C32#295211yescharacteristic, complemented, Sylow
382C23—61no—
383C23—61no—
384C23—91no—
385Q8—92no—
386Q8—92no—
387Q8—181no—
388Q8—181no—
389D4—92no—
390D4—92no—
391D4—184no—
392D4—184no—
393D4—181no—
394D4—181no—
395C2×C4—61no—
396C2×C4—61no—
397C2×C4—64no—
398C2×C4—64no—
399C2×C4—62no—
400C2×C4—62no—
401C2×C4—91no—
402C2×C4—92no—
403C2×C4—92no—
404C2×C4—92no—
405C2×C4—242no—
406C2×C4—721no—
407C2×C4—721no—
408C2×C4—722no—
409C2×C4C2×GO+(4,𝔽2)12yes—
410C2×C4C2×GO+(4,𝔽2)11yescharacteristic
411C8—92no—
412C8—92no—
413C8—182no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—122no—
421C2×C3—122no—
422D3—42no—
423D3—42no—
424D3—122no—
425D3—122no—
426C22—62no—
427C22—62no—
428C22—92no—
429C22—121no—
430C22—121no—
431C22—121no—
432C22—121no—
433C22—181no—
434C22—181no—
435C22C22×GO+(4,𝔽2)11yescharacteristic
436C4—22no—
437C4—62no—
438C4—62no—
439C4—91no—
440C4—91no—
441C4—122no—
442C4—122no—
443C4—182no—
444C4C4×GO+(4,𝔽2)12yes—
445C3—21no—
446C3—21no—
447C2—122no—
448C2—122no—
449C2—182no—
450C2C2×C4×GO+(4,𝔽2)11yescharacteristic
451C2#1059651511yescharacteristic
452C2#1059652111yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC32×C4⋊C4D4
socleC22×C32C22×D4
prime radicalC2×#64223C2
cosocleC2×C3⋊Dic3C24
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#2952
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10594511C2semidirect
3. #10594509C2semidirect
4. #10593748C2semidirect
5. #10593433C2semidirect
6. C4×#3775C2semidirect
7. #10593419C2semidirect
8. #10593387C2semidirect
9. #10593369C2semidirect
10. #10593360C2semidirect
11. #10593360C2semidirect
20. #64223C4semidirect
59. #3798C2×C4semidirect
60. #3798C2×C4semidirect
65. #3787C2×C4semidirect
66. #3776C2×C4semidirect
67. #3775C2×C4semidirect
68. #3775C2×C4semidirect
69. #3774C2×C4semidirect
381. C32#2952semidirect

Maximal subgroups

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

subgroupindex
C2×#642232
#105945112
#105945092
#105937482
#105934332
C4×#37752
#105934192
#105933872
#105933692
#105933602
#29529