Finite Group Databasebeta

← #11860657

Subgroups — #11860657

Order 1152.

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

normal subgroups only

This group has 750 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×#64226C211yesmaximal, characteristic
2#10594511C211yesmaximal, characteristic
3#10594347C211yesmaximal, characteristic, complemented
4#10593748C211yesmaximal, characteristic, complemented
5C4×#3776C212yesmaximal, complemented
6#10593433C212yesmaximal, complemented
7#10593432C212yesmaximal, complemented
8#10593394C211yesmaximal, characteristic, complemented
9#10593375C211yesmaximal, characteristic, complemented
10#10593369C212yesmaximal, complemented
11#10593349C211yesmaximal, characteristic
12C2×#3798C2211yescharacteristic
13C2×#3797C2211yescharacteristic
14C2×#3788C2211yescharacteristic
15C2×#3787C2211yescharacteristic
16C2×#3776C2212yes—
17C2×#3775C2212yes—
18#64226C418yescomplemented
19#64101C2211yescharacteristic
20C3×#892—21no—
21C3×#887—21no—
22C4×#627C2212yes—
23C4×#627C2212yes—
24#63902C2212yes—
25#63900C2211yescharacteristic
26D3×C4⋊Dic3—21no—
27#63880—22no—
28#63874C2211yescharacteristic
29Dic3×Dic6—21no—
30#63838C2212yes—
31#63836—22no—
32#63777C2212yes—
33C4×#622C2212yes—
34#63743C2212yes—
35#63742C2212yes—
36#63740C2211yescharacteristic
37#63740C2211yescharacteristic
38#63740C2212yes—
39#63740C2212yes—
40#63739C2211yescharacteristic
41#63739C2211yescharacteristic
42#5572—61no—
43#5523—61no—
44C2×C4×C3⋊D3C2311yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C3×Dic6—21no—
47C2×#627C2312yes—
48C2×#627C2311yescharacteristic
49C2×#626—21no—
50C2×#625C2311yescharacteristic
51C2×#624—21no—
52C2×#624—21no—
53C2×D3×Dic3—22no—
54#3798—22no—
55#3798C2×C414yes—
56#3797—22no—
57#3797C2×C414yescomplemented
58C2×#622C2311yescharacteristic
59C2×#622C2311yescharacteristic
60C2×#622C2312yes—
61#3788C2×C414yescomplemented
62#3787—22no—
63#3776C2×C418yescomplemented
64#3775C2×C418yescomplemented
65C32×C4⋊C4D411yescharacteristic
66#3752D412yes—
67C4⋊(C3⋊Dic3)D411yescharacteristic
68C4×C3⋊Dic3C2312yes—
69C3×(C2×D3)⋊C4—22no—
70C3×C4⋊Dic3—21no—
71C3×Dic3⋊C4—22no—
72C3×C4×Dic3—22no—
73C3×C4×Dic3—21no—
74C3×C4×Dic3—22no—
75#3724C2311yescharacteristic
76#3724C2311yescharacteristic
77#3724C2312yes—
78Dic3⋊Dic3—22no—
79Dic3⋊Dic3—22no—
80#3722—21no—
81Dic32—22no—
82#2947—91nomaximal, Sylow
83C2×D3×Q8—61no—
84C2×#235—61no—
85C3×C4×Q8—61no—
86C3×#117—61no—
87Q8×Dic3—61no—
88C2×C4⋊Dic3—61no—
89#892—21no—
90#892—61no—
91#892—61no—
92#892—62no—
93D3×C4⋊C4—61no—
94D3×C4⋊C4—61no—
95#887—21no—
96#887—62no—
97#67⋊C4—62no—
98#67⋊C4—62no—
99C4×D12—62no—
100#872—61no—
101#872—62no—
102C4×Dic6—62no—
103C4×Dic6—62no—
104C4×Dic6—61no—
105C22×C3⋊D3C2×D411yescharacteristic
106C22×C3×D3—21no—
107C2×C32×C4C2×D412yes—
108C2×C32×C4C2×D411yescharacteristic
109C2×C3⋊Dic3C2×D412yes—
110C2×C3⋊Dic3C2411yescharacteristic
111C4×C3⋊D3C22×C412yes—
112C4×C3⋊D3#4112yes—
113C2×C3×Dic3—22no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—21no—
117C2×C3×Dic3—22no—
118C3×C4×D3—24no—
119C3×Dic6—24no—
120#627—22no—
121#627—21no—
122#627C22×C414yes—
123#627C22×C412yes—
124#626—24no—
125#625—21no—
126#625C22×C412yes—
127#624—24no—
128#624—81no—
129D3×Dic3—82no—
130#622—21no—
131#622—21no—
132#622C22×C414yes—
133C2×#137—91no—
134#520—91no—
135#519—91no—
136#441—92no—
137#440—92no—
138C4×Q16—92no—
139C4×SD16—92no—
140#428—91no—
141#416—91no—
142C2×#103—91no—
143#405—91no—
144C2×C3×Q8—61no—
145C22×C3×C4—61no—
146C2×#67—61no—
147C2×#67—61no—
148C22×Dic3—62no—
149D3×Q8—64no—
150D3×Q8—64no—
151#235—64no—
152#235—64no—
153C2×D12—61no—
154C2×C4×D3—21no—
155C2×C4×D3—61no—
156C2×C4×D3—61no—
157C2×C4×D3—62no—
158C2×C4×D3—62no—
159C2×C4×D3—62no—
160C2×Dic6—21no—
161C2×Dic6—61no—
162C2×Dic6—62no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—62no—
166C3×C4⋊C4—61no—
167C3×C22⋊C4—62no—
168C3×C42—61no—
169C3×C42—62no—
170C3×C42—62no—
171(C2×D3)⋊C4—22no—
172(C2×D3)⋊C4—62no—
173(C2×D3)⋊C4—62no—
174(C2×D3)⋊C4—61no—
175(C2×D3)⋊C4—61no—
176C4⋊Dic3—21no—
177C4⋊Dic3—61no—
178C4⋊Dic3—61no—
179C4⋊Dic3—62no—
180C4⋊Dic3—62no—
181Dic3⋊C4—22no—
182Dic3⋊C4—61no—
183Dic3⋊C4—62no—
184Dic3⋊C4—61no—
185Dic3⋊C4—62no—
186Dic3⋊C4—62no—
187C4×Dic3—22no—
188C4×Dic3—22no—
189C4×Dic3—21no—
190C4×Dic3—62no—
191C4×Dic3—62no—
192C4×Dic3—62no—
193C4×Dic3—62no—
194C22×C32C22×D411yescharacteristic
195C2×C3⋊D3—21no—
196C2×C3⋊D3—21no—
197C2×C3⋊D3C4×D412yes—
198C2×C3×D3—22no—
199C2×C3×D3—41no—
200C2×C3×D3—41no—
201C32×C4—22no—
202C32×C4C4×D412yes—
203C3⋊Dic3—22no—
204C3⋊Dic3C23×C411yescharacteristic
205C3⋊Dic3C2×#4111yescharacteristic
206C3×Dic3—24no—
207C3×Dic3—22no—
208C3×Dic3—42no—
209C3×Dic3—41no—
210C3×Dic3—41no—
211C2×#41—91no—
212C22×Q8—91no—
213#137—98no—
214C2×Q16—92no—
215C2×SD16—92no—
216C2×M16—91no—
217C22×C8—91no—
218C4×Q8—61no—
219C4×Q8—92no—
220C4×Q8—92no—
221C4×Q8—92no—
222C4×Q8—181no—
223C4×D4—92no—
224C4×D4—182no—
225#117—61no—
226#117—91no—
227#117—91no—
228#117—182no—
229C2×C4⋊C4—91no—
230C2×C4⋊C4—181no—
231#107—92no—
232#106—92no—
233#103—92no—
234#103—92no—
235#103—91no—
236#103—91no—
237#102—91no—
238#102—91no—
239#97—92no—
240C4×C8—92no—
241C23×C3—61no—
242C22×D3—21no—
243C22×D3—61no—
244C22×D3—61no—
245C3×Q8—64no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—22no—
249C2×C3×C4—22no—
250C2×C3×C4—64no—
251C2×C3×C4—62no—
252C2×C3×C4—61no—
253C2×C3×C4—61no—
254C2×C3×C4—61no—
255C2×C3×C4—62no—
256#67—62no—
257#67—64no—
258#67—62no—
259C2×Dic3—21no—
260C2×Dic3—22no—
261C2×Dic3—21no—
262C2×Dic3—21no—
263C2×Dic3—22no—
264C2×Dic3—61no—
265C2×Dic3—61no—
266C2×Dic3—62no—
267C2×Dic3—62no—
268C2×Dic3—242no—
269D12—64no—
270C4×D3—24no—
271C4×D3—62no—
272C4×D3—62no—
273C4×D3—62no—
274C4×D3—62no—
275C4×D3—68no—
276C4×D3—242no—
277C4×D3—242no—
278Dic6—24no—
279Dic6—62no—
280Dic6—64no—
281Dic6—62no—
282Dic6—64no—
283C2×C32C2×C4×D411yescharacteristic
284C2×C32#57711yescharacteristic
285C2×C32#57811yescharacteristic
286C3⋊D3—22no—
287C3×D3—42no—
288#41—94no—
289#41—182no—
290C2×Q8—61no—
291C2×Q8—92no—
292C2×Q8—91no—
293C2×Q8—94no—
294C2×Q8—182no—
295C2×D4—91no—
296C2×D4—181no—
297C22×C4—61no—
298C22×C4—91no—
299C22×C4—181no—
300C22×C4—181no—
301C22×C4—182no—
302Q16—98no—
303SD16—98no—
304M16—94no—
305C2×C8—92no—
306C2×C8—91no—
307C2×C8—91no—
308C2×C8—182no—
309C4⋊C4—61no—
310C4⋊C4—62no—
311C4⋊C4—91no—
312C4⋊C4—91no—
313C4⋊C4—92no—
314C4⋊C4—91no—
315C4⋊C4—182no—
316C4⋊C4—182no—
317C4⋊C4GO+(4,𝔽2)11yescharacteristic
318C22⋊C4—62no—
319C22⋊C4—92no—
320C22⋊C4—181no—
321C42—62no—
322C42—61no—
323C42—62no—
324C42—92no—
325C42—182no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—62no—
329C22×C3—121no—
330C22×C3—121no—
331C2×D3—22no—
332C2×D3—41no—
333C2×D3—41no—
334C2×D3—62no—
335C2×D3—62no—
336C2×D3—121no—
337C2×D3—121no—
338C2×D3—121no—
339C2×D3—121no—
340C3×C4—22no—
341C3×C4—22no—
342C3×C4—42no—
343C3×C4—42no—
344C3×C4—64no—
345C3×C4—62no—
346C3×C4—122no—
347C3×C4—121no—
348C3×C4—121no—
349Dic3—24no—
350Dic3—22no—
351Dic3—42no—
352Dic3—41no—
353Dic3—41no—
354Dic3—61no—
355Dic3—61no—
356Dic3—61no—
357Dic3—61no—
358Dic3—122no—
359Dic3—122no—
360C32#294711yescharacteristic, complemented, Sylow
361C23—61no—
362C23—91no—
363Q8—64no—
364Q8—94no—
365Q8—92no—
366Q8—182no—
367Q8—181no—
368D4—92no—
369D4—184no—
370D4—181no—
371C2×C4—61no—
372C2×C4—62no—
373C2×C4—64no—
374C2×C4—61no—
375C2×C4—61no—
376C2×C4—62no—
377C2×C4—91no—
378C2×C4—92no—
379C2×C4—92no—
380C2×C4—92no—
381C2×C4—184no—
382C2×C4—721no—
383C2×C4—722no—
384C2×C4C2×GO+(4,𝔽2)12yes—
385C2×C4C2×GO+(4,𝔽2)11yescharacteristic
386C8—94no—
387C8—181no—
388C8—181no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—122no—
396D3—42no—
397D3—122no—
398D3—122no—
399C22—62no—
400C22—92no—
401C22—121no—
402C22—121no—
403C22—181no—
404C22—181no—
405C22C22×GO+(4,𝔽2)11yescharacteristic
406C4—22no—
407C4—62no—
408C4—64no—
409C4—91no—
410C4—91no—
411C4—121no—
412C4—122no—
413C4—121no—
414C4—182no—
415C4C4×GO+(4,𝔽2)12yes—
416C3—21no—
417C3—21no—
418C2—122no—
419C2—182no—
420C2C2×C4×GO+(4,𝔽2)11yescharacteristic
421C2#1059651611yescharacteristic
422C2#1059652111yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC32×C4⋊C4D4
socleC22×C32C22×D4
prime radicalC2×#3798C22
cosocleC2×C3⋊Dic3C24
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#2947
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #10594347C2semidirect
4. #10593748C2semidirect
5. C4×#3776C2semidirect
6. #10593433C2semidirect
7. #10593432C2semidirect
8. #10593394C2semidirect
9. #10593375C2semidirect
10. #10593369C2semidirect
18. #64226C4semidirect
57. #3797C2×C4semidirect
61. #3788C2×C4semidirect
63. #3776C2×C4semidirect
64. #3775C2×C4semidirect
360. C32#2947semidirect

Maximal subgroups

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

subgroupindex
C2×#642262
#105945112
#105943472
#105937482
C4×#37762
#105934332
#105934322
#105933942
#105933752
#105933692
#105933492
#29479