Finite Group Databasebeta

← #11899657

Subgroups — #11899657

Order 1152.

770 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 770 conjugacy classes of subgroups — too many to draw. Only its 144 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
1D3×#919C212yesmaximal, complemented
2#10592618C211yesmaximal, characteristic, complemented
3C3×#4918C212yesmaximal, complemented
4#10591049C212yesmaximal, complemented
5#10591047C212yesmaximal, complemented
6#10591038C212yesmaximal, complemented
7#10590245C211yesmaximal, characteristic, complemented
8#10590233C212yesmaximal, complemented
9#10590226C211yesmaximal, characteristic, complemented
10#82039—32nomaximal
11D3×#239—22no—
12#64128C2212yescomplemented
13C3×#919C2212yes—
14C3×D3×Q16C2212yescomplemented
15#63950—22no—
16#63949—22no—
17D3×#215—22no—
18#63810C2212yescomplemented
19#63808C2212yes—
20D3×D24C2212yescomplemented
21D32×C8C2211yescharacteristic
22C32×Q32C2211yescharacteristic, complemented
23#63655C2212yescomplemented
24#63626C2211yescharacteristic, complemented
25C16×C3⋊D3C2211yescharacteristic, complemented
26C3×#829C2212yescomplemented
27C3×#828C2212yescomplemented
28C3×#800C2212yescomplemented
29C3×#798C2212yescomplemented
30#63550C2211yescharacteristic, complemented
31#63549C2212yescomplemented
32#63546C2212yescomplemented
33#63545C2211yescharacteristic, complemented
34#63543C2212yescomplemented
35#63542C2211yescharacteristic, complemented
36D3×#135—32no—
37C2×#919—32no—
38C3×#510—32no—
39#5193—32no—
40#5179—32no—
41#4919—32no—
42#4919—32no—
43#4919—61no—
44#4918—32no—
45#4918D312yescomplemented
46#4916—32no—
47#4916—32no—
48#4914—32no—
49#4914—32no—
50#4908—32no—
51D3×M32—32no—
52#3832—22no—
53C3×#239—22no—
54C3×D3×Q8—22no—
55D3×D12—22no—
56D3×D12—42no—
57C4×D32—42no—
58C4×D32D411yescharacteristic
59#3799—22no—
60#3799—42no—
61#3796—22no—
62#3796—42no—
63C32×Q16C2312yes—
64#3755—22no—
65#3745C2312yes—
66C8×C3⋊D3C2311yescharacteristic
67C3×#216—22no—
68C3×#215—22no—
69C3×Dic12C2312yes—
70C3×D24C2312yes—
71C3×D3×C8C2312yes—
72#3717—22no—
73#3715—22no—
74#3714—22no—
75#3710D411yescharacteristic
76D3×C3⋊C8D412yes—
77C32×C16C2311yescharacteristic
78C3⋊(C3⋊C16)C2311yescharacteristic
79C3×C3⋊C16C2312yes—
80#3414—91noSylow
81D3×#41—62no—
82C2×#239—62no—
83C3×#135—32no—
84C2×C3×Q16—32no—
85#950—62no—
86C2×#215—62no—
87#919—32no—
88#919—32no—
89#919—32no—
90#919—32no—
91#919—62no—
92#919—62no—
93#919—62no—
94#919C2×D312yes—
95D3×Q16C2×D312yescomplemented
96#916—62no—
97D3×SD16—62no—
98#912—32no—
99D3×D8—32no—
100#904—32no—
101C2×D24—32no—
102C2×D3×C8—32no—
103C3×Q32—21no—
104C3×Q32—32no—
105C3×Q32C2×D312yescomplemented
106C3×SD32—32no—
107C3×SD32—32no—
108C3×M32—32no—
109#829—32no—
110#829C2×D312yescomplemented
111#828—32no—
112#828—32no—
113#828—32no—
114#828—62no—
115#828C2×D312yescomplemented
116#826—32no—
117#826—32no—
118#812—32no—
119#800—32no—
120#800C2×D312yescomplemented
121D48—32no—
122D48—32no—
123D48—61no—
124#798—32no—
125#798C2×D312yescomplemented
126D3×C16—32no—
127D3×C16—32no—
128D3×C16—61no—
129C2×D32—42no—
130C2×D32D811yescharacteristic
131C32×Q8—22no—
132C4⋊(C3⋊D3)—22no—
133C4⋊(C3⋊D3)—42no—
134C4×C3⋊D3—42no—
135C4×C3⋊D3C2×D411yescharacteristic
136C3×D12—22no—
137C3×D12—42no—
138C3×C4×D3—42no—
139C3×C4×D3—42no—
140C3×C4×D3C2×D412yes—
141C3×Dic6—22no—
142C3×Dic6—42no—
143#626—42no—
144#626—42no—
145#626—42no—
146#624—42no—
147#624D811yescharacteristic
148D3×Dic3—42no—
149D3×Dic3D812yes—
150C32×C8C2411yescharacteristic
151C3⋊(C3⋊C8)C2×D411yescharacteristic
152C3×C3⋊C8C2×D412yes—
153C2×#135—92no—
154#510—32no—
155#510—92no—
156#509—92no—
157#509—92no—
158#508—91no—
159#508—92no—
160#508—91no—
161C2×M32—91no—
162C3×#41—62no—
163C2×C3×Q8—62no—
164#239—22no—
165#239—62no—
166#239—62no—
167#239—62no—
168#239—62no—
169#239—122no—
170#239—122no—
171#239—122no—
172D3×Q8—22no—
173#237—62no—
174#237—122no—
175D3×D4—62no—
176D3×D4—122no—
177#235—62no—
178#235—122no—
179C2×D12—62no—
180C2×D12—122no—
181C2×C4×D3—32no—
182C2×C4×D3—122no—
183C2×C4×D3—122no—
184C3×Q16—22no—
185C3×Q16—32no—
186C3×Q16—62no—
187C3×Q16C22×D312yes—
188C3×Q16C22×D312yes—
189C3×SD16—62no—
190C3×D8—32no—
191C2×C3×C8—32no—
192#216—22no—
193#215—22no—
194#215—62no—
195#215—62no—
196#215—62no—
197#215—62no—
198#215—122no—
199#214—62no—
200#213—62no—
201C2×C3⋊C8—32no—
202Dic12C22×D312yes—
203D24—32no—
204D24—32no—
205D24—62no—
206D24—62no—
207D24C22×D312yes—
208#204—62no—
209D3×C8—32no—
210D3×C8—32no—
211D3×C8—32no—
212D3×C8—61no—
213D3×C8C22×D312yes—
214C3×C16—21no—
215C3×C16—32no—
216C3×C16C22×D312yes—
217C3⋊C16—32no—
218C3⋊C16—61no—
219C3⋊C16C22×D312yes—
220C2×C3⋊D3—42no—
221C2×C3⋊D3C2×D811yescharacteristic
222C2×C3×D3—42no—
223C2×C3×D3C2×D812yes—
224D32—41no—
225D32—84no—
226C32×C4—42no—
227C32×C4C22×D411yescharacteristic
228C3⋊Dic3C2×D811yescharacteristic
229C3×Dic3—42no—
230C3×Dic3C2×D812yes—
231C2×#41—182no—
232#135—32no—
233#135—92no—
234#135—92no—
235#135—92no—
236#135—182no—
237#135—182no—
238C2×Q16—32no—
239C2×SD16—182no—
240C2×D8—92no—
241C22×C8—91no—
242Q32—32no—
243Q32—91no—
244Q32D3211yescharacteristic, complemented
245SD32—32no—
246SD32—32no—
247SD32—92no—
248SD32—92no—
249D16—92no—
250D16—91no—
251D16—91no—
252M32—32no—
253M32—92no—
254C2×C16—91no—
255C2×C16—91no—
256C22×D3—32no—
257C22×D3—122no—
258C22×D3—122no—
259C3×Q8—22no—
260C3×Q8—22no—
261C3×Q8—42no—
262C3×Q8—62no—
263C3×Q8—122no—
264C3×D4—62no—
265C3×D4—122no—
266C2×C3×C4—32no—
267C2×C3×C4—122no—
268C2×C3×C4—122no—
269#67—122no—
270#67—122no—
271#67—122no—
272C2×Dic3—32no—
273C2×Dic3—122no—
274D12—22no—
275D12—42no—
276D12—62no—
277D12—62no—
278D12—122no—
279D12—122no—
280D12—122no—
281D12—122no—
282D12—122no—
283D12—122no—
284D12—242no—
285C4×D3—32no—
286C4×D3—32no—
287C4×D3—32no—
288C4×D3—42no—
289C4×D3—42no—
290C4×D3—61no—
291C4×D3—122no—
292C4×D3—122no—
293C4×D3—122no—
294C4×D3—122no—
295C4×D3—122no—
296C4×D3—242no—
297C4×D3D3×D412yes—
298Dic6—22no—
299Dic6—42no—
300C3×C8—21no—
301C3×C8—32no—
302C3×C8C23×D312yes—
303C3⋊C8—32no—
304C3⋊C8—61no—
305C3⋊C8D3×D412yes—
306C2×C32C22×D811yescharacteristic
307C3⋊D3—21no—
308C3⋊D3—82no—
309C3×D3—22no—
310C3×D3—82no—
311#41—62no—
312#41—182no—
313#41—182no—
314#41—182no—
315#41—362no—
316#41—362no—
317C2×Q8—62no—
318C2×D4—182no—
319C2×D4—362no—
320C22×C4—91no—
321C22×C4—362no—
322Q16—32no—
323Q16—62no—
324Q16C2×D3212yes—
325SD16—62no—
326SD16—182no—
327SD16—182no—
328SD16—182no—
329D8—32no—
330D8—92no—
331D8—182no—
332C2×C8—32no—
333C2×C8—91no—
334C2×C8—92no—
335C2×C8—91no—
336C16—32no—
337C16—91no—
338C16C2×D3211yescharacteristic
339C22×C3—32no—
340C22×C3—122no—
341C2×D3—32no—
342C2×D3—42no—
343C2×D3—61no—
344C2×D3—122no—
345C2×D3—122no—
346C2×D3—122no—
347C2×D3—242no—
348C2×D3—244no—
349C2×D3—244no—
350C2×D3D3×D812yes—
351C3×C4—21no—
352C3×C4—32no—
353C3×C4—42no—
354C3×C4—42no—
355C3×C4—82no—
356C3×C4—122no—
357C3×C4C2×D3×D412yes—
358Dic3—32no—
359Dic3—42no—
360Dic3—61no—
361Dic3D3×D812yes—
362C32#341411yescharacteristic, complemented, Sylow
363C23—91no—
364C23—362no—
365Q8—22no—
366Q8—62no—
367Q8—122no—
368D4—62no—
369D4—122no—
370D4—182no—
371D4—362no—
372D4—362no—
373D4—362no—
374D4—362no—
375C2×C4—32no—
376C2×C4—91no—
377C2×C4—92no—
378C2×C4—91no—
379C2×C4—122no—
380C2×C4—122no—
381C2×C4—362no—
382C2×C4—362no—
383C2×C4—362no—
384C8—32no—
385C8—91no—
386C8C22×D3211yescharacteristic
387C2×C3—21no—
388C2×C3—62no—
389C2×C3—242no—
390C2×C3C2×D3×D812yes—
391D3—22no—
392D3—62no—
393D3—82no—
394D3—121no—
395D3—242no—
396D3—242no—
397D3—482no—
398C22—32no—
399C22—91no—
400C22—122no—
401C22—361no—
402C22—362no—
403C22—724no—
404C4—32no—
405C4—42no—
406C4—91no—
407C4—122no—
408C4D32×D411yescharacteristic
409C3—21no—
410C3#8203912yescomplemented
411C2—62no—
412C2—181no—
413C2—242no—
414C2—722no—
415C2D32×D811yescharacteristic
subgroupG/H
centerC2D32×D8
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC32×Q32C22
socleC2×C32C22×D8
hypercenterQ32D32
hypocenterC32#3414
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q32

Complements

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

NH ≅ G/Ntype
1. D3×#919C2semidirect
2. #10592618C2semidirect
3. C3×#4918C2semidirect
4. #10591049C2semidirect
5. #10591047C2semidirect
6. #10591038C2semidirect
7. #10590245C2semidirect
8. #10590233C2semidirect
9. #10590226C2semidirect
12. #64128C22semidirect
14. C3×D3×Q16C22semidirect
18. #63810C22semidirect
20. D3×D24C22semidirect
22. C32×Q32C22semidirect
23. #63655C22semidirect
24. #63626C22semidirect
25. C16×C3⋊D3C22semidirect
26. C3×#829C22semidirect
27. C3×#828C22semidirect
28. C3×#800C22semidirect
29. C3×#798C22semidirect
30. #63550C22semidirect
31. #63549C22semidirect
32. #63546C22semidirect
33. #63545C22semidirect
34. #63543C22semidirect
35. #63542C22semidirect
45. #4918D3semidirect
95. D3×Q16C2×D3semidirect
105. C3×Q32C2×D3semidirect
110. #829C2×D3semidirect
115. #828C2×D3semidirect
120. #800C2×D3semidirect
125. #798C2×D3semidirect
244. Q32D32semidirect
362. C32#3414semidirect
410. C3#82039semidirect

Maximal subgroups

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

subgroupindex
D3×#9192
#105926182
C3×#49182
#105910492
#105910472
#105910382
#105902452
#105902332
#105902262
#820393