Finite Group Databasebeta

← C2×#10593782 #11860053

Subgroups — C2×#10593782 #11860053

Order 1152.

842 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 842 conjugacy classes of subgroups — too many to draw. Only its 170 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×Q8×#157C211yesmaximal, characteristic, complemented
2C2×D4×#157C211yesmaximal, characteristic
3C2×SD16×C3⋊D3C211yesmaximal, characteristic
4C2×#63784C211yesmaximal, characteristic, complemented
5C2×#63782C211yesmaximal, characteristic
6#10593782C218yesmaximal, direct product factor
7C2×#63769C211yesmaximal, characteristic, complemented
8C2×#63767C211yesmaximal, characteristic, complemented
9C23×#157—21no—
10C2×Q8×C3⋊D3C2211yescharacteristic
11C2×D4×C3⋊D3C2211yescharacteristic
12C2×C22⋊#157—21no—
13Q8×#157—22no—
14Q8×#157C2214yescomplemented
15D4×#157—22no—
16D4×#157C2214yes—
17C2×C4⋊#157—21no—
18C2×C4⋊#157C2211yescharacteristic
19C2×C4⋊#157C2211yescharacteristic
20C2×C4×#157—21no—
21C2×C4×#157C2211yescharacteristic
22C2×#3787C2211yescharacteristic
23C2×C32×SD16C411yescharacteristic, complemented
24C2×#3755C411yescharacteristic, complemented
25C2×#3754C411yescharacteristic, complemented
26SD16×C3⋊D3C414yescomplemented
27SD16×C3⋊D3C2214yes—
28C2×#3744C411yescharacteristic, complemented
29C2×C8×C3⋊D3C2211yescharacteristic
30#63784C2214yescomplemented
31#63782C2214yes—
32#63769C2214yescomplemented
33#63767C2214yescomplemented
34C2×D3×SD16—62no—
35C23×C3⋊D3—21no—
36C22×#157—21no—
37C22×#157—21no—
38C22×#157—24no—
39C22×#157—44no—
40C22×#157D411yescharacteristic
41C22×#157D411yescharacteristic
42C2×C32×Q8C2×C411yescharacteristic, complemented
43C2×C32×D4C2×C411yescharacteristic
44C2×#638—21no—
45Q8×C3⋊D3—21no—
46Q8×C3⋊D3—21no—
47Q8×C3⋊D3C2×C412yescomplemented
48Q8×C3⋊D3C2312yes—
49D4×C3⋊D3—21no—
50D4×C3⋊D3—21no—
51D4×C3⋊D3C2×C412yes—
52D4×C3⋊D3C2312yes—
53C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
54C2×C4×C3⋊D3—21no—
55C2×C4×C3⋊D3C2311yescharacteristic
56C2×#634—21no—
57C2×#634C2×C411yescharacteristic, complemented
58C22⋊#157—24no—
59C2×#622—21no—
60C4⋊#157—24no—
61C4⋊#157—21no—
62C4⋊#157—21no—
63C4⋊#157C2312yes—
64C4⋊#157C2312yes—
65C4×#157—24no—
66C4×#157D412yes—
67C4×#157C2312yes—
68#3787—21no—
69#3787C2312yes—
70C32×SD16C2×C414yescomplemented
71C2×C32×C8C2×C411yescharacteristic, complemented
72#3755C2×C414yescomplemented
73#3754C2×C414yescomplemented
74C2×C3⋊(C3⋊C8)C2×C411yescharacteristic, complemented
75#3744C2×C414yescomplemented
76C8×C3⋊D3C2×C412yescomplemented
77C8×C3⋊D3C2312yes—
78C2×#440—91nomaximal, Sylow
79C2×D3×Q8—62no—
80C2×D3×D4—62no—
81C2×C3×SD16—22no—
82C2×#215—62no—
83C2×#214—62no—
84D3×SD16—68no—
85D3×SD16—68no—
86C2×#204—62no—
87C2×D3×C8—62no—
88C23×C32—21no—
89C22×C3⋊D3—21no—
90C22×C3⋊D3—22no—
91C22×C3⋊D3—22no—
92C22×C3⋊D3—42no—
93C22×C3⋊D3—42no—
94C22×C3⋊D3C2×D411yescharacteristic
95C2×#157—22no—
96C2×#157—22no—
97C2×#157—22no—
98C2×#157—22no—
99C2×#157—48no—
100C2×#157—42no—
101C2×#157—42no—
102C2×#157C2×D412yes—
103C2×#157C2×D412yes—
104C32×Q8—21no—
105C32×Q8C22×C412yescomplemented
106C32×D4—21no—
107C32×D4C22×C412yes—
108C2×C32×C4—21no—
109C2×C32×C4C22×C411yescharacteristic
110#638—22no—
111#638—22no—
112C2×C3⋊Dic3—21no—
113C2×C3⋊Dic3#4111yescharacteristic
114C4⋊(C3⋊D3)—21no—
115C4⋊(C3⋊D3)C22×C412yes—
116C4×C3⋊D3—22no—
117C4×C3⋊D3—22no—
118C4×C3⋊D3C22×C411yescharacteristic
119C4×C3⋊D3C2×D411yescharacteristic
120C4×C3⋊D3#4111yescharacteristic
121C4×C3⋊D3C2411yescharacteristic
122#634—21no—
123#634—22no—
124#634—22no—
125#634C22×C412yescomplemented
126#622—22no—
127C32×C8C22×C412yescomplemented
128C3⋊(C3⋊C8)C22×C412yescomplemented
129C22×SD16—91no—
130C2×C4×Q8—91no—
131C2×C4×D4—91no—
132#440—98no—
133C2×#107—91no—
134C2×#103—91no—
135C2×#102—91no—
136C2×#97—91no—
137C23×D3—122no—
138C2×C3×Q8—22no—
139C2×C3×D4—22no—
140C2×#67—122no—
141D3×Q8—64no—
142D3×Q8—64no—
143D3×Q8—122no—
144D3×Q8—122no—
145D3×D4—64no—
146D3×D4—64no—
147D3×D4—122no—
148D3×D4—122no—
149C2×D12—62no—
150C2×C4×D3—62no—
151C2×C4×D3—122no—
152C2×Dic6—62no—
153C2×Dic6—122no—
154C3×SD16—28no—
155C2×C3×C8—22no—
156#215—68no—
157#214—68no—
158C2×C3⋊C8—62no—
159#204—68no—
160D3×C8—64no—
161D3×C8—64no—
162C22×C32—22no—
163C22×C32—42no—
164C22×C32C4×D411yescharacteristic
165C2×C3⋊D3—22no—
166C2×C3⋊D3—42no—
167C2×C3⋊D3—42no—
168C2×C3⋊D3—42no—
169C2×C3⋊D3—44no—
170C2×C3⋊D3C4×D411yescharacteristic
171C2×C3⋊D3AGL(1,ℤ/8)12yes—
172C2×C3⋊D3#13712yes—
173C2×C3⋊D3C22×D411yescharacteristic
174#157—22no—
175#157—22no—
176#157—42no—
177#157—42no—
178C32×C4—22no—
179C32×C4C4×D411yescharacteristic
180C32×C4C23×C411yescharacteristic
181C3⋊Dic3—22no—
182C3⋊Dic3C4×D411yescharacteristic
183C3⋊Dic3C2×#4111yescharacteristic
184C22×Q8—91no—
185C22×D4—91no—
186C23×C4—181no—
187C2×SD16—91no—
188C2×SD16—91no—
189C2×SD16—94no—
190C2×SD16—94no—
191C2×SD16—91no—
192C2×SD16#15711yescharacteristic, complemented
193C22×C8—91no—
194C22×C8—91no—
195C4×Q8—94no—
196C4×Q8—182no—
197C4×D4—94no—
198C4×D4—182no—
199C2×C4⋊C4—91no—
200C2×C4⋊C4—91no—
201C2×C4⋊C4—181no—
202C2×C22⋊C4—181no—
203C2×C42—91no—
204C2×C42—181no—
205#107—94no—
206#103—94no—
207#102—94no—
208#97—94no—
209C23×C3—42no—
210C22×D3—62no—
211C22×D3—124no—
212C22×D3—124no—
213C22×D3—122no—
214C22×D3—244no—
215C22×D3—244no—
216C3×Q8—24no—
217C3×Q8—42no—
218C3×D4—24no—
219C3×D4—42no—
220C2×C3×C4—22no—
221C2×C3×C4—42no—
222#67—124no—
223#67—124no—
224C2×Dic3—62no—
225C2×Dic3—122no—
226D12—64no—
227D12—122no—
228C4×D3—62no—
229C4×D3—62no—
230C4×D3—62no—
231C4×D3—62no—
232C4×D3—124no—
233C4×D3—124no—
234Dic6—64no—
235Dic6—124no—
236Dic6—124no—
237Dic6—122no—
238C3×C8—24no—
239C3⋊C8—64no—
240C2×C32—42no—
241C2×C32#44012yescomplemented
242C2×C32C2×C4×D411yescharacteristic
243C3⋊D3—42no—
244C3⋊D3#44012yescomplemented
245C3⋊D3C2×AGL(1,ℤ/8)11yescharacteristic
246C3⋊D3C2×#13711yescharacteristic
247C24—181no—
248C2×Q8—92no—
249C2×Q8—92no—
250C2×Q8—91no—
251C2×Q8—181no—
252C2×Q8—181no—
253C2×Q8—181no—
254C2×Q8C2×#15711yescharacteristic, complemented
255C2×D4—92no—
256C2×D4—92no—
257C2×D4—91no—
258C2×D4—181no—
259C2×D4—181no—
260C2×D4—181no—
261C2×D4C2×#15711yescharacteristic
262C22×C4—91no—
263C22×C4—91no—
264C22×C4—91no—
265C22×C4—181no—
266C22×C4—184no—
267C22×C4—181no—
268C22×C4—181no—
269C22×C4—364no—
270SD16—94no—
271SD16—94no—
272SD16—94no—
273SD16C2×#15714yescomplemented
274C2×C8—91no—
275C2×C8—92no—
276C2×C8—92no—
277C2×C8—92no—
278C2×C8—181no—
279C2×C8—181no—
280C2×C8C2×#15711yescharacteristic, complemented
281C4⋊C4—92no—
282C4⋊C4—92no—
283C4⋊C4—181no—
284C4⋊C4—181no—
285C4⋊C4—184no—
286C22⋊C4—184no—
287C42—92no—
288C42—92no—
289C42—184no—
290C22×C3—22no—
291C22×C3—44no—
292C22×C3—84no—
293C2×D3—62no—
294C2×D3—62no—
295C2×D3—64no—
296C2×D3—64no—
297C2×D3—124no—
298C2×D3—244no—
299C2×D3—244no—
300C2×D3—248no—
301C2×D3—244no—
302C3×C4—22no—
303C3×C4—22no—
304C3×C4—44no—
305Dic3—62no—
306Dic3—62no—
307Dic3—124no—
308C32C2×#44011yescharacteristic, complemented, Sylow
309C23—21no—
310C23—91no—
311C23—182no—
312C23—182no—
313C23—181no—
314C23—362no—
315C23—362no—
316Q8—21no—
317Q8—92no—
318Q8—182no—
319Q8—182no—
320Q8—181no—
321Q8C22×#15712yescomplemented
322D4—21no—
323D4—92no—
324D4—182no—
325D4—182no—
326D4—181no—
327D4C22×#15712yes—
328C2×C4—21no—
329C2×C4—91no—
330C2×C4—91no—
331C2×C4—91no—
332C2×C4—91no—
333C2×C4—91no—
334C2×C4—92no—
335C2×C4—92no—
336C2×C4—182no—
337C2×C4—182no—
338C2×C4—182no—
339C2×C4—182no—
340C2×C4—181no—
341C2×C4—182no—
342C2×C4—182no—
343C2×C4—368no—
344C2×C4—362no—
345C2×C4—362no—
346C2×C4C22×#15711yescharacteristic
347C8—92no—
348C8—182no—
349C8C22×#15712yescomplemented
350C2×C3—22no—
351C2×C3—24no—
352C2×C3—84no—
353D3—62no—
354D3—62no—
355D3—64no—
356D3—244no—
357C22—22no—
358C22—42no—
359C22—91no—
360C22—91no—
361C22—92no—
362C22—92no—
363C22—182no—
364C22—362no—
365C22—362no—
366C22—364no—
367C22—362no—
368C22D4×#15711yescharacteristic
369C4—22no—
370C4—91no—
371C4—91no—
372C4—182no—
373C4—182no—
374C4—182no—
375C4—362no—
376C4—362no—
377C4D4×#15711yescharacteristic
378C4C23×#15711yescharacteristic
379C3—22no—
380C2—42no—
381C2—91no—
382C2—91no—
383C2—92no—
384C2—362no—
385C2#1059378212yesdirect product factor
386C2C2×D4×#15711yescharacteristic
subgroupG/H
centerC22D4×#157
commutatorC32×C4C23×C4
FrattiniC4C23×#157
FittingC2×C32×SD16C4
socleC22×C32C4×D4
prime radicalC2×D4×C3⋊D3C22
cosocleC4×C3⋊D3C24
hypercenterC2×SD16#157
hypocenterC32C2×#440
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×Q8×#157C2semidirect
4. C2×#63784C2semidirect
6. #10593782C2direct (N × H)
7. C2×#63769C2semidirect
8. C2×#63767C2semidirect
14. Q8×#157C22semidirect
23. C2×C32×SD16C4semidirect
24. C2×#3755C4semidirect
25. C2×#3754C4semidirect
26. SD16×C3⋊D3C4semidirect
28. C2×#3744C4semidirect
30. #63784C22semidirect
32. #63769C22semidirect
33. #63767C22semidirect
42. C2×C32×Q8C2×C4semidirect
47. Q8×C3⋊D3C2×C4semidirect
57. C2×#634C2×C4semidirect
70. C32×SD16C2×C4semidirect
71. C2×C32×C8C2×C4semidirect
72. #3755C2×C4semidirect
73. #3754C2×C4semidirect
74. C2×C3⋊(C3⋊C8)C2×C4semidirect
75. #3744C2×C4semidirect
76. C8×C3⋊D3C2×C4semidirect
105. C32×Q8C22×C4semidirect
125. #634C22×C4semidirect
127. C32×C8C22×C4semidirect
128. C3⋊(C3⋊C8)C22×C4semidirect
192. C2×SD16#157semidirect
241. C2×C32#440semidirect
244. C3⋊D3#440semidirect
254. C2×Q8C2×#157semidirect
273. SD16C2×#157semidirect
280. C2×C8C2×#157semidirect
308. C32C2×#440semidirect
321. Q8C22×#157semidirect
349. C8C22×#157semidirect
385. C2#10593782direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×#1572
C2×D4×#1572
C2×SD16×C3⋊D32
C2×#637842
C2×#637822
#105937822
C2×#637692
C2×#637672
C2×#4409