Finite Group Databasebeta

← C2×#10591632 #11873552

Subgroups — C2×#10591632 #11873552

Order 1152.

1037 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 1037 conjugacy classes of subgroups — too many to draw. Only its 212 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×#64156C211yesmaximal, characteristic
2C2×#63919C211yesmaximal, characteristic, complemented
3C2×C3×#835C212yesmaximal, complemented
4#10591632C218yesmaximal, direct product factor
5C2×#63564C212yesmaximal
6C2×#63555C211yesmaximal, characteristic, complemented
7C2×#4794—32nomaximal
8C22×C32×Q8C2211yescharacteristic
9C22×C4⋊(C3⋊D3)C2211yescharacteristic
10C22×#627—21no—
11#64156—22no—
12#64156C2214yes—
13C2×#3752—21no—
14C2×#3752—21no—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2212yes—
17C22×C3×C3⋊C8C2212yes—
18C2×#3724—21no—
19#63919—22no—
20#63919C2214yescomplemented
21C3×#835C2218yescomplemented
22#63564C2218yes—
23#63555C2214yescomplemented
24C2×#947—32no—
25C2×#947—61no—
26C2×#888—32no—
27C2×C3×#103—32no—
28C2×#835D312yescomplemented
29C2×#821—32no—
30C2×#815—32no—
31C2×#809—32no—
32#4794—316no—
33C23×C3⋊D3—21no—
34C2×C32×Q8—21no—
35C2×C32×Q8—24no—
36C2×C32×Q8C2312yes—
37C22×C32×C4—21no—
38C22×C32×C4C2311yescharacteristic
39C22×C3⋊Dic3D411yescharacteristic
40C22×C3⋊Dic3D411yescharacteristic
41C2×C4⋊(C3⋊D3)—24no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)C2312yes—
44C22×C3×Dic3—22no—
45C2×#627—24no—
46C2×#627—44no—
47#3752—24no—
48#3752—24no—
49C4×C3⋊Dic3D412yes—
50C4×C3⋊Dic3C2312yes—
51C3×C4⋊Dic3—22no—
52C3×C4⋊Dic3C2314yes—
53C2×C3×C3⋊C8—24no—
54C2×C3×C3⋊C8C2314yes—
55#3724—24no—
56C2×#489—91noSylow
57C22×C3×Q8—21no—
58C22×C3×Q8C2×D312yes—
59C22×D12—32no—
60C22×D12—61no—
61C22×Dic6—62no—
62C22×C3×C8—32no—
63C2×C3×C4⋊C4—32no—
64#947—38no—
65#947—64no—
66#947—64no—
67#947—64no—
68C2×(C2×D3)⋊C4—62no—
69C2×(C2×D3)⋊C4—62no—
70C2×(C2×D3)⋊C4—62no—
71C2×(C2×D3)⋊C4—62no—
72C2×C4⋊Dic3C2×D312yes—
73C2×Dic3⋊C4—62no—
74C2×C4×Dic3—32no—
75C2×C4×Dic3—61no—
76C22×C3⋊C8C2×D312yes—
77#888—38no—
78#888—64no—
79C3×#103—38no—
80#835C2×D318yescomplemented
81#821—38no—
82#815—38no—
83#809—38no—
84C23×C32C2×D411yescharacteristic
85C22×C3⋊D3—22no—
86C22×C3⋊D3—42no—
87C22×C3⋊D3—42no—
88C22×C3⋊D3—42no—
89C32×Q8—24no—
90C32×Q8—42no—
91C2×C32×C4—22no—
92C2×C32×C4—42no—
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4#4114yes—
95C2×C32×C4C2411yescharacteristic
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3C2×D412yes—
99C2×C3⋊Dic3C2×D412yes—
100C4⋊(C3⋊D3)—24no—
101C4⋊(C3⋊D3)—42no—
102C2×C3×Dic3—24no—
103C2×C3×Dic3—44no—
104#627—48no—
105C3×C3⋊C8—24no—
106C2×C4⋊Q8—91no—
107C2×#124—91no—
108#489—98no—
109C2×#103—32no—
110C2×#102—92no—
111C2×#97—91no—
112C23×D3—62no—
113C23×D3—62no—
114C2×C3×Q8—22no—
115C2×C3×Q8—22no—
116C2×C3×Q8—24no—
117C2×C3×Q8—24no—
118C2×C3×Q8—22no—
119C2×C3×Q8—44no—
120C2×C3×Q8C22×D314yes—
121C22×C3×C4—22no—
122C22×C3×C4—22no—
123C22×C3×C4—21no—
124C22×C3×C4—62no—
125C22×C3×C4C22×D312yes—
126C22×Dic3—22no—
127C22×Dic3—32no—
128C22×Dic3—32no—
129C22×Dic3—61no—
130C22×Dic3—61no—
131C2×D12—34no—
132C2×D12—62no—
133C2×D12—64no—
134C2×D12—64no—
135C2×D12—62no—
136C2×D12—62no—
137C2×D12—124no—
138C2×Dic6—68no—
139C2×Dic6—128no—
140C2×C3×C8—34no—
141C2×C3×C8—64no—
142C3×C4⋊C4—34no—
143C3×C4⋊C4—62no—
144(C2×D3)⋊C4—68no—
145(C2×D3)⋊C4—68no—
146(C2×D3)⋊C4—68no—
147(C2×D3)⋊C4—68no—
148C4⋊Dic3—22no—
149C4⋊Dic3C22×D314yes—
150Dic3⋊C4—68no—
151C4×Dic3—34no—
152C4×Dic3—34no—
153C4×Dic3—62no—
154C4×Dic3—62no—
155C2×C3⋊C8—24no—
156C2×C3⋊C8C22×D314yes—
157C22×C32#12412yes—
158C22×C32AGL(1,ℤ/8)12yes—
159C22×C32#13712yes—
160C22×C32C22×D411yescharacteristic
161C2×C3⋊D3—42no—
162C2×C3⋊D3—42no—
163C2×C3⋊D3—42no—
164C2×C3⋊D3—84no—
165C32×C4—42no—
166C32×C4#12412yes—
167C32×C4C2×#4112yes—
168C3⋊Dic3—22no—
169C3⋊Dic3—22no—
170C3×Dic3—44no—
171C22×Q8—181no—
172C22×Q8D3211yescharacteristic
173C22×D4—91no—
174C22×C8—32no—
175C4⋊Q8—94no—
176C4⋊Q8—182no—
177#124—94no—
178#124—182no—
179C2×C4⋊C4—32no—
180C2×C4⋊C4—181no—
181C2×C22⋊C4—181no—
182C2×C22⋊C4—181no—
183C2×C42—91no—
184#103—38no—
185#102—98no—
186#97—94no—
187C23×C3—21no—
188C23×C3D3×D412yes—
189C22×D3—64no—
190C22×D3—64no—
191C22×D3—124no—
192C22×D3—124no—
193C22×D3—124no—
194C22×D3—124no—
195C22×D3—124no—
196C22×D3—124no—
197C3×Q8—24no—
198C3×Q8—24no—
199C3×Q8—44no—
200C3×Q8—44no—
201C3×Q8—44no—
202C2×C3×C4—24no—
203C2×C3×C4—24no—
204C2×C3×C4—21no—
205C2×C3×C4—24no—
206C2×C3×C4—21no—
207C2×C3×C4—44no—
208C2×C3×C4—44no—
209C2×C3×C4—64no—
210C2×C3×C4—124no—
211C2×C3×C4#23514yes—
212C2×C3×C4D3×D412yes—
213C2×C3×C4#23714yes—
214C2×C3×C4C23×D312yes—
215C2×Dic3—24no—
216C2×Dic3—34no—
217C2×Dic3—34no—
218C2×Dic3—44no—
219C2×Dic3—62no—
220C2×Dic3—62no—
221C2×Dic3—64no—
222C2×Dic3—64no—
223C2×Dic3—122no—
224C2×Dic3—122no—
225D12—64no—
226D12—64no—
227D12—124no—
228D12—124no—
229D12—124no—
230Dic6—1216no—
231C3×C8—64no—
232C3⋊C8—24no—
233C2×C32#48914yescomplemented
234C2×C32C2×#12411yescharacteristic
235C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
236C2×C32C2×#13711yescharacteristic
237C3⋊D3—82no—
238C24—181no—
239C2×Q8—21no—
240C2×Q8—24no—
241C2×Q8—184no—
242C2×Q8—364no—
243C2×Q8C2×D3212yes—
244C2×D4—92no—
245C2×D4—184no—
246C2×D4—181no—
247C22×C4—21no—
248C22×C4—62no—
249C22×C4—91no—
250C22×C4—91no—
251C22×C4C2×D3211yescharacteristic
252C2×C8—34no—
253C2×C8—64no—
254C4⋊C4—34no—
255C4⋊C4—62no—
256C4⋊C4—184no—
257C22⋊C4—184no—
258C22⋊C4—184no—
259C42—92no—
260C42—92no—
261C22×C3—21no—
262C22×C3—22no—
263C22×C3—22no—
264C22×C3—22no—
265C22×C3#88514yes—
266C22×C3#91414yes—
267C22×C3#91814yes—
268C22×C3C2×D3×D412yes—
269C2×D3—124no—
270C2×D3—124no—
271C2×D3—124no—
272C2×D3—124no—
273C2×D3—124no—
274C2×D3—124no—
275C2×D3—248no—
276C2×D3—248no—
277C3×C4—22no—
278C3×C4—22no—
279C3×C4—44no—
280C3×C4—44no—
281C3×C4—124no—
282C3×C4#88514yes—
283C3×C4C2×#23512yes—
284C3×C4C2×#23712yes—
285Dic3—44no—
286Dic3—64no—
287Dic3—64no—
288Dic3—122no—
289Dic3—122no—
290C32C2×#48911yescharacteristic, complemented, Sylow
291C23—182no—
292C23—362no—
293C23—362no—
294C23—362no—
295C23#381111yescharacteristic
296Q8—24no—
297Q8—42no—
298Q8—368no—
299D4—184no—
300D4—362no—
301C2×C4—22no—
302C2×C4—42no—
303C2×C4—64no—
304C2×C4—92no—
305C2×C4—92no—
306C2×C4—124no—
307C2×C4—182no—
308C2×C4—182no—
309C2×C4#380414yes—
310C2×C4#381111yescharacteristic
311C2×C4C22×D3211yescharacteristic
312C8—64no—
313C2×C3—21no—
314C2×C3—24no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3#479418yescomplemented
318C2×C3C2×#88512yes—
319C2×C3C2×#91412yes—
320C2×C3C2×#91812yes—
321D3—244no—
322D3—244no—
323C22—362no—
324C22—362no—
325C22—362no—
326C22—724no—
327C22#6394112yes—
328C22#6394512yes—
329C22#6395312yes—
330C22C2×#381111yescharacteristic
331C4—42no—
332C4—124no—
333C4—182no—
334C4—182no—
335C4#6395312yes—
336C4C2×#380412yes—
337C3—21no—
338C3C2×#479412yescomplemented
339C2—722no—
340C2#1059163214yesdirect product factor
341C2C2×#6394111yescharacteristic
342C2C2×#6394511yescharacteristic
343C2C2×#6395311yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC22×Q8D32
hypocenterC32C2×#489
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#63919C2semidirect
3. C2×C3×#835C2semidirect
4. #10591632C2direct (N × H)
6. C2×#63555C2semidirect
20. #63919C22semidirect
21. C3×#835C22semidirect
23. #63555C22semidirect
28. C2×#835D3semidirect
80. #835C2×D3semidirect
233. C2×C32#489semidirect
290. C32C2×#489semidirect
317. C2×C3#4794semidirect
338. C3C2×#4794semidirect
340. C2#10591632direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641562
C2×#639192
C2×C3×#8352
#105916322
C2×#635642
C2×#635552
C2×#47943