Finite Group Databasebeta

← C2×#10591496 #11873541

Subgroups — C2×#10591496 #11873541

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×#64145C211yesmaximal, characteristic
2C2×#63919C211yesmaximal, characteristic, complemented
3C2×C3×#832C212yesmaximal
4#10591496C218yesmaximal, direct product factor
5C2×#63567C212yesmaximal, complemented
6C2×#63555C211yesmaximal, characteristic, complemented
7C2×#4765—32nomaximal
8C22×C32×D4C2211yescharacteristic
9C22×#634C2211yescharacteristic
10C22×#627—21no—
11C2×#3757—21no—
12C2×#3757—21no—
13#64145—22no—
14#64145C2214yes—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2212yes—
17C22×C3×C3⋊C8C2212yes—
18C2×#3724—21no—
19#63919—22no—
20#63919C2214yescomplemented
21C3×#832C2218yes—
22#63567C2218yescomplemented
23#63555C2214yescomplemented
24C2×#936—32no—
25C2×#936—61no—
26C2×#888—32no—
27C2×C3×#102—32no—
28C2×#832D312yes—
29C2×#816—32no—
30C2×#815—32no—
31C2×#810—32no—
32#4765—316no—
33C24×C32—21no—
34C2×C32×D4—21no—
35C2×C32×D4—24no—
36C2×C32×D4C2312yes—
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3—21no—
39C22×C3⋊Dic3D411yescharacteristic
40C22×C3⋊Dic3D411yescharacteristic
41C2×#634—24no—
42C2×#634—21no—
43C2×#634C2312yes—
44C22×C3×Dic3—22no—
45C2×#627—24no—
46C2×#627—44no—
47#3757—24no—
48#3757—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×D4—21no—
58C22×C3×D4C2×D312yes—
59C22×Dic6—32no—
60C22×Dic6—61no—
61C22×Dic6—62no—
62C22×C3×C8—32no—
63C2×C3×C4⋊C4—32no—
64C2×#217—62no—
65C2×#217—62no—
66C2×#217—62no—
67C2×#217—62no—
68#936—38no—
69#936—64no—
70#936—64no—
71#936—64no—
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×#102—38no—
80#832C2×D318yes—
81#816—38no—
82#815—38no—
83#810—38no—
84C23×C32—22no—
85C23×C32—42no—
86C23×C32—42no—
87C23×C32—42no—
88C23×C32C2×D411yescharacteristic
89C32×D4—24no—
90C32×D4—42no—
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4#4114yes—
93C2×C32×C4C2411yescharacteristic
94C2×C3⋊Dic3—22no—
95C2×C3⋊Dic3—22no—
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3—42no—
98C2×C3⋊Dic3C2×D412yes—
99C2×C3⋊Dic3C2×D412yes—
100#634—24no—
101#634—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—92no—
110C2×#102—32no—
111C2×#97—91no—
112C24×C3—22no—
113C24×C3—22no—
114C2×C3×D4—22no—
115C2×C3×D4—24no—
116C2×C3×D4—22no—
117C2×C3×D4—24no—
118C2×C3×D4—22no—
119C2×C3×D4—44no—
120C2×C3×D4C22×D314yes—
121C22×C3×C4—21no—
122C22×C3×C4—62no—
123C22×C3×C4C22×D312yes—
124C22×Dic3—22no—
125C22×Dic3—32no—
126C22×Dic3—32no—
127C22×Dic3—61no—
128C22×Dic3—61no—
129C22×Dic3—62no—
130C22×Dic3—62no—
131C2×Dic6—34no—
132C2×Dic6—62no—
133C2×Dic6—64no—
134C2×Dic6—64no—
135C2×Dic6—68no—
136C2×Dic6—62no—
137C2×Dic6—62no—
138C2×Dic6—124no—
139C2×Dic6—128no—
140C2×C3×C8—34no—
141C2×C3×C8—64no—
142C3×C4⋊C4—34no—
143C3×C4⋊C4—62no—
144#217—68no—
145#217—68no—
146#217—68no—
147#217—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—42no—
158C22×C32—42no—
159C22×C32—42no—
160C22×C32—84no—
161C22×C32#12412yes—
162C22×C32AGL(1,ℤ/8)12yes—
163C22×C32#13712yes—
164C22×C32C22×D411yescharacteristic
165C32×C4#12412yes—
166C32×C4C2×#4112yes—
167C3⋊Dic3—22no—
168C3⋊Dic3—22no—
169C3⋊Dic3—42no—
170C3×Dic3—44no—
171C22×Q8—91no—
172C22×Q8—181no—
173C22×D4D3211yescharacteristic
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—98no—
185#102—38no—
186#97—94no—
187C23×C3—24no—
188C23×C3—24no—
189C23×C3—21no—
190C23×C3—44no—
191C23×C3—44no—
192C23×C3—44no—
193C23×C3—44no—
194C23×C3—44no—
195C23×C3—44no—
196C23×C3D3×D412yes—
197C3×D4—24no—
198C3×D4—24no—
199C3×D4—44no—
200C3×D4—44no—
201C3×D4—44no—
202C2×C3×C4—21no—
203C2×C3×C4—24no—
204C2×C3×C4—21no—
205C2×C3×C4—64no—
206C2×C3×C4—124no—
207C2×C3×C4#23514yes—
208C2×C3×C4D3×D412yes—
209C2×C3×C4#23714yes—
210C2×C3×C4C23×D312yes—
211C2×Dic3—24no—
212C2×Dic3—34no—
213C2×Dic3—34no—
214C2×Dic3—44no—
215C2×Dic3—62no—
216C2×Dic3—62no—
217C2×Dic3—64no—
218C2×Dic3—64no—
219C2×Dic3—64no—
220C2×Dic3—64no—
221C2×Dic3—122no—
222C2×Dic3—122no—
223C2×Dic3—124no—
224C2×Dic3—124no—
225Dic6—64no—
226Dic6—64no—
227Dic6—124no—
228Dic6—1216no—
229Dic6—124no—
230Dic6—124no—
231C3×C8—64no—
232C3⋊C8—24no—
233C2×C32—82no—
234C2×C32#48914yescomplemented
235C2×C32C2×#12411yescharacteristic
236C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
237C2×C32C2×#13711yescharacteristic
238C24—21no—
239C2×Q8—92no—
240C2×Q8—184no—
241C2×Q8—181no—
242C2×Q8—184no—
243C2×Q8—364no—
244C2×D4—24no—
245C2×D4—21no—
246C2×D4C2×D3212yes—
247C22×C4—62no—
248C22×C4—91no—
249C22×C4—91no—
250C22×C4—181no—
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—44no—
266C22×C3—44no—
267C22×C3—44no—
268C22×C3—44no—
269C22×C3—44no—
270C22×C3—44no—
271C22×C3—88no—
272C22×C3—88no—
273C22×C3#88514yes—
274C22×C3#91114yes—
275C22×C3#91514yes—
276C22×C3C2×D3×D412yes—
277C3×C4—22no—
278C3×C4—22no—
279C3×C4—124no—
280C3×C4#88514yes—
281C3×C4C2×#23512yes—
282C3×C4C2×#23712yes—
283Dic3—44no—
284Dic3—64no—
285Dic3—64no—
286Dic3—122no—
287Dic3—122no—
288Dic3—124no—
289Dic3—124no—
290C32C2×#48911yescharacteristic, complemented, Sylow
291C23—22no—
292C23—42no—
293C23—42no—
294C23—42no—
295C23#381111yescharacteristic
296Q8—184no—
297Q8—368no—
298Q8—362no—
299D4—24no—
300D4—42no—
301C2×C4—64no—
302C2×C4—92no—
303C2×C4—92no—
304C2×C4—124no—
305C2×C4—182no—
306C2×C4—182no—
307C2×C4—182no—
308C2×C4—362no—
309C2×C4#380414yes—
310C2×C4#381111yescharacteristic
311C2×C4C22×D3211yescharacteristic
312C8—64no—
313C2×C3—24no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—84no—
318C2×C3—84no—
319C2×C3#476518yescomplemented
320C2×C3C2×#88512yes—
321C2×C3C2×#91112yes—
322C2×C3C2×#91512yes—
323C22—42no—
324C22—42no—
325C22—42no—
326C22—84no—
327C22#6392712yes—
328C22#6393112yes—
329C22#6395312yes—
330C22C2×#381111yescharacteristic
331C4—124no—
332C4—182no—
333C4—182no—
334C4—362no—
335C4#6395312yes—
336C4C2×#380412yes—
337C3—21no—
338C3C2×#476512yescomplemented
339C2—82no—
340C2#1059149614yesdirect product factor
341C2C2×#6392711yescharacteristic
342C2C2×#6393111yescharacteristic
343C2C2×#6395311yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32C2×#489
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63919C2semidirect
4. #10591496C2direct (N × H)
5. C2×#63567C2semidirect
6. C2×#63555C2semidirect
20. #63919C22semidirect
22. #63567C22semidirect
23. #63555C22semidirect
234. C2×C32#489semidirect
290. C32C2×#489semidirect
319. C2×C3#4765semidirect
338. C3C2×#4765semidirect
340. C2#10591496direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641452
C2×#639192
C2×C3×#8322
#105914962
C2×#635672
C2×#635552
C2×#47653