Finite Group Databasebeta

← C2×#10591497 #11865495

Subgroups — C2×#10591497 #11865495

Order 1152.

1301 conjugacy classes of subgroups; only the 252 normal subgroups are shown.

normal subgroups only

This group has 1301 conjugacy classes of subgroups — too many to draw. Only its 252 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×D4×C3⋊Dic3C211yesmaximal, characteristic
2C22×C3×#214C212yesmaximal
3C2×#63873C211yesmaximal, characteristic, complemented
4#10591497C218yesmaximal, direct product factor
5C2×#63572C211yesmaximal, characteristic, complemented
6C2×#63566C212yesmaximal, complemented
7C2×#5162—32nomaximal
8C22×C32×D4C2211yescharacteristic
9C23×C3⋊Dic3—21no—
10C22×C3×Dic6C2212yes—
11C2×#3757—21no—
12D4×C3⋊Dic3—22no—
13D4×C3⋊Dic3C2214yes—
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C3×#214—28no—
17C2×C3×#214C2218yes—
18C22×C3×C3⋊C8C2212yes—
19C2×#3724—21no—
20C2×#3724—21no—
21#63873—22no—
22#63873C2214yescomplemented
23#63572C2214yescomplemented
24#63566C2218yescomplemented
25C22×C3×SD16—32no—
26C2×#944—32no—
27C2×D4×Dic3—32no—
28C2×D4×Dic3—61no—
29C22×#214D312yes—
30C2×#835—32no—
31#5162—316no—
32C2×#816—32no—
33C2×Dic3⋊C8—32no—
34C24×C32—21no—
35C2×C32×D4—21no—
36C2×C32×D4—22no—
37C2×C32×D4D414yes—
38C2×C32×D4C2312yes—
39C22×C32×C4C2311yescharacteristic
40C22×C3⋊Dic3—21no—
41C22×C3⋊Dic3—24no—
42C22×C3⋊Dic3—44no—
43C22×C3⋊Dic3D411yescharacteristic
44C22×C3⋊Dic3D411yescharacteristic
45C22×C3×Dic3—22no—
46C2×C3×Dic6—24no—
47C2×C3×Dic6—24no—
48C2×C3×Dic6—22no—
49C2×C3×Dic6C2314yes—
50#3757—24no—
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)C2312yes—
53C4×C3⋊Dic3D412yes—
54C4×C3⋊Dic3C2312yes—
55C3×#214—216no—
56C2×C3×C3⋊C8—24no—
57C2×C3×C3⋊C8C2314yes—
58#3724—24no—
59#3724—24no—
60C2×#461—91noSylow
61C22×C3×Q8—32no—
62C22×C3×D4—21no—
63C22×C3×D4C2×D312yes—
64C23×Dic3—62no—
65C23×Dic3—62no—
66C22×Dic6C2×D312yes—
67C2×C3×SD16—38no—
68C2×C3×SD16—68no—
69C22×C3×C8—32no—
70C2×#217—62no—
71C2×#217—62no—
72#944—38no—
73#944—64no—
74D4×Dic3—38no—
75D4×Dic3—64no—
76D4×Dic3—64no—
77D4×Dic3—64no—
78C2×#214—28no—
79C2×#214C2×D318yes—
80C2×C4⋊Dic3—32no—
81C2×C4⋊Dic3—61no—
82C2×Dic3⋊C4—62no—
83C2×Dic3⋊C4—62no—
84C2×C4×Dic3—32no—
85C2×C4×Dic3—61no—
86C22×C3⋊C8C2×D312yes—
87#835—38no—
88#816—38no—
89Dic3⋊C8—38no—
90C23×C32—24no—
91C23×C32—22no—
92C23×C32—42no—
93C23×C32—42no—
94C23×C32C2×D411yescharacteristic
95C32×D4—24no—
96C32×D4—22no—
97C32×D4C2×D414yes—
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D412yes—
100C2×C32×C4#4112yes—
101C2×C32×C4C2411yescharacteristic
102C2×C3⋊Dic3—22no—
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3—42no—
105C2×C3⋊Dic3—48no—
106C2×C3⋊Dic3SD1614yescomplemented
107C2×C3⋊Dic3C2×D412yes—
108C2×C3⋊Dic3C2×D412yes—
109C2×C3×Dic3—24no—
110C2×C3×Dic3—44no—
111C3×Dic6—24no—
112C3×Dic6—24no—
113C3×Dic6—44no—
114C3×C3⋊C8—24no—
115C22×SD16—32no—
116C2×C4⋊Q8—91no—
117C2×C4×D4—91no—
118#461—98no—
119C2×C4⋊C8—91no—
120C2×#103—92no—
121C24×C3—22no—
122C24×C3—22no—
123C2×C3×Q8—34no—
124C2×C3×Q8—62no—
125C2×C3×Q8—64no—
126C2×C3×Q8—64no—
127C2×C3×D4—22no—
128C2×C3×D4—24no—
129C2×C3×D4—22no—
130C2×C3×D4—24no—
131C2×C3×D4—24no—
132C2×C3×D4—22no—
133C2×C3×D4#6718yes—
134C2×C3×D4C22×D314yes—
135C22×C3×C4—21no—
136C22×C3×C4—62no—
137C22×C3×C4C22×D312yes—
138C22×Dic3—22no—
139C22×Dic3—32no—
140C22×Dic3—32no—
141C22×Dic3—61no—
142C22×Dic3—61no—
143C22×Dic3—68no—
144C22×Dic3—62no—
145C22×Dic3—68no—
146C22×Dic3—62no—
147C22×Dic3—128no—
148C22×Dic3—128no—
149C2×Dic6—24no—
150C2×Dic6—24no—
151C2×Dic6—22no—
152C2×Dic6C22×D314yes—
153C3×SD16—616no—
154C2×C3×C8—34no—
155C2×C3×C8—64no—
156#217—68no—
157#217—68no—
158#214—216no—
159C4⋊Dic3—34no—
160C4⋊Dic3—62no—
161C4⋊Dic3—62no—
162C4⋊Dic3—62no—
163Dic3⋊C4—68no—
164Dic3⋊C4—68no—
165C4×Dic3—34no—
166C4×Dic3—34no—
167C4×Dic3—62no—
168C4×Dic3—62no—
169C2×C3⋊C8—24no—
170C2×C3⋊C8C22×D314yes—
171C22×C32—24no—
172C22×C32—42no—
173C22×C32—42no—
174C22×C32—48no—
175C22×C32#12112yes—
176C22×C32C2×SD1612yes—
177C22×C32#13712yes—
178C22×C32C22×D411yescharacteristic
179C32×C4#12112yes—
180C32×C4C22×D411yescharacteristic
181C32×C4C2×#4111yescharacteristic
182C3⋊Dic3—22no—
183C3⋊Dic3—42no—
184C3⋊Dic3C2×SD1614yescomplemented
185C3×Dic3—44no—
186C22×Q8—32no—
187C22×D4D3211yescharacteristic
188C23×C4—181no—
189C2×SD16—38no—
190C2×SD16—68no—
191C22×C8—32no—
192C4⋊Q8—94no—
193C4⋊Q8—182no—
194C4×D4—94no—
195C4×D4—182no—
196C2×C4⋊C4—91no—
197C2×C4⋊C4—181no—
198C2×C4⋊C4—181no—
199C2×C22⋊C4—181no—
200C2×C42—91no—
201C4⋊C8—94no—
202#103—98no—
203C23×C3—24no—
204C23×C3—28no—
205C23×C3—28no—
206C23×C3—24no—
207C23×C3—21no—
208C23×C3—44no—
209C23×C3—44no—
210C23×C3—44no—
211C23×C3—44no—
212C23×C3D3×D412yes—
213C3×Q8—64no—
214C3×Q8—64no—
215C3×Q8—124no—
216C3×D4—24no—
217C3×D4—28no—
218C3×D4—28no—
219C3×D4—24no—
220C3×D4—24no—
221C3×D4C2×#6718yes—
222C2×C3×C4—21no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—21no—
226C2×C3×C4—64no—
227C2×C3×C4—124no—
228C2×C3×C4D3×D412yes—
229C2×C3×C4#23714yes—
230C2×C3×C4C2×#6714yes—
231C2×C3×C4C23×D312yes—
232C2×Dic3—24no—
233C2×Dic3—38no—
234C2×Dic3—34no—
235C2×Dic3—34no—
236C2×Dic3—44no—
237C2×Dic3—64no—
238C2×Dic3—62no—
239C2×Dic3—62no—
240C2×Dic3—64no—
241C2×Dic3—64no—
242C2×Dic3—64no—
243C2×Dic3—122no—
244C2×Dic3—1216no—
245C2×Dic3—1216no—
246C2×Dic3—124no—
247C2×Dic3—124no—
248Dic6—24no—
249Dic6—24no—
250Dic6—44no—
251C3×C8—64no—
252C3⋊C8—24no—
253C2×C32—44no—
254C2×C32#46114yescomplemented
255C2×C32C2×#12111yescharacteristic
256C2×C32C22×SD1611yescharacteristic
257C2×C32C2×#13711yescharacteristic
258C24—21no—
259C2×Q8—34no—
260C2×Q8—62no—
261C2×Q8—64no—
262C2×Q8—64no—
263C2×D4—22no—
264C2×D4—21no—
265C2×D4#62514yes—
266C2×D4C2×D3212yes—
267C22×C4—62no—
268C22×C4—91no—
269C22×C4—91no—
270C22×C4—184no—
271C22×C4—181no—
272C22×C4—364no—
273C22×C4C2×D3211yescharacteristic
274SD16—616no—
275C2×C8—34no—
276C2×C8—64no—
277C4⋊C4—92no—
278C4⋊C4—184no—
279C4⋊C4—184no—
280C4⋊C4—181no—
281C22⋊C4—184no—
282C42—92no—
283C42—92no—
284C22×C3—28no—
285C22×C3—28no—
286C22×C3—21no—
287C22×C3—22no—
288C22×C3—22no—
289C22×C3—22no—
290C22×C3—44no—
291C22×C3—416no—
292C22×C3—44no—
293C22×C3—416no—
294C22×C3—44no—
295C22×C3—44no—
296C22×C3D3×SD1614yes—
297C22×C3#91514yes—
298C22×C3#93914yes—
299C22×C3C2×D3×D412yes—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—22no—
303C3×C4—124no—
304C3×C4#93914yes—
305C3×C4C2×#23712yes—
306C3×C4C22×#6712yes—
307Dic3—38no—
308Dic3—44no—
309Dic3—64no—
310Dic3—64no—
311Dic3—122no—
312Dic3—124no—
313Dic3—124no—
314C32C2×#46111yescharacteristic, complemented, Sylow
315C23—22no—
316C23—24no—
317C23—42no—
318C23—42no—
319C23#381111yescharacteristic
320Q8—64no—
321Q8—64no—
322Q8—124no—
323D4—22no—
324D4—24no—
325D4C2×#62514yes—
326C2×C4—64no—
327C2×C4—92no—
328C2×C4—94no—
329C2×C4—92no—
330C2×C4—124no—
331C2×C4—182no—
332C2×C4—182no—
333C2×C4—368no—
334C2×C4—362no—
335C2×C4#380512yes—
336C2×C4C2×#62512yes—
337C2×C4#381111yescharacteristic
338C2×C4C22×D3211yescharacteristic
339C8—64no—
340C2×C3—24no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—48no—
345C2×C3—48no—
346C2×C3#516218yescomplemented
347C2×C3C2×D3×SD1612yes—
348C2×C3C2×#91512yes—
349C2×C3C2×#93912yes—
350C22—24no—
351C22—48no—
352C22—42no—
353C22—42no—
354C22#6393012yes—
355C22#6393112yes—
356C22#6398012yes—
357C22C2×#381111yescharacteristic
358C4—94no—
359C4—124no—
360C4—182no—
361C4—362no—
362C4#6398012yes—
363C4C2×#380511yescharacteristic
364C4C22×#62511yescharacteristic
365C3—21no—
366C3C2×#516212yescomplemented
367C2—44no—
368C2#1059149714yesdirect product factor
369C2C2×#6393011yescharacteristic
370C2C2×#6393111yescharacteristic
371C2C2×#6398011yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32C2×#461
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
3. C2×#63873C2semidirect
4. #10591497C2direct (N × H)
5. C2×#63572C2semidirect
6. C2×#63566C2semidirect
22. #63873C22semidirect
23. #63572C22semidirect
24. #63566C22semidirect
106. C2×C3⋊Dic3SD16semidirect
184. C3⋊Dic3C2×SD16semidirect
254. C2×C32#461semidirect
314. C32C2×#461semidirect
346. C2×C3#5162semidirect
366. C3C2×#5162semidirect
368. C2#10591497direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C22×C3×#2142
C2×#638732
#105914972
C2×#635722
C2×#635662
C2×#51623