Finite Group Databasebeta

← C2×#10593288 #11866808

Subgroups — C2×#10593288 #11866808

Order 1152.

810 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 127 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×D32⋊Q8C212yesmaximal
2C2×#63802C211yesmaximal, characteristic, complemented
3C2×D32×C8C211yesmaximal, characteristic
4C2×#63769C211yesmaximal, characteristic, complemented
5C2×#63730C212yesmaximal, complemented
6#10593288C218yesmaximal, direct product factor
7C2×C4×D32C2211yescharacteristic
8C2×#3797C2212yes—
9C2×C4⋊#157C2212yes—
10C2×#3773—22no—
11C2×D32⋊C4—22no—
12D32⋊Q8—24no—
13D32⋊Q8C2218yes—
14C2×C8×C3⋊D3C2211yescharacteristic
15C2×C3×Dic12—21no—
16C2×C3×D3×C8—21no—
17C2×#3718—21no—
18C2×#3710C2211yescharacteristic
19C2×D3×C3⋊C8—21no—
20#63802—22no—
21#63802C2214yescomplemented
22D32×C8—22no—
23D32×C8C2214yes—
24#63769C2214yescomplemented
25#63730C2218yescomplemented
26C2×D3×Q16—61no—
27C22×D3×C8—61no—
28C22×D32D411yescharacteristic
29C22×#157—22no—
30C2×C4×C3⋊D3C2311yescharacteristic
31C2×C3×C4×D3—21no—
32C2×C3×Dic6—22no—
33C2×#627—22no—
34C2×#624—22no—
35C2×#624D411yescharacteristic
36C2×D3×Dic3—21no—
37C4×D32—21no—
38C4×D32—21no—
39C4×D32D412yes—
40C4×D32C2312yes—
41#3797—22no—
42#3797—22no—
43#3797—22no—
44#3797C2314yes—
45C4⋊#157—22no—
46C4⋊#157C2314yes—
47#3773—28no—
48D32⋊C4—28no—
49C2×C32×C8D411yescharacteristic
50C2×C3⋊(C3⋊C8)D411yescharacteristic
51C8×C3⋊D3D412yes—
52C8×C3⋊D3C2312yes—
53C2×C3×C3⋊C8—21no—
54C3×Dic12—24no—
55C3×D3×C8—24no—
56#3718—24no—
57#3710—21no—
58#3710C2312yes—
59D3×C3⋊C8—24no—
60C2×#467—91nomaximal, Sylow
61C2×D3×Q8—62no—
62C22×C4×D3—61no—
63C2×C3×Q16—61no—
64C22×C3×C8—61no—
65C2×#216—62no—
66C22×C3⋊C8—61no—
67D3×Q16—64no—
68D3×Q16—64no—
69C2×Dic12—21no—
70C2×D3×C8—21no—
71C2×D3×C8—64no—
72C2×D3×C8—61no—
73C2×D3×C8—61no—
74C2×D3×C8—61no—
75C2×D3×C8—64no—
76C2×D3×C8—61no—
77C22×C3⋊D3C2×D411yescharacteristic
78C22×C3×D3—21no—
79C2×D32—21no—
80C2×D32—22no—
81C2×D32Q1614yescomplemented
82C2×D32C2×D412yes—
83C2×#157—24no—
84C2×#157—44no—
85C2×C32×C4C2×D411yescharacteristic
86C2×C3⋊Dic3#4111yescharacteristic
87C4×C3⋊D3C2×D411yescharacteristic
88C4×C3⋊D3C2×D411yescharacteristic
89C4×C3⋊D3#4111yescharacteristic
90C4×C3⋊D3C2411yescharacteristic
91C2×C3×Dic3—21no—
92C2×C3×Dic3—42no—
93C3×C4×D3—22no—
94C3×C4×D3—22no—
95C3×Dic6—24no—
96C3×Dic6—42no—
97#627—24no—
98#627—42no—
99#624—21no—
100#624—24no—
101#624—42no—
102#624C2×D412yes—
103D3×Dic3—22no—
104D3×Dic3—22no—
105C32×C8C2×D412yes—
106C3⋊(C3⋊C8)C2×D412yes—
107C3×C3⋊C8—22no—
108C22×Q16—91no—
109C23×C8—91no—
110C2×C22⋊Q8—92no—
111#467—98no—
112C2×#107—91no—
113C2×#103—92no—
114C23×D3—61no—
115C2×C3×Q8—62no—
116C22×C3×C4—61no—
117C22×Dic3—61no—
118D3×Q8—64no—
119D3×Q8—64no—
120D3×Q8—122no—
121D3×Q8—122no—
122C2×C4×D3—21no—
123C2×C4×D3—62no—
124C2×C4×D3—62no—
125C2×C4×D3—61no—
126C2×C4×D3—61no—
127C2×C4×D3—61no—
128C2×C4×D3—62no—
129C2×C4×D3—62no—
130C2×C4×D3—61no—
131C2×C4×D3—122no—
132C2×Dic6—22no—
133C2×Dic6—122no—
134C3×Q16—64no—
135C2×C3×C8—21no—
136C2×C3×C8—21no—
137C2×C3×C8—64no—
138C2×C3×C8—61no—
139#216—68no—
140C2×C3⋊C8—21no—
141C2×C3⋊C8—61no—
142C2×C3⋊C8—61no—
143C2×C3⋊C8—64no—
144Dic12—24no—
145D3×C8—24no—
146D3×C8—62no—
147D3×C8—62no—
148D3×C8—62no—
149D3×C8—62no—
150D3×C8—62no—
151D3×C8—62no—
152D3×C8—64no—
153C22×C32#12111yescharacteristic
154C2×C3⋊D3#12111yescharacteristic
155C2×C3⋊D3C2×Q1612yes—
156C2×C3⋊D3#13512yes—
157C2×C3⋊D3C22×D411yescharacteristic
158C2×C3×D3—22no—
159C2×C3×D3—24no—
160D32—22no—
161D32—24no—
162D32C2×Q1614yescomplemented
163#157—44no—
164C32×C4#12111yescharacteristic
165C32×C4C22×D411yescharacteristic
166C3⋊Dic3#12111yescharacteristic
167C3⋊Dic3C2×#4111yescharacteristic
168C3×Dic3—22no—
169C3×Dic3—44no—
170C22×Q8—92no—
171C23×C4—91no—
172C2×Q16—61no—
173C2×Q16—94no—
174C2×Q16—182no—
175C2×Q16—181no—
176C22×C8—61no—
177C22×C8—91no—
178C22×C8—94no—
179C22×C8—91no—
180C22×C8—182no—
181C22×C8—181no—
182C22⋊Q8—98no—
183C22⋊Q8—184no—
184C2×C4⋊C4—92no—
185C2×C4⋊C4—182no—
186C2×C22⋊C4—182no—
187#107—94no—
188#103—98no—
189C23×C3—61no—
190C22×D3—21no—
191C22×D3—64no—
192C22×D3—62no—
193C22×D3—61no—
194C22×D3—61no—
195C22×D3—62no—
196C22×D3—64no—
197C3×Q8—64no—
198C3×Q8—122no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—62no—
202C2×C3×C4—62no—
203C2×C3×C4—61no—
204C2×C3×C4—122no—
205C2×Dic3—21no—
206C2×Dic3—42no—
207C2×Dic3—61no—
208C2×Dic3—61no—
209C2×Dic3—62no—
210C2×Dic3—62no—
211C4×D3—22no—
212C4×D3—22no—
213C4×D3—62no—
214C4×D3—61no—
215C4×D3—61no—
216C4×D3—61no—
217C4×D3—61no—
218C4×D3—61no—
219C4×D3—61no—
220C4×D3—61no—
221C4×D3—61no—
222C4×D3—62no—
223C4×D3—62no—
224C4×D3—62no—
225C4×D3—124no—
226C4×D3—124no—
227Dic6—24no—
228Dic6—42no—
229Dic6—124no—
230Dic6—124no—
231C3×C8—22no—
232C3×C8—22no—
233C3×C8—62no—
234C3⋊C8—22no—
235C3⋊C8—62no—
236C3⋊C8—62no—
237C2×C32#46712yescomplemented
238C2×C32C2×#12111yescharacteristic
239C3⋊D3#46712yescomplemented
240C3⋊D3C22×Q1611yescharacteristic
241C3⋊D3C2×#13511yescharacteristic
242C3×D3—24no—
243C24—91no—
244C2×Q8—62no—
245C2×Q8—94no—
246C2×Q8—182no—
247C2×Q8—182no—
248C2×Q8—182no—
249C2×Q8—182no—
250C22×C4—61no—
251C22×C4—91no—
252C22×C4—92no—
253C22×C4—92no—
254C22×C4—91no—
255C22×C4—181no—
256C22×C4—181no—
257C22×C4—181no—
258C22×C4—182no—
259C22×C4—182no—
260Q16—64no—
261Q16—184no—
262C2×C8—61no—
263C2×C8—64no—
264C2×C8—92no—
265C2×C8—91no—
266C2×C8—92no—
267C2×C8—92no—
268C2×C8—181no—
269C2×C8—184no—
270C2×C8GO+(4,𝔽2)11yescharacteristic
271C4⋊C4—94no—
272C4⋊C4—182no—
273C4⋊C4—188no—
274C22⋊C4—188no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—62no—
278C22×C3—64no—
279C2×D3—22no—
280C2×D3—24no—
281C2×D3—64no—
282C2×D3—61no—
283C2×D3—61no—
284C2×D3—61no—
285C2×D3—61no—
286C2×D3—62no—
287C2×D3—62no—
288C2×D3—62no—
289C2×D3—62no—
290C2×D3—64no—
291C2×D3—68no—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—62no—
297C3×C4—124no—
298Dic3—22no—
299Dic3—44no—
300Dic3—61no—
301Dic3—61no—
302Dic3—61no—
303Dic3—61no—
304C32C2×#46711yescharacteristic, complemented, Sylow
305C23—61no—
306C23—92no—
307C23—94no—
308C23—91no—
309C23—181no—
310C23—182no—
311Q8—64no—
312Q8—122no—
313Q8—184no—
314Q8—362no—
315C2×C4—61no—
316C2×C4—62no—
317C2×C4—62no—
318C2×C4—92no—
319C2×C4—91no—
320C2×C4—91no—
321C2×C4—91no—
322C2×C4—91no—
323C2×C4—91no—
324C2×C4—122no—
325C2×C4—181no—
326C2×C4—182no—
327C2×C4—182no—
328C2×C4—184no—
329C2×C4—184no—
330C2×C4—362no—
331C2×C4—364no—
332C2×C4C2×GO+(4,𝔽2)11yescharacteristic
333C8—62no—
334C8—92no—
335C8C2×GO+(4,𝔽2)12yes—
336C2×C3—22no—
337C2×C3—22no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—64no—
341D3—24no—
342D3—61no—
343D3—61no—
344D3—62no—
345D3—61no—
346D3—61no—
347D3—62no—
348C22—64no—
349C22—62no—
350C22—94no—
351C22—92no—
352C22—92no—
353C22—91no—
354C22—91no—
355C22—182no—
356C22—184no—
357C22#6423011yescharacteristic
358C4—62no—
359C4—91no—
360C4—91no—
361C4—124no—
362C4—364no—
363C4#6423011yescharacteristic
364C4C22×GO+(4,𝔽2)11yescharacteristic
365C3—21no—
366C3—21no—
367C2—64no—
368C2—91no—
369C2—91no—
370C2—92no—
371C2#1059328812yesdirect product factor
372C2C2×#6423011yescharacteristic
subgroupG/H
centerC22#64230
commutator, cosocleC4×C3⋊D3C24
FrattiniC4C22×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#121
prime radicalC22×D32D4
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32C2×#467
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63802C2semidirect
4. C2×#63769C2semidirect
5. C2×#63730C2semidirect
6. #10593288C2direct (N × H)
21. #63802C22semidirect
24. #63769C22semidirect
25. #63730C22semidirect
81. C2×D32Q16semidirect
162. D32C2×Q16semidirect
237. C2×C32#467semidirect
239. C3⋊D3#467semidirect
304. C32C2×#467semidirect
371. C2#10593288direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D32⋊Q82
C2×#638022
C2×D32×C82
C2×#637692
C2×#637302
#105932882
C2×#4679