Finite Group Databasebeta

← C2×#10589727 #11901544

Subgroups — C2×#10589727 #11901544

Order 1152.

1506 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×C22⋊Q8C211yesmaximal, characteristic
2C2×Q8×Dic9C211yesmaximal, characteristic, complemented
3C2×#63506C211yesmaximal, characteristic, complemented
4C2×#63488C211yesmaximal, characteristic
5C2×#63486C211yesmaximal, characteristic
6#10589727C2116yesmaximal, direct product factor
7C2×#63452C211yesmaximal, characteristic, complemented
8C2×#63452C212yesmaximal, complemented
9C2×#63451C212yesmaximal, complemented
10C2×#63449C211yesmaximal, characteristic, complemented
11C2×#63441C212yesmaximal
12C2×#63441C212yesmaximal
13C2×#5625—31nomaximal
14C22×Q8×C9C2211yescharacteristic
15C23×C4×C9C2211yescharacteristic
16C22×Dic18C2211yescharacteristic
17C9×C22⋊Q8C2218yes—
18C2×C9×C4⋊C4C2211yescharacteristic
19C2×C9×C4⋊C4C2212yes—
20C2×C9×C22⋊C4C2212yes—
21C2×#3676C2212yes—
22C2×#3676C2211yescharacteristic
23C2×#3676C2211yescharacteristic
24Q8×Dic9C2218yescomplemented
25#63506C2218yescomplemented
26#63488C2218yes—
27C2×C4⋊Dic9C2212yes—
28C2×C4⋊Dic9C2212yes—
29C2×C4⋊Dic9C2211yescharacteristic
30C2×C4⋊Dic9C2211yescharacteristic
31C2×C4⋊Dic9C2211yescharacteristic
32#63486C2218yes—
33C2×Dic9⋊C4C2212yes—
34C2×Dic9⋊C4C2212yes—
35C2×Dic9⋊C4C2212yes—
36C2×Dic9⋊C4C2212yes—
37C2×Dic9⋊C4C2212yes—
38C2×C4×Dic9C2212yes—
39C2×C4×Dic9C2212yes—
40C2×C4×Dic9C2211yescharacteristic
41C2×C4×Dic9C2211yescharacteristic
42#63452C2218yescomplemented
43#63452C22116yescomplemented
44#63451C22116yescomplemented
45#63449C2218yescomplemented
46#63441C22116yes—
47#63441C22116yes—
48C2×C3×C22⋊Q8D311yescharacteristic
49C2×Q8×Dic3—31no—
50C2×#944—31no—
51C2×#926—31no—
52C2×#924—31no—
53#5625—316no—
54C2×#890—32no—
55C2×#890—31no—
56C2×#889—32no—
57C2×#887—31no—
58C2×#879—32no—
59C2×#879—32no—
60C24×C9C2311yescharacteristic
61C2×Q8×C9—24no—
62C2×Q8×C9C2314yes—
63C22×C4×C9—24no—
64C22×C4×C9C2314yes—
65C22×C4×C9C2312yes—
66C22×C4×C9C2312yes—
67C22×C4×C9C2311yescharacteristic
68C22×C4×C9C2311yescharacteristic
69C22×Dic9C2312yes—
70C22×Dic9C2311yescharacteristic
71C22×Dic9C2311yescharacteristic
72C22×Dic9C2311yescharacteristic
73C22×Dic9C2312yes—
74C22×Dic9C2311yescharacteristic
75C2×Dic18—24no—
76C2×Dic18C2314yes—
77C9×C4⋊C4C2314yes—
78C9×C4⋊C4C2318yes—
79C9×C22⋊C4C2318yes—
80#3676C2314yes—
81#3676C2314yes—
82#3676C2318yes—
83C4⋊Dic9C2314yes—
84C4⋊Dic9C2314yes—
85C4⋊Dic9C2318yes—
86C4⋊Dic9C2314yes—
87C4⋊Dic9C2318yes—
88Dic9⋊C4C2318yes—
89Dic9⋊C4C2318yes—
90Dic9⋊C4C2318yes—
91Dic9⋊C4C2318yes—
92Dic9⋊C4C2318yes—
93C4×Dic9C2314yes—
94C4×Dic9C2314yes—
95C4×Dic9C2318yes—
96C4×Dic9C2318yes—
97C2×#541—91noSylow
98C22×C3×Q8C2×D311yescharacteristic
99C23×C3×C4C2×D311yescharacteristic
100C22×Dic6—31no—
101C3×C22⋊Q8C2×D318yes—
102C2×C3×C4⋊C4C2×D311yescharacteristic
103C2×C3×C4⋊C4C2×D312yes—
104C2×C3×C22⋊C4C2×D312yes—
105C2×#217—32no—
106C2×#217—31no—
107C2×#217—31no—
108Q8×Dic3—38no—
109#944—38no—
110#926—38no—
111C2×C4⋊Dic3—32no—
112C2×C4⋊Dic3—32no—
113C2×C4⋊Dic3—31no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—31no—
116#924—38no—
117C2×Dic3⋊C4—32no—
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—32no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3—32no—
124C2×C4×Dic3—31no—
125C2×C4×Dic3—31no—
126#890—316no—
127#890—38no—
128#889—316no—
129#887—38no—
130#879—316no—
131#879—316no—
132C23×C9—22no—
133C23×C9—22no—
134C23×C9—22no—
135C23×C9C2412yes—
136C23×C9C2411yescharacteristic
137Q8×C9—28no—
138C2×C4×C9—22no—
139C2×C4×C9—24no—
140C2×C4×C9—24no—
141C2×C4×C9—28no—
142C2×C4×C9#4114yes—
143C2×C4×C9C2414yes—
144C2×C4×C9C2414yes—
145C2×C4×C9C2412yes—
146C2×C4×C9C2412yes—
147C2×Dic9—24no—
148C2×Dic9—22no—
149C2×Dic9—24no—
150C2×Dic9—22no—
151C2×Dic9—22no—
152C2×Dic9—22no—
153C2×Dic9C2412yes—
154C2×Dic9C2412yes—
155C2×Dic9C2412yes—
156C2×Dic9C2414yes—
157C2×Dic9C2412yes—
158C2×Dic9C2414yes—
159Dic18—28no—
160#541—916no—
161C2×C4⋊Q8—91no—
162C2×#126—92no—
163C2×#126—92no—
164C2×#125—92no—
165C2×#125—91no—
166C2×#125—92no—
167C2×C22⋊Q8—91no—
168C2×C22⋊Q8D911yescharacteristic
169C2×C4×Q8—91no—
170C2×C4×Q8—91no—
171C2×#117—91no—
172C24×C3C22×D311yescharacteristic
173C2×C3×Q8—24no—
174C2×C3×Q8C22×D314yes—
175C22×C3×C4—24no—
176C22×C3×C4C22×D312yes—
177C22×C3×C4C22×D312yes—
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D314yes—
180C22×C3×C4C22×D311yescharacteristic
181C22×Dic3—31no—
182C22×Dic3—31no—
183C22×Dic3—31no—
184C22×Dic3—32no—
185C22×Dic3—32no—
186C22×Dic3—31no—
187C2×Dic6—34no—
188C2×Dic6—64no—
189C3×C4⋊C4C22×D314yes—
190C3×C4⋊C4C22×D318yes—
191C3×C22⋊C4C22×D318yes—
192#217—38no—
193#217—34no—
194#217—34no—
195C4⋊Dic3—38no—
196C4⋊Dic3—38no—
197C4⋊Dic3—34no—
198C4⋊Dic3—34no—
199C4⋊Dic3—34no—
200Dic3⋊C4—38no—
201Dic3⋊C4—38no—
202Dic3⋊C4—38no—
203Dic3⋊C4—38no—
204Dic3⋊C4—38no—
205C4×Dic3—38no—
206C4×Dic3—38no—
207C4×Dic3—34no—
208C4×Dic3—34no—
209C22×C9—22no—
210C22×C9—22no—
211C22×C9—22no—
212C22×C9—44no—
213C22×C9C2×#4112yes—
214C22×C92−1+412yes—
215C22×C92−1+412yes—
216C22×C9C2511yescharacteristic
217C4×C9—22no—
218C4×C9—24no—
219C4×C9—24no—
220C4×C9C2×#4114yes—
221Dic9—24no—
222Dic9—22no—
223Dic9—22no—
224Dic9—24no—
225Dic9—22no—
226Dic9—22no—
227C22×Q8—91no—
228C22×Q8C2×D911yescharacteristic
229C23×C4C2×D911yescharacteristic
230C4⋊Q8—98no—
231#126—916no—
232#126—916no—
233#125—916no—
234#125—98no—
235#125—916no—
236C22⋊Q8—98no—
237C22⋊Q8C2×D918yes—
238C4×Q8—98no—
239C4×Q8—98no—
240#117—98no—
241C2×C4⋊C4—91no—
242C2×C4⋊C4—91no—
243C2×C4⋊C4—91no—
244C2×C4⋊C4—92no—
245C2×C4⋊C4—92no—
246C2×C4⋊C4—92no—
247C2×C4⋊C4—92no—
248C2×C4⋊C4—92no—
249C2×C4⋊C4—92no—
250C2×C4⋊C4—92no—
251C2×C4⋊C4C2×D911yescharacteristic
252C2×C4⋊C4C2×D912yes—
253C2×C22⋊C4—91no—
254C2×C22⋊C4—91no—
255C2×C22⋊C4—92no—
256C2×C22⋊C4C2×D912yes—
257C2×C42—91no—
258C2×C42—91no—
259C2×C42—92no—
260C2×C42—92no—
261C23×C3—22no—
262C23×C3—22no—
263C23×C3—22no—
264C23×C3C23×D312yes—
265C23×C3C23×D311yescharacteristic
266C3×Q8—28no—
267C2×C3×C4—22no—
268C2×C3×C4—24no—
269C2×C3×C4—24no—
270C2×C3×C4—28no—
271C2×C3×C4#23714yes—
272C2×C3×C4C23×D314yes—
273C2×C3×C4C23×D314yes—
274C2×C3×C4C23×D312yes—
275C2×C3×C4C23×D312yes—
276C2×Dic3—32no—
277C2×Dic3—32no—
278C2×Dic3—32no—
279C2×Dic3—34no—
280C2×Dic3—34no—
281C2×Dic3—32no—
282C2×Dic3—64no—
283C2×Dic3—62no—
284C2×Dic3—64no—
285C2×Dic3—62no—
286C2×Dic3—62no—
287C2×Dic3—62no—
288Dic6—68no—
289C2×C9—42no—
290C2×C9#54114yescomplemented
291C2×C9C22×#4111yescharacteristic
292C2×C9C2×2−1+411yescharacteristic
293C2×C9C2×2−1+411yescharacteristic
294C24C22×D911yescharacteristic
295C2×Q8—24no—
296C2×Q8—94no—
297C2×Q8—184no—
298C2×Q8C22×D914yes—
299C22×C4—24no—
300C22×C4—91no—
301C22×C4—91no—
302C22×C4—91no—
303C22×C4—92no—
304C22×C4—91no—
305C22×C4—92no—
306C22×C4C22×D914yes—
307C22×C4C22×D912yes—
308C22×C4C22×D912yes—
309C22×C4C22×D911yescharacteristic
310C22×C4C22×D911yescharacteristic
311C4⋊C4—94no—
312C4⋊C4—94no—
313C4⋊C4—94no—
314C4⋊C4—98no—
315C4⋊C4—98no—
316C4⋊C4—98no—
317C4⋊C4—98no—
318C4⋊C4—98no—
319C4⋊C4—98no—
320C4⋊C4—98no—
321C4⋊C4C22×D914yes—
322C4⋊C4C22×D918yes—
323C22⋊C4—94no—
324C22⋊C4—94no—
325C22⋊C4—98no—
326C22⋊C4C22×D918yes—
327C42—94no—
328C42—94no—
329C42—98no—
330C42—98no—
331C22×C3—22no—
332C22×C3—22no—
333C22×C3—22no—
334C22×C3—44no—
335C22×C3C2×#23712yes—
336C22×C3#100712yes—
337C22×C3#101012yes—
338C22×C3C24×D311yescharacteristic
339C3×C4—22no—
340C3×C4—24no—
341C3×C4—24no—
342C3×C4C2×#23714yes—
343Dic3—64no—
344Dic3—62no—
345Dic3—64no—
346Dic3—62no—
347Dic3—62no—
348Dic3—62no—
349C9C2×#54111yescharacteristic, complemented, Sylow
350C23—22no—
351C23—22no—
352C23—22no—
353C23C23×D912yes—
354C23C23×D911yescharacteristic
355Q8—28no—
356Q8—188no—
357C2×C4—22no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—28no—
361C2×C4—92no—
362C2×C4—92no—
363C2×C4—92no—
364C2×C4—94no—
365C2×C4—92no—
366C2×C4—94no—
367C2×C4—184no—
368C2×C4—182no—
369C2×C4—182no—
370C2×C4—184no—
371C2×C4—182no—
372C2×C4—182no—
373C2×C4#369914yes—
374C2×C4C23×D914yes—
375C2×C4C23×D914yes—
376C2×C4C23×D912yes—
377C2×C4C23×D912yes—
378C2×C3—42no—
379C2×C3#562514yes—
380C2×C3C22×#23711yescharacteristic
381C2×C3C2×#100711yescharacteristic
382C2×C3C2×#101011yescharacteristic
383C22—22no—
384C22—22no—
385C22—22no—
386C22—44no—
387C22C2×#369912yes—
388C22#6371312yes—
389C22#6371612yes—
390C22C24×D911yescharacteristic
391C4—22no—
392C4—24no—
393C4—24no—
394C4—184no—
395C4—182no—
396C4—182no—
397C4—184no—
398C4—182no—
399C4—182no—
400C4C2×#369914yes—
401C3C2×#562511yescharacteristic
402C2—42no—
403C2#1058972714yesdirect product factor
404C2C22×#369911yescharacteristic
405C2C2×#6371311yescharacteristic
406C2C2×#6371611yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C9×C22⋊Q8C2
socleC23×C3C23×D3
prime radicalC24×C3C22×D3
hypercenterC2×C22⋊Q8D9
hypocenterC9C2×#541
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×Q8×Dic9C2semidirect
3. C2×#63506C2semidirect
6. #10589727C2direct (N × H)
7. C2×#63452C2semidirect
8. C2×#63452C2semidirect
9. C2×#63451C2semidirect
10. C2×#63449C2semidirect
24. Q8×Dic9C22semidirect
25. #63506C22semidirect
42. #63452C22semidirect
43. #63452C22semidirect
44. #63451C22semidirect
45. #63449C22semidirect
290. C2×C9#541semidirect
349. C9C2×#541semidirect
403. C2#10589727direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×C22⋊Q82
C2×Q8×Dic92
C2×#635062
C2×#634882
C2×#634862
#105897272
C2×#634522
C2×#634512
C2×#634492
C2×#634412
C2×#56253