Finite Group Databasebeta

← C2×#10589741 #11902974

Subgroups — C2×#10589741 #11902974

Order 1152.

1686 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#63508C211yesmaximal, characteristic, complemented
3C2×Q8×Dic9C211yesmaximal, characteristic, complemented
4C2×C4×#611C211yesmaximal, characteristic
5C2×#63488C211yesmaximal, characteristic, complemented
6#10589741C2116yesmaximal, direct product factor
7C2×#63454C212yesmaximal, complemented
8C2×C4⋊C4×D9C211yesmaximal, characteristic, complemented
9C2×#63452C211yesmaximal, characteristic, complemented
10C2×#63451C212yesmaximal, complemented
11C2×#63445C212yesmaximal
12C2×#63441C212yesmaximal, complemented
13C2×#5639—31nomaximal
14C22×Q8×C9C2211yescharacteristic
15C23×C4×C9C2211yescharacteristic
16C22×#611C2211yescharacteristic
17C22×C4×D9C2212yes—
18C22×C4×D9C2211yescharacteristic
19C9×C22⋊Q8C2218yescomplemented
20C2×C9×C4⋊C4C2212yes—
21C2×C9×C4⋊C4C2211yescharacteristic
22C2×C9×C22⋊C4C2212yes—
23C2×#3676C2211yescharacteristic
24C2×#3676C2212yes—
25#63508C2218yescomplemented
26Q8×Dic9C2218yescomplemented
27C4×#611C2218yes—
28C2×(C2×D9)⋊C4C2212yes—
29C2×(C2×D9)⋊C4C2211yescharacteristic
30#63488C2218yescomplemented
31C2×C4⋊Dic9C2212yes—
32C2×C4⋊Dic9C2212yes—
33C2×C4⋊Dic9C2211yescharacteristic
34C2×C4⋊Dic9C2211yescharacteristic
35C2×Dic9⋊C4C2212yes—
36C2×Dic9⋊C4C2212yes—
37C2×Dic9⋊C4C2212yes—
38C2×Dic9⋊C4C2211yescharacteristic
39C2×C4×Dic9C2212yes—
40C2×C4×Dic9C2212yes—
41C2×C4×Dic9C2211yescharacteristic
42#63454C22116yescomplemented
43C4⋊C4×D9C2218yescomplemented
44#63452C2218yescomplemented
45#63451C22116yescomplemented
46#63445C22116yes—
47#63441C22116yescomplemented
48C2×C3×C22⋊Q8D311yescharacteristic
49C2×#946—31no—
50C2×Q8×Dic3—31no—
51C2×C4×#67—31no—
52C2×#926—31no—
53#5639—316no—
54C2×#892—32no—
55C2×D3×C4⋊C4—31no—
56C2×#890—31no—
57C2×#889—32no—
58C2×#883—32no—
59C2×#879—32no—
60C24×C9C2311yescharacteristic
61C23×D9C2311yescharacteristic
62C2×Q8×C9—24no—
63C2×Q8×C9C2314yes—
64C22×C4×C9—24no—
65C22×C4×C9C2314yes—
66C22×C4×C9C2312yes—
67C22×C4×C9C2311yescharacteristic
68C22×C4×C9C2312yes—
69C22×C4×C9C2311yescharacteristic
70C2×#611—24no—
71C2×#611C2314yes—
72C22×Dic9C2311yescharacteristic
73C22×Dic9C2312yes—
74C22×Dic9C2312yes—
75C22×Dic9C2311yescharacteristic
76C22×Dic9C2311yescharacteristic
77C2×C4×D9—28no—
78C2×C4×D9—24no—
79C2×C4×D9C2314yes—
80C2×C4×D9C2318yes—
81C9×C4⋊C4C2318yes—
82C9×C4⋊C4C2314yes—
83C9×C22⋊C4C2318yes—
84#3676C2318yes—
85#3676C2314yes—
86(C2×D9)⋊C4C2314yes—
87(C2×D9)⋊C4C2318yes—
88C4⋊Dic9C2314yes—
89C4⋊Dic9C2314yes—
90C4⋊Dic9C2318yes—
91C4⋊Dic9C2318yes—
92Dic9⋊C4C2314yes—
93Dic9⋊C4C2318yes—
94Dic9⋊C4C2318yes—
95Dic9⋊C4C2318yes—
96C4×Dic9C2318yes—
97C4×Dic9C2314yes—
98C4×Dic9C2318yes—
99C2×#552—91noSylow
100C22×C3×Q8C2×D311yescharacteristic
101C23×C3×C4C2×D311yescharacteristic
102C22×#67—31no—
103C22×C4×D3—32no—
104C22×C4×D3—31no—
105C3×C22⋊Q8C2×D318yes—
106C2×C3×C4⋊C4C2×D312yes—
107C2×C3×C4⋊C4C2×D311yescharacteristic
108C2×C3×C22⋊C4C2×D312yes—
109C2×#217—31no—
110C2×#217—32no—
111#946—38no—
112Q8×Dic3—38no—
113C4×#67—38no—
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4—31no—
116#926—38no—
117C2×C4⋊Dic3—32no—
118C2×C4⋊Dic3—32no—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—31no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—31no—
125C2×C4×Dic3—32no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—31no—
128#892—316no—
129D3×C4⋊C4—38no—
130#890—38no—
131#889—316no—
132#883—316no—
133#879—316no—
134C23×C9—22no—
135C23×C9—22no—
136C23×C9—22no—
137C23×C9C2412yes—
138C23×C9C2411yescharacteristic
139C22×D9—22no—
140C22×D9—22no—
141C22×D9#4114yes—
142C22×D9C2412yes—
143Q8×C9—28no—
144C2×C4×C9—24no—
145C2×C4×C9—22no—
146C2×C4×C9—24no—
147C2×C4×C9—28no—
148C2×C4×C9#4114yes—
149C2×C4×C9C2412yes—
150C2×C4×C9C2414yes—
151C2×C4×C9C2414yes—
152C2×C4×C9C2412yes—
153#611—28no—
154C2×Dic9—22no—
155C2×Dic9—24no—
156C2×Dic9—22no—
157C2×Dic9—22no—
158C2×Dic9—24no—
159C2×Dic9C2412yes—
160C2×Dic9C2414yes—
161C2×Dic9C2412yes—
162C2×Dic9C2414yes—
163C2×Dic9C2412yes—
164C4×D9—216no—
165C4×D9—28no—
166#552—916no—
167C2×#126—92no—
168C2×#125—92no—
169C2×#125—91no—
170C2×#123—92no—
171C2×C22⋊Q8—91no—
172C2×C22⋊Q8D911yescharacteristic, complemented
173C2×C4×Q8—91no—
174C2×C4×D4—91no—
175C2×#117—91no—
176C2×#117—92no—
177C22×C4⋊C4—91no—
178C24×C3C22×D311yescharacteristic
179C23×D3—31no—
180C2×C3×Q8—24no—
181C2×C3×Q8C22×D314yes—
182C22×C3×C4—24no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D312yes—
185C22×C3×C4C22×D312yes—
186C22×C3×C4C22×D314yes—
187C22×C3×C4C22×D311yescharacteristic
188C2×#67—34no—
189C2×#67—64no—
190C22×Dic3—31no—
191C22×Dic3—32no—
192C22×Dic3—31no—
193C22×Dic3—32no—
194C22×Dic3—31no—
195C2×C4×D3—38no—
196C2×C4×D3—34no—
197C2×C4×D3—68no—
198C2×C4×D3—64no—
199C3×C4⋊C4C22×D318yes—
200C3×C4⋊C4C22×D314yes—
201C3×C22⋊C4C22×D318yes—
202#217—34no—
203#217—38no—
204(C2×D3)⋊C4—38no—
205(C2×D3)⋊C4—34no—
206C4⋊Dic3—38no—
207C4⋊Dic3—38no—
208C4⋊Dic3—34no—
209C4⋊Dic3—34no—
210Dic3⋊C4—38no—
211Dic3⋊C4—38no—
212Dic3⋊C4—38no—
213Dic3⋊C4—34no—
214C4×Dic3—38no—
215C4×Dic3—38no—
216C4×Dic3—34no—
217C22×C9—22no—
218C22×C9—22no—
219C22×C9—22no—
220C22×C9—44no—
221C22×C9C2×#4112yes—
222C22×C9C2×#4112yes—
223C22×C92−1+412yes—
224C22×C9C2511yescharacteristic
225C2×D9—28no—
226C2×D9—22no—
227C2×D9—22no—
228C2×D9C2×#4114yes—
229C4×C9—24no—
230C4×C9—22no—
231C4×C9—24no—
232C4×C9C2×#4114yes—
233Dic9—22no—
234Dic9—24no—
235Dic9—22no—
236Dic9—22no—
237Dic9—24no—
238C22×Q8C2×D911yescharacteristic
239C22×D4—91no—
240C23×C4—92no—
241C23×C4—91no—
242C23×C4C2×D911yescharacteristic
243#126—916no—
244#125—916no—
245#125—98no—
246#123—916no—
247C22⋊Q8—98no—
248C22⋊Q8C2×D918yescomplemented
249C4×Q8—98no—
250C4×D4—98no—
251#117—98no—
252#117—916no—
253C2×C4⋊C4—91no—
254C2×C4⋊C4—92no—
255C2×C4⋊C4—91no—
256C2×C4⋊C4—92no—
257C2×C4⋊C4—91no—
258C2×C4⋊C4—92no—
259C2×C4⋊C4—92no—
260C2×C4⋊C4—92no—
261C2×C4⋊C4—98no—
262C2×C4⋊C4C2×D911yescharacteristic
263C2×C4⋊C4C2×D912yes—
264C2×C22⋊C4—92no—
265C2×C22⋊C4—91no—
266C2×C22⋊C4—91no—
267C2×C22⋊C4—92no—
268C2×C22⋊C4C2×D912yes—
269C2×C42—92no—
270C2×C42—92no—
271C2×C42—91no—
272C23×C3—22no—
273C23×C3—22no—
274C23×C3—22no—
275C23×C3C23×D312yes—
276C23×C3C23×D311yescharacteristic
277C22×D3—34no—
278C22×D3—32no—
279C22×D3—62no—
280C22×D3—62no—
281C3×Q8—28no—
282C2×C3×C4—22no—
283C2×C3×C4—24no—
284C2×C3×C4—24no—
285C2×C3×C4—28no—
286C2×C3×C4#23714yes—
287C2×C3×C4C23×D312yes—
288C2×C3×C4C23×D314yes—
289C2×C3×C4C23×D314yes—
290C2×C3×C4C23×D312yes—
291#67—68no—
292C2×Dic3—32no—
293C2×Dic3—34no—
294C2×Dic3—32no—
295C2×Dic3—34no—
296C2×Dic3—32no—
297C2×Dic3—62no—
298C2×Dic3—62no—
299C2×Dic3—64no—
300C2×Dic3—64no—
301C2×Dic3—62no—
302C4×D3—616no—
303C4×D3—68no—
304C2×C9—42no—
305C2×C9#55214yescomplemented
306C2×C9C22×#4111yescharacteristic
307C2×C9C22×#4111yescharacteristic
308C2×C9C2×2−1+411yescharacteristic
309D9—24no—
310C24—91no—
311C24C22×D911yescharacteristic
312C2×Q8—24no—
313C2×Q8C22×D914yes—
314C2×D4—94no—
315C2×D4—184no—
316C22×C4—24no—
317C22×C4—91no—
318C22×C4—92no—
319C22×C4—92no—
320C22×C4—91no—
321C22×C4—91no—
322C22×C4—98no—
323C22×C4—94no—
324C22×C4—188no—
325C22×C4—184no—
326C22×C4C22×D914yes—
327C22×C4C22×D911yescharacteristic
328C22×C4C22×D912yes—
329C22×C4C22×D912yes—
330C22×C4C22×D911yescharacteristic
331C4⋊C4—94no—
332C4⋊C4—98no—
333C4⋊C4—94no—
334C4⋊C4—98no—
335C4⋊C4—94no—
336C4⋊C4—98no—
337C4⋊C4—98no—
338C4⋊C4—98no—
339C4⋊C4C22×D914yes—
340C4⋊C4C22×D918yes—
341C22⋊C4—98no—
342C22⋊C4—94no—
343C22⋊C4—94no—
344C22⋊C4—98no—
345C22⋊C4C22×D918yes—
346C42—98no—
347C42—98no—
348C42—94no—
349C22×C3—22no—
350C22×C3—22no—
351C22×C3—22no—
352C22×C3—44no—
353C22×C3C2×#23712yes—
354C22×C3#100712yes—
355C22×C3D3×#4112yes—
356C22×C3C24×D311yescharacteristic
357C2×D3—34no—
358C2×D3—68no—
359C2×D3—62no—
360C2×D3—62no—
361C3×C4—22no—
362C3×C4—24no—
363C3×C4—24no—
364C3×C4C2×#23714yes—
365Dic3—62no—
366Dic3—62no—
367Dic3—64no—
368Dic3—64no—
369Dic3—62no—
370C9C2×#55211yescharacteristic, complemented, Sylow
371C23—22no—
372C23—22no—
373C23—22no—
374C23—92no—
375C23—94no—
376C23—182no—
377C23—182no—
378C23C23×D912yes—
379C23C23×D911yescharacteristic
380Q8—28no—
381D4—188no—
382C2×C4—22no—
383C2×C4—24no—
384C2×C4—24no—
385C2×C4—28no—
386C2×C4—92no—
387C2×C4—94no—
388C2×C4—94no—
389C2×C4—92no—
390C2×C4—92no—
391C2×C4—1816no—
392C2×C4—182no—
393C2×C4—182no—
394C2×C4—184no—
395C2×C4—184no—
396C2×C4—182no—
397C2×C4—188no—
398C2×C4#369914yes—
399C2×C4C23×D912yes—
400C2×C4C23×D914yes—
401C2×C4C23×D914yes—
402C2×C4C23×D912yes—
403C2×C3—42no—
404C2×C3#563914yes—
405C2×C3C22×#23711yescharacteristic
406C2×C3C2×#100711yescharacteristic
407C2×C3C2×D3×#4111yescharacteristic
408D3—64no—
409C22—22no—
410C22—22no—
411C22—22no—
412C22—44no—
413C22—94no—
414C22—188no—
415C22—182no—
416C22—182no—
417C22C2×#369912yes—
418C22#6371312yes—
419C22#41×D912yes—
420C22C24×D911yescharacteristic
421C4—22no—
422C4—24no—
423C4—24no—
424C4—182no—
425C4—182no—
426C4—184no—
427C4—184no—
428C4—182no—
429C4C2×#369914yes—
430C3C2×#563911yescharacteristic
431C2—42no—
432C2—184no—
433C2#1058974114yesdirect product factor
434C2C22×#369911yescharacteristic
435C2C2×#6371311yescharacteristic
436C2C2×#41×D911yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C9×C22⋊Q8C2
socleC23×C3C23×D3
prime radicalC22×#611C22
hypercenterC2×C22⋊Q8D9
hypocenterC9C2×#552
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C9×C22⋊Q8C2semidirect
2. C2×#63508C2semidirect
3. C2×Q8×Dic9C2semidirect
5. C2×#63488C2semidirect
6. #10589741C2direct (N × H)
7. C2×#63454C2semidirect
8. C2×C4⋊C4×D9C2semidirect
9. C2×#63452C2semidirect
10. C2×#63451C2semidirect
12. C2×#63441C2semidirect
19. C9×C22⋊Q8C22semidirect
25. #63508C22semidirect
26. Q8×Dic9C22semidirect
30. #63488C22semidirect
42. #63454C22semidirect
43. C4⋊C4×D9C22semidirect
44. #63452C22semidirect
45. #63451C22semidirect
47. #63441C22semidirect
172. C2×C22⋊Q8D9semidirect
248. C22⋊Q8C2×D9semidirect
305. C2×C9#552semidirect
370. C9C2×#552semidirect
433. C2#10589741direct (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×#635082
C2×Q8×Dic92
C2×C4×#6112
C2×#634882
#105897412
C2×#634542
C2×C4⋊C4×D92
C2×#634522
C2×#634512
C2×#634452
C2×#634412
C2×#56393