Finite Group Databasebeta

← C2×#10589680 #11900813

Subgroups — C2×#10589680 #11900813

Order 1152.

1752 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×C9C211yesmaximal, characteristic, complemented
2C2×#63508C211yesmaximal, characteristic
3C2×#63506C211yesmaximal, characteristic, complemented
4#10589680C2116yesmaximal, direct product factor
5C2×#63459C211yesmaximal, characteristic
6C2×#63458C212yesmaximal
7C2×#63451C212yesmaximal, complemented
8C2×#63450C211yesmaximal, characteristic, complemented
9C2×#63434C212yesmaximal
10C2×C42×D9C211yesmaximal, characteristic
11C2×C4×Dic18C211yesmaximal, characteristic, complemented
12C2×C4×Dic18C212yesmaximal, complemented
13C2×#5578—31nomaximal
14C22×Q8×C9C2211yescharacteristic
15C22×C4×D9C2211yescharacteristic
16C22×C4×D9C2211yescharacteristic
17C22×C4×D9C2211yescharacteristic
18C22×Dic18C2212yes—
19C22×Dic18C2211yescharacteristic
20C4×Q8×C9C2218yescomplemented
21C2×C9×C4⋊C4C2211yescharacteristic
22C2×C9×C4⋊C4C2212yes—
23C2×C42×C9C2211yescharacteristic
24C2×C42×C9C2212yes—
25#63508C2218yes—
26#63506C2218yescomplemented
27C2×(C2×D9)⋊C4C2212yes—
28C2×(C2×D9)⋊C4C2212yes—
29C2×C4⋊Dic9C2211yescharacteristic
30C2×C4⋊Dic9C2212yes—
31C2×Dic9⋊C4C2212yes—
32C2×Dic9⋊C4C2212yes—
33C2×Dic9⋊C4C2212yes—
34C2×Dic9⋊C4C2212yes—
35C2×Dic9⋊C4C2212yes—
36C2×C4×Dic9C2211yescharacteristic
37C2×C4×Dic9C2212yes—
38C2×C4×Dic9C2211yescharacteristic
39C2×C4×Dic9C2211yescharacteristic
40#63459C2218yes—
41#63458C22116yes—
42#63451C22116yescomplemented
43#63450C2218yescomplemented
44#63434C22116yes—
45C42×D9C2218yes—
46C4×Dic18C22116yescomplemented
47C4×Dic18C2218yescomplemented
48C2×C3×C4×Q8D311yescharacteristic
49C2×#946—31no—
50C2×#944—31no—
51#5578—316no—
52C2×#897—31no—
53C2×#896—32no—
54C2×#889—32no—
55C2×#888—31no—
56C2×#872—32no—
57C2×C42×D3—31no—
58C2×C4×Dic6—32no—
59C2×C4×Dic6—31no—
60C23×D9C2311yescharacteristic
61C2×Q8×C9—24no—
62C2×Q8×C9C2314yes—
63C22×C4×C9C2312yes—
64C22×C4×C9C2312yes—
65C22×C4×C9C2311yescharacteristic
66C22×C4×C9C2311yescharacteristic
67C22×C4×C9C2311yescharacteristic
68C22×Dic9C2312yes—
69C22×Dic9C2312yes—
70C22×Dic9C2311yescharacteristic
71C22×Dic9C2311yescharacteristic
72C22×Dic9C2311yescharacteristic
73C2×C4×D9—24no—
74C2×C4×D9—24no—
75C2×C4×D9Q818yescomplemented
76C2×C4×D9C2314yes—
77C2×C4×D9C2314yes—
78C2×C4×D9C2314yes—
79C2×Dic18—24no—
80C2×Dic18—28no—
81C2×Dic18C2314yes—
82C2×Dic18C2318yes—
83C9×C4⋊C4C2314yes—
84C9×C4⋊C4C2318yes—
85C42×C9C2314yes—
86C42×C9C2318yes—
87(C2×D9)⋊C4C2318yes—
88(C2×D9)⋊C4C2318yes—
89C4⋊Dic9C2314yes—
90C4⋊Dic9C2318yes—
91Dic9⋊C4C2318yes—
92Dic9⋊C4C2318yes—
93Dic9⋊C4C2318yes—
94Dic9⋊C4C2318yes—
95Dic9⋊C4C2318yes—
96C4×Dic9C2314yes—
97C4×Dic9C2314yes—
98C4×Dic9C2318yes—
99C4×Dic9C2314yes—
100C2×#533—91noSylow
101C22×C3×Q8C2×D311yescharacteristic
102C22×C4×D3—31no—
103C22×C4×D3—31no—
104C22×C4×D3—31no—
105C22×Dic6—32no—
106C22×Dic6—31no—
107C3×C4×Q8C2×D318yes—
108C2×C3×C4⋊C4C2×D311yescharacteristic
109C2×C3×C4⋊C4C2×D312yes—
110C2×C3×C42C2×D311yescharacteristic
111C2×C3×C42C2×D312yes—
112#946—38no—
113#944—38no—
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4—32no—
116C2×C4⋊Dic3—31no—
117C2×C4⋊Dic3—32no—
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—32no—
123C2×C4×Dic3—31no—
124C2×C4×Dic3—32no—
125C2×C4×Dic3—31no—
126C2×C4×Dic3—31no—
127#897—38no—
128#896—316no—
129#889—316no—
130#888—38no—
131#872—316no—
132C42×D3—38no—
133C4×Dic6—316no—
134C4×Dic6—38no—
135C23×C9C2411yescharacteristic
136C22×D9—22no—
137C22×D9—22no—
138C22×D9C2×Q814yes—
139C22×D9C2412yes—
140Q8×C9—28no—
141C2×C4×C9—24no—
142C2×C4×C9—22no—
143C2×C4×C9—24no—
144C2×C4×C9C2×Q814yes—
145C2×C4×C9#4114yes—
146C2×C4×C9C2412yes—
147C2×C4×C9C2414yes—
148C2×C4×C9C2414yes—
149C2×C4×C9C2412yes—
150C2×C4×C9C2412yes—
151C2×Dic9—24no—
152C2×Dic9—24no—
153C2×Dic9—22no—
154C2×Dic9C2×Q814yes—
155C2×Dic9#4114yes—
156C2×Dic9C2412yes—
157C2×Dic9C2414yes—
158C2×Dic9C2414yes—
159C2×Dic9C2412yes—
160C2×Dic9C2412yes—
161C4×D9—28no—
162C4×D9—28no—
163C4×D9C2×Q8116yescomplemented
164Dic18—28no—
165Dic18—216no—
166#533—916no—
167C2×C4⋊Q8—91no—
168C2×C4⋊Q8—91no—
169C2×#125—92no—
170C2×C22⋊Q8—91no—
171C2×C22⋊Q8—92no—
172C2×C22⋊Q8—91no—
173C2×C4×Q8—91no—
174C2×C4×Q8—92no—
175C2×C4×Q8D911yescharacteristic, complemented
176C2×#117—92no—
177C22×C42—91no—
178C23×D3—31no—
179C2×C3×Q8—24no—
180C2×C3×Q8C22×D314yes—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C22×D312yes—
183C22×C3×C4C22×D312yes—
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C22×Dic3—31no—
187C22×Dic3—31no—
188C22×Dic3—31no—
189C22×Dic3—32no—
190C22×Dic3—32no—
191C2×C4×D3—38no—
192C2×C4×D3—34no—
193C2×C4×D3—34no—
194C2×C4×D3—34no—
195C2×C4×D3—64no—
196C2×C4×D3—64no—
197C2×Dic6—38no—
198C2×Dic6—34no—
199C2×Dic6—68no—
200C2×Dic6—64no—
201C3×C4⋊C4C22×D314yes—
202C3×C4⋊C4C22×D318yes—
203C3×C42C22×D314yes—
204C3×C42C22×D318yes—
205(C2×D3)⋊C4—38no—
206(C2×D3)⋊C4—38no—
207C4⋊Dic3—34no—
208C4⋊Dic3—38no—
209Dic3⋊C4—38no—
210Dic3⋊C4—38no—
211Dic3⋊C4—38no—
212Dic3⋊C4—38no—
213Dic3⋊C4—38no—
214C4×Dic3—34no—
215C4×Dic3—38no—
216C4×Dic3—34no—
217C4×Dic3—34no—
218C22×C9C22×Q812yes—
219C22×C9C2×#4112yes—
220C22×C9C2×#4112yes—
221C22×C9C2511yescharacteristic
222C2×D9—28no—
223C2×D9—22no—
224C2×D9—22no—
225C2×D9C22×Q814yes—
226C4×C9—24no—
227C4×C9—22no—
228C4×C9—24no—
229C4×C9C22×Q814yes—
230C4×C9C2×#4114yes—
231Dic9—24no—
232Dic9—24no—
233Dic9—22no—
234Dic9C22×Q814yes—
235Dic9C2×#4114yes—
236C22×Q8—92no—
237C22×Q8—91no—
238C22×Q8C2×D911yescharacteristic
239C23×C4—91no—
240C23×C4—91no—
241C23×C4—91no—
242C4⋊Q8—98no—
243C4⋊Q8—98no—
244#125—916no—
245C22⋊Q8—98no—
246C22⋊Q8—916no—
247C22⋊Q8—98no—
248C4×Q8—916no—
249C4×Q8—98no—
250C4×Q8C2×D918yescomplemented
251#117—916no—
252C2×C4⋊C4—92no—
253C2×C4⋊C4—92no—
254C2×C4⋊C4—92no—
255C2×C4⋊C4—92no—
256C2×C4⋊C4—92no—
257C2×C4⋊C4—92no—
258C2×C4⋊C4—91no—
259C2×C4⋊C4C2×D912yes—
260C2×C4⋊C4C2×D911yescharacteristic
261C2×C22⋊C4—92no—
262C2×C22⋊C4—92no—
263C2×C42—91no—
264C2×C42—91no—
265C2×C42—92no—
266C2×C42—91no—
267C2×C42—98no—
268C2×C42C2×D912yes—
269C2×C42C2×D911yescharacteristic
270C23×C3C23×D311yescharacteristic
271C22×D3—34no—
272C22×D3—32no—
273C22×D3—62no—
274C22×D3—62no—
275C3×Q8—28no—
276C2×C3×C4—24no—
277C2×C3×C4—24no—
278C2×C3×C4—22no—
279C2×C3×C4#23514yes—
280C2×C3×C4D3×Q814yes—
281C2×C3×C4C23×D312yes—
282C2×C3×C4C23×D314yes—
283C2×C3×C4C23×D314yes—
284C2×C3×C4C23×D312yes—
285C2×C3×C4C23×D312yes—
286C2×Dic3—34no—
287C2×Dic3—34no—
288C2×Dic3—32no—
289C2×Dic3—32no—
290C2×Dic3—32no—
291C2×Dic3—34no—
292C2×Dic3—34no—
293C2×Dic3—64no—
294C2×Dic3—62no—
295C2×Dic3—64no—
296C4×D3—316no—
297C4×D3—68no—
298C4×D3—68no—
299Dic6—616no—
300Dic6—68no—
301C2×C9#53314yescomplemented
302C2×C9C23×Q811yescharacteristic
303C2×C9C22×#4111yescharacteristic
304C2×C9C22×#4111yescharacteristic
305D9—24no—
306C24—91no—
307C2×Q8—24no—
308C2×Q8—98no—
309C2×Q8—94no—
310C2×Q8—188no—
311C2×Q8—184no—
312C2×Q8C22×D914yes—
313C22×C4—91no—
314C22×C4—91no—
315C22×C4—98no—
316C22×C4—94no—
317C22×C4—91no—
318C22×C4—92no—
319C22×C4—92no—
320C22×C4—94no—
321C22×C4—94no—
322C22×C4—184no—
323C22×C4—184no—
324C22×C4C22×D911yescharacteristic
325C22×C4C22×D912yes—
326C22×C4C22×D912yes—
327C22×C4C22×D911yescharacteristic
328C22×C4C22×D911yescharacteristic
329C4⋊C4—98no—
330C4⋊C4—98no—
331C4⋊C4—98no—
332C4⋊C4—98no—
333C4⋊C4—98no—
334C4⋊C4—98no—
335C4⋊C4—94no—
336C4⋊C4C22×D918yes—
337C4⋊C4C22×D914yes—
338C22⋊C4—98no—
339C22⋊C4—98no—
340C42—94no—
341C42—94no—
342C42—94no—
343C42—98no—
344C42C22×D914yes—
345C42C22×D918yes—
346C22×C3C2×#23512yes—
347C22×C3C2×D3×Q812yes—
348C22×C3D3×#4112yes—
349C22×C3C24×D311yescharacteristic
350C2×D3—34no—
351C2×D3—62no—
352C2×D3—62no—
353C2×D3—68no—
354C3×C4—24no—
355C3×C4—24no—
356C3×C4—22no—
357C3×C4C2×#23514yes—
358C3×C4C2×D3×Q814yes—
359Dic3—34no—
360Dic3—34no—
361Dic3—64no—
362Dic3—62no—
363Dic3—64no—
364C9C2×#53311yescharacteristic, complemented, Sylow
365C23—92no—
366C23—94no—
367C23—182no—
368C23—182no—
369C23C23×D911yescharacteristic
370Q8—28no—
371Q8—1816no—
372Q8—188no—
373C2×C4—24no—
374C2×C4—22no—
375C2×C4—24no—
376C2×C4—92no—
377C2×C4—92no—
378C2×C4—94no—
379C2×C4—94no—
380C2×C4—916no—
381C2×C4—92no—
382C2×C4—94no—
383C2×C4—94no—
384C2×C4—188no—
385C2×C4—182no—
386C2×C4—184no—
387C2×C4—184no—
388C2×C4—188no—
389C2×C4#369714yes—
390C2×C4Q8×D914yes—
391C2×C4C23×D912yes—
392C2×C4C23×D914yes—
393C2×C4C23×D914yes—
394C2×C4C23×D912yes—
395C2×C4C23×D912yes—
396C2×C3#557814yes—
397C2×C3C22×#23511yescharacteristic
398C2×C3C22×D3×Q811yescharacteristic
399C2×C3C2×D3×#4111yescharacteristic
400D3—64no—
401C22—94no—
402C22—182no—
403C22—182no—
404C22—188no—
405C22C2×#369712yes—
406C22C2×Q8×D912yes—
407C22#41×D912yes—
408C22C24×D911yescharacteristic
409C4—24no—
410C4—22no—
411C4—24no—
412C4—94no—
413C4—94no—
414C4—182no—
415C4—184no—
416C4—184no—
417C4C2×#369714yes—
418C4C2×Q8×D914yes—
419C3C2×#557811yescharacteristic
420C2—184no—
421C2#1058968014yesdirect product factor
422C2C22×#369711yescharacteristic
423C2C22×Q8×D911yescharacteristic
424C2C2×#41×D911yescharacteristic
subgroupG/H
centerC22×C4C22×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C4×Q8×C9C2
socleC23×C3C23×D3
prime radicalC23×D9C23
hypercenterC2×C4×Q8D9
hypocenterC9C2×#533
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22×C4 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C4×Q8×C9C2semidirect
3. C2×#63506C2semidirect
4. #10589680C2direct (N × H)
7. C2×#63451C2semidirect
8. C2×#63450C2semidirect
11. C2×C4×Dic18C2semidirect
12. C2×C4×Dic18C2semidirect
20. C4×Q8×C9C22semidirect
26. #63506C22semidirect
42. #63451C22semidirect
43. #63450C22semidirect
46. C4×Dic18C22semidirect
47. C4×Dic18C22semidirect
75. C2×C4×D9Q8semidirect
163. C4×D9C2×Q8semidirect
175. C2×C4×Q8D9semidirect
250. C4×Q8C2×D9semidirect
301. C2×C9#533semidirect
364. C9C2×#533semidirect
421. C2#10589680direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×Q8×C92
C2×#635082
C2×#635062
#105896802
C2×#634592
C2×#634582
C2×#634512
C2×#634502
C2×#634342
C2×C42×D92
C2×C4×Dic182
C2×#55783