Finite Group Databasebeta

← C2×#10589792 #11903220

Subgroups — C2×#10589792 #11903220

Order 1152.

1800 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×C9×#125C211yesmaximal, characteristic, complemented
2#10589792C2116yesmaximal, direct product factor
3C2×#63459C212yesmaximal, complemented
4C2×#63458C212yesmaximal, complemented
5C2×#63458C212yesmaximal, complemented
6C2×#63455C211yesmaximal, characteristic
7C2×#63455C211yesmaximal, characteristic
8C2×C4⋊C4×D9C212yesmaximal, complemented
9C2×#63452C211yesmaximal, characteristic, complemented
10C2×#63450C211yesmaximal, characteristic, complemented
11C2×C4×D36C211yesmaximal, characteristic
12C2×C4×Dic18C211yesmaximal, characteristic, complemented
13C2×#5690—31nomaximal
14C22×D36C2211yescharacteristic
15C22×C4×D9C2212yes—
16C22×C4×D9C2212yes—
17C22×C4×D9C2212yes—
18C22×Dic18C2211yescharacteristic
19C22×Dic18C2212yes—
20C9×#125C2218yescomplemented
21C2×C9×C4⋊C4C2211yescharacteristic
22C2×C9×C4⋊C4C2211yescharacteristic
23C2×C9×C4⋊C4C2212yes—
24C2×C9×C4⋊C4C2212yes—
25C2×C42×C9C2211yescharacteristic
26C2×(C2×D9)⋊C4C2212yes—
27C2×(C2×D9)⋊C4C2212yes—
28C2×(C2×D9)⋊C4C2212yes—
29C2×C4⋊Dic9C2211yescharacteristic
30C2×C4⋊Dic9C2211yescharacteristic
31C2×C4⋊Dic9C2212yes—
32C2×Dic9⋊C4C2211yescharacteristic
33C2×Dic9⋊C4C2211yescharacteristic
34C2×Dic9⋊C4C2212yes—
35C2×Dic9⋊C4C2212yes—
36C2×C4×Dic9C2211yescharacteristic
37C2×C4×Dic9C2211yescharacteristic
38#63459C22116yescomplemented
39#63458C22116yescomplemented
40#63458C22116yescomplemented
41#63455C2218yes—
42#63455C2218yes—
43C4⋊C4×D9C22116yescomplemented
44#63452C2218yescomplemented
45#63450C2218yescomplemented
46C4×D36C2218yes—
47C4×Dic18C2218yescomplemented
48C2×C3×#125D311yescharacteristic
49#5690—316no—
50C2×#897—32no—
51C2×#896—32no—
52C2×#896—32no—
53C2×#893—31no—
54C2×#893—31no—
55C2×D3×C4⋊C4—32no—
56C2×#890—31no—
57C2×#888—31no—
58C2×C4×D12—31no—
59C2×C4×Dic6—31no—
60C23×D9C2312yes—
61C22×C4×C9C2311yescharacteristic
62C22×C4×C9C2312yes—
63C22×C4×C9C2312yes—
64C22×C4×C9C2311yescharacteristic
65C22×C4×C9C2311yescharacteristic
66C22×Dic9C2311yescharacteristic
67C22×Dic9C2311yescharacteristic
68C22×Dic9C2312yes—
69C22×Dic9C2311yescharacteristic
70C22×Dic9C2311yescharacteristic
71C2×D36Q818yescomplemented
72C2×D36C2314yes—
73C2×C4×D9—28no—
74C2×C4×D9—44no—
75C2×C4×D9—44no—
76C2×C4×D9C2318yes—
77C2×C4×D9C2318yes—
78C2×C4×D9C2318yes—
79C2×Dic18—24no—
80C2×Dic18—44no—
81C2×Dic18C2314yes—
82C2×Dic18C2318yes—
83C9×C4⋊C4C2314yes—
84C9×C4⋊C4C2314yes—
85C9×C4⋊C4C2318yes—
86C9×C4⋊C4C2318yes—
87C42×C9C2314yes—
88(C2×D9)⋊C4C2318yes—
89(C2×D9)⋊C4C2318yes—
90(C2×D9)⋊C4C2318yes—
91C4⋊Dic9C2314yes—
92C4⋊Dic9C2314yes—
93C4⋊Dic9C2318yes—
94Dic9⋊C4C2314yes—
95Dic9⋊C4C2314yes—
96Dic9⋊C4C2318yes—
97Dic9⋊C4C2318yes—
98C4×Dic9C2314yes—
99C4×Dic9C2314yes—
100C2×#554—91noSylow
101C22×D12—31no—
102C22×C4×D3—32no—
103C22×C4×D3—32no—
104C22×C4×D3—32no—
105C22×Dic6—31no—
106C22×Dic6—32no—
107C3×#125C2×D318yes—
108C2×C3×C4⋊C4C2×D311yescharacteristic
109C2×C3×C4⋊C4C2×D311yescharacteristic
110C2×C3×C4⋊C4C2×D312yes—
111C2×C3×C4⋊C4C2×D312yes—
112C2×C3×C42C2×D311yescharacteristic
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4—32no—
116C2×C4⋊Dic3—31no—
117C2×C4⋊Dic3—31no—
118C2×C4⋊Dic3—32no—
119C2×Dic3⋊C4—31no—
120C2×Dic3⋊C4—31no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—32no—
123C2×C4×Dic3—31no—
124C2×C4×Dic3—31no—
125#897—316no—
126#896—316no—
127#896—316no—
128#893—38no—
129#893—38no—
130D3×C4⋊C4—316no—
131#890—38no—
132#888—38no—
133C4×D12—38no—
134C4×Dic6—38no—
135C23×C9C2411yescharacteristic
136C22×D9—24no—
137C22×D9—24no—
138C22×D9C2×Q818yes—
139C22×D9C2414yes—
140C2×C4×C9—22no—
141C2×C4×C9—24no—
142C2×C4×C9—24no—
143C2×C4×C9—22no—
144C2×C4×C9C2×Q814yes—
145C2×C4×C9C2412yes—
146C2×C4×C9C2414yes—
147C2×C4×C9C2414yes—
148C2×C4×C9C2412yes—
149C2×C4×C9C2412yes—
150C2×Dic9—22no—
151C2×Dic9—22no—
152C2×Dic9—24no—
153C2×Dic9—22no—
154C2×Dic9#4114yes—
155C2×Dic9C2412yes—
156C2×Dic9C2412yes—
157C2×Dic9C2412yes—
158C2×Dic9C2414yes—
159C2×Dic9C2412yes—
160D36C2×Q8116yescomplemented
161C4×D9—216no—
162C4×D9—48no—
163C4×D9—48no—
164Dic18—28no—
165Dic18—48no—
166#554—916no—
167C2×C4⋊Q8—91no—
168C2×#125—91no—
169C2×#125D911yescharacteristic, complemented
170C2×C22⋊Q8—92no—
171C2×C22⋊Q8—92no—
172C2×C22⋊Q8—92no—
173C2×C4×Q8—91no—
174C2×C4×D4—91no—
175C2×C4×D4—91no—
176C2×C4×D4—91no—
177C22×C4⋊C4—92no—
178C23×D3—32no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D312yes—
181C22×C3×C4C22×D312yes—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C22×Dic3—31no—
185C22×Dic3—31no—
186C22×Dic3—31no—
187C22×Dic3—31no—
188C22×Dic3—32no—
189C2×D12—38no—
190C2×D12—34no—
191C2×C4×D3—38no—
192C2×C4×D3—38no—
193C2×C4×D3—38no—
194C2×C4×D3—68no—
195C2×C4×D3—124no—
196C2×C4×D3—124no—
197C2×Dic6—34no—
198C2×Dic6—38no—
199C2×Dic6—64no—
200C2×Dic6—124no—
201C3×C4⋊C4C22×D314yes—
202C3×C4⋊C4C22×D314yes—
203C3×C4⋊C4C22×D318yes—
204C3×C4⋊C4C22×D318yes—
205C3×C42C22×D314yes—
206(C2×D3)⋊C4—38no—
207(C2×D3)⋊C4—38no—
208(C2×D3)⋊C4—38no—
209C4⋊Dic3—34no—
210C4⋊Dic3—34no—
211C4⋊Dic3—38no—
212Dic3⋊C4—34no—
213Dic3⋊C4—34no—
214Dic3⋊C4—38no—
215Dic3⋊C4—38no—
216C4×Dic3—34no—
217C4×Dic3—34no—
218C22×C9C22×Q812yes—
219C22×C9C2×#4112yes—
220C22×C9H(5,𝔽2)12yes—
221C22×C9C2511yescharacteristic
222C2×D9—216no—
223C2×D9—24no—
224C2×D9—24no—
225C2×D9C22×Q818yes—
226C4×C9—22no—
227C4×C9—24no—
228C4×C9—24no—
229C4×C9—22no—
230C4×C9C22×Q814yes—
231Dic9—22no—
232Dic9—22no—
233Dic9—24no—
234Dic9—22no—
235Dic9C2×#4114yes—
236C22×Q8—91no—
237C22×Q8—92no—
238C22×D4—91no—
239C23×C4—92no—
240C23×C4—92no—
241C23×C4—92no—
242C4⋊Q8—98no—
243#125—98no—
244#125C2×D918yescomplemented
245C22⋊Q8—916no—
246C22⋊Q8—916no—
247C22⋊Q8—916no—
248C4×Q8—98no—
249C4×D4—98no—
250C4×D4—98no—
251C4×D4—98no—
252C2×C4⋊C4—91no—
253C2×C4⋊C4—92no—
254C2×C4⋊C4—92no—
255C2×C4⋊C4—91no—
256C2×C4⋊C4—91no—
257C2×C4⋊C4—91no—
258C2×C4⋊C4—92no—
259C2×C4⋊C4—916no—
260C2×C4⋊C4C2×D912yes—
261C2×C4⋊C4C2×D911yescharacteristic
262C2×C4⋊C4C2×D911yescharacteristic
263C2×C4⋊C4C2×D912yes—
264C2×C22⋊C4—92no—
265C2×C22⋊C4—92no—
266C2×C22⋊C4—92no—
267C2×C42—91no—
268C2×C42—91no—
269C2×C42C2×D911yescharacteristic
270C23×C3C23×D311yescharacteristic
271C22×D3—38no—
272C22×D3—34no—
273C22×D3—64no—
274C22×D3—64no—
275C2×C3×C4—22no—
276C2×C3×C4—24no—
277C2×C3×C4—24no—
278C2×C3×C4—22no—
279C2×C3×C4D3×Q814yes—
280C2×C3×C4C23×D312yes—
281C2×C3×C4C23×D314yes—
282C2×C3×C4C23×D314yes—
283C2×C3×C4C23×D312yes—
284C2×C3×C4C23×D312yes—
285C2×Dic3—34no—
286C2×Dic3—32no—
287C2×Dic3—32no—
288C2×Dic3—32no—
289C2×Dic3—32no—
290C2×Dic3—34no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293C2×Dic3—64no—
294C2×Dic3—62no—
295D12—316no—
296C4×D3—616no—
297C4×D3—128no—
298C4×D3—128no—
299Dic6—68no—
300Dic6—128no—
301C2×C9#55414yescomplemented
302C2×C9C23×Q811yescharacteristic
303C2×C9C22×#4111yescharacteristic
304C2×C9C2×H(5,𝔽2)11yescharacteristic
305D9—28no—
306C24—92no—
307C2×Q8—94no—
308C2×Q8—98no—
309C2×Q8—184no—
310C2×Q8—364no—
311C2×D4—98no—
312C2×D4—94no—
313C22×C4—91no—
314C22×C4—91no—
315C22×C4—91no—
316C22×C4—91no—
317C22×C4—92no—
318C22×C4—98no—
319C22×C4—98no—
320C22×C4—98no—
321C22×C4—188no—
322C22×C4—364no—
323C22×C4—364no—
324C22×C4C22×D911yescharacteristic
325C22×C4C22×D911yescharacteristic
326C22×C4C22×D912yes—
327C22×C4C22×D912yes—
328C22×C4C22×D911yescharacteristic
329C4⋊C4—94no—
330C4⋊C4—98no—
331C4⋊C4—98no—
332C4⋊C4—94no—
333C4⋊C4—94no—
334C4⋊C4—94no—
335C4⋊C4—98no—
336C4⋊C4C22×D918yes—
337C4⋊C4C22×D914yes—
338C4⋊C4C22×D914yes—
339C4⋊C4C22×D918yes—
340C22⋊C4—98no—
341C22⋊C4—98no—
342C22⋊C4—98no—
343C42—94no—
344C42—94no—
345C42C22×D914yes—
346C22×C3C2×D3×Q812yes—
347C22×C3D3×#4112yes—
348C22×C3#100912yes—
349C22×C3C24×D311yescharacteristic
350C2×D3—38no—
351C2×D3—616no—
352C2×D3—64no—
353C2×D3—64no—
354C3×C4—22no—
355C3×C4—24no—
356C3×C4—24no—
357C3×C4—22no—
358C3×C4C2×D3×Q814yes—
359Dic3—34no—
360Dic3—62no—
361Dic3—62no—
362Dic3—64no—
363Dic3—62no—
364C9C2×#55411yescharacteristic, complemented, Sylow
365C23—94no—
366C23—98no—
367C23—184no—
368C23—184no—
369C23C23×D911yescharacteristic
370Q8—188no—
371Q8—368no—
372D4—916no—
373C2×C4—24no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—24no—
377C2×C4—92no—
378C2×C4—94no—
379C2×C4—92no—
380C2×C4—92no—
381C2×C4—92no—
382C2×C4—94no—
383C2×C4—1816no—
384C2×C4—182no—
385C2×C4—182no—
386C2×C4—184no—
387C2×C4—182no—
388C2×C4—368no—
389C2×C4—368no—
390C2×C4Q8×D914yes—
391C2×C4C23×D912yes—
392C2×C4C23×D912yes—
393C2×C4C23×D914yes—
394C2×C4C23×D914yes—
395C2×C4C23×D912yes—
396C2×C3#569014yes—
397C2×C3C22×D3×Q811yescharacteristic
398C2×C3C2×D3×#4111yescharacteristic
399C2×C3C2×#100911yescharacteristic
400D3—68no—
401C22—98no—
402C22—1816no—
403C22—184no—
404C22—184no—
405C22C2×Q8×D912yes—
406C22#41×D912yes—
407C22#6371512yes—
408C22C24×D911yescharacteristic
409C4—24no—
410C4—22no—
411C4—22no—
412C4—24no—
413C4—94no—
414C4—182no—
415C4—182no—
416C4—184no—
417C4—182no—
418C4C2×Q8×D914yes—
419C3C2×#569011yescharacteristic
420C2—188no—
421C2#1058979214yesdirect product factor
422C2C22×Q8×D911yescharacteristic
423C2C2×#41×D911yescharacteristic
424C2C2×#6371511yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C9×#125C2
socleC23×C3C23×D3
prime radicalC22×D36C22
hypercenterC2×#125D9
hypocenterC9C2×#554
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. C2×C9×#125C2semidirect
2. #10589792C2direct (N × H)
3. C2×#63459C2semidirect
4. C2×#63458C2semidirect
5. C2×#63458C2semidirect
8. C2×C4⋊C4×D9C2semidirect
9. C2×#63452C2semidirect
10. C2×#63450C2semidirect
12. C2×C4×Dic18C2semidirect
20. C9×#125C22semidirect
38. #63459C22semidirect
39. #63458C22semidirect
40. #63458C22semidirect
43. C4⋊C4×D9C22semidirect
44. #63452C22semidirect
45. #63450C22semidirect
47. C4×Dic18C22semidirect
71. C2×D36Q8semidirect
160. D36C2×Q8semidirect
169. C2×#125D9semidirect
244. #125C2×D9semidirect
301. C2×C9#554semidirect
364. C9C2×#554semidirect
421. C2#10589792direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×#1252
#105897922
C2×#634592
C2×#634582
C2×#634552
C2×C4⋊C4×D92
C2×#634522
C2×#634502
C2×C4×D362
C2×C4×Dic182
C2×#56903