Finite Group Databasebeta

← C2×#10589724 #11900807

Subgroups — C2×#10589724 #11900807

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×C9×C22⋊Q8C211yesmaximal, characteristic
2C2×Q8×Dic9C211yesmaximal, characteristic, complemented
3C2×#63506C211yesmaximal, characteristic, complemented
4C2×#63486C211yesmaximal, characteristic
5C22×C4×Dic9C211yesmaximal, characteristic
6#10589724C2116yesmaximal, direct product factor
7C2×#63451C212yesmaximal, complemented
8C2×#63450C211yesmaximal, characteristic, complemented
9C2×#63449C211yesmaximal, characteristic, complemented
10C2×#63449C212yesmaximal, complemented
11C2×#63440C212yesmaximal
12C2×#63439C212yesmaximal
13C2×#5622—31nomaximal
14C22×Q8×C9C2211yescharacteristic
15C23×C4×C9C2211yescharacteristic
16C23×Dic9C2211yescharacteristic
17C23×Dic9C2211yescharacteristic
18C22×Dic18C2212yes—
19C22×Dic18C2211yescharacteristic
20C9×C22⋊Q8C2218yes—
21C2×C9×C4⋊C4C2211yescharacteristic
22C2×C9×C4⋊C4C2212yes—
23C2×C9×C22⋊C4C2212yes—
24C2×#3676C2212yes—
25Q8×Dic9C2218yescomplemented
26#63506C2218yescomplemented
27C2×C4⋊Dic9C2212yes—
28C2×C4⋊Dic9C2211yescharacteristic
29#63486C2218yes—
30C2×Dic9⋊C4C2212yes—
31C2×Dic9⋊C4C2212yes—
32C2×Dic9⋊C4C2212yes—
33C2×Dic9⋊C4C2212yes—
34C2×Dic9⋊C4C2212yes—
35C2×C4×Dic9C2218yes—
36C2×C4×Dic9C2212yes—
37C2×C4×Dic9C2212yes—
38C2×C4×Dic9C2211yescharacteristic
39C2×C4×Dic9C2211yescharacteristic
40C2×C4×Dic9C2211yescharacteristic
41C2×C4×Dic9C2211yescharacteristic
42#63451C22116yescomplemented
43#63450C2218yescomplemented
44#63449C22116yescomplemented
45#63449C2218yescomplemented
46#63440C22116yes—
47#63439C22116yes—
48C2×C3×C22⋊Q8D311yescharacteristic
49C2×Q8×Dic3—31no—
50C2×#944—31no—
51C2×#924—31no—
52C22×C4×Dic3—31no—
53#5622—316no—
54C2×#889—32no—
55C2×#888—31no—
56C2×#887—31no—
57C2×#887—32no—
58C2×#878—32no—
59C2×#877—32no—
60C24×C9C2311yescharacteristic
61C2×Q8×C9—24no—
62C2×Q8×C9C2314yes—
63C22×C4×C9—24no—
64C22×C4×C9C2312yes—
65C22×C4×C9C2312yes—
66C22×C4×C9C2311yescharacteristic
67C22×C4×C9C2314yes—
68C22×C4×C9C2311yescharacteristic
69C22×Dic9—24no—
70C22×Dic9Q818yescomplemented
71C22×Dic9C2312yes—
72C22×Dic9C2312yes—
73C22×Dic9C2314yes—
74C22×Dic9C2311yescharacteristic
75C22×Dic9C2311yescharacteristic
76C22×Dic9C2311yescharacteristic
77C22×Dic9C2314yes—
78C22×Dic9C2311yescharacteristic
79C2×Dic18—24no—
80C2×Dic18—28no—
81C2×Dic18C2314yes—
82C2×Dic18C2318yes—
83C9×C4⋊C4C2314yes—
84C9×C4⋊C4C2318yes—
85C9×C22⋊C4C2318yes—
86#3676C2318yes—
87C4⋊Dic9C2318yes—
88C4⋊Dic9C2314yes—
89Dic9⋊C4C2318yes—
90Dic9⋊C4C2318yes—
91Dic9⋊C4C2318yes—
92Dic9⋊C4C2318yes—
93Dic9⋊C4C2318yes—
94C4×Dic9C2314yes—
95C4×Dic9C2318yes—
96C4×Dic9C2314yes—
97C4×Dic9C2318yes—
98C4×Dic9C2314yes—
99C4×Dic9C2314yes—
100C2×#533—91noSylow
101C22×C3×Q8C2×D311yescharacteristic
102C23×C3×C4C2×D311yescharacteristic
103C23×Dic3—31no—
104C23×Dic3—31no—
105C22×Dic6—32no—
106C22×Dic6—31no—
107C3×C22⋊Q8C2×D318yes—
108C2×C3×C4⋊C4C2×D311yescharacteristic
109C2×C3×C4⋊C4C2×D312yes—
110C2×C3×C22⋊C4C2×D312yes—
111C2×#217—32no—
112Q8×Dic3—38no—
113#944—38no—
114C2×C4⋊Dic3—32no—
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—
126C2×C4×Dic3—31no—
127C2×C4×Dic3—31no—
128C2×C4×Dic3—38no—
129#889—316no—
130#888—38no—
131#887—38no—
132#887—316no—
133#878—316no—
134#877—316no—
135C23×C9—22no—
136C23×C9—22no—
137C23×C9C2×Q814yes—
138C23×C9C2412yes—
139C23×C9C2411yescharacteristic
140Q8×C9—28no—
141C2×C4×C9—24no—
142C2×C4×C9—22no—
143C2×C4×C9—24no—
144C2×C4×C9—28no—
145C2×C4×C9#4114yes—
146C2×C4×C9C2412yes—
147C2×C4×C9C2414yes—
148C2×C4×C9C2414yes—
149C2×C4×C9C2412yes—
150C2×Dic9—24no—
151C2×Dic9—24no—
152C2×Dic9—22no—
153C2×Dic9—28no—
154C2×Dic9C2×Q814yes—
155C2×Dic9C2×Q814yes—
156C2×Dic9C2×Q8116yescomplemented
157C2×Dic9#4114yes—
158C2×Dic9C2412yes—
159C2×Dic9C2414yes—
160C2×Dic9C2414yes—
161C2×Dic9C2412yes—
162C2×Dic9C2412yes—
163C2×Dic9C2412yes—
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⋊Q8D911yescharacteristic
173C2×C4×Q8—91no—
174C2×C4×Q8—91no—
175C2×C4×Q8—92no—
176C2×#117—92no—
177C22×C42—91no—
178C24×C3C22×D311yescharacteristic
179C2×C3×Q8—24no—
180C2×C3×Q8C22×D314yes—
181C22×C3×C4—24no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D314yes—
184C22×C3×C4C22×D312yes—
185C22×C3×C4C22×D312yes—
186C22×C3×C4C22×D311yescharacteristic
187C22×Dic3—38no—
188C22×Dic3—34no—
189C22×Dic3—31no—
190C22×Dic3—31no—
191C22×Dic3—31no—
192C22×Dic3—34no—
193C22×Dic3—31no—
194C22×Dic3—32no—
195C22×Dic3—32no—
196C22×Dic3—64no—
197C2×Dic6—38no—
198C2×Dic6—34no—
199C2×Dic6—68no—
200C2×Dic6—64no—
201C3×C4⋊C4C22×D314yes—
202C3×C4⋊C4C22×D318yes—
203C3×C22⋊C4C22×D318yes—
204#217—38no—
205C4⋊Dic3—38no—
206C4⋊Dic3—34no—
207Dic3⋊C4—38no—
208Dic3⋊C4—38no—
209Dic3⋊C4—38no—
210Dic3⋊C4—38no—
211Dic3⋊C4—38no—
212C4×Dic3—38no—
213C4×Dic3—38no—
214C4×Dic3—34no—
215C4×Dic3—34no—
216C4×Dic3—34no—
217C4×Dic3—34no—
218C22×C9—28no—
219C22×C9—22no—
220C22×C9—22no—
221C22×C9C22×Q814yes—
222C22×C9C22×Q812yes—
223C22×C9C2×#4112yes—
224C22×C9C2×#4112yes—
225C22×C9C2511yescharacteristic
226C4×C9—24no—
227C4×C9—22no—
228C4×C9—24no—
229C4×C9C2×#4114yes—
230Dic9—24no—
231Dic9—24no—
232Dic9—22no—
233Dic9C22×Q814yes—
234Dic9C22×Q814yes—
235Dic9C2×#4114yes—
236C22×Q8—92no—
237C22×Q8—91no—
238C22×Q8C2×D911yescharacteristic
239C23×C4—91no—
240C23×C4—91no—
241C23×C4C2×D911yescharacteristic
242C4⋊Q8—98no—
243C4⋊Q8—98no—
244#125—916no—
245C22⋊Q8—98no—
246C22⋊Q8—916no—
247C22⋊Q8C2×D918yes—
248C4×Q8—98no—
249C4×Q8—98no—
250C4×Q8—916no—
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⋊C4C2×D912yes—
263C2×C42—92no—
264C2×C42—92no—
265C2×C42—91no—
266C2×C42—91no—
267C2×C42—91no—
268C2×C42—91no—
269C2×C42—98no—
270C23×C3—22no—
271C23×C3—22no—
272C23×C3D3×Q814yes—
273C23×C3C23×D312yes—
274C23×C3C23×D311yescharacteristic
275C3×Q8—28no—
276C2×C3×C4—22no—
277C2×C3×C4—24no—
278C2×C3×C4—24no—
279C2×C3×C4—28no—
280C2×C3×C4#23714yes—
281C2×C3×C4C23×D312yes—
282C2×C3×C4C23×D314yes—
283C2×C3×C4C23×D314yes—
284C2×C3×C4C23×D312yes—
285C2×Dic3—34no—
286C2×Dic3—34no—
287C2×Dic3—316no—
288C2×Dic3—34no—
289C2×Dic3—32no—
290C2×Dic3—32no—
291C2×Dic3—32no—
292C2×Dic3—32no—
293C2×Dic3—34no—
294C2×Dic3—34no—
295C2×Dic3—68no—
296C2×Dic3—64no—
297C2×Dic3—64no—
298C2×Dic3—62no—
299Dic6—616no—
300Dic6—68no—
301C2×C9—24no—
302C2×C9#53314yescomplemented
303C2×C9C23×Q811yescharacteristic
304C2×C9C22×#4111yescharacteristic
305C2×C9C22×#4111yescharacteristic
306C24C22×D911yescharacteristic
307C2×Q8—24no—
308C2×Q8—98no—
309C2×Q8—94no—
310C2×Q8—188no—
311C2×Q8—184no—
312C2×Q8C22×D914yes—
313C22×C4—24no—
314C22×C4—98no—
315C22×C4—94no—
316C22×C4—91no—
317C22×C4—91no—
318C22×C4—91no—
319C22×C4—94no—
320C22×C4—91no—
321C22×C4—92no—
322C22×C4—92no—
323C22×C4—184no—
324C22×C4C22×D914yes—
325C22×C4C22×D911yescharacteristic
326C22×C4C22×D912yes—
327C22×C4C22×D912yes—
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⋊C4C22×D918yes—
340C42—94no—
341C42—94no—
342C42—94no—
343C42—94no—
344C42—98no—
345C42—98no—
346C22×C3—22no—
347C22×C3—22no—
348C22×C3—28no—
349C22×C3C2×#23712yes—
350C22×C3C2×D3×Q814yes—
351C22×C3C2×D3×Q812yes—
352C22×C3D3×#4112yes—
353C22×C3C24×D311yescharacteristic
354C3×C4—22no—
355C3×C4—24no—
356C3×C4—24no—
357C3×C4C2×#23714yes—
358Dic3—34no—
359Dic3—34no—
360Dic3—34no—
361Dic3—64no—
362Dic3—64no—
363Dic3—62no—
364C9C2×#53311yescharacteristic, complemented, Sylow
365C23—22no—
366C23—22no—
367C23Q8×D914yes—
368C23C23×D912yes—
369C23C23×D911yescharacteristic
370Q8—28no—
371Q8—1816no—
372Q8—188no—
373C2×C4—22no—
374C2×C4—24no—
375C2×C4—24no—
376C2×C4—28no—
377C2×C4—92no—
378C2×C4—92no—
379C2×C4—92no—
380C2×C4—916no—
381C2×C4—94no—
382C2×C4—94no—
383C2×C4—94no—
384C2×C4—92no—
385C2×C4—94no—
386C2×C4—94no—
387C2×C4—188no—
388C2×C4—184no—
389C2×C4—182no—
390C2×C4—184no—
391C2×C4#369914yes—
392C2×C4C23×D912yes—
393C2×C4C23×D914yes—
394C2×C4C23×D914yes—
395C2×C4C23×D912yes—
396C2×C3—24no—
397C2×C3#562214yes—
398C2×C3C22×#23711yescharacteristic
399C2×C3C22×D3×Q811yescharacteristic
400C2×C3C2×D3×#4111yescharacteristic
401C22—28no—
402C22—22no—
403C22—22no—
404C22C2×#369912yes—
405C22C2×Q8×D914yes—
406C22C2×Q8×D912yes—
407C22#41×D912yes—
408C22C24×D911yescharacteristic
409C4—22no—
410C4—24no—
411C4—24no—
412C4—94no—
413C4—94no—
414C4—94no—
415C4—184no—
416C4—182no—
417C4—184no—
418C4C2×#369914yes—
419C3C2×#562211yescharacteristic
420C2—24no—
421C2#1058972414yesdirect product factor
422C2C22×#369911yescharacteristic
423C2C22×Q8×D911yescharacteristic
424C2C2×#41×D911yescharacteristic
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×#533
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. #10589724C2direct (N × H)
7. C2×#63451C2semidirect
8. C2×#63450C2semidirect
9. C2×#63449C2semidirect
10. C2×#63449C2semidirect
25. Q8×Dic9C22semidirect
26. #63506C22semidirect
42. #63451C22semidirect
43. #63450C22semidirect
44. #63449C22semidirect
45. #63449C22semidirect
70. C22×Dic9Q8semidirect
156. C2×Dic9C2×Q8semidirect
302. C2×C9#533semidirect
364. C9C2×#533semidirect
421. C2#10589724direct (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×#634862
C22×C4×Dic92
#105897242
C2×#634512
C2×#634502
C2×#634492
C2×#634402
C2×#634392
C2×#56223