Finite Group Databasebeta

← #11906260

Subgroups — #11906260

Order 1152.

1446 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#544C211yesmaximal, characteristic
2#10589824C214yesmaximal, complemented
3#10589823C214yesmaximal, complemented
4#10589787C214yesmaximal, complemented
5#10589787C214yesmaximal, complemented
6#10589725C214yesmaximal
7#10589724C214yesmaximal
8#10589619C212yesmaximal
9#10589618C212yesmaximal
10#10589602C211yesmaximal, characteristic
11C2×#63449C211yesmaximal, characteristic
12#86585—31nomaximal
13C22×Dic18C2211yescharacteristic
14C9×C4⋊Q8C2214yes—
15C9×#125C2214yes—
16C9×C22⋊Q8C2214yes—
17C9×#117C2212yes—
18C2×C9×C4⋊C4C2211yescharacteristic
19Q8×Dic9C2214yes—
20#63506C2214yes—
21#63506C2218yes—
22#63488C2212yes—
23#63486C2214yes—
24C2×Dic9⋊C4C2212yes—
25C2×C4×Dic9C2212yes—
26C2×C4×Dic9C2211yescharacteristic
27#63452C2212yes—
28#63452C2214yes—
29#63452C2212yes—
30#63451C2218yes—
31#63451C2218yes—
32#63451C2218yes—
33#63450C2214yes—
34#63450C2218yes—
35#63450C2212yes—
36#63450C2214yes—
37#63450C2212yes—
38#63449C2214yes—
39#63449C2218yes—
40#63449C2214yes—
41#63449C2214yes—
42#63449C2214yes—
43#63449C2214yes—
44#63440C2214yes—
45#63440C2214yes—
46#63439C2218yes—
47C4×Dic18C2214yes—
48C4×Dic18C2214yes—
49C4×Dic18C2214yes—
50C4×Dic18C2214yes—
51C3×#544D311yescharacteristic
52#5722—34no—
53#5721—34no—
54#5685—34no—
55#5685—34no—
56#5623—34no—
57#5622—34no—
58#5517—32no—
59#5516—32no—
60#5500—31no—
61C2×#887—31no—
62C2×Q8×C9C2314yes—
63C22×C4×C9C2312yes—
64C22×C4×C9C2311yescharacteristic
65C22×Dic9C2311yescharacteristic
66C22×Dic9C2311yescharacteristic
67C22×Dic9C2312yes—
68C2×Dic18Q818yescomplemented
69C2×Dic18C2314yes—
70C2×Dic18C2314yes—
71C2×Dic18C2314yes—
72C2×Dic18C2314yes—
73C9×C4⋊C4C2314yes—
74C9×C4⋊C4C2312yes—
75C9×C4⋊C4C2312yes—
76C9×C4⋊C4C2314yes—
77C9×C4⋊C4C2318yes—
78C9×C22⋊C4C2314yes—
79C42×C9C2314yes—
80#3676C2314yes—
81C4⋊Dic9C2312yes—
82C4⋊Dic9C2312yes—
83C4⋊Dic9C2314yes—
84C4⋊Dic9C2314yes—
85C4⋊Dic9C2314yes—
86Dic9⋊C4C2318yes—
87Dic9⋊C4C2314yes—
88Dic9⋊C4C2314yes—
89Dic9⋊C4C2318yes—
90Dic9⋊C4C2318yes—
91Dic9⋊C4C2318yes—
92Dic9⋊C4C2314yes—
93Dic9⋊C4C2314yes—
94C4×Dic9C2314yes—
95C4×Dic9C2318yes—
96C4×Dic9C2314yes—
97C4×Dic9C2314yes—
98C4×Dic9C2312yes—
99C4×Dic9C2312yes—
100C4×Dic9C2318yes—
101#3502—91noSylow
102C22×Dic6—31no—
103C3×C4⋊Q8C2×D314yes—
104C3×#125C2×D314yes—
105C3×C22⋊Q8C2×D314yes—
106C3×#117C2×D312yes—
107C2×C3×C4⋊C4C2×D311yescharacteristic
108Q8×Dic3—34no—
109#944—38no—
110#944—34no—
111#926—32no—
112#924—34no—
113C2×Dic3⋊C4—32no—
114C2×C4×Dic3—31no—
115C2×C4×Dic3—32no—
116#890—32no—
117#890—34no—
118#890—32no—
119#889—38no—
120#889—38no—
121#889—38no—
122#888—32no—
123#888—34no—
124#888—34no—
125#888—38no—
126#888—32no—
127#887—34no—
128#887—34no—
129#887—34no—
130#887—34no—
131#887—38no—
132#887—34no—
133#878—34no—
134#878—34no—
135#877—38no—
136C4×Dic6—34no—
137C4×Dic6—34no—
138C4×Dic6—34no—
139C4×Dic6—34no—
140C23×C9C2411yescharacteristic
141Q8×C9—44no—
142C2×C4×C9—42no—
143C2×C4×C9C2×Q814yes—
144C2×C4×C9C2414yes—
145C2×C4×C9C2414yes—
146C2×C4×C9C2414yes—
147C2×C4×C9C2412yes—
148C2×Dic9—22no—
149C2×Dic9—41no—
150C2×Dic9C2×Q818yes—
151C2×Dic9C2411yescharacteristic
152C2×Dic9C2414yes—
153C2×Dic9C2414yes—
154C2×Dic9C2412yes—
155C2×Dic9C2414yes—
156C2×Dic9C2411yescharacteristic
157Dic18—28no—
158Dic18—44no—
159Dic18—44no—
160Dic18C2×Q8116yes—
161Q82—94no—
162#557—94no—
163#557—94no—
164#557—94no—
165#544—94no—
166#544—91no—
167#544D911yescharacteristic
168#533—94no—
169#533—92no—
170#519—92no—
171C2×C4×Q8—91no—
172C2×C3×Q8C22×D314yes—
173C22×C3×C4C22×D312yes—
174C22×C3×C4C22×D311yescharacteristic
175C22×Dic3—32no—
176C22×Dic3—31no—
177C22×Dic3—31no—
178C2×Dic6—38no—
179C2×Dic6—34no—
180C2×Dic6—34no—
181C2×Dic6—34no—
182C2×Dic6—34no—
183C3×C4⋊C4C22×D314yes—
184C3×C4⋊C4C22×D312yes—
185C3×C4⋊C4C22×D312yes—
186C3×C4⋊C4C22×D314yes—
187C3×C4⋊C4C22×D318yes—
188C3×C22⋊C4C22×D314yes—
189C3×C42C22×D314yes—
190#217—34no—
191C4⋊Dic3—32no—
192C4⋊Dic3—32no—
193C4⋊Dic3—34no—
194C4⋊Dic3—34no—
195C4⋊Dic3—34no—
196Dic3⋊C4—38no—
197Dic3⋊C4—38no—
198Dic3⋊C4—34no—
199Dic3⋊C4—34no—
200Dic3⋊C4—34no—
201Dic3⋊C4—34no—
202Dic3⋊C4—38no—
203Dic3⋊C4—38no—
204C4×Dic3—32no—
205C4×Dic3—34no—
206C4×Dic3—32no—
207C4×Dic3—38no—
208C4×Dic3—38no—
209C4×Dic3—34no—
210C4×Dic3—34no—
211C22×C9—21no—
212C22×C9—21no—
213C22×C9C22×Q812yes—
214C22×C9C2511yescharacteristic
215C4×C9—24no—
216C4×C9—24no—
217C4×C9—24no—
218C4×C9C22×Q814yes—
219Dic9—24no—
220Dic9—21no—
221Dic9—24no—
222Dic9—22no—
223Dic9C22×Q818yes—
224Dic92−1+412yes—
225C22×Q8—91no—
226C4⋊Q8—94no—
227C4⋊Q8—98no—
228C4⋊Q8—94no—
229C4⋊Q8—92no—
230C4⋊Q8—92no—
231C4⋊Q8—98no—
232C4⋊Q8—94no—
233C4⋊Q8C2×D914yes—
234#125—98no—
235#125—92no—
236#125—92no—
237#125—98no—
238#125—98no—
239#125—94no—
240#125C2×D914yes—
241C22⋊Q8—94no—
242C22⋊Q8—94no—
243C22⋊Q8—94no—
244C22⋊Q8C2×D914yes—
245C4×Q8—94no—
246C4×Q8—94no—
247C4×Q8—94no—
248C4×Q8—94no—
249C4×Q8—94no—
250C4×Q8—94no—
251C4×Q8—98no—
252C4×Q8—94no—
253C4×Q8—94no—
254C4×Q8—94no—
255C4×Q8—94no—
256#117—92no—
257#117—98no—
258#117C2×D912yes—
259C2×C4⋊C4—92no—
260C2×C4⋊C4C2×D911yescharacteristic
261C2×C42—92no—
262C2×C42—91no—
263C23×C3C23×D311yescharacteristic
264C3×Q8—44no—
265C2×C3×C4—42no—
266C2×C3×C4D3×Q814yes—
267C2×C3×C4C23×D314yes—
268C2×C3×C4C23×D314yes—
269C2×C3×C4C23×D314yes—
270C2×C3×C4C23×D312yes—
271C2×Dic3—38no—
272C2×Dic3—34no—
273C2×Dic3—31no—
274C2×Dic3—31no—
275C2×Dic3—34no—
276C2×Dic3—34no—
277C2×Dic3—32no—
278C2×Dic3—62no—
279C2×Dic3—121no—
280Dic6—316no—
281Dic6—68no—
282Dic6—124no—
283Dic6—124no—
284C2×C9—22no—
285C2×C9C23×Q811yescharacteristic
286C2×C9C2×2−1+411yescharacteristic
287C2×C9#58511yescharacteristic
288C2×Q8—98no—
289C2×Q8—94no—
290C2×Q8—94no—
291C2×Q8—94no—
292C2×Q8—94no—
293C2×Q8C22×D914yes—
294C22×C4—92no—
295C22×C4—91no—
296C22×C4—91no—
297C22×C4C22×D912yes—
298C22×C4C22×D911yescharacteristic
299C4⋊C4—98no—
300C4⋊C4—98no—
301C4⋊C4—92no—
302C4⋊C4—98no—
303C4⋊C4—92no—
304C4⋊C4—94no—
305C4⋊C4—94no—
306C4⋊C4—94no—
307C4⋊C4—94no—
308C4⋊C4—94no—
309C4⋊C4—98no—
310C4⋊C4—94no—
311C4⋊C4—94no—
312C4⋊C4C22×D914yes—
313C4⋊C4C22×D912yes—
314C4⋊C4C22×D912yes—
315C4⋊C4C22×D914yes—
316C4⋊C4C22×D918yes—
317C22⋊C4—94no—
318C22⋊C4C22×D914yes—
319C42—94no—
320C42—92no—
321C42—94no—
322C42—92no—
323C42—98no—
324C42—98no—
325C42—94no—
326C42C22×D914yes—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3C2×D3×Q812yes—
330C22×C3C24×D311yescharacteristic
331C3×C4—24no—
332C3×C4—24no—
333C3×C4—24no—
334C3×C4C2×D3×Q814yes—
335Dic3—38no—
336Dic3—32no—
337Dic3—64no—
338Dic3—62no—
339Dic3—64no—
340Dic3—61no—
341C9#350211yescharacteristic, complemented, Sylow
342C23C23×D911yescharacteristic
343Q8—44no—
344Q8—916no—
345Q8—188no—
346Q8—364no—
347Q8—364no—
348C2×C4—42no—
349C2×C4—94no—
350C2×C4—91no—
351C2×C4—98no—
352C2×C4—91no—
353C2×C4—94no—
354C2×C4—94no—
355C2×C4—92no—
356C2×C4—182no—
357C2×C4—361no—
358C2×C4Q8×D914yes—
359C2×C4C23×D914yes—
360C2×C4C23×D914yes—
361C2×C4C23×D914yes—
362C2×C4C23×D912yes—
363C2×C3—22no—
364C2×C3C22×D3×Q811yescharacteristic
365C2×C3#596611yescharacteristic
366C2×C3D3×2−1+411yescharacteristic
367C22—21no—
368C22—21no—
369C22C2×Q8×D912yes—
370C22C24×D911yescharacteristic
371C4—24no—
372C4—24no—
373C4—24no—
374C4—98no—
375C4—92no—
376C4—182no—
377C4—184no—
378C4—181no—
379C4—184no—
380C4C2×Q8×D914yes—
381C3#8658511yescharacteristic
382C2—22no—
383C2C22×Q8×D911yescharacteristic
384C2#1059314111yescharacteristic
385C2D9×2−1+411yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#544C2
prime radicalC23×C3C23×D3
hypercenter#544D9
hypocenterC9#3502
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #544

Complements

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

NH ≅ G/Ntype
2. #10589824C2semidirect
3. #10589823C2semidirect
4. #10589787C2semidirect
5. #10589787C2semidirect
68. C2×Dic18Q8semidirect
341. C9#3502semidirect

Maximal subgroups

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

subgroupindex
C9×#5442
#105898242
#105898232
#105897872
#105897252
#105897242
#105896192
#105896182
#105896022
C2×#634492
#865853