Finite Group Databasebeta

← C4⋊C4×(C22⋊C9)⋊C2 #11920206

Subgroups — C4⋊C4×(C22⋊C9)⋊C2 #11920206

Order 1152.

746 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 746 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×(C22⋊C9)⋊C2C212yesmaximal
2C2×C4×(C22⋊C9)⋊C2C211yesmaximal, characteristic
3C4⋊C4×C22⋊C9C211yesmaximal, characteristic, complemented
4C4⋊((C22⋊C9)⋊C4)C211yesmaximal, characteristic, complemented
5((C22⋊C9)⋊C4)⋊C4C212yesmaximal, complemented
6C4⋊C4×#67—31nomaximal
7C22×(C22⋊C9)⋊C2C2211yescharacteristic
8C2×C4×C22⋊C9C2212yes—
9C2×C4×C22⋊C9C2211yescharacteristic
10C2×(C22⋊C9)⋊C4C2212yes—
11C2×(C22⋊C9)⋊C4C2211yescharacteristic
12C4×(C22⋊C9)⋊C2—24no—
13C4×(C22⋊C9)⋊C2C414yescomplemented
14C4⋊C4×D9—41nomaximal
15C22×C3×C4⋊C4D311yescharacteristic
16C2×C4×#67—31no—
17C2×C4×#67—32no—
18C2×D3×C4⋊C4—31no—
19#5212—31no—
20#5210—32no—
21#4989—32no—
22#4987—31no—
23#4976—32no—
24#4975—31no—
25Dic3×C4⋊C4—31no—
26C22×C22⋊C9C2311yescharacteristic
27C2×(C22⋊C9)⋊C2C2×C412yes—
28C2×(C22⋊C9)⋊C2D412yes—
29C2×(C22⋊C9)⋊C2Q812yes—
30C2×C4×D9—41no—
31C2×C4×D9—42no—
32C4×C22⋊C9—22no—
33C4×C22⋊C9C2×C412yescomplemented
34(C22⋊C9)⋊C4—22no—
35(C22⋊C9)⋊C4C2×C412yescomplemented
36C9×C4⋊C4—41no—
37C4⋊Dic9—41no—
38Dic9⋊C4—42no—
39D4×C4⋊C4—91noSylow
40C23×C3×C4C2×D312yes—
41C23×C3×C4C2×D311yescharacteristic
42C22×#67—31no—
43C22×C4×D3—31no—
44C22×C4×D3—32no—
45C2×C3×C4⋊C4—31no—
46C2×C3×C4⋊C4—31no—
47C2×C3×C4⋊C4—32no—
48C2×#217—31no—
49C2×#217—32no—
50C4×#67—34no—
51C4×#67—34no—
52C4×#67—64no—
53C4×#67—64no—
54C2×(C2×D3)⋊C4—31no—
55C2×(C2×D3)⋊C4—32no—
56C2×C4⋊Dic3—31no—
57C2×C4⋊Dic3—31no—
58C2×Dic3⋊C4—31no—
59C2×Dic3⋊C4—32no—
60C2×Dic3⋊C4—32no—
61C2×Dic3⋊C4—32no—
62C2×C4×Dic3—31no—
63C2×C4×Dic3—32no—
64D3×C4⋊C4—61no—
65D3×C4⋊C4—62no—
66D3×C4⋊C4—61no—
67C3⋊#95—32no—
68C3⋊#95—32no—
69C3⋊#95—32no—
70C22×D9—41no—
71C2×C22⋊C9C22×C411yescharacteristic
72C2×C22⋊C9C2×D411yescharacteristic
73C2×C22⋊C9C2×Q811yescharacteristic
74(C22⋊C9)⋊C2C4⋊C414yesdirect product factor
75C2×C4×C9—41no—
76C2×C4×C9—42no—
77C2×Dic9—41no—
78C2×Dic9—42no—
79C4×D9—44no—
80C4×D9—84no—
81C2×C4×D4—91no—
82C2×C4×D4—92no—
83C22×C4⋊C4—91no—
84C22×C4⋊C4D911yescharacteristic, complemented
85#389—92no—
86#385—92no—
87#385—92no—
88#384—91no—
89#380—91no—
90#380—91no—
91C4×C4⋊C4—91no—
92C24×C3C22×D311yescharacteristic
93C23×D3—31no—
94C22×C3×C4—22no—
95C22×C3×C4—31no—
96C22×C3×C4—31no—
97C22×C3×C4—32no—
98C22×C3×C4—32no—
99C22×C3×C4—32no—
100C22×C3×C4—62no—
101C22×C3×C4C4×D312yes—
102C2×#67—32no—
103C2×#67—32no—
104C2×#67—32no—
105C2×#67—32no—
106C2×#67—32no—
107C2×#67—32no—
108C22×Dic3—31no—
109C22×Dic3—31no—
110C22×Dic3—31no—
111C22×Dic3—32no—
112C22×Dic3—32no—
113C2×C4×D3—34no—
114C2×C4×D3—61no—
115C2×C4×D3—62no—
116C2×C4×D3—61no—
117C2×C4×D3—62no—
118C2×C4×D3—64no—
119C2×C4×D3—62no—
120C2×C4×D3—122no—
121C3×C4⋊C4—32no—
122C3×C4⋊C4—31no—
123C3×C4⋊C4—61no—
124C3×C4⋊C4S411yescharacteristic
125#217—32no—
126#217—32no—
127#217—62no—
128#217—62no—
129(C2×D3)⋊C4—34no—
130(C2×D3)⋊C4—64no—
131C4⋊Dic3—61no—
132C4⋊Dic3—62no—
133C4⋊Dic3—61no—
134Dic3⋊C4—34no—
135Dic3⋊C4—64no—
136Dic3⋊C4—62no—
137Dic3⋊C4—62no—
138Dic3⋊C4—122no—
139C4×Dic3—34no—
140C4×Dic3—64no—
141C22×C9—41no—
142C2×D9—42no—
143C2×D9—42no—
144C2×D9—42no—
145C22⋊C9C2×C4⋊C411yescharacteristic, complemented
146C4×C9—42no—
147C4×C9—82no—
148Dic9—42no—
149Dic9—82no—
150C22×D4—91no—
151C23×C4—91no—
152C23×C4—92no—
153C23×C4C2×D912yes—
154C23×C4C2×D911yescharacteristic
155C4×D4—94no—
156C4×D4—94no—
157C4×D4—184no—
158C4×D4—184no—
159C2×C4⋊C4—31no—
160C2×C4⋊C4—31no—
161C2×C4⋊C4—32no—
162C2×C4⋊C4—91no—
163C2×C4⋊C4—91no—
164C2×C4⋊C4—92no—
165C2×C4⋊C4—92no—
166C2×C4⋊C4—91no—
167C2×C4⋊C4—92no—
168C2×C4⋊C4—181no—
169C2×C4⋊C4—182no—
170C2×C4⋊C4—181no—
171C2×C22⋊C4—91no—
172C2×C22⋊C4—91no—
173C2×C22⋊C4—92no—
174C2×C22⋊C4—92no—
175C2×C42—91no—
176C2×C42—92no—
177#95—92no—
178#95—92no—
179#95—92no—
180C23×C3—31no—
181C23×C3—31no—
182C23×C3—31no—
183C23×C3—31no—
184C23×C3C2×C4×D311yescharacteristic
185C23×C3D3×D411yescharacteristic
186C23×C3D3×Q811yescharacteristic
187C22×D3—32no—
188C22×D3—32no—
189C22×D3—32no—
190C22×D3—61no—
191C22×D3—61no—
192C22×D3—61no—
193C22×D3—61no—
194C2×C3×C4—31no—
195C2×C3×C4—32no—
196C2×C3×C4—32no—
197C2×C3×C4—32no—
198C2×C3×C4—32no—
199C2×C3×C4—62no—
200C2×C3×C4—62no—
201C2×C3×C4—61no—
202C2×C3×C4—62no—
203C2×C3×C4—62no—
204C2×C3×C4C2×S412yes—
205C2×C3×C4C2×S411yescharacteristic
206#67—34no—
207#67—34no—
208#67—34no—
209#67—34no—
210C2×Dic3—32no—
211C2×Dic3—32no—
212C2×Dic3—32no—
213C2×Dic3—32no—
214C2×Dic3—32no—
215C2×Dic3—61no—
216C2×Dic3—61no—
217C2×Dic3—61no—
218C2×Dic3—61no—
219C2×Dic3—62no—
220C2×Dic3—62no—
221C2×Dic3—62no—
222C2×Dic3—62no—
223C2×Dic3—62no—
224C2×Dic3—62no—
225C4×D3—64no—
226C4×D3—64no—
227C4×D3—124no—
228C4×D3—124no—
229C2×C9—41no—
230C2×C9—41no—
231C2×C9—41no—
232D9—44no—
233C24—91no—
234C24C22×D911yescharacteristic
235C2×D4—92no—
236C2×D4—92no—
237C2×D4—92no—
238C2×D4—92no—
239C2×D4—92no—
240C2×D4—92no—
241C22×C4—22no—
242C22×C4—31no—
243C22×C4—31no—
244C22×C4—32no—
245C22×C4—32no—
246C22×C4—32no—
247C22×C4—62no—
248C22×C4—94no—
249C22×C4—91no—
250C22×C4—91no—
251C22×C4—91no—
252C22×C4—92no—
253C22×C4—92no—
254C22×C4—181no—
255C22×C4—182no—
256C22×C4—182no—
257C22×C4—184no—
258C22×C4—181no—
259C22×C4—182no—
260C22×C4—362no—
261C22×C4C4×D912yescomplemented
262C4⋊C4—32no—
263C4⋊C4—31no—
264C4⋊C4—61no—
265C4⋊C4—94no—
266C4⋊C4—182no—
267C4⋊C4—181no—
268C4⋊C4—182no—
269C4⋊C4—184no—
270C4⋊C4—182no—
271C4⋊C4—181no—
272C4⋊C4—362no—
273C4⋊C4(C22⋊C9)⋊C211yescharacteristic, direct product factor
274C22⋊C4—94no—
275C22⋊C4—92no—
276C22⋊C4—92no—
277C22⋊C4—184no—
278C22⋊C4—182no—
279C22⋊C4—182no—
280C42—94no—
281C42—184no—
282C22×C3—31no—
283C22×C3—31no—
284C22×C3—31no—
285C22×C3—31no—
286C22×C3—31no—
287C22×C3—31no—
288C22×C3—31no—
289C22×C3—31no—
290C22×C3—31no—
291C22×C3—61no—
292C22×C3D3×C4⋊C411yescharacteristic
293C22×C3C22×S411yescharacteristic
294C2×D3—34no—
295C2×D3—62no—
296C2×D3—62no—
297C2×D3—62no—
298C2×D3—62no—
299C2×D3—62no—
300C2×D3—62no—
301C3×C4—22no—
302C3×C4—32no—
303C3×C4—62no—
304C3×C4C4×S412yes—
305Dic3—34no—
306Dic3—62no—
307Dic3—62no—
308Dic3—122no—
309Dic3—122no—
310C9—41noSylow
311C23—31no—
312C23—31no—
313C23—31no—
314C23—31no—
315C23—92no—
316C23—92no—
317C23—92no—
318C23—181no—
319C23—181no—
320C23—181no—
321C23—181no—
322C23C2×C4×D911yescharacteristic
323C23D4×D911yescharacteristic
324C23Q8×D911yescharacteristic
325D4—94no—
326D4—94no—
327D4—94no—
328D4—94no—
329C2×C4—31no—
330C2×C4—32no—
331C2×C4—32no—
332C2×C4—32no—
333C2×C4—32no—
334C2×C4—62no—
335C2×C4—62no—
336C2×C4—61no—
337C2×C4—62no—
338C2×C4—62no—
339C2×C4—92no—
340C2×C4—92no—
341C2×C4—92no—
342C2×C4—92no—
343C2×C4—92no—
344C2×C4—184no—
345C2×C4—181no—
346C2×C4—181no—
347C2×C4—181no—
348C2×C4—181no—
349C2×C4—184no—
350C2×C4—182no—
351C2×C4—182no—
352C2×C4—182no—
353C2×C4—182no—
354C2×C4—182no—
355C2×C4—182no—
356C2×C4—364no—
357C2×C4—364no—
358C2×C4C2×(C22⋊C9)⋊C212yes—
359C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
360C2×C3—31no—
361C2×C3—31no—
362C2×C3—31no—
363C2×C3—31no—
364C2×C3C2×C4×S411yescharacteristic
365C2×C3D4×S411yescharacteristic
366C2×C3Q8×S411yescharacteristic
367D3—64no—
368C22—31no—
369C22—31no—
370C22—31no—
371C22—31no—
372C22—31no—
373C22—31no—
374C22—31no—
375C22—31no—
376C22—31no—
377C22—61no—
378C22—94no—
379C22—182no—
380C22—182no—
381C22—182no—
382C22—182no—
383C22—182no—
384C22—182no—
385C22C4⋊C4×D911yescharacteristic, complemented
386C22C22×(C22⋊C9)⋊C211yescharacteristic
387C4—22no—
388C4—32no—
389C4—62no—
390C4—94no—
391C4—182no—
392C4—182no—
393C4—362no—
394C4—362no—
395C4C4×(C22⋊C9)⋊C212yescomplemented
396C3C4⋊C4×S411yescharacteristic
397C2—31no—
398C2—31no—
399C2—31no—
400C2—31no—
401C2—184no—
402C2C2×C4×(C22⋊C9)⋊C211yescharacteristic
403C2D4×(C22⋊C9)⋊C211yescharacteristic
404C2Q8×(C22⋊C9)⋊C211yescharacteristic
subgroupG/H
centerC22C22×(C22⋊C9)⋊C2
commutatorC2×C22⋊C9C22×C4
FrattiniC22×C3C22×S4
FittingC22×C3×C4⋊C4D3
socleC24×C3C22×D3
prime radicalC22×(C22⋊C9)⋊C2C22
cosocleC22×C22⋊C9C23
hypercenterC4⋊C4(C22⋊C9)⋊C2
hypocenterC22⋊C9C2×C4⋊C4
LCSG ▷ C2×C22⋊C9 ▷ C22⋊C9
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C4⋊C4×C22⋊C9C2semidirect
4. C4⋊((C22⋊C9)⋊C4)C2semidirect
5. ((C22⋊C9)⋊C4)⋊C4C2semidirect
13. C4×(C22⋊C9)⋊C2C4semidirect
33. C4×C22⋊C9C2×C4semidirect
35. (C22⋊C9)⋊C4C2×C4semidirect
74. (C22⋊C9)⋊C2C4⋊C4direct (N × H)
84. C22×C4⋊C4D9semidirect
145. C22⋊C9C2×C4⋊C4semidirect
261. C22×C4C4×D9semidirect
273. C4⋊C4(C22⋊C9)⋊C2direct (N × H)
385. C22C4⋊C4×D9semidirect
395. C4C4×(C22⋊C9)⋊C2semidirect

Maximal subgroups

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

subgroupindex
C2×C4×(C22⋊C9)⋊C22
C4⋊C4×C22⋊C92
C4⋊((C22⋊C9)⋊C4)2
((C22⋊C9)⋊C4)⋊C42
C4⋊C4×#673
C4⋊C4×D94