Finite Group Databasebeta

← C22×C22⋊C92 #72244702

Subgroups — C22×C22⋊C92 #72244702

Order 5184.

3018 conjugacy classes of subgroups; only the 245 normal subgroups are shown.

normal subgroups only

This group has 3018 conjugacy classes of subgroups — too many to draw. Only its 245 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×C22⋊C92C213yesmaximal, direct product factor
2C22×C3×C22⋊(C22⋊C9)C312yesmaximal
3C24×C3×C22⋊C9C312yesmaximal
4C22×C9×C22⋊C9—42nomaximal
5C22⋊C92C2211yescharacteristic, direct product factor
6C2×C3×C22⋊(C22⋊C9)C2×C316yes—
7C23×C3×C22⋊C9—32no—
8C23×C3×C22⋊C9—36no—
9C23×C3×C22⋊C9C2×C316yes—
10C2×C9×C22⋊C9—46no—
11C26×C32C3211yescharacteristic
12C22×C22⋊(C22⋊C9)C916yescomplemented
13C24×C22⋊C9C916yescomplemented
14C24×C3×C9—42no—
15C3×C22⋊(C22⋊C9)C22×C312yes—
16C22×C3×C22⋊C9—34no—
17C22×C3×C22⋊C9—36no—
18C22×C3×C22⋊C9—36no—
19C22×C3×C22⋊C9—36no—
20C22×C3×C22⋊C9—44no—
21C22×C3×C22⋊C9—122no—
22C22×C3×C22⋊C9A412yes—
23C22×C3×C22⋊C9C22×C312yes—
24C22×C92—161no—
25C9×C22⋊C9—42no—
26C25×C32—36no—
27C25×C32—32no—
28C25×C32—91no—
29C25×C32—93no—
30C25×C32C2×C3213yes—
31C2×C22⋊(C22⋊C9)C2×C9118yescomplemented
32C23×C22⋊C9—318no—
33C23×C22⋊C9—36no—
34C23×C22⋊C9C2×C9118yescomplemented
35C23×C3×C9—46no—
36C23×C3×C9—122no—
37C23×C3×C9—126no—
38C2×C3×C22⋊C9—36no—
39C2×C3×C22⋊C9—32no—
40C2×C3×C22⋊C9—412no—
41C2×C3×C22⋊C9—126no—
42C2×C3×C22⋊C9C2×A416yes—
43C26×C3C3×C912yes—
44C26×C3C3×C912yes—
45C2×C92—163no—
46C24×C32—34no—
47C24×C32—32no—
48C24×C32—36no—
49C24×C32—36no—
50C24×C32—36no—
51C24×C32—91no—
52C24×C32—93no—
53C24×C32—96no—
54C24×C32—96no—
55C24×C32—96no—
56C24×C32—92no—
57C24×C32—94no—
58C24×C32—912no—
59C24×C32—912no—
60C24×C32—93no—
61C24×C32—96no—
62C24×C32—93no—
63C24×C32C3×A412yes—
64C24×C32C22×C3211yescharacteristic
65C24×C9—46no—
66C22⋊(C22⋊C9)C22×C916yescomplemented
67C22×C22⋊C9—312no—
68C22×C22⋊C9—318no—
69C22×C22⋊C9—318no—
70C22×C22⋊C9—318no—
71C22×C22⋊C9—412no—
72C22×C22⋊C9—126no—
73C22×C22⋊C9C22⋊C916yesdirect product factor
74C22×C22⋊C9C22×C916yescomplemented
75C22×C3×C9—42no—
76C22×C3×C9—42no—
77C22×C3×C9—126no—
78C22×C3×C9—126no—
79C22×C3×C9—124no—
80C22×C3×C9—126no—
81C22×C3×C9—162no—
82C3×C22⋊C9—44no—
83C3×C22⋊C9—122no—
84C3×C22⋊C9C22×A412yes—
85C25×C3—36no—
86C25×C3—312no—
87C25×C3—36no—
88C25×C3—34no—
89C25×C3—32no—
90C25×C3—32no—
91C25×C3—92no—
92C25×C3—92no—
93C25×C3—96no—
94C25×C3—96no—
95C25×C3C2×C3×C916yes—
96C25×C3C2×C3×C916yes—
97C92—161noSylow
98C23×C32—36no—
99C23×C32—32no—
100C23×C32—36no—
101C23×C32—32no—
102C23×C32—36no—
103C23×C32—91no—
104C23×C32—93no—
105C23×C32—96no—
106C23×C32—93no—
107C23×C32—96no—
108C23×C32—912no—
109C23×C32—96no—
110C23×C32—96no—
111C23×C32—96no—
112C23×C32—94no—
113C23×C32—912no—
114C23×C32—912no—
115C23×C32—96no—
116C23×C32—93no—
117C23×C32—912no—
118C23×C32—912no—
119C23×C32—96no—
120C23×C32—96no—
121C23×C32—924no—
122C23×C32—91no—
123C23×C32C2×C3×A416yes—
124C23×C9—418no—
125C23×C9—126no—
126C23×C9—1218no—
127C2×C22⋊C9—318no—
128C2×C22⋊C9—36no—
129C2×C22⋊C9—436no—
130C2×C22⋊C9—1218no—
131C2×C22⋊C9C2×C22⋊C9118yesdirect product factor
132C26C9211yescharacteristic, complemented, Sylow
133C2×C3×C9—46no—
134C2×C3×C9—122no—
135C2×C3×C9—126no—
136C2×C3×C9—166no—
137C24×C3—38no—
138C24×C3—34no—
139C24×C3—34no—
140C24×C3—34no—
141C24×C3—32no—
142C24×C3—32no—
143C24×C3—36no—
144C24×C3—312no—
145C24×C3—36no—
146C24×C3—312no—
147C24×C3—36no—
148C24×C3—312no—
149C24×C3—36no—
150C24×C3—36no—
151C24×C3—36no—
152C24×C3—96no—
153C24×C3—96no—
154C24×C3—92no—
155C24×C3—92no—
156C24×C3—96no—
157C24×C3—912no—
158C24×C3—96no—
159C24×C3—96no—
160C24×C3—912no—
161C24×C3—96no—
162C24×C3—92no—
163C24×C3—92no—
164C24×C3—94no—
165C24×C3—96no—
166C24×C3—912no—
167C24×C3—96no—
168C24×C3—96no—
169C24×C3—96no—
170C24×C3—96no—
171C24×C3—96no—
172C24×C3—912no—
173C24×C3—912no—
174C24×C3—912no—
175C24×C3—924no—
176C24×C3—912no—
177C24×C3—912no—
178C24×C3—924no—
179C24×C3—912no—
180C24×C3—98no—
181C24×C3—94no—
182C24×C3—94no—
183C24×C3C9×A414yes—
184C24×C3C9×A412yes—
185C24×C3C3×C22⋊C912yes—
186C24×C3C22×C3×C912yes—
187C24×C3C22×C3×C912yes—
188C22×C32—36no—
189C22×C32—34no—
190C22×C32—36no—
191C22×C32—36no—
192C22×C32—32no—
193C22×C32—91no—
194C22×C32—96no—
195C22×C32—93no—
196C22×C32—96no—
197C22×C32—92no—
198C22×C32—96no—
199C22×C32—912no—
200C22×C32—912no—
201C22×C32—96no—
202C22×C32—94no—
203C22×C32—93no—
204C22×C32—93no—
205C22×C32A4211yescharacteristic
206C22×C32C22×C3×A412yes—
207C22×C9—46no—
208C22×C9—46no—
209C22×C9—1218no—
210C22×C9—1218no—
211C22×C9—1218no—
212C22×C9—1212no—
213C22×C9—166no—
214C22⋊C9—412no—
215C22⋊C9—126no—
216C22⋊C9C22×C22⋊C916yesdirect product factor
217C25—36no—
218C25—32no—
219C25—91no—
220C25—93no—
221C25C2×C9213yescomplemented
222C3×C9—42no—
223C3×C9—162no—
224C23×C3—36no—
225C23×C3—312no—
226C23×C3—36no—
227C23×C3—32no—
228C23×C3—32no—
229C23×C3—34no—
230C23×C3—36no—
231C23×C3—312no—
232C23×C3—36no—
233C23×C3—312no—
234C23×C3—36no—
235C23×C3—34no—
236C23×C3—32no—
237C23×C3—36no—
238C23×C3—32no—
239C23×C3—92no—
240C23×C3—92no—
241C23×C3—96no—
242C23×C3—96no—
243C23×C3—96no—
244C23×C3—96no—
245C23×C3—912no—
246C23×C3—96no—
247C23×C3—96no—
248C23×C3—96no—
249C23×C3—912no—
250C23×C3—96no—
251C23×C3—96no—
252C23×C3—912no—
253C23×C3—912no—
254C23×C3—924no—
255C23×C3—96no—
256C23×C3—912no—
257C23×C3—96no—
258C23×C3—96no—
259C23×C3—96no—
260C23×C3—96no—
261C23×C3—912no—
262C23×C3—912no—
263C23×C3—94no—
264C23×C3—94no—
265C23×C3—98no—
266C23×C3—912no—
267C23×C3—912no—
268C23×C3—924no—
269C23×C3—912no—
270C23×C3—912no—
271C23×C3—924no—
272C23×C3—96no—
273C23×C3—912no—
274C23×C3—96no—
275C23×C3—96no—
276C23×C3—96no—
277C23×C3—912no—
278C23×C3—924no—
279C23×C3—912no—
280C23×C3—912no—
281C23×C3—924no—
282C23×C3—912no—
283C23×C3—912no—
284C23×C3—96no—
285C23×C3—96no—
286C23×C3—912no—
287C23×C3—912no—
288C23×C3—948no—
289C23×C3—924no—
290C23×C3—924no—
291C23×C3—92no—
292C23×C3—92no—
293C23×C3C2×C9×A4112yes—
294C23×C3C2×C9×A416yes—
295C23×C3C2×C3×C22⋊C916yes—
296C2×C32—36no—
297C2×C32—32no—
298C2×C32—91no—
299C2×C32—93no—
300C2×C32C2×A4213yes—
301C2×C9—418no—
302C2×C9—126no—
303C2×C9—1218no—
304C2×C9—1618no—
305C24—34no—
306C24—32no—
307C24—36no—
308C24—36no—
309C24—36no—
310C24—93no—
311C24—91no—
312C24—96no—
313C24—96no—
314C24—92no—
315C24—96no—
316C24—93no—
317C24—93no—
318C24—96no—
319C24—912no—
320C24—912no—
321C24—94no—
322C24C9×C22⋊C912yescomplemented
323C24C22×C9211yescharacteristic, complemented
324C22×C3—36no—
325C22×C3—312no—
326C22×C3—36no—
327C22×C3—34no—
328C22×C3—34no—
329C22×C3—38no—
330C22×C3—36no—
331C22×C3—36no—
332C22×C3—36no—
333C22×C3—36no—
334C22×C3—312no—
335C22×C3—312no—
336C22×C3—32no—
337C22×C3—34no—
338C22×C3—32no—
339C22×C3—92no—
340C22×C3—92no—
341C22×C3—96no—
342C22×C3—96no—
343C22×C3—912no—
344C22×C3—96no—
345C22×C3—912no—
346C22×C3—96no—
347C22×C3—912no—
348C22×C3—92no—
349C22×C3—96no—
350C22×C3—92no—
351C22×C3—96no—
352C22×C3—94no—
353C22×C3—912no—
354C22×C3—912no—
355C22×C3—912no—
356C22×C3—912no—
357C22×C3—912no—
358C22×C3—924no—
359C22×C3—924no—
360C22×C3—912no—
361C22×C3—96no—
362C22×C3—96no—
363C22×C3—98no—
364C22×C3—94no—
365C22×C3—94no—
366C22×C3—96no—
367C22×C3—96no—
368C22×C3—96no—
369C22×C3—96no—
370C22×C3A4×C22⋊C912yes—
371C22×C3(C22⋊A4)⋊C912yes—
372C22×C3C22×C9×A414yes—
373C22×C3C22×C9×A412yes—
374C22×C3C22×C3×C22⋊C912yes—
375C32C22×A4211yescharacteristic
376C9—46no—
377C9—166no—
378C23—36no—
379C23—32no—
380C23—36no—
381C23—32no—
382C23—36no—
383C23—91no—
384C23—93no—
385C23—96no—
386C23—93no—
387C23—96no—
388C23—96no—
389C23—912no—
390C23—96no—
391C23—96no—
392C23—94no—
393C23—912no—
394C23—912no—
395C23—96no—
396C23—93no—
397C23—912no—
398C23—912no—
399C23—96no—
400C23—96no—
401C23—924no—
402C23—91no—
403C23C2×C9×C22⋊C916yescomplemented
404C2×C3—32no—
405C2×C3—32no—
406C2×C3—36no—
407C2×C3—36no—
408C2×C3—34no—
409C2×C3—312no—
410C2×C3—92no—
411C2×C3—96no—
412C2×C3—92no—
413C2×C3—96no—
414C2×C3C2×A4×C22⋊C916yes—
415C2×C3C2×(C22⋊A4)⋊C916yes—
416C22—36no—
417C22—34no—
418C22—36no—
419C22—36no—
420C22—32no—
421C22—91no—
422C22—96no—
423C22—93no—
424C22—96no—
425C22—92no—
426C22—96no—
427C22—912no—
428C22—912no—
429C22—96no—
430C22—94no—
431C22—93no—
432C22—93no—
433C22C22⋊C9211yescharacteristic, direct product factor
434C22C22×C9×C22⋊C912yescomplemented
435C3C22×A4×C22⋊C912yes—
436C3C22×(C22⋊A4)⋊C912yes—
437C2—32no—
438C2—36no—
439C2—91no—
440C2—93no—
441C2C2×C22⋊C9213yesdirect product factor
subgroupG/H
center, hypercenterC22×C32A42
commutator, hypocenterC24C22×C92
FrattiniC32C22×A42
Fitting, socle, prime radicalC26×C32C32
cosocleC24×C32C22×C32
LCSG ▷ C24
UCSC1 ◁ C22×C32

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊C92C2direct (N × H)
5. C22⋊C92C22direct (N × H)
12. C22×C22⋊(C22⋊C9)C9semidirect
13. C24×C22⋊C9C9semidirect
31. C2×C22⋊(C22⋊C9)C2×C9semidirect
34. C23×C22⋊C9C2×C9semidirect
66. C22⋊(C22⋊C9)C22×C9semidirect
73. C22×C22⋊C9C22⋊C9direct (N × H)
74. C22×C22⋊C9C22×C9semidirect
131. C2×C22⋊C9C2×C22⋊C9direct (N × H)
132. C26C92semidirect
216. C22⋊C9C22×C22⋊C9direct (N × H)
221. C25C2×C92semidirect
322. C24C9×C22⋊C9semidirect
323. C24C22×C92semidirect
403. C23C2×C9×C22⋊C9semidirect
433. C22C22⋊C92direct (N × H)
434. C22C22×C9×C22⋊C9semidirect
441. C2C2×C22⋊C92direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C22⋊C922
C22×C3×C22⋊(C22⋊C9)3
C24×C3×C22⋊C93
C22×C9×C22⋊C94