Finite Group Databasebeta

← #3524⋊C9 #11919769

Subgroups — #3524⋊C9 #11919769

Order 1152.

460 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 91 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
1#557⋊C9C211yesmaximal, characteristic, complemented
2C4⋊(#41⋊C9)C211yesmaximal, characteristic, complemented
3#548⋊C9C211yesmaximal, characteristic, complemented
4#548⋊C9C211yesmaximal, characteristic, complemented
5#520⋊C9C211yesmaximal, characteristic, complemented
6#519⋊C9C211yesmaximal, characteristic, complemented
7C4×#41⋊C9C211yesmaximal, characteristic, complemented
8C3×#3524C311yesmaximal, characteristic
9C2×#41⋊C9C2211yescharacteristic
10C2×#41⋊C9C2211yescharacteristic
11C22×Q8⋊C9C2211yescharacteristic
12C9×#126—41nomaximal
13C4×Q8⋊C9C2211yescharacteristic
14C4×Q8⋊C9C2211yescharacteristic
15C4×Q8⋊C9C2211yescharacteristic
16C4×Q8⋊C9C2211yescharacteristic
17C3×#559—31no—
18C3×#557C2×C311yescharacteristic
19C3×#555—31no—
20C3×#553—31no—
21C3×#552—31no—
22C3×#550C2×C311yescharacteristic
23C3×#548C2×C311yescharacteristic
24C3×#548C2×C311yescharacteristic
25C3×#542—31no—
26C3×#540—31no—
27C3×#529—31no—
28C3×#529—31no—
29C3×#520C2×C311yescharacteristic
30C3×#519C2×C311yescharacteristic
31C3×C4×#41C2×C311yescharacteristic
32#41⋊C9—21no—
33#41⋊C9—21no—
34C2×Q8⋊C9—21no—
35C2×Q8⋊C9C2311yescharacteristic
36C9×C4⋊C4—41no—
37C9×C4⋊C4—41no—
38C9×C4⋊C4—41no—
39C9×C22⋊C4—41no—
40C9×C22⋊C4—41no—
41C9×C22⋊C4—41no—
42C42×C9—41no—
43#3524C911yescharacteristic, complemented, Sylow
44C2×C3×#41C22×C311yescharacteristic
45C2×C3×#41C22×C311yescharacteristic
46C22×C3×Q8C22×C311yescharacteristic
47C3×C4⋊Q8—31no—
48C3×#127—31no—
49C3×#126—32no—
50C3×#126—31no—
51C3×#126A411yescharacteristic
52C3×#125—31no—
53C3×#125—31no—
54C3×#125—31no—
55C3×#124—32no—
56C3×#124—31no—
57C3×#124—31no—
58C3×#124—31no—
59C3×#123—32no—
60C3×#123—32no—
61C3×#123—31no—
62C3×#123—31no—
63C3×C22⋊Q8—31no—
64C3×C22⋊Q8—31no—
65C3×C22⋊Q8—31no—
66C3×#121—31no—
67C3×#121—31no—
68C3×#121—32no—
69C3×#121—31no—
70C3×#121—31no—
71C3×#121—31no—
72C3×C4×Q8—31no—
73C3×C4×Q8—31no—
74C3×C4×Q8—31no—
75C3×C4×Q8C22×C311yescharacteristic
76C3×C4×Q8C22×C311yescharacteristic
77C3×C4×Q8C22×C311yescharacteristic
78C3×C4×Q8C22×C311yescharacteristic
79C3×C4×D4—32no—
80C3×C4×D4—31no—
81C3×C4×D4—31no—
82C3×C4×D4—31no—
83C3×C4×D4—31no—
84C3×C4×D4—31no—
85C3×C4×D4—31no—
86C3×C4×D4—31no—
87C3×#117—32no—
88C3×#117—31no—
89C3×#117—31no—
90C3×#117—31no—
91C3×#117—31no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C42—31no—
94C23×C9—41no—
95C2×C4×C9—41no—
96C2×C4×C9—41no—
97C2×C4×C9—41no—
98C2×C4×C9—41no—
99C2×C4×C9—41no—
100C2×C4×C9—41no—
101Q8⋊C9#4111yescharacteristic
102#559—31no—
103#557C2×C911yescharacteristic, complemented
104#555—31no—
105#553—31no—
106#552—31no—
107#550C2×C911yescharacteristic, complemented
108#548C2×C911yescharacteristic
109#548C2×C911yescharacteristic
110#542—31no—
111#540—31no—
112#529—31no—
113#529—31no—
114#520C2×C911yescharacteristic, complemented
115#519C2×C911yescharacteristic
116C4×#41C2×C911yescharacteristic, complemented
117C3×#41—21no—
118C3×#41—21no—
119C3×#41—61no—
120C3×#41—61no—
121C2×C3×Q8—21no—
122C2×C3×Q8—31no—
123C2×C3×Q8—31no—
124C2×C3×Q8—61no—
125C2×C3×Q8C23×C311yescharacteristic
126C2×C3×D4—31no—
127C2×C3×D4—31no—
128C2×C3×D4—32no—
129C2×C3×D4—31no—
130C2×C3×D4—31no—
131C2×C3×D4—31no—
132C22×C3×C4—31no—
133C22×C3×C4—32no—
134C22×C3×C4—31no—
135C22×C3×C4—31no—
136C22×C3×C4—31no—
137C22×C3×C4—31no—
138C3×C4⋊C4—31no—
139C3×C4⋊C4—31no—
140C3×C4⋊C4—31no—
141C3×C4⋊C4—31no—
142C3×C4⋊C4—32no—
143C3×C4⋊C4—31no—
144C3×C4⋊C4—31no—
145C3×C4⋊C4—31no—
146C3×C4⋊C4—31no—
147C3×C4⋊C4—31no—
148C3×C4⋊C4—31no—
149C3×C4⋊C4—31no—
150C3×C4⋊C4C2×A411yescharacteristic
151C3×C4⋊C4C2×A411yescharacteristic
152C3×C4⋊C4C2×A411yescharacteristic
153C3×C22⋊C4—32no—
154C3×C22⋊C4—32no—
155C3×C22⋊C4—32no—
156C3×C22⋊C4—31no—
157C3×C22⋊C4—31no—
158C3×C22⋊C4—31no—
159C3×C22⋊C4—31no—
160C3×C22⋊C4—31no—
161C3×C22⋊C4—31no—
162C3×C22⋊C4—31no—
163C3×C22⋊C4C2×A411yescharacteristic
164C3×C22⋊C4C2×A411yescharacteristic
165C3×C22⋊C4C2×A411yescharacteristic
166C3×C42—32no—
167C3×C42—31no—
168C3×C42—31no—
169C3×C42—31no—
170C3×C42—31no—
171C3×C42—31no—
172C3×C42C2×A411yescharacteristic
173C22×C9—41no—
174C22×C9—81no—
175C22×C9—81no—
176C22×C9—81no—
177C4×C9—81no—
178C4×C9—81no—
179C4×C9—81no—
180C4×C9—81no—
181C4×C9—81no—
182C4×C9—81no—
183C2×#41C22×C911yescharacteristic
184C2×#41C22×C911yescharacteristic
185C22×Q8C22×C911yescharacteristic
186C4⋊Q8—31no—
187#127—31no—
188#126—32no—
189#126—31no—
190#126C22⋊C911yescharacteristic
191#125—31no—
192#125—31no—
193#125—31no—
194#124—32no—
195#124—31no—
196#124—31no—
197#124—31no—
198#123—32no—
199#123—32no—
200#123—31no—
201#123—31no—
202C22⋊Q8—31no—
203C22⋊Q8—31no—
204C22⋊Q8—31no—
205#121—31no—
206#121—31no—
207#121—32no—
208#121—31no—
209#121—31no—
210#121—31no—
211C4×Q8—31no—
212C4×Q8—31no—
213C4×Q8—31no—
214C4×Q8C22×C911yescharacteristic
215C4×Q8C22×C911yescharacteristic
216C4×Q8C22×C911yescharacteristic
217C4×Q8C22×C911yescharacteristic
218C4×D4—32no—
219C4×D4—31no—
220C4×D4—31no—
221C4×D4—31no—
222C4×D4—31no—
223C4×D4—31no—
224C4×D4—31no—
225C4×D4—31no—
226#117—32no—
227#117—31no—
228#117—31no—
229#117—31no—
230#117—31no—
231C2×C4⋊C4—31no—
232C2×C42—31no—
233C23×C3—31no—
234C23×C3—31no—
235C23×C3C22×A411yescharacteristic
236C3×Q8—31no—
237C3×Q8—61no—
238C3×Q8—61no—
239C3×Q8—121no—
240C3×Q8C3×#4111yescharacteristic
241C3×D4—61no—
242C3×D4—61no—
243C3×D4—61no—
244C3×D4—61no—
245C3×D4—121no—
246C3×D4—121no—
247C3×D4—121no—
248C3×D4—122no—
249C2×C3×C4—31no—
250C2×C3×C4—31no—
251C2×C3×C4—31no—
252C2×C3×C4—31no—
253C2×C3×C4—31no—
254C2×C3×C4—31no—
255C2×C3×C4—61no—
256C2×C3×C4—61no—
257C2×C3×C4—61no—
258C2×C3×C4—61no—
259C2×C3×C4—61no—
260C2×C3×C4—61no—
261C2×C3×C4—121no—
262C2×C3×C4—121no—
263C2×C3×C4—122no—
264C2×C3×C4C22×A411yescharacteristic
265C2×C3×C4C22×A411yescharacteristic
266C2×C3×C4C22×A411yescharacteristic
267C2×C3×C4C22×A411yescharacteristic
268C2×C3×C4C22×A411yescharacteristic
269C2×C3×C4C22×A411yescharacteristic
270C2×C9—41no—
271C2×C9—41no—
272C2×C9—41no—
273C2×C9—161no—
274#41—21no—
275#41—21no—
276#41—61no—
277#41—61no—
278C2×Q8—21no—
279C2×Q8—31no—
280C2×Q8—31no—
281C2×Q8—61no—
282C2×Q8C23×C911yescharacteristic
283C2×D4—31no—
284C2×D4—31no—
285C2×D4—32no—
286C2×D4—31no—
287C2×D4—31no—
288C2×D4—31no—
289C22×C4—31no—
290C22×C4—32no—
291C22×C4—31no—
292C22×C4—31no—
293C22×C4—31no—
294C22×C4—31no—
295C4⋊C4—31no—
296C4⋊C4—31no—
297C4⋊C4—31no—
298C4⋊C4—31no—
299C4⋊C4—32no—
300C4⋊C4—31no—
301C4⋊C4—31no—
302C4⋊C4—31no—
303C4⋊C4—31no—
304C4⋊C4—31no—
305C4⋊C4—31no—
306C4⋊C4—31no—
307C4⋊C4C2×C22⋊C911yescharacteristic
308C4⋊C4C2×C22⋊C911yescharacteristic
309C4⋊C4C2×C22⋊C911yescharacteristic
310C22⋊C4—32no—
311C22⋊C4—32no—
312C22⋊C4—32no—
313C22⋊C4—31no—
314C22⋊C4—31no—
315C22⋊C4—31no—
316C22⋊C4—31no—
317C22⋊C4—31no—
318C22⋊C4—31no—
319C22⋊C4—31no—
320C22⋊C4C2×C22⋊C911yescharacteristic
321C22⋊C4C2×C22⋊C911yescharacteristic
322C22⋊C4C2×C22⋊C911yescharacteristic
323C42—32no—
324C42—31no—
325C42—31no—
326C42—31no—
327C42—31no—
328C42—31no—
329C42C2×C22⋊C911yescharacteristic
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—61no—
334C22×C3—61no—
335C22×C3—61no—
336C22×C3—61no—
337C22×C3—61no—
338C22×C3—61no—
339C22×C3C23×A411yescharacteristic
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—31no—
347C3×C4—31no—
348C3×C4—61no—
349C3×C4—61no—
350C3×C4—61no—
351C3×C4—61no—
352C3×C4—61no—
353C9—41noSylow
354C23—31no—
355C23—31no—
356C23C22×C22⋊C911yescharacteristic
357Q8—31no—
358Q8—61no—
359Q8—61no—
360Q8—121no—
361Q8C9×#4111yescharacteristic
362D4—61no—
363D4—61no—
364D4—61no—
365D4—61no—
366D4—121no—
367D4—121no—
368D4—121no—
369D4—122no—
370C2×C4—31no—
371C2×C4—31no—
372C2×C4—31no—
373C2×C4—31no—
374C2×C4—31no—
375C2×C4—31no—
376C2×C4—61no—
377C2×C4—61no—
378C2×C4—61no—
379C2×C4—61no—
380C2×C4—61no—
381C2×C4—61no—
382C2×C4—121no—
383C2×C4—121no—
384C2×C4—122no—
385C2×C4C22×C22⋊C911yescharacteristic
386C2×C4C22×C22⋊C911yescharacteristic
387C2×C4C22×C22⋊C911yescharacteristic
388C2×C4C22×C22⋊C911yescharacteristic
389C2×C4C22×C22⋊C911yescharacteristic
390C2×C4C22×C22⋊C911yescharacteristic
391C2×C3—41no—
392C2×C3—121no—
393C2×C3—121no—
394C2×C3A4×#4111yescharacteristic
395C2×C3#594511yescharacteristic
396C2×C3#594511yescharacteristic
397C22—21no—
398C22—21no—
399C22—21no—
400C22—61no—
401C22—61no—
402C22—61no—
403C22—61no—
404C22—61no—
405C22—61no—
406C22C23×C22⋊C911yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—31no—
414C4—31no—
415C4—61no—
416C4—61no—
417C4—61no—
418C4—61no—
419C4—61no—
420C3#3524⋊C311yescharacteristic
421C2—41no—
422C2—121no—
423C2—121no—
424C2#41×C22⋊C911yescharacteristic
425C2#1059312011yescharacteristic
426C2#1059312011yescharacteristic
subgroupG/H
center, Frattini, socleC22×C3C23×A4
commutatorC2×Q8C23×C9
Fitting, prime radicalC3×#3524C3
cosocleC2×C3×Q8C23×C3
hypercenterC3×#126A4
hypocenterQ8C9×#41
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C22×C3 ◁ C3×#126

Complements

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

NH ≅ G/Ntype
1. #557⋊C9C2semidirect
2. C4⋊(#41⋊C9)C2semidirect
3. #548⋊C9C2semidirect
4. #548⋊C9C2semidirect
5. #520⋊C9C2semidirect
6. #519⋊C9C2semidirect
7. C4×#41⋊C9C2semidirect
43. #3524C9semidirect
103. #557C2×C9semidirect
107. #550C2×C9semidirect
114. #520C2×C9semidirect
116. C4×#41C2×C9semidirect

Maximal subgroups

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

subgroupindex
#557⋊C92
C4⋊(#41⋊C9)2
#548⋊C92
#520⋊C92
#519⋊C92
C4×#41⋊C92
C3×#35243
C9×#1264