Finite Group Databasebeta

← #3516⋊C9 #11919759

Subgroups — #3516⋊C9 #11919759

Order 1152.

475 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 475 conjugacy classes of subgroups — too many to draw. Only its 95 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
2D4×Q8⋊C9C211yesmaximal, characteristic, complemented
3#548⋊C9C211yesmaximal, characteristic, complemented
4#548⋊C9C211yesmaximal, characteristic, complemented
5#520⋊C9C211yesmaximal, characteristic, complemented
6#519⋊C9C211yesmaximal, characteristic, complemented
7C2×C4×Q8⋊C9C211yesmaximal, characteristic, complemented
8C3×#3516C311yesmaximal, characteristic
9C2×#41⋊C9C2211yescharacteristic
10C22×Q8⋊C9C2211yescharacteristic
11C22×Q8⋊C9C2211yescharacteristic
12C9×#123—41nomaximal
13C4×Q8⋊C9C2211yescharacteristic
14C4×Q8⋊C9C2211yescharacteristic
15C4×Q8⋊C9C2211yescharacteristic
16C4×Q8⋊C9C2211yescharacteristic
17C3×#557C2×C311yescharacteristic
18C3×#556—31no—
19C3×#554—31no—
20C3×#553—31no—
21C3×#552—31no—
22C3×D4×Q8C2×C311yescharacteristic
23C3×#548C2×C311yescharacteristic
24C3×#548C2×C311yescharacteristic
25C3×#542—31no—
26C3×#541—31no—
27C3×#529—31no—
28C3×#529—31no—
29C3×#520C2×C311yescharacteristic
30C3×#519C2×C311yescharacteristic
31C2×C3×C4×Q8C2×C311yescharacteristic
32C2×D4×C9—41no—
33C22×C4×C9—41no—
34#41⋊C9—21no—
35C2×Q8⋊C9—21no—
36C2×Q8⋊C9—21no—
37C2×Q8⋊C9C2311yescharacteristic
38C9×C4⋊C4—41no—
39C9×C4⋊C4—41no—
40C9×C22⋊C4—41no—
41C9×C22⋊C4—41no—
42C9×C22⋊C4—41no—
43#3516C911yescharacteristic, complemented, Sylow
44C2×C3×#41C22×C311yescharacteristic
45C22×C3×Q8C22×C311yescharacteristic
46C22×C3×Q8C22×C311yescharacteristic
47C3×C4⋊Q8—31no—
48C3×C4⋊Q8—31no—
49C3×#126—32no—
50C3×#126—32no—
51C3×#126—31no—
52C3×#126—31no—
53C3×#125—31no—
54C3×#125—31no—
55C3×#125—32no—
56C3×#125—31no—
57C3×#124—31no—
58C3×#124—31no—
59C3×#124—31no—
60C3×#123—32no—
61C3×#123—31no—
62C3×#123A411yescharacteristic
63C3×C22⋊Q8—32no—
64C3×C22⋊Q8—31no—
65C3×C22⋊Q8—31no—
66C3×C22⋊Q8—31no—
67C3×C22⋊Q8—31no—
68C3×C22⋊Q8—31no—
69C3×#121—31no—
70C3×#121—31no—
71C3×#121—31no—
72C3×C4×Q8—31no—
73C3×C4×Q8—31no—
74C3×C4×Q8—31no—
75C3×C4×Q8—31no—
76C3×C4×Q8—31no—
77C3×C4×Q8C22×C311yescharacteristic
78C3×C4×Q8C22×C311yescharacteristic
79C3×C4×Q8C22×C311yescharacteristic
80C3×C4×Q8C22×C311yescharacteristic
81C3×C4×D4—32no—
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—
91C2×C3×C4⋊C4—31no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C42—31no—
94C23×C9—41no—
95C23×C9—41no—
96D4×C9—82no—
97C2×C4×C9—41no—
98C2×C4×C9—41no—
99C2×C4×C9—41no—
100C2×C4×C9—41no—
101C2×C4×C9—41no—
102C2×C4×C9—82no—
103Q8⋊C9#4111yescharacteristic
104#557C2×C911yescharacteristic, complemented
105#556—31no—
106#554—31no—
107#553—31no—
108#552—31no—
109D4×Q8C2×C911yescharacteristic
110#548C2×C911yescharacteristic, complemented
111#548C2×C911yescharacteristic, complemented
112#542—31no—
113#541—31no—
114#529—31no—
115#529—31no—
116#520C2×C911yescharacteristic, complemented
117#519C2×C911yescharacteristic, complemented
118C2×C4×Q8C2×C911yescharacteristic, complemented
119C3×#41—21no—
120C3×#41—61no—
121C2×C3×Q8—21no—
122C2×C3×Q8—21no—
123C2×C3×Q8—31no—
124C2×C3×Q8—31no—
125C2×C3×Q8—31no—
126C2×C3×Q8—61no—
127C2×C3×Q8—61no—
128C2×C3×Q8C23×C311yescharacteristic
129C2×C3×D4—31no—
130C2×C3×D4—31no—
131C2×C3×D4—31no—
132C2×C3×D4C2×A411yescharacteristic
133C22×C3×C4—31no—
134C22×C3×C4—31no—
135C22×C3×C4—32no—
136C22×C3×C4—31no—
137C22×C3×C4—31no—
138C22×C3×C4C2×A411yescharacteristic
139C3×C4⋊C4—31no—
140C3×C4⋊C4—31no—
141C3×C4⋊C4—31no—
142C3×C4⋊C4—31no—
143C3×C4⋊C4—32no—
144C3×C4⋊C4—32no—
145C3×C4⋊C4—32no—
146C3×C4⋊C4—31no—
147C3×C4⋊C4—31no—
148C3×C4⋊C4—31no—
149C3×C4⋊C4—31no—
150C3×C4⋊C4—31no—
151C3×C4⋊C4—31no—
152C3×C4⋊C4—31no—
153C3×C4⋊C4—31no—
154C3×C4⋊C4C2×A411yescharacteristic
155C3×C4⋊C4C2×A411yescharacteristic
156C3×C22⋊C4—32no—
157C3×C22⋊C4—32no—
158C3×C22⋊C4—31no—
159C3×C22⋊C4—31no—
160C3×C22⋊C4—31no—
161C3×C22⋊C4—31no—
162C3×C22⋊C4—31no—
163C3×C22⋊C4—31no—
164C3×C22⋊C4—31no—
165C3×C22⋊C4C2×A411yescharacteristic
166C3×C22⋊C4C2×A411yescharacteristic
167C3×C22⋊C4C2×A411yescharacteristic
168C3×C42—32no—
169C3×C42—31no—
170C3×C42—31no—
171C3×C42—31no—
172C3×C42—31no—
173C3×C42—31no—
174C3×C42—31no—
175C22×C9—42no—
176C22×C9—41no—
177C22×C9—81no—
178C22×C9—81no—
179C22×C9—81no—
180C22×C9—81no—
181C22×C9—81no—
182C4×C9—81no—
183C4×C9—81no—
184C4×C9—81no—
185C4×C9—81no—
186C4×C9—81no—
187C2×#41C22×C911yescharacteristic
188C22×Q8C22×C911yescharacteristic
189C22×Q8C22×C911yescharacteristic
190C4⋊Q8—31no—
191C4⋊Q8—31no—
192#126—32no—
193#126—32no—
194#126—31no—
195#126—31no—
196#125—31no—
197#125—31no—
198#125—32no—
199#125—31no—
200#124—31no—
201#124—31no—
202#124—31no—
203#123—32no—
204#123—31no—
205#123C22⋊C911yescharacteristic
206C22⋊Q8—32no—
207C22⋊Q8—31no—
208C22⋊Q8—31no—
209C22⋊Q8—31no—
210C22⋊Q8—31no—
211C22⋊Q8—31no—
212#121—31no—
213#121—31no—
214#121—31no—
215C4×Q8—31no—
216C4×Q8—31no—
217C4×Q8—31no—
218C4×Q8—31no—
219C4×Q8—31no—
220C4×Q8C22×C911yescharacteristic
221C4×Q8C22×C911yescharacteristic
222C4×Q8C22×C911yescharacteristic
223C4×Q8C22×C911yescharacteristic
224C4×D4—32no—
225C4×D4—31no—
226C4×D4—31no—
227C4×D4—31no—
228C4×D4—31no—
229C4×D4—31no—
230#117—32no—
231#117—31no—
232#117—31no—
233#117—31no—
234C2×C4⋊C4—31no—
235C2×C4⋊C4—31no—
236C2×C42—31no—
237C23×C3—31no—
238C23×C3C22×A411yescharacteristic
239C23×C3C22×A411yescharacteristic
240C3×Q8—31no—
241C3×Q8—61no—
242C3×Q8—61no—
243C3×Q8—61no—
244C3×Q8—61no—
245C3×Q8—121no—
246C3×Q8C3×#4111yescharacteristic
247C3×D4—22no—
248C3×D4—61no—
249C3×D4—61no—
250C3×D4—62no—
251C3×D4—121no—
252C2×C3×C4—22no—
253C2×C3×C4—31no—
254C2×C3×C4—31no—
255C2×C3×C4—31no—
256C2×C3×C4—31no—
257C2×C3×C4—31no—
258C2×C3×C4—31no—
259C2×C3×C4—31no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4—61no—
263C2×C3×C4—61no—
264C2×C3×C4—61no—
265C2×C3×C4—61no—
266C2×C3×C4—121no—
267C2×C3×C4—122no—
268C2×C3×C4C22×A411yescharacteristic
269C2×C3×C4C22×A411yescharacteristic
270C2×C3×C4C22×A411yescharacteristic
271C2×C3×C4C22×A411yescharacteristic
272C2×C3×C4C22×A411yescharacteristic
273C2×C9—41no—
274C2×C9—41no—
275C2×C9—41no—
276C2×C9—82no—
277C2×C9—161no—
278#41—21no—
279#41—61no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—31no—
283C2×Q8—31no—
284C2×Q8—31no—
285C2×Q8—61no—
286C2×Q8—61no—
287C2×Q8C23×C911yescharacteristic
288C2×D4—31no—
289C2×D4—31no—
290C2×D4—31no—
291C2×D4C2×C22⋊C911yescharacteristic
292C22×C4—31no—
293C22×C4—31no—
294C22×C4—32no—
295C22×C4—31no—
296C22×C4—31no—
297C22×C4C2×C22⋊C911yescharacteristic
298C4⋊C4—31no—
299C4⋊C4—31no—
300C4⋊C4—31no—
301C4⋊C4—31no—
302C4⋊C4—32no—
303C4⋊C4—32no—
304C4⋊C4—32no—
305C4⋊C4—31no—
306C4⋊C4—31no—
307C4⋊C4—31no—
308C4⋊C4—31no—
309C4⋊C4—31no—
310C4⋊C4—31no—
311C4⋊C4—31no—
312C4⋊C4—31no—
313C4⋊C4C2×C22⋊C911yescharacteristic
314C4⋊C4C2×C22⋊C911yescharacteristic
315C22⋊C4—32no—
316C22⋊C4—32no—
317C22⋊C4—31no—
318C22⋊C4—31no—
319C22⋊C4—31no—
320C22⋊C4—31no—
321C22⋊C4—31no—
322C22⋊C4—31no—
323C22⋊C4—31no—
324C22⋊C4C2×C22⋊C911yescharacteristic
325C22⋊C4C2×C22⋊C911yescharacteristic
326C22⋊C4C2×C22⋊C911yescharacteristic
327C42—32no—
328C42—31no—
329C42—31no—
330C42—31no—
331C42—31no—
332C42—31no—
333C42—31no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—61no—
340C22×C3—61no—
341C22×C3—61no—
342C22×C32−1+4⋊C312yes—
343C22×C3C23×A411yescharacteristic
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—31no—
350C3×C4—31no—
351C3×C4—61no—
352C3×C4—61no—
353C3×C4—61no—
354C3×C4—61no—
355C3×C4—61no—
356C3×C4—61no—
357C9—41noSylow
358C23—31no—
359C23C22×C22⋊C911yescharacteristic
360C23C22×C22⋊C911yescharacteristic
361Q8—31no—
362Q8—61no—
363Q8—61no—
364Q8—61no—
365Q8—61no—
366Q8—121no—
367Q8C9×#4111yescharacteristic
368D4—22no—
369D4—61no—
370D4—61no—
371D4—62no—
372D4—121no—
373C2×C4—22no—
374C2×C4—31no—
375C2×C4—31no—
376C2×C4—31no—
377C2×C4—31no—
378C2×C4—31no—
379C2×C4—31no—
380C2×C4—31no—
381C2×C4—61no—
382C2×C4—61no—
383C2×C4—61no—
384C2×C4—61no—
385C2×C4—61no—
386C2×C4—61no—
387C2×C4—121no—
388C2×C4—122no—
389C2×C4C22×C22⋊C911yescharacteristic
390C2×C4C22×C22⋊C911yescharacteristic
391C2×C4C22×C22⋊C911yescharacteristic
392C2×C4C22×C22⋊C911yescharacteristic
393C2×C4C22×C22⋊C911yescharacteristic
394C2×C3—22no—
395C2×C3—41no—
396C2×C3—121no—
397C2×C3A4×#4111yescharacteristic
398C2×C3C2×2−1+4⋊C311yescharacteristic
399C2×C3#594511yescharacteristic
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—61no—
406C22—61no—
407C22—61no—
408C222−1+4⋊C912yes—
409C22C23×C22⋊C911yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—31no—
416C4—31no—
417C4—61no—
418C4—61no—
419C4—61no—
420C4—61no—
421C4—61no—
422C4—61no—
423C3#3516⋊C311yescharacteristic
424C2—22no—
425C2—41no—
426C2—121no—
427C2#41×C22⋊C911yescharacteristic
428C2C2×2−1+4⋊C911yescharacteristic
429C2#1059312011yescharacteristic
subgroupG/H
center, Frattini, socleC22×C3C23×A4
commutatorC2×Q8C23×C9
Fitting, prime radicalC3×#3516C3
cosocleC2×C3×Q8C23×C3
hypercenterC3×#123A4
hypocenterQ8C9×#41
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C22×C3 ◁ C3×#123

Complements

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

NH ≅ G/Ntype
1. #557⋊C9C2semidirect
2. D4×Q8⋊C9C2semidirect
3. #548⋊C9C2semidirect
4. #548⋊C9C2semidirect
5. #520⋊C9C2semidirect
6. #519⋊C9C2semidirect
7. C2×C4×Q8⋊C9C2semidirect
43. #3516C9semidirect
104. #557C2×C9semidirect
110. #548C2×C9semidirect
111. #548C2×C9semidirect
116. #520C2×C9semidirect
117. #519C2×C9semidirect
118. C2×C4×Q8C2×C9semidirect

Maximal subgroups

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

subgroupindex
#557⋊C92
D4×Q8⋊C92
#548⋊C92
#520⋊C92
#519⋊C92
C2×C4×Q8⋊C92
C3×#35163
C9×#1234