Finite Group Databasebeta

← #11775912

Subgroups — #11775912

Order 1152.

454 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 98 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#10593874C211yesmaximal, characteristic
2C3×#4705C211yesmaximal, characteristic
3D3×#803C211yesmaximal, characteristic
4#10589331C211yesmaximal, characteristic, complemented
5C3×#4465C211yesmaximal, characteristic, complemented
6#10589089C211yesmaximal, characteristic, complemented
7#10589088C211yesmaximal, characteristic, complemented
8#70813—31nomaximal
9#68365—31nomaximal
10#64079C2211yescharacteristic
11C3×C42×D3C2211yescharacteristic
12C3×#870C2211yescharacteristic
13#63918C411yescharacteristic
14#63918C411yescharacteristic
15#63851—21no—
16#63851—21no—
17#63841C411yescharacteristic
18#63841C411yescharacteristic
19#63837—21no—
20#63837—21no—
21C2×D3×C3⋊C8—21no—
22C32×#97C2211yescharacteristic
23#63630C2211yescharacteristic
24C3×(C2×D3)⋊C8—21no—
25C3×Dic3⋊C8—21no—
26C3×#803C2211yescharacteristic
27C3×#803C2211yescharacteristic
28#63554—21no—
29#5688—31no—
30#5470—31no—
31C3×#432—31no—
32C2×#803—31no—
33#4705D311yescharacteristic
34D3×#97—31no—
35C3×#330—31no—
36#4543—31no—
37#4465—31no—
38#4465—31no—
39#4465—31no—
40#4465—31no—
41#4465—31no—
42#4465—61no—
43#4465D311yescharacteristic, complemented
44C2×C3×C4×D3C2×C411yescharacteristic
45C2×C3×C4×D3D411yescharacteristic
46C2×C3×C4×D3D411yescharacteristic
47C2×#627—21no—
48C2×#627—21no—
49C2×C32×C8—21no—
50C32×C42C2311yescharacteristic
51C4⋊(C3⋊Dic3)C2×C411yescharacteristic
52C4⋊(C3⋊Dic3)C2×C411yescharacteristic
53#3750—21no—
54#3750—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×C4⋊Dic3C2×C411yescharacteristic
57C3×C4⋊Dic3C2×C411yescharacteristic
58C3×Dic3⋊C4—21no—
59C3×Dic3⋊C4—21no—
60C3×C4×Dic3C2×C411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C3×C4×Dic3D411yescharacteristic
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65Dic3⋊Dic3—21no—
66Dic3⋊Dic3—21no—
67(C2×D3)⋊Dic3—21no—
68(C2×D3)⋊Dic3—21no—
69Dic32—21no—
70Dic32—21no—
71D3×C3⋊C8—24no—
72#1531—91noSylow
73C3×#125—31no—
74C2×C3×C42—31no—
75#926—31no—
76#926—31no—
77#924—61no—
78#924—61no—
79C22×C3⋊C8—61no—
80C2×D3×C8—61no—
81#896—61no—
82#896—61no—
83#892—31no—
84#892—31no—
85#888—31no—
86#888—31no—
87#887—61no—
88#887—61no—
89C42×D3C2×D311yescharacteristic
90#870—31no—
91#870—31no—
92#870—61no—
93#870C2×D311yescharacteristic
94#869—31no—
95#869—31no—
96C4×Dic6—61no—
97C4×Dic6—61no—
98C3×C4⋊C8—61no—
99C3×C22⋊C8—61no—
100C3×#97—21no—
101C3×#97—31no—
102C3×#97—31no—
103C3×#97C2×D311yescharacteristic
104C3×#97C2×D311yescharacteristic
105(C2×D3)⋊C8—21no—
106#815—61no—
107Dic3⋊C8—21no—
108#803—31no—
109#803—31no—
110#803—61no—
111#803—61no—
112#803C2×D311yescharacteristic
113#803C2×D311yescharacteristic
114C22×C3×D3C22⋊C411yescharacteristic
115C2×C32×C4C22×C411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—21no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3C22⋊C411yescharacteristic
123C2×C3×Dic3C22⋊C411yescharacteristic
124C2×C3×Dic3C22⋊C411yescharacteristic
125C3×C4×D3—22no—
126C3×C4×D3—22no—
127C3×C4×D3—41no—
128#627—42no—
129#627—42no—
130C32×C8—41no—
131C3⋊(C3⋊C8)—22no—
132C3×C3⋊C8—22no—
133C3×C3⋊C8—41no—
134#533—91no—
135#432—31no—
136C2×#97—91no—
137#330—31no—
138#330—91no—
139#330—91no—
140#330—91no—
141C22×C3×C4—31no—
142C22×C3×C4—31no—
143C22×C3×C4—31no—
144C2×C4×D3C4×D311yescharacteristic
145C2×C4×D3D1211yescharacteristic
146C2×C4×D3#6711yescharacteristic
147C2×Dic6—61no—
148C2×Dic6—61no—
149C2×Dic6—61no—
150C2×Dic6—61no—
151C2×C3×C8—21no—
152C2×C3×C8—21no—
153C2×C3×C8—41no—
154C2×C3×C8—61no—
155C2×C3×C8—61no—
156C3×C4⋊C4—31no—
157C3×C4⋊C4—31no—
158C3×C4⋊C4—61no—
159C3×C4⋊C4—61no—
160C3×C42—21no—
161C3×C42—31no—
162C3×C42—31no—
163C3×C42—31no—
164C3×C42C22×D311yescharacteristic
165C3×C42C22×D311yescharacteristic
166#217—61no—
167#217—61no—
168(C2×D3)⋊C4—61no—
169(C2×D3)⋊C4—61no—
170C4⋊Dic3—31no—
171C4⋊Dic3—31no—
172C4⋊Dic3—31no—
173C4⋊Dic3—31no—
174C4⋊Dic3—61no—
175C4⋊Dic3—61no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178C4⋊Dic3C4×D311yescharacteristic
179C4⋊Dic3C4×D311yescharacteristic
180Dic3⋊C4—21no—
181Dic3⋊C4—21no—
182Dic3⋊C4—61no—
183Dic3⋊C4—61no—
184Dic3⋊C4—61no—
185Dic3⋊C4—61no—
186Dic3⋊C4—61no—
187Dic3⋊C4—61no—
188Dic3⋊C4—121no—
189Dic3⋊C4—121no—
190C4×Dic3—61no—
191C4×Dic3—61no—
192C4×Dic3—61no—
193C4×Dic3—61no—
194C4×Dic3C4×D311yescharacteristic
195C4×Dic3D1211yescharacteristic
196C4×Dic3#6711yescharacteristic
197C2×C3⋊C8—21no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—64no—
200C2×C3⋊C8—61no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—121no—
203D3×C8—64no—
204C22×C32C2×C22⋊C411yescharacteristic
205C2×C3×D3—21no—
206C2×C3×D3—21no—
207C2×C3×D3#10112yes—
208C32×C4—21no—
209C32×C4—21no—
210C32×C4—21no—
211C3⋊Dic3—41no—
212C3⋊Dic3—41no—
213C3×Dic3—21no—
214C3×Dic3—21no—
215C3×Dic3—41no—
216C3×Dic3—41no—
217C3×Dic3#10412yes—
218C22×C8—181no—
219C4⋊Q8—91no—
220C4⋊Q8—91no—
221#125—31no—
222#125—91no—
223C22⋊Q8—181no—
224C22⋊Q8—181no—
225C4×Q8—181no—
226C4×Q8—181no—
227#117—91no—
228#117—91no—
229C2×C42—31no—
230C4⋊C8—61no—
231C22⋊C8—61no—
232#97—31no—
233#97—31no—
234#97—91no—
235#97—181no—
236#97D3211yescharacteristic
237C23×C3—31no—
238C22×D3(C2×D3)⋊C411yescharacteristic
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—31no—
243C2×C3×C4—31no—
244C2×C3×C4—31no—
245C2×C3×C4—62no—
246C2×C3×C4—62no—
247C2×C3×C4—61no—
248C2×C3×C4—61no—
249C2×C3×C4—121no—
250C2×C3×C4C2×C4×D311yescharacteristic
251C2×C3×C4C2×C4×D311yescharacteristic
252C2×C3×C4C2×D1211yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4C2×#6711yescharacteristic
256C2×Dic3—21no—
257C2×Dic3—21no—
258C2×Dic3—61no—
259C2×Dic3—61no—
260C2×Dic3—61no—
261C2×Dic3—61no—
262C2×Dic3—121no—
263C2×Dic3—121no—
264C2×Dic3(C2×D3)⋊C411yescharacteristic
265C2×Dic3(C2×D3)⋊C411yescharacteristic
266C2×Dic3(C2×D3)⋊C411yescharacteristic
267C4×D3—22no—
268C4×D3—22no—
269C4×D3—41no—
270Dic6—122no—
271Dic6—122no—
272Dic6—122no—
273Dic6—122no—
274C3×C8—41no—
275C3×C8—41no—
276C3×C8—42no—
277C3×C8—62no—
278C3×C8—121no—
279C3⋊C8—22no—
280C3⋊C8—41no—
281C3⋊C8—62no—
282C3⋊C8—62no—
283C3⋊C8—122no—
284C2×C32C2×#10111yescharacteristic
285C2×C32C2×#10411yescharacteristic
286C2×C32#42111yescharacteristic
287C3×D3—22no—
288C2×Q8—181no—
289C2×Q8—181no—
290C22×C4—31no—
291C22×C4—31no—
292C22×C4—31no—
293C2×C8—21no—
294C2×C8—61no—
295C2×C8—61no—
296C2×C8—184no—
297C2×C8—181no—
298C4⋊C4—31no—
299C4⋊C4—31no—
300C4⋊C4—61no—
301C4⋊C4—61no—
302C4⋊C4—91no—
303C4⋊C4—91no—
304C4⋊C4—181no—
305C4⋊C4—181no—
306C4⋊C4—181no—
307C4⋊C4—181no—
308C22⋊C4—181no—
309C22⋊C4—181no—
310C42—31no—
311C42—31no—
312C42—31no—
313C42—181no—
314C42—181no—
315C42C2×D3211yescharacteristic
316C22×C3—21no—
317C22×C3—32no—
318C22×C3—61no—
319C22×C3—61no—
320C22×C3D3×C22⋊C411yescharacteristic
321C22×C3C2×(C2×D3)⋊C411yescharacteristic
322C2×D3—21no—
323C2×D3—21no—
324C2×D3#82412yes—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—32no—
332C3×C4—41no—
333C3×C4—41no—
334C3×C4—41no—
335C3×C4—61no—
336C3×C4—61no—
337C3×C4—121no—
338C3×C4—121no—
339Dic3—21no—
340Dic3—21no—
341Dic3—41no—
342Dic3—41no—
343Dic3—121no—
344Dic3—121no—
345Dic3—121no—
346Dic3—121no—
347Dic3—241no—
348Dic3—241no—
349Dic3#82512yes—
350C32#153111yescharacteristic, complemented, Sylow
351C23—31no—
352Q8—362no—
353Q8—362no—
354C2×C4—31no—
355C2×C4—31no—
356C2×C4—31no—
357C2×C4—62no—
358C2×C4—62no—
359C2×C4—61no—
360C2×C4—61no—
361C2×C4—121no—
362C2×C4—181no—
363C2×C4—181no—
364C2×C4C4×D3211yescharacteristic
365C2×C4D3×D1211yescharacteristic
366C2×C4D3×#6711yescharacteristic
367C8—41no—
368C8—62no—
369C8—121no—
370C8—182no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—62no—
375C2×C3D3×#10111yescharacteristic
376C2×C3D3×#10411yescharacteristic
377C2×C3#482111yescharacteristic
378C2×C3#500511yescharacteristic
379C2×C3C2×#82411yescharacteristic
380C2×C3C2×#82511yescharacteristic
381D3—22no—
382C22—32no—
383C22—61no—
384C22—61no—
385C22D3×(C2×D3)⋊C411yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—32no—
390C4—61no—
391C4—61no—
392C4—121no—
393C4—121no—
394C4—361no—
395C4—361no—
396C3—21no—
397C3#6836511yescharacteristic, complemented
398C3#7081311yescharacteristic, complemented
399C2—62no—
400C2#1059039211yescharacteristic
401C2D3×#82411yescharacteristic
402C2D3×#82511yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D3C22⋊C4
cosocleC32×C42C23
hypercenter#97D32
hypocenterC32#1531
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
4. #10589331C2semidirect
5. C3×#4465C2semidirect
6. #10589089C2semidirect
7. #10589088C2semidirect
43. #4465D3semidirect
350. C32#1531semidirect
397. C3#68365semidirect
398. C3#70813semidirect

Maximal subgroups

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

subgroupindex
#105938742
C3×#47052
D3×#8032
#105893312
C3×#44652
#105890892
#105890882
#708133
#683653