Finite Group Databasebeta

← #11780766

Subgroups — #11780766

Order 1152.

418 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C3×#5672C211yesmaximal, characteristic
2#10592754C211yesmaximal, characteristic
3#10590306C211yesmaximal, characteristic, complemented
4#10590295C211yesmaximal, characteristic, complemented
5C3×#4540C211yesmaximal, characteristic
6#10589088C211yesmaximal, characteristic, complemented
7#10589088C211yesmaximal, characteristic, complemented
8#71957—31nomaximal
9#68359—31nomaximal
10C32×#124C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#944—21no—
13C3×#935—21no—
14C3×#879—21no—
15C3×#879—21no—
16C3×#878—21no—
17C3×#878—21no—
18C3×#870C2211yescharacteristic
19C3×#870C2211yescharacteristic
20#63662—21no—
21#63659—21no—
22#63630C2211yescharacteristic
23C3×#803C2211yescharacteristic
24C3×#803C2211yescharacteristic
25#63575—21no—
26#63573—21no—
27#63567—21no—
28#63567—21no—
29C3×#563—31no—
30#5672D311yescharacteristic
31#5069—31no—
32#5064—31no—
33#5055—31no—
34#5055—31no—
35#5055—61no—
36#4703—31no—
37#4702—31no—
38C3×#329—31no—
39#4543—31no—
40#4543—31no—
41#4540D311yescharacteristic
42#4465—31no—
43#4465—31no—
44C2×C32×Q8D411yescharacteristic
45C2×C32×D4D411yescharacteristic
46C2×#634—21no—
47C22×C3×Dic3—21no—
48C2×C3×Dic6—21no—
49C32×C22⋊C4—21no—
50C32×C22⋊C4—21no—
51C32×C42C2311yescharacteristic
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C3×#217—21no—
56C3×#217—21no—
57C3×#217—21no—
58C3×C4⋊Dic3D411yescharacteristic
59C3×C4⋊Dic3D411yescharacteristic
60C3×C4⋊Dic3D411yescharacteristic
61C3×C4⋊Dic3D411yescharacteristic
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—21no—
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×C4×Dic3—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71#1664—91noSylow
72C3×C4⋊Q8—61no—
73C3×#126—61no—
74C3×#126—61no—
75C3×#125—31no—
76C3×#125—31no—
77C3×#124—21no—
78C3×#124C2×D311yescharacteristic
79C3×#124C2×D311yescharacteristic
80C3×#123—61no—
81C3×C22⋊Q8—61no—
82C3×C22⋊Q8—61no—
83#944—21no—
84#935—21no—
85#879—21no—
86#879—21no—
87#878—21no—
88#878—21no—
89#870C2×D311yescharacteristic
90#870C2×D311yescharacteristic
91#869—31no—
92#869—31no—
93#869—61no—
94C3×#97—31no—
95C3×#97—31no—
96#835—62no—
97#835—61no—
98#835—61no—
99#832—62no—
100#832—61no—
101#832—61no—
102#818—61no—
103#817—61no—
104#816—61no—
105#816—61no—
106#810—61no—
107#810—61no—
108#808—61no—
109#807—61no—
110#803—31no—
111#803—31no—
112#803—61no—
113#803C2×D311yescharacteristic
114#803C2×D311yescharacteristic
115C23×C32—21no—
116C32×Q8—41no—
117C32×D4—41no—
118C2×C32×C4—21no—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C3⋊Dic3—41no—
123#634—42no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—81no—
129C3×Dic6—81no—
130C3⋊(C3⋊C8)—41no—
131C3×C3⋊C8—22no—
132C3×C3⋊C8—41no—
133#563—31no—
134#501—91no—
135#491—91no—
136#489—91no—
137#330—91no—
138#330—91no—
139#329—31no—
140C2×C3×Q8—21no—
141C2×C3×Q8—61no—
142C2×C3×Q8D1211yescharacteristic
143C2×C3×Q8#6711yescharacteristic
144C2×C3×D4—21no—
145C2×C3×D4D1211yescharacteristic
146C2×C3×D4#6711yescharacteristic
147C22×C3×C4—61no—
148C22×Dic3—21no—
149C2×Dic6—21no—
150C2×Dic6—61no—
151C2×Dic6—61no—
152C2×Dic6—121no—
153C2×C3×C8—61no—
154C2×C3×C8—61no—
155C3×C4⋊C4—31no—
156C3×C4⋊C4—31no—
157C3×C4⋊C4—31no—
158C3×C4⋊C4—31no—
159C3×C4⋊C4—61no—
160C3×C4⋊C4—61no—
161C3×C4⋊C4—61no—
162C3×C4⋊C4—61no—
163C3×C4⋊C4—61no—
164C3×C4⋊C4—61no—
165C3×C22⋊C4—21no—
166C3×C22⋊C4—21no—
167C3×C22⋊C4—21no—
168C3×C22⋊C4—21no—
169C3×C22⋊C4—41no—
170C3×C22⋊C4—41no—
171C3×C22⋊C4—61no—
172C3×C22⋊C4—61no—
173C3×C22⋊C4—61no—
174C3×C42—21no—
175C3×C42—61no—
176C3×C42C22×D311yescharacteristic
177C3×C42C22×D311yescharacteristic
178#217—21no—
179#217—21no—
180#217—21no—
181C4⋊Dic3—62no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C4⋊Dic3—61no—
185C4⋊Dic3—61no—
186C4⋊Dic3—121no—
187C4⋊Dic3#6711yescharacteristic
188C4⋊Dic3#6711yescharacteristic
189C4⋊Dic3#6711yescharacteristic
190C4⋊Dic3#6711yescharacteristic
191Dic3⋊C4—21no—
192Dic3⋊C4—21no—
193Dic3⋊C4—21no—
194Dic3⋊C4—21no—
195Dic3⋊C4—21no—
196Dic3⋊C4—21no—
197C4×Dic3—21no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—62no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—61no—
203C22×C32—41no—
204C22×C32—41no—
205C22×C32—41no—
206C22×C32#12011yescharacteristic
207C32×C4—21no—
208C32×C4—21no—
209C32×C4—21no—
210C32×C4—41no—
211C3⋊Dic3—81no—
212C3×Dic3—41no—
213C3×Dic3—41no—
214C3×Dic3—41no—
215C3×Dic3—41no—
216C4⋊Q8—61no—
217C4⋊Q8—91no—
218#126—61no—
219#126—61no—
220#125—31no—
221#125—31no—
222#124D3211yescharacteristic
223#123—61no—
224C22⋊Q8—61no—
225C22⋊Q8—61no—
226#107—181no—
227#106—181no—
228#103—181no—
229#103—181no—
230#103—181no—
231#102—181no—
232#97—31no—
233#97—31no—
234#97—91no—
235C23×C3—21no—
236C23×C3—21no—
237C23×C3—41no—
238C3×Q8—41no—
239C3×Q8—41no—
240C3×Q8—42no—
241C3×Q8—241no—
242C3×D4—41no—
243C3×D4—41no—
244C3×D4—42no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—41no—
251C2×C3×C4—61no—
252C2×C3×C4—61no—
253C2×C3×C4—61no—
254C2×C3×C4—61no—
255C2×C3×C4—241no—
256C2×C3×C4C2×D1211yescharacteristic
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4D3×D411yescharacteristic
259C2×C3×C4C2×#6711yescharacteristic
260C2×C3×C4C2×#6711yescharacteristic
261C2×C3×C4C2×#6711yescharacteristic
262C2×Dic3—21no—
263C2×Dic3—21no—
264C2×Dic3—21no—
265C2×Dic3—21no—
266C2×Dic3—81no—
267C2×Dic3—122no—
268C2×Dic3—121no—
269C2×Dic3—121no—
270Dic6—81no—
271Dic6—122no—
272Dic6—122no—
273Dic6—242no—
274C3×C8—62no—
275C3×C8—121no—
276C3⋊C8—22no—
277C3⋊C8—41no—
278C3⋊C8—122no—
279C3⋊C8—121no—
280C3⋊C8—121no—
281C2×C32—81no—
282C2×C32#45411yescharacteristic
283C2×C32#45511yescharacteristic
284C2×C32#45611yescharacteristic
285C2×Q8—61no—
286C2×Q8—181no—
287C2×Q8#62611yescharacteristic
288C2×D4#62611yescharacteristic
289C22×C4—61no—
290C2×C8—61no—
291C2×C8—61no—
292C2×C8—181no—
293C4⋊C4—31no—
294C4⋊C4—31no—
295C4⋊C4—31no—
296C4⋊C4—31no—
297C4⋊C4—61no—
298C4⋊C4—61no—
299C4⋊C4—61no—
300C4⋊C4—61no—
301C4⋊C4—61no—
302C4⋊C4—61no—
303C4⋊C4—181no—
304C4⋊C4—181no—
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—61no—
308C22⋊C4—61no—
309C22⋊C4—61no—
310C42—61no—
311C42C2×D3211yescharacteristic
312C22×C3—21no—
313C22×C3—41no—
314C22×C3—41no—
315C22×C3—41no—
316C22×C3—41no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3—81no—
320C22×C3—81no—
321C22×C3—81no—
322C22×C3#88211yescharacteristic
323C22×C3#95311yescharacteristic
324C3×C4—22no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—41no—
332C3×C4—41no—
333C3×C4—41no—
334C3×C4—41no—
335C3×C4—81no—
336C3×C4—121no—
337C3×C4—121no—
338C3×C4—121no—
339C3×C4—121no—
340Dic3—41no—
341Dic3—41no—
342Dic3—41no—
343Dic3—41no—
344Dic3—242no—
345Dic3—241no—
346Dic3—241no—
347C32#166411yescharacteristic, complemented, Sylow
348C23—21no—
349Q8—41no—
350Q8—241no—
351Q8—362no—
352D4—41no—
353C2×C4—21no—
354C2×C4—61no—
355C2×C4—61no—
356C2×C4—61no—
357C2×C4—61no—
358C2×C4—241no—
359C2×C4—361no—
360C2×C4C2×#62611yescharacteristic
361C2×C4D3×#6711yescharacteristic
362C2×C4D3×#6711yescharacteristic
363C8—62no—
364C8—121no—
365C8—361no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—81no—
370C2×C3—81no—
371C2×C3—161no—
372C2×C3#474611yescharacteristic
373C2×C3#482611yescharacteristic
374C2×C3#482711yescharacteristic
375C2×C3#524211yescharacteristic
376C2×C3#524511yescharacteristic
377C2×C3#524611yescharacteristic
378C22—41no—
379C22—41no—
380C22—41no—
381C22#6397711yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—41no—
386C4—121no—
387C4—121no—
388C4—121no—
389C4—121no—
390C4—721no—
391C3—21no—
392C3#6835911yescharacteristic, complemented
393C3#7195711yescharacteristic, complemented
394C2—81no—
395C2#1059151311yescharacteristic
396C2#1059168511yescharacteristic
397C2#1059168911yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#124C22
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenter#124D32
hypocenterC32#1664
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
3. #10590306C2semidirect
4. #10590295C2semidirect
6. #10589088C2semidirect
7. #10589088C2semidirect
347. C32#1664semidirect
392. C3#68359semidirect
393. C3#71957semidirect

Maximal subgroups

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

subgroupindex
C3×#56722
#105927542
#105903062
#105902952
C3×#45402
#105890882
#719573
#683593