Finite Group Databasebeta

← #11780771

Subgroups — #11780771

Order 1152.

418 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 70 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#10593857C211yesmaximal, characteristic
2#10592413C211yesmaximal, characteristic
3#10590306C211yesmaximal, characteristic, complemented
4#10590295C211yesmaximal, characteristic, complemented
5C3×#4465C211yesmaximal, characteristic, complemented
6C3×#4465C211yesmaximal, characteristic, complemented
7#10589087C211yesmaximal, characteristic
8#68379—31nomaximal
9#68378—31nomaximal
10#64084C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#870C2211yescharacteristic
13C3×#870C2211yescharacteristic
14#63897—21no—
15#63895—21no—
16#63895—21no—
17#63848—21no—
18#63848—21no—
19#63840—21no—
20C32×#97C2211yescharacteristic
21#63648—21no—
22#63643—21no—
23C3×#803C2211yescharacteristic
24C3×#803C2211yescharacteristic
25#63575—21no—
26#63573—21no—
27#63567—21no—
28#63567—21no—
29#5699—31no—
30#5699—31no—
31#5069—31no—
32#5064—31no—
33#4714—31no—
34#4714—31no—
35#4714—61no—
36#4703—31no—
37#4702—31no—
38C3×#330—31no—
39C3×#330—31no—
40#4465D311yescharacteristic, complemented
41#4465D311yescharacteristic, complemented
42#4464—31no—
43#4464—31no—
44C2×C4⋊(C3⋊D3)D411yescharacteristic
45C2×#634—21no—
46C2×#634D411yescharacteristic
47C2×#627—21no—
48C2×#624—21no—
49C2×C32×C8—21no—
50C32×C42C2311yescharacteristic
51#3752—21no—
52#3752—21no—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)—21no—
55C3×C4⋊Dic3D411yescharacteristic
56C3×C4⋊Dic3D411yescharacteristic
57C3×C4⋊Dic3D411yescharacteristic
58C3×C4⋊Dic3D411yescharacteristic
59C3×Dic3⋊C4—21no—
60C3×Dic3⋊C4—21no—
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65Dic3⋊Dic3—21no—
66Dic3⋊Dic3—21no—
67#3722—21no—
68#3722—21no—
69#3722—21no—
70Dic32—21no—
71#1664—91noSylow
72C3×#125—31no—
73C3×#125—31no—
74#898—61no—
75#898—61no—
76#898—61no—
77#898—61no—
78#897—61no—
79#897—61no—
80#896—61no—
81#896—61no—
82#894—61no—
83#894—61no—
84#888—61no—
85#888—61no—
86#875—31no—
87#875—31no—
88#875—61no—
89#870C2×D311yescharacteristic
90#870C2×D311yescharacteristic
91#869—31no—
92#869—31no—
93#869—61no—
94C3×#97—21no—
95C3×#97—31no—
96C3×#97—31no—
97C3×#97C2×D311yescharacteristic
98C3×#97C2×D311yescharacteristic
99#821—61no—
100#821—61no—
101#821—62no—
102#818—61no—
103#817—61no—
104#816—61no—
105#816—61no—
106#816—62no—
107#816—61no—
108#816—61no—
109#810—61no—
110#810—61no—
111#808—61no—
112#807—61no—
113#803C2×D311yescharacteristic
114#803C2×D311yescharacteristic
115C22×C3⋊D3—21no—
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—41no—
121C4⋊(C3⋊D3)—41no—
122#634—41no—
123#634—42no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128#627—81no—
129#624—81no—
130C32×C8—41no—
131C3×C3⋊C8—22no—
132C3×C3⋊C8—41no—
133#563—91no—
134#501—91no—
135#491—91no—
136#489—91no—
137#330—31no—
138#330—31no—
139#329—91no—
140C2×D12—31no—
141C2×D12—31no—
142C2×D12—61no—
143C2×C4×D3—61no—
144C2×C4×D3—61no—
145C2×Dic6—31no—
146C2×Dic6—31no—
147C2×Dic6—61no—
148C2×Dic6—61no—
149C2×Dic6—61no—
150C2×Dic6—61no—
151C2×Dic6—61no—
152C2×Dic6—121no—
153C2×C3×C8—22no—
154C2×C3×C8—21no—
155C2×C3×C8—21no—
156C2×C3×C8—61no—
157C2×C3×C8—61no—
158C3×C4⋊C4—31no—
159C3×C4⋊C4—31no—
160C3×C4⋊C4—31no—
161C3×C4⋊C4—31no—
162C3×C4⋊C4—61no—
163C3×C4⋊C4—61no—
164C3×C4⋊C4—61no—
165C3×C4⋊C4—61no—
166C3×C42—21no—
167C3×C42C22×D311yescharacteristic
168C3×C42C22×D311yescharacteristic
169(C2×D3)⋊C4—61no—
170(C2×D3)⋊C4—61no—
171(C2×D3)⋊C4—61no—
172(C2×D3)⋊C4—61no—
173(C2×D3)⋊C4—61no—
174(C2×D3)⋊C4—61no—
175(C2×D3)⋊C4—61no—
176(C2×D3)⋊C4—61no—
177(C2×D3)⋊C4—61no—
178(C2×D3)⋊C4—61no—
179(C2×D3)⋊C4—121no—
180(C2×D3)⋊C4—121no—
181C4⋊Dic3—61no—
182C4⋊Dic3—61no—
183C4⋊Dic3—62no—
184C4⋊Dic3—61no—
185C4⋊Dic3—61no—
186C4⋊Dic3—61no—
187C4⋊Dic3—61no—
188C4⋊Dic3—121no—
189C4⋊Dic3D1211yescharacteristic
190C4⋊Dic3D1211yescharacteristic
191C4⋊Dic3D1211yescharacteristic
192C4⋊Dic3D1211yescharacteristic
193Dic3⋊C4—21no—
194Dic3⋊C4—21no—
195Dic3⋊C4—21no—
196Dic3⋊C4—21no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199C4×Dic3—61no—
200C4×Dic3—61no—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—21no—
203C22×C32#12011yescharacteristic
204C2×C3⋊D3—41no—
205C2×C3⋊D3—41no—
206C2×C3⋊D3—41no—
207C32×C4—21no—
208C32×C4—21no—
209C32×C4—21no—
210C3⋊Dic3—41no—
211C3⋊Dic3—81no—
212C3×Dic3—41no—
213C3×Dic3—41no—
214C3×Dic3—41no—
215C3×Dic3—41no—
216C4⋊Q8—91no—
217C4⋊Q8—181no—
218#126—181no—
219#126—181no—
220#125—31no—
221#125—31no—
222#124—91no—
223#123—181no—
224C22⋊Q8—181no—
225C22⋊Q8—181no—
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#97D3211yescharacteristic
235C22×D3—61no—
236C22×D3—61no—
237C22×D3—121no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—61no—
242C2×C3×C4—61no—
243C2×C3×C4—61no—
244C2×C3×C4—61no—
245C2×C3×C4C2×D1211yescharacteristic
246C2×C3×C4C2×D1211yescharacteristic
247C2×C3×C4D3×D411yescharacteristic
248C2×C3×C4D3×D411yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×Dic3—21no—
252C2×Dic3—21no—
253C2×Dic3—21no—
254C2×Dic3—21no—
255C2×Dic3—61no—
256C2×Dic3—61no—
257C2×Dic3—121no—
258C2×Dic3—122no—
259C2×Dic3—121no—
260C2×Dic3—121no—
261D12—121no—
262D12—121no—
263D12—122no—
264C4×D3—241no—
265C4×D3—241no—
266Dic6—121no—
267Dic6—121no—
268Dic6—122no—
269Dic6—122no—
270Dic6—122no—
271Dic6—242no—
272Dic6—241no—
273Dic6—241no—
274C3×C8—42no—
275C3×C8—41no—
276C3×C8—41no—
277C3×C8—62no—
278C3×C8—121no—
279C3⋊C8—22no—
280C3⋊C8—41no—
281C2×C32#45411yescharacteristic
282C2×C32#45511yescharacteristic
283C2×C32#45611yescharacteristic
284C3⋊D3—81no—
285C2×Q8—91no—
286C2×Q8—181no—
287C2×Q8—181no—
288C2×D4—91no—
289C22×C4—181no—
290C2×C8—21no—
291C2×C8—61no—
292C2×C8—61no—
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—181no—
302C4⋊C4—181no—
303C4⋊C4—181no—
304C4⋊C4—181no—
305C22⋊C4—181no—
306C22⋊C4—181no—
307C22⋊C4—181no—
308C22⋊C4—181no—
309C22⋊C4—181no—
310C42—181no—
311C42C2×D3211yescharacteristic
312C22×C3—21no—
313C22×C3#88211yescharacteristic
314C22×C3#88211yescharacteristic
315C2×D3—121no—
316C2×D3—121no—
317C2×D3—121no—
318C2×D3—121no—
319C2×D3—121no—
320C2×D3—121no—
321C2×D3—241no—
322C2×D3—241no—
323C2×D3—241no—
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—121no—
334C3×C4—121no—
335C3×C4—121no—
336C3×C4—121no—
337Dic3—41no—
338Dic3—41no—
339Dic3—41no—
340Dic3—41no—
341Dic3—121no—
342Dic3—121no—
343Dic3—241no—
344Dic3—242no—
345Dic3—241no—
346Dic3—241no—
347C32#166411yescharacteristic, complemented, Sylow
348C23—181no—
349Q8—361no—
350Q8—362no—
351Q8—721no—
352D4—361no—
353C2×C4—61no—
354C2×C4—61no—
355C2×C4—61no—
356C2×C4—61no—
357C2×C4—181no—
358C2×C4—361no—
359C2×C4—721no—
360C2×C4D3×D1211yescharacteristic
361C2×C4D3×D1211yescharacteristic
362C2×C4#381111yescharacteristic
363C8—41no—
364C8—62no—
365C8—121no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3#475211yescharacteristic
370C2×C3#475311yescharacteristic
371C2×C3#482511yescharacteristic
372C2×C3#482511yescharacteristic
373C2×C3#482611yescharacteristic
374C2×C3#482711yescharacteristic
375D3—241no—
376D3—241no—
377D3—481no—
378C22—361no—
379C22—361no—
380C22—361no—
381C22#6392311yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—121no—
386C4—121no—
387C4—121no—
388C4—121no—
389C4—361no—
390C4—721no—
391C3—21no—
392C3#6837811yescharacteristic, complemented
393C3#6837911yescharacteristic, complemented
394C2—721no—
395C2#1059039811yescharacteristic
396C2#1059102111yescharacteristic
397C2#1059102211yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32#120
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenter#97D32
hypocenterC32#1664
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
3. #10590306C2semidirect
4. #10590295C2semidirect
5. C3×#4465C2semidirect
6. C3×#4465C2semidirect
40. #4465D3semidirect
41. #4465D3semidirect
347. C32#1664semidirect
392. C3#68378semidirect
393. C3#68379semidirect

Maximal subgroups

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

subgroupindex
#105938572
#105924132
#105903062
#105902952
C3×#44652
#105890872
#683793
#683783