Finite Group Databasebeta

← #11780753

Subgroups — #11780753

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#10592788C211yesmaximal, characteristic
3C3×#5082C211yesmaximal, characteristic, complemented
4C3×#5081C211yesmaximal, characteristic, complemented
5#10589088C211yesmaximal, characteristic, complemented
6#10589088C211yesmaximal, characteristic, complemented
7#10589087C211yesmaximal, characteristic
8#71394—31nomaximal
9#71253—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64084C2211yescharacteristic
12C3×#870C2211yescharacteristic
13C3×#870C2211yescharacteristic
14#63897—21no—
15#63895—21no—
16#63895—21no—
17#63848—21no—
18#63848—21no—
19#63840—21no—
20#63637—21no—
21#63636—21no—
22#63630C2211yescharacteristic
23C3×#835—21no—
24C3×#835—21no—
25C3×#808—21no—
26C3×#807—21no—
27C3×#803C2211yescharacteristic
28C3×#803C2211yescharacteristic
29#5699—31no—
30#5699—31no—
31C3×#501—31no—
32C3×#491—31no—
33#5089—31no—
34#5089—31no—
35#5089—61no—
36#5082D311yescharacteristic, complemented
37#5081D311yescharacteristic, complemented
38#4543—31no—
39#4543—31no—
40#4465—31no—
41#4465—31no—
42#4464—31no—
43#4464—31no—
44C2×C32×Q8—21no—
45C2×C4⋊(C3⋊D3)D411yescharacteristic
46C2×#634D411yescharacteristic
47C2×#627—21no—
48C2×#624—21no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4—21no—
51C32×C42C2311yescharacteristic
52#3752—21no—
53#3752—21no—
54C2×C3⋊(C3⋊C8)—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×C4⋊Q8—21no—
73C3×C4⋊Q8C2×D311yescharacteristic
74C3×C4⋊Q8C2×D311yescharacteristic
75C3×#125—31no—
76C3×#125—31no—
77#898—61no—
78#898—61no—
79#898—61no—
80#898—61no—
81#897—61no—
82#897—61no—
83#896—61no—
84#896—61no—
85#894—61no—
86#894—61no—
87#888—61no—
88#888—61no—
89#875—31no—
90#875—31no—
91#875—61no—
92#870C2×D311yescharacteristic
93#870C2×D311yescharacteristic
94C3×#107—61no—
95C3×#106—61no—
96C3×#103—61no—
97C3×#103—61no—
98C3×#97—31no—
99C3×#97—31no—
100#835—21no—
101#835—21no—
102#810—61no—
103#810—61no—
104#810—62no—
105#809—61no—
106#809—61no—
107#809—62no—
108#808—21no—
109#807—21no—
110#803—31no—
111#803—31no—
112#803—61no—
113#803C2×D311yescharacteristic
114#803C2×D311yescharacteristic
115C22×C3⋊D3—21no—
116C32×Q8—42no—
117C2×C32×C4—41no—
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C3⋊Dic3—21no—
122C4⋊(C3⋊D3)—41no—
123#634—41no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128#627—81no—
129#624—81no—
130C3⋊(C3⋊C8)—41no—
131C3×C3⋊C8—22no—
132C3×C3⋊C8—41no—
133#563—91no—
134#501—31no—
135#491—31no—
136#489—91no—
137#330—91no—
138#330—91no—
139#329—91no—
140C2×C3×Q8—21no—
141C2×C3×Q8—21no—
142C2×C3×Q8—41no—
143C2×D12—31no—
144C2×D12—31no—
145C2×D12—61no—
146C2×C4×D3—61no—
147C2×C4×D3—61no—
148C2×Dic6—31no—
149C2×Dic6—31no—
150C2×Dic6—61no—
151C2×Dic6—61no—
152C2×Dic6—61no—
153C2×C3×C8—61no—
154C2×C3×C8—61no—
155C3×C4⋊C4—22no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4—21no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4—31no—
161C3×C4⋊C4—31no—
162C3×C4⋊C4—31no—
163C3×C4⋊C4—31no—
164C3×C4⋊C4—41no—
165C3×C4⋊C4—61no—
166C3×C4⋊C4—61no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4—61no—
169C3×C42—21no—
170C3×C42C22×D311yescharacteristic
171C3×C42C22×D311yescharacteristic
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—61no—
180(C2×D3)⋊C4—61no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4—121no—
183(C2×D3)⋊C4—121no—
184C4⋊Dic3—61no—
185C4⋊Dic3—61no—
186C4⋊Dic3#6711yescharacteristic
187C4⋊Dic3#6711yescharacteristic
188C4⋊Dic3#6711yescharacteristic
189C4⋊Dic3#6711yescharacteristic
190Dic3⋊C4—21no—
191Dic3⋊C4—21no—
192Dic3⋊C4—21no—
193Dic3⋊C4—21no—
194Dic3⋊C4—61no—
195Dic3⋊C4—61no—
196C4×Dic3—61no—
197C4×Dic3—61no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—62no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—61no—
203C22×C32#12011yescharacteristic
204C2×C3⋊D3—41no—
205C2×C3⋊D3—41no—
206C2×C3⋊D3—41no—
207C32×C4—21no—
208C32×C4—21no—
209C32×C4—21no—
210C32×C4—81no—
211C3⋊Dic3—41no—
212C3×Dic3—41no—
213C3×Dic3—41no—
214C3×Dic3—41no—
215C3×Dic3—41no—
216C4⋊Q8—181no—
217C4⋊Q8D3211yescharacteristic
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—61no—
227#106—61no—
228#103—61no—
229#103—61no—
230#103—181no—
231#102—181no—
232#97—31no—
233#97—31no—
234#97—91no—
235C22×D3—61no—
236C22×D3—61no—
237C22×D3—121no—
238C3×Q8—42no—
239C3×Q8—42no—
240C3×Q8—82no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—42no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—61no—
248C2×C3×C4—61no—
249C2×C3×C4—61no—
250C2×C3×C4—61no—
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4C2×#6711yescharacteristic
256C2×C3×C4C2×#6711yescharacteristic
257C2×Dic3—21no—
258C2×Dic3—21no—
259C2×Dic3—21no—
260C2×Dic3—21no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—121no—
264D12—121no—
265D12—121no—
266D12—122no—
267C4×D3—241no—
268C4×D3—241no—
269Dic6—121no—
270Dic6—121no—
271Dic6—122no—
272Dic6—241no—
273Dic6—241no—
274C3×C8—62no—
275C3×C8—121no—
276C3⋊C8—22no—
277C3⋊C8—41no—
278C3⋊C8—122no—
279C3⋊C8—121no—
280C3⋊C8—121no—
281C2×C32#45411yescharacteristic
282C2×C32#45511yescharacteristic
283C2×C32#45611yescharacteristic
284C3⋊D3—81no—
285C2×Q8—21no—
286C2×Q8—91no—
287C2×Q8—181no—
288C2×D4—91no—
289C22×C4—181no—
290C2×C8—61no—
291C2×C8—61no—
292C2×C8—181no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—31no—
296C4⋊C4—31no—
297C4⋊C4—31no—
298C4⋊C4—31no—
299C4⋊C4—61no—
300C4⋊C4—61no—
301C4⋊C4—61no—
302C4⋊C4—61no—
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#93711yescharacteristic
314C22×C3#93711yescharacteristic
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—82no—
334C3×C4—81no—
335C3×C4—81no—
336C3×C4—121no—
337C3×C4—121no—
338C3×C4—121no—
339C3×C4—121no—
340Dic3—41no—
341Dic3—41no—
342Dic3—41no—
343Dic3—41no—
344Dic3—121no—
345Dic3—121no—
346Dic3—241no—
347C32#166411yescharacteristic, complemented, Sylow
348C23—181no—
349Q8—42no—
350Q8—361no—
351Q8—721no—
352D4—361no—
353C2×C4—41no—
354C2×C4—61no—
355C2×C4—61no—
356C2×C4—61no—
357C2×C4—61no—
358C2×C4—181no—
359C2×C4—721no—
360C2×C4D3×#6711yescharacteristic
361C2×C4D3×#6711yescharacteristic
362C2×C4#381111yescharacteristic
363C8—62no—
364C8—121no—
365C8—361no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3#506211yescharacteristic
370C2×C3#509511yescharacteristic
371C2×C3#520111yescharacteristic
372C2×C3#520211yescharacteristic
373C2×C3#520211yescharacteristic
374C2×C3#520511yescharacteristic
375D3—241no—
376D3—241no—
377D3—481no—
378C22—361no—
379C22—361no—
380C22—361no—
381C22#6398311yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—81no—
386C4—121no—
387C4—121no—
388C4—121no—
389C4—121no—
390C4—361no—
391C3—21no—
392C3#7125311yescharacteristic, complemented
393C3#7139411yescharacteristic, complemented
394C2—721no—
395C2#1059152511yescharacteristic
396C2#1059165811yescharacteristic
397C2#1059166111yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#120
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4⋊Q8D32
hypocenterC32#1664
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. C3×#5082C2semidirect
4. C3×#5081C2semidirect
5. #10589088C2semidirect
6. #10589088C2semidirect
36. #5082D3semidirect
37. #5081D3semidirect
347. C32#1664semidirect
392. C3#71253semidirect
393. C3#71394semidirect

Maximal subgroups

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

subgroupindex
#105938572
#105927882
C3×#50822
C3×#50812
#105890882
#105890872
#713943
#712533