Finite Group Databasebeta

← #11780765

Subgroups — #11780765

Order 1152.

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

normal subgroups only

This group has 403 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
2C3×#4702C211yesmaximal, characteristic, complemented
3#10590294C211yesmaximal, characteristic
4#10590291C211yesmaximal, characteristic, complemented
5#10589330C211yesmaximal, characteristic
6C3×#4465C211yesmaximal, characteristic, complemented
7#10589088C211yesmaximal, characteristic, complemented
8#71394—31nomaximal
9#68379—31nomaximal
10#64084C2211yescharacteristic
11C3×#870C2211yescharacteristic
12C3×#870C2211yescharacteristic
13C3×#869C2211yescharacteristic
14#63897—21no—
15#63895—21no—
16#63895—21no—
17#63848—21no—
18#63848—21no—
19#63840—21no—
20C32×#97C2211yescharacteristic
21#63630C2211yescharacteristic
22C3×#818—21no—
23C3×#817—21no—
24C3×#803C2211yescharacteristic
25#63567—21no—
26#63565—21no—
27#63565—21no—
28#63564—21no—
29#5699—31no—
30#5699—31no—
31C3×#501—31no—
32#5089—31no—
33#5082—31no—
34#5069—31no—
35#4714—31no—
36#4702D311yescharacteristic, complemented
37C3×#330—31no—
38#4543—31no—
39#4465—31no—
40#4465D311yescharacteristic, complemented
41#4464—31no—
42#4464—31no—
43#4464—61no—
44C2×C4⋊(C3⋊D3)D411yescharacteristic
45C2×#634D411yescharacteristic
46C2×C3×Dic6—21no—
47C2×#627—21no—
48C2×#624—21no—
49C2×C32×C8—21no—
50C32×C42C2311yescharacteristic
51#3752—21no—
52#3752—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3D411yescharacteristic
57C3×C4⋊Dic3D411yescharacteristic
58C3×C4⋊Dic3D411yescharacteristic
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—21no—
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—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—31no—
73C3×#125—31no—
74C3×#125—31no—
75#898—61no—
76#898—61no—
77#898—61no—
78#898—61no—
79#897—61no—
80#897—61no—
81#896—61no—
82#896—61no—
83#894—61no—
84#894—61no—
85#888—61no—
86#888—61no—
87#875—31no—
88#875—31no—
89#875—61no—
90#870C2×D311yescharacteristic
91#870C2×D311yescharacteristic
92#869C2×D311yescharacteristic
93C3×#107—61no—
94C3×#106—61no—
95C3×#97—21no—
96C3×#97—31no—
97C3×#97C2×D311yescharacteristic
98C3×#97C2×D311yescharacteristic
99#835—61no—
100#835—61no—
101#821—61no—
102#818—21no—
103#817—21no—
104#816—61no—
105#810—61no—
106#810—61no—
107#810—61no—
108#809—61no—
109#803—31no—
110#803—31no—
111#803—61no—
112#803C2×D311yescharacteristic
113C22×C3⋊D3—21no—
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C3⋊Dic3—21no—
118C4⋊(C3⋊D3)—41no—
119#634—41no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—41no—
125C3×Dic6—42no—
126#627—81no—
127#624—81no—
128C32×C8—22no—
129C3⋊(C3⋊C8)—41no—
130C3×C3⋊C8—41no—
131#563—91no—
132#501—31no—
133#491—91no—
134#489—91no—
135#330—31no—
136#330—91no—
137#329—91no—
138C2×C3×Q8—61no—
139C2×D12—31no—
140C2×D12—31no—
141C2×D12—61no—
142C2×C4×D3—61no—
143C2×C4×D3—61no—
144C2×Dic6—21no—
145C2×Dic6—31no—
146C2×Dic6—31no—
147C2×Dic6—61no—
148C2×Dic6—61no—
149C2×Dic6—61no—
150C2×C3×C8—21no—
151C2×C3×C8—21no—
152C2×C3×C8—41no—
153C2×C3×C8—61no—
154C3×C4⋊C4—31no—
155C3×C4⋊C4—31no—
156C3×C4⋊C4—31no—
157C3×C4⋊C4—31no—
158C3×C4⋊C4—61no—
159C3×C4⋊C4—61no—
160C3×C4⋊C4—61no—
161C3×C4⋊C4—61no—
162C3×C4⋊C4—61no—
163C3×C4⋊C4—61no—
164C3×C42—21no—
165C3×C42C22×D311yescharacteristic
166C3×C42C22×D311yescharacteristic
167(C2×D3)⋊C4—61no—
168(C2×D3)⋊C4—61no—
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—121no—
178(C2×D3)⋊C4—121no—
179C4⋊Dic3—21no—
180C4⋊Dic3—21no—
181C4⋊Dic3—61no—
182C4⋊Dic3—61no—
183C4⋊Dic3D1211yescharacteristic
184C4⋊Dic3D1211yescharacteristic
185C4⋊Dic3#6711yescharacteristic
186C4⋊Dic3#6711yescharacteristic
187Dic3⋊C4—21no—
188Dic3⋊C4—21no—
189Dic3⋊C4—21no—
190Dic3⋊C4—21no—
191Dic3⋊C4—61no—
192Dic3⋊C4—61no—
193C4×Dic3—61no—
194C4×Dic3—61no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—61no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8—121no—
199C22×C32#12011yescharacteristic
200C2×C3⋊D3—41no—
201C2×C3⋊D3—41no—
202C2×C3⋊D3—41no—
203C32×C4—21no—
204C32×C4—21no—
205C32×C4—21no—
206C3⋊Dic3—41no—
207C3×Dic3—41no—
208C3×Dic3—41no—
209C3×Dic3—41no—
210C3×Dic3—41no—
211C3×Dic3—81no—
212C4⋊Q8—31no—
213C4⋊Q8—181no—
214#126—181no—
215#126—181no—
216#125—31no—
217#125—31no—
218#124—91no—
219#123—181no—
220C22⋊Q8—181no—
221C22⋊Q8—181no—
222#107—61no—
223#106—61no—
224#103—181no—
225#103—181no—
226#103—181no—
227#102—181no—
228#97—31no—
229#97—91no—
230#97D3211yescharacteristic
231C22×D3—61no—
232C22×D3—61no—
233C22×D3—121no—
234C3×Q8—122no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—61no—
239C2×C3×C4—61no—
240C2×C3×C4—61no—
241C2×C3×C4—61no—
242C2×C3×C4—121no—
243C2×C3×C4C2×D1211yescharacteristic
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4D3×D411yescharacteristic
247C2×C3×C4D3×D411yescharacteristic
248C2×C3×C4C2×#6711yescharacteristic
249C2×Dic3—21no—
250C2×Dic3—21no—
251C2×Dic3—21no—
252C2×Dic3—21no—
253C2×Dic3—41no—
254C2×Dic3—61no—
255C2×Dic3—61no—
256C2×Dic3—121no—
257D12—121no—
258D12—121no—
259D12—241no—
260C4×D3—241no—
261C4×D3—241no—
262Dic6—42no—
263Dic6—121no—
264Dic6—121no—
265Dic6—241no—
266Dic6—241no—
267Dic6—241no—
268C3×C8—22no—
269C3×C8—22no—
270C3×C8—42no—
271C3×C8—121no—
272C3⋊C8—41no—
273C3⋊C8—121no—
274C3⋊C8—121no—
275C3⋊C8—122no—
276C2×C32#45411yescharacteristic
277C2×C32#45511yescharacteristic
278C2×C32#45611yescharacteristic
279C3⋊D3—81no—
280C2×Q8—61no—
281C2×Q8—91no—
282C2×Q8—181no—
283C2×D4—91no—
284C22×C4—181no—
285C2×C8—21no—
286C2×C8—61no—
287C2×C8—181no—
288C4⋊C4—31no—
289C4⋊C4—31no—
290C4⋊C4—31no—
291C4⋊C4—31no—
292C4⋊C4—61no—
293C4⋊C4—61no—
294C4⋊C4—61no—
295C4⋊C4—61no—
296C4⋊C4—61no—
297C4⋊C4—61no—
298C4⋊C4—181no—
299C4⋊C4—181no—
300C22⋊C4—181no—
301C22⋊C4—181no—
302C22⋊C4—181no—
303C22⋊C4—181no—
304C22⋊C4—181no—
305C42—181no—
306C42C2×D3211yescharacteristic
307C22×C3—21no—
308C22×C3#88211yescharacteristic
309C22×C3#93711yescharacteristic
310C2×D3—121no—
311C2×D3—121no—
312C2×D3—121no—
313C2×D3—121no—
314C2×D3—121no—
315C2×D3—121no—
316C2×D3—241no—
317C2×D3—241no—
318C2×D3—241no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—41no—
326C3×C4—41no—
327C3×C4—41no—
328C3×C4—121no—
329C3×C4—121no—
330C3×C4—121no—
331C3×C4—121no—
332C3×C4—241no—
333Dic3—41no—
334Dic3—41no—
335Dic3—41no—
336Dic3—41no—
337Dic3—81no—
338Dic3—121no—
339Dic3—121no—
340Dic3—241no—
341C32#166411yescharacteristic, complemented, Sylow
342C23—181no—
343Q8—122no—
344Q8—361no—
345Q8—721no—
346D4—361no—
347C2×C4—61no—
348C2×C4—61no—
349C2×C4—61no—
350C2×C4—61no—
351C2×C4—121no—
352C2×C4—181no—
353C2×C4—721no—
354C2×C4D3×D1211yescharacteristic
355C2×C4#380211yescharacteristic
356C2×C4D3×#6711yescharacteristic
357C8—22no—
358C8—121no—
359C8—361no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3#475311yescharacteristic
364C2×C3#482511yescharacteristic
365C2×C3#482611yescharacteristic
366C2×C3#509511yescharacteristic
367C2×C3#520111yescharacteristic
368C2×C3#520211yescharacteristic
369D3—241no—
370D3—241no—
371D3—481no—
372C22—361no—
373C22—361no—
374C22—361no—
375C22#6392211yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—121no—
380C4—121no—
381C4—121no—
382C4—121no—
383C4—241no—
384C4—361no—
385C3—21no—
386C3#6837911yescharacteristic, complemented
387C3#7139411yescharacteristic, complemented
388C2—721no—
389C2#1059039911yescharacteristic
390C2#1059101111yescharacteristic
391C2#1059102011yescharacteristic
subgroupG/H
centerC22#63922
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
2. C3×#4702C2semidirect
4. #10590291C2semidirect
6. C3×#4465C2semidirect
7. #10589088C2semidirect
36. #4702D3semidirect
40. #4465D3semidirect
341. C32#1664semidirect
386. C3#68379semidirect
387. C3#71394semidirect

Maximal subgroups

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

subgroupindex
#105938572
C3×#47022
#105902942
#105902912
#105893302
C3×#44652
#105890882
#713943
#683793