Finite Group Databasebeta

← #11780770

Subgroups — #11780770

Order 1152.

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

normal subgroups only

This group has 398 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#10593952C211yesmaximal, characteristic
2C3×#4714C211yesmaximal, characteristic
3#10590305C211yesmaximal, characteristic, complemented
4#10590291C211yesmaximal, characteristic, complemented
5#10589331C211yesmaximal, characteristic, complemented
6C3×#4465C211yesmaximal, characteristic, complemented
7#10589086C211yesmaximal, characteristic
8#71247—31nomaximal
9#68379—31nomaximal
10#64079C2211yescharacteristic
11C3×#875C2211yescharacteristic
12C3×#870C2211yescharacteristic
13C3×#869C2211yescharacteristic
14#63899—21no—
15#63893—21no—
16#63884—21no—
17#63861—21no—
18#63858—21no—
19#63839—21no—
20C32×#97C2211yescharacteristic
21#63630C2211yescharacteristic
22C3×#821—21no—
23C3×#816—21no—
24C3×#803C2211yescharacteristic
25#63575—21no—
26#63573—21no—
27#63565—21no—
28#63565—21no—
29#5699—31no—
30#5672—31no—
31C3×#489—31no—
32#5082—31no—
33#5081—31no—
34#5069—31no—
35#4714D311yescharacteristic
36#4702—31no—
37C3×#330—31no—
38#4540—31no—
39#4465—31no—
40#4465—31no—
41#4465—61no—
42#4465D311yescharacteristic, complemented
43#4464—31no—
44C2×C3×D12D411yescharacteristic
45C2×C3×Dic6—21no—
46C2×C3×Dic6D411yescharacteristic
47C2×#627—21no—
48C2×D3×Dic3—21no—
49C2×C32×C8—21no—
50C32×C42C2311yescharacteristic
51C4⋊(C3⋊Dic3)D411yescharacteristic
52C4⋊(C3⋊Dic3)D411yescharacteristic
53#3750—21no—
54#3750—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×(C2×D3)⋊C4—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×C4⋊Dic3D411yescharacteristic
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C2×C3×C3⋊C8—21no—
65#3724—21no—
66Dic3⋊Dic3—21no—
67(C2×D3)⋊Dic3—21no—
68(C2×D3)⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70Dic32—21no—
71#1664—91noSylow
72C3×C4⋊Q8—31no—
73C3×#125—31no—
74C3×#124—31no—
75#944—61no—
76#935—61no—
77#898—61no—
78#898—61no—
79#897—61no—
80#896—61no—
81#894—61no—
82#888—61no—
83#879—61no—
84#879—61no—
85#878—61no—
86#878—61no—
87#875C2×D311yescharacteristic
88#870—31no—
89#870—31no—
90#870—61no—
91#870C2×D311yescharacteristic
92#869C2×D311yescharacteristic
93C3×#103—61no—
94C3×#102—61no—
95C3×#97—21no—
96C3×#97—31no—
97C3×#97C2×D311yescharacteristic
98C3×#97C2×D311yescharacteristic
99#835—61no—
100#835—61no—
101#821—21no—
102#818—61no—
103#817—61no—
104#816—21no—
105#810—61no—
106#810—61no—
107#808—61no—
108#807—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—
118C2×C3⋊Dic3—21no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—41no—
123C3×D12—41no—
124C3×Dic6—41no—
125C3×Dic6—42no—
126#627—81no—
127D3×Dic3—81no—
128C32×C8—41no—
129C3⋊(C3⋊C8)—41no—
130C3×C3⋊C8—22no—
131#563—91no—
132#501—91no—
133#491—91no—
134#489—31no—
135#330—31no—
136#330—91no—
137#329—91no—
138C2×C3×Q8—31no—
139C2×C3×Q8—61no—
140C2×C3×D4—31no—
141C22×Dic3—61no—
142C2×D12#6711yescharacteristic
143C2×C4×D3—61no—
144C2×Dic6—21no—
145C2×Dic6—61no—
146C2×Dic6—61no—
147C2×Dic6#6711yescharacteristic
148C2×C3×C8—21no—
149C2×C3×C8—21no—
150C2×C3×C8—41no—
151C2×C3×C8—61no—
152C3×C4⋊C4—31no—
153C3×C4⋊C4—31no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—61no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4—61no—
158C3×C22⋊C4—61no—
159C3×C22⋊C4—61no—
160C3×C42—21no—
161C3×C42C22×D311yescharacteristic
162C3×C42C22×D311yescharacteristic
163#217—61no—
164#217—61no—
165#217—61no—
166(C2×D3)⋊C4—21no—
167(C2×D3)⋊C4—21no—
168(C2×D3)⋊C4—61no—
169(C2×D3)⋊C4—61no—
170(C2×D3)⋊C4—61no—
171C4⋊Dic3—21no—
172C4⋊Dic3—21no—
173C4⋊Dic3—31no—
174C4⋊Dic3—31no—
175C4⋊Dic3—31no—
176C4⋊Dic3—31no—
177C4⋊Dic3—61no—
178C4⋊Dic3—61no—
179C4⋊Dic3—61no—
180C4⋊Dic3D1211yescharacteristic
181C4⋊Dic3D1211yescharacteristic
182Dic3⋊C4—21no—
183Dic3⋊C4—21no—
184Dic3⋊C4—61no—
185Dic3⋊C4—61no—
186Dic3⋊C4—61no—
187Dic3⋊C4—61no—
188Dic3⋊C4—61no—
189Dic3⋊C4—61no—
190Dic3⋊C4—61no—
191Dic3⋊C4—121no—
192Dic3⋊C4—121no—
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—91no—
218#124—31no—
219#123—181no—
220C22⋊Q8—181no—
221C22⋊Q8—181no—
222#107—181no—
223#106—181no—
224#103—61no—
225#103—181no—
226#103—181no—
227#102—61no—
228#97—31no—
229#97—91no—
230#97D3211yescharacteristic
231C23×C3—61no—
232C22×D3—21no—
233C3×Q8—121no—
234C3×Q8—122no—
235C3×D4—121no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
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—41no—
253C2×Dic3—61no—
254C2×Dic3—61no—
255C2×Dic3—61no—
256C2×Dic3—61no—
257C2×Dic3—121no—
258C2×Dic3—121no—
259C2×Dic3—241no—
260D12—41no—
261C4×D3—241no—
262Dic6—41no—
263Dic6—42no—
264Dic6—241no—
265Dic6—241no—
266C3×C8—41no—
267C3×C8—41no—
268C3×C8—42no—
269C3×C8—62no—
270C3⋊C8—22no—
271C3⋊C8—121no—
272C3⋊C8—121no—
273C3⋊C8—122no—
274C2×C32#45411yescharacteristic
275C2×C32#45511yescharacteristic
276C2×C32#45611yescharacteristic
277C3×D3—81no—
278C2×Q8—31no—
279C2×Q8—61no—
280C2×Q8—181no—
281C2×D4—31no—
282C22×C4—181no—
283C2×C8—21no—
284C2×C8—61no—
285C2×C8—181no—
286C4⋊C4—31no—
287C4⋊C4—31no—
288C4⋊C4—61no—
289C4⋊C4—61no—
290C4⋊C4—61no—
291C4⋊C4—61no—
292C4⋊C4—91no—
293C4⋊C4—91no—
294C4⋊C4—181no—
295C4⋊C4—181no—
296C4⋊C4—181no—
297C4⋊C4—181no—
298C22⋊C4—61no—
299C22⋊C4—61no—
300C22⋊C4—181no—
301C22⋊C4—181no—
302C22⋊C4—181no—
303C42—181no—
304C42C2×D3211yescharacteristic
305C22×C3—21no—
306C22×C3—121no—
307C22×C3—121no—
308C22×C3—121no—
309C22×C3#88211yescharacteristic
310C22×C3#93711yescharacteristic
311C2×D3—41no—
312C2×D3—41no—
313C2×D3—41no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—41no—
321C3×C4—41no—
322C3×C4—41no—
323C3×C4—121no—
324C3×C4—121no—
325C3×C4—121no—
326C3×C4—241no—
327Dic3—41no—
328Dic3—41no—
329Dic3—41no—
330Dic3—81no—
331Dic3—121no—
332Dic3—121no—
333Dic3—121no—
334Dic3—121no—
335Dic3—241no—
336Dic3—241no—
337C32#166411yescharacteristic, complemented, Sylow
338C23—61no—
339Q8—121no—
340Q8—122no—
341Q8—721no—
342D4—121no—
343C2×C4—61no—
344C2×C4—61no—
345C2×C4—61no—
346C2×C4—121no—
347C2×C4—181no—
348C2×C4—181no—
349C2×C4—721no—
350C2×C4D3×D1211yescharacteristic
351C2×C4#380211yescharacteristic
352C2×C4D3×#6711yescharacteristic
353C8—41no—
354C8—62no—
355C8—361no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—241no—
360C2×C3#475311yescharacteristic
361C2×C3#482511yescharacteristic
362C2×C3#482611yescharacteristic
363C2×C3#506111yescharacteristic
364C2×C3#520111yescharacteristic
365C2×C3#520511yescharacteristic
366D3—81no—
367C22—121no—
368C22—121no—
369C22—121no—
370C22#6392211yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—121no—
375C4—121no—
376C4—121no—
377C4—241no—
378C4—361no—
379C4—361no—
380C3—21no—
381C3#6837911yescharacteristic, complemented
382C3#7124711yescharacteristic, complemented
383C2—241no—
384C2#1059039611yescharacteristic
385C2#1059101711yescharacteristic
386C2#1059102011yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32#120
prime radicalC2×C3×D12D4
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. #10590305C2semidirect
4. #10590291C2semidirect
5. #10589331C2semidirect
6. C3×#4465C2semidirect
42. #4465D3semidirect
337. C32#1664semidirect
381. C3#68379semidirect
382. C3#71247semidirect

Maximal subgroups

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

subgroupindex
#105939522
C3×#47142
#105903052
#105902912
#105893312
C3×#44652
#105890862
#712473
#683793