Finite Group Databasebeta

← #11780615

Subgroups — #11780615

Order 1152.

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

normal subgroups only

This group has 422 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×#4702C211yesmaximal, characteristic, complemented
3#10590376C211yesmaximal, characteristic
4#10590305C211yesmaximal, characteristic, complemented
5#10589331C211yesmaximal, characteristic, complemented
6C3×#4464C211yesmaximal, characteristic
7#10589088C211yesmaximal, characteristic, complemented
8#71391—31nomaximal
9#68355—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—
20C2×#3718—21no—
21C2×#3715—21no—
22C32×#97C2211yescharacteristic
23#63630C2211yescharacteristic
24C3×#818—21no—
25C3×#817—21no—
26C3×#803C2211yescharacteristic
27#63575—21no—
28#63573—21no—
29#5699—31no—
30#5672—31no—
31C3×#501—31no—
32#5086—31no—
33#5081—31no—
34#5060—31no—
35#4702—31no—
36#4702D311yescharacteristic, complemented
37C3×#329—31no—
38#4543—31no—
39#4465—31no—
40#4465—31no—
41#4465—31no—
42#4465—61no—
43#4464D311yescharacteristic
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#3718—42no—
72#3715—42no—
73#1660—91noSylow
74C3×C4⋊Q8—31no—
75C3×#125—31no—
76C3×#124—31no—
77#944—61no—
78C2×#216—61no—
79C2×#216—61no—
80C2×#215—61no—
81#935—61no—
82C2×#214—61no—
83#898—61no—
84#898—61no—
85#897—61no—
86#896—61no—
87#894—61no—
88#888—61no—
89#879—61no—
90#879—61no—
91#878—61no—
92#878—61no—
93#875C2×D311yescharacteristic
94#870—31no—
95#870—31no—
96#870—61no—
97#870C2×D311yescharacteristic
98#869C2×D311yescharacteristic
99C3×#107—61no—
100C3×#106—61no—
101C3×#97—21no—
102C3×#97—31no—
103C3×#97C2×D311yescharacteristic
104C3×#97C2×D311yescharacteristic
105#818—21no—
106#818—61no—
107#817—21no—
108#817—61no—
109#808—61no—
110#807—61no—
111#803—31no—
112#803—31no—
113#803—61no—
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—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—41no—
125C3×D12—41no—
126C3×Dic6—41no—
127C3×Dic6—41no—
128C3×Dic6—41no—
129#627—81no—
130D3×Dic3—81no—
131C32×C8—22no—
132C3⋊(C3⋊C8)—22no—
133C3×C3⋊C8—22no—
134#563—91no—
135#501—31no—
136#501—91no—
137#497—91no—
138#330—91no—
139#330—91no—
140#329—31no—
141C2×C3×Q8—31no—
142C2×C3×Q8—61no—
143C2×C3×D4—31no—
144C22×Dic3—61no—
145C2×D12D1211yescharacteristic
146C2×C4×D3—61no—
147C2×Dic6—21no—
148C2×Dic6—61no—
149C2×Dic6—61no—
150C2×Dic6D1211yescharacteristic
151C2×C3×C8—21no—
152C2×C3×C8—21no—
153C2×C3×C8—41no—
154C2×C3×C8—61no—
155C3×C4⋊C4—31no—
156C3×C4⋊C4—31no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4—61no—
159C3×C4⋊C4—61no—
160C3×C4⋊C4—61no—
161C3×C22⋊C4—61no—
162C3×C22⋊C4—61no—
163C3×C42—21no—
164C3×C42C22×D311yescharacteristic
165C3×C42C22×D311yescharacteristic
166#217—61no—
167#217—61no—
168#217—61no—
169#216—122no—
170#216—122no—
171#215—122no—
172#214—122no—
173(C2×D3)⋊C4—21no—
174(C2×D3)⋊C4—21no—
175(C2×D3)⋊C4—61no—
176(C2×D3)⋊C4—61no—
177(C2×D3)⋊C4—61no—
178C4⋊Dic3—21no—
179C4⋊Dic3—21no—
180C4⋊Dic3—31no—
181C4⋊Dic3—31no—
182C4⋊Dic3—31no—
183C4⋊Dic3—31no—
184C4⋊Dic3—61no—
185C4⋊Dic3—61no—
186C4⋊Dic3—61no—
187C4⋊Dic3#6711yescharacteristic
188C4⋊Dic3#6711yescharacteristic
189Dic3⋊C4—21no—
190Dic3⋊C4—21no—
191Dic3⋊C4—61no—
192Dic3⋊C4—61no—
193Dic3⋊C4—61no—
194Dic3⋊C4—61no—
195Dic3⋊C4—61no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—121no—
199Dic3⋊C4—121no—
200C4×Dic3—61no—
201C4×Dic3—61no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—121no—
206C22×C32#12011yescharacteristic
207C2×C3×D3—41no—
208C2×C3×D3—41no—
209C2×C3×D3—41no—
210C32×C4—21no—
211C32×C4—21no—
212C32×C4—21no—
213C3⋊Dic3—41no—
214C3⋊Dic3—41no—
215C3×Dic3—41no—
216C3×Dic3—41no—
217C3×Dic3—41no—
218C3×Dic3—81no—
219C2×Q16—181no—
220C2×SD16—181no—
221C4⋊Q8—31no—
222C4⋊Q8—181no—
223#126—181no—
224#126—181no—
225#125—31no—
226#125—91no—
227#124—31no—
228#123—181no—
229C22⋊Q8—181no—
230C22⋊Q8—181no—
231#107—61no—
232#107—181no—
233#106—61no—
234#106—181no—
235#97—31no—
236#97—91no—
237#97D3211yescharacteristic
238C23×C3—61no—
239C22×D3—21no—
240C3×Q8—121no—
241C3×Q8—121no—
242C3×Q8—121no—
243C3×D4—121no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—61no—
248C2×C3×C4—61no—
249C2×C3×C4—61no—
250C2×C3×C4—121no—
251C2×C3×C4C2×D1211yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4C2×#6711yescharacteristic
257C2×Dic3—21no—
258C2×Dic3—21no—
259C2×Dic3—21no—
260C2×Dic3—41no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264C2×Dic3—61no—
265C2×Dic3—121no—
266C2×Dic3—121no—
267C2×Dic3—241no—
268D12—41no—
269C4×D3—241no—
270Dic6—41no—
271Dic6—41no—
272Dic6—41no—
273Dic6—241no—
274Dic6—241no—
275C3×C8—22no—
276C3×C8—22no—
277C3×C8—42no—
278C3×C8—62no—
279C3⋊C8—22no—
280C3⋊C8—62no—
281C3⋊C8—62no—
282C3⋊C8—122no—
283C2×C32#45311yescharacteristic
284C2×C32#45611yescharacteristic
285C2×C32#45611yescharacteristic
286C3×D3—81no—
287C2×Q8—31no—
288C2×Q8—61no—
289C2×Q8—181no—
290C2×D4—31no—
291C22×C4—181no—
292Q16—362no—
293SD16—362no—
294C2×C8—21no—
295C2×C8—61no—
296C2×C8—181no—
297C4⋊C4—31no—
298C4⋊C4—31no—
299C4⋊C4—61no—
300C4⋊C4—61no—
301C4⋊C4—61no—
302C4⋊C4—61no—
303C4⋊C4—91no—
304C4⋊C4—91no—
305C4⋊C4—181no—
306C4⋊C4—181no—
307C4⋊C4—181no—
308C4⋊C4—181no—
309C22⋊C4—61no—
310C22⋊C4—61no—
311C22⋊C4—181no—
312C22⋊C4—181no—
313C22⋊C4—181no—
314C42—181no—
315C42C2×D3211yescharacteristic
316C22×C3—21no—
317C22×C3—121no—
318C22×C3—121no—
319C22×C3—121no—
320C22×C3#88211yescharacteristic
321C22×C3#93711yescharacteristic
322C2×D3—41no—
323C2×D3—41no—
324C2×D3—41no—
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—121no—
335C3×C4—121no—
336C3×C4—121no—
337C3×C4—241no—
338Dic3—41no—
339Dic3—41no—
340Dic3—41no—
341Dic3—81no—
342Dic3—121no—
343Dic3—121no—
344Dic3—121no—
345Dic3—121no—
346Dic3—241no—
347Dic3—241no—
348C32#166011yescharacteristic, complemented, Sylow
349C23—61no—
350Q8—121no—
351Q8—121no—
352Q8—121no—
353Q8—721no—
354D4—121no—
355C2×C4—61no—
356C2×C4—61no—
357C2×C4—61no—
358C2×C4—121no—
359C2×C4—181no—
360C2×C4—181no—
361C2×C4—721no—
362C2×C4D3×D1211yescharacteristic
363C2×C4#380211yescharacteristic
364C2×C4D3×#6711yescharacteristic
365C8—22no—
366C8—62no—
367C8—182no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—241no—
372C2×C3#474711yescharacteristic
373C2×C3#482611yescharacteristic
374C2×C3#482611yescharacteristic
375C2×C3#509511yescharacteristic
376C2×C3#519811yescharacteristic
377C2×C3#520511yescharacteristic
378D3—81no—
379C22—121no—
380C22—121no—
381C22—121no—
382C22#6392211yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—121no—
387C4—121no—
388C4—121no—
389C4—241no—
390C4—361no—
391C4—361no—
392C3—21no—
393C3#6835511yescharacteristic, complemented
394C3#7139111yescharacteristic, complemented
395C2—241no—
396C2#1059039911yescharacteristic
397C2#1059101411yescharacteristic
398C2#1059101711yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenter#97D32
hypocenterC32#1660
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. #10590305C2semidirect
5. #10589331C2semidirect
7. #10589088C2semidirect
36. #4702D3semidirect
348. C32#1660semidirect
393. C3#68355semidirect
394. C3#71391semidirect

Maximal subgroups

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

subgroupindex
#105939522
C3×#47022
#105903762
#105903052
#105893312
C3×#44642
#105890882
#713913
#683553