Finite Group Databasebeta

← #11780764

Subgroups — #11780764

Order 1152.

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

normal subgroups only

This group has 413 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
2#10592401C211yesmaximal, characteristic, complemented
3#10590295C211yesmaximal, characteristic, complemented
4#10590276C211yesmaximal, characteristic
5C3×#4465C211yesmaximal, characteristic, complemented
6C3×#4464C211yesmaximal, characteristic
7#10589089C211yesmaximal, characteristic, complemented
8#68379—31nomaximal
9#68359—31nomaximal
10#64079C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#875C2211yescharacteristic
13C3×#870C2211yescharacteristic
14#63899—21no—
15#63893—21no—
16#63884—21no—
17#63861—21no—
18#63858—21no—
19#63839—21no—
20C32×#97C2211yescharacteristic
21#63645—21no—
22#63644—21no—
23C3×#803C2211yescharacteristic
24C3×#803C2211yescharacteristic
25#63567—21no—
26#63567—21no—
27#63566—21no—
28#63563—21no—
29#5699—31no—
30#5672—31no—
31#5069—31no—
32#5055—31no—
33#4714—31no—
34#4703—31no—
35#4702—31no—
36#4702—31no—
37#4702—61no—
38C3×#330—31no—
39C3×#329—31no—
40#4465—31no—
41#4465—31no—
42#4465D311yescharacteristic, complemented
43#4464D311yescharacteristic
44C2×#634—21no—
45C2×C3×D12D411yescharacteristic
46C2×C3×Dic6D411yescharacteristic
47C2×#627—21no—
48C2×D3×Dic3—21no—
49C2×C32×C8—21no—
50C32×C42C2311yescharacteristic
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)D411yescharacteristic
54C4⋊(C3⋊Dic3)D411yescharacteristic
55#3750—21no—
56#3750—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C2×C3×C3⋊C8—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×#125—31no—
73C3×#124—31no—
74#944—61no—
75#935—61no—
76#898—61no—
77#898—61no—
78#897—61no—
79#896—61no—
80#894—61no—
81#888—61no—
82#879—61no—
83#879—61no—
84#878—61no—
85#878—61no—
86#875C2×D311yescharacteristic
87#870—31no—
88#870—31no—
89#870—61no—
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#835—61no—
100#832—61no—
101#821—61no—
102#818—61no—
103#818—61no—
104#818—62no—
105#817—61no—
106#817—61no—
107#817—62no—
108#816—61no—
109#816—61no—
110#816—61no—
111#810—61no—
112#810—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—21no—
121C2×C3⋊Dic3—41no—
122#634—42no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C3×D12—41no—
127C3×Dic6—41no—
128#627—81no—
129D3×Dic3—81no—
130C32×C8—22no—
131C3×C3⋊C8—41no—
132C3×C3⋊C8—41no—
133#563—91no—
134#501—91no—
135#491—91no—
136#489—91no—
137#330—31no—
138#330—91no—
139#329—31no—
140C2×C3×Q8—31no—
141C2×C3×D4—31no—
142C22×Dic3—61no—
143C2×D12D1211yescharacteristic
144C2×C4×D3—61no—
145C2×Dic6—61no—
146C2×Dic6—61no—
147C2×Dic6—61no—
148C2×Dic6—61no—
149C2×Dic6—121no—
150C2×Dic6D1211yescharacteristic
151C2×C3×C8—22no—
152C2×C3×C8—21no—
153C2×C3×C8—21no—
154C2×C3×C8—61no—
155C2×C3×C8—61no—
156C3×C4⋊C4—31no—
157C3×C4⋊C4—31no—
158C3×C4⋊C4—61no—
159C3×C4⋊C4—61no—
160C3×C22⋊C4—61no—
161C3×C22⋊C4—61no—
162C3×C42—21no—
163C3×C42C22×D311yescharacteristic
164C3×C42C22×D311yescharacteristic
165#217—61no—
166#217—61no—
167#217—61no—
168(C2×D3)⋊C4—21no—
169(C2×D3)⋊C4—21no—
170(C2×D3)⋊C4—61no—
171(C2×D3)⋊C4—61no—
172(C2×D3)⋊C4—61no—
173C4⋊Dic3—31no—
174C4⋊Dic3—31no—
175C4⋊Dic3—31no—
176C4⋊Dic3—31no—
177C4⋊Dic3—61no—
178C4⋊Dic3—61no—
179C4⋊Dic3—61no—
180C4⋊Dic3—62no—
181C4⋊Dic3—61no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C4⋊Dic3—61no—
185C4⋊Dic3—121no—
186C4⋊Dic3D1211yescharacteristic
187C4⋊Dic3D1211yescharacteristic
188Dic3⋊C4—21no—
189Dic3⋊C4—21no—
190Dic3⋊C4—61no—
191Dic3⋊C4—61no—
192Dic3⋊C4—61no—
193Dic3⋊C4—61no—
194Dic3⋊C4—61no—
195Dic3⋊C4—61no—
196Dic3⋊C4—61no—
197Dic3⋊C4—121no—
198Dic3⋊C4—121no—
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—41no—
212C3⋊Dic3—81no—
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—91no—
222#124—31no—
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
235C23×C3—61no—
236C22×D3—21no—
237C3×Q8—121no—
238C3×D4—121no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
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—61no—
255C2×Dic3—61no—
256C2×Dic3—61no—
257C2×Dic3—61no—
258C2×Dic3—121no—
259C2×Dic3—121no—
260C2×Dic3—122no—
261C2×Dic3—121no—
262C2×Dic3—121no—
263C2×Dic3—241no—
264D12—41no—
265C4×D3—241no—
266Dic6—41no—
267Dic6—122no—
268Dic6—122no—
269Dic6—242no—
270Dic6—241no—
271Dic6—241no—
272C3×C8—24no—
273C3×C8—22no—
274C3×C8—22no—
275C3×C8—121no—
276C3×C8—121no—
277C3⋊C8—41no—
278C3⋊C8—41no—
279C2×C32#45411yescharacteristic
280C2×C32#45511yescharacteristic
281C2×C32#45611yescharacteristic
282C3×D3—81no—
283C2×Q8—31no—
284C2×Q8—181no—
285C2×Q8—181no—
286C2×D4—31no—
287C22×C4—181no—
288C2×C8—21no—
289C2×C8—61no—
290C2×C8—61no—
291C4⋊C4—31no—
292C4⋊C4—31no—
293C4⋊C4—61no—
294C4⋊C4—61no—
295C4⋊C4—91no—
296C4⋊C4—91no—
297C4⋊C4—181no—
298C4⋊C4—181no—
299C4⋊C4—181no—
300C4⋊C4—181no—
301C4⋊C4—181no—
302C4⋊C4—181no—
303C22⋊C4—61no—
304C22⋊C4—61no—
305C22⋊C4—181no—
306C22⋊C4—181no—
307C22⋊C4—181no—
308C42—181no—
309C42C2×D3211yescharacteristic
310C22×C3—21no—
311C22×C3—121no—
312C22×C3—121no—
313C22×C3—121no—
314C22×C3#88211yescharacteristic
315C22×C3#88211yescharacteristic
316C2×D3—41no—
317C2×D3—41no—
318C2×D3—41no—
319C3×C4—22no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—41no—
327C3×C4—41no—
328C3×C4—121no—
329C3×C4—121no—
330C3×C4—121no—
331Dic3—41no—
332Dic3—41no—
333Dic3—41no—
334Dic3—121no—
335Dic3—121no—
336Dic3—121no—
337Dic3—121no—
338Dic3—241no—
339Dic3—241no—
340Dic3—242no—
341Dic3—241no—
342Dic3—241no—
343C32#166411yescharacteristic, complemented, Sylow
344C23—61no—
345Q8—121no—
346Q8—362no—
347Q8—721no—
348D4—121no—
349C2×C4—61no—
350C2×C4—61no—
351C2×C4—61no—
352C2×C4—181no—
353C2×C4—181no—
354C2×C4—361no—
355C2×C4—721no—
356C2×C4D3×D1211yescharacteristic
357C2×C4D3×D1211yescharacteristic
358C2×C4#381111yescharacteristic
359C8—22no—
360C8—121no—
361C8—121no—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—241no—
366C2×C3#474611yescharacteristic
367C2×C3#475311yescharacteristic
368C2×C3#482511yescharacteristic
369C2×C3#482611yescharacteristic
370C2×C3#482611yescharacteristic
371C2×C3#482711yescharacteristic
372D3—81no—
373C22—121no—
374C22—121no—
375C22—121no—
376C22#6392311yescharacteristic
377C4—21no—
378C4—21no—
379C4—21no—
380C4—121no—
381C4—121no—
382C4—121no—
383C4—361no—
384C4—361no—
385C4—721no—
386C3—21no—
387C3#6835911yescharacteristic, complemented
388C3#6837911yescharacteristic, complemented
389C2—241no—
390C2#1059040111yescharacteristic
391C2#1059101611yescharacteristic
392C2#1059102211yescharacteristic
subgroupG/H
centerC22#63923
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
2. #10592401C2semidirect
3. #10590295C2semidirect
5. C3×#4465C2semidirect
7. #10589089C2semidirect
42. #4465D3semidirect
343. C32#1664semidirect
387. C3#68359semidirect
388. C3#68379semidirect

Maximal subgroups

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

subgroupindex
#105939522
#105924012
#105902952
#105902762
C3×#44652
C3×#44642
#105890892
#683793
#683593