Finite Group Databasebeta

← #11780534

Subgroups — #11780534

Order 1152.

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

normal subgroups only

This group has 467 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, complemented
2#10592412C211yesmaximal, characteristic, complemented
3#10590351C211yesmaximal, characteristic
4#10590282C211yesmaximal, characteristic, complemented
5C3×#4465C211yesmaximal, characteristic, complemented
6C3×#4464C211yesmaximal, characteristic, complemented
7#10589089C211yesmaximal, characteristic, complemented
8#68371—31nomaximal
9#68354—31nomaximal
10#64083C2211yescharacteristic
11#64079C2211yescharacteristic
12C3×#875C2211yescharacteristic
13C3×#870C2211yescharacteristic
14#63899—21no—
15#63893—21no—
16#63884—21no—
17#63861—21no—
18#63858—21no—
19#63839—21no—
20C2×#3717—21no—
21C2×#3714—21no—
22C32×#97C2211yescharacteristic
23#63648—21no—
24#63648—21no—
25C3×#803C2211yescharacteristic
26C3×#803C2211yescharacteristic
27#63564—21no—
28#63564—21no—
29#5699—31no—
30#5672—31no—
31#5067—31no—
32#5058—31no—
33#4713—31no—
34#4713—31no—
35#4713—31no—
36#4713—61no—
37#4712—31no—
38C3×#330—31no—
39C3×#329—31no—
40#4465—31no—
41#4465—31no—
42#4465D311yescharacteristic, complemented
43#4464D311yescharacteristic, complemented
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C3×D12D411yescharacteristic
48C2×C3×Dic6D411yescharacteristic
49C2×#627—21no—
50C2×D3×Dic3—21no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
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#3717—42no—
72#3714—42no—
73#1657—91noSylow
74C3×#125—31no—
75C3×#124—31no—
76#944—61no—
77C2×#215—61no—
78#935—61no—
79C2×#213—61no—
80C2×D24—61no—
81C2×#204—61no—
82#898—61no—
83#898—61no—
84#897—61no—
85#896—61no—
86#894—61no—
87#888—61no—
88#879—61no—
89#879—61no—
90#878—61no—
91#878—61no—
92#875C2×D311yescharacteristic
93#874—31no—
94#874—31no—
95#874—61no—
96#870—31no—
97#870—31no—
98#870—61no—
99#870C2×D311yescharacteristic
100C3×#97—21no—
101C3×#97—31no—
102C3×#97—31no—
103C3×#97C2×D311yescharacteristic
104C3×#97C2×D311yescharacteristic
105#821—61no—
106#821—61no—
107#821—61no—
108#821—61no—
109#821—62no—
110#821—62no—
111#821—61no—
112#821—61no—
113#809—61no—
114#809—61no—
115#803C2×D311yescharacteristic
116#803C2×D311yescharacteristic
117C22×C3⋊D3—41no—
118C22×C3×D3—21no—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—21no—
124C4⋊(C3⋊D3)—42no—
125C4⋊(C3⋊D3)—41no—
126C4⋊(C3⋊D3)—41no—
127C4⋊(C3⋊D3)—42no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C3×D12—41no—
132C3×Dic6—41no—
133#627—81no—
134D3×Dic3—81no—
135C32×C8—41no—
136C3×C3⋊C8—22no—
137C3×C3⋊C8—41no—
138#563—91no—
139#496—91no—
140#490—91no—
141#490—91no—
142#330—31no—
143#330—91no—
144#329—31no—
145C2×C3×Q8—31no—
146C2×C3×D4—31no—
147C22×Dic3—61no—
148C2×D12—62no—
149C2×D12—61no—
150C2×D12—61no—
151C2×D12—61no—
152C2×D12—61no—
153C2×D12—61no—
154C2×D12—61no—
155C2×D12—121no—
156C2×D12—121no—
157C2×D12D1211yescharacteristic
158C2×C4×D3—61no—
159C2×Dic6—61no—
160C2×Dic6—61no—
161C2×Dic6D1211yescharacteristic
162C2×C3×C8—22no—
163C2×C3×C8—21no—
164C2×C3×C8—21no—
165C2×C3×C8—61no—
166C2×C3×C8—61no—
167C3×C4⋊C4—31no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4—61no—
171C3×C22⋊C4—61no—
172C3×C22⋊C4—61no—
173C3×C42—21no—
174C3×C42C22×D311yescharacteristic
175C3×C42C22×D311yescharacteristic
176#217—61no—
177#217—61no—
178#217—61no—
179#215—122no—
180#213—122no—
181(C2×D3)⋊C4—21no—
182(C2×D3)⋊C4—21no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—61no—
185(C2×D3)⋊C4—61no—
186C4⋊Dic3—31no—
187C4⋊Dic3—31no—
188C4⋊Dic3—31no—
189C4⋊Dic3—31no—
190C4⋊Dic3—61no—
191C4⋊Dic3—61no—
192C4⋊Dic3—61no—
193C4⋊Dic3D1211yescharacteristic
194C4⋊Dic3D1211yescharacteristic
195Dic3⋊C4—21no—
196Dic3⋊C4—21no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—61no—
204Dic3⋊C4—121no—
205Dic3⋊C4—121no—
206C4×Dic3—61no—
207C4×Dic3—61no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—21no—
210D24—122no—
211#204—122no—
212C22×C32#12011yescharacteristic
213C2×C3⋊D3—81no—
214C2×C3⋊D3—81no—
215C2×C3⋊D3—81no—
216C2×C3×D3—41no—
217C2×C3×D3—41no—
218C2×C3×D3—41no—
219C32×C4—21no—
220C32×C4—21no—
221C32×C4—21no—
222C3⋊Dic3—41no—
223C3⋊Dic3—41no—
224C3×Dic3—41no—
225C3×Dic3—41no—
226C3×Dic3—41no—
227C2×SD16—181no—
228C2×D8—181no—
229C4⋊Q8—181no—
230#127—91no—
231#126—181no—
232#126—181no—
233#125—31no—
234#125—91no—
235#124—31no—
236#123—181no—
237C22⋊Q8—181no—
238C22⋊Q8—181no—
239#102—181no—
240#102—181no—
241#102—181no—
242#102—181no—
243#97—31no—
244#97—31no—
245#97D3211yescharacteristic
246C23×C3—61no—
247C22×D3—21no—
248C22×D3—122no—
249C22×D3—121no—
250C22×D3—121no—
251C3×Q8—121no—
252C3×D4—121no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—61no—
257C2×C3×C4—61no—
258C2×C3×C4—61no—
259C2×C3×C4C2×D1211yescharacteristic
260C2×C3×C4C2×D1211yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×Dic3—21no—
266C2×Dic3—21no—
267C2×Dic3—21no—
268C2×Dic3—61no—
269C2×Dic3—61no—
270C2×Dic3—61no—
271C2×Dic3—61no—
272C2×Dic3—121no—
273C2×Dic3—121no—
274C2×Dic3—241no—
275D12—41no—
276D12—121no—
277D12—121no—
278D12—121no—
279D12—121no—
280D12—124no—
281D12—122no—
282D12—122no—
283D12—122no—
284D12—122no—
285D12—241no—
286D12—241no—
287D12—242no—
288C4×D3—241no—
289Dic6—41no—
290Dic6—241no—
291Dic6—241no—
292C3×C8—42no—
293C3×C8—41no—
294C3×C8—41no—
295C3×C8—62no—
296C3×C8—121no—
297C3⋊C8—22no—
298C3⋊C8—41no—
299C2×C32#45311yescharacteristic
300C2×C32#45411yescharacteristic
301C2×C32#45411yescharacteristic
302C3⋊D3—161no—
303C3×D3—81no—
304C2×Q8—31no—
305C2×Q8—181no—
306C2×D4—31no—
307C2×D4—181no—
308C2×D4—181no—
309C2×D4—181no—
310C22×C4—181no—
311SD16—362no—
312D8—362no—
313C2×C8—21no—
314C2×C8—61no—
315C2×C8—61no—
316C4⋊C4—31no—
317C4⋊C4—31no—
318C4⋊C4—61no—
319C4⋊C4—61no—
320C4⋊C4—91no—
321C4⋊C4—91no—
322C4⋊C4—181no—
323C4⋊C4—181no—
324C4⋊C4—181no—
325C4⋊C4—181no—
326C22⋊C4—61no—
327C22⋊C4—61no—
328C22⋊C4—181no—
329C22⋊C4—181no—
330C22⋊C4—181no—
331C42—181no—
332C42C2×D3211yescharacteristic
333C22×C3—21no—
334C22×C3—121no—
335C22×C3—121no—
336C22×C3—121no—
337C22×C3#88211yescharacteristic
338C22×C3#88211yescharacteristic
339C2×D3—41no—
340C2×D3—41no—
341C2×D3—41no—
342C2×D3—242no—
343C2×D3—242no—
344C2×D3—242no—
345C2×D3—241no—
346C2×D3—241no—
347C2×D3—241no—
348C2×D3—241no—
349C2×D3—241no—
350C2×D3—241no—
351C3×C4—22no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—41no—
359C3×C4—41no—
360C3×C4—121no—
361C3×C4—121no—
362C3×C4—121no—
363Dic3—41no—
364Dic3—41no—
365Dic3—41no—
366Dic3—121no—
367Dic3—121no—
368Dic3—121no—
369Dic3—121no—
370Dic3—241no—
371Dic3—241no—
372C32#165711yescharacteristic, complemented, Sylow
373C23—61no—
374C23—361no—
375Q8—121no—
376Q8—721no—
377D4—121no—
378D4—361no—
379D4—361no—
380D4—362no—
381D4—362no—
382C2×C4—61no—
383C2×C4—61no—
384C2×C4—61no—
385C2×C4—181no—
386C2×C4—181no—
387C2×C4—721no—
388C2×C4D3×D1211yescharacteristic
389C2×C4D3×D1211yescharacteristic
390C2×C4#381111yescharacteristic
391C8—41no—
392C8—62no—
393C8—121no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—241no—
398C2×C3#474711yescharacteristic
399C2×C3#475311yescharacteristic
400C2×C3#482211yescharacteristic
401C2×C3#482711yescharacteristic
402C2×C3#482711yescharacteristic
403C2×C3#482711yescharacteristic
404D3—81no—
405D3—482no—
406D3—481no—
407D3—481no—
408C22—121no—
409C22—121no—
410C22—121no—
411C22—721no—
412C22—721no—
413C22—721no—
414C22#6392311yescharacteristic
415C4—21no—
416C4—21no—
417C4—21no—
418C4—121no—
419C4—121no—
420C4—121no—
421C4—361no—
422C4—361no—
423C3—21no—
424C3#6835411yescharacteristic, complemented
425C3#6837111yescharacteristic, complemented
426C2—241no—
427C2—1441no—
428C2#1059040211yescharacteristic
429C2#1059101511yescharacteristic
430C2#1059102211yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32#120
prime radical#10590351C2
hypercenter#97D32
hypocenterC32#1657
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
1. #10593952C2semidirect
2. #10592412C2semidirect
4. #10590282C2semidirect
5. C3×#4465C2semidirect
6. C3×#4464C2semidirect
7. #10589089C2semidirect
42. #4465D3semidirect
43. #4464D3semidirect
372. C32#1657semidirect
424. C3#68354semidirect
425. C3#68371semidirect

Maximal subgroups

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

subgroupindex
#105939522
#105924122
#105903512
#105902822
C3×#44652
C3×#44642
#105890892
#683713
#683543