Finite Group Databasebeta

← #11780535

Subgroups — #11780535

Order 1152.

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

normal subgroups only

This group has 442 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
2C3×#4713C211yesmaximal, characteristic, complemented
3#10590354C211yesmaximal, characteristic
4#10590275C211yesmaximal, characteristic, complemented
5#10589331C211yesmaximal, characteristic, complemented
6C3×#4464C211yesmaximal, characteristic, complemented
7#10589088C211yesmaximal, characteristic, complemented
8#71249—31nomaximal
9#68354—31nomaximal
10#64079C2211yescharacteristic
11C3×#875C2211yescharacteristic
12C3×#874C2211yescharacteristic
13C3×#870C2211yescharacteristic
14#63899—21no—
15#63893—21no—
16#63884—21no—
17#63861—21no—
18#63858—21no—
19#63839—21no—
20C2×#3715—21no—
21C2×#3713—21no—
22C32×#97C2211yescharacteristic
23#63630C2211yescharacteristic
24C3×#821—21no—
25C3×#821—21no—
26C3×#803C2211yescharacteristic
27#63563—21no—
28#63563—21no—
29#5699—31no—
30#5672—31no—
31C3×#490—31no—
32#5074—31no—
33#5071—31no—
34#5058—31no—
35#4713—31no—
36#4713D311yescharacteristic, complemented
37C3×#329—31no—
38#4543—31no—
39#4465—31no—
40#4465—31no—
41#4465—31no—
42#4465—61no—
43#4464D311yescharacteristic, complemented
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—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—
57C2×C3⋊(C3⋊C8)—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—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#3715—42no—
72#3713—42no—
73#1657—91noSylow
74C3×#127—31no—
75C3×#125—31no—
76C3×#124—31no—
77#944—61no—
78C2×#215—61no—
79#935—61no—
80C2×#214—61no—
81C2×#213—61no—
82C2×#213—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#874C2×D311yescharacteristic
95#870—31no—
96#870—31no—
97#870—61no—
98#870C2×D311yescharacteristic
99C3×#102—61no—
100C3×#102—61no—
101C3×#97—21no—
102C3×#97—31no—
103C3×#97C2×D311yescharacteristic
104C3×#97C2×D311yescharacteristic
105#832—61no—
106#832—61no—
107#821—21no—
108#821—21no—
109#821—61no—
110#821—61no—
111#803—31no—
112#803—31no—
113#803—61no—
114#803C2×D311yescharacteristic
115C22×C3×D3—21no—
116C22×C3×D3—41no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—21no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C3×D12—41no—
126C3×D12—41no—
127C3×D12—41no—
128C3×D12—42no—
129C3×D12—42no—
130C3×Dic6—41no—
131#627—81no—
132D3×Dic3—81no—
133C32×C8—41no—
134C3⋊(C3⋊C8)—22no—
135C3×C3⋊C8—41no—
136#563—91no—
137#496—91no—
138#490—31no—
139#490—91no—
140#330—91no—
141#330—91no—
142#329—31no—
143C2×C3×Q8—31no—
144C2×C3×D4—31no—
145C2×C3×D4—61no—
146C2×C3×D4—61no—
147C2×C3×D4—61no—
148C22×Dic3—61no—
149C2×D12—21no—
150C2×D12—21no—
151C2×D12—21no—
152C2×D12D1211yescharacteristic
153C2×C4×D3—61no—
154C2×Dic6—61no—
155C2×Dic6—61no—
156C2×Dic6D1211yescharacteristic
157C2×C3×C8—21no—
158C2×C3×C8—21no—
159C2×C3×C8—41no—
160C2×C3×C8—61no—
161C3×C4⋊C4—31no—
162C3×C4⋊C4—31no—
163C3×C4⋊C4—61no—
164C3×C4⋊C4—61no—
165C3×C22⋊C4—61no—
166C3×C22⋊C4—61no—
167C3×C42—21no—
168C3×C42C22×D311yescharacteristic
169C3×C42C22×D311yescharacteristic
170#217—61no—
171#217—61no—
172#217—61no—
173#215—122no—
174#214—122no—
175#213—122no—
176#213—122no—
177(C2×D3)⋊C4—21no—
178(C2×D3)⋊C4—21no—
179(C2×D3)⋊C4—61no—
180(C2×D3)⋊C4—61no—
181(C2×D3)⋊C4—61no—
182C4⋊Dic3—31no—
183C4⋊Dic3—31no—
184C4⋊Dic3—31no—
185C4⋊Dic3—31no—
186C4⋊Dic3—61no—
187C4⋊Dic3—61no—
188C4⋊Dic3—61no—
189C4⋊Dic3#6711yescharacteristic
190C4⋊Dic3#6711yescharacteristic
191Dic3⋊C4—21no—
192Dic3⋊C4—21no—
193Dic3⋊C4—61no—
194Dic3⋊C4—61no—
195Dic3⋊C4—61no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—121no—
201Dic3⋊C4—121no—
202C4×Dic3—61no—
203C4×Dic3—61no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—121no—
208C22×C32#12011yescharacteristic
209C2×C3×D3—41no—
210C2×C3×D3—41no—
211C2×C3×D3—41no—
212C2×C3×D3—81no—
213C2×C3×D3—81no—
214C2×C3×D3—81no—
215C32×C4—21no—
216C32×C4—21no—
217C32×C4—21no—
218C3⋊Dic3—41no—
219C3⋊Dic3—41no—
220C3×Dic3—41no—
221C3×Dic3—41no—
222C3×Dic3—41no—
223C2×SD16—181no—
224C2×D8—181no—
225C4⋊Q8—181no—
226#127—31no—
227#126—181no—
228#126—181no—
229#125—31no—
230#125—91no—
231#124—31no—
232#123—181no—
233C22⋊Q8—181no—
234C22⋊Q8—181no—
235#102—61no—
236#102—61no—
237#102—181no—
238#102—181no—
239#97—31no—
240#97—91no—
241#97D3211yescharacteristic
242C23×C3—61no—
243C23×C3—121no—
244C22×D3—21no—
245C22×D3—41no—
246C3×Q8—121no—
247C3×D4—121no—
248C3×D4—121no—
249C3×D4—121no—
250C3×D4—122no—
251C3×D4—122no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—61no—
256C2×C3×C4—61no—
257C2×C3×C4—61no—
258C2×C3×C4C2×D1211yescharacteristic
259C2×C3×C4D3×D411yescharacteristic
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4C2×#6711yescharacteristic
264C2×Dic3—21no—
265C2×Dic3—21no—
266C2×Dic3—21no—
267C2×Dic3—61no—
268C2×Dic3—61no—
269C2×Dic3—61no—
270C2×Dic3—61no—
271C2×Dic3—121no—
272C2×Dic3—121no—
273C2×Dic3—241no—
274D12—41no—
275D12—41no—
276D12—41no—
277D12—42no—
278D12—42no—
279C4×D3—241no—
280Dic6—41no—
281Dic6—241no—
282Dic6—241no—
283C3×C8—41no—
284C3×C8—41no—
285C3×C8—42no—
286C3×C8—121no—
287C3⋊C8—41no—
288C3⋊C8—62no—
289C3⋊C8—62no—
290C3⋊C8—122no—
291C2×C32#45311yescharacteristic
292C2×C32#45411yescharacteristic
293C2×C32#45411yescharacteristic
294C3×D3—81no—
295C3×D3—161no—
296C2×Q8—31no—
297C2×Q8—181no—
298C2×D4—31no—
299C2×D4—61no—
300C2×D4—61no—
301C2×D4—61no—
302C22×C4—181no—
303SD16—362no—
304D8—362no—
305C2×C8—21no—
306C2×C8—61no—
307C2×C8—181no—
308C4⋊C4—31no—
309C4⋊C4—31no—
310C4⋊C4—61no—
311C4⋊C4—61no—
312C4⋊C4—91no—
313C4⋊C4—91no—
314C4⋊C4—181no—
315C4⋊C4—181no—
316C4⋊C4—181no—
317C4⋊C4—181no—
318C22⋊C4—61no—
319C22⋊C4—61no—
320C22⋊C4—181no—
321C22⋊C4—181no—
322C22⋊C4—181no—
323C42—181no—
324C42C2×D3211yescharacteristic
325C22×C3—21no—
326C22×C3—121no—
327C22×C3—121no—
328C22×C3—121no—
329C22×C3—241no—
330C22×C3—241no—
331C22×C3—241no—
332C22×C3#88211yescharacteristic
333C22×C3#93711yescharacteristic
334C2×D3—41no—
335C2×D3—41no—
336C2×D3—41no—
337C2×D3—81no—
338C2×D3—81no—
339C2×D3—81no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—41no—
347C3×C4—41no—
348C3×C4—41no—
349C3×C4—121no—
350C3×C4—121no—
351C3×C4—121no—
352Dic3—41no—
353Dic3—41no—
354Dic3—41no—
355Dic3—121no—
356Dic3—121no—
357Dic3—121no—
358Dic3—121no—
359Dic3—241no—
360Dic3—241no—
361C32#165711yescharacteristic, complemented, Sylow
362C23—61no—
363C23—121no—
364Q8—121no—
365Q8—721no—
366D4—121no—
367D4—121no—
368D4—121no—
369D4—122no—
370D4—122no—
371C2×C4—61no—
372C2×C4—61no—
373C2×C4—61no—
374C2×C4—181no—
375C2×C4—181no—
376C2×C4—721no—
377C2×C4D3×D1211yescharacteristic
378C2×C4#380211yescharacteristic
379C2×C4D3×#6711yescharacteristic
380C8—41no—
381C8—121no—
382C8—182no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—241no—
387C2×C3—481no—
388C2×C3#474711yescharacteristic
389C2×C3#482711yescharacteristic
390C2×C3#482711yescharacteristic
391C2×C3#506211yescharacteristic
392C2×C3#519811yescharacteristic
393C2×C3#520111yescharacteristic
394D3—81no—
395D3—161no—
396C22—121no—
397C22—121no—
398C22—121no—
399C22—241no—
400C22—241no—
401C22—241no—
402C22#6392211yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—121no—
407C4—121no—
408C4—121no—
409C4—361no—
410C4—361no—
411C3—21no—
412C3#6835411yescharacteristic, complemented
413C3#7124911yescharacteristic, complemented
414C2—241no—
415C2—481no—
416C2#1059040011yescharacteristic
417C2#1059101411yescharacteristic
418C2#1059101911yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32#120
prime radical#10590354C2
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. C3×#4713C2semidirect
4. #10590275C2semidirect
5. #10589331C2semidirect
6. C3×#4464C2semidirect
7. #10589088C2semidirect
36. #4713D3semidirect
43. #4464D3semidirect
361. C32#1657semidirect
412. C3#68354semidirect
413. C3#71249semidirect

Maximal subgroups

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

subgroupindex
#105939522
C3×#47132
#105903542
#105902752
#105893312
C3×#44642
#105890882
#712493
#683543