Finite Group Databasebeta

← #11780660

Subgroups — #11780660

Order 1152.

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

normal subgroups only

This group has 446 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#10593985C211yesmaximal, characteristic
2C3×#4714C211yesmaximal, characteristic, complemented
3#10590376C211yesmaximal, characteristic, complemented
4#10590305C211yesmaximal, characteristic, complemented
5#10589331C211yesmaximal, characteristic, complemented
6C3×#4464C211yesmaximal, characteristic, complemented
7#10589086C211yesmaximal, characteristic, complemented
8#71245—31nomaximal
9#68356—31nomaximal
10#64079C2211yescharacteristic
11C3×#875C2211yescharacteristic
12C3×#875C2211yescharacteristic
13C3×#869C2211yescharacteristic
14#63891—21no—
15#63891—21no—
16#63887—21no—
17#63887—21no—
18#63885—21no—
19#63885—21no—
20C2×#3718—21no—
21C2×#3715—21no—
22C32×#97C2211yescharacteristic
23#63630C2211yescharacteristic
24C3×#821—21no—
25C3×#816—21no—
26C3×#803C2211yescharacteristic
27#63575—21no—
28#63573—21no—
29#5684—31no—
30#5684—31no—
31C3×#489—31no—
32#5086—31no—
33#5081—31no—
34#5060—31no—
35#4714D311yescharacteristic, complemented
36#4702—31no—
37C3×#329—31no—
38#4540—31no—
39#4465—31no—
40#4465—31no—
41#4465—61no—
42#4464—31no—
43#4464D311yescharacteristic, complemented
44C2×C3×D12D411yescharacteristic
45C2×C3×D12D411yescharacteristic
46C2×C3×Dic6—21no—
47C2×C3×Dic6D411yescharacteristic
48C2×C3×Dic6D411yescharacteristic
49C2×#625—21no—
50C2×#625—21no—
51C2×D3×Dic3—21no—
52C2×D3×Dic3—21no—
53C2×C32×C8—21no—
54C32×C42C2311yescharacteristic
55C4⋊(C3⋊Dic3)D411yescharacteristic
56C4⋊(C3⋊Dic3)D411yescharacteristic
57#3750—21no—
58#3750—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C2×C3×C3⋊C8—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71#3718—42no—
72#3715—42no—
73#1661—91noSylow
74C3×C4⋊Q8—31no—
75C3×#124—31no—
76C3×#124—31no—
77#946—61no—
78#946—61no—
79C2×#216—61no—
80C2×#216—61no—
81C2×#215—61no—
82#939—61no—
83#939—61no—
84C2×#214—61no—
85#886—61no—
86#886—61no—
87#884—61no—
88#884—61no—
89#883—61no—
90#883—61no—
91#878—61no—
92#878—61no—
93#875C2×D311yescharacteristic
94#875C2×D311yescharacteristic
95#870—31no—
96#870—31no—
97#870—61no—
98#869C2×D311yescharacteristic
99C3×#103—61no—
100C3×#102—61no—
101C3×#97—21no—
102C3×#97—31no—
103C3×#97C2×D311yescharacteristic
104C3×#97C2×D311yescharacteristic
105#821—21no—
106#818—61no—
107#817—61no—
108#816—21no—
109#808—61no—
110#807—61no—
111#803—31no—
112#803—31no—
113#803—61no—
114#803C2×D311yescharacteristic
115C22×C3×D3—21no—
116C22×C3×D3—21no—
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—41no—
125C3×D12—41no—
126C3×D12—41no—
127C3×Dic6—41no—
128C3×Dic6—41no—
129C3×Dic6—41no—
130C3×Dic6—41no—
131#625—81no—
132#625—81no—
133D3×Dic3—81no—
134D3×Dic3—81no—
135C32×C8—41no—
136C3⋊(C3⋊C8)—22no—
137C3×C3⋊C8—22no—
138#562—91no—
139#501—91no—
140#497—91no—
141#489—31no—
142#330—91no—
143#329—31no—
144#329—91no—
145C2×C3×Q8—31no—
146C2×C3×Q8—31no—
147C2×C3×Q8—61no—
148C2×C3×D4—31no—
149C2×C3×D4—31no—
150C2×#67—61no—
151C2×#67—61no—
152C2×#67—61no—
153C2×#67—61no—
154C22×Dic3—61no—
155C22×Dic3—61no—
156C2×D12D1211yescharacteristic
157C2×D12#6711yescharacteristic
158C2×C4×D3—61no—
159C2×C4×D3—61no—
160C2×Dic6—21no—
161C2×Dic6D1211yescharacteristic
162C2×Dic6#6711yescharacteristic
163C2×C3×C8—21no—
164C2×C3×C8—21no—
165C2×C3×C8—41no—
166C2×C3×C8—61no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4—61no—
169C3×C22⋊C4—61no—
170C3×C22⋊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#216—122no—
179#216—122no—
180#215—122no—
181#214—122no—
182(C2×D3)⋊C4—21no—
183(C2×D3)⋊C4—21no—
184(C2×D3)⋊C4—21no—
185(C2×D3)⋊C4—21no—
186(C2×D3)⋊C4—61no—
187(C2×D3)⋊C4—61no—
188C4⋊Dic3—21no—
189C4⋊Dic3—21no—
190C4⋊Dic3—31no—
191C4⋊Dic3—31no—
192C4⋊Dic3—31no—
193C4⋊Dic3—31no—
194C4⋊Dic3—61no—
195C4⋊Dic3—61no—
196C4⋊Dic3—61no—
197C4⋊Dic3—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—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—121no—
210C22×C32#12011yescharacteristic
211C2×C3×D3—41no—
212C2×C3×D3—41no—
213C2×C3×D3—41no—
214C2×C3×D3—41no—
215C2×C3×D3—41no—
216C2×C3×D3—41no—
217C32×C4—21no—
218C32×C4—21no—
219C32×C4—21no—
220C3⋊Dic3—41no—
221C3⋊Dic3—41no—
222C3×Dic3—41no—
223C3×Dic3—41no—
224C3×Dic3—81no—
225C2×Q16—181no—
226C2×SD16—181no—
227C4⋊Q8—31no—
228#125—91no—
229#124—31no—
230#124—31no—
231#123—181no—
232#123—181no—
233C22⋊Q8—181no—
234C22⋊Q8—181no—
235#121—181no—
236#121—181no—
237#107—181no—
238#106—181no—
239#103—61no—
240#102—61no—
241#97—31no—
242#97—91no—
243#97D3211yescharacteristic
244C23×C3—61no—
245C23×C3—61no—
246C22×D3—21no—
247C22×D3—21no—
248C3×Q8—121no—
249C3×Q8—121no—
250C3×Q8—121no—
251C3×Q8—121no—
252C3×D4—121no—
253C3×D4—121no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—61no—
258C2×C3×C4—61no—
259C2×C3×C4—121no—
260C2×C3×C4C2×D1211yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4C2×#6711yescharacteristic
266#67—241no—
267#67—241no—
268#67—241no—
269#67—241no—
270C2×Dic3—21no—
271C2×Dic3—21no—
272C2×Dic3—41no—
273C2×Dic3—61no—
274C2×Dic3—61no—
275C2×Dic3—61no—
276C2×Dic3—61no—
277C2×Dic3—121no—
278C2×Dic3—121no—
279C2×Dic3—241no—
280C2×Dic3—241no—
281D12—41no—
282D12—41no—
283C4×D3—241no—
284C4×D3—241no—
285Dic6—41no—
286Dic6—41no—
287Dic6—41no—
288Dic6—41no—
289C3×C8—41no—
290C3×C8—41no—
291C3×C8—42no—
292C3×C8—62no—
293C3⋊C8—22no—
294C3⋊C8—62no—
295C3⋊C8—62no—
296C3⋊C8—122no—
297C2×C32#45311yescharacteristic
298C2×C32#45511yescharacteristic
299C2×C32#45611yescharacteristic
300C3×D3—81no—
301C3×D3—81no—
302C2×Q8—31no—
303C2×Q8—31no—
304C2×Q8—61no—
305C2×D4—31no—
306C2×D4—31no—
307C2×D4—181no—
308C2×D4—181no—
309C22×C4—181no—
310C22×C4—181no—
311Q16—362no—
312SD16—362no—
313C2×C8—21no—
314C2×C8—61no—
315C2×C8—181no—
316C4⋊C4—61no—
317C4⋊C4—61no—
318C4⋊C4—91no—
319C4⋊C4—91no—
320C4⋊C4—181no—
321C4⋊C4—181no—
322C4⋊C4—181no—
323C4⋊C4—181no—
324C22⋊C4—61no—
325C22⋊C4—61no—
326C22⋊C4—61no—
327C22⋊C4—61no—
328C22⋊C4—181no—
329C22⋊C4—181no—
330C42C2×D3211yescharacteristic
331C22×C3—21no—
332C22×C3—121no—
333C22×C3—121no—
334C22×C3—121no—
335C22×C3—121no—
336C22×C3—121no—
337C22×C3—121no—
338C22×C3#88211yescharacteristic
339C22×C3#93711yescharacteristic
340C2×D3—41no—
341C2×D3—41no—
342C2×D3—41no—
343C2×D3—41no—
344C2×D3—41no—
345C2×D3—41no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—41no—
353C3×C4—41no—
354C3×C4—41no—
355C3×C4—121no—
356C3×C4—121no—
357C3×C4—241no—
358Dic3—41no—
359Dic3—41no—
360Dic3—81no—
361Dic3—121no—
362Dic3—121no—
363Dic3—121no—
364Dic3—121no—
365Dic3—241no—
366Dic3—241no—
367C32#166111yescharacteristic, complemented, Sylow
368C23—61no—
369C23—61no—
370Q8—121no—
371Q8—121no—
372Q8—121no—
373Q8—121no—
374D4—121no—
375D4—121no—
376D4—721no—
377D4—721no—
378C2×C4—61no—
379C2×C4—61no—
380C2×C4—121no—
381C2×C4—181no—
382C2×C4—181no—
383C2×C4—721no—
384C2×C4—721no—
385C2×C4D3×D1211yescharacteristic
386C2×C4#380211yescharacteristic
387C2×C4D3×#6711yescharacteristic
388C8—41no—
389C8—62no—
390C8—182no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—241no—
395C2×C3—241no—
396C2×C3#474711yescharacteristic
397C2×C3#482511yescharacteristic
398C2×C3#482611yescharacteristic
399C2×C3#506111yescharacteristic
400C2×C3#519811yescharacteristic
401C2×C3#520511yescharacteristic
402D3—81no—
403D3—81no—
404C22—121no—
405C22—121no—
406C22—121no—
407C22—121no—
408C22—121no—
409C22—121no—
410C22#6392211yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—121no—
415C4—121no—
416C4—241no—
417C4—361no—
418C4—361no—
419C3—21no—
420C3#6835611yescharacteristic, complemented
421C3#7124511yescharacteristic, complemented
422C2—241no—
423C2—241no—
424C2#1059039611yescharacteristic
425C2#1059101411yescharacteristic
426C2#1059101711yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32#120
prime radical#10593985C2
hypercenter#97D32
hypocenterC32#1661
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×#4714C2semidirect
3. #10590376C2semidirect
4. #10590305C2semidirect
5. #10589331C2semidirect
6. C3×#4464C2semidirect
7. #10589086C2semidirect
35. #4714D3semidirect
43. #4464D3semidirect
367. C32#1661semidirect
420. C3#68356semidirect
421. C3#71245semidirect

Maximal subgroups

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

subgroupindex
#105939852
C3×#47142
#105903762
#105903052
#105893312
C3×#44642
#105890862
#712453
#683563