Finite Group Databasebeta

← #11780661

Subgroups — #11780661

Order 1152.

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

normal subgroups only

This group has 466 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#10593953C211yesmaximal, characteristic
2#10592413C211yesmaximal, characteristic, complemented
3#10590372C211yesmaximal, characteristic, complemented
4#10590306C211yesmaximal, characteristic, complemented
5C3×#4465C211yesmaximal, characteristic, complemented
6C3×#4464C211yesmaximal, characteristic, complemented
7#10589087C211yesmaximal, characteristic, complemented
8#68373—31nomaximal
9#68356—31nomaximal
10#64084C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#875C2211yescharacteristic
13C3×#870C2211yescharacteristic
14#63910—21no—
15#63896—21no—
16#63890—21no—
17#63888—21no—
18#63886—21no—
19#63854—21no—
20C2×#3719—21no—
21C2×#3716—21no—
22C32×#97C2211yescharacteristic
23#63648—21no—
24#63643—21no—
25C3×#803C2211yescharacteristic
26C3×#803C2211yescharacteristic
27#63575—21no—
28#63573—21no—
29#5700—31no—
30#5684—31no—
31#5064—31no—
32#5060—31no—
33#4715—31no—
34#4714—31no—
35#4714—31no—
36#4714—61no—
37#4702—31no—
38C3×#330—31no—
39C3×#329—31no—
40#4465D311yescharacteristic, complemented
41#4464—31no—
42#4464—31no—
43#4464D311yescharacteristic, complemented
44C2×C4⋊(C3⋊D3)D411yescharacteristic
45C2×#634—21no—
46C2×#634D411yescharacteristic
47C2×C3×D12D411yescharacteristic
48C2×C3×Dic6D411yescharacteristic
49C2×#626—21no—
50C2×#626—21no—
51C2×#624—21no—
52C2×D3×Dic3—21no—
53C2×C32×C8—21no—
54C32×C42C2311yescharacteristic
55#3752—21no—
56#3752—21no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×C4⋊Dic3D411yescharacteristic
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#3724—21no—
68Dic3⋊Dic3—21no—
69#3722—21no—
70(C2×D3)⋊Dic3—21no—
71#3719—42no—
72#3716—42no—
73#1661—91noSylow
74C3×#125—31no—
75C3×#124—31no—
76#946—61no—
77C2×#216—61no—
78#939—61no—
79C2×#214—61no—
80C2×Dic12—61no—
81C2×#204—61no—
82#896—61no—
83#896—61no—
84#895—61no—
85#895—61no—
86#894—61no—
87#894—61no—
88#886—61no—
89#884—61no—
90#883—61no—
91#878—61no—
92#875—31no—
93#875—31no—
94#875—61no—
95#875C2×D311yescharacteristic
96#870C2×D311yescharacteristic
97#869—31no—
98#869—31no—
99#869—61no—
100C3×#97—21no—
101C3×#97—31no—
102C3×#97—31no—
103C3×#97C2×D311yescharacteristic
104C3×#97C2×D311yescharacteristic
105#821—61no—
106#821—61no—
107#821—62no—
108#818—61no—
109#817—61no—
110#816—61no—
111#816—61no—
112#816—62no—
113#808—61no—
114#807—61no—
115#803C2×D311yescharacteristic
116#803C2×D311yescharacteristic
117C22×C3⋊D3—21no—
118C22×C3×D3—21no—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—41no—
124C4⋊(C3⋊D3)—41no—
125#634—41no—
126#634—41no—
127#634—41no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C3×D12—41no—
132C3×Dic6—41no—
133#626—81no—
134#626—81no—
135#624—81no—
136D3×Dic3—81no—
137C32×C8—41no—
138C3×C3⋊C8—22no—
139C3×C3⋊C8—22no—
140#562—91no—
141#501—91no—
142#497—91no—
143#489—91no—
144#330—31no—
145#329—31no—
146#329—91no—
147C2×C3×Q8—31no—
148C2×C3×D4—31no—
149C2×#67—61no—
150C2×#67—61no—
151C22×Dic3—61no—
152C2×D12—31no—
153C2×D12—31no—
154C2×D12—61no—
155C2×D12—61no—
156C2×D12—61no—
157C2×D12D1211yescharacteristic
158C2×C4×D3—61no—
159C2×C4×D3—61no—
160C2×C4×D3—61no—
161C2×Dic6—31no—
162C2×Dic6—31no—
163C2×Dic6—61no—
164C2×Dic6—61no—
165C2×Dic6—61no—
166C2×Dic6—121no—
167C2×Dic6D1211yescharacteristic
168C2×C3×C8—22no—
169C2×C3×C8—21no—
170C2×C3×C8—21no—
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C3×C4⋊C4—31no—
174C3×C4⋊C4—31no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C22⋊C4—61no—
178C3×C22⋊C4—61no—
179C3×C42—21no—
180C3×C42C22×D311yescharacteristic
181C3×C42C22×D311yescharacteristic
182#217—61no—
183#216—122no—
184#214—122no—
185(C2×D3)⋊C4—21no—
186(C2×D3)⋊C4—21no—
187(C2×D3)⋊C4—61no—
188(C2×D3)⋊C4—61no—
189(C2×D3)⋊C4—61no—
190(C2×D3)⋊C4—61no—
191(C2×D3)⋊C4—61no—
192(C2×D3)⋊C4—61no—
193(C2×D3)⋊C4—61no—
194(C2×D3)⋊C4—121no—
195(C2×D3)⋊C4—121no—
196C4⋊Dic3—61no—
197C4⋊Dic3—62no—
198C4⋊Dic3—61no—
199C4⋊Dic3—61no—
200C4⋊Dic3—61no—
201C4⋊Dic3—61no—
202C4⋊Dic3—121no—
203C4⋊Dic3D1211yescharacteristic
204C4⋊Dic3D1211yescharacteristic
205Dic3⋊C4—21no—
206Dic3⋊C4—21no—
207Dic3⋊C4—61no—
208Dic3⋊C4—61no—
209Dic3⋊C4—61no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—21no—
212Dic12—122no—
213#204—122no—
214C22×C32#12011yescharacteristic
215C2×C3⋊D3—41no—
216C2×C3⋊D3—41no—
217C2×C3⋊D3—41no—
218C2×C3×D3—41no—
219C2×C3×D3—41no—
220C2×C3×D3—41no—
221C32×C4—21no—
222C32×C4—21no—
223C32×C4—21no—
224C3⋊Dic3—41no—
225C3⋊Dic3—81no—
226C3×Dic3—41no—
227C3×Dic3—41no—
228C3×Dic3—41no—
229C2×Q16—181no—
230C2×SD16—181no—
231C4⋊Q8—91no—
232#125—31no—
233#124—31no—
234#124—91no—
235#123—181no—
236#123—181no—
237C22⋊Q8—181no—
238C22⋊Q8—181no—
239#121—181no—
240#121—181no—
241#107—181no—
242#106—181no—
243#103—181no—
244#102—181no—
245#97—31no—
246#97—31no—
247#97D3211yescharacteristic
248C23×C3—61no—
249C22×D3—21no—
250C22×D3—61no—
251C22×D3—61no—
252C22×D3—121no—
253C3×Q8—121no—
254C3×D4—121no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—61no—
259C2×C3×C4—61no—
260C2×C3×C4—61no—
261C2×C3×C4C2×D1211yescharacteristic
262C2×C3×C4C2×D1211yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267#67—241no—
268#67—241no—
269C2×Dic3—21no—
270C2×Dic3—21no—
271C2×Dic3—21no—
272C2×Dic3—61no—
273C2×Dic3—61no—
274C2×Dic3—121no—
275C2×Dic3—122no—
276C2×Dic3—121no—
277C2×Dic3—121no—
278C2×Dic3—241no—
279D12—41no—
280D12—121no—
281D12—121no—
282D12—122no—
283D12—241no—
284D12—241no—
285C4×D3—241no—
286C4×D3—241no—
287C4×D3—241no—
288Dic6—41no—
289Dic6—121no—
290Dic6—121no—
291Dic6—121no—
292Dic6—121no—
293Dic6—121no—
294Dic6—121no—
295Dic6—122no—
296Dic6—241no—
297Dic6—241no—
298C3×C8—42no—
299C3×C8—41no—
300C3×C8—41no—
301C3×C8—62no—
302C3×C8—62no—
303C3⋊C8—22no—
304C3⋊C8—22no—
305C2×C32#45311yescharacteristic
306C2×C32#45511yescharacteristic
307C2×C32#45611yescharacteristic
308C3⋊D3—81no—
309C3×D3—81no—
310C2×Q8—31no—
311C2×Q8—91no—
312C2×Q8—181no—
313C2×D4—31no—
314C2×D4—91no—
315C2×D4—181no—
316C2×D4—181no—
317C22×C4—181no—
318C22×C4—181no—
319Q16—362no—
320SD16—362no—
321C2×C8—21no—
322C2×C8—61no—
323C2×C8—61no—
324C4⋊C4—31no—
325C4⋊C4—31no—
326C4⋊C4—61no—
327C4⋊C4—61no—
328C4⋊C4—181no—
329C4⋊C4—181no—
330C4⋊C4—181no—
331C4⋊C4—181no—
332C22⋊C4—61no—
333C22⋊C4—61no—
334C22⋊C4—181no—
335C22⋊C4—181no—
336C22⋊C4—181no—
337C22⋊C4—181no—
338C42C2×D3211yescharacteristic
339C22×C3—21no—
340C22×C3—121no—
341C22×C3—121no—
342C22×C3—121no—
343C22×C3#88211yescharacteristic
344C22×C3#88211yescharacteristic
345C2×D3—41no—
346C2×D3—41no—
347C2×D3—41no—
348C2×D3—121no—
349C2×D3—121no—
350C2×D3—121no—
351C2×D3—121no—
352C2×D3—121no—
353C2×D3—121no—
354C2×D3—241no—
355C2×D3—241no—
356C2×D3—241no—
357C3×C4—22no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—41no—
365C3×C4—41no—
366C3×C4—121no—
367C3×C4—121no—
368C3×C4—121no—
369Dic3—41no—
370Dic3—41no—
371Dic3—41no—
372Dic3—121no—
373Dic3—121no—
374Dic3—241no—
375Dic3—242no—
376Dic3—241no—
377Dic3—241no—
378C32#166111yescharacteristic, complemented, Sylow
379C23—61no—
380C23—181no—
381Q8—121no—
382Q8—361no—
383Q8—361no—
384Q8—361no—
385D4—121no—
386D4—361no—
387D4—721no—
388D4—721no—
389C2×C4—61no—
390C2×C4—61no—
391C2×C4—61no—
392C2×C4—181no—
393C2×C4—361no—
394C2×C4—721no—
395C2×C4—721no—
396C2×C4D3×D1211yescharacteristic
397C2×C4D3×D1211yescharacteristic
398C2×C4#381111yescharacteristic
399C8—41no—
400C8—62no—
401C8—62no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—241no—
406C2×C3#474711yescharacteristic
407C2×C3#475211yescharacteristic
408C2×C3#482211yescharacteristic
409C2×C3#482511yescharacteristic
410C2×C3#482511yescharacteristic
411C2×C3#482611yescharacteristic
412D3—81no—
413D3—241no—
414D3—241no—
415D3—481no—
416C22—121no—
417C22—121no—
418C22—121no—
419C22—361no—
420C22—361no—
421C22—361no—
422C22#6392311yescharacteristic
423C4—21no—
424C4—21no—
425C4—21no—
426C4—121no—
427C4—121no—
428C4—121no—
429C4—361no—
430C4—721no—
431C3—21no—
432C3#6835611yescharacteristic, complemented
433C3#6837311yescharacteristic, complemented
434C2—241no—
435C2—721no—
436C2#1059039811yescharacteristic
437C2#1059101511yescharacteristic
438C2#1059102111yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32#120
prime radical#10593953C2
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. #10592413C2semidirect
3. #10590372C2semidirect
4. #10590306C2semidirect
5. C3×#4465C2semidirect
6. C3×#4464C2semidirect
7. #10589087C2semidirect
40. #4465D3semidirect
43. #4464D3semidirect
378. C32#1661semidirect
432. C3#68356semidirect
433. C3#68373semidirect

Maximal subgroups

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

subgroupindex
#105939532
#105924132
#105903722
#105903062
C3×#44652
C3×#44642
#105890872
#683733
#683563