Finite Group Databasebeta

← #11780613

Subgroups — #11780613

Order 1152.

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

normal subgroups only

This group has 427 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#10593857C211yesmaximal, characteristic
2C3×#4702C211yesmaximal, characteristic, complemented
3#10590374C211yesmaximal, characteristic
4#10590315C211yesmaximal, characteristic, complemented
5#10589330C211yesmaximal, characteristic
6C3×#4465C211yesmaximal, characteristic, complemented
7#10589088C211yesmaximal, characteristic, complemented
8#71391—31nomaximal
9#68372—31nomaximal
10#64084C2211yescharacteristic
11C3×#870C2211yescharacteristic
12C3×#870C2211yescharacteristic
13C3×#869C2211yescharacteristic
14#63897—21no—
15#63895—21no—
16#63895—21no—
17#63848—21no—
18#63848—21no—
19#63840—21no—
20C2×#3719—21no—
21C2×#3717—21no—
22C32×#97C2211yescharacteristic
23#63630C2211yescharacteristic
24C3×#818—21no—
25C3×#817—21no—
26C3×#803C2211yescharacteristic
27#63576—21no—
28#63574—21no—
29#5699—31no—
30#5699—31no—
31C3×#501—31no—
32#5086—31no—
33#5081—31no—
34#5064—31no—
35#4715—31no—
36#4702D311yescharacteristic, complemented
37C3×#330—31no—
38#4543—31no—
39#4465—31no—
40#4465D311yescharacteristic, complemented
41#4464—31no—
42#4464—31no—
43#4464—61no—
44C2×C4⋊(C3⋊D3)D411yescharacteristic
45C2×#634D411yescharacteristic
46C2×C3×Dic6—21no—
47C2×#627—21no—
48C2×#624—21no—
49C2×C32×C8—21no—
50C32×C42C2311yescharacteristic
51#3752—21no—
52#3752—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3D411yescharacteristic
57C3×C4⋊Dic3D411yescharacteristic
58C3×C4⋊Dic3D411yescharacteristic
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—21no—
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C2×C3×C3⋊C8—21no—
65Dic3⋊Dic3—21no—
66Dic3⋊Dic3—21no—
67#3722—21no—
68#3722—21no—
69#3722—21no—
70Dic32—21no—
71#3719—42no—
72#3717—42no—
73#1660—91noSylow
74C3×C4⋊Q8—31no—
75C3×#125—31no—
76C3×#125—31no—
77C2×#216—61no—
78C2×#215—61no—
79C2×Dic12—61no—
80C2×#204—61no—
81#898—61no—
82#898—61no—
83#898—61no—
84#898—61no—
85#897—61no—
86#897—61no—
87#896—61no—
88#896—61no—
89#894—61no—
90#894—61no—
91#888—61no—
92#888—61no—
93#875—31no—
94#875—31no—
95#875—61no—
96#870C2×D311yescharacteristic
97#870C2×D311yescharacteristic
98#869C2×D311yescharacteristic
99C3×#107—61no—
100C3×#106—61no—
101C3×#97—21no—
102C3×#97—31no—
103C3×#97C2×D311yescharacteristic
104C3×#97C2×D311yescharacteristic
105#818—21no—
106#817—21no—
107#808—61no—
108#808—61no—
109#807—61no—
110#807—61no—
111#803—31no—
112#803—31no—
113#803—61no—
114#803C2×D311yescharacteristic
115C22×C3⋊D3—21no—
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C3⋊Dic3—21no—
120C4⋊(C3⋊D3)—41no—
121#634—41no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—41no—
127C3×Dic6—41no—
128C3×Dic6—41no—
129#627—81no—
130#624—81no—
131C32×C8—22no—
132C3⋊(C3⋊C8)—22no—
133C3×C3⋊C8—22no—
134#563—91no—
135#501—31no—
136#501—91no—
137#497—91no—
138#330—31no—
139#330—91no—
140#329—91no—
141C2×C3×Q8—61no—
142C2×D12—31no—
143C2×D12—31no—
144C2×D12—61no—
145C2×C4×D3—61no—
146C2×C4×D3—61no—
147C2×Dic6—21no—
148C2×Dic6—31no—
149C2×Dic6—31no—
150C2×Dic6—61no—
151C2×Dic6—61no—
152C2×Dic6—61no—
153C2×C3×C8—21no—
154C2×C3×C8—21no—
155C2×C3×C8—41no—
156C2×C3×C8—61no—
157C3×C4⋊C4—31no—
158C3×C4⋊C4—31no—
159C3×C4⋊C4—31no—
160C3×C4⋊C4—31no—
161C3×C4⋊C4—61no—
162C3×C4⋊C4—61no—
163C3×C4⋊C4—61no—
164C3×C4⋊C4—61no—
165C3×C4⋊C4—61no—
166C3×C4⋊C4—61no—
167C3×C42—21no—
168C3×C42C22×D311yescharacteristic
169C3×C42C22×D311yescharacteristic
170#216—122no—
171#215—122no—
172(C2×D3)⋊C4—61no—
173(C2×D3)⋊C4—61no—
174(C2×D3)⋊C4—61no—
175(C2×D3)⋊C4—61no—
176(C2×D3)⋊C4—61no—
177(C2×D3)⋊C4—61no—
178(C2×D3)⋊C4—61no—
179(C2×D3)⋊C4—61no—
180(C2×D3)⋊C4—61no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4—121no—
183(C2×D3)⋊C4—121no—
184C4⋊Dic3—21no—
185C4⋊Dic3—21no—
186C4⋊Dic3—61no—
187C4⋊Dic3—61no—
188C4⋊Dic3D1211yescharacteristic
189C4⋊Dic3D1211yescharacteristic
190C4⋊Dic3#6711yescharacteristic
191C4⋊Dic3#6711yescharacteristic
192Dic3⋊C4—21no—
193Dic3⋊C4—21no—
194Dic3⋊C4—21no—
195Dic3⋊C4—21no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198C4×Dic3—61no—
199C4×Dic3—61no—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—121no—
204Dic12—122no—
205#204—122no—
206C22×C32#12011yescharacteristic
207C2×C3⋊D3—41no—
208C2×C3⋊D3—41no—
209C2×C3⋊D3—41no—
210C32×C4—21no—
211C32×C4—21no—
212C32×C4—21no—
213C3⋊Dic3—41no—
214C3×Dic3—41no—
215C3×Dic3—41no—
216C3×Dic3—41no—
217C3×Dic3—41no—
218C3×Dic3—81no—
219C2×Q16—181no—
220C2×SD16—181no—
221C4⋊Q8—31no—
222C4⋊Q8—181no—
223#126—181no—
224#126—181no—
225#125—31no—
226#125—31no—
227#124—91no—
228#123—181no—
229C22⋊Q8—181no—
230C22⋊Q8—181no—
231#107—61no—
232#107—181no—
233#106—61no—
234#106—181no—
235#97—31no—
236#97—91no—
237#97D3211yescharacteristic
238C22×D3—61no—
239C22×D3—61no—
240C22×D3—121no—
241C3×Q8—121no—
242C3×Q8—121no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—61no—
247C2×C3×C4—61no—
248C2×C3×C4—61no—
249C2×C3×C4—61no—
250C2×C3×C4—121no—
251C2×C3×C4C2×D1211yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4C2×#6711yescharacteristic
257C2×Dic3—21no—
258C2×Dic3—21no—
259C2×Dic3—21no—
260C2×Dic3—21no—
261C2×Dic3—41no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264C2×Dic3—121no—
265D12—121no—
266D12—121no—
267D12—241no—
268C4×D3—241no—
269C4×D3—241no—
270Dic6—41no—
271Dic6—41no—
272Dic6—121no—
273Dic6—121no—
274Dic6—241no—
275Dic6—241no—
276Dic6—241no—
277C3×C8—22no—
278C3×C8—22no—
279C3×C8—42no—
280C3×C8—62no—
281C3⋊C8—22no—
282C3⋊C8—62no—
283C3⋊C8—62no—
284C3⋊C8—122no—
285C2×C32#45311yescharacteristic
286C2×C32#45611yescharacteristic
287C2×C32#45611yescharacteristic
288C3⋊D3—81no—
289C2×Q8—61no—
290C2×Q8—91no—
291C2×Q8—181no—
292C2×D4—91no—
293C22×C4—181no—
294Q16—362no—
295SD16—362no—
296C2×C8—21no—
297C2×C8—61no—
298C2×C8—181no—
299C4⋊C4—31no—
300C4⋊C4—31no—
301C4⋊C4—31no—
302C4⋊C4—31no—
303C4⋊C4—61no—
304C4⋊C4—61no—
305C4⋊C4—61no—
306C4⋊C4—61no—
307C4⋊C4—61no—
308C4⋊C4—61no—
309C4⋊C4—181no—
310C4⋊C4—181no—
311C22⋊C4—181no—
312C22⋊C4—181no—
313C22⋊C4—181no—
314C22⋊C4—181no—
315C22⋊C4—181no—
316C42—181no—
317C42C2×D3211yescharacteristic
318C22×C3—21no—
319C22×C3#88211yescharacteristic
320C22×C3#93711yescharacteristic
321C2×D3—121no—
322C2×D3—121no—
323C2×D3—121no—
324C2×D3—121no—
325C2×D3—121no—
326C2×D3—121no—
327C2×D3—241no—
328C2×D3—241no—
329C2×D3—241no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—41no—
337C3×C4—41no—
338C3×C4—41no—
339C3×C4—121no—
340C3×C4—121no—
341C3×C4—121no—
342C3×C4—121no—
343C3×C4—241no—
344Dic3—41no—
345Dic3—41no—
346Dic3—41no—
347Dic3—41no—
348Dic3—81no—
349Dic3—121no—
350Dic3—121no—
351Dic3—241no—
352C32#166011yescharacteristic, complemented, Sylow
353C23—181no—
354Q8—121no—
355Q8—121no—
356Q8—361no—
357Q8—721no—
358D4—361no—
359C2×C4—61no—
360C2×C4—61no—
361C2×C4—61no—
362C2×C4—61no—
363C2×C4—121no—
364C2×C4—181no—
365C2×C4—721no—
366C2×C4D3×D1211yescharacteristic
367C2×C4#380211yescharacteristic
368C2×C4D3×#6711yescharacteristic
369C8—22no—
370C8—62no—
371C8—182no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3#475211yescharacteristic
376C2×C3#482211yescharacteristic
377C2×C3#482611yescharacteristic
378C2×C3#509511yescharacteristic
379C2×C3#519811yescharacteristic
380C2×C3#520511yescharacteristic
381D3—241no—
382D3—241no—
383D3—481no—
384C22—361no—
385C22—361no—
386C22—361no—
387C22#6392211yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—121no—
392C4—121no—
393C4—121no—
394C4—121no—
395C4—241no—
396C4—361no—
397C3—21no—
398C3#6837211yescharacteristic, complemented
399C3#7139111yescharacteristic, complemented
400C2—721no—
401C2#1059039911yescharacteristic
402C2#1059101311yescharacteristic
403C2#1059101811yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32#120
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenter#97D32
hypocenterC32#1660
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×#4702C2semidirect
4. #10590315C2semidirect
6. C3×#4465C2semidirect
7. #10589088C2semidirect
36. #4702D3semidirect
40. #4465D3semidirect
352. C32#1660semidirect
398. C3#68372semidirect
399. C3#71391semidirect

Maximal subgroups

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

subgroupindex
#105938572
C3×#47022
#105903742
#105903152
#105893302
C3×#44652
#105890882
#713913
#683723