Finite Group Databasebeta

← #11787786

Subgroups — #11787786

Order 1152.

819 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 819 conjugacy classes of subgroups — too many to draw. Only its 124 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#10596303C211yesmaximal, characteristic
2#10594780C211yesmaximal, characteristic, complemented
3C3×#5236C212yesmaximal, complemented
4#10591232C211yesmaximal, characteristic, complemented
5#10589160C212yesmaximal, complemented
6#70417—32nomaximal
7C2×C32×#41C2211yescharacteristic
8C2×#3828C2211yescharacteristic
9#64156C411yescharacteristic, complemented
10#64153C411yescharacteristic, complemented
11#64149C411yescharacteristic, complemented
12#64148—22no—
13#64145C411yescharacteristic, complemented
14C4×#638—22no—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C3×#926C2212yes—
17C2×C3×#208C2212yes—
18#63818—22no—
19#63817—24no—
20C3×#837—24no—
21#63581—22no—
22#5832—32no—
23#5832—61no—
24#5745—32no—
25C3×#421—32no—
26#5236D312yescomplemented
27#5006—32no—
28#4555—32no—
29#4532—32no—
30C32×#41—22no—
31C32×#41—22no—
32C2×C32×Q8C2×C411yescharacteristic
33C2×C32×D4—21no—
34C2×C32×D4C2×C411yescharacteristic
35C22×C32×C4—21no—
36C22×C32×C4C2311yescharacteristic
37C2×#638—22no—
38C2×#638D412yes—
39C22×C3⋊Dic3—21no—
40#3828—22no—
41#3828—22no—
42C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
43C2×C4×C3⋊D3D412yes—
44C2×#634C2×C411yescharacteristic
45#3757—22no—
46#3752—22no—
47#3750—22no—
48C4×C3⋊Dic3—21no—
49C4×C3⋊Dic3C2×C411yescharacteristic
50C4×C3⋊Dic3C2×C411yescharacteristic
51C3×#217—22no—
52C3×C4⋊Dic3—22no—
53C3×C4×Dic3—22no—
54C3×#208—22no—
55C3×#208D414yescomplemented
56C2×C3×C3⋊C8—22no—
57#3712—24no—
58#3710—24no—
59#1884—91noSylow
60C2×C3×#41—21no—
61C2×C3×#41C2×D312yes—
62C2×#235—32no—
63C2×#235—61no—
64C2×C3×M16—32no—
65C3×#117—32no—
66#947—32no—
67#947—61no—
68#944—32no—
69#944—61no—
70#940—32no—
71#940—61no—
72#939—64no—
73#939—64no—
74#936—32no—
75#936—61no—
76C4×#67—64no—
77C4×#67—64no—
78#926C2×D312yes—
79C2×C4×Dic3—32no—
80C2×C4×Dic3—61no—
81C2×#208C2×D312yes—
82#907—64no—
83D3×M16—64no—
84#901—64no—
85C3×#104—64no—
86#837—24no—
87#806—64no—
88C23×C32—21no—
89C23×C32C2×D411yescharacteristic
90C22×C3⋊D3C22⋊C412yes—
91C32×Q8—22no—
92C32×D4—22no—
93C32×D4—42no—
94C2×C32×C4—21no—
95C2×C32×C4—41no—
96C2×C32×C4—41no—
97C2×C32×C4C22×C411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D412yes—
100C2×C32×C4#4112yes—
101#638—24no—
102#638—44no—
103C2×C3⋊Dic3—21no—
104C2×C3⋊Dic3—21no—
105C2×C3⋊Dic3—42no—
106C2×C3⋊Dic3C22⋊C412yes—
107C4⋊(C3⋊D3)—22no—
108C4×C3⋊D3—22no—
109C4×C3⋊D3—22no—
110#634—22no—
111C2×C3×Dic3—42no—
112C3×C3⋊C8—24no—
113#568—91no—
114#532—91no—
115#421—32no—
116#410—91no—
117#339—92no—
118C3×#41—22no—
119C3×#41—22no—
120C3×#41—22no—
121C3×#41—22no—
122C3×#41—42no—
123C3×#41—42no—
124C2×C3×Q8—21no—
125C2×C3×Q8C4×D312yes—
126C2×C3×D4—22no—
127C2×C3×D4—22no—
128C2×C3×D4—21no—
129C2×C3×D4C4×D312yes—
130C22×C3×C4—22no—
131C22×C3×C4—22no—
132C22×C3×C4—21no—
133C22×C3×C4C22×D312yes—
134C2×#67—34no—
135C2×#67—62no—
136C2×#67—64no—
137C2×#67—64no—
138C22×Dic3—62no—
139C22×Dic3—62no—
140#235—62no—
141#235—62no—
142#235—62no—
143#235—62no—
144#235—122no—
145#235—122no—
146C2×D12—32no—
147C2×D12—61no—
148C2×C4×D3—34no—
149C2×C4×D3—62no—
150C2×Dic6—32no—
151C2×Dic6—61no—
152C3×M16—34no—
153C3×M16—62no—
154C2×C3×C8—62no—
155C3×C4⋊C4—62no—
156C3×C22⋊C4—62no—
157C3×C42—62no—
158#217—22no—
159#217—64no—
160#217—64no—
161(C2×D3)⋊C4—64no—
162(C2×D3)⋊C4—64no—
163C4⋊Dic3—22no—
164Dic3⋊C4—64no—
165Dic3⋊C4—64no—
166C4×Dic3—22no—
167C4×Dic3—32no—
168C4×Dic3—32no—
169C4×Dic3—61no—
170C4×Dic3—61no—
171C4×Dic3—62no—
172C4×Dic3—62no—
173#208—22no—
174#208#6714yescomplemented
175C2×C3⋊C8—22no—
176ΓL(1,𝔽25)—68no—
177D3×C8—68no—
178C22×C32—41no—
179C22×C32—42no—
180C22×C32—41no—
181C22×C32C2×C22⋊C411yescharacteristic
182C22×C32#12112yes—
183C2×C3⋊D3—22no—
184C2×C3⋊D3—42no—
185C32×C4—41no—
186C32×C4C4×D412yes—
187C32×C4#12011yescharacteristic
188C32×C4#12311yescharacteristic
189C3⋊Dic3—22no—
190C3⋊Dic3—22no—
191C3⋊Dic3—41no—
192C3×Dic3—82no—
193C2×#41—91no—
194C2×#41D3211yescharacteristic
195#131—184no—
196C2×M16—32no—
197C2×M16—182no—
198C4⋊Q8—91no—
199#127—91no—
200#124—91no—
201#124—91no—
202#121—182no—
203C4×D4—182no—
204#117—32no—
205C2×C42—91no—
206#104—64no—
207#99—182no—
208C23×C3—22no—
209C23×C3—22no—
210C23×C3—21no—
211C23×C3D3×D412yes—
212C22×D3—34no—
213C22×D3—62no—
214C3×Q8—22no—
215C3×Q8—22no—
216C3×Q8—42no—
217C3×D4—22no—
218C3×D4—22no—
219C3×D4—42no—
220C3×D4—44no—
221C3×D4—42no—
222C3×D4—42no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—21no—
227C2×C3×C4—22no—
228C2×C3×C4—21no—
229C2×C3×C4—42no—
230C2×C3×C4—42no—
231C2×C3×C4—42no—
232C2×C3×C4—42no—
233C2×C3×C4—122no—
234C2×C3×C4C2×C4×D312yes—
235C2×C3×C4#23512yes—
236C2×C3×C4D3×D412yes—
237C2×C3×C4D3×D412yes—
238C2×C3×C4#23712yes—
239C2×C3×C4C2×#6712yes—
240#67—64no—
241#67—64no—
242#67—124no—
243#67—128no—
244#67—128no—
245C2×Dic3—34no—
246C2×Dic3—42no—
247C2×Dic3—62no—
248C2×Dic3—62no—
249C2×Dic3—62no—
250C2×Dic3—62no—
251C2×Dic3—62no—
252C2×Dic3—124no—
253C2×Dic3—124no—
254D12—62no—
255D12—62no—
256D12—122no—
257C4×D3—64no—
258C4×D3—64no—
259C4×D3—122no—
260C4×D3—122no—
261Dic6—62no—
262Dic6—62no—
263Dic6—122no—
264C3×C8—64no—
265C3⋊C8—24no—
266C2×C32—21no—
267C2×C32—22no—
268C2×C32—81no—
269C2×C32#38611yescharacteristic
270C3⋊D3—42no—
271#41—22no—
272#41—22no—
273#41—182no—
274#41—182no—
275C2×Q8—91no—
276C2×Q8#62411yescharacteristic
277C2×D4—21no—
278C2×D4—92no—
279C2×D4—91no—
280C2×D4—182no—
281C2×D4#62411yescharacteristic
282C22×C4—21no—
283C22×C4—92no—
284C22×C4—181no—
285C22×C4C2×D3211yescharacteristic
286M16—34no—
287M16—62no—
288M16—184no—
289C2×C8—62no—
290C2×C8—184no—
291C4⋊C4—62no—
292C4⋊C4—182no—
293C22⋊C4—62no—
294C22⋊C4—182no—
295C22⋊C4—182no—
296C42—62no—
297C42—91no—
298C42—91no—
299C42—181no—
300C22×C3—22no—
301C22×C3—21no—
302C22×C3—42no—
303C22×C3—42no—
304C22×C3—44no—
305C22×C3—44no—
306C22×C3—42no—
307C22×C3—42no—
308C22×C3D3×C22⋊C412yes—
309C22×C3#88412yes—
310C22×C3#93812yes—
311C2×D3—64no—
312C2×D3—122no—
313C2×D3—124no—
314C2×D3—124no—
315C3×C4—22no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—42no—
319C3×C4—42no—
320C3×C4—242no—
321C3×C4#67⋊C412yes—
322C3×C4#88312yes—
323C3×C4C4×#6712yes—
324C3×C4#93712yes—
325Dic3—64no—
326Dic3—64no—
327Dic3—64no—
328Dic3—82no—
329Dic3—122no—
330Dic3—122no—
331Dic3—122no—
332C32#188411yescharacteristic, complemented, Sylow
333C23—21no—
334C23—92no—
335C23#381111yescharacteristic
336Q8—22no—
337Q8—182no—
338D4—22no—
339D4—42no—
340D4—184no—
341D4—182no—
342D4—364no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—92no—
347C2×C4—122no—
348C2×C4—181no—
349C2×C4—182no—
350C2×C4—182no—
351C2×C4—181no—
352C2×C4—362no—
353C2×C4#380412yes—
354C2×C4C2×#62411yescharacteristic
355C2×C4D3×#6712yes—
356C2×C4#381111yescharacteristic
357C8—64no—
358C2×C3—22no—
359C2×C3—22no—
360C2×C3—22no—
361C2×C3—22no—
362C2×C3—21no—
363C2×C3—42no—
364C2×C3—82no—
365C2×C3—82no—
366C2×C3#495612yes—
367D3—124no—
368D3—242no—
369C22—41no—
370C22—42no—
371C22—41no—
372C22—182no—
373C22—362no—
374C22#6395812yes—
375C22#6397411yescharacteristic
376C4—41no—
377C4—182no—
378C4—182no—
379C4—242no—
380C4—361no—
381C4#6395212yes—
382C4#6397511yescharacteristic
383C4#6398311yescharacteristic
384C3—21no—
385C3#7041712yescomplemented
386C2—21no—
387C2—22no—
388C2—81no—
389C2—362no—
390C2#1059172211yescharacteristic
subgroupG/H
centerC4#63983
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC2×C32#386
prime radical#10596303C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1884
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10594780C2semidirect
3. C3×#5236C2semidirect
4. #10591232C2semidirect
5. #10589160C2semidirect
9. #64156C4semidirect
10. #64153C4semidirect
11. #64149C4semidirect
13. #64145C4semidirect
26. #5236D3semidirect
55. C3×#208D4semidirect
174. #208#67semidirect
332. C32#1884semidirect
385. C3#70417semidirect

Maximal subgroups

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

subgroupindex
#105963032
#105947802
C3×#52362
#105912322
#105891602
#704173