Finite Group Databasebeta

← #11787051

Subgroups — #11787051

Order 1152.

456 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 63 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#10594707C211yesmaximal, characteristic
2#10593327C211yesmaximal, characteristic, complemented
3#10593325C211yesmaximal, characteristic
4#10593317C211yesmaximal, characteristic
5#10590972C211yesmaximal, characteristic, complemented
6#10590189C211yesmaximal, characteristic, complemented
7#10590044C211yesmaximal, characteristic, complemented
8#64306C2211yescharacteristic
9#64286C2211yescharacteristic
10C2×C4×#157C2211yescharacteristic
11M16×C3⋊D3C2211yescharacteristic
12C3×#907—21no—
13#63818C2211yescharacteristic
14C2×#3710C2211yescharacteristic
15C2×#3710C2211yescharacteristic
16#63814—21no—
17#63804—22no—
18#63791—21no—
19D32×C8—21no—
20#63732—21no—
21#63732—21no—
22#63731—22no—
23#63730C411yescharacteristic, complemented
24#63730C411yescharacteristic, complemented
25#63729C411yescharacteristic, complemented
26#63729C411yescharacteristic, complemented
27C3×#822—21no—
28#63577—21no—
29D3×#131—61no—
30D3×#108—61no—
31C22×#157—21no—
32C2×C4×C3⋊D3C2311yescharacteristic
33C3×#235—21no—
34#3811—21no—
35#3805Q812yes—
36#3802C2×C411yescharacteristic
37C4×D32—21no—
38#3798D412yes—
39#3797C2×C411yescharacteristic
40#3796—21no—
41C22⋊#157—21no—
42C4⋊#157C2×C411yescharacteristic
43C4⋊#157C2×C411yescharacteristic
44C4×#157—21no—
45C4×#157—21no—
46C4×#157—21no—
47C32×M16D411yescharacteristic
48#3748D411yescharacteristic
49#3743—21no—
50C8×C3⋊D3—21no—
51C3×#208—21no—
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8—21no—
54C3×ΓL(1,𝔽25)—22no—
55C3×D3×C8—22no—
56#3712—21no—
57#3711—22no—
58#3710—21no—
59#3710—21no—
60#3710—21no—
61#3710C2×C411yescharacteristic
62#3710C2×C411yescharacteristic
63#3710D411yescharacteristic
64#3710D411yescharacteristic
65D3×C3⋊C8—22no—
66#1866—91nomaximal, Sylow
67D3×#41—61no—
68C3×#131—61no—
69#948—61no—
70#907—21no—
71#907—62no—
72D3×M16—61no—
73D3×M16—61no—
74D3×M16—61no—
75D3×M16—62no—
76#901—62no—
77#901—61no—
78C2×D3×C8—61no—
79C2×D3×C8—61no—
80C2×D3×C8—62no—
81C3×#108—61no—
82#822—21no—
83#822—61no—
84#819—61no—
85C22×C3⋊D3#4111yescharacteristic
86C2×D32—21no—
87C2×#157—22no—
88C2×#157—21no—
89C2×#157—21no—
90C2×#157—41no—
91C2×#157—41no—
92C2×C32×C4C2×D411yescharacteristic
93C2×C3⋊Dic3C2×Q811yescharacteristic
94C4×C3⋊D3C22×C411yescharacteristic
95C4×C3⋊D3C2×D411yescharacteristic
96C4×C3⋊D3C2×D411yescharacteristic
97C4×C3⋊D3#4111yescharacteristic
98C3×#67—22no—
99C3×D12—21no—
100C3×C4×D3—22no—
101C3×Dic6—21no—
102#627C4⋊C412yes—
103#626—22no—
104#625C4⋊C412yes—
105#624—21no—
106D3×Dic3—22no—
107C32×C8—21no—
108C3⋊(C3⋊C8)—21no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—21no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—21no—
113C3×C3⋊C8—41no—
114C2×#131—91no—
115C2×#108—91no—
116#424—91no—
117C2×#104—91no—
118#416—91no—
119#339—91no—
120#336—91no—
121C3×#41—61no—
122#239—61no—
123D3×Q8—61no—
124#237—62no—
125#237—61no—
126D3×D4—61no—
127D3×D4—62no—
128#235—21no—
129#235—62no—
130C2×C4×D3—61no—
131C2×C4×D3—61no—
132C2×C4×D3—62no—
133C3×M16—21no—
134C3×M16—21no—
135C3×M16—62no—
136C3×M16—61no—
137C2×C3×C8—62no—
138C2×C3×C8—61no—
139C2×C3×C8—61no—
140#208—21no—
141#208—61no—
142#208—61no—
143#208—62no—
144C2×C3⋊C8—21no—
145C2×C3⋊C8—21no—
146C2×C3⋊C8—62no—
147ΓL(1,𝔽25)—22no—
148ΓL(1,𝔽25)—62no—
149ΓL(1,𝔽25)—62no—
150ΓL(1,𝔽25)—121no—
151ΓL(1,𝔽25)—121no—
152D3×C8—22no—
153D3×C8—61no—
154D3×C8—61no—
155D3×C8—61no—
156D3×C8—61no—
157D3×C8—61no—
158D3×C8—61no—
159D3×C8—61no—
160D3×C8—61no—
161D3×C8—62no—
162D3×C8—62no—
163D3×C8—121no—
164D3×C8—121no—
165C22×C32C22⋊Q811yescharacteristic
166C2×C3⋊D3—21no—
167C2×C3⋊D3—21no—
168C2×C3⋊D3C4×D411yescharacteristic
169C2×C3⋊D3#12311yescharacteristic
170C2×C3×D3—22no—
171D32—41no—
172D32—41no—
173#157—42no—
174#157—41no—
175#157—41no—
176C32×C4C4×D411yescharacteristic
177C32×C4#12011yescharacteristic
178C3⋊Dic3C2×C4⋊C411yescharacteristic
179C3⋊Dic3C22⋊Q811yescharacteristic
180C3×Dic3—22no—
181C2×#41—91no—
182#131—61no—
183#131—182no—
184#131—181no—
185C2×M16—91no—
186C2×M16—91no—
187C2×M16—181no—
188C22×C8—91no—
189C22×C8—91no—
190C22×C8—181no—
191#117—91no—
192C2×C42—91no—
193#108—61no—
194#108—181no—
195C4⋊C8—181no—
196C4⋊C8—181no—
197#104—182no—
198#103—91no—
199#103—91no—
200#102—91no—
201#102—91no—
202C22×D3—61no—
203C22×D3—61no—
204C22×D3—62no—
205C3×Q8—61no—
206C3×D4—61no—
207C3×D4—62no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—62no—
211#67—22no—
212#67—62no—
213#67—62no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216C2×Dic3—62no—
217D12—21no—
218D12—62no—
219C4×D3—22no—
220C4×D3—61no—
221C4×D3—61no—
222C4×D3—61no—
223C4×D3—61no—
224C4×D3—61no—
225C4×D3—61no—
226C4×D3—61no—
227C4×D3—61no—
228C4×D3—62no—
229C4×D3—62no—
230Dic6—21no—
231Dic6—62no—
232C3×C8—22no—
233C3×C8—41no—
234C3×C8—61no—
235C3×C8—61no—
236C3×C8—61no—
237C3×C8—61no—
238C3×C8—121no—
239C3⋊C8—21no—
240C3⋊C8—21no—
241C3⋊C8—21no—
242C3⋊C8—21no—
243C3⋊C8—41no—
244C3⋊C8—62no—
245C3⋊C8—121no—
246C2×C32—21no—
247C2×C32#38511yescharacteristic
248C3⋊D3—21no—
249C3⋊D3#44311yescharacteristic
250C3⋊D3#44411yescharacteristic
251C3×D3—42no—
252#41—61no—
253#41—92no—
254#41—92no—
255#41—181no—
256C2×Q8—91no—
257C2×D4—91no—
258C2×D4—181no—
259C22×C4—91no—
260C22×C4—181no—
261C22×C4—181no—
262M16—62no—
263M16—61no—
264M16—91no—
265M16—181no—
266M16—182no—
267M16—181no—
268M16GO+(4,𝔽2)11yescharacteristic
269C2×C8—62no—
270C2×C8—61no—
271C2×C8—61no—
272C2×C8—91no—
273C2×C8—91no—
274C2×C8—91no—
275C2×C8—91no—
276C2×C8—181no—
277C2×C8—181no—
278C2×C8—181no—
279C2×C8—182no—
280C2×C8—181no—
281C4⋊C4—91no—
282C4⋊C4—91no—
283C22⋊C4—181no—
284C42—181no—
285C42—181no—
286C42—181no—
287C22×C3—21no—
288C22×C3—21no—
289C22×C3—62no—
290C2×D3—22no—
291C2×D3—61no—
292C2×D3—61no—
293C2×D3—61no—
294C2×D3—61no—
295C2×D3—121no—
296C2×D3—121no—
297C2×D3—121no—
298C2×D3—121no—
299C2×D3—122no—
300C2×D3—122no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—62no—
306Dic3—22no—
307Dic3—61no—
308Dic3—61no—
309Dic3—61no—
310Dic3—61no—
311C32#186611yescharacteristic, complemented, Sylow
312C23—91no—
313C23—181no—
314Q8—61no—
315Q8—92no—
316D4—62no—
317D4—61no—
318D4—92no—
319D4—182no—
320C2×C4—62no—
321C2×C4—91no—
322C2×C4—91no—
323C2×C4—91no—
324C2×C4—91no—
325C2×C4—91no—
326C2×C4—181no—
327C2×C4—182no—
328C2×C4—181no—
329C2×C4—181no—
330C2×C4—182no—
331C2×C4—361no—
332C2×C4—361no—
333C2×C4C2×GO+(4,𝔽2)11yescharacteristic
334C8—21no—
335C8—61no—
336C8—61no—
337C8—61no—
338C8—61no—
339C8—121no—
340C8—181no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—41no—
344C2×C3—41no—
345C2×C3—122no—
346D3—42no—
347D3—61no—
348D3—61no—
349D3—61no—
350D3—61no—
351D3—121no—
352D3—121no—
353C22—62no—
354C22—91no—
355C22—91no—
356C22—181no—
357C22—181no—
358C22—361no—
359C22—361no—
360C22D32⋊Q811yescharacteristic
361C4—62no—
362C4—91no—
363C4—91no—
364C4—361no—
365C4—361no—
366C4—362no—
367C4C4×GO+(4,𝔽2)11yescharacteristic
368C4#6424111yescharacteristic
369C3—21no—
370C3—21no—
371C2—21no—
372C2—91no—
373C2—91no—
374C2—122no—
375C2—181no—
376C2#1059339811yescharacteristic
subgroupG/H
centerC4#64241
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×M16D4
socleC2×C32#385
prime radical#64306C22
cosocleC2×C4×C3⋊D3C23
hypercenterM16GO+(4,𝔽2)
hypocenterC32#1866
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ M16

Complements

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

NH ≅ G/Ntype
2. #10593327C2semidirect
5. #10590972C2semidirect
6. #10590189C2semidirect
7. #10590044C2semidirect
23. #63730C4semidirect
24. #63730C4semidirect
25. #63729C4semidirect
26. #63729C4semidirect
311. C32#1866semidirect

Maximal subgroups

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

subgroupindex
#105947072
#105933272
#105933252
#105933172
#105909722
#105901892
#105900442
#18669