Finite Group Databasebeta

← #11861241

Subgroups — #11861241

Order 1152.

710 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 710 conjugacy classes of subgroups — too many to draw. Only its 147 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
1C2×#64223C211yesmaximal, characteristic
2#10594722C212yesmaximal, complemented
3#10593775C211yesmaximal, characteristic, complemented
4#10593331C211yesmaximal, characteristic, complemented
5#10593323C212yesmaximal, complemented
6#10593299C212yesmaximal, complemented
7#10593298C214yesmaximal, complemented
8#10593297C212yesmaximal, complemented
9C2×#3798C2212yes—
10#64286C2211yescharacteristic
11C2×#3787C2211yescharacteristic
12C2×#3776C411yescharacteristic, complemented
13C2×#3775C412yescomplemented
14C2×#3774C411yescharacteristic, complemented
15#64223C411yescharacteristic, complemented
16#64223C412yescomplemented
17#64223C411yescharacteristic, complemented
18#64223C2211yescharacteristic
19#64223C2212yes—
20#64223C2211yescharacteristic
21M16×C3⋊D3C2211yescharacteristic
22C3×D3×M16—22no—
23#63818C2212yes—
24D3×#208—22no—
25#63805C2214yescomplemented
26#63804—24no—
27#63803C2214yescomplemented
28#63767C2212yescomplemented
29C8×#157C2212yescomplemented
30#63733C2212yescomplemented
31#63733C2212yescomplemented
32#63731C2214yescomplemented
33#63731C2214yescomplemented
34#5745—62no—
35C2×C4×C3⋊D3C2311yescharacteristic
36C2×C3×C4×D3—22no—
37C2×#627C2×C412yes—
38C2×#626—22no—
39C2×#625C2×C412yes—
40#3798—22no—
41#3798—22no—
42#3798C2×C412yes—
43#3798C2×C412yes—
44#3798C2312yes—
45#3798C2312yes—
46C22⋊#157—21no—
47C2×#622C2×C411yescharacteristic
48C2×#622C2×C411yescharacteristic
49C4⋊#157—21no—
50C4×#157C2312yes—
51#3787C2×C411yescharacteristic
52#3787C2×C411yescharacteristic
53#3787C2311yescharacteristic
54#3787C2311yescharacteristic
55#3776C2×C411yescharacteristic
56#3776C2×C412yes—
57#3776C2×C411yescharacteristic
58#3775C2×C412yes—
59#3775C2×C412yes—
60#3775C2×C412yes—
61#3775C2×C412yes—
62#3774C2×C411yescharacteristic
63#3774C2×C412yes—
64#3774C2×C411yescharacteristic
65C32×M16D411yescharacteristic
66#3748D411yescharacteristic
67#3743D412yes—
68C8×C3⋊D3C2312yes—
69C3×#208—22no—
70C3×ΓL(1,𝔽25)—24no—
71C3×D3×C8—24no—
72#3712C2314yes—
73#3711—24no—
74#3710—22no—
75D3×C3⋊C8—24no—
76#2957—91nomaximal, Sylow
77C2×#235—62no—
78C2×C3×M16—62no—
79C2×#208—62no—
80#907—64no—
81#907—64no—
82D3×M16—22no—
83D3×M16—62no—
84D3×M16—62no—
85D3×M16—62no—
86#901—64no—
87#901—64no—
88C22×C3⋊D3#4111yescharacteristic
89C22×C3×D3—22no—
90C2×#157—22no—
91C2×C32×C4C2×D411yescharacteristic
92C2×C3⋊Dic3C22×C411yescharacteristic
93C4×C3⋊D3C22×C411yescharacteristic
94C4×C3⋊D3C2×D411yescharacteristic
95C4×C3⋊D3#4111yescharacteristic
96C4×C3⋊D3C2411yescharacteristic
97C2×C3×Dic3—22no—
98C3×C4×D3—22no—
99C3×C4×D3—22no—
100C3×C4×D3—22no—
101C3×C4×D3—22no—
102#627—22no—
103#627C22×C412yes—
104#627C22×C412yes—
105#626—22no—
106#626—22no—
107#626—22no—
108#626—22no—
109#625—22no—
110#625C22×C412yes—
111#625C22×C412yes—
112#622C22×C411yescharacteristic
113#622C22×C411yescharacteristic
114#622C22×C411yescharacteristic
115#622C22×C411yescharacteristic
116C32×C8C2×D412yes—
117C3⋊(C3⋊C8)C2×D412yes—
118C3×C3⋊C8—24no—
119C2×#135—91no—
120#568—92no—
121#444—94no—
122#443—92no—
123#443—92no—
124C2×#108—91no—
125#421—92no—
126#405—91no—
127C22×C3×C4—62no—
128C2×#67—62no—
129C2×#67—62no—
130#235—62no—
131#235—62no—
132#235—62no—
133#235—62no—
134#235—62no—
135#235—62no—
136#235—62no—
137#235—62no—
138C2×D12—62no—
139C2×C4×D3—22no—
140C2×C4×D3—62no—
141C2×Dic6—62no—
142C3×M16—22no—
143C3×M16—64no—
144C3×M16—62no—
145C2×C3×C8—64no—
146#208—22no—
147#208—62no—
148#208—64no—
149C2×C3⋊C8—64no—
150ΓL(1,𝔽25)—24no—
151ΓL(1,𝔽25)—64no—
152ΓL(1,𝔽25)—64no—
153ΓL(1,𝔽25)—64no—
154D3×C8—24no—
155D3×C8—64no—
156D3×C8—64no—
157D3×C8—64no—
158C22×C32C4×D411yescharacteristic
159C2×C3⋊D3—41no—
160C2×C3⋊D3C4×D411yescharacteristic
161C2×C3⋊D3C2×#4111yescharacteristic
162C2×C3×D3—22no—
163C2×C3×D3—22no—
164C2×C3×D3—82no—
165#157—42no—
166C32×C4C4×D411yescharacteristic
167C32×C4C22×D411yescharacteristic
168C3⋊Dic3C4×D411yescharacteristic
169C3⋊Dic3C23×C411yescharacteristic
170C3×Dic3—22no—
171C3×Dic3—22no—
172C2×#41—92no—
173#135—91no—
174#135—91no—
175#135—92no—
176#135—91no—
177#135—91no—
178#135—92no—
179C2×Q16—91no—
180C2×SD16—92no—
181C2×D8—91no—
182#131—94no—
183#131—94no—
184#131—184no—
185C2×M16—62no—
186C2×M16—91no—
187C2×M16—92no—
188C2×M16—182no—
189C22×C8—91no—
190#117—91no—
191#108—92no—
192#108—92no—
193#104—94no—
194#104—94no—
195#97—92no—
196C4×C8—92no—
197C23×C3—62no—
198C22×D3—22no—
199C22×D3—62no—
200C2×C3×C4—22no—
201C2×C3×C4—62no—
202C2×C3×C4—62no—
203C2×C3×C4—62no—
204C2×C3×C4—62no—
205C2×C3×C4—62no—
206#67—62no—
207#67—62no—
208#67—62no—
209#67—62no—
210#67—62no—
211#67—62no—
212#67—62no—
213#67—62no—
214C2×Dic3—22no—
215C2×Dic3—62no—
216D12—62no—
217D12—62no—
218D12—62no—
219D12—62no—
220C4×D3—22no—
221C4×D3—22no—
222C4×D3—22no—
223C4×D3—22no—
224C4×D3—62no—
225C4×D3—62no—
226C4×D3—62no—
227C4×D3—62no—
228Dic6—62no—
229Dic6—62no—
230Dic6—62no—
231Dic6—62no—
232C3×C8—24no—
233C3×C8—64no—
234C3⋊C8—24no—
235C3⋊C8—64no—
236C2×C32—21no—
237C2×C32C2×C4×D411yescharacteristic
238C3⋊D3—21no—
239C3⋊D3—21no—
240C3×D3—42no—
241C3×D3—42no—
242#41—92no—
243#41—92no—
244#41—92no—
245#41—92no—
246#41—182no—
247#41—182no—
248C2×Q8—92no—
249C2×D4—92no—
250C2×D4—182no—
251C22×C4—62no—
252C22×C4—91no—
253Q16—91no—
254Q16—91no—
255Q16—92no—
256SD16—92no—
257SD16—92no—
258SD16—92no—
259SD16—92no—
260D8—91no—
261D8—91no—
262D8—92no—
263M16—62no—
264M16—64no—
265M16—94no—
266M16—91no—
267M16—92no—
268M16—184no—
269M16GO+(4,𝔽2)11yescharacteristic
270C2×C8—64no—
271C2×C8—91no—
272C2×C8—91no—
273C2×C8—91no—
274C2×C8—91no—
275C2×C8—91no—
276C2×C8—91no—
277C2×C8—92no—
278C2×C8—182no—
279C2×C8—184no—
280C4⋊C4—181no—
281C22⋊C4—181no—
282C42—92no—
283C22×C3—22no—
284C22×C3—62no—
285C22×C3—62no—
286C22×C3—242no—
287C2×D3—22no—
288C2×D3—22no—
289C2×D3—62no—
290C2×D3—62no—
291C2×D3—82no—
292C2×D3—242no—
293C3×C4—22no—
294C3×C4—22no—
295C3×C4—62no—
296C3×C4—62no—
297Dic3—22no—
298Dic3—22no—
299Dic3—62no—
300Dic3—62no—
301C32#295711yescharacteristic, complemented, Sylow
302C23—62no—
303C23—91no—
304Q8—92no—
305Q8—92no—
306Q8—182no—
307D4—92no—
308D4—92no—
309D4—182no—
310D4—182no—
311D4—182no—
312D4—182no—
313D4—182no—
314C2×C4—62no—
315C2×C4—62no—
316C2×C4—62no—
317C2×C4—62no—
318C2×C4—62no—
319C2×C4—91no—
320C2×C4—91no—
321C2×C4—91no—
322C2×C4—91no—
323C2×C4—91no—
324C2×C4—182no—
325C2×C4C2×GO+(4,𝔽2)11yescharacteristic
326C8—64no—
327C8—91no—
328C8—91no—
329C8—91no—
330C8—91no—
331C8—92no—
332C8C2×GO+(4,𝔽2)12yes—
333C2×C3—22no—
334C2×C3—42no—
335C2×C3—122no—
336C2×C3—122no—
337D3—42no—
338D3—42no—
339D3—122no—
340D3—122no—
341C22—62no—
342C22—62no—
343C22—91no—
344C22—91no—
345C22—242no—
346C22—361no—
347C22C4×GO+(4,𝔽2)11yescharacteristic
348C4—62no—
349C4—62no—
350C4—91no—
351C4—91no—
352C4—362no—
353C4C4×GO+(4,𝔽2)11yescharacteristic
354C4C22×GO+(4,𝔽2)11yescharacteristic
355C3—22no—
356C2—21no—
357C2—122no—
358C2—122no—
359C2—181no—
360C2—181no—
361C2C2×C4×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC4C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC32×M16D4
socleC2×C32C2×C4×D4
prime radicalC2×#64223C2
cosocleC4×C3⋊D3C24
hypercenterM16GO+(4,𝔽2)
hypocenterC32#2957
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ M16

Complements

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

NH ≅ G/Ntype
2. #10594722C2semidirect
3. #10593775C2semidirect
4. #10593331C2semidirect
5. #10593323C2semidirect
6. #10593299C2semidirect
7. #10593298C2semidirect
8. #10593297C2semidirect
12. C2×#3776C4semidirect
13. C2×#3775C4semidirect
14. C2×#3774C4semidirect
15. #64223C4semidirect
16. #64223C4semidirect
17. #64223C4semidirect
25. #63805C22semidirect
27. #63803C22semidirect
28. #63767C22semidirect
29. C8×#157C22semidirect
30. #63733C22semidirect
31. #63733C22semidirect
32. #63731C22semidirect
33. #63731C22semidirect
301. C32#2957semidirect

Maximal subgroups

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

subgroupindex
C2×#642232
#105947222
#105937752
#105933312
#105933232
#105932992
#105932982
#105932972
#29579