Finite Group Databasebeta

← #11878680

Subgroups — #11878680

Order 1152.

936 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 936 conjugacy classes of subgroups — too many to draw. Only its 115 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#10595032C211yesmaximal, characteristic, complemented
2C2×#63914C211yesmaximal, characteristic, complemented
3#10593795C211yesmaximal, characteristic, complemented
4#10593519C214yesmaximal, complemented
5#10593418C212yesmaximal, complemented
6#10593417C214yesmaximal, complemented
7#10593348C212yesmaximal, complemented
8C2×C3×#235—21no—
9C22×C3×D12—21no—
10C22×#625—21no—
11C22×#625C2212yes—
12C2×#3774C2218yescomplemented
13C2×C4×C3⋊Dic3C2211yescharacteristic
14#63980—21no—
15#63980C2212yes—
16#63914—21no—
17#63914—21no—
18#63914C2212yes—
19#63914C2212yes—
20#63914C2211yescharacteristic, complemented
21C4×#625—21no—
22C4×#625C2212yescomplemented
23#63873C2211yescharacteristic, complemented
24#63863—21no—
25C22⋊#622C2212yes—
26C4⋊#622C2212yescomplemented
27C4×#622C2212yescomplemented
28#63739C2218yescomplemented
29#5832—61no—
30C2×#940—61no—
31C23×C3×D3—22no—
32C22×C32×C4D411yescharacteristic
33C22×C3⋊Dic3D411yescharacteristic
34C22×C3⋊Dic3C2311yescharacteristic
35C2×C3×#67—22no—
36C3×#235—44no—
37C2×C3×D12—22no—
38C2×C3×D12—22no—
39C2×C3×D12—21no—
40C2×C3×D12—44no—
41C2×C3×C4×D3—22no—
42C2×C3×Dic6—21no—
43C2×#625—22no—
44C2×#625—22no—
45C2×#625—22no—
46C2×#625—21no—
47C2×#625—44no—
48C2×#625—44no—
49C2×#625C2314yes—
50C2×#625C2312yes—
51C2×#622C2314yes—
52#3774—48no—
53C4×C3⋊Dic3D411yescharacteristic
54C4×C3⋊Dic3D411yescharacteristic
55C4×C3⋊Dic3C2311yescharacteristic
56C4×C3⋊Dic3C2311yescharacteristic
57#3724—21no—
58#3724C2312yes—
59(C2×D3)⋊Dic3—22no—
60(C2×D3)⋊Dic3—22no—
61#3205—91nomaximal, Sylow
62C2×C3×#41—61no—
63C22×C3×D4—61no—
64C22×#67—62no—
65C22×#67—62no—
66C2×#235—21no—
67C22×D12—21no—
68#947—61no—
69#944—61no—
70#940—62no—
71#940—62no—
72#940—61no—
73#940—62no—
74#940—62no—
75#939—62no—
76#939—62no—
77#936—61no—
78C4×#67—62no—
79C4×#67—62no—
80C2×C4×Dic3—61no—
81C2×C4×Dic3—61no—
82C23×C32C2×D411yescharacteristic
83C22×C3×D3—24no—
84C22×C3×D3—22no—
85C22×C3×D3—44no—
86C22×C3×D3—44no—
87C22×C3×D3—44no—
88C2×C32×C4D814yescomplemented
89C2×C32×C4C2×D411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C3⋊Dic3—22no—
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3C2×D411yescharacteristic
94C2×C3⋊Dic3C2×D411yescharacteristic
95C2×C3⋊Dic3C2×D411yescharacteristic
96C2×C3⋊Dic3C2411yescharacteristic
97C3×#67—44no—
98C2×C3×Dic3—22no—
99C3×D12—44no—
100C3×D12—44no—
101C3×D12—42no—
102C3×C4×D3—44no—
103C3×Dic6—42no—
104#625—24no—
105#625—28no—
106#625—44no—
107#625—44no—
108#625—42no—
109#625—44no—
110#622—24no—
111#532—91no—
112C2×#127—91no—
113#493—92no—
114#486—92no—
115#459—94no—
116#447—94no—
117#431—91no—
118C24×C3—62no—
119C23×D3—22no—
120C3×#41—124no—
121C2×C3×Q8—61no—
122C2×C3×D4—61no—
123C2×C3×D4—62no—
124C2×C3×D4—62no—
125C2×C3×D4—62no—
126C2×C3×D4—124no—
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C22×C3×C4—62no—
130C2×#67—22no—
131C2×#67—62no—
132C2×#67—64no—
133C2×#67—62no—
134C2×#67—64no—
135C2×#67—64no—
136C2×#67—64no—
137C2×#67—128no—
138C2×#67—128no—
139C22×Dic3—61no—
140C22×Dic3—61no—
141C22×Dic3—61no—
142C22×Dic3—61no—
143#235—44no—
144C2×D12—22no—
145C2×D12—22no—
146C2×D12—21no—
147C2×D12—44no—
148C2×C4×D3—22no—
149C2×Dic6—21no—
150#217—62no—
151#217—62no—
152(C2×D3)⋊C4—62no—
153(C2×D3)⋊C4—62no—
154Dic3⋊C4—62no—
155Dic3⋊C4—62no—
156C4×Dic3—61no—
157C4×Dic3—61no—
158C4×Dic3—61no—
159C4×Dic3—61no—
160C4×Dic3—61no—
161C4×Dic3—61no—
162C4×Dic3—61no—
163C4×Dic3—61no—
164C22×C32—21no—
165C22×C32—21no—
166C22×C32C2×D812yes—
167C22×C32C22×D411yescharacteristic
168C2×C3×D3—44no—
169C2×C3×D3—42no—
170C2×C3×D3—42no—
171C2×C3×D3—44no—
172C2×C3×D3—44no—
173C2×C3×D3—42no—
174C2×C3×D3—88no—
175C32×C4C2×D812yes—
176C32×C4C2×D812yes—
177C3⋊Dic3—21no—
178C3⋊Dic3—21no—
179C3⋊Dic3AGL(1,ℤ/8)12yes—
180C3⋊Dic3H(5,𝔽2)12yes—
181C3×Dic3—42no—
182C2×#41—61no—
183C22×D4—61no—
184C22×D4—92no—
185C22×D4—181no—
186C2×D8—98no—
187C4⋊Q8—91no—
188#127—92no—
189#127—92no—
190#127—91no—
191#127—181no—
192#127—181no—
193#124—181no—
194#121—92no—
195#121—181no—
196C4×D4—92no—
197C4×D4—181no—
198C2×C42—91no—
199C4⋊C8—92no—
200#102—98no—
201C22⋊C8—92no—
202C4×C8—92no—
203C23×C3—21no—
204C23×C3—21no—
205C23×C3—62no—
206C23×C3—64no—
207C23×C3—124no—
208C23×C3—124no—
209C23×C3—124no—
210C22×D3—22no—
211C22×D3—24no—
212C22×D3—44no—
213C22×D3—44no—
214C22×D3—44no—
215C3×Q8—122no—
216C3×D4—124no—
217C3×D4—124no—
218C3×D4—122no—
219C3×D4—124no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—24no—
225C2×C3×C4—24no—
226C2×C3×C4—62no—
227C2×C3×C4—124no—
228#67—44no—
229#67—124no—
230#67—128no—
231#67—124no—
232#67—128no—
233#67—128no—
234#67—128no—
235C2×Dic3—22no—
236C2×Dic3—61no—
237C2×Dic3—61no—
238C2×Dic3—61no—
239C2×Dic3—61no—
240C2×Dic3—61no—
241C2×Dic3—61no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244C2×Dic3—64no—
245C2×Dic3—64no—
246C2×Dic3—122no—
247C2×Dic3—122no—
248D12—44no—
249D12—44no—
250D12—42no—
251C4×D3—44no—
252Dic6—42no—
253C2×C32—22no—
254C2×C32#53511yescharacteristic
255C2×C32C22×D811yescharacteristic
256C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
257C3×D3—82no—
258C3×D3—84no—
259C24—62no—
260#41—124no—
261C2×Q8—61no—
262C2×D4—62no—
263C2×D4—61no—
264C2×D4—62no—
265C2×D4—62no—
266C2×D4—94no—
267C2×D4—92no—
268C2×D4—124no—
269C2×D4—181no—
270C2×D4—182no—
271C2×D4—182no—
272C2×D4—182no—
273C2×D4—364no—
274C2×D4—364no—
275C22×C4—62no—
276C22×C4—91no—
277C22×C4—91no—
278C22×C4GO+(4,𝔽2)11yescharacteristic
279D8—368no—
280C2×C8—94no—
281C4⋊C4—92no—
282C4⋊C4—181no—
283C22⋊C4—182no—
284C22⋊C4—182no—
285C42—91no—
286C42—91no—
287C42—91no—
288C42—91no—
289C22×C3—22no—
290C22×C3—22no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—22no—
294C22×C3—22no—
295C22×C3—41no—
296C22×C3—41no—
297C22×C3—124no—
298C22×C3—124no—
299C22×C3—122no—
300C22×C3—122no—
301C22×C3—122no—
302C22×C3—124no—
303C22×C3—248no—
304C2×D3—42no—
305C2×D3—44no—
306C2×D3—44no—
307C2×D3—44no—
308C2×D3—42no—
309C2×D3—42no—
310C2×D3—88no—
311C3×C4—22no—
312C3×C4—22no—
313C3×C4—22no—
314C3×C4—22no—
315C3×C4—122no—
316Dic3—42no—
317Dic3—62no—
318Dic3—62no—
319Dic3—62no—
320Dic3—62no—
321Dic3—62no—
322Dic3—62no—
323Dic3—121no—
324Dic3—121no—
325C32#320511yescharacteristic, complemented, Sylow
326C23—62no—
327C23—64no—
328C23—124no—
329C23—124no—
330C23—124no—
331C23C2×GO+(4,𝔽2)11yescharacteristic
332Q8—122no—
333D4—124no—
334D4—124no—
335D4—124no—
336D4—122no—
337D4—184no—
338D4—188no—
339D4—364no—
340D4—362no—
341D4—364no—
342D4—364no—
343C2×C4—62no—
344C2×C4—91no—
345C2×C4—91no—
346C2×C4—91no—
347C2×C4—91no—
348C2×C4—124no—
349C2×C4—182no—
350C2×C4—182no—
351C2×C4#377414yescomplemented
352C2×C4C2×GO+(4,𝔽2)11yescharacteristic
353C2×C4C2×GO+(4,𝔽2)11yescharacteristic
354C8—184no—
355C2×C3—24no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—42no—
363C2×C3—244no—
364C2×C3—242no—
365D3—84no—
366D3—82no—
367C22—21no—
368C22—21no—
369C22—124no—
370C22—122no—
371C22—124no—
372C22—122no—
373C22—122no—
374C22—124no—
375C22—248no—
376C22C2×#377412yes—
377C22C22×GO+(4,𝔽2)11yescharacteristic
378C4—92no—
379C4—92no—
380C4—122no—
381C4—181no—
382C4—181no—
383C4C2×#377412yes—
384C4C2×#377412yes—
385C3—21no—
386C3—21no—
387C2—22no—
388C2—244no—
389C2—242no—
390C2#1059650111yescharacteristic
391C2#1059651211yescharacteristic
392C2C22×#377411yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC22×C32×C4D4
socleC22×C32C22×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#3205
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. #10595032C2semidirect
2. C2×#63914C2semidirect
3. #10593795C2semidirect
4. #10593519C2semidirect
5. #10593418C2semidirect
6. #10593417C2semidirect
7. #10593348C2semidirect
12. C2×#3774C22semidirect
20. #63914C22semidirect
22. C4×#625C22semidirect
23. #63873C22semidirect
26. C4⋊#622C22semidirect
27. C4×#622C22semidirect
28. #63739C22semidirect
88. C2×C32×C4D8semidirect
325. C32#3205semidirect
351. C2×C4#3774semidirect

Maximal subgroups

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

subgroupindex
#105950322
C2×#639142
#105937952
#105935192
#105934182
#105934172
#105933482
#32059