Finite Group Databasebeta

← #11878870

Subgroups — #11878870

Order 1152.

848 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 848 conjugacy classes of subgroups — too many to draw. Only its 109 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×#63914C211yesmaximal, characteristic
2#10594810C211yesmaximal, characteristic, complemented
3#10593801C211yesmaximal, characteristic, complemented
4#10593523C214yesmaximal, complemented
5#10593442C212yesmaximal, complemented
6#10593355C214yesmaximal, complemented
7#10593348C212yesmaximal, complemented
8C22×C3×D12—21no—
9C22×#625—21no—
10C22×#625C2212yes—
11C2×#3775C2218yescomplemented
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C3×#924—21no—
14#63982C2212yes—
15#63957—21no—
16#63919C2211yescharacteristic, complemented
17#63914—21no—
18#63914—21no—
19#63914C2212yes—
20#63914C2212yes—
21#63873C2211yescharacteristic, complemented
22#63870—21no—
23#63843—21no—
24#63838C2212yescomplemented
25C22⋊#622C2212yes—
26#63779C2212yescomplemented
27C4×#622C2212yescomplemented
28#63739C2218yescomplemented
29C2×#940—61no—
30#5622—61no—
31C23×C3×D3—22no—
32C22×C32×C4D411yescharacteristic
33C22×C3⋊Dic3D411yescharacteristic
34C22×C3⋊Dic3C2311yescharacteristic
35C2×C3×D12—22no—
36C2×C3×D12—22no—
37C2×C3×D12—44no—
38C2×C3×Dic6—21no—
39C2×#627C2312yes—
40C2×#625—22no—
41C2×#625—22no—
42C2×#625—22no—
43C2×#625—44no—
44C2×#625—44no—
45C2×#625C2314yes—
46C2×#622C2314yes—
47#3775—48no—
48C4×C3⋊Dic3D411yescharacteristic
49C4×C3⋊Dic3D411yescharacteristic
50C4×C3⋊Dic3C2311yescharacteristic
51C4×C3⋊Dic3C2311yescharacteristic
52C3×#217—22no—
53C3×C4⋊Dic3—21no—
54C3×Dic3⋊C4—22no—
55#3724—21no—
56#3724—21no—
57#3724C2312yes—
58Dic3⋊Dic3—22no—
59Dic32—22no—
60#3208—91nomaximal, Sylow
61C22×C3×D4—61no—
62C22×#67—62no—
63C22×#67—62no—
64C22×D12—21no—
65C3×C22⋊Q8—61no—
66Q8×Dic3—61no—
67#944—61no—
68#940—62no—
69#940—62no—
70#940—62no—
71#940—62no—
72#924—21no—
73C2×C4×Dic3—61no—
74C2×C4×Dic3—61no—
75#889—62no—
76#888—61no—
77#887—62no—
78#887—61no—
79#878—62no—
80#877—62no—
81C23×C32C2×D411yescharacteristic
82C22×C3×D3—24no—
83C22×C3×D3—44no—
84C22×C3×D3—44no—
85C22×C3×D3—44no—
86C2×C32×C4—22no—
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4C2×D411yescharacteristic
89C2×C3⋊Dic3—22no—
90C2×C3⋊Dic3SD1614yescomplemented
91C2×C3⋊Dic3C2×D411yescharacteristic
92C2×C3⋊Dic3C2×D411yescharacteristic
93C2×C3⋊Dic3C2×D411yescharacteristic
94C2×C3⋊Dic3C2411yescharacteristic
95C2×C3×Dic3—22no—
96C2×C3×Dic3—22no—
97C3×D12—44no—
98C3×D12—44no—
99C3×Dic6—42no—
100#627—24no—
101#625—28no—
102#625—44no—
103#625—44no—
104#625—44no—
105#622—24no—
106#533—91no—
107C2×#127—91no—
108#492—92no—
109#486—92no—
110#460—94no—
111#450—94no—
112#431—91no—
113C24×C3—62no—
114C23×D3—22no—
115C2×C3×Q8—61no—
116C2×C3×D4—62no—
117C2×C3×D4—62no—
118C2×C3×D4—124no—
119C22×C3×C4—21no—
120C22×C3×C4—21no—
121C2×#67—64no—
122C2×#67—64no—
123C2×#67—64no—
124C2×#67—64no—
125C2×#67—128no—
126C2×#67—128no—
127C22×Dic3—61no—
128C22×Dic3—61no—
129C22×Dic3—61no—
130C22×Dic3—61no—
131C2×D12—22no—
132C2×D12—22no—
133C2×D12—44no—
134C2×Dic6—21no—
135C2×Dic6—62no—
136C3×C4⋊C4—61no—
137C3×C4⋊C4—62no—
138C3×C22⋊C4—62no—
139#217—22no—
140C4⋊Dic3—21no—
141C4⋊Dic3—62no—
142Dic3⋊C4—22no—
143Dic3⋊C4—62no—
144Dic3⋊C4—62no—
145Dic3⋊C4—62no—
146Dic3⋊C4—62no—
147C4×Dic3—61no—
148C4×Dic3—61no—
149C4×Dic3—61no—
150C4×Dic3—61no—
151C4×Dic3—61no—
152C4×Dic3—61no—
153C4×Dic3—61no—
154C4×Dic3—61no—
155C4×Dic3—62no—
156C4×Dic3—62no—
157C22×C32—21no—
158C22×C32—21no—
159C22×C32C2×SD1612yes—
160C22×C32C22×D411yescharacteristic
161C2×C3×D3—44no—
162C2×C3×D3—44no—
163C2×C3×D3—44no—
164C2×C3×D3—88no—
165C32×C4—21no—
166C32×C4AGL(1,ℤ/8)12yes—
167C3⋊Dic3—21no—
168C3⋊Dic3C2×SD1612yes—
169C3⋊Dic3C2×SD1612yes—
170C3⋊Dic3H(5,𝔽2)12yes—
171C3×Dic3—42no—
172C3×Dic3—42no—
173C22×D4—61no—
174C22×D4—92no—
175C22×D4—181no—
176C2×SD16—98no—
177C4⋊Q8—91no—
178C4⋊Q8—91no—
179#127—92no—
180#127—92no—
181#127—181no—
182#127—181no—
183#125—181no—
184C22⋊Q8—61no—
185C22⋊Q8—92no—
186C4×Q8—92no—
187C4×Q8—181no—
188#117—181no—
189C2×C42—91no—
190C4⋊C8—92no—
191#102—98no—
192C22⋊C8—92no—
193C4×C8—92no—
194C23×C3—21no—
195C23×C3—21no—
196C23×C3—64no—
197C23×C3—124no—
198C23×C3—124no—
199C23×C3—124no—
200C22×D3—24no—
201C22×D3—44no—
202C22×D3—44no—
203C22×D3—44no—
204C3×Q8—122no—
205C3×D4—124no—
206C3×D4—124no—
207C2×C3×C4—24no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—42no—
213C2×C3×C4—62no—
214C2×C3×C4—62no—
215#67—128no—
216#67—128no—
217#67—128no—
218#67—128no—
219C2×Dic3—22no—
220C2×Dic3—22no—
221C2×Dic3—64no—
222C2×Dic3—64no—
223C2×Dic3—61no—
224C2×Dic3—61no—
225C2×Dic3—61no—
226C2×Dic3—61no—
227C2×Dic3—61no—
228C2×Dic3—61no—
229C2×Dic3—61no—
230C2×Dic3—61no—
231C2×Dic3—64no—
232C2×Dic3—122no—
233D12—44no—
234D12—44no—
235Dic6—42no—
236Dic6—124no—
237C2×C32—22no—
238C2×C32#53511yescharacteristic
239C2×C32C22×SD1611yescharacteristic
240C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
241C3×D3—84no—
242C24—62no—
243C2×Q8—61no—
244C2×Q8—92no—
245C2×D4—62no—
246C2×D4—62no—
247C2×D4—94no—
248C2×D4—124no—
249C2×D4—182no—
250C2×D4—182no—
251C2×D4—182no—
252C2×D4—364no—
253C2×D4—364no—
254C22×C4—91no—
255C22×C4—91no—
256C22×C4GO+(4,𝔽2)11yescharacteristic
257SD16—368no—
258C2×C8—94no—
259C4⋊C4—62no—
260C4⋊C4—61no—
261C4⋊C4—92no—
262C4⋊C4—181no—
263C4⋊C4—181no—
264C4⋊C4—182no—
265C22⋊C4—62no—
266C42—91no—
267C42—91no—
268C42—91no—
269C42—91no—
270C42—182no—
271C22×C3—22no—
272C22×C3—22no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—22no—
276C22×C3—22no—
277C22×C3—41no—
278C22×C3—41no—
279C22×C3—124no—
280C22×C3—124no—
281C22×C3—124no—
282C22×C3—248no—
283C2×D3—44no—
284C2×D3—44no—
285C2×D3—44no—
286C2×D3—88no—
287C3×C4—22no—
288C3×C4—22no—
289C3×C4—22no—
290C3×C4—41no—
291C3×C4—122no—
292C3×C4—122no—
293Dic3—42no—
294Dic3—42no—
295Dic3—62no—
296Dic3—62no—
297Dic3—62no—
298Dic3—62no—
299Dic3—62no—
300Dic3—62no—
301Dic3—62no—
302Dic3—121no—
303C32#320811yescharacteristic, complemented, Sylow
304C23—64no—
305C23—124no—
306C23—124no—
307C23—124no—
308C23C2×GO+(4,𝔽2)11yescharacteristic
309Q8—122no—
310Q8—184no—
311D4—124no—
312D4—124no—
313D4—188no—
314D4—364no—
315D4—364no—
316D4—364no—
317C2×C4—22no—
318C2×C4—62no—
319C2×C4—62no—
320C2×C4—91no—
321C2×C4—91no—
322C2×C4—91no—
323C2×C4—94no—
324C2×C4—91no—
325C2×C4—182no—
326C2×C4C2×GO+(4,𝔽2)11yescharacteristic
327C2×C4C2×GO+(4,𝔽2)11yescharacteristic
328C8—184no—
329C2×C3—24no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—42no—
337C2×C3—244no—
338D3—84no—
339C22—21no—
340C22—21no—
341C22—124no—
342C22—124no—
343C22—124no—
344C22—248no—
345C22#6422712yes—
346C22C22×GO+(4,𝔽2)11yescharacteristic
347C4—21no—
348C4—92no—
349C4—92no—
350C4—92no—
351C4—122no—
352C4—122no—
353C4—181no—
354C4#6423612yes—
355C3—21no—
356C3—21no—
357C2—22no—
358C2—244no—
359C2C2×#6422711yescharacteristic
360C2#1059651211yescharacteristic
361C2C2×#6423611yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC2×#63914C2
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#3208
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
2. #10594810C2semidirect
3. #10593801C2semidirect
4. #10593523C2semidirect
5. #10593442C2semidirect
6. #10593355C2semidirect
7. #10593348C2semidirect
11. C2×#3775C22semidirect
16. #63919C22semidirect
21. #63873C22semidirect
24. #63838C22semidirect
26. #63779C22semidirect
27. C4×#622C22semidirect
28. #63739C22semidirect
90. C2×C3⋊Dic3SD16semidirect
303. C32#3208semidirect

Maximal subgroups

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

subgroupindex
C2×#639142
#105948102
#105938012
#105935232
#105934422
#105933552
#105933482
#32089