Finite Group Databasebeta

← #11870537

Subgroups — #11870537

Order 1152.

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

normal subgroups only

This group has 772 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×#63902C211yesmaximal, characteristic
2#10594810C211yesmaximal, characteristic, complemented
3#10593801C211yesmaximal, characteristic, complemented
4#10593523C212yesmaximal
5#10593504C212yesmaximal, complemented
6#10593438C212yesmaximal, complemented
7#10593433C214yesmaximal, complemented
8#10593357C212yesmaximal, complemented
9C22×#625C2211yescharacteristic
10C22×D3×Dic3—21no—
11C2×#3775C2214yes—
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×C3×(C2×D3)⋊C4—21no—
14C3×#924—21no—
15#63982C2212yes—
16C2×#3724C2211yescharacteristic
17#63957—21no—
18#63919C2211yescharacteristic, complemented
19#63902—21no—
20#63902—21no—
21#63902C2212yes—
22#63902C2212yes—
23#63873C2211yescharacteristic, complemented
24#63870—21no—
25#63843—21no—
26#63838C2212yescomplemented
27C22⋊#622C2212yes—
28#63779C2212yescomplemented
29C4×#622C2212yescomplemented
30#63742C2214yescomplemented
31#63740C2214yescomplemented
32#63739C2214yes—
33#5622—61no—
34C2×#67⋊C4—61no—
35C23×C3×D3—21no—
36C22×C32×C4D411yescharacteristic
37C22×C3⋊Dic3D411yescharacteristic
38C22×C3⋊Dic3C2311yescharacteristic
39C22×C3×Dic3—21no—
40C2×C3×Dic6—21no—
41C2×#627C2312yes—
42C2×#625—21no—
43C2×#625—24no—
44C2×#625C2312yes—
45C2×D3×Dic3—22no—
46C2×D3×Dic3—22no—
47C2×D3×Dic3—44no—
48C2×#622C2314yes—
49#3775—28no—
50C4×C3⋊Dic3D411yescharacteristic
51C4×C3⋊Dic3D411yescharacteristic
52C4×C3⋊Dic3C2311yescharacteristic
53C4×C3⋊Dic3C2311yescharacteristic
54C3×#217—22no—
55C3×(C2×D3)⋊C4—22no—
56C3×(C2×D3)⋊C4—22no—
57C3×C4⋊Dic3—21no—
58C3×Dic3⋊C4—22no—
59#3724—21no—
60#3724—21no—
61#3724—21no—
62#3724C2312yes—
63#3724C2312yes—
64Dic3⋊Dic3—22no—
65Dic32—22no—
66#3101—91nomaximal, Sylow
67C22×#67—61no—
68C23×Dic3—61no—
69C22×C4×D3—61no—
70C3×C22⋊Q8—61no—
71C2×C3×C22⋊C4—61no—
72Q8×Dic3—61no—
73#944—61no—
74C2×(C2×D3)⋊C4—21no—
75#924—21no—
76C2×Dic3⋊C4—61no—
77C2×C4×Dic3—61no—
78C2×C4×Dic3—61no—
79#889—62no—
80#888—61no—
81#887—62no—
82#887—61no—
83#67⋊C4—62no—
84#67⋊C4—62no—
85#67⋊C4—62no—
86#67⋊C4—62no—
87#878—62no—
88#877—62no—
89C23×C32C2×D411yescharacteristic
90C22×C3×D3—24no—
91C22×C3×D3—22no—
92C22×C3×D3—42no—
93C22×C3×D3—42no—
94C2×C32×C4—41no—
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3SD1614yescomplemented
99C2×C3⋊Dic3C2×D411yescharacteristic
100C2×C3⋊Dic3C2×D411yescharacteristic
101C2×C3⋊Dic3C2×D411yescharacteristic
102C2×C3⋊Dic3C2411yescharacteristic
103C2×C3×Dic3—22no—
104C2×C3×Dic3—22no—
105C2×C3×Dic3—22no—
106C2×C3×Dic3—42no—
107C3×Dic6—42no—
108#627—24no—
109#625—24no—
110#625—22no—
111#625#4114yes—
112D3×Dic3—44no—
113D3×Dic3—44no—
114#622—24no—
115#533—91no—
116C2×C4×D4—91no—
117#483—92no—
118#476—92no—
119#461—92no—
120#450—92no—
121C4×SD16—94no—
122#431—91no—
123C24×C3—61no—
124C23×D3—21no—
125C2×C3×Q8—61no—
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C22×C3×C4—61no—
129C2×#67—62no—
130C2×#67—62no—
131C2×#67—68no—
132C22×Dic3—21no—
133C22×Dic3—61no—
134C22×Dic3—61no—
135C22×Dic3—61no—
136C22×Dic3—61no—
137C22×Dic3—62no—
138C22×Dic3—62no—
139C22×Dic3—124no—
140C2×C4×D3—62no—
141C2×C4×D3—62no—
142C2×C4×D3—124no—
143C2×Dic6—21no—
144C2×Dic6—62no—
145C3×C4⋊C4—61no—
146C3×C4⋊C4—62no—
147C3×C22⋊C4—62no—
148C3×C22⋊C4—62no—
149C3×C22⋊C4—62no—
150#217—22no—
151(C2×D3)⋊C4—22no—
152(C2×D3)⋊C4—22no—
153C4⋊Dic3—21no—
154C4⋊Dic3—62no—
155Dic3⋊C4—22no—
156Dic3⋊C4—62no—
157Dic3⋊C4—62no—
158Dic3⋊C4—62no—
159Dic3⋊C4—62no—
160Dic3⋊C4—62no—
161Dic3⋊C4—62no—
162C4×Dic3—61no—
163C4×Dic3—61no—
164C4×Dic3—61no—
165C4×Dic3—61no—
166C4×Dic3—61no—
167C4×Dic3—61no—
168C4×Dic3—61no—
169C4×Dic3—61no—
170C4×Dic3—62no—
171C4×Dic3—62no—
172C22×C32—21no—
173C22×C32—21no—
174C22×C32C2×SD1612yes—
175C22×C32C22×D411yescharacteristic
176C2×C3×D3—24no—
177C2×C3×D3—48no—
178C2×C3×D3—42no—
179C2×C3×D3—42no—
180C32×C4—21no—
181C32×C4—21no—
182C3⋊Dic3—21no—
183C3⋊Dic3C2×SD1612yes—
184C3⋊Dic3C2×SD1612yes—
185C3⋊Dic3C2×#4112yes—
186C3×Dic3—42no—
187C3×Dic3—42no—
188C3×Dic3—42no—
189C22×D4—91no—
190C23×C4—181no—
191C2×SD16—94no—
192C4⋊Q8—91no—
193C4⋊Q8—91no—
194#125—181no—
195C22⋊Q8—61no—
196C22⋊Q8—92no—
197C4×Q8—92no—
198C4×Q8—181no—
199C4×D4—92no—
200C4×D4—92no—
201C4×D4—181no—
202C4×D4—181no—
203#117—181no—
204C2×C4⋊C4—91no—
205C2×C22⋊C4—61no—
206C2×C42—91no—
207#106—94no—
208C4⋊C8—92no—
209#103—94no—
210#102—94no—
211C22⋊C8—92no—
212C4×C8—92no—
213C23×C3—21no—
214C23×C3—21no—
215C23×C3—62no—
216C23×C3—64no—
217C23×C3—122no—
218C23×C3—122no—
219C22×D3—22no—
220C22×D3—24no—
221C22×D3—42no—
222C22×D3—42no—
223C3×Q8—122no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—42no—
229C2×C3×C4—42no—
230C2×C3×C4—62no—
231C2×C3×C4—62no—
232C2×C3×C4—62no—
233C2×C3×C4—122no—
234#67—64no—
235#67—64no—
236#67—68no—
237C2×Dic3—22no—
238C2×Dic3—22no—
239C2×Dic3—22no—
240C2×Dic3—42no—
241C2×Dic3—64no—
242C2×Dic3—64no—
243C2×Dic3—61no—
244C2×Dic3—61no—
245C2×Dic3—61no—
246C2×Dic3—61no—
247C2×Dic3—61no—
248C2×Dic3—61no—
249C2×Dic3—61no—
250C2×Dic3—61no—
251C2×Dic3—64no—
252C2×Dic3—122no—
253C2×Dic3—124no—
254C2×Dic3—124no—
255C4×D3—124no—
256C4×D3—124no—
257Dic6—42no—
258Dic6—124no—
259C2×C32—22no—
260C2×C32#52511yescharacteristic
261C2×C32C22×SD1611yescharacteristic
262C2×C32#57511yescharacteristic
263C3×D3—44no—
264C24—61no—
265C2×Q8—61no—
266C2×Q8—92no—
267C2×D4—92no—
268C2×D4—181no—
269C2×D4—184no—
270C22×C4—61no—
271C22×C4—91no—
272C22×C4—91no—
273C22×C4—182no—
274C22×C4—182no—
275C22×C4—364no—
276C22×C4GO+(4,𝔽2)11yescharacteristic
277SD16—188no—
278C2×C8—94no—
279C4⋊C4—62no—
280C4⋊C4—61no—
281C4⋊C4—92no—
282C4⋊C4—92no—
283C4⋊C4—181no—
284C4⋊C4—181no—
285C4⋊C4—181no—
286C4⋊C4—182no—
287C22⋊C4—62no—
288C22⋊C4—62no—
289C22⋊C4—62no—
290C42—91no—
291C42—91no—
292C42—91no—
293C42—91no—
294C42—182no—
295C22×C3—22no—
296C22×C3—22no—
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—22no—
300C22×C3—22no—
301C22×C3—41no—
302C22×C3—41no—
303C22×C3—64no—
304C22×C3—122no—
305C22×C3—128no—
306C22×C3—122no—
307C2×D3—24no—
308C2×D3—42no—
309C2×D3—48no—
310C2×D3—42no—
311C3×C4—22no—
312C3×C4—41no—
313C3×C4—41no—
314C3×C4—41no—
315C3×C4—122no—
316C3×C4—122no—
317C3×C4—122no—
318Dic3—42no—
319Dic3—42no—
320Dic3—42no—
321Dic3—62no—
322Dic3—62no—
323Dic3—62no—
324Dic3—62no—
325Dic3—62no—
326Dic3—62no—
327Dic3—62no—
328Dic3—121no—
329C32#310111yescharacteristic, complemented, Sylow
330C23—64no—
331C23—62no—
332C23—122no—
333C23—122no—
334C23C2×GO+(4,𝔽2)11yescharacteristic
335Q8—122no—
336Q8—184no—
337D4—94no—
338D4—182no—
339D4—184no—
340C2×C4—41no—
341C2×C4—62no—
342C2×C4—62no—
343C2×C4—62no—
344C2×C4—91no—
345C2×C4—91no—
346C2×C4—91no—
347C2×C4—94no—
348C2×C4—91no—
349C2×C4—122no—
350C2×C4—182no—
351C2×C4—364no—
352C2×C4—364no—
353C2×C4C2×GO+(4,𝔽2)11yescharacteristic
354C2×C4C2×GO+(4,𝔽2)11yescharacteristic
355C8—184no—
356C2×C3—24no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—42no—
364C2×C3—124no—
365D3—44no—
366C22—21no—
367C22—21no—
368C22—64no—
369C22—128no—
370C22—122no—
371C22—122no—
372C22#6422712yes—
373C22C22×GO+(4,𝔽2)11yescharacteristic
374C4—21no—
375C4—21no—
376C4—92no—
377C4—92no—
378C4—92no—
379C4—122no—
380C4—122no—
381C4—122no—
382C4—181no—
383C3—21no—
384C3—21no—
385C2—22no—
386C2—124no—
387C2C2×#6422711yescharacteristic
388C2#1059651011yescharacteristic
389C2#1059653211yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC22×#625C22
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#3101
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
5. #10593504C2semidirect
6. #10593438C2semidirect
7. #10593433C2semidirect
8. #10593357C2semidirect
18. #63919C22semidirect
23. #63873C22semidirect
26. #63838C22semidirect
28. #63779C22semidirect
29. C4×#622C22semidirect
30. #63742C22semidirect
31. #63740C22semidirect
98. C2×C3⋊Dic3SD16semidirect
329. C32#3101semidirect

Maximal subgroups

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

subgroupindex
C2×#639022
#105948102
#105938012
#105935232
#105935042
#105934382
#105934332
#105933572
#31019