Finite Group Databasebeta

← #11868701

Subgroups — #11868701

Order 1152.

764 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 764 conjugacy classes of subgroups — too many to draw. Only its 113 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#10593805C211yesmaximal, characteristic, complemented
4#10593507C212yesmaximal, complemented
5#10593493C212yesmaximal
6#10593367C212yesmaximal, complemented
7#10593364C214yesmaximal, complemented
8#10593357C212yesmaximal, complemented
9C22×#625C2211yescharacteristic
10C22×D3×Dic3—21no—
11C2×#3792C2212yes—
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×C3×(C2×D3)⋊C4—21no—
14C3×#924—21no—
15#63982—21no—
16C2×#3724C2211yescharacteristic
17#63957C2212yes—
18#63919C2211yescharacteristic, complemented
19#63902—21no—
20#63902—21no—
21#63902C2212yes—
22#63902C2212yes—
23#63873C2211yescharacteristic, complemented
24#63870C2212yescomplemented
25#63843—21no—
26#63838—21no—
27#63779C2212yescomplemented
28C4⋊#622C2212yescomplemented
29#63743C2214yescomplemented
30#63742C2214yescomplemented
31#63739C2214yes—
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×#627—21no—
42C2×#625—21no—
43C2×#625—22no—
44C2×#625Q814yescomplemented
45C2×#625C2312yes—
46C2×D3×Dic3—22no—
47C2×D3×Dic3—22no—
48C2×D3×Dic3—44no—
49#3792—24no—
50C2×#622C2314yes—
51C4×C3⋊Dic3D411yescharacteristic
52C4×C3⋊Dic3D411yescharacteristic
53C4×C3⋊Dic3C2311yescharacteristic
54C4×C3⋊Dic3C2311yescharacteristic
55C3×#217—22no—
56C3×(C2×D3)⋊C4—22no—
57C3×(C2×D3)⋊C4—22no—
58C3×C4⋊Dic3—21no—
59C3×Dic3⋊C4—22no—
60#3724—21no—
61#3724—21no—
62#3724C2312yes—
63#3724C2312yes—
64#3724C2312yes—
65Dic3⋊Dic3—22no—
66Dic32—22no—
67#3077—91nomaximal, Sylow
68C22×#67—61no—
69C23×Dic3—61no—
70C22×C4×D3—61no—
71C3×C22⋊Q8—61no—
72C2×C3×C22⋊C4—61no—
73Q8×Dic3—61no—
74#944—61no—
75C2×(C2×D3)⋊C4—21no—
76#924—21no—
77C2×Dic3⋊C4—61no—
78C2×C4×Dic3—61no—
79C2×C4×Dic3—61no—
80#889—62no—
81#888—61no—
82#887—62no—
83#887—61no—
84#67⋊C4—62no—
85#67⋊C4—62no—
86#67⋊C4—62no—
87#67⋊C4—62no—
88#878—62no—
89#877—62no—
90C23×C32C2×D411yescharacteristic
91C22×C3×D3—24no—
92C22×C3×D3—22no—
93C22×C3×D3—42no—
94C22×C3×D3—42no—
95C2×C32×C4—41no—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3C2×D411yescharacteristic
100C2×C3⋊Dic3C2×D411yescharacteristic
101C2×C3⋊Dic3C2×D411yescharacteristic
102C2×C3⋊Dic3C2×Q812yes—
103C2×C3⋊Dic3#4112yes—
104C2×C3⋊Dic3C2411yescharacteristic
105C2×C3×Dic3—22no—
106C2×C3×Dic3—22no—
107C2×C3×Dic3—22no—
108C2×C3×Dic3—42no—
109C3×Dic6—42no—
110#627—42no—
111#625—24no—
112#625—22no—
113#625C2×Q814yes—
114D3×Dic3—44no—
115D3×Dic3—44no—
116#622—24no—
117#533—91no—
118C2×C4×D4—91no—
119#478—94no—
120#476—92no—
121#474—92no—
122#428—92no—
123#423—91no—
124#418—92no—
125C24×C3—61no—
126C23×D3—21no—
127C2×C3×Q8—61no—
128C22×C3×C4—21no—
129C22×C3×C4—21no—
130C22×C3×C4—61no—
131C2×#67—62no—
132C2×#67—64no—
133C2×#67—62no—
134C2×#67—64no—
135C22×Dic3—21no—
136C22×Dic3—61no—
137C22×Dic3—61no—
138C22×Dic3—61no—
139C22×Dic3—61no—
140C22×Dic3—62no—
141C22×Dic3—62no—
142C22×Dic3—124no—
143C2×C4×D3—62no—
144C2×C4×D3—62no—
145C2×C4×D3—124no—
146C2×Dic6—21no—
147C2×Dic6—62no—
148C3×C4⋊C4—61no—
149C3×C4⋊C4—62no—
150C3×C22⋊C4—62no—
151C3×C22⋊C4—62no—
152C3×C22⋊C4—62no—
153#217—22no—
154(C2×D3)⋊C4—22no—
155(C2×D3)⋊C4—22no—
156C4⋊Dic3—21no—
157C4⋊Dic3—62no—
158Dic3⋊C4—22no—
159Dic3⋊C4—62no—
160Dic3⋊C4—62no—
161Dic3⋊C4—62no—
162Dic3⋊C4—62no—
163Dic3⋊C4—62no—
164Dic3⋊C4—62no—
165C4×Dic3—61no—
166C4×Dic3—61no—
167C4×Dic3—61no—
168C4×Dic3—61no—
169C4×Dic3—61no—
170C4×Dic3—61no—
171C4×Dic3—61no—
172C4×Dic3—61no—
173C4×Dic3—62no—
174C4×Dic3—62no—
175C22×C32—21no—
176C22×C32—21no—
177C22×C32C22⋊Q812yes—
178C22×C32C22×D411yescharacteristic
179C2×C3×D3—24no—
180C2×C3×D3—48no—
181C2×C3×D3—42no—
182C2×C3×D3—42no—
183C32×C4—21no—
184C32×C4—21no—
185C3⋊Dic3—21no—
186C3⋊Dic3C22⋊Q812yes—
187C3⋊Dic3AGL(1,ℤ/8)12yes—
188C3⋊Dic3C22×Q811yescharacteristic
189C3⋊Dic3C2×#4111yescharacteristic
190C3×Dic3—42no—
191C3×Dic3—42no—
192C3×Dic3—42no—
193C22×D4—91no—
194C23×C4—181no—
195C2×M16—92no—
196C4⋊Q8—91no—
197C4⋊Q8—91no—
198#125—92no—
199C22⋊Q8—61no—
200C22⋊Q8—181no—
201C4×Q8—181no—
202C4×Q8—181no—
203C4×D4—92no—
204C4×D4—92no—
205C4×D4—181no—
206C4×D4—181no—
207#117—92no—
208C2×C4⋊C4—91no—
209C2×C22⋊C4—61no—
210C2×C42—91no—
211#107—94no—
212#106—94no—
213C4⋊C8—92no—
214C4⋊C8—92no—
215#102—94no—
216#102—94no—
217C23×C3—21no—
218C23×C3—21no—
219C23×C3—62no—
220C23×C3—64no—
221C23×C3—122no—
222C23×C3—122no—
223C22×D3—22no—
224C22×D3—24no—
225C22×D3—42no—
226C22×D3—42no—
227C3×Q8—122no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—42no—
233C2×C3×C4—42no—
234C2×C3×C4—62no—
235C2×C3×C4—62no—
236C2×C3×C4—62no—
237C2×C3×C4—122no—
238#67—64no—
239#67—68no—
240#67—64no—
241C2×Dic3—22no—
242C2×Dic3—22no—
243C2×Dic3—22no—
244C2×Dic3—42no—
245C2×Dic3—61no—
246C2×Dic3—61no—
247C2×Dic3—61no—
248C2×Dic3—61no—
249C2×Dic3—61no—
250C2×Dic3—62no—
251C2×Dic3—62no—
252C2×Dic3—62no—
253C2×Dic3—62no—
254C2×Dic3—61no—
255C2×Dic3—61no—
256C2×Dic3—61no—
257C2×Dic3—64no—
258C2×Dic3—122no—
259C2×Dic3—124no—
260C2×Dic3—124no—
261C4×D3—124no—
262C4×D3—124no—
263Dic6—42no—
264Dic6—124no—
265C2×C32—22no—
266C2×C32C2×C22⋊Q811yescharacteristic
267C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
268C2×C32#57511yescharacteristic
269C3×D3—44no—
270C24—61no—
271C2×Q8—61no—
272C2×Q8—181no—
273C2×D4—92no—
274C2×D4—94no—
275C2×D4—181no—
276C2×D4—182no—
277C22×C4—61no—
278C22×C4—91no—
279C22×C4—91no—
280C22×C4—182no—
281C22×C4—182no—
282C22×C4—364no—
283C22×C4GO+(4,𝔽2)11yescharacteristic
284M16—184no—
285C2×C8—94no—
286C4⋊C4—62no—
287C4⋊C4—61no—
288C4⋊C4—92no—
289C4⋊C4—92no—
290C4⋊C4—92no—
291C4⋊C4—181no—
292C4⋊C4—182no—
293C4⋊C4—181no—
294C22⋊C4—62no—
295C22⋊C4—62no—
296C22⋊C4—62no—
297C42—91no—
298C42—91no—
299C42—91no—
300C42—91no—
301C42—182no—
302C22×C3—22no—
303C22×C3—22no—
304C22×C3—21no—
305C22×C3—21no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—64no—
311C22×C3—122no—
312C22×C3—128no—
313C22×C3—122no—
314C2×D3—24no—
315C2×D3—42no—
316C2×D3—48no—
317C2×D3—42no—
318C3×C4—22no—
319C3×C4—41no—
320C3×C4—41no—
321C3×C4—41no—
322C3×C4—122no—
323C3×C4—122no—
324C3×C4—122no—
325Dic3—42no—
326Dic3—42no—
327Dic3—42no—
328Dic3—62no—
329Dic3—62no—
330Dic3—62no—
331Dic3—61no—
332Dic3—61no—
333Dic3—62no—
334Dic3—61no—
335Dic3—61no—
336Dic3—62no—
337Dic3—121no—
338C32#307711yescharacteristic, complemented, Sylow
339C23—62no—
340C23—64no—
341C23—122no—
342C23—122no—
343C23C2×GO+(4,𝔽2)11yescharacteristic
344Q8—122no—
345Q8—362no—
346D4—94no—
347D4—182no—
348D4—184no—
349C2×C4—41no—
350C2×C4—62no—
351C2×C4—62no—
352C2×C4—62no—
353C2×C4—91no—
354C2×C4—91no—
355C2×C4—91no—
356C2×C4—92no—
357C2×C4—92no—
358C2×C4—91no—
359C2×C4—122no—
360C2×C4—182no—
361C2×C4—364no—
362C2×C4—364no—
363C2×C4C2×GO+(4,𝔽2)11yescharacteristic
364C2×C4C2×GO+(4,𝔽2)11yescharacteristic
365C8—184no—
366C2×C3—24no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—42no—
374C2×C3—124no—
375D3—44no—
376C22—21no—
377C22—21no—
378C22—64no—
379C22—128no—
380C22—122no—
381C22—122no—
382C22D32⋊Q812yes—
383C22C22×GO+(4,𝔽2)11yescharacteristic
384C4—21no—
385C4—21no—
386C4—91no—
387C4—91no—
388C4—92no—
389C4—92no—
390C4—122no—
391C4—122no—
392C4—122no—
393C4—181no—
394C3—21no—
395C3—21no—
396C2—22no—
397C2—124no—
398C2C2×D32⋊Q811yescharacteristic
399C2#1059650111yescharacteristic
400C2#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#3077
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. #10593805C2semidirect
4. #10593507C2semidirect
6. #10593367C2semidirect
7. #10593364C2semidirect
8. #10593357C2semidirect
18. #63919C22semidirect
23. #63873C22semidirect
24. #63870C22semidirect
27. #63779C22semidirect
28. C4⋊#622C22semidirect
29. #63743C22semidirect
30. #63742C22semidirect
44. C2×#625Q8semidirect
338. C32#3077semidirect

Maximal subgroups

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

subgroupindex
C2×#639022
#105948102
#105938052
#105935072
#105934932
#105933672
#105933642
#105933572
#30779