Finite Group Databasebeta

← #11878681

Subgroups — #11878681

Order 1152.

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

normal subgroups only

This group has 936 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, complemented
2#10594929C211yesmaximal, characteristic, complemented
3#10593801C211yesmaximal, characteristic, complemented
4#10593519C214yesmaximal, complemented
5#10593426C214yesmaximal, complemented
6#10593418C212yesmaximal, complemented
7#10593366C212yesmaximal, complemented
8C22×C3×D12—21no—
9C22×#625—21no—
10C22×#625C2212yes—
11C2×#3805—21no—
12C2×#3774C2218yescomplemented
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C3×#930—21no—
15#63980C2212yes—
16#63919C2211yescharacteristic, complemented
17#63915—21no—
18#63914—21no—
19#63914—21no—
20#63914C2212yes—
21#63914C2212yes—
22#63914C2211yescharacteristic, complemented
23#63902C2212yescomplemented
24#63898—21no—
25C22⋊#622C2212yes—
26#63779C2212yescomplemented
27C4×#622C2212yescomplemented
28#63739C2218yescomplemented
29C2×#940—61no—
30#5596—61no—
31C23×C3×D3—22no—
32C22×C32×C4D411yescharacteristic
33C22×C3⋊Dic3D411yescharacteristic
34C22×C3⋊Dic3C2311yescharacteristic
35C2×C3×#67—22no—
36C2×C3×D12—21no—
37C2×C3×D12—22no—
38C2×C3×D12—22no—
39C2×C3×D12—44no—
40C2×#627—21no—
41C2×#625—21no—
42C2×#625—22no—
43C2×#625—22no—
44C2×#625—22no—
45C2×#625—44no—
46C2×#625—44no—
47C2×#625C2314yes—
48C2×#625C2312yes—
49#3805—44no—
50C2×D3×Dic3—22no—
51C2×#622C2314yes—
52#3774—48no—
53C4×C3⋊Dic3D411yescharacteristic
54C4×C3⋊Dic3D411yescharacteristic
55C4×C3⋊Dic3C2311yescharacteristic
56C4×C3⋊Dic3C2311yescharacteristic
57C3×(C2×D3)⋊C4—22no—
58C3×C4⋊Dic3—21no—
59#3724C2312yes—
60(C2×D3)⋊Dic3—22no—
61#3205—91nomaximal, Sylow
62C22×C3×D4—61no—
63C22×#67—62no—
64C22×#67—62no—
65C2×#237—62no—
66C22×D12—21no—
67C3×#121—61no—
68#940—62no—
69#940—62no—
70#940—61no—
71#940—62no—
72#940—62no—
73#939—62no—
74D4×Dic3—61no—
75#930—21no—
76C2×C4×Dic3—61no—
77C2×C4×Dic3—61no—
78#893—61no—
79#888—61no—
80#885—62no—
81#67⋊C4—62no—
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×C4—22no—
89C2×C32×C4C2×D411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C3⋊Dic3—22no—
92C2×C3⋊Dic3D814yescomplemented
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—42no—
101C3×D12—44no—
102#627—42no—
103#625—24no—
104#625—28no—
105#625—44no—
106#625—42no—
107#625—44no—
108#625—44no—
109D3×Dic3—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—
120C2×C3×D4—61no—
121C2×C3×D4—62no—
122C2×C3×D4—62no—
123C2×C3×D4—62no—
124C2×C3×D4—124no—
125C22×C3×C4—21no—
126C22×C3×C4—21no—
127C2×#67—22no—
128C2×#67—62no—
129C2×#67—64no—
130C2×#67—62no—
131C2×#67—64no—
132C2×#67—64no—
133C2×#67—64no—
134C2×#67—128no—
135C2×#67—128no—
136C22×Dic3—61no—
137C22×Dic3—61no—
138C22×Dic3—61no—
139C22×Dic3—61no—
140C22×Dic3—62no—
141#237—128no—
142C2×D12—21no—
143C2×D12—22no—
144C2×D12—22no—
145C2×D12—44no—
146C2×C4×D3—62no—
147C2×Dic6—62no—
148C3×C4⋊C4—61no—
149C3×C22⋊C4—62no—
150#217—62no—
151(C2×D3)⋊C4—22no—
152(C2×D3)⋊C4—62no—
153C4⋊Dic3—21no—
154Dic3⋊C4—62no—
155C4×Dic3—61no—
156C4×Dic3—61no—
157C4×Dic3—61no—
158C4×Dic3—61no—
159C4×Dic3—61no—
160C4×Dic3—61no—
161C4×Dic3—61no—
162C4×Dic3—61no—
163C22×C32—21no—
164C22×C32—21no—
165C22×C32C2×D812yes—
166C22×C32C22×D411yescharacteristic
167C2×C3×D3—44no—
168C2×C3×D3—42no—
169C2×C3×D3—42no—
170C2×C3×D3—44no—
171C2×C3×D3—44no—
172C2×C3×D3—42no—
173C2×C3×D3—88no—
174C32×C4—21no—
175C32×C4AGL(1,ℤ/8)12yes—
176C3⋊Dic3—21no—
177C3⋊Dic3C2×D812yes—
178C3⋊Dic3C2×D812yes—
179C3⋊Dic3H(5,𝔽2)12yes—
180C3×Dic3—42no—
181C2×#41—181no—
182C22×D4—61no—
183C22×D4—92no—
184C22×D4—181no—
185C2×D8—98no—
186C4⋊Q8—91no—
187#127—92no—
188#127—92no—
189#127—91no—
190#127—181no—
191#127—181no—
192#124—181no—
193#121—61no—
194#121—92no—
195C4×D4—92no—
196C4×D4—181no—
197C2×C42—91no—
198C4⋊C8—92no—
199#102—98no—
200C22⋊C8—92no—
201C4×C8—92no—
202C23×C3—21no—
203C23×C3—21no—
204C23×C3—62no—
205C23×C3—64no—
206C23×C3—124no—
207C23×C3—124no—
208C23×C3—124no—
209C22×D3—22no—
210C22×D3—24no—
211C22×D3—44no—
212C22×D3—44no—
213C22×D3—44no—
214C3×D4—122no—
215C3×D4—124no—
216C3×D4—124no—
217C3×D4—124no—
218C2×C3×C4—24no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—42no—
224C2×C3×C4—62no—
225#67—44no—
226#67—124no—
227#67—128no—
228#67—124no—
229#67—128no—
230#67—128no—
231#67—128no—
232C2×Dic3—22no—
233C2×Dic3—64no—
234C2×Dic3—64no—
235C2×Dic3—61no—
236C2×Dic3—61no—
237C2×Dic3—61no—
238C2×Dic3—61no—
239C2×Dic3—61no—
240C2×Dic3—61no—
241C2×Dic3—61no—
242C2×Dic3—61no—
243C2×Dic3—64no—
244C2×Dic3—122no—
245C2×Dic3—124no—
246D12—42no—
247D12—44no—
248D12—44no—
249C4×D3—124no—
250Dic6—124no—
251C2×C32—22no—
252C2×C32#53511yescharacteristic
253C2×C32C22×D811yescharacteristic
254C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
255C3×D3—82no—
256C3×D3—84no—
257C24—62no—
258#41—364no—
259C2×Q8—181no—
260C2×D4—62no—
261C2×D4—61no—
262C2×D4—62no—
263C2×D4—62no—
264C2×D4—94no—
265C2×D4—92no—
266C2×D4—124no—
267C2×D4—181no—
268C2×D4—182no—
269C2×D4—182no—
270C2×D4—182no—
271C2×D4—364no—
272C2×D4—364no—
273C22×C4—91no—
274C22×C4—91no—
275C22×C4—182no—
276C22×C4GO+(4,𝔽2)11yescharacteristic
277D8—368no—
278C2×C8—94no—
279C4⋊C4—61no—
280C4⋊C4—92no—
281C22⋊C4—62no—
282C22⋊C4—182no—
283C42—91no—
284C42—91no—
285C42—91no—
286C42—91no—
287C22×C3—22no—
288C22×C3—22no—
289C22×C3—21no—
290C22×C3—21no—
291C22×C3—22no—
292C22×C3—22no—
293C22×C3—41no—
294C22×C3—41no—
295C22×C3—122no—
296C22×C3—124no—
297C22×C3—124no—
298C22×C3—122no—
299C22×C3—124no—
300C22×C3—122no—
301C22×C3—248no—
302C2×D3—42no—
303C2×D3—44no—
304C2×D3—42no—
305C2×D3—44no—
306C2×D3—44no—
307C2×D3—42no—
308C2×D3—88no—
309C3×C4—22no—
310C3×C4—22no—
311C3×C4—22no—
312C3×C4—41no—
313C3×C4—122no—
314Dic3—42no—
315Dic3—62no—
316Dic3—62no—
317Dic3—62no—
318Dic3—62no—
319Dic3—62no—
320Dic3—62no—
321Dic3—62no—
322Dic3—121no—
323C32#320511yescharacteristic, complemented, Sylow
324C23—62no—
325C23—64no—
326C23—124no—
327C23—124no—
328C23—124no—
329C23C2×GO+(4,𝔽2)11yescharacteristic
330Q8—362no—
331D4—124no—
332D4—124no—
333D4—124no—
334D4—122no—
335D4—184no—
336D4—188no—
337D4—364no—
338D4—364no—
339D4—362no—
340D4—364no—
341C2×C4—22no—
342C2×C4—62no—
343C2×C4—91no—
344C2×C4—91no—
345C2×C4—91no—
346C2×C4—94no—
347C2×C4—91no—
348C2×C4—182no—
349C2×C4—364no—
350C2×C4C2×GO+(4,𝔽2)11yescharacteristic
351C2×C4C2×GO+(4,𝔽2)11yescharacteristic
352C8—184no—
353C2×C3—24no—
354C2×C3—21no—
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—42no—
361C2×C3—244no—
362C2×C3—242no—
363D3—84no—
364D3—82no—
365C22—21no—
366C22—21no—
367C22—122no—
368C22—124no—
369C22—124no—
370C22—122no—
371C22—124no—
372C22—122no—
373C22—248no—
374C22#6422512yes—
375C22C22×GO+(4,𝔽2)11yescharacteristic
376C4—21no—
377C4—92no—
378C4—92no—
379C4—92no—
380C4—122no—
381C4—181no—
382C4#6423612yes—
383C3—21no—
384C3—21no—
385C2—22no—
386C2—244no—
387C2—242no—
388C2C2×#6422511yescharacteristic
389C2#1059651211yescharacteristic
390C2C2×#6423611yescharacteristic
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. C2×#63914C2semidirect
2. #10594929C2semidirect
3. #10593801C2semidirect
4. #10593519C2semidirect
5. #10593426C2semidirect
6. #10593418C2semidirect
7. #10593366C2semidirect
12. C2×#3774C22semidirect
16. #63919C22semidirect
22. #63914C22semidirect
23. #63902C22semidirect
26. #63779C22semidirect
27. C4×#622C22semidirect
28. #63739C22semidirect
92. C2×C3⋊Dic3D8semidirect
323. C32#3205semidirect

Maximal subgroups

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

subgroupindex
C2×#639142
#105949292
#105938012
#105935192
#105934262
#105934182
#105933662
#32059