Finite Group Databasebeta

← #11868376

Subgroups — #11868376

Order 1152.

774 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 774 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C4×#3802C211yesmaximal, characteristic
2#10593948C211yesmaximal, characteristic, complemented
3#10593726C211yesmaximal, characteristic, complemented
4#10593396C211yesmaximal, characteristic, complemented
5#10593387C211yesmaximal, characteristic, complemented
6#10593365C211yesmaximal, characteristic
7#10593365C211yesmaximal, characteristic
8#10593364C214yesmaximal, complemented
9#10593350C214yesmaximal, complemented
10C2×#3802C2211yescharacteristic
11C2×C4×D32—21no—
12C2×#3787C2211yescharacteristic
13C2×#3787C2211yescharacteristic
14C42×C3⋊D3C2211yescharacteristic
15C3×C4×D12—21no—
16C3×#870—21no—
17#63921—21no—
18#63902C2212yes—
19C4×#625C2212yes—
20#63900C2211yescharacteristic
21#63900C2211yescharacteristic
22#63900C2211yescharacteristic
23#63898—21no—
24#63883—21no—
25#63883—21no—
26#63872—21no—
27#63870C2212yescomplemented
28#63870C2212yescomplemented
29#63779C2212yescomplemented
30C4⋊#622C2212yescomplemented
31#63743C2214yescomplemented
32#63742C2214yescomplemented
33#63739C2214yes—
34#63739C2214yes—
35D3×#125—61no—
36C4×D3×D4—61no—
37C22×D32—21no—
38C2×C4×C3⋊D3D411yescharacteristic
39C2×C4×C3⋊D3D411yescharacteristic
40C2×C4×C3⋊D3C2311yescharacteristic
41C2×C3×D12—21no—
42C2×C3×C4×D3—22no—
43C2×#625C2312yes—
44C2×#624—21no—
45C2×#624—21no—
46C2×#624—21no—
47C2×D3×Dic3—22no—
48#3802—22no—
49#3802Q814yes—
50C4×D32—44no—
51C2×#622C2312yes—
52C2×#622C2312yes—
53#3787—22no—
54#3787—22no—
55C32×C42D411yescharacteristic
56C4×C3⋊Dic3D411yescharacteristic
57C4×C3⋊Dic3C2311yescharacteristic
58C4×C3⋊Dic3C2311yescharacteristic
59C3×(C2×D3)⋊C4—22no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×Dic3⋊C4—22no—
64C3×Dic3⋊C4—22no—
65#3724C2312yes—
66#3724C2312yes—
67#3724C2312yes—
68Dic3⋊Dic3—22no—
69Dic3⋊Dic3—22no—
70(C2×D3)⋊Dic3—22no—
71C2×#478—91nomaximal, Sylow
72C2×D3×D4—61no—
73C22×C4×D3—62no—
74C3×#125—61no—
75C3×C4×D4—61no—
76D4×Dic3—61no—
77C4×#67—62no—
78#893—61no—
79D3×C4⋊C4—61no—
80D3×C4⋊C4—61no—
81D3×C4⋊C4—61no—
82D3×C4⋊C4—62no—
83D3×C4⋊C4—62no—
84#890—61no—
85#890—61no—
86#889—62no—
87#889—62no—
88#67⋊C4—62no—
89D3×C22⋊C4—62no—
90C4×D12—21no—
91C42×D3—61no—
92C42×D3—61no—
93#870—21no—
94C22×C3⋊D3C2×D411yescharacteristic
95C22×C3×D3—22no—
96C2×D32—24no—
97C2×D32—42no—
98C2×D32—42no—
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C3⋊Dic3C2×D411yescharacteristic
103C2×C3⋊Dic3C2×D411yescharacteristic
104C2×C3⋊Dic3C2411yescharacteristic
105C4×C3⋊D3—22no—
106C4×C3⋊D3—22no—
107C4×C3⋊D3C2×Q812yes—
108C4×C3⋊D3#4112yes—
109C2×C3×Dic3—22no—
110C2×C3×Dic3—22no—
111C2×C3×Dic3—22no—
112C3×D12—24no—
113C3×C4×D3—44no—
114#625—22no—
115#625C2×Q814yes—
116#624—42no—
117#624—42no—
118#624—42no—
119D3×Dic3—44no—
120#622—22no—
121#622—22no—
122C2×#125—91no—
123C2×C4×D4—91no—
124#478—94no—
125#478—94no—
126C2×#107—91no—
127C2×#106—91no—
128C2×C4⋊C8—91no—
129C2×#102—91no—
130C2×#102—91no—
131C23×D3—62no—
132C2×C3×D4—61no—
133C22×C3×C4—62no—
134C2×#67—62no—
135C22×Dic3—62no—
136D3×D4—64no—
137D3×D4—64no—
138C2×D12—21no—
139C2×C4×D3—22no—
140C2×C4×D3—61no—
141C2×C4×D3—61no—
142C2×C4×D3—61no—
143C2×C4×D3—61no—
144C2×C4×D3—61no—
145C2×C4×D3—61no—
146C2×C4×D3—62no—
147C2×C4×D3—62no—
148C2×C4×D3—62no—
149C2×C4×D3—62no—
150C2×C4×D3—128no—
151C3×C4⋊C4—62no—
152C3×C4⋊C4—62no—
153C3×C4⋊C4—61no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—61no—
156C3×C22⋊C4—62no—
157C3×C42—21no—
158C3×C42—21no—
159#217—62no—
160(C2×D3)⋊C4—22no—
161(C2×D3)⋊C4—62no—
162C4⋊Dic3—21no—
163C4⋊Dic3—21no—
164C4⋊Dic3—21no—
165C4⋊Dic3—62no—
166C4⋊Dic3—62no—
167Dic3⋊C4—22no—
168Dic3⋊C4—22no—
169Dic3⋊C4—62no—
170Dic3⋊C4—62no—
171Dic3⋊C4—62no—
172Dic3⋊C4—62no—
173Dic3⋊C4—62no—
174C4×Dic3—61no—
175C4×Dic3—61no—
176C4×Dic3—61no—
177C4×Dic3—61no—
178C4×Dic3—61no—
179C4×Dic3—61no—
180C22×C32C22×D411yescharacteristic
181C2×C3⋊D3C22⋊Q812yes—
182C2×C3⋊D3#13512yes—
183C2×C3⋊D3AGL(1,ℤ/8)12yes—
184C2×C3×D3—24no—
185C2×C3×D3—42no—
186C2×C3×D3—42no—
187D32—48no—
188C32×C4—21no—
189C32×C4—21no—
190C32×C4C22⋊Q812yes—
191C3⋊Dic3—21no—
192C3⋊Dic3—21no—
193C3⋊Dic3C22×Q811yescharacteristic
194C3⋊Dic3C2×#4111yescharacteristic
195C3×Dic3—42no—
196C3×Dic3—42no—
197C3×Dic3—42no—
198C22×D4—91no—
199C23×C4—181no—
200C22×C8—91no—
201C22×C8—91no—
202#125—61no—
203#125—92no—
204#125—92no—
205#125—181no—
206C4×D4—61no—
207C4×D4—92no—
208C4×D4—92no—
209C4×D4—181no—
210C2×C4⋊C4—91no—
211C2×C4⋊C4—91no—
212C2×C4⋊C4—91no—
213C2×C4⋊C4—181no—
214C2×C4⋊C4—181no—
215C2×C22⋊C4—181no—
216C2×C42—91no—
217#107—94no—
218#106—94no—
219C4⋊C8—92no—
220C4⋊C8—92no—
221#102—94no—
222#102—94no—
223C23×C3—62no—
224C22×D3—22no—
225C22×D3—61no—
226C22×D3—61no—
227C22×D3—68no—
228C22×D3—124no—
229C22×D3—124no—
230C3×D4—64no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—62no—
238C2×C3×C4—62no—
239C2×C3×C4—62no—
240C2×C3×C4—124no—
241#67—64no—
242#67—64no—
243C2×Dic3—22no—
244C2×Dic3—22no—
245C2×Dic3—22no—
246C2×Dic3—61no—
247C2×Dic3—61no—
248C2×Dic3—61no—
249C2×Dic3—61no—
250C2×Dic3—61no—
251C2×Dic3—61no—
252C2×Dic3—124no—
253D12—24no—
254C4×D3—44no—
255C4×D3—62no—
256C4×D3—62no—
257C4×D3—62no—
258C4×D3—62no—
259C4×D3—64no—
260C4×D3—122no—
261C4×D3—122no—
262C4×D3—122no—
263C4×D3—124no—
264C4×D3—124no—
265C4×D3—124no—
266C4×D3—124no—
267C2×C32C2×C22⋊Q811yescharacteristic
268C2×C32C2×#13511yescharacteristic
269C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
270C3⋊D3#47814yescomplemented
271C3×D3—44no—
272C24—181no—
273C2×D4—61no—
274C2×D4—94no—
275C2×D4—92no—
276C2×D4—182no—
277C22×C4—62no—
278C22×C4—91no—
279C22×C4—91no—
280C22×C4—91no—
281C22×C4—181no—
282C22×C4—181no—
283C22×C4—181no—
284C22×C4—182no—
285C22×C4—364no—
286C2×C8—92no—
287C2×C8—92no—
288C2×C8—182no—
289C2×C8—182no—
290C4⋊C4—61no—
291C4⋊C4—61no—
292C4⋊C4—61no—
293C4⋊C4—62no—
294C4⋊C4—62no—
295C4⋊C4—92no—
296C4⋊C4—92no—
297C4⋊C4—92no—
298C4⋊C4—182no—
299C4⋊C4—182no—
300C22⋊C4—62no—
301C22⋊C4—182no—
302C42—91no—
303C42—91no—
304C42—91no—
305C42GO+(4,𝔽2)11yescharacteristic
306C22×C3—21no—
307C22×C3—21no—
308C22×C3—64no—
309C22×C3—122no—
310C22×C3—122no—
311C2×D3—24no—
312C2×D3—42no—
313C2×D3—42no—
314C2×D3—62no—
315C2×D3—62no—
316C2×D3—62no—
317C2×D3—62no—
318C2×D3—62no—
319C2×D3—62no—
320C2×D3—1216no—
321C3×C4—22no—
322C3×C4—22no—
323C3×C4—22no—
324C3×C4—41no—
325C3×C4—41no—
326C3×C4—41no—
327C3×C4—122no—
328C3×C4—122no—
329C3×C4—122no—
330Dic3—42no—
331Dic3—42no—
332Dic3—42no—
333Dic3—61no—
334Dic3—61no—
335Dic3—61no—
336Dic3—61no—
337Dic3—62no—
338Dic3—121no—
339Dic3—121no—
340Dic3—121no—
341C32C2×#47811yescharacteristic, complemented, Sylow
342C23—62no—
343C23—91no—
344C23—184no—
345C23—362no—
346C23—362no—
347D4—64no—
348D4—94no—
349D4—182no—
350C2×C4—62no—
351C2×C4—62no—
352C2×C4—62no—
353C2×C4—91no—
354C2×C4—92no—
355C2×C4—92no—
356C2×C4—91no—
357C2×C4—91no—
358C2×C4—124no—
359C2×C4—182no—
360C2×C4—182no—
361C2×C4—362no—
362C2×C4—362no—
363C2×C4—362no—
364C2×C4—364no—
365C2×C4C2×GO+(4,𝔽2)11yescharacteristic
366C2×C4C2×GO+(4,𝔽2)11yescharacteristic
367C2×C4C2×GO+(4,𝔽2)11yescharacteristic
368C8—182no—
369C8—182no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—124no—
377D3—44no—
378D3—64no—
379D3—64no—
380C22—64no—
381C22—92no—
382C22—92no—
383C22—92no—
384C22—122no—
385C22—122no—
386C22—368no—
387C22C22×GO+(4,𝔽2)11yescharacteristic
388C4—21no—
389C4—21no—
390C4—91no—
391C4—91no—
392C4—122no—
393C4—122no—
394C4—122no—
395C4—181no—
396C4—181no—
397C4D32⋊Q812yes—
398C3—21no—
399C3—21no—
400C2—94no—
401C2—124no—
402C2C2×D32⋊Q811yescharacteristic
403C2#1059650011yescharacteristic
404C2#1059650111yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenterC42GO+(4,𝔽2)
hypocenterC32C2×#478
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593948C2semidirect
3. #10593726C2semidirect
4. #10593396C2semidirect
5. #10593387C2semidirect
8. #10593364C2semidirect
9. #10593350C2semidirect
27. #63870C22semidirect
28. #63870C22semidirect
29. #63779C22semidirect
30. C4⋊#622C22semidirect
31. #63743C22semidirect
32. #63742C22semidirect
270. C3⋊D3#478semidirect
341. C32C2×#478semidirect

Maximal subgroups

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

subgroupindex
C4×#38022
#105939482
#105937262
#105933962
#105933872
#105933652
#105933642
#105933502
C2×#4789