Finite Group Databasebeta

← #11868849

Subgroups — #11868849

Order 1152.

716 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 117 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×#3805C211yesmaximal, characteristic
2C2×#63873C211yesmaximal, characteristic, complemented
3#10593805C211yesmaximal, characteristic, complemented
4#10593507C212yesmaximal, complemented
5#10593496C212yesmaximal
6#10593391C212yesmaximal, complemented
7#10593376C212yesmaximal, complemented
8#10593357C212yesmaximal, complemented
9#10593347C212yesmaximal, complemented
10C22×C3×Dic6—21no—
11C2×#3805C2211yescharacteristic
12C2×#3792C2212yes—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C3×C4×#67—21no—
15#67⋊Dic3—21no—
16C2×#3724—21no—
17C2×#3724C2212yes—
18#63957C2211yescharacteristic
19C4×#627C2211yescharacteristic
20#63902C2211yescharacteristic
21C4×#625C2211yescharacteristic
22#63878—21no—
23C4×D3×Dic3—21no—
24#63873—21no—
25#63873—21no—
26#63873C2212yes—
27#63873C2212yes—
28#63838C2211yescharacteristic
29#63779C2212yes—
30C4⋊#622C2212yes—
31#63743C2214yes—
32#63742C2214yes—
33#63740C2214yes—
34#63739C2214yes—
35C2×#944—61no—
36C4×#237—61no—
37C22×C32×C4D411yescharacteristic
38C22×C3⋊Dic3D411yescharacteristic
39C22×C3⋊Dic3C2311yescharacteristic
40C2×C3×#67—21no—
41C22×C3×Dic3—22no—
42C2×C3×C4×D3—21no—
43C2×C3×Dic6—22no—
44C2×C3×Dic6—22no—
45C2×C3×Dic6—44no—
46C2×#627C2311yescharacteristic
47C2×#625C2311yescharacteristic
48#3805—22no—
49#3805Q814yescomplemented
50C2×D3×Dic3—21no—
51C2×D3×Dic3—21no—
52#3792—24no—
53C2×#622C2314yes—
54C4×C3⋊Dic3D411yescharacteristic
55C4×C3⋊Dic3D411yescharacteristic
56C4×C3⋊Dic3C2311yescharacteristic
57C4×C3⋊Dic3C2311yescharacteristic
58C3×#217—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×Dic3⋊C4—21no—
61C3×C4×Dic3—21no—
62#3724—22no—
63#3724—22no—
64#3724—22no—
65#3724C2311yescharacteristic
66#3724C2314yes—
67#3724C2311yescharacteristic
68Dic3⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70Dic32—21no—
71Dic32—21no—
72#3079—91nomaximal, Sylow
73C22×C3×Q8—61no—
74C2×#237—61no—
75C22×Dic6—21no—
76C3×C4×D4—61no—
77#944—62no—
78#944—62no—
79#944—62no—
80#944—62no—
81D4×Dic3—61no—
82C4×#67—21no—
83C4×#67—61no—
84C2×Dic3⋊C4—62no—
85C2×Dic3⋊C4—62no—
86C2×C4×Dic3—61no—
87C2×C4×Dic3—61no—
88C2×C4×Dic3—61no—
89#892—61no—
90#887—61no—
91#67⋊C4—61no—
92#67⋊C4—61no—
93#877—61no—
94#877—61no—
95C42×D3—61no—
96C4×Dic6—61no—
97C23×C32C2×D411yescharacteristic
98C22×C3×D3—21no—
99C2×C32×C4—22no—
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C3⋊Dic3—22no—
103C2×C3⋊Dic3C2×D411yescharacteristic
104C2×C3⋊Dic3C2×D411yescharacteristic
105C2×C3⋊Dic3C2×D411yescharacteristic
106C2×C3⋊Dic3C2×Q812yes—
107C2×C3⋊Dic3#4112yes—
108C2×C3⋊Dic3C2411yescharacteristic
109C3×#67—24no—
110C2×C3×Dic3—21no—
111C2×C3×Dic3—21no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—24no—
114C2×C3×Dic3—44no—
115C3×C4×D3—42no—
116C3×Dic6—44no—
117C3×Dic6—44no—
118#627—21no—
119#627C2×Q812yescomplemented
120#625—21no—
121#625C2×Q812yescomplemented
122D3×Dic3—24no—
123D3×Dic3—42no—
124#622—24no—
125C2×C4⋊Q8—91no—
126C4×#41—91no—
127#477—92no—
128#476—92no—
129#475—92no—
130#474—92no—
131#428—92no—
132#423—91no—
133#417—92no—
134C2×C3×Q8—62no—
135C2×C3×Q8—62no—
136C2×C3×Q8—124no—
137C2×C3×D4—61no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—61no—
141C22×C3×C4—62no—
142C2×#67—21no—
143C2×#67—61no—
144C22×Dic3—22no—
145C22×Dic3—61no—
146C22×Dic3—61no—
147C22×Dic3—61no—
148C22×Dic3—61no—
149C22×Dic3—61no—
150C22×Dic3—61no—
151#237—64no—
152#237—64no—
153C2×C4×D3—21no—
154C2×C4×D3—61no—
155C2×C4×D3—61no—
156C2×Dic6—22no—
157C2×Dic6—22no—
158C2×Dic6—44no—
159C2×Dic6—61no—
160C3×C4⋊C4—61no—
161C3×C22⋊C4—61no—
162C3×C22⋊C4—61no—
163C3×C42—61no—
164#217—21no—
165#217—61no—
166(C2×D3)⋊C4—21no—
167(C2×D3)⋊C4—61no—
168C4⋊Dic3—61no—
169Dic3⋊C4—21no—
170Dic3⋊C4—61no—
171Dic3⋊C4—61no—
172Dic3⋊C4—64no—
173Dic3⋊C4—61no—
174Dic3⋊C4—64no—
175Dic3⋊C4—64no—
176Dic3⋊C4—64no—
177C4×Dic3—21no—
178C4×Dic3—61no—
179C4×Dic3—61no—
180C4×Dic3—61no—
181C4×Dic3—61no—
182C4×Dic3—61no—
183C4×Dic3—61no—
184C4×Dic3—61no—
185C4×Dic3—61no—
186C4×Dic3—61no—
187C4×Dic3—61no—
188C4×Dic3—61no—
189C4×Dic3—61no—
190C22×C32—21no—
191C22×C32—21no—
192C22×C32C22⋊Q812yes—
193C22×C32C22×D411yescharacteristic
194C2×C3×D3—22no—
195C2×C3×D3—41no—
196C2×C3×D3—41no—
197C32×C4—21no—
198C32×C4AGL(1,ℤ/8)12yes—
199C3⋊Dic3—21no—
200C3⋊Dic3C22⋊Q812yes—
201C3⋊Dic3#13712yes—
202C3⋊Dic3C22×Q811yescharacteristic
203C3⋊Dic3C2×#4111yescharacteristic
204C3×Dic3—22no—
205C3×Dic3—44no—
206C3×Dic3—41no—
207C3×Dic3—41no—
208C2×#41—91no—
209C22×Q8—61no—
210C2×M16—92no—
211C4⋊Q8—92no—
212C4⋊Q8—92no—
213C4⋊Q8—181no—
214C4⋊Q8—181no—
215C4×Q8—91no—
216C4×Q8—91no—
217C4×D4—61no—
218C4×D4—91no—
219C4×D4—91no—
220C4×D4—181no—
221#117—91no—
222#117—181no—
223C2×C4⋊C4—92no—
224C2×C4⋊C4—181no—
225C2×C42—91no—
226C2×C42—181no—
227#107—94no—
228#106—94no—
229C4⋊C8—92no—
230C4⋊C8—92no—
231#103—94no—
232#102—94no—
233C23×C3—21no—
234C23×C3—21no—
235C23×C3—61no—
236C22×D3—21no—
237C3×Q8—124no—
238C3×Q8—124no—
239C3×D4—64no—
240C2×C3×C4—24no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—42no—
246C2×C3×C4—61no—
247C2×C3×C4—61no—
248C2×C3×C4—61no—
249C2×C3×C4—64no—
250C2×C3×C4—122no—
251C2×C3×C4—124no—
252#67—24no—
253#67—62no—
254#67—62no—
255C2×Dic3—21no—
256C2×Dic3—21no—
257C2×Dic3—21no—
258C2×Dic3—24no—
259C2×Dic3—44no—
260C2×Dic3—61no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264C2×Dic3—61no—
265C2×Dic3—62no—
266C2×Dic3—62no—
267C2×Dic3—62no—
268C2×Dic3—62no—
269C2×Dic3—61no—
270C2×Dic3—61no—
271C2×Dic3—61no—
272C2×Dic3—64no—
273C2×Dic3—64no—
274C2×Dic3—122no—
275C2×Dic3—122no—
276C4×D3—42no—
277C4×D3—64no—
278C4×D3—122no—
279Dic6—44no—
280Dic6—44no—
281Dic6—62no—
282Dic6—62no—
283C2×C32—22no—
284C2×C32C2×C22⋊Q811yescharacteristic
285C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
286C2×C32C2×#13711yescharacteristic
287C3×D3—42no—
288#41—94no—
289#41—182no—
290C2×Q8—62no—
291C2×Q8—62no—
292C2×Q8—91no—
293C2×Q8—124no—
294C2×D4—61no—
295C2×D4—91no—
296C22×C4—62no—
297C22×C4—61no—
298C22×C4—91no—
299C22×C4—91no—
300C22×C4—181no—
301C22×C4—181no—
302C22×C4GO+(4,𝔽2)11yescharacteristic
303M16—184no—
304C2×C8—94no—
305C4⋊C4—61no—
306C4⋊C4—94no—
307C4⋊C4—91no—
308C4⋊C4—91no—
309C4⋊C4—182no—
310C4⋊C4—182no—
311C4⋊C4—182no—
312C4⋊C4—181no—
313C22⋊C4—61no—
314C22⋊C4—61no—
315C22⋊C4—181no—
316C42—61no—
317C42—91no—
318C42—91no—
319C42—91no—
320C42—91no—
321C42—181no—
322C42—181no—
323C22×C3—22no—
324C22×C3—22no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—22no—
328C22×C3—22no—
329C22×C3—41no—
330C22×C3—41no—
331C22×C3—62no—
332C22×C3—121no—
333C22×C3—121no—
334C2×D3—22no—
335C2×D3—41no—
336C2×D3—41no—
337C3×C4—22no—
338C3×C4—22no—
339C3×C4—22no—
340C3×C4—41no—
341C3×C4—62no—
342C3×C4—121no—
343C3×C4—124no—
344C3×C4—121no—
345Dic3—22no—
346Dic3—44no—
347Dic3—41no—
348Dic3—41no—
349Dic3—61no—
350Dic3—61no—
351Dic3—62no—
352Dic3—62no—
353Dic3—62no—
354Dic3—62no—
355Dic3—61no—
356Dic3—61no—
357Dic3—62no—
358Dic3—121no—
359C32#307911yescharacteristic, complemented, Sylow
360C23—61no—
361C23C2×GO+(4,𝔽2)11yescharacteristic
362Q8—92no—
363Q8—124no—
364Q8—124no—
365Q8—181no—
366D4—64no—
367D4—92no—
368D4—181no—
369C2×C4—22no—
370C2×C4—61no—
371C2×C4—61no—
372C2×C4—61no—
373C2×C4—64no—
374C2×C4—91no—
375C2×C4—91no—
376C2×C4—91no—
377C2×C4—92no—
378C2×C4—92no—
379C2×C4—91no—
380C2×C4—124no—
381C2×C4—122no—
382C2×C4—184no—
383C2×C4—182no—
384C2×C4—362no—
385C2×C4C2×GO+(4,𝔽2)11yescharacteristic
386C2×C4C2×GO+(4,𝔽2)11yescharacteristic
387C8—184no—
388C2×C3—24no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—42no—
396C2×C3—122no—
397D3—42no—
398C22—21no—
399C22—21no—
400C22—62no—
401C22—121no—
402C22—121no—
403C22D32⋊Q812yes—
404C22C22×GO+(4,𝔽2)11yescharacteristic
405C4—21no—
406C4—62no—
407C4—91no—
408C4—92no—
409C4—91no—
410C4—92no—
411C4—121no—
412C4—124no—
413C4—121no—
414C4—181no—
415C4#6423612yes—
416C3—21no—
417C3—21no—
418C2—22no—
419C2—122no—
420C2C2×D32⋊Q811yescharacteristic
421C2#1059650511yescharacteristic
422C2C2×#6423611yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC2×#3805C22
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#3079
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. C2×#63873C2semidirect
3. #10593805C2semidirect
4. #10593507C2semidirect
6. #10593391C2semidirect
7. #10593376C2semidirect
8. #10593357C2semidirect
9. #10593347C2semidirect
49. #3805Q8semidirect
119. #627C2×Q8semidirect
121. #625C2×Q8semidirect
359. C32#3079semidirect

Maximal subgroups

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

subgroupindex
C4×#38052
C2×#638732
#105938052
#105935072
#105934962
#105933912
#105933762
#105933572
#105933472
#30799