Finite Group Databasebeta

← #11785175

Subgroups — #11785175

Order 1152.

798 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 798 conjugacy classes of subgroups — too many to draw. Only its 94 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×D4×C3⋊D3C211yesmaximal, characteristic
2C2×#63782C212yesmaximal
3#10593735C211yesmaximal, characteristic, complemented
4#10593726C211yesmaximal, characteristic, complemented
5#10590163C212yesmaximal, complemented
6C2×D4×C3⋊D3C2211yescharacteristic
7C22×C4×C3⋊D3—21no—
8C2×C4⋊#157—21no—
9C2×C4⋊#157—21no—
10C2×C4⋊#157C2212yes—
11C2×#3787C2212yes—
12C32×C4×D4C411yescharacteristic, complemented
13D4×C3⋊Dic3C411yescharacteristic, complemented
14C4×#638—21no—
15#64102C411yescharacteristic, complemented
16C4⋊C4×C3⋊D3C2211yescharacteristic
17#64090—21no—
18C22⋊C4×C3⋊D3—21no—
19C4×C4⋊(C3⋊D3)C411yescharacteristic, complemented
20C42×C3⋊D3C2211yescharacteristic
21#63782—24no—
22#63779—21no—
23C4⋊#622—21no—
24C4×D3×D4—62no—
25C23×C3⋊D3—21no—
26C22×#157—22no—
27C2×C32×D4C2×C411yescharacteristic
28C22×C32×C4—21no—
29C2×#638—21no—
30C22×C3⋊Dic3—21no—
31D4×C3⋊D3—21no—
32D4×C3⋊D3—21no—
33D4×C3⋊D3D412yes—
34D4×C3⋊D3Q812yes—
35C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
36C2×C4×C3⋊D3—21no—
37C2×C4×C3⋊D3—21no—
38C2×C4×C3⋊D3—21no—
39C2×C4×C3⋊D3—42no—
40C2×C4×C3⋊D3—42no—
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C4×C3⋊D3D411yescharacteristic
43C2×C4×C3⋊D3C2311yescharacteristic
44C2×#622—22no—
45C4⋊#157—22no—
46C4⋊#157—22no—
47C4⋊#157—42no—
48C4⋊#157—42no—
49#3787—22no—
50#3787—22no—
51C32×C4⋊C4C2×C411yescharacteristic
52C32×C22⋊C4—21no—
53C32×C42C2×C411yescharacteristic
54#3757—21no—
55#3752—21no—
56#3752—21no—
57C4⋊(C3⋊Dic3)C2×C411yescharacteristic
58#3750—21no—
59C4×C3⋊Dic3C2×C411yescharacteristic
60C4×C3⋊Dic3D411yescharacteristic
61C4×C3⋊Dic3D411yescharacteristic
62#1802—91nomaximal, Sylow
63C2×D3×D4—62no—
64C22×C4×D3—64no—
65C3×C4×D4—22no—
66D4×Dic3—62no—
67C4×#67—64no—
68#893—62no—
69D3×C4⋊C4—62no—
70#67⋊C4—64no—
71D3×C22⋊C4—64no—
72C4×D12—62no—
73C42×D3—62no—
74C23×C32—21no—
75C22×C3⋊D3—21no—
76C22×C3⋊D3—22no—
77C22×C3⋊D3—22no—
78C22×C3⋊D3—41no—
79C22×C3⋊D3—41no—
80C22×C3⋊D3—41no—
81C22×C3⋊D3—41no—
82C22×C3⋊D3C2×D411yescharacteristic
83C2×#157—42no—
84C2×#157—42no—
85C2×#157—42no—
86C32×D4—21no—
87C32×D4C4⋊C412yescomplemented
88C2×C32×C4—21no—
89C2×C32×C4—42no—
90C2×C32×C4C22⋊C411yescharacteristic
91C2×C32×C4C22⋊C411yescharacteristic
92C2×C32×C4C22×C411yescharacteristic
93#638—22no—
94#638—22no—
95C2×C3⋊Dic3—21no—
96C2×C3⋊Dic3—42no—
97C2×C3⋊Dic3C22⋊C411yescharacteristic
98C2×C3⋊Dic3C22⋊C411yescharacteristic
99C2×C3⋊Dic3C2×D411yescharacteristic
100C4⋊(C3⋊D3)—21no—
101C4⋊(C3⋊D3)C4⋊C412yescomplemented
102C4×C3⋊D3—21no—
103C4×C3⋊D3—21no—
104C4×C3⋊D3—41no—
105C4×C3⋊D3—41no—
106C4×C3⋊D3—42no—
107C4×C3⋊D3—42no—
108C4×C3⋊D3D812yes—
109C4×C3⋊D3SD1612yes—
110C4×C3⋊D3C2×D411yescharacteristic
111C4×C3⋊D3C2×Q811yescharacteristic
112C4×C3⋊D3#4111yescharacteristic
113C4×C3⋊D3#4111yescharacteristic
114#622—42no—
115C2×C4×D4—91no—
116C2×C4⋊C8—91no—
117C2×#102—92no—
118#384—91no—
119#340—92no—
120C23×D3—64no—
121C2×C3×D4—22no—
122C22×C3×C4—24no—
123C2×#67—64no—
124C22×Dic3—64no—
125D3×D4—64no—
126D3×D4—64no—
127D3×D4—64no—
128D3×D4—64no—
129C2×D12—62no—
130C2×C4×D3—62no—
131C2×C4×D3—62no—
132C2×C4×D3—62no—
133C2×C4×D3—64no—
134C2×C4×D3—64no—
135C2×C4×D3—64no—
136C2×C4×D3—128no—
137C2×C4×D3—128no—
138C3×C4⋊C4—22no—
139C3×C22⋊C4—24no—
140C3×C42—22no—
141#217—64no—
142(C2×D3)⋊C4—64no—
143(C2×D3)⋊C4—64no—
144C4⋊Dic3—62no—
145Dic3⋊C4—64no—
146C4×Dic3—62no—
147C4×Dic3—62no—
148C4×Dic3—62no—
149C22×C32—22no—
150C22×C32—41no—
151C22×C32—41no—
152C22×C32C2×C22⋊C411yescharacteristic
153C2×C3⋊D3—22no—
154C2×C3⋊D3—41no—
155C2×C3⋊D3—41no—
156C2×C3⋊D3—42no—
157C2×C3⋊D3—42no—
158C2×C3⋊D3—42no—
159C2×C3⋊D3—42no—
160C2×C3⋊D3#12111yescharacteristic
161C2×C3⋊D3C22⋊Q811yescharacteristic
162C2×C3⋊D3C2×D811yescharacteristic
163C2×C3⋊D3C2×SD1611yescharacteristic
164C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
165C2×C3⋊D3#13711yescharacteristic
166#157—82no—
167C32×C4—21no—
168C32×C4—41no—
169C32×C4#10212yescomplemented
170C32×C4C2×C4⋊C411yescharacteristic
171C32×C4#11711yescharacteristic
172C3⋊Dic3—21no—
173C3⋊Dic3—41no—
174C3⋊Dic3#10212yescomplemented
175C3⋊Dic3#12111yescharacteristic
176C3⋊Dic3C22⋊Q811yescharacteristic
177C22×D4—91no—
178C23×C4—181no—
179C22×C8—92no—
180C4×D4—91no—
181C4×D4—91no—
182C4×D4—91no—
183C4×D4—181no—
184C4×D4—181no—
185C4×D4#15711yescharacteristic, complemented
186C2×C4⋊C4—91no—
187C2×C4⋊C4—92no—
188C2×C4⋊C4—181no—
189C2×C4⋊C4—181no—
190C2×C22⋊C4—181no—
191C2×C42—91no—
192C4⋊C8—181no—
193C4⋊C8—181no—
194#102—184no—
195C23×C3—24no—
196C22×D3—62no—
197C22×D3—64no—
198C22×D3—68no—
199C22×D3—68no—
200C22×D3—124no—
201C22×D3—124no—
202C22×D3—124no—
203C22×D3—124no—
204C3×D4—24no—
205C3×D4—24no—
206C2×C3×C4—24no—
207C2×C3×C4—22no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—48no—
211#67—68no—
212#67—68no—
213C2×Dic3—62no—
214C2×Dic3—62no—
215C2×Dic3—62no—
216C2×Dic3—64no—
217C2×Dic3—128no—
218D12—64no—
219D12—64no—
220C4×D3—64no—
221C4×D3—64no—
222C4×D3—62no—
223C4×D3—62no—
224C4×D3—62no—
225C4×D3—62no—
226C4×D3—122no—
227C4×D3—122no—
228C4×D3—128no—
229C4×D3—128no—
230C4×D3—124no—
231C4×D3—124no—
232C2×C32—42no—
233C2×C32#38011yescharacteristic
234C2×C32C2×#10211yescharacteristic
235C2×C32#41711yescharacteristic
236C3⋊D3—42no—
237C3⋊D3#45911yescharacteristic
238C3⋊D3#46111yescharacteristic
239C3⋊D3#47411yescharacteristic
240C3⋊D3#47611yescharacteristic
241C24—181no—
242C2×D4—92no—
243C2×D4—92no—
244C2×D4—91no—
245C2×D4—181no—
246C2×D4—181no—
247C2×D4—181no—
248C2×D4C2×#15711yescharacteristic
249C22×C4—21no—
250C22×C4—91no—
251C22×C4—91no—
252C22×C4—91no—
253C22×C4—181no—
254C22×C4—181no—
255C22×C4—181no—
256C22×C4—181no—
257C22×C4—182no—
258C22×C4—362no—
259C22×C4—362no—
260C2×C8—182no—
261C2×C8—182no—
262C2×C8—182no—
263C4⋊C4—91no—
264C4⋊C4—181no—
265C4⋊C4—182no—
266C4⋊C4—182no—
267C4⋊C4—362no—
268C4⋊C4—362no—
269C4⋊C4C2×#15711yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—181no—
272C22⋊C4—181no—
273C22⋊C4—181no—
274C42—91no—
275C42—91no—
276C42—91no—
277C42C2×#15711yescharacteristic
278C22×C3—28no—
279C22×C3—22no—
280C22×C3—44no—
281C22×C3—44no—
282C2×D3—62no—
283C2×D3—62no—
284C2×D3—62no—
285C2×D3—62no—
286C2×D3—62no—
287C2×D3—62no—
288C2×D3—68no—
289C2×D3—128no—
290C2×D3—128no—
291C2×D3—128no—
292C2×D3—128no—
293C2×D3—124no—
294C2×D3—124no—
295C3×C4—22no—
296C3×C4—22no—
297C3×C4—24no—
298C3×C4—42no—
299C3×C4—44no—
300Dic3—64no—
301Dic3—62no—
302Dic3—62no—
303Dic3—122no—
304Dic3—124no—
305C32#180211yescharacteristic, complemented, Sylow
306C23—21no—
307C23—91no—
308C23—182no—
309C23—182no—
310C23—181no—
311C23—361no—
312C23—361no—
313C23—361no—
314C23—361no—
315D4—21no—
316D4—92no—
317D4—182no—
318D4—182no—
319D4—181no—
320D4C4⋊#15712yescomplemented
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—91no—
324C2×C4—91no—
325C2×C4—91no—
326C2×C4—91no—
327C2×C4—91no—
328C2×C4—91no—
329C2×C4—92no—
330C2×C4—92no—
331C2×C4—91no—
332C2×C4—181no—
333C2×C4—181no—
334C2×C4—181no—
335C2×C4—362no—
336C2×C4—361no—
337C2×C4—361no—
338C2×C4—362no—
339C2×C4—362no—
340C2×C4—362no—
341C2×C4—362no—
342C2×C4—362no—
343C2×C4C22⋊#15711yescharacteristic
344C2×C4C22⋊#15711yescharacteristic
345C2×C4C22×#15711yescharacteristic
346C8—362no—
347C2×C3—22no—
348C2×C3—22no—
349C2×C3—22no—
350C2×C3—48no—
351D3—62no—
352D3—62no—
353D3—62no—
354D3—62no—
355D3—128no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—91no—
360C22—91no—
361C22—91no—
362C22—91no—
363C22—91no—
364C22—91no—
365C22—182no—
366C22—362no—
367C22—362no—
368C22—362no—
369C22—362no—
370C22—361no—
371C22—361no—
372C22C2×C22⋊#15711yescharacteristic
373C4—21no—
374C4—41no—
375C4—91no—
376C4—91no—
377C4—92no—
378C4—181no—
379C4—361no—
380C4—722no—
381C4#6378212yescomplemented
382C4C2×C4⋊#15711yescharacteristic
383C4#6428611yescharacteristic
384C3—22no—
385C2—42no—
386C2—91no—
387C2—91no—
388C2—91no—
389C2—91no—
390C2—362no—
391C2#1059381211yescharacteristic
392C2C2×#6378211yescharacteristic
393C2#1059384011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4×D4C4
socleC22×C32C2×C22⋊C4
prime radicalC2×D4×C3⋊D3C22
cosocleC2×C4×C3⋊D3C23
hypercenterC4×D4#157
hypocenterC32#1802
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #10593735C2semidirect
4. #10593726C2semidirect
5. #10590163C2semidirect
12. C32×C4×D4C4semidirect
13. D4×C3⋊Dic3C4semidirect
15. #64102C4semidirect
19. C4×C4⋊(C3⋊D3)C4semidirect
87. C32×D4C4⋊C4semidirect
101. C4⋊(C3⋊D3)C4⋊C4semidirect
169. C32×C4#102semidirect
174. C3⋊Dic3#102semidirect
185. C4×D4#157semidirect
305. C32#1802semidirect
320. D4C4⋊#157semidirect
381. C4#63782semidirect

Maximal subgroups

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

subgroupindex
C4×D4×C3⋊D32
C2×#637822
#105937352
#105937262
#105901632
#18029