Finite Group Databasebeta

← #11775216

Subgroups — #11775216

Order 1152.

688 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 688 conjugacy classes of subgroups — too many to draw. Only its 61 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
1#10595081C211yesmaximal, characteristic
2#10593803C211yesmaximal, characteristic, complemented
3C4×#3722C211yesmaximal, characteristic, complemented
4#10590071C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×#3811—21no—
7C2×#3802C411yescharacteristic, complemented
8C2×#3788—21no—
9C3×#930—21no—
10C2×C3×C4×Dic3—21no—
11#63980C2212yes—
12C2×#3722—21no—
13#63921—21no—
14#63916—21no—
15#63912C412yescomplemented
16#63900C411yescharacteristic, complemented
17C22⋊#622C2212yescomplemented
18#63778—21no—
19#63579C2212yescomplemented
20D3×#121—61no—
21C4×(C2×D3)⋊C4—61no—
22C23×C3⋊D3D411yescharacteristic
23C22×D32—21no—
24C22×C32×C4D411yescharacteristic
25C22×C3⋊Dic3C2311yescharacteristic
26C2×C4×C3⋊D3—42no—
27C2×C4×C3⋊D3C2×C411yescharacteristic
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3D411yescharacteristic
31C2×C3×#67—22no—
32C22×C3×Dic3—22no—
33C2×C3×D12—21no—
34#3811—44no—
35C2×#626—22no—
36C2×#625C2×C412yes—
37C2×#624—21no—
38#3802—42no—
39C2×#622—22no—
40#3788—42no—
41C3×(C2×D3)⋊C4—22no—
42C3×C4⋊Dic3—21no—
43C3×C4×Dic3—42no—
44#3724C2×C412yes—
45#3722—24no—
46(C2×D3)⋊Dic3—22no—
47#1507—91nomaximal, Sylow
48C2×D3×D4—61no—
49C2×D3×D4—62no—
50C22×C4×D3—61no—
51C22×C4×D3—61no—
52C3×#121—61no—
53C2×C3×C42—61no—
54#939—62no—
55#938—61no—
56#930—21no—
57C2×(C2×D3)⋊C4—62no—
58C2×C4×Dic3—21no—
59#895—61no—
60D3×C4⋊C4—61no—
61#884—62no—
62D3×C22⋊C4—62no—
63C3⋊#95—62no—
64C23×C32C2×D411yescharacteristic
65C22×C3⋊D3—22no—
66C22×C3⋊D3—22no—
67C22×C3⋊D3—41no—
68C22×C3⋊D3C22⋊C411yescharacteristic
69C22×C3⋊D3C22⋊C411yescharacteristic
70C22×C3×D3—22no—
71C2×D32—42no—
72C2×D32—42no—
73C2×D32—42no—
74C2×C32×C4—22no—
75C2×C32×C4C22⋊C411yescharacteristic
76C2×C32×C4C22⋊C411yescharacteristic
77C2×C3⋊Dic3—41no—
78C2×C3⋊Dic3C22×C411yescharacteristic
79C2×C3⋊Dic3C2×D411yescharacteristic
80C4×C3⋊D3—22no—
81C4×C3⋊D3—22no—
82C4×C3⋊D3—41no—
83C4×C3⋊D3—41no—
84C3×#67—44no—
85C2×C3×Dic3—24no—
86C2×C3×Dic3—22no—
87C2×C3×Dic3—42no—
88C2×C3×Dic3—42no—
89C3×D12—42no—
90#626—44no—
91#625—42no—
92#624—42no—
93#622—42no—
94C2×#121—91no—
95#407—91no—
96C4×C22⋊C4—91no—
97#327—94no—
98C23×D3—61no—
99C23×D3—61no—
100C23×D3—62no—
101C2×C3×D4—61no—
102C2×C3×D4—62no—
103C22×C3×C4—21no—
104C22×C3×C4—21no—
105C22×C3×C4—62no—
106C2×#67—22no—
107C2×#67—62no—
108C2×#67—62no—
109C22×Dic3—22no—
110C22×Dic3—61no—
111C22×Dic3—61no—
112D3×D4—124no—
113D3×D4—128no—
114C2×D12—21no—
115C2×D12—62no—
116C2×C4×D3—61no—
117C2×C4×D3—61no—
118C2×C4×D3—61no—
119C2×C4×D3—61no—
120C2×C4×D3—61no—
121C2×C4×D3—61no—
122C2×C4×D3—61no—
123C2×C4×D3—61no—
124C2×C4×D3—62no—
125C2×C4×D3—124no—
126C2×C4×D3—122no—
127C2×C4×D3—122no—
128C3×C4⋊C4—61no—
129C3×C22⋊C4—62no—
130C3×C42—122no—
131#217—62no—
132(C2×D3)⋊C4—22no—
133(C2×D3)⋊C4—68no—
134(C2×D3)⋊C4—62no—
135C4⋊Dic3—21no—
136Dic3⋊C4—62no—
137C4×Dic3—42no—
138C22×C32—21no—
139C22×C32—21no—
140C22×C32C2×C22⋊C411yescharacteristic
141C22×C32AGL(1,ℤ/8)12yes—
142C2×C3⋊D3—21no—
143C2×C3⋊D3—21no—
144C2×C3⋊D3—21no—
145C2×C3⋊D3—21no—
146C2×C3⋊D3—21no—
147C2×C3⋊D3—44no—
148C2×C3⋊D3#10412yes—
149C2×C3×D3—42no—
150C2×C3×D3—42no—
151C2×C3×D3—42no—
152D32—84no—
153C32×C4—21no—
154C32×C4#9912yes—
155C3⋊Dic3—21no—
156C3⋊Dic3—21no—
157C3×Dic3—44no—
158C3×Dic3—42no—
159C22×D4—91no—
160C22×D4—181no—
161C23×C4—91no—
162C2×M16—181no—
163#121—61no—
164#121—92no—
165#121—92no—
166#121—181no—
167C2×C4⋊C4—91no—
168C2×C22⋊C4—181no—
169C2×C22⋊C4—181no—
170C2×C42—61no—
171C22⋊C8—92no—
172C22⋊C8—181no—
173#95—92no—
174C23×C3—21no—
175C23×C3—21no—
176C23×C3—62no—
177C22×D3—22no—
178C22×D3—61no—
179C22×D3—61no—
180C22×D3—61no—
181C22×D3—61no—
182C22×D3—64no—
183C22×D3—64no—
184C22×D3—122no—
185C22×D3—122no—
186C22×D3—124no—
187C22×D3—124no—
188C22×D3—124no—
189C22×D3—122no—
190C22×D3—121no—
191C22×D3—121no—
192C3×D4—122no—
193C3×D4—124no—
194C2×C3×C4—22no—
195C2×C3×C4—22no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—42no—
201C2×C3×C4—62no—
202C2×C3×C4—64no—
203C2×C3×C4—122no—
204C2×C3×C4—122no—
205#67—44no—
206#67—124no—
207#67—124no—
208C2×Dic3—22no—
209C2×Dic3—24no—
210C2×Dic3—42no—
211C2×Dic3—42no—
212C2×Dic3—61no—
213C2×Dic3—61no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216C2×Dic3—122no—
217C2×Dic3—121no—
218C2×Dic3—121no—
219D12—42no—
220D12—124no—
221C4×D3—64no—
222C4×D3—122no—
223C4×D3—122no—
224C4×D3—122no—
225C4×D3—124no—
226C4×D3—122no—
227C4×D3—122no—
228C4×D3—122no—
229C4×D3—122no—
230C2×C32—22no—
231C2×C32C2×#9911yescharacteristic
232C2×C32#41811yescharacteristic
233C2×C32C2×#10411yescharacteristic
234C3⋊D3—22no—
235C3⋊D3—41no—
236C3×D3—82no—
237C24—91no—
238C24—181no—
239C2×D4—62no—
240C2×D4—61no—
241C2×D4—92no—
242C2×D4—182no—
243C2×D4—362no—
244C2×D4—364no—
245C22×C4—62no—
246C22×C4—91no—
247C22×C4—91no—
248C22×C4—91no—
249C22×C4—91no—
250C22×C4—91no—
251C22×C4—181no—
252C22×C4—362no—
253C22×C4GO+(4,𝔽2)11yescharacteristic
254M16—362no—
255C2×C8—182no—
256C4⋊C4—61no—
257C4⋊C4—92no—
258C22⋊C4—62no—
259C22⋊C4—184no—
260C22⋊C4—182no—
261C42—122no—
262C22×C3—22no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—22no—
266C22×C3—22no—
267C22×C3—21no—
268C22×C3—21no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3—122no—
272C22×C3—122no—
273C22×C3—122no—
274C2×D3—42no—
275C2×D3—42no—
276C2×D3—42no—
277C2×D3—62no—
278C2×D3—62no—
279C2×D3—62no—
280C2×D3—62no—
281C2×D3—62no—
282C2×D3—62no—
283C2×D3—121no—
284C2×D3—121no—
285C2×D3—121no—
286C2×D3—121no—
287C2×D3—121no—
288C2×D3—121no—
289C2×D3—128no—
290C2×D3—124no—
291C2×D3—124no—
292C2×D3—248no—
293C3×C4—22no—
294C3×C4—22no—
295C3×C4—22no—
296C3×C4—41no—
297C3×C4—122no—
298C3×C4—124no—
299Dic3—42no—
300Dic3—44no—
301Dic3—62no—
302Dic3—121no—
303Dic3—121no—
304Dic3—121no—
305C32#150711yescharacteristic, complemented, Sylow
306C23—62no—
307C23—91no—
308C23—91no—
309C23—182no—
310C23—182no—
311C23—361no—
312C23—362no—
313C23—362no—
314C23—362no—
315C23C2×GO+(4,𝔽2)11yescharacteristic
316D4—124no—
317D4—122no—
318D4—364no—
319D4—362no—
320C2×C4—22no—
321C2×C4—64no—
322C2×C4—62no—
323C2×C4—91no—
324C2×C4—91no—
325C2×C4—122no—
326C2×C4—122no—
327C2×C4—182no—
328C2×C4—182no—
329C2×C4—361no—
330C2×C4—361no—
331C2×C4—362no—
332C2×C4—361no—
333C2×C4D32⋊C411yescharacteristic
334C2×C4D32⋊C411yescharacteristic
335C8—362no—
336C2×C3—22no—
337C2×C3—22no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—42no—
345C2×C3—242no—
346D3—64no—
347D3—82no—
348D3—122no—
349D3—122no—
350D3—122no—
351C22—21no—
352C22—21no—
353C22—92no—
354C22—122no—
355C22—122no—
356C22—122no—
357C22—181no—
358C22—181no—
359C22—181no—
360C22—181no—
361C22—181no—
362C22—364no—
363C22—724no—
364C22#6422412yes—
365C22C2×D32⋊C411yescharacteristic
366C4—21no—
367C4—124no—
368C4—122no—
369C4—181no—
370C4—181no—
371C4#6373812yes—
372C3—21no—
373C3—21no—
374C2—22no—
375C2—182no—
376C2—242no—
377C2—361no—
378C2#1059336311yescharacteristic
379C2#1059338011yescharacteristic
380C2C2×#6373811yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#10595081C2
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1507
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593803C2semidirect
3. C4×#3722C2semidirect
4. #10590071C2semidirect
7. C2×#3802C4semidirect
15. #63912C4semidirect
16. #63900C4semidirect
17. C22⋊#622C22semidirect
19. #63579C22semidirect
305. C32#1507semidirect

Maximal subgroups

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

subgroupindex
#105950812
#105938032
C4×#37222
#105900712
#15079