Finite Group Databasebeta

← #11786377

Subgroups — #11786377

Order 1152.

618 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C22×#3710C211yesmaximal, characteristic
2C4×C22⋊#157C211yesmaximal, characteristic
3C2×#63732C212yesmaximal, complemented
4#10591152C211yesmaximal, characteristic
5#10590044C212yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C22⋊#157C411yescharacteristic
8C2×C22⋊#157C411yescharacteristic
9C2×C4×#157C2212yes—
10C22×C3×C3⋊C8—21no—
11C2×#3710—21no—
12C2×#3710—24no—
13C2×#3710C2211yescharacteristic
14C2×#3710C2211yescharacteristic
15C2×#3710C2212yes—
16#63781C412yes—
17#63732—24no—
18C3×#830—21no—
19#63557—21no—
20C22×D3×C8—61no—
21D3×C22⋊C8—61no—
22C23×C3⋊D3C2×C411yescharacteristic
23C22×#157C2×C412yes—
24C22×#157C2×C412yes—
25C22×C32×C4D411yescharacteristic
26C22×C3⋊Dic3Q811yescharacteristic
27C2×C4×C3⋊D3—22no—
28C2×C4×C3⋊D3—22no—
29C2×C4×C3⋊D3C2×C411yescharacteristic
30C2×C4×C3⋊D3D411yescharacteristic
31C2×C4×C3⋊D3Q811yescharacteristic
32C2×C4×C3⋊D3C2311yescharacteristic
33C22⋊#157—22no—
34C22⋊#157C814yescomplemented
35C4×#157—22no—
36C4×#157—22no—
37C2×C3×C3⋊C8—24no—
38C2×C3×C3⋊C8—22no—
39C2×C3×C3⋊C8—21no—
40C2×C3×C3⋊C8—21no—
41#3710—24no—
42#3710—22no—
43#3710—22no—
44#3710—22no—
45#3710D414yes—
46#1850—91nomaximal, Sylow
47C22×C4×D3—61no—
48C22×C4×D3—61no—
49C22×C3×C8—61no—
50C22×C3⋊C8—21no—
51C2×D3×C8—62no—
52C2×D3×C8—61no—
53C2×D3×C8—61no—
54C2×D3×C8—68no—
55C2×D3×C8—62no—
56C3×C22⋊C8—61no—
57#830—21no—
58(C2×D3)⋊C8—61no—
59(C2×D3)⋊C8—61no—
60C23×C32C4⋊C411yescharacteristic
61C22×C3⋊D3—22no—
62C22×C3⋊D3—22no—
63C22×C3⋊D3C4⋊C411yescharacteristic
64C22×C3⋊D3C2×C812yes—
65C22×C3⋊D3M1612yes—
66C22×C3⋊D3C22×C411yescharacteristic
67C2×#157—22no—
68C2×#157—22no—
69C2×#157—22no—
70C2×#157—22no—
71C2×#157—22no—
72C2×#157C2×C814yescomplemented
73C2×C32×C4—21no—
74C2×C32×C4—21no—
75C2×C32×C4C4⋊C411yescharacteristic
76C2×C32×C4C2×D411yescharacteristic
77C2×C3⋊Dic3—22no—
78C2×C3⋊Dic3C4⋊C411yescharacteristic
79C2×C3⋊Dic3C2×Q811yescharacteristic
80C4×C3⋊D3—22no—
81C4×C3⋊D3—21no—
82C4×C3⋊D3—21no—
83C4×C3⋊D3—22no—
84C4×C3⋊D3C2×D412yes—
85C4×C3⋊D3#4112yes—
86C3×C3⋊C8—24no—
87C3×C3⋊C8—41no—
88C3×C3⋊C8—41no—
89C23×C8—91no—
90C2×C4⋊C8—92no—
91C2×C22⋊C8—91no—
92C4×C22⋊C4—91no—
93#336—92no—
94C23×D3—61no—
95C23×D3—61no—
96C22×C3×C4—21no—
97C22×C3×C4—21no—
98C22×Dic3—61no—
99C22×Dic3—61no—
100C2×C4×D3—61no—
101C2×C4×D3—61no—
102C2×C4×D3—61no—
103C2×C4×D3—61no—
104C2×C4×D3—61no—
105C2×C4×D3—61no—
106C2×C4×D3—61no—
107C2×C4×D3—61no—
108C2×C4×D3—64no—
109C2×C4×D3—64no—
110C2×C4×D3—122no—
111C2×C4×D3—122no—
112C2×C3×C8—64no—
113C2×C3×C8—62no—
114C2×C3×C8—61no—
115C2×C3×C8—61no—
116C2×C3⋊C8—24no—
117C2×C3⋊C8—22no—
118C2×C3⋊C8—21no—
119C2×C3⋊C8—21no—
120D3×C8—64no—
121D3×C8—64no—
122D3×C8—68no—
123D3×C8—122no—
124D3×C8—122no—
125C22×C32—21no—
126C22×C32—21no—
127C22×C32C4⋊C812yescomplemented
128C22×C32C2×C4⋊C411yescharacteristic
129C2×C3⋊D3—21no—
130C2×C3⋊D3—21no—
131C2×C3⋊D3—24no—
132C2×C3⋊D3—24no—
133C2×C3⋊D3C4⋊C812yescomplemented
134C2×C3⋊D3C4×D412yes—
135C2×C3⋊D3C22×C811yescharacteristic
136C2×C3⋊D3C2×M1611yescharacteristic
137C2×C3⋊D3#13112yes—
138#157—24no—
139#157—42no—
140C32×C4—21no—
141C32×C4#12011yescharacteristic
142C32×C4#12311yescharacteristic
143C3⋊Dic3—21no—
144C3⋊Dic3C22⋊Q812yes—
145C23×C4—91no—
146C22×C8—61no—
147C22×C8—92no—
148C22×C8—91no—
149C22×C8—91no—
150C22×C8—184no—
151C22×C8—181no—
152C2×C22⋊C4—91no—
153C2×C22⋊C4—91no—
154C2×C42—92no—
155C4⋊C8—184no—
156C22⋊C8—61no—
157C22⋊C8—181no—
158#95—92no—
159C23×C3—21no—
160C23×C3—21no—
161C22×D3—61no—
162C22×D3—62no—
163C22×D3—62no—
164C22×D3—61no—
165C22×D3—61no—
166C22×D3—61no—
167C22×D3—62no—
168C22×D3—62no—
169C22×D3—64no—
170C22×D3—64no—
171C22×D3—122no—
172C22×D3—122no—
173C2×C3×C4—22no—
174C2×C3×C4—22no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—41no—
180C2×C3×C4—41no—
181C2×Dic3—61no—
182C2×Dic3—61no—
183C2×Dic3—61no—
184C2×Dic3—61no—
185C2×Dic3—64no—
186C2×Dic3—122no—
187C4×D3—62no—
188C4×D3—62no—
189C4×D3—62no—
190C4×D3—62no—
191C4×D3—62no—
192C4×D3—64no—
193C4×D3—64no—
194C4×D3—62no—
195C4×D3—122no—
196C4×D3—121no—
197C4×D3—121no—
198C4×D3—122no—
199C3×C8—64no—
200C3×C8—121no—
201C3×C8—121no—
202C3⋊C8—24no—
203C3⋊C8—41no—
204C3⋊C8—41no—
205C2×C32—22no—
206C2×C32#38511yescharacteristic
207C2×C32C2×C4⋊C811yescharacteristic
208C2×C32#42411yescharacteristic
209C3⋊D3—22no—
210C3⋊D3C8×D412yes—
211C3⋊D3#43512yes—
212C24—91no—
213C22×C4—91no—
214C22×C4—92no—
215C22×C4—91no—
216C22×C4—91no—
217C22×C4—91no—
218C22×C4—91no—
219C22×C4—92no—
220C22×C4—182no—
221C22×C4—182no—
222C22×C4GO+(4,𝔽2)11yescharacteristic
223C2×C8—64no—
224C2×C8—62no—
225C2×C8—61no—
226C2×C8—61no—
227C2×C8—94no—
228C2×C8—182no—
229C2×C8—184no—
230C2×C8—182no—
231C2×C8—182no—
232C22⋊C4—94no—
233C22⋊C4—182no—
234C42—182no—
235C42—182no—
236C22×C3—22no—
237C22×C3—22no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—22no—
241C22×C3—22no—
242C22×C3—41no—
243C22×C3—41no—
244C2×D3—62no—
245C2×D3—62no—
246C2×D3—62no—
247C2×D3—61no—
248C2×D3—61no—
249C2×D3—61no—
250C2×D3—61no—
251C2×D3—62no—
252C2×D3—62no—
253C2×D3—62no—
254C2×D3—62no—
255C2×D3—68no—
256C2×D3—68no—
257C2×D3—62no—
258C2×D3—124no—
259C2×D3—124no—
260C2×D3—121no—
261C2×D3—121no—
262C3×C4—22no—
263C3×C4—21no—
264C3×C4—21no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—41no—
268Dic3—62no—
269Dic3—62no—
270Dic3—62no—
271Dic3—121no—
272C32#185011yescharacteristic, complemented, Sylow
273C23—91no—
274C23—91no—
275C23—92no—
276C23—92no—
277C23—182no—
278C23—182no—
279C23#377311yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—91no—
283C2×C4—92no—
284C2×C4—92no—
285C2×C4—94no—
286C2×C4—91no—
287C2×C4—182no—
288C2×C4—182no—
289C2×C4—182no—
290C2×C4—182no—
291C2×C4—182no—
292C2×C4—181no—
293C2×C4—181no—
294C2×C4—182no—
295C2×C4—182no—
296C2×C4—182no—
297C2×C4#377311yescharacteristic
298C2×C4C2×GO+(4,𝔽2)11yescharacteristic
299C8—64no—
300C8—121no—
301C8—121no—
302C2×C3—24no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—42no—
310D3—62no—
311D3—62no—
312D3—62no—
313D3—62no—
314D3—64no—
315D3—122no—
316C22—21no—
317C22—21no—
318C22—91no—
319C22—91no—
320C22—92no—
321C22—92no—
322C22—92no—
323C22—184no—
324C22—184no—
325C22—181no—
326C22—181no—
327C22#6373212yescomplemented
328C22C2×#377311yescharacteristic
329C4—21no—
330C4—92no—
331C4—184no—
332C4—181no—
333C4—362no—
334C4#6423311yescharacteristic
335C4#6424111yescharacteristic
336C3—21no—
337C3—21no—
338C2—22no—
339C2—92no—
340C2—92no—
341C2—182no—
342C2C2×#6373211yescharacteristic
343C2#1059332711yescharacteristic
344C2#1059348511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊D3C22×C8
FittingC22×C32×C4D4
socleC22×C32C2×C4⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1850
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. C2×#63732C2semidirect
5. #10590044C2semidirect
34. C22⋊#157C8semidirect
72. C2×#157C2×C8semidirect
127. C22×C32C4⋊C8semidirect
133. C2×C3⋊D3C4⋊C8semidirect
272. C32#1850semidirect
327. C22#63732semidirect

Maximal subgroups

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

subgroupindex
C22×#37102
C4×C22⋊#1572
C2×#637322
#105911522
#105900442
#18509