Finite Group Databasebeta

← #11773745

Subgroups — #11773745

Order 1152.

638 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C2×#63883C211yesmaximal, characteristic
2#10593800C211yesmaximal, characteristic
3#10591152C211yesmaximal, characteristic
4#10590028C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C22×#624C411yescharacteristic
7C22×#624C411yescharacteristic
8C2×#3787—21no—
9C2×C3×Dic3⋊C4—21no—
10C2×Dic3⋊Dic3—21no—
11#63883—21no—
12#63883—21no—
13#63883C412yes—
14#63883C2212yes—
15C2×#3710—21no—
16C22⋊#622—21no—
17#63778C2212yes—
18C3×#830—21no—
19#63557C2212yes—
20C2×D3×C4⋊C4—61no—
21D3×C22⋊C8—61no—
22C23×C3⋊D3C2×C411yescharacteristic
23C22×C32×C4D411yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C2×C4×C3⋊D3—42no—
26C2×C4×C3⋊D3C2×C411yescharacteristic
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C4×C3⋊D3D411yescharacteristic
29C2×C4×C3⋊D3C2311yescharacteristic
30C22×C3×Dic3—21no—
31C22×C3×Dic3—21no—
32C2×#624—21no—
33C2×#624—22no—
34C2×#624—21no—
35C2×#624—42no—
36C2×#624C814yescomplemented
37C2×#624C2×C412yes—
38C2×#624C2×C412yes—
39C2×#622—22no—
40#3787—42no—
41C3×Dic3⋊C4—22no—
42C3×Dic3⋊C4—22no—
43C2×C3×C3⋊C8—22no—
44Dic3⋊Dic3—22no—
45Dic3⋊Dic3—22no—
46#3710—42no—
47C2×#324—91nomaximal, Sylow
48C22×C4×D3—61no—
49C22×C4×D3—61no—
50C22×C4×D3—61no—
51C22×C4×D3—61no—
52C2×C3×C4⋊C4—61no—
53C2×C4⋊Dic3—61no—
54C2×Dic3⋊C4—21no—
55C2×Dic3⋊C4—61no—
56C2×D3×C8—62no—
57D3×C4⋊C4—62no—
58D3×C4⋊C4—62no—
59D3×C4⋊C4—62no—
60D3×C4⋊C4—62no—
61C3×C22⋊C8—61no—
62#830—21no—
63(C2×D3)⋊C8—62no—
64C23×C32C22⋊C411yescharacteristic
65C22×C3⋊D3—22no—
66C22×C3⋊D3—22no—
67C22×C3⋊D3C22⋊C411yescharacteristic
68C22×C3⋊D3C2×C812yes—
69C22×C3⋊D3M1612yes—
70C22×C3⋊D3C22×C411yescharacteristic
71C2×C32×C4—41no—
72C2×C32×C4C22⋊C411yescharacteristic
73C2×C32×C4C2×D411yescharacteristic
74C2×C3⋊Dic3—41no—
75C2×C3⋊Dic3C22⋊C411yescharacteristic
76C2×C3⋊Dic3C2×D411yescharacteristic
77C4×C3⋊D3—22no—
78C4×C3⋊D3—22no—
79C4×C3⋊D3—41no—
80C4×C3⋊D3—41no—
81C2×C3×Dic3—24no—
82C2×C3×Dic3—22no—
83C2×C3×Dic3—22no—
84C2×C3×Dic3—42no—
85#624—24no—
86#624—22no—
87#624—42no—
88#624—42no—
89#624C2×C814yescomplemented
90#622—42no—
91C3×C3⋊C8—42no—
92C22×C4⋊C4—91no—
93C2×C22⋊C8—91no—
94C2×C22⋊C8—91no—
95#324—94no—
96C23×D3—61no—
97C23×D3—61no—
98C22×C3×C4—21no—
99C22×C3×C4—21no—
100C22×C3×C4—61no—
101C22×C3×C4—61no—
102C22×Dic3—21no—
103C22×Dic3—21no—
104C22×Dic3—61no—
105C22×Dic3—61no—
106C2×C4×D3—62no—
107C2×C4×D3—64no—
108C2×C4×D3—61no—
109C2×C4×D3—62no—
110C2×C4×D3—61no—
111C2×C4×D3—61no—
112C2×C4×D3—61no—
113C2×C4×D3—61no—
114C2×C4×D3—61no—
115C2×C4×D3—61no—
116C2×C4×D3—61no—
117C2×C4×D3—62no—
118C2×C4×D3—64no—
119C2×C4×D3—62no—
120C2×C4×D3—124no—
121C2×C4×D3—124no—
122C2×C4×D3—124no—
123C2×C3×C8—62no—
124C3×C4⋊C4—62no—
125C3×C4⋊C4—62no—
126C4⋊Dic3—62no—
127C4⋊Dic3—62no—
128Dic3⋊C4—22no—
129Dic3⋊C4—22no—
130Dic3⋊C4—62no—
131Dic3⋊C4—62no—
132C2×C3⋊C8—22no—
133D3×C8—124no—
134C22×C32—21no—
135C22×C32—21no—
136C22×C32C22⋊C812yes—
137C22×C32C2×C22⋊C411yescharacteristic
138C2×C3⋊D3—21no—
139C2×C3⋊D3—21no—
140C2×C3⋊D3—24no—
141C2×C3⋊D3—24no—
142C2×C3⋊D3C22⋊C812yes—
143C2×C3⋊D3#9912yes—
144C2×C3⋊D3#10112yes—
145C2×C3⋊D3C22×C811yescharacteristic
146C2×C3⋊D3C2×M1611yescharacteristic
147C32×C4—21no—
148C32×C4—21no—
149C3⋊Dic3—21no—
150C3⋊Dic3—21no—
151C3×Dic3—24no—
152C3×Dic3—42no—
153C23×C4—91no—
154C23×C4—91no—
155C23×C4—91no—
156C22×C8—181no—
157C22×C8—181no—
158C2×C4⋊C4—61no—
159C2×C4⋊C4—92no—
160C2×C4⋊C4—92no—
161C2×C4⋊C4—181no—
162C2×C4⋊C4—181no—
163C2×C4⋊C4—181no—
164C22⋊C8—61no—
165C22⋊C8—92no—
166C22⋊C8—92no—
167C22⋊C8—181no—
168C23×C3—21no—
169C23×C3—21no—
170C22×D3—61no—
171C22×D3—61no—
172C22×D3—62no—
173C22×D3—62no—
174C22×D3—61no—
175C22×D3—62no—
176C22×D3—62no—
177C22×D3—61no—
178C22×D3—64no—
179C22×D3—64no—
180C22×D3—122no—
181C22×D3—122no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—42no—
187C2×C3×C4—42no—
188C2×C3×C4—62no—
189C2×C3×C4—64no—
190C2×C3×C4—62no—
191C2×C3×C4—122no—
192C2×Dic3—22no—
193C2×Dic3—24no—
194C2×Dic3—22no—
195C2×Dic3—42no—
196C2×Dic3—61no—
197C2×Dic3—61no—
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—122no—
201C2×Dic3—122no—
202C4×D3—64no—
203C4×D3—68no—
204C4×D3—64no—
205C4×D3—64no—
206C4×D3—122no—
207C4×D3—122no—
208C4×D3—122no—
209C4×D3—124no—
210C4×D3—124no—
211C4×D3—122no—
212C4×D3—122no—
213C4×D3—122no—
214C4×D3—122no—
215C3×C8—122no—
216C3⋊C8—42no—
217C2×C32—22no—
218C2×C32C2×C22⋊C811yescharacteristic
219C2×C32C2×#9911yescharacteristic
220C2×C32C2×#10111yescharacteristic
221C3⋊D3—21no—
222C3⋊D3—21no—
223C3⋊D3#32414yescomplemented
224C24—91no—
225C22×C4—61no—
226C22×C4—61no—
227C22×C4—92no—
228C22×C4—94no—
229C22×C4—92no—
230C22×C4—91no—
231C22×C4—91no—
232C22×C4—91no—
233C22×C4—91no—
234C22×C4—91no—
235C22×C4—181no—
236C22×C4—182no—
237C22×C4—181no—
238C22×C4—362no—
239C22×C4—362no—
240C22×C4GO+(4,𝔽2)11yescharacteristic
241C2×C8—62no—
242C2×C8—182no—
243C2×C8—362no—
244C2×C8—362no—
245C4⋊C4—62no—
246C4⋊C4—62no—
247C4⋊C4—182no—
248C4⋊C4—182no—
249C22×C3—22no—
250C22×C3—22no—
251C22×C3—21no—
252C22×C3—21no—
253C22×C3—22no—
254C22×C3—22no—
255C22×C3—41no—
256C22×C3—41no—
257C2×D3—62no—
258C2×D3—61no—
259C2×D3—61no—
260C2×D3—62no—
261C2×D3—62no—
262C2×D3—62no—
263C2×D3—62no—
264C2×D3—62no—
265C2×D3—61no—
266C2×D3—61no—
267C2×D3—62no—
268C2×D3—68no—
269C2×D3—68no—
270C2×D3—62no—
271C2×D3—124no—
272C2×D3—124no—
273C2×D3—121no—
274C2×D3—121no—
275C3×C4—22no—
276C3×C4—41no—
277C3×C4—41no—
278C3×C4—41no—
279C3×C4—64no—
280C3×C4—122no—
281Dic3—24no—
282Dic3—42no—
283Dic3—62no—
284Dic3—121no—
285Dic3—121no—
286Dic3—121no—
287C32C2×#32411yescharacteristic, complemented, Sylow
288C23—91no—
289C23—91no—
290C23—92no—
291C23—92no—
292C23—182no—
293C23—182no—
294C23D32⋊C411yescharacteristic
295C2×C4—41no—
296C2×C4—62no—
297C2×C4—64no—
298C2×C4—62no—
299C2×C4—94no—
300C2×C4—91no—
301C2×C4—91no—
302C2×C4—122no—
303C2×C4—182no—
304C2×C4—182no—
305C2×C4—184no—
306C2×C4—182no—
307C2×C4—361no—
308C2×C4—361no—
309C2×C4—362no—
310C2×C4—362no—
311C2×C4—361no—
312C2×C4D32⋊C411yescharacteristic
313C2×C4C2×GO+(4,𝔽2)11yescharacteristic
314C8—122no—
315C8—362no—
316C2×C3—24no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—42no—
324D3—64no—
325D3—64no—
326D3—62no—
327D3—62no—
328D3—121no—
329D3—121no—
330C22—21no—
331C22—21no—
332C22—92no—
333C22—92no—
334C22—92no—
335C22—91no—
336C22—91no—
337C22—184no—
338C22—184no—
339C22—181no—
340C22—181no—
341C22D32⋊C812yes—
342C22C2×D32⋊C411yescharacteristic
343C4—21no—
344C4—21no—
345C4—64no—
346C4—122no—
347C4—181no—
348C4—181no—
349C3—21no—
350C3—21no—
351C2—22no—
352C2—94no—
353C2—181no—
354C2—181no—
355C2C2×D32⋊C811yescharacteristic
356C2#1059331511yescharacteristic
357C2#1059349011yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊D3C22×C8
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#324
LCSG ▷ C2×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590028C2semidirect
36. C2×#624C8semidirect
89. #624C2×C8semidirect
223. C3⋊D3#324semidirect
287. C32C2×#324semidirect

Maximal subgroups

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

subgroupindex
C2×#638832
#105938002
#105911522
#105900282
C2×#3249