Finite Group Databasebeta

← #11789119

Subgroups — #11789119

Order 1152.

412 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 75 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×#63742C211yesmaximal, characteristic
2#10591328C211yesmaximal, characteristic
3#10591257C211yesmaximal, characteristic
4#10590207C211yesmaximal, characteristic
5#10590075C211yesmaximal, characteristic
6#10590075C211yesmaximal, characteristic
7#10590075C211yesmaximal, characteristic
8C22×#622C2211yescharacteristic
9C22×#622C2211yescharacteristic
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C2×#3724C2211yescharacteristic
12C2×#3724C2211yescharacteristic
13C2×#3724C2211yescharacteristic
14C2×#3724C2211yescharacteristic
15C2×Dic3⋊Dic3—21no—
16C2×Dic32—21no—
17#63742C414yescomplemented
18C3×C3⋊#95—21no—
19C3×C3⋊#95—21no—
20#4649—61no—
21#4647—61no—
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3D411yescharacteristic
24C22×C3⋊Dic3C2311yescharacteristic
25C22×C3×Dic3—21no—
26C22×C3×Dic3—21no—
27C22×C3×Dic3—21no—
28C22×C3×Dic3—21no—
29C2×#622—21no—
30C2×#622—21no—
31C2×#622—21no—
32C2×#622—21no—
33C2×#622—21no—
34C2×#622C2×C412yes—
35C4×C3⋊Dic3—21no—
36C4×C3⋊Dic3—21no—
37#3724—21no—
38#3724—21no—
39#3724—21no—
40#3724—21no—
41#3724—21no—
42#3724C2×C412yes—
43#3724C2×C412yes—
44#3724Q812yes—
45Dic3⋊Dic3—42no—
46Dic32—42no—
47#1919—91nomaximal, Sylow
48C2×C4⋊Dic3—61no—
49C2×Dic3⋊C4—61no—
50C2×Dic3⋊C4—61no—
51C2×Dic3⋊C4—61no—
52C2×Dic3⋊C4—61no—
53C2×Dic3⋊C4—61no—
54C2×C4×Dic3—61no—
55C2×C4×Dic3—61no—
56C2×C4×Dic3—61no—
57C2×C4×Dic3—61no—
58C3×#95—61no—
59C3×#95—61no—
60C3⋊#95—21no—
61C3⋊#95—21no—
62C23×C32C2×D411yescharacteristic
63C2×C32×C4—21no—
64C2×C32×C4—21no—
65C2×C32×C4—21no—
66C2×C3⋊Dic3—21no—
67C2×C3⋊Dic3—21no—
68C2×C3⋊Dic3SD1612yes—
69C2×C3⋊Dic3C22×C411yescharacteristic
70C2×C3⋊Dic3C2×Q811yescharacteristic
71C2×C3⋊Dic3#4111yescharacteristic
72C2×C3⋊Dic3#4111yescharacteristic
73C2×C3⋊Dic3#4111yescharacteristic
74C2×C3⋊Dic3#4111yescharacteristic
75C2×C3×Dic3—22no—
76C2×C3×Dic3—22no—
77C2×C3×Dic3—22no—
78C2×C3×Dic3—41no—
79C2×C3×Dic3—41no—
80C2×C3×Dic3—41no—
81C2×C3×Dic3—41no—
82C2×C3×Dic3—41no—
83C2×C3×Dic3—41no—
84C2×C3×Dic3—41no—
85C2×C3×Dic3—41no—
86C2×C3×Dic3—41no—
87#622—22no—
88#622—41no—
89C2×#106—91no—
90#389—91no—
91C4×C4⋊C4—91no—
92#340—91no—
93#340—91no—
94#340—91no—
95#336—91no—
96C22×C3×C4—21no—
97C22×C3×C4—21no—
98C22×C3×C4—61no—
99C22×C3×C4—61no—
100C22×C3×C4—61no—
101C22×C3×C4—61no—
102C22×Dic3—21no—
103C22×Dic3—21no—
104C22×Dic3—21no—
105C22×Dic3—21no—
106C22×Dic3—61no—
107C22×Dic3—61no—
108C22×Dic3—61no—
109C22×Dic3—61no—
110C4⋊Dic3—122no—
111Dic3⋊C4—62no—
112Dic3⋊C4—62no—
113Dic3⋊C4—62no—
114Dic3⋊C4—62no—
115Dic3⋊C4—62no—
116Dic3⋊C4—62no—
117Dic3⋊C4—121no—
118Dic3⋊C4—121no—
119Dic3⋊C4—122no—
120C4×Dic3—62no—
121C4×Dic3—62no—
122C4×Dic3—121no—
123C4×Dic3—121no—
124C4×Dic3—122no—
125C4×Dic3—122no—
126C22×C32C4×D411yescharacteristic
127C22×C32C22⋊Q811yescharacteristic
128C22×C32#12311yescharacteristic
129C22×C32C2×SD1611yescharacteristic
130C22×C32#13511yescharacteristic
131C22×C32AGL(1,ℤ/8)11yescharacteristic
132C22×C32#13711yescharacteristic
133C32×C4—41no—
134C3⋊Dic3—22no—
135C3⋊Dic3#11711yescharacteristic
136C3⋊Dic3C4×Q811yescharacteristic
137C3⋊Dic3#12511yescharacteristic
138C3⋊Dic3#12611yescharacteristic
139C3×Dic3—42no—
140C3×Dic3—42no—
141C3×Dic3—42no—
142C3×Dic3—81no—
143C22×C8—91no—
144C22×C8—91no—
145C2×C4⋊C4—91no—
146C2×C4⋊C4—91no—
147C2×C4⋊C4—91no—
148C2×C4⋊C4—91no—
149C2×C4⋊C4—181no—
150C2×C42—91no—
151C2×C42—181no—
152#106—94no—
153#95—61no—
154#95—61no—
155C23×C3—21no—
156C23×C3—21no—
157C2×C3×C4—22no—
158C2×C3×C4—22no—
159C2×C3×C4—41no—
160C2×C3×C4—41no—
161C2×C3×C4—41no—
162C2×C3×C4—41no—
163C2×C3×C4—62no—
164C2×C3×C4—62no—
165C2×C3×C4—62no—
166C2×C3×C4—121no—
167C2×C3×C4—121no—
168C2×C3×C4—121no—
169C2×C3×C4—121no—
170C2×C3×C4—121no—
171C2×C3×C4—121no—
172C2×C3×C4—121no—
173C2×C3×C4—121no—
174C2×C3×C4—121no—
175C2×Dic3—22no—
176C2×Dic3—22no—
177C2×Dic3—22no—
178C2×Dic3—41no—
179C2×Dic3—41no—
180C2×Dic3—41no—
181C2×Dic3—41no—
182C2×Dic3—41no—
183C2×Dic3—41no—
184C2×Dic3—41no—
185C2×Dic3—41no—
186C2×Dic3—41no—
187C2×Dic3—62no—
188C2×Dic3—61no—
189C2×Dic3—61no—
190C2×Dic3—61no—
191C2×Dic3—61no—
192C2×Dic3—61no—
193C2×Dic3—61no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C2×Dic3—61no—
197C2×Dic3—61no—
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—62no—
201C2×Dic3—62no—
202C2×Dic3—62no—
203C2×Dic3—121no—
204C2×Dic3—121no—
205C2×C32#38711yescharacteristic
206C2×C32C4×SD1611yescharacteristic
207C2×C32#44011yescharacteristic
208C2×C32#47511yescharacteristic
209C2×C32#47811yescharacteristic
210C2×C32#48111yescharacteristic
211C2×C32#48511yescharacteristic
212C22×C4—61no—
213C22×C4—61no—
214C22×C4—61no—
215C22×C4—61no—
216C22×C4—91no—
217C22×C4—91no—
218C22×C4GO+(4,𝔽2)11yescharacteristic
219C2×C8—92no—
220C2×C8—181no—
221C2×C8—181no—
222C2×C8—181no—
223C2×C8—181no—
224C2×C8—181no—
225C4⋊C4—92no—
226C4⋊C4—92no—
227C4⋊C4—92no—
228C4⋊C4—181no—
229C4⋊C4—181no—
230C4⋊C4—181no—
231C4⋊C4—181no—
232C4⋊C4—181no—
233C4⋊C4—362no—
234C42—181no—
235C42—181no—
236C42—362no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—21no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—21no—
249C22×C3—21no—
250C22×C3—21no—
251C3×C4—42no—
252C3×C4—42no—
253C3×C4—122no—
254C3×C4—122no—
255C3×C4—122no—
256C3×C4—241no—
257Dic3—42no—
258Dic3—42no—
259Dic3—42no—
260Dic3—61no—
261Dic3—61no—
262Dic3—61no—
263Dic3—61no—
264Dic3—61no—
265Dic3—61no—
266Dic3—61no—
267Dic3—61no—
268Dic3—64no—
269Dic3—81no—
270Dic3—122no—
271C32#191911yescharacteristic, complemented, Sylow
272C23C2×GO+(4,𝔽2)11yescharacteristic
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—62no—
277C2×C4—62no—
278C2×C4—62no—
279C2×C4—91no—
280C2×C4—91no—
281C2×C4—91no—
282C2×C4—91no—
283C2×C4—91no—
284C2×C4—91no—
285C2×C4—92no—
286C2×C4—121no—
287C2×C4—121no—
288C2×C4—121no—
289C2×C4—121no—
290C2×C4—121no—
291C2×C4—121no—
292C2×C4—121no—
293C2×C4—121no—
294C2×C4—121no—
295C2×C4—181no—
296C2×C4—181no—
297C8—182no—
298C8—361no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—21no—
313C22D32⋊Q811yescharacteristic
314C22#6422411yescharacteristic
315C22#6422711yescharacteristic
316C22C4×GO+(4,𝔽2)11yescharacteristic
317C22#6423311yescharacteristic
318C22#6423711yescharacteristic
319C22#6423911yescharacteristic
320C4—41no—
321C4—91no—
322C4—91no—
323C4—91no—
324C4—91no—
325C4—122no—
326C4—122no—
327C4—122no—
328C4—182no—
329C4—241no—
330C3—21no—
331C3—21no—
332C2#1059333811yescharacteristic
333C2#1059336111yescharacteristic
334C2#1059336411yescharacteristic
335C2#1059338511yescharacteristic
336C2#1059343211yescharacteristic
337C2#1059343311yescharacteristic
338C2#1059350111yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1919
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
17. #63742C4semidirect
271. C32#1919semidirect

Maximal subgroups

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

subgroupindex
C2×#637422
#105913282
#105912572
#105902072
#105900752
#19199