Finite Group Databasebeta

← #11789780

Subgroups — #11789780

Order 1152.

418 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 69 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#10593412C211yesmaximal, characteristic
2#10593341C211yesmaximal, characteristic
3C2×#63730C211yesmaximal, characteristic
4#10590672C211yesmaximal, characteristic
5C8×#624C211yesmaximal, characteristic
6#10590182C211yesmaximal, characteristic
7#10590049C211yesmaximal, characteristic
8C2×#3797C2211yescharacteristic
9C2×C4⋊#157C2211yescharacteristic
10C2×C4⋊#157C2211yescharacteristic
11C2×#3773—21no—
12C2×C8×C3⋊D3C2211yescharacteristic
13#63900C2211yescharacteristic
14C4×#624C2211yescharacteristic
15C2×#3710C2211yescharacteristic
16#63737—21no—
17#63737—21no—
18#63737—21no—
19#63730C414yescomplemented
20C3×#816—21no—
21C3×C8×Dic3—21no—
22#63565—21no—
23Dic3×C3⋊C8—21no—
24D3×#103—61no—
25C4×D3×C8—61no—
26C22×#157—21no—
27C22×#157—21no—
28C2×C4×C3⋊D3C2311yescharacteristic
29C2×C3×Dic6—21no—
30C2×#627—21no—
31C2×#624—21no—
32C2×#624—21no—
33C2×#624D411yescharacteristic
34C2×#624D411yescharacteristic
35#3797—21no—
36#3797—21no—
37#3797—21no—
38#3797C2×C412yes—
39C4⋊#157—21no—
40C4⋊#157—21no—
41C4⋊#157—21no—
42C4⋊#157C2×C412yes—
43#3773—42no—
44C2×C32×C8D411yescharacteristic
45C2×C3⋊(C3⋊C8)D411yescharacteristic
46C8×C3⋊D3—21no—
47C8×C3⋊D3—21no—
48C3×C4⋊Dic3—21no—
49C3×C4×Dic3—21no—
50C2×C3×C3⋊C8—21no—
51#3724—21no—
52Dic32—21no—
53#3710—21no—
54#3710C2×C412yes—
55#1933—91nomaximal, Sylow
56C2×D3×Q8—61no—
57C2×D3×C8—61no—
58C2×D3×C8—61no—
59C2×D3×C8—61no—
60D3×C4⋊C4—61no—
61C42×D3—61no—
62C3×#103—61no—
63C3×C4×C8—61no—
64#835—61no—
65#816—21no—
66C8×Dic3—21no—
67C8×Dic3—61no—
68#810—61no—
69C4×C3⋊C8—61no—
70C22×C3⋊D3C2×D411yescharacteristic
71C2×#157—22no—
72C2×#157—41no—
73C2×#157—41no—
74C2×#157—41no—
75C2×#157—41no—
76C2×#157—41no—
77C2×C32×C4C2×D411yescharacteristic
78C2×C3⋊Dic3#4111yescharacteristic
79C4×C3⋊D3C22×C411yescharacteristic
80C4×C3⋊D3#4111yescharacteristic
81C4×C3⋊D3#4111yescharacteristic
82C4×C3⋊D3#4111yescharacteristic
83C2×C3×Dic3—21no—
84C2×C3×Dic3—21no—
85C2×C3×Dic3—41no—
86C2×C3×Dic3—41no—
87C3×Dic6—22no—
88C3×Dic6—41no—
89#627—22no—
90#627—41no—
91#624—21no—
92#624—21no—
93#624—22no—
94#624—41no—
95#624—41no—
96#624—41no—
97#624SD1612yes—
98#624Q1612yes—
99C32×C8—21no—
100C3⋊(C3⋊C8)—21no—
101C3×C3⋊C8—22no—
102C2×#103—91no—
103C2×#103—91no—
104C2×C4×C8—91no—
105#391—91no—
106#389—91no—
107#340—91no—
108#340—91no—
109C2×C3×Q8—61no—
110D3×Q8—62no—
111D3×Q8—62no—
112D3×Q8—121no—
113D3×Q8—121no—
114C2×C4×D3—61no—
115C2×C4×D3—61no—
116C2×C4×D3—61no—
117C2×C4×D3—61no—
118C2×C4×D3—121no—
119C2×C4×D3—121no—
120C2×Dic6—21no—
121C2×Dic6—121no—
122C2×C3×C8—21no—
123C2×C3×C8—21no—
124C2×C3×C8—61no—
125C3×C4⋊C4—61no—
126C3×C42—61no—
127C4⋊Dic3—21no—
128Dic3⋊C4—121no—
129C4×Dic3—21no—
130C4×Dic3—61no—
131C4×Dic3—61no—
132C2×C3⋊C8—21no—
133C2×C3⋊C8—61no—
134C2×C3⋊C8—61no—
135D3×C8—62no—
136D3×C8—62no—
137D3×C8—62no—
138D3×C8—62no—
139D3×C8—121no—
140D3×C8—121no—
141C22×C32#12111yescharacteristic
142C2×C3⋊D3C4×D411yescharacteristic
143C2×C3⋊D3#12411yescharacteristic
144C2×C3⋊D3C2×SD1611yescharacteristic
145C2×C3⋊D3C2×Q1611yescharacteristic
146C2×C3⋊D3#13511yescharacteristic
147C2×C3⋊D3#13511yescharacteristic
148#157—42no—
149#157—81no—
150C32×C4C4×D411yescharacteristic
151C32×C4#12311yescharacteristic
152C3⋊Dic3#11711yescharacteristic
153C3⋊Dic3#12611yescharacteristic
154C3×Dic3—22no—
155C3×Dic3—22no—
156C3×Dic3—42no—
157C3×Dic3—81no—
158C22×Q8—91no—
159C22×C8—91no—
160C22×C8—91no—
161C2×C4⋊C4—91no—
162C2×C4⋊C4—91no—
163C2×C4⋊C4—91no—
164C2×C4⋊C4—181no—
165C2×C42—91no—
166#103—61no—
167#103—94no—
168#103—181no—
169C4×C8—61no—
170C4×C8—181no—
171#95—181no—
172#95—181no—
173#95—181no—
174C22×D3—61no—
175C22×D3—61no—
176C3×Q8—62no—
177C3×Q8—121no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—61no—
181C2×C3×C4—61no—
182C2×C3×C4—121no—
183C2×C3×C4—121no—
184C2×Dic3—21no—
185C2×Dic3—21no—
186C2×Dic3—41no—
187C2×Dic3—41no—
188C2×Dic3—61no—
189C2×Dic3—61no—
190C4×D3—62no—
191C4×D3—62no—
192C4×D3—61no—
193C4×D3—61no—
194C4×D3—61no—
195C4×D3—61no—
196C4×D3—61no—
197C4×D3—61no—
198C4×D3—61no—
199C4×D3—61no—
200C4×D3—62no—
201C4×D3—62no—
202C4×D3—122no—
203C4×D3—122no—
204C4×D3—241no—
205C4×D3—241no—
206Dic6—22no—
207Dic6—41no—
208Dic6—122no—
209Dic6—122no—
210C3×C8—22no—
211C3×C8—41no—
212C3×C8—62no—
213C3⋊C8—22no—
214C3⋊C8—62no—
215C3⋊C8—121no—
216C2×C32#38811yescharacteristic
217C2×C32#46511yescharacteristic
218C2×C32#46711yescharacteristic
219C3⋊D3C4×SD1611yescharacteristic
220C3⋊D3C4×Q1611yescharacteristic
221C3⋊D3#48711yescharacteristic
222C3⋊D3#48811yescharacteristic
223C2×Q8—61no—
224C2×Q8—92no—
225C2×Q8—181no—
226C2×Q8—181no—
227C2×Q8—181no—
228C2×Q8—181no—
229C22×C4—91no—
230C22×C4—91no—
231C22×C4—91no—
232C22×C4—181no—
233C22×C4—181no—
234C22×C4—181no—
235C22×C4—181no—
236C2×C8—61no—
237C2×C8—92no—
238C2×C8—91no—
239C2×C8—181no—
240C2×C8—181no—
241C2×C8—181no—
242C2×C8GO+(4,𝔽2)11yescharacteristic
243C4⋊C4—61no—
244C4⋊C4—92no—
245C4⋊C4—181no—
246C4⋊C4—181no—
247C4⋊C4—181no—
248C4⋊C4—181no—
249C4⋊C4—362no—
250C42—61no—
251C42—181no—
252C22×C3—21no—
253C22×C3—21no—
254C2×D3—61no—
255C2×D3—61no—
256C2×D3—61no—
257C2×D3—61no—
258C2×D3—61no—
259C2×D3—61no—
260C2×D3—61no—
261C2×D3—61no—
262C2×D3—61no—
263C2×D3—61no—
264C2×D3—61no—
265C2×D3—61no—
266C3×C4—21no—
267C3×C4—21no—
268C3×C4—21no—
269C3×C4—21no—
270C3×C4—62no—
271C3×C4—62no—
272C3×C4—122no—
273C3×C4—241no—
274Dic3—22no—
275Dic3—22no—
276Dic3—42no—
277Dic3—61no—
278Dic3—61no—
279Dic3—61no—
280Dic3—61no—
281Dic3—81no—
282C32#193311yescharacteristic, complemented, Sylow
283C23—91no—
284Q8—62no—
285Q8—121no—
286Q8—182no—
287Q8—361no—
288C2×C4—61no—
289C2×C4—61no—
290C2×C4—92no—
291C2×C4—92no—
292C2×C4—91no—
293C2×C4—91no—
294C2×C4—91no—
295C2×C4—91no—
296C2×C4—91no—
297C2×C4—121no—
298C2×C4—121no—
299C2×C4—181no—
300C2×C4—181no—
301C2×C4—182no—
302C2×C4—182no—
303C2×C4—361no—
304C2×C4—361no—
305C2×C4—361no—
306C2×C4—361no—
307C2×C4—361no—
308C2×C4—361no—
309C2×C4—361no—
310C2×C4—361no—
311C2×C4C2×GO+(4,𝔽2)11yescharacteristic
312C8—21no—
313C8—62no—
314C8—181no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—21no—
321D3—61no—
322D3—61no—
323D3—61no—
324D3—61no—
325D3—61no—
326D3—61no—
327D3—61no—
328D3—61no—
329C22—91no—
330C22—91no—
331C22—91no—
332C22—91no—
333C22—91no—
334C22—91no—
335C22#6423011yescharacteristic
336C4—62no—
337C4—62no—
338C4—91no—
339C4—91no—
340C4—122no—
341C4—241no—
342C4—362no—
343C4—721no—
344C4C4×GO+(4,𝔽2)11yescharacteristic
345C4#6423311yescharacteristic
346C3—21no—
347C3—21no—
348C2—91no—
349C2—91no—
350C2—91no—
351C2—91no—
352C2#1059328411yescharacteristic
353C2#1059328811yescharacteristic
354C2#1059339911yescharacteristic
subgroupG/H
centerC22#64230
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#121
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1933
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
19. #63730C4semidirect
282. C32#1933semidirect

Maximal subgroups

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

subgroupindex
#105934122
#105933412
C2×#637302
#105906722
C8×#6242
#105901822
#105900492
#19339