Finite Group Databasebeta

← #11778820

Subgroups — #11778820

Order 1152.

471 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 471 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C3×#5500C211yesmaximal, characteristic
2#10592685C211yesmaximal, characteristic
3#10591103C212yesmaximal
4C3×#4528C211yesmaximal, characteristic
5#10589152C212yesmaximal
6#71899—31nomaximal
7#68141—31nomaximal
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
10C3×#926—21no—
11C3×#924—21no—
12C3×#924C2212yes—
13C3×#890—22no—
14C3×#888—22no—
15#63658—21no—
16#63658—21no—
17#63658C2211yescharacteristic
18C3×#830C2212yes—
19#63575—22no—
20#63566—22no—
21C3×#544—31no—
22#5500D311yescharacteristic
23#5044—32no—
24#4986—31no—
25#4986—31no—
26#4986—61no—
27#4722—32no—
28C3×#324—31no—
29#4538—32no—
30#4528D311yescharacteristic
31#4467—32no—
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3—21no—
37C2×C3×Dic6—21no—
38C2×C3×Dic6D412yes—
39C32×C4⋊C4—22no—
40C4⋊(C3⋊Dic3)—22no—
41C3×#217—22no—
42C3×C4⋊Dic3—21no—
43C3×C4⋊Dic3—21no—
44C3×C4⋊Dic3—21no—
45C3×C4⋊Dic3D412yes—
46C3×Dic3⋊C4—22no—
47C3×Dic3⋊C4—22no—
48C3×C4×Dic3—22no—
49C2×C3×C3⋊C8—22no—
50#1617—91noSylow
51C3×C4⋊Q8—62no—
52C3×#125—62no—
53C3×C22⋊Q8—32no—
54C3×C22⋊Q8—61no—
55C3×#117—61no—
56C2×C3×C4⋊C4—21no—
57C2×C3×C4⋊C4C2×D311yescharacteristic
58C2×C3×C4⋊C4C2×D311yescharacteristic
59#926—21no—
60C2×C4⋊Dic3—31no—
61C2×C4⋊Dic3—31no—
62C2×C4⋊Dic3—61no—
63#924—21no—
64#924C2×D312yes—
65#890—22no—
66#888—22no—
67C3×C22⋊C8—32no—
68#835—62no—
69C3⋊#95—31no—
70C3⋊#95—31no—
71C3⋊#95—61no—
72C3⋊#95—62no—
73C3⋊#95—62no—
74C3⋊#95—61no—
75C3⋊#95—61no—
76C3⋊#95—61no—
77C3⋊#95—61no—
78#830C2×D312yes—
79#818—62no—
80#816—62no—
81#807—62no—
82C23×C32C2×D411yescharacteristic
83C2×C32×C4—21no—
84C2×C32×C4—21no—
85C2×C32×C4—21no—
86C2×C32×C4—41no—
87C2×C32×C4—41no—
88C2×C32×C4Q1612yes—
89C2×C32×C4C2×D412yes—
90C2×C3⋊Dic3—41no—
91C2×C3⋊Dic3—41no—
92C2×C3⋊Dic3—42no—
93C2×C3⋊Dic3—41no—
94C2×C3⋊Dic3—41no—
95C2×C3×Dic3—22no—
96C2×C3×Dic3—22no—
97C3×Dic6—42no—
98C3×Dic6—81no—
99C3×C3⋊C8—42no—
100#544—31no—
101#484—92no—
102#400—91no—
103#328—92no—
104#324—31no—
105C2×C3×Q8—32no—
106C2×C3×Q8—61no—
107C22×C3×C4—21no—
108C22×C3×C4—21no—
109C22×C3×C4—21no—
110C22×C3×C4D1211yescharacteristic
111C22×C3×C4D1211yescharacteristic
112C22×C3×C4#6711yescharacteristic
113C22×C3×C4#6711yescharacteristic
114C22×C3×C4C22×D311yescharacteristic
115C22×C3×C4C22×D311yescharacteristic
116C22×Dic3—62no—
117C22×Dic3—62no—
118C22×Dic3—61no—
119C22×Dic3—61no—
120C22×Dic3—61no—
121C22×Dic3—61no—
122C2×Dic6—21no—
123C2×Dic6#6712yes—
124C2×C3×C8—62no—
125C3×C4⋊C4—22no—
126C3×C4⋊C4—22no—
127C3×C4⋊C4—32no—
128C3×C4⋊C4—42no—
129C3×C4⋊C4—62no—
130C3×C4⋊C4—61no—
131C3×C4⋊C4—61no—
132C3×C4⋊C4—61no—
133C3×C4⋊C4—62no—
134C3×C22⋊C4—62no—
135C3×C42—62no—
136#217—22no—
137C4⋊Dic3—21no—
138C4⋊Dic3—21no—
139C4⋊Dic3—21no—
140C4⋊Dic3—62no—
141C4⋊Dic3—62no—
142C4⋊Dic3—122no—
143C4⋊Dic3#6712yes—
144Dic3⋊C4—22no—
145Dic3⋊C4—22no—
146C4×Dic3—22no—
147C2×C3⋊C8—22no—
148C22×C32—21no—
149C22×C32—21no—
150C22×C32#12011yescharacteristic
151C22×C32C2×Q1611yescharacteristic
152C22×C32#13711yescharacteristic
153C32×C4—22no—
154C32×C4—22no—
155C32×C4—41no—
156C3⋊Dic3—81no—
157C3⋊Dic3—81no—
158C3×Dic3—42no—
159C3×Dic3—42no—
160C4⋊Q8—62no—
161#125—62no—
162C22⋊Q8—32no—
163C22⋊Q8—61no—
164#117—61no—
165C2×C4⋊C4—91no—
166C2×C4⋊C4D3211yescharacteristic
167#107—182no—
168#103—182no—
169C22⋊C8—32no—
170#95—91no—
171#95—181no—
172#95—181no—
173C23×C3—21no—
174C23×C3C2×D1211yescharacteristic
175C23×C3C2×#6711yescharacteristic
176C3×Q8—122no—
177C3×Q8—241no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—22no—
185C2×C3×C4—22no—
186C2×C3×C4—41no—
187C2×C3×C4—41no—
188C2×C3×C4—41no—
189C2×C3×C4—41no—
190C2×C3×C4—41no—
191C2×C3×C4—42no—
192C2×C3×C4—41no—
193C2×C3×C4—41no—
194C2×C3×C4—42no—
195C2×C3×C4—62no—
196C2×C3×C4—62no—
197C2×C3×C4Dic1212yes—
198C2×C3×C4#21612yes—
199C2×C3×C4D3×D412yes—
200C2×C3×C4C2×#6712yes—
201C2×Dic3—22no—
202C2×Dic3—22no—
203C2×Dic3—122no—
204C2×Dic3—122no—
205C2×Dic3—124no—
206C2×Dic3—122no—
207C2×Dic3—121no—
208C2×Dic3—121no—
209C2×Dic3—121no—
210C2×Dic3—121no—
211C2×Dic3—122no—
212C2×Dic3—122no—
213C2×Dic3—122no—
214C2×Dic3—121no—
215C2×Dic3—121no—
216C2×Dic3—121no—
217C2×Dic3—121no—
218Dic6—42no—
219Dic6—81no—
220C3×C8—122no—
221C3⋊C8—42no—
222C2×C32—21no—
223C2×C32—21no—
224C2×C32#45111yescharacteristic
225C2×C32#45411yescharacteristic
226C2×C32#45811yescharacteristic
227C2×Q8—32no—
228C2×Q8—61no—
229C22×C4—181no—
230C22×C4—181no—
231C22×C4#62611yescharacteristic
232C22×C4#62611yescharacteristic
233C22×C4C2×D3211yescharacteristic
234C2×C8—62no—
235C4⋊C4—22no—
236C4⋊C4—32no—
237C4⋊C4—61no—
238C4⋊C4—61no—
239C4⋊C4—61no—
240C4⋊C4—62no—
241C4⋊C4—62no—
242C4⋊C4—182no—
243C22⋊C4—62no—
244C42—62no—
245C22×C3—22no—
246C22×C3—22no—
247C22×C3—21no—
248C22×C3—21no—
249C22×C3—21no—
250C22×C3—21no—
251C22×C3—21no—
252C22×C3—21no—
253C22×C3—21no—
254C22×C3#88211yescharacteristic
255C22×C3C2×Dic1211yescharacteristic
256C22×C3#90911yescharacteristic
257C22×C3#94211yescharacteristic
258C22×C3C2×#21611yescharacteristic
259C22×C3#95311yescharacteristic
260C3×C4—22no—
261C3×C4—22no—
262C3×C4—22no—
263C3×C4—22no—
264C3×C4—42no—
265C3×C4—42no—
266C3×C4—41no—
267C3×C4—41no—
268C3×C4—81no—
269C3×C4—122no—
270C3×C4—122no—
271Dic3—42no—
272Dic3—42no—
273Dic3—242no—
274Dic3—241no—
275Dic3—241no—
276Dic3—242no—
277Dic3—241no—
278Dic3—241no—
279C32#161711yescharacteristic, complemented, Sylow
280C23C2×#62611yescharacteristic
281Q8—122no—
282Q8—241no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—62no—
289C2×C4—62no—
290C2×C4—361no—
291C2×C4—361no—
292C2×C4—362no—
293C2×C4—361no—
294C2×C4—361no—
295C2×C4#371912yes—
296C2×C4D3×#6712yes—
297C8—122no—
298C2×C3—22no—
299C2×C3—22no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3#473911yescharacteristic
308C2×C3#474211yescharacteristic
309C2×C3#475311yescharacteristic
310C2×C3#522811yescharacteristic
311C2×C3#524311yescharacteristic
312C2×C3#524511yescharacteristic
313C22—21no—
314C22—21no—
315C22#6383311yescharacteristic
316C22C2×#371911yescharacteristic
317C22#6397711yescharacteristic
318C4—22no—
319C4—22no—
320C4—41no—
321C4—122no—
322C4—122no—
323C4—721no—
324C4—721no—
325C3—21no—
326C3#6814111yescharacteristic, complemented
327C3#7189911yescharacteristic, complemented
328C2—21no—
329C2—21no—
330C2#1059118611yescharacteristic
331C2#1059153411yescharacteristic
332C2#1059164611yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#1617
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
279. C32#1617semidirect
326. C3#68141semidirect
327. C3#71899semidirect

Maximal subgroups

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

subgroupindex
C3×#55002
#105926852
#105911032
C3×#45282
#105891522
#718993
#681413