Finite Group Databasebeta

← #11778593

Subgroups — #11778593

Order 1152.

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

normal subgroups only

This group has 495 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#10592680C211yesmaximal, characteristic
3#10591126C212yesmaximal
4C3×#4528C211yesmaximal, characteristic
5#10589152C212yesmaximal
6#71898—31nomaximal
7#68140—31nomaximal
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
10C2×#3750—21no—
11C3×#926—21no—
12C3×#924—21no—
13C3×#924C2212yes—
14C3×#890—22no—
15C3×#888—22no—
16#63658—21no—
17#63658C2211yescharacteristic
18C3×#830C2212yes—
19#63573—22no—
20#63566—22no—
21C3×#544—31no—
22#5500D311yescharacteristic
23#5043—32no—
24#4981—31no—
25#4981—31no—
26#4981—61no—
27#4721—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—
41#3750—42no—
42C3×#217—22no—
43C3×C4⋊Dic3—21no—
44C3×C4⋊Dic3—21no—
45C3×C4⋊Dic3—21no—
46C3×C4⋊Dic3D412yes—
47C3×Dic3⋊C4—22no—
48C3×Dic3⋊C4—22no—
49C3×C4×Dic3—22no—
50C2×C3×C3⋊C8—22no—
51#1611—91noSylow
52C3×C4⋊Q8—62no—
53C3×#125—62no—
54C3×C22⋊Q8—32no—
55C3×C22⋊Q8—61no—
56C3×#117—61no—
57C2×C3×C4⋊C4—21no—
58C2×C3×C4⋊C4C2×D311yescharacteristic
59C2×C3×C4⋊C4C2×D311yescharacteristic
60#926—21no—
61C2×C4⋊Dic3—31no—
62C2×C4⋊Dic3—31no—
63C2×C4⋊Dic3—61no—
64#924—21no—
65#924C2×D312yes—
66C2×Dic3⋊C4—62no—
67C2×Dic3⋊C4—61no—
68C2×Dic3⋊C4—61no—
69#890—22no—
70#888—22no—
71C3×C22⋊C8—32no—
72#835—62no—
73C3⋊#95—31no—
74C3⋊#95—31no—
75C3⋊#95—61no—
76C3⋊#95—62no—
77C3⋊#95—61no—
78C3⋊#95—61no—
79#830C2×D312yes—
80#817—62no—
81#816—62no—
82#808—62no—
83C23×C32C2×D411yescharacteristic
84C2×C32×C4—21no—
85C2×C32×C4—21no—
86C2×C32×C4—21no—
87C2×C32×C4—41no—
88C2×C32×C4—41no—
89C2×C32×C4SD1612yes—
90C2×C32×C4C2×D412yes—
91C2×C3⋊Dic3—22no—
92C2×C3⋊Dic3—41no—
93C2×C3⋊Dic3—41no—
94C2×C3⋊Dic3—41no—
95C2×C3⋊Dic3—41no—
96C2×C3⋊Dic3—41no—
97C2×C3×Dic3—22no—
98C2×C3×Dic3—22no—
99C3×Dic6—42no—
100C3×Dic6—81no—
101C3×C3⋊C8—42no—
102#544—31no—
103#483—92no—
104#398—91no—
105#328—92no—
106#324—31no—
107C2×C3×Q8—32no—
108C2×C3×Q8—61no—
109C22×C3×C4—21no—
110C22×C3×C4—21no—
111C22×C3×C4—21no—
112C22×C3×C4D1211yescharacteristic
113C22×C3×C4D1211yescharacteristic
114C22×C3×C4#6711yescharacteristic
115C22×C3×C4#6711yescharacteristic
116C22×C3×C4C22×D311yescharacteristic
117C22×C3×C4C22×D311yescharacteristic
118C22×Dic3—62no—
119C22×Dic3—61no—
120C22×Dic3—61no—
121C22×Dic3—62no—
122C22×Dic3—61no—
123C22×Dic3—61no—
124C2×Dic6—21no—
125C2×Dic6#6712yes—
126C2×C3×C8—62no—
127C3×C4⋊C4—22no—
128C3×C4⋊C4—22no—
129C3×C4⋊C4—32no—
130C3×C4⋊C4—42no—
131C3×C4⋊C4—62no—
132C3×C4⋊C4—61no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—61no—
135C3×C4⋊C4—62no—
136C3×C22⋊C4—62no—
137C3×C42—62no—
138#217—22no—
139C4⋊Dic3—21no—
140C4⋊Dic3—21no—
141C4⋊Dic3—21no—
142C4⋊Dic3—62no—
143C4⋊Dic3—62no—
144C4⋊Dic3—122no—
145C4⋊Dic3#6712yes—
146Dic3⋊C4—22no—
147Dic3⋊C4—22no—
148Dic3⋊C4—124no—
149Dic3⋊C4—122no—
150Dic3⋊C4—122no—
151C4×Dic3—22no—
152C2×C3⋊C8—22no—
153C22×C32—21no—
154C22×C32—21no—
155C22×C32#12011yescharacteristic
156C22×C32C2×SD1611yescharacteristic
157C22×C32#13711yescharacteristic
158C32×C4—22no—
159C32×C4—22no—
160C32×C4—41no—
161C3⋊Dic3—42no—
162C3⋊Dic3—81no—
163C3×Dic3—42no—
164C3×Dic3—42no—
165C4⋊Q8—62no—
166#125—62no—
167C22⋊Q8—32no—
168C22⋊Q8—61no—
169#117—61no—
170C2×C4⋊C4—91no—
171C2×C4⋊C4—181no—
172C2×C4⋊C4D3211yescharacteristic
173#106—182no—
174#103—182no—
175C22⋊C8—32no—
176#95—91no—
177#95—181no—
178C23×C3—21no—
179C23×C3C2×D1211yescharacteristic
180C23×C3C2×#6711yescharacteristic
181C3×Q8—122no—
182C3×Q8—241no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—22no—
190C2×C3×C4—22no—
191C2×C3×C4—41no—
192C2×C3×C4—41no—
193C2×C3×C4—41no—
194C2×C3×C4—41no—
195C2×C3×C4—41no—
196C2×C3×C4—42no—
197C2×C3×C4—41no—
198C2×C3×C4—41no—
199C2×C3×C4—42no—
200C2×C3×C4—62no—
201C2×C3×C4—62no—
202C2×C3×C4#20412yes—
203C2×C3×C4#21512yes—
204C2×C3×C4D3×D412yes—
205C2×C3×C4C2×#6712yes—
206C2×Dic3—22no—
207C2×Dic3—22no—
208C2×Dic3—64no—
209C2×Dic3—62no—
210C2×Dic3—62no—
211C2×Dic3—122no—
212C2×Dic3—122no—
213C2×Dic3—121no—
214C2×Dic3—121no—
215C2×Dic3—121no—
216C2×Dic3—121no—
217C2×Dic3—122no—
218C2×Dic3—122no—
219C2×Dic3—122no—
220C2×Dic3—121no—
221C2×Dic3—121no—
222C2×Dic3—121no—
223C2×Dic3—121no—
224C2×Dic3—121no—
225C2×Dic3—121no—
226Dic6—42no—
227Dic6—81no—
228C3×C8—122no—
229C3⋊C8—42no—
230C2×C32—21no—
231C2×C32—21no—
232C2×C32#44811yescharacteristic
233C2×C32#45611yescharacteristic
234C2×C32#45811yescharacteristic
235C2×Q8—32no—
236C2×Q8—61no—
237C22×C4—181no—
238C22×C4—181no—
239C22×C4#62611yescharacteristic
240C22×C4#62611yescharacteristic
241C22×C4C2×D3211yescharacteristic
242C2×C8—62no—
243C4⋊C4—22no—
244C4⋊C4—32no—
245C4⋊C4—61no—
246C4⋊C4—61no—
247C4⋊C4—61no—
248C4⋊C4—62no—
249C4⋊C4—62no—
250C4⋊C4—182no—
251C4⋊C4—362no—
252C22⋊C4—62no—
253C42—62no—
254C22×C3—22no—
255C22×C3—22no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3#88211yescharacteristic
264C22×C3C2×#20411yescharacteristic
265C22×C3#90911yescharacteristic
266C22×C3C2×#21511yescharacteristic
267C22×C3#94211yescharacteristic
268C22×C3#95311yescharacteristic
269C3×C4—22no—
270C3×C4—22no—
271C3×C4—22no—
272C3×C4—22no—
273C3×C4—42no—
274C3×C4—42no—
275C3×C4—41no—
276C3×C4—41no—
277C3×C4—81no—
278C3×C4—122no—
279C3×C4—122no—
280Dic3—42no—
281Dic3—42no—
282Dic3—124no—
283Dic3—122no—
284Dic3—122no—
285Dic3—242no—
286Dic3—241no—
287Dic3—241no—
288C32#161111yescharacteristic, complemented, Sylow
289C23C2×#62611yescharacteristic
290Q8—122no—
291Q8—241no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—62no—
298C2×C4—62no—
299C2×C4—182no—
300C2×C4—361no—
301C2×C4—361no—
302C2×C4—361no—
303C2×C4—361no—
304C2×C4—361no—
305C2×C4#371712yes—
306C2×C4D3×#6712yes—
307C8—122no—
308C2×C3—22no—
309C2×C3—22no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3#473811yescharacteristic
318C2×C3#474211yescharacteristic
319C2×C3#475211yescharacteristic
320C2×C3#522711yescharacteristic
321C2×C3#524311yescharacteristic
322C2×C3#524611yescharacteristic
323C22—21no—
324C22—21no—
325C22C2×#371711yescharacteristic
326C22#6383311yescharacteristic
327C22#6397711yescharacteristic
328C4—22no—
329C4—22no—
330C4—41no—
331C4—122no—
332C4—122no—
333C4—362no—
334C4—721no—
335C3—21no—
336C3#6814011yescharacteristic, complemented
337C3#7189811yescharacteristic, complemented
338C2—21no—
339C2—21no—
340C2#1059117411yescharacteristic
341C2#1059153411yescharacteristic
342C2#1059164911yescharacteristic
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#1611
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
288. C32#1611semidirect
336. C3#68140semidirect
337. C3#71898semidirect

Maximal subgroups

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

subgroupindex
C3×#55002
#105926802
#105911262
C3×#45282
#105891522
#718983
#681403