Finite Group Databasebeta

← #11778370

Subgroups — #11778370

Order 1152.

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

normal subgroups only

This group has 515 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
2C3×#4979C211yesmaximal, characteristic
3#10591185C212yesmaximal
4#10589394C211yesmaximal, characteristic
5#10589153C212yesmaximal
6#71904—31nomaximal
7#69707—31nomaximal
8C22×C3×Dic6C2211yescharacteristic
9C2×C32×C4⋊C4C2211yescharacteristic
10C3×#926—21no—
11C3×#924—21no—
12C3×#924C2212yes—
13C2×C3×Dic3⋊C4—21no—
14C3×#890—22no—
15C3×#888—22no—
16C2×#3718—22no—
17#63657C2212yes—
18C3×C3⋊#95—21no—
19C3×C3⋊#95C2211yescharacteristic
20#63565—22no—
21C3×#544—31no—
22#5500D311yescharacteristic
23C3×#395—31no—
24#5228—32no—
25#5050—32no—
26#4979D311yescharacteristic
27#4538—32no—
28#4528—31no—
29#4528—31no—
30#4528—61no—
31#4452—32no—
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C22×C3×Dic3—21no—
36C22×C3×Dic3—21no—
37C2×C3×Dic6—22no—
38C2×C3×Dic6—21no—
39C2×C3×Dic6—42no—
40C2×C3×Dic6D412yes—
41C32×C4⋊C4—22no—
42C2×C3⋊(C3⋊C8)—22no—
43C3×#217—22no—
44C3×C4⋊Dic3—21no—
45C3×C4⋊Dic3—21no—
46C3×C4⋊Dic3—21no—
47C3×C4⋊Dic3D412yes—
48C3×Dic3⋊C4—22no—
49C3×Dic3⋊C4—22no—
50C3×Dic3⋊C4—42no—
51C3×C4×Dic3—22no—
52#3718—44no—
53#1605—91noSylow
54C22×C3×Q8—31no—
55C22×Dic6C2×D311yescharacteristic
56C3×C4⋊Q8—62no—
57C3×#125—62no—
58C3×C22⋊Q8—32no—
59C3×C22⋊Q8—61no—
60C3×#117—61no—
61C2×C3×C4⋊C4—21no—
62C2×C3×C4⋊C4—61no—
63C2×C3×C4⋊C4C2×D311yescharacteristic
64C2×C3×C4⋊C4C2×D311yescharacteristic
65C2×#216—62no—
66C2×#216—62no—
67#926—21no—
68#924—21no—
69#924C2×D312yes—
70C2×Dic3⋊C4—21no—
71#890—22no—
72#888—22no—
73C3×#95—31no—
74C3×#95—61no—
75#835—62no—
76C3⋊#95—21no—
77C3⋊#95C2×D311yescharacteristic
78#830—32no—
79#830—32no—
80#830—62no—
81#810—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×C4Q1612yescomplemented
89C2×C32×C4C2×D412yes—
90C2×C3×Dic3—22no—
91C2×C3×Dic3—22no—
92C2×C3×Dic3—22no—
93C2×C3×Dic3—22no—
94C2×C3×Dic3—41no—
95C2×C3×Dic3—41no—
96C2×C3×Dic3—41no—
97C2×C3×Dic3—41no—
98C3×Dic6—24no—
99C3×Dic6—42no—
100C3×Dic6—42no—
101C3×Dic6—81no—
102C3⋊(C3⋊C8)—42no—
103#544—31no—
104#451—92no—
105#395—31no—
106#328—92no—
107#324—91no—
108C2×C3×Q8—32no—
109C2×C3×Q8—61no—
110C2×C3×Q8—62no—
111C2×C3×Q8—122no—
112C22×C3×C4—21no—
113C22×C3×C4—21no—
114C22×C3×C4—21no—
115C22×C3×C4—61no—
116C22×C3×C4—61no—
117C22×C3×C4#6711yescharacteristic
118C22×C3×C4#6711yescharacteristic
119C22×C3×C4#6711yescharacteristic
120C22×C3×C4#6711yescharacteristic
121C22×C3×C4C22×D311yescharacteristic
122C22×C3×C4C22×D311yescharacteristic
123C22×Dic3—21no—
124C22×Dic3—21no—
125C2×Dic6—22no—
126C2×Dic6—21no—
127C2×Dic6—42no—
128C2×Dic6#6712yes—
129C3×C4⋊C4—22no—
130C3×C4⋊C4—22no—
131C3×C4⋊C4—32no—
132C3×C4⋊C4—42no—
133C3×C4⋊C4—62no—
134C3×C4⋊C4—61no—
135C3×C4⋊C4—61no—
136C3×C4⋊C4—61no—
137C3×C4⋊C4—62no—
138C3×C4⋊C4—122no—
139C3×C22⋊C4—62no—
140C3×C42—62no—
141#217—22no—
142#216—124no—
143#216—124no—
144C4⋊Dic3—21no—
145C4⋊Dic3—21no—
146C4⋊Dic3—21no—
147C4⋊Dic3#6712yes—
148Dic3⋊C4—22no—
149Dic3⋊C4—22no—
150Dic3⋊C4—42no—
151C4×Dic3—22no—
152C2×C3⋊C8—62no—
153C2×C3⋊C8—62no—
154C2×C3⋊C8—122no—
155C22×C32—21no—
156C22×C32—21no—
157C22×C32#12011yescharacteristic
158C22×C32C2×Q1611yescharacteristic
159C22×C32#13711yescharacteristic
160C32×C4—22no—
161C32×C4—22no—
162C32×C4—41no—
163C3×Dic3—42no—
164C3×Dic3—42no—
165C3×Dic3—42no—
166C3×Dic3—42no—
167C22×Q8—31no—
168C2×Q16—182no—
169C4⋊Q8—62no—
170#125—62no—
171C22⋊Q8—32no—
172C22⋊Q8—61no—
173#117—61no—
174C2×C4⋊C4—61no—
175C2×C4⋊C4D3211yescharacteristic
176#103—182no—
177C22⋊C8—92no—
178#95—31no—
179#95—61no—
180C23×C3—21no—
181C23×C3C2×#6711yescharacteristic
182C23×C3C2×#6711yescharacteristic
183C3×Q8—64no—
184C3×Q8—122no—
185C3×Q8—122no—
186C3×Q8—241no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—22no—
194C2×C3×C4—22no—
195C2×C3×C4—41no—
196C2×C3×C4—41no—
197C2×C3×C4—41no—
198C2×C3×C4—41no—
199C2×C3×C4—41no—
200C2×C3×C4—41no—
201C2×C3×C4—41no—
202C2×C3×C4—62no—
203C2×C3×C4—62no—
204C2×C3×C4—62no—
205C2×C3×C4—62no—
206C2×C3×C4—81no—
207C2×C3×C4—81no—
208C2×C3×C4—121no—
209C2×C3×C4—121no—
210C2×C3×C4—121no—
211C2×C3×C4—121no—
212C2×C3×C4#21612yescomplemented
213C2×C3×C4#21612yescomplemented
214C2×C3×C4D3×D412yes—
215C2×C3×C4C2×#6712yes—
216C2×Dic3—22no—
217C2×Dic3—22no—
218C2×Dic3—22no—
219C2×Dic3—22no—
220C2×Dic3—41no—
221C2×Dic3—41no—
222C2×Dic3—41no—
223C2×Dic3—41no—
224Dic6—24no—
225Dic6—42no—
226Dic6—42no—
227Dic6—81no—
228C3⋊C8—122no—
229C3⋊C8—122no—
230C3⋊C8—242no—
231C2×C32—21no—
232C2×C32—21no—
233C2×C32#45111yescharacteristic
234C2×C32#45611yescharacteristic
235C2×C32B(4,𝔽2)11yescharacteristic
236C2×Q8—32no—
237C2×Q8—61no—
238C2×Q8—62no—
239C2×Q8—122no—
240C22×C4—61no—
241C22×C4—61no—
242C22×C4#62511yescharacteristic
243C22×C4#62511yescharacteristic
244C22×C4C2×D3211yescharacteristic
245Q16—364no—
246C2×C8—182no—
247C4⋊C4—22no—
248C4⋊C4—32no—
249C4⋊C4—61no—
250C4⋊C4—61no—
251C4⋊C4—61no—
252C4⋊C4—62no—
253C4⋊C4—62no—
254C4⋊C4—122no—
255C22⋊C4—62no—
256C42—62no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3#93711yescharacteristic
267C22×C3#94211yescharacteristic
268C22×C3C2×#21611yescharacteristic
269C22×C3C2×#21611yescharacteristic
270C22×C3#95111yescharacteristic
271C22×C3#95311yescharacteristic
272C3×C4—22no—
273C3×C4—22no—
274C3×C4—22no—
275C3×C4—22no—
276C3×C4—42no—
277C3×C4—42no—
278C3×C4—41no—
279C3×C4—41no—
280C3×C4—81no—
281C3×C4—122no—
282C3×C4—122no—
283C3×C4—122no—
284C3×C4—122no—
285Dic3—42no—
286Dic3—42no—
287Dic3—42no—
288Dic3—42no—
289C32#160511yescharacteristic, complemented, Sylow
290C23C2×#62511yescharacteristic
291Q8—64no—
292Q8—122no—
293Q8—122no—
294Q8—241no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—62no—
301C2×C4—62no—
302C2×C4—62no—
303C2×C4—62no—
304C2×C4—121no—
305C2×C4—121no—
306C2×C4—121no—
307C2×C4—121no—
308C2×C4#371812yescomplemented
309C2×C4D3×#6712yes—
310C8—362no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—41no—
319C2×C3—41no—
320C2×C3#503211yescharacteristic
321C2×C3#505011yescharacteristic
322C2×C3#509511yescharacteristic
323C2×C3#522811yescharacteristic
324C2×C3#524411yescharacteristic
325C2×C3#524611yescharacteristic
326C22—21no—
327C22—21no—
328C22#6382711yescharacteristic
329C22C2×#371811yescharacteristic
330C22#6397611yescharacteristic
331C4—22no—
332C4—22no—
333C4—41no—
334C4—122no—
335C4—122no—
336C4—122no—
337C4—122no—
338C3—21no—
339C3#6970711yescharacteristic, complemented
340C3#7190411yescharacteristic, complemented
341C2—21no—
342C2—21no—
343C2#1059118511yescharacteristic
344C2#1059153011yescharacteristic
345C2#1059164811yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#1605
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
88. C2×C32×C4Q16semidirect
212. C2×C3×C4#216semidirect
213. C2×C3×C4#216semidirect
289. C32#1605semidirect
308. C2×C4#3718semidirect
339. C3#69707semidirect
340. C3#71904semidirect

Maximal subgroups

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

subgroupindex
C3×#55002
C3×#49792
#105911852
#105893942
#105891532
#719043
#697073