Finite Group Databasebeta

← #11775910

Subgroups — #11775910

Order 1152.

535 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595941C211yesmaximal, characteristic
2C3×#4926C211yesmaximal, characteristic
3C2×C3×#803C211yesmaximal, characteristic
4#10589089C214yesmaximal, complemented
5#70813—31nomaximal
6#69801—31nomaximal
7C2×C32×C42C2211yescharacteristic
8#64135C412yes—
9#64133—21no—
10#64133—21no—
11#64079C2212yes—
12#64078C411yescharacteristic
13#64078C411yescharacteristic
14C4×#634—21no—
15C4×#634—21no—
16C22×C3×C3⋊C8—21no—
17C3×#830—21no—
18C3×C4⋊(C3⋊C8)—21no—
19C3×#803—21no—
20C3×#803C2212yes—
21C3×#803C2212yes—
22#5470—31no—
23#5470—31no—
24#5470—61no—
25C3×#432—31no—
26C2×C3×#97—31no—
27#4926D311yescharacteristic
28C2×#803D311yescharacteristic
29#4465—34no—
30#4465—34no—
31C22×C32×C4C2×C411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C2×#634—21no—
35C2×#634—21no—
36C32×C42C2×C411yescharacteristic
37C32×C42D411yescharacteristic
38C32×C42D411yescharacteristic
39C32×C42C2311yescharacteristic
40#3757—22no—
41C4⋊(C3⋊Dic3)—21no—
42C4⋊(C3⋊Dic3)—21no—
43C4⋊(C3⋊Dic3)C2×C412yes—
44C4⋊(C3⋊Dic3)C2×C412yes—
45#3750—22no—
46#3750—22no—
47C4×C3⋊Dic3—22no—
48C2×C3×C3⋊C8—24no—
49C2×C3×C3⋊C8—22no—
50C2×C3×C3⋊C8—22no—
51#1531—91noSylow
52C22×C3×C8—61no—
53C2×C3×C42—21no—
54C2×C3×C42C2×D311yescharacteristic
55C2×C3×C42C2×D311yescharacteristic
56#926—32no—
57#926—32no—
58#926—62no—
59#924—62no—
60#924—62no—
61#924—61no—
62#924—61no—
63#924—61no—
64#924—61no—
65C22×C3⋊C8—21no—
66#870—32no—
67#870—32no—
68#870—62no—
69#869—31no—
70#869—31no—
71#869—31no—
72#869—31no—
73#869—61no—
74#869—61no—
75C4×Dic6—62no—
76C4×Dic6—62no—
77C4×Dic6—61no—
78C4×Dic6—61no—
79C4×Dic6—61no—
80C4×Dic6—61no—
81C3×C4⋊C8—61no—
82C3×C22⋊C8—61no—
83C3×#97—32no—
84C3×#97—32no—
85C3×#97—61no—
86#830—21no—
87C4⋊(C3⋊C8)—21no—
88#803—21no—
89#803C2×D312yes—
90#803C2×D312yes—
91C23×C32C22⋊C411yescharacteristic
92C2×C32×C4—22no—
93C2×C32×C4—22no—
94C2×C32×C4—41no—
95C2×C32×C4C22⋊C411yescharacteristic
96C2×C32×C4C22⋊C411yescharacteristic
97C2×C32×C4C22⋊C411yescharacteristic
98C2×C32×C4C22×C411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—22no—
103#634—42no—
104#634—42no—
105C3×C3⋊C8—24no—
106C3×C3⋊C8—42no—
107#533—91no—
108#432—31no—
109C2×#97—31no—
110#330—94no—
111C22×C3×C4—21no—
112C22×C3×C4—21no—
113C22×C3×C4—21no—
114C22×C3×C4C4×D311yescharacteristic
115C22×C3×C4C4×D311yescharacteristic
116C22×C3×C4D1211yescharacteristic
117C22×C3×C4D1211yescharacteristic
118C22×C3×C4#6711yescharacteristic
119C22×C3×C4#6711yescharacteristic
120C2×Dic6—62no—
121C2×Dic6—62no—
122C2×Dic6—61no—
123C2×Dic6—61no—
124C2×Dic6—61no—
125C2×Dic6—61no—
126C2×C3×C8—64no—
127C2×C3×C8—62no—
128C2×C3×C8—62no—
129C3×C42—21no—
130C3×C42—21no—
131C3×C42—21no—
132C3×C42—21no—
133C3×C42C4×D311yescharacteristic
134C3×C42C4×D311yescharacteristic
135C3×C42D1211yescharacteristic
136C3×C42D1211yescharacteristic
137C3×C42#6711yescharacteristic
138C3×C42#6711yescharacteristic
139C3×C42C22×D311yescharacteristic
140C3×C42C22×D311yescharacteristic
141#217—64no—
142#217—62no—
143#217—62no—
144C4⋊Dic3—32no—
145C4⋊Dic3—32no—
146C4⋊Dic3—32no—
147C4⋊Dic3—32no—
148C4⋊Dic3—62no—
149C4⋊Dic3—62no—
150C4⋊Dic3—62no—
151C4⋊Dic3—62no—
152C4⋊Dic3—61no—
153C4⋊Dic3—61no—
154C4⋊Dic3—61no—
155C4⋊Dic3—61no—
156Dic3⋊C4—64no—
157Dic3⋊C4—64no—
158Dic3⋊C4—62no—
159Dic3⋊C4—62no—
160Dic3⋊C4—62no—
161Dic3⋊C4—62no—
162C4×Dic3—64no—
163C4×Dic3—62no—
164C4×Dic3—62no—
165C2×C3⋊C8—24no—
166C2×C3⋊C8—22no—
167C2×C3⋊C8—22no—
168C22×C32—21no—
169C22×C32—21no—
170C22×C32#10112yes—
171C22×C32C2×C22⋊C411yescharacteristic
172C32×C4—21no—
173C32×C4—21no—
174C32×C4—21no—
175C32×C4—21no—
176C32×C4—21no—
177C32×C4#10412yes—
178C3⋊Dic3—42no—
179C3⋊Dic3—42no—
180C22×C8—61no—
181C4⋊Q8—91no—
182C4⋊Q8—91no—
183#125—92no—
184C22⋊Q8—181no—
185C22⋊Q8—181no—
186C4×Q8—181no—
187C4×Q8—181no—
188#117—92no—
189C2×C42D3211yescharacteristic
190C4⋊C8—61no—
191C22⋊C8—61no—
192#97—32no—
193#97—32no—
194#97—61no—
195C23×C3—21no—
196C23×C3(C2×D3)⋊C411yescharacteristic
197C23×C3(C2×D3)⋊C411yescharacteristic
198C2×C3×C4—24no—
199C2×C3×C4—22no—
200C2×C3×C4—22no—
201C2×C3×C4—22no—
202C2×C3×C4—22no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—42no—
210C2×C3×C4—41no—
211C2×C3×C4—41no—
212C2×C3×C4—42no—
213C2×C3×C4(C2×D3)⋊C411yescharacteristic
214C2×C3×C4(C2×D3)⋊C411yescharacteristic
215C2×C3×C4(C2×D3)⋊C411yescharacteristic
216C2×C3×C4(C2×D3)⋊C411yescharacteristic
217C2×C3×C4(C2×D3)⋊C411yescharacteristic
218C2×C3×C4(C2×D3)⋊C411yescharacteristic
219C2×C3×C4C2×C4×D311yescharacteristic
220C2×C3×C4C2×C4×D311yescharacteristic
221C2×C3×C4C2×D1211yescharacteristic
222C2×C3×C4C2×D1211yescharacteristic
223C2×C3×C4C2×#6711yescharacteristic
224C2×C3×C4C2×#6711yescharacteristic
225C2×Dic3—64no—
226C2×Dic3—64no—
227C2×Dic3—62no—
228C2×Dic3—62no—
229C2×Dic3—62no—
230C2×Dic3—62no—
231Dic6—124no—
232Dic6—122no—
233Dic6—122no—
234Dic6—124no—
235Dic6—122no—
236Dic6—122no—
237C3×C8—64no—
238C3×C8—122no—
239C3⋊C8—24no—
240C3⋊C8—42no—
241C2×C32—22no—
242C2×C32C2×#10111yescharacteristic
243C2×C32C2×#10411yescharacteristic
244C2×C32#42111yescharacteristic
245C2×Q8—181no—
246C2×Q8—181no—
247C22×C4#62411yescharacteristic
248C22×C4#62611yescharacteristic
249C22×C4#62611yescharacteristic
250C2×C8—64no—
251C2×C8—62no—
252C2×C8—62no—
253C4⋊C4—92no—
254C4⋊C4—92no—
255C4⋊C4—181no—
256C4⋊C4—181no—
257C4⋊C4—182no—
258C4⋊C4—182no—
259C22⋊C4—182no—
260C42—182no—
261C42#62411yescharacteristic
262C42#62611yescharacteristic
263C42#62611yescharacteristic
264C42C2×D3211yescharacteristic
265C22×C3—21no—
266C22×C3—21no—
267C22×C3—21no—
268C22×C3—21no—
269C22×C3—22no—
270C22×C3—21no—
271C22×C3—41no—
272C22×C3—41no—
273C22×C3#82412yes—
274C22×C3#82412yes—
275C22×C3C2×(C2×D3)⋊C411yescharacteristic
276C22×C3C2×(C2×D3)⋊C411yescharacteristic
277C3×C4—22no—
278C3×C4—22no—
279C3×C4—22no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—22no—
291C3×C4—41no—
292C3×C4—41no—
293C3×C4#80512yes—
294C3×C4#82512yes—
295Dic3—124no—
296Dic3—124no—
297Dic3—122no—
298Dic3—122no—
299Dic3—122no—
300Dic3—122no—
301C32#153111yescharacteristic, complemented, Sylow
302C23#372211yescharacteristic
303Q8—362no—
304Q8—362no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—41no—
308C2×C4—182no—
309C2×C4—182no—
310C2×C4#372211yescharacteristic
311C2×C4#372211yescharacteristic
312C2×C4#372211yescharacteristic
313C2×C4C2×#62411yescharacteristic
314C2×C4C2×#62611yescharacteristic
315C2×C4C2×#62611yescharacteristic
316C8—64no—
317C8—122no—
318C2×C3—22no—
319C2×C3—22no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—42no—
324C2×C3C2×#80511yescharacteristic
325C2×C3#500511yescharacteristic
326C2×C3C2×#82411yescharacteristic
327C2×C3C2×#82411yescharacteristic
328C2×C3C2×#82511yescharacteristic
329C2×C3#513911yescharacteristic
330C22—21no—
331C22—21no—
332C22#6356112yes—
333C22C2×#372211yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—362no—
340C4—362no—
341C4#6357012yes—
342C3—21no—
343C3#6980111yescharacteristic, complemented
344C3#7081311yescharacteristic, complemented
345C2—22no—
346C2C2×#6356111yescharacteristic
347C2C2×#6357011yescharacteristic
348C2#1059111311yescharacteristic
subgroupG/H
centerC22C2×#3722
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22⋊C4
cosocleC32×C42C23
hypercenterC2×C42D32
hypocenterC32#1531
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. #10589089C2semidirect
301. C32#1531semidirect
343. C3#69801semidirect
344. C3#70813semidirect

Maximal subgroups

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

subgroupindex
#105959412
C3×#49262
C2×C3×#8032
#105890892
#708133
#698013