Finite Group Databasebeta

← #11777935

Subgroups — #11777935

Order 1152.

351 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 351 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C4×#3756C211yesmaximal, characteristic
2C3×#5024C211yesmaximal, characteristic
3#10590296C211yesmaximal, characteristic
4C3×#4535C211yesmaximal, characteristic
5#10589098C211yesmaximal, characteristic
6#10589085C211yesmaximal, characteristic
7#10589079C211yesmaximal, characteristic
8#70952—31nomaximal
9#68227—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11C2×#3756C411yescharacteristic
12C4×#634C2211yescharacteristic
13#63662C411yescharacteristic
14#63637C411yescharacteristic
15#63634C411yescharacteristic
16C4×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×C4⋊(C3⋊C8)—21no—
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×#803—21no—
21C3×C4×C3⋊C8C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23#63572—21no—
24#63555—21no—
25C3×#446—31no—
26C4×#216—31no—
27C4×#216—31no—
28C4×#216—61no—
29#5024D311yescharacteristic
30#4831—31no—
31#4679—31no—
32C3×Q8⋊C8—31no—
33#4535D311yescharacteristic
34#4484—31no—
35#4480—31no—
36#4480—31no—
37#4456—31no—
38#4454—31no—
39#4454—31no—
40C2×C32×Q8C2×C411yescharacteristic
41C2×#634C2×C411yescharacteristic
42C32×C4⋊C4—21no—
43C32×C4⋊C4C2×C411yescharacteristic
44C32×C42—21no—
45C32×C42C2311yescharacteristic
46#3756—22no—
47C4⋊(C3⋊Dic3)C2×C411yescharacteristic
48#3750—21no—
49C4×C3⋊Dic3—21no—
50C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
51C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#1593—91noSylow
58C3×C4×Q8—21no—
59C3×C4×Q8C2×D311yescharacteristic
60C3×C4×Q8C2×D311yescharacteristic
61C2×#216—31no—
62C2×#216—31no—
63C2×#216—61no—
64C4×Dic6—31no—
65C4×Dic6—31no—
66C4×Dic6—61no—
67C3×C4⋊C8—31no—
68C3×C4⋊C8—31no—
69C3×C4⋊C8—61no—
70C3×#97—61no—
71C3×C4×C8—31no—
72C3×C4×C8—31no—
73#835—31no—
74#835—31no—
75#835—61no—
76#815—61no—
77#815—61no—
78Dic3⋊C8—61no—
79Dic3⋊C8—61no—
80#810—31no—
81#810—31no—
82#810—61no—
83#807—31no—
84#807—31no—
85#807—61no—
86C4⋊(C3⋊C8)—21no—
87C4⋊(C3⋊C8)C2×D311yescharacteristic
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89#803—21no—
90C4×C3⋊C8—31no—
91C4×C3⋊C8—31no—
92C4×C3⋊C8—61no—
93C4×C3⋊C8C2×D311yescharacteristic
94C4×C3⋊C8C2×D311yescharacteristic
95C32×Q8—21no—
96C32×Q8—21no—
97C2×C32×C4—21no—
98C2×C32×C4—21no—
99C2×C32×C4C22×C411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C3⋊Dic3—21no—
103C2×C3⋊Dic3—21no—
104#634—21no—
105#634—21no—
106C3⋊(C3⋊C8)—21no—
107C3⋊(C3⋊C8)M1612yes—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112C3×C3⋊C8—41no—
113#446—31no—
114#446—91no—
115C4×Q16—91no—
116#334—91no—
117Q8⋊C8—31no—
118Q8⋊C8—91no—
119#322—91no—
120C2×C3×Q8—21no—
121C2×C3×Q8C4×D311yescharacteristic
122C2×C3×Q8C4×D311yescharacteristic
123C2×Dic6—31no—
124C2×Dic6—31no—
125C2×Dic6—61no—
126C2×C3×C8—31no—
127C2×C3×C8—31no—
128C2×C3×C8—61no—
129C2×C3×C8—61no—
130C2×C3×C8—61no—
131C3×C4⋊C4—21no—
132C3×C4⋊C4—21no—
133C3×C4⋊C4—21no—
134C3×C4⋊C4—41no—
135C3×C4⋊C4C4×D311yescharacteristic
136C3×C4⋊C4C4×D311yescharacteristic
137C3×C42—21no—
138C3×C42—21no—
139C3×C42—21no—
140C3×C42—41no—
141C3×C42C22×D311yescharacteristic
142C3×C42C22×D311yescharacteristic
143#216—62no—
144#216—62no—
145#216—64no—
146C4⋊Dic3—31no—
147C4⋊Dic3—31no—
148C4⋊Dic3—61no—
149Dic3⋊C4—61no—
150Dic3⋊C4—61no—
151Dic3⋊C4—121no—
152C4×Dic3—61no—
153C4×Dic3—61no—
154C4×Dic3—121no—
155C2×C3⋊C8—21no—
156C2×C3⋊C8—21no—
157C2×C3⋊C8—21no—
158C2×C3⋊C8—31no—
159C2×C3⋊C8—31no—
160C2×C3⋊C8—31no—
161C2×C3⋊C8—31no—
162C2×C3⋊C8—61no—
163C2×C3⋊C8—61no—
164C2×C3⋊C8#6711yescharacteristic
165C2×C3⋊C8#6711yescharacteristic
166C22×C32C4×D411yescharacteristic
167C32×C4—21no—
168C32×C4—41no—
169C32×C4—41no—
170C32×C4C2×M1611yescharacteristic
171C32×C4#13111yescharacteristic
172C32×C4#13711yescharacteristic
173C32×C4#13711yescharacteristic
174C3⋊Dic3—41no—
175C3⋊Dic3—41no—
176C2×Q16—91no—
177C4×Q8—91no—
178C4×Q8D3211yescharacteristic
179#107—91no—
180C4⋊C8—31no—
181C4⋊C8—31no—
182C4⋊C8—61no—
183C4⋊C8—181no—
184#103—91no—
185#103—91no—
186#97—61no—
187#97—181no—
188C4×C8—31no—
189C4×C8—31no—
190C4×C8—91no—
191C3×Q8—22no—
192C3×Q8—21no—
193C3×Q8—21no—
194C3×Q8—21no—
195C3×Q8—21no—
196C3×Q8—41no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—41no—
205C2×C3×C4—41no—
206C2×C3×C4C2×C4×D311yescharacteristic
207C2×C3×C4C2×C4×D311yescharacteristic
208C2×C3×C4#23511yescharacteristic
209C2×C3×C4D3×D411yescharacteristic
210C2×C3×C4#23711yescharacteristic
211C2×C3×C4C2×#6711yescharacteristic
212C2×Dic3—61no—
213C2×Dic3—61no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216C2×Dic3—121no—
217C2×Dic3—121no—
218Dic6—62no—
219Dic6—61no—
220Dic6—61no—
221Dic6—61no—
222Dic6—61no—
223Dic6—121no—
224C3×C8—61no—
225C3×C8—61no—
226C3×C8—121no—
227C3×C8—121no—
228C3×C8—121no—
229C3⋊C8—21no—
230C3⋊C8—21no—
231C3⋊C8—32no—
232C3⋊C8—32no—
233C3⋊C8—41no—
234C3⋊C8—41no—
235C3⋊C8—41no—
236C3⋊C8—62no—
237C3⋊C8—61no—
238C3⋊C8—61no—
239C3⋊C8—121no—
240C2×C32#43611yescharacteristic
241C2×C32#44111yescharacteristic
242C2×C32#44411yescharacteristic
243C2×Q8—91no—
244C2×Q8#62411yescharacteristic
245Q16—182no—
246C2×C8—31no—
247C2×C8—31no—
248C2×C8—61no—
249C2×C8—61no—
250C2×C8—61no—
251C2×C8—91no—
252C2×C8—91no—
253C4⋊C4—21no—
254C4⋊C4—91no—
255C4⋊C4—181no—
256C4⋊C4#62411yescharacteristic
257C42—21no—
258C42—181no—
259C42C2×D3211yescharacteristic
260C22×C3—21no—
261C22×C3#67⋊C411yescharacteristic
262C22×C3C4×#6711yescharacteristic
263C3×C4—21no—
264C3×C4—21no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—21no—
268C3×C4—21no—
269C3×C4—41no—
270C3×C4—42no—
271C3×C4—41no—
272C3×C4—41no—
273C3×C4—41no—
274C3×C4—41no—
275C3×C4—81no—
276C3×C4#90111yescharacteristic
277C3×C4D3×M1611yescharacteristic
278C3×C4D3×M1611yescharacteristic
279C3×C4#90711yescharacteristic
280C3×C4#91511yescharacteristic
281C3×C4#91811yescharacteristic
282C3×C4#94211yescharacteristic
283C3×C4#95111yescharacteristic
284Dic3—122no—
285Dic3—121no—
286Dic3—121no—
287Dic3—121no—
288Dic3—121no—
289Dic3—241no—
290C32#159311yescharacteristic, complemented, Sylow
291Q8—21no—
292Q8—21no—
293Q8—181no—
294Q8—181no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—181no—
298C2×C4—181no—
299C2×C4#380411yescharacteristic
300C2×C4C2×#62411yescharacteristic
301C2×C4D3×#6711yescharacteristic
302C8—61no—
303C8—61no—
304C8—92no—
305C8—121no—
306C8—121no—
307C8—121no—
308C8—181no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3#472911yescharacteristic
313C2×C3#478911yescharacteristic
314C2×C3#482311yescharacteristic
315C2×C3#503011yescharacteristic
316C2×C3#512811yescharacteristic
317C2×C3#514511yescharacteristic
318C22#6395211yescharacteristic
319C4—21no—
320C4—41no—
321C4—41no—
322C4—361no—
323C4—361no—
324C4#6381711yescharacteristic
325C4#6381811yescharacteristic
326C4#6394311yescharacteristic
327C4#6394611yescharacteristic
328C3—21no—
329C3#6822711yescharacteristic, complemented
330C3#7095211yescharacteristic, complemented
331C2#1059105111yescharacteristic
332C2#1059154111yescharacteristic
333C2#1059166311yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socle, prime radicalC22×C32C4×D4
cosocleC32×C42C23
hypercenterC4×Q8D32
hypocenterC32#1593
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
290. C32#1593semidirect
329. C3#68227semidirect
330. C3#70952semidirect

Maximal subgroups

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

subgroupindex
C4×#37562
C3×#50242
#105902962
C3×#45352
#105890982
#105890852
#105890792
#709523
#682273