Finite Group Databasebeta

← #11779597

Subgroups — #11779597

Order 1152.

408 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 90 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
1#10593860C211yesmaximal, characteristic
2C3×#4850C211yesmaximal, characteristic
3#10590310C211yesmaximal, characteristic
4#10590287C211yesmaximal, characteristic
5#10589352C211yesmaximal, characteristic
6C3×#4484C211yesmaximal, characteristic
7#10589084C211yesmaximal, characteristic
8#71158—31nomaximal
9#68268—31nomaximal
10#64078C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14#63869—21no—
15#63866—21no—
16#63845—22no—
17#63844—21no—
18Dic3×Dic6—21no—
19C32×C4⋊C8C2211yescharacteristic
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C3×#818—21no—
22C3×#816—21no—
23C3×C4×C3⋊C8C2211yescharacteristic
24#63576—21no—
25#63566—22no—
26#63565—21no—
27#5570—31no—
28#5567—31no—
29C3×#477—31no—
30#5091—31no—
31#5079—31no—
32#5021—31no—
33#4850D311yescharacteristic
34#4681—31no—
35C3×Q8⋊C8—31no—
36#4535—31no—
37#4486—31no—
38#4486—31no—
39#4486—61no—
40#4484D311yescharacteristic
41#4456—31no—
42C2×#634—21no—
43C2×C3×Dic6—21no—
44C2×C3×Dic6D411yescharacteristic
45C2×C3×Dic6D411yescharacteristic
46C2×C32×C8—21no—
47C32×C42C2311yescharacteristic
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)D412yes—
50C2×C3⋊(C3⋊C8)—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3D411yescharacteristic
54C3×C4⋊Dic3D411yescharacteristic
55C3×Dic3⋊C4—21no—
56C3×Dic3⋊C4—21no—
57C3×C4×Dic3—21no—
58C3×C4×Dic3—21no—
59C2×C3×C3⋊C8—21no—
60#3724—22no—
61Dic3⋊Dic3—22no—
62Dic3⋊Dic3—22no—
63Dic32—22no—
64#1636—91noSylow
65C3×C4⋊Q8—31no—
66C3×C4×Q8—31no—
67C3×C4×Q8—31no—
68Q8×Dic3—61no—
69#944—61no—
70#890—61no—
71#890—62no—
72#889—62no—
73#887—61no—
74#870—61no—
75#869—31no—
76#869—31no—
77#869—61no—
78#869—61no—
79#869C2×D311yescharacteristic
80C4×Dic6—61no—
81C4×Dic6—61no—
82C4×Dic6C2×D311yescharacteristic
83C4×Dic6C2×D311yescharacteristic
84C3×#107—61no—
85C3×C4⋊C8—21no—
86C3×C4⋊C8C2×D311yescharacteristic
87C3×C4⋊C8C2×D311yescharacteristic
88C3×#103—61no—
89C3×C4×C8—31no—
90#835—62no—
91#835—61no—
92#818—21no—
93#816—21no—
94#816—62no—
95#810—61no—
96#807—61no—
97#807—61no—
98C4⋊(C3⋊C8)—31no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—61no—
101C4×C3⋊C8C2×D311yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C3⋊Dic3—22no—
106#634—41no—
107#634—41no—
108C2×C3×Dic3—21no—
109C2×C3×Dic3—21no—
110C2×C3×Dic3—21no—
111C2×C3×Dic3—21no—
112C2×C3×Dic3—41no—
113C3×Dic6—21no—
114C3×Dic6—21no—
115C3×Dic6—21no—
116C3×Dic6—42no—
117C3×Dic6Q1612yes—
118C32×C8—41no—
119C3⋊(C3⋊C8)—41no—
120C3×C3⋊C8—41no—
121#557—91no—
122#487—91no—
123#477—31no—
124#477—91no—
125#332—91no—
126Q8⋊C8—31no—
127Q8⋊C8—91no—
128C2×C3×Q8—31no—
129C2×C3×Q8—31no—
130C2×C3×Q8—61no—
131C2×Dic6—21no—
132C2×Dic6—61no—
133C2×Dic6—61no—
134C2×Dic6—121no—
135C2×Dic6D1211yescharacteristic
136C2×Dic6#6711yescharacteristic
137C2×C3×C8—21no—
138C2×C3×C8—21no—
139C2×C3×C8—41no—
140C2×C3×C8—61no—
141C3×C4⋊C4—31no—
142C3×C4⋊C4—31no—
143C3×C4⋊C4—61no—
144C3×C4⋊C4—61no—
145C3×C4⋊C4—61no—
146C3×C4⋊C4—61no—
147C3×C42—21no—
148C3×C42—61no—
149C3×C42—61no—
150C3×C42C22×D311yescharacteristic
151C3×C42C22×D311yescharacteristic
152C4⋊Dic3—21no—
153C4⋊Dic3—21no—
154C4⋊Dic3—32no—
155C4⋊Dic3—32no—
156C4⋊Dic3—62no—
157C4⋊Dic3—62no—
158C4⋊Dic3—62no—
159C4⋊Dic3—61no—
160C4⋊Dic3—61no—
161C4⋊Dic3—121no—
162C4⋊Dic3D1211yescharacteristic
163C4⋊Dic3#6711yescharacteristic
164Dic3⋊C4—21no—
165Dic3⋊C4—21no—
166Dic3⋊C4—62no—
167Dic3⋊C4—62no—
168Dic3⋊C4—62no—
169Dic3⋊C4—62no—
170C4×Dic3—21no—
171C4×Dic3—21no—
172C4×Dic3—62no—
173C4×Dic3—62no—
174C2×C3⋊C8—21no—
175C2×C3⋊C8—61no—
176C2×C3⋊C8—61no—
177C2×C3⋊C8—121no—
178C22×C32#12011yescharacteristic
179C32×C4—21no—
180C32×C4C2×Q1611yescharacteristic
181C32×C4#13511yescharacteristic
182C32×C4#13711yescharacteristic
183C32×C4#13711yescharacteristic
184C3⋊Dic3—42no—
185C3×Dic3—22no—
186C3×Dic3—41no—
187C3×Dic3—41no—
188C3×Dic3—41no—
189C3×Dic3—81no—
190C4⋊Q8—31no—
191C4⋊Q8—91no—
192C4⋊Q8—181no—
193#125—181no—
194#125—182no—
195C4×Q8—31no—
196C4×Q8—31no—
197C4×Q8—181no—
198C4×Q8—181no—
199#107—61no—
200#107—181no—
201C4⋊C8—91no—
202C4⋊C8D3211yescharacteristic
203#103—61no—
204#103—181no—
205#103—182no—
206C4×C8—31no—
207C3×Q8—32no—
208C3×Q8—61no—
209C3×Q8—61no—
210C3×Q8—61no—
211C3×Q8—122no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—61no—
216C2×C3×C4—61no—
217C2×C3×C4—61no—
218C2×C3×C4—61no—
219C2×C3×C4—121no—
220C2×C3×C4C2×D1211yescharacteristic
221C2×C3×C4D3×D411yescharacteristic
222C2×C3×C4D3×D411yescharacteristic
223C2×C3×C4D3×D411yescharacteristic
224C2×C3×C4D3×D411yescharacteristic
225C2×C3×C4C2×#6711yescharacteristic
226C2×Dic3—21no—
227C2×Dic3—21no—
228C2×Dic3—21no—
229C2×Dic3—21no—
230C2×Dic3—41no—
231C2×Dic3—62no—
232C2×Dic3—62no—
233C2×Dic3—122no—
234Dic6—21no—
235Dic6—21no—
236Dic6—21no—
237Dic6—42no—
238Dic6—121no—
239Dic6—121no—
240Dic6—121no—
241Dic6—121no—
242Dic6—241no—
243Dic6—241no—
244Dic6#21612yes—
245C3×C8—41no—
246C3×C8—41no—
247C3×C8—81no—
248C3×C8—121no—
249C3⋊C8—41no—
250C3⋊C8—121no—
251C3⋊C8—121no—
252C3⋊C8—241no—
253C2×C32#45111yescharacteristic
254C2×C32#45211yescharacteristic
255C2×C32#45411yescharacteristic
256C2×Q8—31no—
257C2×Q8—31no—
258C2×Q8—61no—
259C2×Q8—181no—
260C2×C8—21no—
261C2×C8—61no—
262C2×C8—181no—
263C4⋊C4—31no—
264C4⋊C4—31no—
265C4⋊C4—61no—
266C4⋊C4—61no—
267C4⋊C4—61no—
268C4⋊C4—61no—
269C4⋊C4—92no—
270C4⋊C4—182no—
271C4⋊C4—182no—
272C4⋊C4—182no—
273C4⋊C4—181no—
274C42—61no—
275C42—61no—
276C42—182no—
277C42C2×D3211yescharacteristic
278C22×C3—21no—
279C22×C3#88211yescharacteristic
280C22×C3#93711yescharacteristic
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—41no—
288C3×C4—62no—
289C3×C4—121no—
290C3×C4—121no—
291C3×C4—121no—
292C3×C4—241no—
293C3×C4#90411yescharacteristic
294C3×C4#90911yescharacteristic
295C3×C4#91511yescharacteristic
296C3×C4D3×Q1611yescharacteristic
297C3×C4#91811yescharacteristic
298C3×C4#91911yescharacteristic
299C3×C4C2×#21611yescharacteristic
300C3×C4#95111yescharacteristic
301Dic3—22no—
302Dic3—41no—
303Dic3—41no—
304Dic3—41no—
305Dic3—81no—
306Dic3—122no—
307Dic3—122no—
308Dic3—242no—
309C32#163611yescharacteristic, complemented, Sylow
310Q8—32no—
311Q8—61no—
312Q8—61no—
313Q8—61no—
314Q8—122no—
315Q8—361no—
316Q8—361no—
317C2×C4—61no—
318C2×C4—61no—
319C2×C4—61no—
320C2×C4—61no—
321C2×C4—121no—
322C2×C4—182no—
323C2×C4D3×D1211yescharacteristic
324C2×C4#380211yescharacteristic
325C2×C4D3×#6711yescharacteristic
326C8—41no—
327C8—121no—
328C8—361no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3#473311yescharacteristic
333C2×C3#480911yescharacteristic
334C2×C3#482711yescharacteristic
335C2×C3#505011yescharacteristic
336C2×C3#518711yescharacteristic
337C2×C3#520111yescharacteristic
338C22#6392211yescharacteristic
339C4—21no—
340C4—62no—
341C4—121no—
342C4—121no—
343C4—121no—
344C4—241no—
345C4—362no—
346C4#6380111yescharacteristic
347C4#6380811yescharacteristic
348C4#6392911yescharacteristic
349C4D3×#21611yescharacteristic
350C3—21no—
351C3#6826811yescharacteristic, complemented
352C3#7115811yescharacteristic, complemented
353C2#1059060411yescharacteristic
354C2#1059096611yescharacteristic
355C2#1059101911yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#120
hypercenterC4⋊C8D32
hypocenterC32#1636
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
309. C32#1636semidirect
351. C3#68268semidirect
352. C3#71158semidirect

Maximal subgroups

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

subgroupindex
#105938602
C3×#48502
#105903102
#105902872
#105893522
C3×#44842
#105890842
#711583
#682683