Finite Group Databasebeta

← #11779599

Subgroups — #11779599

Order 1152.

424 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 88 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#10593864C211yesmaximal, characteristic
2#10592549C211yesmaximal, characteristic
3#10590288C211yesmaximal, characteristic
4#10590283C211yesmaximal, characteristic
5C3×#4486C211yesmaximal, characteristic
6C3×#4484C211yesmaximal, characteristic
7#10589085C211yesmaximal, characteristic
8#68458—31nomaximal
9#68268—31nomaximal
10#64078C2211yescharacteristic
11C4×#634C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14#63873—21no—
15#63869—21no—
16#63847—22no—
17#63844—21no—
18#63843—21no—
19C32×C4⋊C8C2211yescharacteristic
20#63645—21no—
21#63643—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24#63575—21no—
25#63567—22no—
26#63566—21no—
27#5721—31no—
28#5567—31no—
29#5093—31no—
30#5021—31no—
31#4850—31no—
32#4850—31no—
33#4850—31no—
34#4850—61no—
35#4681—31no—
36C3×#332—31no—
37C3×Q8⋊C8—31no—
38#4486D311yescharacteristic
39#4484—31no—
40#4484D311yescharacteristic
41#4456—31no—
42C2×#634—21no—
43C2×#634D411yescharacteristic
44C2×C3×Dic6—21no—
45C2×C3×Dic6D411yescharacteristic
46C2×C32×C8—21no—
47C32×C42C2311yescharacteristic
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)D411yescharacteristic
51#3750—21no—
52C4×C3⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3D412yes—
55C3×C4⋊Dic3D411yescharacteristic
56C3×Dic3⋊C4—21no—
57C3×C4×Dic3—21no—
58C2×C3×C3⋊C8—21no—
59C2×C3×C3⋊C8—21no—
60#3724—22no—
61#3724—22no—
62Dic3⋊Dic3—22no—
63Dic32—22no—
64#1636—91noSylow
65C3×C4⋊Q8—31no—
66C3×C4×Q8—31no—
67Q8×Dic3—61no—
68#944—61no—
69#944—61no—
70#890—61no—
71#889—62no—
72#889—62no—
73#887—61no—
74#887—61no—
75#870—61no—
76#869—31no—
77#869—31no—
78#869—61no—
79#869C2×D311yescharacteristic
80C4×Dic6—31no—
81C4×Dic6—31no—
82C4×Dic6—61no—
83C4×Dic6—61no—
84C4×Dic6C2×D311yescharacteristic
85C3×C4⋊C8—21no—
86C3×C4⋊C8—31no—
87C3×C4⋊C8C2×D311yescharacteristic
88C3×C4⋊C8C2×D311yescharacteristic
89C3×C4×C8—31no—
90#835—61no—
91#818—61no—
92#818—61no—
93#818—62no—
94#818—61no—
95#816—61no—
96#816—61no—
97#816—62no—
98#816—61no—
99#816—62no—
100#810—62no—
101#807—61no—
102C4⋊(C3⋊C8)C2×D311yescharacteristic
103C4×C3⋊C8C2×D311yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C3⋊Dic3—21no—
108C2×C3⋊Dic3—21no—
109C2×C3⋊Dic3—41no—
110#634—21no—
111#634—42no—
112#634Q1612yes—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—21no—
116C3×Dic6—21no—
117C3×Dic6—21no—
118C3×Dic6—41no—
119C3×Dic6—41no—
120C32×C8—41no—
121C3×C3⋊C8—41no—
122C3×C3⋊C8—41no—
123#557—91no—
124#487—91no—
125#477—91no—
126#477—91no—
127#332—31no—
128Q8⋊C8—31no—
129Q8⋊C8—91no—
130C2×C3×Q8—31no—
131C2×C3×Q8—61no—
132C2×Dic6—21no—
133C2×Dic6—31no—
134C2×Dic6—31no—
135C2×Dic6—61no—
136C2×Dic6—61no—
137C2×Dic6—61no—
138C2×Dic6—121no—
139C2×Dic6D1211yescharacteristic
140C2×C3×C8—22no—
141C2×C3×C8—21no—
142C2×C3×C8—21no—
143C2×C3×C8—61no—
144C2×C3×C8—61no—
145C3×C4⋊C4—31no—
146C3×C4⋊C4—32no—
147C3×C4⋊C4—61no—
148C3×C4⋊C4—61no—
149C3×C42—21no—
150C3×C42—61no—
151C3×C42C22×D311yescharacteristic
152C3×C42C22×D311yescharacteristic
153C4⋊Dic3—21no—
154C4⋊Dic3—31no—
155C4⋊Dic3—31no—
156C4⋊Dic3—61no—
157C4⋊Dic3—62no—
158C4⋊Dic3—62no—
159C4⋊Dic3—61no—
160C4⋊Dic3—61no—
161C4⋊Dic3—61no—
162C4⋊Dic3—61no—
163C4⋊Dic3—121no—
164C4⋊Dic3D1212yes—
165C4⋊Dic3D1211yescharacteristic
166Dic3⋊C4—21no—
167Dic3⋊C4—62no—
168Dic3⋊C4—62no—
169Dic3⋊C4—62no—
170Dic3⋊C4—62no—
171Dic3⋊C4—62no—
172Dic3⋊C4—61no—
173Dic3⋊C4—61no—
174Dic3⋊C4—121no—
175C4×Dic3—21no—
176C4×Dic3—62no—
177C4×Dic3—62no—
178C4×Dic3—61no—
179C4×Dic3—61no—
180C4×Dic3—121no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—21no—
183C22×C32#12011yescharacteristic
184C32×C4—21no—
185C32×C4C2×Q1611yescharacteristic
186C32×C4#13511yescharacteristic
187C32×C4#13711yescharacteristic
188C32×C4#13711yescharacteristic
189C3⋊Dic3—22no—
190C3⋊Dic3—41no—
191C3⋊Dic3—81no—
192C3×Dic3—41no—
193C3×Dic3—42no—
194C3×Dic3—41no—
195C4⋊Q8—31no—
196C4⋊Q8—91no—
197C4⋊Q8—181no—
198#125—181no—
199#125—182no—
200C4×Q8—31no—
201C4×Q8—91no—
202C4×Q8—181no—
203C4×Q8—181no—
204#107—181no—
205#107—181no—
206C4⋊C8—31no—
207C4⋊C8D3211yescharacteristic
208#103—182no—
209#103—181no—
210#103—181no—
211C4×C8—31no—
212C3×Q8—61no—
213C3×Q8—61no—
214C3×Q8—121no—
215C3×Q8—121no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—61no—
220C2×C3×C4—62no—
221C2×C3×C4—61no—
222C2×C3×C4C2×D1211yescharacteristic
223C2×C3×C4C2×D1211yescharacteristic
224C2×C3×C4D3×D411yescharacteristic
225C2×C3×C4D3×D411yescharacteristic
226C2×C3×C4D3×D411yescharacteristic
227C2×C3×C4D3×D411yescharacteristic
228C2×Dic3—21no—
229C2×Dic3—21no—
230C2×Dic3—22no—
231C2×Dic3—61no—
232C2×Dic3—61no—
233C2×Dic3—61no—
234C2×Dic3—61no—
235C2×Dic3—121no—
236C2×Dic3—121no—
237C2×Dic3—122no—
238C2×Dic3—121no—
239C2×Dic3—121no—
240Dic6—21no—
241Dic6—21no—
242Dic6—32no—
243Dic6—32no—
244Dic6—41no—
245Dic6—41no—
246Dic6—62no—
247Dic6—61no—
248Dic6—61no—
249Dic6—121no—
250Dic6—122no—
251Dic6—122no—
252Dic6—242no—
253C3×C8—42no—
254C3×C8—41no—
255C3×C8—41no—
256C3×C8—121no—
257C3×C8—121no—
258C3⋊C8—41no—
259C3⋊C8—41no—
260C2×C32#45111yescharacteristic
261C2×C32#45211yescharacteristic
262C2×C32#45411yescharacteristic
263C2×Q8—31no—
264C2×Q8—61no—
265C2×Q8—91no—
266C2×Q8—181no—
267C2×C8—21no—
268C2×C8—61no—
269C2×C8—61no—
270C4⋊C4—32no—
271C4⋊C4—31no—
272C4⋊C4—61no—
273C4⋊C4—61no—
274C4⋊C4—91no—
275C4⋊C4—182no—
276C4⋊C4—182no—
277C4⋊C4—182no—
278C4⋊C4—181no—
279C4⋊C4—181no—
280C4⋊C4—181no—
281C42—61no—
282C42—182no—
283C42—181no—
284C42C2×D3211yescharacteristic
285C22×C3—21no—
286C22×C3#88211yescharacteristic
287C22×C3#88211yescharacteristic
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—41no—
295C3×C4—122no—
296C3×C4—121no—
297C3×C4—121no—
298C3×C4#90411yescharacteristic
299C3×C4#90911yescharacteristic
300C3×C4#91211yescharacteristic
301C3×C4#91511yescharacteristic
302C3×C4#91511yescharacteristic
303C3×C4#91511yescharacteristic
304C3×C4D3×Q1611yescharacteristic
305C3×C4D3×Q1611yescharacteristic
306Dic3—41no—
307Dic3—42no—
308Dic3—41no—
309Dic3—62no—
310Dic3—62no—
311Dic3—122no—
312Dic3—121no—
313Dic3—121no—
314Dic3—241no—
315Dic3—242no—
316Dic3—241no—
317Dic3—241no—
318C32#163611yescharacteristic, complemented, Sylow
319Q8—61no—
320Q8—61no—
321Q8—92no—
322Q8—121no—
323Q8—121no—
324Q8—181no—
325Q8—362no—
326C2×C4—61no—
327C2×C4—61no—
328C2×C4—62no—
329C2×C4—181no—
330C2×C4—181no—
331C2×C4—361no—
332C2×C4D3×D1211yescharacteristic
333C2×C4D3×D1211yescharacteristic
334C2×C4#381111yescharacteristic
335C8—41no—
336C8—121no—
337C8—121no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3#473311yescharacteristic
342C2×C3#475311yescharacteristic
343C2×C3#478311yescharacteristic
344C2×C3#480911yescharacteristic
345C2×C3#480911yescharacteristic
346C2×C3#482711yescharacteristic
347C22#6392311yescharacteristic
348C4—21no—
349C4—121no—
350C4—121no—
351C4—122no—
352C4—182no—
353C4—361no—
354C4—721no—
355C4#6380011yescharacteristic
356C4#6380711yescharacteristic
357C4#6393111yescharacteristic
358C4#6394411yescharacteristic
359C3—21no—
360C3#6826811yescharacteristic, complemented
361C3#6845811yescharacteristic, complemented
362C2#1059060511yescharacteristic
363C2#1059096911yescharacteristic
364C2#1059102211yescharacteristic
subgroupG/H
centerC22#63923
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
318. C32#1636semidirect
360. C3#68268semidirect
361. C3#68458semidirect

Maximal subgroups

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

subgroupindex
#105938642
#105925492
#105902882
#105902832
C3×#44862
C3×#44842
#105890852
#684583
#682683