Finite Group Databasebeta

← #11781940

Subgroups — #11781940

Order 1152.

392 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 86 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#10592540C211yesmaximal, characteristic
2#10590379C211yesmaximal, characteristic
3#10590338C211yesmaximal, characteristic
4#10590311C211yesmaximal, characteristic, complemented
5C3×#4482C211yesmaximal, characteristic, complemented
6C3×#4480C211yesmaximal, characteristic, complemented
7#10589094C211yesmaximal, characteristic, complemented
8#68542—31nomaximal
9#68451—31nomaximal
10C2×#3744—21no—
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12#64078C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C2×#3717—21no—
15C2×#3712—21no—
16C32×C4⋊C8C2211yescharacteristic
17#63643—21no—
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4×C3⋊C8C2211yescharacteristic
21#63575—21no—
22#63575—21no—
23#63566—21no—
24#63557—21no—
25#5083—31no—
26#5078—31no—
27#4841—31no—
28#4841—31no—
29#4841—31no—
30#4841—61no—
31#4838—31no—
32#4688—31no—
33#4682—31no—
34C3×#334—31no—
35C3×#332—31no—
36#4486—31no—
37#4482—31no—
38#4482D311yescharacteristic, complemented
39#4480D311yescharacteristic, complemented
40C2×C4⋊(C3⋊D3)D411yescharacteristic
41C2×C4×C3⋊D3—21no—
42C2×#634—21no—
43C2×C3×Dic6—21no—
44C2×C32×C8—21no—
45C32×C42C2311yescharacteristic
46#3752—21no—
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)D411yescharacteristic
50#3744—42no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#3717—42no—
58#3712—42no—
59#1693—91noSylow
60C3×C4⋊Q8—31no—
61C2×#215—61no—
62C2×#204—61no—
63C2×#204—61no—
64C2×#204—62no—
65C2×#204—61no—
66C2×ΓL(1,𝔽25)—61no—
67C2×ΓL(1,𝔽25)—61no—
68C4×D12—31no—
69C4×D12—31no—
70C4×D12—61no—
71#869—31no—
72#869—31no—
73#869—61no—
74#869C2×D311yescharacteristic
75C3×C4⋊C8—21no—
76C3×C4⋊C8—31no—
77C3×C4⋊C8—31no—
78C3×C4⋊C8C2×D311yescharacteristic
79C3×C4⋊C8C2×D311yescharacteristic
80C3×C4×C8—31no—
81#835—61no—
82(C2×D3)⋊C8—61no—
83(C2×D3)⋊C8—61no—
84#818—61no—
85#818—61no—
86#816—61no—
87#816—61no—
88#816—61no—
89#816—62no—
90#807—61no—
91#807—61no—
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C4⋊(C3⋊C8)C2×D311yescharacteristic
94C4×C3⋊C8C2×D311yescharacteristic
95C22×C3⋊D3—21no—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—41no—
101C4⋊(C3⋊D3)—21no—
102C4⋊(C3⋊D3)—21no—
103C4×C3⋊D3—41no—
104C4×C3⋊D3—41no—
105#634—41no—
106#634—41no—
107C2×C3×Dic3—41no—
108C3×Dic6—41no—
109C3×Dic6—41no—
110C32×C8—41no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—41no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8SD1612yescomplemented
115#500—91no—
116#461—91no—
117#461—91no—
118#436—91no—
119#334—31no—
120#332—31no—
121#332—91no—
122C2×C3×Q8—61no—
123C2×D12—31no—
124C2×D12—31no—
125C2×D12—61no—
126C2×C4×D3—61no—
127C2×C4×D3—61no—
128C2×C4×D3—121no—
129C2×Dic6—21no—
130C2×Dic6—62no—
131C2×Dic6—61no—
132C2×Dic6—61no—
133C2×C3×C8—22no—
134C2×C3×C8—21no—
135C2×C3×C8—21no—
136C2×C3×C8—31no—
137C2×C3×C8—31no—
138C2×C3×C8—61no—
139C2×C3×C8—61no—
140C3×C4⋊C4—61no—
141C3×C4⋊C4—61no—
142C3×C42—21no—
143C3×C42C22×D311yescharacteristic
144C3×C42C22×D311yescharacteristic
145#215—122no—
146(C2×D3)⋊C4—61no—
147(C2×D3)⋊C4—61no—
148(C2×D3)⋊C4—121no—
149C4⋊Dic3—21no—
150C4⋊Dic3—21no—
151C4⋊Dic3—31no—
152C4⋊Dic3—31no—
153C4⋊Dic3—61no—
154C4⋊Dic3—61no—
155C4⋊Dic3—61no—
156C4⋊Dic3—61no—
157C4⋊Dic3—61no—
158C4⋊Dic3—121no—
159C4⋊Dic3—121no—
160C2×C3⋊C8—21no—
161C2×C3⋊C8—21no—
162C2×C3⋊C8D1211yescharacteristic
163C2×C3⋊C8D1211yescharacteristic
164#204—124no—
165#204—122no—
166#204—122no—
167#204—122no—
168ΓL(1,𝔽25)—122no—
169ΓL(1,𝔽25)—122no—
170C22×C32#12111yescharacteristic
171C2×C3⋊D3—41no—
172C2×C3⋊D3—41no—
173C2×C3⋊D3—41no—
174C32×C4—21no—
175C32×C4C2×SD1611yescharacteristic
176C32×C4AGL(1,ℤ/8)11yescharacteristic
177C32×C4AGL(1,ℤ/8)11yescharacteristic
178C32×C4#13711yescharacteristic
179C3⋊Dic3—41no—
180C3⋊Dic3—81no—
181C3×Dic3—81no—
182C2×SD16—181no—
183C2×SD16—181no—
184C2×M16—181no—
185C4⋊Q8—31no—
186C4⋊Q8—91no—
187C4×D4—91no—
188#107—181no—
189#107—181no—
190C4⋊C8—31no—
191C4⋊C8—31no—
192C4⋊C8D3211yescharacteristic
193#103—181no—
194#103—181no—
195C22⋊C8—181no—
196C4×C8—31no—
197C22×D3—61no—
198C22×D3—61no—
199C22×D3—121no—
200C3×Q8—121no—
201C3×Q8—121no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—121no—
206C2×C3×C4C2×D1211yescharacteristic
207C2×C3×C4#23511yescharacteristic
208C2×C3×C4D3×D411yescharacteristic
209C2×C3×C4D3×D411yescharacteristic
210C2×C3×C4D3×D411yescharacteristic
211C2×C3×C4#23911yescharacteristic
212C2×Dic3—41no—
213C2×Dic3—61no—
214C2×Dic3—61no—
215C2×Dic3—121no—
216C2×Dic3—122no—
217C2×Dic3—121no—
218C2×Dic3—121no—
219D12—62no—
220D12—61no—
221D12—61no—
222D12—61no—
223D12—61no—
224D12—121no—
225C4×D3—121no—
226C4×D3—121no—
227C4×D3—121no—
228C4×D3—121no—
229C4×D3—241no—
230C4×D3—241no—
231Dic6—41no—
232Dic6—41no—
233Dic6—122no—
234Dic6—122no—
235Dic6—121no—
236Dic6—121no—
237Dic6—121no—
238Dic6—121no—
239C3×C8—32no—
240C3×C8—42no—
241C3×C8—41no—
242C3×C8—41no—
243C3×C8—61no—
244C3×C8—121no—
245C3×C8—121no—
246C3⋊C8—21no—
247C3⋊C8—41no—
248C3⋊C8—41no—
249C3⋊C8#20412yescomplemented
250C2×C32#46111yescharacteristic
251C2×C32#46911yescharacteristic
252C2×C32#47311yescharacteristic
253C3⋊D3—81no—
254C2×Q8—61no—
255C2×Q8—181no—
256C2×D4—91no—
257C22×C4—181no—
258SD16—362no—
259SD16—362no—
260M16—362no—
261C2×C8—21no—
262C2×C8—31no—
263C2×C8—31no—
264C2×C8—61no—
265C2×C8—61no—
266C4⋊C4—61no—
267C4⋊C4—61no—
268C4⋊C4—91no—
269C4⋊C4—181no—
270C4⋊C4—181no—
271C22⋊C4—181no—
272C42C2×D3211yescharacteristic
273C22×C3—21no—
274C22×C3#88411yescharacteristic
275C22×C3#89511yescharacteristic
276C2×D3—122no—
277C2×D3—121no—
278C2×D3—121no—
279C2×D3—121no—
280C2×D3—121no—
281C2×D3—121no—
282C2×D3—121no—
283C2×D3—241no—
284C2×D3—241no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—41no—
292C3×C4—241no—
293C3×C4C2×#20411yescharacteristic
294C3×C4#90911yescharacteristic
295C3×C4#91111yescharacteristic
296C3×C4D3×SD1611yescharacteristic
297C3×C4#91411yescharacteristic
298C3×C4#91411yescharacteristic
299C3×C4#91411yescharacteristic
300C3×C4#91811yescharacteristic
301Dic3—81no—
302Dic3—121no—
303Dic3—121no—
304Dic3—241no—
305Dic3—242no—
306Dic3—241no—
307Dic3—241no—
308C32#169311yescharacteristic, complemented, Sylow
309C23—181no—
310Q8—121no—
311Q8—121no—
312Q8—361no—
313Q8—361no—
314D4—181no—
315D4—181no—
316C2×C4—121no—
317C2×C4—181no—
318C2×C4—361no—
319C2×C4—361no—
320C2×C4—361no—
321C2×C4#379911yescharacteristic
322C2×C4D3×D1211yescharacteristic
323C2×C4#381111yescharacteristic
324C8—32no—
325C8—41no—
326C8—61no—
327C8—121no—
328C8—121no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3#475511yescharacteristic
333C2×C3#478211yescharacteristic
334C2×C3#481811yescharacteristic
335C2×C3#484111yescharacteristic
336C2×C3#486511yescharacteristic
337C2×C3#489611yescharacteristic
338D3—242no—
339D3—241no—
340D3—241no—
341C22—361no—
342C22—361no—
343C22—361no—
344C22#6391011yescharacteristic
345C4—21no—
346C4—241no—
347C4—361no—
348C4—721no—
349C4D3×#20411yescharacteristic
350C4#6380111yescharacteristic
351C4#6393711yescharacteristic
352C4#6394111yescharacteristic
353C3—21no—
354C3#6845111yescharacteristic, complemented
355C3#6854211yescharacteristic, complemented
356C2—721no—
357C2#1059050811yescharacteristic
358C2#1059076011yescharacteristic
359C2#1059099211yescharacteristic
subgroupG/H
centerC22#63910
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4⋊C8D32
hypocenterC32#1693
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
4. #10590311C2semidirect
5. C3×#4482C2semidirect
6. C3×#4480C2semidirect
7. #10589094C2semidirect
38. #4482D3semidirect
39. #4480D3semidirect
114. C3×C3⋊C8SD16semidirect
249. C3⋊C8#204semidirect
308. C32#1693semidirect
354. C3#68451semidirect
355. C3#68542semidirect

Maximal subgroups

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

subgroupindex
#105925402
#105903792
#105903382
#105903112
C3×#44822
C3×#44802
#105890942
#685423
#684513