Finite Group Databasebeta

← #11781773

Subgroups — #11781773

Order 1152.

393 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 393 conjugacy classes of subgroups — too many to draw. Only its 84 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#10592791C211yesmaximal, characteristic, complemented
2C3×#5087C211yesmaximal, characteristic
3#10590339C211yesmaximal, characteristic
4#10590272C211yesmaximal, characteristic
5C3×#4547C211yesmaximal, characteristic, complemented
6#10589098C211yesmaximal, characteristic, complemented
7#10589094C211yesmaximal, characteristic, complemented
8#71105—31nomaximal
9#68449—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C2×#3756—21no—
12C2×#3756—21no—
13#64078C2211yescharacteristic
14C3×C4×D12C2211yescharacteristic
15C2×#3711—21no—
16C4×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#809—21no—
18C3×#807—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22#63575—21no—
23#63563—21no—
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×#474—31no—
26#5092—31no—
27#5092—31no—
28#5092—61no—
29#5087D311yescharacteristic
30#5012—31no—
31#5007—31no—
32#4846—31no—
33#4838—31no—
34C3×#332—31no—
35#4547D311yescharacteristic, complemented
36#4486—31no—
37#4482—31no—
38#4480—31no—
39#4480—31no—
40C2×C32×Q8—21no—
41C2×#634—21no—
42C2×C3×D12D411yescharacteristic
43C2×C3×C4×D3—21no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4—21no—
46C32×C42C2311yescharacteristic
47#3756—42no—
48#3756—42no—
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)—21no—
51C2×C3⋊(C3⋊C8)D411yescharacteristic
52C2×C3⋊(C3⋊C8)D411yescharacteristic
53C3×(C2×D3)⋊C4—21no—
54C3×C4⋊Dic3D411yescharacteristic
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8—21no—
58#3711—42no—
59#1689—91noSylow
60C3×C4⋊Q8—21no—
61C3×C4⋊Q8C2×D311yescharacteristic
62C3×C4⋊Q8C2×D311yescharacteristic
63C3×C4×D4—31no—
64C2×#216—61no—
65C2×#216—61no—
66C2×#216—61no—
67C2×#216—61no—
68C2×#216—62no—
69C2×#216—62no—
70C2×#208—61no—
71C2×ΓL(1,𝔽25)—61no—
72C4×D12C2×D311yescharacteristic
73#869—31no—
74#869—31no—
75#869—61no—
76C3×#107—61no—
77C3×C4⋊C8—31no—
78C3×C4⋊C8—31no—
79C3×C4⋊C8—31no—
80C3×#102—61no—
81#832—61no—
82#830—61no—
83#821—61no—
84(C2×D3)⋊C8—61no—
85#818—61no—
86#809—21no—
87#807—21no—
88#807—61no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4×C3⋊C8—31no—
93C4×C3⋊C8—31no—
94C4×C3⋊C8—61no—
95C22×C3×D3—21no—
96C32×Q8—41no—
97C32×Q8—41no—
98C2×C32×C4—41no—
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C3⋊Dic3—41no—
103#634—41no—
104#634—41no—
105C2×C3×Dic3—21no—
106C3×D12—21no—
107C3×D12—21no—
108C3×C4×D3—41no—
109C3×C4×D3—41no—
110C3⋊(C3⋊C8)—21no—
111C3⋊(C3⋊C8)D812yes—
112C3×C3⋊C8—41no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8—41no—
115#494—91no—
116#474—31no—
117#474—91no—
118#436—91no—
119#334—91no—
120#332—31no—
121#332—91no—
122C2×C3×Q8—22no—
123C2×C3×Q8—21no—
124C2×C3×Q8—21no—
125C2×C3×D4—31no—
126C22×C3×C4—61no—
127C2×D12#6711yescharacteristic
128C2×C4×D3—21no—
129C2×Dic6—62no—
130C2×Dic6—61no—
131C2×Dic6—61no—
132C2×C3×C8—61no—
133C2×C3×C8—61no—
134C2×C3×C8—61no—
135C3×C4⋊C4—21no—
136C3×C4⋊C4—21no—
137C3×C4⋊C4—21no—
138C3×C4⋊C4—21no—
139C3×C4⋊C4—31no—
140C3×C4⋊C4—41no—
141C3×C4⋊C4—41no—
142C3×C22⋊C4—61no—
143C3×C42—21no—
144C3×C42C22×D311yescharacteristic
145C3×C42C22×D311yescharacteristic
146#216—122no—
147#216—122no—
148#216—124no—
149#216—124no—
150#216—122no—
151#216—122no—
152(C2×D3)⋊C4—21no—
153C4⋊Dic3—61no—
154C4⋊Dic3—61no—
155C4⋊Dic3—61no—
156C4⋊Dic3—61no—
157C4⋊Dic3—121no—
158C4⋊Dic3—121no—
159C4⋊Dic3#6711yescharacteristic
160#208—122no—
161C2×C3⋊C8—21no—
162C2×C3⋊C8—21no—
163C2×C3⋊C8—21no—
164C2×C3⋊C8—31no—
165C2×C3⋊C8—31no—
166C2×C3⋊C8—31no—
167C2×C3⋊C8—31no—
168C2×C3⋊C8—61no—
169C2×C3⋊C8—61no—
170ΓL(1,𝔽25)—122no—
171C22×C32#12111yescharacteristic
172C2×C3×D3—41no—
173C2×C3×D3—41no—
174C2×C3×D3—41no—
175C32×C4—21no—
176C32×C4—81no—
177C32×C4C2×D811yescharacteristic
178C32×C4AGL(1,ℤ/8)11yescharacteristic
179C32×C4#13711yescharacteristic
180C32×C4#13711yescharacteristic
181C3⋊Dic3—81no—
182C3×Dic3—41no—
183C2×Q16—181no—
184C2×Q16—181no—
185C2×M16—181no—
186C4⋊Q8—91no—
187C4⋊Q8D3211yescharacteristic
188C4×D4—31no—
189#107—61no—
190#107—181no—
191C4⋊C8—31no—
192C4⋊C8—31no—
193C4⋊C8—31no—
194#102—61no—
195#102—181no—
196C22⋊C8—181no—
197C4×C8—91no—
198C23×C3—61no—
199C22×D3—21no—
200C3×Q8—42no—
201C3×Q8—42no—
202C3×Q8—41no—
203C3×Q8—41no—
204C3×Q8—41no—
205C3×Q8—41no—
206C3×D4—61no—
207C3×D4—61no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—42no—
212C2×C3×C4—41no—
213C2×C3×C4—41no—
214C2×C3×C4—61no—
215C2×C3×C4—121no—
216C2×C3×C4—121no—
217C2×C3×C4#23511yescharacteristic
218C2×C3×C4D3×D411yescharacteristic
219C2×C3×C4D3×D411yescharacteristic
220C2×C3×C4D3×D411yescharacteristic
221C2×C3×C4#23711yescharacteristic
222C2×C3×C4C2×#6711yescharacteristic
223C2×Dic3—21no—
224C2×Dic3—122no—
225C2×Dic3—121no—
226C2×Dic3—121no—
227D12—21no—
228D12—21no—
229C4×D3—41no—
230C4×D3—41no—
231Dic6—122no—
232Dic6—122no—
233Dic6—121no—
234Dic6—121no—
235Dic6—121no—
236Dic6—121no—
237C3×C8—121no—
238C3×C8—121no—
239C3×C8—121no—
240C3⋊C8—32no—
241C3⋊C8—32no—
242C3⋊C8—41no—
243C3⋊C8—41no—
244C3⋊C8—41no—
245C3⋊C8—62no—
246C3⋊C8—62no—
247C3⋊C8—61no—
248C3⋊C8—61no—
249C2×C32#45911yescharacteristic
250C2×C32#47011yescharacteristic
251C2×C32#47311yescharacteristic
252C3×D3—81no—
253C2×Q8—21no—
254C2×Q8—181no—
255C2×D4—31no—
256C22×C4—61no—
257Q16—362no—
258Q16—362no—
259M16—362no—
260C2×C8—61no—
261C2×C8—61no—
262C2×C8—61no—
263C2×C8—91no—
264C2×C8—91no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—31no—
268C4⋊C4—181no—
269C4⋊C4—181no—
270C22⋊C4—61no—
271C42C2×D3211yescharacteristic
272C22×C3—21no—
273C22×C3—121no—
274C22×C3—121no—
275C22×C3—121no—
276C22×C3#88411yescharacteristic
277C22×C3#93911yescharacteristic
278C2×D3—41no—
279C2×D3—41no—
280C2×D3—41no—
281C3×C4—22no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—82no—
289C3×C4—81no—
290C3×C4—81no—
291C3×C4—121no—
292C3×C4D3×D811yescharacteristic
293C3×C4D3×D811yescharacteristic
294C3×C4#91111yescharacteristic
295C3×C4#91411yescharacteristic
296C3×C4#91511yescharacteristic
297C3×C4#91811yescharacteristic
298C3×C4#94211yescharacteristic
299C3×C4#95111yescharacteristic
300Dic3—41no—
301Dic3—242no—
302Dic3—241no—
303Dic3—241no—
304C32#168911yescharacteristic, complemented, Sylow
305C23—61no—
306Q8—41no—
307Q8—41no—
308Q8—361no—
309Q8—361no—
310D4—61no—
311D4—61no—
312C2×C4—41no—
313C2×C4—61no—
314C2×C4—121no—
315C2×C4—121no—
316C2×C4—361no—
317C2×C4#380411yescharacteristic
318C2×C4D3×#6711yescharacteristic
319C2×C4#381111yescharacteristic
320C8—92no—
321C8—121no—
322C8—121no—
323C8—121no—
324C8—181no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—241no—
329C2×C3#475511yescharacteristic
330C2×C3#478611yescharacteristic
331C2×C3#481611yescharacteristic
332C2×C3#505211yescharacteristic
333C2×C3#515011yescharacteristic
334C2×C3#520411yescharacteristic
335D3—81no—
336C22—121no—
337C22—121no—
338C22—121no—
339C22#6397111yescharacteristic
340C4—21no—
341C4—81no—
342C4—121no—
343C4—721no—
344C4#6392611yescharacteristic
345C4#6393711yescharacteristic
346C4#6394311yescharacteristic
347C4#6394611yescharacteristic
348C3—21no—
349C3#6844911yescharacteristic, complemented
350C3#7110511yescharacteristic, complemented
351C2—241no—
352C2#1059143311yescharacteristic
353C2#1059159811yescharacteristic
354C2#1059164411yescharacteristic
subgroupG/H
centerC22#63971
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#121
prime radicalC2×C3×D12D4
hypercenterC4⋊Q8D32
hypocenterC32#1689
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10592791C2semidirect
5. C3×#4547C2semidirect
6. #10589098C2semidirect
7. #10589094C2semidirect
35. #4547D3semidirect
304. C32#1689semidirect
349. C3#68449semidirect
350. C3#71105semidirect

Maximal subgroups

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

subgroupindex
#105927912
C3×#50872
#105903392
#105902722
C3×#45472
#105890982
#105890942
#711053
#684493