Finite Group Databasebeta

← #11779440

Subgroups — #11779440

Order 1152.

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

normal subgroups only

This group has 460 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#10593960C211yesmaximal, characteristic
2C3×#4850C211yesmaximal, characteristic, complemented
3#10590386C211yesmaximal, characteristic, complemented
4#10590266C211yesmaximal, characteristic
5#10589347C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic
7#10589084C211yesmaximal, characteristic, complemented
8#71156—31nomaximal
9#68202—31nomaximal
10#64078C2211yescharacteristic
11C3×C4×D12C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14#63896—22no—
15Dic3×D12—21no—
16D3×C4⋊Dic3—21no—
17#63869—21no—
18#63856—21no—
19C2×#3719—22no—
20C32×C4⋊C8C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×#818—21no—
23C3×#816—21no—
24C3×C4×C3⋊C8C2211yescharacteristic
25#63574—21no—
26#63562—21no—
27#5579—31no—
28#5543—31no—
29C3×#477—31no—
30#5092—31no—
31#5084—31no—
32#5008—31no—
33#4850D311yescharacteristic, complemented
34#4699—31no—
35C3×D4⋊C8—31no—
36#4535—31no—
37#4483D311yescharacteristic
38#4481—31no—
39#4481—31no—
40#4481—61no—
41#4456—31no—
42C2×#634D412yes—
43C2×C3×D12D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×Dic6—21no—
46C2×C3×Dic6D411yescharacteristic
47C2×D3×Dic3—22no—
48C2×C32×C8—21no—
49C32×C42C2311yescharacteristic
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C3×(C2×D3)⋊C4—21no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3D411yescharacteristic
57C3×C4⋊Dic3D411yescharacteristic
58C3×Dic3⋊C4—21no—
59C3×C4×Dic3—21no—
60C2×C3×C3⋊C8—21no—
61#3724—22no—
62Dic3⋊Dic3—22no—
63(C2×D3)⋊Dic3—22no—
64#3719—44no—
65#1632—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4×Q8—31no—
68C3×C4×D4—31no—
69#946—61no—
70C2×#216—62no—
71D4×Dic3—61no—
72C2×C4⋊Dic3—61no—
73#924—61no—
74C2×Dic12—62no—
75#896—62no—
76D3×C4⋊C4—61no—
77#890—61no—
78#878—62no—
79C4×D12—61no—
80C4×D12C2×D311yescharacteristic
81#870—61no—
82#869—31no—
83#869—31no—
84#869—61no—
85#869C2×D311yescharacteristic
86C4×Dic6C2×D311yescharacteristic
87C3×#107—61no—
88C3×C4⋊C8—21no—
89C3×C4⋊C8C2×D311yescharacteristic
90C3×C4⋊C8C2×D311yescharacteristic
91C3×#103—61no—
92C3×C4×C8—31no—
93#832—61no—
94#818—21no—
95#816—21no—
96#809—61no—
97#808—61no—
98#808—61no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—61no—
102C4×C3⋊C8C2×D311yescharacteristic
103C22×C3×D3—21no—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C3⋊Dic3—22no—
108#634—42no—
109C2×C3×Dic3—21no—
110C2×C3×Dic3—21no—
111C2×C3×Dic3—21no—
112C2×C3×Dic3—41no—
113C3×D12—21no—
114C3×D12Q1612yescomplemented
115C3×C4×D3—41no—
116C3×C4×D3—41no—
117C3×Dic6—21no—
118C3×Dic6—21no—
119C3×Dic6—42no—
120D3×Dic3—82no—
121C32×C8—41no—
122C3⋊(C3⋊C8)—41no—
123C3×C3⋊C8—22no—
124#554—91no—
125#494—91no—
126#477—31no—
127#476—91no—
128#333—91no—
129Q8⋊C8—91no—
130D4⋊C8—31no—
131C2×C3×Q8—31no—
132C2×C3×Q8—61no—
133C2×C3×D4—31no—
134C22×C3×C4—61no—
135C22×Dic3—62no—
136C2×D12D1211yescharacteristic
137C2×C4×D3—21no—
138C2×C4×D3—62no—
139C2×Dic6—21no—
140C2×Dic6—32no—
141C2×Dic6—32no—
142C2×Dic6—62no—
143C2×Dic6#6711yescharacteristic
144C2×C3×C8—21no—
145C2×C3×C8—21no—
146C2×C3×C8—41no—
147C2×C3×C8—61no—
148C3×C4⋊C4—31no—
149C3×C4⋊C4—31no—
150C3×C4⋊C4—61no—
151C3×C4⋊C4—61no—
152C3×C4⋊C4—61no—
153C3×C22⋊C4—61no—
154C3×C42—21no—
155C3×C42—61no—
156C3×C42C22×D311yescharacteristic
157C3×C42C22×D311yescharacteristic
158#217—62no—
159#216—124no—
160(C2×D3)⋊C4—21no—
161(C2×D3)⋊C4—62no—
162C4⋊Dic3—21no—
163C4⋊Dic3—21no—
164C4⋊Dic3—62no—
165C4⋊Dic3—61no—
166C4⋊Dic3—61no—
167C4⋊Dic3—61no—
168C4⋊Dic3—61no—
169C4⋊Dic3—121no—
170C4⋊Dic3—121no—
171C4⋊Dic3D1211yescharacteristic
172C4⋊Dic3#6711yescharacteristic
173Dic3⋊C4—21no—
174Dic3⋊C4—62no—
175Dic3⋊C4—62no—
176Dic3⋊C4—62no—
177C4×Dic3—21no—
178C2×C3⋊C8—21no—
179C2×C3⋊C8—61no—
180C2×C3⋊C8—61no—
181C2×C3⋊C8—121no—
182Dic12—124no—
183C22×C32#12011yescharacteristic
184C2×C3×D3—22no—
185C2×C3×D3—41no—
186C2×C3×D3—41no—
187C32×C4—21no—
188C32×C4C2×Q1611yescharacteristic
189C32×C4#13511yescharacteristic
190C32×C4#13711yescharacteristic
191C32×C4#13711yescharacteristic
192C3⋊Dic3—42no—
193C3×Dic3—41no—
194C3×Dic3—41no—
195C3×Dic3—41no—
196C3×Dic3—81no—
197C2×Q16—182no—
198C4⋊Q8—31no—
199C4⋊Q8—91no—
200#125—181no—
201C22⋊Q8—182no—
202C22⋊Q8—181no—
203C4×Q8—31no—
204C4×D4—31no—
205C4×D4—181no—
206C2×C4⋊C4—181no—
207#107—61no—
208#106—181no—
209C4⋊C8—91no—
210C4⋊C8D3211yescharacteristic
211#103—61no—
212#102—181no—
213C4×C8—31no—
214C23×C3—61no—
215C22×D3—21no—
216C3×Q8—61no—
217C3×Q8—61no—
218C3×Q8—122no—
219C3×D4—32no—
220C3×D4—61no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—61no—
225C2×C3×C4—61no—
226C2×C3×C4—61no—
227C2×C3×C4—121no—
228C2×C3×C4—121no—
229C2×C3×C4—121no—
230C2×C3×C4C2×D1211yescharacteristic
231C2×C3×C4D3×D411yescharacteristic
232C2×C3×C4D3×D411yescharacteristic
233C2×C3×C4D3×D411yescharacteristic
234C2×C3×C4D3×D411yescharacteristic
235C2×C3×C4C2×#6711yescharacteristic
236C2×Dic3—21no—
237C2×Dic3—21no—
238C2×Dic3—21no—
239C2×Dic3—41no—
240C2×Dic3—62no—
241C2×Dic3—62no—
242C2×Dic3—122no—
243C2×Dic3—242no—
244D12—21no—
245D12Dic1212yescomplemented
246C4×D3—41no—
247C4×D3—41no—
248C4×D3—242no—
249Dic6—21no—
250Dic6—21no—
251Dic6—42no—
252Dic6—122no—
253Dic6—122no—
254Dic6—242no—
255C3×C8—41no—
256C3×C8—41no—
257C3×C8—62no—
258C3×C8—81no—
259C3⋊C8—22no—
260C3⋊C8—121no—
261C3⋊C8—121no—
262C3⋊C8—241no—
263C2×C32#45111yescharacteristic
264C2×C32#45211yescharacteristic
265C2×C32#45311yescharacteristic
266C3×D3—42no—
267C2×Q8—31no—
268C2×Q8—61no—
269C2×Q8—92no—
270C2×D4—31no—
271C22×C4—61no—
272C22×C4—182no—
273Q16—364no—
274C2×C8—21no—
275C2×C8—61no—
276C2×C8—181no—
277C4⋊C4—31no—
278C4⋊C4—31no—
279C4⋊C4—61no—
280C4⋊C4—61no—
281C4⋊C4—61no—
282C4⋊C4—182no—
283C4⋊C4—182no—
284C4⋊C4—181no—
285C4⋊C4—181no—
286C22⋊C4—61no—
287C22⋊C4—182no—
288C42—61no—
289C42C2×D3211yescharacteristic
290C22×C3—21no—
291C22×C3—62no—
292C22×C3—121no—
293C22×C3—121no—
294C22×C3#88211yescharacteristic
295C22×C3#93711yescharacteristic
296C2×D3—22no—
297C2×D3—41no—
298C2×D3—41no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—41no—
306C3×C4—121no—
307C3×C4—121no—
308C3×C4—121no—
309C3×C4—241no—
310C3×C4C2×Dic1211yescharacteristic
311C3×C4#90911yescharacteristic
312C3×C4#91211yescharacteristic
313C3×C4#91511yescharacteristic
314C3×C4D3×Q1611yescharacteristic
315C3×C4#91811yescharacteristic
316C3×C4#94211yescharacteristic
317C3×C4#95011yescharacteristic
318Dic3—41no—
319Dic3—41no—
320Dic3—41no—
321Dic3—81no—
322Dic3—122no—
323Dic3—122no—
324Dic3—242no—
325C32#163211yescharacteristic, complemented, Sylow
326C23—61no—
327Q8—61no—
328Q8—61no—
329Q8—122no—
330Q8—362no—
331D4—32no—
332D4—61no—
333C2×C4—61no—
334C2×C4—61no—
335C2×C4—61no—
336C2×C4—121no—
337C2×C4—121no—
338C2×C4—121no—
339C2×C4—182no—
340C2×C4—722no—
341C2×C4D3×D1211yescharacteristic
342C2×C4#380211yescharacteristic
343C2×C4D3×#6711yescharacteristic
344C8—41no—
345C8—62no—
346C8—361no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—122no—
351C2×C3#473911yescharacteristic
352C2×C3#478311yescharacteristic
353C2×C3#482211yescharacteristic
354C2×C3#504711yescharacteristic
355C2×C3#518611yescharacteristic
356C2×C3#519811yescharacteristic
357D3—42no—
358C22—62no—
359C22—121no—
360C22—121no—
361C22#6392211yescharacteristic
362C4—21no—
363C4—121no—
364C4—121no—
365C4—121no—
366C4—241no—
367C4—362no—
368C4D3×Dic1211yescharacteristic
369C4#6380111yescharacteristic
370C4#6393311yescharacteristic
371C4#6394611yescharacteristic
372C3—21no—
373C3#6820211yescharacteristic, complemented
374C3#7115611yescharacteristic, complemented
375C2—122no—
376C2#1059061411yescharacteristic
377C2#1059094911yescharacteristic
378C2#1059101311yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC4⋊C8D32
hypocenterC32#1632
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
2. C3×#4850C2semidirect
3. #10590386C2semidirect
5. #10589347C2semidirect
7. #10589084C2semidirect
33. #4850D3semidirect
114. C3×D12Q16semidirect
245. D12Dic12semidirect
325. C32#1632semidirect
373. C3#68202semidirect
374. C3#71156semidirect

Maximal subgroups

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

subgroupindex
#105939602
C3×#48502
#105903862
#105902662
#105893472
C3×#44832
#105890842
#711563
#682023