Finite Group Databasebeta

← #11779972

Subgroups — #11779972

Order 1152.

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

normal subgroups only

This group has 470 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#10593956C211yesmaximal, characteristic
2#10592548C211yesmaximal, characteristic, complemented
3#10590287C211yesmaximal, characteristic, complemented
4#10590272C211yesmaximal, characteristic
5C3×#4483C211yesmaximal, characteristic
6C3×#4481C211yesmaximal, characteristic, complemented
7#10589085C211yesmaximal, characteristic, complemented
8#68506—31nomaximal
9#68191—31nomaximal
10C2×#3746—21no—
11#64078C2211yescharacteristic
12C4×#634C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×#869C2211yescharacteristic
15#63898—21no—
16D3×C4⋊Dic3—21no—
17#63887—22no—
18#63872—21no—
19#63857—21no—
20C32×C4⋊C8C2211yescharacteristic
21#63643—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24#63575—21no—
25#63566—22no—
26#63563—21no—
27#5730—31no—
28#5543—31no—
29#5079—31no—
30#5007—31no—
31#4849—31no—
32#4849—31no—
33#4849—61no—
34#4846—31no—
35#4681—31no—
36C3×#333—31no—
37C3×D4⋊C8—31no—
38#4484—31no—
39#4483D311yescharacteristic
40#4481D311yescharacteristic, complemented
41#4456—31no—
42C2×#634—21no—
43C2×#634D411yescharacteristic
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C3×Dic6D412yes—
47C2×D3×Dic3—22no—
48C2×C32×C8—21no—
49C32×C42C2311yescharacteristic
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)D411yescharacteristic
53#3750—21no—
54C4×C3⋊Dic3—21no—
55#3746—42no—
56C3×(C2×D3)⋊C4—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62Dic3⋊Dic3—22no—
63Dic3⋊Dic3—22no—
64(C2×D3)⋊Dic3—22no—
65#1644—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4×D4—31no—
68#946—62no—
69D4×Dic3—61no—
70C2×C4⋊Dic3—61no—
71#924—61no—
72C2×Dic12—61no—
73C2×Dic12—61no—
74C2×Dic12—62no—
75#897—61no—
76#893—61no—
77D3×C4⋊C4—61no—
78#890—61no—
79#890—61no—
80#878—62no—
81C4×D12C2×D311yescharacteristic
82#869—31no—
83#869—31no—
84#869—61no—
85#869C2×D311yescharacteristic
86C4×Dic6—31no—
87C4×Dic6—31no—
88C4×Dic6—61no—
89C3×C4⋊C8—21no—
90C3×C4⋊C8—31no—
91C3×C4⋊C8C2×D311yescharacteristic
92C3×C4⋊C8C2×D311yescharacteristic
93C3×C4×C8—31no—
94#835—62no—
95#832—61no—
96#821—61no—
97#818—61no—
98#816—61no—
99#816—61no—
100#816—62no—
101#816—62no—
102#807—61no—
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C4×C3⋊C8C2×D311yescharacteristic
105C22×C3×D3—21no—
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C3⋊Dic3—21no—
110C2×C3⋊Dic3—21no—
111C2×C3⋊Dic3—41no—
112#634—21no—
113#634—21no—
114#634—41no—
115#634—41no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—21no—
118C3×D12—21no—
119C3×D12Q1612yescomplemented
120C3×C4×D3—41no—
121C3×C4×D3—41no—
122C3×Dic6—42no—
123D3×Dic3—82no—
124C32×C8—41no—
125C3×C3⋊C8—41no—
126C3×C3⋊C8—41no—
127#554—91no—
128#487—91no—
129#474—91no—
130#462—91no—
131#333—31no—
132Q8⋊C8—91no—
133D4⋊C8—31no—
134C2×C3×Q8—32no—
135C2×C3×D4—31no—
136C22×C3×C4—61no—
137C22×Dic3—62no—
138C2×D12D1211yescharacteristic
139C2×C4×D3—21no—
140C2×C4×D3—62no—
141C2×Dic6—31no—
142C2×Dic6—31no—
143C2×Dic6—61no—
144C2×Dic6—62no—
145C2×Dic6—61no—
146C2×Dic6—61no—
147C2×Dic6D1212yes—
148C2×C3×C8—22no—
149C2×C3×C8—21no—
150C2×C3×C8—21no—
151C2×C3×C8—61no—
152C2×C3×C8—61no—
153C3×C4⋊C4—31no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—61no—
156C3×C22⋊C4—61no—
157C3×C42—21no—
158C3×C42C22×D311yescharacteristic
159C3×C42C22×D311yescharacteristic
160#217—62no—
161(C2×D3)⋊C4—21no—
162(C2×D3)⋊C4—62no—
163C4⋊Dic3—21no—
164C4⋊Dic3—21no—
165C4⋊Dic3—31no—
166C4⋊Dic3—31no—
167C4⋊Dic3—61no—
168C4⋊Dic3—62no—
169C4⋊Dic3—62no—
170C4⋊Dic3—61no—
171C4⋊Dic3—61no—
172C4⋊Dic3—61no—
173C4⋊Dic3—61no—
174C4⋊Dic3—121no—
175C4⋊Dic3—121no—
176C4⋊Dic3D1211yescharacteristic
177Dic3⋊C4—62no—
178Dic3⋊C4—62no—
179Dic3⋊C4—61no—
180Dic3⋊C4—61no—
181Dic3⋊C4—121no—
182C4×Dic3—61no—
183C4×Dic3—61no—
184C4×Dic3—121no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—21no—
187Dic12—124no—
188Dic12—122no—
189Dic12—122no—
190C22×C32#12011yescharacteristic
191C2×C3×D3—22no—
192C2×C3×D3—41no—
193C2×C3×D3—41no—
194C32×C4—21no—
195C32×C4C2×Q1611yescharacteristic
196C32×C4#13511yescharacteristic
197C32×C4AGL(1,ℤ/8)11yescharacteristic
198C32×C4#13711yescharacteristic
199C3⋊Dic3—41no—
200C3⋊Dic3—41no—
201C3⋊Dic3—81no—
202C3×Dic3—41no—
203C3×Dic3—42no—
204C2×Q16—181no—
205C4⋊Q8—31no—
206C4⋊Q8—91no—
207#125—181no—
208C22⋊Q8—182no—
209C22⋊Q8—181no—
210C4×Q8—91no—
211C4×D4—31no—
212C4×D4—181no—
213C2×C4⋊C4—181no—
214#107—181no—
215C4⋊C8—31no—
216C4⋊C8D3211yescharacteristic
217#103—181no—
218#103—182no—
219#102—181no—
220C4×C8—31no—
221C23×C3—61no—
222C22×D3—21no—
223C3×Q8—122no—
224C3×D4—32no—
225C3×D4—61no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—61no—
230C2×C3×C4—62no—
231C2×C3×C4—121no—
232C2×C3×C4—121no—
233C2×C3×C4C2×D1211yescharacteristic
234C2×C3×C4C2×D1211yescharacteristic
235C2×C3×C4D3×D411yescharacteristic
236C2×C3×C4D3×D411yescharacteristic
237C2×C3×C4D3×D411yescharacteristic
238C2×C3×C4D3×D411yescharacteristic
239C2×Dic3—21no—
240C2×Dic3—22no—
241C2×Dic3—61no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244C2×Dic3—61no—
245C2×Dic3—121no—
246C2×Dic3—121no—
247C2×Dic3—122no—
248C2×Dic3—121no—
249C2×Dic3—121no—
250C2×Dic3—242no—
251D12—21no—
252D12Dic1212yescomplemented
253C4×D3—41no—
254C4×D3—41no—
255C4×D3—242no—
256Dic6—42no—
257Dic6—62no—
258Dic6—61no—
259Dic6—61no—
260Dic6—61no—
261Dic6—61no—
262Dic6—121no—
263Dic6—122no—
264Dic6—122no—
265Dic6—121no—
266Dic6—121no—
267Dic6—121no—
268Dic6—121no—
269C3×C8—42no—
270C3×C8—41no—
271C3×C8—41no—
272C3×C8—121no—
273C3×C8—121no—
274C3⋊C8—41no—
275C3⋊C8—41no—
276C2×C32#44911yescharacteristic
277C2×C32#45111yescharacteristic
278C2×C32#45511yescharacteristic
279C3×D3—42no—
280C2×Q8—32no—
281C2×Q8—91no—
282C2×Q8—181no—
283C2×D4—31no—
284C22×C4—61no—
285C22×C4—182no—
286Q16—362no—
287C2×C8—21no—
288C2×C8—61no—
289C2×C8—61no—
290C4⋊C4—31no—
291C4⋊C4—61no—
292C4⋊C4—61no—
293C4⋊C4—91no—
294C4⋊C4—182no—
295C4⋊C4—182no—
296C4⋊C4—181no—
297C4⋊C4—181no—
298C4⋊C4—181no—
299C22⋊C4—61no—
300C22⋊C4—182no—
301C42—181no—
302C42C2×D3211yescharacteristic
303C22×C3—21no—
304C22×C3—62no—
305C22×C3—121no—
306C22×C3—121no—
307C22×C3#88211yescharacteristic
308C22×C3#88211yescharacteristic
309C2×D3—22no—
310C2×D3—41no—
311C2×D3—41no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—41no—
319C3×C4—121no—
320C3×C4—122no—
321C3×C4C2×Dic1211yescharacteristic
322C3×C4#90911yescharacteristic
323C3×C4#91111yescharacteristic
324C3×C4#91411yescharacteristic
325C3×C4#91511yescharacteristic
326C3×C4#91611yescharacteristic
327C3×C4D3×Q1611yescharacteristic
328C3×C4#91911yescharacteristic
329Dic3—42no—
330Dic3—41no—
331Dic3—122no—
332Dic3—121no—
333Dic3—121no—
334Dic3—121no—
335Dic3—121no—
336Dic3—241no—
337Dic3—242no—
338Dic3—241no—
339Dic3—241no—
340C32#164411yescharacteristic, complemented, Sylow
341C23—61no—
342Q8—122no—
343Q8—181no—
344Q8—181no—
345Q8—361no—
346Q8—361no—
347D4—32no—
348D4—61no—
349C2×C4—61no—
350C2×C4—62no—
351C2×C4—121no—
352C2×C4—121no—
353C2×C4—181no—
354C2×C4—181no—
355C2×C4—361no—
356C2×C4—722no—
357C2×C4D3×D1211yescharacteristic
358C2×C4D3×D1211yescharacteristic
359C2×C4#381111yescharacteristic
360C8—41no—
361C8—121no—
362C8—121no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—122no—
367C2×C3#473911yescharacteristic
368C2×C3#474611yescharacteristic
369C2×C3#478111yescharacteristic
370C2×C3#480911yescharacteristic
371C2×C3#481011yescharacteristic
372C2×C3#482511yescharacteristic
373D3—42no—
374C22—62no—
375C22—121no—
376C22—121no—
377C22#6392311yescharacteristic
378C4—21no—
379C4—122no—
380C4—121no—
381C4—361no—
382C4—361no—
383C4—721no—
384C4D3×Dic1211yescharacteristic
385C4#6380011yescharacteristic
386C4#6393711yescharacteristic
387C4#6395011yescharacteristic
388C3—21no—
389C3#6819111yescharacteristic, complemented
390C3#6850611yescharacteristic, complemented
391C2—122no—
392C2#1059061711yescharacteristic
393C2#1059095211yescharacteristic
394C2#1059101611yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC4⋊C8D32
hypocenterC32#1644
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. #10592548C2semidirect
3. #10590287C2semidirect
6. C3×#4481C2semidirect
7. #10589085C2semidirect
40. #4481D3semidirect
119. C3×D12Q16semidirect
252. D12Dic12semidirect
340. C32#1644semidirect
389. C3#68191semidirect
390. C3#68506semidirect

Maximal subgroups

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

subgroupindex
#105939562
#105925482
#105902872
#105902722
C3×#44832
C3×#44812
#105890852
#685063
#681913