Finite Group Databasebeta

← #11779961

Subgroups — #11779961

Order 1152.

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

normal subgroups only

This group has 470 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#10593958C211yesmaximal, characteristic
2#10592786C211yesmaximal, characteristic
3C3×#5093C211yesmaximal, characteristic, complemented
4C3×#5090C211yesmaximal, characteristic, complemented
5#10589095C211yesmaximal, characteristic, complemented
6#10589084C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic
8#71238—31nomaximal
9#71062—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×C3×#216—21no—
13C3×#869C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63900—21no—
16#63894—21no—
17#63888—22no—
18#63871—21no—
19#63869—21no—
20#63636—21no—
21#63634—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×#835—21no—
24C3×#810—22no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27#5730—31no—
28#5579—31no—
29C3×#487—31no—
30C3×#462—31no—
31#5093D311yescharacteristic, complemented
32#5090D311yescharacteristic, complemented
33#5087—31no—
34#5087—31no—
35#5087—61no—
36#4546—31no—
37#4535—31no—
38#4483—31no—
39#4481—31no—
40#4459—31no—
41#4456—31no—
42C2×C32×Q8—21no—
43C2×C4⋊(C3⋊D3)D411yescharacteristic
44C2×C4×C3⋊D3—21no—
45C2×C3×Dic6D411yescharacteristic
46C2×C3×Dic6D412yes—
47C2×#624—22no—
48C32×C4⋊C4—21no—
49C32×C4⋊C4—21no—
50C32×C42C2311yescharacteristic
51#3752—21no—
52C4⋊(C3⋊Dic3)D411yescharacteristic
53C2×C3⋊(C3⋊C8)—21no—
54C3×#216—42no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3D411yescharacteristic
58C3×Dic3⋊C4—21no—
59C3×C4×Dic3—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62#3724—22no—
63Dic3⋊Dic3—22no—
64#3722—22no—
65#1644—91noSylow
66C2×C3×Q16—61no—
67C3×C4⋊Q8—21no—
68C3×C4⋊Q8—31no—
69C3×C4⋊Q8C2×D311yescharacteristic
70C3×C4⋊Q8C2×D311yescharacteristic
71C3×C4×Q8—31no—
72#946—62no—
73#946—61no—
74C2×#216—21no—
75#897—61no—
76#896—62no—
77#893—61no—
78D3×C4⋊C4—61no—
79D3×C4⋊C4—61no—
80#890—61no—
81C4×D12—31no—
82C4×D12—31no—
83C4×D12—61no—
84C4×D12—61no—
85#870—61no—
86#869C2×D311yescharacteristic
87C4×Dic6C2×D311yescharacteristic
88C3×C4⋊C8—31no—
89C3×#103—62no—
90C3×#103—61no—
91C3×C4×C8—31no—
92#835—21no—
93#810—22no—
94#809—61no—
95#809—61no—
96#809—62no—
97#807—61no—
98#807—61no—
99#807—62no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—61no—
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C4×C3⋊C8C2×D311yescharacteristic
105C22×C3⋊D3—21no—
106C32×Q8—41no—
107C32×Q8—41no—
108C2×C32×C4—41no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3⋊Dic3—21no—
113C4⋊(C3⋊D3)—21no—
114C4⋊(C3⋊D3)Q1612yescomplemented
115C4×C3⋊D3—41no—
116C4×C3⋊D3—41no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—22no—
119C2×C3×Dic3—21no—
120C3×Dic6—21no—
121C3×Dic6—21no—
122C3×Dic6—42no—
123#624—82no—
124C3⋊(C3⋊C8)—41no—
125C3×C3⋊C8—41no—
126C3×C3⋊C8—41no—
127#554—91no—
128#487—31no—
129#474—91no—
130#462—31no—
131#333—91no—
132Q8⋊C8—91no—
133D4⋊C8—91no—
134C2×C3×Q8—21no—
135C2×C3×Q8—21no—
136C2×C3×Q8—31no—
137C2×C3×Q8—32no—
138C2×C3×Q8—41no—
139C2×D12—31no—
140C2×D12—31no—
141C2×D12—61no—
142C2×C4×D3—61no—
143C2×C4×D3—61no—
144C2×C4×D3—62no—
145C2×C4×D3—62no—
146C2×C4×D3—121no—
147C2×Dic6#6711yescharacteristic
148C2×Dic6#6712yes—
149C3×Q16—122no—
150C2×C3×C8—61no—
151C2×C3×C8—61no—
152C3×C4⋊C4—22no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—31no—
158C3×C4⋊C4—41no—
159C3×C4⋊C4—61no—
160C3×C4⋊C4—61no—
161C3×C4⋊C4—61no—
162C3×C42—21no—
163C3×C42—61no—
164C3×C42C22×D311yescharacteristic
165C3×C42C22×D311yescharacteristic
166#216—42no—
167(C2×D3)⋊C4—62no—
168(C2×D3)⋊C4—62no—
169(C2×D3)⋊C4—61no—
170(C2×D3)⋊C4—61no—
171(C2×D3)⋊C4—121no—
172C4⋊Dic3—21no—
173C4⋊Dic3—21no—
174C4⋊Dic3—31no—
175C4⋊Dic3—31no—
176C4⋊Dic3—61no—
177C4⋊Dic3—62no—
178C4⋊Dic3#6711yescharacteristic
179Dic3⋊C4—21no—
180Dic3⋊C4—62no—
181Dic3⋊C4—62no—
182Dic3⋊C4—62no—
183C4×Dic3—21no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—62no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8—61no—
189C22×C32#12011yescharacteristic
190C2×C3⋊D3—22no—
191C2×C3⋊D3—41no—
192C2×C3⋊D3—41no—
193C32×C4—21no—
194C32×C4—81no—
195C32×C4C2×Q1611yescharacteristic
196C32×C4#13511yescharacteristic
197C32×C4AGL(1,ℤ/8)11yescharacteristic
198C32×C4#13711yescharacteristic
199C3⋊Dic3—41no—
200C3×Dic3—41no—
201C3×Dic3—41no—
202C3×Dic3—42no—
203C2×Q16—61no—
204C4⋊Q8—31no—
205C4⋊Q8D3211yescharacteristic
206#125—181no—
207C22⋊Q8—182no—
208C22⋊Q8—181no—
209C4×Q8—31no—
210C4×D4—91no—
211C4×D4—181no—
212C2×C4⋊C4—181no—
213#107—181no—
214C4⋊C8—31no—
215C4⋊C8—91no—
216#103—62no—
217#103—61no—
218#102—181no—
219C4×C8—31no—
220C22×D3—61no—
221C22×D3—61no—
222C22×D3—121no—
223C3×Q8—41no—
224C3×Q8—41no—
225C3×Q8—41no—
226C3×Q8—41no—
227C3×Q8—61no—
228C3×Q8—61no—
229C3×Q8—81no—
230C3×Q8—81no—
231C3×Q8—122no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—42no—
236C2×C3×C4—41no—
237C2×C3×C4—41no—
238C2×C3×C4—61no—
239C2×C3×C4—61no—
240C2×C3×C4—62no—
241C2×C3×C4D3×D411yescharacteristic
242C2×C3×C4D3×D411yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4C2×#6711yescharacteristic
246C2×C3×C4C2×#6711yescharacteristic
247C2×Dic3—21no—
248C2×Dic3—21no—
249C2×Dic3—22no—
250C2×Dic3—61no—
251C2×Dic3—61no—
252C2×Dic3—121no—
253D12—32no—
254D12—32no—
255D12—62no—
256D12—61no—
257D12—61no—
258D12—121no—
259C4×D3—121no—
260C4×D3—121no—
261C4×D3—121no—
262C4×D3—121no—
263C4×D3—241no—
264C4×D3—241no—
265C4×D3—242no—
266C4×D3—242no—
267Dic6—21no—
268Dic6—21no—
269Dic6—42no—
270C3×C8—121no—
271C3×C8—121no—
272C3⋊C8—41no—
273C3⋊C8—41no—
274C3⋊C8—122no—
275C3⋊C8—121no—
276C3⋊C8—121no—
277C2×C32#44911yescharacteristic
278C2×C32#45111yescharacteristic
279C2×C32#45511yescharacteristic
280C3⋊D3—42no—
281C2×Q8—21no—
282C2×Q8—31no—
283C2×Q8—32no—
284C2×D4—91no—
285C22×C4—182no—
286C22×C4—181no—
287Q16—122no—
288C2×C8—61no—
289C2×C8—61no—
290C2×C8—181no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—31no—
294C4⋊C4—61no—
295C4⋊C4—61no—
296C4⋊C4—61no—
297C4⋊C4—91no—
298C4⋊C4—182no—
299C4⋊C4—182no—
300C22⋊C4—182no—
301C22⋊C4—181no—
302C42—61no—
303C42C2×D3211yescharacteristic
304C22×C3—21no—
305C22×C3#93711yescharacteristic
306C22×C3#93711yescharacteristic
307C2×D3—62no—
308C2×D3—62no—
309C2×D3—122no—
310C2×D3—121no—
311C2×D3—121no—
312C2×D3—121no—
313C2×D3—121no—
314C2×D3—241no—
315C2×D3—241no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—41no—
323C3×C4—82no—
324C3×C4—81no—
325C3×C4—81no—
326C3×C4—121no—
327C3×C4—122no—
328C3×C4—121no—
329C3×C4#91411yescharacteristic
330C3×C4#91611yescharacteristic
331C3×C4D3×Q1611yescharacteristic
332C3×C4D3×Q1611yescharacteristic
333C3×C4#91811yescharacteristic
334C3×C4#91811yescharacteristic
335C3×C4#93211yescharacteristic
336C3×C4#95011yescharacteristic
337Dic3—41no—
338Dic3—41no—
339Dic3—42no—
340Dic3—121no—
341Dic3—121no—
342Dic3—241no—
343C32#164411yescharacteristic, complemented, Sylow
344C23—181no—
345Q8—41no—
346Q8—41no—
347Q8—61no—
348Q8—61no—
349Q8—122no—
350D4—92no—
351D4—181no—
352C2×C4—41no—
353C2×C4—61no—
354C2×C4—61no—
355C2×C4—62no—
356C2×C4—181no—
357C2×C4—361no—
358C2×C4—361no—
359C2×C4—722no—
360C2×C4D3×#6711yescharacteristic
361C2×C4D3×#6711yescharacteristic
362C2×C4#381111yescharacteristic
363C8—121no—
364C8—121no—
365C8—361no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3#503711yescharacteristic
370C2×C3#506111yescharacteristic
371C2×C3#517211yescharacteristic
372C2×C3#518611yescharacteristic
373C2×C3#518611yescharacteristic
374C2×C3#520211yescharacteristic
375D3—122no—
376D3—122no—
377D3—242no—
378C22—182no—
379C22—361no—
380C22—361no—
381C22#6398311yescharacteristic
382C4—21no—
383C4—81no—
384C4—121no—
385C4—121no—
386C4—122no—
387C4—361no—
388C4#6393411yescharacteristic
389C4#6393511yescharacteristic
390C4#6394411yescharacteristic
391C4#6394511yescharacteristic
392C3—21no—
393C3#7106211yescharacteristic, complemented
394C3#7123811yescharacteristic, complemented
395C2—362no—
396C2#1059152111yescharacteristic
397C2#1059165411yescharacteristic
398C2#1059165911yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#120
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4⋊Q8D32
hypocenterC32#1644
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
3. C3×#5093C2semidirect
4. C3×#5090C2semidirect
5. #10589095C2semidirect
6. #10589084C2semidirect
31. #5093D3semidirect
32. #5090D3semidirect
114. C4⋊(C3⋊D3)Q16semidirect
343. C32#1644semidirect
393. C3#71062semidirect
394. C3#71238semidirect

Maximal subgroups

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

subgroupindex
#105939582
#105927862
C3×#50932
C3×#50902
#105890952
#105890842
#105890822
#712383
#710623