Finite Group Databasebeta

← #11779966

Subgroups — #11779966

Order 1152.

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

normal subgroups only

This group has 530 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#10596050C211yesmaximal, characteristic
2C3×#5031C211yesmaximal, characteristic, complemented
3#10590313C211yesmaximal, characteristic
4#10590288C211yesmaximal, characteristic, complemented
5C3×#4535C211yesmaximal, characteristic, complemented
6#10589096C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic
8#71062—31nomaximal
9#68270—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11#64155—21no—
12#64105—22no—
13C4⋊C4×C3⋊D3—21no—
14C4×C4⋊(C3⋊D3)—21no—
15C4×C4⋊(C3⋊D3)C2211yescharacteristic
16#64079—21no—
17#64078C2211yescharacteristic
18C2×C3×#216—21no—
19C3×#869C2211yescharacteristic
20C3×#810—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24#63575—21no—
25#63567—22no—
26#63564—21no—
27#5579—31no—
28#5579—31no—
29#5579—61no—
30C3×#462—31no—
31#5093—31no—
32#5087—31no—
33#5031D311yescharacteristic, complemented
34#4846—31no—
35#4681—31no—
36C3×Q8⋊C8—31no—
37#4535D311yescharacteristic, complemented
38#4483—31no—
39#4481—31no—
40#4481—31no—
41#4459—31no—
42C2×C32×Q8D411yescharacteristic
43C2×C4⋊(C3⋊D3)D411yescharacteristic
44C2×C4×C3⋊D3—21no—
45C2×C4×C3⋊D3—22no—
46C2×#634D412yes—
47C2×C3×Dic6—21no—
48C32×C4⋊C4—21no—
49C32×C4⋊C4D411yescharacteristic
50C32×C42—21no—
51C32×C42C2311yescharacteristic
52#3752—22no—
53#3752—21no—
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)D411yescharacteristic
57#3750—22no—
58#3750—22no—
59C3×#216—42no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#1644—91noSylow
66C2×C3×Q16—61no—
67C3×C4⋊Q8—31no—
68C3×C4×Q8—21no—
69C3×C4×Q8C2×D311yescharacteristic
70C3×C4×Q8C2×D311yescharacteristic
71#946—62no—
72#946—61no—
73#946—61no—
74C2×#216—21no—
75#896—62no—
76#896—62no—
77#896—64no—
78D3×C4⋊C4—62no—
79D3×C4⋊C4—61no—
80D3×C4⋊C4—61no—
81C4×D12—31no—
82C4×D12—31no—
83C4×D12—61no—
84C4×D12—61no—
85C4×D12—61no—
86C4×D12—62no—
87#870—61no—
88#870—61no—
89#870—62no—
90#869—31no—
91#869—31no—
92#869—61no—
93#869C2×D311yescharacteristic
94C3×C4⋊C8—31no—
95C3×C4⋊C8—31no—
96C3×#103—61no—
97C3×C4×C8—31no—
98#821—61no—
99#818—61no—
100#816—62no—
101#810—21no—
102#810—62no—
103#809—61no—
104#807—61no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4⋊(C3⋊C8)C2×D311yescharacteristic
107C4×C3⋊C8C2×D311yescharacteristic
108C22×C3⋊D3—21no—
109C32×Q8—21no—
110C32×Q8—21no—
111C2×C32×C4—21no—
112C2×C32×C4—21no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C3⋊Dic3—21no—
117C2×C3⋊Dic3—22no—
118C4⋊(C3⋊D3)—21no—
119C4⋊(C3⋊D3)Q1612yescomplemented
120C4×C3⋊D3—41no—
121C4×C3⋊D3—41no—
122C4×C3⋊D3—82no—
123#634—42no—
124C2×C3×Dic3—41no—
125C3×Dic6—41no—
126C3×Dic6—41no—
127C3×C3⋊C8—41no—
128C3×C3⋊C8—41no—
129C3×C3⋊C8—41no—
130#554—91no—
131#487—91no—
132#474—91no—
133#462—31no—
134#333—91no—
135Q8⋊C8—31no—
136D4⋊C8—91no—
137C2×C3×Q8—21no—
138C2×C3×Q8—61no—
139C2×C3×Q8D1211yescharacteristic
140C2×C3×Q8#6711yescharacteristic
141C2×D12—31no—
142C2×D12—31no—
143C2×D12—61no—
144C2×C4×D3—62no—
145C2×C4×D3—61no—
146C2×C4×D3—61no—
147C2×C4×D3—64no—
148C2×C4×D3—62no—
149C2×C4×D3—62no—
150C2×Dic6—21no—
151C2×Dic6—32no—
152C2×Dic6—32no—
153C2×Dic6—62no—
154C3×Q16—122no—
155C2×C3×C8—61no—
156C2×C3×C8—61no—
157C2×C3×C8—61no—
158C3×C4⋊C4—22no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4—21no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—61no—
163C3×C4⋊C4—61no—
164C3×C4⋊C4D1211yescharacteristic
165C3×C4⋊C4#6711yescharacteristic
166C3×C42—22no—
167C3×C42—21no—
168C3×C42—21no—
169C3×C42—21no—
170C3×C42C22×D311yescharacteristic
171C3×C42C22×D311yescharacteristic
172#216—42no—
173(C2×D3)⋊C4—62no—
174(C2×D3)⋊C4—64no—
175(C2×D3)⋊C4—62no—
176(C2×D3)⋊C4—62no—
177(C2×D3)⋊C4—61no—
178(C2×D3)⋊C4—61no—
179C4⋊Dic3—21no—
180C4⋊Dic3—21no—
181C4⋊Dic3—31no—
182C4⋊Dic3—31no—
183C4⋊Dic3—61no—
184C4⋊Dic3—62no—
185C4⋊Dic3—62no—
186C4⋊Dic3—61no—
187C4⋊Dic3—61no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190Dic3⋊C4—64no—
191Dic3⋊C4—62no—
192Dic3⋊C4—62no—
193Dic3⋊C4—64no—
194Dic3⋊C4—62no—
195Dic3⋊C4—62no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—21no—
199C22×C32#12011yescharacteristic
200C2×C3⋊D3—22no—
201C2×C3⋊D3—41no—
202C2×C3⋊D3—41no—
203C32×C4—21no—
204C32×C4—41no—
205C32×C4—41no—
206C32×C4C2×Q1611yescharacteristic
207C32×C4#13511yescharacteristic
208C32×C4AGL(1,ℤ/8)11yescharacteristic
209C32×C4#13711yescharacteristic
210C3⋊Dic3—41no—
211C3⋊Dic3—42no—
212C3×Dic3—81no—
213C2×Q16—61no—
214C4⋊Q8—31no—
215C4⋊Q8—91no—
216#125—181no—
217C22⋊Q8—182no—
218C22⋊Q8—181no—
219C4×Q8D3211yescharacteristic
220C4×D4—91no—
221C4×D4—181no—
222C2×C4⋊C4—181no—
223#107—181no—
224C4⋊C8—31no—
225C4⋊C8—31no—
226#103—61no—
227#103—182no—
228#102—181no—
229C4×C8—31no—
230C22×D3—62no—
231C22×D3—61no—
232C22×D3—61no—
233C3×Q8—21no—
234C3×Q8—21no—
235C3×Q8—21no—
236C3×Q8—21no—
237C3×Q8—41no—
238C3×Q8—41no—
239C3×Q8—121no—
240C3×Q8—121no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—121no—
251C2×C3×C4C2×D1211yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4C2×#6711yescharacteristic
257C2×Dic3—41no—
258C2×Dic3—62no—
259C2×Dic3—64no—
260C2×Dic3—61no—
261C2×Dic3—62no—
262C2×Dic3—61no—
263C2×Dic3—62no—
264D12—32no—
265D12—32no—
266D12—62no—
267D12—62no—
268D12—61no—
269D12—61no—
270C4×D3—122no—
271C4×D3—122no—
272C4×D3—121no—
273C4×D3—121no—
274C4×D3—121no—
275C4×D3—121no—
276C4×D3—244no—
277C4×D3—242no—
278C4×D3—242no—
279Dic6—41no—
280Dic6—41no—
281Dic6—122no—
282Dic6—122no—
283Dic6—242no—
284C3×C8—121no—
285C3×C8—121no—
286C3×C8—121no—
287C3⋊C8—41no—
288C3⋊C8—41no—
289C3⋊C8—41no—
290C2×C32#44911yescharacteristic
291C2×C32#45111yescharacteristic
292C2×C32#45511yescharacteristic
293C3⋊D3—42no—
294C2×Q8—61no—
295C2×Q8—92no—
296C2×Q8#62611yescharacteristic
297C2×D4—91no—
298C22×C4—182no—
299C22×C4—181no—
300Q16—122no—
301C2×C8—61no—
302C2×C8—61no—
303C2×C8—61no—
304C4⋊C4—21no—
305C4⋊C4—61no—
306C4⋊C4—61no—
307C4⋊C4—91no—
308C4⋊C4—182no—
309C4⋊C4—182no—
310C4⋊C4—181no—
311C4⋊C4—181no—
312C4⋊C4#62611yescharacteristic
313C22⋊C4—182no—
314C22⋊C4—181no—
315C42—21no—
316C42C2×D3211yescharacteristic
317C22×C3—21no—
318C22×C3#88211yescharacteristic
319C22×C3#93711yescharacteristic
320C2×D3—64no—
321C2×D3—62no—
322C2×D3—62no—
323C2×D3—122no—
324C2×D3—122no—
325C2×D3—121no—
326C2×D3—121no—
327C2×D3—121no—
328C2×D3—121no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—41no—
336C3×C4—42no—
337C3×C4—42no—
338C3×C4—41no—
339C3×C4—41no—
340C3×C4—41no—
341C3×C4—41no—
342C3×C4—241no—
343C3×C4#90411yescharacteristic
344C3×C4#90811yescharacteristic
345C3×C4#91511yescharacteristic
346C3×C4D3×Q1611yescharacteristic
347C3×C4D3×Q1611yescharacteristic
348C3×C4#91811yescharacteristic
349C3×C4#93211yescharacteristic
350C3×C4#95011yescharacteristic
351Dic3—81no—
352Dic3—124no—
353Dic3—122no—
354Dic3—122no—
355Dic3—121no—
356Dic3—121no—
357Dic3—122no—
358C32#164411yescharacteristic, complemented, Sylow
359C23—181no—
360Q8—21no—
361Q8—21no—
362Q8—121no—
363Q8—121no—
364Q8—362no—
365D4—92no—
366D4—181no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—121no—
370C2×C4—181no—
371C2×C4—182no—
372C2×C4—361no—
373C2×C4—361no—
374C2×C4—722no—
375C2×C4C2×#62611yescharacteristic
376C2×C4#381111yescharacteristic
377C2×C4#381111yescharacteristic
378C8—121no—
379C8—121no—
380C8—121no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3#473411yescharacteristic
385C2×C3#480911yescharacteristic
386C2×C3#482511yescharacteristic
387C2×C3#503711yescharacteristic
388C2×C3#518611yescharacteristic
389C2×C3#520211yescharacteristic
390D3—124no—
391D3—122no—
392D3—122no—
393C22—182no—
394C22—361no—
395C22—361no—
396C22#6398111yescharacteristic
397C4—21no—
398C4—41no—
399C4—41no—
400C4—241no—
401C4—362no—
402C4—361no—
403C4#6382911yescharacteristic
404C4#6383011yescharacteristic
405C4#6394411yescharacteristic
406C4#6395111yescharacteristic
407C3—21no—
408C3#6827011yescharacteristic, complemented
409C3#7106211yescharacteristic, complemented
410C2—362no—
411C2#1059118211yescharacteristic
412C2#1059160311yescharacteristic
413C2#1059169011yescharacteristic
subgroupG/H
centerC22#63981
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
2. C3×#5031C2semidirect
4. #10590288C2semidirect
5. C3×#4535C2semidirect
6. #10589096C2semidirect
33. #5031D3semidirect
37. #4535D3semidirect
119. C4⋊(C3⋊D3)Q16semidirect
358. C32#1644semidirect
408. C3#68270semidirect
409. C3#71062semidirect

Maximal subgroups

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

subgroupindex
#105960502
C3×#50312
#105903132
#105902882
C3×#45352
#105890962
#105890822
#710623
#682703