Finite Group Databasebeta

← #11779026

Subgroups — #11779026

Order 1152.

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

normal subgroups only

This group has 586 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, complemented
2C3×#5027C211yesmaximal, characteristic, complemented
3#10590369C211yesmaximal, characteristic, complemented
4#10590355C211yesmaximal, characteristic
5C3×#4535C211yesmaximal, characteristic, complemented
6#10589096C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic, complemented
8#71028—31nomaximal
9#68244—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×#215—21no—
19C3×#874C2211yescharacteristic
20C2×#3716—22no—
21C2×#3714—21no—
22C3×#809—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×C4×C3⋊C8C2211yescharacteristic
26#63563—21no—
27#5579—31no—
28#5579—31no—
29#5579—61no—
30C3×#460—31no—
31#5076—31no—
32#5072—31no—
33#5027D311yescharacteristic, complemented
34#4843—31no—
35#4693—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×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C32×C4⋊C4—21no—
51C32×C4⋊C4D411yescharacteristic
52C32×C42—21no—
53C32×C42C2311yescharacteristic
54#3752—22no—
55#3752—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)D411yescharacteristic
59#3750—22no—
60#3750—22no—
61C3×#215—42no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#3716—44no—
66#3714—42no—
67#1622—91noSylow
68C2×C3×SD16—61no—
69C3×#127—31no—
70C3×C4×Q8—21no—
71C3×C4×Q8C2×D311yescharacteristic
72C3×C4×Q8C2×D311yescharacteristic
73#946—62no—
74#946—61no—
75#946—61no—
76C2×#215—21no—
77C2×#214—62no—
78C2×#213—61no—
79C2×D24—61no—
80C2×#204—62no—
81#896—62no—
82#896—62no—
83#896—64no—
84D3×C4⋊C4—62no—
85D3×C4⋊C4—61no—
86D3×C4⋊C4—61no—
87#874C2×D311yescharacteristic
88C4×D12—31no—
89C4×D12—31no—
90C4×D12—61no—
91C4×D12—61no—
92C4×D12—61no—
93C4×D12—62no—
94#870—61no—
95#870—61no—
96#870—62no—
97#869—31no—
98#869—31no—
99#869—61no—
100C3×C4⋊C8—31no—
101C3×C4⋊C8—31no—
102C3×#102—61no—
103C3×C4×C8—31no—
104#832—61no—
105#821—61no—
106#809—21no—
107C4⋊(C3⋊C8)C2×D311yescharacteristic
108C4⋊(C3⋊C8)C2×D311yescharacteristic
109C4×C3⋊C8C2×D311yescharacteristic
110C22×C3⋊D3—21no—
111C22×C3×D3—41no—
112C32×Q8—21no—
113C32×Q8—21no—
114C2×C32×C4—21no—
115C2×C32×C4—21no—
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—22no—
121C4⋊(C3⋊D3)—21no—
122C4⋊(C3⋊D3)SD1612yescomplemented
123C4×C3⋊D3—41no—
124C4×C3⋊D3—41no—
125C4×C3⋊D3—82no—
126#634—42no—
127C3×D12—42no—
128C3×D12—41no—
129C3×D12—41no—
130C3×D12—41no—
131C3×D12—41no—
132C3×C3⋊C8—22no—
133C3×C3⋊C8—41no—
134C3×C3⋊C8—41no—
135#554—91no—
136#492—91no—
137#460—31no—
138#459—91no—
139#333—91no—
140Q8⋊C8—31no—
141D4⋊C8—91no—
142C2×C3×Q8—21no—
143C2×C3×Q8D1211yescharacteristic
144C2×C3×Q8#6711yescharacteristic
145C2×C3×D4—61no—
146C2×C3×D4—61no—
147C2×C3×D4—61no—
148C2×D12—21no—
149C2×D12—21no—
150C2×D12—21no—
151C2×D12—31no—
152C2×D12—31no—
153C2×D12—61no—
154C2×C4×D3—62no—
155C2×C4×D3—61no—
156C2×C4×D3—61no—
157C2×C4×D3—64no—
158C2×C4×D3—62no—
159C2×C4×D3—62no—
160C2×Dic6—32no—
161C2×Dic6—32no—
162C2×Dic6—62no—
163C3×SD16—122no—
164C2×C3×C8—61no—
165C2×C3×C8—61no—
166C2×C3×C8—61no—
167C3×C4⋊C4—22no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4D1211yescharacteristic
172C3×C4⋊C4#6711yescharacteristic
173C3×C42—22no—
174C3×C42—21no—
175C3×C42—21no—
176C3×C42—21no—
177C3×C42C22×D311yescharacteristic
178C3×C42C22×D311yescharacteristic
179#215—42no—
180#214—124no—
181#213—122no—
182(C2×D3)⋊C4—62no—
183(C2×D3)⋊C4—64no—
184(C2×D3)⋊C4—62no—
185(C2×D3)⋊C4—62no—
186(C2×D3)⋊C4—61no—
187(C2×D3)⋊C4—61no—
188C4⋊Dic3—31no—
189C4⋊Dic3—31no—
190C4⋊Dic3—61no—
191C4⋊Dic3—62no—
192C4⋊Dic3—62no—
193C4⋊Dic3—61no—
194C4⋊Dic3—61no—
195C4⋊Dic3—61no—
196C4⋊Dic3—61no—
197Dic3⋊C4—64no—
198Dic3⋊C4—62no—
199Dic3⋊C4—62no—
200Dic3⋊C4—64no—
201Dic3⋊C4—62no—
202Dic3⋊C4—62no—
203C2×C3⋊C8—21no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—21no—
206D24—122no—
207#204—124no—
208C22×C32#12011yescharacteristic
209C2×C3⋊D3—22no—
210C2×C3⋊D3—41no—
211C2×C3⋊D3—41no—
212C2×C3×D3—81no—
213C2×C3×D3—81no—
214C2×C3×D3—81no—
215C32×C4—21no—
216C32×C4—41no—
217C32×C4—41no—
218C32×C4C2×SD1611yescharacteristic
219C32×C4#13511yescharacteristic
220C32×C4AGL(1,ℤ/8)11yescharacteristic
221C32×C4#13711yescharacteristic
222C3⋊Dic3—41no—
223C3⋊Dic3—42no—
224C2×SD16—61no—
225C2×SD16—182no—
226C2×D8—181no—
227C4⋊Q8—91no—
228#127—31no—
229#125—181no—
230C22⋊Q8—182no—
231C22⋊Q8—181no—
232C4×Q8D3211yescharacteristic
233C4×D4—91no—
234C4×D4—181no—
235C2×C4⋊C4—181no—
236C4⋊C8—31no—
237C4⋊C8—31no—
238#102—61no—
239#102—181no—
240C4×C8—31no—
241C23×C3—121no—
242C22×D3—41no—
243C22×D3—62no—
244C22×D3—61no—
245C22×D3—61no—
246C3×Q8—21no—
247C3×Q8—21no—
248C3×Q8—21no—
249C3×Q8—21no—
250C3×Q8—41no—
251C3×Q8—41no—
252C3×D4—122no—
253C3×D4—121no—
254C3×D4—121no—
255C3×D4—121no—
256C3×D4—121no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4C2×D1211yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4D3×D411yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272C2×Dic3—62no—
273C2×Dic3—64no—
274C2×Dic3—61no—
275C2×Dic3—62no—
276C2×Dic3—61no—
277C2×Dic3—62no—
278D12—32no—
279D12—32no—
280D12—42no—
281D12—41no—
282D12—41no—
283D12—41no—
284D12—41no—
285D12—62no—
286D12—62no—
287D12—61no—
288D12—61no—
289C4×D3—122no—
290C4×D3—122no—
291C4×D3—121no—
292C4×D3—121no—
293C4×D3—121no—
294C4×D3—121no—
295C4×D3—244no—
296C4×D3—242no—
297C4×D3—242no—
298Dic6—122no—
299Dic6—122no—
300Dic6—242no—
301C3×C8—62no—
302C3×C8—121no—
303C3×C8—121no—
304C3⋊C8—22no—
305C3⋊C8—41no—
306C3⋊C8—41no—
307C2×C32#44811yescharacteristic
308C2×C32#44911yescharacteristic
309C2×C32#45311yescharacteristic
310C3⋊D3—42no—
311C3×D3—161no—
312C2×Q8—92no—
313C2×Q8#62611yescharacteristic
314C2×D4—61no—
315C2×D4—61no—
316C2×D4—61no—
317C2×D4—91no—
318C22×C4—182no—
319C22×C4—181no—
320SD16—122no—
321SD16—364no—
322D8—362no—
323C2×C8—61no—
324C2×C8—61no—
325C2×C8—61no—
326C4⋊C4—21no—
327C4⋊C4—91no—
328C4⋊C4—182no—
329C4⋊C4—182no—
330C4⋊C4—181no—
331C4⋊C4—181no—
332C4⋊C4#62611yescharacteristic
333C22⋊C4—182no—
334C22⋊C4—181no—
335C42—21no—
336C42C2×D3211yescharacteristic
337C22×C3—21no—
338C22×C3—241no—
339C22×C3—241no—
340C22×C3—241no—
341C22×C3#88211yescharacteristic
342C22×C3#93711yescharacteristic
343C2×D3—64no—
344C2×D3—62no—
345C2×D3—62no—
346C2×D3—81no—
347C2×D3—81no—
348C2×D3—81no—
349C2×D3—122no—
350C2×D3—122no—
351C2×D3—121no—
352C2×D3—121no—
353C2×D3—121no—
354C2×D3—121no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—41no—
362C3×C4—42no—
363C3×C4—42no—
364C3×C4—41no—
365C3×C4—41no—
366C3×C4—41no—
367C3×C4—41no—
368C3×C4#90411yescharacteristic
369C3×C4#90811yescharacteristic
370C3×C4D3×SD1611yescharacteristic
371C3×C4D3×SD1611yescharacteristic
372C3×C4#91511yescharacteristic
373C3×C4#91811yescharacteristic
374C3×C4#93211yescharacteristic
375C3×C4#95011yescharacteristic
376Dic3—124no—
377Dic3—122no—
378Dic3—122no—
379Dic3—121no—
380Dic3—121no—
381Dic3—122no—
382C32#162211yescharacteristic, complemented, Sylow
383C23—121no—
384C23—181no—
385Q8—21no—
386Q8—21no—
387Q8—362no—
388D4—92no—
389D4—122no—
390D4—121no—
391D4—121no—
392D4—121no—
393D4—121no—
394D4—181no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—181no—
398C2×C4—182no—
399C2×C4—361no—
400C2×C4—361no—
401C2×C4—722no—
402C2×C4C2×#62611yescharacteristic
403C2×C4#381111yescharacteristic
404C2×C4#381111yescharacteristic
405C8—62no—
406C8—121no—
407C8—121no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—481no—
412C2×C3#473411yescharacteristic
413C2×C3#480611yescharacteristic
414C2×C3#482211yescharacteristic
415C2×C3#503711yescharacteristic
416C2×C3#517011yescharacteristic
417C2×C3#519811yescharacteristic
418D3—124no—
419D3—122no—
420D3—122no—
421D3—161no—
422C22—182no—
423C22—241no—
424C22—241no—
425C22—241no—
426C22—361no—
427C22—361no—
428C22#6398111yescharacteristic
429C4—21no—
430C4—41no—
431C4—41no—
432C4—362no—
433C4—361no—
434C4#6382911yescharacteristic
435C4#6383011yescharacteristic
436C4#6394011yescharacteristic
437C4#6395111yescharacteristic
438C3—21no—
439C3#6824411yescharacteristic, complemented
440C3#7102811yescharacteristic, complemented
441C2—362no—
442C2—481no—
443C2#1059118211yescharacteristic
444C2#1059159211yescharacteristic
445C2#1059166711yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32#120
prime radical#10590355C2
hypercenterC4×Q8D32
hypocenterC32#1622
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. #10596050C2semidirect
2. C3×#5027C2semidirect
3. #10590369C2semidirect
5. C3×#4535C2semidirect
6. #10589096C2semidirect
7. #10589082C2semidirect
33. #5027D3semidirect
37. #4535D3semidirect
122. C4⋊(C3⋊D3)SD16semidirect
382. C32#1622semidirect
439. C3#68244semidirect
440. C3#71028semidirect

Maximal subgroups

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

subgroupindex
#105960502
C3×#50272
#105903692
#105903552
C3×#45352
#105890962
#105890822
#710283
#682443