Finite Group Databasebeta

← #11779014

Subgroups — #11779014

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#10596201C211yesmaximal, characteristic, complemented
2C3×#5085C211yesmaximal, characteristic, complemented
3#10590377C211yesmaximal, characteristic, complemented
4#10590355C211yesmaximal, characteristic
5C3×#4546C211yesmaximal, characteristic, complemented
6#10589085C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic, complemented
8#71264—31nomaximal
9#68490—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64155—22no—
12#64106—21no—
13#64102—21no—
14C4⋊C4×C3⋊D3—21no—
15#64099—21no—
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C2×C3×#215—22no—
19C3×#874C2211yescharacteristic
20C2×#3716—21no—
21C2×#3714—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63563—21no—
26#63563—21no—
27#5730—31no—
28#5730—31no—
29#5730—61no—
30C3×#492—31no—
31#5085D311yescharacteristic, complemented
32#5075—31no—
33#5072—31no—
34#4848—31no—
35#4843—31no—
36C3×#333—31no—
37#4546D311yescharacteristic, complemented
38#4484—31no—
39#4483—31no—
40#4459—31no—
41#4456—31no—
42C2×C32×Q8D412yes—
43C2×C4⋊(C3⋊D3)D411yescharacteristic
44C2×C4×C3⋊D3—21no—
45C2×C4×C3⋊D3—22no—
46C2×#634D411yescharacteristic
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C32×C4⋊C4—21no—
51C32×C4⋊C4—21no—
52C32×C42C2311yescharacteristic
53#3752—22no—
54#3752—21no—
55C4⋊(C3⋊Dic3)—22no—
56C4⋊(C3⋊Dic3)D411yescharacteristic
57C4⋊(C3⋊Dic3)D411yescharacteristic
58#3750—22no—
59#3750—21no—
60C4×C3⋊Dic3—21no—
61C3×#215—44no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#3716—42no—
66#3714—42no—
67#1622—91noSylow
68C2×C3×SD16—62no—
69C3×C4⋊Q8—21no—
70C3×C4⋊Q8C2×D311yescharacteristic
71C3×C4⋊Q8C2×D311yescharacteristic
72C3×#127—31no—
73#946—64no—
74#946—62no—
75#946—62no—
76C2×#215—22no—
77C2×#214—61no—
78C2×#213—61no—
79C2×D24—61no—
80C2×#204—61no—
81#897—61no—
82#897—61no—
83#897—62no—
84#893—61no—
85#893—61no—
86#893—62no—
87D3×C4⋊C4—61no—
88D3×C4⋊C4—61no—
89D3×C4⋊C4—62no—
90#890—61no—
91#890—61no—
92#890—62no—
93#874C2×D311yescharacteristic
94C4×D12—31no—
95C4×D12—31no—
96C4×D12—61no—
97C4×Dic6—31no—
98C4×Dic6—31no—
99C4×Dic6—61no—
100C3×C4⋊C8—31no—
101C3×C4⋊C8—31no—
102C3×C4×C8—31no—
103#832—61no—
104#832—61no—
105#821—61no—
106#821—61no—
107C4⋊(C3⋊C8)C2×D311yescharacteristic
108C4⋊(C3⋊C8)C2×D311yescharacteristic
109C4×C3⋊C8C2×D311yescharacteristic
110C22×C3⋊D3—21no—
111C22×C3×D3—41no—
112C32×Q8—42no—
113C2×C32×C4—22no—
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C3⋊Dic3—21no—
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—21no—
120C4⋊(C3⋊D3)—21no—
121C4⋊(C3⋊D3)SD1612yescomplemented
122C4×C3⋊D3—41no—
123C4×C3⋊D3—41no—
124C4×C3⋊D3—82no—
125#634—21no—
126#634—21no—
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—31no—
137#460—91no—
138#459—91no—
139#333—31no—
140Q8⋊C8—91no—
141D4⋊C8—91no—
142C2×C3×Q8—22no—
143C2×C3×Q8D1212yes—
144C2×C3×Q8#6712yes—
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—31no—
161C2×Dic6—31no—
162C2×Dic6—61no—
163C3×SD16—124no—
164C2×C3×C8—61no—
165C2×C3×C8—61no—
166C2×C3×C8—61no—
167C3×C4⋊C4—22no—
168C3×C4⋊C4—22no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C42—21no—
174C3×C42C22×D311yescharacteristic
175C3×C42C22×D311yescharacteristic
176#215—44no—
177#214—122no—
178#213—122no—
179(C2×D3)⋊C4—62no—
180(C2×D3)⋊C4—64no—
181(C2×D3)⋊C4—62no—
182(C2×D3)⋊C4—62no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—61no—
185C4⋊Dic3—31no—
186C4⋊Dic3—31no—
187C4⋊Dic3—31no—
188C4⋊Dic3—31no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3—64no—
192C4⋊Dic3—62no—
193C4⋊Dic3—62no—
194Dic3⋊C4—62no—
195Dic3⋊C4—64no—
196Dic3⋊C4—62no—
197Dic3⋊C4—62no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200C4×Dic3—62no—
201C4×Dic3—61no—
202C4×Dic3—61no—
203C2×C3⋊C8—21no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—21no—
206D24—122no—
207#204—122no—
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—42no—
217C32×C4C2×SD1611yescharacteristic
218C32×C4#13511yescharacteristic
219C32×C4AGL(1,ℤ/8)11yescharacteristic
220C32×C4#13711yescharacteristic
221C3⋊Dic3—41no—
222C3⋊Dic3—41no—
223C3⋊Dic3—41no—
224C2×SD16—62no—
225C2×SD16—181no—
226C2×D8—181no—
227C4⋊Q8D3211yescharacteristic
228#127—31no—
229#125—181no—
230C22⋊Q8—181no—
231C22⋊Q8—182no—
232C4×Q8—91no—
233C4×D4—91no—
234C4×D4—181no—
235C2×C4⋊C4—181no—
236C4⋊C8—31no—
237C4⋊C8—31no—
238#102—181no—
239#102—181no—
240C4×C8—31no—
241C23×C3—121no—
242C22×D3—41no—
243C22×D3—62no—
244C22×D3—61no—
245C22×D3—61no—
246C3×Q8—42no—
247C3×Q8—42no—
248C3×Q8—82no—
249C3×D4—122no—
250C3×D4—121no—
251C3×D4—121no—
252C3×D4—121no—
253C3×D4—121no—
254C2×C3×C4—24no—
255C2×C3×C4—22no—
256C2×C3×C4—22no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4C2×D1211yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4C2×#6711yescharacteristic
266C2×Dic3—62no—
267C2×Dic3—62no—
268C2×Dic3—62no—
269C2×Dic3—61no—
270C2×Dic3—61no—
271C2×Dic3—61no—
272C2×Dic3—61no—
273C2×Dic3—61no—
274C2×Dic3—61no—
275D12—32no—
276D12—32no—
277D12—42no—
278D12—41no—
279D12—41no—
280D12—41no—
281D12—41no—
282D12—62no—
283D12—62no—
284D12—61no—
285D12—61no—
286C4×D3—122no—
287C4×D3—122no—
288C4×D3—121no—
289C4×D3—121no—
290C4×D3—121no—
291C4×D3—121no—
292C4×D3—244no—
293C4×D3—242no—
294C4×D3—242no—
295Dic6—61no—
296Dic6—61no—
297Dic6—61no—
298Dic6—61no—
299Dic6—121no—
300Dic6—121no—
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—91no—
313C2×Q8#62612yes—
314C2×D4—61no—
315C2×D4—61no—
316C2×D4—61no—
317C2×D4—91no—
318C22×C4—182no—
319C22×C4—181no—
320SD16—124no—
321SD16—362no—
322D8—362no—
323C2×C8—61no—
324C2×C8—61no—
325C2×C8—61no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—91no—
329C4⋊C4—91no—
330C4⋊C4—182no—
331C4⋊C4—182no—
332C4⋊C4—181no—
333C22⋊C4—182no—
334C22⋊C4—181no—
335C42—181no—
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—44no—
363C3×C4—42no—
364C3×C4—42no—
365C3×C4D3×SD1611yescharacteristic
366C3×C4D3×SD1611yescharacteristic
367C3×C4#91411yescharacteristic
368C3×C4#91411yescharacteristic
369C3×C4#91511yescharacteristic
370C3×C4#91611yescharacteristic
371C3×C4#91811yescharacteristic
372C3×C4#91911yescharacteristic
373Dic3—122no—
374Dic3—122no—
375Dic3—122no—
376Dic3—121no—
377Dic3—121no—
378Dic3—121no—
379Dic3—121no—
380Dic3—121no—
381Dic3—121no—
382C32#162211yescharacteristic, complemented, Sylow
383C23—121no—
384C23—181no—
385Q8—42no—
386Q8—181no—
387Q8—181no—
388D4—92no—
389D4—122no—
390D4—121no—
391D4—121no—
392D4—121no—
393D4—121no—
394D4—181no—
395C2×C4—22no—
396C2×C4—181no—
397C2×C4—181no—
398C2×C4—181no—
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#474711yescharacteristic
413C2×C3#480611yescharacteristic
414C2×C3#481011yescharacteristic
415C2×C3#507711yescharacteristic
416C2×C3#517011yescharacteristic
417C2×C3#517211yescharacteristic
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—42no—
431C4—361no—
432C4—361no—
433C4—361no—
434C4#6394011yescharacteristic
435C4#6394111yescharacteristic
436C4#6395011yescharacteristic
437C4#6395111yescharacteristic
438C3—21no—
439C3#6849011yescharacteristic, complemented
440C3#7126411yescharacteristic, complemented
441C2—362no—
442C2—481no—
443C2#1059151111yescharacteristic
444C2#1059159211yescharacteristic
445C2#1059159311yescharacteristic
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. #10596201C2semidirect
2. C3×#5085C2semidirect
3. #10590377C2semidirect
5. C3×#4546C2semidirect
6. #10589085C2semidirect
7. #10589082C2semidirect
31. #5085D3semidirect
37. #4546D3semidirect
121. C4⋊(C3⋊D3)SD16semidirect
382. C32#1622semidirect
439. C3#68490semidirect
440. C3#71264semidirect

Maximal subgroups

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

subgroupindex
#105962012
C3×#50852
#105903772
#105903552
C3×#45462
#105890852
#105890822
#712643
#684903