Finite Group Databasebeta

← #11779229

Subgroups — #11779229

Order 1152.

564 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 92 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#10593904C211yesmaximal, characteristic, complemented
2#10592547C211yesmaximal, characteristic, complemented
3#10590349C211yesmaximal, characteristic
4#10590281C211yesmaximal, characteristic, complemented
5C3×#4483C211yesmaximal, characteristic, complemented
6C3×#4482C211yesmaximal, characteristic, complemented
7#10589085C211yesmaximal, characteristic, complemented
8#68457—31nomaximal
9#68187—31nomaximal
10C2×D3×Dic6—21no—
11C2×#3744—21no—
12#64083C2211yescharacteristic
13C4×#634C2211yescharacteristic
14C3×C4×D12C2211yescharacteristic
15C3×#869C2211yescharacteristic
16#63919—21no—
17#63899—22no—
18#63898—21no—
19#63856—21no—
20C2×#3714—21no—
21C32×C4⋊C8C2211yescharacteristic
22#63648—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63564—22no—
26#63564—21no—
27#5727—31no—
28D4×Dic6—31no—
29#5088—31no—
30#5015—31no—
31#4848—31no—
32#4848—31no—
33#4848—61no—
34#4843—31no—
35#4694—31no—
36C3×#332—31no—
37C3×D4⋊C8—31no—
38#4484—31no—
39#4483D311yescharacteristic, complemented
40#4482D311yescharacteristic, complemented
41#4456—31no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×#634D411yescharacteristic
46C2×C3×D12D411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×Dic6—21no—
49C2×#627—22no—
50C2×D3×Dic3—22no—
51D3×Dic6—42no—
52D3×Dic6—42no—
53C2×C32×C8—21no—
54C32×C42C2311yescharacteristic
55C4⋊(C3⋊Dic3)D411yescharacteristic
56#3750—21no—
57C4×C3⋊Dic3—21no—
58#3744—42no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D412yes—
62C3×C4⋊Dic3D411yescharacteristic
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#3724—22no—
66(C2×D3)⋊Dic3—22no—
67#3714—42no—
68#1627—91noSylow
69C2×D3×Q8—61no—
70C22×Dic6—61no—
71C3×C4⋊Q8—31no—
72C3×C4×D4—31no—
73#946—61no—
74D4×Dic3—61no—
75C2×#213—61no—
76#924—61no—
77C2×D24—61no—
78C2×#204—61no—
79C2×#204—61no—
80C2×#204—62no—
81#896—62no—
82#893—61no—
83#888—61no—
84#888—61no—
85#878—62no—
86#874—31no—
87#874—31no—
88#874—61no—
89C4×D12C2×D311yescharacteristic
90#869C2×D311yescharacteristic
91C4×Dic6—31no—
92C4×Dic6—31no—
93C4×Dic6—61no—
94C3×C4⋊C8—21no—
95C3×C4⋊C8—31no—
96C3×C4⋊C8C2×D311yescharacteristic
97C3×C4⋊C8C2×D311yescharacteristic
98C3×C4×C8—31no—
99#821—61no—
100#821—61no—
101#821—62no—
102#821—62no—
103#821—61no—
104#809—61no—
105#809—62no—
106C4⋊(C3⋊C8)C2×D311yescharacteristic
107C4×C3⋊C8C2×D311yescharacteristic
108C22×C3⋊D3—41no—
109C22×C3×D3—21no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C3⋊Dic3—21no—
114C2×C3⋊Dic3—21no—
115C4⋊(C3⋊D3)—41no—
116C4⋊(C3⋊D3)—41no—
117C4⋊(C3⋊D3)—42no—
118C4⋊(C3⋊D3)—41no—
119C4⋊(C3⋊D3)—41no—
120#634—21no—
121#634D812yescomplemented
122C2×C3×Dic3—22no—
123C2×C3×Dic3—21no—
124C3×D12—21no—
125C3×D12SD1612yescomplemented
126C3×C4×D3—41no—
127C3×C4×D3—41no—
128C3×Dic6—41no—
129C3×Dic6—41no—
130#627—44no—
131D3×Dic3—44no—
132C32×C8—41no—
133C3×C3⋊C8—41no—
134C3×C3⋊C8—41no—
135D4×Q8—91no—
136#486—91no—
137#460—91no—
138#459—91no—
139#332—31no—
140Q8⋊C8—91no—
141D4⋊C8—31no—
142C2×C3×Q8—61no—
143C2×C3×D4—31no—
144C22×C3×C4—61no—
145C22×Dic3—62no—
146D3×Q8—122no—
147D3×Q8—122no—
148C2×D12—62no—
149C2×D12—61no—
150C2×D12—61no—
151C2×D12—61no—
152C2×D12—61no—
153C2×D12—61no—
154C2×D12—61no—
155C2×D12—121no—
156C2×D12—121no—
157C2×D12D1211yescharacteristic
158C2×C4×D3—21no—
159C2×C4×D3—62no—
160C2×Dic6—21no—
161C2×Dic6—31no—
162C2×Dic6—31no—
163C2×Dic6—61no—
164C2×Dic6—62no—
165C2×Dic6—62no—
166C2×Dic6—122no—
167C2×Dic6—122no—
168C2×C3×C8—22no—
169C2×C3×C8—21no—
170C2×C3×C8—21no—
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C3×C4⋊C4—31no—
174C3×C4⋊C4—32no—
175C3×C4⋊C4—61no—
176C3×C22⋊C4—61no—
177C3×C42—21no—
178C3×C42C22×D311yescharacteristic
179C3×C42C22×D311yescharacteristic
180#217—62no—
181#213—122no—
182(C2×D3)⋊C4—21no—
183(C2×D3)⋊C4—62no—
184C4⋊Dic3—21no—
185C4⋊Dic3—31no—
186C4⋊Dic3—31no—
187C4⋊Dic3—61no—
188C4⋊Dic3D1212yes—
189C4⋊Dic3D1211yescharacteristic
190Dic3⋊C4—62no—
191Dic3⋊C4—62no—
192Dic3⋊C4—61no—
193Dic3⋊C4—61no—
194Dic3⋊C4—121no—
195C4×Dic3—61no—
196C4×Dic3—61no—
197C4×Dic3—121no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200D24—122no—
201#204—122no—
202#204—122no—
203#204—124no—
204C22×C32#12011yescharacteristic
205C2×C3⋊D3—81no—
206C2×C3⋊D3—81no—
207C2×C3⋊D3—81no—
208C2×C3×D3—22no—
209C2×C3×D3—41no—
210C2×C3×D3—41no—
211C32×C4—21no—
212C32×C4C2×D811yescharacteristic
213C32×C4C2×SD1611yescharacteristic
214C32×C4AGL(1,ℤ/8)11yescharacteristic
215C32×C4#13711yescharacteristic
216C3⋊Dic3—22no—
217C3⋊Dic3—41no—
218C3×Dic3—42no—
219C3×Dic3—41no—
220C22×Q8—181no—
221C2×SD16—181no—
222C2×D8—181no—
223C4⋊Q8—31no—
224C4⋊Q8—181no—
225#127—91no—
226C22⋊Q8—182no—
227C22⋊Q8—181no—
228C4×Q8—91no—
229C4×D4—31no—
230C4×D4—181no—
231C4⋊C8—31no—
232C4⋊C8D3211yescharacteristic
233#102—181no—
234#102—182no—
235#102—181no—
236C4×C8—31no—
237C23×C3—61no—
238C22×D3—21no—
239C22×D3—122no—
240C22×D3—121no—
241C22×D3—121no—
242C3×Q8—121no—
243C3×Q8—121no—
244C3×D4—32no—
245C3×D4—61no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—61no—
250C2×C3×C4—62no—
251C2×C3×C4—121no—
252C2×C3×C4—121no—
253C2×C3×C4C2×D1211yescharacteristic
254C2×C3×C4C2×D1211yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4D3×D411yescharacteristic
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4D3×D411yescharacteristic
259C2×Dic3—21no—
260C2×Dic3—22no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264C2×Dic3—61no—
265C2×Dic3—121no—
266C2×Dic3—121no—
267C2×Dic3—124no—
268D12—21no—
269D12—122no—
270D12—122no—
271D12—122no—
272D12—122no—
273D12—121no—
274D12—121no—
275D12—121no—
276D12—121no—
277D12—121no—
278D12—121no—
279D12—121no—
280D12—121no—
281D12—241no—
282D12—241no—
283D12—242no—
284D12#20412yescomplemented
285C4×D3—41no—
286C4×D3—41no—
287C4×D3—124no—
288Dic6—32no—
289Dic6—32no—
290Dic6—41no—
291Dic6—41no—
292Dic6—62no—
293Dic6—61no—
294Dic6—61no—
295Dic6—121no—
296Dic6—124no—
297Dic6—124no—
298C3×C8—42no—
299C3×C8—41no—
300C3×C8—41no—
301C3×C8—121no—
302C3×C8—121no—
303C3⋊C8—41no—
304C3⋊C8—41no—
305C2×C32#44711yescharacteristic
306C2×C32#44811yescharacteristic
307C2×C32#45411yescharacteristic
308C3⋊D3—161no—
309C3×D3—42no—
310C2×Q8—61no—
311C2×Q8—91no—
312C2×Q8—182no—
313C2×Q8—362no—
314C2×Q8—362no—
315C2×D4—31no—
316C2×D4—181no—
317C2×D4—181no—
318C2×D4—181no—
319C22×C4—61no—
320C22×C4—182no—
321SD16—362no—
322D8—362no—
323C2×C8—21no—
324C2×C8—61no—
325C2×C8—61no—
326C4⋊C4—31no—
327C4⋊C4—32no—
328C4⋊C4—61no—
329C4⋊C4—91no—
330C4⋊C4—182no—
331C4⋊C4—181no—
332C22⋊C4—61no—
333C22⋊C4—182no—
334C42—181no—
335C42C2×D3211yescharacteristic
336C22×C3—21no—
337C22×C3—62no—
338C22×C3—121no—
339C22×C3—121no—
340C22×C3#88211yescharacteristic
341C22×C3#88211yescharacteristic
342C2×D3—22no—
343C2×D3—41no—
344C2×D3—41no—
345C2×D3—242no—
346C2×D3—242no—
347C2×D3—242no—
348C2×D3—241no—
349C2×D3—241no—
350C2×D3—241no—
351C2×D3—241no—
352C2×D3—241no—
353C2×D3—241no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—41no—
361C3×C4—121no—
362C3×C4—122no—
363C3×C4C2×#20411yescharacteristic
364C3×C4#90911yescharacteristic
365C3×C4D3×D811yescharacteristic
366C3×C4D3×D811yescharacteristic
367C3×C4D3×SD1611yescharacteristic
368C3×C4#91411yescharacteristic
369C3×C4#91411yescharacteristic
370C3×C4#91811yescharacteristic
371Dic3—42no—
372Dic3—41no—
373Dic3—62no—
374Dic3—62no—
375Dic3—122no—
376Dic3—121no—
377Dic3—121no—
378Dic3—241no—
379C32#162711yescharacteristic, complemented, Sylow
380C23—61no—
381C23—361no—
382Q8—92no—
383Q8—121no—
384Q8—121no—
385Q8—181no—
386Q8—364no—
387D4—32no—
388D4—61no—
389D4—362no—
390D4—361no—
391D4—361no—
392D4—361no—
393D4—361no—
394C2×C4—61no—
395C2×C4—62no—
396C2×C4—121no—
397C2×C4—121no—
398C2×C4—181no—
399C2×C4—181no—
400C2×C4—364no—
401C2×C4D3×D1211yescharacteristic
402C2×C4D3×D1211yescharacteristic
403C2×C4#381111yescharacteristic
404C8—41no—
405C8—121no—
406C8—121no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—122no—
411C2×C3#473811yescharacteristic
412C2×C3#475311yescharacteristic
413C2×C3#477311yescharacteristic
414C2×C3#477311yescharacteristic
415C2×C3#480611yescharacteristic
416C2×C3#482711yescharacteristic
417D3—42no—
418D3—482no—
419D3—481no—
420D3—481no—
421C22—62no—
422C22—121no—
423C22—121no—
424C22—721no—
425C22—721no—
426C22—721no—
427C22#6392311yescharacteristic
428C4—21no—
429C4—121no—
430C4—122no—
431C4—182no—
432C4—361no—
433C4D3×#20411yescharacteristic
434C4#6380111yescharacteristic
435C4#6392611yescharacteristic
436C4#6394111yescharacteristic
437C3—21no—
438C3#6818711yescharacteristic, complemented
439C3#6845711yescharacteristic, complemented
440C2—122no—
441C2—1441no—
442C2#1059059811yescharacteristic
443C2#1059095111yescharacteristic
444C2#1059102211yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10590349C2
hypercenterC4⋊C8D32
hypocenterC32#1627
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
1. #10593904C2semidirect
2. #10592547C2semidirect
4. #10590281C2semidirect
5. C3×#4483C2semidirect
6. C3×#4482C2semidirect
7. #10589085C2semidirect
39. #4483D3semidirect
40. #4482D3semidirect
121. #634D8semidirect
125. C3×D12SD16semidirect
284. D12#204semidirect
379. C32#1627semidirect
438. C3#68187semidirect
439. C3#68457semidirect

Maximal subgroups

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

subgroupindex
#105939042
#105925472
#105903492
#105902812
C3×#44832
C3×#44822
#105890852
#684573
#681873