Finite Group Databasebeta

← #11779872

Subgroups — #11779872

Order 1152.

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

normal subgroups only

This group has 559 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#10593902C211yesmaximal, characteristic
2#10592393C211yesmaximal, characteristic, complemented
3#10590365C211yesmaximal, characteristic, complemented
4#10590301C211yesmaximal, characteristic, complemented
5C3×#4459C211yesmaximal, characteristic, complemented
6C3×#4456C211yesmaximal, characteristic, complemented
7#10589091C211yesmaximal, characteristic, complemented
8#68248—31nomaximal
9#68197—31nomaximal
10C2×#3799—21no—
11#64083C2211yescharacteristic
12#64078C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63911—21no—
16#63910—22no—
17#63909—21no—
18#63894—21no—
19C2×#3716—21no—
20C32×C4×C8C2211yescharacteristic
21#63648—22no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24#63573—21no—
25#63567—21no—
26#63566—21no—
27#5577—31no—
28#5553—31no—
29#5020—31no—
30#5019—31no—
31#4851—31no—
32#4841—31no—
33#4694—31no—
34#4694—31no—
35#4694—61no—
36C3×Q8⋊C8—31no—
37C3×D4⋊C8—31no—
38#4485—31no—
39#4485—31no—
40#4459D311yescharacteristic, complemented
41#4456D311yescharacteristic, complemented
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)D412yes—
45C2×#634—21no—
46C2×C3×D12D411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×Dic6D411yescharacteristic
49C2×#626—22no—
50C2×#626—22no—
51C2×#624—22no—
52#3799—42no—
53#3799—42no—
54C2×C32×C8—21no—
55C32×C42C2311yescharacteristic
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×C4×Dic3—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#3722—22no—
66#3716—42no—
67#1642—91noSylow
68C2×#239—61no—
69C2×#235—61no—
70C3×C4×Q8—31no—
71C3×C4×D4—31no—
72#940—61no—
73C2×#214—61no—
74#930—61no—
75C2×#204—61no—
76#895—62no—
77#895—61no—
78#893—61no—
79#884—62no—
80#874—31no—
81#874—31no—
82#874—61no—
83#874—61no—
84C4×D12—61no—
85C4×D12C2×D311yescharacteristic
86#869—31no—
87#869—31no—
88#869—61no—
89C4×Dic6C2×D311yescharacteristic
90C3×C4⋊C8—31no—
91C3×C4⋊C8—31no—
92C3×C4×C8—21no—
93C3×C4×C8C2×D311yescharacteristic
94C3×C4×C8C2×D311yescharacteristic
95#835—61no—
96#821—62no—
97#821—62no—
98#821—64no—
99#817—61no—
100#816—61no—
101#816—61no—
102#810—61no—
103#808—61no—
104C4⋊(C3⋊C8)C2×D311yescharacteristic
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C22×C3⋊D3—22no—
107C22×C3×D3—21no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C3⋊Dic3—41no—
112C4⋊(C3⋊D3)—42no—
113C4⋊(C3⋊D3)—41no—
114C4⋊(C3⋊D3)—41no—
115C4⋊(C3⋊D3)—41no—
116C4⋊(C3⋊D3)—41no—
117#634—41no—
118#634—41no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—21no—
122C3×D12—21no—
123C3×D12—21no—
124C3×C4×D3—41no—
125C3×C4×D3—41no—
126C3×Dic6—21no—
127C3×Dic6SD1612yescomplemented
128#626—44no—
129#626—82no—
130#624—44no—
131C32×C8—41no—
132C3×C3⋊C8—41no—
133C3×C3⋊C8—41no—
134#550—91no—
135#486—91no—
136#475—91no—
137#461—91no—
138#331—91no—
139Q8⋊C8—31no—
140D4⋊C8—31no—
141C2×C3×Q8—31no—
142C2×C3×D4—31no—
143C22×C3×C4—61no—
144C2×#67—62no—
145C2×#67—62no—
146#239—122no—
147#239—122no—
148#235—122no—
149#235—122no—
150C2×D12—32no—
151C2×D12—32no—
152C2×D12—62no—
153C2×D12—62no—
154C2×D12—61no—
155C2×D12—61no—
156C2×D12—61no—
157C2×D12—61no—
158C2×D12—62no—
159C2×D12—121no—
160C2×D12—121no—
161C2×D12D1211yescharacteristic
162C2×C4×D3—21no—
163C2×C4×D3—62no—
164C2×C4×D3—62no—
165C2×Dic6—61no—
166C2×Dic6—61no—
167C2×Dic6—121no—
168C2×Dic6D1211yescharacteristic
169C2×C3×C8—22no—
170C2×C3×C8—21no—
171C2×C3×C8—21no—
172C2×C3×C8—61no—
173C2×C3×C8—61no—
174C3×C4⋊C4—31no—
175C3×C4⋊C4—31no—
176C3×C4⋊C4—61no—
177C3×C22⋊C4—61no—
178C3×C42—21no—
179C3×C42—61no—
180C3×C42C22×D311yescharacteristic
181C3×C42C22×D311yescharacteristic
182#214—122no—
183(C2×D3)⋊C4—21no—
184(C2×D3)⋊C4—62no—
185(C2×D3)⋊C4—62no—
186C4⋊Dic3—62no—
187C4⋊Dic3—61no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3—121no—
192C4⋊Dic3D1211yescharacteristic
193C4⋊Dic3D1211yescharacteristic
194Dic3⋊C4—21no—
195C4×Dic3—21no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—21no—
198#204—122no—
199C22×C32#12011yescharacteristic
200C2×C3⋊D3—42no—
201C2×C3⋊D3—42no—
202C2×C3⋊D3—42no—
203C2×C3×D3—41no—
204C2×C3×D3—41no—
205C2×C3×D3—41no—
206C32×C4—21no—
207C32×C4C2×SD1611yescharacteristic
208C32×C4#13511yescharacteristic
209C32×C4AGL(1,ℤ/8)11yescharacteristic
210C32×C4AGL(1,ℤ/8)11yescharacteristic
211C3⋊Dic3—81no—
212C3×Dic3—22no—
213C3×Dic3—41no—
214C3×Dic3—41no—
215C2×#41—181no—
216C2×SD16—181no—
217C4⋊Q8—91no—
218#127—91no—
219#127—181no—
220#121—182no—
221#121—181no—
222C4×Q8—31no—
223C4×D4—31no—
224C4×D4—181no—
225#106—181no—
226C4⋊C8—31no—
227C4⋊C8—31no—
228#103—181no—
229#103—181no—
230#102—182no—
231C4×C8D3211yescharacteristic
232C23×C3—61no—
233C22×D3—21no—
234C22×D3—62no—
235C22×D3—62no—
236C22×D3—122no—
237C3×Q8—32no—
238C3×Q8—61no—
239C3×D4—61no—
240C3×D4—61no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—61no—
245C2×C3×C4—61no—
246C2×C3×C4—61no—
247C2×C3×C4—121no—
248C2×C3×C4—121no—
249C2×C3×C4C2×D1211yescharacteristic
250C2×C3×C4C2×D1211yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255#67—124no—
256#67—242no—
257C2×Dic3—21no—
258C2×Dic3—21no—
259C2×Dic3—21no—
260C2×Dic3—122no—
261C2×Dic3—121no—
262C2×Dic3—121no—
263D12—21no—
264D12—21no—
265D12—122no—
266D12—122no—
267D12—124no—
268D12—124no—
269D12—121no—
270D12—121no—
271D12—121no—
272D12—121no—
273D12—121no—
274D12—121no—
275D12—121no—
276D12—121no—
277D12—241no—
278D12—241no—
279D12—241no—
280D12—241no—
281D12—242no—
282C4×D3—41no—
283C4×D3—41no—
284C4×D3—124no—
285C4×D3—124no—
286Dic6—21no—
287Dic6—121no—
288Dic6—121no—
289Dic6—121no—
290Dic6—121no—
291Dic6—241no—
292Dic6—241no—
293Dic6#20412yescomplemented
294C3×C8—42no—
295C3×C8—41no—
296C3×C8—41no—
297C3×C8—121no—
298C3×C8—121no—
299C3⋊C8—41no—
300C3⋊C8—41no—
301C2×C32#44911yescharacteristic
302C2×C32#45011yescharacteristic
303C2×C32#45511yescharacteristic
304C3⋊D3—82no—
305C3×D3—81no—
306#41—362no—
307#41—362no—
308C2×Q8—31no—
309C2×Q8—181no—
310C2×D4—31no—
311C2×D4—92no—
312C2×D4—182no—
313C2×D4—182no—
314C2×D4—181no—
315C2×D4—181no—
316C22×C4—61no—
317C22×C4—182no—
318SD16—362no—
319C2×C8—21no—
320C2×C8—61no—
321C2×C8—61no—
322C4⋊C4—31no—
323C4⋊C4—31no—
324C4⋊C4—61no—
325C4⋊C4—181no—
326C4⋊C4—181no—
327C22⋊C4—61no—
328C22⋊C4—182no—
329C42—61no—
330C42C2×D3211yescharacteristic
331C22×C3—21no—
332C22×C3—121no—
333C22×C3—121no—
334C22×C3—121no—
335C22×C3#88211yescharacteristic
336C22×C3#88211yescharacteristic
337C2×D3—41no—
338C2×D3—41no—
339C2×D3—41no—
340C2×D3—122no—
341C2×D3—122no—
342C2×D3—122no—
343C2×D3—122no—
344C2×D3—122no—
345C2×D3—122no—
346C2×D3—242no—
347C2×D3—242no—
348C2×D3—242no—
349C3×C4—22no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—62no—
357C3×C4—121no—
358C3×C4—121no—
359C3×C4C2×#20411yescharacteristic
360C3×C4#90411yescharacteristic
361C3×C4#90811yescharacteristic
362C3×C4#90811yescharacteristic
363C3×C4#91111yescharacteristic
364C3×C4D3×SD1611yescharacteristic
365C3×C4#91411yescharacteristic
366C3×C4#91911yescharacteristic
367Dic3—22no—
368Dic3—41no—
369Dic3—41no—
370Dic3—242no—
371Dic3—241no—
372Dic3—241no—
373C32#164211yescharacteristic, complemented, Sylow
374C23—61no—
375C23—182no—
376Q8—32no—
377Q8—61no—
378Q8—361no—
379Q8—361no—
380D4—61no—
381D4—61no—
382D4—362no—
383D4—364no—
384D4—361no—
385D4—361no—
386D4—361no—
387D4—361no—
388D4—722no—
389C2×C4—61no—
390C2×C4—61no—
391C2×C4—61no—
392C2×C4—121no—
393C2×C4—121no—
394C2×C4—364no—
395C2×C4—361no—
396C2×C4D3×D1211yescharacteristic
397C2×C4D3×D1211yescharacteristic
398C2×C4#381111yescharacteristic
399C8—41no—
400C8—121no—
401C8—121no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—241no—
406C2×C3#473111yescharacteristic
407C2×C3#473411yescharacteristic
408C2×C3#477611yescharacteristic
409C2×C3#481011yescharacteristic
410C2×C3#482511yescharacteristic
411C2×C3#482511yescharacteristic
412D3—81no—
413D3—242no—
414D3—242no—
415D3—482no—
416C22—121no—
417C22—121no—
418C22—121no—
419C22—362no—
420C22—362no—
421C22—362no—
422C22#6392311yescharacteristic
423C4—21no—
424C4—62no—
425C4—121no—
426C4—121no—
427C4—721no—
428C4D3×#20411yescharacteristic
429C4#6379411yescharacteristic
430C4#6379511yescharacteristic
431C4#6380811yescharacteristic
432C3—21no—
433C3#6819711yescharacteristic, complemented
434C3#6824811yescharacteristic, complemented
435C2—241no—
436C2—722no—
437C2#1059039811yescharacteristic
438C2#1059094611yescharacteristic
439C2#1059096711yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#120
prime radical#10593902C2
hypercenterC4×C8D32
hypocenterC32#1642
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
2. #10592393C2semidirect
3. #10590365C2semidirect
4. #10590301C2semidirect
5. C3×#4459C2semidirect
6. C3×#4456C2semidirect
7. #10589091C2semidirect
40. #4459D3semidirect
41. #4456D3semidirect
127. C3×Dic6SD16semidirect
293. Dic6#204semidirect
373. C32#1642semidirect
433. C3#68197semidirect
434. C3#68248semidirect

Maximal subgroups

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

subgroupindex
#105939022
#105923932
#105903652
#105903012
C3×#44592
C3×#44562
#105890912
#682483
#681973