Finite Group Databasebeta

← #11779236

Subgroups — #11779236

Order 1152.

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

normal subgroups only

This group has 570 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#10593903C211yesmaximal, characteristic, complemented
2#10592542C211yesmaximal, characteristic
3#10590367C211yesmaximal, characteristic, complemented
4#10590281C211yesmaximal, characteristic, complemented
5C3×#4486C211yesmaximal, characteristic, complemented
6C3×#4484C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic, complemented
8#68457—31nomaximal
9#68266—31nomaximal
10C2×#3797—21no—
11C2×#3745—21no—
12#64083C2211yescharacteristic
13C4×C4⋊(C3⋊D3)C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C3×C4×Dic6C2211yescharacteristic
16#63918—21no—
17#63895—22no—
18#63894—21no—
19#63871—21no—
20C2×#3717—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—
28Q8×D12—31no—
29#5088—31no—
30#5027—31no—
31#4848—31no—
32#4843—31no—
33#4843—31no—
34#4843—61no—
35#4694—31no—
36C3×#332—31no—
37C3×Q8⋊C8—31no—
38#4486D311yescharacteristic, complemented
39#4484D311yescharacteristic, complemented
40#4483—31no—
41#4459—31no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)D411yescharacteristic
46C2×C4×C3⋊D3—21no—
47C2×C3×Dic6—21no—
48C2×C3×Dic6D411yescharacteristic
49C2×#627—22no—
50C2×#624—22no—
51#3797—42no—
52#3797—42no—
53C2×C32×C8—21no—
54C32×C42C2311yescharacteristic
55#3752—21no—
56C4⋊(C3⋊Dic3)D411yescharacteristic
57#3745—42no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×C4⋊Dic3D412yes—
61C3×Dic3⋊C4—21no—
62C3×C4×Dic3—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65Dic3⋊Dic3—22no—
66#3722—22no—
67#3717—42no—
68#1627—91noSylow
69C2×D3×Q8—61no—
70C2×D3×Q8—61no—
71C3×C4⋊Q8—31no—
72C3×C4×Q8—31no—
73#946—61no—
74C2×#215—61no—
75C2×D24—61no—
76C2×D24—61no—
77C2×D24—62no—
78C2×#204—61no—
79#897—61no—
80#897—62no—
81#896—62no—
82#893—61no—
83#888—61no—
84#874—31no—
85#874—31no—
86#874—61no—
87C4×D12—31no—
88C4×D12—31no—
89C4×D12—61no—
90C4×D12—61no—
91#869—61no—
92#869C2×D311yescharacteristic
93C4×Dic6C2×D311yescharacteristic
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—21no—
109C22×C3⋊D3—41no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C3⋊Dic3—21no—
114C4⋊(C3⋊D3)—21no—
115C4⋊(C3⋊D3)—41no—
116C4⋊(C3⋊D3)—41no—
117C4⋊(C3⋊D3)—42no—
118C4⋊(C3⋊D3)—41no—
119C4⋊(C3⋊D3)—41no—
120C4⋊(C3⋊D3)SD1612yescomplemented
121C4×C3⋊D3—41no—
122C4×C3⋊D3—41no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—22no—
126C3×Dic6—21no—
127C3×Dic6—41no—
128C3×Dic6—41no—
129C3×Dic6D812yescomplemented
130#627—44no—
131#624—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—31no—
141D4⋊C8—91no—
142C2×C3×Q8—31no—
143C2×C3×Q8—61no—
144D3×Q8—122no—
145D3×Q8—122no—
146D3×Q8—122no—
147D3×Q8—122no—
148C2×D12—31no—
149C2×D12—31no—
150C2×D12—61no—
151C2×D12—62no—
152C2×D12—61no—
153C2×D12—61no—
154C2×D12—61no—
155C2×D12—61no—
156C2×D12—61no—
157C2×D12—61no—
158C2×D12—121no—
159C2×D12—121no—
160C2×C4×D3—62no—
161C2×C4×D3—62no—
162C2×C4×D3—61no—
163C2×C4×D3—61no—
164C2×C4×D3—121no—
165C2×Dic6—21no—
166C2×Dic6—62no—
167C2×Dic6—62no—
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—32no—
175C3×C4⋊C4—31no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C42—21no—
179C3×C42—61no—
180C3×C42C22×D311yescharacteristic
181C3×C42C22×D311yescharacteristic
182#215—122no—
183(C2×D3)⋊C4—62no—
184(C2×D3)⋊C4—62no—
185(C2×D3)⋊C4—61no—
186(C2×D3)⋊C4—61no—
187(C2×D3)⋊C4—121no—
188C4⋊Dic3—21no—
189C4⋊Dic3—31no—
190C4⋊Dic3—31no—
191C4⋊Dic3—61no—
192C4⋊Dic3—62no—
193C4⋊Dic3D1211yescharacteristic
194C4⋊Dic3D1212yes—
195Dic3⋊C4—21no—
196Dic3⋊C4—62no—
197C4×Dic3—21no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200D24—122no—
201D24—122no—
202D24—124no—
203#204—122no—
204C22×C32#12011yescharacteristic
205C2×C3⋊D3—22no—
206C2×C3⋊D3—41no—
207C2×C3⋊D3—41no—
208C2×C3⋊D3—81no—
209C2×C3⋊D3—81no—
210C2×C3⋊D3—81no—
211C32×C4—21no—
212C32×C4C2×D811yescharacteristic
213C32×C4C2×SD1611yescharacteristic
214C32×C4AGL(1,ℤ/8)11yescharacteristic
215C32×C4#13711yescharacteristic
216C3⋊Dic3—41no—
217C3×Dic3—22no—
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—31no—
229C4×D4—91no—
230C4×D4—181no—
231C4⋊C8—31no—
232C4⋊C8D3211yescharacteristic
233#102—181no—
234#102—182no—
235#102—181no—
236C4×C8—31no—
237C22×D3—61no—
238C22×D3—61no—
239C22×D3—121no—
240C22×D3—122no—
241C22×D3—121no—
242C22×D3—121no—
243C3×Q8—32no—
244C3×Q8—61no—
245C3×Q8—121no—
246C3×Q8—121no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—61no—
251C2×C3×C4—62no—
252C2×C3×C4—61no—
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—21no—
261C2×Dic3—22no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264C2×Dic3—121no—
265D12—32no—
266D12—32no—
267D12—62no—
268D12—61no—
269D12—61no—
270D12—121no—
271D12—122no—
272D12—122no—
273D12—122no—
274D12—122no—
275D12—121no—
276D12—121no—
277D12—121no—
278D12—121no—
279D12—121no—
280D12—121no—
281D12—121no—
282D12—121no—
283D12—241no—
284D12—241no—
285D12—242no—
286C4×D3—124no—
287C4×D3—124no—
288C4×D3—121no—
289C4×D3—121no—
290C4×D3—121no—
291C4×D3—121no—
292C4×D3—241no—
293C4×D3—241no—
294Dic6—21no—
295Dic6—41no—
296Dic6—41no—
297Dic6—124no—
298Dic6—124no—
299Dic6D2412yescomplemented
300C3×C8—42no—
301C3×C8—41no—
302C3×C8—41no—
303C3×C8—121no—
304C3×C8—121no—
305C3⋊C8—41no—
306C3⋊C8—41no—
307C2×C32#44711yescharacteristic
308C2×C32#44811yescharacteristic
309C2×C32#45411yescharacteristic
310C3⋊D3—42no—
311C3⋊D3—161no—
312C2×Q8—31no—
313C2×Q8—61no—
314C2×Q8—182no—
315C2×Q8—362no—
316C2×Q8—362no—
317C2×D4—91no—
318C2×D4—181no—
319C2×D4—181no—
320C2×D4—181no—
321C22×C4—182no—
322C22×C4—181no—
323SD16—362no—
324D8—362no—
325C2×C8—21no—
326C2×C8—61no—
327C2×C8—61no—
328C4⋊C4—31no—
329C4⋊C4—32no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C4⋊C4—91no—
333C4⋊C4—182no—
334C22⋊C4—182no—
335C22⋊C4—181no—
336C42—61no—
337C42C2×D3211yescharacteristic
338C22×C3—21no—
339C22×C3#88211yescharacteristic
340C22×C3#88211yescharacteristic
341C2×D3—62no—
342C2×D3—62no—
343C2×D3—122no—
344C2×D3—121no—
345C2×D3—121no—
346C2×D3—121no—
347C2×D3—121no—
348C2×D3—241no—
349C2×D3—241no—
350C2×D3—242no—
351C2×D3—242no—
352C2×D3—242no—
353C2×D3—241no—
354C2×D3—241no—
355C2×D3—241no—
356C2×D3—241no—
357C2×D3—241no—
358C2×D3—241no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—41no—
366C3×C4—62no—
367C3×C4—122no—
368C3×C4—121no—
369C3×C4C2×D2411yescharacteristic
370C3×C4#90811yescharacteristic
371C3×C4D3×D811yescharacteristic
372C3×C4D3×SD1611yescharacteristic
373C3×C4D3×SD1611yescharacteristic
374C3×C4#91411yescharacteristic
375C3×C4#91811yescharacteristic
376C3×C4#91811yescharacteristic
377Dic3—22no—
378Dic3—42no—
379Dic3—41no—
380Dic3—121no—
381Dic3—121no—
382Dic3—241no—
383C32#162711yescharacteristic, complemented, Sylow
384C23—181no—
385C23—361no—
386Q8—32no—
387Q8—61no—
388Q8—121no—
389Q8—121no—
390Q8—364no—
391D4—92no—
392D4—181no—
393D4—362no—
394D4—361no—
395D4—361no—
396D4—361no—
397D4—361no—
398C2×C4—61no—
399C2×C4—61no—
400C2×C4—62no—
401C2×C4—181no—
402C2×C4—364no—
403C2×C4—361no—
404C2×C4—361no—
405C2×C4D3×D1211yescharacteristic
406C2×C4D3×D1211yescharacteristic
407C2×C4#381111yescharacteristic
408C8—41no—
409C8—121no—
410C8—121no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3#473211yescharacteristic
415C2×C3#475311yescharacteristic
416C2×C3#477311yescharacteristic
417C2×C3#480611yescharacteristic
418C2×C3#480611yescharacteristic
419C2×C3#482711yescharacteristic
420D3—122no—
421D3—122no—
422D3—242no—
423D3—482no—
424D3—481no—
425D3—481no—
426C22—182no—
427C22—361no—
428C22—361no—
429C22—721no—
430C22—721no—
431C22—721no—
432C22#6392311yescharacteristic
433C4—21no—
434C4—62no—
435C4—121no—
436C4—122no—
437C4—361no—
438C4D3×D2411yescharacteristic
439C4#6379411yescharacteristic
440C4#6393011yescharacteristic
441C4#6394511yescharacteristic
442C3—21no—
443C3#6826611yescharacteristic, complemented
444C3#6845711yescharacteristic, complemented
445C2—362no—
446C2—1441no—
447C2#1059060611yescharacteristic
448C2#1059094711yescharacteristic
449C2#1059102211yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10592542C2
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. #10593903C2semidirect
3. #10590367C2semidirect
4. #10590281C2semidirect
5. C3×#4486C2semidirect
6. C3×#4484C2semidirect
7. #10589082C2semidirect
38. #4486D3semidirect
39. #4484D3semidirect
120. C4⋊(C3⋊D3)SD16semidirect
129. C3×Dic6D8semidirect
299. Dic6D24semidirect
383. C32#1627semidirect
443. C3#68266semidirect
444. C3#68457semidirect

Maximal subgroups

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

subgroupindex
#105939032
#105925422
#105903672
#105902812
C3×#44862
C3×#44842
#105890822
#684573
#682663