Finite Group Databasebeta

← #11779225

Subgroups — #11779225

Order 1152.

559 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 559 conjugacy classes of subgroups — too many to draw. Only its 94 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
1Dic6×D12C211yesmaximal, characteristic, complemented
2#10592393C211yesmaximal, characteristic, complemented
3#10590367C211yesmaximal, characteristic, complemented
4#10590349C211yesmaximal, characteristic
5C3×#4459C211yesmaximal, characteristic, complemented
6C3×#4456C211yesmaximal, characteristic, complemented
7#10589094C211yesmaximal, characteristic, complemented
8#68266—31nomaximal
9#68187—31nomaximal
10C2×D3×Dic6—21no—
11#64083C2211yescharacteristic
12#64078C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63918—21no—
16#63893—22no—
17Dic3×D12—21no—
18#63857—21no—
19C2×#3717—21no—
20C2×#3714—21no—
21C32×C4×C8C2211yescharacteristic
22#63648—22no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63564—21no—
26#63564—21no—
27Q8×D12—31no—
28D4×Dic6—31no—
29#5027—31no—
30#5015—31no—
31#4848—31no—
32#4843—31no—
33#4694—31no—
34#4694—31no—
35#4694—61no—
36C3×Q8⋊C8—31no—
37C3×D4⋊C8—31no—
38#4486—31no—
39#4482—31no—
40#4459D311yescharacteristic, complemented
41#4456D311yescharacteristic, complemented
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×#634—21no—
46C2×C3×D12D411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×Dic6D411yescharacteristic
49C2×#627—22no—
50C2×D3×Dic3—22no—
51D3×Dic6—42no—
52D3×Dic6—42no—
53C2×C32×C8—21no—
54C32×C42C2311yescharacteristic
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)D412yes—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3D411yescharacteristic
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—21no—
61C3×C4×Dic3—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64Dic3⋊Dic3—22no—
65(C2×D3)⋊Dic3—22no—
66#3717—42no—
67#3714—42no—
68#1627—91noSylow
69C2×D3×Q8—61no—
70C22×Dic6—61no—
71C3×C4×Q8—31no—
72C3×C4×D4—31no—
73C2×#215—61no—
74D4×Dic3—61no—
75C2×#213—61no—
76#924—61no—
77C2×D24—61no—
78C2×#204—61no—
79#897—62no—
80#897—61no—
81#888—61no—
82#878—62no—
83#874—31no—
84#874—31no—
85#874—61no—
86C4×D12—61no—
87C4×D12C2×D311yescharacteristic
88#869—31no—
89#869—31no—
90#869—61no—
91#869—61no—
92C4×Dic6C2×D311yescharacteristic
93C3×C4⋊C8—31no—
94C3×C4⋊C8—31no—
95C3×C4×C8—21no—
96C3×C4×C8C2×D311yescharacteristic
97C3×C4×C8C2×D311yescharacteristic
98#821—62no—
99#821—62no—
100#821—64no—
101#821—61no—
102#821—61no—
103#809—61no—
104#809—61no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4⋊(C3⋊C8)C2×D311yescharacteristic
107C22×C3⋊D3—41no—
108C22×C3×D3—21no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3⋊Dic3—22no—
113C4⋊(C3⋊D3)—42no—
114C4⋊(C3⋊D3)—41no—
115C4⋊(C3⋊D3)—41no—
116C4⋊(C3⋊D3)—41no—
117C4⋊(C3⋊D3)—41no—
118#634—41no—
119#634—41no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—21no—
123C3×D12—21no—
124C3×D12SD1612yescomplemented
125C3×C4×D3—41no—
126C3×C4×D3—41no—
127C3×Dic6—21no—
128C3×Dic6D812yescomplemented
129#627—44no—
130D3×Dic3—44no—
131C32×C8—41no—
132C3×C3⋊C8—41no—
133C3×C3⋊C8—41no—
134D4×Q8—91no—
135#486—91no—
136#460—91no—
137#459—91no—
138#332—91no—
139Q8⋊C8—31no—
140D4⋊C8—31no—
141C2×C3×Q8—31no—
142C2×C3×D4—31no—
143C22×C3×C4—61no—
144C22×Dic3—62no—
145D3×Q8—122no—
146D3×Q8—122no—
147C2×D12—62no—
148C2×D12—61no—
149C2×D12—61no—
150C2×D12—61no—
151C2×D12—61no—
152C2×D12—61no—
153C2×D12—61no—
154C2×D12—121no—
155C2×D12—121no—
156C2×D12D1211yescharacteristic
157C2×C4×D3—21no—
158C2×C4×D3—62no—
159C2×Dic6—62no—
160C2×Dic6—62no—
161C2×Dic6—61no—
162C2×Dic6—61no—
163C2×Dic6—121no—
164C2×Dic6—122no—
165C2×Dic6—122no—
166C2×Dic6D1211yescharacteristic
167C2×C3×C8—22no—
168C2×C3×C8—21no—
169C2×C3×C8—21no—
170C2×C3×C8—61no—
171C2×C3×C8—61no—
172C3×C4⋊C4—31no—
173C3×C4⋊C4—31no—
174C3×C4⋊C4—61no—
175C3×C22⋊C4—61no—
176C3×C42—21no—
177C3×C42—61no—
178C3×C42C22×D311yescharacteristic
179C3×C42C22×D311yescharacteristic
180#217—62no—
181#215—122no—
182#213—122no—
183(C2×D3)⋊C4—21no—
184(C2×D3)⋊C4—62no—
185C4⋊Dic3—32no—
186C4⋊Dic3—32no—
187C4⋊Dic3—62no—
188C4⋊Dic3—62no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3—121no—
192C4⋊Dic3D1211yescharacteristic
193C4⋊Dic3D1211yescharacteristic
194Dic3⋊C4—21no—
195Dic3⋊C4—62no—
196C4×Dic3—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—21no—
199D24—122no—
200#204—122no—
201C22×C32#12011yescharacteristic
202C2×C3⋊D3—81no—
203C2×C3⋊D3—81no—
204C2×C3⋊D3—81no—
205C2×C3×D3—22no—
206C2×C3×D3—41no—
207C2×C3×D3—41no—
208C32×C4—21no—
209C32×C4C2×D811yescharacteristic
210C32×C4C2×SD1611yescharacteristic
211C32×C4AGL(1,ℤ/8)11yescharacteristic
212C32×C4#13711yescharacteristic
213C3⋊Dic3—42no—
214C3×Dic3—22no—
215C3×Dic3—41no—
216C3×Dic3—41no—
217C22×Q8—181no—
218C2×SD16—181no—
219C2×D8—181no—
220C4⋊Q8—91no—
221C4⋊Q8—181no—
222#127—91no—
223C22⋊Q8—182no—
224C22⋊Q8—181no—
225C4×Q8—31no—
226C4×D4—31no—
227C4×D4—181no—
228C4⋊C8—31no—
229C4⋊C8—31no—
230#102—181no—
231#102—181no—
232#102—182no—
233C4×C8D3211yescharacteristic
234C23×C3—61no—
235C22×D3—21no—
236C22×D3—122no—
237C22×D3—121no—
238C22×D3—121no—
239C3×Q8—32no—
240C3×Q8—61no—
241C3×D4—32no—
242C3×D4—61no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—61no—
247C2×C3×C4—61no—
248C2×C3×C4—61no—
249C2×C3×C4—121no—
250C2×C3×C4—121no—
251C2×C3×C4C2×D1211yescharacteristic
252C2×C3×C4C2×D1211yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4D3×D411yescharacteristic
257C2×Dic3—21no—
258C2×Dic3—21no—
259C2×Dic3—21no—
260C2×Dic3—62no—
261C2×Dic3—62no—
262C2×Dic3—122no—
263C2×Dic3—124no—
264D12—21no—
265D12—124no—
266D12—122no—
267D12—122no—
268D12—121no—
269D12—121no—
270D12—121no—
271D12—121no—
272D12—121no—
273D12—121no—
274D12—121no—
275D12—121no—
276D12—241no—
277D12—241no—
278D12—241no—
279D12—241no—
280D12#20412yescomplemented
281C4×D3—41no—
282C4×D3—41no—
283C4×D3—124no—
284Dic6—21no—
285Dic6—124no—
286Dic6—124no—
287Dic6—121no—
288Dic6—121no—
289Dic6—121no—
290Dic6—121no—
291Dic6—241no—
292Dic6—241no—
293Dic6D2412yescomplemented
294C3×C8—42no—
295C3×C8—41no—
296C3×C8—41no—
297C3×C8—121no—
298C3×C8—121no—
299C3⋊C8—41no—
300C3⋊C8—41no—
301C2×C32#44711yescharacteristic
302C2×C32#44811yescharacteristic
303C2×C32#45411yescharacteristic
304C3⋊D3—161no—
305C3×D3—42no—
306C2×Q8—31no—
307C2×Q8—182no—
308C2×Q8—181no—
309C2×Q8—362no—
310C2×Q8—362no—
311C2×D4—31no—
312C2×D4—181no—
313C2×D4—181no—
314C2×D4—181no—
315C22×C4—61no—
316C22×C4—182no—
317SD16—362no—
318D8—362no—
319C2×C8—21no—
320C2×C8—61no—
321C2×C8—61no—
322C4⋊C4—31no—
323C4⋊C4—31no—
324C4⋊C4—61no—
325C4⋊C4—92no—
326C4⋊C4—182no—
327C4⋊C4—181no—
328C22⋊C4—61no—
329C22⋊C4—182no—
330C42—61no—
331C42C2×D3211yescharacteristic
332C22×C3—21no—
333C22×C3—62no—
334C22×C3—121no—
335C22×C3—121no—
336C22×C3#88211yescharacteristic
337C22×C3#88211yescharacteristic
338C2×D3—22no—
339C2×D3—41no—
340C2×D3—41no—
341C2×D3—242no—
342C2×D3—242no—
343C2×D3—242no—
344C2×D3—241no—
345C2×D3—241no—
346C2×D3—241no—
347C2×D3—241no—
348C2×D3—241no—
349C2×D3—241no—
350C3×C4—22no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—62no—
358C3×C4—121no—
359C3×C4—121no—
360C3×C4C2×#20411yescharacteristic
361C3×C4C2×D2411yescharacteristic
362C3×C4#90811yescharacteristic
363C3×C4#90911yescharacteristic
364C3×C4D3×D811yescharacteristic
365C3×C4D3×SD1611yescharacteristic
366C3×C4#91411yescharacteristic
367C3×C4#91811yescharacteristic
368Dic3—22no—
369Dic3—41no—
370Dic3—41no—
371Dic3—122no—
372Dic3—122no—
373Dic3—242no—
374C32#162711yescharacteristic, complemented, Sylow
375C23—61no—
376C23—361no—
377Q8—32no—
378Q8—61no—
379Q8—364no—
380Q8—361no—
381Q8—361no—
382D4—32no—
383D4—61no—
384D4—362no—
385D4—361no—
386D4—361no—
387D4—361no—
388D4—361no—
389C2×C4—61no—
390C2×C4—61no—
391C2×C4—61no—
392C2×C4—121no—
393C2×C4—121no—
394C2×C4—182no—
395C2×C4—364no—
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—122no—
406C2×C3#473211yescharacteristic
407C2×C3#473811yescharacteristic
408C2×C3#477311yescharacteristic
409C2×C3#480611yescharacteristic
410C2×C3#482711yescharacteristic
411C2×C3#482711yescharacteristic
412D3—42no—
413D3—482no—
414D3—481no—
415D3—481no—
416C22—62no—
417C22—121no—
418C22—121no—
419C22—721no—
420C22—721no—
421C22—721no—
422C22#6392311yescharacteristic
423C4—21no—
424C4—62no—
425C4—121no—
426C4—121no—
427C4—362no—
428C4D3×#20411yescharacteristic
429C4D3×D2411yescharacteristic
430C4#6379411yescharacteristic
431C4#6380111yescharacteristic
432C3—21no—
433C3#6818711yescharacteristic, complemented
434C3#6826611yescharacteristic, complemented
435C2—122no—
436C2—1441no—
437C2#1059040211yescharacteristic
438C2#1059094711yescharacteristic
439C2#1059095111yescharacteristic
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. Dic6×D12C2semidirect
2. #10592393C2semidirect
3. #10590367C2semidirect
5. C3×#4459C2semidirect
6. C3×#4456C2semidirect
7. #10589094C2semidirect
40. #4459D3semidirect
41. #4456D3semidirect
124. C3×D12SD16semidirect
128. C3×Dic6D8semidirect
280. D12#204semidirect
293. Dic6D24semidirect
374. C32#1627semidirect
433. C3#68187semidirect
434. C3#68266semidirect

Maximal subgroups

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

subgroupindex
Dic6×D122
#105923932
#105903672
#105903492
C3×#44592
C3×#44562
#105890942
#682663
#681873