Finite Group Databasebeta

← #11796682

Subgroups — #11796682

Order 1152.

497 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 497 conjugacy classes of subgroups — too many to draw. Only its 114 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
1C2×#63808C211yesmaximal, characteristic
2C3×D3×#107C211yesmaximal, characteristic, complemented
3C2×#63543C211yesmaximal, characteristic, complemented
4#10589357C211yesmaximal, characteristic, complemented
5C3×#4492C211yesmaximal, characteristic, complemented
6#10589117C211yesmaximal, characteristic, complemented
7#10589116C211yesmaximal, characteristic, complemented
8#70598—31nomaximal
9#69221—31nomaximal
10C2×#3799—21no—
11C2×#3745C2211yescharacteristic
12C2×C3×Dic12C2211yescharacteristic
13C2×C3×D3×C8C2211yescharacteristic
14C3×D3×C4⋊C4—21no—
15C2×#3717—21no—
16#63808—22no—
17#63808C414yescomplemented
18C32×#107C2211yescharacteristic
19C2×C3⋊(C3⋊C16)C2211yescharacteristic
20C3×#818C2211yescharacteristic
21C2×C3×C3⋊C16C2211yescharacteristic
22C3×#807—21no—
23#63543—22no—
24C2×#919—31no—
25C2×#904—31no—
26C2×C3×#107—31no—
27C2×#812—31no—
28C2×#798—31no—
29D3×#107D311yescharacteristic, complemented
30C3×#358—31no—
31#4564—31no—
32#4509—31no—
33#4492—31no—
34#4492D311yescharacteristic, complemented
35#4491—31no—
36#4491—31no—
37#4491—31no—
38#4491—61no—
39C2×C4⋊(C3⋊D3)—21no—
40C2×C3×C4×D3—41no—
41C2×C3×C4×D3D411yescharacteristic
42C2×C3×Dic6—21no—
43C2×#626—41no—
44C2×#624—41no—
45#3799—24no—
46#3799—42no—
47C2×C32×C8C2311yescharacteristic
48C32×C4⋊C4—21no—
49#3745—21no—
50#3745C2×C412yescomplemented
51C3×C4⋊Dic3—21no—
52C3×Dic3⋊C4—41no—
53C2×C3×C3⋊C8D411yescharacteristic
54C3×Dic12—21no—
55C3×Dic12C2×C412yescomplemented
56C3×D3×C8C2×C412yes—
57C3×D3×C8D412yes—
58#3717—24no—
59C3⋊(C3⋊C16)—21no—
60C3×C3⋊C16—21no—
61#2139—91noSylow
62C2×#239—61no—
63C2×#235—61no—
64C2×C3×Q16—31no—
65C22×C3×C8—31no—
66C2×C3×C4⋊C4—61no—
67C2×#215—61no—
68#919—34no—
69#919—62no—
70C2×Dic12C2×D311yescharacteristic
71#904—34no—
72#904—62no—
73C2×D24—31no—
74C2×D24—31no—
75C2×D24—61no—
76C2×#204—61no—
77C2×D3×C8C2×D311yescharacteristic
78D3×C4⋊C4—21no—
79C2×C3×C16—31no—
80C3×#107—21no—
81C3×#107—31no—
82C3×#107—61no—
83C3×#107C2×D311yescharacteristic
84C3×#107C2×D311yescharacteristic
85#818C2×D311yescharacteristic
86#812—62no—
87C2×C3⋊C16—31no—
88C2×C3⋊C16—31no—
89C2×C3⋊C16—61no—
90C2×C3⋊C16C2×D311yescharacteristic
91#807—21no—
92#798—62no—
93C22×C3⋊D3—41no—
94C22×C3×D3D811yescharacteristic
95C2×C32×C4—41no—
96C2×C32×C4C2×D411yescharacteristic
97C4⋊(C3⋊D3)—22no—
98C4⋊(C3⋊D3)—41no—
99C2×C3×Dic3—41no—
100C2×C3×Dic3—41no—
101C2×C3×Dic3D811yescharacteristic
102C3×C4×D3—82no—
103C3×C4×D3C22⋊C412yes—
104C3×C4×D3SD1612yes—
105C3×Dic6—22no—
106C3×Dic6—41no—
107#626—44no—
108#624—44no—
109C32×C8C22×C411yescharacteristic
110C32×C8C2×D411yescharacteristic
111C3×C3⋊C8C22⋊C412yes—
112C2×#135—91no—
113C2×M32—91no—
114C2×#107—31no—
115#358—31no—
116#358—91no—
117#357—91no—
118#357—91no—
119C2×C3×Q8—61no—
120C22×C3×C4—31no—
121C22×C3×C4—121no—
122C2×#67—121no—
123#239—64no—
124#239—122no—
125#235—64no—
126#235—122no—
127C2×D12—61no—
128C2×D12—61no—
129C2×D12—121no—
130C2×D12—121no—
131C2×C4×D3—41no—
132C2×C4×D3—121no—
133C2×C4×D3—121no—
134C2×C4×D3#6711yescharacteristic
135C2×Dic6—21no—
136C3×Q16—32no—
137C3×Q16—61no—
138C2×C3×C8—21no—
139C2×C3×C8—31no—
140C2×C3×C8—32no—
141C2×C3×C8—32no—
142C2×C3×C8C22×D311yescharacteristic
143C2×C3×C8C22×D311yescharacteristic
144C3×C4⋊C4—21no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—41no—
147C3×C4⋊C4—61no—
148C3×C4⋊C4—121no—
149#215—64no—
150C4⋊Dic3—21no—
151Dic3⋊C4—41no—
152C2×C3⋊C8#6711yescharacteristic
153Dic12—21no—
154Dic12C4×D312yescomplemented
155D24—32no—
156D24—32no—
157D24—62no—
158D24—61no—
159D24—61no—
160D24—121no—
161#204—64no—
162D3×C8C4×D312yes—
163D3×C8D1212yes—
164C3×C16—61no—
165C3⋊C16—21no—
166C3⋊C16—61no—
167C3⋊C16—61no—
168C3⋊C16—121no—
169C22×C32C2×D811yescharacteristic
170C2×C3⋊D3—42no—
171C2×C3⋊D3—81no—
172C2×C3⋊D3—81no—
173C2×C3×D3—21no—
174C2×C3×D3—21no—
175C2×C3×D3#10212yes—
176C32×C4—81no—
177C32×C4C2×C22⋊C411yescharacteristic
178C32×C4C2×SD1611yescharacteristic
179C3×Dic3—42no—
180C3×Dic3—81no—
181C3×Dic3#10212yes—
182C2×#41—181no—
183#135—94no—
184#135—182no—
185C2×Q16—31no—
186C2×SD16—181no—
187C2×D8—91no—
188C22×C8—31no—
189C2×C4⋊C4—61no—
190M32—182no—
191C2×C16—31no—
192C2×C16—91no—
193#107—31no—
194#107—61no—
195#107D3211yescharacteristic
196C23×C3—31no—
197C22×D3—121no—
198C22×D3—121no—
199C22×D3—241no—
200C22×D3#21311yescharacteristic
201C3×Q8—62no—
202C3×Q8—121no—
203C2×C3×C4—21no—
204C2×C3×C4—31no—
205C2×C3×C4—32no—
206C2×C3×C4—32no—
207C2×C3×C4—41no—
208C2×C3×C4—41no—
209C2×C3×C4—81no—
210C2×C3×C4—121no—
211C2×C3×C4—121no—
212C2×C3×C4—242no—
213C2×C3×C4D3×D411yescharacteristic
214C2×C3×C4C2×#6711yescharacteristic
215#67—124no—
216C2×Dic3—41no—
217C2×Dic3—41no—
218C2×Dic3#21311yescharacteristic
219D12—62no—
220D12—62no—
221D12—122no—
222D12—124no—
223D12—121no—
224D12—121no—
225D12—241no—
226C4×D3—82no—
227C4×D3—124no—
228C4×D3—124no—
229C4×D3(C2×D3)⋊C412yes—
230C4×D3#21512yes—
231Dic6—22no—
232Dic6—41no—
233C3×C8—21no—
234C3×C8—21no—
235C3×C8—32no—
236C3×C8C2×C4×D311yescharacteristic
237C3×C8C2×C4×D311yescharacteristic
238C3×C8C2×D1211yescharacteristic
239C3×C8D3×D411yescharacteristic
240C3⋊C8(C2×D3)⋊C412yes—
241C2×C32C2×#10211yescharacteristic
242C2×C32#50911yescharacteristic
243C2×C32#51011yescharacteristic
244C3⋊D3—82no—
245C3×D3—22no—
246#41—184no—
247#41—362no—
248C2×Q8—61no—
249C2×D4—181no—
250C2×D4—361no—
251C22×C4—31no—
252C22×C4—121no—
253C22×C4—361no—
254Q16—32no—
255Q16—61no—
256SD16—184no—
257D8—92no—
258D8—181no—
259C2×C8—31no—
260C2×C8—32no—
261C2×C8—32no—
262C2×C8C2×D3211yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—61no—
265C4⋊C4—121no—
266C16—61no—
267C16—181no—
268C22×C3—21no—
269C22×C3—32no—
270C22×C3—61no—
271C22×C3—61no—
272C22×C3D3×D811yescharacteristic
273C22×C3C2×#21311yescharacteristic
274C2×D3—21no—
275C2×D3—21no—
276C2×D3—122no—
277C2×D3—122no—
278C2×D3—242no—
279C2×D3—241no—
280C2×D3—241no—
281C2×D3—241no—
282C2×D3—241no—
283C2×D3—481no—
284C2×D3—481no—
285C2×D3#80912yes—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—32no—
289C3×C4—81no—
290C3×C4—81no—
291C3×C4—122no—
292C3×C4—161no—
293C3×C4—241no—
294C3×C4D3×C22⋊C411yescharacteristic
295C3×C4D3×SD1611yescharacteristic
296C3×C4C2×(C2×D3)⋊C411yescharacteristic
297C3×C4C2×#21511yescharacteristic
298Dic3—42no—
299Dic3—81no—
300Dic3#80912yes—
301C32#213911yescharacteristic, complemented, Sylow
302C23—31no—
303C23—361no—
304Q8—62no—
305Q8—121no—
306D4—182no—
307D4—364no—
308D4—361no—
309C2×C4—31no—
310C2×C4—32no—
311C2×C4—32no—
312C2×C4—41no—
313C2×C4—121no—
314C2×C4—121no—
315C2×C4—242no—
316C2×C4—364no—
317C2×C4D3×#6711yescharacteristic
318C8—32no—
319C8C4×D3211yescharacteristic
320C8D3×D1211yescharacteristic
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—62no—
325C2×C3D3×#10211yescharacteristic
326C2×C3#491411yescharacteristic
327C2×C3#491811yescharacteristic
328C2×C3C2×#80911yescharacteristic
329C2×C3#514711yescharacteristic
330C2×C3#517911yescharacteristic
331D3—22no—
332D3—242no—
333D3—242no—
334D3—482no—
335C22—32no—
336C22—61no—
337C22—61no—
338C22—362no—
339C22—721no—
340C22—721no—
341C22D3×#21311yescharacteristic
342C4—32no—
343C4—81no—
344C4—122no—
345C4—241no—
346C4D3×(C2×D3)⋊C411yescharacteristic
347C4D3×#21511yescharacteristic
348C3—21no—
349C3#6922111yescharacteristic, complemented
350C3#7059811yescharacteristic, complemented
351C2—62no—
352C2—722no—
353C2D3×#80911yescharacteristic
354C2#1059103311yescharacteristic
355C2#1059104711yescharacteristic
subgroupG/H
centerC22D3×#213
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×#107C22
socleC22×C32C2×D8
prime radicalC2×#63808C2
cosocleC2×C32×C8C23
hypercenter#107D32
hypocenterC32#2139
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C3×D3×#107C2semidirect
3. C2×#63543C2semidirect
4. #10589357C2semidirect
5. C3×#4492C2semidirect
6. #10589117C2semidirect
7. #10589116C2semidirect
17. #63808C4semidirect
29. D3×#107D3semidirect
34. #4492D3semidirect
50. #3745C2×C4semidirect
55. C3×Dic12C2×C4semidirect
154. Dic12C4×D3semidirect
301. C32#2139semidirect
349. C3#69221semidirect
350. C3#70598semidirect

Maximal subgroups

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

subgroupindex
C2×#638082
C3×D3×#1072
C2×#635432
#105893572
C3×#44922
#105891172
#105891162
#705983
#692213