Finite Group Databasebeta

← #11798985

Subgroups — #11798985

Order 1152.

389 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 389 conjugacy classes of subgroups — too many to draw. Only its 84 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×#63653C211yesmaximal, characteristic
2C3×Dic3×D8C211yesmaximal, characteristic, complemented
3C2×C3×#827C211yesmaximal, characteristic, complemented
4#10590865C211yesmaximal, characteristic, complemented
5Dic3⋊(C3⋊C16)C211yesmaximal, characteristic, complemented
6#10589117C211yesmaximal, characteristic, complemented
7#10589116C211yesmaximal, characteristic, complemented
8#71477—31nomaximal
9#70890—31nomaximal
10C2×C32×D8C2211yescharacteristic
11C2×#3745C2211yescharacteristic
12C3×D4×Dic3—21no—
13C2×C3×Dic12C2211yescharacteristic
14#63864—21no—
15C2×#3717—21no—
16#63653—22no—
17C2×C3⋊(C3⋊C16)C2211yescharacteristic
18C3×#832—21no—
19C3×#827—22no—
20C3×#818C2211yescharacteristic
21C3×C8×Dic3C2211yescharacteristic
22C2×C3×C3⋊C16C2211yescharacteristic
23C2×C3×SD32—31no—
24C3×C4×D8—31no—
25#5191—31no—
26Dic3×D8D311yescharacteristic, complemented
27C2×#827D311yescharacteristic, complemented
28C2×#826—31no—
29C2×#826—31no—
30C2×#826—61no—
31#4696—31no—
32#4564—31no—
33#4509—31no—
34Dic3⋊C16—31no—
35#4492—31no—
36#4491—31no—
37C4⋊(C3⋊C16)—31no—
38C2×C32×D4—21no—
39C2×C4⋊(C3⋊D3)—21no—
40C22×C3×Dic3—41no—
41C2×C3×Dic6—21no—
42C32×D8—21no—
43C32×D8D412yes—
44C2×C32×C8C2311yescharacteristic
45#3745—21no—
46#3745—21no—
47C3×#217—41no—
48C3×C4⋊Dic3—21no—
49C3×C4×Dic3D411yescharacteristic
50C2×C3×C3⋊C8D411yescharacteristic
51C3×Dic12—21no—
52C3×Dic12—21no—
53#3722—41no—
54#3722—41no—
55#3717—42no—
56C3⋊(C3⋊C16)—21no—
57C3×C3⋊C16—21no—
58#2210—91noSylow
59C2×C3×Q16—31no—
60C2×C3×D8—21no—
61C2×C3×D8C2×D311yescharacteristic
62C2×C3×D8C2×D311yescharacteristic
63C3×C4×D4—61no—
64#947—61no—
65C2×#215—61no—
66D4×Dic3—21no—
67C2×Dic12C2×D311yescharacteristic
68C2×D24—31no—
69C2×D24—31no—
70C2×D24—61no—
71C2×#204—61no—
72#875—61no—
73C3×SD32—62no—
74C2×C3×C16—31no—
75C3×#107—31no—
76C3×#102—61no—
77C3×C4×C8—31no—
78#832—21no—
79#827—22no—
80#826—64no—
81#826—62no—
82#826—62no—
83#818C2×D311yescharacteristic
84C8×Dic3C2×D311yescharacteristic
85C2×C3⋊C16—31no—
86C2×C3⋊C16—31no—
87C2×C3⋊C16—61no—
88C2×C3⋊C16C2×D311yescharacteristic
89C23×C32—41no—
90C22×C3⋊D3—41no—
91C32×D4—22no—
92C32×D4—41no—
93C2×C32×C4C2×D411yescharacteristic
94C4⋊(C3⋊D3)—41no—
95C4⋊(C3⋊D3)—41no—
96C2×C3×Dic3—41no—
97C2×C3×Dic3—41no—
98C2×C3×Dic3—82no—
99C2×C3×Dic3D811yescharacteristic
100C2×C3×Dic3D811yescharacteristic
101C3×Dic6—41no—
102C3×Dic6—41no—
103C32×C8C2×D411yescharacteristic
104C32×C8#4111yescharacteristic
105C3×C3⋊C8—21no—
106C2×SD32—31no—
107C2×D16—91no—
108#495—91no—
109C4×D8—31no—
110C4⋊C16—91no—
111#358—91no—
112#357—91no—
113C2×C3×Q8—61no—
114C2×C3×D4—21no—
115C2×C3×D4—21no—
116C2×C3×D4—41no—
117C22×C3×C4—121no—
118C22×Dic3—41no—
119C2×D12—61no—
120C2×D12—61no—
121C2×D12—121no—
122C2×Dic6—21no—
123C3×Q16—61no—
124C3×Q16—61no—
125C3×D8—21no—
126C3×D8—21no—
127C3×D8—22no—
128C3×D8—41no—
129C3×D8D1212yes—
130C3×D8#6712yes—
131C2×C3×C8—21no—
132C2×C3×C8—31no—
133C2×C3×C8C22×D311yescharacteristic
134C2×C3×C8C22×D311yescharacteristic
135C3×C4⋊C4—61no—
136C3×C22⋊C4—121no—
137C3×C42—31no—
138#217—41no—
139#215—122no—
140(C2×D3)⋊C4—121no—
141(C2×D3)⋊C4—121no—
142(C2×D3)⋊C4—121no—
143(C2×D3)⋊C4—121no—
144C4⋊Dic3—21no—
145C4×Dic3#6711yescharacteristic
146C2×C3⋊C8#6711yescharacteristic
147Dic12—21no—
148Dic12—21no—
149D24—62no—
150D24—61no—
151D24—61no—
152D24—61no—
153D24—61no—
154D24—121no—
155#204—122no—
156C3×C16—61no—
157C3⋊C16—21no—
158C3⋊C16—62no—
159C3⋊C16—61no—
160C3⋊C16—61no—
161C22×C32—42no—
162C22×C32—81no—
163C22×C32—81no—
164C22×C32C2×D811yescharacteristic
165C2×C3⋊D3—81no—
166C2×C3⋊D3—81no—
167C2×C3⋊D3—81no—
168C32×C4#12111yescharacteristic
169C32×C4AGL(1,ℤ/8)11yescharacteristic
170C3×Dic3—21no—
171C3×Dic3—21no—
172C3×Dic3—81no—
173C3×Dic3—81no—
174C2×Q16—31no—
175C2×SD16—181no—
176C2×D8—91no—
177C2×D8D3211yescharacteristic
178#124—181no—
179C4×D4—61no—
180SD32—62no—
181D16—182no—
182C2×C16—31no—
183C2×C16—91no—
184#107—31no—
185#102—61no—
186C4×C8—31no—
187C23×C3—41no—
188C23×C3—41no—
189C23×C3—81no—
190C22×D3—121no—
191C22×D3—121no—
192C22×D3—241no—
193C3×Q8—121no—
194C3×Q8—121no—
195C3×D4—22no—
196C3×D4—22no—
197C3×D4—42no—
198C3×D4—41no—
199C3×D4—41no—
200C3×D4—81no—
201C2×C3×C4—21no—
202C2×C3×C4—31no—
203C2×C3×C4—31no—
204C2×C3×C4—121no—
205C2×C3×C4—121no—
206C2×C3×C4—242no—
207C2×C3×C4D3×D411yescharacteristic
208C2×C3×C4C2×#6711yescharacteristic
209C2×Dic3—41no—
210C2×Dic3—41no—
211C2×Dic3—82no—
212C2×Dic3#21311yescharacteristic
213C2×Dic3#21311yescharacteristic
214D12—122no—
215D12—121no—
216D12—121no—
217D12—121no—
218D12—121no—
219D12—241no—
220Dic6—41no—
221Dic6—41no—
222C3×C8—21no—
223C3×C8—21no—
224C3×C8—61no—
225C3×C8C2×D1211yescharacteristic
226C3×C8#23511yescharacteristic
227C3×C8#23711yescharacteristic
228C3×C8C2×#6711yescharacteristic
229C3⋊C8—21no—
230C2×C32—82no—
231C2×C32#45911yescharacteristic
232C2×C32#50811yescharacteristic
233C2×C32#50911yescharacteristic
234C3⋊D3—161no—
235C2×Q8—61no—
236C2×D4—21no—
237C2×D4—181no—
238C22×C4—121no—
239Q16—61no—
240Q16—61no—
241SD16—362no—
242D8—21no—
243D8—181no—
244D8—181no—
245D8#62612yes—
246C2×C8—31no—
247C2×C8C2×D3211yescharacteristic
248C4⋊C4—61no—
249C22⋊C4—121no—
250C22⋊C4—361no—
251C22⋊C4—361no—
252C42—31no—
253C16—61no—
254C16—181no—
255C22×C3—21no—
256C22×C3—42no—
257C22×C3—42no—
258C22×C3—82no—
259C22×C3—81no—
260C22×C3—81no—
261C22×C3—81no—
262C22×C3—81no—
263C22×C3—161no—
264C22×C3—161no—
265C22×C3D3×D811yescharacteristic
266C22×C3C2×#21311yescharacteristic
267C2×D3—242no—
268C2×D3—241no—
269C2×D3—241no—
270C2×D3—241no—
271C2×D3—241no—
272C2×D3—241no—
273C2×D3—241no—
274C2×D3—481no—
275C2×D3—481no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—61no—
279C3×C4—61no—
280C3×C4—241no—
281C3×C4—241no—
282C3×C4#91111yescharacteristic
283C3×C4#93011yescharacteristic
284C3×C4#93911yescharacteristic
285C3×C4#94911yescharacteristic
286Dic3—21no—
287Dic3—21no—
288Dic3—81no—
289Dic3—81no—
290C32#221011yescharacteristic, complemented, Sylow
291C23—41no—
292C23—361no—
293Q8—121no—
294Q8—121no—
295D4—22no—
296D4—41no—
297D4—361no—
298D4—361no—
299C2×C4—31no—
300C2×C4—31no—
301C2×C4—121no—
302C2×C4—121no—
303C2×C4—242no—
304C2×C4D3×#6711yescharacteristic
305C8—61no—
306C8#380411yescharacteristic
307C8C2×#62611yescharacteristic
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—82no—
312C2×C3—82no—
313C2×C3—162no—
314C2×C3#491411yescharacteristic
315C2×C3#491611yescharacteristic
316C2×C3#501511yescharacteristic
317C2×C3#514711yescharacteristic
318C2×C3#515011yescharacteristic
319C2×C3#519411yescharacteristic
320D3—482no—
321D3—481no—
322D3—481no—
323C22—42no—
324C22—81no—
325C22—81no—
326C22—721no—
327C22—721no—
328C22—721no—
329C22D3×#21311yescharacteristic
330C4—61no—
331C4—61no—
332C4—241no—
333C4—241no—
334C4#6392511yescharacteristic
335C4#6397811yescharacteristic
336C3—21no—
337C3#7089011yescharacteristic, complemented
338C3#7147711yescharacteristic, complemented
339C2—82no—
340C2—1441no—
341C2#1059103311yescharacteristic
342C2#1059103411yescharacteristic
343C2#1059148111yescharacteristic
subgroupG/H
centerC22D3×#213
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×D8C22
socleC22×C32C2×D8
prime radicalC2×#63653C2
hypercenterC2×D8D32
hypocenterC32#2210
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. C3×Dic3×D8C2semidirect
3. C2×C3×#827C2semidirect
4. #10590865C2semidirect
5. Dic3⋊(C3⋊C16)C2semidirect
6. #10589117C2semidirect
7. #10589116C2semidirect
26. Dic3×D8D3semidirect
27. C2×#827D3semidirect
290. C32#2210semidirect
337. C3#70890semidirect
338. C3#71477semidirect

Maximal subgroups

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

subgroupindex
C2×#636532
C3×Dic3×D82
C2×C3×#8272
#105908652
Dic3⋊(C3⋊C16)2
#105891172
#105891162
#714773
#708903