Finite Group Databasebeta

← #11774554

Subgroups — #11774554

Order 1152.

738 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C4×D4×C3⋊D3C211yesmaximal, characteristic
2#10593728C211yesmaximal, characteristic, complemented
3#10593727C211yesmaximal, characteristic, complemented
4D4⋊#622C212yesmaximal, complemented
5#10590160C212yesmaximal, complemented
6C2×D4×C3⋊D3C411yescharacteristic
7C22×C4×C3⋊D3—21no—
8C2×#3788—21no—
9C32×C4×D4C411yescharacteristic
10D4×C3⋊Dic3C2211yescharacteristic
11C4×#638—21no—
12#64102C2211yescharacteristic
13C4⋊C4×C3⋊D3C411yescharacteristic
14#64090—21no—
15C22⋊C4×C3⋊D3—21no—
16C4×C4⋊(C3⋊D3)C411yescharacteristic
17C42×C3⋊D3C2211yescharacteristic
18#63778—21no—
19C4⋊#622—21no—
20C4⋊#622—21no—
21C4⋊#622C2212yescomplemented
22C4×#622C2212yescomplemented
23C4×D3×D4—62no—
24C23×C3⋊D3—21no—
25C2×C32×D4C2×C411yescharacteristic
26C22×C32×C4—21no—
27C2×#638—21no—
28C22×C3⋊Dic3—21no—
29D4×C3⋊D3—22no—
30D4×C3⋊D3—22no—
31C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
32C2×C4×C3⋊D3—21no—
33C2×C4×C3⋊D3—21no—
34C2×C4×C3⋊D3—21no—
35C2×C4×C3⋊D3—42no—
36C2×C4×C3⋊D3—42no—
37C2×C4×C3⋊D3C2×C411yescharacteristic
38C2×C4×C3⋊D3D411yescharacteristic
39C2×C4×C3⋊D3D411yescharacteristic
40C2×#622—22no—
41C2×#622—22no—
42#3788—42no—
43C32×C4⋊C4C2×C411yescharacteristic
44C32×C22⋊C4—21no—
45C32×C42C2×C411yescharacteristic
46#3757—21no—
47#3752—21no—
48#3752—21no—
49C4⋊(C3⋊Dic3)C2×C411yescharacteristic
50#3750—21no—
51C4×C3⋊Dic3D411yescharacteristic
52C4×C3⋊Dic3D411yescharacteristic
53C4×C3⋊Dic3C2311yescharacteristic
54#1486—91nomaximal, Sylow
55C2×D3×D4—62no—
56C22×C4×D3—64no—
57C3×C4×D4—22no—
58D4×Dic3—62no—
59C4×#67—64no—
60#893—62no—
61D3×C4⋊C4—62no—
62#67⋊C4—64no—
63D3×C22⋊C4—64no—
64C4×D12—62no—
65C42×D3—62no—
66C23×C32—21no—
67C22×C3⋊D3—24no—
68C22×C3⋊D3—21no—
69C22×C3⋊D3—42no—
70C22×C3⋊D3—42no—
71C22×C3⋊D3C22⋊C411yescharacteristic
72C32×D4—21no—
73C32×D4M1612yescomplemented
74C2×C32×C4—21no—
75C2×C32×C4—42no—
76C2×C32×C4C22⋊C411yescharacteristic
77C2×C32×C4C22⋊C411yescharacteristic
78C2×C32×C4C22×C411yescharacteristic
79#638—24no—
80C2×C3⋊Dic3—21no—
81C2×C3⋊Dic3—41no—
82C2×C3⋊Dic3—41no—
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C2×D411yescharacteristic
85C2×C3⋊Dic3C2×D411yescharacteristic
86C4⋊(C3⋊D3)—21no—
87C4⋊(C3⋊D3)M1612yescomplemented
88C4×C3⋊D3—21no—
89C4×C3⋊D3—21no—
90C4×C3⋊D3—41no—
91C4×C3⋊D3—42no—
92C4×C3⋊D3—42no—
93C4×C3⋊D3—41no—
94C4×C3⋊D3—41no—
95C4×C3⋊D3D812yes—
96C4×C3⋊D3SD1612yes—
97#622—42no—
98#622—42no—
99C2×C4×D4—91no—
100#431—91no—
101#423—91no—
102D4⋊C8—92no—
103D4⋊C8—92no—
104C23×D3—64no—
105C2×C3×D4—22no—
106C22×C3×C4—24no—
107C2×#67—64no—
108C22×Dic3—64no—
109D3×D4—68no—
110D3×D4—68no—
111C2×D12—62no—
112C2×C4×D3—62no—
113C2×C4×D3—62no—
114C2×C4×D3—62no—
115C2×C4×D3—64no—
116C2×C4×D3—64no—
117C2×C4×D3—64no—
118C2×C4×D3—128no—
119C2×C4×D3—128no—
120C3×C4⋊C4—22no—
121C3×C22⋊C4—24no—
122C3×C42—22no—
123#217—64no—
124(C2×D3)⋊C4—64no—
125(C2×D3)⋊C4—64no—
126C4⋊Dic3—62no—
127Dic3⋊C4—64no—
128C4×Dic3—62no—
129C4×Dic3—62no—
130C4×Dic3—62no—
131C22×C32—22no—
132C22×C32—41no—
133C22×C32—41no—
134C22×C32C2×C22⋊C411yescharacteristic
135C2×C3⋊D3—21no—
136C2×C3⋊D3—21no—
137C2×C3⋊D3—22no—
138C2×C3⋊D3—48no—
139C2×C3⋊D3—41no—
140C2×C3⋊D3—41no—
141C2×C3⋊D3#10212yes—
142C32×C4—21no—
143C32×C4—41no—
144C32×C4#10212yes—
145C32×C4C2×M1611yescharacteristic
146C32×C4C2×M1611yescharacteristic
147C3⋊Dic3—21no—
148C3⋊Dic3—21no—
149C3⋊Dic3—41no—
150C3⋊Dic3C2×D811yescharacteristic
151C3⋊Dic3C2×SD1611yescharacteristic
152C22×D4—91no—
153C23×C4—181no—
154C2×M16—181no—
155C4×D4—91no—
156C4×D4—91no—
157C4×D4—91no—
158C4×D4—181no—
159C4×D4—181no—
160C4×D4#15711yescharacteristic
161C2×C4⋊C4—91no—
162C2×C22⋊C4—181no—
163C2×C42—91no—
164C4⋊C8—92no—
165C4⋊C8—181no—
166C4⋊C8—181no—
167C22⋊C8—181no—
168C4×C8—92no—
169C23×C3—24no—
170C22×D3—62no—
171C22×D3—64no—
172C22×D3—616no—
173C22×D3—128no—
174C22×D3—128no—
175C3×D4—24no—
176C3×D4—24no—
177C2×C3×C4—24no—
178C2×C3×C4—22no—
179C2×C3×C4—22no—
180C2×C3×C4—22no—
181C2×C3×C4—48no—
182#67—616no—
183C2×Dic3—62no—
184C2×Dic3—62no—
185C2×Dic3—62no—
186C2×Dic3—64no—
187C2×Dic3—124no—
188C2×Dic3—124no—
189D12—64no—
190D12—64no—
191C4×D3—64no—
192C4×D3—64no—
193C4×D3—64no—
194C4×D3—64no—
195C4×D3—124no—
196C4×D3—124no—
197C4×D3—128no—
198C4×D3—124no—
199C4×D3—128no—
200C2×C32—42no—
201C2×C32#40711yescharacteristic
202C2×C32C2×#10211yescharacteristic
203C2×C32#42111yescharacteristic
204C3⋊D3—22no—
205C3⋊D3—42no—
206C24—181no—
207C2×D4—91no—
208C2×D4—181no—
209C2×D4—182no—
210C2×D4—182no—
211C2×D4C2×#15711yescharacteristic
212C22×C4—21no—
213C22×C4—91no—
214C22×C4—91no—
215C22×C4—91no—
216C22×C4—181no—
217C22×C4—181no—
218C22×C4—181no—
219C22×C4—181no—
220C22×C4—362no—
221C22×C4—362no—
222M16—362no—
223C2×C8—182no—
224C2×C8—182no—
225C4⋊C4—91no—
226C4⋊C4—181no—
227C4⋊C4C2×#15711yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—181no—
230C22⋊C4—181no—
231C22⋊C4—181no—
232C42—91no—
233C42—91no—
234C42—91no—
235C42C2×#15711yescharacteristic
236C22×C3—28no—
237C22×C3—22no—
238C22×C3—44no—
239C22×C3—44no—
240C2×D3—64no—
241C2×D3—64no—
242C2×D3—64no—
243C2×D3—68no—
244C2×D3—1232no—
245C2×D3—124no—
246C2×D3—124no—
247C3×C4—22no—
248C3×C4—22no—
249C3×C4—24no—
250C3×C4—42no—
251C3×C4—44no—
252Dic3—62no—
253Dic3—62no—
254Dic3—64no—
255Dic3—122no—
256Dic3—124no—
257C32#148611yescharacteristic, complemented, Sylow
258C23—21no—
259C23—91no—
260C23—184no—
261C23—181no—
262C23—362no—
263C23—362no—
264D4—21no—
265D4—92no—
266D4—184no—
267D4—181no—
268D4#378812yescomplemented
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—91no—
272C2×C4—92no—
273C2×C4—92no—
274C2×C4—91no—
275C2×C4—91no—
276C2×C4—181no—
277C2×C4—181no—
278C2×C4—181no—
279C2×C4—361no—
280C2×C4—361no—
281C2×C4—361no—
282C2×C4—362no—
283C2×C4—361no—
284C2×C4—361no—
285C2×C4—362no—
286C2×C4C22⋊#15711yescharacteristic
287C2×C4C22⋊#15711yescharacteristic
288C2×C4C22×#15711yescharacteristic
289C8—362no—
290C8—362no—
291C2×C3—22no—
292C2×C3—22no—
293C2×C3—22no—
294C2×C3—48no—
295D3—68no—
296D3—128no—
297C22—22no—
298C22—41no—
299C22—41no—
300C22—92no—
301C22—181no—
302C22—181no—
303C22—182no—
304C22—368no—
305C22—361no—
306C22—361no—
307C22C2×C22⋊#15711yescharacteristic
308C4—21no—
309C4—41no—
310C4—91no—
311C4—91no—
312C4—181no—
313C4—181no—
314C4—361no—
315C4#6378212yes—
316C4C2×#378811yescharacteristic
317C4#6428311yescharacteristic
318C3—22no—
319C2—42no—
320C2—182no—
321C2—362no—
322C2#1059380311yescharacteristic
323C2C2×#6378211yescharacteristic
324C2#1059384211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4×D4C4
socleC22×C32C2×C22⋊C4
prime radicalC2×D4×C3⋊D3C4
cosocleC4×C3⋊Dic3C23
hypercenterC4×D4#157
hypocenterC32#1486
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593728C2semidirect
3. #10593727C2semidirect
4. D4⋊#622C2semidirect
5. #10590160C2semidirect
21. C4⋊#622C22semidirect
22. C4×#622C22semidirect
73. C32×D4M16semidirect
87. C4⋊(C3⋊D3)M16semidirect
257. C32#1486semidirect
268. D4#3788semidirect

Maximal subgroups

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

subgroupindex
C4×D4×C3⋊D32
#105937282
#105937272
D4⋊#6222
#105901602
#14869