Finite Group Databasebeta

← #11789898

Subgroups — #11789898

Order 1152.

486 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 68 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#10593827C211yesmaximal, characteristic
2C2×#63782C211yesmaximal, characteristic
3C2×#63767C211yesmaximal, characteristic, complemented
4#10593759C211yesmaximal, characteristic, complemented
5C3⋊D3×#102C211yesmaximal, characteristic
6#10590182C211yesmaximal, characteristic, complemented
7#10590163C211yesmaximal, characteristic, complemented
8C2×D4×C3⋊D3C2211yescharacteristic
9C2×C22⋊#157—21no—
10C2×C22⋊#157—21no—
11C2×C4⋊#157—21no—
12C2×C4⋊#157C2211yescharacteristic
13C2×C4⋊#157C2211yescharacteristic
14C2×C4×#157C2211yescharacteristic
15C2×#3787C2211yescharacteristic
16C2×C8×C3⋊D3C2211yescharacteristic
17C4⋊C4×C3⋊D3C2211yescharacteristic
18#63782—22no—
19#63781—21no—
20#63767—22no—
21C32×#102C411yescharacteristic, complemented
22#63659C411yescharacteristic, complemented
23#63648C411yescharacteristic, complemented
24#63636C411yescharacteristic, complemented
25D3×#102—62no—
26C23×C3⋊D3—21no—
27C22×#157—21no—
28C22×#157—21no—
29C22×#157D411yescharacteristic
30C22×#157D411yescharacteristic
31C2×C32×D4C2×C411yescharacteristic
32C2×#638—21no—
33D4×C3⋊D3—21no—
34D4×C3⋊D3—21no—
35D4×C3⋊D3—21no—
36D4×C3⋊D3—21no—
37C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
38C2×C4×C3⋊D3—21no—
39C2×C4×C3⋊D3C2311yescharacteristic
40C22⋊#157—42no—
41C22⋊#157—42no—
42C2×#622—21no—
43C4⋊#157—21no—
44C4⋊#157—21no—
45C4⋊#157—21no—
46C4⋊#157—21no—
47C4⋊#157—42no—
48C4×#157—21no—
49C4×#157—21no—
50#3787—21no—
51#3787D412yes—
52C2×C32×C8C2×C411yescharacteristic
53C32×C4⋊C4C2×C411yescharacteristic
54C4⋊(C3⋊Dic3)C2×C411yescharacteristic
55#3750—21no—
56C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
57C8×C3⋊D3—21no—
58C8×C3⋊D3—21no—
59#1936—91nomaximal, Sylow
60C2×D3×D4—62no—
61C2×D3×C8—62no—
62D3×C4⋊C4—62no—
63C3×#102—22no—
64#832—62no—
65#821—62no—
66#809—62no—
67C23×C32—21no—
68C22×C3⋊D3—21no—
69C22×C3⋊D3—41no—
70C22×C3⋊D3—41no—
71C22×C3⋊D3—41no—
72C22×C3⋊D3—41no—
73C22×C3⋊D3—41no—
74C22×C3⋊D3—41no—
75C22×C3⋊D3C2×D411yescharacteristic
76C2×#157—21no—
77C2×#157—21no—
78C2×#157—21no—
79C2×#157—21no—
80C2×#157—21no—
81C2×#157—21no—
82C2×#157—41no—
83C2×#157—41no—
84C2×#157—41no—
85C2×#157—41no—
86C2×#157—41no—
87C2×#157—41no—
88C32×D4—21no—
89C32×D4—21no—
90C2×C32×C4—21no—
91C2×C32×C4C22×C411yescharacteristic
92#638—41no—
93#638—41no—
94C2×C3⋊Dic3—21no—
95C2×C3⋊Dic3#4111yescharacteristic
96C4⋊(C3⋊D3)—21no—
97C4⋊(C3⋊D3)—21no—
98C4×C3⋊D3—41no—
99C4×C3⋊D3—41no—
100C4×C3⋊D3C2×D411yescharacteristic
101C4×C3⋊D3#4111yescharacteristic
102C4×C3⋊D3#4111yescharacteristic
103C4×C3⋊D3#4111yescharacteristic
104#622—22no—
105C32×C8—21no—
106C3⋊(C3⋊C8)—21no—
107C2×#102—91no—
108C2×#102—91no—
109C2×#97—91no—
110#390—91no—
111#389—91no—
112#340—91no—
113#340—91no—
114C23×D3—122no—
115C2×C3×D4—22no—
116C2×#67—122no—
117D3×D4—64no—
118D3×D4—64no—
119D3×D4—122no—
120D3×D4—122no—
121C2×D12—62no—
122C2×C4×D3—62no—
123C2×C4×D3—122no—
124C2×C3×C8—22no—
125C3×C4⋊C4—22no—
126C4⋊Dic3—62no—
127Dic3⋊C4—122no—
128C2×C3⋊C8—62no—
129D3×C8—122no—
130D3×C8—122no—
131C22×C32—41no—
132C22×C32—41no—
133C22×C32—41no—
134C22×C32C4×D411yescharacteristic
135C2×C3⋊D3—41no—
136C2×C3⋊D3—41no—
137C2×C3⋊D3—41no—
138C2×C3⋊D3—81no—
139C2×C3⋊D3—81no—
140C2×C3⋊D3—81no—
141C2×C3⋊D3—81no—
142C2×C3⋊D3#12111yescharacteristic
143C2×C3⋊D3#12411yescharacteristic
144C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
145C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
146C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
147C2×C3⋊D3#13711yescharacteristic
148#157—41no—
149#157—41no—
150#157—81no—
151#157—81no—
152C32×C4—41no—
153C32×C4#11711yescharacteristic
154C32×C4C4×D411yescharacteristic
155C3⋊Dic3—41no—
156C3⋊Dic3#12311yescharacteristic
157C3⋊Dic3#12611yescharacteristic
158C22×D4—91no—
159C22×C8—91no—
160C22×C8—91no—
161C2×C4⋊C4—91no—
162C2×C4⋊C4—91no—
163C2×C4⋊C4—91no—
164C2×C4⋊C4—181no—
165C2×C22⋊C4—181no—
166C2×C22⋊C4—181no—
167C2×C42—91no—
168#102—91no—
169#102—91no—
170#102—91no—
171#102—182no—
172#102#15711yescharacteristic, complemented
173#97—182no—
174#95—181no—
175C23×C3—42no—
176C22×D3—62no—
177C22×D3—122no—
178C22×D3—124no—
179C22×D3—124no—
180C22×D3—242no—
181C22×D3—242no—
182C22×D3—242no—
183C22×D3—242no—
184C3×D4—24no—
185C3×D4—42no—
186C2×C3×C4—22no—
187C2×C3×C4—42no—
188#67—124no—
189#67—124no—
190C2×Dic3—62no—
191C2×Dic3—122no—
192D12—64no—
193D12—122no—
194C4×D3—62no—
195C4×D3—62no—
196C4×D3—62no—
197C4×D3—62no—
198C4×D3—242no—
199C4×D3—242no—
200C3×C8—42no—
201C3⋊C8—122no—
202C2×C32—81no—
203C2×C32#38811yescharacteristic
204C2×C32#44011yescharacteristic
205C2×C32#44211yescharacteristic
206C3⋊D3—81no—
207C3⋊D3#46811yescharacteristic
208C3⋊D3#46911yescharacteristic
209C3⋊D3#48911yescharacteristic
210C3⋊D3#49011yescharacteristic
211C24—181no—
212C2×D4—91no—
213C2×D4—181no—
214C2×D4—181no—
215C2×D4—181no—
216C2×D4—181no—
217C2×D4—181no—
218C2×D4C2×#15711yescharacteristic
219C22×C4—91no—
220C22×C4—91no—
221C22×C4—91no—
222C22×C4—181no—
223C22×C4—181no—
224C22×C4—181no—
225C2×C8—92no—
226C2×C8—91no—
227C2×C8—181no—
228C2×C8—181no—
229C2×C8—181no—
230C2×C8—181no—
231C2×C8C2×#15711yescharacteristic
232C4⋊C4—91no—
233C4⋊C4—181no—
234C4⋊C4—181no—
235C4⋊C4—181no—
236C4⋊C4—181no—
237C4⋊C4—181no—
238C4⋊C4—362no—
239C4⋊C4C2×#15711yescharacteristic
240C22⋊C4—362no—
241C22⋊C4—362no—
242C42—181no—
243C42—181no—
244C22×C3—22no—
245C22×C3—44no—
246C22×C3—82no—
247C22×C3—82no—
248C2×D3—62no—
249C2×D3—62no—
250C2×D3—62no—
251C2×D3—62no—
252C2×D3—62no—
253C2×D3—62no—
254C2×D3—124no—
255C2×D3—242no—
256C2×D3—242no—
257C2×D3—244no—
258C2×D3—244no—
259C2×D3—244no—
260C2×D3—244no—
261C3×C4—22no—
262C3×C4—22no—
263C3×C4—82no—
264Dic3—62no—
265Dic3—62no—
266Dic3—242no—
267C32#193611yescharacteristic, complemented, Sylow
268C23—21no—
269C23—91no—
270C23—181no—
271C23—361no—
272C23—361no—
273C23—361no—
274C23—361no—
275C23—361no—
276C23—361no—
277D4—21no—
278D4—21no—
279D4—181no—
280D4—181no—
281D4—361no—
282D4—361no—
283C2×C4—21no—
284C2×C4—91no—
285C2×C4—91no—
286C2×C4—91no—
287C2×C4—91no—
288C2×C4—91no—
289C2×C4—181no—
290C2×C4—181no—
291C2×C4—181no—
292C2×C4—181no—
293C2×C4—181no—
294C2×C4—181no—
295C2×C4—181no—
296C2×C4—361no—
297C2×C4—361no—
298C2×C4—361no—
299C2×C4—361no—
300C2×C4—361no—
301C2×C4—361no—
302C2×C4—361no—
303C2×C4—361no—
304C2×C4C22×#15711yescharacteristic
305C8—21no—
306C8—182no—
307C8—181no—
308C2×C3—22no—
309C2×C3—22no—
310C2×C3—22no—
311C2×C3—84no—
312D3—62no—
313D3—62no—
314D3—62no—
315D3—62no—
316D3—244no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—91no—
321C22—91no—
322C22—91no—
323C22—91no—
324C22—91no—
325C22—91no—
326C22—361no—
327C22—361no—
328C22—361no—
329C22—721no—
330C22—721no—
331C22—721no—
332C22—721no—
333C22D4×#15711yescharacteristic
334C4—41no—
335C4—91no—
336C4—91no—
337C4—361no—
338C4—361no—
339C4—361no—
340C4—721no—
341C4—721no—
342C4#6428611yescharacteristic
343C4D4×#15711yescharacteristic
344C3—22no—
345C2—81no—
346C2—91no—
347C2—91no—
348C2—91no—
349C2—91no—
350C2—721no—
351C2#1059374711yescharacteristic
352C2#1059377811yescharacteristic
353C2#1059378211yescharacteristic
subgroupG/H
centerC22D4×#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#102C4
socleC22×C32C4×D4
prime radicalC2×D4×C3⋊D3C22
cosocleC2×C4×C3⋊D3C23
hypercenter#102#157
hypocenterC32#1936
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
3. C2×#63767C2semidirect
4. #10593759C2semidirect
6. #10590182C2semidirect
7. #10590163C2semidirect
21. C32×#102C4semidirect
22. #63659C4semidirect
23. #63648C4semidirect
24. #63636C4semidirect
172. #102#157semidirect
267. C32#1936semidirect

Maximal subgroups

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

subgroupindex
#105938272
C2×#637822
C2×#637672
#105937592
C3⋊D3×#1022
#105901822
#105901632
#19369