Finite Group Databasebeta

← #11786928

Subgroups — #11786928

Order 1152.

564 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 80 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×D4×#157C211yesmaximal, characteristic
2C2×#63782C211yesmaximal, characteristic
3C2×#63768C211yesmaximal, characteristic, complemented
4#10593759C211yesmaximal, characteristic, complemented
5C3⋊D3×#102C211yesmaximal, characteristic
6#10590181C211yesmaximal, characteristic, complemented
7#10590163C211yesmaximal, characteristic, complemented
8C23×#157—21no—
9C2×D4×C3⋊D3C2211yescharacteristic
10C2×C22⋊#157—21no—
11D4×#157—22no—
12D4×#157—22no—
13C2×C4⋊#157—21no—
14C2×C4⋊#157C2211yescharacteristic
15C2×C4⋊#157C2211yescharacteristic
16C2×C4×#157C2211yescharacteristic
17C2×#3787C2211yescharacteristic
18C2×C8×C3⋊D3C2211yescharacteristic
19C4⋊C4×C3⋊D3C2211yescharacteristic
20#63782—22no—
21#63781—21no—
22#63768—22no—
23C32×#102C411yescharacteristic, complemented
24#63659C411yescharacteristic, complemented
25#63648C411yescharacteristic, complemented
26#63636C411yescharacteristic, complemented
27D3×#102—62no—
28C23×C3⋊D3—21no—
29C22×#157—24no—
30C22×#157—21no—
31C22×#157—21no—
32C22×#157—42no—
33C22×#157—42no—
34C22×#157D411yescharacteristic
35C22×#157D411yescharacteristic
36C2×C32×D4C2×C411yescharacteristic
37C2×#638—21no—
38D4×C3⋊D3—21no—
39D4×C3⋊D3—21no—
40D4×C3⋊D3D412yes—
41D4×C3⋊D3Q812yes—
42C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
43C2×C4×C3⋊D3—21no—
44C2×C4×C3⋊D3C2311yescharacteristic
45C22⋊#157—24no—
46C2×#622—21no—
47C4⋊#157—21no—
48C4⋊#157—21no—
49C4⋊#157—21no—
50C4⋊#157—42no—
51C4⋊#157D412yes—
52C4×#157—21no—
53C4×#157—21no—
54#3787—21no—
55#3787—21no—
56C2×C32×C8C2×C411yescharacteristic, complemented
57C32×C4⋊C4C2×C411yescharacteristic, complemented
58C4⋊(C3⋊Dic3)C2×C411yescharacteristic, complemented
59#3750—21no—
60C2×C3⋊(C3⋊C8)C2×C411yescharacteristic, complemented
61C8×C3⋊D3—21no—
62C8×C3⋊D3—21no—
63#1864—91nomaximal, Sylow
64C2×D3×D4—62no—
65C2×D3×C8—62no—
66D3×C4⋊C4—62no—
67C3×#102—22no—
68#832—62no—
69#821—62no—
70#809—62no—
71C23×C32—21no—
72C22×C3⋊D3—21no—
73C22×C3⋊D3—22no—
74C22×C3⋊D3—22no—
75C22×C3⋊D3—41no—
76C22×C3⋊D3—41no—
77C22×C3⋊D3—41no—
78C22×C3⋊D3—41no—
79C22×C3⋊D3C2×D411yescharacteristic
80C2×#157—21no—
81C2×#157—21no—
82C2×#157—22no—
83C2×#157—21no—
84C2×#157—21no—
85C2×#157—21no—
86C2×#157—48no—
87C2×#157—41no—
88C2×#157—41no—
89C2×#157—41no—
90C2×#157—41no—
91C2×#157—41no—
92C2×#157SD1612yes—
93C32×D4—21no—
94C32×D4C4⋊C412yescomplemented
95C2×C32×C4—21no—
96C2×C32×C4C22×C411yescharacteristic
97#638—22no—
98#638—22no—
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3#4111yescharacteristic
101C4⋊(C3⋊D3)—21no—
102C4⋊(C3⋊D3)C4⋊C412yescomplemented
103C4×C3⋊D3—41no—
104C4×C3⋊D3—41no—
105C4×C3⋊D3C2×D411yescharacteristic
106C4×C3⋊D3C2×D411yescharacteristic
107C4×C3⋊D3C2×Q811yescharacteristic
108C4×C3⋊D3#4111yescharacteristic
109#622—41no—
110C32×C8—21no—
111C3⋊(C3⋊C8)—21no—
112C2×C4×D4—91no—
113C2×#106—91no—
114C2×#102—91no—
115C2×#102—91no—
116#389—91no—
117#340—91no—
118#336—91no—
119C23×D3—122no—
120C2×C3×D4—22no—
121C2×#67—122no—
122D3×D4—64no—
123D3×D4—64no—
124D3×D4—122no—
125D3×D4—122no—
126C2×D12—62no—
127C2×C4×D3—62no—
128C2×C4×D3—122no—
129C2×C3×C8—22no—
130C3×C4⋊C4—22no—
131C4⋊Dic3—62no—
132Dic3⋊C4—122no—
133C2×C3⋊C8—62no—
134D3×C8—122no—
135D3×C8—122no—
136C22×C32—22no—
137C22×C32—41no—
138C22×C32—41no—
139C22×C32C4×D411yescharacteristic
140C2×C3⋊D3—22no—
141C2×C3⋊D3—41no—
142C2×C3⋊D3—41no—
143C2×C3⋊D3—42no—
144C2×C3⋊D3—42no—
145C2×C3⋊D3—42no—
146C2×C3⋊D3—42no—
147C2×C3⋊D3#12011yescharacteristic
148C2×C3⋊D3C22⋊Q811yescharacteristic
149C2×C3⋊D3C2×SD1611yescharacteristic
150C2×C3⋊D3#13511yescharacteristic
151C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
152C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
153#157—22no—
154#157—41no—
155#157—42no—
156#157—81no—
157C32×C4—41no—
158C32×C4C2×C4⋊C411yescharacteristic
159C32×C4C4×D411yescharacteristic
160C3⋊Dic3—41no—
161C3⋊Dic3C22⋊Q811yescharacteristic
162C3⋊Dic3#12311yescharacteristic
163C22×D4—91no—
164C23×C4—181no—
165C22×C8—91no—
166C22×C8—91no—
167C4×D4—182no—
168C4×D4—182no—
169C2×C4⋊C4—91no—
170C2×C4⋊C4—91no—
171C2×C4⋊C4—91no—
172C2×C4⋊C4—181no—
173C2×C22⋊C4—181no—
174C2×C42—91no—
175#106—182no—
176#102—91no—
177#102—91no—
178#102—91no—
179#102—182no—
180#102#15711yescharacteristic, complemented
181#95—181no—
182C23×C3—42no—
183C22×D3—62no—
184C22×D3—124no—
185C22×D3—124no—
186C22×D3—122no—
187C22×D3—242no—
188C22×D3—242no—
189C22×D3—242no—
190C22×D3—242no—
191C3×D4—24no—
192C3×D4—42no—
193C2×C3×C4—22no—
194C2×C3×C4—42no—
195#67—124no—
196#67—124no—
197C2×Dic3—62no—
198C2×Dic3—122no—
199D12—64no—
200D12—122no—
201C4×D3—62no—
202C4×D3—62no—
203C4×D3—62no—
204C4×D3—62no—
205C4×D3—242no—
206C4×D3—242no—
207C3×C8—42no—
208C3⋊C8—122no—
209C2×C32—42no—
210C2×C32#38511yescharacteristic
211C2×C32C4×SD1611yescharacteristic
212C2×C32#44211yescharacteristic
213C3⋊D3—42no—
214C3⋊D3#44911yescharacteristic
215C3⋊D3#45011yescharacteristic
216C3⋊D3#47611yescharacteristic
217C3⋊D3#47811yescharacteristic
218C24—181no—
219C2×D4—92no—
220C2×D4—92no—
221C2×D4—91no—
222C2×D4—181no—
223C2×D4—181no—
224C2×D4—181no—
225C2×D4C2×#15711yescharacteristic
226C22×C4—91no—
227C22×C4—91no—
228C22×C4—91no—
229C22×C4—181no—
230C22×C4—181no—
231C22×C4—184no—
232C22×C4—181no—
233C22×C4—362no—
234C22×C4—362no—
235C2×C8—91no—
236C2×C8—181no—
237C2×C8—181no—
238C2×C8—181no—
239C2×C8—181no—
240C2×C8—181no—
241C2×C8C2×#15711yescharacteristic, complemented
242C4⋊C4—92no—
243C4⋊C4—91no—
244C4⋊C4—181no—
245C4⋊C4—181no—
246C4⋊C4—181no—
247C4⋊C4—181no—
248C4⋊C4—362no—
249C4⋊C4C2×#15711yescharacteristic, complemented
250C22⋊C4—184no—
251C42—181no—
252C42—181no—
253C22×C3—22no—
254C22×C3—44no—
255C22×C3—82no—
256C22×C3—82no—
257C2×D3—62no—
258C2×D3—62no—
259C2×D3—62no—
260C2×D3—62no—
261C2×D3—62no—
262C2×D3—62no—
263C2×D3—124no—
264C2×D3—244no—
265C2×D3—244no—
266C2×D3—244no—
267C2×D3—244no—
268C2×D3—242no—
269C2×D3—242no—
270C3×C4—22no—
271C3×C4—22no—
272C3×C4—82no—
273Dic3—62no—
274Dic3—62no—
275Dic3—242no—
276C32#186411yescharacteristic, complemented, Sylow
277C23—21no—
278C23—91no—
279C23—182no—
280C23—182no—
281C23—181no—
282C23—361no—
283C23—361no—
284C23—361no—
285C23—361no—
286D4—21no—
287D4—92no—
288D4—182no—
289D4—182no—
290D4—181no—
291D4C4⋊#15712yescomplemented
292C2×C4—21no—
293C2×C4—91no—
294C2×C4—91no—
295C2×C4—91no—
296C2×C4—91no—
297C2×C4—91no—
298C2×C4—92no—
299C2×C4—181no—
300C2×C4—181no—
301C2×C4—181no—
302C2×C4—182no—
303C2×C4—181no—
304C2×C4—181no—
305C2×C4—181no—
306C2×C4—361no—
307C2×C4—361no—
308C2×C4—368no—
309C2×C4—361no—
310C2×C4—361no—
311C2×C4—361no—
312C2×C4—361no—
313C2×C4—361no—
314C2×C4C22×#15711yescharacteristic
315C8—21no—
316C8—181no—
317C8—361no—
318C2×C3—22no—
319C2×C3—22no—
320C2×C3—22no—
321C2×C3—84no—
322D3—62no—
323D3—62no—
324D3—62no—
325D3—62no—
326D3—244no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—91no—
331C22—91no—
332C22—91no—
333C22—91no—
334C22—91no—
335C22—91no—
336C22—182no—
337C22—362no—
338C22—362no—
339C22—362no—
340C22—362no—
341C22—361no—
342C22—361no—
343C22D4×#15711yescharacteristic
344C4—41no—
345C4—91no—
346C4—91no—
347C4—182no—
348C4—361no—
349C4—362no—
350C4—361no—
351C4—721no—
352C4C2×C4⋊#15711yescharacteristic
353C4D4×#15711yescharacteristic
354C3—22no—
355C2—42no—
356C2—91no—
357C2—91no—
358C2—91no—
359C2—91no—
360C2—362no—
361C2#1059374611yescharacteristic
362C2#1059377811yescharacteristic
363C2SD16×#15711yescharacteristic
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#1864
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×#63768C2semidirect
4. #10593759C2semidirect
6. #10590181C2semidirect
7. #10590163C2semidirect
23. C32×#102C4semidirect
24. #63659C4semidirect
25. #63648C4semidirect
26. #63636C4semidirect
56. C2×C32×C8C2×C4semidirect
57. C32×C4⋊C4C2×C4semidirect
58. C4⋊(C3⋊Dic3)C2×C4semidirect
60. C2×C3⋊(C3⋊C8)C2×C4semidirect
94. C32×D4C4⋊C4semidirect
102. C4⋊(C3⋊D3)C4⋊C4semidirect
180. #102#157semidirect
241. C2×C8C2×#157semidirect
249. C4⋊C4C2×#157semidirect
276. C32#1864semidirect
291. D4C4⋊#157semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#1572
C2×#637822
C2×#637682
#105937592
C3⋊D3×#1022
#105901812
#105901632
#18649