Finite Group Databasebeta

← #13080708

Subgroups — #13080708

Order 1408.

382 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623355C211yesmaximal, characteristic
2#10623060C211yesmaximal, characteristic, complemented
3C11×#416C211yesmaximal, characteristic, complemented
4#10622852C211yesmaximal, characteristic, complemented
5#10622729C211yesmaximal, characteristic, complemented
6#10622724C211yesmaximal, characteristic, complemented
7#10622609C211yesmaximal, characteristic, complemented
8#10622429C211yesmaximal, characteristic, complemented
9#10622422C211yesmaximal, characteristic, complemented
10#10622410C211yesmaximal, characteristic, complemented
11#10622406C211yesmaximal, characteristic, complemented
12#10622396C211yesmaximal, characteristic, complemented
13#10622384C211yesmaximal, characteristic, complemented
14#10622379C211yesmaximal, characteristic, complemented
15#10622370C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C22×C8×C11C2211yescharacteristic
19C11×#117C2211yescharacteristic
20#66999C2211yescharacteristic
21#66997C2211yescharacteristic
22C2×#4326C2211yescharacteristic
23#66992—21no—
24#66988—21no—
25D4×Dic11C2211yescharacteristic
26C2×#4324C2211yescharacteristic
27#66982—21no—
28C4×C22⋊D11C2211yescharacteristic
29#66977C2211yescharacteristic
30#66977C2211yescharacteristic
31C2×Dic11⋊C4—21no—
32C2×Dic44C2211yescharacteristic
33C2×#4313C2211yescharacteristic
34#66950C2211yescharacteristic
35C4⋊C4×D11C2211yescharacteristic
36#66943C2211yescharacteristic
37#66940C2211yescharacteristic
38#66936—21no—
39#66932—21no—
40#66925—21no—
41#66923—21no—
42C11×#103C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#102C2211yescharacteristic
45C11×#102C2211yescharacteristic
46#66899C2211yescharacteristic
47#66896C2211yescharacteristic
48C22⋊(C11⋊C8)C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50#66882C2211yescharacteristic
51#66880C2211yescharacteristic
52#66880C2211yescharacteristic
53#66879C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55#66874C2211yescharacteristic
56#66874C2211yescharacteristic
57#66872C2211yescharacteristic
58#66871C2211yescharacteristic
59C11×#41—22no—
60C11×#41—41no—
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11—21no—
63C2×D4×C11C2311yescharacteristic
64C22×C4×C11—21no—
65C22×C4×C11C2311yescharacteristic
66C2×C22⋊D11—21no—
67C2×C22⋊D11D411yescharacteristic
68C22×Dic11—21no—
69C22×Dic11—21no—
70#4341—22no—
71#4341—41no—
72C2×C4×D11—21no—
73C2×C4×D11C2311yescharacteristic
74C2×Dic22C2311yescharacteristic
75C2×Dic22C2311yescharacteristic
76C2×C8×C11—41no—
77C2×C8×C11C2311yescharacteristic
78C2×C8×C11C2311yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C11×C4⋊C4C2311yescharacteristic
81C11×C22⋊C4—21no—
82C42×C11—21no—
83C22⋊Dic11—21no—
84C22⋊Dic11—21no—
85C22⋊Dic11—21no—
86C22⋊Dic11D411yescharacteristic
87#4326—41no—
88#4324—22no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4D411yescharacteristic
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4D411yescharacteristic
105C4×Dic11—21no—
106C4×Dic11C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109Dic44—41no—
110#4313—41no—
111#3315—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11C2×D411yescharacteristic
114C22×D11C2×D411yescharacteristic
115Q8×C11—21no—
116Q8×C11—21no—
117D4×C11—21no—
118D4×C11—42no—
119D4×C11#4112yes—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—42no—
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2411yescharacteristic
128C22⋊D11—41no—
129C22⋊D11—42no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—42no—
135C2×Dic11—42no—
136C2×Dic11C2×D411yescharacteristic
137C2×Dic11C2×D411yescharacteristic
138C2×Dic11C2×D411yescharacteristic
139C4×D11—21no—
140C4×D11—21no—
141C4×D11—42no—
142Dic22—21no—
143Dic22—21no—
144Dic22—21no—
145Dic22—21no—
146C8×C11—21no—
147C8×C11—21no—
148C11⋊C8—21no—
149C11⋊C8—21no—
150#552—111no—
151#547—111no—
152#491—111no—
153#485—111no—
154#484—111no—
155#478—111no—
156#470—111no—
157#467—111no—
158#462—111no—
159#452—111no—
160#452—111no—
161#440—111no—
162#435—111no—
163#417—111no—
164#416D1111yescharacteristic, complemented
165C22×C11—21no—
166C22×C11—22no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11C22×D411yescharacteristic
172C2×D11—21no—
173C2×D11—21no—
174C2×D11—21no—
175C4×C11—21no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11C2×#4111yescharacteristic
180C4×C11H(5,𝔽2)11yescharacteristic
181Dic11—21no—
182Dic11—21no—
183Dic11—21no—
184Dic11—41no—
185Dic11—41no—
186Dic11—41no—
187Dic11—41no—
188C2×#41—111no—
189C2×#41C2×D1111yescharacteristic
190C2×Q16—111no—
191C2×Q16—111no—
192C2×SD16—111no—
193C2×M16—111no—
194C22×C8C2×D1111yescharacteristic
195C4⋊Q8—111no—
196#126—221no—
197#125—111no—
198#125—221no—
199#123—221no—
200#123—221no—
201#123—221no—
202C22⋊Q8—111no—
203C22⋊Q8—111no—
204C22⋊Q8—111no—
205C22⋊Q8—111no—
206#121—221no—
207C4×Q8—111no—
208C4×D4—111no—
209C4×D4—111no—
210#117—221no—
211#117C2×D1111yescharacteristic
212C2×C4⋊C4—111no—
213C2×C4⋊C4—221no—
214#107—111no—
215#107—111no—
216#106—111no—
217C4⋊C8—111no—
218#103—111no—
219#103—111no—
220#103—111no—
221#103—111no—
222#103—111no—
223#103C2×D1111yescharacteristic
224#103C2×D1111yescharacteristic
225#102—111no—
226#102C2×D1111yescharacteristic
227#102C2×D1111yescharacteristic
228C22⋊C8—111no—
229C22⋊C8—111no—
230#97—111no—
231C2×C11—41no—
232C2×C11—42no—
233C2×C11#54611yescharacteristic
234C2×C11#57511yescharacteristic
235C2×C11#57811yescharacteristic
236D11—41no—
237#41—22no—
238#41—41no—
239#41—222no—
240#41—441no—
241C2×Q8—111no—
242C2×Q8—111no—
243C2×Q8C22×D1111yescharacteristic
244C2×D4—21no—
245C2×D4—111no—
246C2×D4—221no—
247C2×D4C22×D1111yescharacteristic
248C22×C4—21no—
249C22×C4—111no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4C22×D1111yescharacteristic
254Q16—441no—
255Q16—441no—
256SD16—222no—
257M16—441no—
258C2×C8—41no—
259C2×C8—111no—
260C2×C8—111no—
261C2×C8C22×D1111yescharacteristic
262C2×C8C22×D1111yescharacteristic
263C4⋊C4—111no—
264C4⋊C4—111no—
265C4⋊C4—111no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4C22×D1111yescharacteristic
277C4⋊C4C22×D1111yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—111no—
280C22⋊C4—111no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C22⋊C4—221no—
284C22⋊C4—221no—
285C22⋊C4—221no—
286C42—21no—
287C42—111no—
288C42—221no—
289C11#331511yescharacteristic, complemented, Sylow
290C23—21no—
291C23—111no—
292C23D4×D1111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—221no—
296Q8—221no—
297Q8—221no—
298Q8—221no—
299D4—21no—
300D4—42no—
301D4—441no—
302D4—442no—
303D4#433912yes—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—111no—
311C2×C4—111no—
312C2×C4—111no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—442no—
320C2×C4—442no—
321C2×C4—442no—
322C2×C4D4×D1111yescharacteristic
323C2×C4C23×D1111yescharacteristic
324C8—21no—
325C8—21no—
326C8—221no—
327C8—221no—
328C22—21no—
329C22—22no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—221no—
335C22—221no—
336C22—221no—
337C22C2×D4×D1111yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—221no—
343C4—221no—
344C4—221no—
345C4—441no—
346C4—441no—
347C4—441no—
348C4—441no—
349C4C2×#433911yescharacteristic
350C4#6703711yescharacteristic
351C2—41no—
352C2—42no—
353C2—441no—
354C2#1062302111yescharacteristic
355C2#1062329911yescharacteristic
356C2#1062330211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#416C2
socleC22×C11C22×D4
prime radical#10623355C2
hypercenter#416D11
hypocenterC11#3315
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. #10623060C2semidirect
3. C11×#416C2semidirect
4. #10622852C2semidirect
5. #10622729C2semidirect
6. #10622724C2semidirect
7. #10622609C2semidirect
8. #10622429C2semidirect
9. #10622422C2semidirect
10. #10622410C2semidirect
11. #10622406C2semidirect
12. #10622396C2semidirect
13. #10622384C2semidirect
14. #10622379C2semidirect
15. #10622370C2semidirect
164. #416D11semidirect
289. C11#3315semidirect

Maximal subgroups

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

subgroupindex
#106233552
#106230602
C11×#4162
#106228522
#106227292
#106227242
#106226092
#106224292
#106224222
#106224102
#106224062
#106223962
#106223842
#106223792
#106223702
#331511