Finite Group Databasebeta

← #14910397

Subgroups — #14910397

Order 2816.

664 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622792C212yesmaximal, complemented
2#13080338C211yesmaximal, characteristic
3#13070868C211yesmaximal, characteristic, complemented
4#13070722C212yesmaximal, complemented
5#13070666C211yesmaximal, characteristic, complemented
6#13070658C211yesmaximal, characteristic, complemented
7#13070554C212yesmaximal, complemented
8#13070550C212yesmaximal, complemented
9C4×#66892C211yesmaximal, characteristic, complemented
10#13070448C211yesmaximal, characteristic, complemented
11D4×C11×Q16C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2212yes—
13D4×Q8×C11—21no—
14C2×#66957C2212yes—
15#10623082—21no—
16C11×#494C2211yescharacteristic
17C11×#467C2212yes—
18C11×#462—21no—
19C11×#451—22no—
20C4×C11×Q16C2211yescharacteristic
21C8×D4×C11C2211yescharacteristic
22C2×#66893C2212yes—
23C2×#66893C2212yes—
24C2×#66893C2212yes—
25#10622792—28no—
26C2×#66892C2212yes—
27C2×#66892C2211yescharacteristic
28#10622729C2212yes—
29C2×#66876C2212yes—
30#10622454—21no—
31#10622346—22no—
32#10622312C2211yescharacteristic
33C4×D88C2211yescharacteristic
34#10622202C2212yes—
35#10622202C2211yescharacteristic
36C22⋊(C11⋊C16)C2212yes—
37#10622130C2212yes—
38#10622129C2211yescharacteristic
39#10622128C2211yescharacteristic
40C4⋊(C11⋊C16)C2211yescharacteristic
41C4×C11⋊C16C2211yescharacteristic
42C22×Q8×C11—22no—
43C2×#4339—22no—
44C2×C11×Q16—24no—
45C2×C11×Q16—22no—
46C2×C11×Q16—21no—
47C2×C11×Q16—42no—
48C2×C11×Q16C2312yes—
49C2×C11×Q16C2311yescharacteristic
50C22×C8×C11C2312yes—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—41no—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8—42no—
55C4×Q8×C11—21no—
56C4×D4×C11—41no—
57C4×D4×C11D411yescharacteristic
58#66991—41no—
59#66977—22no—
60C2×Dic44—21no—
61C2×Dic44C2312yes—
62#66957—24no—
63#66957—42no—
64C2×D88C2311yescharacteristic
65C2×#4314—22no—
66C4⋊C4×D11—41no—
67#66936—42no—
68C4×D44—21no—
69#66922—21no—
70C11×#107C2311yescharacteristic
71C11×C4⋊C8D411yescharacteristic
72C11×#103—21no—
73C11×#103—22no—
74C11×C22⋊C8D412yes—
75C4×C8×C11C2311yescharacteristic
76#66893—24no—
77#66893—24no—
78#66893—42no—
79#66892—24no—
80#66892D414yescomplemented
81#66885—21no—
82#66882C2311yescharacteristic
83#66880—22no—
84#66876—24no—
85C2×C11⋊C16C2312yes—
86C2×C11⋊C16C2311yescharacteristic
87C2×C11⋊C16C2311yescharacteristic
88#33842—111nomaximal, Sylow
89C2×Q8×C11—21no—
90C2×Q8×C11—22no—
91C2×Q8×C11—44no—
92C2×Q8×C11—42no—
93C2×Q8×C11—82no—
94C2×D4×C11D811yescharacteristic
95C22×C4×C11—42no—
96C22×C4×C11C2×D412yes—
97C2×C22⋊D11—42no—
98#4339—44no—
99#4339—82no—
100C2×D44—21no—
101C2×C4×D11—41no—
102C2×C4×D11—42no—
103C2×Dic22—22no—
104C11×Q16—21no—
105C11×Q16—22no—
106C11×Q16—22no—
107C11×Q16—44no—
108C11×Q16—81no—
109C11×Q16C2×D412yes—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11C2×D412yes—
113C2×C8×C11C2×D411yescharacteristic
114C2×C8×C11C2411yescharacteristic
115C11×C4⋊C4—21no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—42no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4D811yescharacteristic
121C11×C22⋊C4—42no—
122C11×C22⋊C4D812yes—
123C42×C11—41no—
124C42×C11C2×D411yescharacteristic
125C22⋊Dic11—42no—
126(C2×D11)⋊C4—41no—
127C4⋊Dic11—21no—
128C4⋊Dic11—41no—
129C4⋊Dic11—41no—
130Dic11⋊C4—42no—
131Dic44—22no—
132Dic44—22no—
133Dic44—81no—
134D88—21no—
135D88C2×D412yes—
136#4314—44no—
137C11⋊C16—22no—
138C11⋊C16—21no—
139C11⋊C16C2×D412yes—
140C2×#510—112no—
141D4×Q16D1111yescharacteristic, complemented
142#3283—111no—
143#2247—111no—
144#2219—112no—
145#2209—111no—
146#2208—111no—
147#2189—112no—
148#2188—112no—
149C4×SD32—111no—
150#2169—111no—
151C23×C11C2×D812yes—
152C22×D11—41no—
153Q8×C11—22no—
154Q8×C11—41no—
155Q8×C11—42no—
156Q8×C11—42no—
157Q8×C11—84no—
158D4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—42no—
164C2×C4×C11—84no—
165C2×C4×C11C2×D812yes—
166C2×C4×C11C2×D811yescharacteristic
167C2×C4×C11C2×D811yescharacteristic
168C2×C4×C11C22×D411yescharacteristic
169C22⋊D11—84no—
170C2×Dic11—41no—
171C2×Dic11—42no—
172D44—22no—
173D44—41no—
174C4×D11—84no—
175C4×D11—82no—
176Dic22—42no—
177Dic22—42no—
178C8×C11—22no—
179C8×C11—21no—
180C8×C11C22×D411yescharacteristic
181C8×C11H(5,𝔽2)11yescharacteristic
182C2×#135—112no—
183C22×Q16C2×D1112yes—
184D4×Q8—21no—
185#547—221no—
186#510—228no—
187C2×Q32—112no—
188C2×Q32—112no—
189C2×Q32—112no—
190C2×SD32—111no—
191C2×SD32—112no—
192C2×M32—112no—
193#494—111no—
194#494C2×D1111yescharacteristic
195#467—112no—
196#467C2×D1112yes—
197#462—21no—
198#461—221no—
199#452—222no—
200#451—22no—
201C4×Q16C2×D1111yescharacteristic
202C4×D8—111no—
203C8×D4C2×D1111yescharacteristic
204#367—111no—
205C4⋊C16—111no—
206#358—111no—
207#358—112no—
208#358—112no—
209#357—111no—
210C22⋊C16—112no—
211C4×C16—111no—
212C22×C11—22no—
213C22×C11—22no—
214C22×C11—22no—
215C22×C11C22×D811yescharacteristic
216C2×D11—42no—
217C2×D11—81no—
218C2×D11—81no—
219C4×C11—21no—
220C4×C11—22no—
221C4×C11—42no—
222C4×C11—81no—
223C4×C11—82no—
224C4×C11#51012yescomplemented
225C4×C11D4211yescharacteristic
226C4×C11#57611yescharacteristic
227Dic11—81no—
228Dic11—82no—
229C2×#41—222no—
230C22×Q8—22no—
231#135—224no—
232#135—442no—
233C2×Q16—24no—
234C2×Q16—22no—
235C2×Q16—21no—
236C2×Q16—42no—
237C2×Q16—112no—
238C2×Q16—221no—
239C2×Q16C22×D1112yes—
240C2×Q16C22×D1111yescharacteristic
241C2×SD16—222no—
242C2×D8—111no—
243C22×C8C22×D1112yes—
244C4⋊Q8—21no—
245C4⋊Q8—41no—
246C4⋊Q8—221no—
247#123—442no—
248C22⋊Q8—22no—
249C22⋊Q8—42no—
250C22⋊Q8—222no—
251#121—441no—
252C4×Q8—21no—
253C4×D4—41no—
254C4×D4—221no—
255C4×D4C22⋊D1111yescharacteristic
256C2×C4⋊C4—441no—
257Q32—224no—
258Q32—224no—
259Q32—442no—
260SD32—114no—
261SD32—224no—
262M32—224no—
263C2×C16—111no—
264C2×C16—111no—
265C2×C16—112no—
266#107—111no—
267#107C22×D1111yescharacteristic
268C4⋊C8C22⋊D1111yescharacteristic
269#103—21no—
270#103—22no—
271#103—222no—
272#102—221no—
273C22⋊C8C22⋊D1112yes—
274C4×C8C22×D1111yescharacteristic
275C2×C11—42no—
276C2×C11D4×D811yescharacteristic
277C2×C11C2×#51011yescharacteristic
278C2×C11#341711yescharacteristic
279D11—82no—
280#41—444no—
281#41—882no—
282C2×Q8—21no—
283C2×Q8—22no—
284C2×Q8—44no—
285C2×Q8—42no—
286C2×Q8—82no—
287C2×Q8—222no—
288C2×D4—221no—
289C2×D4—442no—
290C2×D4#432311yescharacteristic
291C22×C4—42no—
292C22×C4—441no—
293C22×C4—442no—
294C22×C4C2×C22⋊D1112yes—
295Q16—22no—
296Q16—21no—
297Q16—22no—
298Q16—44no—
299Q16—81no—
300Q16—222no—
301Q16—222no—
302Q16—881no—
303Q16D4×D1112yes—
304SD16—444no—
305D8—112no—
306D8—221no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8C2×C22⋊D1111yescharacteristic
310C2×C8C2×C22⋊D1112yes—
311C2×C8C23×D1111yescharacteristic
312C4⋊C4—21no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—42no—
316C4⋊C4—41no—
317C4⋊C4—221no—
318C4⋊C4—441no—
319C4⋊C4—442no—
320C4⋊C4—441no—
321C4⋊C4#432311yescharacteristic
322C22⋊C4—42no—
323C22⋊C4—442no—
324C22⋊C4—441no—
325C22⋊C4#432312yes—
326C42—41no—
327C42C2×C22⋊D1111yescharacteristic
328C16—112no—
329C16—222no—
330C16—221no—
331C11#3384211yescharacteristic, complemented, Sylow
332C23—441no—
333C23C2×#432312yes—
334Q8—22no—
335Q8—41no—
336Q8—42no—
337Q8—42no—
338Q8—84no—
339Q8—442no—
340Q8—442no—
341D4—22no—
342D4—222no—
343D4—441no—
344D4—884no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—84no—
351C2×C4—441no—
352C2×C4—442no—
353C2×C4—884no—
354C2×C4—882no—
355C2×C4C2×#432311yescharacteristic
356C2×C4C2×#432312yes—
357C2×C4C2×#432311yescharacteristic
358C2×C4C22×C22⋊D1111yescharacteristic
359C8—22no—
360C8—21no—
361C8C2×D4×D1111yescharacteristic
362C8#6703711yescharacteristic
363C22—22no—
364C22—22no—
365C22—22no—
366C22—442no—
367C22—881no—
368C22—881no—
369C22C22×#432311yescharacteristic
370C4—21no—
371C4—22no—
372C4—42no—
373C4—81no—
374C4—82no—
375C4—881no—
376C4—882no—
377C4#1062279212yescomplemented
378C4D4×C22⋊D1111yescharacteristic
379C4#1062336611yescharacteristic
380C2—42no—
381C2—882no—
382C2D4×#432311yescharacteristic
383C2C2×#1062279211yescharacteristic
384C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingD4×C11×Q16C2
socleC22×C11C22×D8
prime radical#13080338C2
hypercenterD4×Q16D11
hypocenterC11#33842
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#10622792C2semidirect
3. #13070868C2semidirect
4. #13070722C2semidirect
5. #13070666C2semidirect
6. #13070658C2semidirect
7. #13070554C2semidirect
8. #13070550C2semidirect
9. C4×#66892C2semidirect
10. #13070448C2semidirect
11. D4×C11×Q16C2semidirect
80. #66892D4semidirect
141. D4×Q16D11semidirect
224. C4×C11#510semidirect
331. C11#33842semidirect
377. C4#10622792semidirect

Maximal subgroups

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

subgroupindex
C2×#106227922
#130803382
#130708682
#130707222
#130706662
#130706582
#130705542
#130705502
C4×#668922
#130704482
D4×C11×Q162
#3384211