Finite Group Databasebeta

← #14672186

Subgroups — #14672186

Order 2816.

410 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622807C211yesmaximal, characteristic
2#13070398C211yesmaximal, characteristic, complemented
3#13070352C211yesmaximal, characteristic, complemented
4#13070351C211yesmaximal, characteristic, complemented
5#13070213C211yesmaximal, characteristic, complemented
6#13069514C211yesmaximal, characteristic, complemented
7C11×#1976C211yesmaximal, characteristic, complemented
8C2×C11×#135C2211yescharacteristic
9C2×#66957C2211yescharacteristic
10C11×#427C2211yescharacteristic
11C11×#421—21no—
12C11×#410—21no—
13C11×#405C2211yescharacteristic
14#10622807—21no—
15#10622807—21no—
16#10622807—21no—
17#10622807—21no—
18C2×#66893C411yescharacteristic, complemented
19C2×#66892C411yescharacteristic, complemented
20C2×#66891C411yescharacteristic, complemented
21C2×#66890C411yescharacteristic, complemented
22#10622752—21no—
23#10622719C2211yescharacteristic
24C2×#66876C2211yescharacteristic
25C22×C11⋊C16C2211yescharacteristic
26#10622619—21no—
27#10622204—22no—
28#10622128—21no—
29#10622127—21no—
30#10622126—22no—
31#10622099—21no—
32C4×C11⋊C16—21no—
33C2×C11×#41—21no—
34C2×#4339—21no—
35C11×#135—21no—
36C11×#135—21no—
37C11×#135—21no—
38C11×#135—21no—
39C2×C11×Q16C2×C411yescharacteristic
40C2×C11×SD16—21no—
41C2×C11×D8C2×C411yescharacteristic
42C2×C11×M16D411yescharacteristic
43C22×C8×C11C2311yescharacteristic
44C11×#117—21no—
45C11×#117D411yescharacteristic
46#66979—21no—
47C2×Dic44C2×C411yescharacteristic
48#66957—21no—
49#66957—21no—
50#66957—21no—
51#66957—21no—
52C2×D88C2×C411yescharacteristic
53C2×#4314—21no—
54C11×#107—21no—
55C11×#106—21no—
56C11×#104—42no—
57C11×#99—42no—
58C11×#97—21no—
59C4×C8×C11—21no—
60#66893—21no—
61#66893—21no—
62#66892—21no—
63#66892—21no—
64#66891—21no—
65#66891—21no—
66#66890—21no—
67#66890—21no—
68#66889—42no—
69#66882—21no—
70#66881—21no—
71#66876—21no—
72#66876D412yes—
73C2×C11⋊C16—21no—
74C2×C11⋊C16C2×C411yescharacteristic
75C2×C11⋊C16C2×C411yescharacteristic
76C2×C11⋊C16D411yescharacteristic
77C2×C11⋊C16D411yescharacteristic
78C2×C11⋊C16D411yescharacteristic
79C2×C11⋊C16D411yescharacteristic
80#66870—42no—
81#13243—111nomaximal, Sylow
82C11×#41—41no—
83C11×#41—41no—
84C11×#41—41no—
85C11×#41—41no—
86C2×Q8×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11C2×D411yescharacteristic
91C2×C22⋊D11—41no—
92#4339—41no—
93#4339—41no—
94#4339—41no—
95#4339—41no—
96C2×D44—21no—
97C2×C4×D11—41no—
98C2×Dic22—21no—
99C11×Q16—21no—
100C11×Q16—21no—
101C11×SD16—41no—
102C11×SD16—41no—
103C11×D8—21no—
104C11×D8—21no—
105C11×M16—21no—
106C11×M16D812yes—
107C2×C8×C11—21no—
108C2×C8×C11C22×C411yescharacteristic
109C2×C8×C11C2×D411yescharacteristic
110C2×C8×C11C2×D411yescharacteristic
111C2×C8×C11C2×D411yescharacteristic
112C2×C8×C11#4111yescharacteristic
113C2×C8×C11#4111yescharacteristic
114C11×C4⋊C4—21no—
115C11×C4⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4D812yes—
118C42×C11—21no—
119C42×C11—41no—
120C22⋊Dic11—41no—
121C4⋊Dic11—41no—
122C4×Dic11—41no—
123Dic44—21no—
124Dic44—21no—
125D88—21no—
126D88—21no—
127#4314—41no—
128#4314—41no—
129C11⋊C16—22no—
130C11⋊C16C22⋊C411yescharacteristic
131C11⋊C16C22⋊C411yescharacteristic
132C11⋊C16C22⋊C411yescharacteristic
133C11⋊C16C22⋊C411yescharacteristic
134C2×#508—111no—
135#2158—111no—
136#2145—111no—
137#2145—111no—
138#2108—111no—
139#1976—111no—
140#1976D1111yescharacteristic, complemented
141C23×C11—41no—
142C23×C11C2×D811yescharacteristic
143C22×D11—41no—
144Q8×C11—41no—
145Q8×C11—41no—
146D4×C11—41no—
147D4×C11—41no—
148D4×C11—81no—
149D4×C11—81no—
150C2×C4×C11—22no—
151C2×C4×C11—41no—
152C2×C4×C11—81no—
153C2×C4×C11—81no—
154C2×C4×C11—81no—
155C2×C4×C11C4×D411yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12711yescharacteristic
158C2×C4×C11C2×D811yescharacteristic
159C2×C4×C11#13511yescharacteristic
160C2×C4×C11#13511yescharacteristic
161C22⋊D11—81no—
162C22⋊D11—81no—
163C2×Dic11—41no—
164C2×Dic11—81no—
165D44—41no—
166D44—41no—
167C4×D11—81no—
168C4×D11—81no—
169Dic22—41no—
170Dic22—41no—
171C8×C11—22no—
172C8×C11C2×C22⋊C411yescharacteristic
173C8×C11C4×D411yescharacteristic
174C8×C11#12111yescharacteristic
175C8×C11#12411yescharacteristic
176C2×#135—111no—
177C2×#135C2×D1111yescharacteristic
178#508—221no—
179#508—221no—
180#508—221no—
181#508—221no—
182C2×Q32—111no—
183C2×SD32—111no—
184C2×SD32—111no—
185C2×D16—111no—
186C2×M32—111no—
187C22×C16—111no—
188#427—111no—
189#427C2×D1111yescharacteristic
190#421—21no—
191#421—221no—
192#410—21no—
193#410—221no—
194#405C2×D1111yescharacteristic
195#367—221no—
196#366—221no—
197#360—222no—
198#360—222no—
199#346—221no—
200C4×C16—221no—
201C22×C11—41no—
202C22×C11—81no—
203C22×C11—161no—
204C22×C11C4×D811yescharacteristic
205C22×C11#46611yescharacteristic
206C22×C11#49311yescharacteristic
207C2×D11—81no—
208C2×D11—161no—
209C4×C11—42no—
210C4×C11—81no—
211C4×C11—161no—
212C4×C11#39011yescharacteristic
213C4×C11C4×D811yescharacteristic
214C4×C11#46611yescharacteristic
215C4×C11#49511yescharacteristic
216Dic11—81no—
217Dic11—161no—
218C2×#41—21no—
219C2×#41—221no—
220#135—21no—
221#135—21no—
222#135—21no—
223#135—21no—
224#135—221no—
225#135—221no—
226#135—221no—
227#135—221no—
228C2×Q16—111no—
229C2×Q16C4×D1111yescharacteristic
230C2×SD16—21no—
231C2×SD16—221no—
232C2×D8—111no—
233C2×D8C4×D1111yescharacteristic
234C2×M16C22⋊D1111yescharacteristic
235C22×C8C22×D1111yescharacteristic
236#117—21no—
237#117—221no—
238#117C22⋊D1111yescharacteristic
239Q32—221no—
240Q32—221no—
241SD32—221no—
242SD32—221no—
243SD32—221no—
244SD32—221no—
245D16—221no—
246D16—221no—
247M32—112no—
248M32—221no—
249C2×C16—111no—
250C2×C16—111no—
251C2×C16—111no—
252C2×C16—111no—
253C2×C16—111no—
254C2×C16—111no—
255C2×C16—221no—
256#107—21no—
257#107—221no—
258#106—21no—
259#106—221no—
260#104—42no—
261#104—442no—
262#99—42no—
263#99—442no—
264#97—21no—
265C4×C8—21no—
266C2×C11—21no—
267C2×C11—21no—
268C2×C11—21no—
269C2×C11—161no—
270C2×C11#197011yescharacteristic
271D11—161no—
272#41—41no—
273#41—41no—
274#41—41no—
275#41—41no—
276#41—441no—
277#41—441no—
278#41—441no—
279#41—441no—
280C2×Q8—21no—
281C2×Q8—221no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4—221no—
285C2×D4—441no—
286C22×C4—41no—
287C22×C4—441no—
288C22×C4C2×C22⋊D1111yescharacteristic
289Q16—21no—
290Q16—21no—
291Q16—221no—
292Q16—221no—
293SD16—41no—
294SD16—41no—
295SD16—441no—
296SD16—441no—
297D8—21no—
298D8—21no—
299D8—221no—
300D8—221no—
301M16—21no—
302M16#432312yes—
303C2×C8—21no—
304C2×C8C2×C4×D1111yescharacteristic
305C2×C8#433911yescharacteristic
306C2×C8D4×D1111yescharacteristic
307C2×C8D4×D1111yescharacteristic
308C2×C8D4×D1111yescharacteristic
309C2×C8#434111yescharacteristic
310C4⋊C4—21no—
311C4⋊C4—41no—
312C4⋊C4—441no—
313C22⋊C4—41no—
314C22⋊C4—441no—
315C22⋊C4#432312yes—
316C42—21no—
317C42—41no—
318C42—441no—
319C16—111no—
320C16—111no—
321C16—111no—
322C16—111no—
323C16—222no—
324C11#1324311yescharacteristic, complemented, Sylow
325C23—41no—
326C23—441no—
327C23C2×#432311yescharacteristic
328Q8—41no—
329Q8—41no—
330Q8—441no—
331Q8—441no—
332D4—41no—
333D4—41no—
334D4—81no—
335D4—81no—
336D4—441no—
337D4—441no—
338D4—881no—
339D4—881no—
340C2×C4—22no—
341C2×C4—41no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—441no—
346C2×C4—881no—
347C2×C4—881no—
348C2×C4—881no—
349C2×C4C4×C22⋊D1111yescharacteristic
350C2×C4C2×#432311yescharacteristic
351C2×C4#6699211yescharacteristic
352C2×C4#6699311yescharacteristic
353C2×C4#6700311yescharacteristic
354C2×C4#6700311yescharacteristic
355C8—22no—
356C8C22⋊C4×D1111yescharacteristic
357C8(C22⋊D11)⋊C411yescharacteristic
358C8#6693711yescharacteristic
359C8#6693811yescharacteristic
360C22—41no—
361C22—81no—
362C22—161no—
363C22—881no—
364C22—1761no—
365C22C4×#432311yescharacteristic
366C22#1062265111yescharacteristic
367C22#1062268611yescharacteristic
368C4—42no—
369C4—81no—
370C4—161no—
371C4—881no—
372C4—1761no—
373C4#1062257011yescharacteristic
374C4C4×#432311yescharacteristic
375C4#1062265111yescharacteristic
376C4#1062267211yescharacteristic
377C2—21no—
378C2—21no—
379C2—21no—
380C2—161no—
381C2—1761no—
382C2#1306948111yescharacteristic
subgroupG/H
centerC4#10622651
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1976C2
socleC2×C11#1970
prime radicalC2×#10622807C2
cosocleC22×C8×C11C23
hypercenter#1976D11
hypocenterC11#13243
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #405 ◁ #1976

Complements

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

NH ≅ G/Ntype
2. #13070398C2semidirect
3. #13070352C2semidirect
4. #13070351C2semidirect
5. #13070213C2semidirect
6. #13069514C2semidirect
7. C11×#1976C2semidirect
18. C2×#66893C4semidirect
19. C2×#66892C4semidirect
20. C2×#66891C4semidirect
21. C2×#66890C4semidirect
140. #1976D11semidirect
324. C11#13243semidirect

Maximal subgroups

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

subgroupindex
C2×#106228072
#130703982
#130703522
#130703512
#130702132
#130695142
C11×#19762
#1324311