Finite Group Databasebeta

← #14672176

Subgroups — #14672176

Order 2816.

426 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
1C2×#10622807C211yesmaximal, characteristic
2C2×#10622131C211yesmaximal, characteristic, complemented
3C2×#10622205C211yesmaximal, characteristic, complemented
4C2×#10622135C211yesmaximal, characteristic, complemented
5C2×C4×C11⋊C16C211yesmaximal, characteristic, complemented
6#13069504C211yesmaximal, characteristic, complemented
7C11×#1974C211yesmaximal, characteristic, complemented
8C2×C11×#135C2211yescharacteristic
9C2×#66957C2211yescharacteristic
10C2×C11×#108C2211yescharacteristic
11C2×C11×#104—21no—
12C11×#408—21no—
13C2×C4×C8×C11C2211yescharacteristic
14#10622807—22no—
15#10622807—22no—
16C2×#66893C411yescharacteristic, complemented
17C2×#66892C411yescharacteristic, complemented
18C2×#66891C411yescharacteristic, complemented
19C2×#66890C411yescharacteristic, complemented
20#10622723—21no—
21C2×#66883C2211yescharacteristic
22C22×C11⋊C16C2211yescharacteristic
23C22×C11⋊C16C2211yescharacteristic
24C2×#66869—21no—
25#10622205—22no—
26#10622135—22no—
27#10622131—22no—
28C4×C11⋊C16—22no—
29C2×C11×#41—21no—
30C2×#4339—21no—
31C11×#135—21no—
32C11×#135—21no—
33C11×#135—21no—
34C11×#135—21no—
35C2×C11×Q16C2×C411yescharacteristic
36C2×C11×SD16—21no—
37C2×C11×D8C2×C411yescharacteristic
38C2×C11×M16—21no—
39C22×C8×C11D411yescharacteristic
40C22×C8×C11C2311yescharacteristic
41C2×C42×C11D411yescharacteristic
42C2×#4318—21no—
43C2×Dic44C2×C411yescharacteristic
44#66957—21no—
45#66957—21no—
46#66957—21no—
47#66957—21no—
48C2×D88C2×C411yescharacteristic
49C2×#4314—21no—
50C11×#108—21no—
51C11×#108—21no—
52C11×#104—42no—
53C11×C22⋊C8—42no—
54C4×C8×C11—21no—
55C4×C8×C11—21no—
56#66893—22no—
57#66892—22no—
58#66891—22no—
59#66890—22no—
60(C2×D11)⋊C8—42no—
61#66883—21no—
62#66883—21no—
63C2×C11⋊C16—21no—
64C2×C11⋊C16—21no—
65C2×C11⋊C16C2×C411yescharacteristic
66C2×C11⋊C16C2×C411yescharacteristic
67C2×C11⋊C16D412yes—
68C2×C11⋊C16D412yes—
69C2×C11⋊C16D412yes—
70#66869—42no—
71#13241—111nomaximal, Sylow
72C11×#41—41no—
73C11×#41—41no—
74C11×#41—41no—
75C11×#41—41no—
76C2×Q8×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—41no—
79C22×C4×C11—21no—
80C22×C4×C11—41no—
81C22×C4×C11C2×D411yescharacteristic
82C2×C22⋊D11—41no—
83#4339—41no—
84#4339—41no—
85#4339—41no—
86#4339—41no—
87C2×D44—21no—
88C2×C4×D11—41no—
89C2×Dic22—21no—
90C11×Q16—21no—
91C11×Q16—21no—
92C11×SD16—41no—
93C11×SD16—41no—
94C11×D8—21no—
95C11×D8—21no—
96C11×M16—41no—
97C11×M16—41no—
98C2×C8×C11—21no—
99C2×C8×C11—21no—
100C2×C8×C11—41no—
101C2×C8×C11D812yes—
102C2×C8×C11C22×C411yescharacteristic
103C2×C8×C11C2×D411yescharacteristic
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11#4111yescharacteristic
107C2×C8×C11#4111yescharacteristic
108C42×C11—21no—
109C42×C11D812yes—
110#4318—41no—
111#4318—41no—
112C2×C11⋊C8—41no—
113Dic44—21no—
114Dic44—21no—
115D88—21no—
116D88—21no—
117#4314—41no—
118#4314—41no—
119C11⋊C16—22no—
120C11⋊C16C22⋊C412yes—
121C11⋊C16C22⋊C412yes—
122C2×#508—111no—
123C2×#368—111no—
124C2×#359—111no—
125C2×#359—111no—
126C2×C4×C16—111no—
127#1974—111no—
128#1974D1111yescharacteristic, complemented
129C23×C11—41no—
130C23×C11#13511yescharacteristic
131C22×D11—41no—
132Q8×C11—41no—
133Q8×C11—41no—
134D4×C11—41no—
135D4×C11—41no—
136D4×C11—81no—
137D4×C11—81no—
138C2×C4×C11—24no—
139C2×C4×C11—22no—
140C2×C4×C11—41no—
141C2×C4×C11—81no—
142C2×C4×C11—81no—
143C2×C4×C11C4×D411yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12711yescharacteristic
146C2×C4×C11C2×D811yescharacteristic
147C2×C4×C11C2×D811yescharacteristic
148C2×C4×C11#13511yescharacteristic
149C22⋊D11—81no—
150C22⋊D11—81no—
151C2×Dic11—41no—
152D44—41no—
153D44—41no—
154C4×D11—81no—
155C4×D11—81no—
156Dic22—41no—
157Dic22—41no—
158C8×C11—22no—
159C8×C11—81no—
160C8×C11C2×C22⋊C411yescharacteristic
161C8×C11C4×D411yescharacteristic
162C8×C11#12111yescharacteristic
163C8×C11#12411yescharacteristic
164C11⋊C8—81no—
165C2×#135—111no—
166C2×#135C2×D1111yescharacteristic
167#508—222no—
168#508—222no—
169C2×Q32—111no—
170C2×SD32—111no—
171C2×SD32—111no—
172C2×D16—111no—
173C22×C16—111no—
174C22×C16—111no—
175C2×#108—111no—
176C2×#108C2×D1111yescharacteristic
177C2×#104—21no—
178C2×#104—221no—
179#408—21no—
180#408—221no—
181C2×C4×C8C2×D1111yescharacteristic
182#368—222no—
183#359—222no—
184#359—222no—
185C4×C16—222no—
186C22×C11—22no—
187C22×C11—82no—
188C22×C11—81no—
189C22×C11C4×D811yescharacteristic
190C22×C11#46611yescharacteristic
191C22×C11#49511yescharacteristic
192C2×D11—82no—
193C2×D11—81no—
194C4×C11—24no—
195C4×C11—81no—
196C4×C11#39011yescharacteristic
197C4×C11C4×D811yescharacteristic
198C4×C11#46611yescharacteristic
199C4×C11#49311yescharacteristic
200Dic11—81no—
201C2×#41—21no—
202C2×#41—221no—
203#135—21no—
204#135—21no—
205#135—21no—
206#135—21no—
207#135—221no—
208#135—221no—
209#135—221no—
210#135—221no—
211C2×Q16—111no—
212C2×Q16C4×D1111yescharacteristic
213C2×SD16—21no—
214C2×SD16—221no—
215C2×D8—111no—
216C2×D8C4×D1111yescharacteristic
217C2×M16—21no—
218C2×M16—221no—
219C22×C8C22⋊D1111yescharacteristic
220C22×C8C22×D1111yescharacteristic
221C2×C42C22⋊D1111yescharacteristic
222Q32—222no—
223SD32—222no—
224SD32—222no—
225D16—222no—
226C2×C16—111no—
227C2×C16—111no—
228C2×C16—112no—
229C2×C16—112no—
230C2×C16—112no—
231C2×C16—221no—
232C2×C16—221no—
233#108—21no—
234#108—21no—
235#108—221no—
236#108—221no—
237#104—42no—
238#104—442no—
239C22⋊C8—42no—
240C22⋊C8—442no—
241C4×C8—21no—
242C4×C8—21no—
243C2×C11—21no—
244C2×C11—21no—
245C2×C11—161no—
246C2×C11#197011yescharacteristic
247C2×C11#217812yes—
248D11—161no—
249#41—41no—
250#41—41no—
251#41—41no—
252#41—41no—
253#41—441no—
254#41—441no—
255#41—441no—
256#41—441no—
257C2×Q8—21no—
258C2×Q8—221no—
259C2×D4—21no—
260C2×D4—41no—
261C2×D4—221no—
262C2×D4—441no—
263C22×C4—21no—
264C22×C4—41no—
265C22×C4—441no—
266C22×C4C2×C22⋊D1111yescharacteristic
267Q16—21no—
268Q16—21no—
269Q16—221no—
270Q16—221no—
271SD16—41no—
272SD16—41no—
273SD16—441no—
274SD16—441no—
275D8—21no—
276D8—21no—
277D8—221no—
278D8—221no—
279M16—41no—
280M16—41no—
281M16—441no—
282M16—441no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—41no—
286C2×C8—441no—
287C2×C8#432312yes—
288C2×C8C2×C4×D1111yescharacteristic
289C2×C8#433911yescharacteristic
290C2×C8D4×D1111yescharacteristic
291C2×C8D4×D1111yescharacteristic
292C2×C8D4×D1111yescharacteristic
293C2×C8#434111yescharacteristic
294C42—21no—
295C42#432312yes—
296C16—112no—
297C16—112no—
298C16—222no—
299C11#1324111yescharacteristic, complemented, Sylow
300C23—41no—
301C23—441no—
302C23#6700311yescharacteristic
303Q8—41no—
304Q8—41no—
305Q8—441no—
306Q8—441no—
307D4—41no—
308D4—41no—
309D4—81no—
310D4—81no—
311D4—441no—
312D4—441no—
313D4—881no—
314D4—881no—
315C2×C4—24no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—441no—
321C2×C4—881no—
322C2×C4—881no—
323C2×C4C4×C22⋊D1111yescharacteristic
324C2×C4C2×#432311yescharacteristic
325C2×C4C2×#432311yescharacteristic
326C2×C4#6699211yescharacteristic
327C2×C4#6699311yescharacteristic
328C2×C4#6700311yescharacteristic
329C8—22no—
330C8—81no—
331C8—881no—
332C8C22⋊C4×D1111yescharacteristic
333C8(C22⋊D11)⋊C411yescharacteristic
334C8#6693711yescharacteristic
335C8#6693811yescharacteristic
336C22—22no—
337C22—82no—
338C22—81no—
339C22—882no—
340C22—881no—
341C22C4×#432311yescharacteristic
342C22#1062265111yescharacteristic
343C22#1062267211yescharacteristic
344C4—24no—
345C4—81no—
346C4—881no—
347C4#1062257011yescharacteristic
348C4C4×#432311yescharacteristic
349C4#1062265111yescharacteristic
350C4#1062268611yescharacteristic
351C2—21no—
352C2—21no—
353C2—161no—
354C2—1761no—
355C2#1306948111yescharacteristic
356C2#1307049512yes—
subgroupG/H
centerC2×C4C2×#4323
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1974C2
socleC22×C11C4×D8
prime radicalC2×#10622807C2
cosocleC22×C8×C11C23
hypercenter#1974D11
hypocenterC11#13241
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4×C8 ◁ #1974

Complements

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

NH ≅ G/Ntype
2. C2×#10622131C2semidirect
3. C2×#10622205C2semidirect
4. C2×#10622135C2semidirect
5. C2×C4×C11⋊C16C2semidirect
6. #13069504C2semidirect
7. C11×#1974C2semidirect
16. C2×#66893C4semidirect
17. C2×#66892C4semidirect
18. C2×#66891C4semidirect
19. C2×#66890C4semidirect
128. #1974D11semidirect
299. C11#13241semidirect

Maximal subgroups

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

subgroupindex
C2×#106228072
C2×#106221312
C2×#106222052
C2×#106221352
C2×C4×C11⋊C162
#130695042
C11×#19742
#1324111