Finite Group Databasebeta

← #14670824

Subgroups — #14670824

Order 2816.

476 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×#10622517C211yesmaximal, characteristic
2C2×#10622508C211yesmaximal, characteristic, complemented
3C2×#10622135C211yesmaximal, characteristic, complemented
4C2×#10622135C211yesmaximal, characteristic, complemented
5#13069502C211yesmaximal, characteristic, complemented
6#13066693C211yesmaximal, characteristic, complemented
7C11×#1381C211yesmaximal, characteristic, complemented
8C2×#66960—21no—
9C2×#66957C2211yescharacteristic
10C2×#66957C2211yescharacteristic
11C22×C11×C16C2211yescharacteristic
12C2×C11×#108C2211yescharacteristic
13C2×C11×#108C2211yescharacteristic
14C2×#66889—21no—
15C2×#66889—21no—
16#10622742—21no—
17C2×C8×Dic11C2211yescharacteristic
18C22×C11⋊C16C2211yescharacteristic
19C2×Dic88C411yescharacteristic, complemented
20#10622517—22no—
21#10622517—22no—
22C2×#66864C411yescharacteristic, complemented
23C2×#66864C411yescharacteristic, complemented
24C2×D176C411yescharacteristic, complemented
25#10622508—22no—
26#10622508—22no—
27#10622135—22no—
28#10622135—22no—
29C2×#4339—21no—
30C2×#4339—21no—
31C2×C11×M16—21no—
32C2×C11×M16—21no—
33C22×C8×C11C2311yescharacteristic
34C2×C4×Dic11D411yescharacteristic
35C22×C11⋊C8D411yescharacteristic
36#66960—24no—
37#66960—42no—
38C2×Dic44C2×C411yescharacteristic
39C2×Dic44C2×C411yescharacteristic
40#66957—21no—
41#66957—21no—
42#66957—21no—
43#66957—21no—
44#66957—21no—
45#66957—21no—
46#66957D412yes—
47#66957D412yes—
48C2×D88C2×C411yescharacteristic
49C2×D88C2×C411yescharacteristic
50C2×#4314—21no—
51C2×#4314—21no—
52C2×#4313—41no—
53C2×C8×D11—41no—
54C2×C11×C16—21no—
55C2×C11×C16—21no—
56C2×C11×C16C2×C411yescharacteristic
57C2×C11×C16C2×C411yescharacteristic
58C11×#108—21no—
59C11×#108—21no—
60C11×#108—21no—
61C11×#108D412yes—
62#66889—24no—
63#66889—42no—
64(C2×D11)⋊C8—41no—
65(C2×D11)⋊C8—41no—
66C8×Dic11—21no—
67C8×Dic11—21no—
68C2×C11⋊C16—21no—
69C2×C11⋊C16—21no—
70C2×C11⋊C16—21no—
71Dic88—22no—
72#66864—22no—
73#66864—22no—
74D176—22no—
75#13011—111nomaximal, Sylow
76C22×C4×C11C2×D411yescharacteristic
77C2×C22⋊D11—41no—
78C2×C22⋊D11—41no—
79C22×Dic11—21no—
80#4339—22no—
81#4339—22no—
82#4339—41no—
83#4339—41no—
84#4339—41no—
85#4339—41no—
86#4339—41no—
87#4339—41no—
88C2×D44—21no—
89C2×D44—21no—
90C2×C4×D11—41no—
91C2×C4×D11—41no—
92C2×Dic22—21no—
93C2×Dic22—21no—
94C11×M16—22no—
95C11×M16—41no—
96C11×M16—41no—
97C11×M16—41no—
98C2×C8×C11—41no—
99C2×C8×C11—41no—
100C2×C8×C11C22×C411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11C2×D411yescharacteristic
104C2×C8×C11#4111yescharacteristic
105C2×C8×C11#4111yescharacteristic
106C4×Dic11—21no—
107C4×Dic11—21no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8—21no—
110C2×C11⋊C8D811yescharacteristic
111C2×C11⋊C8D811yescharacteristic
112Dic44—21no—
113Dic44—21no—
114Dic44—21no—
115Dic44C22⋊C412yes—
116D88—21no—
117D88—21no—
118D88—21no—
119D88C22⋊C412yes—
120#4314—22no—
121#4314—22no—
122#4314—41no—
123#4314—41no—
124#4313—44no—
125C8×D11—44no—
126C11×C16—21no—
127C11×C16—21no—
128C11⋊C16—41no—
129C2×#508—111no—
130C2×#443—111no—
131C2×#359—111no—
132C2×#359—111no—
133#1974—111no—
134#1381D1111yescharacteristic, complemented
135#1374—111no—
136C23×C11#13511yescharacteristic
137C22×D11—41no—
138C22×D11—41no—
139C2×C4×C11C4×D411yescharacteristic
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11C2×D811yescharacteristic
143C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
145C22⋊D11—42no—
146C22⋊D11—42no—
147C22⋊D11—81no—
148C22⋊D11—81no—
149C2×Dic11—22no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154D44—22no—
155D44—41no—
156D44—41no—
157D44—41no—
158C4×D11—42no—
159C4×D11—42no—
160C4×D11—81no—
161C4×D11—81no—
162Dic22—22no—
163Dic22—41no—
164Dic22—41no—
165Dic22—41no—
166C8×C11—42no—
167C8×C11—81no—
168C8×C11C2×C22⋊C411yescharacteristic
169C8×C11C4×D411yescharacteristic
170C8×C11#12111yescharacteristic
171C8×C11#12311yescharacteristic
172C11⋊C8—21no—
173C11⋊C8—21no—
174C2×#135—111no—
175C2×#135—111no—
176C2×#131—221no—
177#508—222no—
178#508—222no—
179C2×Q32—111no—
180C2×SD32—111no—
181C2×SD32—111no—
182C2×D16—111no—
183C22×C16—111no—
184C22×C16C2×D1111yescharacteristic
185#443—222no—
186#443—222no—
187C2×#108C2×D1111yescharacteristic
188C2×#108C2×D1111yescharacteristic
189C2×#104—221no—
190C2×#104—221no—
191#408—221no—
192C2×C4×C8—111no—
193#359—222no—
194#359—222no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11C4×D811yescharacteristic
198C22×C11#44911yescharacteristic
199C22×C11#46311yescharacteristic
200C2×D11—42no—
201C2×D11—81no—
202C2×D11—81no—
203C2×D11—81no—
204C2×D11—81no—
205C2×D11—81no—
206C4×C11#38611yescharacteristic
207C4×C11#44211yescharacteristic
208C4×C11#44711yescharacteristic
209C4×C11#45911yescharacteristic
210Dic11—42no—
211Dic11—42no—
212Dic11—81no—
213C2×#41—221no—
214C2×#41—221no—
215#135—112no—
216#135—112no—
217#135—221no—
218#135—221no—
219#135—221no—
220#135—221no—
221#135—221no—
222#135—221no—
223C2×Q16—111no—
224C2×Q16—111no—
225C2×SD16—221no—
226C2×SD16—221no—
227C2×D8—111no—
228C2×D8—111no—
229#131—224no—
230#131—442no—
231C2×M16—21no—
232C2×M16—21no—
233C2×M16—441no—
234C22×C8—111no—
235C22×C8—441no—
236C22×C8C22×D1111yescharacteristic
237C2×C42—111no—
238Q32—222no—
239SD32—222no—
240SD32—222no—
241D16—222no—
242C2×C16—21no—
243C2×C16—21no—
244C2×C16—221no—
245C2×C16—221no—
246C2×C16—221no—
247C2×C16C4×D1111yescharacteristic
248C2×C16C4×D1111yescharacteristic
249#108—21no—
250#108—21no—
251#108—21no—
252#108D4412yes—
253#104—224no—
254#104—442no—
255C22⋊C8—441no—
256C22⋊C8—441no—
257C4×C8—221no—
258C4×C8—221no—
259C2×C11—21no—
260C2×C11—21no—
261C2×C11#187911yescharacteristic
262C2×C11#217811yescharacteristic
263C2×C11#217911yescharacteristic
264D11—82no—
265D11—161no—
266#41—222no—
267#41—222no—
268#41—441no—
269#41—441no—
270#41—441no—
271#41—441no—
272#41—441no—
273#41—441no—
274C2×Q8—221no—
275C2×Q8—221no—
276C2×D4—221no—
277C2×D4—221no—
278C2×D4—441no—
279C2×D4—441no—
280C22×C4—221no—
281C22×C4—441no—
282C22×C4—441no—
283C22×C4D4×D1111yescharacteristic
284Q16—112no—
285Q16—221no—
286Q16—221no—
287Q16—221no—
288SD16—222no—
289SD16—222no—
290SD16—441no—
291SD16—441no—
292D8—112no—
293D8—221no—
294D8—221no—
295D8—221no—
296M16—22no—
297M16—41no—
298M16—41no—
299M16—41no—
300M16—444no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—111no—
304C2×C8—111no—
305C2×C8—221no—
306C2×C8—221no—
307C2×C8—444no—
308C2×C8C2×C4×D1111yescharacteristic
309C2×C8C2×D4411yescharacteristic
310C2×C8#433911yescharacteristic
311C2×C8D4×D1111yescharacteristic
312C2×C8D4×D1111yescharacteristic
313C2×C8#434311yescharacteristic
314C42—221no—
315C42—221no—
316C16—21no—
317C16—21no—
318C16—441no—
319C11#1301111yescharacteristic, complemented, Sylow
320C23—441no—
321C23—441no—
322C23#6697211yescharacteristic
323Q8—222no—
324Q8—441no—
325Q8—441no—
326Q8—441no—
327D4—222no—
328D4—442no—
329D4—442no—
330D4—441no—
331D4—441no—
332D4—441no—
333D4—881no—
334D4—881no—
335C2×C4—222no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—442no—
340C2×C4—442no—
341C2×C4—441no—
342C2×C4—881no—
343C2×C4—881no—
344C2×C4#6693511yescharacteristic
345C2×C4#6693711yescharacteristic
346C2×C4#6694611yescharacteristic
347C2×C4D8×D1111yescharacteristic
348C2×C4#6696711yescharacteristic
349C2×C4#6696711yescharacteristic
350C8—42no—
351C8—81no—
352C8—221no—
353C8—221no—
354C8C4×D4411yescharacteristic
355C8C22⋊C4×D1111yescharacteristic
356C8#6694711yescharacteristic
357C8#6694811yescharacteristic
358C22—21no—
359C22—21no—
360C22—442no—
361C22—881no—
362C22—881no—
363C22—881no—
364C22—881no—
365C22—881no—
366C22#1062242411yescharacteristic
367C22#1062243211yescharacteristic
368C22#1062248511yescharacteristic
369C4—442no—
370C4—442no—
371C4—881no—
372C4#1062227811yescharacteristic
373C4#1062238611yescharacteristic
374C4#1062239911yescharacteristic
375C4#1062248211yescharacteristic
376C2—21no—
377C2—21no—
378C2—882no—
379C2—1761no—
380C2#1306896511yescharacteristic
381C2#1307049611yescharacteristic
382C2#1307050111yescharacteristic
subgroupG/H
centerC2×C4D8×D11
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1381C2
socleC22×C11C4×D8
prime radicalC2×#10622517C2
cosocleC22×C8×C11C23
hypercenter#1381D11
hypocenterC11#13011
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #1381

Complements

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

NH ≅ G/Ntype
2. C2×#10622508C2semidirect
3. C2×#10622135C2semidirect
4. C2×#10622135C2semidirect
5. #13069502C2semidirect
6. #13066693C2semidirect
7. C11×#1381C2semidirect
19. C2×Dic88C4semidirect
22. C2×#66864C4semidirect
23. C2×#66864C4semidirect
24. C2×D176C4semidirect
134. #1381D11semidirect
319. C11#13011semidirect

Maximal subgroups

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

subgroupindex
C2×#106225172
C2×#106225082
C2×#106221352
#130695022
#130666932
C11×#13812
#1301111