Finite Group Databasebeta

← #14908842

Subgroups — #14908842

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66957C211yesmaximal, characteristic, complemented
2#13070804C212yesmaximal, complemented
3#13070755C211yesmaximal, characteristic, complemented
4#13070750C211yesmaximal, characteristic, complemented
5#13070653C211yesmaximal, characteristic, complemented
6#13070648C211yesmaximal, characteristic, complemented
7#13070537C212yesmaximal, complemented
8#13070490C212yesmaximal, complemented
9#13070480C212yesmaximal, complemented
10#13070419C211yesmaximal, characteristic, complemented
11C11×#3169C211yesmaximal, characteristic, complemented
12C11×#532—21no—
13C2×#66957C2211yescharacteristic
14C4×#4339—21no—
15C11×#500C2211yescharacteristic
16C11×#493C2211yescharacteristic
17C11×#486—21no—
18C11×#466—21no—
19C11×#466C2212yes—
20C4×C11×D8—21no—
21C4×C11×D8C2212yes—
22C2×C4×C8×C11C2211yescharacteristic
23C2×#66891C2212yes—
24C2×#66890C2212yes—
25#10622726—21no—
26#10622719C2211yescharacteristic
27C4×Dic44C2211yescharacteristic
28C4×Dic44C2211yescharacteristic
29C4×D88C2211yescharacteristic
30C4×D88C2211yescharacteristic
31C4×#4314—21no—
32C4×#4314—21no—
33#10622200C2212yes—
34#10622200C2212yes—
35C22⋊(C11⋊C16)C2212yes—
36#10622130C2212yes—
37#10622129C2212yes—
38#10622128C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C4⋊(C11⋊C16)C2211yescharacteristic
42#10622099C2212yes—
43C2×C11×#41—41no—
44C2×#4339—21no—
45C2×C11×D8—21no—
46C2×C11×D8C2312yes—
47C22×C8×C11D411yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×C4⋊Q8—21no—
50C11×#127—21no—
51C11×#124—41no—
52C11×#121—22no—
53C11×#121—41no—
54C4×D4×C11—22no—
55C4×D4×C11—41no—
56C2×C42×C11D411yescharacteristic
57C4×C22⋊D11—41no—
58C4×C22⋊D11—41no—
59#66979—21no—
60C2×Dic44C2311yescharacteristic
61#66957—22no—
62#66957—22no—
63C2×D88C2311yescharacteristic
64C2×#4314—21no—
65C4×D44—21no—
66C4×D44—21no—
67#66925—41no—
68C42×D11—41no—
69C4×Dic22—21no—
70C4×Dic22—21no—
71C11×#107—21no—
72C11×#107C2312yes—
73C11×#102—22no—
74C11×#102—22no—
75C4×C8×C11D411yescharacteristic
76C4×C8×C11D411yescharacteristic
77C4×C8×C11C2311yescharacteristic
78C4×C8×C11C2311yescharacteristic
79#66891—24no—
80#66890—24no—
81#66885—21no—
82#66885—21no—
83#66882C2311yescharacteristic
84#66882C2311yescharacteristic
85#66881—21no—
86#66880—21no—
87#66880—21no—
88C2×C11⋊C16C2312yes—
89C2×C11⋊C16C2312yes—
90#33675—111nomaximal, Sylow
91C11×#41—84no—
92C2×Q8×C11—41no—
93C2×D4×C11—22no—
94C2×D4×C11—42no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C22×C4×C11—42no—
98C22×C4×C11D811yescharacteristic
99C22×C4×C11D811yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C2×C22⋊D11—41no—
102#4339—24no—
103#4339—42no—
104C2×D44—21no—
105C2×C4×D11—41no—
106C2×C4×D11—41no—
107C2×C4×D11—41no—
108C2×Dic22—21no—
109C11×D8—22no—
110C11×D8—22no—
111C11×D8—42no—
112C2×C8×C11—21no—
113C2×C8×C11—21no—
114C2×C8×C11—41no—
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11C2411yescharacteristic
119C11×C4⋊C4—22no—
120C11×C4⋊C4—41no—
121C11×C22⋊C4—42no—
122C11×C22⋊C4—42no—
123C42×C11D811yescharacteristic
124C42×C11D811yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C22⋊Dic11—41no—
128(C2×D11)⋊C4—41no—
129(C2×D11)⋊C4—41no—
130C4⋊Dic11—21no—
131C4⋊Dic11—21no—
132Dic11⋊C4—41no—
133Dic11⋊C4—41no—
134C4×Dic11—41no—
135C4×Dic11—41no—
136C4×Dic11—41no—
137Dic44—21no—
138Dic44#4112yescomplemented
139D88—21no—
140D88#4112yescomplemented
141#4314—24no—
142C11⋊C16—22no—
143C11⋊C16—22no—
144#3169D1111yescharacteristic, complemented
145C4×#135—111no—
146#2234—112no—
147#2225—111no—
148#2224—111no—
149#2207—111no—
150#2206—111no—
151#2186—112no—
152#2177—112no—
153#2175—112no—
154#2163—111no—
155C23×C11—42no—
156C23×C11C2×D811yescharacteristic
157C22×D11—41no—
158Q8×C11—82no—
159D4×C11—42no—
160D4×C11—42no—
161D4×C11—82no—
162D4×C11—84no—
163D4×C11—82no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—22no—
167C2×C4×C11—41no—
168C2×C4×C11—42no—
169C2×C4×C11—84no—
170C2×C4×C11C2×D811yescharacteristic
171C2×C4×C11C2×D811yescharacteristic
172C2×C4×C11C2×D811yescharacteristic
173C2×C4×C11C2×D811yescharacteristic
174C2×C4×C11C2×D811yescharacteristic
175C2×C4×C11C22×D411yescharacteristic
176C22⋊D11—44no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180D44—22no—
181D44—41no—
182C4×D11—44no—
183C4×D11—82no—
184C4×D11—82no—
185Dic22—22no—
186Dic22—41no—
187C8×C11—21no—
188C8×C11—21no—
189C8×C11—21no—
190C8×C11C2×#4111yescharacteristic
191C8×C11C2×#4111yescharacteristic
192C2×#135—111no—
193#532—21no—
194C4×#41—221no—
195C2×SD32—112no—
196C2×D16—112no—
197#500C2×D1111yescharacteristic
198#493C2×D1111yescharacteristic
199#486—21no—
200#466—21no—
201#466C2×D1112yes—
202C4×Q16—111no—
203C4×Q16—111no—
204C4×SD16—221no—
205C4×SD16—221no—
206C4×D8—21no—
207C4×D8—111no—
208C4×D8—111no—
209C4×D8C2×D1112yes—
210#427—111no—
211#416—221no—
212C2×C4×C8C2×D1111yescharacteristic
213#367—112no—
214#366—112no—
215C4⋊C16—111no—
216C4⋊C16—111no—
217#358—112no—
218#357—112no—
219#357—112no—
220#357—112no—
221C22⋊C16—112no—
222#346—112no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—82no—
227C22×C11—82no—
228C22×C11—82no—
229C22×C11C22×D811yescharacteristic
230C2×D11—42no—
231C2×D11—81no—
232C2×D11—81no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—82no—
238C4×C11#50912yes—
239C4×C11#52511yescharacteristic
240C4×C11#57511yescharacteristic
241Dic11—42no—
242Dic11—81no—
243Dic11—81no—
244C2×#41—41no—
245C2×#41—221no—
246#135—222no—
247#135—222no—
248C2×Q16—111no—
249C2×SD16—221no—
250C2×D8—21no—
251C2×D8—111no—
252C2×D8C22×D1112yes—
253C22×C8C22⋊D1111yescharacteristic
254C22×C8C22×D1111yescharacteristic
255C4⋊Q8—21no—
256#127—21no—
257#124—41no—
258#121—22no—
259#121—41no—
260C4×Q8—221no—
261C4×Q8—221no—
262C4×D4—22no—
263C4×D4—41no—
264C4×D4—221no—
265C4×D4—221no—
266C4×D4—441no—
267C4×D4—441no—
268#117—221no—
269#117—441no—
270C2×C42—441no—
271C2×C42C22⋊D1111yescharacteristic
272SD32—224no—
273D16—224no—
274C2×C16—112no—
275C2×C16—112no—
276#107—21no—
277#107—111no—
278#107—111no—
279#107C22×D1112yes—
280#106—221no—
281#103—221no—
282#103—221no—
283#102—22no—
284#102—22no—
285#102—221no—
286#102—221no—
287C4×C8C22⋊D1111yescharacteristic
288C4×C8C22⋊D1111yescharacteristic
289C4×C8C22×D1111yescharacteristic
290C4×C8C22×D1111yescharacteristic
291C2×C11—41no—
292C2×C11—162no—
293C2×C11#310011yescharacteristic
294C2×C11C2×#50911yescharacteristic
295C2×C11#341411yescharacteristic
296D11—82no—
297#41—84no—
298#41—224no—
299#41—442no—
300C2×Q8—41no—
301C2×Q8—221no—
302C2×D4—22no—
303C2×D4—42no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—221no—
307C2×D4—441no—
308C22×C4—42no—
309C22×C4—441no—
310C22×C4—441no—
311C22×C4—441no—
312C22×C4#432311yescharacteristic
313C22×C4#432311yescharacteristic
314C22×C4C2×C22⋊D1111yescharacteristic
315Q16—112no—
316Q16—221no—
317SD16—224no—
318D8—22no—
319D8—22no—
320D8—42no—
321D8—112no—
322D8—221no—
323C2×C8—21no—
324C2×C8—21no—
325C2×C8—41no—
326C2×C8C2×C22⋊D1111yescharacteristic
327C2×C8C2×C22⋊D1111yescharacteristic
328C2×C8C2×C22⋊D1111yescharacteristic
329C2×C8C23×D1111yescharacteristic
330C4⋊C4—22no—
331C4⋊C4—41no—
332C4⋊C4—221no—
333C4⋊C4—221no—
334C4⋊C4—441no—
335C4⋊C4—441no—
336C22⋊C4—42no—
337C22⋊C4—42no—
338C22⋊C4—441no—
339C22⋊C4—441no—
340C22⋊C4—441no—
341C42—441no—
342C42—441no—
343C42—441no—
344C42#432311yescharacteristic
345C42#432311yescharacteristic
346C42C2×C22⋊D1111yescharacteristic
347C42C2×C22⋊D1111yescharacteristic
348C16—222no—
349C16—222no—
350C11#3367511yescharacteristic, complemented, Sylow
351C23—42no—
352C23—441no—
353C23C2×#432311yescharacteristic
354Q8—82no—
355Q8—222no—
356Q8—441no—
357D4—42no—
358D4—42no—
359D4—82no—
360D4—84no—
361D4—82no—
362D4—222no—
363D4—444no—
364D4—441no—
365C2×C4—22no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—84no—
371C2×C4—444no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—882no—
376C2×C4—882no—
377C2×C4C2×#432311yescharacteristic
378C2×C4C2×#432311yescharacteristic
379C2×C4C2×#432311yescharacteristic
380C2×C4C2×#432311yescharacteristic
381C2×C4C2×#432311yescharacteristic
382C2×C4C22×C22⋊D1111yescharacteristic
383C8—21no—
384C8—21no—
385C8—21no—
386C8#41×D1111yescharacteristic
387C8#41×D1111yescharacteristic
388C22—21no—
389C22—21no—
390C22—21no—
391C22—82no—
392C22—82no—
393C22—82no—
394C22—442no—
395C22—881no—
396C22—881no—
397C22C22×#432311yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—82no—
403C4—442no—
404C4—881no—
405C4—881no—
406C4#1062276012yes—
407C4#1062335311yescharacteristic
408C4#1062335911yescharacteristic
409C2—41no—
410C2—162no—
411C2—882no—
412C2#1307861211yescharacteristic
413C2C2×#1062276011yescharacteristic
414C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3169C2
socleC22×C11C22×D8
hypercenter#3169D11
hypocenterC11#33675
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. C4×#66957C2semidirect
2. #13070804C2semidirect
3. #13070755C2semidirect
4. #13070750C2semidirect
5. #13070653C2semidirect
6. #13070648C2semidirect
7. #13070537C2semidirect
8. #13070490C2semidirect
9. #13070480C2semidirect
10. #13070419C2semidirect
11. C11×#3169C2semidirect
138. Dic44#41semidirect
140. D88#41semidirect
144. #3169D11semidirect
350. C11#33675semidirect

Maximal subgroups

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

subgroupindex
C4×#669572
#130708042
#130707552
#130707502
#130706532
#130706482
#130705372
#130704902
#130704802
#130704192
C11×#31692
#3367511