Finite Group Databasebeta

← #14908322

Subgroups — #14908322

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622522C211yesmaximal, characteristic, complemented
2#13078286C211yesmaximal, characteristic
3#13078271C211yesmaximal, characteristic, complemented
4#13070729C212yesmaximal, complemented
5#13070724C212yesmaximal, complemented
6#13070712C212yesmaximal, complemented
7#13070707C212yesmaximal, complemented
8#13070404C211yesmaximal, characteristic, complemented
9#13070324C211yesmaximal, characteristic, complemented
10C2×#10622141C211yesmaximal, characteristic, complemented
11C2×C11×#504C211yesmaximal, characteristic, complemented
12C2×C11×#131C2211yescharacteristic
13#10623364—21no—
14#10623356—21no—
15C22×Dic44C2211yescharacteristic
16C2×#66957C2211yescharacteristic
17C11×#504—24no—
18C2×C11×M32C2212yes—
19C2×C11×M32C2211yescharacteristic
20C22×C11×C16C2212yes—
21C22×C11×C16C2211yescharacteristic
22#10622750—22no—
23#10622747—22no—
24#10622746—21no—
25#10622733—21no—
26#10622729C2212yes—
27#10622729C2212yes—
28#10622729C2212yes—
29#10622728C2212yes—
30#10622719C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32#10622522—24no—
33C2×Dic88C2212yes—
34C2×#66864C2212yes—
35#10622147C2211yescharacteristic
36#10622147C2211yescharacteristic
37#10622143C2212yes—
38#10622142C2212yes—
39#10622141C2211yescharacteristic
40#10622141C2212yes—
41#10622141C2211yescharacteristic
42#10622141C2212yes—
43C2×C11×#41D411yescharacteristic
44C2×#4339—21no—
45C22×Dic22—21no—
46C11×#131—22no—
47C11×#131—22no—
48C2×C11×M16D411yescharacteristic
49C2×C11×M16D412yes—
50C22×C8×C11C2312yes—
51C22×C8×C11C2311yescharacteristic
52#66999—41no—
53#66997—41no—
54#66992—42no—
55#66991—41no—
56#66989—41no—
57#66988—42no—
58#66983—22no—
59#66979—21no—
60C2×C4⋊Dic11—21no—
61#66977—22no—
62#66977—22no—
63#66977—22no—
64C2×Dic44—22no—
65C2×Dic44—22no—
66C2×Dic44—21no—
67C2×Dic44C2311yescharacteristic
68C2×Dic44C2312yes—
69#66957—22no—
70#66957—22no—
71C2×D88C2311yescharacteristic
72C2×#4314—21no—
73C11×M32—24no—
74C11×M32D414yescomplemented
75C2×C11×C16—22no—
76C2×C11×C16—24no—
77C2×C11×C16C2311yescharacteristic
78C2×C11×C16C2311yescharacteristic
79C2×C11×C16C2312yes—
80#66885—22no—
81#66882—21no—
82#66882C2312yes—
83#66882C2311yescharacteristic
84#66882C2311yescharacteristic
85#66881—21no—
86#66880—22no—
87#66880—22no—
88#66880—22no—
89Dic88—24no—
90#66864—24no—
91#33613—111nomaximal, Sylow
92C11×#41—22no—
93C11×#41—22no—
94C2×Q8×C11D811yescharacteristic
95C2×D4×C11D812yes—
96C2×D4×C11D811yescharacteristic
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D411yescharacteristic
99C2×C22⋊D11—41no—
100C2×C22⋊D11—42no—
101C22×Dic11—41no—
102C22×Dic11—41no—
103#4339—42no—
104#4339—42no—
105C2×D44—21no—
106C2×C4×D11—41no—
107C2×Dic22—21no—
108C2×Dic22—22no—
109C2×Dic22—42no—
110C2×Dic22—41no—
111C2×Dic22—42no—
112C11×M16—24no—
113C11×M16—22no—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C2×C8×C11C2×D412yes—
117C2×C8×C11C2×D412yes—
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11#4112yes—
120C2×C8×C11C2411yescharacteristic
121C22⋊Dic11—42no—
122C22⋊Dic11—42no—
123C22⋊Dic11—42no—
124C22⋊Dic11—41no—
125(C2×D11)⋊C4—42no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128C4⋊Dic11—22no—
129C4⋊Dic11—41no—
130Dic11⋊C4—42no—
131Dic11⋊C4—42no—
132Dic11⋊C4—42no—
133C4×Dic11—41no—
134Dic44—22no—
135Dic44—21no—
136Dic44—21no—
137Dic44—22no—
138Dic44—42no—
139D88—21no—
140D88—21no—
141#4314—42no—
142C11×C16—21no—
143C11×C16—21no—
144C11×C16C2×D414yes—
145C2×#510—111no—
146C2×#504D1111yescharacteristic, complemented
147#3061—111no—
148#3059—111no—
149#2220—112no—
150#2219—112no—
151#2217—112no—
152#2216—112no—
153#2159—111no—
154#2138—111no—
155C2×#358—111no—
156C23×C11C2×D812yes—
157C23×C11C2×D811yescharacteristic
158C22×D11—41no—
159Q8×C11—22no—
160D4×C11—24no—
161D4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11#12112yes—
165C2×C4×C11C2×D812yes—
166C2×C4×C11C2×D811yescharacteristic
167C2×C4×C11#13512yes—
168C2×C4×C11C22×D411yescharacteristic
169C22⋊D11—82no—
170C22⋊D11—162no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—42no—
174C2×Dic11—41no—
175C2×Dic11—42no—
176C2×Dic11—82no—
177C2×Dic11—161no—
178D44—41no—
179D44—41no—
180C4×D11—82no—
181Dic22—41no—
182Dic22—42no—
183Dic22—42no—
184Dic22—41no—
185Dic22—82no—
186C8×C11—22no—
187C8×C11#12112yes—
188C8×C11C22×D411yescharacteristic
189C8×C11C2×#4111yescharacteristic
190C2×#135—111no—
191C22×Q16—111no—
192C2×#131C2×D1111yescharacteristic
193#537—221no—
194#536—221no—
195#510—224no—
196C2×Q32—112no—
197C2×SD32—112no—
198#504—24no—
199C2×M32C2×D1112yes—
200C2×M32C2×D1111yescharacteristic
201C22×C16C2×D1111yescharacteristic
202C22×C16C2×D1112yes—
203#470—222no—
204#468—222no—
205#467—112no—
206#467—112no—
207#467—112no—
208#466—112no—
209#427—111no—
210C2×#107—111no—
211#419—221no—
212#417—221no—
213#367—112no—
214#366—112no—
215#358—112no—
216#358—112no—
217#358—111no—
218#358—111no—
219#357—111no—
220#357—111no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—22no—
224C22×C11—22no—
225C22×C11—22no—
226C22×C11#46612yes—
227C22×C11C22×D811yescharacteristic
228C2×D11—81no—
229C2×D11—81no—
230C2×D11—81no—
231C4×C11—22no—
232C4×C11#46612yes—
233C4×C11C2×#12111yescharacteristic
234C4×C11C2×#13511yescharacteristic
235Dic11—81no—
236Dic11—82no—
237Dic11—81no—
238Dic11—82no—
239Dic11—81no—
240C2×#41—221no—
241C2×#41D4411yescharacteristic
242C22×Q8—221no—
243#135—222no—
244#135—222no—
245C2×Q16—112no—
246C2×Q16—111no—
247C2×Q16—221no—
248C2×Q16—222no—
249C2×Q16—222no—
250C2×SD16—221no—
251C2×D8—111no—
252#131—22no—
253#131—22no—
254C2×M16D4411yescharacteristic
255C2×M16D4412yes—
256C22×C8C22×D1112yes—
257C22×C8C22×D1111yescharacteristic
258C4⋊Q8—441no—
259#124—441no—
260#123—442no—
261C22⋊Q8—222no—
262C22⋊Q8—222no—
263C22⋊Q8—222no—
264C22⋊Q8—441no—
265#121—222no—
266#121—441no—
267#121—442no—
268#117—221no—
269C2×C4⋊C4—221no—
270Q32—224no—
271SD32—224no—
272M32—24no—
273M32C22⋊D1114yescomplemented
274C2×C16—22no—
275C2×C16—24no—
276C2×C16C22×D1111yescharacteristic
277C2×C16C22×D1111yescharacteristic
278C2×C16C22×D1112yes—
279#107—111no—
280#107—111no—
281#107—112no—
282#107—221no—
283#106—221no—
284#103—222no—
285#103—222no—
286#103—222no—
287#102—222no—
288C2×C11—22no—
289C2×C11—42no—
290C2×C11C2×#46611yescharacteristic
291C2×C11#341611yescharacteristic
292C2×C11#341711yescharacteristic
293D11—161no—
294#41—22no—
295#41—22no—
296#41—442no—
297#41—442no—
298C2×Q8—221no—
299C2×Q8—222no—
300C2×Q8—441no—
301C2×Q8—442no—
302C2×Q8—442no—
303C2×Q8D8811yescharacteristic
304C2×D4—221no—
305C2×D4—441no—
306C2×D4—442no—
307C2×D4D8812yes—
308C2×D4D8811yescharacteristic
309C22×C4—441no—
310C22×C4—441no—
311C22×C4—441no—
312C22×C4C2×D4412yes—
313C22×C4C2×D4411yescharacteristic
314Q16—222no—
315Q16—221no—
316Q16—222no—
317Q16—221no—
318Q16—442no—
319SD16—442no—
320D8—221no—
321D8—221no—
322M16—22no—
323M16—24no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8C2×D4412yes—
327C2×C8C2×D4411yescharacteristic
328C2×C8#433912yes—
329C2×C8C2×C22⋊D1112yes—
330C2×C8C23×D1111yescharacteristic
331C4⋊C4—222no—
332C4⋊C4—221no—
333C4⋊C4—221no—
334C4⋊C4—441no—
335C4⋊C4—442no—
336C4⋊C4—442no—
337C4⋊C4—442no—
338C22⋊C4—441no—
339C22⋊C4—442no—
340C22⋊C4—442no—
341C22⋊C4—442no—
342C22⋊C4—442no—
343C42—441no—
344C16—21no—
345C16—21no—
346C16C2×C22⋊D1114yes—
347C11#3361311yescharacteristic, complemented, Sylow
348C23—441no—
349C23C2×D8812yes—
350C23C2×D8811yescharacteristic
351Q8—22no—
352Q8—442no—
353Q8—441no—
354Q8—441no—
355Q8—442no—
356Q8—882no—
357D4—24no—
358D4—22no—
359D4—441no—
360D4—441no—
361D4—882no—
362D4—1762no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—442no—
368C2×C4—441no—
369C2×C4—442no—
370C2×C4—882no—
371C2×C4—882no—
372C2×C4—1761no—
373C2×C4C2×D8812yes—
374C2×C4C2×D8811yescharacteristic
375C2×C4#6695712yes—
376C2×C4#6698312yes—
377C2×C4C22×D4411yescharacteristic
378C8—22no—
379C8#6698312yes—
380C8C2×#433911yescharacteristic
381C8C22×C22⋊D1111yescharacteristic
382C22—21no—
383C22—21no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—881no—
388C22—881no—
389C22—881no—
390C22#1062272812yes—
391C22C22×D8811yescharacteristic
392C4—22no—
393C4—882no—
394C4—881no—
395C4—881no—
396C4—882no—
397C4—881no—
398C4#1062272812yes—
399C4C2×#6695711yescharacteristic
400C4C2×#6698311yescharacteristic
401C2—22no—
402C2—42no—
403C2—1761no—
404C2C2×#1062272811yescharacteristic
405C2#1308176411yescharacteristic
406C2#1308176911yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#504C2
socleC22×C11C22×D8
prime radical#13078286C2
hypercenterC2×#504D11
hypocenterC11#33613
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ C2×#504

Complements

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

NH ≅ G/Ntype
1. C2×#10622522C2semidirect
3. #13078271C2semidirect
4. #13070729C2semidirect
5. #13070724C2semidirect
6. #13070712C2semidirect
7. #13070707C2semidirect
8. #13070404C2semidirect
9. #13070324C2semidirect
10. C2×#10622141C2semidirect
11. C2×C11×#504C2semidirect
74. C11×M32D4semidirect
146. C2×#504D11semidirect
273. M32C22⋊D11semidirect
347. C11#33613semidirect

Maximal subgroups

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

subgroupindex
C2×#106225222
#130782862
#130782712
#130707292
#130707242
#130707122
#130707072
#130704042
#130703242
C2×#106221412
C2×C11×#5042
#3361311