Finite Group Databasebeta

← #14908325

Subgroups — #14908325

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×#10622808C211yesmaximal, characteristic, complemented
2C2×#10622514C211yesmaximal, characteristic, complemented
3#13078282C211yesmaximal, characteristic
4#13078272C211yesmaximal, characteristic, complemented
5#13070728C212yesmaximal, complemented
6#13070723C212yesmaximal, complemented
7#13070711C212yesmaximal, complemented
8#13070706C212yesmaximal, complemented
9#13070405C211yesmaximal, characteristic, complemented
10C2×#10622141C211yesmaximal, characteristic, complemented
11C11×#2138C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13#10623364—21no—
14C22×Dic44C2211yescharacteristic
15C2×#66954C2211yescharacteristic
16#10623057—21no—
17C22×C11×C16C2211yescharacteristic
18C11×#427C2211yescharacteristic
19#10622845—21no—
20#10622808—24no—
21#10622801C2212yes—
22C2×#66893C2212yes—
23#10622787—22no—
24#10622770C2212yes—
25C2×#66891C2212yes—
26C2×#66882C2211yescharacteristic
27C2×#66876C2211yescharacteristic
28#10622617—21no—
29#10622514—24no—
30C2×#66862C2212yes—
31C2×C16×D11C2212yes—
32#10622500C2212yes—
33#10622500C2212yes—
34#10622481—22no—
35C11×#358C2211yescharacteristic
36C11×#358C2211yescharacteristic
37C11×#357C2211yescharacteristic
38C11×#357C2211yescharacteristic
39#10622141C2212yes—
40#10622141C2212yes—
41#10622128C2212yes—
42#10622127C2212yes—
43C2×C11×#41—21no—
44C2×#4339D411yescharacteristic
45C22×Dic22—21no—
46C11×#135—22no—
47C11×#135—22no—
48C2×C11×Q16C2311yescharacteristic
49C2×C11×SD16—21no—
50C2×C11×D8C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C11×#117—21no—
53#66999—22no—
54#66992—42no—
55#66991—22no—
56#66983—41no—
57C2×C4⋊Dic11—21no—
58#66977—41no—
59C2×#4318D411yescharacteristic
60C2×Dic44—22no—
61C2×Dic44—22no—
62C2×Dic44—21no—
63C2×Dic44C2312yes—
64#66954—22no—
65#66954—22no—
66C2×#4313D412yes—
67C2×C8×D11C2312yes—
68#66950—22no—
69#66950—22no—
70#66939—42no—
71#66928—41no—
72#66922—41no—
73C2×C11×C16—22no—
74C2×C11×C16C2311yescharacteristic
75C2×C11×C16C2311yescharacteristic
76C11×#107C2311yescharacteristic
77C11×#107C2311yescharacteristic
78C11×#106—21no—
79#66899—22no—
80#66896—22no—
81#66893—24no—
82#66891—24no—
83#66882—21no—
84#66882C2312yes—
85#66876D414yescomplemented
86C2×C11⋊C16C2312yes—
87#66874—22no—
88#66874—22no—
89#66862—24no—
90C16×D11—24no—
91#33613—111nomaximal, Sylow
92C11×#41—42no—
93C11×#41—42no—
94C2×Q8×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11C2×D411yescharacteristic
99C2×C22⋊D11—42no—
100C2×C22⋊D11D812yes—
101C22×Dic11—41no—
102C22×Dic11—41no—
103#4339—22no—
104#4339—22no—
105C2×D44D811yescharacteristic
106C2×C4×D11C2×D412yes—
107C2×Dic22—22no—
108C2×Dic22—42no—
109C2×Dic22—41no—
110C2×Dic22—42no—
111C2×Dic22D811yescharacteristic
112C11×Q16—21no—
113C11×Q16—21no—
114C11×SD16—42no—
115C11×D8—21no—
116C11×D8—21no—
117C2×C8×C11C2×D412yes—
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11#4112yes—
120C2×C8×C11C2411yescharacteristic
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C22⋊C4—41no—
124C42×C11—41no—
125C22⋊Dic11—42no—
126(C2×D11)⋊C4—42no—
127(C2×D11)⋊C4—42no—
128(C2×D11)⋊C4—42no—
129C4⋊Dic11—22no—
130C4⋊Dic11—42no—
131C4⋊Dic11—42no—
132C4⋊Dic11—41no—
133Dic11⋊C4—42no—
134#4318—22no—
135C2×C11⋊C8C2×D412yes—
136Dic44—22no—
137Dic44—22no—
138Dic44—42no—
139#4313—24no—
140C8×D11—22no—
141C8×D11—22no—
142C11×C16—21no—
143C11×C16—21no—
144C11⋊C16C2×D414yes—
145C2×#510—111no—
146C2×#504—111no—
147#3061—111no—
148#3059—111no—
149#2220—112no—
150#2219—112no—
151#2217—112no—
152#2216—112no—
153#2159—111no—
154#2138D1111yescharacteristic, complemented
155C2×#358—111no—
156C23×C11—41no—
157C23×C11C2×D811yescharacteristic
158C22×D11C2×D812yes—
159Q8×C11—41no—
160Q8×C11—41no—
161D4×C11—41no—
162D4×C11—41no—
163D4×C11—82no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—82no—
168C2×C4×C11#12112yes—
169C2×C4×C11C2×D811yescharacteristic
170C2×C4×C11#13512yes—
171C2×C4×C11C22×D411yescharacteristic
172C22⋊D11—24no—
173C22⋊D11—162no—
174C2×Dic11—42no—
175C2×Dic11—42no—
176C2×Dic11—82no—
177C2×Dic11—161no—
178C2×Dic11C2×D812yes—
179D44—22no—
180C4×D11—22no—
181C4×D11—22no—
182Dic22—22no—
183Dic22—42no—
184Dic22—42no—
185Dic22—82no—
186C8×C11#12112yes—
187C8×C11C22×D411yescharacteristic
188C8×C11C2×#4111yescharacteristic
189C11⋊C8—22no—
190C2×#135C2×D1111yescharacteristic
191C22×Q16—111no—
192C2×#131—111no—
193#537—221no—
194#536—221no—
195#510—224no—
196C2×Q32—112no—
197C2×SD32—112no—
198#504—224no—
199C2×M32—111no—
200C2×M32—112no—
201C22×C16—112no—
202C22×C16C2×D1111yescharacteristic
203#470—222no—
204#468—222no—
205#467—112no—
206#467—112no—
207#467—112no—
208#466—112no—
209#427C2×D1111yescharacteristic
210C2×#107—111no—
211#419—221no—
212#417—221no—
213#367—112no—
214#366—112no—
215#358—112no—
216#358—112no—
217#358C2×D1111yescharacteristic
218#358C2×D1111yescharacteristic
219#357C2×D1111yescharacteristic
220#357C2×D1111yescharacteristic
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11—81no—
226C22×C11#46612yes—
227C22×C11C22×D811yescharacteristic
228C2×D11—22no—
229C2×D11—22no—
230C2×D11—22no—
231C4×C11—81no—
232C4×C11—81no—
233C4×C11—81no—
234C4×C11#46612yes—
235C4×C11C2×#12111yescharacteristic
236C4×C11C2×#13511yescharacteristic
237Dic11—22no—
238Dic11—82no—
239Dic11—82no—
240C2×#41—21no—
241C2×#41—111no—
242C22×Q8—221no—
243#135—22no—
244#135—22no—
245C2×Q16—112no—
246C2×Q16—222no—
247C2×Q16—222no—
248C2×Q16—221no—
249C2×Q16C22×D1111yescharacteristic
250C2×SD16—21no—
251C2×D8C22×D1111yescharacteristic
252#131—222no—
253#131—222no—
254C2×M16—111no—
255C2×M16—112no—
256C22×C8—112no—
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—21no—
269C2×C4⋊C4—221no—
270Q32—224no—
271SD32—224no—
272M32—114no—
273M32—224no—
274C2×C16—22no—
275C2×C16—112no—
276C2×C16—224no—
277C2×C16C22×D1111yescharacteristic
278C2×C16C22×D1111yescharacteristic
279#107—112no—
280#107—221no—
281#107C22×D1111yescharacteristic
282#107C22×D1111yescharacteristic
283#106—21no—
284#103—222no—
285#103—222no—
286#103—222no—
287#102—222no—
288C2×C11—22no—
289C2×C11—161no—
290C2×C11C2×#46611yescharacteristic
291C2×C11#341611yescharacteristic
292C2×C11#341711yescharacteristic
293D11—42no—
294#41—42no—
295#41—42no—
296#41—222no—
297#41—222no—
298C2×Q8—21no—
299C2×Q8—111no—
300C2×Q8—222no—
301C2×Q8—441no—
302C2×Q8—442no—
303C2×Q8—442no—
304C2×D4—21no—
305C2×D4—41no—
306C2×D4—112no—
307C2×D4—111no—
308C2×D4—442no—
309C22×C4—41no—
310C22×C4—112no—
311C22×C4—441no—
312C22×C4—441no—
313C22×C4D4×D1111yescharacteristic
314Q16—21no—
315Q16—21no—
316Q16—222no—
317Q16—222no—
318Q16—442no—
319SD16—42no—
320D8—21no—
321D8—21no—
322M16—222no—
323M16—224no—
324C2×C8—112no—
325C2×C8—222no—
326C2×C8—222no—
327C2×C8#433912yes—
328C2×C8D4×D1111yescharacteristic
329C2×C8D4×D1112yes—
330C2×C8C23×D1111yescharacteristic
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—222no—
334C4⋊C4—442no—
335C4⋊C4—442no—
336C4⋊C4—442no—
337C4⋊C4—441no—
338C22⋊C4—41no—
339C22⋊C4—442no—
340C22⋊C4—442no—
341C22⋊C4—442no—
342C22⋊C4—442no—
343C42—41no—
344C16—21no—
345C16—21no—
346C16—114no—
347C11#3361311yescharacteristic, complemented, Sylow
348C23—41no—
349C23—112no—
350C23D8×D1111yescharacteristic
351Q8—41no—
352Q8—41no—
353Q8—222no—
354Q8—442no—
355Q8—442no—
356Q8—882no—
357D4—41no—
358D4—41no—
359D4—82no—
360D4—224no—
361D4—222no—
362D4—1762no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—82no—
367C2×C4—112no—
368C2×C4—222no—
369C2×C4—222no—
370C2×C4—442no—
371C2×C4—442no—
372C2×C4—882no—
373C2×C4—1761no—
374C2×C4#6693712yes—
375C2×C4D8×D1111yescharacteristic
376C2×C4#6696912yes—
377C2×C4C2×D4×D1111yescharacteristic
378C8—222no—
379C8#6693712yes—
380C8C2×#433911yescharacteristic
381C8C2×D4×D1111yescharacteristic
382C22—21no—
383C22—21no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—222no—
388C22—222no—
389C22—222no—
390C22#1062238812yes—
391C22C2×D8×D1111yescharacteristic
392C4—81no—
393C4—81no—
394C4—81no—
395C4—222no—
396C4—882no—
397C4—882no—
398C4#1062238812yes—
399C4C2×#6693711yescharacteristic
400C4C2×#6696911yescharacteristic
401C2—22no—
402C2—161no—
403C2—442no—
404C2C2×#1062238811yescharacteristic
405C2#1308175911yescharacteristic
406C2#1308176611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2138C2
socleC22×C11C22×D8
prime radical#13078282C2
hypercenter#2138D11
hypocenterC11#33613
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2138

Complements

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

NH ≅ G/Ntype
1. C2×#10622808C2semidirect
2. C2×#10622514C2semidirect
4. #13078272C2semidirect
5. #13070728C2semidirect
6. #13070723C2semidirect
7. #13070711C2semidirect
8. #13070706C2semidirect
9. #13070405C2semidirect
10. C2×#10622141C2semidirect
11. C11×#2138C2semidirect
85. #66876D4semidirect
154. #2138D11semidirect
347. C11#33613semidirect

Maximal subgroups

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

subgroupindex
C2×#106228082
C2×#106225142
#130782822
#130782722
#130707282
#130707232
#130707112
#130707062
#130704052
C2×#106221412
C11×#21382
#3361311