Finite Group Databasebeta

← #14737129

Subgroups — #14737129

Order 2816.

562 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079795C212yesmaximal
2#13077591C211yesmaximal, characteristic
3#13068195C212yesmaximal, complemented
4#13068188C212yesmaximal, complemented
5#13068017C211yesmaximal, characteristic, complemented
6#13068012C211yesmaximal, characteristic, complemented
7#13067983C211yesmaximal, characteristic, complemented
8#13067978C211yesmaximal, characteristic, complemented
9#13067364C211yesmaximal, characteristic, complemented
10#13067326C212yesmaximal, complemented
11C11×#3170C211yesmaximal, characteristic, complemented
12C11×#533C2212yes—
13#10623010C2211yescharacteristic
14C11×#500C2211yescharacteristic
15C11×#494C2211yescharacteristic
16C11×#487C2212yes—
17C11×#467—21no—
18C11×#467—21no—
19C4×C11×Q16—21no—
20C4×C11×Q16—21no—
21C2×C4×C8×C11C2211yescharacteristic
22#10622724—21no—
23C8×C22⋊D11—21no—
24#10622707C2212yes—
25#10622704C2212yes—
26#10622700C2212yes—
27#10622697C2212yes—
28#10622681—22no—
29#10622677—22no—
30#10622616—22no—
31#10622609—22no—
32#10622539C2211yescharacteristic
33#10622538C2212yes—
34#10622303—21no—
35#10622302—21no—
36#10622301C2211yescharacteristic
37C8×D44C2211yescharacteristic
38#10622292C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40#10622185C2212yes—
41#10622185C2212yes—
42#10622184C2212yes—
43#10622184C2212yes—
44#10622096C2211yescharacteristic
45#10622096C2211yescharacteristic
46#10622095C2212yes—
47C2×C11×Q16—21no—
48C2×C11×Q16—21no—
49C22×C8×C11D411yescharacteristic
50C22×C8×C11D411yescharacteristic
51C11×C4⋊Q8C2312yes—
52C11×C4⋊Q8C2312yes—
53C11×#125—22no—
54C11×C22⋊Q8—22no—
55C11×C22⋊Q8—22no—
56C4×Q8×C11—22no—
57C4×Q8×C11—22no—
58C11×#117—22no—
59C2×C42×C11C2311yescharacteristic
60#66983D411yescharacteristic
61#66982—21no—
62C4×C22⋊D11—21no—
63#66977D411yescharacteristic
64C2×#4313—21no—
65C2×C8×D11—21no—
66#66929—21no—
67#66928D411yescharacteristic
68C4×D44C2311yescharacteristic
69#66925—21no—
70#66923D411yescharacteristic
71C4×Dic22C2311yescharacteristic
72C11×#107—21no—
73C11×#107—21no—
74C11×#103—22no—
75C11×#103—22no—
76C4×C8×C11D411yescharacteristic
77C4×C8×C11D411yescharacteristic
78C4×C8×C11C2311yescharacteristic
79C4×C8×C11C2311yescharacteristic
80C22⋊(C11⋊C8)—21no—
81C22⋊(C11⋊C8)—22no—
82(C2×D11)⋊C8—21no—
83(C2×D11)⋊C8—21no—
84#66879—21no—
85Dic11⋊C8—21no—
86Dic11⋊C8—21no—
87C8×Dic11—21no—
88#66874—22no—
89#66874—22no—
90#66873—22no—
91#66873—22no—
92#66872—22no—
93#66872—22no—
94#66871—22no—
95#66871—22no—
96C4⋊(C11⋊C8)C2312yes—
97C4⋊(C11⋊C8)C2312yes—
98C4⋊(C11⋊C8)C2311yescharacteristic
99C4⋊(C11⋊C8)C2311yescharacteristic
100#66867—21no—
101C4×C11⋊C8—22no—
102#19220—111nomaximal, Sylow
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C2×C22⋊D11—21no—
109C2×D44C2×D411yescharacteristic
110C2×C4×D11—21no—
111C2×Dic22C2×D411yescharacteristic
112C11×Q16—42no—
113C11×Q16—42no—
114C2×C8×C11—22no—
115C2×C8×C11—41no—
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×D411yescharacteristic
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—42no—
125C11×C4⋊C4—42no—
126C11×C22⋊C4—42no—
127C42×C11—42no—
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11#4111yescharacteristic
131C42×C11C2411yescharacteristic
132C22⋊Dic11—21no—
133(C2×D11)⋊C4—21no—
134(C2×D11)⋊C4—21no—
135(C2×D11)⋊C4—21no—
136(C2×D11)⋊C4—21no—
137C4⋊Dic11C2×D411yescharacteristic
138C4⋊Dic11C2×D411yescharacteristic
139Dic11⋊C4—21no—
140Dic11⋊C4—21no—
141Dic11⋊C4—21no—
142Dic11⋊C4—21no—
143C4×Dic11—21no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—21no—
148#4313—42no—
149C8×D11—42no—
150#3233—112no—
151#3170D1111yescharacteristic, complemented
152#2966—111no—
153#1704—112no—
154#1703—112no—
155#1676—111no—
156#1675—111no—
157#1670—111no—
158#1669—111no—
159#1564—111no—
160#1554—112no—
161C23×C11#12111yescharacteristic
162C22×D11—21no—
163Q8×C11—42no—
164Q8×C11—42no—
165Q8×C11—82no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11C22×D411yescharacteristic
177C2×C4×C11C22×D411yescharacteristic
178C2×C4×C11C2×#4111yescharacteristic
179C22⋊D11—42no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183D44—21no—
184D44—21no—
185C4×D11—41no—
186C4×D11—41no—
187Dic22—21no—
188Dic22—21no—
189C8×C11—21no—
190C8×C11—21no—
191C8×C11—21no—
192C8×C11#13512yes—
193C11⋊C8—41no—
194C11⋊C8—41no—
195C11⋊C8—42no—
196C11⋊C8—42no—
197#533C2×D1112yes—
198#529—111no—
199#500C2×D1111yescharacteristic
200#499—222no—
201#494C2×D1111yescharacteristic
202#488—222no—
203#487C2×D1112yes—
204#485—222no—
205#482—222no—
206#477—112no—
207#476—112no—
208#475—112no—
209#474—112no—
210#467—21no—
211#467—21no—
212#446—111no—
213C8×Q8—111no—
214C4×Q16—21no—
215C4×Q16—21no—
216#436—111no—
217#435—221no—
218C8×D4—111no—
219C8×D4—221no—
220#433—221no—
221#432—111no—
222#431—112no—
223#405—221no—
224C2×C4×C8C2×D1111yescharacteristic
225#335—111no—
226#335—111no—
227#334—112no—
228#333—112no—
229#333—112no—
230#332—112no—
231#332—112no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11C2×#12111yescharacteristic
236C2×D11—41no—
237C2×D11—41no—
238C2×D11—41no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—82no—
244C4×C11—82no—
245C4×C11C2×#13511yescharacteristic
246C4×C11#57511yescharacteristic
247C4×C11#57811yescharacteristic
248C4×C11#57811yescharacteristic
249Dic11—41no—
250Dic11—41no—
251Dic11—41no—
252C2×Q16—21no—
253C2×Q16—21no—
254C2×M16—221no—
255C22×C8—221no—
256C22×C8C22⋊D1111yescharacteristic
257C22×C8C22⋊D1111yescharacteristic
258C4⋊Q8C22×D1112yes—
259C4⋊Q8C22×D1112yes—
260#126—221no—
261#125—22no—
262#125—111no—
263#124—111no—
264#123—221no—
265C22⋊Q8—22no—
266C22⋊Q8—22no—
267C22⋊Q8—111no—
268#121—111no—
269C4×Q8—22no—
270C4×Q8—22no—
271C4×Q8—111no—
272C4×D4—111no—
273C4×D4—221no—
274#117—22no—
275#117—221no—
276C2×C42C22×D1111yescharacteristic
277#107—21no—
278#107—21no—
279#107—222no—
280#107—222no—
281#106—222no—
282#106—222no—
283C4⋊C8—111no—
284C4⋊C8—111no—
285C4⋊C8—112no—
286C4⋊C8—112no—
287C4⋊C8—221no—
288C4⋊C8—221no—
289#103—22no—
290#103—22no—
291#103—222no—
292#103—222no—
293#102—222no—
294#102—222no—
295C22⋊C8—222no—
296C22⋊C8—221no—
297C22⋊C8—221no—
298C22⋊C8—221no—
299#97—221no—
300#97—221no—
301C4×C8—221no—
302C4×C8—222no—
303C4×C8C22⋊D1111yescharacteristic
304C4×C8C22⋊D1111yescharacteristic
305C4×C8C22×D1111yescharacteristic
306C4×C8C22×D1111yescharacteristic
307C2×C11—41no—
308C2×C11#303511yescharacteristic
309C2×C11#305911yescharacteristic
310C2×C11#306711yescharacteristic
311D11—81no—
312C2×Q8—22no—
313C2×Q8—22no—
314C2×Q8—111no—
315C2×D4—111no—
316C2×D4—221no—
317C22×C4—221no—
318C22×C4D4×D1111yescharacteristic
319C22×C4#434111yescharacteristic
320C22×C4C2×C22⋊D1111yescharacteristic
321Q16—42no—
322Q16—42no—
323M16—442no—
324C2×C8—22no—
325C2×C8—41no—
326C2×C8—222no—
327C2×C8—222no—
328C2×C8—221no—
329C2×C8—221no—
330C2×C8—442no—
331C2×C8C2×C22⋊D1111yescharacteristic
332C2×C8C2×C22⋊D1111yescharacteristic
333C2×C8C2×C22⋊D1111yescharacteristic
334C2×C8C2×C22⋊D1111yescharacteristic
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—42no—
340C4⋊C4—42no—
341C4⋊C4—111no—
342C4⋊C4—111no—
343C4⋊C4—221no—
344C4⋊C4—221no—
345C4⋊C4—221no—
346C4⋊C4—221no—
347C22⋊C4—42no—
348C22⋊C4—221no—
349C22⋊C4—221no—
350C22⋊C4—221no—
351C22⋊C4—221no—
352C22⋊C4—221no—
353C42—42no—
354C42—221no—
355C42D4×D1111yescharacteristic
356C42#434111yescharacteristic
357C42C2×C22⋊D1111yescharacteristic
358C42C23×D1111yescharacteristic
359C11#1922011yescharacteristic, complemented, Sylow
360C23—221no—
361C23#6699111yescharacteristic
362Q8—42no—
363Q8—42no—
364Q8—82no—
365Q8—221no—
366Q8—221no—
367D4—221no—
368D4—221no—
369D4—442no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—221no—
378C2×C4—221no—
379C2×C4—221no—
380C2×C4—441no—
381C2×C4—441no—
382C2×C4#6699111yescharacteristic
383C2×C4#6699111yescharacteristic
384C2×C4#6699111yescharacteristic
385C2×C4C2×D4×D1111yescharacteristic
386C2×C4C2×#434111yescharacteristic
387C2×C4C22×C22⋊D1111yescharacteristic
388C8—21no—
389C8—21no—
390C8—21no—
391C8—442no—
392C8—442no—
393C8—441no—
394C8—441no—
395C8#6700312yes—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—441no—
400C22—441no—
401C22—441no—
402C22C2×#6699111yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—82no—
408C4—82no—
409C4—441no—
410C4—441no—
411C4—441no—
412C4#1062329711yescharacteristic
413C4#1062329711yescharacteristic
414C4C2×#6700311yescharacteristic
415C4#1062335311yescharacteristic
416C2—41no—
417C2—881no—
418C2#1307806511yescharacteristic
419C2#1307826711yescharacteristic
420C2#1307833211yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3170C2
socleC22×C11C2×#121
prime radical#66983D4
hypercenter#3170D11
hypocenterC11#19220
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3170

Complements

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

NH ≅ G/Ntype
3. #13068195C2semidirect
4. #13068188C2semidirect
5. #13068017C2semidirect
6. #13068012C2semidirect
7. #13067983C2semidirect
8. #13067978C2semidirect
9. #13067364C2semidirect
10. #13067326C2semidirect
11. C11×#3170C2semidirect
151. #3170D11semidirect
359. C11#19220semidirect

Maximal subgroups

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

subgroupindex
#130797952
#130775912
#130681952
#130681882
#130680172
#130680122
#130679832
#130679782
#130673642
#130673262
C11×#31702
#1922011