Finite Group Databasebeta

← #14737166

Subgroups — #14737166

Order 2816.

584 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079947C212yesmaximal
2#13077591C211yesmaximal, characteristic
3#13068167C212yesmaximal, complemented
4#13068160C212yesmaximal, complemented
5#13068007C211yesmaximal, characteristic, complemented
6#13068002C211yesmaximal, characteristic, complemented
7#13067983C211yesmaximal, characteristic, complemented
8#13067978C211yesmaximal, characteristic, complemented
9C2×#10622096C211yesmaximal, characteristic, complemented
10#13067316C212yesmaximal, 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#10622703C2212yes—
26#10622700C2212yes—
27#10622696C2212yes—
28#10622664—22no—
29#10622661—22no—
30#10622641—22no—
31#10622635—22no—
32#10622539C2211yescharacteristic
33C2×C4⋊(C11⋊C8)C2212yes—
34#10622303—21no—
35#10622302—21no—
36#10622301C2211yescharacteristic
37C8×D44C2211yescharacteristic
38#10622292C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40#10622185C2212yes—
41#10622185C2212yes—
42#10622185C2212yes—
43#10622185C2212yes—
44#10622096C2212yes—
45#10622096C2211yescharacteristic
46#10622096C2211yescharacteristic
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
60C2×#4326—22no—
61C2×#4325—22no—
62#66983D411yescharacteristic
63#66982—21no—
64C4×C22⋊D11—21no—
65#66977D411yescharacteristic
66C22×C11⋊C8—22no—
67C2×#4313—21no—
68C2×C8×D11—21no—
69#66929—21no—
70#66928D411yescharacteristic
71C4×D44C2311yescharacteristic
72#66925—21no—
73#66923D411yescharacteristic
74C4×Dic22C2311yescharacteristic
75C11×#107—21no—
76C11×#107—21no—
77C11×#103—22no—
78C11×#103—22no—
79C4×C8×C11D411yescharacteristic
80C4×C8×C11D411yescharacteristic
81C4×C8×C11C2311yescharacteristic
82C4×C8×C11C2311yescharacteristic
83#66899—22no—
84#66899—22no—
85C22⋊(C11⋊C8)—21no—
86(C2×D11)⋊C8—21no—
87(C2×D11)⋊C8—21no—
88#66879—21no—
89Dic11⋊C8—21no—
90Dic11⋊C8—21no—
91C8×Dic11—21no—
92#66874—22no—
93#66873—22no—
94#66872—22no—
95#66871—22no—
96C4⋊(C11⋊C8)—22no—
97C4⋊(C11⋊C8)C2312yes—
98C4⋊(C11⋊C8)C2312yes—
99C4⋊(C11⋊C8)C2311yescharacteristic
100C4⋊(C11⋊C8)C2311yescharacteristic
101#66867—21no—
102#19223—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#4326—82no—
134#4325—82no—
135(C2×D11)⋊C4—21no—
136(C2×D11)⋊C4—21no—
137(C2×D11)⋊C4—21no—
138(C2×D11)⋊C4—21no—
139C4⋊Dic11C2×D411yescharacteristic
140C4⋊Dic11C2×D411yescharacteristic
141Dic11⋊C4—21no—
142Dic11⋊C4—21no—
143Dic11⋊C4—21no—
144Dic11⋊C4—21no—
145C4×Dic11—21no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—82no—
151#4313—42no—
152C8×D11—42no—
153#3248—112no—
154#3170D1111yescharacteristic, complemented
155#2966—111no—
156#1700—112no—
157#1699—112no—
158#1674—111no—
159#1673—111no—
160#1670—111no—
161#1669—111no—
162C2×#335—111no—
163#1552—112no—
164C23×C11#12111yescharacteristic
165C22×D11—21no—
166Q8×C11—42no—
167Q8×C11—42no—
168Q8×C11—42no—
169Q8×C11—42no—
170C2×C4×C11—22no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11C22×D411yescharacteristic
181C2×C4×C11C22×D411yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C22⋊D11—42no—
184C2×Dic11—21no—
185C2×Dic11—21no—
186C2×Dic11—21no—
187D44—21no—
188D44—21no—
189C4×D11—41no—
190C4×D11—41no—
191Dic22—21no—
192Dic22—21no—
193C8×C11—21no—
194C8×C11—21no—
195C8×C11—21no—
196C8×C11#13512yes—
197C11⋊C8—41no—
198C11⋊C8—41no—
199C11⋊C8—42no—
200C11⋊C8—42no—
201#533C2×D1112yes—
202#529—111no—
203#500C2×D1111yescharacteristic
204#494C2×D1111yescharacteristic
205#487C2×D1112yes—
206#479—222no—
207#475—112no—
208#474—112no—
209#467—21no—
210#467—21no—
211#467—222no—
212#465—222no—
213#464—222no—
214#462—112no—
215#461—112no—
216#446—111no—
217C8×Q8—111no—
218C4×Q16—21no—
219C4×Q16—21no—
220#436—111no—
221#435—221no—
222C8×D4—111no—
223C8×D4—221no—
224#433—221no—
225#432—111no—
226C2×C4⋊C8—112no—
227#405—221no—
228C2×C4×C8C2×D1111yescharacteristic
229#335—111no—
230#335—111no—
231#335—112no—
232#332—112no—
233#332—112no—
234#332—112no—
235#332—112no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11#47312yes—
239C22×C11C2×#12111yescharacteristic
240C2×D11—41no—
241C2×D11—41no—
242C2×D11—41no—
243C4×C11—21no—
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—82no—
248C4×C11—82no—
249C4×C11C2×#13511yescharacteristic
250C4×C11#57511yescharacteristic
251C4×C11#57611yescharacteristic
252C4×C11#57811yescharacteristic
253Dic11—41no—
254Dic11—41no—
255Dic11—41no—
256C2×Q16—21no—
257C2×Q16—21no—
258C2×Q16—222no—
259C2×SD16—222no—
260C2×M16—221no—
261C22×C8—222no—
262C22×C8—221no—
263C22×C8C22⋊D1111yescharacteristic
264C22×C8C22⋊D1111yescharacteristic
265C4⋊Q8C22×D1112yes—
266C4⋊Q8C22×D1112yes—
267#126—221no—
268#125—22no—
269#125—111no—
270#124—111no—
271#123—221no—
272C22⋊Q8—22no—
273C22⋊Q8—22no—
274C22⋊Q8—111no—
275#121—111no—
276C4×Q8—22no—
277C4×Q8—22no—
278C4×Q8—111no—
279C4×D4—111no—
280C4×D4—221no—
281#117—22no—
282#117—221no—
283C2×C42C22×D1111yescharacteristic
284#107—21no—
285#107—21no—
286#107—222no—
287#106—222no—
288C4⋊C8—111no—
289C4⋊C8—111no—
290C4⋊C8—112no—
291C4⋊C8—112no—
292C4⋊C8—221no—
293C4⋊C8—221no—
294C4⋊C8—222no—
295#103—22no—
296#103—22no—
297#103—222no—
298#103—222no—
299#103—222no—
300#102—222no—
301C22⋊C8—221no—
302C22⋊C8—221no—
303C22⋊C8—221no—
304#97—221no—
305#97—221no—
306C4×C8—221no—
307C4×C8C22⋊D1111yescharacteristic
308C4×C8C22⋊D1111yescharacteristic
309C4×C8C22×D1111yescharacteristic
310C4×C8C22×D1111yescharacteristic
311C2×C11—22no—
312C2×C11#303511yescharacteristic
313C2×C11#306111yescharacteristic
314C2×C11C2×#47311yescharacteristic
315D11—81no—
316C2×Q8—22no—
317C2×Q8—22no—
318C2×Q8—111no—
319C2×D4—111no—
320C2×D4—221no—
321C22×C4—221no—
322C22×C4D4×D1111yescharacteristic
323C22×C4#434111yescharacteristic
324C22×C4C2×C22⋊D1111yescharacteristic
325Q16—42no—
326Q16—42no—
327Q16—882no—
328SD16—882no—
329M16—442no—
330C2×C8—22no—
331C2×C8—41no—
332C2×C8—222no—
333C2×C8—222no—
334C2×C8—221no—
335C2×C8—221no—
336C2×C8—442no—
337C2×C8—882no—
338C2×C8C2×C22⋊D1111yescharacteristic
339C2×C8C2×C22⋊D1111yescharacteristic
340C2×C8C2×C22⋊D1111yescharacteristic
341C2×C8C2×C22⋊D1111yescharacteristic
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—42no—
347C4⋊C4—42no—
348C4⋊C4—111no—
349C4⋊C4—111no—
350C4⋊C4—221no—
351C4⋊C4—221no—
352C4⋊C4—221no—
353C4⋊C4—221no—
354C22⋊C4—42no—
355C22⋊C4—221no—
356C22⋊C4—221no—
357C22⋊C4—221no—
358C22⋊C4—221no—
359C22⋊C4—221no—
360C42—42no—
361C42—221no—
362C42D4×D1111yescharacteristic
363C42#434111yescharacteristic
364C42C2×C22⋊D1111yescharacteristic
365C42C23×D1111yescharacteristic
366C11#1922311yescharacteristic, complemented, Sylow
367C23—221no—
368C23#6699111yescharacteristic
369Q8—42no—
370Q8—42no—
371Q8—42no—
372Q8—42no—
373Q8—221no—
374Q8—221no—
375D4—221no—
376D4—221no—
377D4—442no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—221no—
386C2×C4—221no—
387C2×C4—221no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4#6699111yescharacteristic
391C2×C4#6699111yescharacteristic
392C2×C4#6699111yescharacteristic
393C2×C4C2×D4×D1111yescharacteristic
394C2×C4C2×#434111yescharacteristic
395C2×C4C22×C22⋊D1111yescharacteristic
396C8—21no—
397C8—21no—
398C8—21no—
399C8—442no—
400C8—442no—
401C8—441no—
402C8—441no—
403C8#6700312yes—
404C22—21no—
405C22—21no—
406C22—441no—
407C22—441no—
408C22—441no—
409C22#1062280512yes—
410C22C2×#6699111yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—82no—
416C4—82no—
417C4—441no—
418C4—441no—
419C4—441no—
420C4#1062330011yescharacteristic
421C4#1062330211yescharacteristic
422C4C2×#6700311yescharacteristic
423C4#1062335311yescharacteristic
424C2—22no—
425C2—881no—
426C2#1307806511yescharacteristic
427C2#1307828211yescharacteristic
428C2C2×#1062280511yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3170C2
socleC22×C11C2×#121
prime radical#66983D4
hypercenter#3170D11
hypocenterC11#19223
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. #13068167C2semidirect
4. #13068160C2semidirect
5. #13068007C2semidirect
6. #13068002C2semidirect
7. #13067983C2semidirect
8. #13067978C2semidirect
9. C2×#10622096C2semidirect
10. #13067316C2semidirect
11. C11×#3170C2semidirect
154. #3170D11semidirect
366. C11#19223semidirect

Maximal subgroups

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

subgroupindex
#130799472
#130775912
#130681672
#130681602
#130680072
#130680022
#130679832
#130679782
C2×#106220962
#130673162
C11×#31702
#1922311