Finite Group Databasebeta

← #14737214

Subgroups — #14737214

Order 2816.

628 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079936C212yesmaximal, complemented
2#13077591C211yesmaximal, characteristic, complemented
3#13068141C211yesmaximal, characteristic, complemented
4#13068136C211yesmaximal, characteristic, complemented
5#13068097C211yesmaximal, characteristic, complemented
6#13068092C211yesmaximal, characteristic, complemented
7#13068029C212yesmaximal, complemented
8#13068022C212yesmaximal, complemented
9C2×#10622095C211yesmaximal, characteristic, complemented
10#13067311C212yesmaximal, complemented
11C11×#3169C211yesmaximal, characteristic, complemented
12C11×#532C2212yes—
13#10623010C2211yescharacteristic
14C11×#500C2211yescharacteristic
15C11×#493C2211yescharacteristic
16C11×#486C2212yes—
17C11×#466—21no—
18C11×#466—21no—
19C4×C11×D8—21no—
20C4×C11×D8—21no—
21C2×C4×C8×C11C2211yescharacteristic
22#10622724—21no—
23C8×C22⋊D11—21no—
24#10622704C2212yes—
25#10622697C2212yes—
26#10622688C2212yes—
27#10622685C2212yes—
28#10622654—22no—
29#10622651—22no—
30#10622629—22no—
31#10622622—22no—
32#10622539C2211yescharacteristic
33C2×C4⋊(C11⋊C8)C2212yes—
34#10622303—21no—
35#10622302—21no—
36#10622301C2211yescharacteristic
37C8×D44C2211yescharacteristic
38#10622292C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40#10622184C2212yes—
41#10622184C2212yes—
42#10622182C2212yes—
43#10622182C2212yes—
44#10622095C2211yescharacteristic
45#10622095C2211yescharacteristic
46#10622095C2212yes—
47C2×C11×#41—22no—
48C2×C11×D8—21no—
49C2×C11×D8—21no—
50C22×C8×C11D411yescharacteristic
51C22×C8×C11D411yescharacteristic
52C11×C4⋊Q8C2312yes—
53C11×#127C2312yes—
54C11×#124—22no—
55C11×#121—22no—
56C11×#121—22no—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C2×C42×C11C2311yescharacteristic
60C2×#4324—22no—
61C2×#4323—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×#102—22no—
78C11×#102—22no—
79C4×C8×C11D411yescharacteristic
80C4×C8×C11D411yescharacteristic
81C4×C8×C11C2311yescharacteristic
82C4×C8×C11C2311yescharacteristic
83#66896—22no—
84#66896—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#19227—111nomaximal, Sylow
103C11×#41—84no—
104C2×Q8×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C2×C22⋊D11—21no—
114C2×D44C2×D411yescharacteristic
115C2×C4×D11—21no—
116C2×Dic22C2×D411yescharacteristic
117C11×D8—42no—
118C11×D8—42no—
119C2×C8×C11—22no—
120C2×C8×C11—41no—
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11C2×D411yescharacteristic
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C22⋊C4—42no—
128C11×C22⋊C4—42no—
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11#4111yescharacteristic
132C42×C11C2411yescharacteristic
133C22⋊Dic11—21no—
134#4324—82no—
135#4323—82no—
136(C2×D11)⋊C4—21no—
137(C2×D11)⋊C4—21no—
138(C2×D11)⋊C4—21no—
139(C2×D11)⋊C4—21no—
140C4⋊Dic11C2×D411yescharacteristic
141C4⋊Dic11C2×D411yescharacteristic
142Dic11⋊C4—21no—
143Dic11⋊C4—21no—
144Dic11⋊C4—21no—
145Dic11⋊C4—21no—
146C4×Dic11—21no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—82no—
152#4313—42no—
153C8×D11—42no—
154#3247—112no—
155#3169D1111yescharacteristic, complemented
156#2966—111no—
157#1696—111no—
158#1695—111no—
159#1688—111no—
160#1687—111no—
161#1678—112no—
162#1677—112no—
163C2×#334—111no—
164#1551—112no—
165C23×C11—42no—
166C23×C11#12111yescharacteristic
167C22×D11—21no—
168Q8×C11—82no—
169D4×C11—42no—
170D4×C11—42no—
171D4×C11—42no—
172D4×C11—42no—
173D4×C11—82no—
174D4×C11—84no—
175C2×C4×C11—22no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—22no—
179C2×C4×C11—42no—
180C2×C4×C11—84no—
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C22⋊D11—42no—
188C2×Dic11—21no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191D44—22no—
192C4×D11—41no—
193C4×D11—41no—
194Dic22—22no—
195C8×C11—21no—
196C8×C11—21no—
197C8×C11—21no—
198C8×C11#13512yes—
199C11⋊C8—41no—
200C11⋊C8—41no—
201C11⋊C8—42no—
202C11⋊C8—42no—
203#532C2×D1112yes—
204#529—111no—
205#500C2×D1111yescharacteristic
206#493C2×D1111yescharacteristic
207#486C2×D1112yes—
208#478—222no—
209#477—112no—
210#476—112no—
211#466—21no—
212#466—21no—
213#466—222no—
214#465—222no—
215#463—222no—
216#460—112no—
217#459—112no—
218#446—111no—
219C8×Q8—111no—
220C4×D8—21no—
221C4×D8—21no—
222#436—111no—
223#435—221no—
224C8×D4—111no—
225C8×D4—221no—
226#433—221no—
227#432—111no—
228C2×C4⋊C8—112no—
229#405—221no—
230C2×C4×C8C2×D1111yescharacteristic
231#334—112no—
232#334—111no—
233#334—111no—
234#333—112no—
235#333—112no—
236#331—112no—
237#331—112no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—82no—
241C22×C11—82no—
242C22×C11—82no—
243C22×C11#47212yes—
244C22×C11C2×#12111yescharacteristic
245C2×D11—41no—
246C2×D11—41no—
247C2×D11—41no—
248C4×C11—21no—
249C4×C11—21no—
250C4×C11—21no—
251C4×C11—21no—
252C4×C11—82no—
253C4×C11C2×#13511yescharacteristic
254C4×C11#57511yescharacteristic
255C4×C11#57712yes—
256Dic11—41no—
257Dic11—41no—
258Dic11—41no—
259C2×#41—22no—
260C2×SD16—222no—
261C2×D8—21no—
262C2×D8—21no—
263C2×D8—222no—
264C2×M16—221no—
265C22×C8—222no—
266C22×C8—221no—
267C22×C8C22⋊D1111yescharacteristic
268C22×C8C22⋊D1111yescharacteristic
269C4⋊Q8C22×D1112yes—
270#127C22×D1112yes—
271#126—221no—
272#125—111no—
273#124—22no—
274#124—111no—
275#123—221no—
276C22⋊Q8—111no—
277#121—22no—
278#121—22no—
279#121—111no—
280C4×Q8—111no—
281C4×D4—22no—
282C4×D4—22no—
283C4×D4—111no—
284C4×D4—221no—
285#117—221no—
286C2×C42C22×D1111yescharacteristic
287#107—21no—
288#107—21no—
289#107—222no—
290#106—222no—
291C4⋊C8—111no—
292C4⋊C8—111no—
293C4⋊C8—112no—
294C4⋊C8—112no—
295C4⋊C8—221no—
296C4⋊C8—221no—
297C4⋊C8—222no—
298#103—222no—
299#102—22no—
300#102—22no—
301#102—222no—
302#102—222no—
303#102—222no—
304C22⋊C8—221no—
305C22⋊C8—221no—
306C22⋊C8—221no—
307#97—221no—
308#97—221no—
309C4×C8—221no—
310C4×C8C22⋊D1111yescharacteristic
311C4×C8C22⋊D1111yescharacteristic
312C4×C8C22×D1111yescharacteristic
313C4×C8C22×D1111yescharacteristic
314C2×C11—22no—
315C2×C11—162no—
316C2×C11#303511yescharacteristic
317C2×C11#306011yescharacteristic
318C2×C11C2×#47211yescharacteristic
319D11—81no—
320#41—84no—
321C2×Q8—22no—
322C2×Q8—111no—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—42no—
327C2×D4—111no—
328C2×D4—221no—
329C22×C4—42no—
330C22×C4—221no—
331C22×C4D4×D1111yescharacteristic
332C22×C4#434111yescharacteristic
333C22×C4C2×C22⋊D1111yescharacteristic
334SD16—882no—
335D8—42no—
336D8—42no—
337D8—882no—
338M16—442no—
339C2×C8—22no—
340C2×C8—41no—
341C2×C8—222no—
342C2×C8—222no—
343C2×C8—221no—
344C2×C8—221no—
345C2×C8—442no—
346C2×C8—882no—
347C2×C8C2×C22⋊D1111yescharacteristic
348C2×C8C2×C22⋊D1111yescharacteristic
349C2×C8C2×C22⋊D1111yescharacteristic
350C2×C8C2×C22⋊D1111yescharacteristic
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—111no—
354C4⋊C4—111no—
355C4⋊C4—221no—
356C4⋊C4—221no—
357C4⋊C4—221no—
358C4⋊C4—221no—
359C22⋊C4—42no—
360C22⋊C4—42no—
361C22⋊C4—221no—
362C22⋊C4—221no—
363C22⋊C4—221no—
364C22⋊C4—221no—
365C22⋊C4—221no—
366C42—221no—
367C42D4×D1111yescharacteristic
368C42#434111yescharacteristic
369C42C2×C22⋊D1111yescharacteristic
370C42C23×D1111yescharacteristic
371C11#1922711yescharacteristic, complemented, Sylow
372C23—42no—
373C23—221no—
374C23#6699111yescharacteristic
375Q8—82no—
376Q8—222no—
377D4—42no—
378D4—42no—
379D4—42no—
380D4—42no—
381D4—82no—
382D4—84no—
383D4—222no—
384D4—442no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—42no—
390C2×C4—84no—
391C2×C4—221no—
392C2×C4—221no—
393C2×C4—221no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4#6699111yescharacteristic
397C2×C4#6699111yescharacteristic
398C2×C4#6699111yescharacteristic
399C2×C4C2×D4×D1111yescharacteristic
400C2×C4C2×#434111yescharacteristic
401C2×C4C22×C22⋊D1111yescharacteristic
402C8—21no—
403C8—21no—
404C8—21no—
405C8—442no—
406C8—442no—
407C8—441no—
408C8—441no—
409C8#6700312yes—
410C22—21no—
411C22—21no—
412C22—82no—
413C22—82no—
414C22—82no—
415C22—441no—
416C22—441no—
417C22—441no—
418C22#1062277312yes—
419C22C2×#6699111yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—21no—
424C4—82no—
425C4—441no—
426C4—441no—
427C4—441no—
428C4#1062330112yes—
429C4C2×#6700311yescharacteristic
430C4#1062335311yescharacteristic
431C2—22no—
432C2—162no—
433C2—881no—
434C2#1307806511yescharacteristic
435C2#1307827411yescharacteristic
436C2C2×#1062277311yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3169C2
socleC22×C11C2×#121
hypercenter#3169D11
hypocenterC11#19227
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #13079936C2semidirect
2. #13077591C2semidirect
3. #13068141C2semidirect
4. #13068136C2semidirect
5. #13068097C2semidirect
6. #13068092C2semidirect
7. #13068029C2semidirect
8. #13068022C2semidirect
9. C2×#10622095C2semidirect
10. #13067311C2semidirect
11. C11×#3169C2semidirect
155. #3169D11semidirect
371. C11#19227semidirect

Maximal subgroups

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

subgroupindex
#130799362
#130775912
#130681412
#130681362
#130680972
#130680922
#130680292
#130680222
C2×#106220952
#130673112
C11×#31692
#1922711