Finite Group Databasebeta

← #14737155

Subgroups — #14737155

Order 2816.

628 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079936C212yesmaximal, complemented
2#13077591C211yesmaximal, characteristic, complemented
3#13068153C212yesmaximal, complemented
4#13068146C212yesmaximal, complemented
5#13068017C211yesmaximal, characteristic, complemented
6#13068012C211yesmaximal, characteristic, complemented
7#13067973C211yesmaximal, characteristic, complemented
8#13067968C211yesmaximal, characteristic, complemented
9C2×#10622096C211yesmaximal, 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#10622096C2212yes—
45#10622096C2211yescharacteristic
46#10622096C2211yescharacteristic
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#19222—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#1698—112no—
158#1697—112no—
159#1676—111no—
160#1675—111no—
161#1668—111no—
162#1667—111no—
163C2×#335—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—21no—
179C2×C4×C11—21no—
180C2×C4×C11—42no—
181C2×C4×C11—84no—
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C22⋊D11—42no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—21no—
192D44—21no—
193D44—21no—
194C4×D11—41no—
195C4×D11—41no—
196Dic22—21no—
197Dic22—21no—
198C8×C11—21no—
199C8×C11—21no—
200C8×C11—21no—
201C8×C11#13512yes—
202C11⋊C8—41no—
203C11⋊C8—41no—
204C11⋊C8—42no—
205C11⋊C8—42no—
206#532C2×D1112yes—
207#529—111no—
208#500C2×D1111yescharacteristic
209#493C2×D1111yescharacteristic
210#486C2×D1112yes—
211#478—222no—
212#477—112no—
213#476—112no—
214#466—21no—
215#466—21no—
216#466—222no—
217#465—222no—
218#463—222no—
219#460—112no—
220#459—112no—
221#446—111no—
222C8×Q8—111no—
223C4×D8—21no—
224C4×D8—21no—
225#436—111no—
226#435—221no—
227C8×D4—111no—
228C8×D4—221no—
229#433—221no—
230#432—111no—
231C2×C4⋊C8—112no—
232#405—221no—
233C2×C4×C8C2×D1111yescharacteristic
234#335—111no—
235#335—111no—
236#335—112no—
237#333—112no—
238#333—112no—
239#331—112no—
240#331—112no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—82no—
244C22×C11—82no—
245C22×C11—82no—
246C22×C11#47212yes—
247C22×C11C2×#12111yescharacteristic
248C2×D11—41no—
249C2×D11—41no—
250C2×D11—41no—
251C4×C11—21no—
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—21no—
255C4×C11—82no—
256C4×C11C2×#13511yescharacteristic
257C4×C11#57511yescharacteristic
258C4×C11#57611yescharacteristic
259C4×C11#57811yescharacteristic
260Dic11—41no—
261Dic11—41no—
262Dic11—41no—
263C2×#41—22no—
264C2×SD16—222no—
265C2×D8—21no—
266C2×D8—21no—
267C2×D8—222no—
268C2×M16—221no—
269C22×C8—222no—
270C22×C8—221no—
271C22×C8C22⋊D1111yescharacteristic
272C22×C8C22⋊D1111yescharacteristic
273C4⋊Q8C22×D1112yes—
274#127C22×D1112yes—
275#126—221no—
276#125—111no—
277#124—22no—
278#124—111no—
279#123—221no—
280C22⋊Q8—111no—
281#121—22no—
282#121—22no—
283#121—111no—
284C4×Q8—111no—
285C4×D4—22no—
286C4×D4—22no—
287C4×D4—111no—
288C4×D4—221no—
289#117—221no—
290C2×C42C22×D1111yescharacteristic
291#107—21no—
292#107—21no—
293#107—222no—
294#106—222no—
295C4⋊C8—111no—
296C4⋊C8—111no—
297C4⋊C8—112no—
298C4⋊C8—112no—
299C4⋊C8—221no—
300C4⋊C8—221no—
301C4⋊C8—222no—
302#103—222no—
303#102—22no—
304#102—22no—
305#102—222no—
306#102—222no—
307#102—222no—
308C22⋊C8—221no—
309C22⋊C8—221no—
310C22⋊C8—221no—
311#97—221no—
312#97—221no—
313C4×C8—221no—
314C4×C8C22⋊D1111yescharacteristic
315C4×C8C22⋊D1111yescharacteristic
316C4×C8C22×D1111yescharacteristic
317C4×C8C22×D1111yescharacteristic
318C2×C11—22no—
319C2×C11—162no—
320C2×C11#303511yescharacteristic
321C2×C11#306111yescharacteristic
322C2×C11C2×#47211yescharacteristic
323D11—81no—
324#41—84no—
325C2×Q8—22no—
326C2×Q8—111no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—42no—
331C2×D4—111no—
332C2×D4—221no—
333C22×C4—42no—
334C22×C4—221no—
335C22×C4D4×D1111yescharacteristic
336C22×C4#434111yescharacteristic
337C22×C4C2×C22⋊D1111yescharacteristic
338SD16—882no—
339D8—42no—
340D8—42no—
341D8—882no—
342M16—442no—
343C2×C8—22no—
344C2×C8—41no—
345C2×C8—222no—
346C2×C8—222no—
347C2×C8—221no—
348C2×C8—221no—
349C2×C8—442no—
350C2×C8—882no—
351C2×C8C2×C22⋊D1111yescharacteristic
352C2×C8C2×C22⋊D1111yescharacteristic
353C2×C8C2×C22⋊D1111yescharacteristic
354C2×C8C2×C22⋊D1111yescharacteristic
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—111no—
358C4⋊C4—111no—
359C4⋊C4—221no—
360C4⋊C4—221no—
361C4⋊C4—221no—
362C4⋊C4—221no—
363C22⋊C4—42no—
364C22⋊C4—42no—
365C22⋊C4—221no—
366C22⋊C4—221no—
367C22⋊C4—221no—
368C22⋊C4—221no—
369C22⋊C4—221no—
370C42—221no—
371C42D4×D1111yescharacteristic
372C42#434111yescharacteristic
373C42C2×C22⋊D1111yescharacteristic
374C42C23×D1111yescharacteristic
375C11#1922211yescharacteristic, complemented, Sylow
376C23—42no—
377C23—221no—
378C23#6699111yescharacteristic
379Q8—82no—
380Q8—221no—
381Q8—221no—
382D4—42no—
383D4—42no—
384D4—42no—
385D4—42no—
386D4—82no—
387D4—84no—
388D4—221no—
389D4—221no—
390D4—442no—
391C2×C4—22no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—42no—
397C2×C4—84no—
398C2×C4—221no—
399C2×C4—221no—
400C2×C4—221no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4#6699111yescharacteristic
404C2×C4#6699111yescharacteristic
405C2×C4#6699111yescharacteristic
406C2×C4C2×D4×D1111yescharacteristic
407C2×C4C2×#434111yescharacteristic
408C2×C4C22×C22⋊D1111yescharacteristic
409C8—21no—
410C8—21no—
411C8—21no—
412C8—442no—
413C8—442no—
414C8—441no—
415C8—441no—
416C8#6700312yes—
417C22—21no—
418C22—21no—
419C22—82no—
420C22—82no—
421C22—82no—
422C22—441no—
423C22—441no—
424C22—441no—
425C22#1062277312yes—
426C22C2×#6699111yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—82no—
432C4—441no—
433C4—441no—
434C4—441no—
435C4#1062330011yescharacteristic
436C4#1062330211yescharacteristic
437C4C2×#6700311yescharacteristic
438C4#1062335311yescharacteristic
439C2—22no—
440C2—162no—
441C2—881no—
442C2#1307806511yescharacteristic
443C2#1307828211yescharacteristic
444C2C2×#1062277311yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3169C2
socleC22×C11C2×#121
hypercenter#3169D11
hypocenterC11#19222
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. #13068153C2semidirect
4. #13068146C2semidirect
5. #13068017C2semidirect
6. #13068012C2semidirect
7. #13067973C2semidirect
8. #13067968C2semidirect
9. C2×#10622096C2semidirect
10. #13067311C2semidirect
11. C11×#3169C2semidirect
155. #3169D11semidirect
375. C11#19222semidirect

Maximal subgroups

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

subgroupindex
#130799362
#130775912
#130681532
#130681462
#130680172
#130680122
#130679732
#130679682
C2×#106220962
#130673112
C11×#31692
#1922211