Finite Group Databasebeta

← #14737161

Subgroups — #14737161

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#13079942C212yesmaximal, complemented
2#13079195C211yesmaximal, characteristic, complemented
3#13068156C212yesmaximal, complemented
4#13068149C212yesmaximal, complemented
5#13068020C211yesmaximal, characteristic, complemented
6#13068015C211yesmaximal, characteristic, complemented
7#13067976C211yesmaximal, characteristic, complemented
8#13067971C211yesmaximal, characteristic, complemented
9C2×#10622096C211yesmaximal, characteristic, complemented
10#13067312C212yesmaximal, complemented
11C11×#2966C211yesmaximal, characteristic, complemented
12C11×#529C2211yescharacteristic
13#10623008C2212yes—
14C11×#446C2211yescharacteristic
15C8×Q8×C11C2211yescharacteristic
16C11×#436C2211yescharacteristic
17C11×#435—21no—
18C8×D4×C11—21no—
19C8×D4×C11C2211yescharacteristic
20C11×#433—21no—
21C11×#432C2211yescharacteristic
22C11×#405—21no—
23C2×C4×C8×C11C2211yescharacteristic
24#10622728—21no—
25#10622728—21no—
26#10622679—22no—
27#10622670—22no—
28#10622661—22no—
29#10622651—22no—
30#10622640C2212yes—
31#10622634C2212yes—
32#10622628C2212yes—
33#10622621C2212yes—
34C2×C4⋊(C11⋊C8)C2212yes—
35#10622308C2211yescharacteristic
36#10622307C2212yes—
37C4×D88—21no—
38C4×D88—21no—
39#10622295C2211yescharacteristic
40#10622123C2212yes—
41#10622123C2212yes—
42#10622119C2212yes—
43#10622119C2212yes—
44#10622096C2212yes—
45#10622096C2211yescharacteristic
46#10622096C2211yescharacteristic
47C2×#4339—22no—
48C2×C11×M16—21no—
49C22×C8×C11—21no—
50C22×C8×C11D411yescharacteristic
51C22×C8×C11D411yescharacteristic
52C11×#126—21no—
53C11×#125D411yescharacteristic
54C11×#124D411yescharacteristic
55C11×#123—21no—
56C11×C22⋊Q8D411yescharacteristic
57C11×#121D411yescharacteristic
58C4×Q8×C11C2311yescharacteristic
59C4×D4×C11—21no—
60C4×D4×C11C2311yescharacteristic
61C11×#117—21no—
62C2×C42×C11C2311yescharacteristic
63C2×#4325—22no—
64C2×#4323—22no—
65#66983—22no—
66#66983—22no—
67C22×C11⋊C8—22no—
68C2×D88—21no—
69C2×D88—21no—
70#66928—22no—
71#66927C2312yes—
72C4×D44—22no—
73C4×D44—22no—
74#66922C2312yes—
75C11×C4⋊C8—21no—
76C11×C4⋊C8—21no—
77C11×C4⋊C8C2311yescharacteristic
78C11×C4⋊C8C2311yescharacteristic
79C11×C22⋊C8—21no—
80C11×C22⋊C8—21no—
81C11×C22⋊C8—21no—
82C11×#97—21no—
83C11×#97—21no—
84C4×C8×C11—21no—
85C4×C8×C11D411yescharacteristic
86C4×C8×C11D411yescharacteristic
87C4×C8×C11C2311yescharacteristic
88C4×C8×C11C2311yescharacteristic
89#66899—22no—
90#66896—22no—
91#66885—22no—
92#66885—22no—
93#66882—21no—
94#66882—21no—
95#66873—22no—
96#66873—22no—
97#66872—22no—
98#66871—22no—
99C4⋊(C11⋊C8)—22no—
100C4⋊(C11⋊C8)C2312yes—
101C4⋊(C11⋊C8)C2312yes—
102#19222—111nomaximal, Sylow
103C2×Q8×C11C2×D411yescharacteristic
104C2×D4×C11—21no—
105C2×D4×C11C2×D411yescharacteristic
106C22×C4×C11—21no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11#4111yescharacteristic
110C2×C22⋊D11—42no—
111#4339—84no—
112C2×D44—22no—
113C2×D44—22no—
114C2×D44—22no—
115C2×C4×D11—42no—
116C2×Dic22—22no—
117C11×M16—42no—
118C2×C8×C11—22no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11—41no—
122C2×C8×C11—42no—
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2×D411yescharacteristic
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4C2×D411yescharacteristic
132C11×C4⋊C4C2×D411yescharacteristic
133C11×C22⋊C4—21no—
134C11×C22⋊C4—21no—
135C11×C22⋊C4—21no—
136C11×C22⋊C4—21no—
137C11×C22⋊C4—21no—
138C42×C11—21no—
139C42×C11C2×D411yescharacteristic
140C42×C11C2×D411yescharacteristic
141C42×C11#4111yescharacteristic
142C42×C11C2411yescharacteristic
143#4325—82no—
144#4323—82no—
145(C2×D11)⋊C4—42no—
146(C2×D11)⋊C4—42no—
147C4⋊Dic11—22no—
148C4⋊Dic11—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—82no—
152D88—42no—
153D88—42no—
154#3247—112no—
155#3169—111no—
156#2966D1111yescharacteristic, complemented
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—21no—
166C23×C11#12111yescharacteristic
167C22×D11—42no—
168Q8×C11—21no—
169Q8×C11—21no—
170D4×C11—21no—
171D4×C11—21no—
172D4×C11—42no—
173C2×C4×C11—22no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C22×D411yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C22⋊D11—84no—
190C2×Dic11—42no—
191D44—42no—
192D44—42no—
193D44—42no—
194D44—42no—
195D44—82no—
196C4×D11—84no—
197Dic22—82no—
198C8×C11—21no—
199C8×C11—21no—
200C8×C11—21no—
201C8×C11—41no—
202C8×C11—41no—
203C8×C11#13512yes—
204C11⋊C8—42no—
205C11⋊C8—42no—
206#532—112no—
207#529C2×D1111yescharacteristic
208#500—111no—
209#493—111no—
210#486—112no—
211#478—222no—
212#477—112no—
213#476—112no—
214#466—221no—
215#466—221no—
216#466—222no—
217#465—222no—
218#463—222no—
219#460—112no—
220#459—112no—
221#446C2×D1111yescharacteristic
222C8×Q8C2×D1111yescharacteristic
223C4×D8—221no—
224C4×D8—221no—
225#436C2×D1111yescharacteristic
226#435—21no—
227C8×D4—21no—
228C8×D4C2×D1111yescharacteristic
229#433—21no—
230#432C2×D1111yescharacteristic
231C2×C4⋊C8—112no—
232#405—21no—
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—41no—
244C22×C11—41no—
245C22×C11—41no—
246C22×C11#47212yes—
247C22×C11C2×#12111yescharacteristic
248C2×D11—82no—
249C2×D11—82no—
250C2×D11—82no—
251C4×C11—21no—
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—21no—
255C4×C11—41no—
256C4×C11—41no—
257C4×C11—41no—
258C4×C11C2×#13511yescharacteristic
259C4×C11#57511yescharacteristic
260C4×C11#57611yescharacteristic
261C4×C11#57811yescharacteristic
262Dic11—82no—
263C2×#41—222no—
264C2×SD16—222no—
265C2×D8—222no—
266C2×D8—221no—
267C2×D8—221no—
268C2×M16—21no—
269C22×C8—21no—
270C22×C8—222no—
271C22×C8C22⋊D1111yescharacteristic
272C22×C8C22⋊D1111yescharacteristic
273C4⋊Q8—112no—
274#127—112no—
275#126—21no—
276#125D4411yescharacteristic
277#124—222no—
278#124D4411yescharacteristic
279#123—21no—
280C22⋊Q8D4411yescharacteristic
281#121—222no—
282#121—222no—
283#121D4411yescharacteristic
284C4×Q8C22×D1111yescharacteristic
285C4×D4—21no—
286C4×D4—222no—
287C4×D4—222no—
288C4×D4C22×D1111yescharacteristic
289#117—21no—
290C2×C42C22×D1111yescharacteristic
291#107—221no—
292#107—221no—
293#107—222no—
294#106—222no—
295C4⋊C8—21no—
296C4⋊C8—21no—
297C4⋊C8—112no—
298C4⋊C8—112no—
299C4⋊C8—222no—
300C4⋊C8C22×D1111yescharacteristic
301C4⋊C8C22×D1111yescharacteristic
302#103—222no—
303#102—222no—
304#102—222no—
305#102—222no—
306#102—222no—
307#102—222no—
308C22⋊C8—21no—
309C22⋊C8—21no—
310C22⋊C8—21no—
311#97—21no—
312#97—21no—
313C4×C8—21no—
314C4×C8C22⋊D1111yescharacteristic
315C4×C8C22⋊D1111yescharacteristic
316C4×C8C22×D1111yescharacteristic
317C4×C8C22×D1111yescharacteristic
318C2×C11—22no—
319C2×C11—81no—
320C2×C11#303511yescharacteristic
321C2×C11#306111yescharacteristic
322C2×C11C2×#47211yescharacteristic
323D11—162no—
324#41—884no—
325C2×Q8—222no—
326C2×Q8C2×D4411yescharacteristic
327C2×D4—21no—
328C2×D4—222no—
329C2×D4—222no—
330C2×D4—222no—
331C2×D4—442no—
332C2×D4C2×D4411yescharacteristic
333C22×C4—21no—
334C22×C4—442no—
335C22×C4C2×D4411yescharacteristic
336C22×C4#433911yescharacteristic
337C22×C4C2×C22⋊D1111yescharacteristic
338SD16—882no—
339D8—442no—
340D8—442no—
341D8—882no—
342M16—42no—
343C2×C8—22no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—41no—
347C2×C8—42no—
348C2×C8—222no—
349C2×C8—222no—
350C2×C8—882no—
351C2×C8C2×C22⋊D1111yescharacteristic
352C2×C8C2×C22⋊D1111yescharacteristic
353C2×C8C2×C22⋊D1111yescharacteristic
354C2×C8C2×C22⋊D1111yescharacteristic
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—222no—
360C4⋊C4—222no—
361C4⋊C4C2×D4411yescharacteristic
362C4⋊C4C2×D4411yescharacteristic
363C22⋊C4—21no—
364C22⋊C4—21no—
365C22⋊C4—21no—
366C22⋊C4—21no—
367C22⋊C4—21no—
368C22⋊C4—442no—
369C22⋊C4—442no—
370C42—21no—
371C42C2×D4411yescharacteristic
372C42#433911yescharacteristic
373C42C2×C22⋊D1111yescharacteristic
374C42C23×D1111yescharacteristic
375C11#1922211yescharacteristic, complemented, Sylow
376C23—21no—
377C23—442no—
378C23#6698311yescharacteristic
379Q8—21no—
380Q8—21no—
381Q8—882no—
382D4—21no—
383D4—21no—
384D4—42no—
385D4—442no—
386D4—442no—
387D4—442no—
388D4—442no—
389D4—882no—
390D4—884no—
391C2×C4—22no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—442no—
402C2×C4—884no—
403C2×C4#6698311yescharacteristic
404C2×C4#6698311yescharacteristic
405C2×C4#6698311yescharacteristic
406C2×C4C22×D4411yescharacteristic
407C2×C4C2×#433911yescharacteristic
408C2×C4C22×C22⋊D1111yescharacteristic
409C8—21no—
410C8—21no—
411C8—21no—
412C8—41no—
413C8—41no—
414C8—442no—
415C8—442no—
416C8#6700312yes—
417C22—21no—
418C22—21no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—882no—
423C22—882no—
424C22—882no—
425C22#1062275512yes—
426C22C2×#6698311yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—41no—
432C4—41no—
433C4—41no—
434C4—882no—
435C4#1062328311yescharacteristic
436C4#1062328411yescharacteristic
437C4C2×#6700311yescharacteristic
438C4#1062335311yescharacteristic
439C2—22no—
440C2—81no—
441C2—1762no—
442C2#1307807111yescharacteristic
443C2#1307828611yescharacteristic
444C2C2×#1062275511yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2966C2
socleC22×C11C2×#121
hypercenter#2966D11
hypocenterC11#19222
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2966

Complements

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

NH ≅ G/Ntype
1. #13079942C2semidirect
2. #13079195C2semidirect
3. #13068156C2semidirect
4. #13068149C2semidirect
5. #13068020C2semidirect
6. #13068015C2semidirect
7. #13067976C2semidirect
8. #13067971C2semidirect
9. C2×#10622096C2semidirect
10. #13067312C2semidirect
11. C11×#2966C2semidirect
156. #2966D11semidirect
375. C11#19222semidirect

Maximal subgroups

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

subgroupindex
#130799422
#130791952
#130681562
#130681492
#130680202
#130680152
#130679762
#130679712
C2×#106220962
#130673122
C11×#29662
#1922211