Finite Group Databasebeta

← #14739268

Subgroups — #14739268

Order 2816.

608 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078425C211yesmaximal, characteristic
2#13078398C211yesmaximal, characteristic
3#13077724C211yesmaximal, characteristic
4#13068071C212yesmaximal, complemented
5#13068064C212yesmaximal, complemented
6#13068017C212yesmaximal, complemented
7#13068012C212yesmaximal, complemented
8#13067391C211yesmaximal, characteristic, complemented
9#13067306C211yesmaximal, characteristic, complemented
10C2×#10622184C211yesmaximal, characteristic, complemented
11C11×#3230C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C4×#4339C2211yescharacteristic
15C11×#500C2212yes—
16C11×#487C2212yes—
17C11×#484—22no—
18C11×#477—21no—
19C11×#477—21no—
20C11×#431C2211yescharacteristic
21#10622707—21no—
22#10622707C2211yescharacteristic
23#10622704C2212yes—
24#10622704C2211yescharacteristic
25#10622700—21no—
26#10622700C2211yescharacteristic
27#10622697C2212yes—
28#10622697C2211yescharacteristic
29#10622679—21no—
30#10622676—21no—
31#10622615—21no—
32#10622611—21no—
33#10622579—21no—
34#10622577—21no—
35#10622537C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622446—21no—
39D11×C4⋊C8—21no—
40(C22⋊D11)⋊C8—22no—
41C8×D44C2212yes—
42C8×Dic22C2212yes—
43#10622185C2212yes—
44#10622184C2212yes—
45#10622184C2212yes—
46#10622184C2212yes—
47#10622096C2212yes—
48#10622096C2212yes—
49C22×Q8×C11—21no—
50C2×#4339D411yescharacteristic
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8C2311yescharacteristic
55C11×C4⋊Q8C2312yes—
56C11×C4⋊Q8C2311yescharacteristic
57C11×#125—21no—
58C11×C22⋊Q8—21no—
59C11×C22⋊Q8—21no—
60C4×Q8×C11—21no—
61C4×Q8×C11—21no—
62C11×#117—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C42×C11C2311yescharacteristic
66C4×C22⋊D11—21no—
67C4×C22⋊D11—21no—
68#66979D411yescharacteristic
69C2×#4318—21no—
70C22×C11⋊C8—21no—
71C22×C11⋊C8—21no—
72C2×C8×D11—22no—
73C4×D44D411yescharacteristic
74C4×D44C2311yescharacteristic
75#66925—21no—
76C42×D11—21no—
77C4×Dic22D411yescharacteristic
78C4×Dic22C2311yescharacteristic
79C11×#107—22no—
80C11×#107—22no—
81C11×C4⋊C8D411yescharacteristic
82C11×C4⋊C8D411yescharacteristic
83C11×#103—22no—
84C11×#103—22no—
85C11×C22⋊C8D412yes—
86C4×C8×C11C2312yes—
87(C2×D11)⋊C8—22no—
88Dic11⋊C8—22no—
89C8×Dic11—22no—
90#66874—22no—
91#66874—21no—
92#66874—21no—
93#66873—22no—
94#66873—21no—
95#66873—21no—
96#66872—22no—
97#66872—21no—
98#66872—21no—
99#66871—22no—
100#66871—21no—
101#66871—21no—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)C2312yes—
106C4⋊(C11⋊C8)C2311yescharacteristic
107C4⋊(C11⋊C8)C2311yescharacteristic
108C4⋊(C11⋊C8)C2312yes—
109#19417—111nomaximal, Sylow
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—41no—
114C2×Q8×C11—82no—
115C22×C4×C11—41no—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11#4111yescharacteristic
119C2×C22⋊D11—21no—
120#4339—22no—
121#4339Q1614yes—
122C2×D44C2×D411yescharacteristic
123C2×C4×D11—21no—
124C2×C4×D11—21no—
125C2×C4×D11—21no—
126C2×Dic22C2×D411yescharacteristic
127C2×C8×C11C2×D412yes—
128C2×C8×C11C2×D412yes—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—41no—
136C11×C4⋊C4—41no—
137C11×C4⋊C4—41no—
138C11×C4⋊C4—41no—
139C11×C22⋊C4—41no—
140C42×C11—41no—
141C42×C11C2×D411yescharacteristic
142C42×C11C2×D411yescharacteristic
143C42×C11#4111yescharacteristic
144C42×C11C2411yescharacteristic
145C22⋊Dic11—21no—
146(C2×D11)⋊C4—21no—
147(C2×D11)⋊C4—21no—
148C4⋊Dic11C2×D411yescharacteristic
149C4⋊Dic11C2×D411yescharacteristic
150Dic11⋊C4—21no—
151Dic11⋊C4—21no—
152C4×Dic11—21no—
153C4×Dic11—21no—
154C4×Dic11—21no—
155#4318—42no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—42no—
161C2×C11⋊C8—81no—
162C8×D11—82no—
163#3230D1111yescharacteristic, complemented
164#3079—111no—
165#3076—111no—
166#2988—111no—
167#1684—112no—
168#1683—112no—
169#1676—112no—
170#1675—112no—
171#1571—111no—
172#1550—111no—
173C2×#333—111no—
174C23×C11#12111yescharacteristic
175C22×D11—21no—
176Q8×C11—41no—
177Q8×C11—41no—
178Q8×C11—81no—
179Q8×C11—82no—
180Q8×C11—82no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—42no—
187C2×C4×C11—82no—
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11#12111yescharacteristic
191C2×C4×C11C2×Q1612yes—
192C2×C4×C11#13512yes—
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C22⋊D11—24no—
197C2×Dic11—21no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200D44—21no—
201D44C2×Q1612yes—
202C4×D11—24no—
203C4×D11—41no—
204C4×D11—41no—
205C4×D11—81no—
206Dic22—21no—
207Dic22C2×Q1612yes—
208C8×C11—22no—
209C8×C11—22no—
210C11⋊C8—41no—
211C11⋊C8—41no—
212C11⋊C8—42no—
213C11⋊C8—42no—
214#533C2×D1111yescharacteristic
215C2×C4⋊Q8C2×D1111yescharacteristic
216C4×#41—111no—
217#500C2×D1112yes—
218#487C2×D1112yes—
219#484—22no—
220#479—221no—
221#478—221no—
222#477—21no—
223#477—21no—
224#477—111no—
225#477—112no—
226#476—111no—
227#476—112no—
228#475—111no—
229#475—221no—
230#474—111no—
231#474—221no—
232C8×Q8—112no—
233C8×D4—112no—
234C8×D4—222no—
235#431—221no—
236#431C2×D1111yescharacteristic
237#428—221no—
238#427—221no—
239#423—111no—
240C2×C4⋊C8—111no—
241C2×C4⋊C8—111no—
242C2×C4⋊C8—221no—
243#417—221no—
244#416—221no—
245#335—112no—
246#335—112no—
247#333—112no—
248#333—112no—
249#333—112no—
250#332—112no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11#46712yes—
254C22×C11C2×#12111yescharacteristic
255C2×D11—22no—
256C2×D11—41no—
257C2×D11—41no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—81no—
262C4×C11—82no—
263C4×C11—81no—
264C4×C11#46712yes—
265C4×C11C22×Q1611yescharacteristic
266C4×C11C2×#13511yescharacteristic
267C4×C11#57711yescharacteristic
268C4×C11#57811yescharacteristic
269Dic11—22no—
270Dic11—41no—
271Dic11—41no—
272C2×#41—111no—
273C22×Q8—21no—
274C2×M16—221no—
275C22×C8—221no—
276C22×C8—221no—
277C22×C8—222no—
278C4⋊Q8—21no—
279C4⋊Q8—21no—
280C4⋊Q8—21no—
281C4⋊Q8C22×D1112yes—
282C4⋊Q8C22×D1111yescharacteristic
283C4⋊Q8C22×D1111yescharacteristic
284#125—21no—
285C22⋊Q8—21no—
286C22⋊Q8—21no—
287C4×Q8—21no—
288C4×Q8—21no—
289C4×Q8—111no—
290C4×Q8—111no—
291C4×D4—111no—
292C4×D4—111no—
293C4×D4—221no—
294C4×D4—221no—
295#117—21no—
296#117—111no—
297#117—221no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C42—221no—
301C2×C42C22×D1111yescharacteristic
302#107—22no—
303#107—22no—
304#107—221no—
305#107—221no—
306#107—222no—
307#106—221no—
308#106—221no—
309#106—222no—
310C4⋊C8—112no—
311C4⋊C8—112no—
312C4⋊C8—111no—
313C4⋊C8—111no—
314C4⋊C8—222no—
315C4⋊C8—221no—
316C4⋊C8—221no—
317C4⋊C8—221no—
318C4⋊C8C22⋊D1111yescharacteristic
319C4⋊C8C22⋊D1111yescharacteristic
320#103—22no—
321#103—22no—
322#103—221no—
323#103—221no—
324#103—222no—
325#102—221no—
326#102—221no—
327#102—222no—
328C22⋊C8—222no—
329C22⋊C8C22⋊D1112yes—
330C4×C8—222no—
331C4×C8C22×D1112yes—
332C2×C11—22no—
333C2×C11#304611yescharacteristic
334C2×C11C2×#46711yescharacteristic
335C2×C11#306811yescharacteristic
336D11—42no—
337#41—114no—
338#41—222no—
339C2×Q8—21no—
340C2×Q8—22no—
341C2×Q8—21no—
342C2×Q8—41no—
343C2×Q8—82no—
344C2×Q8—111no—
345C2×D4—111no—
346C2×D4—221no—
347C22×C4—41no—
348C22×C4—221no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4D4×D1111yescharacteristic
352C22×C4#434111yescharacteristic
353C22×C4C2×C22⋊D1111yescharacteristic
354M16—442no—
355C2×C8—221no—
356C2×C8—222no—
357C2×C8—221no—
358C2×C8—222no—
359C2×C8—442no—
360C2×C8—882no—
361C2×C8—881no—
362C2×C8C2×C22⋊D1112yes—
363C2×C8C2×C22⋊D1112yes—
364C4⋊C4—22no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—21no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—111no—
375C4⋊C4—111no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C22⋊C4—41no—
379C22⋊C4—221no—
380C22⋊C4—221no—
381C22⋊C4—221no—
382C42—41no—
383C42—221no—
384C42—221no—
385C42—221no—
386C42D4×D1111yescharacteristic
387C42#434111yescharacteristic
388C42C2×C22⋊D1111yescharacteristic
389C42C23×D1111yescharacteristic
390C11#1941711yescharacteristic, complemented, Sylow
391C23—221no—
392C23#6699111yescharacteristic
393Q8—41no—
394Q8—41no—
395Q8—81no—
396Q8—82no—
397Q8—82no—
398Q8—112no—
399Q8—221no—
400D4—112no—
401D4—224no—
402D4—221no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—82no—
410C2×C4—221no—
411C2×C4—224no—
412C2×C4—221no—
413C2×C4—221no—
414C2×C4—441no—
415C2×C4—441no—
416C2×C4—881no—
417C2×C4Q16×D1112yes—
418C2×C4#6697212yes—
419C2×C4#6699111yescharacteristic
420C2×C4#6699111yescharacteristic
421C2×C4#6699111yescharacteristic
422C2×C4C2×D4×D1111yescharacteristic
423C2×C4C2×#434111yescharacteristic
424C2×C4C22×C22⋊D1111yescharacteristic
425C8—22no—
426C8—22no—
427C8—441no—
428C8—441no—
429C8—442no—
430C8—442no—
431C22—21no—
432C22—21no—
433C22—222no—
434C22—441no—
435C22—441no—
436C22#1062280112yes—
437C22C2×#6699111yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—82no—
442C4—81no—
443C4—81no—
444C4—222no—
445C4—441no—
446C4—441no—
447C4#1062280112yes—
448C4C2×Q16×D1111yescharacteristic
449C4C2×#6697211yescharacteristic
450C4#1062336811yescharacteristic
451C4#1062336911yescharacteristic
452C2—22no—
453C2—442no—
454C2#1307816211yescharacteristic
455C2C2×#1062280111yescharacteristic
456C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3230C2
socleC22×C11C2×#121
prime radicalC2×#4339D4
hypercenter#3230D11
hypocenterC11#19417
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
4. #13068071C2semidirect
5. #13068064C2semidirect
6. #13068017C2semidirect
7. #13068012C2semidirect
8. #13067391C2semidirect
9. #13067306C2semidirect
10. C2×#10622184C2semidirect
11. C11×#3230C2semidirect
163. #3230D11semidirect
390. C11#19417semidirect

Maximal subgroups

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

subgroupindex
#130784252
#130783982
#130777242
#130680712
#130680642
#130680172
#130680122
#130673912
#130673062
C2×#106221842
C11×#32302
#1941711