Finite Group Databasebeta

← #14737328

Subgroups — #14737328

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079923C211yesmaximal, characteristic
2#13079541C211yesmaximal, characteristic, complemented
3#13077362C211yesmaximal, characteristic, complemented
4#13068174C212yesmaximal, complemented
5#13068160C212yesmaximal, complemented
6#13068050C212yesmaximal, complemented
7#13068036C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9#13067265C211yesmaximal, characteristic, complemented
10C2×#10622185C211yesmaximal, characteristic, complemented
11C11×#3141C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#66960—21no—
15#10623008C2211yescharacteristic
16C11×#489—22no—
17C11×#487C2212yes—
18C11×#486C2212yes—
19C11×#417—21no—
20C11×#417—21no—
21C4×C11×M16C2211yescharacteristic
22#10622840—22no—
23#10622742—21no—
24#10622700C2212yes—
25#10622698—21no—
26#10622696C2212yes—
27#10622696C2212yes—
28#10622694—21no—
29#10622685C2212yes—
30#10622651—22no—
31#10622628—21no—
32#10622620—21no—
33#10622538C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622319—22no—
37#10622301C2212yes—
38C8×D44C2212yes—
39#10622185C2211yescharacteristic
40#10622185C2211yescharacteristic
41#10622185C2212yes—
42#10622185C2212yes—
43#10622182C2211yescharacteristic
44#10622182C2211yescharacteristic
45#10622096C2212yes—
46#10622095C2212yes—
47C2×C11×#41—21no—
48C22×Q8×C11—21no—
49C2×#4339—21no—
50C2×C11×M16D411yescharacteristic
51C2×C11×M16D411yescharacteristic
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8C2312yes—
56C11×C4⋊Q8C2311yescharacteristic
57C11×#127C2311yescharacteristic
58C11×#124—21no—
59C11×#121—21no—
60C11×#121—21no—
61C4×D4×C11—21no—
62C4×D4×C11—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C42×C11C2311yescharacteristic
66C2×#4325—22no—
67C2×#4325—22no—
68C2×#4323—22no—
69#66983—21no—
70#66983D412yes—
71C22×C11⋊C8—21no—
72C22×C11⋊C8—21no—
73#66960—44no—
74C2×#4313—22no—
75C2×C8×D11—22no—
76#66928—21no—
77#66927D411yescharacteristic
78C4×D44—21no—
79C4×D44C2312yes—
80#66922D411yescharacteristic
81C11×#103—22no—
82C11×#103—22no—
83C11×#102—22no—
84C11×#102—22no—
85C11×#97D412yes—
86C4×C8×C11C2312yes—
87#66899—22no—
88#66899—22no—
89#66896—22no—
90C22⋊(C11⋊C8)—21no—
91(C2×D11)⋊C8—22no—
92(C2×D11)⋊C8—22no—
93#66873—22no—
94#66871—22no—
95C4⋊(C11⋊C8)—21no—
96C4⋊(C11⋊C8)—21no—
97C4⋊(C11⋊C8)C2311yescharacteristic
98C4⋊(C11⋊C8)C2311yescharacteristic
99C4⋊(C11⋊C8)C2312yes—
100C4⋊(C11⋊C8)C2311yescharacteristic
101C4⋊(C11⋊C8)C2311yescharacteristic
102C4×C11⋊C8—21no—
103#19237—111nomaximal, Sylow
104C11×#41—42no—
105C11×#41—42no—
106C2×Q8×C11—22no—
107C2×Q8×C11—21no—
108C2×Q8×C11—41no—
109C2×Q8×C11—81no—
110C2×Q8×C11—81no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—41no—
115C22×C4×C11—41no—
116C22×C4×C11—41no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11#4111yescharacteristic
120C2×C22⋊D11—22no—
121#4339—42no—
122#4339—42no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44C2×D412yes—
126C2×C4×D11—22no—
127C2×Dic22—21no—
128C11×M16—22no—
129C11×M16—22no—
130C2×C8×C11C2×D412yes—
131C2×C8×C11C2×D412yes—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—41no—
137C11×C4⋊C4—41no—
138C11×C22⋊C4—41no—
139C11×C22⋊C4—41no—
140C42×C11C2×D411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C42×C11#4111yescharacteristic
143C42×C11C2411yescharacteristic
144#4325—82no—
145#4325—82no—
146#4323—82no—
147(C2×D11)⋊C4—22no—
148(C2×D11)⋊C4—22no—
149C4⋊Dic11—21no—
150C4⋊Dic11C2×D412yes—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—42no—
157C2×C11⋊C8—81no—
158#4313—44no—
159C8×D11—44no—
160#3245—111no—
161#3206—111no—
162#3141D1111yescharacteristic, complemented
163#2935—111no—
164#1701—112no—
165#1699—112no—
166#1681—112no—
167#1679—112no—
168#1565—111no—
169#1540—111no—
170C2×#332—111no—
171C23×C11—41no—
172C23×C11#12111yescharacteristic
173C22×D11—22no—
174Q8×C11—41no—
175Q8×C11—41no—
176Q8×C11—42no—
177Q8×C11—42no—
178Q8×C11—82no—
179D4×C11—41no—
180D4×C11—41no—
181D4×C11—41no—
182D4×C11—41no—
183D4×C11—81no—
184D4×C11—82no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—82no—
191C2×C4×C11—82no—
192C2×C4×C11#12111yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11#12111yescharacteristic
195C2×C4×C11#13512yes—
196C2×C4×C11AGL(1,ℤ/8)12yes—
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C22⋊D11—44no—
201C2×Dic11—22no—
202D44—22no—
203D44—22no—
204D44—42no—
205D44—81no—
206C4×D11—42no—
207C4×D11—42no—
208Dic22—42no—
209C8×C11—22no—
210C8×C11—22no—
211C11⋊C8—41no—
212C11⋊C8—41no—
213C11⋊C8—42no—
214C11⋊C8—41no—
215C11⋊C8—41no—
216C2×#131—221no—
217#532—111no—
218#532C2×D1111yescharacteristic
219C2×C4⋊Q8C2×D1111yescharacteristic
220#492—221no—
221#489—22no—
222#487—221no—
223#487C2×D1112yes—
224#486C2×D1112yes—
225#474—112no—
226#474—221no—
227#466—222no—
228#461—112no—
229#461—112no—
230#459—112no—
231#459—221no—
232#448—222no—
233#436—112no—
234#435—222no—
235C8×D4—112no—
236#431—111no—
237C2×C4⋊C8—111no—
238C2×C4⋊C8—111no—
239#417—21no—
240#417—21no—
241#408—221no—
242C4×M16C2×D1111yescharacteristic
243#335—112no—
244#334—112no—
245#332—112no—
246#332—112no—
247#332—111no—
248#332—111no—
249#331—111no—
250#331—111no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—81no—
254C22×C11—81no—
255C22×C11—81no—
256C22×C11#46312yes—
257C22×C11C2×#12111yescharacteristic
258C2×D11—42no—
259C2×D11—42no—
260C2×D11—42no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—81no—
265C4×C11—82no—
266C4×C11#46312yes—
267C4×C11C2×#13511yescharacteristic
268C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
269C4×C11#57611yescharacteristic
270C4×C11#57711yescharacteristic
271Dic11—42no—
272C2×#41—21no—
273C2×#41—221no—
274C22×Q8—21no—
275C2×SD16—222no—
276C2×SD16—222no—
277C2×D8—222no—
278#131—444no—
279C2×M16—222no—
280C2×M16C22⋊D1111yescharacteristic
281C2×M16C22⋊D1111yescharacteristic
282C22×C8—221no—
283C22×C8—221no—
284C22×C8—222no—
285C4⋊Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8—111no—
289C4⋊Q8C22×D1112yes—
290C4⋊Q8C22×D1111yescharacteristic
291#127—111no—
292#127C22×D1111yescharacteristic
293#124—21no—
294#124—221no—
295#121—21no—
296#121—21no—
297#121—112no—
298#121—221no—
299C4×D4—21no—
300C4×D4—21no—
301C4×D4—112no—
302C4×D4—221no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C42C22×D1111yescharacteristic
306#107—222no—
307C4⋊C8—111no—
308C4⋊C8—111no—
309C4⋊C8—111no—
310C4⋊C8—111no—
311C4⋊C8—112no—
312C4⋊C8—221no—
313C4⋊C8—221no—
314#103—22no—
315#103—22no—
316#103—222no—
317#103—222no—
318#102—22no—
319#102—22no—
320#102—222no—
321#102—222no—
322C22⋊C8—221no—
323C22⋊C8—222no—
324C22⋊C8—222no—
325#97C22⋊D1112yes—
326C4×C8—221no—
327C4×C8C22×D1112yes—
328C2×C11—22no—
329C2×C11—161no—
330C2×C11C2×#46311yescharacteristic
331C2×C11#306211yescharacteristic
332C2×C11#306911yescharacteristic
333D11—82no—
334#41—42no—
335#41—42no—
336#41—442no—
337#41—442no—
338C2×Q8—22no—
339C2×Q8—21no—
340C2×Q8—41no—
341C2×Q8—81no—
342C2×Q8—81no—
343C2×Q8—221no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—41no—
348C2×D4—112no—
349C2×D4—222no—
350C2×D4—221no—
351C2×D4—221no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—222no—
355C22×C4D4×D1111yescharacteristic
356C22×C4#434111yescharacteristic
357C22×C4C2×C22⋊D1111yescharacteristic
358SD16—882no—
359SD16—882no—
360D8—882no—
361M16—22no—
362M16—22no—
363M16—444no—
364C2×C8—221no—
365C2×C8—221no—
366C2×C8—222no—
367C2×C8—221no—
368C2×C8—221no—
369C2×C8—444no—
370C2×C8—442no—
371C2×C8—881no—
372C2×C8C2×C22⋊D1112yes—
373C2×C8C2×C22⋊D1112yes—
374C4⋊C4—21no—
375C4⋊C4—22no—
376C4⋊C4—21no—
377C4⋊C4—22no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—112no—
381C4⋊C4—221no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—222no—
385C22⋊C4—222no—
386C42D4×D1111yescharacteristic
387C42#434111yescharacteristic
388C42C2×C22⋊D1111yescharacteristic
389C42C23×D1111yescharacteristic
390C11#1923711yescharacteristic, complemented, Sylow
391C23—41no—
392C23—222no—
393C23#6699111yescharacteristic
394Q8—42no—
395Q8—42no—
396Q8—41no—
397Q8—41no—
398Q8—82no—
399Q8—442no—
400D4—41no—
401D4—41no—
402D4—41no—
403D4—41no—
404D4—81no—
405D4—82no—
406D4—222no—
407D4—222no—
408D4—444no—
409D4—442no—
410D4—881no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—82no—
417C2×C4—82no—
418C2×C4—222no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4#6699111yescharacteristic
422C2×C4#6699111yescharacteristic
423C2×C4#6699111yescharacteristic
424C2×C4#6700212yes—
425C2×C4#6700312yes—
426C2×C4C2×D4×D1111yescharacteristic
427C2×C4C2×#434111yescharacteristic
428C2×C4C22×C22⋊D1111yescharacteristic
429C8—22no—
430C8—22no—
431C8—442no—
432C8—441no—
433C8—441no—
434C8—441no—
435C8—441no—
436C22—21no—
437C22—21no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—442no—
442C22—442no—
443C22—442no—
444C22#1062267012yes—
445C22C2×#6699111yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—82no—
450C4—81no—
451C4—442no—
452C4#1062267012yes—
453C4#1062330511yescharacteristic
454C4#1062330611yescharacteristic
455C4C2×#6700211yescharacteristic
456C4C2×#6700311yescharacteristic
457C2—22no—
458C2—161no—
459C2—882no—
460C2C2×#1062267011yescharacteristic
461C2#1307829011yescharacteristic
462C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3141C2
socleC22×C11C2×#121
prime radical#13079923C2
hypercenter#3141D11
hypocenterC11#19237
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
2. #13079541C2semidirect
3. #13077362C2semidirect
4. #13068174C2semidirect
5. #13068160C2semidirect
6. #13068050C2semidirect
7. #13068036C2semidirect
8. #13067368C2semidirect
9. #13067265C2semidirect
10. C2×#10622185C2semidirect
11. C11×#3141C2semidirect
162. #3141D11semidirect
390. C11#19237semidirect

Maximal subgroups

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

subgroupindex
#130799232
#130795412
#130773622
#130681742
#130681602
#130680502
#130680362
#130673682
#130672652
C2×#106221852
C11×#31412
#1923711