Finite Group Databasebeta

← #14736530

Subgroups — #14736530

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079202C211yesmaximal, characteristic, complemented
2#13078687C212yesmaximal
3#13068170C212yesmaximal, complemented
4#13068163C212yesmaximal, complemented
5#13068134C211yesmaximal, characteristic, complemented
6#13068129C211yesmaximal, characteristic, complemented
7#13068110C211yesmaximal, characteristic, complemented
8#13068105C211yesmaximal, characteristic, complemented
9#13067364C211yesmaximal, characteristic, complemented
10#13067280C212yesmaximal, complemented
11C11×#2965C211yesmaximal, characteristic
12C4×C11×#41C2211yescharacteristic
13#10623001C2212yes—
14C11×#446C2211yescharacteristic
15C11×#446C2211yescharacteristic
16C11×#436C2211yescharacteristic
17C11×#436C2211yescharacteristic
18C11×#435—21no—
19C11×#435—21no—
20C11×#431—21no—
21C11×#431C2211yescharacteristic
22C4×C11×M16—21no—
23C2×C4×C8×C11C2211yescharacteristic
24#10622852—22no—
25#10622729—21no—
26#10622729—21no—
27#10622644C2212yes—
28C4×#4326—22no—
29#10622633C2212yes—
30#10622632C2212yes—
31C4×#4324—22no—
32#10622620C2212yes—
33#10622609—22no—
34#10622538C2212yes—
35#10622312C2211yescharacteristic
36C4×Dic44—21no—
37C4×Dic44—21no—
38#10622295C2211yescharacteristic
39#10622294C2212yes—
40#10622124C2212yes—
41#10622124C2212yes—
42#10622120C2212yes—
43#10622120C2212yes—
44#10622096C2212yes—
45#10622095C2211yescharacteristic
46#10622095C2211yescharacteristic
47C2×C11×#41D411yescharacteristic
48C2×C11×M16—21no—
49C2×C11×M16—21no—
50C22×C8×C11D411yescharacteristic
51C22×C8×C11D411yescharacteristic
52C4×Q8×C11D411yescharacteristic
53C4×Q8×C11C2311yescharacteristic
54C4×D4×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11D411yescharacteristic
57C4×D4×C11C2311yescharacteristic
58C11×#117—21no—
59C11×#117D411yescharacteristic
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62C2×#4326—22no—
63C2×#4324—22no—
64#66979—22no—
65#66977—22no—
66#66977—22no—
67C2×Dic44—21no—
68C2×Dic44—21no—
69#66923—22no—
70#66922C2312yes—
71#66922C2312yes—
72C4×Dic22—22no—
73C4×Dic22—22no—
74C11×C4⋊C8—21no—
75C11×C4⋊C8—21no—
76C11×C4⋊C8C2311yescharacteristic
77C11×C4⋊C8C2311yescharacteristic
78C11×C22⋊C8—21no—
79C11×C22⋊C8—21no—
80C11×C22⋊C8—21no—
81C11×#97—21no—
82C11×#97—21no—
83C4×C8×C11—21no—
84C4×C8×C11D411yescharacteristic
85C4×C8×C11D411yescharacteristic
86C4×C8×C11C2311yescharacteristic
87C4×C8×C11C2311yescharacteristic
88#66899—22no—
89#66896—22no—
90C22⋊(C11⋊C8)—22no—
91#66882—21no—
92#66882—21no—
93#66880—22no—
94#66880—22no—
95#66874—22no—
96#66874—22no—
97#66872—22no—
98#66871—22no—
99C4⋊(C11⋊C8)C2312yes—
100C4⋊(C11⋊C8)C2312yes—
101C4×C11⋊C8—22no—
102#19161—111nomaximal, Sylow
103C11×#41—42no—
104C2×Q8×C11C2×D411yescharacteristic
105C2×D4×C11—21no—
106C2×D4×C11C2×D411yescharacteristic
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C2×Dic22—22no—
114C2×Dic22—22no—
115C11×M16—42no—
116C11×M16—42no—
117C2×C8×C11—22no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11—41no—
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11C2×D411yescharacteristic
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4C2×D411yescharacteristic
128C11×C4⋊C4C2×D411yescharacteristic
129C11×C22⋊C4—21no—
130C11×C22⋊C4—21no—
131C11×C22⋊C4—21no—
132C42×C11—21no—
133C42×C11—21no—
134C42×C11—21no—
135C42×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11#4111yescharacteristic
138C42×C11C2411yescharacteristic
139C22⋊Dic11—42no—
140#4326—44no—
141#4324—44no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146Dic11⋊C4—42no—
147Dic11⋊C4—42no—
148C4×Dic11—42no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151Dic44—42no—
152Dic44—42no—
153#3170—111no—
154#3107—112no—
155#2965D1111yescharacteristic
156#1700—112no—
157#1699—112no—
158#1694—111no—
159#1693—111no—
160#1690—111no—
161#1689—111no—
162#1564—111no—
163#1544—112no—
164C23×C11—21no—
165C23×C11#12111yescharacteristic
166Q8×C11—22no—
167D4×C11—22no—
168D4×C11—42no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11C22×D411yescharacteristic
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C2×Dic11—42no—
187C2×Dic11—42no—
188Dic22—42no—
189Dic22—42no—
190Dic22—42no—
191Dic22—42no—
192C8×C11—21no—
193C8×C11—21no—
194C8×C11—21no—
195C8×C11—41no—
196C8×C11—41no—
197C8×C11#13512yes—
198C11⋊C8—42no—
199C11⋊C8—42no—
200#533—112no—
201C4×#41C2×D1111yescharacteristic
202#500—111no—
203#494—111no—
204#487—112no—
205#485—222no—
206#475—112no—
207#474—112no—
208#467—221no—
209#467—221no—
210#462—112no—
211#461—112no—
212#452—222no—
213#446C2×D1111yescharacteristic
214#446C2×D1111yescharacteristic
215C4×Q16—222no—
216C4×Q16—221no—
217C4×Q16—221no—
218C4×SD16—222no—
219#436C2×D1111yescharacteristic
220#436C2×D1111yescharacteristic
221#435—21no—
222#435—21no—
223#431—21no—
224#431—112no—
225#431C2×D1111yescharacteristic
226C4×M16—21no—
227C2×C4×C8C2×D1111yescharacteristic
228#335—112no—
229#334—111no—
230#334—111no—
231#332—112no—
232#332—112no—
233#332—112no—
234#332—112no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—41no—
241C22×C11C2×#12111yescharacteristic
242C4×C11—21no—
243C4×C11—21no—
244C4×C11—21no—
245C4×C11—41no—
246C4×C11—41no—
247C4×C11—41no—
248C4×C11#47312yes—
249C4×C11C2×#13511yescharacteristic
250C4×C11#57512yes—
251C4×C11#57511yescharacteristic
252Dic11—82no—
253Dic11—82no—
254C2×#41D4411yescharacteristic
255C2×Q16—222no—
256C2×Q16—221no—
257C2×Q16—221no—
258C2×SD16—222no—
259C2×M16—21no—
260C2×M16—21no—
261C22×C8C22⋊D1111yescharacteristic
262C22×C8C22⋊D1111yescharacteristic
263C4⋊Q8—112no—
264C4⋊Q8—112no—
265#125—222no—
266C22⋊Q8—222no—
267C22⋊Q8—222no—
268C4×Q8—222no—
269C4×Q8—222no—
270C4×Q8D4411yescharacteristic
271C4×Q8C22×D1111yescharacteristic
272C4×D4—21no—
273C4×D4—21no—
274C4×D4D4411yescharacteristic
275C4×D4C22×D1111yescharacteristic
276#117—21no—
277#117—222no—
278#117D4411yescharacteristic
279C2×C42—21no—
280C2×C42C22×D1111yescharacteristic
281#107—221no—
282#107—221no—
283#107—222no—
284#106—222no—
285C4⋊C8—21no—
286C4⋊C8—21no—
287C4⋊C8—112no—
288C4⋊C8—112no—
289C4⋊C8C22×D1111yescharacteristic
290C4⋊C8C22×D1111yescharacteristic
291#103—222no—
292#103—222no—
293#103—222no—
294#103—222no—
295#103—222no—
296#102—222no—
297C22⋊C8—21no—
298C22⋊C8—21no—
299C22⋊C8—21no—
300C22⋊C8—222no—
301#97—21no—
302#97—21no—
303C4×C8—21no—
304C4×C8—222no—
305C4×C8C22⋊D1111yescharacteristic
306C4×C8C22⋊D1111yescharacteristic
307C4×C8C22×D1111yescharacteristic
308C4×C8C22×D1111yescharacteristic
309C2×C11—41no—
310C2×C11—81no—
311C2×C11#303511yescharacteristic
312C2×C11#305411yescharacteristic
313C2×C11C2×#47311yescharacteristic
314#41—42no—
315C2×Q8—222no—
316C2×Q8—222no—
317C2×Q8C2×D4411yescharacteristic
318C2×D4—21no—
319C2×D4C2×D4411yescharacteristic
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4C2×D4411yescharacteristic
324C22×C4#433911yescharacteristic
325C22×C4C2×C22⋊D1111yescharacteristic
326Q16—442no—
327Q16—444no—
328Q16—442no—
329SD16—444no—
330M16—42no—
331M16—42no—
332C2×C8—22no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—41no—
336C2×C8—222no—
337C2×C8—222no—
338C2×C8C2×C22⋊D1111yescharacteristic
339C2×C8C2×C22⋊D1111yescharacteristic
340C2×C8C2×C22⋊D1111yescharacteristic
341C2×C8C2×C22⋊D1111yescharacteristic
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—222no—
345C4⋊C4—222no—
346C4⋊C4—222no—
347C4⋊C4—222no—
348C4⋊C4—442no—
349C4⋊C4—442no—
350C4⋊C4C2×D4411yescharacteristic
351C4⋊C4C2×D4411yescharacteristic
352C22⋊C4—21no—
353C22⋊C4—21no—
354C22⋊C4—21no—
355C22⋊C4—442no—
356C42—21no—
357C42—21no—
358C42—21no—
359C42—442no—
360C42C2×D4411yescharacteristic
361C42#433911yescharacteristic
362C42C2×C22⋊D1111yescharacteristic
363C42C23×D1111yescharacteristic
364C11#1916111yescharacteristic, complemented, Sylow
365C23—21no—
366C23#6698311yescharacteristic
367Q8—22no—
368Q8—442no—
369Q8—442no—
370Q8—442no—
371Q8—442no—
372D4—22no—
373D4—42no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—442no—
386C2×C4—442no—
387C2×C4#6698311yescharacteristic
388C2×C4#6698311yescharacteristic
389C2×C4#6698311yescharacteristic
390C2×C4C22×D4411yescharacteristic
391C2×C4C2×#433911yescharacteristic
392C2×C4C22×C22⋊D1111yescharacteristic
393C8—21no—
394C8—21no—
395C8—21no—
396C8—41no—
397C8—41no—
398C8—442no—
399C8—442no—
400C8#6700312yes—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22C2×#6698311yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—882no—
415C4—882no—
416C4#1062275612yes—
417C4#1062327912yes—
418C4C2×#6700311yescharacteristic
419C4#1062335311yescharacteristic
420C2—41no—
421C2—81no—
422C2#1307807111yescharacteristic
423C2#1307822511yescharacteristic
424C2C2×#1062275611yescharacteristic
subgroupG/H
centerC2×C4#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2965C2
socleC22×C11C2×#121
prime radicalC2×C11×#41D4
hypercenter#2965D11
hypocenterC11#19161
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2965

Complements

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

NH ≅ G/Ntype
1. #13079202C2semidirect
3. #13068170C2semidirect
4. #13068163C2semidirect
5. #13068134C2semidirect
6. #13068129C2semidirect
7. #13068110C2semidirect
8. #13068105C2semidirect
9. #13067364C2semidirect
10. #13067280C2semidirect
364. C11#19161semidirect

Maximal subgroups

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

subgroupindex
#130792022
#130786872
#130681702
#130681632
#130681342
#130681292
#130681102
#130681052
#130673642
#130672802
C11×#29652
#1916111