Finite Group Databasebeta

← #14737231

Subgroups — #14737231

Order 2816.

584 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079953C212yesmaximal
2#13079202C211yesmaximal, characteristic, complemented
3#13068134C211yesmaximal, characteristic, complemented
4#13068129C211yesmaximal, characteristic, complemented
5#13068110C211yesmaximal, characteristic, complemented
6#13068105C211yesmaximal, characteristic, complemented
7#13068046C212yesmaximal, complemented
8#13068039C212yesmaximal, complemented
9C2×#10622095C211yesmaximal, characteristic, complemented
10#13067317C212yesmaximal, complemented
11C11×#2966C211yesmaximal, characteristic
12C11×#529C2211yescharacteristic
13#10623001C2212yes—
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#10622729—21no—
25#10622729—21no—
26#10622676—22no—
27#10622667—22no—
28#10622664—22no—
29#10622654—22no—
30#10622644C2212yes—
31#10622633C2212yes—
32#10622632C2212yes—
33#10622620C2212yes—
34C2×C4⋊(C11⋊C8)C2212yes—
35#10622312C2211yescharacteristic
36C4×Dic44—21no—
37C4×Dic44—21no—
38#10622295C2211yescharacteristic
39#10622294C2212yes—
40#10622124C2212yes—
41#10622124C2212yes—
42#10622120C2212yes—
43#10622120C2212yes—
44#10622095C2212yes—
45#10622095C2211yescharacteristic
46#10622095C2211yescharacteristic
47C2×C11×M16—21no—
48C22×C8×C11—21no—
49C22×C8×C11D411yescharacteristic
50C22×C8×C11D411yescharacteristic
51C11×#126—21no—
52C11×#125D411yescharacteristic
53C11×#124D411yescharacteristic
54C11×#123—21no—
55C11×C22⋊Q8D411yescharacteristic
56C11×#121D411yescharacteristic
57C4×Q8×C11C2311yescharacteristic
58C4×D4×C11—21no—
59C4×D4×C11C2311yescharacteristic
60C11×#117—21no—
61C2×C42×C11C2311yescharacteristic
62C2×#4326—22no—
63C2×#4324—22no—
64#66979—22no—
65#66977—22no—
66#66977—22no—
67C22×C11⋊C8—22no—
68C2×Dic44—21no—
69C2×Dic44—21no—
70#66923—22no—
71#66922C2312yes—
72#66922C2312yes—
73C4×Dic22—22no—
74C4×Dic22—22no—
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#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)—22no—
100C4⋊(C11⋊C8)C2312yes—
101C4⋊(C11⋊C8)C2312yes—
102#19228—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×Dic22—22no—
111C2×Dic22—22no—
112C11×M16—42no—
113C2×C8×C11—22no—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—41no—
117C2×C8×C11—42no—
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4C2×D411yescharacteristic
127C11×C4⋊C4C2×D411yescharacteristic
128C11×C22⋊C4—21no—
129C11×C22⋊C4—21no—
130C11×C22⋊C4—21no—
131C11×C22⋊C4—21no—
132C11×C22⋊C4—21no—
133C42×C11—21no—
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11#4111yescharacteristic
137C42×C11C2411yescharacteristic
138C22⋊Dic11—42no—
139#4326—82no—
140#4324—82no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145Dic11⋊C4—42no—
146Dic11⋊C4—42no—
147C4×Dic11—42no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—82no—
151Dic44—42no—
152Dic44—42no—
153#3248—112no—
154#3170—111no—
155#2966D1111yescharacteristic
156#1694—111no—
157#1693—111no—
158#1690—111no—
159#1689—111no—
160#1680—112no—
161#1679—112no—
162C2×#334—111no—
163#1552—112no—
164C23×C11—21no—
165C23×C11#12111yescharacteristic
166Q8×C11—22no—
167D4×C11—22no—
168D4×C11—42no—
169C2×C4×C11—22no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—22no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11C22×D411yescharacteristic
182C2×C4×C11C22×D411yescharacteristic
183C2×C4×C11C2×#4111yescharacteristic
184C2×Dic11—42no—
185C2×Dic11—42no—
186Dic22—42no—
187Dic22—42no—
188Dic22—42no—
189Dic22—42no—
190C8×C11—21no—
191C8×C11—21no—
192C8×C11—21no—
193C8×C11—41no—
194C8×C11—41no—
195C8×C11#13512yes—
196C11⋊C8—42no—
197C11⋊C8—42no—
198#533—112no—
199#529C2×D1111yescharacteristic
200#500—111no—
201#494—111no—
202#487—112no—
203#479—222no—
204#475—112no—
205#474—112no—
206#467—221no—
207#467—221no—
208#467—222no—
209#465—222no—
210#464—222no—
211#462—112no—
212#461—112no—
213#446C2×D1111yescharacteristic
214C8×Q8C2×D1111yescharacteristic
215C4×Q16—221no—
216C4×Q16—221no—
217#436C2×D1111yescharacteristic
218#435—21no—
219C8×D4—21no—
220C8×D4C2×D1111yescharacteristic
221#433—21no—
222#432C2×D1111yescharacteristic
223C2×C4⋊C8—112no—
224#405—21no—
225C2×C4×C8C2×D1111yescharacteristic
226#334—112no—
227#334—111no—
228#334—111no—
229#332—112no—
230#332—112no—
231#332—112no—
232#332—112no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—41no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11#47312yes—
239C22×C11C2×#12111yescharacteristic
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—21no—
244C4×C11—41no—
245C4×C11—41no—
246C4×C11—41no—
247C4×C11C2×#13511yescharacteristic
248C4×C11#57511yescharacteristic
249C4×C11#57712yes—
250Dic11—82no—
251Dic11—82no—
252C2×Q16—222no—
253C2×Q16—221no—
254C2×Q16—221no—
255C2×SD16—222no—
256C2×M16—21no—
257C22×C8—21no—
258C22×C8—222no—
259C22×C8C22⋊D1111yescharacteristic
260C22×C8C22⋊D1111yescharacteristic
261C4⋊Q8—112no—
262C4⋊Q8—112no—
263#126—21no—
264#125—222no—
265#125D4411yescharacteristic
266#124D4411yescharacteristic
267#123—21no—
268C22⋊Q8—222no—
269C22⋊Q8—222no—
270C22⋊Q8D4411yescharacteristic
271#121D4411yescharacteristic
272C4×Q8—222no—
273C4×Q8—222no—
274C4×Q8C22×D1111yescharacteristic
275C4×D4—21no—
276C4×D4C22×D1111yescharacteristic
277#117—21no—
278#117—222no—
279C2×C42C22×D1111yescharacteristic
280#107—221no—
281#107—221no—
282#107—222no—
283#106—222no—
284C4⋊C8—21no—
285C4⋊C8—21no—
286C4⋊C8—112no—
287C4⋊C8—112no—
288C4⋊C8—222no—
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—
300#97—21no—
301#97—21no—
302C4×C8—21no—
303C4×C8C22⋊D1111yescharacteristic
304C4×C8C22⋊D1111yescharacteristic
305C4×C8C22×D1111yescharacteristic
306C4×C8C22×D1111yescharacteristic
307C2×C11—22no—
308C2×C11—81no—
309C2×C11#303511yescharacteristic
310C2×C11#306011yescharacteristic
311C2×C11C2×#47311yescharacteristic
312C2×Q8—222no—
313C2×Q8—222no—
314C2×Q8C2×D4411yescharacteristic
315C2×D4—21no—
316C2×D4C2×D4411yescharacteristic
317C22×C4—21no—
318C22×C4C2×D4411yescharacteristic
319C22×C4#433911yescharacteristic
320C22×C4C2×C22⋊D1111yescharacteristic
321Q16—442no—
322Q16—442no—
323Q16—882no—
324SD16—882no—
325M16—42no—
326C2×C8—22no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—41no—
330C2×C8—42no—
331C2×C8—222no—
332C2×C8—222no—
333C2×C8—882no—
334C2×C8C2×C22⋊D1111yescharacteristic
335C2×C8C2×C22⋊D1111yescharacteristic
336C2×C8C2×C22⋊D1111yescharacteristic
337C2×C8C2×C22⋊D1111yescharacteristic
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—222no—
343C4⋊C4—222no—
344C4⋊C4—222no—
345C4⋊C4—222no—
346C4⋊C4—442no—
347C4⋊C4—442no—
348C4⋊C4C2×D4411yescharacteristic
349C4⋊C4C2×D4411yescharacteristic
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—21no—
353C22⋊C4—21no—
354C22⋊C4—21no—
355C22⋊C4—442no—
356C42—21no—
357C42—442no—
358C42C2×D4411yescharacteristic
359C42#433911yescharacteristic
360C42C2×C22⋊D1111yescharacteristic
361C42C23×D1111yescharacteristic
362C11#1922811yescharacteristic, complemented, Sylow
363C23—21no—
364C23#6698311yescharacteristic
365Q8—22no—
366Q8—442no—
367Q8—442no—
368Q8—442no—
369Q8—442no—
370D4—22no—
371D4—42no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—442no—
382C2×C4—442no—
383C2×C4#6698311yescharacteristic
384C2×C4#6698311yescharacteristic
385C2×C4#6698311yescharacteristic
386C2×C4C22×D4411yescharacteristic
387C2×C4C2×#433911yescharacteristic
388C2×C4C22×C22⋊D1111yescharacteristic
389C8—21no—
390C8—21no—
391C8—21no—
392C8—41no—
393C8—41no—
394C8—442no—
395C8—442no—
396C8#6700312yes—
397C22—21no—
398C22—21no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22#1062275612yes—
403C22C2×#6698311yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—41no—
409C4—41no—
410C4—41no—
411C4—882no—
412C4—882no—
413C4#1062328212yes—
414C4C2×#6700311yescharacteristic
415C4#1062335311yescharacteristic
416C2—22no—
417C2—81no—
418C2#1307807111yescharacteristic
419C2#1307827811yescharacteristic
420C2C2×#1062275611yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2966C2
socleC22×C11C2×#121
prime radicalC11×#121D4
hypercenter#2966D11
hypocenterC11#19228
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
2. #13079202C2semidirect
3. #13068134C2semidirect
4. #13068129C2semidirect
5. #13068110C2semidirect
6. #13068105C2semidirect
7. #13068046C2semidirect
8. #13068039C2semidirect
9. C2×#10622095C2semidirect
10. #13067317C2semidirect
362. C11#19228semidirect

Maximal subgroups

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

subgroupindex
#130799532
#130792022
#130681342
#130681292
#130681102
#130681052
#130680462
#130680392
C2×#106220952
#130673172
C11×#29662
#1922811