Finite Group Databasebeta

← #14908859

Subgroups — #14908859

Order 2816.

548 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079202C211yesmaximal, characteristic, complemented
2#13070824C212yesmaximal, complemented
3#13070768C211yesmaximal, characteristic, complemented
4#13070763C211yesmaximal, characteristic, complemented
5#13070666C211yesmaximal, characteristic, complemented
6#13070661C211yesmaximal, characteristic, complemented
7#13070556C212yesmaximal
8#13070485C212yesmaximal, complemented
9#13070480C212yesmaximal, complemented
10#13070419C211yesmaximal, characteristic, complemented
11C4×C11×#135C211yesmaximal, characteristic
12C2×C11×#135C2211yescharacteristic
13C4×C11×#41—21no—
14#10623001—21no—
15C4×C11×Q16C2211yescharacteristic
16C4×C11×Q16C2211yescharacteristic
17C4×C11×SD16—21no—
18C4×C11×SD16—21no—
19C4×C11×D8C2211yescharacteristic
20C4×C11×D8C2211yescharacteristic
21C11×#427C2211yescharacteristic
22C11×#416—21no—
23C2×C4×C8×C11C2211yescharacteristic
24C2×#66893C2212yes—
25C2×#66891C2212yes—
26#10622729—21no—
27#10622729C2212yes—
28#10622312C2211yescharacteristic
29C4×Dic44—21no—
30C4×Dic44C2212yes—
31#10622295C2211yescharacteristic
32#10622294—21no—
33#10622202C2212yes—
34#10622200C2212yes—
35C22⋊(C11⋊C16)C2212yes—
36#10622130C2212yes—
37#10622130C2212yes—
38#10622128C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C4⋊(C11⋊C16)C2211yescharacteristic
42#10622099C2212yes—
43C2×C11×#41—21no—
44C11×#135—22no—
45C11×#135—22no—
46C2×C11×Q16C2311yescharacteristic
47C2×C11×SD16—21no—
48C2×C11×D8C2311yescharacteristic
49C22×C8×C11D411yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C4×Q8×C11—21no—
52C4×Q8×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C4×D4×C11—41no—
56C4×D4×C11—41no—
57C11×#117—21no—
58C11×#117—41no—
59C2×C42×C11—41no—
60C2×C42×C11D411yescharacteristic
61#66979—41no—
62#66977—22no—
63#66977—41no—
64C2×Dic44—21no—
65C2×Dic44C2312yes—
66#66923—41no—
67#66922—21no—
68#66922—21no—
69C4×Dic22—22no—
70C4×Dic22—41no—
71C11×#107C2311yescharacteristic
72C11×#107C2311yescharacteristic
73C11×#106—21no—
74C11×#103—21no—
75C11×#103—21no—
76C11×#102—21no—
77C11×#102—21no—
78C4×C8×C11D411yescharacteristic
79C4×C8×C11D411yescharacteristic
80C4×C8×C11C2311yescharacteristic
81C4×C8×C11C2311yescharacteristic
82#66893—24no—
83#66891—24no—
84#66882—21no—
85#66882C2312yes—
86#66880—22no—
87#66880—22no—
88C2×C11⋊C16C2312yes—
89C2×C11⋊C16C2312yes—
90#33676—111nomaximal, Sylow
91C11×#41—24no—
92C11×#41—42no—
93C2×Q8×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11D811yescharacteristic
100C22×C4×C11D811yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C2×Dic22—22no—
103C2×Dic22—41no—
104C11×Q16—21no—
105C11×Q16#4112yes—
106C11×SD16—24no—
107C11×D8—21no—
108C11×D8#4112yes—
109C2×C8×C11—21no—
110C2×C8×C11—21no—
111C2×C8×C11—41no—
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11C2×D411yescharacteristic
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2411yescharacteristic
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C42×C11—41no—
124C42×C11—41no—
125C42×C11—41no—
126C42×C11D811yescharacteristic
127C42×C11D811yescharacteristic
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C22⋊Dic11—42no—
131C4⋊Dic11—22no—
132C4⋊Dic11—41no—
133C4⋊Dic11—41no—
134C4⋊Dic11—41no—
135Dic11⋊C4—42no—
136Dic11⋊C4—42no—
137C4×Dic11—42no—
138Dic44—22no—
139Dic44—22no—
140Dic44—42no—
141C11⋊C16—22no—
142C11⋊C16—22no—
143#3170—111no—
144C4×#135D1111yescharacteristic
145#2237—112no—
146#2227—111no—
147#2226—111no—
148#2209—111no—
149#2208—111no—
150#2189—112no—
151#2176—112no—
152#2175—112no—
153#2163—111no—
154C23×C11—41no—
155C23×C11C2×D811yescharacteristic
156Q8×C11—22no—
157Q8×C11—41no—
158D4×C11—22no—
159D4×C11—44no—
160D4×C11—41no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—22no—
164C2×C4×C11—41no—
165C2×C4×C11—44no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—82no—
170C2×C4×C11—82no—
171C2×C4×C11C2×D811yescharacteristic
172C2×C4×C11C2×D811yescharacteristic
173C2×C4×C11C2×D811yescharacteristic
174C2×C4×C11C2×D811yescharacteristic
175C2×C4×C11C2×D811yescharacteristic
176C2×C4×C11C22×D411yescharacteristic
177C2×Dic11—42no—
178C2×Dic11—42no—
179Dic22—42no—
180Dic22—42no—
181Dic22—82no—
182C8×C11—21no—
183C8×C11—21no—
184C8×C11—21no—
185C8×C11C2×#4111yescharacteristic
186C8×C11C2×#4111yescharacteristic
187C2×#135C2×D1111yescharacteristic
188#533—221no—
189C4×#41—21no—
190C2×Q32—112no—
191C2×SD32—112no—
192#500—111no—
193#494—111no—
194#487—221no—
195#467—112no—
196#467—221no—
197C4×Q16—112no—
198C4×Q16—221no—
199C4×Q16C2×D1111yescharacteristic
200C4×Q16C2×D1111yescharacteristic
201C4×SD16—21no—
202C4×SD16—21no—
203C4×D8C2×D1111yescharacteristic
204C4×D8C2×D1111yescharacteristic
205#427C2×D1111yescharacteristic
206#416—21no—
207C2×C4×C8C2×D1111yescharacteristic
208#367—112no—
209#366—112no—
210C4⋊C16—111no—
211C4⋊C16—111no—
212#358—112no—
213#358—112no—
214#358—112no—
215#357—112no—
216C22⋊C16—112no—
217#346—112no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—42no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11C22×D811yescharacteristic
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—42no—
230C4×C11—81no—
231C4×C11—81no—
232C4×C11#51012yes—
233C4×C11#52511yescharacteristic
234C4×C11#57511yescharacteristic
235Dic11—82no—
236Dic11—82no—
237C2×#41—21no—
238#135—22no—
239#135—22no—
240C2×Q16—112no—
241C2×Q16—221no—
242C2×Q16C22×D1111yescharacteristic
243C2×SD16—21no—
244C2×D8C22×D1111yescharacteristic
245C22×C8C22⋊D1111yescharacteristic
246C22×C8C22×D1111yescharacteristic
247C4⋊Q8—221no—
248C4⋊Q8—221no—
249#125—441no—
250C22⋊Q8—222no—
251C22⋊Q8—441no—
252C4×Q8—21no—
253C4×Q8—21no—
254C4×Q8—222no—
255C4×Q8—441no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—41no—
259C4×D4—41no—
260#117—21no—
261#117—41no—
262#117—441no—
263C2×C42—41no—
264C2×C42C22⋊D1111yescharacteristic
265Q32—224no—
266SD32—224no—
267C2×C16—112no—
268C2×C16—112no—
269#107—112no—
270#107—221no—
271#107C22×D1111yescharacteristic
272#107C22×D1111yescharacteristic
273#106—21no—
274#103—21no—
275#103—21no—
276#103—222no—
277#103—222no—
278#102—21no—
279#102—21no—
280C4×C8C22⋊D1111yescharacteristic
281C4×C8C22⋊D1111yescharacteristic
282C4×C8C22×D1111yescharacteristic
283C4×C8C22×D1111yescharacteristic
284C2×C11—41no—
285C2×C11—82no—
286C2×C11#310011yescharacteristic
287C2×C11C2×#51011yescharacteristic
288C2×C11#341411yescharacteristic
289#41—24no—
290#41—42no—
291C2×Q8—21no—
292C2×Q8—222no—
293C2×Q8—441no—
294C2×D4—21no—
295C2×D4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4#432311yescharacteristic
300C22×C4#432311yescharacteristic
301C22×C4C2×C22⋊D1111yescharacteristic
302Q16—21no—
303Q16—222no—
304Q16—222no—
305Q16—442no—
306Q16#433912yes—
307SD16—24no—
308D8—21no—
309D8#433912yes—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—41no—
313C2×C8C2×C22⋊D1111yescharacteristic
314C2×C8C2×C22⋊D1111yescharacteristic
315C2×C8C2×C22⋊D1111yescharacteristic
316C2×C8C23×D1111yescharacteristic
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—222no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C4⋊C4—442no—
325C4⋊C4—442no—
326C4⋊C4—441no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—442no—
331C42—41no—
332C42—41no—
333C42—41no—
334C42—442no—
335C42#432311yescharacteristic
336C42#432311yescharacteristic
337C42C2×C22⋊D1111yescharacteristic
338C42C2×C22⋊D1111yescharacteristic
339C16—222no—
340C16—222no—
341C11#3367611yescharacteristic, complemented, Sylow
342C23—41no—
343C23C2×#432311yescharacteristic
344Q8—22no—
345Q8—41no—
346Q8—442no—
347Q8—442no—
348Q8—882no—
349D4—22no—
350D4—44no—
351D4—41no—
352C2×C4—22no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—44no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—82no—
361C2×C4—82no—
362C2×C4—442no—
363C2×C4—442no—
364C2×C4C2×#432311yescharacteristic
365C2×C4C2×#432311yescharacteristic
366C2×C4C2×#432311yescharacteristic
367C2×C4C2×#432311yescharacteristic
368C2×C4C2×#432311yescharacteristic
369C2×C4C22×C22⋊D1111yescharacteristic
370C8—21no—
371C8—21no—
372C8—21no—
373C8C2×#433911yescharacteristic
374C8C2×#433911yescharacteristic
375C22—21no—
376C22—21no—
377C22—21no—
378C22—42no—
379C22—81no—
380C22—81no—
381C22C22×#432311yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—42no—
387C4—81no—
388C4—81no—
389C4—882no—
390C4—882no—
391C4#1062280812yes—
392C4#1062332211yescharacteristic
393C4#1062335311yescharacteristic
394C2—41no—
395C2—82no—
396C2#1307861611yescharacteristic
397C2C2×#1062280811yescharacteristic
398C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×#135C2
socleC22×C11C22×D8
prime radicalC2×C11×#135C22
hypercenterC4×#135D11
hypocenterC11#33676
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
1. #13079202C2semidirect
2. #13070824C2semidirect
3. #13070768C2semidirect
4. #13070763C2semidirect
5. #13070666C2semidirect
6. #13070661C2semidirect
8. #13070485C2semidirect
9. #13070480C2semidirect
10. #13070419C2semidirect
341. C11#33676semidirect

Maximal subgroups

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

subgroupindex
#130792022
#130708242
#130707682
#130707632
#130706662
#130706612
#130705562
#130704852
#130704802
#130704192
C4×C11×#1352
#3367611