Finite Group Databasebeta

← #14908822

Subgroups — #14908822

Order 2816.

542 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079197C211yesmaximal, characteristic
2C2×Q16×Dic11C211yesmaximal, characteristic
3#13070814C211yesmaximal, characteristic
4#13070811C211yesmaximal, characteristic
5#13070756C212yesmaximal, complemented
6#13070664C212yesmaximal, complemented
7#13070550C211yesmaximal, characteristic
8#13070487C212yesmaximal, complemented
9#13070484C212yesmaximal, complemented
10#13070416C211yesmaximal, characteristic
11C11×#2188C211yesmaximal, characteristic
12C22×C11×Q16C2211yescharacteristic
13C2×Q8×Dic11—21no—
14#10623153—21no—
15C2×C11×Q32C2212yes—
16C11×#467C2211yescharacteristic
17C2×#66899—21no—
18Q16×Dic11—21no—
19Q16×Dic11—21no—
20Q16×Dic11C2212yes—
21Q16×Dic11C2212yes—
22Q16×Dic11C2211yescharacteristic
23#10622794C2211yescharacteristic
24C2×#66893C2212yes—
25#10622729C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×C8×Dic11C2211yescharacteristic
28#10622664—21no—
29#10622487C2211yescharacteristic
30#10622486C2211yescharacteristic
31#10622405—21no—
32#10622403—21no—
33C11×#358C2212yes—
34C11×C22⋊C16C2211yescharacteristic
35#10622202C2212yes—
36#10622202C2212yes—
37C22⋊(C11⋊C16)C2211yescharacteristic
38#10622143C2212yes—
39#10622141C2212yes—
40#10622140C2212yes—
41Dic11⋊C16C2212yes—
42#10622128C2212yes—
43C22×Q8×C11—21no—
44C2×C11×Q16—24no—
45C2×C11×Q16—21no—
46C2×C11×Q16C2311yescharacteristic
47C2×C11×Q16C2312yes—
48C22×C8×C11C2311yescharacteristic
49C11×C22⋊Q8—21no—
50Q8×Dic11—22no—
51Q8×Dic11—22no—
52Q8×Dic11—21no—
53Q8×Dic11—41no—
54Q8×Dic11—41no—
55#66997—21no—
56C2×#4326—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—41no—
59#66977—21no—
60C2×C4×Dic11—41no—
61C2×C4×Dic11D411yescharacteristic
62C22×C11⋊C8D411yescharacteristic
63C2×Dic44C2311yescharacteristic
64#66942—41no—
65#66941—21no—
66#66940—21no—
67#66940—41no—
68#66931—41no—
69#66930—41no—
70C11×Q32—24no—
71C2×C11×C16C2312yes—
72C11×#107C2311yescharacteristic
73C11×#103—21no—
74#66899—22no—
75#66899—22no—
76#66899—21no—
77#66893—24no—
78#66882—21no—
79#66882C2311yescharacteristic
80#66882C2312yes—
81#66880—21no—
82C8×Dic11D411yescharacteristic
83C8×Dic11D411yescharacteristic
84C8×Dic11C2311yescharacteristic
85C8×Dic11C2311yescharacteristic
86C2×C11⋊C16C2312yes—
87#66874—21no—
88#66871—21no—
89#33673—111nomaximal, Sylow
90C2×Q8×C11—24no—
91C2×Q8×C11—22no—
92C2×Q8×C11—21no—
93C2×Q8×C11—42no—
94C2×Q8×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11C2×D411yescharacteristic
97C22×Dic11—41no—
98C22×Dic11D811yescharacteristic
99C22×Dic11D811yescharacteristic
100C2×Dic22—21no—
101C2×Dic22—41no—
102C11×Q16—24no—
103C11×Q16—22no—
104C11×Q16—22no—
105C11×Q16#4114yes—
106C2×C8×C11—22no—
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11C2411yescharacteristic
109C11×C4⋊C4—21no—
110C11×C4⋊C4—41no—
111C11×C22⋊C4—41no—
112C22⋊Dic11—41no—
113#4326—42no—
114C4⋊Dic11—21no—
115C4⋊Dic11—22no—
116C4⋊Dic11—41no—
117C4⋊Dic11—42no—
118C4⋊Dic11—42no—
119C4⋊Dic11—41no—
120Dic11⋊C4—41no—
121Dic11⋊C4—41no—
122Dic11⋊C4—41no—
123Dic11⋊C4—41no—
124Dic11⋊C4—41no—
125C4×Dic11—41no—
126C4×Dic11—41no—
127C4×Dic11—42no—
128C4×Dic11—42no—
129C4×Dic11D811yescharacteristic
130C4×Dic11D811yescharacteristic
131C4×Dic11C2×D411yescharacteristic
132C4×Dic11C2×D411yescharacteristic
133C2×C11⋊C8—41no—
134C2×C11⋊C8C2×D411yescharacteristic
135C2×C11⋊C8C2×D411yescharacteristic
136Dic44—22no—
137C11×C16—22no—
138C11⋊C16—22no—
139#3170—111no—
140C2×C4×Q16—111no—
141#2235—111no—
142#2235—111no—
143#2225—112no—
144#2209—112no—
145#2188—111no—
146#2188D1111yescharacteristic
147#2176—112no—
148#2176—112no—
149#2163—111no—
150C23×C11C2×D811yescharacteristic
151Q8×C11—24no—
152Q8×C11—44no—
153Q8×C11—42no—
154Q8×C11—41no—
155Q8×C11—41no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—44no—
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11C2×D811yescharacteristic
163C2×C4×C11C22×D411yescharacteristic
164C2×Dic11—22no—
165C2×Dic11—22no—
166C2×Dic11—42no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—82no—
170C2×Dic11C2×D811yescharacteristic
171C2×Dic11C2×D811yescharacteristic
172C2×Dic11C2×D811yescharacteristic
173C2×Dic11C2×D811yescharacteristic
174Dic22—41no—
175Dic22—41no—
176Dic22—82no—
177C8×C11—21no—
178C8×C11C2×#4112yes—
179C11⋊C8—21no—
180C11⋊C8—21no—
181C22×Q16C2×D1111yescharacteristic
182#533—221no—
183C2×C4×Q8—221no—
184C2×Q32—112no—
185C2×Q32C2×D1112yes—
186#500—111no—
187#494—111no—
188#487—221no—
189#467—111no—
190#467—221no—
191#467C2×D1111yescharacteristic
192C4×Q16—111no—
193C4×Q16—112no—
194C4×Q16—112no—
195C4×Q16—111no—
196C4×Q16—221no—
197C4×Q16—221no—
198C4×Q16—221no—
199C2×#107—111no—
200C2×#103—221no—
201C2×C4×C8—111no—
202#367—112no—
203#367—112no—
204C4⋊C16—112no—
205#358—112no—
206#358—112no—
207#358—112no—
208#358C2×D1112yes—
209C22⋊C16—111no—
210C22⋊C16C2×D1111yescharacteristic
211#346—112no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11#51012yes—
215C22×C11C22×D811yescharacteristic
216C4×C11—21no—
217C4×C11—44no—
218C4×C11—81no—
219C4×C11—81no—
220C4×C11#52511yescharacteristic
221C4×C11#57511yescharacteristic
222Dic11—21no—
223Dic11—21no—
224Dic11—21no—
225Dic11—81no—
226Dic11—81no—
227Dic11—82no—
228Dic11#51012yes—
229C22×Q8—21no—
230C2×Q16—24no—
231C2×Q16—21no—
232C2×Q16—111no—
233C2×Q16—221no—
234C2×Q16C22×D1111yescharacteristic
235C2×Q16C22×D1112yes—
236C22×C8—111no—
237C22×C8C22×D1111yescharacteristic
238C4⋊Q8—221no—
239C4⋊Q8—221no—
240#125—441no—
241C22⋊Q8—21no—
242C22⋊Q8—221no—
243C22⋊Q8—441no—
244C4×Q8—221no—
245C4×Q8—222no—
246C4×Q8—222no—
247C4×Q8—221no—
248C4×Q8—441no—
249C4×Q8—441no—
250C4×Q8—441no—
251#117—441no—
252C2×C4⋊C4—221no—
253C2×C4⋊C4—441no—
254C2×C42—111no—
255C2×C42—441no—
256Q32—24no—
257Q32—224no—
258C2×C16—112no—
259C2×C16C22×D1112yes—
260#107—112no—
261#107—111no—
262#107—221no—
263#107—221no—
264#107C22×D1111yescharacteristic
265#103—21no—
266#103—221no—
267#103—222no—
268#103—222no—
269#103—221no—
270#103—221no—
271C4×C8—111no—
272C4×C8—111no—
273C4×C8—111no—
274C4×C8—111no—
275C2×C11—22no—
276C2×C11#310011yescharacteristic
277C2×C11C2×#51011yescharacteristic
278C2×C11C2×#51011yescharacteristic
279C2×Q8—24no—
280C2×Q8—22no—
281C2×Q8—21no—
282C2×Q8—42no—
283C2×Q8—41no—
284C2×Q8—221no—
285C2×Q8—441no—
286C22×C4—41no—
287C22×C4—111no—
288C22×C4—111no—
289C22×C4—441no—
290C22×C4D4×D1111yescharacteristic
291Q16—24no—
292Q16—22no—
293Q16—22no—
294Q16—222no—
295Q16—442no—
296Q16#434114yes—
297C2×C8—22no—
298C2×C8—111no—
299C2×C8—111no—
300C2×C8—441no—
301C2×C8D4×D1111yescharacteristic
302C2×C8C23×D1111yescharacteristic
303C4⋊C4—21no—
304C4⋊C4—41no—
305C4⋊C4—222no—
306C4⋊C4—221no—
307C4⋊C4—442no—
308C4⋊C4—442no—
309C4⋊C4—441no—
310C4⋊C4—441no—
311C4⋊C4—441no—
312C4⋊C4—441no—
313C4⋊C4—441no—
314C4⋊C4—441no—
315C4⋊C4—441no—
316C22⋊C4—41no—
317C22⋊C4—441no—
318C42—111no—
319C42—111no—
320C42—111no—
321C42—111no—
322C42—442no—
323C42—442no—
324C42—441no—
325C42—441no—
326C16—22no—
327C16—222no—
328C11#3367311yescharacteristic, complemented, Sylow
329C23D8×D1111yescharacteristic
330Q8—24no—
331Q8—44no—
332Q8—42no—
333Q8—41no—
334Q8—41no—
335Q8—441no—
336Q8—441no—
337Q8—882no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—44no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—111no—
345C2×C4—111no—
346C2×C4—111no—
347C2×C4—111no—
348C2×C4—222no—
349C2×C4—222no—
350C2×C4—442no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—882no—
354C2×C4D8×D1111yescharacteristic
355C2×C4C2×D4×D1111yescharacteristic
356C8—21no—
357C8—221no—
358C8—221no—
359C8C2×#434112yes—
360C22—21no—
361C22—21no—
362C22#1062253112yes—
363C22C2×D8×D1111yescharacteristic
364C4—21no—
365C4—44no—
366C4—81no—
367C4—81no—
368C4—112no—
369C4—221no—
370C4—221no—
371C4—221no—
372C4—881no—
373C4—881no—
374C4—882no—
375C4#1062311711yescharacteristic
376C4#1062330411yescharacteristic
377C2—22no—
378C2#1307861111yescharacteristic
379C2D11×#51011yescharacteristic
380C2C2×#1062253111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2188C2
socleC22×C11C22×D8
prime radicalC23×C11C2×D8
hypercenter#2188D11
hypocenterC11#33673
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2188

Complements

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

NH ≅ G/Ntype
5. #13070756C2semidirect
6. #13070664C2semidirect
8. #13070487C2semidirect
9. #13070484C2semidirect
328. C11#33673semidirect

Maximal subgroups

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

subgroupindex
#130791972
C2×Q16×Dic112
#130708142
#130708112
#130707562
#130706642
#130705502
#130704872
#130704842
#130704162
C11×#21882
#3367311