Finite Group Databasebeta

← #14648236

Subgroups — #14648236

Order 2816.

476 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071705C211yesmaximal, characteristic
2#13069417C211yesmaximal, characteristic
3#13069377C211yesmaximal, characteristic
4C2×#10622119C211yesmaximal, characteristic
5#13066457C211yesmaximal, characteristic
6#13066455C211yesmaximal, characteristic
7C11×#1948C211yesmaximal, characteristic
8C2×#66922C2211yescharacteristic
9C2×C11×#106—21no—
10C2×C11×C4⋊C8C2211yescharacteristic
11C11×#384C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13C4⋊C4×Dic11—21no—
14#10622586—21no—
15C2×#66874—22no—
16C2×#66872—21no—
17C4×C4⋊Dic11—21no—
18C4×C4⋊Dic11C2211yescharacteristic
19#10622541—21no—
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×C4×C11⋊C8C2211yescharacteristic
22#10622259—22no—
23C11×#340—21no—
24#10622167—21no—
25#10622119C414yescomplemented
26C22×Dic22D412yes—
27C22×C8×C11—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C42×C11—21no—
34C2×C42×C11C2311yescharacteristic
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11D411yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×Dic11⋊C4—22no—
40C2×C4×Dic11—21no—
41C2×C4×Dic11—22no—
42C22×C11⋊C8—21no—
43C22×C11⋊C8—21no—
44#66922—21no—
45#66922—21no—
46#66922C2×C412yes—
47#66922Q812yes—
48C11×#106—42no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8C2×C412yes—
51C11×#95—21no—
52C11⋊#95—22no—
53C11⋊#95—22no—
54C11⋊#95—21no—
55#66874—44no—
56#66872—42no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)C2×C412yes—
59C4×C11⋊C8—21no—
60C4×C11⋊C8—21no—
61#8928—111nomaximal, Sylow
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—41no—
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—21no—
69C22×Dic11—22no—
70C22×Dic11—21no—
71C2×Dic22—22no—
72C2×Dic22—42no—
73C2×Dic22—42no—
74C2×Dic22C4⋊C414yes—
75C2×C8×C11—22no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—42no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4SD1612yes—
87C42×C11—41no—
88C42×C11—41no—
89C42×C11C22×C411yescharacteristic
90C42×C11C2×Q811yescharacteristic
91C42×C11#4111yescharacteristic
92C42×C11#4111yescharacteristic
93C4⋊Dic11—22no—
94C4⋊Dic11—22no—
95C4⋊Dic11—22no—
96C4⋊Dic11—22no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11—21no—
100C4⋊Dic11SD1612yes—
101Dic11⋊C4—82no—
102C4×Dic11—41no—
103C4×Dic11—41no—
104C4×Dic11—82no—
105C2×C11⋊C8—22no—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111#2369—111no—
112#1956—111no—
113#1948—111no—
114#1948D1111yescharacteristic
115C2×#333—111no—
116#1279—111no—
117#1279—111no—
118C23×C11#12011yescharacteristic
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—22no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—81no—
128C2×C4×C11—81no—
129C2×C4×C11—81no—
130C2×C4×C11C2×C4⋊C411yescharacteristic
131C2×C4×C11C4×D411yescharacteristic
132C2×C4×C11C4×D411yescharacteristic
133C2×C4×C11C22⋊Q811yescharacteristic
134C2×C4×C11C22⋊Q811yescharacteristic
135C2×C4×C11#12311yescharacteristic
136C2×C4×C11C2×SD1611yescharacteristic
137C2×C4×C11C2×SD1611yescharacteristic
138C2×C4×C11#13511yescharacteristic
139C2×C4×C11#13511yescharacteristic
140C2×C4×C11#13711yescharacteristic
141C2×C4×C11#13711yescharacteristic
142C2×C4×C11#13711yescharacteristic
143C2×C4×C11#13711yescharacteristic
144C2×Dic11—24no—
145C2×Dic11—22no—
146C2×Dic11—41no—
147C2×Dic11—42no—
148C2×Dic11—41no—
149C2×Dic11—42no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153Dic22—44no—
154Dic22—82no—
155C8×C11—42no—
156C11⋊C8—42no—
157C11⋊C8—42no—
158C2×C4⋊Q8—111no—
159C2×#106—21no—
160C2×#106—221no—
161C2×C4⋊C8—111no—
162C2×C4⋊C8C2×D1111yescharacteristic
163C2×#103—222no—
164C2×C4×C8—111no—
165#391—222no—
166#389—221no—
167#389—221no—
168#384C2×D1111yescharacteristic
169C4×C4⋊C4—111no—
170C4×C4⋊C4—221no—
171C4×C4⋊C4—221no—
172C4×C4⋊C4C2×D1111yescharacteristic
173#340—21no—
174#340—221no—
175#333—114no—
176C22×C11#38511yescharacteristic
177C22×C11#44811yescharacteristic
178C22×C11#44811yescharacteristic
179C22×C11#45211yescharacteristic
180C22×C11#45211yescharacteristic
181C22×C11#45311yescharacteristic
182C22×C11#45511yescharacteristic
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—42no—
186C4×C11—81no—
187C4×C11—161no—
188C4×C11C4×SD1611yescharacteristic
189C4×C11C4×SD1611yescharacteristic
190C4×C11#44111yescharacteristic
191C4×C11#44111yescharacteristic
192C4×C11#47511yescharacteristic
193C4×C11#47511yescharacteristic
194C4×C11#47911yescharacteristic
195C4×C11#47911yescharacteristic
196Dic11—44no—
197Dic11—42no—
198Dic11—81no—
199C22×Q8—112no—
200C22×C8—21no—
201C22×C8—221no—
202C22×C8—221no—
203C4⋊Q8—112no—
204C4⋊Q8—112no—
205C4⋊Q8—221no—
206C4⋊Q8—221no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—111no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—222no—
215C2×C4⋊C4C22⋊D1111yescharacteristic
216C2×C4⋊C4C22⋊D1111yescharacteristic
217C2×C42—21no—
218C2×C42—221no—
219C2×C42—222no—
220C2×C42C22×D1111yescharacteristic
221#106—42no—
222#106—442no—
223C4⋊C8—21no—
224C4⋊C8—112no—
225C4⋊C8—221no—
226C4⋊C8C4×D1112yes—
227#103—444no—
228C4×C8—221no—
229C4×C8—221no—
230#95—21no—
231#95—222no—
232#95—222no—
233#95—221no—
234C2×C11#162311yescharacteristic
235C2×C11#163411yescharacteristic
236C2×C11#164311yescharacteristic
237C2×C11#164311yescharacteristic
238C2×C11#185611yescharacteristic
239C2×C11#186511yescharacteristic
240C2×C11#186511yescharacteristic
241C2×Q8—114no—
242C2×Q8—222no—
243C2×Q8—442no—
244C2×Q8—442no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—41no—
248C22×C4—221no—
249C22×C4—222no—
250C22×C4—221no—
251C22×C4D4×D1111yescharacteristic
252C22×C4D4×D1111yescharacteristic
253C22×C4C2×C22⋊D1111yescharacteristic
254C2×C8—22no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—222no—
258C2×C8—222no—
259C2×C8—441no—
260C2×C8—441no—
261C2×C8—441no—
262C2×C8—441no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—42no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—112no—
272C4⋊C4—222no—
273C4⋊C4—222no—
274C4⋊C4—221no—
275C4⋊C4—222no—
276C4⋊C4—222no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—882no—
280C4⋊C4#432412yes—
281C42—41no—
282C42—41no—
283C42—441no—
284C42—441no—
285C42—882no—
286C42C2×C4×D1111yescharacteristic
287C42#433911yescharacteristic
288C42Q8×D1111yescharacteristic
289C42#434311yescharacteristic
290C11#892811yescharacteristic, complemented, Sylow
291C23#6699011yescharacteristic
292Q8—444no—
293Q8—882no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—222no—
306C2×C4—224no—
307C2×C4—442no—
308C2×C4—441no—
309C2×C4—442no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4C4⋊C4×D1111yescharacteristic
315C2×C4#6694611yescharacteristic
316C2×C4#6694711yescharacteristic
317C2×C4#6694911yescharacteristic
318C2×C4SD16×D1111yescharacteristic
319C2×C4#6696811yescharacteristic
320C2×C4#6696811yescharacteristic
321C2×C4#6696911yescharacteristic
322C2×C4C4×C22⋊D1111yescharacteristic
323C2×C4C2×#432411yescharacteristic
324C2×C4#6699511yescharacteristic
325C2×C4#6699911yescharacteristic
326C2×C4#6700311yescharacteristic
327C2×C4#6700411yescharacteristic
328C8—42no—
329C8—442no—
330C8—442no—
331C22#1062260211yescharacteristic
332C22#1062265311yescharacteristic
333C22#1062266011yescharacteristic
334C22#1062278311yescharacteristic
335C22#1062278611yescharacteristic
336C22#1062281111yescharacteristic
337C22#1062281511yescharacteristic
338C4—21no—
339C4—21no—
340C4—42no—
341C4—81no—
342C4—161no—
343C4—444no—
344C4—442no—
345C4—881no—
346C4#1062246511yescharacteristic
347C4#1062246611yescharacteristic
348C4#1062246711yescharacteristic
349C4#1062247011yescharacteristic
350C4C4×#432411yescharacteristic
351C4#1062264311yescharacteristic
352C4#1062267611yescharacteristic
353C4#1062270711yescharacteristic
354C2#1306769311yescharacteristic
355C2#1306776011yescharacteristic
356C2#1306782111yescharacteristic
357C2#1306782211yescharacteristic
358C2#1306882411yescharacteristic
359C2#1306888111yescharacteristic
360C2#1306888311yescharacteristic
subgroupG/H
centerC23#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1948C2
socle, prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#1948D11
hypocenterC11#8928
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
25. #10622119C4semidirect
290. C11#8928semidirect

Maximal subgroups

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

subgroupindex
#130717052
#130694172
#130693772
C2×#106221192
#130664572
#130664552
C11×#19482
#892811