Finite Group Databasebeta

← #14657258

Subgroups — #14657258

Order 2816.

460 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076667C211yesmaximal, characteristic
2#13069584C211yesmaximal, characteristic, complemented
3#13068782C211yesmaximal, characteristic, complemented
4C2×#10622103C211yesmaximal, characteristic, complemented
5C2×#10622178C211yesmaximal, characteristic
6#13066498C211yesmaximal, characteristic, complemented
7C11×#1959C211yesmaximal, characteristic
8C2×C11×#124C2211yescharacteristic
9C2×#66923C2211yescharacteristic
10C2×C11×#103—21no—
11C2×C11×#102—21no—
12C2×C11×#97C2211yescharacteristic
13C11×#384C2211yescharacteristic
14#10622842—21no—
15#10622835—21no—
16C2×#66872—21no—
17C2×#66871—21no—
18#10622566—21no—
19#10622562—21no—
20#10622561—21no—
21#10622561—21no—
22#10622549C2211yescharacteristic
23C2×#66867C2211yescharacteristic
24C2×#66867C2211yescharacteristic
25#10622178—22no—
26#10622167—21no—
27#10622167—21no—
28#10622103—22no—
29C22×Q8×C11D411yescharacteristic
30C22×D4×C11D411yescharacteristic
31C22×C8×C11—21no—
32C11×#124—21no—
33C11×#124—21no—
34C11×#124—21no—
35C11×#124—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C42×C11C2311yescharacteristic
42C2×C22⋊Dic11—21no—
43C2×C22⋊Dic11—21no—
44C2×C22⋊Dic11—21no—
45C2×C22⋊Dic11—21no—
46C2×C4⋊Dic11D411yescharacteristic
47C2×C4⋊Dic11D411yescharacteristic
48C2×C4⋊Dic11D411yescharacteristic
49C2×C4⋊Dic11D411yescharacteristic
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4—21no—
52C2×Dic11⋊C4—21no—
53C2×Dic11⋊C4—21no—
54C22×C11⋊C8—21no—
55C22×C11⋊C8—21no—
56#66923—21no—
57#66923—21no—
58#66923—21no—
59#66923—21no—
60C11×#103—42no—
61C11×#102—42no—
62C11×#97—21no—
63C11×#97—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68#66872—42no—
69#66871—42no—
70#66867—21no—
71#66867—21no—
72#66867—21no—
73#66867D412yes—
74#10427—111nomaximal, Sylow
75C24×C11—21no—
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C22×C4×C11—21no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C2×C8×C11—22no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—42no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C42×C11C2×D411yescharacteristic
106C42×C11#4111yescharacteristic
107C42×C11#4111yescharacteristic
108C42×C11#4111yescharacteristic
109C22⋊Dic11—81no—
110C22⋊Dic11—81no—
111C22⋊Dic11—81no—
112C22⋊Dic11—81no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—41no—
118C4⋊Dic11—41no—
119Dic11⋊C4—41no—
120Dic11⋊C4—41no—
121Dic11⋊C4—41no—
122Dic11⋊C4—41no—
123Dic11⋊C4—81no—
124Dic11⋊C4—81no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—41no—
131#2820—111no—
132#1992—111no—
133#1959D1111yescharacteristic
134#1847—111no—
135C2×#330—111no—
136C2×#329—111no—
137#1295—111no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11#12011yescharacteristic
146Q8×C11—42no—
147Q8×C11—81no—
148D4×C11—42no—
149D4×C11—81no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C2×C4×C11—81no—
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12311yescharacteristic
166C2×C4×C11#12311yescharacteristic
167C2×C4×C11#12411yescharacteristic
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C8×C11—42no—
181C11⋊C8—24no—
182C11⋊C8—42no—
183C2×#125—111no—
184C2×#124C2×D1111yescharacteristic
185C2×#107—221no—
186C2×#106—221no—
187C2×#103—21no—
188C2×#102—21no—
189C2×#97—111no—
190C2×#97—111no—
191C2×#97C2×D1111yescharacteristic
192#399—221no—
193#397—221no—
194#396—221no—
195#396—221no—
196#395—221no—
197#394—221no—
198#384C2×D1111yescharacteristic
199#382—111no—
200#340—221no—
201#340—221no—
202#330—222no—
203#329—222no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11—81no—
210C22×C11—81no—
211C22×C11#39411yescharacteristic
212C22×C11#45311yescharacteristic
213C22×C11#45311yescharacteristic
214C22×C11#45411yescharacteristic
215C22×C11#45511yescharacteristic
216C22×C11#45611yescharacteristic
217C22×C11#45611yescharacteristic
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—81no—
225C4×C11—161no—
226Dic11—81no—
227Dic11—81no—
228Dic11—81no—
229Dic11—81no—
230C22×Q8C22⋊D1111yescharacteristic
231C22×D4C22⋊D1111yescharacteristic
232C22×C8—21no—
233C22×C8—221no—
234C22×C8—221no—
235#125—221no—
236#125—221no—
237#125—221no—
238#125—221no—
239#124—21no—
240#124—21no—
241#124—21no—
242#124—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—111no—
247C2×C4⋊C4—111no—
248C2×C4⋊C4—111no—
249C2×C4⋊C4—111no—
250C2×C4⋊C4—221no—
251C2×C4⋊C4—221no—
252C2×C4⋊C4—221no—
253C2×C4⋊C4—221no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C22⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C42C22×D1111yescharacteristic
261#107—442no—
262#106—442no—
263#103—42no—
264#102—42no—
265#97—21no—
266#97—21no—
267#97—112no—
268#97—221no—
269#97—221no—
270#97—221no—
271#95—221no—
272#95—221no—
273#95—221no—
274#95—221no—
275C2×C11—161no—
276C2×C11#165611yescharacteristic
277C2×C11#166011yescharacteristic
278C2×C11#166111yescharacteristic
279C2×C11#166411yescharacteristic
280C2×C11#203711yescharacteristic
281C2×C11#203811yescharacteristic
282C2×C11#203911yescharacteristic
283C24—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—41no—
291C2×D4—41no—
292C22×C4—21no—
293C22×C4—41no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4—221no—
298C22×C4D4×D1111yescharacteristic
299C22×C4D4×D1111yescharacteristic
300C22×C4C2×C22⋊D1111yescharacteristic
301C2×C8—22no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—222no—
305C2×C8—222no—
306C2×C8—222no—
307C2×C8—222no—
308C2×C8—441no—
309C2×C8—441no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—42no—
315C4⋊C4—221no—
316C4⋊C4—221no—
317C4⋊C4—221no—
318C4⋊C4—221no—
319C4⋊C4—441no—
320C4⋊C4—441no—
321C4⋊C4—441no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C4⋊C4—441no—
325C4⋊C4—881no—
326C4⋊C4—881no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—881no—
332C22⋊C4—881no—
333C22⋊C4—881no—
334C22⋊C4—881no—
335C42#433911yescharacteristic
336C42#433911yescharacteristic
337C42D4×D1111yescharacteristic
338C42#434111yescharacteristic
339C11#1042711yescharacteristic, complemented, Sylow
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23#6699011yescharacteristic
348Q8—42no—
349Q8—81no—
350D4—42no—
351D4—81no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—441no—
376C2×C4#6693611yescharacteristic
377C2×C4#6693711yescharacteristic
378C2×C4#6693711yescharacteristic
379C2×C4#6693811yescharacteristic
380C2×C4#6698211yescharacteristic
381C2×C4#6699211yescharacteristic
382C8—42no—
383C8—224no—
384C8—442no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22#1062257211yescharacteristic
393C22#1062267411yescharacteristic
394C22#1062269011yescharacteristic
395C22#1062281111yescharacteristic
396C22#1062281411yescharacteristic
397C22#1062281811yescharacteristic
398C22#1062281811yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—81no—
406C4—161no—
407C4—881no—
408C4—881no—
409C4—881no—
410C4—881no—
411C2—161no—
412C2#1306790711yescharacteristic
413C2#1306792511yescharacteristic
414C2#1306793211yescharacteristic
415C2#1306794911yescharacteristic
416C2#1306982611yescharacteristic
417C2#1306983111yescharacteristic
418C2#1306983811yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1959C2
socleC23×C11#120
prime radicalC22×D4×C11D4
hypercenter#1959D11
hypocenterC11#10427
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1959

Complements

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

NH ≅ G/Ntype
2. #13069584C2semidirect
3. #13068782C2semidirect
4. C2×#10622103C2semidirect
6. #13066498C2semidirect
339. C11#10427semidirect

Maximal subgroups

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

subgroupindex
#130766672
#130695842
#130687822
C2×#106221032
C2×#106221782
#130664982
C11×#19592
#1042711