Finite Group Databasebeta

← #14655800

Subgroups — #14655800

Order 2816.

528 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 101 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#13079760C211yesmaximal, characteristic, complemented
2#13078415C211yesmaximal, characteristic
3C2×#10622696C211yesmaximal, characteristic
4#13067020C211yesmaximal, characteristic, complemented
5#13066936C211yesmaximal, characteristic
6#13066511C211yesmaximal, characteristic, complemented
7C11×#1546C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C22×#4325—21no—
10C2×C4×D44C2211yescharacteristic
11#10623001C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#423C2211yescharacteristic
14C2×#66899—21no—
15#10622744—21no—
16#10622734—21no—
17#10622707—22no—
18#10622706—21no—
19#10622696—22no—
20#10622696—22no—
21#10622692—21no—
22#10622584—22no—
23#10622538C2211yescharacteristic
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25#10622460—22no—
26#10622459—21no—
27#10622455—21no—
28C11×#332—22no—
29#10622106—22no—
30#10622094—22no—
31C22×Q8×C11—21no—
32C22×D44D411yescharacteristic
33C22×C4×D11—21no—
34C2×C11×M16—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8D412yes—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C42×C11C2311yescharacteristic
42C2×#4325—24no—
43C2×#4325—42no—
44C2×#4325—42no—
45C2×(C2×D11)⋊C4—21no—
46#66979—21no—
47C2×C4⋊Dic11D411yescharacteristic
48#66977—21no—
49#66977—21no—
50C22×C11⋊C8—21no—
51C4×D44—21no—
52C4×D44—21no—
53C4×D44—21no—
54C4×D44—21no—
55#66923—21no—
56#66922D411yescharacteristic
57#66922D411yescharacteristic
58C4×Dic22—21no—
59C4×Dic22—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8D412yes—
63C11×C22⋊C8—21no—
64C4×C8×C11—21no—
65#66899—24no—
66C22⋊(C11⋊C8)D412yes—
67#66885—22no—
68#66885—22no—
69#66882—22no—
70#66881—22no—
71#66874—24no—
72#66872—24no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)D412yes—
76C4×C11⋊C8—21no—
77#10186—111nomaximal, Sylow
78C23×D11—21no—
79C2×Q8×C11—22no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C22×Dic11—21no—
90C2×D44—21no—
91C2×D44—21no—
92C2×D44—21no—
93C2×D44—21no—
94C2×D44—21no—
95C2×D44SD1612yes—
96C2×C4×D11—41no—
97C2×C4×D11—41no—
98C2×C4×D11—82no—
99C2×Dic22—21no—
100C2×Dic22—21no—
101C11×M16—41no—
102C11×M16—41no—
103C2×C8×C11—22no—
104C2×C8×C11—41no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C22⋊Dic11—41no—
114#4325—48no—
115(C2×D11)⋊C4—41no—
116(C2×D11)⋊C4—41no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123Dic11⋊C4—41no—
124Dic11⋊C4—41no—
125C4×Dic11—41no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—41no—
129C2×C11⋊C8—41no—
130#3229—111no—
131#3077—111no—
132C2×#461—111no—
133#1546D1111yescharacteristic, complemented
134#1481—111no—
135#1460—111no—
136#1301—111no—
137C23×C11#12111yescharacteristic
138C22×D11—22no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—81no—
142C22×D11—81no—
143Q8×C11—42no—
144Q8×C11—42no—
145Q8×C11—81no—
146Q8×C11—81no—
147C2×C4×C11—22no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—81no—
151C2×C4×C11—81no—
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12711yescharacteristic
158C2×C4×C11C2×SD1611yescharacteristic
159C2×C4×C11#13511yescharacteristic
160C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C11#13711yescharacteristic
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—81no—
166D44—22no—
167D44—22no—
168D44—41no—
169D44—41no—
170C4×D11—82no—
171C4×D11—82no—
172Dic22—42no—
173Dic22—42no—
174C8×C11—42no—
175C8×C11—81no—
176C11⋊C8—42no—
177C11⋊C8—42no—
178C22×SD16—221no—
179#533—111no—
180C2×C4⋊Q8C2×D1111yescharacteristic
181C2×C4×D4—111no—
182#498—221no—
183#487—221no—
184#483—222no—
185#478—222no—
186#476—221no—
187#475—222no—
188#474—221no—
189#461—222no—
190#461—222no—
191#431—111no—
192#431C2×D1111yescharacteristic
193#428—221no—
194#423C2×D1111yescharacteristic
195C2×C4⋊C8—111no—
196#418—221no—
197C2×#103—221no—
198#332—22no—
199Q8⋊C8—222no—
200#323—222no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11#39211yescharacteristic
204C22×C11#46511yescharacteristic
205C22×C11#46811yescharacteristic
206C2×D11—42no—
207C2×D11—82no—
208C2×D11—81no—
209C2×D11—81no—
210C2×D11—82no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—82no—
215C4×C11#44811yescharacteristic
216C4×C11#44911yescharacteristic
217C4×C11#45011yescharacteristic
218C4×C11#45211yescharacteristic
219C4×C11#47112yes—
220Dic11—81no—
221Dic11—81no—
222Dic11—81no—
223C22×Q8—21no—
224C22×D4—111no—
225C23×C4—221no—
226C2×SD16—224no—
227C2×SD16—442no—
228C2×SD16—442no—
229C2×M16—21no—
230C22×C8—221no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—111no—
235C4⋊Q8—111no—
236C4⋊Q8D4412yes—
237#125—221no—
238C22⋊Q8—221no—
239C22⋊Q8—221no—
240C4×Q8—221no—
241C4×Q8—221no—
242C4×D4—221no—
243C4×D4—221no—
244C4×D4—221no—
245C4×D4—221no—
246#117—221no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—111no—
250C2×C22⋊C4—221no—
251C2×C42C22×D1111yescharacteristic
252#107—222no—
253#106—224no—
254#106—222no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—112no—
258C4⋊C8—221no—
259C4⋊C8—221no—
260C4⋊C8C22⋊D1112yes—
261#103—224no—
262#103—224no—
263#102—222no—
264#102—222no—
265C22⋊C8—21no—
266C22⋊C8—112no—
267C4×C8—21no—
268C4×C8—221no—
269C2×C11—21no—
270C2×C11—21no—
271C2×C11#200011yescharacteristic
272C2×C11#200911yescharacteristic
273C2×C11#201911yescharacteristic
274D11—82no—
275C24—221no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—221no—
283C2×Q8—221no—
284C2×D4—112no—
285C2×D4—221no—
286C2×D4—221no—
287C2×D4—221no—
288C2×D4—221no—
289C2×D4—221no—
290C22×C4—41no—
291C22×C4—221no—
292C22×C4—441no—
293C22×C4—441no—
294C22×C4—882no—
295C22×C4#433911yescharacteristic
296C22×C4D4×D1111yescharacteristic
297C22×C4D4×D1111yescharacteristic
298SD16—448no—
299M16—41no—
300M16—41no—
301C2×C8—22no—
302C2×C8—41no—
303C2×C8—222no—
304C2×C8—222no—
305C2×C8—441no—
306C2×C8—441no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—221no—
312C4⋊C4—221no—
313C4⋊C4—221no—
314C4⋊C4—221no—
315C4⋊C4—221no—
316C4⋊C4—221no—
317C4⋊C4—441no—
318C4⋊C4—441no—
319C22⋊C4—441no—
320C22⋊C4—441no—
321C22⋊C4—441no—
322C42—441no—
323C42C2×D4411yescharacteristic
324C42D4×D1111yescharacteristic
325C42D4×D1111yescharacteristic
326C42C2×C22⋊D1111yescharacteristic
327C11#1018611yescharacteristic, complemented, Sylow
328C23—222no—
329C23—441no—
330C23—441no—
331C23—881no—
332C23—881no—
333C23#6693711yescharacteristic
334Q8—42no—
335Q8—42no—
336Q8—81no—
337Q8—81no—
338Q8—442no—
339Q8—442no—
340D4—222no—
341D4—222no—
342D4—441no—
343D4—441no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—882no—
353C2×C4—882no—
354C2×C4—881no—
355C2×C4#6693511yescharacteristic
356C2×C4#6693511yescharacteristic
357C2×C4#6693711yescharacteristic
358C2×C4#6696411yescharacteristic
359C2×C4#6696511yescharacteristic
360C2×C4SD16×D1111yescharacteristic
361C2×C4#6696811yescharacteristic
362C2×C4#6698311yescharacteristic
363C2×C4#6699011yescharacteristic
364C2×C4#6699311yescharacteristic
365C8—42no—
366C8—81no—
367C8—442no—
368C8—442no—
369C22—21no—
370C22—21no—
371C22—442no—
372C22—882no—
373C22—882no—
374C22—881no—
375C22—881no—
376C22#1062239111yescharacteristic
377C22#1062239311yescharacteristic
378C22#1062257311yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—82no—
383C4—881no—
384C4—881no—
385C4—881no—
386C4#1062236712yes—
387C4#1062238911yescharacteristic
388C4#1062239611yescharacteristic
389C4#1062277111yescharacteristic
390C4#1062278311yescharacteristic
391C2—21no—
392C2—21no—
393C2—882no—
394C2#1306962011yescharacteristic
395C2#1306967811yescharacteristic
396C2#1306972911yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1546C2
socleC22×C11#392
prime radicalC22×D44D4
hypercenter#1546D11
hypocenterC11#10186
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
1. #13079760C2semidirect
4. #13067020C2semidirect
6. #13066511C2semidirect
7. C11×#1546C2semidirect
133. #1546D11semidirect
327. C11#10186semidirect

Maximal subgroups

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

subgroupindex
#130797602
#130784152
C2×#106226962
#130670202
#130669362
#130665112
C11×#15462
#1018611