Finite Group Databasebeta

← #14656262

Subgroups — #14656262

Order 2816.

528 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079932C211yesmaximal, characteristic
2#13078421C211yesmaximal, characteristic, complemented
3#13069553C211yesmaximal, characteristic, complemented
4#13067070C211yesmaximal, characteristic, complemented
5#13067067C211yesmaximal, characteristic
6#13066490C211yesmaximal, characteristic, complemented
7C11×#3037C211yesmaximal, characteristic
8C2×C11×#137—21no—
9C11×#532C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11#10623001C2211yescharacteristic
12C11×#464—22no—
13C11×#462—21no—
14C11×#460—21no—
15C11×#423C2211yescharacteristic
16C11×#417—21no—
17#10622838—21no—
18#10622707—21no—
19#10622688—21no—
20#10622654—22no—
21#10622635—22no—
22#10622634—21no—
23#10622633—21no—
24#10622632—21no—
25#10622621—21no—
26#10622577—21no—
27#10622537C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29C2×C4×C11⋊C8C2211yescharacteristic
30D4⋊(C11⋊C8)—22no—
31#10622162—22no—
32#10622122—22no—
33C2×C11×#41—21no—
34C22×Q8×C11D411yescharacteristic
35C11×#137—42no—
36C11×#137—42no—
37C2×C11×Q16—22no—
38C2×C11×SD16—22no—
39C2×C11×M16—21no—
40C11×C4⋊Q8D411yescharacteristic
41C11×#127D411yescharacteristic
42C11×#124—21no—
43C11×#121—21no—
44C11×#121—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C42×C11—21no—
54C2×C42×C11C2311yescharacteristic
55C2×#4324—22no—
56#66979—21no—
57#66977—21no—
58#66977—21no—
59C2×#4318—21no—
60C22×C11⋊C8—21no—
61C22×C11⋊C8D412yes—
62#66923—21no—
63#66922D411yescharacteristic
64#66922D411yescharacteristic
65C4×Dic22—21no—
66C4×Dic22—21no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8D412yes—
69C11×#103—22no—
70C11×#102—22no—
71#66899—22no—
72#66899—22no—
73#66896—22no—
74#66874—22no—
75#66872—22no—
76#66872—22no—
77#66871—22no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)D412yes—
82C4×C11⋊C8—21no—
83C4×C11⋊C8—21no—
84#10257—111nomaximal, Sylow
85C11×#41—41no—
86C11×#41—41no—
87C11×#41—41no—
88C11×#41—41no—
89C2×Q8×C11—21no—
90C2×Q8×C11—21no—
91C2×Q8×C11—21no—
92C2×Q8×C11—21no—
93C2×Q8×C11—21no—
94C2×Q8×C11—21no—
95C2×Q8×C11SD1612yescomplemented
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—41no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—41no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11#4111yescharacteristic
106C2×Dic22—21no—
107C2×Dic22—21no—
108C11×Q16—44no—
109C11×SD16—44no—
110C11×M16—41no—
111C11×M16—41no—
112C2×C8×C11—22no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C42×C11—41no—
122C42×C11—41no—
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C22⋊Dic11—41no—
128#4324—82no—
129C4⋊Dic11—21no—
130C4⋊Dic11—21no—
131C4⋊Dic11—21no—
132C4⋊Dic11—21no—
133Dic11⋊C4—41no—
134Dic11⋊C4—41no—
135C4×Dic11—41no—
136#4318—41no—
137#4318—41no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—42no—
142C2×C11⋊C8—41no—
143C2×C11⋊C8—41no—
144#3246—111no—
145#3078—111no—
146#3037D1111yescharacteristic
147#1984—111no—
148#1493—111no—
149#1492—111no—
150#1292—111no—
151C23×C11—41no—
152C23×C11#12111yescharacteristic
153Q8×C11—22no—
154Q8×C11—22no—
155Q8×C11—41no—
156Q8×C11—41no—
157Q8×C11—41no—
158Q8×C11—41no—
159D4×C11—42no—
160D4×C11—41no—
161D4×C11—41no—
162D4×C11—41no—
163D4×C11—41no—
164D4×C11—81no—
165D4×C11—81no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—22no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—42no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—81no—
176C2×C4×C11—81no—
177C2×C4×C11#12011yescharacteristic
178C2×C4×C11#12011yescharacteristic
179C2×C4×C11#12011yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12711yescharacteristic
183C2×C4×C11C2×SD1611yescharacteristic
184C2×C4×C11#13511yescharacteristic
185C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C11#13711yescharacteristic
187C2×Dic11—41no—
188C2×Dic11—41no—
189Dic22—42no—
190Dic22—41no—
191Dic22—41no—
192C8×C11—42no—
193C11⋊C8—42no—
194C11⋊C8—42no—
195C11⋊C8—42no—
196C2×#137—21no—
197#533—111no—
198#532C2×D1111yescharacteristic
199C2×C4×Q8C2×D1111yescharacteristic
200#479—222no—
201#477—221no—
202#476—221no—
203#475—221no—
204#475—221no—
205#465—222no—
206#464—22no—
207#462—21no—
208#461—221no—
209#460—21no—
210#460—221no—
211#428—221no—
212#423—111no—
213#423C2×D1111yescharacteristic
214C2×C4⋊C8—111no—
215#419—221no—
216#417—21no—
217C2×C4×C8—111no—
218#336—222no—
219Q8⋊C8—222no—
220D4⋊C8—222no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11—81no—
226C22×C11#39211yescharacteristic
227C22×C11#46511yescharacteristic
228C22×C11#46811yescharacteristic
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—42no—
233C4×C11—81no—
234C4×C11—81no—
235C4×C11#44811yescharacteristic
236C4×C11#44911yescharacteristic
237C4×C11#45011yescharacteristic
238C4×C11#45211yescharacteristic
239C4×C11#45511yescharacteristic
240C4×C11#45611yescharacteristic
241Dic11—81no—
242Dic11—81no—
243C2×#41—21no—
244C22×Q8C22⋊D1111yescharacteristic
245#137—42no—
246#137—42no—
247C2×Q16—22no—
248C2×SD16—22no—
249C2×SD16—222no—
250C2×M16—21no—
251C2×M16—221no—
252C22×C8—112no—
253C22×C8—221no—
254C4⋊Q8—111no—
255C4⋊Q8—111no—
256C4⋊Q8C22⋊D1111yescharacteristic
257#127C22⋊D1111yescharacteristic
258#125—221no—
259#124—21no—
260C22⋊Q8—221no—
261C22⋊Q8—221no—
262#121—21no—
263#121—21no—
264C4×Q8—21no—
265C4×Q8—21no—
266C4×Q8—21no—
267C4×Q8—21no—
268C4×Q8—221no—
269C4×Q8—221no—
270C4×D4—21no—
271C4×D4—21no—
272#117—221no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4C22⋊D1111yescharacteristic
275C2×C42—21no—
276C2×C42C22×D1111yescharacteristic
277#107—222no—
278#106—222no—
279#106—222no—
280C4⋊C8—21no—
281C4⋊C8—112no—
282C4⋊C8—221no—
283C4⋊C8—221no—
284C4⋊C8—221no—
285C4⋊C8C22⋊D1112yes—
286#103—22no—
287#103—222no—
288#103—222no—
289#103—222no—
290#102—22no—
291#102—222no—
292C4×C8—221no—
293C4×C8—221no—
294C2×C11—21no—
295C2×C11—21no—
296C2×C11—161no—
297C2×C11#200011yescharacteristic
298C2×C11#200711yescharacteristic
299C2×C11#201711yescharacteristic
300#41—41no—
301#41—41no—
302#41—41no—
303#41—41no—
304C2×Q8—21no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—221no—
311C2×Q8—221no—
312C2×Q8#432412yescomplemented
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—41no—
320C22×C4D4×D1111yescharacteristic
321C22×C4#434111yescharacteristic
322C22×C4C2×C22⋊D1111yescharacteristic
323Q16—44no—
324SD16—44no—
325SD16—882no—
326M16—41no—
327M16—41no—
328M16—441no—
329M16—441no—
330C2×C8—22no—
331C2×C8—222no—
332C2×C8—222no—
333C2×C8—222no—
334C2×C8—441no—
335C2×C8—441no—
336C2×C8—442no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—221no—
344C4⋊C4—221no—
345C4⋊C4—221no—
346C4⋊C4—221no—
347C4⋊C4—441no—
348C4⋊C4—441no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—441no—
352C42—41no—
353C42—41no—
354C42—441no—
355C42D4×D1111yescharacteristic
356C42D4×D1111yescharacteristic
357C42C2×C22⋊D1111yescharacteristic
358C42C2×C22⋊D1111yescharacteristic
359C11#1025711yescharacteristic, complemented, Sylow
360C23—41no—
361C23#6699211yescharacteristic
362Q8—22no—
363Q8—22no—
364Q8—41no—
365Q8—41no—
366Q8—41no—
367Q8—41no—
368Q8—442no—
369Q8—441no—
370Q8—441no—
371D4—42no—
372D4—41no—
373D4—41no—
374D4—41no—
375D4—41no—
376D4—81no—
377D4—81no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—22no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4#6698511yescharacteristic
392C2×C4C2×#432411yescharacteristic
393C2×C4#6699011yescharacteristic
394C2×C4#6699011yescharacteristic
395C2×C4#6699111yescharacteristic
396C2×C4#6699211yescharacteristic
397C2×C4#6699311yescharacteristic
398C2×C4#6700311yescharacteristic
399C2×C4#6700411yescharacteristic
400C2×C4#6700611yescharacteristic
401C8—42no—
402C8—442no—
403C8—442no—
404C8—442no—
405C22—21no—
406C22—21no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22#1062265411yescharacteristic
411C22#1062265511yescharacteristic
412C22#1062283611yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—42no—
417C4—81no—
418C4—81no—
419C4—881no—
420C4—881no—
421C4#1062265011yescharacteristic
422C4#1062265311yescharacteristic
423C4#1062281511yescharacteristic
424C4#1062281811yescharacteristic
425C4#1062283111yescharacteristic
426C4#1062285211yescharacteristic
427C2—21no—
428C2—21no—
429C2—161no—
430C2#1306961911yescharacteristic
431C2#1306966111yescharacteristic
432C2#1306971911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3037C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3037D11
hypocenterC11#10257
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3037

Complements

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

NH ≅ G/Ntype
2. #13078421C2semidirect
3. #13069553C2semidirect
4. #13067070C2semidirect
6. #13066490C2semidirect
95. C2×Q8×C11SD16semidirect
312. C2×Q8#4324semidirect
359. C11#10257semidirect

Maximal subgroups

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

subgroupindex
#130799322
#130784212
#130695532
#130670702
#130670672
#130664902
C11×#30372
#1025711