Finite Group Databasebeta

← #14656137

Subgroups — #14656137

Order 2816.

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

normal subgroups only

This group has 610 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#13079734C211yesmaximal, characteristic, complemented
2#13073608C211yesmaximal, characteristic, complemented
3#13067289C211yesmaximal, characteristic, complemented
4#13067111C211yesmaximal, characteristic, complemented
5#13067007C211yesmaximal, characteristic, complemented
6#13066517C211yesmaximal, characteristic, complemented
7C11×#3036C211yesmaximal, characteristic
8C2×C11×AGL(1,ℤ/8)—21no—
9C11×#532C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66989—21no—
12C2×#66922C2211yescharacteristic
13C11×#463—22no—
14C11×#461—21no—
15C11×#459—21no—
16C11×#423C2211yescharacteristic
17C11×#417—21no—
18#10622825—22no—
19#10622691—21no—
20#10622683—21no—
21#10622646—22no—
22#10622620—22no—
23#10622587—21no—
24#10622566—22no—
25C4×C4⋊Dic11C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622538C2211yescharacteristic
28#10622175—22no—
29D4⋊(C11⋊C8)—22no—
30#10622120—22no—
31C2×C11×#41—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C22×Dic22—21no—
35C11×AGL(1,ℤ/8)—42no—
36C11×AGL(1,ℤ/8)—42no—
37C2×C11×SD16—22no—
38C2×C11×D8—22no—
39C2×C11×M16—21no—
40C11×C4⋊Q8D411yescharacteristic
41C11×#127D411yescharacteristic
42C11×#124—21no—
43C11×#121—21no—
44C11×#121—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C22⋊C4—21no—
53C2×C42×C11C2311yescharacteristic
54C2×C22⋊Dic11—24no—
55#66989—42no—
56#66989—42no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11D412yes—
60C2×C4×Dic11—21no—
61#66922—21no—
62#66922—21no—
63#66922—21no—
64#66922—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8D412yes—
67C11×#103—22no—
68C11×#102—22no—
69#66896—24no—
70C11⋊#95—24no—
71C11⋊#95D412yes—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74#66871—24no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)D412yes—
77C4×C11⋊C8—21no—
78C4×C11⋊C8—21no—
79#10239—111nomaximal, Sylow
80C24×C11—21no—
81C11×#41—41no—
82C11×#41—41no—
83C11×#41—41no—
84C11×#41—41no—
85C2×Q8×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—41no—
95C2×D4×C11D812yes—
96C22×C4×C11—21no—
97C22×C4×C11—44no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×Dic11—22no—
105C22×Dic11—22no—
106C2×Dic22—41no—
107C2×Dic22—41no—
108C2×Dic22—41no—
109C2×Dic22—41no—
110C2×Dic22—41no—
111C2×Dic22—41no—
112C11×SD16—44no—
113C11×D8—44no—
114C11×M16—41no—
115C11×M16—41no—
116C2×C8×C11—22no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11#4111yescharacteristic
129C22⋊Dic11—48no—
130C4⋊Dic11—22no—
131C4⋊Dic11—22no—
132C4⋊Dic11—42no—
133C4⋊Dic11—41no—
134C4⋊Dic11—41no—
135C4×Dic11—41no—
136C4×Dic11—41no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—41no—
139#3226—111no—
140#3036D1111yescharacteristic
141#2547—111no—
142#1546—111no—
143#1502—111no—
144#1478—111no—
145#1303—111no—
146C23×C11—22no—
147C23×C11—42no—
148C23×C11—42no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11#12011yescharacteristic
153Q8×C11—41no—
154Q8×C11—41no—
155D4×C11—22no—
156D4×C11—22no—
157D4×C11—41no—
158D4×C11—41no—
159D4×C11—41no—
160D4×C11—42no—
161D4×C11—41no—
162D4×C11—81no—
163D4×C11—81no—
164D4×C11—81no—
165C2×C4×C11—22no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—82no—
171C2×C4×C11—82no—
172C2×C4×C11—81no—
173C2×C4×C11—81no—
174C2×C4×C11#12011yescharacteristic
175C2×C4×C11#12011yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12711yescharacteristic
180C2×C4×C11C2×D811yescharacteristic
181C2×C4×C11#13511yescharacteristic
182C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190Dic22—81no—
191Dic22—81no—
192Dic22—81no—
193Dic22—81no—
194C8×C11—42no—
195C11⋊C8—42no—
196C11⋊C8—81no—
197C2×AGL(1,ℤ/8)—21no—
198#532C2×D1111yescharacteristic
199C2×C4⋊Q8—111no—
200C2×#124—221no—
201C2×C4×D4C2×D1111yescharacteristic
202#500—221no—
203#486—221no—
204#480—222no—
205#474—222no—
206#463—22no—
207#461—21no—
208#459—21no—
209#431—111no—
210#431—111no—
211#423C2×D1111yescharacteristic
212#417—21no—
213#397—222no—
214#391—221no—
215#380—222no—
216C4×C4⋊C4—111no—
217#332—222no—
218#327—222no—
219D4⋊C8—222no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—44no—
223C22×C11—42no—
224C22×C11—82no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11—81no—
228C22×C11—81no—
229C22×C11—81no—
230C22×C11#39211yescharacteristic
231C22×C11#44711yescharacteristic
232C22×C11#44911yescharacteristic
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—81no—
237C4×C11—81no—
238C4×C11#44711yescharacteristic
239C4×C11#44911yescharacteristic
240C4×C11#45412yes—
241C4×C11#46611yescharacteristic
242C4×C11#46911yescharacteristic
243Dic11—82no—
244Dic11—82no—
245C2×#41—21no—
246C22×Q8—221no—
247C22×D4C22⋊D1111yescharacteristic
248C23×C4—21no—
249AGL(1,ℤ/8)—42no—
250AGL(1,ℤ/8)—42no—
251C2×SD16—22no—
252C2×D8—22no—
253C2×M16—21no—
254C4⋊Q8—221no—
255C4⋊Q8—221no—
256C4⋊Q8—221no—
257C4⋊Q8—221no—
258C4⋊Q8C22⋊D1111yescharacteristic
259#127C22⋊D1111yescharacteristic
260#124—21no—
261#124—442no—
262#124—442no—
263#121—21no—
264#121—21no—
265C4×D4—21no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—21no—
271C2×C4⋊C4—112no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4—221no—
274C2×C4⋊C4C22⋊D1111yescharacteristic
275C2×C22⋊C4—21no—
276C2×C22⋊C4—224no—
277C2×C42—221no—
278C2×C42C22×D1111yescharacteristic
279#107—224no—
280C4⋊C8—21no—
281C4⋊C8—112no—
282C4⋊C8—221no—
283C4⋊C8C22⋊D1112yes—
284#103—22no—
285#102—22no—
286#102—224no—
287C22⋊C8—221no—
288C22⋊C8—221no—
289C4×C8—221no—
290C4×C8—221no—
291#95—112no—
292#95—224no—
293C2×C11—21no—
294C2×C11—21no—
295C2×C11—82no—
296C2×C11—161no—
297C2×C11#199911yescharacteristic
298C2×C11#200311yescharacteristic
299C2×C11#200911yescharacteristic
300C24—21no—
301#41—41no—
302#41—41no—
303#41—41no—
304#41—41no—
305C2×Q8—21no—
306C2×Q8—441no—
307C2×Q8—441no—
308C2×Q8—441no—
309C2×Q8—441no—
310C2×Q8—441no—
311C2×Q8—441no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—41no—
321C2×D4#432312yes—
322C22×C4—21no—
323C22×C4—44no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—222no—
328C22×C4—222no—
329C22×C4D4×D1111yescharacteristic
330C22×C4D4×D1111yescharacteristic
331C22×C4C2×C22⋊D1111yescharacteristic
332SD16—44no—
333D8—44no—
334M16—41no—
335M16—41no—
336C2×C8—22no—
337C2×C8—222no—
338C2×C8—441no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—222no—
344C4⋊C4—222no—
345C4⋊C4—442no—
346C4⋊C4—441no—
347C4⋊C4—441no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—448no—
353C42—441no—
354C42—441no—
355C42D4×D1111yescharacteristic
356C42#434111yescharacteristic
357C42C2×C22⋊D1111yescharacteristic
358C42C2×C22⋊D1111yescharacteristic
359C11#1023911yescharacteristic, complemented, Sylow
360C23—22no—
361C23—42no—
362C23—42no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23#6699011yescharacteristic
367Q8—41no—
368Q8—41no—
369Q8—881no—
370Q8—881no—
371Q8—881no—
372Q8—881no—
373D4—22no—
374D4—22no—
375D4—42no—
376D4—41no—
377D4—41no—
378D4—41no—
379D4—41no—
380D4—81no—
381D4—81no—
382D4—81no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—82no—
389C2×C4—82no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—442no—
393C2×C4—442no—
394C2×C4—442no—
395C2×C4—442no—
396C2×C4—442no—
397C2×C4—442no—
398C2×C4C2×#432311yescharacteristic
399C2×C4#6698511yescharacteristic
400C2×C4#6699011yescharacteristic
401C2×C4#6699111yescharacteristic
402C2×C4#6699211yescharacteristic
403C2×C4#6699211yescharacteristic
404C2×C4#6699311yescharacteristic
405C2×C4#6700211yescharacteristic
406C2×C4#6700311yescharacteristic
407C2×C4#6700611yescharacteristic
408C8—42no—
409C8—442no—
410C8—881no—
411C22—21no—
412C22—21no—
413C22—44no—
414C22—42no—
415C22—82no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22#1062264911yescharacteristic
422C22#1062265011yescharacteristic
423C22#1062283611yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—81no—
428C4—81no—
429C4—882no—
430C4—882no—
431C4#1062265111yescharacteristic
432C4#1062265211yescharacteristic
433C4#1062281412yes—
434C4#1062283011yescharacteristic
435C4#1062285111yescharacteristic
436C2—21no—
437C2—21no—
438C2—82no—
439C2—161no—
440C2#1306961211yescharacteristic
441C2#1306963511yescharacteristic
442C2#1306967311yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3036C2
socleC22×C11#392
hypercenter#3036D11
hypocenterC11#10239
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #13079734C2semidirect
2. #13073608C2semidirect
3. #13067289C2semidirect
4. #13067111C2semidirect
5. #13067007C2semidirect
6. #13066517C2semidirect
359. C11#10239semidirect

Maximal subgroups

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

subgroupindex
#130797342
#130736082
#130672892
#130671112
#130670072
#130665172
C11×#30362
#1023911