Finite Group Databasebeta

← #14656167

Subgroups — #14656167

Order 2816.

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

normal subgroups only

This group has 578 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#13079734C211yesmaximal, characteristic
2#13078084C211yesmaximal, characteristic
3#13073604C211yesmaximal, characteristic, complemented
4#13067287C211yesmaximal, characteristic, complemented
5#13067012C211yesmaximal, characteristic, complemented
6#13066519C211yesmaximal, characteristic, complemented
7C11×#1502C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#67004—21no—
10C2×#66922—21no—
11C2×#66922C2211yescharacteristic
12C2×C4×Dic22C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C4×C11×C4⋊C4C2211yescharacteristic
15#10622845—21no—
16#10622703—21no—
17#10622691—21no—
18#10622688—21no—
19#10622683—21no—
20#10622667—22no—
21#10622646—22no—
22#10622620—22no—
23#10622598—22no—
24#10622542—21no—
25#10622538C2211yescharacteristic
26#10622537C2211yescharacteristic
27#10622274—22no—
28C11×#327—22no—
29#10622124—22no—
30#10622094—22no—
31C2×C11×#41—21no—
32C22×Dic22—21no—
33C22×Dic22D411yescharacteristic
34C11×C4⋊Q8D411yescharacteristic
35C11×#127D411yescharacteristic
36C11×#124—21no—
37C11×#121—21no—
38C11×#121—21no—
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C2×C11×C4⋊C4—21no—
42C2×C42×C11—21no—
43C2×C42×C11C2311yescharacteristic
44#67004—42no—
45#67004—42no—
46C2×#4326—22no—
47C2×#4324—22no—
48C2×C4⋊Dic11—24no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11D411yescharacteristic
51C2×C4⋊Dic11D412yes—
52C2×Dic11⋊C4—21no—
53C2×C4×Dic11—21no—
54C2×#4318—21no—
55#66922—21no—
56#66922—21no—
57#66922—21no—
58#66922—21no—
59#66922—42no—
60#66922—42no—
61C4×Dic22—21no—
62C4×Dic22—21no—
63C4×Dic22—21no—
64C4×Dic22—21no—
65C11×C4⋊C8—21no—
66C11×C22⋊C8—21no—
67C4×C8×C11—21no—
68C11×#95D412yes—
69#66899—22no—
70#66896—22no—
71#66896—24no—
72C11⋊#95—24no—
73C22⋊(C11⋊C8)—21no—
74#66871—24no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)D412yes—
77C4⋊(C11⋊C8)D412yes—
78C4×C11⋊C8—21no—
79#10243—111nomaximal, Sylow
80C11×#41—41no—
81C11×#41—41no—
82C11×#41—41no—
83C11×#41—41no—
84C2×Q8×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—41no—
89C22×C4×C11—22no—
90C22×C4×C11—41no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—22no—
97C2×Dic22—21no—
98C2×Dic22—21no—
99C2×Dic22—21no—
100C2×Dic22—21no—
101C2×Dic22—21no—
102C2×Dic22—41no—
103C2×Dic22—41no—
104C2×Dic22—41no—
105C2×Dic22—41no—
106C2×Dic22—41no—
107C2×Dic22—41no—
108C2×Dic22D812yes—
109C2×C8×C11—41no—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C42×C11—41no—
116C42×C11—41no—
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11#4111yescharacteristic
121#4326—44no—
122#4324—44no—
123C4⋊Dic11—22no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11—22no—
127C4⋊Dic11—48no—
128C4⋊Dic11—41no—
129C4⋊Dic11—41no—
130Dic11⋊C4—41no—
131Dic11⋊C4—41no—
132C4×Dic11—41no—
133C4×Dic11—41no—
134#4318—41no—
135#4318—41no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138#3226—111no—
139#3037—111no—
140#2546—111no—
141#1546—111no—
142#1502D1111yescharacteristic
143#1479—111no—
144#1303—111no—
145C23×C11—41no—
146C23×C11#12011yescharacteristic
147Q8×C11—41no—
148Q8×C11—41no—
149D4×C11—41no—
150D4×C11—41no—
151D4×C11—42no—
152D4×C11—81no—
153D4×C11—81no—
154D4×C11—81no—
155C2×C4×C11—22no—
156C2×C4×C11—24no—
157C2×C4×C11—41no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—81no—
162C2×C4×C11—81no—
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12711yescharacteristic
169C2×C4×C11C2×D811yescharacteristic
170C2×C4×C11#13511yescharacteristic
171C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
173C2×Dic11—22no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—42no—
177C2×Dic11—41no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181Dic22—22no—
182Dic22—22no—
183Dic22—41no—
184Dic22—41no—
185Dic22—81no—
186Dic22—81no—
187Dic22—81no—
188Dic22—81no—
189C8×C11—81no—
190C11⋊C8—42no—
191C11⋊C8—42no—
192C2×#137—221no—
193#532C2×D1111yescharacteristic
194C2×C4⋊Q8—111no—
195C2×C4⋊Q8—221no—
196C2×C4×Q8—111no—
197#500—221no—
198#486—221no—
199#480—222no—
200#474—222no—
201#464—222no—
202#462—221no—
203#460—221no—
204#431—111no—
205#431C2×D1111yescharacteristic
206#423—111no—
207#417—221no—
208#398—222no—
209#391—221no—
210#389—222no—
211C4×C4⋊C4C2×D1111yescharacteristic
212#332—222no—
213#327—22no—
214Q8⋊C8—222no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11#39211yescharacteristic
221C22×C11#44711yescharacteristic
222C22×C11#44911yescharacteristic
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—44no—
227C4×C11—81no—
228C4×C11#44711yescharacteristic
229C4×C11#44911yescharacteristic
230C4×C11#45612yes—
231C4×C11#46611yescharacteristic
232C4×C11#46911yescharacteristic
233Dic11—42no—
234Dic11—82no—
235Dic11—81no—
236C2×#41—21no—
237C22×Q8—111no—
238C22×Q8—221no—
239#137—442no—
240#137—442no—
241C2×Q16—222no—
242C2×SD16—222no—
243C2×M16—221no—
244C4⋊Q8—221no—
245C4⋊Q8—221no—
246C4⋊Q8—221no—
247C4⋊Q8—221no—
248C4⋊Q8—442no—
249C4⋊Q8—442no—
250C4⋊Q8D4411yescharacteristic
251#127D4411yescharacteristic
252#124—21no—
253#121—21no—
254#121—21no—
255C4×Q8—221no—
256C4×Q8—221no—
257C4×Q8—221no—
258C4×Q8—221no—
259C4×D4—21no—
260C4×D4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—111no—
263C2×C4⋊C4—112no—
264C2×C4⋊C4—224no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—221no—
267C2×C42—21no—
268C2×C42—221no—
269C2×C42C22×D1111yescharacteristic
270#107—224no—
271C4⋊C8—21no—
272C4⋊C8—112no—
273C4⋊C8—112no—
274C4⋊C8—221no—
275#103—222no—
276#102—222no—
277#102—224no—
278C22⋊C8—21no—
279C22⋊C8—221no—
280C4×C8—21no—
281C4×C8—221no—
282#95—224no—
283#95C22⋊D1112yes—
284C2×C11—21no—
285C2×C11—21no—
286C2×C11—161no—
287C2×C11#199911yescharacteristic
288C2×C11#200511yescharacteristic
289C2×C11#200911yescharacteristic
290#41—41no—
291#41—41no—
292#41—41no—
293#41—41no—
294C2×Q8—21no—
295C2×Q8—112no—
296C2×Q8—221no—
297C2×Q8—221no—
298C2×Q8—221no—
299C2×Q8—221no—
300C2×Q8—221no—
301C2×Q8—441no—
302C2×Q8—441no—
303C2×Q8—441no—
304C2×Q8—441no—
305C2×Q8—441no—
306C2×Q8—441no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—41no—
311C22×C4—22no—
312C22×C4—41no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—222no—
316C22×C4D4×D1111yescharacteristic
317C22×C4D4×D1111yescharacteristic
318C22×C4C2×C22⋊D1111yescharacteristic
319Q16—444no—
320SD16—444no—
321M16—441no—
322M16—441no—
323C2×C8—41no—
324C2×C8—222no—
325C2×C8—222no—
326C4⋊C4—24no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—221no—
330C4⋊C4—222no—
331C4⋊C4—221no—
332C4⋊C4—222no—
333C4⋊C4—448no—
334C4⋊C4—441no—
335C4⋊C4—441no—
336C4⋊C4—441no—
337C4⋊C4—441no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C42—41no—
341C42—41no—
342C42—441no—
343C42—441no—
344C42C2×D4411yescharacteristic
345C42#433911yescharacteristic
346C42D4×D1111yescharacteristic
347C42D4×D1111yescharacteristic
348C11#1024311yescharacteristic, complemented, Sylow
349C23—41no—
350C23#6699011yescharacteristic
351Q8—41no—
352Q8—41no—
353Q8—222no—
354Q8—222no—
355Q8—441no—
356Q8—441no—
357Q8—881no—
358Q8—881no—
359Q8—881no—
360Q8—881no—
361D4—41no—
362D4—41no—
363D4—42no—
364D4—81no—
365D4—81no—
366D4—81no—
367C2×C4—22no—
368C2×C4—24no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—222no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—442no—
379C2×C4—442no—
380C2×C4—442no—
381C2×C4—441no—
382C2×C4—442no—
383C2×C4#6693511yescharacteristic
384C2×C4#6693511yescharacteristic
385C2×C4#6693711yescharacteristic
386C2×C4#6693711yescharacteristic
387C2×C4D8×D1111yescharacteristic
388C2×C4#6696411yescharacteristic
389C2×C4#6696711yescharacteristic
390C2×C4#6696911yescharacteristic
391C2×C4#6698311yescharacteristic
392C2×C4#6699311yescharacteristic
393C8—81no—
394C8—442no—
395C8—442no—
396C22—21no—
397C22—21no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22#1062257311yescharacteristic
402C22#1062276911yescharacteristic
403C22#1062278511yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—44no—
408C4—81no—
409C4—442no—
410C4—882no—
411C4—881no—
412C4#1062238611yescharacteristic
413C4#1062238811yescharacteristic
414C4#1062239411yescharacteristic
415C4#1062239511yescharacteristic
416C4#1062243912yes—
417C2—21no—
418C2—21no—
419C2—161no—
420C2#1306961311yescharacteristic
421C2#1306965111yescharacteristic
422C2#1306967511yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1502C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#1502D11
hypocenterC11#10243
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1502

Complements

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

NH ≅ G/Ntype
3. #13073604C2semidirect
4. #13067287C2semidirect
5. #13067012C2semidirect
6. #13066519C2semidirect
348. C11#10243semidirect

Maximal subgroups

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

subgroupindex
#130797342
#130780842
#130736042
#130672872
#130670122
#130665192
C11×#15022
#1024311