Finite Group Databasebeta

← #14656169

Subgroups — #14656169

Order 2816.

578 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079739C211yesmaximal, characteristic
2#13078088C211yesmaximal, characteristic
3#13073601C211yesmaximal, characteristic, complemented
4#13067287C211yesmaximal, characteristic, complemented
5#13067112C211yesmaximal, characteristic
6#13066518C211yesmaximal, characteristic, complemented
7C11×#1479C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#66997—21no—
10C2×#66995—21no—
11#10623008C2211yescharacteristic
12C2×#66922C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C11×#431C2211yescharacteristic
15#10622644—21no—
16#10622641—22no—
17#10622640—21no—
18#10622596—22no—
19#10622587—21no—
20#10622579—21no—
21C4×C4⋊Dic11C2211yescharacteristic
22#10622541—22no—
23#10622537C2211yescharacteristic
24#10622459—22no—
25#10622349—22no—
26#10622307—21no—
27#10622295—21no—
28C11×Q8⋊C8—22no—
29#10622124—22no—
30#10622108—22no—
31C22×Q8×C11D411yescharacteristic
32C2×#4339—21no—
33C22×Dic22—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C42×C11—21no—
41C2×C42×C11C2311yescharacteristic
42#66997—42no—
43#66997—42no—
44C2×#4326—22no—
45#66995—42no—
46#66995—42no—
47C2×#4325—22no—
48#66983—21no—
49#66983—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11D412yes—
53C2×Dic11⋊C4—24no—
54C2×C4×Dic11—21no—
55C2×#4318—21no—
56#66928—21no—
57#66927D411yescharacteristic
58C4×D44—21no—
59C4×D44—21no—
60#66922—21no—
61#66922—21no—
62#66922—21no—
63#66922—21no—
64#66922D411yescharacteristic
65C11×C4⋊C8—21no—
66C11×C4⋊C8D412yes—
67C11×C22⋊C8—21no—
68C11×C22⋊C8—21no—
69C4×C8×C11—21no—
70C4×C8×C11—21no—
71C11⋊#95—24no—
72C11⋊#95D412yes—
73#66885—24no—
74#66882—24no—
75#66874—22no—
76#66873—22no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)D412yes—
79#10243—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11D812yes—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C2×C22⋊D11—41no—
92C22×Dic11—22no—
93C22×Dic11—22no—
94#4339—41no—
95#4339—41no—
96#4339—41no—
97#4339—41no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44—21no—
101C2×C4×D11—41no—
102C2×Dic22—21no—
103C2×Dic22—41no—
104C2×Dic22—41no—
105C2×Dic22—41no—
106C2×Dic22—41no—
107C2×Dic22—41no—
108C2×Dic22—41no—
109C2×C8×C11—22no—
110C2×C8×C11—41no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C42×C11—41no—
116C42×C11—41no—
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11#4111yescharacteristic
121#4326—44no—
122#4325—44no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—41no—
125C4⋊Dic11—24no—
126C4⋊Dic11—21no—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11—21no—
130C4⋊Dic11—41no—
131C4⋊Dic11—41no—
132Dic11⋊C4—48no—
133C4×Dic11—41no—
134C4×Dic11—41no—
135#4318—41no—
136#4318—41no—
137C2×C11⋊C8—22no—
138#3226—111no—
139#3037—111no—
140#2546—111no—
141#1546—111no—
142#1502—111no—
143#1479D1111yescharacteristic, complemented
144#1303—111no—
145C23×C11#12011yescharacteristic
146C22×D11—41no—
147Q8×C11—22no—
148Q8×C11—22no—
149Q8×C11—41no—
150Q8×C11—41no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12711yescharacteristic
164C2×C4×C11C2×D811yescharacteristic
165C2×C4×C11#13511yescharacteristic
166C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
168C22⋊D11—81no—
169C22⋊D11—81no—
170C2×Dic11—24no—
171C2×Dic11—42no—
172C2×Dic11—42no—
173C2×Dic11—42no—
174C2×Dic11—41no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177D44—41no—
178D44—41no—
179D44—42no—
180D44—81no—
181C4×D11—81no—
182C4×D11—81no—
183Dic22—41no—
184Dic22—41no—
185Dic22—81no—
186Dic22—81no—
187Dic22—81no—
188Dic22—81no—
189C8×C11—42no—
190C8×C11—81no—
191C11⋊C8—42no—
192C2×#137—221no—
193#532—111no—
194C2×C4⋊Q8—111no—
195C2×C4⋊Q8—221no—
196C2×C4×Q8C2×D1111yescharacteristic
197#500—221no—
198#486—221no—
199#480—222no—
200#474—222no—
201#464—222no—
202#462—221no—
203#460—221no—
204#431C2×D1111yescharacteristic
205#431C2×D1111yescharacteristic
206#423—111no—
207#417—221no—
208#398—222no—
209#391—221no—
210#389—222no—
211C4×C4⋊C4—111no—
212#332—222no—
213#327—222no—
214Q8⋊C8—22no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11#39211yescharacteristic
218C22×C11#44711yescharacteristic
219C22×C11#44911yescharacteristic
220C2×D11—81no—
221C2×D11—81no—
222C2×D11—81no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—42no—
227C4×C11—81no—
228C4×C11#44711yescharacteristic
229C4×C11#44911yescharacteristic
230C4×C11#45612yes—
231C4×C11#46611yescharacteristic
232C4×C11#46911yescharacteristic
233Dic11—44no—
234Dic11—81no—
235Dic11—82no—
236C2×#41—221no—
237C22×Q8—221no—
238C22×Q8D4411yescharacteristic
239#137—442no—
240#137—442no—
241C2×Q16—222no—
242C2×SD16—222no—
243C2×M16—221no—
244C4⋊Q8—111no—
245C4⋊Q8—221no—
246C4⋊Q8—221no—
247C4⋊Q8—221no—
248C4⋊Q8—221no—
249C4⋊Q8—442no—
250C4⋊Q8—442no—
251#127—111no—
252#124—221no—
253#121—221no—
254#121—221no—
255C4×Q8—21no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×D4—221no—
260C4×D4—221no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—112no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4—224no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4D4411yescharacteristic
267C2×C42—21no—
268C2×C42—221no—
269C2×C42C22×D1111yescharacteristic
270#107—224no—
271C4⋊C8—21no—
272C4⋊C8—112no—
273C4⋊C8—221no—
274C4⋊C8C22⋊D1112yes—
275#103—222no—
276#102—222no—
277#102—224no—
278C22⋊C8—21no—
279C22⋊C8—21no—
280C4×C8—21no—
281C4×C8—21no—
282#95—112no—
283#95—224no—
284C2×C11—21no—
285C2×C11—21no—
286C2×C11#199911yescharacteristic
287C2×C11#200511yescharacteristic
288C2×C11#200911yescharacteristic
289D11—161no—
290#41—441no—
291#41—441no—
292#41—441no—
293#41—441no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—221no—
300C2×Q8—441no—
301C2×Q8—441no—
302C2×Q8—441no—
303C2×Q8—441no—
304C2×Q8—441no—
305C2×Q8—441no—
306C2×Q8D8812yes—
307C2×D4—221no—
308C2×D4—221no—
309C2×D4—221no—
310C2×D4—441no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—222no—
314C22×C4—222no—
315C22×C4—441no—
316C22×C4C2×D4411yescharacteristic
317C22×C4D4×D1111yescharacteristic
318C22×C4D4×D1111yescharacteristic
319Q16—444no—
320SD16—444no—
321M16—441no—
322M16—441no—
323C2×C8—22no—
324C2×C8—41no—
325C2×C8—222no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—224no—
331C4⋊C4—222no—
332C4⋊C4—221no—
333C4⋊C4—222no—
334C4⋊C4—221no—
335C4⋊C4—448no—
336C4⋊C4—441no—
337C4⋊C4—441no—
338C22⋊C4—441no—
339C22⋊C4—441no—
340C42—41no—
341C42—41no—
342C42—441no—
343C42—441no—
344C42#433911yescharacteristic
345C42D4×D1111yescharacteristic
346C42D4×D1111yescharacteristic
347C42C2×C22⋊D1111yescharacteristic
348C11#1024311yescharacteristic, complemented, Sylow
349C23—441no—
350C23#6693511yescharacteristic
351Q8—22no—
352Q8—22no—
353Q8—41no—
354Q8—41no—
355Q8—441no—
356Q8—441no—
357Q8—881no—
358Q8—881no—
359Q8—881no—
360Q8—881no—
361D4—442no—
362D4—441no—
363D4—441no—
364D4—881no—
365D4—881no—
366D4—881no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—224no—
375C2×C4—442no—
376C2×C4—442no—
377C2×C4—441no—
378C2×C4—442no—
379C2×C4—442no—
380C2×C4—442no—
381C2×C4—881no—
382C2×C4—881no—
383C2×C4#6693511yescharacteristic
384C2×C4#6693711yescharacteristic
385C2×C4#6693711yescharacteristic
386C2×C4C2×D8811yescharacteristic
387C2×C4#6695711yescharacteristic
388C2×C4#6696111yescharacteristic
389C2×C4#6696111yescharacteristic
390C2×C4#6698311yescharacteristic
391C2×C4#6699011yescharacteristic
392C2×C4#6699311yescharacteristic
393C8—42no—
394C8—81no—
395C8—442no—
396C22—21no—
397C22—21no—
398C22—881no—
399C22—881no—
400C22—881no—
401C22#1062234511yescharacteristic
402C22#1062234711yescharacteristic
403C22#1062257311yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—42no—
408C4—81no—
409C4—444no—
410C4—882no—
411C4—881no—
412C4#1062234511yescharacteristic
413C4#1062234711yescharacteristic
414C4#1062272811yescharacteristic
415C4#1062274811yescharacteristic
416C4#1062281812yes—
417C2—21no—
418C2—21no—
419C2—1761no—
420C2#1306961411yescharacteristic
421C2#1306965311yescharacteristic
422C2#1306967711yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1479C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#1479D11
hypocenterC11#10243
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
3. #13073601C2semidirect
4. #13067287C2semidirect
6. #13066518C2semidirect
7. C11×#1479C2semidirect
143. #1479D11semidirect
348. C11#10243semidirect

Maximal subgroups

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

subgroupindex
#130797392
#130780882
#130736012
#130672872
#130671122
#130665182
C11×#14792
#1024311