Finite Group Databasebeta

← #14655761

Subgroups — #14655761

Order 2816.

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

normal subgroups only

This group has 562 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#13079543C211yesmaximal, characteristic, complemented
2C2×#10622621C211yesmaximal, characteristic, complemented
3#13078080C211yesmaximal, characteristic
4#13067300C211yesmaximal, characteristic, complemented
5#13067016C211yesmaximal, characteristic, complemented
6#13066512C211yesmaximal, characteristic, complemented
7C11×#1460C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9C2×#66985—21no—
10#10623008C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C2×#66896—21no—
15#10622632—21no—
16#10622629—22no—
17#10622628—21no—
18#10622621—22no—
19#10622621—22no—
20#10622579—21no—
21C2×#66872—21no—
22#10622537C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622454—22no—
25#10622351—22no—
26#10622306—21no—
27#10622294—21no—
28C11×#323—22no—
29#10622120—22no—
30#10622097—22no—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11—21no—
33C2×#4339—21no—
34C22×Dic22—21no—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C4×D4×C11—21no—
38C4×D4×C11—21no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C42×C11C2311yescharacteristic
42C2×#4324—22no—
43#66985—42no—
44#66985—42no—
45C2×#4323—22no—
46#66983—21no—
47#66983—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—21no—
50C2×#4318—21no—
51C22×C11⋊C8—21no—
52C2×#4314—24no—
53#66928—21no—
54#66927D411yescharacteristic
55C4×D44—21no—
56C4×D44—21no—
57#66922—21no—
58#66922—21no—
59#66922—21no—
60#66922D412yes—
61#66922D411yescharacteristic
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C22⋊C8—21no—
65C11×C22⋊C8D412yes—
66C4×C8×C11—21no—
67C4×C8×C11—21no—
68#66896—24no—
69#66880—24no—
70#66874—22no—
71#66873—22no—
72#66872—24no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)D412yes—
76C4⋊(C11⋊C8)D412yes—
77#10180—111nomaximal, Sylow
78C24×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11SD1612yescomplemented
85C22×C4×C11—21no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—82no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C2×C22⋊D11—41no—
93C22×Dic11—41no—
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—22no—
104C2×Dic22—41no—
105C2×Dic22—82no—
106C2×C8×C11—22no—
107C2×C8×C11—41no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116#4324—44no—
117#4323—44no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—41no—
120C4⋊Dic11—22no—
121C4⋊Dic11—21no—
122C4⋊Dic11—22no—
123C4⋊Dic11—21no—
124C4⋊Dic11—41no—
125C4⋊Dic11—41no—
126#4318—41no—
127#4318—41no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132#4314—84no—
133#3206—111no—
134C2×#476—111no—
135#3036—111no—
136#1549—111no—
137#1480—111no—
138#1460D1111yescharacteristic, complemented
139#1301—111no—
140C23×C11—22no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—81no—
144C23×C11—81no—
145C23×C11#12111yescharacteristic
146C22×D11—41no—
147D4×C11—22no—
148D4×C11—22no—
149D4×C11—41no—
150D4×C11—41no—
151C2×C4×C11—22no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—82no—
155C2×C4×C11—82no—
156C2×C4×C11—81no—
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12711yescharacteristic
163C2×C4×C11C2×SD1611yescharacteristic
164C2×C4×C11#13511yescharacteristic
165C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C11#13711yescharacteristic
167C22⋊D11—81no—
168C22⋊D11—81no—
169C2×Dic11—42no—
170C2×Dic11—41no—
171C2×Dic11—82no—
172D44—42no—
173D44—41no—
174D44—41no—
175D44—42no—
176C4×D11—81no—
177C4×D11—81no—
178Dic22—44no—
179Dic22—41no—
180Dic22—41no—
181Dic22—82no—
182C8×C11—42no—
183C8×C11—81no—
184C11⋊C8—42no—
185C11⋊C8—42no—
186C2×AGL(1,ℤ/8)—221no—
187#532—111no—
188C2×C4⋊Q8—111no—
189C2×C4×D4C2×D1111yescharacteristic
190#492—221no—
191#487—221no—
192#476—222no—
193#476—222no—
194#463—222no—
195#461—222no—
196#461—221no—
197#459—221no—
198#448—222no—
199#431C2×D1111yescharacteristic
200#431C2×D1111yescharacteristic
201C2×#106—221no—
202#423—111no—
203C2×C4⋊C8—111no—
204#417—221no—
205C2×#102—221no—
206#332—222no—
207D4⋊C8—222no—
208#323—22no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—42no—
212C22×C11—82no—
213C22×C11—82no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11#39211yescharacteristic
217C22×C11#46511yescharacteristic
218C22×C11#46811yescharacteristic
219C2×D11—81no—
220C2×D11—81no—
221C2×D11—81no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—81no—
226C4×C11#44811yescharacteristic
227C4×C11#44911yescharacteristic
228C4×C11#45011yescharacteristic
229C4×C11#45211yescharacteristic
230C4×C11#47112yes—
231Dic11—81no—
232Dic11—82no—
233C2×#41—221no—
234C22×Q8—221no—
235C22×D4D4411yescharacteristic
236C23×C4—21no—
237AGL(1,ℤ/8)—442no—
238AGL(1,ℤ/8)—442no—
239C2×SD16—224no—
240C2×SD16—222no—
241C2×D8—222no—
242C2×M16—221no—
243C22×C8—221no—
244C4⋊Q8—112no—
245C4⋊Q8—111no—
246C4⋊Q8—221no—
247C4⋊Q8—221no—
248C4⋊Q8—221no—
249#127—111no—
250#124—221no—
251#121—221no—
252#121—221no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4—21no—
256C4×D4—21no—
257C4×D4—221no—
258C4×D4—221no—
259C2×C4⋊C4—221no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4D4411yescharacteristic
262C2×C22⋊C4—21no—
263C2×C42C22×D1111yescharacteristic
264#106—224no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—112no—
268C4⋊C8—112no—
269C4⋊C8—221no—
270C4⋊C8—221no—
271#103—222no—
272#103—224no—
273#102—222no—
274#102—224no—
275C22⋊C8—21no—
276C22⋊C8C22⋊D1112yes—
277C4×C8—21no—
278C4×C8—21no—
279C2×C11—21no—
280C2×C11—21no—
281C2×C11—82no—
282C2×C11#200011yescharacteristic
283C2×C11#200811yescharacteristic
284C2×C11#201911yescharacteristic
285D11—161no—
286C24—21no—
287#41—441no—
288#41—441no—
289#41—441no—
290#41—441no—
291C2×Q8—221no—
292C2×Q8—222no—
293C2×Q8—441no—
294C2×Q8—882no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—221no—
301C2×D4—221no—
302C2×D4—221no—
303C2×D4—441no—
304C2×D4#431412yescomplemented
305C22×C4—21no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—82no—
309C22×C4—441no—
310C22×C4—441no—
311C22×C4C2×D4411yescharacteristic
312C22×C4#433911yescharacteristic
313C22×C4C2×C22⋊D1111yescharacteristic
314SD16—444no—
315SD16—884no—
316D8—444no—
317M16—441no—
318M16—441no—
319C2×C8—22no—
320C2×C8—41no—
321C2×C8—222no—
322C2×C8—222no—
323C2×C8—441no—
324C2×C8—441no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—222no—
328C4⋊C4—222no—
329C4⋊C4—221no—
330C4⋊C4—221no—
331C4⋊C4—441no—
332C4⋊C4—441no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—441no—
336C22⋊C4—441no—
337C42D4×D1111yescharacteristic
338C42D4×D1111yescharacteristic
339C42D4×D1111yescharacteristic
340C42D4×D1111yescharacteristic
341C11#1018011yescharacteristic, complemented, Sylow
342C23—22no—
343C23—41no—
344C23—41no—
345C23—81no—
346C23—81no—
347C23—441no—
348C23#6698311yescharacteristic
349Q8—444no—
350Q8—441no—
351Q8—441no—
352Q8—882no—
353D4—22no—
354D4—22no—
355D4—41no—
356D4—41no—
357D4—442no—
358D4—441no—
359D4—441no—
360D4—442no—
361D4—881no—
362D4—881no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—82no—
367C2×C4—82no—
368C2×C4—81no—
369C2×C4—441no—
370C2×C4—442no—
371C2×C4—882no—
372C2×C4—881no—
373C2×C4—881no—
374C2×C4#6693511yescharacteristic
375C2×C4#6693511yescharacteristic
376C2×C4#6693711yescharacteristic
377C2×C4#6693711yescharacteristic
378C2×C4C2×#431411yescharacteristic
379C2×C4#6695711yescharacteristic
380C2×C4#6696111yescharacteristic
381C2×C4#6696211yescharacteristic
382C2×C4#6699011yescharacteristic
383C2×C4#6699311yescharacteristic
384C8—42no—
385C8—81no—
386C8—442no—
387C8—442no—
388C22—21no—
389C22—21no—
390C22—42no—
391C22—82no—
392C22—82no—
393C22—81no—
394C22—81no—
395C22—881no—
396C22—881no—
397C22—881no—
398C22#1062257311yescharacteristic
399C22#1062272711yescharacteristic
400C22#1062274711yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—81no—
405C4—881no—
406C4—882no—
407C4#1062234411yescharacteristic
408C4#1062234611yescharacteristic
409C4#1062234711yescharacteristic
410C4#1062235111yescharacteristic
411C4#1062236112yes—
412C2—21no—
413C2—21no—
414C2—82no—
415C2—1761no—
416C2#1306962111yescharacteristic
417C2#1306966811yescharacteristic
418C2#1306973211yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1460C2
socleC22×C11#392
prime radical#13078080C2
hypercenter#1460D11
hypocenterC11#10180
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
1. #13079543C2semidirect
2. C2×#10622621C2semidirect
4. #13067300C2semidirect
5. #13067016C2semidirect
6. #13066512C2semidirect
7. C11×#1460C2semidirect
84. C2×D4×C11SD16semidirect
138. #1460D11semidirect
304. C2×D4#4314semidirect
341. C11#10180semidirect

Maximal subgroups

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

subgroupindex
#130795432
C2×#106226212
#130780802
#130673002
#130670162
#130665122
C11×#14602
#1018011