Finite Group Databasebeta

← #14655796

Subgroups — #14655796

Order 2816.

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

normal subgroups only

This group has 550 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
3C2×#10622644C211yesmaximal, characteristic, complemented
4#13067287C211yesmaximal, characteristic, complemented
5#13067016C211yesmaximal, characteristic
6#13066512C211yesmaximal, characteristic, complemented
7C11×#1461C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C22×#4326—21no—
10C2×#66995—21no—
11#10623008C2211yescharacteristic
12C2×#66922C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C11×#431C2211yescharacteristic
15#10622644—22no—
16#10622644—21no—
17#10622644—22no—
18#10622641—22no—
19#10622640—21no—
20C2×#66874—21no—
21#10622579—21no—
22#10622537C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622459—22no—
25#10622349—22no—
26#10622307—21no—
27#10622295—21no—
28C11×#324—22no—
29#10622124—22no—
30#10622097—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
42C2×#4326—22no—
43C2×#4326—24no—
44C2×#4326—42no—
45C2×#4326—42no—
46#66995—42no—
47#66995—42no—
48C2×#4325—22no—
49#66983—21no—
50#66983—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×#4318—21no—
54C22×C11⋊C8—21no—
55#66928—21no—
56#66927D411yescharacteristic
57C4×D44—21no—
58C4×D44—21no—
59#66922—21no—
60#66922—21no—
61#66922—21no—
62#66922D412yes—
63#66922D411yescharacteristic
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C22⋊C8—21no—
67C11×C22⋊C8D412yes—
68C4×C8×C11—21no—
69C4×C8×C11—21no—
70#66885—24no—
71#66882—24no—
72#66874—22no—
73#66874—24no—
74#66873—22no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)D412yes—
78C4⋊(C11⋊C8)D412yes—
79#10185—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×C11#4111yescharacteristic
91C2×C22⋊D11—41no—
92C22×Dic11—41no—
93#4339—41no—
94#4339—41no—
95#4339—41no—
96#4339—41no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×C4×D11—41no—
101C2×Dic22—22no—
102C2×Dic22—21no—
103C2×Dic22—41no—
104C2×Dic22—41no—
105C2×Dic22—41no—
106C2×Dic22—41no—
107C2×Dic22—41no—
108C2×C8×C11—22no—
109C2×C8×C11—41no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C42×C11—41no—
115C42×C11—41no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120#4326—44no—
121#4326—48no—
122#4325—44no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—41no—
125C4⋊Dic11—21no—
126C4⋊Dic11—22no—
127C4⋊Dic11—22no—
128C4⋊Dic11—21no—
129C4⋊Dic11—41no—
130C4⋊Dic11—41no—
131#4318—41no—
132#4318—41no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—41no—
136C2×C11⋊C8—41no—
137#3226—111no—
138#3037—111no—
139C2×#462—111no—
140#1546—111no—
141#1480—111no—
142#1461D1111yescharacteristic, complemented
143#1301—111no—
144C23×C11#12111yescharacteristic
145C22×D11—41no—
146Q8×C11—22no—
147Q8×C11—22no—
148Q8×C11—41no—
149Q8×C11—41no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
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×D811yescharacteristic
164C2×C4×C11#13511yescharacteristic
165C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
167C22⋊D11—81no—
168C22⋊D11—81no—
169C2×Dic11—42no—
170C2×Dic11—41no—
171C2×Dic11—81no—
172C2×Dic11—81no—
173D44—42no—
174D44—41no—
175D44—41no—
176D44—42no—
177C4×D11—81no—
178C4×D11—81no—
179Dic22—42no—
180Dic22—41no—
181Dic22—42no—
182Dic22—41no—
183Dic22—81no—
184Dic22—81no—
185C8×C11—42no—
186C8×C11—81no—
187C11⋊C8—42no—
188C11⋊C8—42no—
189C2×#137—221no—
190C22×Q16—221no—
191#532—111no—
192C2×C4⋊Q8—111no—
193C2×C4×Q8C2×D1111yescharacteristic
194#500—221no—
195#486—221no—
196#480—222no—
197#474—222no—
198#464—222no—
199#462—222no—
200#462—222no—
201#462—221no—
202#460—221no—
203#431C2×D1111yescharacteristic
204#431C2×D1111yescharacteristic
205#423—111no—
206C2×C4⋊C8—111no—
207#417—221no—
208C2×#103—221no—
209#332—222no—
210D4⋊C8—222no—
211#324—22no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11#39211yescharacteristic
215C22×C11#46611yescharacteristic
216C22×C11#46911yescharacteristic
217C2×D11—81no—
218C2×D11—81no—
219C2×D11—81no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—42no—
224C4×C11—81no—
225C4×C11#44711yescharacteristic
226C4×C11#44711yescharacteristic
227C4×C11#44911yescharacteristic
228C4×C11#44911yescharacteristic
229C4×C11#47312yes—
230Dic11—82no—
231Dic11—81no—
232C2×#41—221no—
233C22×Q8—221no—
234C22×Q8D4411yescharacteristic
235#137—442no—
236#137—442no—
237C2×Q16—224no—
238C2×Q16—222no—
239C2×Q16—442no—
240C2×Q16—442no—
241C2×SD16—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×Q8—21no—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×Q8—21no—
257C4×D4—221no—
258C4×D4—221no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4—221no—
262C2×C4⋊C4D4411yescharacteristic
263C2×C42—21no—
264C2×C42C22×D1111yescharacteristic
265#107—224no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—112no—
269C4⋊C8—112no—
270C4⋊C8—221no—
271C4⋊C8—221no—
272#103—224no—
273#103—222no—
274#102—222no—
275#102—224no—
276C22⋊C8—21no—
277C22⋊C8C22⋊D1112yes—
278C4×C8—21no—
279C4×C8—21no—
280C2×C11—21no—
281C2×C11—21no—
282C2×C11#199911yescharacteristic
283C2×C11#200911yescharacteristic
284C2×C11#202011yescharacteristic
285D11—161no—
286#41—441no—
287#41—441no—
288#41—441no—
289#41—441no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—221no—
296C2×Q8—222no—
297C2×Q8—441no—
298C2×Q8—441no—
299C2×Q8—441no—
300C2×Q8—441no—
301C2×Q8—441no—
302C2×Q8D8812yes—
303C2×D4—221no—
304C2×D4—221no—
305C2×D4—221no—
306C2×D4—441no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—441no—
310C22×C4—441no—
311C22×C4C2×D4411yescharacteristic
312C22×C4#433911yescharacteristic
313C22×C4C2×C22⋊D1111yescharacteristic
314Q16—448no—
315Q16—444no—
316SD16—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—41no—
328C4⋊C4—41no—
329C4⋊C4—222no—
330C4⋊C4—221no—
331C4⋊C4—222no—
332C4⋊C4—221no—
333C4⋊C4—441no—
334C4⋊C4—441no—
335C22⋊C4—441no—
336C22⋊C4—441no—
337C42—41no—
338C42—41no—
339C42D4×D1111yescharacteristic
340C42D4×D1111yescharacteristic
341C42D4×D1111yescharacteristic
342C42D4×D1111yescharacteristic
343C11#1018511yescharacteristic, complemented, Sylow
344C23—441no—
345C23#6698311yescharacteristic
346Q8—22no—
347Q8—22no—
348Q8—41no—
349Q8—41no—
350Q8—442no—
351Q8—441no—
352Q8—442no—
353Q8—441no—
354Q8—881no—
355Q8—881no—
356D4—442no—
357D4—441no—
358D4—441no—
359D4—442no—
360D4—881no—
361D4—881no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—81no—
369C2×C4—441no—
370C2×C4—442no—
371C2×C4—881no—
372C2×C4—881no—
373C2×C4—881no—
374C2×C4—881no—
375C2×C4#6693511yescharacteristic
376C2×C4#6693511yescharacteristic
377C2×C4#6693711yescharacteristic
378C2×C4#6693711yescharacteristic
379C2×C4C2×D8811yescharacteristic
380C2×C4#6695711yescharacteristic
381C2×C4#6696111yescharacteristic
382C2×C4#6696111yescharacteristic
383C2×C4#6699011yescharacteristic
384C2×C4#6699311yescharacteristic
385C8—42no—
386C8—81no—
387C8—442no—
388C8—442no—
389C22—21no—
390C22—21no—
391C22—881no—
392C22—881no—
393C22—881no—
394C22#1062257311yescharacteristic
395C22#1062272811yescharacteristic
396C22#1062274811yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—42no—
401C4—81no—
402C4—881no—
403C4—882no—
404C4#1062234511yescharacteristic
405C4#1062234511yescharacteristic
406C4#1062234711yescharacteristic
407C4#1062234711yescharacteristic
408C4#1062236812yes—
409C2—21no—
410C2—21no—
411C2—1761no—
412C2#1306961411yescharacteristic
413C2#1306967511yescharacteristic
414C2#1306973611yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1461C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#1461D11
hypocenterC11#10185
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
3. C2×#10622644C2semidirect
4. #13067287C2semidirect
6. #13066512C2semidirect
7. C11×#1461C2semidirect
142. #1461D11semidirect
343. C11#10185semidirect

Maximal subgroups

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

subgroupindex
#130797392
#130780882
C2×#106226442
#130672872
#130670162
#130665122
C11×#14612
#1018511