Finite Group Databasebeta

← #14656174

Subgroups — #14656174

Order 2816.

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

normal subgroups only

This group has 554 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#13079538C211yesmaximal, characteristic
2#13078084C211yesmaximal, characteristic
3#13073831C211yesmaximal, characteristic, complemented
4#13067296C211yesmaximal, characteristic, complemented
5#13067012C211yesmaximal, characteristic, complemented
6#13066519C211yesmaximal, characteristic, complemented
7C11×#1502C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#67004—21no—
10C2×#66922C2211yescharacteristic
11C2×C4×Dic22C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C4×C11×C4⋊C4C2211yescharacteristic
14#10622845—21no—
15#10622706—21no—
16#10622703—21no—
17#10622689—21no—
18#10622688—21no—
19#10622667—22no—
20#10622653—22no—
21#10622632—22no—
22#10622587—22no—
23#10622549—21no—
24#10622542—21no—
25#10622538C2211yescharacteristic
26#10622537C2211yescharacteristic
27#10622272—22no—
28C11×#327—22no—
29#10622119—22no—
30#10622094—22no—
31C2×C11×#41—21no—
32C22×Dic22D411yescharacteristic
33C22×Dic22D412yes—
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×#4324—24no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11D411yescharacteristic
52C2×Dic11⋊C4—21no—
53C2×C4×Dic11—21no—
54C2×#4318—21no—
55#66922—21no—
56#66922—21no—
57#66922—21no—
58#66922—21no—
59C4×Dic22—21no—
60C4×Dic22—21no—
61C4×Dic22—21no—
62C4×Dic22—21no—
63C11×C4⋊C8—21no—
64C11×C22⋊C8—21no—
65C4×C8×C11—21no—
66C11×#95D412yes—
67#66899—22no—
68#66896—22no—
69C11⋊#95—24no—
70C11⋊#95—24no—
71C22⋊(C11⋊C8)—21no—
72#66874—24no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)D412yes—
75C4⋊(C11⋊C8)D412yes—
76C4×C11⋊C8—21no—
77#10244—111nomaximal, Sylow
78C11×#41—41no—
79C11×#41—41no—
80C11×#41—41no—
81C11×#41—41no—
82C2×Q8×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—41no—
87C22×C4×C11—22no—
88C22×C4×C11—41no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11—22no—
95C2×Dic22—21no—
96C2×Dic22—22no—
97C2×Dic22—21no—
98C2×Dic22—22no—
99C2×Dic22—21no—
100C2×Dic22—21no—
101C2×Dic22—21no—
102C2×Dic22—44no—
103C2×Dic22SD1612yescomplemented
104C2×C8×C11—41no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—42no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C42×C11—41no—
111C42×C11—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116#4326—44no—
117#4324—44no—
118#4324—84no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123C4⋊Dic11—41no—
124C4⋊Dic11—41no—
125Dic11⋊C4—41no—
126Dic11⋊C4—41no—
127C4×Dic11—41no—
128C4×Dic11—41no—
129#4318—41no—
130#4318—41no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133#3206—111no—
134#3037—111no—
135#2568—111no—
136#1548—111no—
137#1502D1111yescharacteristic
138#1479—111no—
139#1303—111no—
140C23×C11—41no—
141C23×C11#12011yescharacteristic
142Q8×C11—41no—
143Q8×C11—41no—
144D4×C11—41no—
145D4×C11—41no—
146D4×C11—42no—
147D4×C11—81no—
148D4×C11—81no—
149D4×C11—81no—
150C2×C4×C11—22no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—41no—
155C2×C4×C11—42no—
156C2×C4×C11—81no—
157C2×C4×C11—81no—
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×SD1611yescharacteristic
165C2×C4×C11#13511yescharacteristic
166C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C11#13711yescharacteristic
168C2×Dic11—22no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—44no—
172C2×Dic11—42no—
173C2×Dic11—41no—
174C2×Dic11—42no—
175Dic22—22no—
176Dic22—22no—
177Dic22—41no—
178Dic22—41no—
179Dic22—44no—
180Dic22—82no—
181C8×C11—81no—
182C11⋊C8—42no—
183C11⋊C8—42no—
184C2×#137—221no—
185#532C2×D1111yescharacteristic
186C2×C4⋊Q8—111no—
187C2×C4×Q8—111no—
188#492—221no—
189#487—221no—
190#464—222no—
191#462—221no—
192#461—222no—
193#460—221no—
194#448—222no—
195#431—111no—
196#431C2×D1111yescharacteristic
197#423—111no—
198#417—221no—
199#400—222no—
200#391—221no—
201#391—222no—
202#382—221no—
203C4×C4⋊C4C2×D1111yescharacteristic
204#333—222no—
205#327—22no—
206Q8⋊C8—222no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—81no—
210C22×C11—81no—
211C22×C11—81no—
212C22×C11#39211yescharacteristic
213C22×C11#44811yescharacteristic
214C22×C11#44911yescharacteristic
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—82no—
219C4×C11—81no—
220C4×C11#45011yescharacteristic
221C4×C11#45211yescharacteristic
222C4×C11#45512yes—
223C4×C11#46511yescharacteristic
224C4×C11#46811yescharacteristic
225Dic11—42no—
226Dic11—82no—
227Dic11—81no—
228C2×#41—21no—
229C22×Q8—111no—
230C22×Q8—112no—
231#137—442no—
232#137—442no—
233C2×Q16—222no—
234C2×SD16—222no—
235C2×SD16—224no—
236C2×M16—221no—
237C4⋊Q8—221no—
238C4⋊Q8—221no—
239C4⋊Q8—221no—
240C4⋊Q8—221no—
241C4⋊Q8D4411yescharacteristic
242#127D4411yescharacteristic
243#124—21no—
244#121—21no—
245#121—21no—
246C4×Q8—221no—
247C4×Q8—221no—
248C4×Q8—221no—
249C4×Q8—221no—
250C4×D4—21no—
251C4×D4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—111no—
254C2×C4⋊C4—221no—
255C2×C4⋊C4—221no—
256C2×C4⋊C4—221no—
257C2×C42—21no—
258C2×C42—221no—
259C2×C42C22×D1111yescharacteristic
260C4⋊C8—21no—
261C4⋊C8—112no—
262C4⋊C8—112no—
263C4⋊C8—221no—
264#103—224no—
265#103—222no—
266#102—222no—
267C22⋊C8—21no—
268C22⋊C8—221no—
269C4×C8—21no—
270C4×C8—221no—
271#95—224no—
272#95—224no—
273#95C22⋊D1112yes—
274C2×C11—21no—
275C2×C11—21no—
276C2×C11—161no—
277C2×C11#200011yescharacteristic
278C2×C11#200411yescharacteristic
279C2×C11#200911yescharacteristic
280#41—41no—
281#41—41no—
282#41—41no—
283#41—41no—
284C2×Q8—21no—
285C2×Q8—112no—
286C2×Q8—221no—
287C2×Q8—221no—
288C2×Q8—222no—
289C2×Q8—221no—
290C2×Q8—222no—
291C2×Q8—221no—
292C2×Q8—221no—
293C2×Q8—444no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C22×C4—22no—
299C22×C4—41no—
300C22×C4—221no—
301C22×C4—221no—
302C22×C4—222no—
303C22×C4D4×D1111yescharacteristic
304C22×C4D4×D1111yescharacteristic
305C22×C4C2×C22⋊D1111yescharacteristic
306Q16—444no—
307SD16—444no—
308SD16—884no—
309M16—441no—
310M16—441no—
311C2×C8—41no—
312C2×C8—222no—
313C2×C8—222no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—42no—
317C4⋊C4—221no—
318C4⋊C4—221no—
319C4⋊C4—441no—
320C4⋊C4—441no—
321C4⋊C4—441no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C4⋊C4—441no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C42—41no—
328C42—41no—
329C42—441no—
330C42—441no—
331C42C2×D4411yescharacteristic
332C42#433911yescharacteristic
333C42D4×D1111yescharacteristic
334C42D4×D1111yescharacteristic
335C11#1024411yescharacteristic, complemented, Sylow
336C23—41no—
337C23#6699011yescharacteristic
338Q8—41no—
339Q8—41no—
340Q8—222no—
341Q8—222no—
342Q8—441no—
343Q8—441no—
344Q8—444no—
345Q8—882no—
346D4—41no—
347D4—41no—
348D4—42no—
349D4—81no—
350D4—81no—
351D4—81no—
352C2×C4—22no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—222no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—444no—
364C2×C4—442no—
365C2×C4—441no—
366C2×C4—442no—
367C2×C4#6693511yescharacteristic
368C2×C4#6693511yescharacteristic
369C2×C4#6693711yescharacteristic
370C2×C4#6693711yescharacteristic
371C2×C4#6696411yescharacteristic
372C2×C4#6696511yescharacteristic
373C2×C4SD16×D1111yescharacteristic
374C2×C4#6696811yescharacteristic
375C2×C4#6698311yescharacteristic
376C2×C4#6699311yescharacteristic
377C8—81no—
378C8—442no—
379C8—442no—
380C22—21no—
381C22—21no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22#1062257311yescharacteristic
386C22#1062277111yescharacteristic
387C22#1062278311yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—82no—
392C4—81no—
393C4—442no—
394C4—882no—
395C4—881no—
396C4#1062238911yescharacteristic
397C4#1062239111yescharacteristic
398C4#1062239311yescharacteristic
399C4#1062239611yescharacteristic
400C4#1062243812yes—
401C2—21no—
402C2—21no—
403C2—161no—
404C2#1306962011yescharacteristic
405C2#1306964411yescharacteristic
406C2#1306967511yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1502C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#1502D11
hypocenterC11#10244
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. #13073831C2semidirect
4. #13067296C2semidirect
5. #13067012C2semidirect
6. #13066519C2semidirect
103. C2×Dic22SD16semidirect
335. C11#10244semidirect

Maximal subgroups

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

subgroupindex
#130795382
#130780842
#130738312
#130672962
#130670122
#130665192
C11×#15022
#1024411