Finite Group Databasebeta

← #14666654

Subgroups — #14666654

Order 2816.

422 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 55 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#13076700C211yesmaximal, characteristic
2#13069968C211yesmaximal, characteristic, complemented
3#13067539C211yesmaximal, characteristic
4#13066637C211yesmaximal, characteristic, complemented
5#13066614C211yesmaximal, characteristic
6#13066565C211yesmaximal, characteristic, complemented
7C11×#1602C211yesmaximal, characteristic, complemented
8C11×#543C2211yescharacteristic
9C11×#451—21no—
10C11×#393C2211yescharacteristic
11#10622844—21no—
12#10622659—21no—
13#10622574—21no—
14#10622573C2211yescharacteristic
15#10622571—21no—
16#10622559—21no—
17#10622559C2211yescharacteristic
18#10622287—21no—
19#10622285—21no—
20#10622273—21no—
21C11×#328—21no—
22C11×#323C2211yescharacteristic
23#10622176—21no—
24#10622164—21no—
25#10622164C2211yescharacteristic
26#10622163C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×C22⋊D11—21no—
29C23×Dic11D411yescharacteristic
30C22×D44D411yescharacteristic
31C2×C11×Q16—41no—
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8—21no—
34C11×C22⋊Q8—41no—
35C11×C22⋊Q8—41no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4C2311yescharacteristic
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11D411yescharacteristic
41C2×#4325—41no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×C4⋊Dic11—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—41no—
50C11×#103—41no—
51C11×C22⋊C8—21no—
52C11×#95—21no—
53C11×#95D411yescharacteristic
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—41no—
59C11⋊#95D411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61#66873—41no—
62#12230—111nomaximal, Sylow
63C24×C11C2×D411yescharacteristic
64C23×D11—21no—
65C2×Q8×C11—21no—
66C2×Q8×C11—21no—
67C2×Q8×C11—41no—
68C2×Q8×C11—81no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C2×C22⋊D11—41no—
76C2×C22⋊D11—41no—
77C2×C22⋊D11—81no—
78C2×C22⋊D11—81no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—41no—
83C22×Dic11—41no—
84C22×Dic11—81no—
85C2×D44—41no—
86C2×D44—81no—
87C11×Q16—82no—
88C2×C8×C11—41no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—81no—
97C22⋊Dic11—22no—
98C22⋊Dic11—21no—
99C22⋊Dic11—21no—
100C22⋊Dic11—41no—
101#4325—82no—
102(C2×D11)⋊C4—81no—
103(C2×D11)⋊C4—81no—
104(C2×D11)⋊C4—81no—
105(C2×D11)⋊C4—81no—
106(C2×D11)⋊C4—81no—
107C4⋊Dic11—81no—
108Dic11⋊C4—81no—
109Dic11⋊C4—82no—
110C2×C11⋊C8—41no—
111#2824—111no—
112#2062—111no—
113#1602D1111yescharacteristic, complemented
114#1596—111no—
115#1351—111no—
116#1343—111no—
117#1326—111no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11#12011yescharacteristic
123C23×C11#13511yescharacteristic
124C23×C11#13711yescharacteristic
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132Q8×C11—42no—
133Q8×C11—81no—
134Q8×C11—81no—
135Q8×C11—81no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—81no—
149C2×C4×C11—81no—
150C22⋊D11—82no—
151C22⋊D11—82no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—81no—
164C2×Dic11—81no—
165C2×Dic11—81no—
166D44—42no—
167D44—81no—
168C8×C11—81no—
169C11⋊C8—81no—
170#543C2×D1111yescharacteristic
171#451—21no—
172#450—221no—
173#400—221no—
174#397—221no—
175#394—221no—
176#394—221no—
177#393—221no—
178#393C2×D1111yescharacteristic
179#392—111no—
180#386—221no—
181#385—111no—
182#385—221no—
183#342—111no—
184#342—221no—
185#328—21no—
186#328—221no—
187#323—111no—
188#323C2×D1111yescharacteristic
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—81no—
198C22×C11#45211yescharacteristic
199C22×C11#45611yescharacteristic
200C22×C11B(4,𝔽2)11yescharacteristic
201C2×D11—81no—
202C2×D11—81no—
203C2×D11—81no—
204C2×D11—81no—
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—81no—
208C4×C11—41no—
209C4×C11—41no—
210C4×C11—81no—
211C4×C11—81no—
212C4×C11—81no—
213C4×C11—81no—
214Dic11—81no—
215Dic11—81no—
216Dic11—82no—
217Dic11—81no—
218C22×Q8C22⋊D1111yescharacteristic
219C22×D4—111no—
220C22×D4—221no—
221C23×C4—111no—
222C2×Q16—41no—
223C2×SD16—441no—
224C22⋊Q8—21no—
225C22⋊Q8—21no—
226C22⋊Q8—41no—
227C22⋊Q8—41no—
228C2×C4⋊C4—221no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—441no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—111no—
234C2×C22⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C22⋊C4—221no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C22⋊C4—221no—
240C2×C22⋊C4C22×D1111yescharacteristic
241#103—41no—
242#102—441no—
243C22⋊C8—21no—
244C22⋊C8—221no—
245#95—21no—
246#95—111no—
247#95—221no—
248#95—221no—
249#95—221no—
250#95—221no—
251#95—441no—
252#95C22⋊D1111yescharacteristic
253C2×C11—21no—
254C2×C11—21no—
255C2×C11—41no—
256C2×C11—41no—
257C2×C11#160311yescharacteristic
258C2×C11#219911yescharacteristic
259C2×C11#220011yescharacteristic
260D11—161no—
261C24—221no—
262C24D4×D1111yescharacteristic
263C2×Q8—21no—
264C2×Q8—21no—
265C2×Q8—41no—
266C2×Q8—81no—
267C2×D4—441no—
268C2×D4—441no—
269C2×D4—441no—
270C2×D4—881no—
271C2×D4—881no—
272C2×D4—881no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—441no—
281C22×C4—441no—
282C22×C4—881no—
283C22×C4D4×D1111yescharacteristic
284C22×C4C2×C22⋊D1111yescharacteristic
285Q16—82no—
286SD16—882no—
287C2×C8—41no—
288C2×C8—441no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—881no—
294C4⋊C4—881no—
295C4⋊C4—882no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—81no—
300C22⋊C4—222no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C22⋊C4—441no—
304C22⋊C4—881no—
305C22⋊C4—881no—
306C22⋊C4—881no—
307C22⋊C4—881no—
308C22⋊C4—881no—
309C11#1223011yescharacteristic, complemented, Sylow
310C23—21no—
311C23—21no—
312C23—41no—
313C23—41no—
314C23—441no—
315C23—441no—
316C23—441no—
317C23—441no—
318C23—441no—
319C23—441no—
320C23—441no—
321C23#6697111yescharacteristic
322C23#6697211yescharacteristic
323C23#6699011yescharacteristic
324Q8—42no—
325Q8—81no—
326Q8—81no—
327Q8—81no—
328D4—442no—
329D4—881no—
330D4—882no—
331D4—882no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—442no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—442no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—881no—
358C2×C4—881no—
359C2×C4—881no—
360C8—81no—
361C8—881no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—81no—
371C22—881no—
372C22—881no—
373C22—881no—
374C22—881no—
375C22—881no—
376C22—881no—
377C22—881no—
378C22#1062264511yescharacteristic
379C22#1062280011yescharacteristic
380C22#1062281811yescharacteristic
381C4—41no—
382C4—41no—
383C4—81no—
384C4—81no—
385C4—81no—
386C4—81no—
387C4—881no—
388C4—881no—
389C4—882no—
390C4—881no—
391C2—21no—
392C2—21no—
393C2—41no—
394C2—41no—
395C2—1761no—
396C2#1306757811yescharacteristic
397C2#1307061611yescharacteristic
398C2#1307062111yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1602C2
socleC22×C11B(4,𝔽2)
prime radical#10622573C22
hypercenter#1602D11
hypocenterC11#12230
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1602

Complements

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

NH ≅ G/Ntype
2. #13069968C2semidirect
4. #13066637C2semidirect
6. #13066565C2semidirect
7. C11×#1602C2semidirect
113. #1602D11semidirect
309. C11#12230semidirect

Maximal subgroups

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

subgroupindex
#130767002
#130699682
#130675392
#130666372
#130666142
#130665652
C11×#16022
#1223011