Finite Group Databasebeta

← #14655801

Subgroups — #14655801

Order 2816.

528 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079757C211yesmaximal, characteristic, complemented
2C2×#10622632C211yesmaximal, characteristic
3#13067289C211yesmaximal, characteristic, complemented
4#13067019C211yesmaximal, characteristic, complemented
5#13066937C211yesmaximal, characteristic
6#13066511C211yesmaximal, characteristic, complemented
7C11×#3077C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10C22×#4324—21no—
11C2×#66922C2211yescharacteristic
12C11×#478—22no—
13C11×#476—21no—
14C11×#474—21no—
15C11×#428—21no—
16C11×#423C2211yescharacteristic
17C11×#418—21no—
18#10622694—21no—
19#10622692—21no—
20#10622656—22no—
21#10622633—22no—
22#10622632—22no—
23#10622632—22no—
24C2×#66874—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28Q8⋊(C11⋊C8)—22no—
29#10622163—22no—
30#10622120—22no—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11—21no—
33C22×Dic22—21no—
34C2×C11×M16—21no—
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×#125—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C11×#117—21no—
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C22⋊C4—21no—
49C2×C42×C11C2311yescharacteristic
50C2×#4324—24no—
51C2×#4324—42no—
52C2×#4324—42no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—21no—
55C22×C11⋊C8—21no—
56#66922—21no—
57#66922—21no—
58#66922—21no—
59#66922D412yes—
60C11×#107—22no—
61C11×#106—22no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8D412yes—
64C11×#102—22no—
65C11×#102—22no—
66#66899—24no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)D412yes—
69#66874—24no—
70#66872—24no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)D412yes—
75C4×C11⋊C8—21no—
76C4×C11⋊C8—21no—
77#10186—111nomaximal, Sylow
78C24×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11SD1612yes—
87C22×C4×C11—21no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—82no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×Dic11—41no—
95C2×Dic22—22no—
96C2×Dic22—41no—
97C2×Dic22—41no—
98C2×Dic22—41no—
99C2×Dic22—41no—
100C2×Dic22—41no—
101C11×M16—41no—
102C11×M16—41no—
103C2×C8×C11—22no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C42×C11—41no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120#4324—48no—
121C4⋊Dic11—22no—
122C4⋊Dic11—22no—
123C4⋊Dic11—41no—
124C4⋊Dic11—41no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—41no—
128C2×C11⋊C8—41no—
129C2×C11⋊C8—41no—
130#3229—111no—
131#3077D1111yescharacteristic
132C2×#461—111no—
133#1546—111no—
134#1481—111no—
135#1460—111no—
136#1301—111no—
137C23×C11—22no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—81no—
141C23×C11—81no—
142C23×C11#12111yescharacteristic
143Q8×C11—42no—
144Q8×C11—42no—
145D4×C11—22no—
146D4×C11—22no—
147D4×C11—41no—
148D4×C11—41no—
149C2×C4×C11—22no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
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
167C2×Dic11—42no—
168C2×Dic11—81no—
169C2×Dic11—81no—
170Dic22—42no—
171Dic22—42no—
172Dic22—81no—
173Dic22—81no—
174C8×C11—42no—
175C11⋊C8—42no—
176C11⋊C8—42no—
177C11⋊C8—81no—
178C22×SD16—221no—
179#533C2×D1111yescharacteristic
180C2×C4⋊Q8—111no—
181C2×C4×D4C2×D1111yescharacteristic
182#498—221no—
183#487—221no—
184#483—222no—
185#478—22no—
186#476—21no—
187#475—222no—
188#474—21no—
189#461—222no—
190#461—222no—
191#431—111no—
192#431—111no—
193#428—21no—
194#423C2×D1111yescharacteristic
195C2×C4⋊C8—111no—
196#418—21no—
197C2×#103—221no—
198#332—222no—
199Q8⋊C8—222no—
200#323—222no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—42no—
204C22×C11—82no—
205C22×C11—82no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11#39211yescharacteristic
209C22×C11#46511yescharacteristic
210C22×C11#46811yescharacteristic
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—81no—
215C4×C11—81no—
216C4×C11—81no—
217C4×C11#44811yescharacteristic
218C4×C11#44911yescharacteristic
219C4×C11#45011yescharacteristic
220C4×C11#45211yescharacteristic
221C4×C11#47112yes—
222Dic11—82no—
223C22×Q8—221no—
224C22×D4C22⋊D1111yescharacteristic
225C23×C4—21no—
226C2×SD16—224no—
227C2×SD16—442no—
228C2×SD16—442no—
229C2×M16—21no—
230C22×C8—221no—
231C4⋊Q8—112no—
232C4⋊Q8—221no—
233C4⋊Q8—221no—
234C4⋊Q8—221no—
235C4⋊Q8C22⋊D1111yescharacteristic
236C4⋊Q8C22⋊D1111yescharacteristic
237#125—21no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C4×Q8—21no—
241C4×Q8—21no—
242C4×D4—21no—
243C4×D4—21no—
244C4×D4—21no—
245C4×D4—21no—
246#117—21no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4C22⋊D1111yescharacteristic
250C2×C22⋊C4—21no—
251C2×C42C22×D1111yescharacteristic
252#107—22no—
253#106—22no—
254#106—224no—
255C4⋊C8—21no—
256C4⋊C8—112no—
257C4⋊C8—221no—
258C4⋊C8—221no—
259C4⋊C8—221no—
260C4⋊C8C22⋊D1112yes—
261#103—224no—
262#103—224no—
263#102—22no—
264#102—22no—
265C22⋊C8—112no—
266C22⋊C8—221no—
267C4×C8—221no—
268C4×C8—221no—
269C2×C11—21no—
270C2×C11—21no—
271C2×C11—82no—
272C2×C11#200011yescharacteristic
273C2×C11#200911yescharacteristic
274C2×C11#201911yescharacteristic
275C24—21no—
276C2×Q8—21no—
277C2×Q8—21no—
278C2×Q8—222no—
279C2×Q8—441no—
280C2×Q8—441no—
281C2×Q8—441no—
282C2×Q8—441no—
283C2×Q8—441no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4#432512yes—
290C22×C4—21no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—82no—
294C22×C4—441no—
295C22×C4D4×D1111yescharacteristic
296C22×C4#434111yescharacteristic
297C22×C4C2×C22⋊D1111yescharacteristic
298SD16—448no—
299M16—41no—
300M16—41no—
301C2×C8—22no—
302C2×C8—222no—
303C2×C8—222no—
304C2×C8—441no—
305C2×C8—441no—
306C2×C8—441no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—222no—
316C4⋊C4—222no—
317C4⋊C4—441no—
318C4⋊C4—441no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C42—41no—
323C42D4×D1111yescharacteristic
324C42D4×D1111yescharacteristic
325C42C2×C22⋊D1111yescharacteristic
326C42C2×C22⋊D1111yescharacteristic
327C11#1018611yescharacteristic, complemented, Sylow
328C23—22no—
329C23—41no—
330C23—41no—
331C23—81no—
332C23—81no—
333C23#6699211yescharacteristic
334Q8—42no—
335Q8—42no—
336Q8—442no—
337Q8—442no—
338Q8—881no—
339Q8—881no—
340D4—22no—
341D4—22no—
342D4—41no—
343D4—41no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—81no—
352C2×C4—442no—
353C2×C4—881no—
354C2×C4—881no—
355C2×C4#6699011yescharacteristic
356C2×C4#6699011yescharacteristic
357C2×C4#6699111yescharacteristic
358C2×C4#6699211yescharacteristic
359C2×C4#6699311yescharacteristic
360C2×C4C2×#432511yescharacteristic
361C2×C4#6699511yescharacteristic
362C2×C4#6700211yescharacteristic
363C2×C4#6700311yescharacteristic
364C2×C4#6700611yescharacteristic
365C8—42no—
366C8—442no—
367C8—442no—
368C8—881no—
369C22—21no—
370C22—21no—
371C22—42no—
372C22—82no—
373C22—82no—
374C22—81no—
375C22—81no—
376C22#1062266111yescharacteristic
377C22#1062266211yescharacteristic
378C22#1062283611yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—81no—
383C4—81no—
384C4—81no—
385C4—882no—
386C4#1062265911yescharacteristic
387C4#1062266011yescharacteristic
388C4#1062281312yes—
389C4#1062284011yescharacteristic
390C4#1062285111yescharacteristic
391C2—21no—
392C2—21no—
393C2—82no—
394C2#1306961711yescharacteristic
395C2#1306967311yescharacteristic
396C2#1306973011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3077C2
socleC22×C11#392
prime radicalC22×D4×C11D4
hypercenter#3077D11
hypocenterC11#10186
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #13079757C2semidirect
3. #13067289C2semidirect
4. #13067019C2semidirect
6. #13066511C2semidirect
327. C11#10186semidirect

Maximal subgroups

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

subgroupindex
#130797572
C2×#106226322
#130672892
#130670192
#130669372
#130665112
C11×#30772
#1018611