Finite Group Databasebeta

← #14655785

Subgroups — #14655785

Order 2816.

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

normal subgroups only

This group has 582 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#13079737C211yesmaximal, characteristic, complemented
2#13078080C211yesmaximal, characteristic
3#13067288C211yesmaximal, characteristic, complemented
4#13067014C211yesmaximal, characteristic, complemented
5#13066937C211yesmaximal, characteristic, complemented
6#13066513C211yesmaximal, characteristic, complemented
7C2×C11×#461C211yesmaximal, characteristic, complemented
8C22×C11×SD16—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66985—21no—
12#10623008C2211yescharacteristic
13C11×#461—22no—
14C11×#461—22no—
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#103—21no—
17#10622701—21no—
18#10622700—22no—
19#10622691—21no—
20#10622632—21no—
21#10622629—22no—
22#10622628—21no—
23#10622580—22no—
24#10622579—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622185—22no—
29#10622163—22no—
30#10622121—22no—
31C22×Q8×C11—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C2×#4339—21no—
35C2×C11×SD16—24no—
36C2×C11×SD16—42no—
37C2×C11×SD16—42no—
38C22×C8×C11—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8D412yes—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C22⋊C4—21no—
51C2×C42×C11C2311yescharacteristic
52C2×#4324—22no—
53#66985—42no—
54#66985—42no—
55C2×#4323—22no—
56#66983—21no—
57#66983—21no—
58C2×#4318—21no—
59#66928—21no—
60#66927D411yescharacteristic
61C4×D44—21no—
62C4×D44—21no—
63#66922D411yescharacteristic
64C11×C4⋊C8—21no—
65C11×C4⋊C8D412yes—
66C11×#103—24no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)D412yes—
69#66874—22no—
70#66873—22no—
71#66873—24no—
72#66871—24no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)D412yes—
77C4×C11⋊C8—21no—
78C4×C11⋊C8—21no—
79#10184—111nomaximal, Sylow
80C24×C11—21no—
81C2×Q8×C11—22no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11D812yes—
93C22×C4×C11—21no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—82no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11#4111yescharacteristic
101C2×C22⋊D11—41no—
102#4339—41no—
103#4339—41no—
104#4339—41no—
105#4339—41no—
106C2×D44—21no—
107C2×D44—21no—
108C2×D44—21no—
109C2×C4×D11—41no—
110C2×Dic22—21no—
111C11×SD16—48no—
112C2×C8×C11—22no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127#4324—44no—
128#4323—44no—
129(C2×D11)⋊C4—41no—
130(C2×D11)⋊C4—41no—
131C4⋊Dic11—21no—
132C4⋊Dic11—21no—
133#4318—41no—
134#4318—41no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—41no—
138#3226—111no—
139#3036—111no—
140C2×#461D1111yescharacteristic, complemented
141#1546—111no—
142#1480—111no—
143#1460—111no—
144#1301—111no—
145C23×C11—22no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—81no—
149C23×C11—81no—
150C23×C11#12111yescharacteristic
151C22×D11—41no—
152Q8×C11—42no—
153Q8×C11—42no—
154Q8×C11—81no—
155Q8×C11—81no—
156D4×C11—22no—
157D4×C11—22no—
158D4×C11—41no—
159D4×C11—41no—
160C2×C4×C11—22no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—42no—
164C2×C4×C11—82no—
165C2×C4×C11—81no—
166C2×C4×C11—81no—
167C2×C4×C11—82no—
168C2×C4×C11—81no—
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12711yescharacteristic
175C2×C4×C11C2×D811yescharacteristic
176C2×C4×C11#13511yescharacteristic
177C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
179C22⋊D11—81no—
180C22⋊D11—81no—
181C2×Dic11—41no—
182D44—42no—
183D44—41no—
184D44—41no—
185D44—42no—
186C4×D11—81no—
187C4×D11—81no—
188Dic22—41no—
189Dic22—41no—
190C8×C11—42no—
191C11⋊C8—42no—
192C11⋊C8—42no—
193C11⋊C8—81no—
194C2×AGL(1,ℤ/8)—221no—
195C22×SD16—21no—
196#532—111no—
197C2×C4⋊Q8C2×D1111yescharacteristic
198C2×C4×D4C2×D1111yescharacteristic
199#500—221no—
200#486—221no—
201#480—222no—
202#474—222no—
203#463—222no—
204#461—22no—
205#461—22no—
206#461—221no—
207#459—221no—
208#431—111no—
209#431—111no—
210#423—111no—
211C2×C4⋊C8C2×D1111yescharacteristic
212#417—221no—
213C2×#103—21no—
214#332—222no—
215D4⋊C8—222no—
216#323—222no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—42no—
220C22×C11—82no—
221C22×C11—82no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11#39211yescharacteristic
225C22×C11#46611yescharacteristic
226C22×C11#46911yescharacteristic
227C2×D11—81no—
228C2×D11—81no—
229C2×D11—81no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—82no—
234C4×C11—81no—
235C4×C11#44711yescharacteristic
236C4×C11#44711yescharacteristic
237C4×C11#44911yescharacteristic
238C4×C11#44911yescharacteristic
239C4×C11#47112yes—
240Dic11—81no—
241C2×#41—221no—
242C22×Q8—21no—
243C22×D4C22⋊D1111yescharacteristic
244C23×C4—21no—
245AGL(1,ℤ/8)—442no—
246AGL(1,ℤ/8)—442no—
247C2×SD16—24no—
248C2×SD16—42no—
249C2×SD16—42no—
250C2×SD16—222no—
251C2×D8—222no—
252C2×M16—221no—
253C22×C8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—111no—
258C4⋊Q8C22⋊D1112yes—
259#127—111no—
260#124—221no—
261#121—221no—
262#121—221no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—21no—
267C4×D4—221no—
268C4×D4—221no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4C22⋊D1111yescharacteristic
272C2×C22⋊C4—21no—
273C2×C42C22×D1111yescharacteristic
274#107—224no—
275C4⋊C8—21no—
276C4⋊C8—112no—
277C4⋊C8—221no—
278C4⋊C8—221no—
279C4⋊C8—221no—
280C4⋊C8C22⋊D1112yes—
281#103—24no—
282#103—222no—
283#102—222no—
284#102—224no—
285C22⋊C8—112no—
286C22⋊C8—221no—
287C4×C8—221no—
288C4×C8—221no—
289C2×C11—21no—
290C2×C11—21no—
291C2×C11—82no—
292C2×C11#199911yescharacteristic
293C2×C11#200911yescharacteristic
294C2×C11#201911yescharacteristic
295D11—161no—
296C24—21no—
297#41—441no—
298#41—441no—
299#41—441no—
300#41—441no—
301C2×Q8—22no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—221no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—221no—
314C2×D4—221no—
315C2×D4—221no—
316C2×D4—441no—
317C2×D4#432312yes—
318C22×C4—21no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—82no—
323C22×C4—441no—
324C22×C4D4×D1111yescharacteristic
325C22×C4#434111yescharacteristic
326C22×C4C2×C22⋊D1111yescharacteristic
327SD16—48no—
328SD16—444no—
329D8—444no—
330M16—441no—
331M16—441no—
332C2×C8—22no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—222no—
336C2×C8—222no—
337C2×C8—441no—
338C4⋊C4—21no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—21no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—221no—
345C4⋊C4—221no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—441no—
349C22⋊C4—441no—
350C42D4×D1111yescharacteristic
351C42D4×D1111yescharacteristic
352C42C2×C22⋊D1111yescharacteristic
353C42C2×C22⋊D1111yescharacteristic
354C11#1018411yescharacteristic, complemented, Sylow
355C23—22no—
356C23—41no—
357C23—41no—
358C23—81no—
359C23—81no—
360C23—441no—
361C23#6699211yescharacteristic
362Q8—42no—
363Q8—42no—
364Q8—81no—
365Q8—81no—
366Q8—441no—
367Q8—441no—
368D4—22no—
369D4—22no—
370D4—41no—
371D4—41no—
372D4—442no—
373D4—442no—
374D4—441no—
375D4—441no—
376D4—881no—
377D4—881no—
378C2×C4—22no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—82no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—82no—
386C2×C4—81no—
387C2×C4—441no—
388C2×C4—881no—
389C2×C4—881no—
390C2×C4C2×#432311yescharacteristic
391C2×C4#6698511yescharacteristic
392C2×C4#6699011yescharacteristic
393C2×C4#6699011yescharacteristic
394C2×C4#6699111yescharacteristic
395C2×C4#6699211yescharacteristic
396C2×C4#6699311yescharacteristic
397C2×C4#6700211yescharacteristic
398C2×C4#6700311yescharacteristic
399C2×C4#6700611yescharacteristic
400C8—42no—
401C8—442no—
402C8—442no—
403C8—881no—
404C22—21no—
405C22—21no—
406C22—42no—
407C22—82no—
408C22—82no—
409C22—81no—
410C22—81no—
411C22—881no—
412C22—881no—
413C22—881no—
414C22#1062265111yescharacteristic
415C22#1062265211yescharacteristic
416C22#1062283611yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—82no—
421C4—81no—
422C4—881no—
423C4#1062264911yescharacteristic
424C4#1062265011yescharacteristic
425C4#1062279012yes—
426C4#1062283011yescharacteristic
427C4#1062285111yescharacteristic
428C2—21no—
429C2—21no—
430C2—82no—
431C2—1761no—
432C2#1306961211yescharacteristic
433C2#1306967411yescharacteristic
434C2#1306972811yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#461C2
socleC22×C11#392
prime radical#13078080C2
hypercenterC2×#461D11
hypocenterC11#10184
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. #13079737C2semidirect
3. #13067288C2semidirect
4. #13067014C2semidirect
5. #13066937C2semidirect
6. #13066513C2semidirect
7. C2×C11×#461C2semidirect
140. C2×#461D11semidirect
354. C11#10184semidirect

Maximal subgroups

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

subgroupindex
#130797372
#130780802
#130672882
#130670142
#130669372
#130665132
C2×C11×#4612
#1018411