Finite Group Databasebeta

← #14655729

Subgroups — #14655729

Order 2816.

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

normal subgroups only

This group has 646 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#13079534C211yesmaximal, characteristic, complemented
2#13078080C211yesmaximal, characteristic, complemented
3#13067284C211yesmaximal, characteristic, complemented
4#13067014C211yesmaximal, characteristic, complemented
5#13066937C211yesmaximal, characteristic, complemented
6#13066513C211yesmaximal, characteristic, complemented
7C2×C11×#459C211yesmaximal, characteristic, complemented
8C22×C11×D8—21no—
9C2×C11×#127C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66985—21no—
12#10623008C2211yescharacteristic
13C11×#459—22no—
14C11×#459—22no—
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#102—21no—
17#10622830—22no—
18#10622686—21no—
19#10622685—22no—
20#10622683—21no—
21#10622632—21no—
22#10622629—22no—
23#10622628—21no—
24#10622579—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622182—22no—
29#10622163—22no—
30#10622121—22no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11D411yescharacteristic
35C23×C4×C11—21no—
36C2×#4339—21no—
37C2×C11×D8—24no—
38C2×C11×D8—42no—
39C2×C11×D8—42no—
40C22×C8×C11—21no—
41C11×#127—21no—
42C11×#127—21no—
43C11×#127—21no—
44C11×#127D412yes—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—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—
56C2×#4323—24no—
57#66983—21no—
58#66983—21no—
59C2×#4318—21no—
60#66928—21no—
61#66927D411yescharacteristic
62C4×D44—21no—
63C4×D44—21no—
64#66922D411yescharacteristic
65C11×C4⋊C8—21no—
66C11×C4⋊C8D412yes—
67C11×#102—24no—
68#66896—24no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)D412yes—
71#66874—22no—
72#66873—22no—
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#10176—111nomaximal, Sylow
80C24×C11—21no—
81C24×C11—41no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—22no—
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—82no—
98C2×D4×C11—82no—
99C2×D4×C11D812yescomplemented
100C22×C4×C11—21no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—82no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11#4111yescharacteristic
107C2×C22⋊D11—41no—
108#4339—41no—
109#4339—41no—
110#4339—41no—
111#4339—41no—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44—21no—
115C2×C4×D11—41no—
116C2×Dic22—21no—
117C11×D8—48no—
118C2×C8×C11—22no—
119C2×C8×C11—41no—
120C2×C8×C11—41no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11C2×D411yescharacteristic
129#4324—44no—
130#4323—44no—
131#4323—84no—
132(C2×D11)⋊C4—41no—
133(C2×D11)⋊C4—41no—
134C4⋊Dic11—21no—
135C4⋊Dic11—21no—
136#4318—41no—
137#4318—41no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—41no—
141#3205—111no—
142#3036—111no—
143C2×#459D1111yescharacteristic, complemented
144#1545—111no—
145#1480—111no—
146#1460—111no—
147#1301—111no—
148C23×C11—22no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—42no—
152C23×C11—81no—
153C23×C11—81no—
154C23×C11—82no—
155C23×C11—82no—
156C23×C11—81no—
157C23×C11—81no—
158C23×C11#12111yescharacteristic
159C22×D11—41no—
160D4×C11—22no—
161D4×C11—22no—
162D4×C11—44no—
163D4×C11—42no—
164D4×C11—41no—
165D4×C11—41no—
166D4×C11—42no—
167D4×C11—82no—
168D4×C11—82no—
169D4×C11—81no—
170D4×C11—81no—
171D4×C11—82no—
172C2×C4×C11—22no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—82no—
176C2×C4×C11—82no—
177C2×C4×C11—81no—
178C2×C4×C11#12011yescharacteristic
179C2×C4×C11#12011yescharacteristic
180C2×C4×C11#12011yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12711yescharacteristic
184C2×C4×C11C2×D811yescharacteristic
185C2×C4×C11#13511yescharacteristic
186C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
188C22⋊D11—81no—
189C22⋊D11—81no—
190C2×Dic11—41no—
191D44—42no—
192D44—41no—
193D44—41no—
194D44—42no—
195C4×D11—81no—
196C4×D11—81no—
197Dic22—41no—
198Dic22—41no—
199C8×C11—42no—
200C11⋊C8—42no—
201C11⋊C8—42no—
202C11⋊C8—81no—
203C2×AGL(1,ℤ/8)—221no—
204C22×D8—21no—
205#532—111no—
206C2×#127C2×D1111yescharacteristic
207C2×C4×D4C2×D1111yescharacteristic
208#493—221no—
209#486—221no—
210#463—222no—
211#461—221no—
212#459—22no—
213#459—22no—
214#459—221no—
215#459—222no—
216#447—222no—
217#431—111no—
218#431—111no—
219#423—111no—
220C2×C4⋊C8C2×D1111yescharacteristic
221#417—221no—
222C2×#102—21no—
223#331—222no—
224D4⋊C8—222no—
225#323—222no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—42no—
229C22×C11—82no—
230C22×C11—82no—
231C22×C11—81no—
232C22×C11—81no—
233C22×C11—82no—
234C22×C11—82no—
235C22×C11—82no—
236C22×C11—162no—
237C22×C11—162no—
238C22×C11#39211yescharacteristic
239C22×C11#46611yescharacteristic
240C22×C11#46911yescharacteristic
241C2×D11—81no—
242C2×D11—81no—
243C2×D11—81no—
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—81no—
248C4×C11#44711yescharacteristic
249C4×C11#44711yescharacteristic
250C4×C11#44911yescharacteristic
251C4×C11#44911yescharacteristic
252C4×C11#47212yes—
253Dic11—81no—
254C2×#41—221no—
255C22×D4—21no—
256C22×D4—21no—
257C22×D4—21no—
258C22×D4C22⋊D1111yescharacteristic
259C23×C4—21no—
260AGL(1,ℤ/8)—442no—
261AGL(1,ℤ/8)—442no—
262C2×SD16—222no—
263C2×D8—24no—
264C2×D8—42no—
265C2×D8—42no—
266C2×D8—222no—
267C2×D8—224no—
268C2×M16—221no—
269C22×C8—21no—
270C4⋊Q8—111no—
271#127—21no—
272#127—21no—
273#127—21no—
274#127—111no—
275#127C22⋊D1112yes—
276#124—221no—
277#121—221no—
278#121—221no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C4×D4—221no—
284C4×D4—221no—
285C2×C4⋊C4C22⋊D1111yescharacteristic
286C2×C22⋊C4—21no—
287C2×C42C22×D1111yescharacteristic
288C4⋊C8—21no—
289C4⋊C8—112no—
290C4⋊C8—221no—
291C4⋊C8—221no—
292C4⋊C8—221no—
293C4⋊C8C22⋊D1112yes—
294#103—222no—
295#102—24no—
296#102—222no—
297#102—224no—
298C22⋊C8—112no—
299C22⋊C8—221no—
300C4×C8—221no—
301C4×C8—221no—
302C2×C11—21no—
303C2×C11—21no—
304C2×C11—82no—
305C2×C11—162no—
306C2×C11#199911yescharacteristic
307C2×C11#200811yescharacteristic
308C2×C11#201811yescharacteristic
309D11—161no—
310C24—21no—
311C24—41no—
312#41—441no—
313#41—441no—
314#41—441no—
315#41—441no—
316C2×Q8—221no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—22no—
320C2×D4—22no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—22no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—41no—
328C2×D4—41no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—82no—
333C2×D4—82no—
334C2×D4—221no—
335C2×D4—221no—
336C2×D4—221no—
337C2×D4—441no—
338C2×D4#432312yescomplemented
339C22×C4—21no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—82no—
343C22×C4—441no—
344C22×C4D4×D1111yescharacteristic
345C22×C4#434111yescharacteristic
346C22×C4C2×C22⋊D1111yescharacteristic
347SD16—444no—
348D8—48no—
349D8—444no—
350D8—884no—
351M16—441no—
352M16—441no—
353C2×C8—22no—
354C2×C8—41no—
355C2×C8—41no—
356C2×C8—222no—
357C2×C8—222no—
358C2×C8—441no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—221no—
362C4⋊C4—221no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—441no—
366C22⋊C4—441no—
367C42D4×D1111yescharacteristic
368C42D4×D1111yescharacteristic
369C42C2×C22⋊D1111yescharacteristic
370C42C2×C22⋊D1111yescharacteristic
371C11#1017611yescharacteristic, complemented, Sylow
372C23—22no—
373C23—41no—
374C23—41no—
375C23—42no—
376C23—81no—
377C23—81no—
378C23—82no—
379C23—82no—
380C23—81no—
381C23—81no—
382C23—441no—
383C23#6699211yescharacteristic
384Q8—441no—
385Q8—441no—
386D4—22no—
387D4—22no—
388D4—44no—
389D4—42no—
390D4—41no—
391D4—42no—
392D4—41no—
393D4—82no—
394D4—82no—
395D4—82no—
396D4—81no—
397D4—81no—
398D4—442no—
399D4—442no—
400D4—441no—
401D4—441no—
402D4—881no—
403D4—881no—
404C2×C4—22no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4—81no—
410C2×C4—441no—
411C2×C4—881no—
412C2×C4—881no—
413C2×C4C2×#432311yescharacteristic
414C2×C4#6698511yescharacteristic
415C2×C4#6699011yescharacteristic
416C2×C4#6699011yescharacteristic
417C2×C4#6699111yescharacteristic
418C2×C4#6699211yescharacteristic
419C2×C4#6699311yescharacteristic
420C2×C4#6700211yescharacteristic
421C2×C4#6700311yescharacteristic
422C2×C4#6700611yescharacteristic
423C8—42no—
424C8—442no—
425C8—442no—
426C8—881no—
427C22—21no—
428C22—21no—
429C22—42no—
430C22—82no—
431C22—82no—
432C22—81no—
433C22—81no—
434C22—82no—
435C22—82no—
436C22—82no—
437C22—162no—
438C22—162no—
439C22—881no—
440C22—881no—
441C22—881no—
442C22#1062265111yescharacteristic
443C22#1062265211yescharacteristic
444C22#1062283611yescharacteristic
445C4—21no—
446C4—21no—
447C4—21no—
448C4—81no—
449C4—881no—
450C4#1062264911yescharacteristic
451C4#1062265011yescharacteristic
452C4#1062277312yes—
453C4#1062283011yescharacteristic
454C4#1062285111yescharacteristic
455C2—21no—
456C2—21no—
457C2—82no—
458C2—162no—
459C2—1761no—
460C2#1306961211yescharacteristic
461C2#1306966711yescharacteristic
462C2#1306972311yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#459C2
socleC22×C11#392
hypercenterC2×#459D11
hypocenterC11#10176
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. #13079534C2semidirect
2. #13078080C2semidirect
3. #13067284C2semidirect
4. #13067014C2semidirect
5. #13066937C2semidirect
6. #13066513C2semidirect
7. C2×C11×#459C2semidirect
99. C2×D4×C11D8semidirect
143. C2×#459D11semidirect
338. C2×D4#4323semidirect
371. C11#10176semidirect

Maximal subgroups

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

subgroupindex
#130795342
#130780802
#130672842
#130670142
#130669372
#130665132
C2×C11×#4592
#1017611