Finite Group Databasebeta

← #14655731

Subgroups — #14655731

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#13079531C211yesmaximal, characteristic, complemented
2C2×#10622628C211yesmaximal, characteristic, complemented
3#13067285C211yesmaximal, characteristic, complemented
4#13067015C211yesmaximal, characteristic, complemented
5#13066937C211yesmaximal, characteristic, complemented
6#13066511C211yesmaximal, characteristic, complemented
7C11×#3036C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—21no—
9C11×#532C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C22×#4323—21no—
12C2×#66927C2211yescharacteristic
13C11×#463—22no—
14C11×#461—21no—
15C11×#459—21no—
16C11×#423C2211yescharacteristic
17C11×#417—21no—
18#10622701—21no—
19#10622686—21no—
20#10622649—22no—
21#10622628—22no—
22#10622628—22no—
23#10622628—22no—
24C2×#66873—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28D4⋊(C11⋊C8)—22no—
29#10622163—22no—
30#10622123—22no—
31C2×C11×#41—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C22×D44—21no—
35C22×D44—21no—
36C22×D44—21no—
37C11×AGL(1,ℤ/8)—42no—
38C11×AGL(1,ℤ/8)—42no—
39C2×C11×SD16—22no—
40C2×C11×D8—22no—
41C2×C11×M16—21no—
42C11×C4⋊Q8D411yescharacteristic
43C11×#127D411yescharacteristic
44C11×#124—21no—
45C11×#121—21no—
46C11×#121—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C11×C22⋊C4—21no—
55C2×C42×C11C2311yescharacteristic
56C2×#4323—24no—
57C2×#4323—24no—
58C2×#4323—42no—
59C2×#4323—42no—
60C22×C11⋊C8—21no—
61#66927—21no—
62#66927—21no—
63#66927—21no—
64#66927D412yes—
65C11×C4⋊C8—21no—
66C11×C4⋊C8D412yes—
67C11×#103—22no—
68C11×#102—22no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)D412yes—
71#66873—24no—
72#66873—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#10176—111nomaximal, Sylow
80C24×C11—21no—
81C23×D11—41no—
82C11×#41—41no—
83C11×#41—41no—
84C11×#41—41no—
85C11×#41—41no—
86C2×Q8×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—41no—
96C2×D4×C11D812yescomplemented
97C22×C4×C11—21no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—82no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C2×D44—22no—
106C2×D44—22no—
107C2×D44—22no—
108C2×D44—41no—
109C2×D44—41no—
110C2×D44—41no—
111C2×D44—41no—
112C2×D44—41no—
113C2×D44—41no—
114C2×D44—41no—
115C2×D44—82no—
116C2×D44—82no—
117C11×SD16—44no—
118C11×D8—44no—
119C11×M16—41no—
120C11×M16—41no—
121C2×C8×C11—22no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—41no—
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11C2×D411yescharacteristic
133C42×C11C2×D411yescharacteristic
134#4323—48no—
135#4323—84no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—41no—
139C2×C11⋊C8—41no—
140C2×C11⋊C8—41no—
141#3205—111no—
142#3036D1111yescharacteristic, complemented
143C2×#459—111no—
144#1545—111no—
145#1480—111no—
146#1460—111no—
147#1301—111no—
148C23×C11—22no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—81no—
153C23×C11—81no—
154C23×C11#12111yescharacteristic
155C22×D11—42no—
156C22×D11—82no—
157C22×D11—82no—
158C22×D11—81no—
159C22×D11—81no—
160Q8×C11—41no—
161Q8×C11—41no—
162D4×C11—22no—
163D4×C11—22no—
164D4×C11—42no—
165D4×C11—41no—
166D4×C11—41no—
167D4×C11—41no—
168D4×C11—41no—
169D4×C11—42no—
170D4×C11—81no—
171D4×C11—81no—
172C2×C4×C11—22no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—82no—
177C2×C4×C11—81no—
178C2×C4×C11—81no—
179C2×C4×C11—82no—
180C2×C4×C11—81no—
181C2×C4×C11#12011yescharacteristic
182C2×C4×C11#12011yescharacteristic
183C2×C4×C11#12011yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12711yescharacteristic
187C2×C4×C11C2×D811yescharacteristic
188C2×C4×C11#13511yescharacteristic
189C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
191D44—44no—
192D44—42no—
193D44—42no—
194D44—82no—
195D44—82no—
196D44—81no—
197D44—81no—
198D44—82no—
199C8×C11—42no—
200C11⋊C8—42no—
201C11⋊C8—42no—
202C11⋊C8—81no—
203C2×AGL(1,ℤ/8)—21no—
204C22×D8—221no—
205#532C2×D1111yescharacteristic
206C2×#127—111no—
207C2×C4×D4C2×D1111yescharacteristic
208#493—221no—
209#486—221no—
210#463—22no—
211#461—21no—
212#459—21no—
213#459—222no—
214#459—222no—
215#459—222no—
216#447—222no—
217#431—111no—
218#431—111no—
219#423C2×D1111yescharacteristic
220C2×C4⋊C8—111no—
221#417—21no—
222C2×#102—221no—
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—81no—
234C22×C11—81no—
235C22×C11—81no—
236C22×C11#39211yescharacteristic
237C22×C11#46611yescharacteristic
238C22×C11#46911yescharacteristic
239C2×D11—82no—
240C2×D11—82no—
241C2×D11—82no—
242C2×D11—162no—
243C2×D11—162no—
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—81no—
248C4×C11—81no—
249C4×C11#44711yescharacteristic
250C4×C11#44711yescharacteristic
251C4×C11#44911yescharacteristic
252C4×C11#44911yescharacteristic
253C4×C11#47212yes—
254C2×#41—21no—
255C22×D4—221no—
256C22×D4—221no—
257C22×D4—221no—
258C22×D4C22⋊D1111yescharacteristic
259C23×C4—21no—
260AGL(1,ℤ/8)—42no—
261AGL(1,ℤ/8)—42no—
262C2×SD16—22no—
263C2×D8—22no—
264C2×D8—224no—
265C2×D8—224no—
266C2×D8—442no—
267C2×D8—442no—
268C2×M16—21no—
269C22×C8—221no—
270C4⋊Q8C22⋊D1111yescharacteristic
271#127—112no—
272#127—221no—
273#127—221no—
274#127—221no—
275#127C22⋊D1111yescharacteristic
276#124—21no—
277#121—21no—
278#121—21no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C4×D4—21no—
284C4×D4—21no—
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—22no—
295#102—22no—
296#102—224no—
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—161no—
306C2×C11#199911yescharacteristic
307C2×C11#200811yescharacteristic
308C2×C11#201811yescharacteristic
309D11—162no—
310C24—21no—
311C24—441no—
312#41—41no—
313#41—41no—
314#41—41no—
315#41—41no—
316C2×Q8—21no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—41no—
326C2×D4—222no—
327C2×D4—222no—
328C2×D4—222no—
329C2×D4—441no—
330C2×D4—441no—
331C2×D4—441no—
332C2×D4—441no—
333C2×D4—441no—
334C2×D4—441no—
335C2×D4—441no—
336C2×D4—882no—
337C2×D4—882no—
338C2×D4#432312yescomplemented
339C22×C4—21no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—82no—
344C22×C4D4×D1111yescharacteristic
345C22×C4#434111yescharacteristic
346C22×C4C2×C22⋊D1111yescharacteristic
347SD16—44no—
348D8—44no—
349D8—448no—
350D8—884no—
351M16—41no—
352M16—41no—
353C2×C8—22no—
354C2×C8—222no—
355C2×C8—222no—
356C2×C8—441no—
357C2×C8—441no—
358C2×C8—441no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C42D4×D1111yescharacteristic
368C42D4×D1111yescharacteristic
369C42C2×C22⋊D1111yescharacteristic
370C42C2×C22⋊D1111yescharacteristic
371C11#1017611yescharacteristic, complemented, Sylow
372C23—22no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—81no—
377C23—81no—
378C23—442no—
379C23—882no—
380C23—882no—
381C23—881no—
382C23—881no—
383C23#6699211yescharacteristic
384Q8—41no—
385Q8—41no—
386D4—22no—
387D4—22no—
388D4—42no—
389D4—42no—
390D4—41no—
391D4—41no—
392D4—41no—
393D4—41no—
394D4—81no—
395D4—81no—
396D4—444no—
397D4—442no—
398D4—442no—
399D4—882no—
400D4—882no—
401D4—882no—
402D4—881no—
403D4—881no—
404C2×C4—22no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—82no—
409C2×C4—82no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4—81no—
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—81no—
435C22—81no—
436C22—81no—
437C22—882no—
438C22—882no—
439C22—882no—
440C22—1762no—
441C22—1762no—
442C22#1062265111yescharacteristic
443C22#1062265211yescharacteristic
444C22#1062283611yescharacteristic
445C4—21no—
446C4—21no—
447C4—21no—
448C4—81no—
449C4—81no—
450C4#1062264911yescharacteristic
451C4#1062265011yescharacteristic
452C4#1062281212yes—
453C4#1062283011yescharacteristic
454C4#1062285111yescharacteristic
455C2—21no—
456C2—21no—
457C2—82no—
458C2—161no—
459C2—1762no—
460C2#1306961211yescharacteristic
461C2#1306966611yescharacteristic
462C2#1306972211yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3036C2
socleC22×C11#392
hypercenter#3036D11
hypocenterC11#10176
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #13079531C2semidirect
2. C2×#10622628C2semidirect
3. #13067285C2semidirect
4. #13067015C2semidirect
5. #13066937C2semidirect
6. #13066511C2semidirect
7. C11×#3036C2semidirect
96. C2×D4×C11D8semidirect
142. #3036D11semidirect
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
#130795312
C2×#106226282
#130672852
#130670152
#130669372
#130665112
C11×#30362
#1017611