Finite Group Databasebeta

← #14656247

Subgroups — #14656247

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#13079923C211yesmaximal, characteristic
2#13078088C211yesmaximal, characteristic, complemented
3#13069553C211yesmaximal, characteristic, complemented
4#13067067C211yesmaximal, characteristic, complemented
5#13067066C211yesmaximal, characteristic, complemented
6#13066490C211yesmaximal, characteristic, complemented
7C11×#3037C211yesmaximal, characteristic, complemented
8C2×C11×#137—21no—
9C11×#532C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C2×#66995—21no—
12#10623008C2211yescharacteristic
13C11×#464—22no—
14C11×#462—21no—
15C11×#460—21no—
16C11×#423C2211yescharacteristic
17C11×#417—21no—
18#10622700—21no—
19#10622685—21no—
20#10622651—22no—
21#10622644—21no—
22#10622641—22no—
23#10622640—21no—
24#10622628—21no—
25#10622620—21no—
26#10622579—21no—
27#10622537C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29C2×C4×C11⋊C8C2211yescharacteristic
30D4⋊(C11⋊C8)—22no—
31#10622162—22no—
32#10622121—22no—
33C2×C11×#41—21no—
34C22×Q8×C11D411yescharacteristic
35C2×#4339—21no—
36C11×#137—42no—
37C11×#137—42no—
38C2×C11×Q16—22no—
39C2×C11×SD16—22no—
40C2×C11×M16—21no—
41C11×C4⋊Q8D411yescharacteristic
42C11×#127D411yescharacteristic
43C11×#124—21no—
44C11×#121—21no—
45C11×#121—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C42×C11—21no—
55C2×C42×C11C2311yescharacteristic
56C2×#4326—22no—
57#66995—42no—
58#66995—42no—
59C2×#4325—22no—
60C2×#4323—22no—
61#66983—21no—
62#66983—21no—
63C2×#4318—21no—
64C22×C11⋊C8—21no—
65C22×C11⋊C8D412yes—
66#66928—21no—
67#66927D411yescharacteristic
68C4×D44—21no—
69C4×D44—21no—
70#66922D411yescharacteristic
71C11×C4⋊C8—21no—
72C11×C4⋊C8D412yes—
73C11×#103—22no—
74C11×#102—22no—
75#66896—22no—
76#66874—22no—
77#66873—22no—
78#66873—22no—
79#66871—22no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)—21no—
83C4⋊(C11⋊C8)D412yes—
84C4×C11⋊C8—21no—
85C4×C11⋊C8—21no—
86#10255—111nomaximal, Sylow
87C11×#41—41no—
88C11×#41—41no—
89C11×#41—41no—
90C11×#41—41no—
91C2×Q8×C11—21no—
92C2×Q8×C11—21no—
93C2×Q8×C11—21no—
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11D812yescomplemented
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—41no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—41no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C2×C22⋊D11—41no—
109#4339—41no—
110#4339—41no—
111#4339—41no—
112#4339—41no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44—21no—
116C2×C4×D11—41no—
117C2×Dic22—21no—
118C11×Q16—44no—
119C11×SD16—44no—
120C11×M16—41no—
121C11×M16—41no—
122C2×C8×C11—22no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4—41no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—41no—
131C42×C11—41no—
132C42×C11—41no—
133C42×C11C2×D411yescharacteristic
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137#4326—44no—
138#4325—44no—
139#4323—82no—
140(C2×D11)⋊C4—41no—
141(C2×D11)⋊C4—41no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144#4318—41no—
145#4318—41no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—42no—
150C2×C11⋊C8—41no—
151C2×C11⋊C8—41no—
152#3245—111no—
153#3037—111no—
154#3037D1111yescharacteristic, complemented
155#1984—111no—
156#1492—111no—
157#1492—111no—
158#1292—111no—
159C23×C11—41no—
160C23×C11#12111yescharacteristic
161C22×D11—41no—
162Q8×C11—22no—
163Q8×C11—22no—
164Q8×C11—41no—
165Q8×C11—41no—
166Q8×C11—41no—
167Q8×C11—41no—
168D4×C11—42no—
169D4×C11—41no—
170D4×C11—41no—
171D4×C11—41no—
172D4×C11—41no—
173D4×C11—81no—
174D4×C11—81no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—22no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—81no—
185C2×C4×C11—81no—
186C2×C4×C11#12011yescharacteristic
187C2×C4×C11#12011yescharacteristic
188C2×C4×C11#12011yescharacteristic
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11#12111yescharacteristic
191C2×C4×C11#12711yescharacteristic
192C2×C4×C11C2×D811yescharacteristic
193C2×C4×C11#13511yescharacteristic
194C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
195C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
196C22⋊D11—81no—
197C22⋊D11—81no—
198C2×Dic11—41no—
199D44—42no—
200D44—41no—
201D44—41no—
202D44—41no—
203D44—41no—
204C4×D11—81no—
205C4×D11—81no—
206Dic22—41no—
207Dic22—41no—
208C8×C11—42no—
209C11⋊C8—42no—
210C11⋊C8—42no—
211C11⋊C8—42no—
212C2×#137—21no—
213C2×#137—221no—
214#532—111no—
215#532C2×D1111yescharacteristic
216C2×C4×Q8C2×D1111yescharacteristic
217#474—221no—
218#474—221no—
219#466—222no—
220#464—22no—
221#464—222no—
222#462—21no—
223#462—221no—
224#460—21no—
225#460—221no—
226#459—221no—
227#459—221no—
228#423—111no—
229#423C2×D1111yescharacteristic
230C2×C4⋊C8—111no—
231#417—21no—
232#417—221no—
233C2×C4×C8—111no—
234#336—222no—
235D4⋊C8—222no—
236D4⋊C8—222no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11—81no—
242C22×C11#39211yescharacteristic
243C22×C11#46611yescharacteristic
244C22×C11#46911yescharacteristic
245C2×D11—81no—
246C2×D11—81no—
247C2×D11—81no—
248C4×C11—21no—
249C4×C11—21no—
250C4×C11—21no—
251C4×C11—42no—
252C4×C11—81no—
253C4×C11—81no—
254C4×C11#44711yescharacteristic
255C4×C11#44711yescharacteristic
256C4×C11#44911yescharacteristic
257C4×C11#44911yescharacteristic
258C4×C11#45511yescharacteristic
259C4×C11#45611yescharacteristic
260Dic11—81no—
261C2×#41—21no—
262C2×#41—221no—
263C22×Q8C22⋊D1111yescharacteristic
264#137—42no—
265#137—42no—
266#137—442no—
267#137—442no—
268C2×Q16—22no—
269C2×Q16—222no—
270C2×SD16—22no—
271C2×SD16—222no—
272C2×D8—222no—
273C2×M16—21no—
274C2×M16—221no—
275C22×C8—112no—
276C22×C8—221no—
277C4⋊Q8—111no—
278C4⋊Q8C22⋊D1111yescharacteristic
279#127—111no—
280#127C22⋊D1111yescharacteristic
281#124—21no—
282#124—221no—
283#121—21no—
284#121—21no—
285#121—221no—
286#121—221no—
287C4×Q8—21no—
288C4×Q8—21no—
289C4×Q8—21no—
290C4×Q8—21no—
291C4×D4—21no—
292C4×D4—21no—
293C4×D4—221no—
294C4×D4—221no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4C22⋊D1111yescharacteristic
297C2×C42—21no—
298C2×C42C22×D1111yescharacteristic
299#107—222no—
300C4⋊C8—21no—
301C4⋊C8—112no—
302C4⋊C8—221no—
303C4⋊C8—221no—
304C4⋊C8—221no—
305C4⋊C8C22⋊D1112yes—
306#103—22no—
307#103—222no—
308#102—22no—
309#102—222no—
310#102—222no—
311#102—222no—
312C4×C8—221no—
313C4×C8—221no—
314C2×C11—21no—
315C2×C11—21no—
316C2×C11—161no—
317C2×C11#199911yescharacteristic
318C2×C11#200711yescharacteristic
319C2×C11#201711yescharacteristic
320D11—161no—
321#41—41no—
322#41—41no—
323#41—41no—
324#41—41no—
325#41—441no—
326#41—441no—
327#41—441no—
328#41—441no—
329C2×Q8—21no—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8—221no—
336C2×Q8#432312yescomplemented
337C2×D4—21no—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—41no—
341C2×D4—221no—
342C2×D4—221no—
343C2×D4—221no—
344C2×D4—441no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—41no—
348C22×C4—441no—
349C22×C4D4×D1111yescharacteristic
350C22×C4#434111yescharacteristic
351C22×C4C2×C22⋊D1111yescharacteristic
352Q16—44no—
353Q16—444no—
354SD16—44no—
355SD16—444no—
356D8—882no—
357M16—41no—
358M16—41no—
359M16—441no—
360M16—441no—
361C2×C8—22no—
362C2×C8—222no—
363C2×C8—222no—
364C2×C8—222no—
365C2×C8—441no—
366C2×C8—441no—
367C2×C8—442no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—441no—
379C22⋊C4—441no—
380C42—41no—
381C42—41no—
382C42D4×D1111yescharacteristic
383C42D4×D1111yescharacteristic
384C42C2×C22⋊D1111yescharacteristic
385C42C2×C22⋊D1111yescharacteristic
386C11#1025511yescharacteristic, complemented, Sylow
387C23—41no—
388C23—441no—
389C23#6699211yescharacteristic
390Q8—22no—
391Q8—22no—
392Q8—41no—
393Q8—41no—
394Q8—41no—
395Q8—41no—
396Q8—441no—
397Q8—441no—
398D4—42no—
399D4—41no—
400D4—41no—
401D4—41no—
402D4—41no—
403D4—81no—
404D4—81no—
405D4—442no—
406D4—441no—
407D4—441no—
408D4—441no—
409D4—441no—
410D4—881no—
411D4—881no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—441no—
424C2×C4—881no—
425C2×C4—881no—
426C2×C4C2×#432311yescharacteristic
427C2×C4#6698511yescharacteristic
428C2×C4#6699011yescharacteristic
429C2×C4#6699011yescharacteristic
430C2×C4#6699111yescharacteristic
431C2×C4#6699211yescharacteristic
432C2×C4#6699311yescharacteristic
433C2×C4#6700211yescharacteristic
434C2×C4#6700311yescharacteristic
435C2×C4#6700611yescharacteristic
436C8—42no—
437C8—442no—
438C8—442no—
439C8—442no—
440C22—21no—
441C22—21no—
442C22—81no—
443C22—81no—
444C22—81no—
445C22—881no—
446C22—881no—
447C22—881no—
448C22#1062265111yescharacteristic
449C22#1062265211yescharacteristic
450C22#1062283611yescharacteristic
451C4—21no—
452C4—21no—
453C4—21no—
454C4—42no—
455C4—81no—
456C4—81no—
457C4—881no—
458C4#1062264911yescharacteristic
459C4#1062265011yescharacteristic
460C4#1062281511yescharacteristic
461C4#1062281811yescharacteristic
462C4#1062283011yescharacteristic
463C4#1062285111yescharacteristic
464C2—21no—
465C2—21no—
466C2—161no—
467C2—1761no—
468C2#1306961211yescharacteristic
469C2#1306966111yescharacteristic
470C2#1306971911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3037C2
socleC22×C11#392
prime radical#13079923C2
hypercenter#3037D11
hypocenterC11#10255
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3037

Complements

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

NH ≅ G/Ntype
2. #13078088C2semidirect
3. #13069553C2semidirect
4. #13067067C2semidirect
5. #13067066C2semidirect
6. #13066490C2semidirect
7. C11×#3037C2semidirect
97. C2×Q8×C11D8semidirect
154. #3037D11semidirect
336. C2×Q8#4323semidirect
386. C11#10255semidirect

Maximal subgroups

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

subgroupindex
#130799232
#130780882
#130695532
#130670672
#130670662
#130664902
C11×#30372
#1025511