Finite Group Databasebeta

← #14804181

Subgroups — #14804181

Order 2816.

732 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079012C211yesmaximal, characteristic
2#13078088C211yesmaximal, characteristic
3#13077359C211yesmaximal, characteristic
4#13070062C212yesmaximal, complemented
5#13069916C212yesmaximal, complemented
6#13069606C211yesmaximal, characteristic, complemented
7#13069392C211yesmaximal, characteristic, complemented
8#13069134C212yesmaximal, complemented
9#13068676C212yesmaximal, complemented
10C4×#66900C211yesmaximal, characteristic, complemented
11C2×C11×#475C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×#66995C2212yes—
15C2×#66954C2212yes—
16#10623008C2211yescharacteristic
17C11×#475—21no—
18C11×#475—22no—
19C11×#475—21no—
20C2×C11×#106C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#103C2212yes—
23C2×#66900C2211yescharacteristic
24C2×#66900C2211yescharacteristic
25#10622723C2212yes—
26C2×#66883C2212yes—
27#10622706—21no—
28#10622702—22no—
29#10622701—21no—
30#10622644—21no—
31#10622641—22no—
32#10622640—21no—
33#10622579C2212yes—
34#10622579C2212yes—
35#10622579C2212yes—
36#10622537C2211yescharacteristic
37C4×#4318C2211yescharacteristic
38C4×#4318C2211yescharacteristic
39#10622451—21no—
40#10622449—22no—
41#10622447—21no—
42#10622190C2212yes—
43#10622168C2212yes—
44#10622168C2212yes—
45#10622168C2211yescharacteristic
46#10622168C2211yescharacteristic
47C22×Q8×C11—21no—
48C22×Q8×C11C2311yescharacteristic
49C2×#4339C2312yes—
50C22×C8×C11C2312yes—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C4×Q8×C11—21no—
56C4×Q8×C11—21no—
57C4×Q8×C11—21no—
58C4×Q8×C11—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2312yes—
63C2×C42×C11—21no—
64C2×C42×C11C2311yescharacteristic
65C2×#4326—22no—
66#66995—24no—
67#66995—42no—
68C2×#4325—22no—
69#66983—21no—
70#66983—21no—
71C2×#4318C2311yescharacteristic
72C2×#4318C2312yes—
73C2×#4318C2311yescharacteristic
74C2×#4318C2311yescharacteristic
75C2×#4318C2311yescharacteristic
76#66954—24no—
77#66954—42no—
78C2×#4313—22no—
79C2×C8×D11—22no—
80#66928D412yes—
81#66927D411yescharacteristic
82C4×D44—21no—
83C4×D44—21no—
84#66922D411yescharacteristic
85C11×#106—22no—
86C11×#106—22no—
87C11×C4⋊C8D411yescharacteristic
88C11×C4⋊C8D412yes—
89C11×C4⋊C8D411yescharacteristic
90C11×#103—22no—
91C11×#103—22no—
92#66900—22no—
93#66900—22no—
94(C2×D11)⋊C8—22no—
95(C2×D11)⋊C8—22no—
96#66883—42no—
97#66874—22no—
98#66874—22no—
99#66874—22no—
100#66873—22no—
101#66873—22no—
102#66873—22no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)—21no—
105#66867—21no—
106#66867—21no—
107C4×C11⋊C8—21no—
108C4×C11⋊C8—21no—
109#25361—111nomaximal, Sylow
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—41no—
116C2×Q8×C11—41no—
117C2×Q8×C11—82no—
118C2×Q8×C11#4112yes—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11#4111yescharacteristic
123C22×C4×C11#4111yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C2×C22⋊D11—22no—
126#4339—22no—
127#4339—22no—
128#4339—22no—
129#4339—22no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44C2×D412yes—
133C2×C4×D11—22no—
134C2×Dic22C2×D412yes—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11C2×D412yes—
138C2×C8×C11C2×D412yes—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—41no—
144C11×C4⋊C4—41no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4—41no—
147C42×C11—41no—
148C42×C11—41no—
149C42×C11C2×D411yescharacteristic
150C42×C11C2×D411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153#4326—44no—
154#4325—44no—
155(C2×D11)⋊C4—22no—
156(C2×D11)⋊C4—22no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159#4318—21no—
160#4318—21no—
161#4318—21no—
162#4318—22no—
163#4318—21no—
164#4318—21no—
165#4318—22no—
166#4318—21no—
167#4318—21no—
168#4318#4112yes—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—22no—
174#4313—44no—
175C8×D11—44no—
176#3141—111no—
177C2×#475D1111yescharacteristic, complemented
178#3037—111no—
179#2935—111no—
180#2079—112no—
181#2052—112no—
182#1997—111no—
183#1950—111no—
184#1908—112no—
185#1815—112no—
186C4×#101—111no—
187C23×C11C2×#4111yescharacteristic
188C22×D11—22no—
189Q8×C11—22no—
190Q8×C11—22no—
191Q8×C11—41no—
192Q8×C11—41no—
193Q8×C11—82no—
194Q8×C11—82no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—42no—
202C2×C4×C11—81no—
203C2×C4×C11—82no—
204C2×C4×C11#12111yescharacteristic
205C2×C4×C11#12111yescharacteristic
206C2×C4×C11#12111yescharacteristic
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C11H(5,𝔽2)11yescharacteristic
213C2×C4×C112−1+411yescharacteristic
214C22⋊D11—42no—
215C22⋊D11—42no—
216C2×Dic11—22no—
217D44—22no—
218D44—22no—
219D44—42no—
220D44—81no—
221C4×D11—42no—
222C4×D11—42no—
223Dic22—22no—
224Dic22—22no—
225C8×C11—22no—
226C8×C11—22no—
227C11⋊C8—22no—
228C11⋊C8—41no—
229C11⋊C8—42no—
230C11⋊C8—41no—
231C11⋊C8—41no—
232C2×#137—112no—
233C2×#131—112no—
234#532—111no—
235C2×C4⋊Q8C2×D1111yescharacteristic
236C2×C4×Q8C2×D1111yescharacteristic
237#489—222no—
238#487—221no—
239#486—221no—
240#475—21no—
241#475—22no—
242#475—21no—
243#464—222no—
244#462—221no—
245#460—221no—
246#436—221no—
247#435—222no—
248C8×D4—221no—
249C2×#108—112no—
250C2×#106C2×D1112yes—
251#423—111no—
252C2×C4⋊C8C2×D1111yescharacteristic
253#417—112no—
254#417—112no—
255#417—112no—
256C2×#103C2×D1112yes—
257C2×#101—111no—
258C2×#101—111no—
259#408—112no—
260C4×M16—111no—
261C4×M16—111no—
262#343—112no—
263#343—111no—
264#343—112no—
265#343—111no—
266#341—112no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11C2×#12111yescharacteristic
270C22×C11#52911yescharacteristic
271C22×C11#54211yescharacteristic
272C2×D11—42no—
273C2×D11—42no—
274C2×D11—42no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—42no—
279C4×C11—82no—
280C4×C11—81no—
281C4×C11#47112yes—
282C4×C11#54611yescharacteristic
283C4×C11#54611yescharacteristic
284C4×C11#54711yescharacteristic
285C4×C11#54811yescharacteristic
286Dic11—42no—
287C2×#41—112no—
288C22×Q8—21no—
289C22×Q8C22×D1111yescharacteristic
290#137—224no—
291#137—442no—
292C2×Q16—222no—
293C2×SD16—222no—
294#131—224no—
295#131—442no—
296C2×M16—111no—
297C2×M16—112no—
298C2×M16—111no—
299C2×M16—111no—
300C2×M16—111no—
301C2×M16—222no—
302C22×C8—222no—
303C22×C8C22×D1112yes—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8—111no—
309#127—111no—
310#124—112no—
311#121—221no—
312#121—221no—
313C4×Q8—21no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×Q8—21no—
317C4×D4—221no—
318C4×D4—221no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4C22×D1111yescharacteristic
322C2×C4⋊C4C22×D1112yes—
323C2×C42—21no—
324C2×C42C22×D1111yescharacteristic
325#108—442no—
326#106—22no—
327#106—22no—
328C4⋊C8—221no—
329C4⋊C8—221no—
330C4⋊C8C22⋊D1111yescharacteristic
331C4⋊C8C22⋊D1112yes—
332C4⋊C8C22⋊D1111yescharacteristic
333#103—22no—
334#103—22no—
335#103—222no—
336#103—222no—
337#103—222no—
338#102—222no—
339#102—222no—
340#102—222no—
341#101—222no—
342#101—222no—
343C22⋊C8—222no—
344C22⋊C8—222no—
345#97—221no—
346#97—221no—
347C4×C8—221no—
348C4×C8—221no—
349C2×C11—21no—
350C2×C11—21no—
351C2×C11#242711yescharacteristic
352C2×C11C2×#47111yescharacteristic
353C2×C11#306911yescharacteristic
354D11—82no—
355#41—222no—
356#41—222no—
357#41—222no—
358#41—222no—
359C2×Q8—21no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—41no—
365C2×Q8—41no—
366C2×Q8—82no—
367C2×Q8—112no—
368C2×Q8#434312yes—
369C2×D4—112no—
370C2×D4—222no—
371C2×D4—221no—
372C2×D4—221no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—222no—
377C22×C4#434111yescharacteristic
378C22×C4#434111yescharacteristic
379C22×C4C23×D1111yescharacteristic
380Q16—444no—
381SD16—444no—
382M16—112no—
383M16—221no—
384M16—221no—
385M16—221no—
386M16—222no—
387M16—221no—
388M16—221no—
389M16—221no—
390M16—221no—
391M16—222no—
392M16—444no—
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—221no—
396C2×C8—221no—
397C2×C8—221no—
398C2×C8—222no—
399C2×C8—221no—
400C2×C8—444no—
401C2×C8C2×C22⋊D1112yes—
402C2×C8C2×C22⋊D1112yes—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C22⋊C4—222no—
414C22⋊C4—222no—
415C42—41no—
416C42—41no—
417C42D4×D1111yescharacteristic
418C42D4×D1111yescharacteristic
419C42C2×C22⋊D1111yescharacteristic
420C42C2×C22⋊D1111yescharacteristic
421C11#2536111yescharacteristic, complemented, Sylow
422C23—222no—
423C23C2×#434111yescharacteristic
424Q8—22no—
425Q8—22no—
426Q8—41no—
427Q8—41no—
428Q8—82no—
429Q8—82no—
430Q8—222no—
431Q8—222no—
432D4—222no—
433D4—222no—
434D4—442no—
435D4—442no—
436D4—442no—
437D4—881no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—81no—
446C2×C4—82no—
447C2×C4—222no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4#6699111yescharacteristic
451C2×C4#6699111yescharacteristic
452C2×C4#6699111yescharacteristic
453C2×C4#6699111yescharacteristic
454C2×C4C2×D4×D1111yescharacteristic
455C2×C4C2×#434311yescharacteristic
456C2×C4#6704011yescharacteristic
457C2×C4#41×D1111yescharacteristic
458C2×C4#6704211yescharacteristic
459C2×C4C22×C22⋊D1111yescharacteristic
460C8—22no—
461C8—22no—
462C8—222no—
463C8—441no—
464C8—442no—
465C8—441no—
466C8—441no—
467C22—21no—
468C22—21no—
469C22—442no—
470C22—442no—
471C22—442no—
472C22#1062315511yescharacteristic
473C22#1062317411yescharacteristic
474C22C2×#6699111yescharacteristic
475C4—21no—
476C4—21no—
477C4—21no—
478C4—42no—
479C4—82no—
480C4—81no—
481C4—442no—
482C4#1062279012yes—
483C4#1062316111yescharacteristic
484C4#1062316211yescharacteristic
485C4#1062334811yescharacteristic
486C4#1062336011yescharacteristic
487C2—21no—
488C2—21no—
489C2—882no—
490C2#1307218911yescharacteristic
491C2C2×#1062279011yescharacteristic
492C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#475C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenterC2×#475D11
hypocenterC11#25361
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
4. #13070062C2semidirect
5. #13069916C2semidirect
6. #13069606C2semidirect
7. #13069392C2semidirect
8. #13069134C2semidirect
9. #13068676C2semidirect
10. C4×#66900C2semidirect
11. C2×C11×#475C2semidirect
177. C2×#475D11semidirect
421. C11#25361semidirect

Maximal subgroups

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

subgroupindex
#130790122
#130780882
#130773592
#130700622
#130699162
#130696062
#130693922
#130691342
#130686762
C4×#669002
C2×C11×#4752
#2536111