Finite Group Databasebeta

← #14807133

Subgroups — #14807133

Order 2816.

1126 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623072C211yesmaximal, characteristic
2C2×#10622695C211yesmaximal, characteristic, complemented
3C2×#10622703C211yesmaximal, characteristic, complemented
4#13069624C212yesmaximal, complemented
5#13069624C212yesmaximal, complemented
6#13069573C211yesmaximal, characteristic, complemented
7#13069415C211yesmaximal, characteristic
8#13068929C212yesmaximal, complemented
9#13068924C212yesmaximal, complemented
10#13068449C211yesmaximal, characteristic, complemented
11C11×#2542C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C22⋊Q8C2212yes—
14C2×C11×C22⋊Q8C2212yes—
15C2×C4×D4×C11C2211yescharacteristic
16C22×#4326C2212yes—
17C2×#66988—21no—
18C2×#66979C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22#10623072—24no—
23#10623072—24no—
24C2×#66942—21no—
25C2×#66932—21no—
26C2×#66930—21no—
27C2×#66923C2211yescharacteristic
28C2×C4×Dic22C2211yescharacteristic
29C11×#399—21no—
30C11×#399—21no—
31C11×#390—21no—
32C11×#384—21no—
33C4×C11×C4⋊C4C2211yescharacteristic
34C2×#66899C2212yes—
35C2×#66899C2212yes—
36C2×#66899C2212yes—
37C2×C22⋊(C11⋊C8)C2212yes—
38C2×C22⋊(C11⋊C8)C2212yes—
39#10622703—24no—
40#10622695—24no—
41C2×#66874C2212yes—
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×#66867C2211yescharacteristic
44#10622167C2212yes—
45#10622167C2212yes—
46#10622167C2212yes—
47C22×Q8×C11C2312yes—
48C22×D4×C11D411yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×Dic11—21no—
52C22×Dic22C2311yescharacteristic
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8—22no—
55C11×C22⋊Q8—24no—
56C11×C22⋊Q8—24no—
57C11×C22⋊Q8—42no—
58C11×C22⋊Q8—42no—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4D411yescharacteristic
70C2×C11×C22⋊C4D411yescharacteristic
71C2×C42×C11—21no—
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×#4326—24no—
77C2×#4326—42no—
78C2×#4326—42no—
79#66988—28no—
80#66979—22no—
81#66979—22no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88#66977—22no—
89#66977—22no—
90#66977—22no—
91#66977—22no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C22×C11⋊C8C2312yes—
100C22×C11⋊C8C2312yes—
101#66942—28no—
102#66932—28no—
103#66930—28no—
104#66923—22no—
105#66923D414yes—
106C4×Dic22—22no—
107C4×Dic22D414yes—
108C11×#95—21no—
109#66899—24no—
110#66899—24no—
111#66899—24no—
112C22⋊(C11⋊C8)—42no—
113C22⋊(C11⋊C8)—42no—
114#66874—24no—
115C4⋊(C11⋊C8)—22no—
116#66867—22no—
117#25584—111nomaximal, Sylow
118C24×C11C2×D411yescharacteristic
119C24×C11C2×D411yescharacteristic
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—41no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—24no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—42no—
150C22×Dic11—42no—
151C2×Dic22—21no—
152C2×Dic22—22no—
153C2×Dic22—22no—
154C2×Dic22C2×D412yes—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—44no—
158C11×C4⋊C4—44no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4#4114yes—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—44no—
165C11×C22⋊C4—44no—
166C42×C11—42no—
167C42×C11C2×D412yes—
168C42×C11C2×D412yes—
169C22⋊Dic11—24no—
170C22⋊Dic11—24no—
171C22⋊Dic11—24no—
172#4326—48no—
173C4⋊Dic11—24no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11C2×D412yes—
178C4⋊Dic11C2×D412yes—
179C4⋊Dic11C2×D412yes—
180Dic11⋊C4—24no—
181Dic11⋊C4—24no—
182Dic11⋊C4—24no—
183Dic11⋊C4—24no—
184Dic11⋊C4—24no—
185C4×Dic11—24no—
186C4×Dic11—24no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×#552—111no—
194C2×#491—111no—
195C2×#462—111no—
196#2542D1111yescharacteristic
197#2001—112no—
198#2001—112no—
199#1989—111no—
200#1955—111no—
201#1873—112no—
202#1872—112no—
203#1763—111no—
204C23×C11—21no—
205C23×C11—22no—
206C23×C11—21no—
207C23×C11—22no—
208C23×C11—21no—
209C23×C11—22no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—22no—
213C23×C11#13712yes—
214C23×C11C22×D411yescharacteristic
215Q8×C11—42no—
216Q8×C11—42no—
217Q8×C11—42no—
218Q8×C11—42no—
219D4×C11—44no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11#12012yes—
240C2×C4×C11#12012yes—
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4112yes—
244C2×C4×C11H(5,𝔽2)12yes—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—48no—
250C2×Dic11—42no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—42no—
256Dic22—22no—
257Dic22—22no—
258Dic22—42no—
259C11⋊C8—42no—
260C11⋊C8—42no—
261C22×Q16—112no—
262#552—224no—
263#552—224no—
264C2×C4⋊Q8C2×D1111yescharacteristic
265C2×#126—221no—
266C2×#125—111no—
267C2×#125—221no—
268C2×#123—221no—
269C2×C22⋊Q8—111no—
270C2×C22⋊Q8—111no—
271C2×C22⋊Q8C2×D1112yes—
272C2×C22⋊Q8C2×D1112yes—
273C2×C4×Q8—111no—
274C2×C4×D4C2×D1111yescharacteristic
275C2×#117—111no—
276C2×#117—221no—
277C22×C4⋊C4—111no—
278#491—224no—
279#462—224no—
280C2×C4⋊C8—111no—
281C2×#103—112no—
282C2×#103—112no—
283C2×#103—112no—
284C2×#103—112no—
285C2×C22⋊C8—112no—
286C2×C22⋊C8—112no—
287C2×#97—111no—
288#399—21no—
289#399—21no—
290#390—21no—
291#384—21no—
292C4×C4⋊C4C2×D1111yescharacteristic
293#340—112no—
294#340—112no—
295#340—112no—
296C22×C11—22no—
297C22×C11—24no—
298C22×C11—41no—
299C22×C11—41no—
300C22×C11—42no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11C2×#12011yescharacteristic
307C22×C11#54612yes—
308C22×C11C2×#13711yescharacteristic
309C22×C11#57511yescharacteristic
310C22×C11#57812yes—
311C4×C11—22no—
312C4×C11—22no—
313C4×C11—41no—
314C4×C11—41no—
315C4×C11—44no—
316C4×C11—82no—
317C4×C11#53211yescharacteristic
318C4×C11#53511yescharacteristic
319C4×C11#55012yes—
320Dic11—42no—
321Dic11—42no—
322Dic11—42no—
323Dic11—42no—
324C22×Q8—111no—
325C22×Q8C22×D1112yes—
326C22×D4C22⋊D1111yescharacteristic
327C23×C4—221no—
328C23×C4C22×D1111yescharacteristic
329C23×C4C22×D1111yescharacteristic
330C2×Q16—224no—
331C2×Q16—442no—
332C2×Q16—442no—
333C22×C8—112no—
334C22×C8—112no—
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337#126—228no—
338#125—114no—
339#125—228no—
340#125—222no—
341#123—228no—
342C22⋊Q8—24no—
343C22⋊Q8—24no—
344C22⋊Q8—42no—
345C22⋊Q8—42no—
346C22⋊Q8—222no—
347C22⋊Q8—222no—
348C22⋊Q8—222no—
349C22⋊Q8—222no—
350C4×Q8—114no—
351C4×Q8—222no—
352C4×D4—22no—
353C4×D4—22no—
354#117—228no—
355#117—222no—
356#117—222no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—222no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4C22⋊D1111yescharacteristic
373C2×C4⋊C4C22×D1112yes—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—221no—
377C2×C22⋊C4—221no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4C22⋊D1111yescharacteristic
380C2×C22⋊C4C22⋊D1111yescharacteristic
381C2×C42—21no—
382C2×C42—221no—
383C2×C42—221no—
384C2×C42C22×D1111yescharacteristic
385C4⋊C8—222no—
386#103—224no—
387#103—224no—
388#103—224no—
389#103—224no—
390C22⋊C8—442no—
391C22⋊C8—442no—
392#97—222no—
393#95—21no—
394C2×C11—42no—
395C2×C11—81no—
396C2×C11#243111yescharacteristic
397C2×C11#300711yescharacteristic
398C2×C11#301111yescharacteristic
399C2×C11#331212yes—
400C2×C11#331512yes—
401C24C2×C22⋊D1111yescharacteristic
402C24C2×C22⋊D1111yescharacteristic
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—112no—
410C2×Q8—221no—
411C2×Q8—222no—
412C2×Q8—222no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—41no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—224no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—442no—
432C22×C4—442no—
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C2×C22⋊D1111yescharacteristic
436C22×C4C2×C22⋊D1111yescharacteristic
437C22×C4C23×D1111yescharacteristic
438Q16—448no—
439C2×C8—222no—
440C2×C8—222no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—222no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—44no—
448C4⋊C4—44no—
449C4⋊C4—42no—
450C4⋊C4—42no—
451C4⋊C4—112no—
452C4⋊C4—112no—
453C4⋊C4—112no—
454C4⋊C4—224no—
455C4⋊C4—224no—
456C4⋊C4—224no—
457C4⋊C4—224no—
458C4⋊C4—224no—
459C4⋊C4—224no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4#434114yes—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—44no—
467C22⋊C4—44no—
468C22⋊C4—224no—
469C22⋊C4—224no—
470C22⋊C4—224no—
471C42—42no—
472C42—224no—
473C42—224no—
474C42D4×D1112yes—
475C42D4×D1112yes—
476C11#2558411yescharacteristic, complemented, Sylow
477C23—21no—
478C23—22no—
479C23—21no—
480C23—22no—
481C23—21no—
482C23—22no—
483C23—21no—
484C23—21no—
485C23—22no—
486C23#6699512yes—
487C23C22×C22⋊D1111yescharacteristic
488Q8—42no—
489Q8—42no—
490Q8—42no—
491Q8—42no—
492Q8—222no—
493Q8—222no—
494Q8—442no—
495D4—44no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—448no—
520C2×C4—442no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—442no—
526C2×C4#6699012yes—
527C2×C4#6699012yes—
528C2×C4C2×D4×D1111yescharacteristic
529C2×C4C2×D4×D1111yescharacteristic
530C2×C4C2×#434112yes—
531C2×C4#6703712yes—
532C8—442no—
533C8—442no—
534C22—24no—
535C22—22no—
536C22—41no—
537C22—42no—
538C22—41no—
539C22—42no—
540C22—41no—
541C22—41no—
542C22—42no—
543C22—41no—
544C22C2×#6699011yescharacteristic
545C22#1062333712yes—
546C22C2×#6699511yescharacteristic
547C22#1062335311yescharacteristic
548C22#1062336912yes—
549C4—22no—
550C4—22no—
551C4—41no—
552C4—41no—
553C4—44no—
554C4—82no—
555C4—442no—
556C4—442no—
557C4—442no—
558C4—442no—
559C4#1062324611yescharacteristic
560C4#1062324711yescharacteristic
561C4#1062324912yes—
562C2—42no—
563C2—81no—
564C2#1307223211yescharacteristic
565C2#1307787411yescharacteristic
566C2#1307790911yescharacteristic
567C2#1308066712yes—
568C2#1308071212yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2542C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#2542D11
hypocenterC11#25584
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2542

Complements

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

NH ≅ G/Ntype
2. C2×#10622695C2semidirect
3. C2×#10622703C2semidirect
4. #13069624C2semidirect
5. #13069624C2semidirect
6. #13069573C2semidirect
8. #13068929C2semidirect
9. #13068924C2semidirect
10. #13068449C2semidirect
476. C11#25584semidirect

Maximal subgroups

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

subgroupindex
C2×#106230722
C2×#106226952
C2×#106227032
#130696242
#130695732
#130694152
#130689292
#130689242
#130684492
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