Finite Group Databasebeta

← #14826379

Subgroups — #14826379

Order 2816.

690 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072488C211yesmaximal, characteristic
2#13070001C211yesmaximal, characteristic
3#13069954C211yesmaximal, characteristic, complemented
4#13069951C211yesmaximal, characteristic, complemented
5#13069759C211yesmaximal, characteristic
6#13069573C211yesmaximal, characteristic, complemented
7#13069356C211yesmaximal, characteristic, complemented
8#13069243C211yesmaximal, characteristic
9#13069236C211yesmaximal, characteristic
10#13069194C211yesmaximal, characteristic, complemented
11#13069187C211yesmaximal, characteristic, complemented
12#13069182C211yesmaximal, characteristic, complemented
13#13068876C211yesmaximal, characteristic
14#13068444C211yesmaximal, characteristic
15C11×#2370C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C2×#66923C2211yescharacteristic
19C11×#389—21no—
20C11×#389C2211yescharacteristic
21C11×#389C2211yescharacteristic
22C11×#387—21no—
23C11×#387—21no—
24C4×C11×C4⋊C4—21no—
25C4×C11×C4⋊C4C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29#10622605—21no—
30#10622602—21no—
31C2×#66873C2211yescharacteristic
32C2×#66873C2211yescharacteristic
33C2×#66873C2211yescharacteristic
34C2×#66873C2211yescharacteristic
35C2×#66872C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39#10622552C2211yescharacteristic
40#10622552C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45#10622289—21no—
46#10622280—21no—
47#10622167C2211yescharacteristic
48#10622167C2211yescharacteristic
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C11×#125—22no—
62C11×#125—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11—21no—
74C2×C42×C11—21no—
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C4×D44—22no—
96C4×D44—41no—
97#66923—22no—
98#66923—41no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95D411yescharacteristic
105C11×#95D411yescharacteristic
106C11⋊#95—21no—
107C11⋊#95—21no—
108#66873—22no—
109#66873—22no—
110#66873—41no—
111#66873Q814yes—
112#66872—22no—
113#66872—22no—
114#66871—22no—
115#66871—41no—
116C4⋊(C11⋊C8)—41no—
117#66867—41no—
118#27027—111nomaximal, Sylow
119C23×D11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2411yescharacteristic
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44C2×Q812yes—
140C2×C4×D11—42no—
141C2×C4×D11—42no—
142C2×C4×D11—81no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—41no—
151C11×C4⋊C4—41no—
152C11×C4⋊C4—42no—
153C11×C4⋊C4—81no—
154C11×C4⋊C4C2×Q812yes—
155C11×C4⋊C4#4112yes—
156C11×C4⋊C4#4112yes—
157C42×C11—21no—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11—42no—
164C42×C11—81no—
165C42×C11—81no—
166(C2×D11)⋊C4—42no—
167(C2×D11)⋊C4—42no—
168(C2×D11)⋊C4—81no—
169(C2×D11)⋊C4—81no—
170(C2×D11)⋊C4—81no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11#4112yes—
177Dic11⋊C4—42no—
178Dic11⋊C4—42no—
179Dic11⋊C4—81no—
180Dic11⋊C4—81no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8C2×Q812yes—
193#2454—111no—
194#2370D1111yescharacteristic, complemented
195#2067—111no—
196#2059—111no—
197#2059—111no—
198#2025—111no—
199#1989—111no—
200#1944—111no—
201#1926—111no—
202#1925—111no—
203#1919—111no—
204#1918—111no—
205#1917—111no—
206#1864—111no—
207#1762—111no—
208C23×C11C22×D411yescharacteristic
209C22×D11—22no—
210C22×D11—41no—
211C22×D11—41no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—22no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11C22×Q811yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11H(5,𝔽2)11yescharacteristic
251C2×C4×C112−1+411yescharacteristic
252C2×Dic11—22no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261D44—22no—
262D44—22no—
263D44—41no—
264D44—41no—
265C4×D11—84no—
266C11⋊C8—22no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C2×#125—111no—
271C2×#125C2×D1111yescharacteristic
272C2×C4×D4—111no—
273C2×#107—111no—
274C2×#107—111no—
275C2×#106—111no—
276C2×#106—111no—
277C2×C4⋊C8—111no—
278C2×#102—111no—
279C2×#102—111no—
280C2×#102—111no—
281C2×#102—111no—
282C2×#97—111no—
283#399—221no—
284#396—221no—
285#390—111no—
286#390—111no—
287#389—21no—
288#389—111no—
289#389—111no—
290#389C2×D1111yescharacteristic
291#389C2×D1111yescharacteristic
292#387—21no—
293#387—21no—
294#385—221no—
295#380—221no—
296C4×C4⋊C4—21no—
297C4×C4⋊C4C2×D1111yescharacteristic
298C4×C4⋊C4C2×D1111yescharacteristic
299C4×C4⋊C4C2×D1111yescharacteristic
300C4×C4⋊C4C2×D1111yescharacteristic
301#340—111no—
302#340—111no—
303#340—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#336—111no—
310#336—111no—
311#336—111no—
312#336—111no—
313C22×C11#52511yescharacteristic
314C22×C11#54611yescharacteristic
315C22×C11D4×Q811yescharacteristic
316C22×C11#57511yescharacteristic
317C22×C11#57511yescharacteristic
318C22×C11#57611yescharacteristic
319C22×C11#57711yescharacteristic
320C2×D11—42no—
321C2×D11—42no—
322C2×D11—42no—
323C2×D11—81no—
324C2×D11—81no—
325C2×D11—81no—
326C2×D11—81no—
327C4×C11—41no—
328C4×C11—42no—
329C4×C11—41no—
330C4×C11—42no—
331C4×C11—42no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—81no—
337C4×C11#53311yescharacteristic
338C4×C11#54211yescharacteristic
339C4×C11#55411yescharacteristic
340C4×C11#55611yescharacteristic
341Dic11—42no—
342Dic11—81no—
343Dic11—81no—
344C22×D4—111no—
345C23×C4—221no—
346C22×C8—111no—
347C22×C8—111no—
348C22×C8—111no—
349C22×C8—111no—
350#125—22no—
351#125—22no—
352#125—222no—
353#125—441no—
354C4×D4—222no—
355C4×D4—441no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4C22⋊D1111yescharacteristic
368C2×C4⋊C4C22⋊D1111yescharacteristic
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C22⋊C4—221no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C22⋊C4—221no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42C22×D1111yescharacteristic
382C2×C42C22×D1111yescharacteristic
383C2×C42C22×D1111yescharacteristic
384#107—222no—
385#107—441no—
386#106—222no—
387#106—222no—
388C4⋊C8—441no—
389#102—114no—
390#102—222no—
391#102—222no—
392#102—441no—
393#97—441no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—221no—
400#95—221no—
401#95C22⋊D1111yescharacteristic
402#95C22⋊D1111yescharacteristic
403C2×C11#246511yescharacteristic
404C2×C11#311111yescharacteristic
405C2×C11#311911yescharacteristic
406C2×C11#330911yescharacteristic
407C2×C11#332311yescharacteristic
408C2×C11#338811yescharacteristic
409C2×C11#338911yescharacteristic
410D11—82no—
411C24—221no—
412C2×D4—112no—
413C2×D4—221no—
414C2×D4—221no—
415C2×D4—221no—
416C2×D4—221no—
417C2×D4—221no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—442no—
426C22×C4—442no—
427C22×C4—881no—
428C22×C4C2×C22⋊D1111yescharacteristic
429C22×C4C2×C22⋊D1111yescharacteristic
430C22×C4C2×C22⋊D1111yescharacteristic
431C22×C4C2×C22⋊D1111yescharacteristic
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C23×D1111yescharacteristic
435C2×C8—112no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C4⋊C4—24no—
448C4⋊C4—24no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—42no—
457C4⋊C4—81no—
458C4⋊C4—112no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—442no—
465C4⋊C4—442no—
466C4⋊C4—881no—
467C4⋊C4—881no—
468C4⋊C4#433912yes—
469C4⋊C4#433912yes—
470C4⋊C4Q8×D1112yes—
471C22⋊C4—442no—
472C22⋊C4—442no—
473C22⋊C4—881no—
474C22⋊C4—881no—
475C22⋊C4—881no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—42no—
483C42—81no—
484C42—81no—
485C11#2702711yescharacteristic, complemented, Sylow
486C23—222no—
487C23—441no—
488C23—441no—
489C23—441no—
490C23—441no—
491C23—441no—
492C23—441no—
493C23C22×C22⋊D1111yescharacteristic
494D4—222no—
495D4—222no—
496D4—441no—
497D4—441no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—222no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—884no—
538C2×C4C2×#433911yescharacteristic
539C2×C4C2×#433911yescharacteristic
540C2×C4C2×Q8×D1111yescharacteristic
541C2×C4#6704011yescharacteristic
542C2×C4#41×D1111yescharacteristic
543C2×C4#6704211yescharacteristic
544C8—222no—
545C8—441no—
546C8—441no—
547C8—441no—
548C22—442no—
549C22—442no—
550C22—442no—
551C22—881no—
552C22—881no—
553C22—881no—
554C22—881no—
555C22#1062332211yescharacteristic
556C22Q8×C22⋊D1111yescharacteristic
557C22#1062335311yescharacteristic
558C22#1062335311yescharacteristic
559C22#1062336011yescharacteristic
560C22#1062336611yescharacteristic
561C22#1062336811yescharacteristic
562C4—41no—
563C4—42no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—42no—
568C4—42no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—442no—
573C4—881no—
574C4—881no—
575C4#1062309911yescharacteristic
576C4#1062310911yescharacteristic
577C4#1062311011yescharacteristic
578C4#1062311311yescharacteristic
579C2—882no—
580C2#1307263111yescharacteristic
581C2#1307872511yescharacteristic
582C2#1307881511yescharacteristic
583C2#1308061611yescharacteristic
584C2#1308082611yescharacteristic
585C2#1308155511yescharacteristic
586C2#1308157011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2370C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2370D11
hypocenterC11#27027
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2370

Complements

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

NH ≅ G/Ntype
3. #13069954C2semidirect
4. #13069951C2semidirect
6. #13069573C2semidirect
7. #13069356C2semidirect
10. #13069194C2semidirect
11. #13069187C2semidirect
12. #13069182C2semidirect
15. C11×#2370C2semidirect
194. #2370D11semidirect
485. C11#27027semidirect

Maximal subgroups

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

subgroupindex
#130724882
#130700012
#130699542
#130699512
#130697592
#130695732
#130693562
#130692432
#130692362
#130691942
#130691872
#130691822
#130688762
#130684442
C11×#23702
#2702711