Finite Group Databasebeta

← #14826364

Subgroups — #14826364

Order 2816.

726 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072466C211yesmaximal, characteristic
2#13069987C211yesmaximal, characteristic
3#13069951C211yesmaximal, characteristic, complemented
4#13069949C211yesmaximal, characteristic, complemented
5#13069759C211yesmaximal, characteristic
6#13069568C211yesmaximal, characteristic, complemented
7#13069351C211yesmaximal, characteristic, complemented
8#13069243C211yesmaximal, characteristic
9#13069236C211yesmaximal, characteristic
10#13069201C211yesmaximal, characteristic, complemented
11#13069201C211yesmaximal, characteristic, complemented
12#13069182C211yesmaximal, characteristic, complemented
13#13068876C211yesmaximal, characteristic
14#13068444C211yesmaximal, characteristic
15C11×#2370C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×#66949—21no—
18C2×C4×D44C2211yescharacteristic
19C2×#66922C2211yescharacteristic
20C11×#389—21no—
21C11×#389C2211yescharacteristic
22C11×#389C2211yescharacteristic
23C11×#387—21no—
24C11×#387—21no—
25C4×C11×C4⋊C4—21no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30#10622607—21no—
31C2×#66873C2211yescharacteristic
32C2×#66873C2211yescharacteristic
33C2×#66873C2211yescharacteristic
34C2×#66873C2211yescharacteristic
35C2×#66872C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39#10622552C2211yescharacteristic
40#10622552C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45#10622286—21no—
46#10622281—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—
61C22×Dic22—21no—
62C11×#125—22no—
63C11×#125—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11—21no—
75C2×C42×C11—21no—
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95#66949—44no—
96C4×D44—22no—
97C4×D44—41no—
98#66922—22no—
99#66922—41no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95D411yescharacteristic
106C11×#95D411yescharacteristic
107C11⋊#95—21no—
108C11⋊#95—21no—
109#66873—22no—
110#66873—22no—
111#66873—41no—
112#66873Q814yescomplemented
113#66872—22no—
114#66872—22no—
115#66872—41no—
116#66871—22no—
117C4⋊(C11⋊C8)—41no—
118#66867—41no—
119#27026—111nomaximal, Sylow
120C23×D11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44C2×Q812yes—
141C2×C4×D11—42no—
142C2×C4×D11—42no—
143C2×C4×D11—81no—
144C2×Dic22—42no—
145C2×Dic22—42no—
146C2×Dic22—81no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—41no—
156C11×C4⋊C4—42no—
157C11×C4⋊C4—81no—
158C11×C4⋊C4C2×Q812yes—
159C11×C4⋊C4#4112yes—
160C11×C4⋊C4#4112yes—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—42no—
168C42×C11—81no—
169C42×C11—81no—
170(C2×D11)⋊C4—42no—
171(C2×D11)⋊C4—42no—
172(C2×D11)⋊C4—42no—
173(C2×D11)⋊C4—42no—
174(C2×D11)⋊C4—81no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—42no—
181C4⋊Dic11#4112yes—
182Dic11⋊C4—42no—
183Dic11⋊C4—42no—
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⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8C2×Q812yes—
196#2452—111no—
197#2370D1111yescharacteristic, complemented
198#2065—111no—
199#2059—111no—
200#2058—111no—
201#2025—111no—
202#1988—111no—
203#1943—111no—
204#1926—111no—
205#1925—111no—
206#1920—111no—
207#1920—111no—
208#1917—111no—
209#1864—111no—
210#1762—111no—
211C23×C11C22×D411yescharacteristic
212C22×D11—22no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—41no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
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—21no—
238C2×C4×C11—21no—
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×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11AGL(1,ℤ/8)12yes—
249C2×C4×C11C22×Q811yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
254C2×C4×C112−1+411yescharacteristic
255C2×Dic11—22no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264D44—22no—
265D44—22no—
266D44—41no—
267D44—41no—
268C4×D11—84no—
269Dic22—84no—
270C11⋊C8—22no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C2×C4⋊Q8—111no—
275C2×#125C2×D1111yescharacteristic
276C2×C22⋊Q8—221no—
277C2×C4×D4—111no—
278C2×#107—111no—
279C2×#106—111no—
280C2×#106—111no—
281C2×#106—111no—
282C2×C4⋊C8—111no—
283C2×#102—111no—
284C2×#102—111no—
285C2×#102—111no—
286C2×#102—111no—
287C2×#97—111no—
288#396—221no—
289#393—221no—
290#390—111no—
291#390—111no—
292#389—21no—
293#389—111no—
294#389—111no—
295#389C2×D1111yescharacteristic
296#389C2×D1111yescharacteristic
297#387—21no—
298#387—21no—
299#385—221no—
300C4×C4⋊C4—21no—
301C4×C4⋊C4C2×D1111yescharacteristic
302C4×C4⋊C4C2×D1111yescharacteristic
303C4×C4⋊C4C2×D1111yescharacteristic
304C4×C4⋊C4C2×D1111yescharacteristic
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#336—111no—
314#336—111no—
315#336—111no—
316#336—111no—
317C22×C11#52511yescharacteristic
318C22×C11#54611yescharacteristic
319C22×C11D4×Q811yescharacteristic
320C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
321C22×C11#57511yescharacteristic
322C22×C11#57711yescharacteristic
323C22×C11#57711yescharacteristic
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—42no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—81no—
330C2×D11—81no—
331C4×C11—22no—
332C4×C11—41no—
333C4×C11—42no—
334C4×C11—41no—
335C4×C11—42no—
336C4×C11—42no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—81no—
341C4×C11#53311yescharacteristic
342C4×C11#54211yescharacteristic
343C4×C11#55411yescharacteristic
344C4×C11#55611yescharacteristic
345Dic11—42no—
346Dic11—81no—
347Dic11—81no—
348C22×Q8—221no—
349C22×D4—111no—
350C23×C4—221no—
351C22×C8—111no—
352C22×C8—111no—
353C22×C8—111no—
354C22×C8—111no—
355C4⋊Q8—222no—
356C4⋊Q8—441no—
357#125—22no—
358#125—22no—
359C22⋊Q8—444no—
360C4×D4—222no—
361C4×D4—441no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4C22⋊D1111yescharacteristic
373C2×C4⋊C4C22⋊D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C22⋊C4—221no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—221no—
381C2×C22⋊C4—221no—
382C2×C22⋊C4—221no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42C22×D1111yescharacteristic
387C2×C42C22×D1111yescharacteristic
388C2×C42C22×D1111yescharacteristic
389#107—222no—
390#106—222no—
391#106—222no—
392#106—441no—
393C4⋊C8—441no—
394#102—114no—
395#102—222no—
396#102—222no—
397#102—441no—
398#97—441no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—221no—
405#95—221no—
406#95C22⋊D1111yescharacteristic
407#95C22⋊D1111yescharacteristic
408C2×C11#246511yescharacteristic
409C2×C11#311511yescharacteristic
410C2×C11#312511yescharacteristic
411C2×C11#331011yescharacteristic
412C2×C11#332611yescharacteristic
413C2×C11#338411yescharacteristic
414C2×C11#338811yescharacteristic
415D11—82no—
416C24—221no—
417C2×Q8—442no—
418C2×Q8—442no—
419C2×Q8—881no—
420C2×D4—112no—
421C2×D4—221no—
422C2×D4—221no—
423C2×D4—221no—
424C2×D4—221no—
425C2×D4—221no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—442no—
434C22×C4—442no—
435C22×C4—881no—
436C22×C4C2×C22⋊D1111yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438C22×C4C2×C22⋊D1111yescharacteristic
439C22×C4C2×C22⋊D1111yescharacteristic
440C22×C4C2×C22⋊D1111yescharacteristic
441C22×C4C2×C22⋊D1111yescharacteristic
442C22×C4C23×D1111yescharacteristic
443C2×C8—112no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C4⋊C4—24no—
456C4⋊C4—24no—
457C4⋊C4—22no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—42no—
465C4⋊C4—81no—
466C4⋊C4—112no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—442no—
473C4⋊C4—442no—
474C4⋊C4—442no—
475C4⋊C4#433912yes—
476C4⋊C4#433912yes—
477C4⋊C4Q8×D1112yes—
478C22⋊C4—442no—
479C22⋊C4—442no—
480C22⋊C4—442no—
481C22⋊C4—442no—
482C22⋊C4—881no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—42no—
490C42—81no—
491C42—81no—
492C11#2702611yescharacteristic, complemented, Sylow
493C23—222no—
494C23—441no—
495C23—441no—
496C23—441no—
497C23—441no—
498C23—441no—
499C23—441no—
500C23C22×C22⋊D1111yescharacteristic
501Q8—884no—
502D4—222no—
503D4—222no—
504D4—441no—
505D4—441no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—222no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—884no—
545C2×C4#6700212yes—
546C2×C4C2×#433911yescharacteristic
547C2×C4C2×#433911yescharacteristic
548C2×C4C2×Q8×D1111yescharacteristic
549C2×C4#6704011yescharacteristic
550C2×C4#41×D1111yescharacteristic
551C2×C4#6704211yescharacteristic
552C8—222no—
553C8—441no—
554C8—441no—
555C8—441no—
556C22—442no—
557C22—442no—
558C22—442no—
559C22—881no—
560C22—881no—
561C22—881no—
562C22—881no—
563C22#1062332211yescharacteristic
564C22Q8×C22⋊D1111yescharacteristic
565C22C2×#6700211yescharacteristic
566C22#1062335311yescharacteristic
567C22#1062336011yescharacteristic
568C22#1062336711yescharacteristic
569C22#1062336811yescharacteristic
570C4—22no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—42no—
576C4—42no—
577C4—41no—
578C4—42no—
579C4—81no—
580C4—442no—
581C4—881no—
582C4—881no—
583C4#1062309911yescharacteristic
584C4#1062310911yescharacteristic
585C4#1062311011yescharacteristic
586C4#1062311311yescharacteristic
587C2—882no—
588C2#1307263111yescharacteristic
589C2#1307876711yescharacteristic
590C2#1307889311yescharacteristic
591C2#1308063111yescharacteristic
592C2#1308086311yescharacteristic
593C2#1308151511yescharacteristic
594C2#1308155511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2370C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2370D11
hypocenterC11#27026
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. #13069951C2semidirect
4. #13069949C2semidirect
6. #13069568C2semidirect
7. #13069351C2semidirect
10. #13069201C2semidirect
11. #13069201C2semidirect
12. #13069182C2semidirect
15. C11×#2370C2semidirect
112. #66873Q8semidirect
197. #2370D11semidirect
492. C11#27026semidirect

Maximal subgroups

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

subgroupindex
#130724662
#130699872
#130699512
#130699492
#130697592
#130695682
#130693512
#130692432
#130692362
#130692012
#130691822
#130688762
#130684442
C11×#23702
#2702611