Finite Group Databasebeta

← #14805685

Subgroups — #14805685

Order 2816.

754 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622460C211yesmaximal, characteristic
2#13074004C211yesmaximal, characteristic, complemented
3#13073974C211yesmaximal, characteristic
4#13070114C211yesmaximal, characteristic, complemented
5#13070104C211yesmaximal, characteristic, complemented
6#13070003C211yesmaximal, characteristic
7#13069989C211yesmaximal, characteristic
8#13069581C211yesmaximal, characteristic, complemented
9#13069386C211yesmaximal, characteristic, complemented
10#13069359C211yesmaximal, characteristic, complemented
11#13069354C211yesmaximal, characteristic, complemented
12#13069313C211yesmaximal, characteristic
13#13069313C211yesmaximal, characteristic
14C4×#66885C211yesmaximal, characteristic
15C2×C11×#446C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C2×#66923C2211yescharacteristic
19C11×#446—24no—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#97C2211yescharacteristic
24C2×C11×#97C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26#10622844—21no—
27#10622842—21no—
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36#10622605—21no—
37#10622602—21no—
38#10622602—21no—
39#10622593—21no—
40#10622585—21no—
41#10622585—21no—
42#10622552C2211yescharacteristic
43#10622552C2211yescharacteristic
44#10622549C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49#10622541C2211yescharacteristic
50#10622541C2211yescharacteristic
51#10622541C2211yescharacteristic
52#10622460—24no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C22×Q8×C11D411yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C4×Q8×C11—22no—
69C4×Q8×C11—22no—
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C4×D44—22no—
98C4×D44—22no—
99#66923—22no—
100#66923—22no—
101C11×C4⋊C8—22no—
102C11×C4⋊C8—22no—
103C11×C4⋊C8D414yes—
104C11×#97—22no—
105C11×#97—22no—
106C4×C8×C11—22no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116#66885—22no—
117#66885—22no—
118#66885—22no—
119#66885Q814yescomplemented
120#66882—22no—
121#66882—22no—
122#66881—22no—
123#66881—22no—
124#25475—111nomaximal, Sylow
125C23×D11—21no—
126C2×Q8×C11—22no—
127C2×Q8×C11—41no—
128C2×Q8×C11—41no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44C2×Q812yes—
149C2×C4×D11—42no—
150C2×C4×D11—81no—
151C2×C4×D11—81no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11C2×D412yes—
162C2×C8×C11C2×D412yes—
163C2×C8×C11C2×Q812yes—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11C2×D412yes—
172C42×C11#4112yes—
173(C2×D11)⋊C4—42no—
174(C2×D11)⋊C4—42no—
175(C2×D11)⋊C4—42no—
176(C2×D11)⋊C4—81no—
177(C2×D11)⋊C4—81no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11C2×Q812yes—
191C4⋊Dic11#4112yes—
192Dic11⋊C4—42no—
193Dic11⋊C4—42no—
194Dic11⋊C4—42no—
195Dic11⋊C4—42no—
196Dic11⋊C4—81no—
197Dic11⋊C4—81no—
198Dic11⋊C4—81no—
199Dic11⋊C4—81no—
200C4×Dic11—81no—
201C2×#478—111no—
202C2×#446D1111yescharacteristic, complemented
203#2584—111no—
204#2580—111no—
205#2088—111no—
206#2086—111no—
207#2067—111no—
208#2065—111no—
209#1991—111no—
210#1949—111no—
211#1944—111no—
212#1943—111no—
213#1936—111no—
214#1936—111no—
215C4×#102—111no—
216C23×C11C22×D411yescharacteristic
217C22×D11—22no—
218C22×D11—41no—
219C22×D11—41no—
220C22×D11—41no—
221C22×D11—41no—
222C22×D11—41no—
223C22×D11—41no—
224Q8×C11—44no—
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—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11#12112yes—
242C2×C4×C11#12112yes—
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×Q811yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C112−1+411yescharacteristic
248C2×C4×C112−1+411yescharacteristic
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270D44—22no—
271D44—22no—
272D44—41no—
273D44—41no—
274C4×D11—84no—
275C8×C11—22no—
276C8×C11—22no—
277C8×C11—22no—
278C8×C11—41no—
279C2×#125—111no—
280C2×C4×Q8C2×D1111yescharacteristic
281C2×C4×D4—111no—
282#478—224no—
283#446—24no—
284C2×#107—111no—
285C2×#107—111no—
286C2×#106—111no—
287C2×#106—111no—
288C2×C4⋊C8C2×D1111yescharacteristic
289C2×C4⋊C8C2×D1111yescharacteristic
290C2×C4⋊C8C2×D1111yescharacteristic
291C2×#102—111no—
292C2×#102—111no—
293C2×#102—111no—
294C2×#102—111no—
295C2×#97C2×D1111yescharacteristic
296C2×#97C2×D1111yescharacteristic
297C2×C4×C8C2×D1111yescharacteristic
298#399—221no—
299#398—221no—
300#395—221no—
301#393—221no—
302#390—111no—
303#390—111no—
304#389—111no—
305#389—111no—
306#389—111no—
307#389—111no—
308#389—111no—
309#389—111no—
310#389—221no—
311#389—221no—
312#385—221no—
313#385—221no—
314#382—111no—
315C4×C4⋊C4—111no—
316#340—111no—
317#340—111no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324C22×C11C2×#12111yescharacteristic
325C22×C11#54811yescharacteristic
326C22×C11D4×Q811yescharacteristic
327C22×C11#57511yescharacteristic
328C22×C11#57511yescharacteristic
329C22×C11#57611yescharacteristic
330C22×C11#57711yescharacteristic
331C2×D11—42no—
332C2×D11—42no—
333C2×D11—42no—
334C2×D11—81no—
335C2×D11—81no—
336C2×D11—81no—
337C2×D11—81no—
338C4×C11—22no—
339C4×C11—22no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11#53311yescharacteristic
345C4×C11#54111yescharacteristic
346C4×C11#54711yescharacteristic
347C4×C11D4×Q811yescharacteristic
348Dic11—42no—
349Dic11—42no—
350Dic11—81no—
351Dic11—81no—
352Dic11—81no—
353Dic11—81no—
354Dic11—81no—
355C22×Q8D4411yescharacteristic
356C22×D4—111no—
357C23×C4—221no—
358C22×C8C22×D1111yescharacteristic
359C22×C8C22×D1111yescharacteristic
360C22×C8C22×D1111yescharacteristic
361C22×C8C22×D1111yescharacteristic
362#125—222no—
363#125—222no—
364C4×Q8—22no—
365C4×Q8—22no—
366C4×D4—222no—
367C4×D4—222no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4D4411yescharacteristic
384C2×C4⋊C4D4411yescharacteristic
385C2×C4⋊C4D4411yescharacteristic
386C2×C22⋊C4—221no—
387C2×C22⋊C4—221no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C42—221no—
392C2×C42C22×D1111yescharacteristic
393C2×C42C22×D1111yescharacteristic
394C2×C42C22×D1111yescharacteristic
395#107—222no—
396#107—222no—
397#106—222no—
398#106—222no—
399C4⋊C8—22no—
400C4⋊C8—22no—
401C4⋊C8C22⋊D1114yes—
402#102—114no—
403#102—222no—
404#102—222no—
405#102—222no—
406#97—22no—
407#97—22no—
408C4×C8—22no—
409#95—221no—
410#95—221no—
411#95—221no—
412#95—221no—
413#95—221no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95—221no—
418C2×C11#242911yescharacteristic
419C2×C11#305411yescharacteristic
420C2×C11#306211yescharacteristic
421C2×C11#337011yescharacteristic
422C2×C11#337111yescharacteristic
423C2×C11#338811yescharacteristic
424C2×C11#338911yescharacteristic
425D11—82no—
426C24—221no—
427C2×Q8—22no—
428C2×Q8—41no—
429C2×Q8—41no—
430C2×D4—112no—
431C2×D4—221no—
432C2×D4—221no—
433C2×D4—221no—
434C2×D4—221no—
435C2×D4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—442no—
444C22×C4—881no—
445C22×C4—881no—
446C22×C4C2×D4411yescharacteristic
447C22×C4C2×D4411yescharacteristic
448C22×C4C2×D4411yescharacteristic
449C22×C4C2×D4411yescharacteristic
450C22×C4C2×D4411yescharacteristic
451C22×C4C2×D4411yescharacteristic
452C22×C4C23×D1111yescharacteristic
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8Q8×D1112yes—
463C2×C8C2×C22⋊D1112yes—
464C2×C8C2×C22⋊D1112yes—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—112no—
469C4⋊C4—112no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—442no—
483C4⋊C4—442no—
484C4⋊C4—442no—
485C4⋊C4—442no—
486C4⋊C4—881no—
487C4⋊C4—881no—
488C4⋊C4—881no—
489C4⋊C4—881no—
490C22⋊C4—442no—
491C22⋊C4—442no—
492C22⋊C4—442no—
493C22⋊C4—881no—
494C22⋊C4—881no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—881no—
500C42#433912yes—
501C42C2×C22⋊D1112yes—
502C11#2547511yescharacteristic, complemented, Sylow
503C23—222no—
504C23—441no—
505C23—441no—
506C23—441no—
507C23—441no—
508C23—441no—
509C23—441no—
510C23C22×D4411yescharacteristic
511Q8—44no—
512D4—222no—
513D4—222no—
514D4—441no—
515D4—441no—
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—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—441no—
535C2×C4—441no—
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—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—884no—
554C2×C4#6698312yes—
555C2×C4#6698312yes—
556C2×C4C2×#433911yescharacteristic
557C2×C4C2×Q8×D1111yescharacteristic
558C2×C4#6704011yescharacteristic
559C2×C4#41×D1111yescharacteristic
560C2×C4#6704311yescharacteristic
561C2×C4C22×C22⋊D1111yescharacteristic
562C8—22no—
563C8—22no—
564C8—22no—
565C8—41no—
566C22—442no—
567C22—442no—
568C22—442no—
569C22—881no—
570C22—881no—
571C22—881no—
572C22—881no—
573C22Q8×D4411yescharacteristic
574C22#1062310711yescharacteristic
575C22#1062327911yescharacteristic
576C22#1062327911yescharacteristic
577C22#1062328211yescharacteristic
578C22#1062328311yescharacteristic
579C22C2×#6698311yescharacteristic
580C4—22no—
581C4—22no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—442no—
587C4—442no—
588C4—881no—
589C4—881no—
590C4—881no—
591C4—881no—
592C4—881no—
593C4#1062310911yescharacteristic
594C4#1062311411yescharacteristic
595C4Q8×C22⋊D1111yescharacteristic
596C4#1062335511yescharacteristic
597C2—882no—
598C2#1307220911yescharacteristic
599C2#1307822511yescharacteristic
600C2#1307829611yescharacteristic
601C2#1308137111yescharacteristic
602C2#1308138611yescharacteristic
603C2#1308156311yescharacteristic
604C2#1308157611yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#446C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×#446D11
hypocenterC11#25475
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #13074004C2semidirect
4. #13070114C2semidirect
5. #13070104C2semidirect
8. #13069581C2semidirect
9. #13069386C2semidirect
10. #13069359C2semidirect
11. #13069354C2semidirect
15. C2×C11×#446C2semidirect
119. #66885Q8semidirect
202. C2×#446D11semidirect
502. C11#25475semidirect

Maximal subgroups

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

subgroupindex
C2×#106224602
#130740042
#130739742
#130701142
#130701042
#130700032
#130699892
#130695812
#130693862
#130693592
#130693542
#130693132
C4×#668852
C2×C11×#4462
#2547511