Finite Group Databasebeta

← #16797632

Subgroups — #16797632

Order 3328.

850 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719077C211yesmaximal, characteristic
2C2×#11719079C211yesmaximal, characteristic
3#13130636C211yesmaximal, characteristic, complemented
4#13130635C211yesmaximal, characteristic, complemented
5#13130632C211yesmaximal, characteristic, complemented
6#13130631C211yesmaximal, characteristic, complemented
7#13130624C211yesmaximal, characteristic, complemented
8#13130624C211yesmaximal, characteristic, complemented
9#13130622C211yesmaximal, characteristic, complemented
10#13130621C211yesmaximal, characteristic, complemented
11#13130577C211yesmaximal, characteristic
12#13130577C211yesmaximal, characteristic
13#13130574C211yesmaximal, characteristic
14#13130574C211yesmaximal, characteristic
15#13117328C211yesmaximal, characteristic
16C22×#6118C2211yescharacteristic
17C22×D13⋊C8C2211yescharacteristic
18C2×#88146C2211yescharacteristic
19C2×#88112C2211yescharacteristic
20C2×#88112C2211yescharacteristic
21C2×#88112C2211yescharacteristic
22C2×#88111C2211yescharacteristic
23C2×#88111C2211yescharacteristic
24C2×#88110C2211yescharacteristic
25C2×#88110C2211yescharacteristic
26C2×#88110C2211yescharacteristic
27C2×#88110C2211yescharacteristic
28C2×#88110C2211yescharacteristic
29C2×#88110C2211yescharacteristic
30C2×#88110C2211yescharacteristic
31C2×C4⋊#1057C2211yescharacteristic
32C2×C4⋊#1057C2211yescharacteristic
33C2×C4⋊#1057C2211yescharacteristic
34C2×C4×#1057C2211yescharacteristic
35C2×C4×#1057C2211yescharacteristic
36C2×C4×#1057C2211yescharacteristic
37#11719079C418yescomplemented
38#11719077C418yescomplemented
39C13×#387C411yescharacteristic
40#11718651C411yescharacteristic
41#11718642C411yescharacteristic
42C4⋊C4×Dic13C2211yescharacteristic
43#11718601C411yescharacteristic
44C42×Dic13C2211yescharacteristic
45#11718331C411yescharacteristic
46#11718330C411yescharacteristic
47#11718327C2211yescharacteristic
48#11718327C2211yescharacteristic
49#11718315C411yescharacteristic
50#11718314C411yescharacteristic
51#11718310C2211yescharacteristic
52#11718309C2211yescharacteristic
53#11718290C2211yescharacteristic
54#11718290C2211yescharacteristic
55#11718290C2211yescharacteristic
56#11718290C2211yescharacteristic
57#11718290C2211yescharacteristic
58#11718290C2211yescharacteristic
59#11718290C2211yescharacteristic
60#11718290C2211yescharacteristic
61C22×C4×D13C2311yescharacteristic
62C22×#1057C2311yescharacteristic
63C22×#1057C2311yescharacteristic
64C22×#1057C2311yescharacteristic
65C22×#1057C2311yescharacteristic
66C22×#1057C2311yescharacteristic
67C22×#1057C2311yescharacteristic
68C22×#1057C2311yescharacteristic
69C22×#1057C2311yescharacteristic
70C2×#6118—41no—
71C2×#6118—41no—
72C2×#6118C2×C414yes—
73C2×D13⋊C8—41no—
74C2×D13⋊C8—41no—
75C2×D13⋊C8C2×C414yes—
76C2×C13×C4⋊C4C2×C411yescharacteristic
77C2×C13×C4⋊C4C2×C411yescharacteristic
78C2×C42×C13C2×C411yescharacteristic
79C2×#6103C2×C411yescharacteristic
80C2×#6103C2×C411yescharacteristic
81C2×#6103C2×C411yescharacteristic
82C2×#6103C2×C411yescharacteristic
83C2×#6103C2×C411yescharacteristic
84C2×#6103C2×C411yescharacteristic
85C2×C4⋊Dic13C2×C411yescharacteristic
86C2×C4⋊Dic13C2×C411yescharacteristic
87C2×#6101C2×C411yescharacteristic
88C2×#6101C2×C411yescharacteristic
89C2×C4×Dic13C2×C411yescharacteristic
90C2×C4×Dic13C2×C411yescharacteristic
91C2×C4×Dic13C2×C411yescharacteristic
92C2×C4×Dic13C2311yescharacteristic
93C2×C4×Dic13C2311yescharacteristic
94C2×C4×Dic13C2311yescharacteristic
95C2×C4×Dic13C2311yescharacteristic
96C2×C4×Dic13C2311yescharacteristic
97C2×C4×Dic13C2311yescharacteristic
98#88146C2×C414yes—
99#88146C2×C414yes—
100#88112C2×C414yes—
101#88112C2×C414yes—
102#88112C2×C414yes—
103#88111C2×C414yes—
104#88111C2×C414yes—
105#88110—41no—
106#88110—41no—
107#88110—41no—
108#88110—41no—
109#88110—41no—
110#88110—41no—
111#88110C2×C414yes—
112C4⋊#1057C2×C414yes—
113C4⋊#1057C2×C414yes—
114C4⋊#1057C2×C414yes—
115C4×#1057—41no—
116C4×#1057—41no—
117C4×#1057C2×C414yes—
118C13×#95C2×C411yescharacteristic
119C13×#95C2×C411yescharacteristic
120C13×#95C2×C411yescharacteristic
121C13×#95C2×C411yescharacteristic
122#88071C2×C411yescharacteristic
123#88071C2×C411yescharacteristic
124#88071C2×C411yescharacteristic
125#88071C2×C411yescharacteristic
126#88071C2×C411yescharacteristic
127#88071C2×C411yescharacteristic
128#88071C2×C411yescharacteristic
129#88071C2×C411yescharacteristic
130#20554—131nomaximal, Sylow
131C23×D13C22×C411yescharacteristic
132C22×C4×C13C22×C411yescharacteristic
133C22×C4×C13C22×C411yescharacteristic
134C22×C4×C13C22×C411yescharacteristic
135C22×C4×C13C22×C411yescharacteristic
136C22×C4×C13C22×C411yescharacteristic
137C22×C4×C13C22×C411yescharacteristic
138C22×C4×C13C22×C411yescharacteristic
139C22×Dic13C22×C411yescharacteristic
140C22×Dic13C22×C411yescharacteristic
141C22×Dic13C22×C411yescharacteristic
142C22×Dic13C22×C411yescharacteristic
143C22×Dic13C22×C411yescharacteristic
144C22×Dic13C22×C411yescharacteristic
145C22×Dic13C2411yescharacteristic
146C2×C4×D13—21no—
147C2×C4×D13—21no—
148C2×C4×D13—21no—
149C2×C4×D13—21no—
150C2×C4×D13C22×C412yes—
151C2×C4×D13C22×C412yes—
152C2×#1057—21no—
153C2×#1057—21no—
154C2×#1057—21no—
155C2×#1057—21no—
156C2×#1057—21no—
157C2×#1057—21no—
158C2×#1057—21no—
159C2×#1057—21no—
160C2×#1057—21no—
161C2×#1057—21no—
162C2×#1057—21no—
163C2×#1057—21no—
164C2×#1057—21no—
165C2×#1057—21no—
166C2×#1057—21no—
167C2×#1057—21no—
168C2×#1057C22×C412yes—
169C2×#1057C22×C412yes—
170C2×#1057C22×C412yes—
171C2×#1057C22×C412yes—
172C2×#1057C22×C412yes—
173C2×#1057C22×C412yes—
174C2×#1057C22×C412yes—
175C2×#1057C22×C412yes—
176#6118—44no—
177D13⋊C8—44no—
178C13×C4⋊C4—41no—
179C13×C4⋊C4C4214yes—
180C42×C13—41no—
181#6103—41no—
182#6103—41no—
183#6103—41no—
184#6103—41no—
185#6103C4214yes—
186#6103C4214yes—
187C4⋊Dic13—41no—
188C4⋊Dic13C4214yes—
189#6101—41no—
190#6101—41no—
191C4×Dic13—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195C4×Dic13—21no—
196C4×Dic13—21no—
197C4×Dic13—21no—
198C4×Dic13—21no—
199C4×Dic13—41no—
200C4×Dic13—41no—
201C4×Dic13—41no—
202C4×Dic13C22×C412yes—
203C4×Dic13C22×C412yes—
204C4×Dic13C22×C412yes—
205C4×Dic13C22×C412yes—
206C2×#433—131no—
207C2×#424—131no—
208#2298—131no—
209#1771—131no—
210#1771—131no—
211#1770—131no—
212#1770—131no—
213#1768—131no—
214#1768—131no—
215#1767—131no—
216#1767—131no—
217#1753—131no—
218#1753—131no—
219#1752—131no—
220#1752—131no—
221C23×C13C23×C411yescharacteristic
222C22×D13—21no—
223C22×D13—21no—
224C22×D13—21no—
225C22×D13—21no—
226C22×D13—21no—
227C22×D13—21no—
228C22×D13C2×C4212yes—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13C2×C4212yes—
248C2×C4×C13C2×C4212yes—
249C2×C4×C13C2×C4212yes—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—21no—
266C2×Dic13C2×C4212yes—
267C2×Dic13C2×C4212yes—
268C2×Dic13C23×C411yescharacteristic
269C2×Dic13C23×C411yescharacteristic
270C2×Dic13H(5,𝔽2)11yescharacteristic
271C2×Dic13H(5,𝔽2)11yescharacteristic
272C2×Dic132−1+411yescharacteristic
273C2×Dic132−1+411yescharacteristic
274C4×D13—22no—
275C4×D13—22no—
276C4×D13—22no—
277C4×D13—22no—
278#1057—22no—
279#1057—22no—
280#1057—22no—
281#1057—22no—
282#1057—22no—
283#1057—22no—
284#1057—22no—
285#1057—22no—
286C22×M16—131no—
287C23×C8—131no—
288C2×#117—131no—
289#433—138no—
290#424—138no—
291C2×C4⋊C8—131no—
292C2×C4⋊C8—131no—
293C2×C4⋊C8—131no—
294C2×C4⋊C8—131no—
295C2×C4⋊C8—131no—
296C2×C4⋊C8—131no—
297C2×C22⋊C8—131no—
298C2×C22⋊C8—131no—
299C2×#97—131no—
300C2×#97—131no—
301C2×#97—131no—
302C2×#97—131no—
303C2×#97—131no—
304C2×#97—131no—
305C2×#97—131no—
306C2×C4×C8—131no—
307C2×C4×C8—131no—
308C2×C4×C8—131no—
309#388—131no—
310#388—131no—
311#388—131no—
312#388—131no—
313#387—131no—
314#387—131no—
315#387—131no—
316#387#26111yescharacteristic
317C4×C4⋊C4—131no—
318C4×C4⋊C4—131no—
319C4×C22⋊C4—131no—
320C4×C22⋊C4—131no—
321#376—131no—
322C43—131no—
323#336—131no—
324#336—131no—
325#336—131no—
326#336—131no—
327#336—131no—
328#336—131no—
329#336—131no—
330#336—131no—
331C22×C13C22×C4211yescharacteristic
332C22×C13#52011yescharacteristic
333C22×C13#52011yescharacteristic
334C22×C13#56811yescharacteristic
335C22×C13#56811yescharacteristic
336C22×C13#56811yescharacteristic
337C22×C13#56811yescharacteristic
338C2×D13—22no—
339C2×D13—22no—
340C2×D13—22no—
341C2×D13—41no—
342C2×D13—41no—
343C2×D13—41no—
344C2×D13—41no—
345C4×C13—22no—
346C4×C13—22no—
347C4×C13—22no—
348C4×C13—41no—
349C4×C13—41no—
350C4×C13—41no—
351C4×C13—41no—
352Dic13—22no—
353Dic13—22no—
354Dic13—41no—
355Dic13—41no—
356Dic13—41no—
357Dic13—41no—
358Dic13#51811yescharacteristic
359Dic13#51911yescharacteristic
360Dic13#52011yescharacteristic
361Dic13#52011yescharacteristic
362C23×C4—131no—
363C2×M16—134no—
364C2×M16—521no—
365C2×M16—521no—
366C22×C8—131no—
367C22×C8—131no—
368C22×C8—131no—
369C22×C8—131no—
370C22×C8—131no—
371C22×C8—131no—
372C22×C8—131no—
373C22×C8—131no—
374C22×C8—134no—
375C22×C8—521no—
376C22×C8—521no—
377#117—134no—
378#117—134no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4C2×#26111yescharacteristic
384C2×C4⋊C4C2×#26111yescharacteristic
385C2×C22⋊C4—131no—
386C2×C22⋊C4—131no—
387C2×C22⋊C4—131no—
388C2×C22⋊C4—131no—
389C2×C22⋊C4—131no—
390C2×C22⋊C4—131no—
391C2×C42—131no—
392C2×C42—131no—
393C2×C42—131no—
394C2×C42—131no—
395C2×C42—131no—
396C2×C42—131no—
397C2×C42—131no—
398C2×C42—131no—
399C2×C42—131no—
400C2×C42C2×#26111yescharacteristic
401C4⋊C8—134no—
402C4⋊C8—134no—
403C4⋊C8—134no—
404C4⋊C8—134no—
405C4⋊C8—134no—
406C4⋊C8—134no—
407C22⋊C8—134no—
408C22⋊C8—134no—
409#97—134no—
410#97—521no—
411#97—521no—
412#97—521no—
413#97—521no—
414#97—521no—
415#97—521no—
416C4×C8—134no—
417C4×C8—521no—
418C4×C8—521no—
419#95—131no—
420#95—131no—
421#95—131no—
422#95—131no—
423#95—131no—
424#95—131no—
425#95—131no—
426#95—131no—
427#95C2×#26111yescharacteristic
428#95C2×#26111yescharacteristic
429#95C2×#26111yescharacteristic
430#95C2×#26111yescharacteristic
431C2×C13#227411yescharacteristic
432C2×C13#287511yescharacteristic
433C2×C13#287511yescharacteristic
434C2×C13#299511yescharacteristic
435C2×C13#299511yescharacteristic
436C2×C13#299511yescharacteristic
437C2×C13#299511yescharacteristic
438D13—42no—
439C24—131no—
440C22×C4—131no—
441C22×C4—131no—
442C22×C4—131no—
443C22×C4—132no—
444C22×C4—132no—
445C22×C4—131no—
446C22×C4—131no—
447C22×C4—131no—
448C22×C4—131no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—261no—
453C22×C4C22×#26111yescharacteristic
454C22×C4C22×#26111yescharacteristic
455C22×C4C22×#26111yescharacteristic
456C22×C4C22×#26111yescharacteristic
457C22×C4C22×#26111yescharacteristic
458C22×C4C22×#26111yescharacteristic
459C22×C4C22×#26111yescharacteristic
460M16—524no—
461C2×C8—132no—
462C2×C8—132no—
463C2×C8—132no—
464C2×C8—132no—
465C2×C8—132no—
466C2×C8—132no—
467C2×C8—132no—
468C2×C8—132no—
469C2×C8—261no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C2×C8—261no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8—261no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—524no—
486C4⋊C4—41no—
487C4⋊C4—134no—
488C4⋊C4—521no—
489C4⋊C4—521no—
490C4⋊C4—521no—
491C4⋊C4C4×#26114yes—
492C22⋊C4—134no—
493C22⋊C4—134no—
494C22⋊C4—521no—
495C22⋊C4—521no—
496C22⋊C4—521no—
497C22⋊C4—521no—
498C42—41no—
499C42—132no—
500C42—132no—
501C42—132no—
502C42—132no—
503C42—261no—
504C42—261no—
505C42—261no—
506C42—261no—
507C42—261no—
508C42—261no—
509C42—261no—
510C42—261no—
511C42—521no—
512C42—521no—
513C42—521no—
514C13#2055411yescharacteristic, complemented, Sylow
515C23—132no—
516C23—261no—
517C23—261no—
518C23—261no—
519C23—261no—
520C23—261no—
521C23—261no—
522C23C23×#26111yescharacteristic
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—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—131no—
542C2×C4—131no—
543C2×C4—131no—
544C2×C4—131no—
545C2×C4—131no—
546C2×C4—131no—
547C2×C4—132no—
548C2×C4—132no—
549C2×C4—262no—
550C2×C4—262no—
551C2×C4—262no—
552C2×C4—262no—
553C2×C4—261no—
554C2×C4—261no—
555C2×C4—261no—
556C2×C4—261no—
557C2×C4—261no—
558C2×C4—261no—
559C2×C4—261no—
560C2×C4—261no—
561C2×C4—261no—
562C2×C4—261no—
563C2×C4—261no—
564C2×C4—261no—
565C2×C4—261no—
566C2×C4—261no—
567C2×C4—261no—
568C2×C4—261no—
569C2×C4C2×C4×#26112yes—
570C2×C4C2×C4×#26112yes—
571C2×C4C2×C4×#26112yes—
572C8—262no—
573C8—262no—
574C8—262no—
575C8—262no—
576C8—262no—
577C8—262no—
578C8—262no—
579C8—262no—
580C22—262no—
581C22—262no—
582C22—262no—
583C22—521no—
584C22—521no—
585C22—521no—
586C22—521no—
587C22C22×C4×#26111yescharacteristic
588C22#1171962111yescharacteristic
589C22#1171962511yescharacteristic
590C22#1171962911yescharacteristic
591C22#1171962911yescharacteristic
592C22#1171963111yescharacteristic
593C22#1171963111yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—131no—
602C4—131no—
603C4—131no—
604C4—131no—
605C4—262no—
606C4—262no—
607C4—521no—
608C4—521no—
609C4—521no—
610C4—521no—
611C2—522no—
612C2#1313127311yescharacteristic
613C2#1313140711yescharacteristic
614C2#1313140811yescharacteristic
615C2#1313179011yescharacteristic
616C2#1313179111yescharacteristic
617C2#1313179311yescharacteristic
618C2#1313179411yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC13×#387C4
socleC23×C13C23×C4
prime radicalC23×D13C22×C4
cosocleC22×Dic13C24
hypercenter#387#261
hypocenterC13#20554
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
3. #13130636C2semidirect
4. #13130635C2semidirect
5. #13130632C2semidirect
6. #13130631C2semidirect
7. #13130624C2semidirect
8. #13130624C2semidirect
9. #13130622C2semidirect
10. #13130621C2semidirect
37. #11719079C4semidirect
38. #11719077C4semidirect
514. C13#20554semidirect

Maximal subgroups

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

subgroupindex
C2×#117190772
C2×#117190792
#131306362
#131306352
#131306322
#131306312
#131306242
#131306222
#131306212
#131305772
#131305742
#131173282
#2055413