Finite Group Databasebeta

← #15832179

Subgroups — #15832179

Order 3328.

588 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123803C211yesmaximal, characteristic
2#13123502C211yesmaximal, characteristic
3#13113627C211yesmaximal, characteristic, complemented
4#13113624C211yesmaximal, characteristic, complemented
5#13113622C211yesmaximal, characteristic, complemented
6#13113619C211yesmaximal, characteristic, complemented
7#13113617C211yesmaximal, characteristic, complemented
8#13113614C211yesmaximal, characteristic, complemented
9#13113604C211yesmaximal, characteristic, complemented
10#13113601C211yesmaximal, characteristic, complemented
11#13113597C211yesmaximal, characteristic, complemented
12#13113589C211yesmaximal, characteristic, complemented
13#13113586C211yesmaximal, characteristic, complemented
14#13113582C211yesmaximal, characteristic, complemented
15C13×#2925C211yesmaximal, characteristic
16C4×C13×#41C2211yescharacteristic
17C13×#433—21no—
18C13×#433—21no—
19C13×#432C2211yescharacteristic
20C13×#432C2211yescharacteristic
21C13×#431C2211yescharacteristic
22C13×#431C2211yescharacteristic
23C13×#423C2211yescharacteristic
24C2×C13×C4⋊C8C2211yescharacteristic
25C13×#408—21no—
26C13×#405—21no—
27#11718895—21no—
28#11718685C411yescharacteristic
29#11718685C411yescharacteristic
30#11718673C411yescharacteristic
31#11718673C411yescharacteristic
32#11718672C411yescharacteristic
33#11718672C411yescharacteristic
34#11718672C411yescharacteristic
35#11718672C411yescharacteristic
36#11718661—21no—
37#11718661—21no—
38#11718658—21no—
39#11718587C2211yescharacteristic
40#11718587C2211yescharacteristic
41#11718586C2211yescharacteristic
42#11718586C2211yescharacteristic
43#11718586C2211yescharacteristic
44#11718586C2211yescharacteristic
45#11718586C2211yescharacteristic
46#11718585C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48C4×#6099C2211yescharacteristic
49C4×#6099C2211yescharacteristic
50C2×C4×#1055C2211yescharacteristic
51#11718072C2211yescharacteristic
52#11718072C2211yescharacteristic
53#11718072C2211yescharacteristic
54#11718072C2211yescharacteristic
55#11718072C2211yescharacteristic
56#11718072C2211yescharacteristic
57#11718072C2211yescharacteristic
58#11718072C2211yescharacteristic
59#11718071C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718071C2211yescharacteristic
62#11718071C2211yescharacteristic
63#11718071C2211yescharacteristic
64#11718071C2211yescharacteristic
65#11718071C2211yescharacteristic
66#11718071C2211yescharacteristic
67C2×C13×#41D411yescharacteristic
68C2×C13×M16—21no—
69C22×C8×C13—21no—
70C4×Q8×C13C2×C411yescharacteristic
71C4×Q8×C13Q811yescharacteristic
72C4×D4×C13C2×C411yescharacteristic
73C4×D4×C13C2×C411yescharacteristic
74C4×D4×C13C2×C411yescharacteristic
75C4×D4×C13Q811yescharacteristic
76C4×D4×C13Q811yescharacteristic
77C4×D4×C13Q811yescharacteristic
78C13×#117D411yescharacteristic
79C13×#117D411yescharacteristic
80C13×#117D411yescharacteristic
81C2×C42×C13C2311yescharacteristic
82C2×C42×C13C2311yescharacteristic
83C2×C42×C13C2311yescharacteristic
84C2×#6099—21no—
85C2×#6099C2×C411yescharacteristic
86C2×#6099C2×C411yescharacteristic
87C2×#6099C2×C411yescharacteristic
88C2×#6099C2×C411yescharacteristic
89C22×#1055—21no—
90C22×#1055C2×C411yescharacteristic
91C22×#1055C2×C411yescharacteristic
92C13×C4⋊C8—21no—
93C13×C4⋊C8—21no—
94C13×C4⋊C8C2311yescharacteristic
95C13×C4⋊C8C2311yescharacteristic
96C13×C4⋊C8C2311yescharacteristic
97C13×C4⋊C8C2311yescharacteristic
98C13×C22⋊C8—21no—
99C13×C22⋊C8—21no—
100C13×C22⋊C8—21no—
101C13×C22⋊C8—21no—
102C13×#97—21no—
103C13×#97—21no—
104C4×C8×C13—21no—
105C4×C8×C13—21no—
106C22⋊#1055—21no—
107C22⋊#1055—21no—
108C22⋊#1055—21no—
109C22⋊#1055—21no—
110C22⋊#1055C2×C411yescharacteristic
111C22⋊#1055C2×C411yescharacteristic
112C22⋊#1055C2×C411yescharacteristic
113C22⋊#1055C2×C411yescharacteristic
114C22⋊#1055C2×C411yescharacteristic
115C22⋊#1055C2×C411yescharacteristic
116C4⋊#1055—21no—
117C4⋊#1055—21no—
118C4⋊#1055C2×C411yescharacteristic
119C4⋊#1055C2×C411yescharacteristic
120C4⋊#1055C2×C411yescharacteristic
121C4⋊#1055C2×C411yescharacteristic
122C4⋊#1055C2×C411yescharacteristic
123C4⋊#1055C2×C411yescharacteristic
124C4⋊#1055C2311yescharacteristic
125C4⋊#1055C2311yescharacteristic
126C4⋊#1055C2311yescharacteristic
127C4⋊#1055C2311yescharacteristic
128#88043—21no—
129#88043—21no—
130#88043C2×C411yescharacteristic
131#88043C2×C411yescharacteristic
132#88043C2×C411yescharacteristic
133#88043C2×C411yescharacteristic
134C4×#1055—21no—
135C4×#1055—21no—
136C4×#1055C2×C411yescharacteristic
137C4×#1055C2×C411yescharacteristic
138C4×#1055C2311yescharacteristic
139C4×#1055C2311yescharacteristic
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142#17831—131nomaximal, Sylow
143C13×#41—41no—
144C13×#41—41no—
145C2×Q8×C13C4⋊C411yescharacteristic
146C2×D4×C13C4⋊C411yescharacteristic
147C2×D4×C13C4⋊C411yescharacteristic
148C2×D4×C13C4⋊C411yescharacteristic
149C22×C4×C13C22×C411yescharacteristic
150C22×C4×C13C22×C411yescharacteristic
151C22×C4×C13C22×C411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×Q811yescharacteristic
156C22×C4×C13C2×Q811yescharacteristic
157C22×C4×C13C2×Q811yescharacteristic
158C13×M16—42no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—42no—
164C13×C4⋊C4C4⋊C411yescharacteristic
165C13×C4⋊C4C4⋊C411yescharacteristic
166C13×C4⋊C4C4⋊C411yescharacteristic
167C13×C4⋊C4C4⋊C411yescharacteristic
168C13×C4⋊C4C4⋊C411yescharacteristic
169C13×C4⋊C4C4⋊C411yescharacteristic
170C13×C22⋊C4C4⋊C411yescharacteristic
171C13×C22⋊C4C4⋊C411yescharacteristic
172C13×C22⋊C4C4⋊C411yescharacteristic
173C13×C22⋊C4C4⋊C411yescharacteristic
174C13×C22⋊C4C4⋊C411yescharacteristic
175C13×C22⋊C4C4⋊C411yescharacteristic
176C42×C13C22×C411yescharacteristic
177C42×C13C22×C411yescharacteristic
178C42×C13C22×C411yescharacteristic
179C42×C13C2×D411yescharacteristic
180C42×C13C2×D411yescharacteristic
181C42×C13C2×D411yescharacteristic
182C42×C13C2×Q811yescharacteristic
183C42×C13C2×Q811yescharacteristic
184C42×C13C2×Q811yescharacteristic
185C42×C13C2411yescharacteristic
186#6099—22no—
187#6099—22no—
188#6099—41no—
189#6099—41no—
190#6099—42no—
191C2×#1055—22no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—41no—
197C2×#1055—42no—
198C2×#1055C22×C411yescharacteristic
199C2×#1055C22×C411yescharacteristic
200C2×#1055C22×C411yescharacteristic
201C2×#1055C22×C411yescharacteristic
202C2×#1055C22×C411yescharacteristic
203C2×#1055C22×C411yescharacteristic
204C2×#1055C22×C411yescharacteristic
205C2×#1055C22×C411yescharacteristic
206#2965—131no—
207#2925—131no—
208#2925D1311yescharacteristic
209#1574—131no—
210#1574—131no—
211#1573—131no—
212#1573—131no—
213#1572—131no—
214#1572—131no—
215#1569—131no—
216#1569—131no—
217#1568—131no—
218#1565—131no—
219#1565—131no—
220#1564—131no—
221C23×C13C2×C4⋊C411yescharacteristic
222C23×C13C2×C4⋊C411yescharacteristic
223C23×C13C2×C4⋊C411yescharacteristic
224Q8×C13—41no—
225D4×C13—41no—
226D4×C13—41no—
227D4×C13—41no—
228C2×C4×C13—21no—
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—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13C2×C4⋊C411yescharacteristic
244C2×C4×C13C2×C4⋊C411yescharacteristic
245C2×C4×C13C2×C4⋊C411yescharacteristic
246C2×C4×C13C2×C4⋊C411yescharacteristic
247C2×C4×C13C2×C4⋊C411yescharacteristic
248C2×C4×C13C2×C4⋊C411yescharacteristic
249C2×C4×C13C2×C4⋊C411yescharacteristic
250C2×C4×C13C2×C4⋊C411yescharacteristic
251C2×C4×C13C2×C4⋊C411yescharacteristic
252C2×C4×C13C23×C411yescharacteristic
253C2×C4×C13C22×D411yescharacteristic
254C2×C4×C13C22×Q811yescharacteristic
255C8×C13—41no—
256C8×C13—41no—
257C8×C13—41no—
258C8×C13—41no—
259#1055—21no—
260#1055—21no—
261#1055—21no—
262#1055—21no—
263#1055—21no—
264#1055—21no—
265#1055—21no—
266#1055—41no—
267#1055—41no—
268#1055—41no—
269#1055—41no—
270#1055#13112yes—
271C4×#41C2×D1311yescharacteristic
272#446—131no—
273#446—131no—
274#436—131no—
275#436—131no—
276#435—131no—
277#435—131no—
278#435—131no—
279#435—131no—
280#433—21no—
281#433—21no—
282#433—261no—
283#433—261no—
284#432—131no—
285#432—131no—
286#432C2×D1311yescharacteristic
287#432C2×D1311yescharacteristic
288#431—131no—
289#431—131no—
290#431—131no—
291#431—131no—
292#431—131no—
293#431C2×D1311yescharacteristic
294#431C2×D1311yescharacteristic
295#423—131no—
296#423C2×D1311yescharacteristic
297C2×C4⋊C8—131no—
298C2×C4⋊C8C2×D1311yescharacteristic
299#408—21no—
300#408—261no—
301#405—21no—
302#405—261no—
303C4×M16—131no—
304C4×M16—131no—
305C2×C4×C8—131no—
306#335—131no—
307#335—131no—
308#335—131no—
309#335—131no—
310#335—131no—
311#335—131no—
312#335—131no—
313#335—131no—
314#334—131no—
315#334—131no—
316#334—131no—
317#334—131no—
318#334—131no—
319#334—131no—
320#334—131no—
321#334—131no—
322C22×C13—21no—
323C22×C13—21no—
324C22×C13—21no—
325C22×C13—21no—
326C22×C13—21no—
327C22×C13—21no—
328C22×C13—21no—
329C22×C13—21no—
330C22×C13—21no—
331C22×C13C22×C4⋊C411yescharacteristic
332C4×C13—21no—
333C4×C13—21no—
334C4×C13—21no—
335C4×C13—21no—
336C4×C13—21no—
337C4×C13—21no—
338C4×C13—21no—
339C4×C13—21no—
340C4×C13—21no—
341C4×C13—21no—
342C4×C13C2×#13111yescharacteristic
343C4×C13#56811yescharacteristic
344C4×C13#57511yescharacteristic
345C4×C13#57511yescharacteristic
346C2×#41C22⋊D1311yescharacteristic
347C2×M16—21no—
348C2×M16—131no—
349C2×M16—131no—
350C2×M16—131no—
351C2×M16—131no—
352C2×M16—261no—
353C22×C8—21no—
354C22×C8—131no—
355C22×C8—131no—
356C22×C8—261no—
357C4×Q8Dic2611yescharacteristic
358C4×Q8C4×D1311yescharacteristic
359C4×D4Dic2611yescharacteristic
360C4×D4Dic2611yescharacteristic
361C4×D4Dic2611yescharacteristic
362C4×D4C4×D1311yescharacteristic
363C4×D4C4×D1311yescharacteristic
364C4×D4C4×D1311yescharacteristic
365#117C22⋊D1311yescharacteristic
366#117C22⋊D1311yescharacteristic
367#117C22⋊D1311yescharacteristic
368C2×C42C22×D1311yescharacteristic
369C2×C42C22×D1311yescharacteristic
370C2×C42C22×D1311yescharacteristic
371C4⋊C8—21no—
372C4⋊C8—21no—
373C4⋊C8—131no—
374C4⋊C8—131no—
375C4⋊C8—131no—
376C4⋊C8—131no—
377C4⋊C8—131no—
378C4⋊C8—131no—
379C4⋊C8—131no—
380C4⋊C8—131no—
381C4⋊C8—131no—
382C4⋊C8—131no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8C22×D1311yescharacteristic
386C4⋊C8C22×D1311yescharacteristic
387C4⋊C8C22×D1311yescharacteristic
388C4⋊C8C22×D1311yescharacteristic
389C22⋊C8—21no—
390C22⋊C8—21no—
391C22⋊C8—21no—
392C22⋊C8—21no—
393C22⋊C8—131no—
394C22⋊C8—131no—
395C22⋊C8—131no—
396C22⋊C8—131no—
397C22⋊C8—131no—
398C22⋊C8—131no—
399C22⋊C8—261no—
400C22⋊C8—261no—
401C22⋊C8—261no—
402C22⋊C8—261no—
403#97—21no—
404#97—21no—
405#97—131no—
406#97—131no—
407#97—131no—
408#97—131no—
409#97—261no—
410#97—261no—
411C4×C8—21no—
412C4×C8—21no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—131no—
416C4×C8—131no—
417C4×C8—131no—
418C4×C8—131no—
419C4×C8—261no—
420C4×C8—261no—
421C2×C13—41no—
422C2×C13—41no—
423C2×C13—41no—
424C2×C13#290611yescharacteristic
425C2×C13#291111yescharacteristic
426C2×C13#291611yescharacteristic
427#41—41no—
428#41—41no—
429C2×Q8#610111yescharacteristic
430C2×D4#610111yescharacteristic
431C2×D4#610111yescharacteristic
432C2×D4#610111yescharacteristic
433C22×C4C2×Dic2611yescharacteristic
434C22×C4C2×Dic2611yescharacteristic
435C22×C4C2×Dic2611yescharacteristic
436C22×C4C2×C4×D1311yescharacteristic
437C22×C4C2×C4×D1311yescharacteristic
438C22×C4C2×C4×D1311yescharacteristic
439C22×C4C2×C22⋊D1311yescharacteristic
440C22×C4C2×C22⋊D1311yescharacteristic
441C22×C4C2×C22⋊D1311yescharacteristic
442M16—42no—
443M16—262no—
444M16—262no—
445M16—521no—
446M16—521no—
447M16—522no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—42no—
453C2×C8—131no—
454C2×C8—131no—
455C2×C8—131no—
456C2×C8—131no—
457C2×C8—131no—
458C2×C8—131no—
459C2×C8—131no—
460C2×C8—131no—
461C2×C8—262no—
462C2×C8—261no—
463C2×C8—261no—
464C2×C8—261no—
465C2×C8—261no—
466C2×C8—521no—
467C2×C8—522no—
468C4⋊C4#610111yescharacteristic
469C4⋊C4#610111yescharacteristic
470C4⋊C4#610111yescharacteristic
471C4⋊C4#610111yescharacteristic
472C4⋊C4#610111yescharacteristic
473C4⋊C4#610111yescharacteristic
474C22⋊C4#610111yescharacteristic
475C22⋊C4#610111yescharacteristic
476C22⋊C4#610111yescharacteristic
477C22⋊C4#610111yescharacteristic
478C22⋊C4#610111yescharacteristic
479C22⋊C4#610111yescharacteristic
480C42C2×Dic2611yescharacteristic
481C42C2×Dic2611yescharacteristic
482C42C2×Dic2611yescharacteristic
483C42C2×C4×D1311yescharacteristic
484C42C2×C4×D1311yescharacteristic
485C42C2×C4×D1311yescharacteristic
486C42C2×C22⋊D1311yescharacteristic
487C42C2×C22⋊D1311yescharacteristic
488C42C2×C22⋊D1311yescharacteristic
489C42C23×D1311yescharacteristic
490C13#1783111yescharacteristic, complemented, Sylow
491C23C2×#610111yescharacteristic
492C23C2×#610111yescharacteristic
493C23C2×#610111yescharacteristic
494Q8—41no—
495D4—41no—
496D4—41no—
497D4—41no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4C2×#610111yescharacteristic
514C2×C4C2×#610111yescharacteristic
515C2×C4C2×#610111yescharacteristic
516C2×C4C2×#610111yescharacteristic
517C2×C4C2×#610111yescharacteristic
518C2×C4C2×#610111yescharacteristic
519C2×C4C2×#610111yescharacteristic
520C2×C4C2×#610111yescharacteristic
521C2×C4C2×#610111yescharacteristic
522C2×C4C22×Dic2611yescharacteristic
523C2×C4C22×C4×D1311yescharacteristic
524C2×C4C22×C22⋊D1311yescharacteristic
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—132no—
530C8—261no—
531C8—261no—
532C8—261no—
533C8—261no—
534C8—261no—
535C8—261no—
536C8—261no—
537C8—521no—
538C8—521no—
539C8—521no—
540C8—521no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22C22×#610111yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4D13×#13111yescharacteristic
562C4#1171945511yescharacteristic
563C4#1171952711yescharacteristic
564C4#1171952711yescharacteristic
565C2—41no—
566C2—41no—
567C2—41no—
568C2#1312340211yescharacteristic
569C2#1312342511yescharacteristic
570C2#1312344511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2925C2
socleC22×C13C22×C4⋊C4
prime radicalC2×C13×#41D4
cosocleC42×C13C24
hypercenter#2925D13
hypocenterC13#17831
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2925

Complements

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

NH ≅ G/Ntype
3. #13113627C2semidirect
4. #13113624C2semidirect
5. #13113622C2semidirect
6. #13113619C2semidirect
7. #13113617C2semidirect
8. #13113614C2semidirect
9. #13113604C2semidirect
10. #13113601C2semidirect
11. #13113597C2semidirect
12. #13113589C2semidirect
13. #13113586C2semidirect
14. #13113582C2semidirect
490. C13#17831semidirect

Maximal subgroups

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

subgroupindex
#131238032
#131235022
#131136272
#131136242
#131136222
#131136192
#131136172
#131136142
#131136042
#131136012
#131135972
#131135892
#131135862
#131135822
C13×#29252
#1783113