Finite Group Databasebeta

← #15834309

Subgroups — #15834309

Order 3328.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124871C211yesmaximal, characteristic
2#13123923C211yesmaximal, characteristic
3#13113743C211yesmaximal, characteristic, complemented
4#13113731C211yesmaximal, characteristic, complemented
5#13113707C211yesmaximal, characteristic, complemented
6#13113705C211yesmaximal, characteristic, complemented
7#13113686C211yesmaximal, characteristic, complemented
8#13113684C211yesmaximal, characteristic, complemented
9#13113653C211yesmaximal, characteristic, complemented
10C8×#6107C211yesmaximal, characteristic, complemented
11#13113614C211yesmaximal, characteristic
12#13113309C211yesmaximal, characteristic
13#13113230C211yesmaximal, characteristic
14#13113136C211yesmaximal, characteristic
15C13×#2986C211yesmaximal, characteristic
16C13×#533C2211yescharacteristic
17C2×C4×Dic26C2211yescharacteristic
18C13×#446—21no—
19C13×#446C2211yescharacteristic
20C13×#446C2211yescharacteristic
21C8×Q8×C13—21no—
22C8×Q8×C13C2211yescharacteristic
23C8×Q8×C13C2211yescharacteristic
24C13×#433—21no—
25C13×#433—21no—
26C13×#431C2211yescharacteristic
27C13×#431C2211yescharacteristic
28#11718752C411yescharacteristic
29#11718752C411yescharacteristic
30#11718751C411yescharacteristic
31#11718751C411yescharacteristic
32#11718711C411yescharacteristic
33#11718711C411yescharacteristic
34#11718705C411yescharacteristic
35#11718705C411yescharacteristic
36C4×#6107C2211yescharacteristic
37C4×#6107C2211yescharacteristic
38C4×#6107C2211yescharacteristic
39C4×#6107C2211yescharacteristic
40#11718587C2211yescharacteristic
41#11718586C2211yescharacteristic
42#11718586C2211yescharacteristic
43#11718489—21no—
44#11718489—21no—
45#11718380—21no—
46#11718379—21no—
47#11718340C2211yescharacteristic
48#11718340C2211yescharacteristic
49C8×Dic26C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51Q8⋊#1055C2211yescharacteristic
52Q8⋊#1055C2211yescharacteristic
53Q8⋊#1055C2211yescharacteristic
54Q8⋊#1055C2211yescharacteristic
55#11718076C2211yescharacteristic
56#11718076C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718072C2211yescharacteristic
61#11718071C2211yescharacteristic
62#11718071C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C22×Dic26C2×C411yescharacteristic
68C13×C4⋊Q8C2×C411yescharacteristic
69C13×C4⋊Q8C2×C411yescharacteristic
70C13×#125—21no—
71C13×C22⋊Q8—21no—
72C13×C22⋊Q8C2×C411yescharacteristic
73C13×C22⋊Q8C2×C411yescharacteristic
74C4×Q8×C13—21no—
75C4×Q8×C13C2311yescharacteristic
76C4×Q8×C13C2311yescharacteristic
77C13×#117—21no—
78C2×C42×C13C2311yescharacteristic
79C2×#6107C2×C411yescharacteristic
80C2×#6107C2×C411yescharacteristic
81C2×#6107C2×C411yescharacteristic
82C2×#6107C2×C411yescharacteristic
83C2×C4⋊Dic13C2×C411yescharacteristic
84C2×#6101—21no—
85C2×C4×Dic13—21no—
86C4×Dic26—21no—
87C4×Dic26—21no—
88C4×Dic26C2×C411yescharacteristic
89C4×Dic26C2×C411yescharacteristic
90C4×Dic26C2311yescharacteristic
91C4×Dic26C2311yescharacteristic
92C13×C4⋊C8—21no—
93C13×C4⋊C8—21no—
94C13×C4⋊C8—21no—
95C13×C4⋊C8—21no—
96C13×C4⋊C8D411yescharacteristic
97C13×C4⋊C8D411yescharacteristic
98C13×C4⋊C8C2311yescharacteristic
99C13×C4⋊C8C2311yescharacteristic
100C13×C22⋊C8—21no—
101C13×C22⋊C8D411yescharacteristic
102C13×C22⋊C8D411yescharacteristic
103C13×#97—21no—
104C13×#97—21no—
105C4×C8×C13—21no—
106C4×C8×C13—21no—
107C4×C8×C13—21no—
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110#88075C2×C411yescharacteristic
111#88075C2×C411yescharacteristic
112#88075C2×C411yescharacteristic
113#88075C2×C411yescharacteristic
114C22⋊#1055—21no—
115C22⋊#1055—21no—
116C22⋊#1055C2×C411yescharacteristic
117C22⋊#1055C2×C411yescharacteristic
118#88055—21no—
119#88055—21no—
120#88054—21no—
121#88054—21no—
122#88054—21no—
123#88054—21no—
124C8×Dic13—21no—
125C8×Dic13—21no—
126#88050C2×C411yescharacteristic
127#88050C2×C411yescharacteristic
128#88050C2×C411yescharacteristic
129#88050C2×C411yescharacteristic
130#88047C2×C411yescharacteristic
131#88047C2×C411yescharacteristic
132#88047C2×C411yescharacteristic
133#88047C2×C411yescharacteristic
134C4⋊#1055—21no—
135C4⋊#1055C2×C411yescharacteristic
136C4⋊#1055C2×C411yescharacteristic
137C4⋊#1055C2311yescharacteristic
138C4⋊#1055C2311yescharacteristic
139#88043—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18032—131nomaximal, Sylow
145C2×Q8×C13—21no—
146C2×Q8×C13C22×C411yescharacteristic
147C2×Q8×C13C22×C411yescharacteristic
148C22×C4×C13C22×C411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13#4111yescharacteristic
151C22×Dic13—21no—
152C22×Dic13—21no—
153C2×Dic26—22no—
154C2×Dic26—21no—
155C2×Dic26—41no—
156C2×Dic26C22×C411yescharacteristic
157C2×Dic26C22×C411yescharacteristic
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13C2×D411yescharacteristic
161C2×C8×C13C2×D411yescharacteristic
162C2×C8×C13C2×D411yescharacteristic
163C2×C8×C13C2×D411yescharacteristic
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4C22×C411yescharacteristic
172C13×C4⋊C4C22×C411yescharacteristic
173C13×C22⋊C4—21no—
174C13×C22⋊C4—21no—
175C42×C13—21no—
176C42×C13—21no—
177C42×C13C22×C411yescharacteristic
178C42×C13C2×D411yescharacteristic
179C42×C13#4111yescharacteristic
180C42×C13C2411yescharacteristic
181#6107—22no—
182#6107—22no—
183#6107—41no—
184#6107—41no—
185C4⋊Dic13—21no—
186C4⋊Dic13C22×C411yescharacteristic
187C4⋊Dic13C22×C411yescharacteristic
188#6101—21no—
189#6101—21no—
190#6101—21no—
191#6101—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195C4×Dic13—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055C22×C411yescharacteristic
201C2×#1055C22×C411yescharacteristic
202C2×#1055C22×C411yescharacteristic
203C2×#1055C22×C411yescharacteristic
204#3104—131no—
205#2986D1311yescharacteristic
206#2984—131no—
207#1593—131no—
208#1591—131no—
209#1587—131no—
210#1587—131no—
211#1584—131no—
212#1584—131no—
213#1579—131no—
214C8×Q16—131no—
215#1572—131no—
216#1497—131no—
217#1479—131no—
218#1454—131no—
219C23×C13C4×D411yescharacteristic
220Q8×C13—21no—
221Q8×C13—21no—
222Q8×C13—21no—
223Q8×C13—21no—
224Q8×C13—42no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—41no—
234C2×C4×C13C4×D411yescharacteristic
235C2×C4×C13C4×D411yescharacteristic
236C2×C4×C13C4×D411yescharacteristic
237C2×C4×C13C23×C411yescharacteristic
238C2×C4×C13C22×D411yescharacteristic
239C2×C4×C13C2×#4111yescharacteristic
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—42no—
245C2×Dic13—42no—
246Dic26—21no—
247Dic26—21no—
248Dic26—21no—
249Dic26—42no—
250Dic26#13112yes—
251C8×C13—21no—
252C8×C13—21no—
253C8×C13—21no—
254C8×C13—21no—
255C8×C13—41no—
256C8×C13—41no—
257#1055—21no—
258#1055—21no—
259#1055—21no—
260#1055—21no—
261#1055—41no—
262#1055—41no—
263#1055—41no—
264#1055—41no—
265#533C2×D1311yescharacteristic
266C2×C4×Q8—131no—
267#484—131no—
268#484—131no—
269#477—131no—
270#477—131no—
271#462—131no—
272#462—131no—
273#451—131no—
274#451—131no—
275#446—21no—
276#446—131no—
277#446—131no—
278#446—261no—
279#446—261no—
280#446C2×D1311yescharacteristic
281#446C2×D1311yescharacteristic
282C8×Q8—21no—
283C8×Q8—131no—
284C8×Q8—131no—
285C8×Q8C2×D1311yescharacteristic
286C8×Q8C2×D1311yescharacteristic
287C4×Q16—131no—
288C4×Q16—131no—
289C4×Q16—131no—
290C4×Q16—131no—
291#433—21no—
292#433—21no—
293#432—131no—
294#432—261no—
295#431—131no—
296#431—131no—
297#431—261no—
298#431C2×D1311yescharacteristic
299#431C2×D1311yescharacteristic
300#335—131no—
301#335—131no—
302#334—131no—
303#334—131no—
304Q8⋊C8—131no—
305Q8⋊C8—131no—
306Q8⋊C8—131no—
307Q8⋊C8—131no—
308Q8⋊C8—131no—
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312#322—131no—
313#322—131no—
314#322—131no—
315C82—131no—
316C22×C13—21no—
317C22×C13—21no—
318C22×C13—21no—
319C22×C13C2×C4×D411yescharacteristic
320C4×C13—21no—
321C4×C13—21no—
322C4×C13—21no—
323C4×C13—21no—
324C4×C13—41no—
325C4×C13—41no—
326C4×C13—41no—
327C4×C13—41no—
328C4×C13C2×#13111yescharacteristic
329C4×C13#56811yescharacteristic
330C4×C13#57811yescharacteristic
331C4×C13#57811yescharacteristic
332Dic13—22no—
333Dic13—41no—
334Dic13—41no—
335Dic13—41no—
336C22×Q8—131no—
337C2×Q16—131no—
338C2×Q16—131no—
339C2×Q16—131no—
340C2×Q16—131no—
341C4⋊Q8C4×D1311yescharacteristic
342C4⋊Q8C4×D1311yescharacteristic
343#125—21no—
344C22⋊Q8—21no—
345C22⋊Q8C4×D1311yescharacteristic
346C22⋊Q8C4×D1311yescharacteristic
347C4×Q8—21no—
348C4×Q8—131no—
349C4×Q8—131no—
350C4×Q8—131no—
351C4×Q8—131no—
352C4×Q8—261no—
353C4×Q8—261no—
354C4×Q8C22×D1311yescharacteristic
355C4×Q8C22×D1311yescharacteristic
356#117—21no—
357C2×C4⋊C4—131no—
358C2×C4⋊C4—261no—
359C2×C42—261no—
360C2×C42C22×D1311yescharacteristic
361#107—131no—
362#107—131no—
363#107—131no—
364#107—131no—
365C4⋊C8—21no—
366C4⋊C8—21no—
367C4⋊C8—21no—
368C4⋊C8—21no—
369C4⋊C8—131no—
370C4⋊C8—131no—
371C4⋊C8—131no—
372C4⋊C8—131no—
373C4⋊C8—261no—
374C4⋊C8—261no—
375C4⋊C8—261no—
376C4⋊C8—261no—
377C4⋊C8—261no—
378C4⋊C8C22⋊D1311yescharacteristic
379C4⋊C8C22⋊D1311yescharacteristic
380C4⋊C8C22×D1311yescharacteristic
381C4⋊C8C22×D1311yescharacteristic
382#103—131no—
383#103—131no—
384#103—131no—
385#103—131no—
386#103—131no—
387#103—131no—
388#103—131no—
389#103—131no—
390C22⋊C8—21no—
391C22⋊C8—131no—
392C22⋊C8—131no—
393C22⋊C8—261no—
394C22⋊C8—261no—
395C22⋊C8C22⋊D1311yescharacteristic
396C22⋊C8C22⋊D1311yescharacteristic
397#97—21no—
398#97—21no—
399#97—261no—
400#97—261no—
401#97—261no—
402C4×C8—21no—
403C4×C8—21no—
404C4×C8—21no—
405C4×C8—131no—
406C4×C8—131no—
407C4×C8—131no—
408C4×C8—131no—
409C4×C8—261no—
410C4×C8—261no—
411C4×C8C22×D1311yescharacteristic
412C4×C8C22×D1311yescharacteristic
413C2×C13—41no—
414C2×C13#293311yescharacteristic
415C2×C13#295011yescharacteristic
416C2×C13#295511yescharacteristic
417C2×Q8—21no—
418C2×Q8—131no—
419C2×Q8—131no—
420C2×Q8—262no—
421C2×Q8—261no—
422C2×Q8—521no—
423C2×Q8C2×C4×D1311yescharacteristic
424C2×Q8C2×C4×D1311yescharacteristic
425C22×C4—261no—
426C22×C4—261no—
427C22×C4C2×C4×D1311yescharacteristic
428C22×C4#612711yescharacteristic
429C22×C4C2×C22⋊D1311yescharacteristic
430Q16—262no—
431Q16—262no—
432Q16—521no—
433Q16—521no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—131no—
437C2×C8—131no—
438C2×C8—131no—
439C2×C8—131no—
440C2×C8—261no—
441C2×C8—261no—
442C2×C8—261no—
443C2×C8—261no—
444C2×C8C2×C22⋊D1311yescharacteristic
445C2×C8C2×C22⋊D1311yescharacteristic
446C2×C8C2×C22⋊D1311yescharacteristic
447C2×C8C2×C22⋊D1311yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—131no—
456C4⋊C4—131no—
457C4⋊C4—261no—
458C4⋊C4—261no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4C2×C4×D1311yescharacteristic
463C4⋊C4C2×C4×D1311yescharacteristic
464C22⋊C4—21no—
465C22⋊C4—21no—
466C42—21no—
467C42—21no—
468C42—261no—
469C42—261no—
470C42—261no—
471C42—261no—
472C42C2×C4×D1311yescharacteristic
473C42#612711yescharacteristic
474C42C2×C22⋊D1311yescharacteristic
475C42C23×D1311yescharacteristic
476C13#1803211yescharacteristic, complemented, Sylow
477C23C4×C22⋊D1311yescharacteristic
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—42no—
483Q8—132no—
484Q8—261no—
485Q8—261no—
486Q8—261no—
487Q8—522no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—261no—
498C2×C4—261no—
499C2×C4—261no—
500C2×C4—261no—
501C2×C4—522no—
502C2×C4—522no—
503C2×C4C4×C22⋊D1311yescharacteristic
504C2×C4C4×C22⋊D1311yescharacteristic
505C2×C4C4×C22⋊D1311yescharacteristic
506C2×C4C22×C4×D1311yescharacteristic
507C2×C4C2×#612711yescharacteristic
508C2×C4C22×C22⋊D1311yescharacteristic
509C8—21no—
510C8—21no—
511C8—21no—
512C8—21no—
513C8—41no—
514C8—41no—
515C8—261no—
516C8—261no—
517C8—261no—
518C8—261no—
519C8—521no—
520C8—521no—
521C8—521no—
522C8—521no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×C4×C22⋊D1311yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—262no—
536C4—521no—
537C4—521no—
538C4—521no—
539C4D13×#13111yescharacteristic
540C4#1171945511yescharacteristic
541C4#1171954311yescharacteristic
542C4#1171954311yescharacteristic
543C2—41no—
544C2#1312355811yescharacteristic
545C2#1312370211yescharacteristic
546C2#1312373711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2986C2
socleC22×C13C2×C4×D4
prime radicalC23×C13C4×D4
cosocleC42×C13C24
hypercenter#2986D13
hypocenterC13#18032
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2986

Complements

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

NH ≅ G/Ntype
3. #13113743C2semidirect
4. #13113731C2semidirect
5. #13113707C2semidirect
6. #13113705C2semidirect
7. #13113686C2semidirect
8. #13113684C2semidirect
9. #13113653C2semidirect
10. C8×#6107C2semidirect
476. C13#18032semidirect

Maximal subgroups

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

subgroupindex
#131248712
#131239232
#131137432
#131137312
#131137072
#131137052
#131136862
#131136842
#131136532
C8×#61072
#131136142
#131133092
#131132302
#131131362
C13×#29862
#1803213