Finite Group Databasebeta

← #15834106

Subgroups — #15834106

Order 3328.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124916C211yesmaximal, characteristic
2#13123992C211yesmaximal, characteristic
3#13123925C211yesmaximal, characteristic, complemented
4#13113730C211yesmaximal, characteristic, complemented
5#13113723C211yesmaximal, characteristic, complemented
6#13113711C211yesmaximal, characteristic, complemented
7#13113710C211yesmaximal, characteristic, complemented
8#13113704C211yesmaximal, characteristic, complemented
9#13113696C211yesmaximal, characteristic, complemented
10#13113640C211yesmaximal, characteristic, complemented
11#13113633C211yesmaximal, characteristic, complemented
12#13113619C211yesmaximal, characteristic, complemented
13#13113297C211yesmaximal, characteristic
14#13113119C211yesmaximal, characteristic, complemented
15C2×C13×Q8⋊C8C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C13C2211yescharacteristic
17#11719184C2211yescharacteristic
18C2×C13×C4⋊C8C2211yescharacteristic
19C2×C4×C8×C13C2211yescharacteristic
20#11718889C411yescharacteristic
21#11718888C411yescharacteristic
22#11718772—21no—
23C8×C22⋊D13—21no—
24C4×#6107C2211yescharacteristic
25C4×#6107C2211yescharacteristic
26#11718689C411yescharacteristic
27#11718689C411yescharacteristic
28C4×#6106C2211yescharacteristic
29C4×#6106C2211yescharacteristic
30#11718685—21no—
31#11718685—21no—
32#11718685C2211yescharacteristic
33#11718685C2211yescharacteristic
34Q8×#1055C2211yescharacteristic
35Q8×#1055C2211yescharacteristic
36#11718683C411yescharacteristic
37#11718683C411yescharacteristic
38#11718632C411yescharacteristic
39#11718628C411yescharacteristic
40#11718587—21no—
41#11718587C2211yescharacteristic
42#11718586—21no—
43#11718586C2211yescharacteristic
44#11718586C2211yescharacteristic
45#11718501—21no—
46#11718500—21no—
47#11718499C2211yescharacteristic
48#11718495C2211yescharacteristic
49#11718492C2211yescharacteristic
50#11718491C2211yescharacteristic
51C13×Q8⋊C8C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×Q8⋊C8C2211yescharacteristic
54C13×Q8⋊C8C2211yescharacteristic
55#11718072C2211yescharacteristic
56#11718072C2211yescharacteristic
57#11718071C2211yescharacteristic
58#11718071C2211yescharacteristic
59#11718051C2211yescharacteristic
60#11718051C2211yescharacteristic
61#11718048C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718047C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C22×Q8×C13C2×C411yescharacteristic
68C22×C8×C13—21no—
69C22×C8×C13—21no—
70C4×Q8×C13—21no—
71C4×Q8×C13—21no—
72C4×Q8×C13C2×C411yescharacteristic
73C4×Q8×C13C2×C411yescharacteristic
74C4×Q8×C13C2311yescharacteristic
75C4×Q8×C13C2311yescharacteristic
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4C2×C411yescharacteristic
78C2×C42×C13—21no—
79C2×C42×C13C2311yescharacteristic
80C2×#6107C2×C411yescharacteristic
81C2×#6107C2×C411yescharacteristic
82C2×#6106C2×C411yescharacteristic
83C2×#6106C2×C411yescharacteristic
84#88184C2×C411yescharacteristic
85#88183—21no—
86C4×C22⋊D13—21no—
87#88178C2×C411yescharacteristic
88C2×#6094—21no—
89C2×C8×D13—21no—
90#88130—21no—
91#88129C2×C411yescharacteristic
92C4×D52C2311yescharacteristic
93#88126—21no—
94#88124C2×C411yescharacteristic
95C4×Dic26C2311yescharacteristic
96C13×C4⋊C8—21no—
97C13×C4⋊C8C2311yescharacteristic
98C13×C4⋊C8C2311yescharacteristic
99C4×C8×C13—21no—
100C4×C8×C13C2311yescharacteristic
101C4×C8×C13C2311yescharacteristic
102#88075C2×C411yescharacteristic
103#88075C2×C411yescharacteristic
104#88075C2×C411yescharacteristic
105#88075C2×C411yescharacteristic
106C22⋊#1055—21no—
107C22⋊#1055C2×C411yescharacteristic
108C22⋊#1055C2×C411yescharacteristic
109C22⋊#1055D411yescharacteristic
110C22⋊#1055D411yescharacteristic
111#88060—21no—
112#88060—21no—
113#88055—21no—
114#88054—21no—
115#88054—21no—
116C8×Dic13—21no—
117#88050C2×C411yescharacteristic
118#88050C2×C411yescharacteristic
119#88049C2×C411yescharacteristic
120#88049C2×C411yescharacteristic
121#88048C2×C411yescharacteristic
122#88048C2×C411yescharacteristic
123#88047C2×C411yescharacteristic
124#88047C2×C411yescharacteristic
125C4⋊#1055—21no—
126C4⋊#1055—21no—
127C4⋊#1055—21no—
128C4⋊#1055—21no—
129C4⋊#1055C2×C411yescharacteristic
130C4⋊#1055C2×C411yescharacteristic
131C4⋊#1055D411yescharacteristic
132C4⋊#1055D411yescharacteristic
133C4⋊#1055C2311yescharacteristic
134C4⋊#1055C2311yescharacteristic
135#88043—21no—
136#88043—21no—
137#88043—21no—
138C4×#1055—21no—
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18017—131nomaximal, Sylow
145C2×Q8×C13—21no—
146C2×Q8×C13—22no—
147C2×Q8×C13—41no—
148C2×Q8×C13C22×C411yescharacteristic
149C2×Q8×C13C22×C411yescharacteristic
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13C22×C411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13#4111yescharacteristic
155C2×C22⋊D13—21no—
156C2×D52C22×C411yescharacteristic
157C2×C4×D13—21no—
158C2×Dic26C22×C411yescharacteristic
159C2×C8×C13—24no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13—81no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4C22×C411yescharacteristic
171C13×C4⋊C4C22×C411yescharacteristic
172C42×C13—21no—
173C42×C13—21no—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13C22×C411yescharacteristic
177C42×C13C2×D411yescharacteristic
178C42×C13#4111yescharacteristic
179C42×C13C2411yescharacteristic
180C22⋊Dic13—21no—
181#6107—22no—
182#6107—41no—
183#6106—22no—
184#6106—41no—
185#6103—21no—
186#6103—21no—
187#6103—21no—
188#6103—21no—
189C4⋊Dic13C22×C411yescharacteristic
190C4⋊Dic13C22×C411yescharacteristic
191#6101—21no—
192#6101—21no—
193#6101—21no—
194#6101—21no—
195C4×Dic13—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055C22×C411yescharacteristic
199C2×#1055C22×C411yescharacteristic
200C2×#1055C22×C411yescharacteristic
201C2×#1055C22×C411yescharacteristic
202C2×#1055C2×D411yescharacteristic
203C2×#1055C2×D411yescharacteristic
204C2×#1055C2×D411yescharacteristic
205C2×#1055C2×D411yescharacteristic
206#6094—81no—
207C8×D13—81no—
208#3108—131no—
209#2994—131no—
210#2984—131no—
211#1591—131no—
212#1590—131no—
213#1588—131no—
214#1587—131no—
215#1587—131no—
216#1585—131no—
217C8×Q16—131no—
218C8×SD16—131no—
219#1573—131no—
220#1494—131no—
221C2×Q8⋊C8D1311yescharacteristic, complemented
222#1450—131no—
223C23×C13C4×D411yescharacteristic
224C22×D13—21no—
225Q8×C13—21no—
226Q8×C13—21no—
227Q8×C13—21no—
228Q8×C13—42no—
229Q8×C13#13112yes—
230C2×C4×C13—21no—
231C2×C4×C13—22no—
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—42no—
240C2×C4×C13—42no—
241C2×C4×C13C4×D411yescharacteristic
242C2×C4×C13C4×D411yescharacteristic
243C2×C4×C13C4×D411yescharacteristic
244C2×C4×C13C23×C411yescharacteristic
245C2×C4×C13C22×D411yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C22⋊D13—42no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251D52—21no—
252D52—21no—
253C4×D13—41no—
254C4×D13—41no—
255Dic26—21no—
256Dic26—21no—
257C8×C13—22no—
258C8×C13—22no—
259C8×C13—41no—
260C8×C13—41no—
261#1055—21no—
262#1055—21no—
263#1055—21no—
264#1055—21no—
265#1055—21no—
266#1055—21no—
267#1055—21no—
268#1055—21no—
269#1055—41no—
270#1055—41no—
271#529—131no—
272C2×C4×Q8C2×D1311yescharacteristic
273#483—131no—
274#480—131no—
275#479—131no—
276#479—131no—
277#464—131no—
278#464—131no—
279#451—131no—
280#448—131no—
281#446—131no—
282#446—131no—
283#446—131no—
284#446—261no—
285#446—261no—
286C8×Q8—131no—
287C8×Q8—131no—
288C8×Q8—131no—
289C4×Q16—131no—
290C4×Q16—131no—
291C4×SD16—131no—
292C4×SD16—131no—
293#436—131no—
294#435—261no—
295C8×D4—131no—
296C8×D4—261no—
297#433—261no—
298#432—131no—
299#432—261no—
300#431—131no—
301#431—131no—
302#431—261no—
303#424—261no—
304C2×C4⋊C8C2×D1311yescharacteristic
305C2×C4×C8C2×D1311yescharacteristic
306#335—131no—
307#335—131no—
308#334—131no—
309#334—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8C2×D1311yescharacteristic
313Q8⋊C8C2×D1311yescharacteristic
314Q8⋊C8C2×D1311yescharacteristic
315Q8⋊C8C2×D1311yescharacteristic
316D4⋊C8—131no—
317D4⋊C8—131no—
318#322—131no—
319#322—131no—
320C82—131no—
321C82—131no—
322C22×C13—21no—
323C22×C13—21no—
324C22×C13#44312yes—
325C22×C13C2×C4×D411yescharacteristic
326C2×D13—41no—
327C2×D13—41no—
328C2×D13—41no—
329C4×C13—21no—
330C4×C13—22no—
331C4×C13—21no—
332C4×C13—21no—
333C4×C13—21no—
334C4×C13—41no—
335C4×C13—41no—
336C4×C13—41no—
337C4×C13C2×#13111yescharacteristic
338C4×C13#56811yescharacteristic
339C4×C13#57711yescharacteristic
340C4×C13#57811yescharacteristic
341Dic13—41no—
342Dic13—41no—
343Dic13—41no—
344C22×Q8C4×D1311yescharacteristic
345C2×Q16—131no—
346C2×Q16—131no—
347C2×SD16—131no—
348C2×SD16—131no—
349C2×M16—261no—
350C22×C8—21no—
351C22×C8—21no—
352C22×C8—261no—
353#126—261no—
354#125—131no—
355#124—131no—
356#123—261no—
357C22⋊Q8—131no—
358#121—131no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8—131no—
362C4×Q8C4×D1311yescharacteristic
363C4×Q8C4×D1311yescharacteristic
364C4×Q8C22×D1311yescharacteristic
365C4×Q8C22×D1311yescharacteristic
366C4×D4—131no—
367C4×D4—261no—
368#117—261no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4C4×D1311yescharacteristic
371C2×C42—21no—
372C2×C42C22×D1311yescharacteristic
373#107—131no—
374#107—131no—
375#106—131no—
376#106—131no—
377C4⋊C8—21no—
378C4⋊C8—131no—
379C4⋊C8—131no—
380C4⋊C8—131no—
381C4⋊C8—131no—
382C4⋊C8—131no—
383C4⋊C8—131no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8—261no—
389C4⋊C8—261no—
390C4⋊C8C22×D1311yescharacteristic
391C4⋊C8C22×D1311yescharacteristic
392#103—131no—
393#103—131no—
394#103—131no—
395#103—131no—
396#103—131no—
397#103—131no—
398#102—131no—
399#102—131no—
400C22⋊C8—131no—
401C22⋊C8—131no—
402C22⋊C8—131no—
403C22⋊C8—131no—
404C22⋊C8—261no—
405C22⋊C8—261no—
406C22⋊C8—261no—
407#97—261no—
408#97—261no—
409#97—261no—
410#97—261no—
411C4×C8—21no—
412C4×C8—131no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—131no—
416C4×C8—261no—
417C4×C8—261no—
418C4×C8—261no—
419C4×C8C22×D1311yescharacteristic
420C4×C8C22×D1311yescharacteristic
421C2×C13—22no—
422C2×C13#293311yescharacteristic
423C2×C13#294711yescharacteristic
424C2×C13C2×#44311yescharacteristic
425D13—81no—
426C2×Q8—21no—
427C2×Q8—22no—
428C2×Q8—41no—
429C2×Q8—131no—
430C2×Q8C2×C4×D1311yescharacteristic
431C2×Q8C2×C4×D1311yescharacteristic
432C2×D4—131no—
433C2×D4—261no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—261no—
437C22×C4C2×C4×D1311yescharacteristic
438C22×C4D4×D1311yescharacteristic
439C22×C4#612911yescharacteristic
440Q16—262no—
441Q16—521no—
442SD16—262no—
443SD16—521no—
444M16—1041no—
445C2×C8—24no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—81no—
451C2×C8—131no—
452C2×C8—131no—
453C2×C8—131no—
454C2×C8—131no—
455C2×C8—131no—
456C2×C8—131no—
457C2×C8—131no—
458C2×C8—131no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—1041no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—131no—
468C4⋊C4—131no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4C2×C4×D1311yescharacteristic
474C4⋊C4C2×C4×D1311yescharacteristic
475C22⋊C4—261no—
476C22⋊C4—261no—
477C22⋊C4—261no—
478C22⋊C4—261no—
479C22⋊C4—261no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—261no—
485C42C2×C4×D1311yescharacteristic
486C42D4×D1311yescharacteristic
487C42#612911yescharacteristic
488C42C23×D1311yescharacteristic
489C13#1801711yescharacteristic, complemented, Sylow
490C23—261no—
491C23#8813511yescharacteristic
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—42no—
496Q8—261no—
497Q8—261no—
498Q8#8815512yes—
499D4—261no—
500D4—261no—
501D4—522no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—521no—
517C2×C4—521no—
518C2×C4#8813511yescharacteristic
519C2×C4#8813511yescharacteristic
520C2×C4#8813511yescharacteristic
521C2×C4C22×C4×D1311yescharacteristic
522C2×C4C2×D4×D1311yescharacteristic
523C2×C4C2×#612911yescharacteristic
524C8—22no—
525C8—22no—
526C8—41no—
527C8—41no—
528C8—261no—
529C8—261no—
530C8—261no—
531C8—261no—
532C8—261no—
533C8—261no—
534C8—261no—
535C8—261no—
536C8—521no—
537C8—521no—
538C22—21no—
539C22—21no—
540C22—521no—
541C22—521no—
542C22—521no—
543C22#1171848512yes—
544C22C2×#8813511yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—22no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—521no—
554C4—521no—
555C4—521no—
556C4C2×#8815511yescharacteristic
557C4#1171945011yescharacteristic
558C4#1171946711yescharacteristic
559C4#1171947111yescharacteristic
560C2—22no—
561C2—1041no—
562C2#1312355711yescharacteristic
563C2#1312367311yescharacteristic
564C2C2×#1171848511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC2×C13×Q8⋊C8C2
socleC22×C13C2×C4×D4
prime radical#88184C2×C4
cosocleC42×C13C24
hypercenterC2×Q8⋊C8D13
hypocenterC13#18017
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
3. #13123925C2semidirect
4. #13113730C2semidirect
5. #13113723C2semidirect
6. #13113711C2semidirect
7. #13113710C2semidirect
8. #13113704C2semidirect
9. #13113696C2semidirect
10. #13113640C2semidirect
11. #13113633C2semidirect
12. #13113619C2semidirect
14. #13113119C2semidirect
15. C2×C13×Q8⋊C8C2semidirect
221. C2×Q8⋊C8D13semidirect
489. C13#18017semidirect

Maximal subgroups

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

subgroupindex
#131249162
#131239922
#131239252
#131137302
#131137232
#131137112
#131137102
#131137042
#131136962
#131136402
#131136332
#131136192
#131132972
#131131192
C2×C13×Q8⋊C82
#1801713