Finite Group Databasebeta

← #16808844

Subgroups — #16808844

Order 3328.

1702 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
1#13131747C213yesmaximal, complemented
2#13131745C213yesmaximal, complemented
3#13131741C213yesmaximal, complemented
4#13131740C213yesmaximal, complemented
5#13131739C211yesmaximal, characteristic, complemented
6#13131738C211yesmaximal, characteristic, complemented
7#13131730C211yesmaximal, characteristic, complemented
8#13131729C211yesmaximal, characteristic, complemented
9Q8×#6122C211yesmaximal, characteristic, complemented
10#13131631C213yesmaximal, complemented
11#13131624C213yesmaximal, complemented
12C2×Q8×#1057C211yesmaximal, characteristic, complemented
13#13131531C213yesmaximal
14#13131519C213yesmaximal
15Q8×#6129C211yesmaximal, characteristic
16D4×Q8×C13C411yescharacteristic
17Q8×C22⋊D13C411yescharacteristic
18Q8×C22⋊D13C411yescharacteristic
19C2×Q8×Dic13C2211yescharacteristic
20C2×Q8×Dic13C2211yescharacteristic
21#11719433C2213yes—
22#11719426C413yes—
23#11719340C413yes—
24#11719340C413yes—
25#11719327C2213yes—
26#11719327C2213yes—
27C4×Q8×D13C2211yescharacteristic
28Q8×Dic26C411yescharacteristic
29#11719248C413yes—
30C4×#6129C2213yes—
31#11719158C2213yes—
32#11719158C2213yes—
33#11719158C2213yes—
34#11719158C2213yes—
35Q8×#1057C2211yescharacteristic
36Q8×#1057C2211yescharacteristic
37Q8×#1057C2213yes—
38Q8×#1057C2213yes—
39Q8×#1057C2213yes—
40Q8×#1057C2213yes—
41Q8×#1057C2211yescharacteristic
42Q8×#1057C2211yescharacteristic
43#11719146C2213yes—
44#11719146C2211yescharacteristic
45#11719130C2213yes—
46#11719129C2213yes—
47#11719125C2213yes—
48C4×#6122C2213yes—
49#11719119C2213yes—
50#11719119C2213yes—
51C2×C4⋊#1057C2213yes—
52C2×C4×#1057C2213yes—
53#11719080C2213yes—
54#11719080C2213yes—
55#11719080C2216yes—
56#11719078C2216yes—
57#11719078C2216yes—
58#11719077C2216yes—
59#11719077C2213yes—
60#11719077C2213yes—
61#11719074C2213yes—
62#11719074C2216yes—
63#11719074C2213yes—
64#11719068C2216yes—
65#11719068C2213yes—
66#11719068C2213yes—
67#11719067C2213yes—
68#11719067C2213yes—
69#11719062C2216yes—
70#11719054C2213yes—
71#11719051C2213yes—
72#11719051C2213yes—
73#11719049C2213yes—
74C22×Q8×C13C2×C411yescharacteristic
75C22×Q8×C13C2×C411yescharacteristic
76C2×Q8×D13C2×C411yescharacteristic
77C2×#6129C2311yescharacteristic
78C2×#6122C2313yes—
79C2×#6122C2311yescharacteristic
80C22×#1057C2313yes—
81C22×#1057C2311yescharacteristic
82C13×C4⋊Q8C2×C413yes—
83C13×C22⋊Q8C2×C413yes—
84C13×C22⋊Q8C2×C413yes—
85C4×Q8×C13C2×C411yescharacteristic
86C4×D4×C13C2×C413yes—
87#88200C2×C413yes—
88#88200C2×C413yes—
89Q8×Dic13C2×C413yes—
90Q8×Dic13C2×C413yes—
91Q8×Dic13C2×C411yescharacteristic
92Q8×Dic13C2×C411yescharacteristic
93Q8×Dic13C2313yes—
94Q8×Dic13C2313yes—
95Q8×Dic13C2311yescharacteristic
96#88198C2×C413yes—
97#88198C2×C413yes—
98D4×Dic13C2×C413yes—
99C4×C22⋊D13C2×C413yes—
100C4×C22⋊D13C2×C413yes—
101C2×C4⋊Dic13C2×C413yes—
102C2×C4⋊Dic13C2×C413yes—
103#88178C2×C413yes—
104#88178C2×C413yes—
105C2×C4×Dic13C2313yes—
106C2×C4×Dic13C2313yes—
107#88151C2×C416yes—
108#88146C2313yes—
109C4⋊C4×D13C2×C413yes—
110#88144C2×C416yes—
111#88143C2×C416yes—
112#88143C2×C416yes—
113#88142C2×C413yes—
114#88142C2×C413yes—
115#88141C2×C413yes—
116#88141C2316yes—
117#88141C2313yes—
118#88135C2×C413yes—
119#88135C2×C413yes—
120#88132C2×C416yes—
121#88132C2×C416yes—
122#88131C2313yes—
123#88131C2313yes—
124C42×D13C2313yes—
125#88123C2×C413yes—
126C4×Dic26C2×C413yes—
127C4×Dic26C2×C413yes—
128C22⋊#1057C2313yes—
129C22⋊#1057C2311yescharacteristic
130C22⋊#1057C2311yescharacteristic
131C22⋊#1057C2313yes—
132#88112C2313yes—
133#88112C2313yes—
134#88112C2313yes—
135#88112C2313yes—
136#88112C2316yes—
137#88111C2311yescharacteristic
138#88111C2313yes—
139#88111C2311yescharacteristic
140#88111C2313yes—
141#88110C2316yes—
142#88110C2316yes—
143#88110C2313yes—
144#88110C2313yes—
145C4⋊#1057C2313yes—
146C4⋊#1057C2313yes—
147C4⋊#1057C2313yes—
148C4⋊#1057C2313yes—
149C4⋊#1057C2313yes—
150C4⋊#1057C2313yes—
151C4⋊#1057C2313yes—
152C4⋊#1057C2313yes—
153C4⋊#1057C2316yes—
154C4×#1057C2313yes—
155C4×#1057C2313yes—
156C4×#1057C2316yes—
157C4×#1057C2313yes—
158C4×#1057C2313yes—
159C4×#1057C2316yes—
160C4×#1057C2313yes—
161C4×#1057C2313yes—
162#60253—131nomaximal, Sylow
163C2×Q8×C13—24no—
164C2×Q8×C13—24no—
165C2×Q8×C13C22×C413yes—
166C2×Q8×C13C22×C413yes—
167C2×Q8×C13C22×C411yescharacteristic
168C2×D4×C13C22×C411yescharacteristic
169C22×C4×C13C22×C413yes—
170C22×C4×C13C22×C413yes—
171C2×C22⋊D13C22×C411yescharacteristic
172C2×C22⋊D13C22×C411yescharacteristic
173C22×Dic13C22×C413yes—
174C22×Dic13C22×C413yes—
175C22×Dic13C2411yescharacteristic
176C22×Dic13C2411yescharacteristic
177Q8×D13—24no—
178#6129—22no—
179#6129—22no—
180C2×C4×D13C22×C413yes—
181C2×C4×D13C22×C413yes—
182C2×C4×D13C2411yescharacteristic
183C2×Dic26C22×C411yescharacteristic
184C2×Dic26C22×C413yes—
185C2×Dic26C22×C416yes—
186#6122—22no—
187#6122—26no—
188C2×#1057—26no—
189C2×#1057—22no—
190C2×#1057C2413yes—
191C2×#1057C2411yescharacteristic
192C2×#1057C2411yescharacteristic
193C2×#1057C2411yescharacteristic
194C2×#1057C2413yes—
195C2×#1057C2413yes—
196C2×#1057C2411yescharacteristic
197C2×#1057C2413yes—
198C13×C4⋊C4C22×C413yes—
199C13×C4⋊C4C22×C413yes—
200C13×C4⋊C4C22×C416yes—
201C13×C22⋊C4C22×C413yes—
202C13×C22⋊C4C22×C413yes—
203C42×C13C22×C413yes—
204C22⋊Dic13C22×C413yes—
205C22⋊Dic13C22×C413yes—
206#6103C22×C413yes—
207#6103C22×C413yes—
208C4⋊Dic13C22×C413yes—
209C4⋊Dic13C22×C413yes—
210C4⋊Dic13C22×C413yes—
211C4⋊Dic13C22×C413yes—
212C4⋊Dic13C22×C416yes—
213C4⋊Dic13C22×C416yes—
214#6101C22×C413yes—
215#6101C22×C413yes—
216#6101C22×C416yes—
217#6101C22×C413yes—
218#6101C22×C413yes—
219#6101C22×C416yes—
220#6101C22×C416yes—
221C4×Dic13C22×C413yes—
222C4×Dic13C22×C413yes—
223C4×Dic13C22×C413yes—
224C4×Dic13C22×C413yes—
225C4×Dic13C22×C413yes—
226C4×Dic13C2413yes—
227C4×Dic13C2413yes—
228C4×Dic13C2413yes—
229C4×Dic13C2413yes—
230Q8×#41—131no—
231#2986—133no—
232#2986—133no—
233#2985—133no—
234#2985—133no—
235#2984—131no—
236#2984—131no—
237#2982—131no—
238#2982—131no—
239Q8×M16—131no—
240#2962—133no—
241#2960—133no—
242C2×C8×Q8—131no—
243#2925—133no—
244#2922—133no—
245C23×C13C23×C411yescharacteristic
246C23×C13C23×C411yescharacteristic
247C22×D13C23×C411yescharacteristic
248Q8×C13—26no—
249Q8×C13—26no—
250Q8×C13#13114yes—
251D4×C13—22no—
252C2×C4×C13—26no—
253C2×C4×C13—26no—
254C2×C4×C13C23×C411yescharacteristic
255C2×C4×C13C23×C413yes—
256C2×C4×C13C23×C413yes—
257C2×C4×C13C23×C413yes—
258C2×C4×C13C23×C413yes—
259C22⋊D13—22no—
260C22⋊D13—22no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—43no—
264C2×Dic13—43no—
265C2×Dic13C23×C411yescharacteristic
266C2×Dic13C23×C413yes—
267C2×Dic13C23×C413yes—
268C2×Dic13C23×C413yes—
269C2×Dic13C23×C413yes—
270C2×Dic13C23×C411yescharacteristic
271C2×Dic132−1+412yes—
272C2×Dic132−1+412yes—
273C2×Dic13C2511yescharacteristic
274C4×D13—26no—
275C4×D13—21no—
276C4×D13—21no—
277C4×D13—43no—
278Dic26—26no—
279Dic26—22no—
280Dic26—46no—
281#1057—23no—
282#1057—21no—
283#1057—21no—
284#1057—23no—
285#1057—21no—
286#1057—23no—
287#1057—23no—
288#1057—21no—
289Q82—131no—
290#557—133no—
291#554—133no—
292#554—133no—
293#554—133no—
294D4×Q8—131no—
295D4×Q8—131no—
296D4×Q8#26111yescharacteristic
297#533—133no—
298#533—133no—
299#533—133no—
300C4×#41—133no—
301C2×C4×Q8—131no—
302C2×C4×Q8—131no—
303C2×C4×Q8—131no—
304#446—136no—
305#446—133no—
306#446—133no—
307#446—136no—
308#446—133no—
309#446—133no—
310#446—136no—
311#446—133no—
312#446—133no—
313C8×Q8—131no—
314C8×Q8—131no—
315C8×Q8—133no—
316C8×Q8—133no—
317C8×Q8—133no—
318C8×Q8—136no—
319C8×Q8—133no—
320C8×Q8—133no—
321C8×Q8—133no—
322C8×Q8—131no—
323C8×Q8—131no—
324#433—133no—
325#433—133no—
326#433—133no—
327#433—133no—
328#433—136no—
329#433—136no—
330#432—133no—
331#432—133no—
332#431—133no—
333#431—133no—
334#431—133no—
335#431—133no—
336#431—133no—
337#431—133no—
338#424—133no—
339#424—133no—
340#423—133no—
341C2×C4⋊C8—133no—
342#408—131no—
343#408—133no—
344#405—136no—
345C4×M16—133no—
346C2×C4×C8—133no—
347C22×C13—21no—
348C22×C13—21no—
349C22×C13—21no—
350C22×C13—21no—
351C22×C13—21no—
352C22×C13#51912yes—
353C22×C13C24×C411yescharacteristic
354C2×D13—21no—
355C2×D13—21no—
356C2×D13—21no—
357C4×C13—21no—
358C4×C13—23no—
359C4×C13—23no—
360C4×C13—23no—
361C4×C13C2×#13116yes—
362Dic13—21no—
363Dic13—23no—
364Dic13—23no—
365Dic13—23no—
366Dic13—23no—
367Dic13#51912yes—
368Dic13C2×2−1+411yescharacteristic
369Dic13C2×2−1+411yescharacteristic
370C2×#41—131no—
371C22×Q8—131no—
372C22×Q8C2×#26111yescharacteristic
373C22×Q8C2×#26111yescharacteristic
374C2×M16—131no—
375C2×M16—133no—
376C22×C8—131no—
377C22×C8—133no—
378C4⋊Q8—133no—
379C4⋊Q8—133no—
380C4⋊Q8—133no—
381C4⋊Q8—133no—
382C4⋊Q8—133no—
383C4⋊Q8C2×#26113yes—
384#125—136no—
385#125—136no—
386#125—136no—
387C22⋊Q8—133no—
388C22⋊Q8—133no—
389C22⋊Q8—133no—
390C22⋊Q8—133no—
391C22⋊Q8—136no—
392C22⋊Q8—136no—
393C22⋊Q8—136no—
394C22⋊Q8C2×#26113yes—
395C22⋊Q8C2×#26113yes—
396C4×Q8—131no—
397C4×Q8—133no—
398C4×Q8—133no—
399C4×Q8—131no—
400C4×Q8—131no—
401C4×Q8—133no—
402C4×Q8—133no—
403C4×Q8—133no—
404C4×Q8—133no—
405C4×Q8—136no—
406C4×Q8—133no—
407C4×Q8—133no—
408C4×Q8C2×#26111yescharacteristic
409C4×D4—133no—
410C4×D4—133no—
411C4×D4—133no—
412C4×D4—133no—
413C4×D4—133no—
414C4×D4C2×#26113yes—
415#117—133no—
416#117—133no—
417#117—133no—
418C2×C4⋊C4—133no—
419C2×C4⋊C4—133no—
420C2×C4⋊C4—133no—
421C2×C42—133no—
422C2×C42—133no—
423C2×C42—133no—
424C4⋊C8—133no—
425C4⋊C8—133no—
426C4⋊C8—136no—
427C4⋊C8—133no—
428C4⋊C8—133no—
429C4⋊C8—133no—
430C4⋊C8—133no—
431C4⋊C8—133no—
432C4⋊C8—133no—
433C4⋊C8—136no—
434C4⋊C8—133no—
435C4⋊C8—133no—
436C4⋊C8—133no—
437C4⋊C8—133no—
438C22⋊C8—131no—
439C22⋊C8—133no—
440C22⋊C8—131no—
441C22⋊C8—133no—
442C22⋊C8—131no—
443C22⋊C8—133no—
444C22⋊C8—131no—
445C22⋊C8—133no—
446#97—133no—
447#97—133no—
448#97—136no—
449#97—136no—
450C4×C8—133no—
451C4×C8—133no—
452C4×C8—133no—
453C4×C8—133no—
454C4×C8—133no—
455C4×C8—133no—
456C4×C8—136no—
457C4×C8—136no—
458C2×C13—22no—
459C2×C13—41no—
460C2×C13C2×#51911yescharacteristic
461C2×C13C22×#13111yescharacteristic
462C2×C13#357311yescharacteristic
463D13—41no—
464#41—262no—
465#41—262no—
466C2×Q8—24no—
467C2×Q8—24no—
468C2×Q8—131no—
469C2×Q8—133no—
470C2×Q8—136no—
471C2×Q8—264no—
472C2×Q8C22×#26113yes—
473C2×Q8C22×#26113yes—
474C2×Q8C22×#26111yescharacteristic
475C2×D4—131no—
476C2×D4—131no—
477C2×D4C22×#26111yescharacteristic
478C22×C4—131no—
479C22×C4—131no—
480C22×C4—133no—
481C22×C4—133no—
482C22×C4—131no—
483C22×C4—133no—
484C22×C4—133no—
485C22×C4C22×#26113yes—
486C22×C4C22×#26113yes—
487M16—262no—
488M16—266no—
489C2×C8—131no—
490C2×C8—133no—
491C2×C8—131no—
492C2×C8—131no—
493C2×C8—131no—
494C2×C8—133no—
495C2×C8—133no—
496C2×C8—133no—
497C2×C8—266no—
498C2×C8—262no—
499C4⋊C4—133no—
500C4⋊C4—136no—
501C4⋊C4—136no—
502C4⋊C4—136no—
503C4⋊C4—133no—
504C4⋊C4—133no—
505C4⋊C4—133no—
506C4⋊C4—133no—
507C4⋊C4—133no—
508C4⋊C4—133no—
509C4⋊C4—133no—
510C4⋊C4—136no—
511C4⋊C4—136no—
512C4⋊C4C22×#26113yes—
513C4⋊C4C22×#26113yes—
514C4⋊C4C22×#26116yes—
515C22⋊C4—133no—
516C22⋊C4—133no—
517C22⋊C4—133no—
518C22⋊C4—133no—
519C22⋊C4C22×#26113yes—
520C22⋊C4C22×#26113yes—
521C42—133no—
522C42—133no—
523C42—133no—
524C42—133no—
525C42—133no—
526C42—133no—
527C42—133no—
528C42—133no—
529C42—133no—
530C42C22×#26113yes—
531C13#6025311yescharacteristic, complemented, Sylow
532C23—131no—
533C23C23×#26111yescharacteristic
534C23C23×#26111yescharacteristic
535Q8—26no—
536Q8—26no—
537Q8—262no—
538Q8—266no—
539Q8—526no—
540Q8#8823814yes—
541D4—22no—
542D4—262no—
543D4—262no—
544C2×C4—26no—
545C2×C4—26no—
546C2×C4—132no—
547C2×C4—132no—
548C2×C4—131no—
549C2×C4—131no—
550C2×C4—131no—
551C2×C4—133no—
552C2×C4—133no—
553C2×C4—133no—
554C2×C4—133no—
555C2×C4—261no—
556C2×C4—261no—
557C2×C4—261no—
558C2×C4—261no—
559C2×C4—266no—
560C2×C4—523no—
561C2×C4—523no—
562C2×C4—523no—
563C2×C4C23×#26111yescharacteristic
564C2×C4C23×#26113yes—
565C2×C4C23×#26113yes—
566C2×C4C23×#26113yes—
567C2×C4C23×#26113yes—
568C8—263no—
569C8—261no—
570C8—261no—
571C8—263no—
572C8—261no—
573C8—261no—
574C8—263no—
575C8—263no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—261no—
582C22—261no—
583C22—261no—
584C22#1171962712yes—
585C22C24×#26111yescharacteristic
586C4—21no—
587C4—23no—
588C4—23no—
589C4—23no—
590C4—132no—
591C4—131no—
592C4—131no—
593C4—261no—
594C4—263no—
595C4—263no—
596C4—263no—
597C4—263no—
598C4C2×#8823816yes—
599C2—22no—
600C2—41no—
601C2—521no—
602C2C2×#1171962711yescharacteristic
603C2C22×#8823811yescharacteristic
604C2#1313183211yescharacteristic
subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingD4×Q8×C13C4
prime radicalC2×#6129C23
cosocleC2×Dic13C25
hypercenterD4×Q8#261
hypocenterC13#60253
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. #13131747C2semidirect
2. #13131745C2semidirect
3. #13131741C2semidirect
4. #13131740C2semidirect
5. #13131739C2semidirect
6. #13131738C2semidirect
7. #13131730C2semidirect
8. #13131729C2semidirect
9. Q8×#6122C2semidirect
10. #13131631C2semidirect
11. #13131624C2semidirect
12. C2×Q8×#1057C2semidirect
531. C13#60253semidirect

Maximal subgroups

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

subgroupindex
#131317472
#131317452
#131317412
#131317402
#131317392
#131317382
#131317302
#131317292
Q8×#61222
#131316312
#131316242
C2×Q8×#10572
#131315312
#131315192
Q8×#61292
#6025313