Finite Group Databasebeta

← #15935525

Subgroups — #15935525

Order 3328.

690 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118708C211yesmaximal, characteristic
2#13116221C211yesmaximal, characteristic
3#13116174C211yesmaximal, characteristic, complemented
4#13116171C211yesmaximal, characteristic, complemented
5#13115979C211yesmaximal, characteristic
6#13115793C211yesmaximal, characteristic, complemented
7#13115576C211yesmaximal, characteristic, complemented
8#13115463C211yesmaximal, characteristic
9#13115456C211yesmaximal, characteristic
10#13115414C211yesmaximal, characteristic, complemented
11#13115407C211yesmaximal, characteristic, complemented
12#13115402C211yesmaximal, characteristic, complemented
13#13115096C211yesmaximal, characteristic
14#13114664C211yesmaximal, characteristic
15C13×#2370C211yesmaximal, characteristic, complemented
16C2×C13×#125C2211yescharacteristic
17C2×C4×D52C2211yescharacteristic
18C2×#88124C2211yescharacteristic
19C13×#389—21no—
20C13×#389C2211yescharacteristic
21C13×#389C2211yescharacteristic
22C13×#387—21no—
23C13×#387—21no—
24C4×C13×C4⋊C4—21no—
25C4×C13×C4⋊C4C2211yescharacteristic
26C4×C13×C4⋊C4C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29#11718653—21no—
30#11718650—21no—
31C2×#88049C2211yescharacteristic
32C2×#88049C2211yescharacteristic
33C2×#88049C2211yescharacteristic
34C2×#88049C2211yescharacteristic
35C2×#88048C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88047C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39#11718600C2211yescharacteristic
40#11718600C2211yescharacteristic
41#11718589C2211yescharacteristic
42#11718589C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44C2×#88043C2211yescharacteristic
45#11718337—21no—
46#11718328—21no—
47#11718121C2211yescharacteristic
48#11718121C2211yescharacteristic
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718116C2211yescharacteristic
56#11718116C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×D52C2311yescharacteristic
60C22×C4×D13—21no—
61C13×#125—22no—
62C13×#125—22no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4D411yescharacteristic
68C2×C13×C4⋊C4D411yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C42×C13—21no—
74C2×C42×C13—21no—
75C2×C42×C13—21no—
76C2×C42×C13C2311yescharacteristic
77C2×C42×C13C2311yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×#6103—21no—
80C2×#6103—21no—
81C2×#6103—21no—
82C2×#6103—21no—
83C2×#6103—21no—
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×#6101—21no—
88C2×#6101—21no—
89C2×#6101—21no—
90C2×#6101—21no—
91C22×#1055C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C4×D52—22no—
96C4×D52—41no—
97#88124—22no—
98#88124—41no—
99C13×#95—21no—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95—21no—
104C13×#95D411yescharacteristic
105C13×#95D411yescharacteristic
106#88071—21no—
107#88071—21no—
108#88049—22no—
109#88049—22no—
110#88049—41no—
111#88049Q814yes—
112#88048—22no—
113#88048—22no—
114#88047—22no—
115#88047—41no—
116C4⋊#1055—41no—
117#88043—41no—
118#27027—131nomaximal, Sylow
119C23×D13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2411yescharacteristic
131C22×Dic13—21no—
132C22×Dic13—21no—
133C22×Dic13—21no—
134C2×D52—21no—
135C2×D52—21no—
136C2×D52—21no—
137C2×D52—21no—
138C2×D52—21no—
139C2×D52C2×Q812yes—
140C2×C4×D13—42no—
141C2×C4×D13—42no—
142C2×C4×D13—81no—
143C13×C4⋊C4—24no—
144C13×C4⋊C4—24no—
145C13×C4⋊C4—21no—
146C13×C4⋊C4—21no—
147C13×C4⋊C4—21no—
148C13×C4⋊C4—21no—
149C13×C4⋊C4—21no—
150C13×C4⋊C4—41no—
151C13×C4⋊C4—41no—
152C13×C4⋊C4—42no—
153C13×C4⋊C4—81no—
154C13×C4⋊C4C2×Q812yes—
155C13×C4⋊C4#4112yes—
156C13×C4⋊C4#4112yes—
157C42×C13—21no—
158C42×C13—21no—
159C42×C13—21no—
160C42×C13—21no—
161C42×C13—21no—
162C42×C13—21no—
163C42×C13—42no—
164C42×C13—81no—
165C42×C13—81no—
166#6103—42no—
167#6103—42no—
168#6103—81no—
169#6103—81no—
170#6103—81no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13#4112yes—
177#6101—42no—
178#6101—42no—
179#6101—81no—
180#6101—81no—
181C2×#1055—21no—
182C2×#1055—21no—
183C2×#1055—21no—
184C2×#1055—21no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055C2×Q812yes—
193#2454—131no—
194#2370D1311yescharacteristic, complemented
195#2067—131no—
196#2059—131no—
197#2059—131no—
198#2025—131no—
199#1989—131no—
200#1944—131no—
201#1926—131no—
202#1925—131no—
203#1919—131no—
204#1918—131no—
205#1917—131no—
206#1864—131no—
207#1762—131no—
208C23×C13C22×D411yescharacteristic
209C22×D13—22no—
210C22×D13—41no—
211C22×D13—41no—
212C22×D13—41no—
213C22×D13—41no—
214C22×D13—41no—
215C22×D13—41no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—22no—
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—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13C22×Q811yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C2×C4×C13H(5,𝔽2)11yescharacteristic
251C2×C4×C132−1+411yescharacteristic
252C2×Dic13—22no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261D52—22no—
262D52—22no—
263D52—41no—
264D52—41no—
265C4×D13—84no—
266#1055—22no—
267#1055—41no—
268#1055—41no—
269#1055—41no—
270C2×#125—131no—
271C2×#125C2×D1311yescharacteristic
272C2×C4×D4—131no—
273C2×#107—131no—
274C2×#107—131no—
275C2×#106—131no—
276C2×#106—131no—
277C2×C4⋊C8—131no—
278C2×#102—131no—
279C2×#102—131no—
280C2×#102—131no—
281C2×#102—131no—
282C2×#97—131no—
283#399—261no—
284#396—261no—
285#390—131no—
286#390—131no—
287#389—21no—
288#389—131no—
289#389—131no—
290#389C2×D1311yescharacteristic
291#389C2×D1311yescharacteristic
292#387—21no—
293#387—21no—
294#385—261no—
295#380—261no—
296C4×C4⋊C4—21no—
297C4×C4⋊C4C2×D1311yescharacteristic
298C4×C4⋊C4C2×D1311yescharacteristic
299C4×C4⋊C4C2×D1311yescharacteristic
300C4×C4⋊C4C2×D1311yescharacteristic
301#340—131no—
302#340—131no—
303#340—131no—
304#340—131no—
305#340—131no—
306#340—131no—
307#340—131no—
308#340—131no—
309#336—131no—
310#336—131no—
311#336—131no—
312#336—131no—
313C22×C13#52511yescharacteristic
314C22×C13#54611yescharacteristic
315C22×C13D4×Q811yescharacteristic
316C22×C13#57511yescharacteristic
317C22×C13#57511yescharacteristic
318C22×C13#57611yescharacteristic
319C22×C13#57711yescharacteristic
320C2×D13—42no—
321C2×D13—42no—
322C2×D13—42no—
323C2×D13—81no—
324C2×D13—81no—
325C2×D13—81no—
326C2×D13—81no—
327C4×C13—41no—
328C4×C13—42no—
329C4×C13—41no—
330C4×C13—42no—
331C4×C13—42no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13—41no—
336C4×C13—81no—
337C4×C13#53311yescharacteristic
338C4×C13#54211yescharacteristic
339C4×C13#55411yescharacteristic
340C4×C13#55611yescharacteristic
341Dic13—42no—
342Dic13—81no—
343Dic13—81no—
344C22×D4—131no—
345C23×C4—261no—
346C22×C8—131no—
347C22×C8—131no—
348C22×C8—131no—
349C22×C8—131no—
350#125—22no—
351#125—22no—
352#125—262no—
353#125—521no—
354C4×D4—262no—
355C4×D4—521no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—261no—
364C2×C4⋊C4—261no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4C22⋊D1311yescharacteristic
368C2×C4⋊C4C22⋊D1311yescharacteristic
369C2×C4⋊C4C22×D1311yescharacteristic
370C2×C4⋊C4C22×D1311yescharacteristic
371C2×C4⋊C4C22×D1311yescharacteristic
372C2×C4⋊C4C22×D1311yescharacteristic
373C2×C22⋊C4—261no—
374C2×C22⋊C4—261no—
375C2×C22⋊C4—261no—
376C2×C22⋊C4—261no—
377C2×C22⋊C4—261no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42C22×D1311yescharacteristic
382C2×C42C22×D1311yescharacteristic
383C2×C42C22×D1311yescharacteristic
384#107—262no—
385#107—521no—
386#106—262no—
387#106—262no—
388C4⋊C8—521no—
389#102—134no—
390#102—262no—
391#102—262no—
392#102—521no—
393#97—521no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—261no—
400#95—261no—
401#95C22⋊D1311yescharacteristic
402#95C22⋊D1311yescharacteristic
403C2×C13#246511yescharacteristic
404C2×C13#311111yescharacteristic
405C2×C13#311911yescharacteristic
406C2×C13#330911yescharacteristic
407C2×C13#332311yescharacteristic
408C2×C13#338811yescharacteristic
409C2×C13#338911yescharacteristic
410D13—82no—
411C24—261no—
412C2×D4—132no—
413C2×D4—261no—
414C2×D4—261no—
415C2×D4—261no—
416C2×D4—261no—
417C2×D4—261no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—261no—
423C22×C4—261no—
424C22×C4—261no—
425C22×C4—522no—
426C22×C4—522no—
427C22×C4—1041no—
428C22×C4C2×C22⋊D1311yescharacteristic
429C22×C4C2×C22⋊D1311yescharacteristic
430C22×C4C2×C22⋊D1311yescharacteristic
431C22×C4C2×C22⋊D1311yescharacteristic
432C22×C4C2×C22⋊D1311yescharacteristic
433C22×C4C2×C22⋊D1311yescharacteristic
434C22×C4C23×D1311yescharacteristic
435C2×C8—132no—
436C2×C8—261no—
437C2×C8—261no—
438C2×C8—261no—
439C2×C8—261no—
440C2×C8—261no—
441C2×C8—261no—
442C2×C8—261no—
443C2×C8—261no—
444C2×C8—261no—
445C2×C8—261no—
446C2×C8—261no—
447C4⋊C4—24no—
448C4⋊C4—24no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—42no—
457C4⋊C4—81no—
458C4⋊C4—132no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—522no—
465C4⋊C4—522no—
466C4⋊C4—1041no—
467C4⋊C4—1041no—
468C4⋊C4#612712yes—
469C4⋊C4#612712yes—
470C4⋊C4Q8×D1312yes—
471C22⋊C4—522no—
472C22⋊C4—522no—
473C22⋊C4—1041no—
474C22⋊C4—1041no—
475C22⋊C4—1041no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—42no—
483C42—81no—
484C42—81no—
485C13#2702711yescharacteristic, complemented, Sylow
486C23—262no—
487C23—521no—
488C23—521no—
489C23—521no—
490C23—521no—
491C23—521no—
492C23—521no—
493C23C22×C22⋊D1311yescharacteristic
494D4—262no—
495D4—262no—
496D4—521no—
497D4—521no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—262no—
529C2×C4—521no—
530C2×C4—521no—
531C2×C4—521no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4—1044no—
538C2×C4C2×#612711yescharacteristic
539C2×C4C2×#612711yescharacteristic
540C2×C4C2×Q8×D1311yescharacteristic
541C2×C4#8825411yescharacteristic
542C2×C4#41×D1311yescharacteristic
543C2×C4#8825611yescharacteristic
544C8—262no—
545C8—521no—
546C8—521no—
547C8—521no—
548C22—522no—
549C22—522no—
550C22—522no—
551C22—1041no—
552C22—1041no—
553C22—1041no—
554C22—1041no—
555C22#1171949611yescharacteristic
556C22Q8×C22⋊D1311yescharacteristic
557C22#1171952711yescharacteristic
558C22#1171952711yescharacteristic
559C22#1171953411yescharacteristic
560C22#1171954011yescharacteristic
561C22#1171954211yescharacteristic
562C4—41no—
563C4—42no—
564C4—42no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—42no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—522no—
573C4—1041no—
574C4—1041no—
575C4#1171927311yescharacteristic
576C4#1171928311yescharacteristic
577C4#1171928411yescharacteristic
578C4#1171928711yescharacteristic
579C2—1042no—
580C2#1311885111yescharacteristic
581C2#1312494511yescharacteristic
582C2#1312503511yescharacteristic
583C2#1312683611yescharacteristic
584C2#1312704611yescharacteristic
585C2#1312777511yescharacteristic
586C2#1312779011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2370C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenter#2370D13
hypocenterC13#27027
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2370

Complements

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

NH ≅ G/Ntype
3. #13116174C2semidirect
4. #13116171C2semidirect
6. #13115793C2semidirect
7. #13115576C2semidirect
10. #13115414C2semidirect
11. #13115407C2semidirect
12. #13115402C2semidirect
15. C13×#2370C2semidirect
194. #2370D13semidirect
485. C13#27027semidirect

Maximal subgroups

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

subgroupindex
#131187082
#131162212
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