Finite Group Databasebeta

← #15920518

Subgroups — #15920518

Order 3328.

802 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117703C211yesmaximal, characteristic
2#13116393C211yesmaximal, characteristic, complemented
3#13116327C211yesmaximal, characteristic, complemented
4#13116327C211yesmaximal, characteristic, complemented
5#13116161C211yesmaximal, characteristic, complemented
6#13115789C211yesmaximal, characteristic, complemented
7#13115592C211yesmaximal, characteristic, complemented
8#13115404C211yesmaximal, characteristic, complemented
9#13115404C211yesmaximal, characteristic, complemented
10#13115024C211yesmaximal, characteristic
11#13115016C211yesmaximal, characteristic
12#13114920C211yesmaximal, characteristic
13#13114863C211yesmaximal, characteristic
14C2×#11718121C211yesmaximal, characteristic
15C13×#2440C211yesmaximal, characteristic
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×C22⋊Q8—21no—
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C23×#1055C2211yescharacteristic
21C2×#88131—21no—
22C13×#398—21no—
23C13×#395—21no—
24C13×#389C2211yescharacteristic
25C13×#389C2211yescharacteristic
26C13×#385—21no—
27C13×#384C2211yescharacteristic
28C13×#380C2211yescharacteristic
29C4×C13×C22⋊C4C2211yescharacteristic
30#11718873C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32C2×#88047C2211yescharacteristic
33C2×#88047C2211yescharacteristic
34C2×#88047C2211yescharacteristic
35C2×#88047C2211yescharacteristic
36#11718604—21no—
37C4×C4⋊Dic13C2211yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39#11718589C2211yescharacteristic
40#11718589C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43#11718314—21no—
44#11718314—21no—
45#11718121C2211yescharacteristic
46#11718121C2211yescharacteristic
47#11718121C2211yescharacteristic
48#11718121C2211yescharacteristic
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×Q8×C13—21no—
60C23×C4×C13—21no—
61C23×C4×C13C2311yescharacteristic
62C23×Dic13—21no—
63C13×C4⋊Q8—22no—
64C13×C4⋊Q8—41no—
65C13×C22⋊Q8—44no—
66C2×C13×C4⋊C4—22no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—41no—
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4D411yescharacteristic
80C2×C13×C22⋊C4D411yescharacteristic
81C2×C42×C13C2311yescharacteristic
82C2×C42×C13C2311yescharacteristic
83C2×C22⋊Dic13—21no—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13—22no—
86C2×C4⋊Dic13Q814yescomplemented
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×#6101—21no—
92C2×#6101—21no—
93C2×C4×Dic13—21no—
94C2×C4×Dic13—21no—
95C22×#1055—22no—
96C22×#1055—22no—
97C22×#1055—41no—
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102#88131—44no—
103C13×#95—21no—
104C13×#95—21no—
105C13×#95—21no—
106C13×#95D411yescharacteristic
107C13×#95D411yescharacteristic
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113C22⋊#1055—22no—
114#88047—22no—
115#88047—22no—
116#88047—41no—
117#88047—41no—
118C4⋊#1055—22no—
119C4⋊#1055—41no—
120#25988—131nomaximal, Sylow
121C24×C13C2×D411yescharacteristic
122C2×Q8×C13—42no—
123C2×Q8×C13—42no—
124C2×Q8×C13—81no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—42no—
134C22×C4×C13—42no—
135C22×C4×C13—81no—
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×Q812yes—
142C22×C4×C13#4112yes—
143C22×C4×C13C2411yescharacteristic
144C22×Dic13—24no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—42no—
150C22×Dic13—42no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—42no—
159C13×C4⋊C4—42no—
160C13×C4⋊C4—42no—
161C13×C4⋊C4—42no—
162C13×C4⋊C4—42no—
163C13×C4⋊C4—81no—
164C13×C4⋊C4#4112yes—
165C13×C22⋊C4—22no—
166C13×C22⋊C4—42no—
167C13×C22⋊C4D814yes—
168C42×C13—21no—
169C42×C13—21no—
170C42×C13—21no—
171C42×C13—21no—
172C22⋊Dic13—42no—
173C4⋊Dic13—24no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13C2×Q812yes—
181C4⋊Dic13C2×Q812yes—
182#6101—42no—
183#6101—42no—
184C4×Dic13—42no—
185C4×Dic13—42no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—44no—
198C2×#1055#4112yes—
199#2440D1311yescharacteristic
200#2344—131no—
201#2099—131no—
202#2086—131no—
203#2086—131no—
204#2057—131no—
205#1988—131no—
206#1947—131no—
207#1918—131no—
208#1918—131no—
209#1852—131no—
210#1850—131no—
211#1823—131no—
212#1808—131no—
213C2×#340—131no—
214C23×C13—21no—
215C23×C13—21no—
216C23×C13—21no—
217C23×C13—21no—
218C23×C13C22⋊Q812yes—
219C23×C13C2×D812yes—
220C23×C13#13712yes—
221C23×C13C22×D411yescharacteristic
222Q8×C13—84no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—21no—
234C2×C4×C13—22no—
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×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—84no—
252C2×C4×C13C22⋊Q812yes—
253C2×C4×C13C2×D812yes—
254C2×C4×C13C2×D812yes—
255C2×C4×C13C22×Q811yescharacteristic
256C2×C4×C13C2×#4111yescharacteristic
257C2×C4×C13C2×#4111yescharacteristic
258C2×C4×C13C2×#4111yescharacteristic
259C2×C4×C13H(5,𝔽2)11yescharacteristic
260C2×C4×C132−1+411yescharacteristic
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—48no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274#1055—22no—
275#1055—41no—
276#1055—41no—
277#1055—41no—
278C23×C8—131no—
279C2×C4⋊Q8C2×D1311yescharacteristic
280C2×C22⋊Q8—21no—
281C2×#117—261no—
282C22×C4⋊C4—131no—
283C22×C4⋊C4C2×D1311yescharacteristic
284C2×#107—131no—
285C2×#107—131no—
286C2×#107—131no—
287C2×#107—131no—
288C2×C4⋊C8—131no—
289C2×C4⋊C8—131no—
290C2×C22⋊C8—131no—
291#398—21no—
292#395—21no—
293#389—131no—
294#389—131no—
295#389C2×D1311yescharacteristic
296#389C2×D1311yescharacteristic
297#387—261no—
298#387—261no—
299#385—21no—
300#384C2×D1311yescharacteristic
301#381—261no—
302#380—131no—
303#380C2×D1311yescharacteristic
304C4×C4⋊C4—131no—
305C4×C4⋊C4—131no—
306C4×C22⋊C4C2×D1311yescharacteristic
307#340—131no—
308#340—131no—
309#340—131no—
310#340—131no—
311#340—131no—
312#340—131no—
313#340—131no—
314#340—131no—
315#340—131no—
316#340—131no—
317#340—131no—
318#340—131no—
319#336—131no—
320#336—131no—
321C22×C13—22no—
322C22×C13—22no—
323C22×C13—22no—
324C22×C13—22no—
325C22×C13—22no—
326C22×C13—22no—
327C22×C13#47414yes—
328C22×C13C2×C22⋊Q811yescharacteristic
329C22×C13#54611yescharacteristic
330C22×C13#54711yescharacteristic
331C22×C13C22×D811yescharacteristic
332C22×C13C2×#13711yescharacteristic
333C22×C13#57711yescharacteristic
334C22×C13#57811yescharacteristic
335C4×C13—22no—
336C4×C13—22no—
337C4×C13—22no—
338C4×C13—41no—
339C4×C13—42no—
340C4×C13—41no—
341C4×C13—81no—
342C4×C13—81no—
343C4×C13—81no—
344C4×C13#53311yescharacteristic
345C4×C13#54411yescharacteristic
346C4×C13#55111yescharacteristic
347C4×C13#55211yescharacteristic
348Dic13—42no—
349Dic13—42no—
350Dic13—81no—
351Dic13—81no—
352C22×Q8—21no—
353C23×C4—21no—
354C23×C4—261no—
355C23×C4C22×D1311yescharacteristic
356C22×C8—131no—
357C22×C8—131no—
358C22×C8—131no—
359C22×C8—131no—
360C22×C8—262no—
361C22×C8—262no—
362C22×C8—521no—
363C4⋊Q8—22no—
364C4⋊Q8—41no—
365C22⋊Q8—44no—
366#117—524no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—41no—
375C2×C4⋊C4—134no—
376C2×C4⋊C4—131no—
377C2×C4⋊C4—131no—
378C2×C4⋊C4—131no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—262no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4C22×D1311yescharacteristic
385C2×C4⋊C4C22×D1311yescharacteristic
386C2×C4⋊C4C22×D1311yescharacteristic
387C2×C4⋊C4C22×D1311yescharacteristic
388C2×C22⋊C4—21no—
389C2×C22⋊C4—261no—
390C2×C22⋊C4C22⋊D1311yescharacteristic
391C2×C22⋊C4C22⋊D1311yescharacteristic
392C2×C42—261no—
393C2×C42—261no—
394C2×C42C22×D1311yescharacteristic
395C2×C42C22×D1311yescharacteristic
396#107—262no—
397#107—262no—
398#107—521no—
399#107—521no—
400C4⋊C8—262no—
401C4⋊C8—521no—
402C22⋊C8—262no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—261no—
407#95—261no—
408#95—261no—
409#95—261no—
410#95—261no—
411#95C22⋊D1311yescharacteristic
412#95C22⋊D1311yescharacteristic
413C2×C13—24no—
414C2×C13#243811yescharacteristic
415C2×C13C2×#47411yescharacteristic
416C2×C13#308211yescharacteristic
417C2×C13#329411yescharacteristic
418C2×C13#331211yescharacteristic
419C2×C13#333411yescharacteristic
420C2×C13#334411yescharacteristic
421C24C2×C22⋊D1311yescharacteristic
422C2×Q8—42no—
423C2×Q8—42no—
424C2×Q8—81no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—81no—
436C22×C4—264no—
437C22×C4—261no—
438C22×C4—261no—
439C22×C4—261no—
440C22×C4—261no—
441C22×C4—522no—
442C22×C4—522no—
443C22×C4Q8×D1312yes—
444C22×C4#613112yes—
445C22×C4C2×C22⋊D1311yescharacteristic
446C22×C4C2×C22⋊D1311yescharacteristic
447C22×C4C2×C22⋊D1311yescharacteristic
448C22×C4C2×C22⋊D1311yescharacteristic
449C22×C4C2×C22⋊D1311yescharacteristic
450C22×C4C23×D1311yescharacteristic
451C2×C8—132no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—261no—
462C2×C8—261no—
463C2×C8—524no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—42no—
472C4⋊C4—42no—
473C4⋊C4—42no—
474C4⋊C4—42no—
475C4⋊C4—42no—
476C4⋊C4—81no—
477C4⋊C4—132no—
478C4⋊C4—132no—
479C4⋊C4—264no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—522no—
487C4⋊C4—522no—
488C4⋊C4#612912yes—
489C22⋊C4—22no—
490C22⋊C4—42no—
491C22⋊C4—522no—
492C22⋊C4#610414yes—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—522no—
498C42—522no—
499C13#2598811yescharacteristic, complemented, Sylow
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23C2×#610412yes—
505C23#8819612yes—
506C23#8820012yes—
507C23C22×C22⋊D1311yescharacteristic
508Q8—84no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—84no—
538C2×C4—262no—
539C2×C4—262no—
540C2×C4—521no—
541C2×C4—521no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—528no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4C2×#610412yes—
552C2×C4C2×#610412yes—
553C2×C4#8820012yes—
554C2×C4C2×#612911yescharacteristic
555C2×C4#8825111yescharacteristic
556C2×C4C2×Q8×D1311yescharacteristic
557C2×C4C2×#613111yescharacteristic
558C2×C4#41×D1311yescharacteristic
559C2×C4#8825711yescharacteristic
560C8—262no—
561C8—521no—
562C8—521no—
563C8—521no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22#1171874814yes—
571C22C22×#610411yescharacteristic
572C22#1171951111yescharacteristic
573C22C2×#8819611yescharacteristic
574C22C2×#8820011yescharacteristic
575C22#1171952911yescharacteristic
576C22#1171954111yescharacteristic
577C22#1171954311yescharacteristic
578C4—22no—
579C4—22no—
580C4—22no—
581C4—41no—
582C4—41no—
583C4—42no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4—522no—
588C4—522no—
589C4—1041no—
590C4—1041no—
591C4#1171932711yescharacteristic
592C4#1171932811yescharacteristic
593C4#1171934211yescharacteristic
594C4#1171934711yescharacteristic
595C2—24no—
596C2#1311850811yescharacteristic
597C2C2×#1171874811yescharacteristic
598C2#1312467211yescharacteristic
599C2#1312664911yescharacteristic
600C2#1312688711yescharacteristic
601C2#1312717911yescharacteristic
602C2#1312728511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2440C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2440D13
hypocenterC13#25988
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2440

Complements

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

NH ≅ G/Ntype
2. #13116393C2semidirect
3. #13116327C2semidirect
4. #13116327C2semidirect
5. #13116161C2semidirect
6. #13115789C2semidirect
7. #13115592C2semidirect
8. #13115404C2semidirect
9. #13115404C2semidirect
86. C2×C4⋊Dic13Q8semidirect
499. C13#25988semidirect

Maximal subgroups

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

subgroupindex
#131177032
#131163932
#131163272
#131161612
#131157892
#131155922
#131154042
#131150242
#131150162
#131149202
#131148632
C2×#117181212
C13×#24402
#2598813