Finite Group Databasebeta

← #15898309

Subgroups — #15898309

Order 3328.

1438 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718751C211yesmaximal, characteristic, complemented
2C2×#11718900C212yesmaximal, complemented
3C2×C4×#6105C211yesmaximal, characteristic, complemented
4#13119758C211yesmaximal, characteristic, complemented
5#13116029C212yesmaximal, complemented
6#13115844C212yesmaximal, complemented
7#13115639C211yesmaximal, characteristic, complemented
8#13115631C211yesmaximal, characteristic, complemented
9#13114836C211yesmaximal, characteristic, complemented
10#13114776C212yesmaximal, complemented
11C2×C13×#547C211yesmaximal, characteristic
12C22×C13×#41C2212yes—
13C13×#547—24no—
14C13×#547—24no—
15C2×C13×C4⋊Q8C2211yescharacteristic
16C2×C13×#123—22no—
17C2×C13×C22⋊Q8C2212yes—
18C2×C13×#121—21no—
19C2×C4×D4×C13C2211yescharacteristic
20C2×C4×D4×C13C2211yescharacteristic
21C22×C13×C4⋊C4—21no—
22C22×#6107C2212yes—
23C22×#6105C2211yescharacteristic
24C2×#88178C2212yes—
25C2×C4×Dic26C2211yescharacteristic
26#11718900—28no—
27C2×#88075C2212yes—
28C2×#88075C2212yes—
29C2×#88075C2212yes—
30#11718882—21no—
31C2×#88072C2211yescharacteristic
32C2×#88072C2212yes—
33#11718873C2212yes—
34C2×C22⋊#1055C2212yes—
35C2×C22⋊#1055C2212yes—
36#11718751—24no—
37C4×#6105—24no—
38#11718634—21no—
39C2×#88050C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41#11718609—22no—
42#11718596C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44C2×C4×#1055C2211yescharacteristic
45#11718121C2212yes—
46C2×C13×#41—24no—
47C2×C13×#41—24no—
48C2×C13×#41—24no—
49C2×C13×#41—24no—
50C2×C13×#41—42no—
51C2×C13×#41—42no—
52C22×Q8×C13C2312yes—
53C22×D4×C13—22no—
54C22×D4×C13D411yescharacteristic
55C22×D4×C13C2311yescharacteristic
56C23×C4×C13—21no—
57C23×C4×C13—22no—
58C23×C4×C13C2312yes—
59C22×Dic26C2311yescharacteristic
60C13×C4⋊Q8—22no—
61C13×C4⋊Q8D414yes—
62C13×#123—216no—
63C13×C22⋊Q8—24no—
64C13×C22⋊Q8—24no—
65C13×#121—28no—
66C4×D4×C13—22no—
67C4×D4×C13—22no—
68C4×D4×C13—22no—
69C4×D4×C13D414yes—
70C2×C13×C4⋊C4—28no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4D411yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C22⋊C4—22no—
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4D412yes—
79C2×C42×C13C2311yescharacteristic
80C2×C22⋊Dic13—22no—
81C2×C22⋊Dic13—22no—
82C2×#6107—24no—
83C2×#6107—24no—
84C2×#6107—42no—
85C2×#6105—22no—
86C2×#6105—22no—
87C2×#6105D414yescomplemented
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2312yes—
92#88178—24no—
93#88178—42no—
94C2×#6101—21no—
95C2×#6101—22no—
96C2×C4×Dic13—21no—
97C22×#1055C2312yes—
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C4×Dic26—22no—
101C4×Dic26—22no—
102#88075—24no—
103#88075—24no—
104#88075—42no—
105#88072—22no—
106#88072—24no—
107#88071—22no—
108C22⋊#1055—24no—
109C22⋊#1055—42no—
110#88050—22no—
111#88048—22no—
112C4⋊#1055—22no—
113C4×#1055—22no—
114#24241—131nomaximal, Sylow
115C24×C13—21no—
116C24×C13C2×D412yes—
117C13×#41—48no—
118C13×#41—48no—
119C13×#41—48no—
120C13×#41—48no—
121C2×Q8×C13—22no—
122C2×Q8×C13—22no—
123C2×Q8×C13—22no—
124C2×Q8×C13—22no—
125C2×Q8×C13—22no—
126C2×Q8×C13C2×D414yes—
127C2×D4×C13—28no—
128C2×D4×C13—22no—
129C2×D4×C13—22no—
130C2×D4×C13—22no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13—21no—
134C2×D4×C13—44no—
135C2×D4×C13—44no—
136C2×D4×C13C2×D412yes—
137C2×D4×C13C2×D412yes—
138C2×D4×C13#4112yes—
139C22×C4×C13—28no—
140C22×C4×C13—21no—
141C22×C4×C13—22no—
142C22×C4×C13—24no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—44no—
150C22×C4×C13—44no—
151C22×C4×C13—42no—
152C22×C4×C13—42no—
153C22×C4×C13C2×D412yes—
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2411yescharacteristic
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—22no—
160C2×Dic26—21no—
161C2×Dic26—21no—
162C2×Dic26—21no—
163C2×Dic26—21no—
164C2×Dic26—21no—
165C2×Dic26C2×D412yes—
166C13×C4⋊C4—28no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—24no—
169C13×C4⋊C4—24no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4C2×D412yes—
172C13×C22⋊C4—28no—
173C13×C22⋊C4—24no—
174C13×C22⋊C4—24no—
175C42×C13C2×D412yes—
176C42×C13C2×D412yes—
177C22⋊Dic13—44no—
178C22⋊Dic13—82no—
179#6107—48no—
180#6105—28no—
181C4⋊Dic13—22no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—22no—
185C4⋊Dic13—42no—
186C4⋊Dic13—81no—
187#6101—44no—
188#6101—42no—
189C4×Dic13—42no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055—22no—
193C2×#1055—21no—
194C2×#1055—22no—
195C2×#1055—21no—
196C2×#1055—22no—
197C2×#1055—21no—
198C2×#1055C2×D412yes—
199C2×#547D1311yescharacteristic
200C2×#462—131no—
201C2×#452—132no—
202C2×C4×SD16—131no—
203#2538—131no—
204#2035—132no—
205#2001—132no—
206#1956—131no—
207#1954—131no—
208#1802—131no—
209#1788—132no—
210C23×C13—22no—
211C23×C13—22no—
212C23×C13—22no—
213C23×C13—22no—
214C23×C13—22no—
215C23×C13—22no—
216C23×C13—22no—
217C23×C13—22no—
218C23×C13—22no—
219C23×C13—22no—
220C23×C13—41no—
221C23×C13—41no—
222C23×C13—41no—
223C23×C13—41no—
224C23×C13C22×D411yescharacteristic
225Q8×C13—24no—
226Q8×C13—24no—
227Q8×C13—42no—
228Q8×C13—42no—
229D4×C13—22no—
230D4×C13—22no—
231D4×C13—22no—
232D4×C13—416no—
233D4×C13—44no—
234D4×C13#12114yes—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—24no—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—416no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—48no—
252C2×C4×C13#12012yes—
253C2×C4×C13#12012yes—
254C2×C4×C13#13512yes—
255C2×C4×C13#13712yes—
256C2×C4×C13C22×D411yescharacteristic
257C2×C4×C13C22×D411yescharacteristic
258C2×C4×C13C22×D411yescharacteristic
259C2×C4×C13C2×#4111yescharacteristic
260C2×C4×C13H(5,𝔽2)11yescharacteristic
261C2×C4×C13H(5,𝔽2)11yescharacteristic
262C2×Dic13—22no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—42no—
267C2×Dic13—42no—
268C2×Dic13—42no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271Dic26—22no—
272Dic26—22no—
273Dic26—41no—
274Dic26—41no—
275#1055—22no—
276#1055—41no—
277#1055—42no—
278C22×#41C2×D1312yes—
279C22×Q16—132no—
280C22×SD16—131no—
281#547—24no—
282#547—24no—
283C2×C4⋊Q8C2×D1311yescharacteristic
284C2×#123—22no—
285C2×C22⋊Q8—132no—
286C2×C22⋊Q8C2×D1312yes—
287C2×#121—21no—
288C2×C4×Q8—131no—
289C2×C4×D4C2×D1311yescharacteristic
290C2×C4×D4C2×D1311yescharacteristic
291C22×C4⋊C4—21no—
292#462—264no—
293#452—268no—
294C4×SD16—264no—
295C2×#106—131no—
296C2×C4⋊C8—131no—
297C2×#103—132no—
298C2×#103—132no—
299C2×#103—131no—
300C2×#103—132no—
301C2×#102—132no—
302C2×#102—131no—
303C2×C22⋊C8—132no—
304C2×C22⋊C8—132no—
305C2×C4×C8—131no—
306#396—262no—
307#390—261no—
308#389—261no—
309#384—131no—
310#380—132no—
311#340—132no—
312C22×C13—24no—
313C22×C13—42no—
314C22×C13—42no—
315C22×C13—42no—
316C22×C13—42no—
317C22×C13—42no—
318C22×C13—42no—
319C22×C13—42no—
320C22×C13—42no—
321C22×C13—42no—
322C22×C13—42no—
323C22×C13—42no—
324C22×C13—42no—
325C22×C13—42no—
326C22×C13C2×#12011yescharacteristic
327C22×C13D4211yescharacteristic
328C22×C13#54611yescharacteristic
329C22×C13C2×#13511yescharacteristic
330C22×C13C2×#13711yescharacteristic
331C22×C13#57711yescharacteristic
332C22×C13#57811yescharacteristic
333C4×C13—22no—
334C4×C13—42no—
335C4×C13—44no—
336C4×C13—42no—
337C4×C13#45214yescomplemented
338C4×C13C2×#12111yescharacteristic
339C4×C13#53511yescharacteristic
340C4×C13D4211yescharacteristic
341C4×C13#54611yescharacteristic
342Dic13—42no—
343Dic13—81no—
344Dic13—82no—
345C2×#41—24no—
346C2×#41—24no—
347C2×#41—24no—
348C2×#41—24no—
349C2×#41—42no—
350C2×#41—42no—
351C22×Q8—131no—
352C22×Q8C22×D1312yes—
353C22×D4—22no—
354C22×D4C22⋊D1311yescharacteristic
355C22×D4C22×D1311yescharacteristic
356C23×C4—21no—
357C23×C4—22no—
358C23×C4C22×D1312yes—
359C2×Q16—264no—
360C2×Q16—264no—
361C2×Q16—522no—
362C2×SD16—134no—
363C2×SD16—262no—
364C2×SD16—262no—
365C22×C8—131no—
366C22×C8—132no—
367C22×C8—131no—
368C4⋊Q8—22no—
369C4⋊Q8C22⋊D1314yes—
370#123—216no—
371C22⋊Q8—24no—
372C22⋊Q8—24no—
373C22⋊Q8—264no—
374C22⋊Q8—522no—
375#121—28no—
376C4×Q8—262no—
377C4×Q8—262no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4C22⋊D1314yes—
382C2×C4⋊C4—28no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—131no—
387C2×C4⋊C4—132no—
388C2×C4⋊C4—261no—
389C2×C4⋊C4—262no—
390C2×C4⋊C4—261no—
391C2×C4⋊C4—261no—
392C2×C4⋊C4C22⋊D1311yescharacteristic
393C2×C4⋊C4C22×D1311yescharacteristic
394C2×C22⋊C4—22no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—262no—
397C2×C22⋊C4—262no—
398C2×C22⋊C4C22⋊D1312yes—
399C2×C42—261no—
400C2×C42C22×D1311yescharacteristic
401#106—262no—
402C4⋊C8—262no—
403#103—264no—
404#103—264no—
405#103—262no—
406#103—522no—
407#102—264no—
408#102—262no—
409C22⋊C8—264no—
410C22⋊C8—522no—
411C4×C8—262no—
412#95—262no—
413C2×C13—44no—
414C2×C13—82no—
415C2×C13#240811yescharacteristic
416C2×C13C2×#45211yescharacteristic
417C2×C13#301311yescharacteristic
418C2×C13#327611yescharacteristic
419C2×C13#328411yescharacteristic
420C2×C13#330211yescharacteristic
421C2×C13#333111yescharacteristic
422C24—21no—
423C24C2×C22⋊D1312yes—
424#41—48no—
425#41—48no—
426#41—48no—
427#41—48no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—132no—
434C2×Q8—261no—
435C2×Q8—261no—
436C2×Q8—261no—
437C2×Q8—261no—
438C2×Q8—261no—
439C2×Q8C2×C22⋊D1314yes—
440C2×D4—28no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—44no—
448C2×D4—44no—
449C2×D4D4×D1312yes—
450C2×D4#612912yes—
451C2×D4C2×C22⋊D1312yes—
452C22×C4—28no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—44no—
463C22×C4—44no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4—262no—
469C22×C4C2×C22⋊D1312yes—
470C22×C4C2×C22⋊D1311yescharacteristic
471C22×C4C2×C22⋊D1311yescharacteristic
472C22×C4C23×D1311yescharacteristic
473Q16—528no—
474SD16—268no—
475C2×C8—132no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8—262no—
479C2×C8—261no—
480C2×C8—262no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—262no—
484C4⋊C4—28no—
485C4⋊C4—22no—
486C4⋊C4—24no—
487C4⋊C4—24no—
488C4⋊C4—21no—
489C4⋊C4—262no—
490C4⋊C4—262no—
491C4⋊C4—261no—
492C4⋊C4—261no—
493C4⋊C4—524no—
494C4⋊C4—522no—
495C4⋊C4—522no—
496C4⋊C4—1041no—
497C4⋊C4C2×C22⋊D1312yes—
498C22⋊C4—28no—
499C22⋊C4—24no—
500C22⋊C4—24no—
501C22⋊C4—524no—
502C22⋊C4—1042no—
503C42—522no—
504C42C2×C22⋊D1312yes—
505C42C2×C22⋊D1312yes—
506C13#2424111yescharacteristic, complemented, Sylow
507C23—22no—
508C23—22no—
509C23—22no—
510C23—22no—
511C23—22no—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—22no—
516C23—22no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23C22×C22⋊D1311yescharacteristic
522Q8—24no—
523Q8—24no—
524Q8—42no—
525Q8—42no—
526Q8—262no—
527Q8—262no—
528Q8—521no—
529Q8—521no—
530D4—22no—
531D4—22no—
532D4—22no—
533D4—416no—
534D4—44no—
535D4#8819214yes—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—416no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—48no—
553C2×C4—262no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—522no—
557C2×C4—522no—
558C2×C4—521no—
559C2×C4—522no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4#8820412yes—
563C2×C4#8820512yes—
564C2×C4#8820712yes—
565C2×C4#8820712yes—
566C2×C4C2×D4×D1311yescharacteristic
567C2×C4C2×#612911yescharacteristic
568C2×C4#8825111yescharacteristic
569C2×C4#8825111yescharacteristic
570C2×C4C22×C22⋊D1311yescharacteristic
571C2×C4C22×C22⋊D1311yescharacteristic
572C8—262no—
573C8—522no—
574C8—521no—
575C22—24no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22D4×C22⋊D1311yescharacteristic
590C22#1171951111yescharacteristic
591C22C2×#8820411yescharacteristic
592C22C2×#8820511yescharacteristic
593C22#1171954211yescharacteristic
594C22#1171954311yescharacteristic
595C22C2×#8820711yescharacteristic
596C4—22no—
597C4—42no—
598C4—42no—
599C4—44no—
600C4—522no—
601C4—1041no—
602C4—1042no—
603C4#1171890014yescomplemented
604C4C2×#8819211yescharacteristic
605C4D4×C22⋊D1311yescharacteristic
606C4#1171951011yescharacteristic
607C4#1171951111yescharacteristic
608C2—44no—
609C2—82no—
610C2#1311818611yescharacteristic
611C2C2×#1171890011yescharacteristic
612C2#1312415111yescharacteristic
613C2#1312647811yescharacteristic
614C2#1312656211yescharacteristic
615C2#1312675311yescharacteristic
616C2#1312715211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#547C2
socleC23×C13C22×D4
hypercenterC2×#547D13
hypocenterC13#24241
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#11718751C2semidirect
2. C2×#11718900C2semidirect
3. C2×C4×#6105C2semidirect
4. #13119758C2semidirect
5. #13116029C2semidirect
6. #13115844C2semidirect
7. #13115639C2semidirect
8. #13115631C2semidirect
9. #13114836C2semidirect
10. #13114776C2semidirect
87. C2×#6105D4semidirect
337. C4×C13#452semidirect
506. C13#24241semidirect
603. C4#11718900semidirect

Maximal subgroups

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

subgroupindex
C2×#117187512
C2×#117189002
C2×C4×#61052
#131197582
#131160292
#131158442
#131156392
#131156312
#131148362
#131147762
C2×C13×#5472
#2424113