Finite Group Databasebeta

← #15880706

Subgroups — #15880706

Order 3328.

916 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C4⋊C4×D13C211yesmaximal, characteristic
2#13115553C211yesmaximal, characteristic, complemented
3#13115551C211yesmaximal, characteristic, complemented
4#13115395C211yesmaximal, characteristic, complemented
5#13115394C211yesmaximal, characteristic, complemented
6#13115392C211yesmaximal, characteristic, complemented
7#13114815C211yesmaximal, characteristic
8#13114815C211yesmaximal, characteristic
9#13114813C211yesmaximal, characteristic
10C8×#6101C211yesmaximal, characteristic, complemented
11#13114697C211yesmaximal, characteristic, complemented
12C4×#88060C211yesmaximal, characteristic
13#13114593C211yesmaximal, characteristic
14#13114593C211yesmaximal, characteristic
15C13×#1916C211yesmaximal, characteristic, complemented
16C2×C4⋊C4×D13C411yescharacteristic
17C2×C4⋊C4×D13C411yescharacteristic
18C2×C42×D13C2211yescharacteristic
19C2×C42×D13C2211yescharacteristic
20C2×C42×D13C2211yescharacteristic
21C2×C13×C4⋊C8C2211yescharacteristic
22C2×C4×C8×C13C2211yescharacteristic
23C4×C13×C4⋊C4C2211yescharacteristic
24C2×#88060C2211yescharacteristic
25C2×#88060C2211yescharacteristic
26C2×#88060C2211yescharacteristic
27C2×#88060C2211yescharacteristic
28C2×#88054C2211yescharacteristic
29C2×#88054C2211yescharacteristic
30C2×#88054C2211yescharacteristic
31C2×#88054C2211yescharacteristic
32C2×C8×Dic13C2211yescharacteristic
33C2×C8×Dic13C2211yescharacteristic
34C2×C8×Dic13C2211yescharacteristic
35C2×C8×Dic13C2211yescharacteristic
36C4⋊C4×Dic13C411yescharacteristic
37C4⋊C4×Dic13C411yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39C4×#6101C2211yescharacteristic
40C4×#6101C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42C2×C4×#1055C2211yescharacteristic
43D13×#95C411yescharacteristic
44D13×#95C411yescharacteristic
45#11718310C411yescharacteristic
46#11718310C411yescharacteristic
47C13×#336C2211yescharacteristic
48C13×#336C2211yescharacteristic
49C13×#336C2211yescharacteristic
50C13×#336C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718116C2211yescharacteristic
56#11718116C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×C4×D13C2×C411yescharacteristic
60C22×C4×D13C2×C411yescharacteristic
61C22×C4×D13C2×C411yescharacteristic
62C22×C4×D13C2×C411yescharacteristic
63C22×C4×D13C2×C411yescharacteristic
64C22×C4×D13C2×C411yescharacteristic
65C22×C4×D13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C2×C13×C4⋊C4C2×C411yescharacteristic
71C2×C13×C4⋊C4C2×C411yescharacteristic
72C2×C42×C13C2311yescharacteristic
73C2×C42×C13C2311yescharacteristic
74C2×C42×C13C2311yescharacteristic
75C2×C4⋊Dic13C2×C411yescharacteristic
76C2×C4⋊Dic13C2×C411yescharacteristic
77C2×#6101C2×C411yescharacteristic
78C2×#6101C2×C411yescharacteristic
79C2×#6101C2×C411yescharacteristic
80C2×#6101C2×C411yescharacteristic
81C2×C4×Dic13C2×C411yescharacteristic
82C2×C4×Dic13C2×C411yescharacteristic
83C2×C4×Dic13C2×C411yescharacteristic
84C2×C4×Dic13C2×C411yescharacteristic
85C2×C4×Dic13C2×C411yescharacteristic
86C2×C4×Dic13C2×C411yescharacteristic
87C2×C4×Dic13C2311yescharacteristic
88C2×C4×Dic13C2311yescharacteristic
89C2×C4×Dic13C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C4⋊C4×D13—24no—
95C4⋊C4×D13C818yescomplemented
96C42×D13—22no—
97C42×D13—22no—
98C42×D13—41no—
99C42×D13—41no—
100C42×D13—41no—
101C42×D13—41no—
102C13×C4⋊C8—41no—
103C4×C8×C13—41no—
104C13×#95C2×C411yescharacteristic
105C13×#95C2×C411yescharacteristic
106#88071C2×C411yescharacteristic
107#88071C2×C411yescharacteristic
108#88071C2×C411yescharacteristic
109#88071C2×C411yescharacteristic
110#88071C2×C411yescharacteristic
111#88071C2×C411yescharacteristic
112#88060—22no—
113#88060—22no—
114#88060—22no—
115#88060Q814yes—
116#88054—22no—
117#88054—22no—
118#88054—41no—
119#88054—41no—
120C8×Dic13—22no—
121C8×Dic13—22no—
122C8×Dic13—41no—
123C8×Dic13—41no—
124C4⋊#1055—41no—
125C4×#1055—41no—
126#22625—131nomaximal, Sylow
127C23×D13C22×C411yescharacteristic
128C22×C4×C13C22×C411yescharacteristic
129C22×C4×C13C22×C411yescharacteristic
130C22×C4×C13C22×C411yescharacteristic
131C22×C4×C13C22×C411yescharacteristic
132C22×C4×C13C22×C411yescharacteristic
133C22×C4×C13C22×C411yescharacteristic
134C22×C4×C13C2411yescharacteristic
135C22×Dic13C22×C411yescharacteristic
136C22×Dic13C22×C411yescharacteristic
137C22×Dic13C22×C411yescharacteristic
138C22×Dic13C22×C411yescharacteristic
139C22×Dic13C22×C411yescharacteristic
140C22×Dic13C22×C411yescharacteristic
141C22×Dic13C22×C411yescharacteristic
142C2×C4×D13—21no—
143C2×C4×D13—21no—
144C2×C4×D13—21no—
145C2×C4×D13—21no—
146C2×C4×D13—22no—
147C2×C4×D13—22no—
148C2×C4×D13—22no—
149C2×C4×D13—22no—
150C2×C4×D13—22no—
151C2×C4×D13—22no—
152C2×C4×D13—22no—
153C2×C4×D13—22no—
154C2×C4×D13—41no—
155C2×C4×D13—41no—
156C2×C4×D13—41no—
157C2×C4×D13—41no—
158C2×C4×D13—41no—
159C2×C4×D13—41no—
160C2×C4×D13—41no—
161C2×C4×D13C2×C814yes—
162C2×C4×D13C2×C814yes—
163C2×C4×D13C2×C814yes—
164C2×C4×D13C2×Q812yes—
165C2×C4×D13#4112yes—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C2×C8×C13—21no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C2×C8×C13—21no—
177C2×C8×C13C2×Q812yes—
178C13×C4⋊C4—22no—
179C13×C4⋊C4C2×C814yes—
180C42×C13—21no—
181C42×C13—21no—
182C42×C13—21no—
183C42×C13—21no—
184C42×C13—21no—
185C42×C13—21no—
186C4⋊Dic13—22no—
187C4⋊Dic13C2×C814yes—
188#6101—22no—
189#6101C2×C814yes—
190#6101C2×C814yes—
191#6101M1614yes—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195C4×Dic13—21no—
196C4×Dic13—22no—
197C4×Dic13—22no—
198C4×Dic13—41no—
199C4×Dic13—41no—
200C4×Dic13—41no—
201C4×Dic13—41no—
202C4×Dic13#4112yes—
203C4×Dic13#4112yes—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055C2×Q812yes—
216C2×C4×C4⋊C4—131no—
217#1939—131no—
218#1939—131no—
219#1916—131no—
220#1916—131no—
221#1916—131no—
222#1916D1311yescharacteristic, complemented
223#1797—131no—
224#1797—131no—
225#1797—131no—
226C8×C4⋊C4—131no—
227C8×C4⋊C4—131no—
228C4×C22⋊C8—131no—
229C4×C22⋊C8—131no—
230C4×C22⋊C8—131no—
231C23×C13C23×C411yescharacteristic
232C22×D13—21no—
233C22×D13—21no—
234C22×D13—21no—
235C22×D13—21no—
236C22×D13C4×Q812yes—
237C22×D13C22×C812yes—
238C22×D13#13112yes—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13C22×C812yes—
254C2×C4×C13C22×C812yes—
255C2×C4×C13C22×C812yes—
256C2×C4×C13C2×M1612yes—
257C2×C4×C13C22×Q811yescharacteristic
258C2×C4×C13C2×#4111yescharacteristic
259C2×C4×C13C2×#4111yescharacteristic
260C2×C4×C13C2×#4111yescharacteristic
261C2×C4×C13H(5,𝔽2)11yescharacteristic
262C2×C4×C13H(5,𝔽2)11yescharacteristic
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—21no—
266C2×Dic13—21no—
267C2×Dic13—21no—
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—21no—
271C2×Dic13—21no—
272C2×Dic13—21no—
273C2×Dic13—21no—
274C2×Dic13—21no—
275C2×Dic13—21no—
276C2×Dic13#11712yes—
277C2×Dic13#11712yes—
278C2×Dic13C4×Q812yes—
279C2×Dic13C22×C812yes—
280C2×Dic13C22×C812yes—
281C2×Dic13C22×C812yes—
282C2×Dic13C2×M1612yes—
283C2×Dic13C2×M1612yes—
284C4×D13—22no—
285C4×D13—22no—
286C4×D13—22no—
287C4×D13—22no—
288C4×D13—28no—
289C4×D13—44no—
290C4×D13—44no—
291C4×D13—44no—
292C4×D13—44no—
293C4×D13—44no—
294C8×C13—22no—
295C8×C13—41no—
296C8×C13—41no—
297C8×C13—41no—
298#1055—22no—
299#1055—41no—
300#1055—41no—
301#1055—41no—
302C22×C4⋊C4—131no—
303C22×C4⋊C4—131no—
304C22×C42—131no—
305C22×C42—131no—
306C22×C42—131no—
307C2×C4⋊C8—131no—
308C2×C4⋊C8—131no—
309C2×C4⋊C8—131no—
310C2×C4⋊C8—131no—
311C2×C4⋊C8—131no—
312C2×C4⋊C8C2×D1311yescharacteristic
313C2×C22⋊C8—131no—
314C2×C22⋊C8—131no—
315C2×C22⋊C8—131no—
316C2×C22⋊C8—131no—
317C2×C4×C8—131no—
318C2×C4×C8—131no—
319C2×C4×C8—131no—
320C2×C4×C8—131no—
321C2×C4×C8—131no—
322C2×C4×C8C2×D1311yescharacteristic
323C4×C4⋊C4—131no—
324C4×C4⋊C4—131no—
325C4×C4⋊C4—131no—
326C4×C4⋊C4—131no—
327C4×C4⋊C4—131no—
328C4×C4⋊C4—131no—
329C4×C4⋊C4—131no—
330C4×C4⋊C4C2×D1311yescharacteristic
331C2×#95—131no—
332C2×#95—131no—
333#336—131no—
334#336—131no—
335#336—131no—
336#336—131no—
337#336—131no—
338#336—131no—
339#336—131no—
340#336—131no—
341#336C2×D1311yescharacteristic
342#336C2×D1311yescharacteristic
343#336C2×D1311yescharacteristic
344#336C2×D1311yescharacteristic
345C22×C13C2×#11711yescharacteristic
346C22×C13C2×C4×Q811yescharacteristic
347C22×C13#51811yescharacteristic
348C22×C13C23×C811yescharacteristic
349C22×C13C22×M1611yescharacteristic
350C22×C13C2×#13111yescharacteristic
351C22×C13#56811yescharacteristic
352C2×D13—22no—
353C2×D13—22no—
354C2×D13—22no—
355C2×D13—22no—
356C2×D13—22no—
357C2×D13—22no—
358C2×D13C8×Q814yes—
359C4×C13—22no—
360C4×C13—22no—
361C4×C13—22no—
362C4×C13—22no—
363C4×C13—41no—
364C4×C13—41no—
365C4×C13#55311yescharacteristic
366C4×C13#55311yescharacteristic
367C4×C13#55411yescharacteristic
368C4×C13#55411yescharacteristic
369Dic13—22no—
370Dic13—22no—
371Dic13—22no—
372Dic13—22no—
373Dic13—22no—
374Dic13—41no—
375Dic13#43114yes—
376C23×C4—131no—
377C23×C4—131no—
378C23×C4—131no—
379C23×C4—131no—
380C23×C4—131no—
381C23×C4—131no—
382C23×C4—131no—
383C22×C8—131no—
384C22×C8—131no—
385C22×C8—131no—
386C22×C8—131no—
387C22×C8C22×D1311yescharacteristic
388C22×C8C22×D1311yescharacteristic
389C22×C8C22×D1311yescharacteristic
390C22×C8C22×D1311yescharacteristic
391C2×C4⋊C4—131no—
392C2×C4⋊C4—131no—
393C2×C4⋊C4—131no—
394C2×C4⋊C4—131no—
395C2×C4⋊C4—138no—
396C2×C4⋊C4—131no—
397C2×C4⋊C4—131no—
398C2×C4⋊C4—264no—
399C2×C4⋊C4C4×D1311yescharacteristic
400C2×C4⋊C4C4×D1311yescharacteristic
401C2×C42—131no—
402C2×C42—131no—
403C2×C42—131no—
404C2×C42—131no—
405C2×C42—131no—
406C2×C42—131no—
407C2×C42—131no—
408C2×C42—131no—
409C2×C42—131no—
410C2×C42—262no—
411C2×C42—262no—
412C2×C42—521no—
413C2×C42—521no—
414C2×C42—521no—
415C2×C42—521no—
416C2×C42C22×D1311yescharacteristic
417C2×C42C22×D1311yescharacteristic
418C2×C42C22×D1311yescharacteristic
419C4⋊C8—41no—
420C4⋊C8—262no—
421C4⋊C8—262no—
422C4⋊C8—521no—
423C4⋊C8—521no—
424C4⋊C8—521no—
425C22⋊C8—134no—
426C22⋊C8—262no—
427C22⋊C8—262no—
428C22⋊C8—262no—
429C4×C8—41no—
430C4×C8—262no—
431C4×C8—262no—
432C4×C8—521no—
433C4×C8—521no—
434C4×C8—521no—
435#95—131no—
436#95—131no—
437#95—131no—
438#95—131no—
439#95—131no—
440#95—131no—
441#95C4×D1311yescharacteristic
442#95C4×D1311yescharacteristic
443C2×C13#234511yescharacteristic
444C2×C13C2×#43111yescharacteristic
445C2×C13#292411yescharacteristic
446C2×C13C2×C8×Q811yescharacteristic
447C2×C13Q8×M1611yescharacteristic
448C2×C13#297211yescharacteristic
449C2×C13#297411yescharacteristic
450D13—24no—
451C24—131no—
452C22×C4—131no—
453C22×C4—131no—
454C22×C4—131no—
455C22×C4—131no—
456C22×C4—131no—
457C22×C4—131no—
458C22×C4—134no—
459C22×C4—132no—
460C22×C4—132no—
461C22×C4—134no—
462C22×C4—134no—
463C22×C4—131no—
464C22×C4—262no—
465C22×C4—262no—
466C22×C4—262no—
467C22×C4—262no—
468C22×C4—262no—
469C22×C4—262no—
470C22×C4—262no—
471C22×C4—261no—
472C22×C4—261no—
473C22×C4—261no—
474C22×C4—261no—
475C22×C4—262no—
476C22×C4—521no—
477C22×C4—521no—
478C22×C4—521no—
479C22×C4—521no—
480C22×C4—521no—
481C22×C4—521no—
482C22×C4—521no—
483C22×C4C2×C4×D1311yescharacteristic
484C22×C4C2×C4×D1311yescharacteristic
485C22×C4C2×C4×D1311yescharacteristic
486C22×C4C2×C4×D1311yescharacteristic
487C22×C4C2×C4×D1311yescharacteristic
488C22×C4C2×C4×D1311yescharacteristic
489C22×C4C23×D1311yescharacteristic
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—132no—
502C2×C8—261no—
503C2×C8—261no—
504C2×C8—261no—
505C2×C8—261no—
506C2×C8—261no—
507C2×C8—261no—
508C2×C8—261no—
509C2×C8—261no—
510C2×C8—261no—
511C2×C8—261no—
512C2×C8—261no—
513C2×C8Q8×D1312yes—
514C4⋊C4—22no—
515C4⋊C4—134no—
516C4⋊C4—134no—
517C4⋊C4—134no—
518C4⋊C4—134no—
519C4⋊C4—262no—
520C4⋊C4—262no—
521C4⋊C4C8×D1314yes—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—132no—
529C42—132no—
530C42—262no—
531C42—262no—
532C42—261no—
533C42—261no—
534C42—261no—
535C42—261no—
536C42—521no—
537C42—521no—
538C42—521no—
539C42—521no—
540C13#2262511yescharacteristic, complemented, Sylow
541C23—132no—
542C23—132no—
543C23—132no—
544C23—261no—
545C23—261no—
546C23—261no—
547C23—261no—
548C23C22×C4×D1311yescharacteristic
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—132no—
564C2×C4—132no—
565C2×C4—132no—
566C2×C4—132no—
567C2×C4—132no—
568C2×C4—132no—
569C2×C4—132no—
570C2×C4—132no—
571C2×C4—268no—
572C2×C4—261no—
573C2×C4—261no—
574C2×C4—261no—
575C2×C4—261no—
576C2×C4—261no—
577C2×C4—261no—
578C2×C4—261no—
579C2×C4—261no—
580C2×C4—261no—
581C2×C4—261no—
582C2×C4—262no—
583C2×C4—262no—
584C2×C4—262no—
585C2×C4—262no—
586C2×C4—261no—
587C2×C4—261no—
588C2×C4—261no—
589C2×C4—524no—
590C2×C4—524no—
591C2×C4—524no—
592C2×C4—524no—
593C2×C4—524no—
594C2×C4C2×C8×D1312yes—
595C2×C4C2×C8×D1312yes—
596C2×C4C2×C8×D1312yes—
597C2×C4M16×D1312yes—
598C2×C4#8825111yescharacteristic
599C2×C4C2×Q8×D1311yescharacteristic
600C2×C4#41×D1311yescharacteristic
601C2×C4#41×D1311yescharacteristic
602C2×C4#41×D1311yescharacteristic
603C2×C4#8825611yescharacteristic
604C8—22no—
605C8—41no—
606C8—41no—
607C8—41no—
608C8—262no—
609C8—521no—
610C8—521no—
611C8—521no—
612C22—134no—
613C22—262no—
614C22—262no—
615C22—262no—
616C22—262no—
617C22—262no—
618C22—262no—
619C22D13×#11711yescharacteristic
620C22#1171925011yescharacteristic
621C22C4×Q8×D1311yescharacteristic
622C22C22×C8×D1311yescharacteristic
623C22C2×M16×D1311yescharacteristic
624C22D13×#13111yescharacteristic
625C22#1171945511yescharacteristic
626C4—22no—
627C4—22no—
628C4—22no—
629C4—22no—
630C4—41no—
631C4—41no—
632C4—134no—
633C4—262no—
634C4—262no—
635C4—262no—
636C4—262no—
637C4—262no—
638C4—521no—
639C4#1171934111yescharacteristic
640C4#1171936611yescharacteristic
641C4#1171939511yescharacteristic
642C4#1171941411yescharacteristic
643C2—264no—
644C2#1311771011yescharacteristic
645C2D13×#43111yescharacteristic
646C2#1312349211yescharacteristic
647C2C8×Q8×D1311yescharacteristic
648C2#1312378811yescharacteristic
649C2#1312385711yescharacteristic
650C2#1312386611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutatorC22×C13C23×C8
FittingC13×#1916C2
socleC23×C13C23×C4
prime radicalC23×D13C22×C4
cosocleC22×C4×C13C24
hypercenter#1916D13
hypocenterC13#22625
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
2. #13115553C2semidirect
3. #13115551C2semidirect
4. #13115395C2semidirect
5. #13115394C2semidirect
6. #13115392C2semidirect
10. C8×#6101C2semidirect
11. #13114697C2semidirect
15. C13×#1916C2semidirect
95. C4⋊C4×D13C8semidirect
222. #1916D13semidirect
540. C13#22625semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊C4×D132
#131155532
#131155512
#131153952
#131153942
#131153922
#131148152
#131148132
C8×#61012
#131146972
C4×#880602
#131145932
C13×#19162
#2262513