Finite Group Databasebeta

← #15873282

Subgroups — #15873282

Order 3328.

790 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718501C211yesmaximal, characteristic
2C2×#11718351C211yesmaximal, characteristic
3#13117316C211yesmaximal, characteristic
4#13115560C211yesmaximal, characteristic, complemented
5#13115558C211yesmaximal, characteristic, complemented
6#13115557C211yesmaximal, characteristic, complemented
7#13115556C211yesmaximal, characteristic, complemented
8#13115554C211yesmaximal, characteristic, complemented
9#13115553C211yesmaximal, characteristic, complemented
10#13115551C211yesmaximal, characteristic, complemented
11#13114819C211yesmaximal, characteristic
12#13114817C211yesmaximal, characteristic
13#13114815C211yesmaximal, characteristic
14#13114813C211yesmaximal, characteristic
15C13×#1939C211yesmaximal, characteristic, complemented
16C2×#88126C2211yescharacteristic
17C2×#88126C2211yescharacteristic
18C2×C42×D13C2211yescharacteristic
19C2×C13×C4⋊C8C2211yescharacteristic
20C2×C13×C4⋊C8C2211yescharacteristic
21C2×C13×C4⋊C8C2211yescharacteristic
22C2×C4×C8×C13C2211yescharacteristic
23C4×C13×C4⋊C4C2211yescharacteristic
24C2×#88060C2211yescharacteristic
25C2×#88060C2211yescharacteristic
26C2×#88060C2211yescharacteristic
27C2×#88060C2211yescharacteristic
28C2×#88055C2211yescharacteristic
29C2×#88054C2211yescharacteristic
30C2×#88054C2211yescharacteristic
31C2×#88054C2211yescharacteristic
32C2×#88054C2211yescharacteristic
33C2×#88054C2211yescharacteristic
34C2×#88054C2211yescharacteristic
35C2×C8×Dic13C2211yescharacteristic
36#11718650C411yescharacteristic
37#11718650C411yescharacteristic
38#11718633C411yescharacteristic
39#11718633C411yescharacteristic
40C4×C4⋊Dic13C2211yescharacteristic
41C4×#6101C2211yescharacteristic
42C4×#6101C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44C2×C4⋊#1055C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×#88043C2211yescharacteristic
47#11718501—24no—
48#11718351—24no—
49#11718329C411yescharacteristic
50#11718329C411yescharacteristic
51#11718308C411yescharacteristic
52#11718308C411yescharacteristic
53C13×#336C2211yescharacteristic
54C13×#336C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×C4×D13C2×C411yescharacteristic
62C22×C4×D13C2×C411yescharacteristic
63C22×C4×D13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C2×C13×C4⋊C4C2×C411yescharacteristic
69C2×C13×C4⋊C4C2×C411yescharacteristic
70C2×C42×C13C2311yescharacteristic
71C2×C42×C13C2311yescharacteristic
72C2×C42×C13C2311yescharacteristic
73C2×#6103C2×C411yescharacteristic
74C2×#6103C2×C411yescharacteristic
75C2×#6103C2×C411yescharacteristic
76C2×#6103C2×C411yescharacteristic
77C2×C4⋊Dic13C2×C411yescharacteristic
78C2×C4⋊Dic13C2×C411yescharacteristic
79C2×#6101C2×C411yescharacteristic
80C2×#6101C2×C411yescharacteristic
81C2×#6101C2×C411yescharacteristic
82C2×#6101C2×C411yescharacteristic
83C2×#6101C2×C411yescharacteristic
84C2×#6101C2×C411yescharacteristic
85C2×#6101C2×C411yescharacteristic
86C2×#6101C2×C411yescharacteristic
87C2×C4×Dic13C2×C411yescharacteristic
88C2×C4×Dic13C2×C411yescharacteristic
89C2×C4×Dic13C2311yescharacteristic
90C2×C4×Dic13C2311yescharacteristic
91C2×C4×Dic13C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96#88126—41no—
97#88126—41no—
98#88126D414yes—
99#88126Q814yes—
100C42×D13—41no—
101C42×D13—41no—
102C13×C4⋊C8—22no—
103C13×C4⋊C8—41no—
104C13×C4⋊C8—41no—
105C4×C8×C13—22no—
106C13×#95C2×C411yescharacteristic
107C13×#95C2×C411yescharacteristic
108#88071C2×C411yescharacteristic
109#88071C2×C411yescharacteristic
110#88071C2×C411yescharacteristic
111#88071C2×C411yescharacteristic
112#88071C2×C411yescharacteristic
113#88071C2×C411yescharacteristic
114#88060—22no—
115#88060—22no—
116#88060—22no—
117#88060—22no—
118#88055—22no—
119#88054—22no—
120#88054—22no—
121#88054—41no—
122#88054—41no—
123#88054—41no—
124#88054—41no—
125C8×Dic13—22no—
126C4⋊#1055—22no—
127C4⋊#1055—41no—
128C4⋊#1055—41no—
129#88043—22no—
130#21958—131nomaximal, Sylow
131C23×D13C22×C411yescharacteristic
132C22×C4×C13C22×C411yescharacteristic
133C22×C4×C13C22×C411yescharacteristic
134C22×C4×C13C22×C411yescharacteristic
135C22×C4×C13C22×C411yescharacteristic
136C22×C4×C13C22×C411yescharacteristic
137C22×C4×C13C22×C411yescharacteristic
138C22×C4×C13C2411yescharacteristic
139C22×Dic13C22×C411yescharacteristic
140C22×Dic13C22×C411yescharacteristic
141C22×Dic13C22×C411yescharacteristic
142C22×Dic13C22×C411yescharacteristic
143C22×Dic13C22×C411yescharacteristic
144C22×Dic13C22×C411yescharacteristic
145C22×Dic13C22×C411yescharacteristic
146C2×C4×D13—21no—
147C2×C4×D13—21no—
148C2×C4×D13—21no—
149C2×C4×D13—21no—
150C2×C4×D13—22no—
151C2×C4×D13—22no—
152C2×C4×D13—41no—
153C2×C4×D13—41no—
154C2×C4×D13—41no—
155C2×C4×D13—41no—
156C2×C4×D13C2×D412yes—
157C2×C4×D13C2×Q812yes—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C13×C4⋊C4—22no—
171C13×C4⋊C4—41no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13C2×D412yes—
177C42×C13C2×Q812yes—
178#6103—41no—
179#6103—41no—
180#6103C4⋊C414yes—
181#6103C4⋊C414yes—
182C4⋊Dic13—22no—
183C4⋊Dic13—41no—
184#6101—22no—
185#6101—22no—
186#6101—41no—
187#6101—41no—
188#6101—41no—
189#6101—41no—
190#6101C4⋊C414yes—
191#6101C4⋊C414yes—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195C4×Dic13—21no—
196C4×Dic13—41no—
197C4×Dic13—41no—
198C4×Dic13C2×D412yes—
199C4×Dic13C2×Q812yes—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
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×#433—131no—
213C2×#433—131no—
214#2296—131no—
215#1940—131no—
216#1940—131no—
217#1940—131no—
218#1940—131no—
219#1939—131no—
220#1939—131no—
221#1939—131no—
222#1939D1311yescharacteristic, complemented
223#1798—131no—
224#1798—131no—
225#1797—131no—
226#1797—131no—
227C23×C13C23×C411yescharacteristic
228C22×D13—21no—
229C22×D13—21no—
230C22×D13—21no—
231C22×D13—21no—
232C22×D13—21no—
233C22×D13—21no—
234C22×D13C2×C4⋊C412yes—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
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×C13C2×C4⋊C412yes—
251C2×C4×C13C2×C4⋊C412yes—
252C2×C4×C13#13112yes—
253C2×C4×C13C22×D411yescharacteristic
254C2×C4×C13C22×Q811yescharacteristic
255C2×C4×C13H(5,𝔽2)11yescharacteristic
256C2×C4×C13H(5,𝔽2)11yescharacteristic
257C2×C4×C132−1+411yescharacteristic
258C2×C4×C132−1+411yescharacteristic
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—21no—
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×Dic13C2×C4⋊C412yes—
277C2×Dic13C2×C4⋊C412yes—
278C2×Dic13C2×C4⋊C412yes—
279C2×Dic13#13112yes—
280C4×D13—22no—
281C4×D13—22no—
282C4×D13—22no—
283C4×D13—22no—
284C4×D13—44no—
285C4×D13—44no—
286C8×C13—41no—
287C8×C13—41no—
288C8×C13—41no—
289C8×C13—41no—
290#1055—41no—
291#1055—41no—
292#1055—41no—
293#1055—41no—
294C2×#117—131no—
295C2×#117—131no—
296C22×C42—131no—
297#433—264no—
298#433—264no—
299C2×C4⋊C8—131no—
300C2×C4⋊C8—131no—
301C2×C4⋊C8—131no—
302C2×C4⋊C8—131no—
303C2×C4⋊C8—131no—
304C2×C4⋊C8—131no—
305C2×C4⋊C8—131no—
306C2×C4⋊C8—131no—
307C2×C4⋊C8—131no—
308C2×C4⋊C8C2×D1311yescharacteristic
309C2×C4⋊C8C2×D1311yescharacteristic
310C2×C4⋊C8C2×D1311yescharacteristic
311C2×C22⋊C8—131no—
312C2×C22⋊C8—131no—
313C2×C22⋊C8—131no—
314C2×C22⋊C8—131no—
315C2×#97—131no—
316C2×#97—131no—
317C2×C4×C8—131no—
318C2×C4×C8C2×D1311yescharacteristic
319#389—131no—
320#389—131no—
321#389—131no—
322#389—131no—
323#385—131no—
324#385—131no—
325#385—131no—
326#385—131no—
327C4×C4⋊C4—131no—
328C4×C4⋊C4—131no—
329C4×C4⋊C4—131no—
330C4×C4⋊C4C2×D1311yescharacteristic
331#336—131no—
332#336—131no—
333#336—131no—
334#336—131no—
335#336—131no—
336#336—131no—
337#336C2×D1311yescharacteristic
338#336C2×D1311yescharacteristic
339C22×C13C22×C4⋊C411yescharacteristic
340C22×C13#51811yescharacteristic
341C22×C13#51911yescharacteristic
342C22×C13C2×#13111yescharacteristic
343C22×C13C2×#13111yescharacteristic
344C22×C13#56811yescharacteristic
345C22×C13#56811yescharacteristic
346C2×D13—22no—
347C2×D13—22no—
348C2×D13—22no—
349C2×D13—41no—
350C2×D13—41no—
351C2×D13—41no—
352C2×D13—41no—
353C4×C13—22no—
354C4×C13—22no—
355C4×C13—22no—
356C4×C13—41no—
357C4×C13—41no—
358C4×C13—41no—
359C4×C13#53711yescharacteristic
360C4×C13#53711yescharacteristic
361C4×C13#54411yescharacteristic
362C4×C13#54411yescharacteristic
363Dic13—22no—
364Dic13—22no—
365Dic13—22no—
366Dic13—22no—
367Dic13—41no—
368Dic13—41no—
369Dic13—41no—
370C23×C4—131no—
371C23×C4—131no—
372C23×C4—131no—
373C22×C8—131no—
374C22×C8—131no—
375C22×C8—131no—
376C22×C8—131no—
377C22×C8C22×D1311yescharacteristic
378C22×C8C22×D1311yescharacteristic
379C22×C8C22×D1311yescharacteristic
380C22×C8C22×D1311yescharacteristic
381#117—134no—
382#117—134no—
383#117—521no—
384#117—521no—
385C2×C4⋊C4—131no—
386C2×C4⋊C4—131no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—131no—
389C2×C4⋊C4—131no—
390C2×C4⋊C4—131no—
391C2×C4⋊C4—131no—
392C2×C4⋊C4—131no—
393C2×C4⋊C4—131no—
394C2×C4⋊C4—131no—
395C2×C4⋊C4C4×D1311yescharacteristic
396C2×C4⋊C4C4×D1311yescharacteristic
397C2×C22⋊C4—131no—
398C2×C22⋊C4—131no—
399C2×C22⋊C4—131no—
400C2×C22⋊C4—131no—
401C2×C42—131no—
402C2×C42—131no—
403C2×C42—131no—
404C2×C42—131no—
405C2×C42—131no—
406C2×C42—521no—
407C2×C42—521no—
408C2×C42C22×D1311yescharacteristic
409C2×C42C22×D1311yescharacteristic
410C2×C42C22×D1311yescharacteristic
411C4⋊C8—22no—
412C4⋊C8—41no—
413C4⋊C8—41no—
414C4⋊C8—262no—
415C4⋊C8—262no—
416C4⋊C8—262no—
417C4⋊C8—521no—
418C4⋊C8—521no—
419C4⋊C8—521no—
420C4⋊C8—521no—
421C4⋊C8—521no—
422C4⋊C8—521no—
423C22⋊C8—262no—
424C22⋊C8—262no—
425C22⋊C8—262no—
426C22⋊C8—262no—
427#97—262no—
428#97—262no—
429C4×C8—22no—
430C4×C8—262no—
431#95—131no—
432#95—131no—
433#95—131no—
434#95—131no—
435#95—131no—
436#95—131no—
437#95C4×D1311yescharacteristic
438#95C4×D1311yescharacteristic
439C2×C13#231611yescharacteristic
440C2×C13#290611yescharacteristic
441C2×C13#290611yescharacteristic
442C2×C13#297711yescharacteristic
443C2×C13#297811yescharacteristic
444C2×C13#298511yescharacteristic
445C2×C13#298511yescharacteristic
446D13—42no—
447C24—131no—
448C22×C4—131no—
449C22×C4—131no—
450C22×C4—131no—
451C22×C4—131no—
452C22×C4—132no—
453C22×C4—132no—
454C22×C4—131no—
455C22×C4—131no—
456C22×C4—131no—
457C22×C4—262no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—261no—
462C22×C4—262no—
463C22×C4—521no—
464C22×C4—521no—
465C22×C4—521no—
466C22×C4—521no—
467C22×C4C2×C4×D1311yescharacteristic
468C22×C4C2×C4×D1311yescharacteristic
469C22×C4C2×C4×D1311yescharacteristic
470C22×C4C2×C4×D1311yescharacteristic
471C22×C4C2×C4×D1311yescharacteristic
472C22×C4C2×C4×D1311yescharacteristic
473C22×C4C23×D1311yescharacteristic
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—261no—
487C2×C8—261no—
488C2×C8—261no—
489C2×C8—261no—
490C2×C8—261no—
491C2×C8—261no—
492C2×C8—261no—
493C2×C8—261no—
494C2×C8—261no—
495C2×C8—261no—
496C2×C8—261no—
497C2×C8—261no—
498C4⋊C4—22no—
499C4⋊C4—41no—
500C4⋊C4—134no—
501C4⋊C4—134no—
502C4⋊C4—262no—
503C4⋊C4—262no—
504C4⋊C4—262no—
505C4⋊C4—521no—
506C4⋊C4—521no—
507C4⋊C4—521no—
508C4⋊C4—521no—
509C4⋊C4—521no—
510C22⋊C4—134no—
511C22⋊C4—134no—
512C22⋊C4—521no—
513C22⋊C4—521no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—132no—
519C42—132no—
520C42—261no—
521C42—261no—
522C42—261no—
523C42—261no—
524C42—521no—
525C42—521no—
526C42D4×D1312yes—
527C42Q8×D1312yes—
528C13#2195811yescharacteristic, complemented, Sylow
529C23—132no—
530C23—261no—
531C23—261no—
532C23—261no—
533C23—261no—
534C23—261no—
535C23—261no—
536C23C22×C4×D1311yescharacteristic
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—132no—
553C2×C4—132no—
554C2×C4—132no—
555C2×C4—132no—
556C2×C4—261no—
557C2×C4—261no—
558C2×C4—261no—
559C2×C4—261no—
560C2×C4—261no—
561C2×C4—261no—
562C2×C4—261no—
563C2×C4—261no—
564C2×C4—262no—
565C2×C4—262no—
566C2×C4—262no—
567C2×C4—262no—
568C2×C4—261no—
569C2×C4—261no—
570C2×C4—261no—
571C2×C4—261no—
572C2×C4—261no—
573C2×C4—261no—
574C2×C4—261no—
575C2×C4—261no—
576C2×C4—261no—
577C2×C4—524no—
578C2×C4—524no—
579C2×C4C4⋊C4×D1312yes—
580C2×C4C4⋊C4×D1312yes—
581C2×C4#8815512yes—
582C2×C4C2×D4×D1311yescharacteristic
583C2×C4#8825111yescharacteristic
584C2×C4C2×Q8×D1311yescharacteristic
585C2×C4#8825411yescharacteristic
586C2×C4#8825611yescharacteristic
587C2×C4#8825711yescharacteristic
588C8—41no—
589C8—41no—
590C8—41no—
591C8—41no—
592C8—521no—
593C8—521no—
594C8—521no—
595C8—521no—
596C22—262no—
597C22—262no—
598C22—262no—
599C22—521no—
600C22—521no—
601C22—521no—
602C22—521no—
603C22C2×C4⋊C4×D1311yescharacteristic
604C22#1171925011yescharacteristic
605C22#1171927711yescharacteristic
606C22C2×#8815511yescharacteristic
607C22#1171945011yescharacteristic
608C22D13×#13111yescharacteristic
609C22#1171945511yescharacteristic
610C4—22no—
611C4—22no—
612C4—22no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—262no—
617C4—262no—
618C4—262no—
619C4—262no—
620C4—521no—
621C4—521no—
622C4—521no—
623C4#1171931311yescharacteristic
624C4#1171933411yescharacteristic
625C4#1171939411yescharacteristic
626C4#1171943411yescharacteristic
627C2—522no—
628C2#1311745111yescharacteristic
629C2#1312340111yescharacteristic
630C2#1312340311yescharacteristic
631C2#1312388911yescharacteristic
632C2#1312389311yescharacteristic
633C2#1312392711yescharacteristic
634C2#1312392911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1939C2
prime radicalC23×D13C22×C4
cosocleC22×C4×C13C24
hypercenter#1939D13
hypocenterC13#21958
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
4. #13115560C2semidirect
5. #13115558C2semidirect
6. #13115557C2semidirect
7. #13115556C2semidirect
8. #13115554C2semidirect
9. #13115553C2semidirect
10. #13115551C2semidirect
15. C13×#1939C2semidirect
222. #1939D13semidirect
528. C13#21958semidirect

Maximal subgroups

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

subgroupindex
C2×#117185012
C2×#117183512
#131173162
#131155602
#131155582
#131155572
#131155562
#131155542
#131155532
#131155512
#131148192
#131148172
#131148152
#131148132
C13×#19392
#2195813