Finite Group Databasebeta

← #15880783

Subgroups — #15880783

Order 3328.

828 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88131C211yesmaximal, characteristic
2#13115553C211yesmaximal, characteristic, complemented
3#13115551C211yesmaximal, characteristic, complemented
4#13115445C211yesmaximal, characteristic
5#13115444C211yesmaximal, characteristic
6#13115439C211yesmaximal, characteristic
7#13114952C211yesmaximal, characteristic, complemented
8#13114951C211yesmaximal, characteristic, complemented
9#13114814C211yesmaximal, characteristic
10C8×#6101C211yesmaximal, characteristic, complemented
11#13114697C211yesmaximal, characteristic, complemented
12C22⋊C8×Dic13C211yesmaximal, characteristic
13#13114581C211yesmaximal, characteristic, complemented
14#13114580C211yesmaximal, characteristic, complemented
15C13×#1923C211yesmaximal, characteristic
16C22×C4×Dic13C2211yescharacteristic
17C2×#88131C411yescharacteristic
18C2×#88131C411yescharacteristic
19C2×C13×C4⋊C8C2211yescharacteristic
20C2×C13×C22⋊C8C2211yescharacteristic
21C2×C13×C22⋊C8C2211yescharacteristic
22C2×C4×C8×C13C2211yescharacteristic
23C4×C13×C22⋊C4C2211yescharacteristic
24C4×C22⋊Dic13C2211yescharacteristic
25C2×C22⋊#1055C2211yescharacteristic
26C2×C22⋊#1055C2211yescharacteristic
27C2×#88054C2211yescharacteristic
28C2×#88054C2211yescharacteristic
29C2×#88054C2211yescharacteristic
30C2×#88054C2211yescharacteristic
31C2×C8×Dic13C2211yescharacteristic
32C2×C8×Dic13C2211yescharacteristic
33C2×C8×Dic13C2211yescharacteristic
34C2×C8×Dic13C2211yescharacteristic
35C22⋊C4×Dic13C411yescharacteristic
36C22⋊C4×Dic13C411yescharacteristic
37C4×#6101C2211yescharacteristic
38C4×#6101C2211yescharacteristic
39C42×Dic13C2211yescharacteristic
40C42×Dic13C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42C2×C4×#1055C2211yescharacteristic
43#11718310C411yescharacteristic
44#11718310C411yescharacteristic
45#11718309C411yescharacteristic
46#11718309C411yescharacteristic
47C13×#336C2211yescharacteristic
48C13×#336C2211yescharacteristic
49#11718142C2211yescharacteristic
50#11718142C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×Dic13C2×C411yescharacteristic
61C23×Dic13C2×C411yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C2×C13×C22⋊C4C2×C411yescharacteristic
67C2×C13×C22⋊C4C2×C411yescharacteristic
68C2×C42×C13C2311yescharacteristic
69C2×C42×C13C2311yescharacteristic
70C2×C22⋊Dic13C2×C411yescharacteristic
71C2×C22⋊Dic13C2×C411yescharacteristic
72C2×#6101C2×C411yescharacteristic
73C2×#6101C2×C411yescharacteristic
74C2×#6101C2×C411yescharacteristic
75C2×#6101C2×C411yescharacteristic
76C2×C4×Dic13—22no—
77C2×C4×Dic13—22no—
78C2×C4×Dic13C2×C411yescharacteristic
79C2×C4×Dic13C2×C411yescharacteristic
80C2×C4×Dic13C2×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×Dic13C2×C411yescharacteristic
88C2×C4×Dic13C2311yescharacteristic
89C2×C4×Dic13C2311yescharacteristic
90C2×C4×Dic13C2311yescharacteristic
91C2×C4×Dic13C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96#88131—24no—
97#88131C818yescomplemented
98C13×C4⋊C8—41no—
99C13×C22⋊C8—22no—
100C13×C22⋊C8—41no—
101C4×C8×C13—22no—
102C13×#95C2×C411yescharacteristic
103C13×#95C2×C411yescharacteristic
104#88071C2×C411yescharacteristic
105#88071C2×C411yescharacteristic
106#88071C2×C411yescharacteristic
107#88071C2×C411yescharacteristic
108#88071C2×C411yescharacteristic
109#88071C2×C411yescharacteristic
110C22⋊#1055—22no—
111C22⋊#1055—41no—
112#88054—22no—
113#88054—22no—
114#88054—41no—
115#88054—41no—
116C8×Dic13—22no—
117C8×Dic13—22no—
118C8×Dic13—22no—
119C8×Dic13—22no—
120C4⋊#1055—41no—
121C4×#1055—22no—
122#22632—131nomaximal, Sylow
123C24×C13C22×C411yescharacteristic
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13C22×C411yescharacteristic
131C22×C4×C13C22×C411yescharacteristic
132C22×C4×C13C22×C411yescharacteristic
133C22×C4×C13C22×C411yescharacteristic
134C22×C4×C13C22×C411yescharacteristic
135C22×C4×C13C2411yescharacteristic
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—41no—
141C22×Dic13C2×C814yes—
142C22×Dic13C22×C411yescharacteristic
143C22×Dic13C22×C411yescharacteristic
144C22×Dic13C22×C411yescharacteristic
145C22×Dic13C22×C411yescharacteristic
146C22×Dic13C22×C411yescharacteristic
147C22×Dic13C22×C411yescharacteristic
148C22×Dic13C22×C411yescharacteristic
149C22×Dic13C22×C411yescharacteristic
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13#4112yes—
162C13×C22⋊C4—22no—
163C13×C22⋊C4C2×C814yes—
164C42×C13—21no—
165C42×C13—21no—
166C42×C13—21no—
167C42×C13—21no—
168C22⋊Dic13—22no—
169C22⋊Dic13C2×C814yes—
170#6101—22no—
171#6101C2×C814yes—
172#6101C2×C814yes—
173#6101M1614yes—
174C4×Dic13—22no—
175C4×Dic13—21no—
176C4×Dic13—21no—
177C4×Dic13—21no—
178C4×Dic13—21no—
179C4×Dic13—21no—
180C4×Dic13—21no—
181C4×Dic13—22no—
182C4×Dic13—22no—
183C4×Dic13—22no—
184C4×Dic13—22no—
185C4×Dic13—22no—
186C4×Dic13—41no—
187C4×Dic13—41no—
188C4×Dic13C2×C814yes—
189C4×Dic13C2×C814yes—
190C4×Dic13#4112yes—
191C4×Dic13#4112yes—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055#4112yes—
204C4×#117—131no—
205#1939—131no—
206#1939—131no—
207#1923—131no—
208#1923—131no—
209#1923—131no—
210#1923D1311yescharacteristic
211#1831—131no—
212#1831—131no—
213#1797—131no—
214C8×C4⋊C4—131no—
215C8×C4⋊C4—131no—
216C4×C22⋊C8—131no—
217#1744—131no—
218#1744—131no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13—21no—
224C23×C13—21no—
225C23×C13C22×C812yes—
226C23×C13C23×C411yescharacteristic
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—21no—
238C2×C4×C13—21no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13C22×C812yes—
244C2×C4×C13C22×C812yes—
245C2×C4×C13C2×M1612yes—
246C2×C4×C13C2×#4111yescharacteristic
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—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—28no—
265C2×Dic13—21no—
266C2×Dic13—21no—
267C2×Dic13—21no—
268C2×Dic13—44no—
269C2×Dic13#11712yes—
270C2×Dic13#11712yes—
271C2×Dic13C22×C812yes—
272C2×Dic13C22×C812yes—
273C2×Dic13C22×C812yes—
274C2×Dic13C22×C812yes—
275C2×Dic13C2×M1612yes—
276C2×Dic13C2×M1612yes—
277C2×Dic13#13112yes—
278C8×C13—22no—
279C8×C13—41no—
280C8×C13—41no—
281C8×C13—41no—
282#1055—22no—
283#1055—41no—
284#1055—41no—
285#1055—41no—
286C2×#117—131no—
287C2×#117—131no—
288C22×C42—131no—
289C2×C4⋊C8—131no—
290C2×C4⋊C8—131no—
291C2×C4⋊C8—131no—
292C2×C4⋊C8—131no—
293C2×C4⋊C8—131no—
294C2×C4⋊C8C2×D1311yescharacteristic
295C2×C22⋊C8—131no—
296C2×C22⋊C8—131no—
297C2×C22⋊C8C2×D1311yescharacteristic
298C2×C22⋊C8C2×D1311yescharacteristic
299C2×C4×C8—131no—
300C2×C4×C8—131no—
301C2×C4×C8—131no—
302C2×C4×C8—131no—
303C2×C4×C8—131no—
304C2×C4×C8C2×D1311yescharacteristic
305C4×C4⋊C4—131no—
306C4×C4⋊C4—131no—
307C4×C4⋊C4—131no—
308C4×C4⋊C4—131no—
309C4×C22⋊C4—131no—
310C4×C22⋊C4—131no—
311C4×C22⋊C4—131no—
312C4×C22⋊C4C2×D1311yescharacteristic
313#376—131no—
314#376—131no—
315C43—131no—
316C43—131no—
317#336—131no—
318#336—131no—
319#336—131no—
320#336—131no—
321#336—131no—
322#336—131no—
323#336—131no—
324#336—131no—
325#336—131no—
326#336—131no—
327#336C2×D1311yescharacteristic
328#336C2×D1311yescharacteristic
329C22×C13—22no—
330C22×C13—22no—
331C22×C13—22no—
332C22×C13—41no—
333C22×C13—41no—
334C22×C13—41no—
335C22×C13—41no—
336C22×C13C2×#11711yescharacteristic
337C22×C13C4×#4111yescharacteristic
338C22×C13#52011yescharacteristic
339C22×C13C23×C811yescharacteristic
340C22×C13C22×M1611yescharacteristic
341C22×C13C2×#13111yescharacteristic
342C22×C13#56811yescharacteristic
343C4×C13—22no—
344C4×C13—22no—
345C4×C13—22no—
346C4×C13—41no—
347C4×C13—41no—
348C4×C13#55211yescharacteristic
349C4×C13#55211yescharacteristic
350C4×C13#55511yescharacteristic
351C4×C13#55511yescharacteristic
352Dic13—22no—
353Dic13—22no—
354Dic13—22no—
355Dic13—22no—
356Dic13—22no—
357Dic13—22no—
358Dic13—41no—
359Dic13#43114yes—
360C23×C4—131no—
361C23×C4—131no—
362C23×C4C22×D1311yescharacteristic
363C22×C8—131no—
364C22×C8—131no—
365C22×C8—131no—
366C22×C8—131no—
367C22×C8C22×D1311yescharacteristic
368C22×C8C22×D1311yescharacteristic
369C22×C8C22×D1311yescharacteristic
370C22×C8C22×D1311yescharacteristic
371#117—138no—
372#117—264no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—131no—
376C2×C4⋊C4—131no—
377C2×C22⋊C4—131no—
378C2×C22⋊C4—131no—
379C2×C22⋊C4C4×D1311yescharacteristic
380C2×C22⋊C4C4×D1311yescharacteristic
381C2×C42—131no—
382C2×C42—131no—
383C2×C42—131no—
384C2×C42—131no—
385C2×C42—131no—
386C2×C42—131no—
387C2×C42—131no—
388C2×C42—131no—
389C2×C42—131no—
390C2×C42—131no—
391C2×C42—131no—
392C2×C42—131no—
393C2×C42—131no—
394C2×C42—131no—
395C2×C42—262no—
396C2×C42—262no—
397C2×C42C22×D1311yescharacteristic
398C2×C42C22×D1311yescharacteristic
399C4⋊C8—41no—
400C4⋊C8—262no—
401C4⋊C8—262no—
402C4⋊C8—521no—
403C4⋊C8—521no—
404C4⋊C8—521no—
405C22⋊C8—22no—
406C22⋊C8—41no—
407C22⋊C8—262no—
408C22⋊C8—521no—
409C4×C8—22no—
410C4×C8—262no—
411C4×C8—262no—
412C4×C8—262no—
413C4×C8—262no—
414C4×C8—262no—
415#95—131no—
416#95—131no—
417#95—131no—
418#95—131no—
419#95—131no—
420#95—131no—
421#95C4×D1311yescharacteristic
422#95C4×D1311yescharacteristic
423C2×C13—42no—
424C2×C13#234611yescharacteristic
425C2×C13C2×#43111yescharacteristic
426C2×C13#292411yescharacteristic
427C2×C13C8×#4111yescharacteristic
428C2×C13#297011yescharacteristic
429C2×C13#298811yescharacteristic
430C2×C13#299111yescharacteristic
431C24C2×C4×D1311yescharacteristic
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—131no—
439C22×C4—134no—
440C22×C4—131no—
441C22×C4—131no—
442C22×C4—131no—
443C22×C4—131no—
444C22×C4—131no—
445C22×C4—131no—
446C22×C4—131no—
447C22×C4—262no—
448C22×C4—262no—
449C22×C4—262no—
450C22×C4—262no—
451C22×C4—521no—
452C22×C4C2×C4×D1311yescharacteristic
453C22×C4C2×C4×D1311yescharacteristic
454C22×C4C2×C4×D1311yescharacteristic
455C22×C4C2×C4×D1311yescharacteristic
456C22×C4C2×C4×D1311yescharacteristic
457C22×C4C23×D1311yescharacteristic
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—132no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C2×C8—261no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8—261no—
480C2×C8—261no—
481C2×C8#612912yes—
482C4⋊C4—134no—
483C4⋊C4—134no—
484C4⋊C4—134no—
485C4⋊C4—262no—
486C22⋊C4—22no—
487C22⋊C4—134no—
488C22⋊C4—262no—
489C22⋊C4C8×D1314yes—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—134no—
495C42—134no—
496C42—132no—
497C42—132no—
498C42—262no—
499C42—262no—
500C42—262no—
501C42—262no—
502C42—262no—
503C42—262no—
504C42—261no—
505C42—261no—
506C42—261no—
507C42—261no—
508C42—261no—
509C42—261no—
510C42—521no—
511C42—521no—
512C13#2263211yescharacteristic, complemented, Sylow
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23C2×C8×D1312yes—
520C23C22×C4×D1311yescharacteristic
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—132no—
538C2×C4—132no—
539C2×C4—132no—
540C2×C4—132no—
541C2×C4—132no—
542C2×C4—132no—
543C2×C4—132no—
544C2×C4—132no—
545C2×C4—132no—
546C2×C4—268no—
547C2×C4—261no—
548C2×C4—261no—
549C2×C4—261no—
550C2×C4—261no—
551C2×C4—261no—
552C2×C4—261no—
553C2×C4—261no—
554C2×C4—261no—
555C2×C4—261no—
556C2×C4—261no—
557C2×C4—261no—
558C2×C4—261no—
559C2×C4—261no—
560C2×C4—261no—
561C2×C4—261no—
562C2×C4—524no—
563C2×C4C2×C8×D1312yes—
564C2×C4C2×C8×D1312yes—
565C2×C4M16×D1312yes—
566C2×C4C2×#612911yescharacteristic
567C2×C4#8825111yescharacteristic
568C2×C4#41×D1311yescharacteristic
569C2×C4#41×D1311yescharacteristic
570C2×C4#41×D1311yescharacteristic
571C2×C4#8825711yescharacteristic
572C8—22no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—262no—
577C8—521no—
578C8—521no—
579C8—521no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22D13×#11711yescharacteristic
588C22C4×#612911yescharacteristic
589C22#1171925111yescharacteristic
590C22C22×C8×D1311yescharacteristic
591C22C2×M16×D1311yescharacteristic
592C22D13×#13111yescharacteristic
593C22#1171945511yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—41no—
598C4—41no—
599C4—134no—
600C4—262no—
601C4—262no—
602C4—262no—
603C4—262no—
604C4—262no—
605C4—262no—
606C4—521no—
607C4#1171932111yescharacteristic
608C4#1171935511yescharacteristic
609C4#1171937511yescharacteristic
610C4#1171941311yescharacteristic
611C2—42no—
612C2#1311771811yescharacteristic
613C2D13×#43111yescharacteristic
614C2#1312349211yescharacteristic
615C2C8×#612911yescharacteristic
616C2#1312384611yescharacteristic
617C2#1312394311yescharacteristic
618C2#1312396411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutatorC22×C13C23×C8
FittingC13×#1923C2
socleC23×C13C23×C4
prime radicalC24×C13C22×C4
cosocleC22×C4×C13C24
hypercenter#1923D13
hypocenterC13#22632
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
2. #13115553C2semidirect
3. #13115551C2semidirect
7. #13114952C2semidirect
8. #13114951C2semidirect
10. C8×#6101C2semidirect
11. #13114697C2semidirect
13. #13114581C2semidirect
14. #13114580C2semidirect
97. #88131C8semidirect
512. C13#22632semidirect

Maximal subgroups

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

subgroupindex
C4×#881312
#131155532
#131155512
#131154452
#131154442
#131154392
#131149522
#131149512
#131148142
C8×#61012
#131146972
C22⋊C8×Dic132
#131145812
#131145802
C13×#19232
#2263213