Finite Group Databasebeta

← #15925870

Subgroups — #15925870

Order 3328.

968 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718668C211yesmaximal, characteristic, complemented
2C2×C4×#6104C211yesmaximal, characteristic
3#13118686C211yesmaximal, characteristic, complemented
4#13116365C211yesmaximal, characteristic, complemented
5#13116308C211yesmaximal, characteristic, complemented
6#13116221C211yesmaximal, characteristic, complemented
7#13116164C211yesmaximal, characteristic, complemented
8#13115566C211yesmaximal, characteristic, complemented
9#13115395C211yesmaximal, characteristic, complemented
10#13115184C211yesmaximal, characteristic
11#13115184C211yesmaximal, characteristic
12#13115083C211yesmaximal, characteristic, complemented
13#13115083C211yesmaximal, characteristic, complemented
14#13115082C211yesmaximal, characteristic, complemented
15D4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
16C2×C4×D4×C13C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C22×C13×C4⋊C4—21no—
20C22×#6104C2211yescharacteristic
21C2×#88150—21no—
22C2×C4×D52C2211yescharacteristic
23C2×#88123C2211yescharacteristic
24C13×#389C2211yescharacteristic
25C13×#389C2211yescharacteristic
26C13×#385—21no—
27C13×#385—21no—
28C13×#384C2211yescharacteristic
29C13×#380—21no—
30C4×C13×C4⋊C4C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34C4×#6104—24no—
35#11718668—24no—
36#11718655—21no—
37C2×#88049C2211yescharacteristic
38C2×#88049C2211yescharacteristic
39C2×#88049C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45#11718600C2211yescharacteristic
46#11718600C2211yescharacteristic
47#11718589C2211yescharacteristic
48#11718589C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4×#1055C2211yescharacteristic
51#11718334—21no—
52#11718329—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×D4×C13C2311yescharacteristic
62C23×C4×C13—21no—
63C23×C4×C13—21no—
64C23×C4×C13—21no—
65C22×D52C2311yescharacteristic
66C22×C4×D13—21no—
67C22×Dic26—21no—
68C4×D4×C13—22no—
69C4×D4×C13—22no—
70C4×D4×C13—22no—
71C4×D4×C13—22no—
72C4×D4×C13—41no—
73C4×D4×C13—41no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—44no—
79C2×C13×C4⋊C4D411yescharacteristic
80C2×C13×C4⋊C4D411yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C4⋊C4C2311yescharacteristic
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4—21no—
86C2×C13×C22⋊C4—21no—
87C2×C42×C13C2311yescharacteristic
88C2×C42×C13C2311yescharacteristic
89C2×C42×C13C2311yescharacteristic
90C2×#6104—22no—
91C2×#6104—22no—
92C2×#6104Q814yescomplemented
93C2×#6103—21no—
94C2×#6103—21no—
95C2×#6103—21no—
96C2×#6103—21no—
97C2×#6103—21no—
98C2×C4⋊Dic13—21no—
99C2×C4⋊Dic13C2311yescharacteristic
100C2×C4⋊Dic13C2311yescharacteristic
101C2×C4⋊Dic13C2311yescharacteristic
102C2×#6101—21no—
103C2×#6101—21no—
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108#88150—44no—
109C4×D52—22no—
110C4×D52—41no—
111#88123—22no—
112#88123—41no—
113C13×#95—21no—
114C13×#95—21no—
115C13×#95D411yescharacteristic
116C13×#95D411yescharacteristic
117#88072—22no—
118#88072—22no—
119#88072D414yes—
120#88071—21no—
121#88071—21no—
122#88049—22no—
123#88049—22no—
124#88049—41no—
125#88047—22no—
126#88047—22no—
127#88047—22no—
128#88047—22no—
129#88047—41no—
130C4⋊#1055—22no—
131C4×#1055—22no—
132#26368—131nomaximal, Sylow
133C24×C13—21no—
134C23×D13—21no—
135C2×D4×C13—21no—
136C2×D4×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13C2×D412yes—
139C2×D4×C13C2×Q812yes—
140C2×D4×C13#4112yes—
141C22×C4×C13—24no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—42no—
146C22×C4×C13—42no—
147C22×C4×C13—42no—
148C22×C4×C13—42no—
149C22×C4×C13—42no—
150C22×C4×C13—42no—
151C22×C4×C13—81no—
152C22×C4×C13—81no—
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2411yescharacteristic
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C2×D52—21no—
164C2×D52—21no—
165C2×D52—21no—
166C2×D52—21no—
167C2×D52—21no—
168C2×D52C2×Q812yes—
169C2×C4×D13—42no—
170C2×C4×D13—42no—
171C2×C4×D13—81no—
172C2×Dic26—42no—
173C2×Dic26—42no—
174C2×Dic26—81no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—41no—
181C13×C4⋊C4—42no—
182C13×C4⋊C4—42no—
183C13×C4⋊C4—42no—
184C13×C4⋊C4—81no—
185C13×C4⋊C4D814yescomplemented
186C13×C4⋊C4#4112yes—
187C13×C22⋊C4—24no—
188C13×C22⋊C4—42no—
189C13×C22⋊C4—42no—
190C42×C13—21no—
191C42×C13—21no—
192C42×C13—21no—
193C42×C13—21no—
194C42×C13—21no—
195C42×C13—21no—
196#6104—28no—
197#6103—42no—
198#6103—42no—
199#6103—42no—
200#6103—42no—
201#6103—81no—
202C4⋊Dic13—21no—
203C4⋊Dic13—21no—
204C4⋊Dic13—21no—
205C4⋊Dic13—21no—
206C4⋊Dic13—21no—
207C4⋊Dic13—42no—
208C4⋊Dic13C2×D412yes—
209#6101—42no—
210#6101—42no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055—21no—
219C2×#1055—21no—
220C2×#1055—21no—
221C2×#1055C2×D412yes—
222C2×#1055C2×Q812yes—
223C2×#474—131no—
224C2×C4×D8—131no—
225#2452—131no—
226D4×C4⋊C4D1311yescharacteristic, complemented
227#2093—131no—
228#2083—131no—
229#2067—131no—
230#2057—131no—
231#1942—131no—
232#1916—131no—
233#1879—131no—
234#1879—131no—
235#1862—131no—
236#1862—131no—
237#1862—131no—
238C23×C13—22no—
239C23×C13—22no—
240C23×C13—22no—
241C23×C13—41no—
242C23×C13—41no—
243C23×C13—41no—
244C23×C13—41no—
245C23×C13C22×D411yescharacteristic
246C22×D13—22no—
247C22×D13—41no—
248C22×D13—41no—
249C22×D13—41no—
250C22×D13—41no—
251C22×D13—41no—
252C22×D13—41no—
253D4×C13—22no—
254D4×C13—22no—
255D4×C13—22no—
256D4×C13C22⋊Q814yescomplemented
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—22no—
265C2×C4×C13—21no—
266C2×C4×C13—21no—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—21no—
273C2×C4×C13—48no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C2×C4×C13—41no—
278C2×C4×C13—41no—
279C2×C4×C13—41no—
280C2×C4×C13—41no—
281C2×C4×C13—41no—
282C2×C4×C13—84no—
283C2×C4×C13—84no—
284C2×C4×C13C2×D812yes—
285C2×C4×C13C2×D812yes—
286C2×C4×C13C2×D812yes—
287C2×C4×C13C22×D411yescharacteristic
288C2×C4×C13C22×Q811yescharacteristic
289C2×C4×C13C2×#4111yescharacteristic
290C2×C4×C13C2×#4111yescharacteristic
291C2×C4×C13H(5,𝔽2)11yescharacteristic
292C2×C4×C132−1+411yescharacteristic
293C2×Dic13—22no—
294C2×Dic13—41no—
295C2×Dic13—41no—
296C2×Dic13—41no—
297C2×Dic13—41no—
298C2×Dic13—41no—
299C2×Dic13—41no—
300C2×Dic13—41no—
301C2×Dic13—41no—
302D52—22no—
303D52—22no—
304D52—41no—
305D52—41no—
306C4×D13—84no—
307Dic26—84no—
308#1055—22no—
309#1055—22no—
310#1055—41no—
311#1055—41no—
312C22×D8—131no—
313C2×C4⋊Q8—131no—
314C2×C22⋊Q8—261no—
315C2×C4×D4—131no—
316C2×C4×D4C2×D1311yescharacteristic
317C2×C4×D4C2×D1311yescharacteristic
318C2×C4×D4C2×D1311yescharacteristic
319C22×C4⋊C4—21no—
320#474—264no—
321C4×D8—264no—
322C2×#107—131no—
323C2×#107—131no—
324C2×#107—131no—
325C2×#107—131no—
326C2×#107—131no—
327C2×C4⋊C8—131no—
328C2×#102—131no—
329C2×#102—131no—
330C2×#102—131no—
331C2×#102—131no—
332C2×#102—131no—
333C2×#102—131no—
334C2×C4×C8—131no—
335#396—261no—
336#393—261no—
337#390—131no—
338#390—131no—
339#389—131no—
340#389—131no—
341#389C2×D1311yescharacteristic
342#389C2×D1311yescharacteristic
343#385—21no—
344#385—21no—
345#385—261no—
346#384C2×D1311yescharacteristic
347#380—21no—
348C4×C4⋊C4C2×D1311yescharacteristic
349#340—131no—
350#340—131no—
351#340—131no—
352#340—131no—
353#336—131no—
354#336—131no—
355#336—131no—
356#336—131no—
357C22×C13—24no—
358C22×C13—42no—
359C22×C13—42no—
360C22×C13—42no—
361C22×C13—42no—
362C22×C13—42no—
363C22×C13—42no—
364C22×C13#52511yescharacteristic
365C22×C13D4211yescharacteristic
366C22×C13D4×Q811yescharacteristic
367C22×C13C22×D811yescharacteristic
368C22×C13#57511yescharacteristic
369C22×C13#57611yescharacteristic
370C22×C13#57811yescharacteristic
371C2×D13—42no—
372C2×D13—42no—
373C2×D13—42no—
374C2×D13—81no—
375C2×D13—81no—
376C2×D13—81no—
377C2×D13—81no—
378C4×C13—22no—
379C4×C13—22no—
380C4×C13—22no—
381C4×C13—42no—
382C4×C13—41no—
383C4×C13—41no—
384C4×C13—41no—
385C4×C13—81no—
386C4×C13—81no—
387C4×C13C2×C22⋊Q811yescharacteristic
388C4×C13#53911yescharacteristic
389C4×C13#54711yescharacteristic
390C4×C13#55411yescharacteristic
391Dic13—42no—
392Dic13—81no—
393Dic13—81no—
394C22×Q8—261no—
395C22×D4—131no—
396C22×D4C22×D1311yescharacteristic
397C23×C4—21no—
398C23×C4—21no—
399C23×C4—21no—
400C23×C4—261no—
401C2×D8—134no—
402C2×D8—262no—
403C2×D8—262no—
404C22×C8—131no—
405C22×C8—131no—
406C22×C8—131no—
407C22×C8—131no—
408C4⋊Q8—262no—
409C4⋊Q8—521no—
410C22⋊Q8—524no—
411C4×D4—22no—
412C4×D4—22no—
413C4×D4—22no—
414C4×D4—22no—
415C4×D4—41no—
416C4×D4—41no—
417C4×D4—262no—
418C4×D4—521no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—44no—
424C2×C4⋊C4—131no—
425C2×C4⋊C4—131no—
426C2×C4⋊C4—131no—
427C2×C4⋊C4—261no—
428C2×C4⋊C4—261no—
429C2×C4⋊C4—261no—
430C2×C4⋊C4C22⋊D1311yescharacteristic
431C2×C4⋊C4C22⋊D1311yescharacteristic
432C2×C4⋊C4C22×D1311yescharacteristic
433C2×C4⋊C4C22×D1311yescharacteristic
434C2×C4⋊C4C22×D1311yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—261no—
439C2×C22⋊C4—261no—
440C2×C22⋊C4—261no—
441C2×C22⋊C4—261no—
442C2×C22⋊C4—261no—
443C2×C42C22×D1311yescharacteristic
444C2×C42C22×D1311yescharacteristic
445C2×C42C22×D1311yescharacteristic
446#107—262no—
447#107—262no—
448#107—262no—
449#107—262no—
450#107—521no—
451C4⋊C8—262no—
452#102—134no—
453#102—262no—
454#102—262no—
455#102—262no—
456#102—262no—
457#102—521no—
458C4×C8—262no—
459#95—21no—
460#95—21no—
461#95—261no—
462#95—261no—
463#95C22⋊D1311yescharacteristic
464#95C22⋊D1311yescharacteristic
465C2×C13—44no—
466C2×C13#244911yescharacteristic
467C2×C13#310011yescharacteristic
468C2×C13#312411yescharacteristic
469C2×C13#326911yescharacteristic
470C2×C13D4×D811yescharacteristic
471C2×C13Q8×D811yescharacteristic
472C2×C13#338911yescharacteristic
473D13—82no—
474C24—21no—
475C24—261no—
476C2×Q8—522no—
477C2×Q8—522no—
478C2×Q8—1041no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—132no—
483C2×D4—261no—
484C2×D4—261no—
485C2×D4—261no—
486C2×D4—261no—
487C2×D4—261no—
488C2×D4#612712yes—
489C2×D4D4×D1312yes—
490C2×D4Q8×D1312yes—
491C22×C4—24no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—81no—
502C22×C4—81no—
503C22×C4—261no—
504C22×C4—261no—
505C22×C4—261no—
506C22×C4—522no—
507C22×C4—522no—
508C22×C4—1041no—
509C22×C4C2×C22⋊D1311yescharacteristic
510C22×C4C2×C22⋊D1311yescharacteristic
511C22×C4C2×C22⋊D1311yescharacteristic
512C22×C4C2×C22⋊D1311yescharacteristic
513C22×C4C2×C22⋊D1311yescharacteristic
514C22×C4C2×C22⋊D1311yescharacteristic
515C22×C4C23×D1311yescharacteristic
516D8—268no—
517C2×C8—132no—
518C2×C8—132no—
519C2×C8—261no—
520C2×C8—261no—
521C2×C8—261no—
522C2×C8—261no—
523C2×C8—261no—
524C2×C8—261no—
525C2×C8—261no—
526C2×C8—261no—
527C2×C8—261no—
528C2×C8—261no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—41no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—81no—
539C4⋊C4—132no—
540C4⋊C4—261no—
541C4⋊C4—261no—
542C4⋊C4—261no—
543C4⋊C4—261no—
544C4⋊C4—261no—
545C4⋊C4—522no—
546C4⋊C4—522no—
547C4⋊C4—522no—
548C4⋊C4#610414yescomplemented
549C4⋊C4#612712yes—
550C22⋊C4—24no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—522no—
554C22⋊C4—522no—
555C22⋊C4—522no—
556C22⋊C4—522no—
557C22⋊C4—1041no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—21no—
564C13#2636811yescharacteristic, complemented, Sylow
565C23—22no—
566C23—22no—
567C23—22no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—262no—
573C23—521no—
574C23—521no—
575C23—521no—
576C23—521no—
577C23—521no—
578C23—521no—
579C23C22×C22⋊D1311yescharacteristic
580Q8—1044no—
581D4—22no—
582D4—22no—
583D4—22no—
584D4—262no—
585D4—262no—
586D4—521no—
587D4—521no—
588D4#8815014yescomplemented
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—48no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—84no—
615C2×C4—84no—
616C2×C4—262no—
617C2×C4—521no—
618C2×C4—521no—
619C2×C4—521no—
620C2×C4—521no—
621C2×C4—521no—
622C2×C4—521no—
623C2×C4—521no—
624C2×C4—521no—
625C2×C4—1044no—
626C2×C4C2×#610412yes—
627C2×C4C2×#610412yes—
628C2×C4C2×#610412yes—
629C2×C4C2×#612711yescharacteristic
630C2×C4C2×#612711yescharacteristic
631C2×C4C2×D4×D1311yescharacteristic
632C2×C4#8825111yescharacteristic
633C2×C4C2×Q8×D1311yescharacteristic
634C2×C4#8825411yescharacteristic
635C8—262no—
636C8—262no—
637C8—521no—
638C8—521no—
639C22—24no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—522no—
647C22—522no—
648C22—522no—
649C22—1041no—
650C22—1041no—
651C22—1041no—
652C22—1041no—
653C22#1171949611yescharacteristic
654C22C22×#610411yescharacteristic
655C22D4×C22⋊D1311yescharacteristic
656C22Q8×C22⋊D1311yescharacteristic
657C22#1171952711yescharacteristic
658C22#1171954011yescharacteristic
659C22#1171954311yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—42no—
664C4—41no—
665C4—41no—
666C4—41no—
667C4—81no—
668C4—81no—
669C4—522no—
670C4—1041no—
671C4—1041no—
672C4#1171921211yescharacteristic
673C4C2×#8815011yescharacteristic
674C4#1171921611yescharacteristic
675C4#1171922011yescharacteristic
676C2—44no—
677C2—1042no—
678C2#1311864511yescharacteristic
679C2#1312483611yescharacteristic
680C2#1312509811yescharacteristic
681C2#1312638711yescharacteristic
682C2D4×#610411yescharacteristic
683C2Q8×#610411yescharacteristic
684C2#1312779011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingD4×C13×C4⋊C4C2
socleC23×C13C22×D4
prime radicalC22×#6104C22
hypercenterD4×C4⋊C4D13
hypocenterC13#26368
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11718668C2semidirect
3. #13118686C2semidirect
4. #13116365C2semidirect
5. #13116308C2semidirect
6. #13116221C2semidirect
7. #13116164C2semidirect
8. #13115566C2semidirect
9. #13115395C2semidirect
12. #13115083C2semidirect
13. #13115083C2semidirect
14. #13115082C2semidirect
15. D4×C13×C4⋊C4C2semidirect
92. C2×#6104Q8semidirect
185. C13×C4⋊C4D8semidirect
226. D4×C4⋊C4D13semidirect
256. D4×C13C22⋊Q8semidirect
548. C4⋊C4#6104semidirect
564. C13#26368semidirect
588. D4#88150semidirect

Maximal subgroups

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

subgroupindex
C2×#117186682
C2×C4×#61042
#131186862
#131163652
#131163082
#131162212
#131161642
#131155662
#131153952
#131151842
#131150832
#131150822
D4×C13×C4⋊C42
#2636813