Finite Group Databasebeta

← #29737517

Subgroups — #29737517

Order 15616.

988 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840059C211yesmaximal, characteristic, complemented
2C2×#16839761C211yesmaximal, characteristic
3#21448650C211yesmaximal, characteristic
4#21447370C211yesmaximal, characteristic, complemented
5#21447211C211yesmaximal, characteristic, complemented
6#21447211C211yesmaximal, characteristic, complemented
7#21446967C211yesmaximal, characteristic, complemented
8#21446065C211yesmaximal, characteristic, complemented
9#21446065C211yesmaximal, characteristic, complemented
10#21446007C211yesmaximal, characteristic, complemented
11#21446004C211yesmaximal, characteristic, complemented
12#21445850C211yesmaximal, characteristic, complemented
13#21445826C211yesmaximal, characteristic, complemented
14#21445757C211yesmaximal, characteristic
15C61×#2442C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20#16840059—24no—
21C2×#14519710C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519710C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×C4⋊#92418C2211yescharacteristic
27#16839761—24no—
28C2×#14519700C2211yescharacteristic
29C2×#14519700C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37#16839668C2211yescharacteristic
38#16839668C2211yescharacteristic
39#16839638—21no—
40#16839638—21no—
41#16839624—21no—
42#16839622C2211yescharacteristic
43#95×D61—21no—
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C2×#125×C61C2211yescharacteristic
51C22×C4⋊C4×C61C2211yescharacteristic
52C61×#400—21no—
53C61×#398—21no—
54C61×#389C2211yescharacteristic
55C61×#389C2211yescharacteristic
56C61×#385—21no—
57C61×#382C2211yescharacteristic
58C61×#380—21no—
59C61×#380C2211yescharacteristic
60C4×C22⋊C4×C61C2211yescharacteristic
61C2×#11758222—22no—
62C2×#11758222—22no—
63C2×#11758222—22no—
64C2×#11758222—41no—
65C2×#11758222—41no—
66C2×#11758222Q814yes—
67C22×Dic122C2311yescharacteristic
68C22×D244C2311yescharacteristic
69C22×C22⋊D61—21no—
70C22×C4×D61—21no—
71C22×C4×D61—21no—
72C22×C4×D61—21no—
73C2×#11758194—22no—
74C2×#11758194—22no—
75C2×#11758194—41no—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C4×D244—22no—
81C4×D244—22no—
82C4×D244—41no—
83C4×D244—41no—
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C22⋊Dic61—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89#14519710—22no—
90#14519710—41no—
91#14519710—41no—
92#14519708—22no—
93C4⋊#92418—22no—
94C4⋊#92418—41no—
95#14519700—22no—
96#14519700—22no—
97#14519700—41no—
98#14519700—41no—
99#14519697—22no—
100#14519697—22no—
101#14519697—22no—
102#14519697D414yes—
103C22⋊#92418—22no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109C23×C4×C61—21no—
110C23×C4×C61C2311yescharacteristic
111#125×C61—22no—
112#125×C61—41no—
113C2×C4⋊C4×C61—22no—
114C2×C4⋊C4×C61—21no—
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61—21no—
117C2×C4⋊C4×C61—21no—
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61—41no—
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61D411yescharacteristic
126C2×C22⋊C4×C61D411yescharacteristic
127C2×C42×C61C2311yescharacteristic
128C2×C42×C61C2311yescharacteristic
129#95×C61—21no—
130#95×C61—21no—
131#95×C61—21no—
132#95×C61—21no—
133#95×C61—21no—
134#95×C61D411yescharacteristic
135#95×C61D411yescharacteristic
136C24×C61C2×D411yescharacteristic
137C23×D61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—42no—
147C22×C4×C61—42no—
148C22×C4×C61—81no—
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×Q812yes—
155C22×C4×C61#4112yes—
156C22×C4×C61C2411yescharacteristic
157C2×C22⋊D61—24no—
158C2×C22⋊D61—42no—
159C2×C22⋊D61—42no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163#11758222—28no—
164#11758222—44no—
165#11758222—44no—
166#11758222—44no—
167C2×D244—21no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244C2×D412yes—
171C2×D244C2×Q812yes—
172C2×D244#4112yes—
173C2×C4×D61—24no—
174C2×C4×D61—42no—
175C2×C4×D61—42no—
176C2×C4×D61—42no—
177C2×C4×D61—42no—
178C2×C4×D61—42no—
179C2×C4×D61—42no—
180C2×C4×D61—81no—
181C2×C4×D61—81no—
182C2×Dic122—21no—
183C2×Dic122—21no—
184C2×Dic122—21no—
185C2×Dic122—21no—
186C2×Dic122—21no—
187C2×Dic122C2×Q812yes—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—42no—
196C4⋊C4×C61—42no—
197C4⋊C4×C61—42no—
198C4⋊C4×C61—81no—
199C4⋊C4×C61—81no—
200C4⋊C4×C61C2×D412yes—
201C22⋊C4×C61—41no—
202C22⋊C4×C61—41no—
203C22⋊C4×C61—42no—
204C42×C61—21no—
205C42×C61—21no—
206C42×C61—21no—
207C42×C61—21no—
208C22⋊Dic61—81no—
209#11758198—42no—
210#11758198—42no—
211C4⋊Dic61—21no—
212C4⋊Dic61—21no—
213C4⋊Dic61—21no—
214C4⋊Dic61—21no—
215#11758194—44no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—21no—
219C2×#92418—21no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418—21no—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418C2×D412yes—
228C23×C61—21no—
229C23×C61—21no—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61C22⋊Q812yes—
235C23×C61C22×D411yescharacteristic
236C22×D61—22no—
237C22×D61—22no—
238C22×D61—22no—
239C22×D61—41no—
240C22×D61—41no—
241C22×D61—41no—
242C22×D61—41no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—22no—
248C2×C4×C61—22no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—22no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—84no—
274C2×C4×C61C22⋊Q812yes—
275C2×C4×C61C22×D411yescharacteristic
276C2×C4×C61C22×Q811yescharacteristic
277C2×C4×C61C2×#4111yescharacteristic
278C2×C4×C61C2×#4111yescharacteristic
279C2×C4×C61H(5,𝔽2)11yescharacteristic
280C2×C4×C61H(5,𝔽2)11yescharacteristic
281C22⋊D61—48no—
282C2×Dic61—22no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289C2×Dic61—41no—
290C2×Dic61—41no—
291D244—22no—
292D244—22no—
293D244—22no—
294D244C22⋊Q814yes—
295C4×D61—48no—
296C4×D61—84no—
297C4×D61—84no—
298Dic122—22no—
299Dic122—22no—
300Dic122—41no—
301Dic122—41no—
302#92418—22no—
303#92418—41no—
304#92418—41no—
305#92418—41no—
306#25980—611nomaximal, Sylow
307C22×C61—22no—
308C22×C61—22no—
309C22×C61—22no—
310C22×C61—41no—
311C22×C61—41no—
312C22×C61—41no—
313C22×C61—41no—
314C22×C61C2×C22⋊Q811yescharacteristic
315C22×C61D4211yescharacteristic
316C22×C61#54611yescharacteristic
317C22×C61#57511yescharacteristic
318C22×C61#57511yescharacteristic
319C22×C61#57611yescharacteristic
320C22×C61#57811yescharacteristic
321C2×D61—24no—
322C2×D61—42no—
323C2×D61—42no—
324C2×D61—42no—
325C2×D61—42no—
326C2×D61—42no—
327C2×D61—42no—
328C4×C61—22no—
329C4×C61—41no—
330C4×C61—41no—
331C4×C61—42no—
332C4×C61—41no—
333C4×C61—41no—
334C4×C61—81no—
335C4×C61—81no—
336C4×C61—81no—
337C4×C61C2×C22⋊Q811yescharacteristic
338C4×C61#54311yescharacteristic
339C4×C61#54611yescharacteristic
340C4×C61#55111yescharacteristic
341Dic61—42no—
342Dic61—81no—
343Dic61—81no—
344C2×#478—611no—
345C2×#417—611no—
346#2442D6111yescharacteristic, complemented
347#2339—611no—
348#2097—611no—
349#2068—611no—
350#2068—611no—
351#2026—611no—
352#1862—611no—
353#1862—611no—
354#1852—611no—
355#1851—611no—
356#1809—611no—
357#1804—611no—
358#1788—611no—
359C2×C61—42no—
360C2×C61#243711yescharacteristic
361C2×C61#308011yescharacteristic
362C2×C61#308311yescharacteristic
363C2×C61#326911yescharacteristic
364C2×C61#327311yescharacteristic
365C2×C61#331511yescharacteristic
366C2×C61#332211yescharacteristic
367D61—44no—
368C22×#41—611no—
369C22×M16—611no—
370C2×#125C2×D6111yescharacteristic
371C2×C4×D4—611no—
372C2×C4×D4—611no—
373C22×C4⋊C4C2×D6111yescharacteristic
374#478—1224no—
375C2×#107—611no—
376C2×#107—611no—
377C2×#107—611no—
378C2×#106—611no—
379C2×C4⋊C8—611no—
380C2×C4⋊C8—611no—
381#417—1224no—
382C2×#103—611no—
383C2×#103—611no—
384C2×#103—611no—
385C2×#103—611no—
386C2×#102—611no—
387C2×#102—611no—
388C2×#102—611no—
389C2×#102—611no—
390C2×C22⋊C8—611no—
391#400—21no—
392#398—21no—
393#391—611no—
394#391—611no—
395#389C2×D6111yescharacteristic
396#389C2×D6111yescharacteristic
397#386—1221no—
398#386—1221no—
399#385—21no—
400#382C2×D6111yescharacteristic
401#381—1221no—
402#380—21no—
403#380—611no—
404#380C2×D6111yescharacteristic
405C4×C22⋊C4C2×D6111yescharacteristic
406C2×#95—1221no—
407#340—611no—
408#340—611no—
409#340—611no—
410#340—611no—
411#336—611no—
412#336—611no—
413C61#2598011yescharacteristic, complemented, Sylow
414C2×#41—614no—
415C2×#41—1222no—
416C2×#41—1222no—
417C2×#41—1222no—
418C2×#41—2441no—
419C2×#41—2441no—
420C22×Q8—611no—
421C22×D4—611no—
422C22×D4—1221no—
423C23×C4—21no—
424C23×C4—1221no—
425C23×C4—1221no—
426C23×C4—1221no—
427C23×C4C22×D6111yescharacteristic
428C2×M16—1222no—
429C2×M16—1222no—
430C2×M16—2441no—
431C22×C8—611no—
432C22×C8—611no—
433C22×C8—611no—
434C22×C8—611no—
435#125—22no—
436#125—41no—
437C4×D4—1222no—
438C4×D4—1222no—
439C4×D4—2441no—
440C4×D4—2441no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—41no—
448C2×C4⋊C4—611no—
449C2×C4⋊C4—611no—
450C2×C4⋊C4C22×D6111yescharacteristic
451C2×C4⋊C4C22×D6111yescharacteristic
452C2×C4⋊C4C22×D6111yescharacteristic
453C2×C4⋊C4C22×D6111yescharacteristic
454C2×C22⋊C4—21no—
455C2×C22⋊C4—1221no—
456C2×C22⋊C4—1221no—
457C2×C22⋊C4—1221no—
458C2×C22⋊C4C22⋊D6111yescharacteristic
459C2×C22⋊C4C22⋊D6111yescharacteristic
460C2×C42C22×D6111yescharacteristic
461C2×C42C22×D6111yescharacteristic
462#107—1222no—
463#107—2441no—
464#107—2441no—
465#106—1222no—
466C4⋊C8—1222no—
467C4⋊C8—2441no—
468#103—1222no—
469#103—1222no—
470#103—2441no—
471#103—2441no—
472#102—614no—
473#102—1222no—
474#102—1222no—
475#102—1222no—
476C22⋊C8—1222no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—1221no—
483#95—1221no—
484#95—1221no—
485#95—1221no—
486#95—1221no—
487#95C22⋊D6111yescharacteristic
488#95C22⋊D6111yescharacteristic
489C24—1221no—
490C24C2×C22⋊D6111yescharacteristic
491#41—1228no—
492#41—2444no—
493#41—2444no—
494#41—2444no—
495C2×Q8—612no—
496C2×Q8—1221no—
497C2×Q8—1221no—
498C2×Q8—1221no—
499C2×Q8—1221no—
500C2×Q8—1221no—
501C2×D4—612no—
502C2×D4—612no—
503C2×D4—612no—
504C2×D4—1224no—
505C2×D4—1221no—
506C2×D4—1221no—
507C2×D4—1221no—
508C2×D4—2442no—
509C2×D4—2442no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—81no—
521C22×C4—1221no—
522C22×C4—1224no—
523C22×C4—1221no—
524C22×C4—1221no—
525C22×C4—4881no—
526C22×C4—4881no—
527C22×C4—2442no—
528C22×C4—2442no—
529C22×C4—2442no—
530C22×C4—2442no—
531C22×C4—2442no—
532C22×C4—2442no—
533C22×C4Q8×D6112yes—
534C22×C4#1175822612yes—
535C22×C4C2×C22⋊D6111yescharacteristic
536C22×C4C2×C22⋊D6111yescharacteristic
537C22×C4C2×C22⋊D6111yescharacteristic
538C22×C4C2×C22⋊D6111yescharacteristic
539C22×C4C2×C22⋊D6111yescharacteristic
540C22×C4C23×D6111yescharacteristic
541M16—2444no—
542C2×C8—612no—
543C2×C8—1221no—
544C2×C8—1221no—
545C2×C8—1221no—
546C2×C8—1221no—
547C2×C8—1221no—
548C2×C8—1221no—
549C2×C8—1221no—
550C2×C8—1221no—
551C2×C8—1221no—
552C2×C8—1221no—
553C2×C8—1221no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—81no—
565C4⋊C4—81no—
566C4⋊C4—1221no—
567C4⋊C4—1221no—
568C4⋊C4—1221no—
569C4⋊C4—1221no—
570C4⋊C4D4×D6112yes—
571C22⋊C4—41no—
572C22⋊C4—41no—
573C22⋊C4—42no—
574C22⋊C4—4881no—
575C22⋊C4—2442no—
576C22⋊C4—2442no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—1222no—
588C23—1222no—
589C23—1222no—
590C23—2441no—
591C23—2441no—
592C23—2441no—
593C23—2441no—
594C23#1451975312yes—
595C23C22×C22⋊D6111yescharacteristic
596Q8—1222no—
597Q8—1222no—
598Q8—2441no—
599Q8—2441no—
600D4—614no—
601D4—1222no—
602D4—1222no—
603D4—1222no—
604D4—2448no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—84no—
636C2×C4—1222no—
637C2×C4—4884no—
638C2×C4—4884no—
639C2×C4—2448no—
640C2×C4—2441no—
641C2×C4—2441no—
642C2×C4—2441no—
643C2×C4—2441no—
644C2×C4—2441no—
645C2×C4—2441no—
646C2×C4—2441no—
647C2×C4—2441no—
648C2×C4#1451975312yes—
649C2×C4C2×D4×D6111yescharacteristic
650C2×C4C2×Q8×D6111yescharacteristic
651C2×C4#41×D6111yescharacteristic
652C2×C4C2×#1175822611yescharacteristic
653C2×C4#1451982211yescharacteristic
654C2×C4#1451982311yescharacteristic
655C8—1222no—
656C8—2441no—
657C8—2441no—
658C8—2441no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—1224no—
667C22—2442no—
668C22—2442no—
669C22—2442no—
670C22—2442no—
671C22—2442no—
672C22—2442no—
673C22C2×#1451975311yescharacteristic
674C22D4×C22⋊D6111yescharacteristic
675C22#1684040011yescharacteristic
676C22#1684056011yescharacteristic
677C22#1684056011yescharacteristic
678C22#1684056511yescharacteristic
679C22#1684057711yescharacteristic
680C4—22no—
681C4—41no—
682C4—42no—
683C4—41no—
684C4—41no—
685C4—41no—
686C4—81no—
687C4—81no—
688C4—81no—
689C4—4881no—
690C4—4881no—
691C4—2442no—
692C4C22⋊Q8×D6111yescharacteristic
693C4#1684038711yescharacteristic
694C4#1684040311yescharacteristic
695C4#1684043911yescharacteristic
696C2—42no—
697C2—2444no—
698C2#2144948211yescharacteristic
699C2#2145563711yescharacteristic
700C2#2145566611yescharacteristic
701C2#2145737511yescharacteristic
702C2#2145742611yescharacteristic
703C2#2145790911yescharacteristic
704C2#2145801411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2442C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
hypercenter#2442D61
hypocenterC61#25980
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2442

Complements

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

NH ≅ G/Ntype
1. C2×#16840059C2semidirect
4. #21447370C2semidirect
5. #21447211C2semidirect
6. #21447211C2semidirect
7. #21446967C2semidirect
8. #21446065C2semidirect
9. #21446065C2semidirect
10. #21446007C2semidirect
11. #21446004C2semidirect
12. #21445850C2semidirect
13. #21445826C2semidirect
15. C61×#2442C2semidirect
346. #2442D61semidirect
413. C61#25980semidirect

Maximal subgroups

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

subgroupindex
C2×#168400592
C2×#168397612
#214486502
#214473702
#214472112
#214469672
#214460652
#214460072
#214460042
#214458502
#214458262
#214457572
C61×#24422
#2598061