Finite Group Databasebeta

← #29737242

Subgroups — #29737242

Order 15616.

958 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840068C211yesmaximal, characteristic, complemented
2C2×#16839759C211yesmaximal, characteristic
3#21449533C211yesmaximal, characteristic, complemented
4#21448656C211yesmaximal, characteristic
5#21447344C211yesmaximal, characteristic, complemented
6#21447202C211yesmaximal, characteristic, complemented
7#21447194C211yesmaximal, characteristic, complemented
8#21446964C211yesmaximal, characteristic, complemented
9#21446074C211yesmaximal, characteristic, complemented
10#21446070C211yesmaximal, characteristic, complemented
11#21446016C211yesmaximal, characteristic, complemented
12#21445997C211yesmaximal, characteristic, complemented
13#21445823C211yesmaximal, characteristic, complemented
14#21445757C211yesmaximal, characteristic
15C61×#1808C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#14519768C2211yescharacteristic
18C2×#14519742C2211yescharacteristic
19C2×#14519742C2211yescharacteristic
20C2×#14519736C2211yescharacteristic
21#16840068—24no—
22C2×#14519710C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26#16839759—24no—
27C2×#14519702C2211yescharacteristic
28C2×#14519702C2211yescharacteristic
29C2×#14519700C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36#16839698—21no—
37#16839685—21no—
38#16839663C2211yescharacteristic
39#16839663C2211yescharacteristic
40#16839662—21no—
41#16839662—21no—
42#16839661C2211yescharacteristic
43#16839659—21no—
44#16839658C2211yescharacteristic
45#16839649—21no—
46#16839631C2211yescharacteristic
47#16839621—21no—
48C4×C22⋊Dic61C2211yescharacteristic
49#16839609—21no—
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C23×C8×C61C2211yescharacteristic
55C2×#107×C61C2211yescharacteristic
56C2×#107×C61C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#380C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
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×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73#14519768—22no—
74#14519768—41no—
75#14519742—22no—
76#14519742—22no—
77#14519742—41no—
78#14519742—41no—
79#14519736—22no—
80#14519736—41no—
81C2×C4⋊Dic61—21no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×#11758196—21no—
90C2×#11758196—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61D411yescharacteristic
93C2×C22⋊Dic61D411yescharacteristic
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61—21no—
100C2×C4×Dic61—21no—
101C2×C4×Dic61C2311yescharacteristic
102C2×C4×Dic61C2311yescharacteristic
103#14519710—41no—
104#14519708—22no—
105#14519706—22no—
106#14519706—41no—
107#14519702—22no—
108#14519702D414yes—
109#14519700—22no—
110#14519700—22no—
111#14519699—22no—
112#14519699—22no—
113#14519697—41no—
114#14519697—41no—
115C22⋊#92418—22no—
116#14519684—21no—
117#14519684—21no—
118#14519684D411yescharacteristic
119#14519684D411yescharacteristic
120C23×C4×C61C2311yescharacteristic
121C22×C8×C61—22no—
122C22×C8×C61—22no—
123C22×C8×C61—41no—
124C22×C8×C61C2311yescharacteristic
125C22×C8×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132#107×C61—22no—
133#107×C61—41no—
134#95×C61—21no—
135#95×C61—21no—
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×C61C2×D411yescharacteristic
147C22×C4×C61C2×Q812yes—
148C22×C4×C61#4112yes—
149C22×C4×C61C2411yescharacteristic
150C2×C22⋊D61—24no—
151C2×C22⋊D61—42no—
152C2×C22⋊D61—42no—
153C22×Dic61—21no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61C2×D411yescharacteristic
157C22×Dic61C2×D411yescharacteristic
158C22×Dic61C2×D411yescharacteristic
159C22×Dic61C2×D411yescharacteristic
160#11758222—28no—
161#11758222—44no—
162#11758222—44no—
163#11758222—44no—
164C2×D244—21no—
165C2×D244—21no—
166C2×D244—21no—
167C2×D244—21no—
168C2×D244—21no—
169C2×D244C2×Q812yes—
170C2×C4×D61—24no—
171C2×C4×D61—42no—
172C2×C4×D61—42no—
173C2×Dic122—21no—
174C2×Dic122—21no—
175C2×Dic122—21no—
176C2×Dic122C2×D412yes—
177C2×Dic122C2×Q812yes—
178C2×Dic122#4112yes—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C2×C8×C61—44no—
185C2×C8×C61C2×D412yes—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—21no—
194C22⋊C4×C61—81no—
195C22⋊C4×C61—81no—
196C22⋊Dic61—22no—
197C22⋊Dic61—41no—
198C22⋊Dic61—42no—
199#11758198—42no—
200#11758198—42no—
201#11758198—81no—
202#11758198—81no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61—42no—
207C4⋊Dic61—81no—
208C4⋊Dic61C2×D412yes—
209#11758196—42no—
210#11758196—42no—
211#11758196—42no—
212#11758196—42no—
213#11758196—42no—
214#11758196—81no—
215C4×Dic61—21no—
216C4×Dic61—21no—
217C4×Dic61—21no—
218C4×Dic61—21no—
219C4×Dic61—42no—
220C4×Dic61—42no—
221C4×Dic61—42no—
222C2×#92418—21no—
223C2×#92418—21no—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—21no—
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—41no—
238C22×D61—41no—
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—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61C22⋊Q812yes—
262C2×C4×C61C22×D411yescharacteristic
263C2×C4×C61C22×Q811yescharacteristic
264C2×C4×C61C2×#4111yescharacteristic
265C2×C4×C61C2×#4111yescharacteristic
266C2×C4×C61H(5,𝔽2)11yescharacteristic
267C2×C4×C61H(5,𝔽2)11yescharacteristic
268C22⋊D61—48no—
269C2×Dic61—22no—
270C2×Dic61—22no—
271C2×Dic61—21no—
272C2×Dic61—22no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—22no—
277C2×Dic61—21no—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—21no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289C2×Dic61#13512yes—
290D244—22no—
291D244—22no—
292D244—41no—
293D244—41no—
294C4×D61—48no—
295Dic122—22no—
296Dic122—22no—
297Dic122—22no—
298Dic122C22⋊Q814yes—
299C8×C61—22no—
300C8×C61—41no—
301#92418—41no—
302#92418—41no—
303#25961—611nomaximal, Sylow
304C22×C61—22no—
305C22×C61—22no—
306C22×C61—22no—
307C22×C61—41no—
308C22×C61—41no—
309C22×C61—41no—
310C22×C61—41no—
311C22×C61C2×C22⋊Q811yescharacteristic
312C22×C61D4211yescharacteristic
313C22×C61#54611yescharacteristic
314C22×C61C2×#13511yescharacteristic
315C22×C61#57511yescharacteristic
316C22×C61#57611yescharacteristic
317C22×C61#57811yescharacteristic
318C2×D61—42no—
319C2×D61—42no—
320C2×D61—42no—
321C2×D61—81no—
322C2×D61—81no—
323C2×D61—81no—
324C2×D61—81no—
325C4×C61—22no—
326C4×C61—81no—
327C4×C61—81no—
328C4×C61—81no—
329C4×C61—81no—
330C4×C61C2×C22⋊Q811yescharacteristic
331C4×C61#54311yescharacteristic
332C4×C61#54611yescharacteristic
333C4×C61#55111yescharacteristic
334Dic61—24no—
335Dic61—22no—
336Dic61—41no—
337Dic61—42no—
338Dic61—41no—
339Dic61—41no—
340Dic61—81no—
341C2×#479—611no—
342C2×#416—611no—
343#2441—611no—
344#2341—611no—
345#2093—611no—
346#2067—611no—
347#2065—611no—
348#2025—611no—
349#1863—611no—
350#1863—611no—
351#1854—611no—
352#1850—611no—
353#1808D6111yescharacteristic, complemented
354#1803—611no—
355#1788—611no—
356C2×C61—42no—
357C2×C61#243711yescharacteristic
358C2×C61#307611yescharacteristic
359C2×C61#308311yescharacteristic
360C2×C61#326911yescharacteristic
361C2×C61#328711yescharacteristic
362C2×C61#330011yescharacteristic
363C2×C61#330911yescharacteristic
364D61—82no—
365C22×#41—611no—
366C23×C8C2×D6111yescharacteristic
367C2×#125—611no—
368C2×C4×Q8—611no—
369C2×C4×Q8—611no—
370C2×#117—611no—
371#479—1224no—
372C2×#107—611no—
373C2×#107C2×D6111yescharacteristic
374C2×#107C2×D6111yescharacteristic
375C2×#106—611no—
376C2×C4⋊C8—611no—
377C2×C4⋊C8—611no—
378#416—1224no—
379C2×#103—611no—
380C2×#103—611no—
381C2×#103—611no—
382C2×#103—611no—
383C2×#102—611no—
384C2×#102—611no—
385C2×#102—611no—
386C2×#102—611no—
387C2×C22⋊C8—611no—
388#399—1221no—
389#396—1221no—
390#390—611no—
391#390—611no—
392#390—1221no—
393#390—1221no—
394#389—611no—
395#389—611no—
396#389—1221no—
397#387—1221no—
398#384—611no—
399#380—1221no—
400#380C2×D6111yescharacteristic
401#380C2×D6111yescharacteristic
402C4×C22⋊C4—611no—
403C4×C22⋊C4—1221no—
404#340—611no—
405#340—611no—
406#340C2×D6111yescharacteristic
407#340C2×D6111yescharacteristic
408#336—611no—
409#336—611no—
410C61#2596111yescharacteristic, complemented, Sylow
411C2×#41—614no—
412C2×#41—1222no—
413C2×#41—1222no—
414C2×#41—1222no—
415C2×#41—2441no—
416C2×#41—2441no—
417C22×Q8—611no—
418C22×D4—611no—
419C22×D4—1221no—
420C23×C4—1221no—
421C23×C4C22×D6111yescharacteristic
422C22×C8—22no—
423C22×C8—22no—
424C22×C8—41no—
425C22×C8—611no—
426C22×C8—611no—
427C22×C8C22×D6111yescharacteristic
428C22×C8C22×D6111yescharacteristic
429#125—1222no—
430#125—2441no—
431C4×Q8—1222no—
432C4×Q8—1222no—
433C4×Q8—2441no—
434C4×Q8—2441no—
435#117—1222no—
436#117—2441no—
437C2×C4⋊C4—611no—
438C2×C4⋊C4—611no—
439C2×C4⋊C4—1221no—
440C2×C4⋊C4—1221no—
441C2×C4⋊C4—1221no—
442C2×C4⋊C4—1221no—
443C2×C4⋊C4—1221no—
444C2×C4⋊C4—1221no—
445C2×C4⋊C4—1221no—
446C2×C4⋊C4—1221no—
447C2×C4⋊C4C22×D6111yescharacteristic
448C2×C4⋊C4C22×D6111yescharacteristic
449C2×C4⋊C4C22×D6111yescharacteristic
450C2×C4⋊C4C22×D6111yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—611no—
454C2×C22⋊C4—611no—
455C2×C22⋊C4—1221no—
456C2×C22⋊C4—1221no—
457C2×C22⋊C4—1221no—
458C2×C22⋊C4—1221no—
459C2×C22⋊C4—1221no—
460C2×C42—611no—
461C2×C42—611no—
462C2×C42—1221no—
463C2×C42—1221no—
464C2×C42—1221no—
465#107—22no—
466#107—41no—
467#107—2441no—
468#106—1222no—
469C4⋊C8—1222no—
470C4⋊C8—2441no—
471#103—614no—
472#103—1222no—
473#103—1222no—
474#103—1222no—
475#102—1222no—
476#102—1222no—
477#102—2441no—
478#102—2441no—
479C22⋊C8—1222no—
480#95—21no—
481#95—21no—
482#95—611no—
483#95—611no—
484#95—1221no—
485#95—1221no—
486C24—1221no—
487C24D4×D6111yescharacteristic
488#41—1228no—
489#41—2444no—
490#41—2444no—
491#41—2444no—
492C2×Q8—612no—
493C2×Q8—612no—
494C2×Q8—612no—
495C2×Q8—1221no—
496C2×Q8—1221no—
497C2×Q8—1221no—
498C2×D4—612no—
499C2×D4—1224no—
500C2×D4—1221no—
501C2×D4—1221no—
502C2×D4—1221no—
503C2×D4—1221no—
504C2×D4—1221no—
505C2×D4—2442no—
506C2×D4—2442no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—611no—
516C22×C4—611no—
517C22×C4—611no—
518C22×C4—611no—
519C22×C4—1221no—
520C22×C4—1221no—
521C22×C4—1224no—
522C22×C4—1221no—
523C22×C4—2442no—
524C22×C4—2442no—
525C22×C4#1175822212yes—
526C22×C4D4×D6111yescharacteristic
527C22×C4Q8×D6112yes—
528C22×C4C23×D6111yescharacteristic
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—44no—
535C2×C8—1221no—
536C2×C8—1221no—
537C2×C8—1221no—
538C2×C8—1221no—
539C2×C8—1221no—
540C2×C8—1221no—
541C2×C8D4×D6112yes—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—612no—
551C4⋊C4—1221no—
552C4⋊C4—1221no—
553C4⋊C4—1221no—
554C4⋊C4—4881no—
555C4⋊C4—4881no—
556C4⋊C4—2442no—
557C4⋊C4—2442no—
558C4⋊C4—2442no—
559C4⋊C4—2442no—
560C4⋊C4—2442no—
561C4⋊C4—2442no—
562C22⋊C4—81no—
563C22⋊C4—81no—
564C22⋊C4—1222no—
565C22⋊C4—4881no—
566C22⋊C4—4881no—
567C22⋊C4—2442no—
568C22⋊C4—2442no—
569C22⋊C4—2441no—
570C22⋊C4—2442no—
571C42—1221no—
572C42—1221no—
573C42—1221no—
574C42—1221no—
575C42—2442no—
576C42—2442no—
577C42—2442no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—1222no—
585C23—2441no—
586C23—2441no—
587C23—2441no—
588C23—2441no—
589C23—2441no—
590C23—2441no—
591C23#1451975512yes—
592C23C2×D4×D6111yescharacteristic
593Q8—614no—
594Q8—1222no—
595Q8—1222no—
596Q8—1222no—
597D4—1222no—
598D4—1222no—
599D4—2448no—
600D4—2441no—
601D4—2441no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—612no—
621C2×C4—1222no—
622C2×C4—1221no—
623C2×C4—1222no—
624C2×C4—1221no—
625C2×C4—1222no—
626C2×C4—1221no—
627C2×C4—1221no—
628C2×C4—1221no—
629C2×C4—1221no—
630C2×C4—1221no—
631C2×C4—1221no—
632C2×C4—1221no—
633C2×C4—1221no—
634C2×C4—1222no—
635C2×C4—1221no—
636C2×C4—2448no—
637C2×C4—2441no—
638C2×C4—2441no—
639C2×C4—2441no—
640C2×C4—2441no—
641C2×C4—2441no—
642C2×C4#1451975512yes—
643C2×C4C2×D4×D6111yescharacteristic
644C2×C4C2×Q8×D6111yescharacteristic
645C2×C4#41×D6111yescharacteristic
646C2×C4C2×#1175822211yescharacteristic
647C2×C4#1451982211yescharacteristic
648C2×C4#1451982311yescharacteristic
649C8—22no—
650C8—41no—
651C8—2441no—
652C8—2441no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—4881no—
661C22—4881no—
662C22—4881no—
663C22—4881no—
664C22—2442no—
665C22—2442no—
666C22—2442no—
667C22C2×#1451975511yescharacteristic
668C22#1684039611yescharacteristic
669C22#1684040111yescharacteristic
670C22#135×D6111yescharacteristic
671C22#1684055911yescharacteristic
672C22#1684056311yescharacteristic
673C22#1684057511yescharacteristic
674C4—22no—
675C4—81no—
676C4—81no—
677C4—81no—
678C4—81no—
679C4—1224no—
680C4—1222no—
681C4—4881no—
682C4—2441no—
683C4—2441no—
684C4—2441no—
685C4—2442no—
686C4C22⋊Q8×D6111yescharacteristic
687C4#1684038711yescharacteristic
688C4#1684040211yescharacteristic
689C4#1684043611yescharacteristic
690C2—42no—
691C2—4882no—
692C2#2144948711yescharacteristic
693C2#2145560511yescharacteristic
694C2#2145567511yescharacteristic
695C2#2145737111yescharacteristic
696C2#2145757611yescharacteristic
697C2#2145770111yescharacteristic
698C2#2145783111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1808C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
hypercenter#1808D61
hypocenterC61#25961
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1808

Complements

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

NH ≅ G/Ntype
1. C2×#16840068C2semidirect
3. #21449533C2semidirect
5. #21447344C2semidirect
6. #21447202C2semidirect
7. #21447194C2semidirect
8. #21446964C2semidirect
9. #21446074C2semidirect
10. #21446070C2semidirect
11. #21446016C2semidirect
12. #21445997C2semidirect
13. #21445823C2semidirect
15. C61×#1808C2semidirect
353. #1808D61semidirect
410. C61#25961semidirect

Maximal subgroups

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

subgroupindex
C2×#168400682
C2×#168397592
#214495332
#214486562
#214473442
#214472022
#214471942
#214469642
#214460742
#214460702
#214460162
#214459972
#214458232
#214457572
C61×#18082
#2596161