Finite Group Databasebeta

← #29734437

Subgroups — #29734437

Order 15616.

968 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840372C211yesmaximal, characteristic
2C2×#16840169C211yesmaximal, characteristic, complemented
3C2×#16840111C211yesmaximal, characteristic, complemented
4#21451644C211yesmaximal, characteristic
5#21447023C211yesmaximal, characteristic
6#21447022C211yesmaximal, characteristic
7#21447012C211yesmaximal, characteristic
8#21446782C211yesmaximal, characteristic, complemented
9#21446637C211yesmaximal, characteristic, complemented
10#21446088C211yesmaximal, characteristic, complemented
11#21446084C211yesmaximal, characteristic, complemented
12#21446075C211yesmaximal, characteristic, complemented
13#21446071C211yesmaximal, characteristic, complemented
14#21445587C211yesmaximal, characteristic
15C61×#2035C211yesmaximal, characteristic
16#16840372—24no—
17#16840372—24no—
18C2×#14519776C2211yescharacteristic
19C2×#14519775C2211yescharacteristic
20C2×#14519770—21no—
21C2×#14519770—21no—
22C2×#14519768—21no—
23C2×#14519768C2211yescharacteristic
24C2×#14519767—21no—
25C2×#14519756C2211yescharacteristic
26C2×Q8×Dic61C2211yescharacteristic
27C2×#14519742C2211yescharacteristic
28C2×#14519736C2211yescharacteristic
29#16840169—24no—
30#16840111—24no—
31C2×#14519711C2211yescharacteristic
32C2×#14519710C2211yescharacteristic
33C2×#14519708C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519702C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×#14519687C2211yescharacteristic
42C2×C8×Dic61C2211yescharacteristic
43#16839704—21no—
44#16839698—21no—
45#16839683—21no—
46#16839674—21no—
47#16839661C2211yescharacteristic
48#16839658C2211yescharacteristic
49#16839627C2211yescharacteristic
50#16839622C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C2×C22⋊Q8×C61C2211yescharacteristic
57C2×#106×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C22×Dic122—21no—
64C22×Dic122C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67#14519776—22no—
68#14519776—22no—
69#14519775—22no—
70#14519775D414yes—
71#14519770—28no—
72#14519770—28no—
73#14519768—28no—
74#14519768—22no—
75#14519768D414yes—
76#14519767—28no—
77#14519756—22no—
78#14519756—22no—
79Q8×Dic61—22no—
80Q8×Dic61—22no—
81#14519742—22no—
82#14519742—22no—
83#14519736—22no—
84#14519736—22no—
85C2×C4⋊Dic61—21no—
86C2×C4⋊Dic61—21no—
87C2×C4⋊Dic61—21no—
88C2×C4⋊Dic61D411yescharacteristic
89C2×C4⋊Dic61D411yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×C22⋊Dic61—21no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61D411yescharacteristic
103C2×C22⋊Dic61D411yescharacteristic
104C2×C4×Dic61—21no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61C2311yescharacteristic
107C2×C4×Dic61C2311yescharacteristic
108#14519711—22no—
109#14519710—22no—
110#14519708—22no—
111#14519702—22no—
112#14519702—22no—
113#14519701—22no—
114#14519701—22no—
115#14519700—22no—
116#14519700—22no—
117C22⋊#92418—22no—
118#14519687—22no—
119C8×Dic61—22no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125C22×Q8×C61C2311yescharacteristic
126C23×C4×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C22⋊Q8×C61—22no—
130C22⋊Q8×C61—22no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61—21no—
137#106×C61—22no—
138#103×C61—22no—
139#103×C61—22no—
140C22⋊C8×C61—22no—
141#95×C61—21no—
142C24×C61C2×D411yescharacteristic
143C2×Q8×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61C2×D412yes—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2411yescharacteristic
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61C2×D411yescharacteristic
166C22×Dic61C2×D411yescharacteristic
167C22×Dic61C2×D411yescharacteristic
168C22×Dic61C2×D411yescharacteristic
169C2×Dic122—21no—
170C2×Dic122—21no—
171C2×Dic122—21no—
172C2×Dic122—21no—
173C2×Dic122—21no—
174C2×Dic122—42no—
175C2×Dic122—81no—
176C2×Dic122—81no—
177C2×Dic122C2×D412yes—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61#4112yes—
184C4⋊C4×C61—24no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61C2×D412yes—
191C22⋊C4×C61—24no—
192C22⋊C4×C61—81no—
193C22⋊Dic61—24no—
194C22⋊Dic61—22no—
195C22⋊Dic61—22no—
196C22⋊Dic61—81no—
197C4⋊Dic61—24no—
198C4⋊Dic61—21no—
199C4⋊Dic61—24no—
200C4⋊Dic61—22no—
201C4⋊Dic61—22no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61—81no—
207C4⋊Dic61C2×D412yes—
208#11758196—24no—
209#11758196—24no—
210#11758196—24no—
211#11758196—24no—
212#11758196—24no—
213#11758196—42no—
214#11758196—81no—
215C4×Dic61—24no—
216C4×Dic61—24no—
217C4×Dic61—21no—
218C4×Dic61—21no—
219C4×Dic61C2×D412yes—
220C4×Dic61C2×D412yes—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418—21no—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418#4112yes—
227C23×C61—21no—
228C23×C61—21no—
229C23×C61—21no—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61C22×D411yescharacteristic
235Q8×C61—22no—
236Q8×C61—22no—
237Q8×C61—41no—
238Q8×C61—41no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
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×C61C22×D411yescharacteristic
259C2×C4×C61C22×D411yescharacteristic
260C2×C4×C61C2×#4111yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C2×C4×C612−1+411yescharacteristic
263C2×C4×C612−1+411yescharacteristic
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—22no—
271C2×Dic61—22no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61#12012yes—
287C2×Dic61#12012yes—
288Dic122—22no—
289Dic122—22no—
290Dic122—41no—
291Dic122—41no—
292Dic122—84no—
293C8×C61—22no—
294C8×C61—41no—
295#92418—22no—
296#92418—41no—
297#25686—611nomaximal, Sylow
298C22×C61—41no—
299C22×C61—41no—
300C22×C61—41no—
301C22×C61—41no—
302C22×C61—41no—
303C22×C61—41no—
304C22×C61—41no—
305C22×C61C2×#12011yescharacteristic
306C22×C61#53211yescharacteristic
307C22×C61#53611yescharacteristic
308C22×C61#57711yescharacteristic
309C22×C61#57711yescharacteristic
310C22×C61#57811yescharacteristic
311C22×C61#57811yescharacteristic
312C4×C61—41no—
313C4×C61—42no—
314C4×C61—42no—
315C4×C61—81no—
316C4×C61—81no—
317C4×C61#54711yescharacteristic
318C4×C61#54711yescharacteristic
319C4×C61#54811yescharacteristic
320C4×C61#54811yescharacteristic
321Dic61—22no—
322Dic61—22no—
323Dic61—42no—
324Dic61—41no—
325Dic61—42no—
326Dic61—41no—
327Dic61—81no—
328Dic61—81no—
329C2×#541—611no—
330C2×#501—611no—
331C2×#487—611no—
332#2628—611no—
333#2036—611no—
334#2036—611no—
335#2035—611no—
336#2035D6111yescharacteristic
337#1991—611no—
338#1960—611no—
339#1865—611no—
340#1865—611no—
341#1863—611no—
342#1863—611no—
343#1750—611no—
344C2×C61—81no—
345C2×C61#243211yescharacteristic
346C2×C61#301011yescharacteristic
347C2×C61#301111yescharacteristic
348C2×C61#317811yescharacteristic
349C2×C61#317811yescharacteristic
350C2×C61#324211yescharacteristic
351C2×C61#324211yescharacteristic
352#541—1224no—
353#541—1224no—
354C2×C4⋊Q8—611no—
355C2×C4⋊Q8—611no—
356C2×#126—1221no—
357C2×#126—1221no—
358C2×#125—611no—
359C2×#125—1221no—
360C2×#125—1221no—
361C2×C22⋊Q8—611no—
362C2×C22⋊Q8C2×D6111yescharacteristic
363C2×C4×Q8—611no—
364C2×C4×Q8—611no—
365C2×#117—611no—
366#501—1224no—
367#487—1224no—
368C2×#107—611no—
369C2×#107—611no—
370C2×#106—611no—
371C2×#106C2×D6111yescharacteristic
372C2×#103—611no—
373C2×#103—611no—
374C2×#103—611no—
375C2×#103—611no—
376C2×#103—611no—
377C2×#103—611no—
378C2×#103C2×D6111yescharacteristic
379C2×#103C2×D6111yescharacteristic
380C2×C22⋊C8—611no—
381C2×C22⋊C8C2×D6111yescharacteristic
382C2×#97—611no—
383C2×C4×C8—611no—
384#400—1221no—
385#399—1221no—
386#395—1221no—
387#393—1221no—
388#389—611no—
389#389—611no—
390#382—611no—
391#380—611no—
392#380C2×D6111yescharacteristic
393#340—611no—
394#340—611no—
395#340—611no—
396#340C2×D6111yescharacteristic
397#336—611no—
398#336—611no—
399C61#2568611yescharacteristic, complemented, Sylow
400C22×Q8—611no—
401C22×Q8—1221no—
402C22×Q8C22×D6111yescharacteristic
403C23×C4C22×D6111yescharacteristic
404C22×C8—611no—
405C22×C8—611no—
406C22×C8C22×D6111yescharacteristic
407C22×C8C22×D6111yescharacteristic
408C4⋊Q8—614no—
409C4⋊Q8—1222no—
410C4⋊Q8—1222no—
411C4⋊Q8—1222no—
412#126—1228no—
413#126—1228no—
414#125—614no—
415#125—1222no—
416#125—1228no—
417#125—1228no—
418C22⋊Q8—22no—
419C22⋊Q8—22no—
420C22⋊Q8—1222no—
421C22⋊Q8—1222no—
422C4×Q8—1222no—
423C4×Q8—1222no—
424C4×Q8—1222no—
425C4×Q8—1222no—
426#117—1222no—
427#117—1222no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—611no—
430C2×C4⋊C4—611no—
431C2×C4⋊C4—611no—
432C2×C4⋊C4—611no—
433C2×C4⋊C4—611no—
434C2×C4⋊C4—1221no—
435C2×C4⋊C4—1221no—
436C2×C4⋊C4—1221no—
437C2×C4⋊C4—1221no—
438C2×C4⋊C4—1221no—
439C2×C4⋊C4—1221no—
440C2×C4⋊C4—1221no—
441C2×C4⋊C4—1221no—
442C2×C4⋊C4—1221no—
443C2×C4⋊C4—1221no—
444C2×C4⋊C4C22×D6111yescharacteristic
445C2×C4⋊C4C22×D6111yescharacteristic
446C2×C4⋊C4C22×D6111yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—611no—
450C2×C22⋊C4—611no—
451C2×C22⋊C4—1221no—
452C2×C22⋊C4—1221no—
453C2×C42—611no—
454C2×C42—611no—
455C2×C42—1221no—
456C2×C42—1221no—
457#107—1222no—
458#107—1222no—
459#106—22no—
460#106—1222no—
461#103—22no—
462#103—22no—
463#103—1222no—
464#103—1222no—
465#103—1222no—
466#103—1222no—
467#103—1222no—
468#103—1222no—
469C22⋊C8—22no—
470C22⋊C8—1222no—
471#97—1222no—
472C4×C8—1222no—
473#95—21no—
474#95—1221no—
475#95—1221no—
476#95—1221no—
477#95—1221no—
478#95—1221no—
479C24D4×D6111yescharacteristic
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—612no—
486C2×Q8—1221no—
487C2×Q8—1221no—
488C2×Q8—1221no—
489C2×Q8—1221no—
490C2×Q8—1221no—
491C2×Q8—4881no—
492C2×Q8—4881no—
493C2×Q8—2442no—
494C2×Q8D4×D6112yes—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—611no—
506C22×C4—611no—
507C22×C4—611no—
508C22×C4—611no—
509C22×C4—1221no—
510C22×C4—1221no—
511C22×C4—1221no—
512C22×C4—1221no—
513C22×C4D4×D6111yescharacteristic
514C22×C4C23×D6111yescharacteristic
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—612no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8—1221no—
524C2×C8—1221no—
525C2×C8—1221no—
526C2×C8#1175822412yes—
527C4⋊C4—24no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—612no—
534C4⋊C4—1222no—
535C4⋊C4—1222no—
536C4⋊C4—1224no—
537C4⋊C4—1224no—
538C4⋊C4—1224no—
539C4⋊C4—1224no—
540C4⋊C4—1224no—
541C4⋊C4—1224no—
542C4⋊C4—1224no—
543C4⋊C4—1221no—
544C4⋊C4—1221no—
545C4⋊C4—1221no—
546C4⋊C4—1221no—
547C4⋊C4—1221no—
548C4⋊C4—4881no—
549C4⋊C4—4881no—
550C4⋊C4—2442no—
551C4⋊C4D4×D6112yes—
552C22⋊C4—24no—
553C22⋊C4—81no—
554C22⋊C4—1222no—
555C22⋊C4—1222no—
556C22⋊C4—1224no—
557C22⋊C4—4881no—
558C42—612no—
559C42—612no—
560C42—1224no—
561C42—1224no—
562C42—1221no—
563C42—1221no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23C2×D4×D6111yescharacteristic
572Q8—22no—
573Q8—22no—
574Q8—41no—
575Q8—41no—
576Q8—1222no—
577Q8—1222no—
578Q8—4884no—
579Q8—2441no—
580Q8—2441no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—612no—
601C2×C4—612no—
602C2×C4—1221no—
603C2×C4—1221no—
604C2×C4—1221no—
605C2×C4—1221no—
606C2×C4—1221no—
607C2×C4—1221no—
608C2×C4—1222no—
609C2×C4—1222no—
610C2×C4—1221no—
611C2×C4—1221no—
612C2×C4—1221no—
613C2×C4—1221no—
614C2×C4—2441no—
615C2×C4—2441no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4—2441no—
619C2×C4—2441no—
620C2×C4—2441no—
621C2×C4—2441no—
622C2×C4—2441no—
623C2×C4—2441no—
624C2×C4C2×D4×D6111yescharacteristic
625C2×C4C2×D4×D6111yescharacteristic
626C2×C4#41×D6111yescharacteristic
627C2×C4C2×#1175822411yescharacteristic
628C2×C4#1451982411yescharacteristic
629C2×C4#1451982411yescharacteristic
630C8—22no—
631C8—41no—
632C8—1222no—
633C8—2441no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22#120×D6111yescharacteristic
642C22#1684030711yescharacteristic
643C22#1684033411yescharacteristic
644C22#1684056811yescharacteristic
645C22#1684057111yescharacteristic
646C22#1684057611yescharacteristic
647C22#1684057811yescharacteristic
648C4—42no—
649C4—41no—
650C4—42no—
651C4—81no—
652C4—81no—
653C4—1222no—
654C4—1222no—
655C4—4881no—
656C4—4881no—
657C4—2441no—
658C4—2442no—
659C4—2441no—
660C4—2442no—
661C4#1684041011yescharacteristic
662C4#1684041211yescharacteristic
663C4#1684041811yescharacteristic
664C4#1684042011yescharacteristic
665C2—81no—
666C2#2144944211yescharacteristic
667C2#2145510011yescharacteristic
668C2#2145511111yescharacteristic
669C2#2145648211yescharacteristic
670C2#2145648811yescharacteristic
671C2#2145708311yescharacteristic
672C2#2145708511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2035C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
hypercenter#2035D61
hypocenterC61#25686
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2035

Complements

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

NH ≅ G/Ntype
2. C2×#16840169C2semidirect
3. C2×#16840111C2semidirect
8. #21446782C2semidirect
9. #21446637C2semidirect
10. #21446088C2semidirect
11. #21446084C2semidirect
12. #21446075C2semidirect
13. #21446071C2semidirect
399. C61#25686semidirect

Maximal subgroups

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

subgroupindex
C2×#168403722
C2×#168401692
C2×#168401112
#214516442
#214470232
#214470222
#214470122
#214467822
#214466372
#214460882
#214460842
#214460752
#214460712
#214455872
C61×#20352
#2568661