Finite Group Databasebeta

← #30622321

Subgroups — #30622321

Order 15616.

766 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840811C211yesmaximal, characteristic, complemented
2C2×#16840787C211yesmaximal, characteristic
3#21461991C211yesmaximal, characteristic, complemented
4#21461918C211yesmaximal, characteristic, complemented
5#21461895C211yesmaximal, characteristic
6#21461891C211yesmaximal, characteristic
7#21461890C211yesmaximal, characteristic
8#21461890C211yesmaximal, characteristic
9#21461878C211yesmaximal, characteristic, complemented
10#21461874C211yesmaximal, characteristic, complemented
11#21461618C211yesmaximal, characteristic, complemented
12#21461618C211yesmaximal, characteristic, complemented
13#21461611C211yesmaximal, characteristic, complemented
14#21461548C211yesmaximal, characteristic
15#21449092C211yesmaximal, characteristic
16#16840811—24no—
17#16840787—24no—
18C2×#14519844C2211yescharacteristic
19C2×#14519844C2211yescharacteristic
20C2×#14519844C2211yescharacteristic
21C2×#14519844C2211yescharacteristic
22C2×C4⋊#92420C2211yescharacteristic
23C2×C4⋊#92420C2211yescharacteristic
24C2×#14519834C2211yescharacteristic
25C2×#14519834C2211yescharacteristic
26C2×#14519834C2211yescharacteristic
27C2×#14519834C2211yescharacteristic
28C2×#14519832C2211yescharacteristic
29C2×#14519832C2211yescharacteristic
30C2×#14519832C2211yescharacteristic
31C2×C4×#92420C2211yescharacteristic
32C2×C4×#92420C2211yescharacteristic
33C2×C4×#92420C2211yescharacteristic
34C2×C4×#92420C2211yescharacteristic
35C2×C4×#92420C2211yescharacteristic
36#16840628C2211yescharacteristic
37#16840628C2211yescharacteristic
38#16840628C2211yescharacteristic
39#16840628C2211yescharacteristic
40#16840628C2211yescharacteristic
41#16840628C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46C2×#14519742C2211yescharacteristic
47C2×#14519735C2211yescharacteristic
48#16839697C411yescharacteristic
49#16839696C411yescharacteristic
50#16839696C411yescharacteristic
51#16839686C411yescharacteristic
52#16839686C411yescharacteristic
53#16839682C411yescharacteristic
54#16839675C411yescharacteristic
55#16839613C2211yescharacteristic
56#16839613C2211yescharacteristic
57#16839613C2211yescharacteristic
58#16839609C2211yescharacteristic
59#16839609C2211yescharacteristic
60C61×#400C411yescharacteristic
61C22×#92420C2311yescharacteristic
62C22×#92420C2311yescharacteristic
63C22×#92420C2311yescharacteristic
64C22×#92420C2311yescharacteristic
65C22×#92420C2311yescharacteristic
66C22×#92420C2311yescharacteristic
67C22×#92420C2311yescharacteristic
68C22×#92420C2311yescharacteristic
69#14519844—22no—
70#14519844—22no—
71#14519844—22no—
72#14519844—22no—
73C4⋊#92420—22no—
74C4⋊#92420D414yes—
75#14519834—22no—
76#14519834—22no—
77#14519834—22no—
78#14519834—22no—
79#14519832—22no—
80#14519832—22no—
81#14519832—22no—
82C4×#92420—22no—
83C4×#92420—22no—
84C4×#92420—22no—
85C4×#92420—22no—
86C4×#92420—22no—
87C22×Dic122C2×C411yescharacteristic
88C22×C4×D61C2311yescharacteristic
89#14519742—22no—
90#14519742—22no—
91#14519735—22no—
92#14519735—22no—
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×#11758196C2×C411yescharacteristic
95C2×#11758196C2×C411yescharacteristic
96C2×#11758196C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×#11758196C2×C411yescharacteristic
99C2×#11758196C2×C411yescharacteristic
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×#11758198C2×C411yescharacteristic
103C2×#11758198C2×C411yescharacteristic
104C2×#11758198C2×C411yescharacteristic
105C2×#11758198C2×C411yescharacteristic
106C2×#11758198C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×C4×Dic61C2311yescharacteristic
109C2×C4×Dic61C2311yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112C2×C4×Dic61C2311yescharacteristic
113C2×C4×Dic61C2311yescharacteristic
114#14519684C2×C411yescharacteristic
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
117#14519684C2×C411yescharacteristic
118#14519684C2×C411yescharacteristic
119C2×C4⋊C4×C61C2×C411yescharacteristic
120C2×C4⋊C4×C61C2×C411yescharacteristic
121#95×C61C2×C411yescharacteristic
122#95×C61C2×C411yescharacteristic
123#95×C61C2×C411yescharacteristic
124#95×C61C2×C411yescharacteristic
125#95×C61C2×C411yescharacteristic
126C23×D61C22×C411yescharacteristic
127C22×C4×C61C22×C411yescharacteristic
128C22×C4×C61C22×C411yescharacteristic
129C22×C4×C61C22×C411yescharacteristic
130C22×C4×C61C22×C411yescharacteristic
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C22×C411yescharacteristic
134C22×Dic61C22×C411yescharacteristic
135C22×Dic61C22×C411yescharacteristic
136C22×Dic61C22×C411yescharacteristic
137C22×Dic61C22×C411yescharacteristic
138C22×Dic61C22×C411yescharacteristic
139C22×Dic61C22×C411yescharacteristic
140C22×Dic61C2411yescharacteristic
141C2×C4×D61—21no—
142C2×C4×D61—21no—
143C2×C4×D61—21no—
144C2×C4×D61—21no—
145C2×C4×D61—21no—
146C2×C4×D61—21no—
147C2×Dic122—22no—
148C2×Dic122—22no—
149C2×Dic122—22no—
150C2×#92420—21no—
151C2×#92420—21no—
152C2×#92420—21no—
153C2×#92420—21no—
154C2×#92420—21no—
155C2×#92420—21no—
156C2×#92420—21no—
157C2×#92420—21no—
158C2×#92420—21no—
159C2×#92420—21no—
160C2×#92420—21no—
161C2×#92420—21no—
162C2×#92420—21no—
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420C2×D412yes—
171C2×#92420C2×D412yes—
172C2×#92420#4112yes—
173C2×#92420#4112yes—
174C4⋊C4×C61—22no—
175C4⋊C4×C61—22no—
176#11758198—22no—
177#11758198—22no—
178#11758198—22no—
179#11758198—22no—
180#11758198—22no—
181#11758198—41no—
182C4⋊Dic61—22no—
183#11758196—22no—
184#11758196—22no—
185#11758196—22no—
186#11758196—22no—
187#11758196—22no—
188#11758196—22no—
189#11758196—41no—
190#11758196—41no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61—21no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61C2×D412yes—
202C4×Dic61#4112yes—
203C23×C61C23×C411yescharacteristic
204C22×D61—21no—
205C22×D61—21no—
206C22×D61—21no—
207C22×D61—21no—
208C22×D61—21no—
209C22×D61—21no—
210C22×D61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61C4×D412yes—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61C4×D412yes—
247C2×Dic61#13112yes—
248C2×Dic61#13112yes—
249C2×Dic61#13112yes—
250C2×Dic61C22×D411yescharacteristic
251C2×Dic61C2×#4111yescharacteristic
252C2×Dic61C2×#4111yescharacteristic
253C2×Dic61C2×#4111yescharacteristic
254C2×Dic612−1+411yescharacteristic
255C2×Dic612−1+411yescharacteristic
256C4×D61—41no—
257C4×D61—41no—
258C4×D61—41no—
259C4×D61—41no—
260Dic122—28no—
261#92420—22no—
262#92420—22no—
263#92420—22no—
264#92420—22no—
265#92420—41no—
266#92420—41no—
267#92420—41no—
268#92420—41no—
269#23056—611nomaximal, Sylow
270C22×C61C2×C4×D411yescharacteristic
271C22×C61C4×#4111yescharacteristic
272C22×C61#51911yescharacteristic
273C22×C61C2×#13111yescharacteristic
274C22×C61C2×#13111yescharacteristic
275C22×C61C2×#13111yescharacteristic
276C22×C61#56811yescharacteristic
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C2×D61—41no—
282C2×D61—41no—
283C2×D61—41no—
284C4×C61—22no—
285C4×C61—41no—
286C4×C61—41no—
287C4×C61—41no—
288C4×C61—41no—
289C4×C61—41no—
290C4×C61—41no—
291Dic61—22no—
292Dic61—22no—
293Dic61—22no—
294Dic61—22no—
295Dic61—41no—
296Dic61—41no—
297Dic61#54711yescharacteristic
298Dic61#54811yescharacteristic
299Dic61#55211yescharacteristic
300Dic61#55611yescharacteristic
301C2×C8×Q8—611no—
302C2×#433—611no—
303#2396—611no—
304#1985—611no—
305#1939—611no—
306#1924—611no—
307#1923—611no—
308#1923—611no—
309#1923—611no—
310#1917—611no—
311#1916—611no—
312#1771—611no—
313#1771—611no—
314C8×C4⋊C4—611no—
315#1750—611no—
316C2×C61#236211yescharacteristic
317C2×C61#292911yescharacteristic
318C2×C61#293511yescharacteristic
319C2×C61#296611yescharacteristic
320C2×C61#296911yescharacteristic
321C2×C61#298511yescharacteristic
322C2×C61#298611yescharacteristic
323D61—81no—
324C2×C4×Q8—611no—
325C2×#117—611no—
326C8×Q8—1224no—
327#433—1224no—
328C2×C4⋊C8—611no—
329C2×C4⋊C8—611no—
330C2×C4⋊C8—611no—
331C2×C4⋊C8—611no—
332C2×C4⋊C8—611no—
333C2×C4⋊C8—611no—
334C2×C22⋊C8—611no—
335C2×C22⋊C8—611no—
336C2×C22⋊C8—611no—
337C2×C22⋊C8—611no—
338C2×#97—611no—
339C2×#97—611no—
340C2×#97—611no—
341C2×C4×C8—611no—
342C2×C4×C8—611no—
343C2×C4×C8—611no—
344C2×C4×C8—611no—
345C2×C4×C8—611no—
346#400#692311yescharacteristic
347#399—611no—
348#398—611no—
349#398—611no—
350#396—611no—
351#396—611no—
352#395—611no—
353#393—611no—
354C4×C4⋊C4—611no—
355C4×C4⋊C4—611no—
356C4×C4⋊C4—611no—
357C4×C22⋊C4—611no—
358C4×C22⋊C4—611no—
359#336—611no—
360#336—611no—
361#336—611no—
362#336—611no—
363#336—611no—
364#336—611no—
365#336—611no—
366#336—611no—
367#336—611no—
368#336—611no—
369C61#2305611yescharacteristic, complemented, Sylow
370C22×Q8—611no—
371C23×C4—611no—
372C22×C8—611no—
373C22×C8—611no—
374C22×C8—611no—
375C22×C8—611no—
376C22×C8—611no—
377C22×C8—611no—
378C22×C8—611no—
379C22×C8—611no—
380C4×Q8—1222no—
381C4×Q8—1222no—
382#117—1222no—
383#117—1222no—
384C2×C4⋊C4—611no—
385C2×C4⋊C4—611no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4—611no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—611no—
390C2×C4⋊C4—611no—
391C2×C4⋊C4—611no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4C2×#692311yescharacteristic
394C2×C4⋊C4C2×#692311yescharacteristic
395C2×C22⋊C4—611no—
396C2×C22⋊C4—611no—
397C2×C22⋊C4—611no—
398C2×C22⋊C4—611no—
399C2×C22⋊C4—611no—
400C2×C22⋊C4—611no—
401C2×C42—611no—
402C2×C42—611no—
403C2×C42—611no—
404C2×C42—611no—
405C2×C42—611no—
406C2×C42—611no—
407C4⋊C8—614no—
408C4⋊C8—1222no—
409C4⋊C8—1222no—
410C4⋊C8—1222no—
411C4⋊C8—1222no—
412C4⋊C8—1222no—
413C22⋊C8—1222no—
414C22⋊C8—1222no—
415C22⋊C8—1222no—
416C22⋊C8—1222no—
417#97—1222no—
418#97—1222no—
419#97—1222no—
420C4×C8—1222no—
421C4×C8—1222no—
422C4×C8—1222no—
423C4×C8—1222no—
424C4×C8—1222no—
425#95—611no—
426#95—611no—
427#95—611no—
428#95—611no—
429#95—611no—
430#95C2×#692311yescharacteristic
431#95C2×#692311yescharacteristic
432#95C2×#692311yescharacteristic
433#95C2×#692311yescharacteristic
434#95C2×#692311yescharacteristic
435C24—611no—
436C2×Q8—1222no—
437C2×Q8—1222no—
438C2×Q8—1222no—
439C22×C4—611no—
440C22×C4—611no—
441C22×C4—611no—
442C22×C4—611no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—1221no—
447C22×C4—1221no—
448C22×C4—1221no—
449C22×C4—1221no—
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4C22×#692311yescharacteristic
453C22×C4C22×#692311yescharacteristic
454C22×C4C22×#692311yescharacteristic
455C22×C4C22×#692311yescharacteristic
456C22×C4C22×#692311yescharacteristic
457C22×C4C22×#692311yescharacteristic
458C22×C4C22×#692311yescharacteristic
459C2×C8—612no—
460C2×C8—612no—
461C2×C8—612no—
462C2×C8—612no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—1222no—
486C4⋊C4—1222no—
487C4⋊C4—1222no—
488C4⋊C4—1222no—
489C4⋊C4—1222no—
490C4⋊C4—1222no—
491C4⋊C4—1222no—
492C4⋊C4—2441no—
493C4⋊C4—2441no—
494C22⋊C4—1222no—
495C22⋊C4—1222no—
496C22⋊C4—1222no—
497C22⋊C4—1222no—
498C22⋊C4—1222no—
499C22⋊C4—2441no—
500C42—612no—
501C42—612no—
502C42—1221no—
503C42—1221no—
504C42—1221no—
505C42—1221no—
506C42—1221no—
507C42—1221no—
508C42—1221no—
509C42—1221no—
510C42—1221no—
511C42—1221no—
512C23—1221no—
513C23—1221no—
514C23—1221no—
515C23—1221no—
516C23—1221no—
517C23—1221no—
518C23—1221no—
519C23C23×#692311yescharacteristic
520Q8—1228no—
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—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—611no—
542C2×C4—611no—
543C2×C4—611no—
544C2×C4—611no—
545C2×C4—611no—
546C2×C4—611no—
547C2×C4—612no—
548C2×C4—612no—
549C2×C4—612no—
550C2×C4—612no—
551C2×C4—1221no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—1221no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4D4×#692312yes—
570C8—1222no—
571C8—1222no—
572C8—1222no—
573C8—1222no—
574C8—2441no—
575C8—2441no—
576C8—2441no—
577C8—2441no—
578C22—2441no—
579C22—2441no—
580C22—2441no—
581C22—2441no—
582C22—2441no—
583C22—2441no—
584C22—2441no—
585C22C2×D4×#692311yescharacteristic
586C22#41×#692311yescharacteristic
587C22#1684083011yescharacteristic
588C22D61⋊#13111yescharacteristic
589C22D61⋊#13111yescharacteristic
590C22D61⋊#13111yescharacteristic
591C22#1684084111yescharacteristic
592C4—22no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—611no—
600C4—611no—
601C4—611no—
602C4—611no—
603C4—1222no—
604C4—1222no—
605C4—1222no—
606C4—1222no—
607C4—2441no—
608C4—2441no—
609C2—4881no—
610C2#2146234511yescharacteristic
611C2#2146253611yescharacteristic
612C2#2146256411yescharacteristic
613C2#2146263711yescharacteristic
614C2#2146265411yescharacteristic
615C2#2146272611yescharacteristic
616C2#2146272911yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#400C4
prime radicalC23×D61C22×C4
cosocleC22×Dic61C24
hypercenter#400#6923
hypocenterC61#23056
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#16840811C2semidirect
3. #21461991C2semidirect
4. #21461918C2semidirect
9. #21461878C2semidirect
10. #21461874C2semidirect
11. #21461618C2semidirect
12. #21461618C2semidirect
13. #21461611C2semidirect
369. C61#23056semidirect

Maximal subgroups

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

subgroupindex
C2×#168408112
C2×#168407872
#214619912
#214619182
#214618952
#214618912
#214618902
#214618782
#214618742
#214616182
#214616112
#214615482
#214490922
#2305661