Finite Group Databasebeta

← #29685434

Subgroups — #29685434

Order 15616.

810 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519733C211yesmaximal, characteristic
2#21446435C211yesmaximal, characteristic
3#21446434C211yesmaximal, characteristic
4#21446429C211yesmaximal, characteristic
5#21446386C211yesmaximal, characteristic, complemented
6#21446383C211yesmaximal, characteristic, complemented
7#21446381C211yesmaximal, characteristic, complemented
8#21446380C211yesmaximal, characteristic, complemented
9C4⋊C8×Dic61C211yesmaximal, characteristic, complemented
10#21445667C211yesmaximal, characteristic, complemented
11C22⋊C8×Dic61C211yesmaximal, characteristic
12C22⋊C8×Dic61C211yesmaximal, characteristic
13#21445563C211yesmaximal, characteristic, complemented
14#97×Dic61C211yesmaximal, characteristic, complemented
15C61×#1924C211yesmaximal, characteristic
16C2×#14519733C411yescharacteristic
17C2×#14519733C411yescharacteristic
18C22×C4×Dic61C2211yescharacteristic
19C2×C4⋊#92418C2211yescharacteristic
20C2×#14519706C2211yescharacteristic
21C2×#14519706C2211yescharacteristic
22C2×C22⋊#92418C2211yescharacteristic
23C2×C22⋊#92418C2211yescharacteristic
24C2×#14519688C2211yescharacteristic
25C2×#14519687C2211yescharacteristic
26C2×#14519687C2211yescharacteristic
27C2×C8×Dic61C2211yescharacteristic
28C2×C8×Dic61C2211yescharacteristic
29C2×C8×Dic61C2211yescharacteristic
30C2×C8×Dic61C2211yescharacteristic
31C4×#11758196C2211yescharacteristic
32C4×#11758196C2211yescharacteristic
33#16839613C411yescharacteristic
34#16839613C411yescharacteristic
35C22⋊C4×Dic61C411yescharacteristic
36C22⋊C4×Dic61C411yescharacteristic
37C4×C22⋊Dic61C2211yescharacteristic
38#16839607C411yescharacteristic
39#16839607C411yescharacteristic
40C42×Dic61C2211yescharacteristic
41C42×Dic61C2211yescharacteristic
42#16839517C2211yescharacteristic
43#16839517C2211yescharacteristic
44#16839516C2211yescharacteristic
45#16839516C2211yescharacteristic
46#16839516C2211yescharacteristic
47#16839516C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×C4⋊C8×C61C2211yescharacteristic
53C2×C22⋊C8×C61C2211yescharacteristic
54C2×C22⋊C8×C61C2211yescharacteristic
55C2×#97×C61C2211yescharacteristic
56C4×C22⋊C4×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C23×Dic61C2×C411yescharacteristic
60C23×Dic61C2×C411yescharacteristic
61C22×#92418C2311yescharacteristic
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65#14519733—24no—
66#14519733—24no—
67C2×#11758196C2×C411yescharacteristic
68C2×#11758196C2×C411yescharacteristic
69C2×#11758196C2×C411yescharacteristic
70C2×#11758196C2×C411yescharacteristic
71C2×C22⋊Dic61C2×C411yescharacteristic
72C2×C22⋊Dic61C2×C411yescharacteristic
73C2×C4×Dic61—22no—
74C2×C4×Dic61—22no—
75C2×C4×Dic61C2×C411yescharacteristic
76C2×C4×Dic61C2×C411yescharacteristic
77C2×C4×Dic61C2×C411yescharacteristic
78C2×C4×Dic61C2×C411yescharacteristic
79C2×C4×Dic61C2×C411yescharacteristic
80C2×C4×Dic61C2×C411yescharacteristic
81C2×C4×Dic61C2×C411yescharacteristic
82C2×C4×Dic61C2×C411yescharacteristic
83C2×C4×Dic61C2×C411yescharacteristic
84C2×C4×Dic61C2×C411yescharacteristic
85C2×C4×Dic61C2311yescharacteristic
86C2×C4×Dic61C2311yescharacteristic
87C2×C4×Dic61C2311yescharacteristic
88C2×C4×Dic61C2311yescharacteristic
89C4⋊#92418—22no—
90#14519706—22no—
91#14519706—22no—
92C22⋊#92418—22no—
93C22⋊#92418—22no—
94#14519688—22no—
95#14519687—22no—
96#14519687—22no—
97C8×Dic61—22no—
98C8×Dic61—22no—
99C8×Dic61—22no—
100C8×Dic61—22no—
101#14519684C2×C411yescharacteristic
102#14519684C2×C411yescharacteristic
103#14519684C2×C411yescharacteristic
104#14519684C2×C411yescharacteristic
105#14519684C2×C411yescharacteristic
106#14519684C2×C411yescharacteristic
107C23×C4×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110C22×C8×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112C2×C22⋊C4×C61C2×C411yescharacteristic
113C2×C22⋊C4×C61C2×C411yescharacteristic
114C2×C42×C61C2311yescharacteristic
115C2×C42×C61C2311yescharacteristic
116C4⋊C8×C61—22no—
117C22⋊C8×C61—22no—
118C22⋊C8×C61—22no—
119#97×C61—22no—
120#95×C61C2×C411yescharacteristic
121#95×C61C2×C411yescharacteristic
122C24×C61C22×C411yescharacteristic
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61C22×C411yescharacteristic
130C22×C4×C61C22×C411yescharacteristic
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C2411yescharacteristic
135C22×Dic61—22no—
136C22×Dic61—22no—
137C22×Dic61—22no—
138C22×Dic61—22no—
139C22×Dic61—22no—
140C22×Dic61M1614yes—
141C22×Dic61C22×C411yescharacteristic
142C22×Dic61C22×C411yescharacteristic
143C22×Dic61C22×C411yescharacteristic
144C22×Dic61C22×C411yescharacteristic
145C22×Dic61C22×C411yescharacteristic
146C22×Dic61C22×C411yescharacteristic
147C22×Dic61C22×C411yescharacteristic
148C22×Dic61C22×C411yescharacteristic
149C2×C8×C61—21no—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C2×C8×C61—21no—
154C2×C8×C61—21no—
155C2×C8×C61—21no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61#4112yes—
160C2×C8×C61#4112yes—
161C22⋊C4×C61—22no—
162C22⋊C4×C61—22no—
163C42×C61—21no—
164C42×C61—21no—
165C42×C61—21no—
166C42×C61—21no—
167C22⋊Dic61—22no—
168C22⋊Dic61—22no—
169#11758196—22no—
170#11758196—22no—
171#11758196—22no—
172#11758196—22no—
173C4×Dic61—21no—
174C4×Dic61—21no—
175C4×Dic61—21no—
176C4×Dic61—21no—
177C4×Dic61—21no—
178C4×Dic61—21no—
179C4×Dic61—22no—
180C4×Dic61—22no—
181C4×Dic61—22no—
182C4×Dic61—22no—
183C4×Dic61—22no—
184C4×Dic61—22no—
185C4×Dic61—22no—
186C4×Dic61—22no—
187C4×Dic61—22no—
188C4×Dic61M1614yes—
189C4×Dic61#4112yes—
190C4×Dic61#4112yes—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418#4112yes—
202C2×#92418#4112yes—
203C23×C61—21no—
204C23×C61—21no—
205C23×C61—21no—
206C23×C61—21no—
207C23×C61—21no—
208C23×C61—21no—
209C23×C61C2×M1612yes—
210C23×C61C23×C411yescharacteristic
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—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61C2×M1612yes—
230C2×C4×C61C2×#4111yescharacteristic
231C2×C4×C61C2×#4111yescharacteristic
232C2×C4×C61C2×#4111yescharacteristic
233C2×C4×C61C2×#4111yescharacteristic
234C2×C4×C61C2×#4111yescharacteristic
235C2×C4×C61C2×#4111yescharacteristic
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—28no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—44no—
254C2×Dic61#11712yes—
255C2×Dic61#11712yes—
256C2×Dic61C2×M1612yes—
257C2×Dic61C2×M1612yes—
258C2×Dic61C2×M1612yes—
259C2×Dic61C2×M1612yes—
260C2×Dic61#13112yes—
261C2×Dic61#13112yes—
262C8×C61—22no—
263C8×C61—22no—
264C8×C61—41no—
265C8×C61—41no—
266#92418—22no—
267#92418—22no—
268#92418—41no—
269#92418—41no—
270#21431—611nomaximal, Sylow
271C22×C61—22no—
272C22×C61—22no—
273C22×C61—22no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61C2×#11711yescharacteristic
279C22×C61C4×#4111yescharacteristic
280C22×C61C4×#4111yescharacteristic
281C22×C61C22×M1611yescharacteristic
282C22×C61C22×M1611yescharacteristic
283C22×C61C2×#13111yescharacteristic
284C22×C61C2×#13111yescharacteristic
285C4×C61—22no—
286C4×C61—41no—
287C4×C61—41no—
288C4×C61—41no—
289C4×C61—41no—
290C4×C61#52911yescharacteristic
291C4×C61#52911yescharacteristic
292C4×C61#52911yescharacteristic
293C4×C61#52911yescharacteristic
294Dic61—22no—
295Dic61—22no—
296Dic61—41no—
297Dic61—41no—
298Dic61—41no—
299Dic61—41no—
300Dic61#43214yes—
301Dic61#43314yes—
302C4×#117—611no—
303#1924—611no—
304#1924—611no—
305#1924—611no—
306#1924D6111yescharacteristic
307#1917—611no—
308#1917—611no—
309#1917—611no—
310#1917—611no—
311C4×C4⋊C8—611no—
312C4×C4⋊C8—611no—
313C4×C22⋊C8—611no—
314C4×C22⋊C8—611no—
315#1744—611no—
316C4×#97—611no—
317C2×C61—42no—
318C2×C61#229811yescharacteristic
319C2×C61C2×#43211yescharacteristic
320C2×C61C2×#43311yescharacteristic
321C2×C61#296511yescharacteristic
322C2×C61#296511yescharacteristic
323C2×C61#296511yescharacteristic
324C2×C61#296511yescharacteristic
325C2×#117—611no—
326C2×#117—611no—
327C22×C42—611no—
328C2×C4⋊C8—611no—
329C2×C4⋊C8—611no—
330C2×C4⋊C8—611no—
331C2×C4⋊C8C2×D6111yescharacteristic
332C2×C22⋊C8—611no—
333C2×C22⋊C8—611no—
334C2×C22⋊C8C2×D6111yescharacteristic
335C2×C22⋊C8C2×D6111yescharacteristic
336C2×#97—611no—
337C2×#97—611no—
338C2×#97—611no—
339C2×#97C2×D6111yescharacteristic
340C2×C4×C8—611no—
341C2×C4×C8—611no—
342C2×C4×C8—611no—
343C2×C4×C8—611no—
344C4×C4⋊C4—611no—
345C4×C4⋊C4—611no—
346C4×C4⋊C4—611no—
347C4×C4⋊C4—611no—
348C4×C22⋊C4—611no—
349C4×C22⋊C4—611no—
350C4×C22⋊C4—611no—
351C4×C22⋊C4C2×D6111yescharacteristic
352#376—611no—
353#376—611no—
354C43—611no—
355C43—611no—
356#336—611no—
357#336—611no—
358#336—611no—
359#336—611no—
360#336—611no—
361#336—611no—
362#336—611no—
363#336—611no—
364#336—611no—
365#336—611no—
366#336C2×D6111yescharacteristic
367#336C2×D6111yescharacteristic
368C61#2143111yescharacteristic, complemented, Sylow
369C23×C4—611no—
370C23×C4—611no—
371C23×C4C22×D6111yescharacteristic
372C22×C8—611no—
373C22×C8—611no—
374C22×C8—611no—
375C22×C8—611no—
376C22×C8C22×D6111yescharacteristic
377C22×C8C22×D6111yescharacteristic
378C22×C8C22×D6111yescharacteristic
379C22×C8C22×D6111yescharacteristic
380#117—1224no—
381#117—1224no—
382C2×C4⋊C4—611no—
383C2×C4⋊C4—611no—
384C2×C4⋊C4—611no—
385C2×C4⋊C4—611no—
386C2×C22⋊C4—611no—
387C2×C22⋊C4—611no—
388C2×C22⋊C4C4×D6111yescharacteristic
389C2×C22⋊C4C4×D6111yescharacteristic
390C2×C42—611no—
391C2×C42—611no—
392C2×C42—611no—
393C2×C42—611no—
394C2×C42—611no—
395C2×C42—611no—
396C2×C42—611no—
397C2×C42—611no—
398C2×C42—611no—
399C2×C42—611no—
400C2×C42—611no—
401C2×C42—611no—
402C2×C42—611no—
403C2×C42—611no—
404C2×C42—1222no—
405C2×C42—1222no—
406C2×C42C22×D6111yescharacteristic
407C2×C42C22×D6111yescharacteristic
408C4⋊C8—22no—
409C4⋊C8—1222no—
410C4⋊C8—1222no—
411C4⋊C8—1222no—
412C22⋊C8—22no—
413C22⋊C8—22no—
414C22⋊C8—1222no—
415C22⋊C8—1222no—
416#97—22no—
417#97—1222no—
418#97—1222no—
419#97—1222no—
420C4×C8—1222no—
421C4×C8—1222no—
422C4×C8—1222no—
423C4×C8—1222no—
424#95—611no—
425#95—611no—
426#95—611no—
427#95—611no—
428#95—611no—
429#95—611no—
430#95C4×D6111yescharacteristic
431#95C4×D6111yescharacteristic
432C24C2×C4×D6111yescharacteristic
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—611no—
440C22×C4—611no—
441C22×C4—611no—
442C22×C4—611no—
443C22×C4—614no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—611no—
447C22×C4—611no—
448C22×C4—1222no—
449C22×C4—1222no—
450C22×C4—1222no—
451C22×C4—1222no—
452C22×C4—1222no—
453C22×C4C2×C4×D6111yescharacteristic
454C22×C4C2×C4×D6111yescharacteristic
455C22×C4C2×C4×D6111yescharacteristic
456C22×C4C2×C4×D6111yescharacteristic
457C22×C4C2×C4×D6111yescharacteristic
458C22×C4C23×D6111yescharacteristic
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—612no—
470C2×C8—612no—
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#1175822412yes—
482C2×C8#1175822412yes—
483C4⋊C4—1222no—
484C4⋊C4—1222no—
485C4⋊C4—1222no—
486C4⋊C4—1222no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—1222no—
490C22⋊C4—1222no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—612no—
496C42—612no—
497C42—614no—
498C42—1222no—
499C42—1222no—
500C42—1222no—
501C42—1222no—
502C42—1222no—
503C42—1222no—
504C42—1222no—
505C42—1222no—
506C42—1222no—
507C42—1221no—
508C42—1221no—
509C42—1221no—
510C42—1221no—
511C42—1221no—
512C42—1221no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23M16×D6112yes—
520C23C22×C4×D6111yescharacteristic
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—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—612no—
540C2×C4—612no—
541C2×C4—612no—
542C2×C4—612no—
543C2×C4—612no—
544C2×C4—612no—
545C2×C4—612no—
546C2×C4—612no—
547C2×C4—1228no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—1221no—
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—2444no—
565C2×C4M16×D6112yes—
566C2×C4#41×D6111yescharacteristic
567C2×C4#41×D6111yescharacteristic
568C2×C4#41×D6111yescharacteristic
569C2×C4#41×D6111yescharacteristic
570C2×C4C2×#1175822411yescharacteristic
571C2×C4C2×#1175822411yescharacteristic
572C8—22no—
573C8—22no—
574C8—41no—
575C8—41no—
576C8—1222no—
577C8—1222no—
578C8—2441no—
579C8—2441no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22#117×D6111yescharacteristic
588C22C4×#1175822411yescharacteristic
589C22C4×#1175822411yescharacteristic
590C22C2×M16×D6111yescharacteristic
591C22C2×M16×D6111yescharacteristic
592C22#131×D6111yescharacteristic
593C22#131×D6111yescharacteristic
594C4—22no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—614no—
600C4—614no—
601C4—1222no—
602C4—1222no—
603C4—2441no—
604C4—2441no—
605C4—2441no—
606C4—2441no—
607C4#1684028911yescharacteristic
608C4#1684029111yescharacteristic
609C4#1684029311yescharacteristic
610C4#1684029511yescharacteristic
611C2—42no—
612C2#2144831311yescharacteristic
613C2#432×D6111yescharacteristic
614C2#433×D6111yescharacteristic
615C2#2145477911yescharacteristic
616C2#2145477911yescharacteristic
617C2#2145477911yescharacteristic
618C2#2145478211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1924C2
prime radicalC24×C61C22×C4
cosocleC22×C4×C61C24
hypercenter#1924D61
hypocenterC61#21431
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
5. #21446386C2semidirect
6. #21446383C2semidirect
7. #21446381C2semidirect
8. #21446380C2semidirect
9. C4⋊C8×Dic61C2semidirect
10. #21445667C2semidirect
13. #21445563C2semidirect
14. #97×Dic61C2semidirect
368. C61#21431semidirect

Maximal subgroups

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

subgroupindex
C4×#145197332
#214464352
#214464342
#214464292
#214463862
#214463832
#214463812
#214463802
C4⋊C8×Dic612
#214456672
C22⋊C8×Dic612
#214455632
#97×Dic612
C61×#19242
#2143161