Finite Group Databasebeta

← #29698167

Subgroups — #29698167

Order 15616.

1042 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839804C211yesmaximal, characteristic, complemented
2C22×#14519709C211yesmaximal, characteristic, complemented
3#21448748C211yesmaximal, characteristic
4D4×C4⋊Dic61C211yesmaximal, characteristic
5#21446589C211yesmaximal, characteristic, complemented
6#21446583C211yesmaximal, characteristic, complemented
7#21446020C211yesmaximal, characteristic, complemented
8#21446014C211yesmaximal, characteristic, complemented
9#21446014C211yesmaximal, characteristic, complemented
10#21446009C211yesmaximal, characteristic, complemented
11#21445987C211yesmaximal, characteristic, complemented
12#21445852C211yesmaximal, characteristic, complemented
13#21445848C211yesmaximal, characteristic, complemented
14#21445716C211yesmaximal, characteristic, complemented
15C2×C61×#435C211yesmaximal, characteristic
16C2×D4×Dic61—21no—
17C2×#14519736C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21#16839804—24no—
22C2×#14519711C2211yescharacteristic
23C2×#14519711C2211yescharacteristic
24C2×#14519711C2211yescharacteristic
25C2×#14519711C2211yescharacteristic
26C2×#14519709—24no—
27C2×#14519709C2211yescharacteristic
28C2×#14519709C2211yescharacteristic
29C2×#14519709C2211yescharacteristic
30C2×#14519709C2211yescharacteristic
31C2×#14519709C2211yescharacteristic
32C2×#14519709C2211yescharacteristic
33#16839661—21no—
34#16839655—21no—
35#16839648—21no—
36#16839642—21no—
37#16839637—21no—
38#16839637—21no—
39#16839632C2211yescharacteristic
40#16839628C2211yescharacteristic
41#16839622C2211yescharacteristic
42#16839622C2211yescharacteristic
43#16839622C2211yescharacteristic
44#16839622C2211yescharacteristic
45C4×C4⋊Dic61C2211yescharacteristic
46C4×C4⋊Dic61C2211yescharacteristic
47C22⋊C4×Dic61—21no—
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54C22×M16×C61C2211yescharacteristic
55C23×C8×C61C2211yescharacteristic
56C2×C4×D4×C61C2211yescharacteristic
57C61×#435C418yescomplemented
58C2×C4⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C2×#97×C61C2211yescharacteristic
62C23×Dic61—21no—
63C23×Dic61—21no—
64C23×Dic61—21no—
65D4×Dic61—44no—
66#14519736—22no—
67#14519736—41no—
68C2×C4⋊Dic61—22no—
69C2×C4⋊Dic61—22no—
70C2×C4⋊Dic61—22no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61—41no—
77C2×C4⋊Dic61—41no—
78C2×C4⋊Dic61—41no—
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C4×Dic61—21no—
93C2×C4×Dic61—21no—
94C2×C4×Dic61—21no—
95#14519711—22no—
96#14519711—22no—
97#14519711—22no—
98#14519711—41no—
99#14519709—22no—
100#14519709—22no—
101#14519709—22no—
102#14519709—22no—
103#14519709—41no—
104#14519709D414yescomplemented
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113C22×D4×C61D411yescharacteristic
114C23×C4×C61C2311yescharacteristic
115C23×C4×C61C2311yescharacteristic
116C2×M16×C61—22no—
117C2×M16×C61—22no—
118C2×M16×C61C2×C414yescomplemented
119C22×C8×C61—22no—
120C22×C8×C61—22no—
121C22×C8×C61C2×C414yescomplemented
122C22×C8×C61C2311yescharacteristic
123C22×C8×C61C2311yescharacteristic
124C22×C8×C61C2311yescharacteristic
125C22×C8×C61C2311yescharacteristic
126C4×D4×C61C2×C414yes—
127C4×D4×C61Q814yes—
128C2×C4⋊C4×C61D411yescharacteristic
129C2×C22⋊C4×C61D411yescharacteristic
130C2×C22⋊C4×C61D411yescharacteristic
131C2×C42×C61C2311yescharacteristic
132C4⋊C8×C61C2×C414yescomplemented
133C22⋊C8×C61C2×C414yescomplemented
134C22⋊C8×C61C2×C414yescomplemented
135#97×C61C2×C414yescomplemented
136C24×C61C2×D411yescharacteristic
137C24×C61C2×D411yescharacteristic
138C2×D4×C61—22no—
139C2×D4×C61—22no—
140C2×D4×C61C4⋊C414yes—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61C22×C412yes—
150C22×C4×C61C22×C412yes—
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×Q812yes—
156C22×C4×C61C2×Q812yes—
157C22×C4×C61C2411yescharacteristic
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—42no—
167C22×Dic61—42no—
168C22×Dic61—42no—
169C22×Dic61—42no—
170C22×Dic61—42no—
171C22×Dic61—42no—
172C22×Dic61—81no—
173C22×Dic61—81no—
174C22×Dic61—81no—
175M16×C61—28no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—28no—
183C2×C8×C61C22×C412yes—
184C2×C8×C61C22×C412yes—
185C2×C8×C61C22×C412yes—
186C2×C8×C61C22×C412yes—
187C2×C8×C61C2×D412yes—
188C2×C8×C61#4112yes—
189C4⋊C4×C61C4⋊C414yes—
190C22⋊C4×C61C4⋊C414yes—
191C22⋊C4×C61C4⋊C414yes—
192C42×C61C22×C412yes—
193C42×C61C2×Q812yes—
194C22⋊Dic61—42no—
195C22⋊Dic61—42no—
196C22⋊Dic61—42no—
197C22⋊Dic61—42no—
198C22⋊Dic61—81no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61—21no—
207C4⋊Dic61—21no—
208C4⋊Dic61—21no—
209C4⋊Dic61—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61—21no—
213C4⋊Dic61—42no—
214C4⋊Dic61—42no—
215C4⋊Dic61—42no—
216C4⋊Dic61—42no—
217C4⋊Dic61—81no—
218C4⋊Dic61C2×D412yes—
219C4⋊Dic61C2×D412yes—
220C4×Dic61—42no—
221C4×Dic61—42no—
222C4×Dic61—81no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61—21no—
227C23×C61—21no—
228C23×C61—21no—
229C23×C61—21no—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61C2×C4⋊C412yes—
234C23×C61C2×C4⋊C412yes—
235C23×C61AGL(1,ℤ/8)12yes—
236C23×C61#13712yes—
237C23×C61C22×D411yescharacteristic
238D4×C61—28no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—22no—
248C2×C4×C61—22no—
249C2×C4×C61—22no—
250C2×C4×C61—22no—
251C2×C4×C61—22no—
252C2×C4×C61—22no—
253C2×C4×C61—22no—
254C2×C4×C61—22no—
255C2×C4×C61C2×C4⋊C412yes—
256C2×C4×C61C2×C4⋊C412yes—
257C2×C4×C61C2×C4⋊C412yes—
258C2×C4×C61C2×C4⋊C412yes—
259C2×C4×C61C23×C411yescharacteristic
260C2×C4×C61C22×D411yescharacteristic
261C2×C4×C61C22×Q811yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C2×C4×C61H(5,𝔽2)11yescharacteristic
264C2×C4×C612−1+411yescharacteristic
265C2×Dic61—22no—
266C2×Dic61—22no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—41no—
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—41no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289C2×Dic61—84no—
290C2×Dic61—84no—
291C2×Dic61—84no—
292C8×C61—22no—
293C8×C61—22no—
294C8×C61—22no—
295C8×C61C4×D414yescomplemented
296#22659—611nomaximal, Sylow
297C22×C61—22no—
298C22×C61—22no—
299C22×C61—22no—
300C22×C61—22no—
301C22×C61—22no—
302C22×C61—22no—
303C22×C61—22no—
304C22×C61—22no—
305C22×C61—22no—
306C22×C61—41no—
307C22×C61—41no—
308C22×C61—41no—
309C22×C61—41no—
310C22×C61#42814yescomplemented
311C22×C61C22×C4⋊C411yescharacteristic
312C22×C61D4211yescharacteristic
313C22×C61#54711yescharacteristic
314C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
315C22×C61C2×#13711yescharacteristic
316C22×C61#57711yescharacteristic
317C22×C61#57711yescharacteristic
318C4×C61—22no—
319C4×C61—22no—
320C4×C61—22no—
321C4×C61—22no—
322C4×C61C2×C4×D411yescharacteristic
323C4×C61#52011yescharacteristic
324C4×C61D4×Q811yescharacteristic
325C4×C61#55411yescharacteristic
326Dic61—42no—
327Dic61—42no—
328Dic61—81no—
329Dic61—81no—
330Dic61—81no—
331Dic61—81no—
332Dic61—81no—
333Dic61—81no—
334C2×#435D6111yescharacteristic
335C2×#428—611no—
336C22×#106—611no—
337#2352—611no—
338D4×C4⋊C4—611no—
339#1949—611no—
340#1948—611no—
341#1854—611no—
342#1853—611no—
343#1853—611no—
344#1852—611no—
345#1847—611no—
346#1809—611no—
347#1808—611no—
348#1776—611no—
349C2×C61—24no—
350C2×C61—42no—
351C2×C61D4×C4⋊C411yescharacteristic
352C2×C61C2×#42811yescharacteristic
353C2×C61#291211yescharacteristic
354C2×C61#326511yescharacteristic
355C2×C61#326611yescharacteristic
356C2×C61#334411yescharacteristic
357C2×C61#334511yescharacteristic
358C22×M16C2×D6111yescharacteristic
359C23×C8C2×D6111yescharacteristic
360C2×C4×D4—1221no—
361C2×C4×D4C2×D6111yescharacteristic
362C2×#117—611no—
363C22×C4⋊C4—611no—
364C22×C4⋊C4—611no—
365C22×C4⋊C4—611no—
366#435Dic6118yescomplemented
367#428—1224no—
368C2×#107—611no—
369C2×#107—611no—
370C2×#107—611no—
371C2×#107—611no—
372C2×#106—611no—
373C2×#106—611no—
374C2×#106—611no—
375C2×#106—611no—
376C2×#106—611no—
377C2×#106—611no—
378C2×#106—1224no—
379C2×C4⋊C8C2×D6111yescharacteristic
380C2×C22⋊C8C2×D6111yescharacteristic
381C2×C22⋊C8C2×D6111yescharacteristic
382C2×#97C2×D6111yescharacteristic
383#389—1221no—
384#388—1221no—
385#387—1221no—
386#386—1221no—
387#385—1221no—
388#385—1221no—
389#384—611no—
390#382—611no—
391#380—611no—
392#380—611no—
393#380—611no—
394#380—611no—
395C4×C4⋊C4—611no—
396C4×C4⋊C4—611no—
397C4×C22⋊C4—1221no—
398#340—611no—
399#340—611no—
400#340—611no—
401#340—611no—
402#340—611no—
403#340—611no—
404C61#2265911yescharacteristic, complemented, Sylow
405C22×D4D24411yescharacteristic
406C23×C4—1221no—
407C23×C4—1221no—
408C23×C4—1221no—
409C23×C4C22×D6111yescharacteristic
410C23×C4C22×D6111yescharacteristic
411C2×M16—22no—
412C2×M16—22no—
413C2×M16C2×Dic6114yescomplemented
414C22×C8—22no—
415C22×C8—22no—
416C22×C8C2×Dic6114yescomplemented
417C22×C8C22×D6111yescharacteristic
418C22×C8C22×D6111yescharacteristic
419C22×C8C22×D6111yescharacteristic
420C22×C8C22×D6111yescharacteristic
421C4×D4—2444no—
422C4×D4Dic12214yes—
423C4×D4C2×Dic6114yes—
424#117—1222no—
425#117—2441no—
426C2×C4⋊C4—611no—
427C2×C4⋊C4—611no—
428C2×C4⋊C4—611no—
429C2×C4⋊C4—611no—
430C2×C4⋊C4—611no—
431C2×C4⋊C4—611no—
432C2×C4⋊C4—611no—
433C2×C4⋊C4—611no—
434C2×C4⋊C4—1222no—
435C2×C4⋊C4—1222no—
436C2×C4⋊C4—1222no—
437C2×C4⋊C4—1221no—
438C2×C4⋊C4—1221no—
439C2×C4⋊C4—1221no—
440C2×C4⋊C4—1221no—
441C2×C4⋊C4—1221no—
442C2×C4⋊C4—2441no—
443C2×C4⋊C4—2441no—
444C2×C4⋊C4—2441no—
445C2×C4⋊C4D24411yescharacteristic
446C2×C22⋊C4—1221no—
447C2×C22⋊C4—1221no—
448C2×C22⋊C4—1221no—
449C2×C22⋊C4—1221no—
450C2×C22⋊C4—1221no—
451C2×C22⋊C4D24411yescharacteristic
452C2×C22⋊C4D24411yescharacteristic
453C2×C42—1221no—
454C2×C42—1221no—
455C2×C42—1221no—
456C2×C42C22×D6111yescharacteristic
457#107—1222no—
458#107—1222no—
459#107—1222no—
460#107—2441no—
461#106—614no—
462#106—1222no—
463#106—1222no—
464#106—1222no—
465#106—1222no—
466#106—2441no—
467C4⋊C8C2×Dic6114yescomplemented
468C22⋊C8C2×Dic6114yescomplemented
469C22⋊C8C2×Dic6114yescomplemented
470#97C2×Dic6114yescomplemented
471#95—1221no—
472#95—1221no—
473#95—1221no—
474#95—1221no—
475#95—1221no—
476#95—1221no—
477#95—1221no—
478#95—1221no—
479C24C2×D24411yescharacteristic
480C24C2×D24411yescharacteristic
481C2×D4—22no—
482C2×D4—22no—
483C2×D4C4⋊Dic6114yes—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—1221no—
493C22×C4—1221no—
494C22×C4—1221no—
495C22×C4—1221no—
496C22×C4—1221no—
497C22×C4—1221no—
498C22×C4—1221no—
499C22×C4—1221no—
500C22×C4—4881no—
501C22×C4—4881no—
502C22×C4—4881no—
503C22×C4—2442no—
504C22×C4—2442no—
505C22×C4—2442no—
506C22×C4—2442no—
507C22×C4—2442no—
508C22×C4—2442no—
509C22×C4C2×Dic12212yes—
510C22×C4C2×Dic12212yes—
511C22×C4C2×D24411yescharacteristic
512C22×C4C2×D24411yescharacteristic
513C22×C4C2×D24411yescharacteristic
514C22×C4C2×D24411yescharacteristic
515C22×C4C22×Dic6112yes—
516C22×C4C22×Dic6112yes—
517C22×C4C23×D6111yescharacteristic
518M16—28no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—28no—
526C2×C8D4×D6112yes—
527C2×C8#1175822412yes—
528C2×C8C22×Dic6112yes—
529C2×C8C22×Dic6112yes—
530C2×C8C22×Dic6112yes—
531C2×C8C22×Dic6112yes—
532C4⋊C4—612no—
533C4⋊C4—612no—
534C4⋊C4—1221no—
535C4⋊C4—1221no—
536C4⋊C4—1221no—
537C4⋊C4—1221no—
538C4⋊C4—1221no—
539C4⋊C4—1221no—
540C4⋊C4—1221no—
541C4⋊C4—1221no—
542C4⋊C4—1221no—
543C4⋊C4—1221no—
544C4⋊C4—1221no—
545C4⋊C4—1221no—
546C4⋊C4—1221no—
547C4⋊C4—1221no—
548C4⋊C4—4881no—
549C4⋊C4—2442no—
550C4⋊C4—2442no—
551C4⋊C4—2442no—
552C4⋊C4—2442no—
553C4⋊C4C4⋊Dic6114yes—
554C22⋊C4—4881no—
555C22⋊C4—2442no—
556C22⋊C4—2442no—
557C22⋊C4—2442no—
558C22⋊C4—2442no—
559C22⋊C4C4⋊Dic6114yes—
560C22⋊C4C4⋊Dic6114yes—
561C42—4881no—
562C42—2442no—
563C42—2442no—
564C42C2×Dic12212yes—
565C42C22×Dic6112yes—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23C2×C4⋊Dic6112yes—
577C23C2×C4⋊Dic6112yes—
578C23#1451980512yes—
579C23#1451981012yes—
580C23C22×D24411yescharacteristic
581D4—28no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—1222no—
599C2×C4—1222no—
600C2×C4—4884no—
601C2×C4—4884no—
602C2×C4—4884no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4—2441no—
606C2×C4—2441no—
607C2×C4—2441no—
608C2×C4—2441no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4—2441no—
612C2×C4—2441no—
613C2×C4—2441no—
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×C4—2441no—
625C2×C4C2×C4⋊Dic6112yes—
626C2×C4C2×C4⋊Dic6112yes—
627C2×C4C2×C4⋊Dic6112yes—
628C2×C4C2×C4⋊Dic6112yes—
629C2×C4C23×Dic6111yescharacteristic
630C2×C4C2×D4×D6111yescharacteristic
631C2×C4C22×Dic12211yescharacteristic
632C2×C4C2×#1175822411yescharacteristic
633C2×C4#1451982311yescharacteristic
634C2×C4#1451982411yescharacteristic
635C8—22no—
636C8—22no—
637C8—22no—
638C8D4×Dic6114yescomplemented
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22#1683980414yescomplemented
653C22C22×C4⋊Dic6111yescharacteristic
654C22D4×D24411yescharacteristic
655C22#1684041611yescharacteristic
656C22C2×#1451980511yescharacteristic
657C22C2×#1451981011yescharacteristic
658C22#1684057411yescharacteristic
659C22#1684057411yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—4881no—
665C4—4881no—
666C4—4881no—
667C4—4881no—
668C4—4881no—
669C4—4881no—
670C4—2442no—
671C4—2442no—
672C4C2×D4×Dic6111yescharacteristic
673C4#1684024511yescharacteristic
674C4D4×Dic12211yescharacteristic
675C4#1684046911yescharacteristic
676C2—24no—
677C2—42no—
678C2D4×C4⋊Dic6111yescharacteristic
679C2C2×#1683980411yescharacteristic
680C2#2145441411yescharacteristic
681C2#2145731911yescharacteristic
682C2#2145733411yescharacteristic
683C2#2145827611yescharacteristic
684C2#2145829111yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#435C2
socleC23×C61C22×D4
prime radicalC22×D4×C61D4
cosocleC22×C4×C61C24
hypercenterC2×#435D61
hypocenterC61#22659
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#16839804C2semidirect
2. C22×#14519709C2semidirect
5. #21446589C2semidirect
6. #21446583C2semidirect
7. #21446020C2semidirect
8. #21446014C2semidirect
9. #21446014C2semidirect
10. #21446009C2semidirect
11. #21445987C2semidirect
12. #21445852C2semidirect
13. #21445848C2semidirect
14. #21445716C2semidirect
57. C61×#435C4semidirect
104. #14519709D4semidirect
118. C2×M16×C61C2×C4semidirect
121. C22×C8×C61C2×C4semidirect
132. C4⋊C8×C61C2×C4semidirect
133. C22⋊C8×C61C2×C4semidirect
134. C22⋊C8×C61C2×C4semidirect
135. #97×C61C2×C4semidirect
295. C8×C61C4×D4semidirect
310. C22×C61#428semidirect
366. #435Dic61semidirect
404. C61#22659semidirect
413. C2×M16C2×Dic61semidirect
416. C22×C8C2×Dic61semidirect
467. C4⋊C8C2×Dic61semidirect
468. C22⋊C8C2×Dic61semidirect
469. C22⋊C8C2×Dic61semidirect
470. #97C2×Dic61semidirect
638. C8D4×Dic61semidirect
652. C22#16839804semidirect

Maximal subgroups

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

subgroupindex
C2×#168398042
C22×#145197092
#214487482
D4×C4⋊Dic612
#214465892
#214465832
#214460202
#214460142
#214460092
#214459872
#214458522
#214458482
#214457162
C2×C61×#4352
#2265961