Finite Group Databasebeta

← #29697333

Subgroups — #29697333

Order 15616.

1150 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839766C211yesmaximal, characteristic
2C22⋊C4×D244C211yesmaximal, characteristic
3#21446515C211yesmaximal, characteristic, complemented
4#21446501C211yesmaximal, characteristic, complemented
5#21446446C211yesmaximal, characteristic, complemented
6#21446439C211yesmaximal, characteristic, complemented
7#21446079C211yesmaximal, characteristic, complemented
8#21446065C211yesmaximal, characteristic, complemented
9#21445914C211yesmaximal, characteristic, complemented
10#21445850C211yesmaximal, characteristic, complemented
11#21445749C211yesmaximal, characteristic
12#21445647C211yesmaximal, characteristic, complemented
13C4×#14519697C211yesmaximal, characteristic, complemented
14#21445603C211yesmaximal, characteristic, complemented
15C61×#2346C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20C2×C22⋊C4×D61—21no—
21C2×#14519710C2211yescharacteristic, complemented
22C2×#14519708C2211yescharacteristic, complemented
23#16839766C418yescomplemented
24C2×#14519697C2211yescharacteristic
25C2×#14519697C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×#14519688C2211yescharacteristic, complemented
34C2×C4×#92418C2211yescharacteristic, complemented
35#16839664C2211yescharacteristic
36#16839664C2211yescharacteristic
37#16839640—21no—
38#16839640—21no—
39#16839622C2211yescharacteristic
40#16839617—21no—
41#16839524C2211yescharacteristic, complemented
42#16839524C2211yescharacteristic, complemented
43#16839524C2211yescharacteristic, complemented
44#16839524C2211yescharacteristic, complemented
45#16839524C2211yescharacteristic, complemented
46#16839524C2211yescharacteristic, complemented
47#16839517C2211yescharacteristic, complemented
48#16839517C2211yescharacteristic, complemented
49C2×#117×C61C2211yescharacteristic
50C61×#389C2211yescharacteristic, complemented
51C61×#389C2211yescharacteristic, complemented
52C61×#388—21no—
53C61×#388—21no—
54C61×#382—21no—
55C61×#380C2211yescharacteristic
56C4×C4⋊C4×C61C2211yescharacteristic, complemented
57C4×C4⋊C4×C61C2211yescharacteristic, complemented
58C4×C22⋊C4×C61C2211yescharacteristic
59C61×#376—21no—
60C24×D61—21no—
61C22×D244—22no—
62C22×D244—22no—
63C22×D244—21no—
64C22×D244—22no—
65C22×D244—41no—
66C22×D244—41no—
67C22×D244C2×C414yes—
68C22×D244C2311yescharacteristic
69C22×D244C2311yescharacteristic
70C22×C4×D61—21no—
71C22×C4×D61—21no—
72C2×#11758194—41no—
73C2×#11758194—41no—
74C2×#11758194C2×C414yescomplemented
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C4×D244—22no—
80C4×D244—22no—
81C4×D244—41no—
82C4×D244—41no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C22⋊Dic61—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C22⋊C4×D61—44no—
93#14519710—41no—
94#14519708—41no—
95#14519697—22no—
96#14519697—22no—
97#14519697—41no—
98#14519697—41no—
99#14519697C2×C414yes—
100#14519697C2×C414yes—
101#14519697C2×C414yescomplemented
102#14519697C2×C414yescomplemented
103C22⋊#92418—22no—
104#14519688—41no—
105C4×#92418—41no—
106#14519684—21no—
107C23×C4×C61C2311yescharacteristic
108#117×C61—22no—
109#117×C61C2×C414yescomplemented
110C2×C4⋊C4×C61—21no—
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C22⋊C4×C61—21no—
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61D411yescharacteristic
119C2×C22⋊C4×C61D411yescharacteristic
120C2×C42×C61—21no—
121C2×C42×C61—21no—
122C2×C42×C61—21no—
123C2×C42×C61C2311yescharacteristic
124C2×C42×C61C2311yescharacteristic
125#95×C61—21no—
126#95×C61—21no—
127#95×C61—21no—
128#95×C61—21no—
129#95×C61—21no—
130#95×C61D411yescharacteristic
131#95×C61D411yescharacteristic
132C24×C61C2×D411yescharacteristic
133C23×D61—21no—
134C23×D61—21no—
135C23×D61—24no—
136C23×D61—42no—
137C23×D61—42no—
138C23×D61—42no—
139C23×D61—42no—
140C23×D61—81no—
141C23×D61—81no—
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×C61—21no—
150C22×C4×C61C22×C412yes—
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61#4112yes—
157C22×C4×C61C2411yescharacteristic
158C22×Dic61—21no—
159C22×Dic61—21no—
160C2×D244—21no—
161C2×D244—21no—
162C2×D244—21no—
163C2×D244—21no—
164C2×D244—21no—
165C2×D244—21no—
166C2×D244—21no—
167C2×D244—28no—
168C2×D244—24no—
169C2×D244—21no—
170C2×D244—44no—
171C2×D244—44no—
172C2×D244—44no—
173C2×D244—42no—
174C2×D244—42no—
175C2×D244C22×C412yes—
176C2×D244C22×C412yes—
177C2×D244#4112yes—
178C2×D244#4112yes—
179C2×C4×D61—42no—
180C2×C4×D61—42no—
181C2×C4×D61—42no—
182C2×C4×D61—42no—
183C2×C4×D61—81no—
184C2×C4×D61—81no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—81no—
192C4⋊C4×C61—81no—
193C4⋊C4×C61C22×C412yes—
194C4⋊C4×C61C22×C412yes—
195C22⋊C4×C61—24no—
196C22⋊C4×C61—22no—
197C22⋊C4×C61—41no—
198C22⋊C4×C61—81no—
199C42×C61—24no—
200C42×C61—21no—
201C42×C61—21no—
202C42×C61—21no—
203C42×C61—21no—
204C42×C61—42no—
205C42×C61—42no—
206C22⋊Dic61—42no—
207#11758198—42no—
208#11758198—42no—
209#11758198—42no—
210#11758198—42no—
211#11758198—81no—
212#11758198—81no—
213C4⋊Dic61—21no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217#11758194—44no—
218C2×#92418—21no—
219C2×#92418—21no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418—21no—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418C22×C412yes—
229C2×#92418C22×C412yes—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61C4×D412yes—
237C23×C61C22×D411yescharacteristic
238C22×D61—22no—
239C22×D61—22no—
240C22×D61—22no—
241C22×D61—22no—
242C22×D61—48no—
243C22×D61—41no—
244C22×D61—41no—
245C22×D61—41no—
246C22×D61—41no—
247C22×D61—48no—
248C22×D61—41no—
249C22×D61—41no—
250C22×D61—41no—
251C22×D61—41no—
252C22×D61—41no—
253C22×D61—41no—
254C22×D61—84no—
255C22×D61—84no—
256C22×D61—84no—
257C22×D61—84no—
258C22×D61—84no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61C4×D412yes—
289C2×C4×C61AGL(1,ℤ/8)12yes—
290C2×C4×C61C23×C411yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61H(5,𝔽2)11yescharacteristic
295C2×C4×C61H(5,𝔽2)11yescharacteristic
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302D244—22no—
303D244—22no—
304D244—22no—
305D244—22no—
306D244—22no—
307D244—48no—
308D244—41no—
309D244—41no—
310D244#11714yes—
311C4×D61—84no—
312C4×D61—84no—
313#92418—22no—
314#92418—22no—
315#92418—41no—
316#92418—41no—
317#22584—611nomaximal, Sylow
318C22×C61—22no—
319C22×C61—22no—
320C22×C61—22no—
321C22×C61—41no—
322C22×C61—41no—
323C22×C61—41no—
324C22×C61—41no—
325C22×C61C2×C4×D411yescharacteristic
326C22×C61#54611yescharacteristic
327C22×C61#54611yescharacteristic
328C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
329C22×C61#57511yescharacteristic
330C22×C61#57611yescharacteristic
331C22×C61#57711yescharacteristic
332C2×D61—24no—
333C2×D61—42no—
334C2×D61—42no—
335C2×D61—42no—
336C2×D61—42no—
337C2×D61—42no—
338C2×D61—42no—
339C2×D61—42no—
340C2×D61—42no—
341C2×D61—42no—
342C2×D61—816no—
343C2×D61—81no—
344C2×D61—81no—
345C2×D61—81no—
346C2×D61—81no—
347C4×C61—22no—
348C4×C61—22no—
349C4×C61—42no—
350C4×C61—42no—
351C4×C61—41no—
352C4×C61—41no—
353C4×C61—41no—
354C4×C61—81no—
355C4×C61—81no—
356C4×C61C2×#11711yescharacteristic
357C4×C61#51811yescharacteristic
358C4×C61#55111yescharacteristic
359C4×C61#55111yescharacteristic
360Dic61—81no—
361Dic61—81no—
362C2×#418—611no—
363#2346D6111yescharacteristic, complemented
364D4×C22⋊C4—611no—
365#1936—611no—
366#1934—611no—
367#1926—611no—
368#1925—611no—
369#1864—611no—
370#1862—611no—
371#1825—611no—
372#1809—611no—
373#1786—611no—
374#1762—611no—
375C4×#102—611no—
376#1753—611no—
377C2×C61—42no—
378C2×C61#234211yescharacteristic
379C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
380C2×C61#294611yescharacteristic
381C2×C61#331011yescharacteristic
382C2×C61#331911yescharacteristic
383C2×C61#332311yescharacteristic
384C2×C61#332511yescharacteristic
385D61—44no—
386D61—82no—
387C23×D4—611no—
388C22×M16—611no—
389C2×C4×D4—611no—
390C2×C4×D4—611no—
391C2×#117C2×D6111yescharacteristic
392C22×C22⋊C4—1221no—
393C2×#107—611no—
394C2×#106—611no—
395#418—618no—
396C2×#102—611no—
397C2×#102—611no—
398C2×#102—611no—
399C2×#102—611no—
400C2×#102—611no—
401C2×#102—611no—
402C2×#102—611no—
403C2×#102—611no—
404C2×C22⋊C8—611no—
405C2×#97—611no—
406C2×C4×C8—611no—
407#390—611no—
408#390—611no—
409#389C2×D6111yescharacteristic, complemented
410#389C2×D6111yescharacteristic, complemented
411#388—21no—
412#388—21no—
413#386—1221no—
414#386—1221no—
415#382—21no—
416#380—611no—
417#380C2×D6111yescharacteristic
418#379—1221no—
419C4×C4⋊C4C2×D6111yescharacteristic, complemented
420C4×C4⋊C4C2×D6111yescharacteristic, complemented
421C4×C22⋊C4C2×D6111yescharacteristic
422#376—21no—
423#340—611no—
424#340—611no—
425#340—611no—
426#340—611no—
427#340—611no—
428#340—611no—
429#336—611no—
430#336—611no—
431C61#2258411yescharacteristic, complemented, Sylow
432C25—1221no—
433C22×D4—614no—
434C22×D4—611no—
435C22×D4—611no—
436C22×D4—1222no—
437C22×D4—1222no—
438C22×D4—1222no—
439C22×D4—1221no—
440C22×D4—2441no—
441C22×D4—2441no—
442C23×C4—1221no—
443C23×C4—1221no—
444C23×C4C22×D6111yescharacteristic
445C2×M16—614no—
446C2×M16—2441no—
447C2×M16—2441no—
448C22×C8—611no—
449C22×C8—611no—
450C22×C8—611no—
451C22×C8—611no—
452C4×D4—1222no—
453C4×D4—1222no—
454C4×D4—2441no—
455C4×D4—2441no—
456#117—22no—
457#117C4×D6114yescomplemented
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—611no—
461C2×C4⋊C4—611no—
462C2×C4⋊C4C22×D6111yescharacteristic
463C2×C4⋊C4C22×D6111yescharacteristic
464C2×C4⋊C4C22×D6111yescharacteristic
465C2×C4⋊C4C22×D6111yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—1221no—
469C2×C22⋊C4—1221no—
470C2×C22⋊C4—1221no—
471C2×C22⋊C4—1221no—
472C2×C22⋊C4—1221no—
473C2×C22⋊C4—1221no—
474C2×C22⋊C4—1221no—
475C2×C22⋊C4—2444no—
476C2×C22⋊C4C22⋊D6111yescharacteristic
477C2×C22⋊C4C22⋊D6111yescharacteristic
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42C22×D6111yescharacteristic
482C2×C42C22×D6111yescharacteristic
483#107—2441no—
484#106—2441no—
485#102—614no—
486#102—614no—
487#102—614no—
488#102—614no—
489#102—1222no—
490#102—1222no—
491#102—2441no—
492#102—2441no—
493C22⋊C8—1222no—
494#97—2441no—
495C4×C8—2441no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—1221no—
502#95C22⋊D6111yescharacteristic
503#95C22⋊D6111yescharacteristic
504C24—1221no—
505C24—1224no—
506C24—1221no—
507C24—4881no—
508C24—4881no—
509C24—2442no—
510C24—2442no—
511C24—2442no—
512C24—2442no—
513C24C2×C22⋊D6111yescharacteristic
514C2×D4—612no—
515C2×D4—612no—
516C2×D4—612no—
517C2×D4—612no—
518C2×D4—1228no—
519C2×D4—1221no—
520C2×D4—1221no—
521C2×D4—1221no—
522C2×D4—1221no—
523C2×D4—1221no—
524C2×D4—1221no—
525C2×D4—1221no—
526C2×D4—1221no—
527C2×D4—1224no—
528C2×D4—2444no—
529C2×D4—2444no—
530C2×D4—2444no—
531C2×D4—2442no—
532C2×D4—2442no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—1221no—
542C22×C4—1221no—
543C22×C4—4881no—
544C22×C4—4881no—
545C22×C4—2442no—
546C22×C4—2442no—
547C22×C4—2442no—
548C22×C4—2442no—
549C22×C4C2×C4×D6112yes—
550C22×C4#1175822212yes—
551C22×C4C2×C22⋊D6111yescharacteristic
552C22×C4C2×C22⋊D6111yescharacteristic
553C22×C4C2×C22⋊D6111yescharacteristic
554C22×C4C2×C22⋊D6111yescharacteristic
555C22×C4C2×C22⋊D6111yescharacteristic
556C22×C4C23×D6111yescharacteristic
557M16—2444no—
558C2×C8—612no—
559C2×C8—612no—
560C2×C8—1221no—
561C2×C8—1221no—
562C2×C8—1221no—
563C2×C8—1221no—
564C2×C8—1221no—
565C2×C8—1221no—
566C2×C8—1221no—
567C2×C8—1221no—
568C2×C8—1221no—
569C2×C8—1221no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—81no—
577C4⋊C4—81no—
578C4⋊C4—1221no—
579C4⋊C4—1221no—
580C4⋊C4—1221no—
581C4⋊C4—1221no—
582C4⋊C4C2×C4×D6112yes—
583C4⋊C4C2×C4×D6112yes—
584C22⋊C4—24no—
585C22⋊C4—22no—
586C22⋊C4—41no—
587C22⋊C4—81no—
588C22⋊C4—4881no—
589C22⋊C4—4881no—
590C22⋊C4—2442no—
591C22⋊C4—2442no—
592C22⋊C4—2442no—
593C22⋊C4—2442no—
594C22⋊C4—2442no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—24no—
600C42—42no—
601C42—42no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—1222no—
609C23—1222no—
610C23—1222no—
611C23—1222no—
612C23—4884no—
613C23—4884no—
614C23—4884no—
615C23—4884no—
616C23—4884no—
617C23—2448no—
618C23—2448no—
619C23—2441no—
620C23—2441no—
621C23—2441no—
622C23—2441no—
623C23—2441no—
624C23—2441no—
625C23—2441no—
626C23—2441no—
627C23—2441no—
628C23—2441no—
629C23C4×C22⋊D6112yes—
630C23C22×C22⋊D6111yescharacteristic
631D4—614no—
632D4—1222no—
633D4—1222no—
634D4—1222no—
635D4—1222no—
636D4—1222no—
637D4—2448no—
638D4—2441no—
639D4—2441no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—4884no—
670C2×C4—4884no—
671C2×C4—2441no—
672C2×C4—2441no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4C4×C22⋊D6112yes—
678C2×C4#1451980212yes—
679C2×C4C22×C4×D6111yescharacteristic
680C2×C4#41×D6111yescharacteristic
681C2×C4#41×D6111yescharacteristic
682C2×C4C2×#1175822211yescharacteristic
683C2×C4#1451982311yescharacteristic
684C2×C4#1451982311yescharacteristic
685C8—1222no—
686C8—1222no—
687C8—2441no—
688C8—2441no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—1224no—
697C22—48816no—
698C22—4881no—
699C22—4881no—
700C22—4881no—
701C22—4881no—
702C22—2442no—
703C22—2442no—
704C22—2442no—
705C22—2442no—
706C22—2442no—
707C22—2442no—
708C22—2442no—
709C22—2442no—
710C22—2442no—
711C22C2×C4×C22⋊D6111yescharacteristic
712C22#1684040011yescharacteristic
713C22#1684040011yescharacteristic
714C22C2×#1451980211yescharacteristic
715C22#1684056011yescharacteristic
716C22#1684056511yescharacteristic
717C22#1684057011yescharacteristic
718C4—22no—
719C4—22no—
720C4—42no—
721C4—41no—
722C4—42no—
723C4—41no—
724C4—41no—
725C4—81no—
726C4—81no—
727C4—4881no—
728C4—4881no—
729C4#117×D6111yescharacteristic
730C4#1684023611yescharacteristic
731C4#1684043611yescharacteristic
732C4#1684043611yescharacteristic
733C2—42no—
734C2—4882no—
735C2—2444no—
736C2#2144866911yescharacteristic
737C2C4×#1451980211yescharacteristic
738C2#2145464711yescharacteristic
739C2#2145783411yescharacteristic
740C2#2145796911yescharacteristic
741C2#2145802911yescharacteristic
742C2#2145805511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2346C2
socleC23×C61C22×D4
prime radicalC23×D244C22
cosocleC22×C4×C61C24
hypercenter#2346D61
hypocenterC61#22584
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2346

Complements

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

NH ≅ G/Ntype
3. #21446515C2semidirect
4. #21446501C2semidirect
5. #21446446C2semidirect
6. #21446439C2semidirect
7. #21446079C2semidirect
8. #21446065C2semidirect
9. #21445914C2semidirect
10. #21445850C2semidirect
12. #21445647C2semidirect
13. C4×#14519697C2semidirect
14. #21445603C2semidirect
15. C61×#2346C2semidirect
21. C2×#14519710C22semidirect
22. C2×#14519708C22semidirect
23. #16839766C4semidirect
33. C2×#14519688C22semidirect
34. C2×C4×#92418C22semidirect
41. #16839524C22semidirect
42. #16839524C22semidirect
43. #16839524C22semidirect
44. #16839524C22semidirect
45. #16839524C22semidirect
46. #16839524C22semidirect
47. #16839517C22semidirect
48. #16839517C22semidirect
50. C61×#389C22semidirect
51. C61×#389C22semidirect
56. C4×C4⋊C4×C61C22semidirect
57. C4×C4⋊C4×C61C22semidirect
74. C2×#11758194C2×C4semidirect
101. #14519697C2×C4semidirect
102. #14519697C2×C4semidirect
109. #117×C61C2×C4semidirect
363. #2346D61semidirect
409. #389C2×D61semidirect
410. #389C2×D61semidirect
419. C4×C4⋊C4C2×D61semidirect
420. C4×C4⋊C4C2×D61semidirect
431. C61#22584semidirect
457. #117C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168397662
C22⋊C4×D2442
#214465152
#214465012
#214464462
#214464392
#214460792
#214460652
#214459142
#214458502
#214457492
#214456472
C4×#145196972
#214456032
C61×#23462
#2258461