Finite Group Databasebeta

← #29698108

Subgroups — #29698108

Order 15616.

1126 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839825C211yesmaximal, characteristic
2C22×#14519708C211yesmaximal, characteristic, complemented
3C2×#106×D61C211yesmaximal, characteristic, complemented
4C4⋊C4×C22⋊D61C211yesmaximal, characteristic
5#21448715C211yesmaximal, characteristic
6#21446581C211yesmaximal, characteristic, complemented
7#21446579C211yesmaximal, characteristic, complemented
8#21446014C211yesmaximal, characteristic, complemented
9#21446013C211yesmaximal, characteristic, complemented
10#21446010C211yesmaximal, characteristic, complemented
11#21445974C211yesmaximal, characteristic, complemented
12#21445843C211yesmaximal, characteristic, complemented
13#21445842C211yesmaximal, characteristic, complemented
14#21445707C211yesmaximal, characteristic, complemented
15C61×#1853C211yesmaximal, characteristic, complemented
16C23×#92418C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C2×C4×C22⋊D61—21no—
19C2×C4×C22⋊D61C2211yescharacteristic
20C2×#14519737—21no—
21C22×C4⋊Dic61C2211yescharacteristic
22C2×C4⋊C4×D61C2211yescharacteristic
23C2×C4⋊C4×D61C2211yescharacteristic
24#16839825C418yescomplemented
25C2×#14519709C2211yescharacteristic
26C2×#14519709C2211yescharacteristic
27C2×#14519708—24no—
28C2×#14519708C2211yescharacteristic
29C2×#14519708C2211yescharacteristic
30C2×#14519708C2211yescharacteristic
31C2×#14519708C2211yescharacteristic
32C2×#14519708C2211yescharacteristic
33C2×#14519708C2211yescharacteristic
34#106×D61—24no—
35C2×#14519706C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×C8×Dic61C2211yescharacteristic
38#16839659—21no—
39#16839657—21no—
40#16839636—21no—
41#16839635—21no—
42#16839634—21no—
43#16839633—21no—
44#16839631C2211yescharacteristic
45#16839631C2211yescharacteristic
46#16839622C2211yescharacteristic
47#16839619C2211yescharacteristic
48#16839619C2211yescharacteristic
49C4⋊C4×Dic61C2211yescharacteristic
50C4⋊C4×Dic61C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C22×C4⋊C4×C61C2211yescharacteristic
56C2×#106×C61C2211yescharacteristic
57C2×#106×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C22×C22⋊D61D411yescharacteristic
63C23×Dic61—21no—
64C22×C4×D61—21no—
65C22×C4×D61—21no—
66C22×C4×D61C2311yescharacteristic
67C22×#92418—22no—
68C22×#92418—22no—
69C22×#92418C2×C414yescomplemented
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C2×C8×D61—22no—
73C2×C8×D61—22no—
74C2×C8×D61C2×C414yescomplemented
75C4×C22⋊D61—44no—
76C4×C22⋊D61C2×C414yes—
77C4×C22⋊D61Q814yes—
78#14519737—44no—
79C2×C4⋊Dic61—22no—
80C2×C4⋊Dic61—21no—
81C2×C4⋊Dic61—41no—
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×#11758196—21no—
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×#11758196D411yescharacteristic
93C4⋊C4×D61—22no—
94C4⋊C4×D61—22no—
95C4⋊C4×D61—41no—
96C4⋊C4×D61—41no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61D411yescharacteristic
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198D411yescharacteristic
102C2×C4×Dic61—21no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61C2311yescharacteristic
105#14519709—22no—
106#14519709—41no—
107#14519708—22no—
108#14519708—22no—
109#14519708—22no—
110#14519708—22no—
111#14519708—22no—
112#14519708D414yescomplemented
113#14519706C2×C414yescomplemented
114#14519689C2×C414yescomplemented
115C8×Dic61C2×C414yescomplemented
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121C23×C4×C61—21no—
122C23×C4×C61C2311yescharacteristic
123C22×C8×C61C2311yescharacteristic
124C22×C8×C61C2311yescharacteristic
125C2×C4⋊C4×C61—22no—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61—41no—
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C22⋊C4×C61—21no—
133#106×C61—22no—
134#106×C61—41no—
135C22⋊C8×C61C2×C414yescomplemented
136#95×C61—21no—
137C24×C61C2×D411yescharacteristic
138C23×D61C2×D411yescharacteristic
139C22×C4×C61—21no—
140C22×C4×C61—21no—
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—42no—
148C22×C4×C61—42no—
149C22×C4×C61—81no—
150C22×C4×C61C22×C412yes—
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×Q812yes—
153C22×C4×C61C2411yescharacteristic
154C2×C22⋊D61C4⋊C414yes—
155C2×C22⋊D61SD1614yes—
156C2×C22⋊D61SD1614yes—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—42no—
162C22×Dic61—42no—
163C22×Dic61—81no—
164C22×Dic61C2×D411yescharacteristic
165C22×Dic61C2×D411yescharacteristic
166C22×Dic61C2×D411yescharacteristic
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—42no—
172C2×C4×D61—42no—
173C2×C4×D61—42no—
174C2×C4×D61—42no—
175C2×C4×D61—81no—
176C2×C4×D61—81no—
177C2×C4×D61C22×C412yes—
178C2×C4×D61C2×Q812yes—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61C22×C412yes—
184C2×C8×C61C22×C412yes—
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—21no—
192C4⋊C4×C61—42no—
193C4⋊C4×C61C2×D412yes—
194C22⋊C4×C61—42no—
195C22⋊Dic61—42no—
196C22⋊Dic61C4⋊C414yes—
197#11758198—42no—
198#11758198—42no—
199#11758198C4⋊C414yes—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61—21no—
207C4⋊Dic61—42no—
208C4⋊Dic61C2×D412yes—
209#11758196—42no—
210#11758196—42no—
211#11758196—42no—
212#11758196—42no—
213#11758196—81no—
214#11758196—81no—
215#11758196C4⋊C414yes—
216C4×Dic61—42no—
217C4×Dic61—42no—
218C4×Dic61C22×C412yes—
219C4×Dic61C2×Q812yes—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418—28no—
223C2×#92418C22×C412yes—
224C2×#92418C22×C412yes—
225C2×#92418C2×D412yes—
226C2×#92418#4112yes—
227C8×D61—28no—
228C23×C61—21no—
229C23×C61—21no—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61C2×C4⋊C412yes—
233C23×C61C2×SD1612yes—
234C23×C61C2×SD1612yes—
235C23×C61C22×D411yescharacteristic
236C22×D61—21no—
237C22×D61—21no—
238C22×D61—21no—
239C22×D61—21no—
240C22×D61C2×C4⋊C412yes—
241C22×D61C2×SD1612yes—
242C22×D61C2×SD1612yes—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—22no—
248C2×C4×C61—22no—
249C2×C4×C61—22no—
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×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—84no—
262C2×C4×C61C2×C4⋊C412yes—
263C2×C4×C61C23×C411yescharacteristic
264C2×C4×C61C22×D411yescharacteristic
265C2×C4×C61C22×Q811yescharacteristic
266C2×C4×C61C2×#4111yescharacteristic
267C2×C4×C61H(5,𝔽2)11yescharacteristic
268C2×C4×C612−1+411yescharacteristic
269C22⋊D61#106116yescomplemented
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—22no—
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—84no—
287C2×Dic61C2×C4⋊C412yes—
288C2×Dic61C2×C4⋊C412yes—
289C2×Dic61C2×C4⋊C412yes—
290C2×Dic61C2×SD1612yes—
291C2×Dic61C2×SD1612yes—
292C4×D61—22no—
293C4×D61—22no—
294C4×D61—22no—
295C4×D61—22no—
296C4×D61—84no—
297C4×D61—84no—
298C8×C61—22no—
299C8×C61—22no—
300#92418—22no—
301#92418C4×D414yescomplemented
302D4×#106—611nomaximal, Sylow
303C22×C61—22no—
304C22×C61—22no—
305C22×C61—22no—
306C22×C61—22no—
307C22×C61—22no—
308C22×C61—22no—
309C22×C61C2×#10614yescomplemented
310C22×C61C22×C4⋊C411yescharacteristic
311C22×C61D4211yescharacteristic
312C22×C61#54711yescharacteristic
313C22×C61C22×SD1611yescharacteristic
314C22×C61C22×SD1611yescharacteristic
315C22×C61#57711yescharacteristic
316C22×C61#57711yescharacteristic
317C2×D61—22no—
318C2×D61—22no—
319C2×D61—22no—
320C2×D61—22no—
321C2×D61—22no—
322C2×D61—22no—
323C2×D61C2×#10614yescomplemented
324C4×C61—22no—
325C4×C61—42no—
326C4×C61—81no—
327C4×C61—81no—
328C4×C61—81no—
329C4×C61C2×C4×D411yescharacteristic
330C4×C61#52011yescharacteristic
331C4×C61D4×Q811yescharacteristic
332C4×C61#55411yescharacteristic
333Dic61—22no—
334Dic61—22no—
335Dic61—42no—
336Dic61—81no—
337Dic61—81no—
338Dic61—81no—
339Dic61C2×#10614yescomplemented
340C2×C8×D4—611no—
341C22×#106—611no—
342C22×#106—611no—
343D4×C4⋊C4—611no—
344D4×C4⋊C4—611no—
345#1948—611no—
346#1948—611no—
347#1853—611no—
348#1853—611no—
349#1853—611no—
350#1853D6111yescharacteristic, complemented
351#1844—611no—
352#1807—611no—
353#1807—611no—
354C4×#106—611no—
355C2×C61—24no—
356C2×C61D4×C4⋊C411yescharacteristic
357C2×C61C22×#10611yescharacteristic
358C2×C61#291211yescharacteristic
359C2×C61D4×SD1611yescharacteristic
360C2×C61D4×SD1611yescharacteristic
361C2×C61#333511yescharacteristic
362C2×C61#333511yescharacteristic
363D61—24no—
364C23×C8—611no—
365C23×C8—611no—
366C2×C4×D4—611no—
367C2×C4×D4—1221no—
368C2×C4×D4—1221no—
369C22×C4⋊C4—611no—
370C22×C4⋊C4—611no—
371C22×C4⋊C4—611no—
372C22×C4⋊C4C2×D6111yescharacteristic
373C8×D4—618no—
374C2×#106—611no—
375C2×#106—611no—
376C2×#106—611no—
377C2×#106—611no—
378C2×#106—611no—
379C2×#106—611no—
380C2×#106—611no—
381C2×#106—611no—
382C2×#106—1224no—
383C2×#106—1224no—
384C2×#106C2×D6111yescharacteristic
385C2×#106C2×D6111yescharacteristic
386C2×C4⋊C8—611no—
387C2×C22⋊C8—611no—
388C2×C22⋊C8C2×D6111yescharacteristic
389C2×C4×C8—611no—
390#389—1221no—
391#389—1221no—
392#385—1221no—
393#385—1221no—
394#385—1221no—
395#385—1221no—
396#384—611no—
397#384—611no—
398#380—611no—
399#380—611no—
400#380—611no—
401#380C2×D6111yescharacteristic
402C4×C4⋊C4—611no—
403C4×C4⋊C4—611no—
404#340—611no—
405#340—611no—
406#340—611no—
407#340—611no—
408#340C2×D6111yescharacteristic
409#340C2×D6111yescharacteristic
410C61D4×#10611yescharacteristic, complemented, Sylow
411C22×D4—611no—
412C23×C4—21no—
413C23×C4—611no—
414C23×C4—1221no—
415C23×C4—1221no—
416C23×C4—1221no—
417C23×C4C22×D6111yescharacteristic
418C22×C8—611no—
419C22×C8—614no—
420C22×C8—611no—
421C22×C8—614no—
422C22×C8—1222no—
423C22×C8—1222no—
424C22×C8—1222no—
425C22×C8—1222no—
426C22×C8C22×D6111yescharacteristic
427C22×C8C22×D6111yescharacteristic
428C4×D4—614no—
429C4×D4—614no—
430C4×D4—2444no—
431C4×D4—2444no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—41no—
435C2×C4⋊C4—611no—
436C2×C4⋊C4—611no—
437C2×C4⋊C4—611no—
438C2×C4⋊C4—611no—
439C2×C4⋊C4—611no—
440C2×C4⋊C4—1222no—
441C2×C4⋊C4—1222no—
442C2×C4⋊C4—1222no—
443C2×C4⋊C4—1221no—
444C2×C4⋊C4—1221no—
445C2×C4⋊C4—1221no—
446C2×C4⋊C4—1221no—
447C2×C4⋊C4—1221no—
448C2×C4⋊C4—1221no—
449C2×C4⋊C4—1221no—
450C2×C4⋊C4—2441no—
451C2×C4⋊C4—2441no—
452C2×C4⋊C4—2441no—
453C2×C4⋊C4C22×D6111yescharacteristic
454C2×C4⋊C4C22×D6111yescharacteristic
455C2×C4⋊C4C22×D6111yescharacteristic
456C2×C4⋊C4C22×D6111yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—611no—
459C2×C22⋊C4—611no—
460C2×C22⋊C4—1221no—
461C2×C22⋊C4—1221no—
462C2×C22⋊C4—1221no—
463C2×C42—611no—
464C2×C42—1221no—
465C2×C42—1221no—
466#106—22no—
467#106—41no—
468#106—614no—
469#106—1222no—
470#106—1222no—
471#106—1222no—
472#106—1222no—
473#106—1222no—
474#106—1222no—
475#106—2441no—
476C4⋊C8—614no—
477C22⋊C8—614no—
478C22⋊C8C4×D6114yescomplemented
479C4×C8—614no—
480#95—21no—
481#95—1221no—
482#95—1221no—
483#95—1221no—
484#95—1221no—
485#95—1221no—
486C24—611no—
487C24D4×D6111yescharacteristic
488C2×D4—614no—
489C2×D4—614no—
490C2×D4—614no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—81no—
502C22×C4—611no—
503C22×C4—611no—
504C22×C4—611no—
505C22×C4—612no—
506C22×C4—612no—
507C22×C4—1221no—
508C22×C4—1221no—
509C22×C4—1221no—
510C22×C4—1221no—
511C22×C4—1221no—
512C22×C4—1221no—
513C22×C4—1221no—
514C22×C4—1221no—
515C22×C4—4881no—
516C22×C4—4881no—
517C22×C4—4881no—
518C22×C4—2442no—
519C22×C4—2442no—
520C22×C4—2442no—
521C22×C4—2442no—
522C22×C4—2442no—
523C22×C4—2442no—
524C22×C4C2×C4×D6112yes—
525C22×C4D4×D6111yescharacteristic
526C22×C4Q8×D6112yes—
527C22×C4C23×D6111yescharacteristic
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—612no—
533C2×C8—612no—
534C2×C8—612no—
535C2×C8—612no—
536C2×C8—1228no—
537C2×C8—1228no—
538C2×C8—1221no—
539C2×C8—1221no—
540C2×C8C2×C4×D6112yes—
541C2×C8C2×C4×D6112yes—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—42no—
550C4⋊C4—614no—
551C4⋊C4—612no—
552C4⋊C4—1221no—
553C4⋊C4—1221no—
554C4⋊C4—1221no—
555C4⋊C4—1221no—
556C4⋊C4—1221no—
557C4⋊C4—1221no—
558C4⋊C4—1221no—
559C4⋊C4—4881no—
560C4⋊C4—4881no—
561C4⋊C4—2442no—
562C4⋊C4—2442no—
563C4⋊C4—2442no—
564C4⋊C4—2442no—
565C4⋊C4—2442no—
566C4⋊C4D4×D6112yes—
567C22⋊C4—42no—
568C22⋊C4—614no—
569C22⋊C4—614no—
570C22⋊C4—2442no—
571C22⋊C4—2442no—
572C22⋊C4—2442no—
573C42—612no—
574C42—612no—
575C42—2442no—
576C42—2442no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—612no—
582C23—612no—
583C23—612no—
584C23—1221no—
585C23—1221no—
586C23—1221no—
587C23—1221no—
588C23C4⋊C4×D6112yes—
589C23SD16×D6112yes—
590C23SD16×D6112yes—
591C23C2×D4×D6111yescharacteristic
592D4—6116no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—84no—
612C2×C4—612no—
613C2×C4—612no—
614C2×C4—612no—
615C2×C4—612no—
616C2×C4—612no—
617C2×C4—1221no—
618C2×C4—1221no—
619C2×C4—1221no—
620C2×C4—1221no—
621C2×C4—1222no—
622C2×C4—1222no—
623C2×C4—1222no—
624C2×C4—1222no—
625C2×C4—1222no—
626C2×C4—4884no—
627C2×C4—4884no—
628C2×C4—4884no—
629C2×C4—2441no—
630C2×C4—2441no—
631C2×C4—2441no—
632C2×C4—2441no—
633C2×C4—2441no—
634C2×C4—2441no—
635C2×C4—2441no—
636C2×C4—2441no—
637C2×C4—2441no—
638C2×C4—2441no—
639C2×C4—2441no—
640C2×C4C4⋊C4×D6112yes—
641C2×C4C22×C4×D6111yescharacteristic
642C2×C4C2×D4×D6111yescharacteristic
643C2×C4C2×Q8×D6111yescharacteristic
644C2×C4#41×D6111yescharacteristic
645C2×C4#1451982211yescharacteristic
646C2×C4#1451982411yescharacteristic
647C8—22no—
648C8—22no—
649C8—614no—
650C8—1222no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—22no—
657C22—614no—
658C22—1222no—
659C22—1222no—
660C22—1222no—
661C22—1222no—
662C22—1222no—
663C22—1222no—
664C22#106×D6114yescomplemented
665C22C2×C4⋊C4×D6111yescharacteristic
666C22#1684039411yescharacteristic
667C22#1684041011yescharacteristic
668C22C2×SD16×D6111yescharacteristic
669C22C2×SD16×D6111yescharacteristic
670C22#1684057111yescharacteristic
671C22#1684057211yescharacteristic
672C4—22no—
673C4—42no—
674C4—81no—
675C4—81no—
676C4—81no—
677C4—614no—
678C4—1222no—
679C4—1222no—
680C4—4881no—
681C4—4881no—
682C4—4881no—
683C4—2442no—
684C4C4×D4×D6111yescharacteristic
685C4#1684024111yescharacteristic
686C4#1684042511yescharacteristic
687C4#1684046611yescharacteristic
688C2—24no—
689C2—1224no—
690C2#2144871711yescharacteristic
691C2C2×#106×D6111yescharacteristic
692C2#2145441311yescharacteristic
693C2#2145750811yescharacteristic
694C2#2145751311yescharacteristic
695C2#2145816911yescharacteristic
696C2#2145817411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1853C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
cosocleC22×C4×C61C24
hypercenter#1853D61
hypocenterC61D4×#106
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
2. C22×#14519708C2semidirect
3. C2×#106×D61C2semidirect
6. #21446581C2semidirect
7. #21446579C2semidirect
8. #21446014C2semidirect
9. #21446013C2semidirect
10. #21446010C2semidirect
11. #21445974C2semidirect
12. #21445843C2semidirect
13. #21445842C2semidirect
14. #21445707C2semidirect
15. C61×#1853C2semidirect
24. #16839825C4semidirect
69. C22×#92418C2×C4semidirect
74. C2×C8×D61C2×C4semidirect
112. #14519708D4semidirect
113. #14519706C2×C4semidirect
114. #14519689C2×C4semidirect
115. C8×Dic61C2×C4semidirect
135. C22⋊C8×C61C2×C4semidirect
269. C22⋊D61#106semidirect
301. #92418C4×D4semidirect
309. C22×C61C2×#106semidirect
323. C2×D61C2×#106semidirect
339. Dic61C2×#106semidirect
350. #1853D61semidirect
410. C61D4×#106semidirect
478. C22⋊C8C4×D61semidirect
664. C22#106×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398252
C22×#145197082
C2×#106×D612
C4⋊C4×C22⋊D612
#214487152
#214465812
#214465792
#214460142
#214460132
#214460102
#214459742
#214458432
#214458422
#214457072
C61×#18532
D4×#10661