Finite Group Databasebeta

← C2×#21458361 #30558653

Subgroups — C2×#21458361 #30558653

Order 15616.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840485C211yesmaximal, characteristic, complemented
2C2×#16840465C211yesmaximal, characteristic
3#21458361C2116yesmaximal, direct product factor
4C2×#16840172C211yesmaximal, characteristic, complemented
5C2×#16840101C211yesmaximal, characteristic, complemented
6C2×#16840089C211yesmaximal, characteristic, complemented
7C2×#16840088C211yesmaximal, characteristic, complemented
8C2×#16840091C211yesmaximal, characteristic, complemented
9C2×#16840053C211yesmaximal, characteristic, complemented
10C2×#16840011C211yesmaximal, characteristic, complemented
11C2×#16839994C211yesmaximal, characteristic, complemented
12C2×#16839860C211yesmaximal, characteristic, complemented
13C2×#16839832C211yesmaximal, characteristic, complemented
14C2×#16839803C211yesmaximal, characteristic, complemented
15C2×#16839797C211yesmaximal, characteristic, complemented
16C2×C61×#479C211yesmaximal, characteristic, complemented
17C22×#11758201C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840485—24no—
21#16840485C2218yescomplemented
22#16840465—24no—
23#16840465C2218yes—
24C2×#14519777C2211yescharacteristic
25C2×#14519772—21no—
26C2×#14519772—21no—
27C2×#14519772—21no—
28C2×#14519765—21no—
29C2×#14519762—21no—
30C2×#14519753C2211yescharacteristic
31C2×#14519753C2211yescharacteristic
32C2×#14519752—21no—
33C2×#14519752C2211yescharacteristic
34C2×#14519752C2211yescharacteristic
35C2×C4×Dic122—21no—
36C2×C4×D244C2211yescharacteristic
37C2×C4×D244C2211yescharacteristic
38C2×#14519739—21no—
39C2×#14519735C2211yescharacteristic
40C2×#14519735C2211yescharacteristic
41C2×#14519735C2211yescharacteristic
42C2×C4⋊C4×D61C2211yescharacteristic
43#16840172C2218yescomplemented
44#16840101C2218yescomplemented
45#16840091C2218yescomplemented
46#16840089C2218yescomplemented
47#16840088C2218yescomplemented
48#16840053C2218yescomplemented
49#16840011C2218yescomplemented
50#16839994C2218yescomplemented
51#16839860C2218yescomplemented
52#16839832C2218yescomplemented
53#16839803C2218yescomplemented
54#16839797C2218yescomplemented
55C2×#14519710C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519710C2211yescharacteristic
58C2×#14519709C2211yescharacteristic
59C2×#14519709C2211yescharacteristic
60C2×#14519708C2211yescharacteristic
61C2×#14519708C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519688C2211yescharacteristic
69C2×#125×C61C2211yescharacteristic
70C2×C4×Q8×C61C2211yescharacteristic
71C61×#479C2218yescomplemented
72C2×#107×C61C2211yescharacteristic
73C2×#106×C61C2211yescharacteristic
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#103×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×D244—21no—
79C22×D244—21no—
80C22×D244D411yescharacteristic
81C22×D244C2311yescharacteristic
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61C2311yescharacteristic
85C22×C4×D61C2311yescharacteristic
86C2×#11758201—24no—
87C2×#11758201C2314yes—
88C2×#11758189—24no—
89C2×#11758189C2314yes—
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92C2×C8×D61—24no—
93C2×C8×D61C2314yes—
94#14519777—22no—
95#14519777C2314yes—
96#14519772—28no—
97#14519772—28no—
98#14519772—28no—
99#14519765—28no—
100#14519762—28no—
101#14519753—22no—
102#14519753—22no—
103#14519753C2314yes—
104#14519753C2314yes—
105#14519752—28no—
106#14519752—22no—
107#14519752—22no—
108#14519752C2314yes—
109#14519752C2314yes—
110C4×Dic122—28no—
111C4×D244—22no—
112C4×D244D414yes—
113C4×D244C2314yes—
114C4×D244C2314yes—
115#14519739—28no—
116#14519735—22no—
117#14519735—22no—
118#14519735—22no—
119#14519735C2314yes—
120#14519735C2314yes—
121#14519735C2314yes—
122C2×C4⋊Dic61—21no—
123C2×C4⋊Dic61D411yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×C4⋊Dic61C2311yescharacteristic
126C2×C4⋊Dic61C2311yescharacteristic
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C4⋊C4×D61—22no—
131C4⋊C4×D61C2314yes—
132C2×#11758198—21no—
133C2×#11758198—21no—
134C2×#11758198—21no—
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198D411yescharacteristic
141C2×#11758198D411yescharacteristic
142C2×C4×Dic61—21no—
143C2×C4×Dic61—21no—
144C2×C4×Dic61—21no—
145#14519710C2314yes—
146#14519710C2314yes—
147#14519710C2314yes—
148#14519709C2314yes—
149#14519709C2314yes—
150#14519708C2314yes—
151#14519708C2314yes—
152#14519701C2314yes—
153#14519699C2314yes—
154#14519699C2314yes—
155#14519697C2314yes—
156#14519689C2314yes—
157#14519689C2314yes—
158#14519688C2314yes—
159C22×Q8×C61C2311yescharacteristic
160C22×C8×C61C2311yescharacteristic
161C22×C8×C61C2311yescharacteristic
162#125×C61—22no—
163#125×C61C2314yes—
164C4×Q8×C61—22no—
165C4×Q8×C61C2314yes—
166C2×C4⋊C4×C61—21no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61—21no—
169C2×C4⋊C4×C61C2311yescharacteristic
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C42×C61—21no—
173C2×C42×C61C2311yescharacteristic
174#107×C61C2314yes—
175#106×C61C2314yes—
176C4⋊C8×C61C2314yes—
177#103×C61C2314yes—
178#103×C61C2314yes—
179C23×D61—21no—
180C23×D61C2×D411yescharacteristic
181C23×D61C2×D411yescharacteristic
182C2×Q8×C61—21no—
183C2×Q8×C61—22no—
184C2×Q8×C61—22no—
185C2×Q8×C61C2412yes—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2411yescharacteristic
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61C2×D411yescharacteristic
197C22×Dic61C2×D411yescharacteristic
198C2×D244—22no—
199C2×D244—22no—
200C2×D244—24no—
201C2×D244—21no—
202C2×D244—24no—
203C2×D244—42no—
204C2×D244—44no—
205C2×D244—82no—
206C2×D244C2×D414yes—
207C2×D244C2412yes—
208C2×C4×D61—22no—
209C2×C4×D61—22no—
210C2×C4×D61—22no—
211C2×C4×D61—22no—
212C2×C4×D61—24no—
213C2×C4×D61—24no—
214C2×C4×D61—82no—
215C2×C4×D61—82no—
216C2×C4×D61C2×D412yes—
217C2×C4×D61C2×D412yes—
218C2×C4×D61C2412yes—
219C2×C4×D61C2412yes—
220C2×Dic122—24no—
221C2×Dic122—44no—
222C2×C8×C61—22no—
223C2×C8×C61—22no—
224C2×C8×C61C2412yes—
225C2×C8×C61C2412yes—
226C4⋊C4×C61—24no—
227C4⋊C4×C61—24no—
228C4⋊C4×C61—24no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61C2412yes—
233C4⋊C4×C61C2412yes—
234C4⋊C4×C61C2412yes—
235C42×C61—24no—
236C42×C61C2×D412yes—
237C42×C61C2412yes—
238#11758201—28no—
239#11758198—24no—
240#11758198—24no—
241#11758198—24no—
242#11758198—24no—
243#11758198—24no—
244#11758198—24no—
245#11758198—24no—
246#11758198—24no—
247#11758198C2×D414yes—
248#11758198C2×D414yes—
249C4⋊Dic61—21no—
250C4⋊Dic61—24no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61C2×D414yes—
254C4⋊Dic61C2412yes—
255C4⋊Dic61C2412yes—
256C4⋊Dic61C2412yes—
257#11758196—24no—
258#11758196—24no—
259#11758196—24no—
260C4×Dic61—24no—
261C4×Dic61—24no—
262C4×Dic61—24no—
263C2×#92418—22no—
264C2×#92418#4114yes—
265C2×#92418C2412yes—
266C2×#92418C2412yes—
267#11758189—28no—
268C8×D61—28no—
269C23×C61C22×D411yescharacteristic
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—42no—
278C22×D61—42no—
279C22×D61—42no—
280C22×D61C22×D412yes—
281C22×D61C22×D412yes—
282Q8×C61—22no—
283Q8×C61—22no—
284Q8×C61—42no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—42no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61—42no—
295C2×C4×C61C22×D412yes—
296C2×C4×C61C22×D412yes—
297C2×C4×C61C22×D411yescharacteristic
298C2×C4×C61C2×#4112yes—
299C2×C4×C612−1+412yes—
300C2×C4×C61C2511yescharacteristic
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—42no—
307C2×Dic61—42no—
308C2×Dic61—42no—
309C2×Dic61C22×D412yes—
310C2×Dic61C22×D412yes—
311D244—22no—
312D244—22no—
313D244—44no—
314D244—48no—
315D244—42no—
316D244—84no—
317C4×D61—24no—
318C4×D61—24no—
319C4×D61—22no—
320C4×D61—22no—
321C4×D61—22no—
322C4×D61—22no—
323C4×D61—84no—
324C4×D61—84no—
325Dic122—48no—
326C8×C61—22no—
327C8×C61—22no—
328#92418—22no—
329#92418C2×#4114yes—
330C2×#3350—611nomaximal, Sylow
331C22×C61#54712yes—
332C22×C61#57512yes—
333C22×C61#57712yes—
334C22×C61C23×D411yescharacteristic
335C2×D61—22no—
336C2×D61—22no—
337C2×D61—22no—
338C2×D61—22no—
339C2×D61—22no—
340C2×D61—22no—
341C2×D61—44no—
342C2×D61—44no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—42no—
346C2×D61—84no—
347C4×C61—22no—
348C4×C61—22no—
349C4×C61—42no—
350C4×C61—42no—
351C4×C61—42no—
352C4×C61—42no—
353C4×C61#54712yes—
354C4×C61C22×#4111yescharacteristic
355C4×C61C2×2−1+411yescharacteristic
356Dic61—22no—
357Dic61—22no—
358Dic61—42no—
359Dic61—42no—
360Dic61—42no—
361C2×#556—611no—
362C2×#553—611no—
363#3350—6116no—
364C2×#501—611no—
365C2×#485—611no—
366C2×#482—611no—
367C2×#482—611no—
368C2×#483—611no—
369C2×#479D6111yescharacteristic, complemented
370C2×#476—611no—
371C2×#468—611no—
372C2×#465—611no—
373C2×#440—611no—
374C2×#435—611no—
375C2×#428—611no—
376C2×#427—611no—
377C2×C61#335014yescomplemented
378C2×C61C2×#54711yescharacteristic
379C2×C61C2×#57511yescharacteristic
380C2×C61C2×#57711yescharacteristic
381D61—42no—
382D61—42no—
383D61—82no—
384C22×SD16—611no—
385C22×M16—611no—
386C23×C8—611no—
387#556—618no—
388#556—1224no—
389#553—618no—
390#553—1224no—
391C2×C4⋊Q8—611no—
392C2×#126—1221no—
393C2×#126—1221no—
394C2×#126—1221no—
395C2×#125C2×D6111yescharacteristic
396C2×#124—1221no—
397C2×#123—1221no—
398C2×C22⋊Q8—611no—
399C2×C22⋊Q8—611no—
400C2×#121—611no—
401C2×#121—611no—
402C2×#121—1221no—
403C2×C4×Q8—1221no—
404C2×C4×Q8C2×D6111yescharacteristic
405C2×C4×D4—611no—
406C2×C4×D4—611no—
407C2×C4×D4—1221no—
408C2×#117—611no—
409C2×#117—611no—
410C2×#117—611no—
411C22×C4⋊C4—611no—
412#501—618no—
413#485—618no—
414#483—618no—
415#482—618no—
416#482—618no—
417#479C2×D6118yescomplemented
418#476—618no—
419#468—618no—
420#465—618no—
421#440—618no—
422#435—618no—
423#428—618no—
424#427—618no—
425C2×#107—611no—
426C2×#107—611no—
427C2×#107—611no—
428C2×#107C2×D6111yescharacteristic
429C2×#106—611no—
430C2×#106—611no—
431C2×#106—611no—
432C2×#106—611no—
433C2×#106C2×D6111yescharacteristic
434C2×C4⋊C8C2×D6111yescharacteristic
435C2×#103—611no—
436C2×#103C2×D6111yescharacteristic
437C2×#103C2×D6111yescharacteristic
438C2×#102—611no—
439C2×#102—611no—
440C2×#102—611no—
441C2×C22⋊C8—611no—
442C2×C22⋊C8—611no—
443C2×#97—611no—
444C61C2×#335011yescharacteristic, complemented, Sylow
445C22×Q8—1221no—
446C22×Q8C22×D6111yescharacteristic
447C22×D4—611no—
448C22×D4—611no—
449C22×D4—1221no—
450C22×D4—1221no—
451C23×C4—611no—
452C23×C4—611no—
453C23×C4—1221no—
454C23×C4—1221no—
455C2×SD16—614no—
456C2×SD16—1224no—
457C2×M16—614no—
458C2×M16—1224no—
459C22×C8—611no—
460C22×C8—611no—
461C22×C8—614no—
462C22×C8—1224no—
463C22×C8C22×D6111yescharacteristic
464C22×C8C22×D6111yescharacteristic
465C4⋊Q8—614no—
466C4⋊Q8—1222no—
467#126—1228no—
468#126—1228no—
469#126—1228no—
470#125—22no—
471#125C22×D6114yes—
472#124—1228no—
473#123—1228no—
474C22⋊Q8—614no—
475C22⋊Q8—614no—
476C22⋊Q8—1222no—
477C22⋊Q8—1222no—
478#121—614no—
479#121—614no—
480#121—1222no—
481#121—1222no—
482#121—1228no—
483C4×Q8—22no—
484C4×Q8—1228no—
485C4×Q8C22×D6114yes—
486C4×D4—614no—
487C4×D4—614no—
488C4×D4—614no—
489C4×D4—1228no—
490C4×D4—1222no—
491#117—614no—
492#117—614no—
493#117—614no—
494#117—1222no—
495#117—1222no—
496#117—1222no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—614no—
505C2×C4⋊C4—1222no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4C22×D6111yescharacteristic
511C2×C4⋊C4C22×D6111yescharacteristic
512C2×C4⋊C4C22×D6111yescharacteristic
513C2×C22⋊C4—611no—
514C2×C22⋊C4—611no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C42—21no—
524C2×C42—1221no—
525C2×C42—1221no—
526C2×C42—1221no—
527C2×C42C22×D6111yescharacteristic
528#107—614no—
529#107—614no—
530#107—614no—
531#107C22×D6114yes—
532#106—614no—
533#106—614no—
534#106—614no—
535#106—614no—
536#106C22×D6114yes—
537C4⋊C8C22×D6114yes—
538#103—614no—
539#103C22×D6114yes—
540#103C22×D6114yes—
541#102—614no—
542#102—614no—
543#102—614no—
544C22⋊C8—614no—
545C22⋊C8—614no—
546#97—614no—
547C24—611no—
548C24—611no—
549C24—1221no—
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—1224no—
554C2×Q8—2444no—
555C2×Q8C23×D6112yes—
556C2×D4—614no—
557C2×D4—612no—
558C2×D4—1224no—
559C2×D4—1224no—
560C2×D4—1221no—
561C2×D4—1222no—
562C2×D4—1222no—
563C2×D4—4882no—
564C2×D4—2442no—
565C2×D4—2444no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—611no—
571C22×C4—611no—
572C22×C4—612no—
573C22×C4—612no—
574C22×C4—612no—
575C22×C4—612no—
576C22×C4—1224no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1224no—
585C22×C4—4882no—
586C22×C4—4882no—
587C22×C4D4×D6111yescharacteristic
588C22×C4D4×D6111yescharacteristic
589C22×C4C23×D6111yescharacteristic
590SD16—1228no—
591M16—1228no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—614no—
595C2×C8—612no—
596C2×C8—612no—
597C2×C8—1228no—
598C2×C8—1222no—
599C2×C8C23×D6112yes—
600C2×C8C23×D6112yes—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—614no—
608C4⋊C4—612no—
609C4⋊C4—612no—
610C4⋊C4—612no—
611C4⋊C4—1224no—
612C4⋊C4—1224no—
613C4⋊C4—1224no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—1224no—
618C4⋊C4C23×D6112yes—
619C4⋊C4C23×D6112yes—
620C4⋊C4C23×D6112yes—
621C22⋊C4—614no—
622C22⋊C4—614no—
623C22⋊C4—1224no—
624C22⋊C4—1224no—
625C22⋊C4—1224no—
626C22⋊C4—1224no—
627C22⋊C4—1224no—
628C22⋊C4—1224no—
629C22⋊C4—1224no—
630C22⋊C4—1224no—
631C42—24no—
632C42—1224no—
633C42—1224no—
634C42—1224no—
635C42D4×D6112yes—
636C42C23×D6112yes—
637C23—612no—
638C23—612no—
639C23—1222no—
640C23—1222no—
641C23—1222no—
642C23—1222no—
643C23—1222no—
644C23—1222no—
645C23—1222no—
646C23—2442no—
647C23—2442no—
648C23—2442no—
649C23C2×D4×D6111yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—2448no—
654D4—1222no—
655D4—1222no—
656D4—4884no—
657D4—2444no—
658D4—2448no—
659D4—2442no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—612no—
671C2×C4—612no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1224no—
679C2×C4—1224no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—4884no—
684C2×C4—4884no—
685C2×C4—2442no—
686C2×C4—2442no—
687C2×C4—2442no—
688C2×C4C2×D4×D6112yes—
689C2×C4C2×D4×D6112yes—
690C2×C4C2×D4×D6111yescharacteristic
691C2×C4#41×D6112yes—
692C2×C4#1451982512yes—
693C2×C4C24×D6111yescharacteristic
694C8—22no—
695C8—22no—
696C8—614no—
697C8—1222no—
698C22—1222no—
699C22—1222no—
700C22—1222no—
701C22—1222no—
702C22—1222no—
703C22—1222no—
704C22—4884no—
705C22—2442no—
706C22—2442no—
707C22—2442no—
708C22—2444no—
709C22—2444no—
710C22#1684041412yes—
711C22#1684056112yes—
712C22#1684056912yes—
713C22C22×D4×D6111yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—1222no—
721C4—1222no—
722C4—2442no—
723C4—2442no—
724C4—2442no—
725C4#1684041412yes—
726C4C2×#41×D6111yescharacteristic
727C4C2×#1451982511yescharacteristic
728C2—4882no—
729C2—2442no—
730C2—2442no—
731C2#2145836114yesdirect product factor
732C2C2×#1684041411yescharacteristic
733C2C2×#1684056111yescharacteristic
734C2C2×#1684056911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#479C2
socleC23×C61C22×D4
prime radicalC2×#16840465C2
hypercenterC2×#479D61
hypocenterC61C2×#3350
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
1. C2×#16840485C2semidirect
3. #21458361C2direct (N × H)
4. C2×#16840172C2semidirect
5. C2×#16840101C2semidirect
6. C2×#16840089C2semidirect
7. C2×#16840088C2semidirect
8. C2×#16840091C2semidirect
9. C2×#16840053C2semidirect
10. C2×#16840011C2semidirect
11. C2×#16839994C2semidirect
12. C2×#16839860C2semidirect
13. C2×#16839832C2semidirect
14. C2×#16839803C2semidirect
15. C2×#16839797C2semidirect
16. C2×C61×#479C2semidirect
21. #16840485C22semidirect
43. #16840172C22semidirect
44. #16840101C22semidirect
45. #16840091C22semidirect
46. #16840089C22semidirect
47. #16840088C22semidirect
48. #16840053C22semidirect
49. #16840011C22semidirect
50. #16839994C22semidirect
51. #16839860C22semidirect
52. #16839832C22semidirect
53. #16839803C22semidirect
54. #16839797C22semidirect
71. C61×#479C22semidirect
369. C2×#479D61semidirect
377. C2×C61#3350semidirect
417. #479C2×D61semidirect
444. C61C2×#3350semidirect
731. C2#21458361direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404852
C2×#168404652
#214583612
C2×#168401722
C2×#168401012
C2×#168400892
C2×#168400882
C2×#168400912
C2×#168400532
C2×#168400112
C2×#168399942
C2×#168398602
C2×#168398322
C2×#168398032
C2×#168397972
C2×C61×#4792
C2×#335061