Finite Group Databasebeta

← C2×#21458386 #30558698

Subgroups — C2×#21458386 #30558698

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×#16840462C211yesmaximal, characteristic
2C2×#16840450C211yesmaximal, characteristic, complemented
3#21458386C2116yesmaximal, direct product factor
4C2×#16840161C211yesmaximal, characteristic, complemented
5C2×#16840079C211yesmaximal, characteristic, complemented
6C2×#16840105C211yesmaximal, characteristic, complemented
7C2×#16840084C211yesmaximal, characteristic, complemented
8C2×#16840094C211yesmaximal, characteristic, complemented
9C2×#16840070C211yesmaximal, characteristic, complemented
10C2×#16840007C211yesmaximal, characteristic, complemented
11C2×#16840007C211yesmaximal, characteristic, complemented
12C2×C4×#11758200C211yesmaximal, characteristic, complemented
13C2×#16839839C211yesmaximal, characteristic, complemented
14C2×#16839803C211yesmaximal, characteristic, complemented
15C2×#16839801C211yesmaximal, characteristic, complemented
16C2×C61×#478C211yesmaximal, characteristic, complemented
17C22×#11758200C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20#16840462—24no—
21#16840462C2218yes—
22#16840450—24no—
23#16840450C2218yescomplemented
24C2×#14519772—21no—
25C2×#14519770—21no—
26C2×#14519769C2211yescharacteristic
27C2×#14519768—21no—
28C2×#14519762—21no—
29C2×#14519760—21no—
30C2×#14519757C2211yescharacteristic
31C2×#14519757C2211yescharacteristic
32C2×#14519750—21no—
33C2×#14519748C2211yescharacteristic
34C2×#14519748C2211yescharacteristic
35C2×C4×Dic122C2211yescharacteristic
36C2×C4×D244C2211yescharacteristic
37C2×C4×C22⋊D61—21no—
38C2×#14519735—21no—
39C2×#14519735C2211yescharacteristic
40C2×#14519735C2211yescharacteristic
41C2×C4⋊C4×D61C2211yescharacteristic
42C2×C4⋊C4×D61C2211yescharacteristic
43#16840161C2218yescomplemented
44#16840105C2218yescomplemented
45#16840094C2218yescomplemented
46#16840084C2218yescomplemented
47#16840079C2218yescomplemented
48#16840070C2218yescomplemented
49#16840007C2218yescomplemented
50#16840007C2218yescomplemented
51C4×#11758200C2218yescomplemented
52#16839839C2218yescomplemented
53#16839803C2218yescomplemented
54#16839801C2218yescomplemented
55C2×#14519711C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519710C2211yescharacteristic
58C2×#14519709C2211yescharacteristic
59C2×#14519708C2211yescharacteristic
60C2×#14519708C2211yescharacteristic
61C2×#14519708C2211yescharacteristic
62C2×#14519702C2211yescharacteristic
63C2×#14519702C2211yescharacteristic
64C2×#14519700C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C4×#92418C2211yescharacteristic
69C2×#125×C61C2211yescharacteristic
70C2×C4×D4×C61C2211yescharacteristic
71C61×#478C2218yescomplemented
72C2×#107×C61C2211yescharacteristic
73C2×#106×C61C2211yescharacteristic
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×Dic122C2311yescharacteristic
78C22×D244D411yescharacteristic
79C22×C22⋊D61—21no—
80C22×C22⋊D61—21no—
81C22×C4×D61—21no—
82C22×C4×D61—21no—
83C22×C4×D61C2311yescharacteristic
84C22×C4×D61C2311yescharacteristic
85C2×#11758200—24no—
86C2×#11758200C2314yes—
87C2×#11758189—24no—
88C2×#11758189—24no—
89C2×#11758189C2314yes—
90C2×#11758189C2314yes—
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93#14519772—28no—
94#14519770—28no—
95#14519769—22no—
96#14519769C2314yes—
97#14519768—28no—
98#14519762—28no—
99#14519760—28no—
100#14519757—22no—
101#14519757—22no—
102#14519757C2314yes—
103#14519757C2314yes—
104#14519750—28no—
105#14519748—22no—
106#14519748—22no—
107#14519748C2314yes—
108#14519748C2314yes—
109C4×Dic122—22no—
110C4×Dic122C2314yes—
111C4×D244D414yes—
112C4×D244C2314yes—
113C4×C22⋊D61—28no—
114#14519735—22no—
115#14519735—22no—
116#14519735—28no—
117#14519735C2314yes—
118#14519735C2314yes—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61—21no—
121C2×C4⋊Dic61D411yescharacteristic
122C2×C4⋊Dic61C2311yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C4⋊C4×D61—22no—
131C4⋊C4×D61—22no—
132C4⋊C4×D61C2314yes—
133C4⋊C4×D61C2314yes—
134C2×C22⋊Dic61—21no—
135C2×C22⋊Dic61—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#14519711C2314yes—
146#14519710C2314yes—
147#14519710C2314yes—
148#14519709C2314yes—
149#14519708C2314yes—
150#14519708C2314yes—
151#14519708C2314yes—
152#14519702C2314yes—
153#14519702C2314yes—
154#14519700C2314yes—
155#14519698C2314yes—
156#14519689C2314yes—
157#14519689C2314yes—
158C4×#92418C2314yes—
159C22×D4×C61C2311yescharacteristic
160C23×C4×C61—21no—
161C22×C8×C61C2311yescharacteristic
162C22×C8×C61C2311yescharacteristic
163#125×C61—22no—
164#125×C61C2314yes—
165C4×D4×C61—22no—
166C4×D4×C61C2314yes—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61—21no—
169C2×C4⋊C4×C61C2311yescharacteristic
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C22⋊C4×C61—21no—
173C2×C42×C61C2311yescharacteristic
174#107×C61C2314yes—
175#106×C61C2314yes—
176C4⋊C8×C61C2314yes—
177#102×C61C2314yes—
178#102×C61C2314yes—
179C24×C61—21no—
180C23×D61C2×D411yescharacteristic
181C23×D61C2×D411yescharacteristic
182C2×D4×C61—21no—
183C2×D4×C61—22no—
184C2×D4×C61—22no—
185C2×D4×C61C2412yes—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—24no—
190C22×C4×C61—82no—
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2411yescharacteristic
194C2×C22⋊D61—24no—
195C2×C22⋊D61—24no—
196C2×C22⋊D61—44no—
197C2×C22⋊D61—82no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61C2×D411yescharacteristic
203C22×Dic61C2×D411yescharacteristic
204C2×D244—42no—
205C2×D244C2×D414yes—
206C2×C4×D61—22no—
207C2×C4×D61—22no—
208C2×C4×D61—22no—
209C2×C4×D61—22no—
210C2×C4×D61—24no—
211C2×C4×D61—24no—
212C2×C4×D61—44no—
213C2×C4×D61—82no—
214C2×C4×D61C2×D412yes—
215C2×C4×D61C2×D412yes—
216C2×C4×D61C2412yes—
217C2×C4×D61C2412yes—
218C2×Dic122—22no—
219C2×Dic122—22no—
220C2×Dic122—21no—
221C2×Dic122C2412yes—
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—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61C2412yes—
232C4⋊C4×C61C2412yes—
233C4⋊C4×C61C2412yes—
234C22⋊C4×C61—24no—
235C42×C61C2×D412yes—
236C42×C61C2412yes—
237C22⋊Dic61—24no—
238C22⋊Dic61—24no—
239#11758200—28no—
240#11758198—24no—
241#11758198—24no—
242#11758198—24no—
243#11758198—24no—
244#11758198C2×D414yes—
245#11758198C2×D414yes—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61—21no—
249C4⋊Dic61—24no—
250C4⋊Dic61—24no—
251C4⋊Dic61C2×D414yes—
252C4⋊Dic61C2412yes—
253C4⋊Dic61C2412yes—
254C4⋊Dic61C2412yes—
255#11758196—24no—
256#11758196—24no—
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—
268#11758189—28no—
269C23×C61—22no—
270C23×C61—42no—
271C23×C61—42no—
272C23×C61—42no—
273C23×C61C22×D411yescharacteristic
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—22no—
280C22×D61C22×D412yes—
281C22×D61C22×D412yes—
282D4×C61—22no—
283D4×C61—22no—
284D4×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—42no—
291C2×C4×C61—42no—
292C2×C4×C61—42no—
293C2×C4×C61—84no—
294C2×C4×C61C22×D412yes—
295C2×C4×C61C22×D412yes—
296C2×C4×C61C22×D411yescharacteristic
297C2×C4×C61C2×#4112yes—
298C2×C4×C612−1+412yes—
299C2×C4×C61C2511yescharacteristic
300C22⋊D61—48no—
301C22⋊D61—84no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61—42no—
311C2×Dic61—42no—
312C2×Dic61C22×D412yes—
313C2×Dic61C22×D412yes—
314D244—44no—
315C4×D61—24no—
316C4×D61—24no—
317C4×D61—22no—
318C4×D61—22no—
319C4×D61—22no—
320C4×D61—22no—
321C4×D61—48no—
322C4×D61—84no—
323Dic122—22no—
324Dic122—22no—
325Dic122—42no—
326C8×C61—22no—
327C8×C61—22no—
328#92418—22no—
329#92418C2×#4114yes—
330C2×#3351—611nomaximal, Sylow
331C22×C61—42no—
332C22×C61—42no—
333C22×C61—42no—
334C22×C61—84no—
335C22×C61#54712yes—
336C22×C61#57512yes—
337C22×C61#57712yes—
338C22×C61C23×D411yescharacteristic
339C2×D61—22no—
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—22no—
343C2×D61—22no—
344C2×D61—22no—
345C2×D61—44no—
346C2×D61—44no—
347C4×C61—22no—
348C4×C61—22no—
349C4×C61—42no—
350C4×C61—42no—
351C4×C61—42no—
352C4×C61#54712yes—
353C4×C61C22×#4111yescharacteristic
354C4×C61C2×2−1+411yescharacteristic
355Dic61—22no—
356Dic61—22no—
357Dic61—42no—
358Dic61—42no—
359Dic61—42no—
360Dic61—42no—
361C2×#553—611no—
362C2×#552—611no—
363#3351—6116no—
364C2×#499—611no—
365C2×#481—611no—
366C2×#485—611no—
367C2×#482—611no—
368C2×#483—611no—
369C2×#479—611no—
370C2×#478D6111yescharacteristic, complemented
371C2×#468—611no—
372C2×#468—611no—
373C2×C4×SD16—611no—
374C2×#436—611no—
375C2×#428—611no—
376C2×#428—611no—
377C2×C61—82no—
378C2×C61#335114yescomplemented
379C2×C61C2×#54711yescharacteristic
380C2×C61C2×#57511yescharacteristic
381C2×C61C2×#57711yescharacteristic
382D61—42no—
383D61—42no—
384C22×SD16—611no—
385C22×M16—611no—
386C22×M16—611no—
387#553—618no—
388#553—1224no—
389#552—618no—
390#552—1224no—
391C2×#126—1221no—
392C2×#126—1221no—
393C2×#125—611no—
394C2×#125—1221no—
395C2×#125C2×D6111yescharacteristic
396C2×#123—1221no—
397C2×#123—1221no—
398C2×C22⋊Q8—611no—
399C2×C22⋊Q8—611no—
400C2×#121—611no—
401C2×#121—611no—
402C2×#121—1221no—
403C2×C4×Q8—611no—
404C2×C4×D4—611no—
405C2×C4×D4—1221no—
406C2×C4×D4C2×D6111yescharacteristic
407C2×#117—611no—
408C2×#117—611no—
409C2×#117—1221no—
410C22×C4⋊C4—611no—
411C22×C4⋊C4—611no—
412#499—618no—
413#485—618no—
414#483—618no—
415#482—618no—
416#481—618no—
417#479—618no—
418#478C2×D6118yescomplemented
419#468—618no—
420#468—618no—
421C4×SD16—618no—
422#436—618no—
423#428—618no—
424#428—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×#103—611no—
437C2×#103—611no—
438C2×#102—611no—
439C2×#102C2×D6111yescharacteristic
440C2×#102C2×D6111yescharacteristic
441C2×C22⋊C8—611no—
442C2×C22⋊C8—611no—
443C2×C4×C8—611no—
444C61C2×#335111yescharacteristic, complemented, Sylow
445C22×Q8—611no—
446C22×D4—611no—
447C22×D4—1221no—
448C22×D4—1221no—
449C22×D4C22×D6111yescharacteristic
450C23×C4—21no—
451C23×C4—611no—
452C23×C4—611no—
453C23×C4—1221no—
454C23×C4—1221no—
455C2×SD16—614no—
456C2×SD16—1224no—
457C2×M16—614no—
458C2×M16—614no—
459C2×M16—1224no—
460C2×M16—1224no—
461C22×C8—611no—
462C22×C8—611no—
463C22×C8C22×D6111yescharacteristic
464C22×C8C22×D6111yescharacteristic
465#126—1228no—
466#126—1228no—
467#125—22no—
468#125—614no—
469#125—1228no—
470#125—1222no—
471#125C22×D6114yes—
472#123—1228no—
473#123—1228no—
474C22⋊Q8—614no—
475C22⋊Q8—614no—
476C22⋊Q8—1222no—
477C22⋊Q8—1222no—
478#121—614no—
479#121—614no—
480#121—1228no—
481#121—1222no—
482#121—1222no—
483C4×Q8—614no—
484C4×Q8—1222no—
485C4×D4—22no—
486C4×D4—614no—
487C4×D4—614no—
488C4×D4—1228no—
489C4×D4C22×D6114yes—
490#117—614no—
491#117—614no—
492#117—1228no—
493#117—1222no—
494#117—1222no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—614no—
502C2×C4⋊C4—614no—
503C2×C4⋊C4—1222no—
504C2×C4⋊C4—1222no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4C22×D6111yescharacteristic
513C2×C4⋊C4C22×D6111yescharacteristic
514C2×C4⋊C4C22×D6111yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—611no—
517C2×C22⋊C4—611no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
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#103—614no—
540#103—614no—
541#102—614no—
542#102C22×D6114yes—
543#102C22×D6114yes—
544C22⋊C8—614no—
545C22⋊C8—614no—
546C4×C8—614no—
547C24—21no—
548C24—611no—
549C24—611no—
550C2×Q8—612no—
551C2×Q8—1221no—
552C2×Q8—1222no—
553C2×Q8—1222no—
554C2×D4—21no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—614no—
558C2×D4—1224no—
559C2×D4—1224no—
560C2×D4—4882no—
561C2×D4—2442no—
562C2×D4—2444no—
563C2×D4C23×D6112yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—24no—
568C22×C4—82no—
569C22×C4—611no—
570C22×C4—611no—
571C22×C4—612no—
572C22×C4—612no—
573C22×C4—612no—
574C22×C4—612no—
575C22×C4—1224no—
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—1221no—
585C22×C4—4882no—
586C22×C4—2444no—
587C22×C4D4×D6111yescharacteristic
588C22×C4D4×D6111yescharacteristic
589C22×C4C23×D6111yescharacteristic
590SD16—1228no—
591M16—1228no—
592M16—1228no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—614no—
596C2×C8—612no—
597C2×C8—612no—
598C2×C8—1222no—
599C2×C8C23×D6112yes—
600C2×C8C23×D6112yes—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—614no—
607C4⋊C4—612no—
608C4⋊C4—612no—
609C4⋊C4—612no—
610C4⋊C4—1224no—
611C4⋊C4—1224no—
612C4⋊C4—1224no—
613C4⋊C4—1224no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—1224no—
618C4⋊C4—1224no—
619C4⋊C4—1224no—
620C4⋊C4C23×D6112yes—
621C4⋊C4C23×D6112yes—
622C4⋊C4C23×D6112yes—
623C22⋊C4—24no—
624C22⋊C4—614no—
625C22⋊C4—614no—
626C22⋊C4—1224no—
627C22⋊C4—1224no—
628C22⋊C4—1224no—
629C22⋊C4—1224no—
630C22⋊C4—1224no—
631C22⋊C4—1224no—
632C42—1224no—
633C42—1224no—
634C42—1224no—
635C42D4×D6112yes—
636C42C23×D6112yes—
637C23—22no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—612no—
642C23—612no—
643C23—1222no—
644C23—1222no—
645C23—1222no—
646C23—1222no—
647C23—1222no—
648C23—1222no—
649C23C2×D4×D6111yescharacteristic
650Q8—1222no—
651Q8—1222no—
652Q8—2442no—
653D4—22no—
654D4—22no—
655D4—42no—
656D4—4884no—
657D4—2444no—
658D4—2448no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—84no—
668C2×C4—612no—
669C2×C4—612no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1224no—
677C2×C4—1224no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—4884no—
683C2×C4—2448no—
684C2×C4—2442no—
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—42no—
699C22—42no—
700C22—42no—
701C22—84no—
702C22—1222no—
703C22—1222no—
704C22—1222no—
705C22—1222no—
706C22—1222no—
707C22—1222no—
708C22—2444no—
709C22—2444no—
710C22#1684041412yes—
711C22#1684055912yes—
712C22#1684057212yes—
713C22C22×D4×D6111yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—1222no—
720C4—1222no—
721C4—2442no—
722C4—2442no—
723C4—2442no—
724C4—2442no—
725C4#1684041412yes—
726C4C2×#41×D6111yescharacteristic
727C4C2×#1451982511yescharacteristic
728C2—82no—
729C2—2442no—
730C2—2442no—
731C2#2145838614yesdirect product factor
732C2C2×#1684041411yescharacteristic
733C2C2×#1684055911yescharacteristic
734C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#478C2
socleC23×C61C22×D4
prime radicalC2×#16840462C2
hypercenterC2×#478D61
hypocenterC61C2×#3351
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
2. C2×#16840450C2semidirect
3. #21458386C2direct (N × H)
4. C2×#16840161C2semidirect
5. C2×#16840079C2semidirect
6. C2×#16840105C2semidirect
7. C2×#16840084C2semidirect
8. C2×#16840094C2semidirect
9. C2×#16840070C2semidirect
10. C2×#16840007C2semidirect
11. C2×#16840007C2semidirect
12. C2×C4×#11758200C2semidirect
13. C2×#16839839C2semidirect
14. C2×#16839803C2semidirect
15. C2×#16839801C2semidirect
16. C2×C61×#478C2semidirect
23. #16840450C22semidirect
43. #16840161C22semidirect
44. #16840105C22semidirect
45. #16840094C22semidirect
46. #16840084C22semidirect
47. #16840079C22semidirect
48. #16840070C22semidirect
49. #16840007C22semidirect
50. #16840007C22semidirect
51. C4×#11758200C22semidirect
52. #16839839C22semidirect
53. #16839803C22semidirect
54. #16839801C22semidirect
71. C61×#478C22semidirect
370. C2×#478D61semidirect
378. C2×C61#3351semidirect
418. #478C2×D61semidirect
444. C61C2×#3351semidirect
731. C2#21458386direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404622
C2×#168404502
#214583862
C2×#168401612
C2×#168400792
C2×#168401052
C2×#168400842
C2×#168400942
C2×#168400702
C2×#168400072
C2×C4×#117582002
C2×#168398392
C2×#168398032
C2×#168398012
C2×C61×#4782
C2×#335161