Finite Group Databasebeta

← C2×#21446276 #29681799

Subgroups — C2×#21446276 #29681799

Order 15616.

2066 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
1C22×#14519761C211yesmaximal, characteristic
2C22×#14519733C211yesmaximal, characteristic, complemented
3C22×#14519691C211yesmaximal, characteristic
4C22×#14519691C211yesmaximal, characteristic
5C2×#16839623C211yesmaximal, characteristic, complemented
6#21446276C218yesmaximal, direct product factor
7C2×#16839529C211yesmaximal, characteristic, complemented
8C2×C61×#342C211yesmaximal, characteristic, complemented
9C23×C22⋊D61C2211yescharacteristic
10C24×Dic61C2211yescharacteristic
11C2×#14519761—21no—
12C2×#14519761—21no—
13C2×#14519761—22no—
14C2×#14519761—22no—
15C2×#14519761—22no—
16C2×#14519761C414yescomplemented
17C2×#14519761C2214yes—
18C2×#14519733—24no—
19C2×#14519733—24no—
20C2×#14519733—22no—
21C2×#14519733C2214yescomplemented
22C22×C4⋊Dic61C412yescomplemented
23C22×#11758196—21no—
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×#11758198C412yescomplemented
27C22×C4×Dic61—21no—
28C2×#14519691—24no—
29C2×#14519691—24no—
30C2×#14519691C2214yes—
31C2×#14519691C2214yes—
32#16839623—22no—
33#16839623C2214yescomplemented
34C2×#14519684—22no—
35#16839529C2214yescomplemented
36C22×C22⋊C4×C61C2211yescharacteristic
37C22×C22⋊C4×C61C2211yescharacteristic
38C22×C22⋊C4×C61C2211yescharacteristic
39C61×#342C2214yescomplemented
40C24×D61C2×C411yescharacteristic
41C22×C22⋊D61—22no—
42C22×C22⋊D61—22no—
43C22×C22⋊D61—21no—
44C22×C22⋊D61—21no—
45C22×C22⋊D61—21no—
46C22×C22⋊D61—21no—
47C22×C22⋊D61—22no—
48C22×C22⋊D61—22no—
49C22×C22⋊D61C2×C412yes—
50C22×C22⋊D61C2312yes—
51C23×Dic61—22no—
52C23×Dic61—22no—
53C23×Dic61—22no—
54C23×Dic61—22no—
55C23×Dic61—21no—
56C23×Dic61—21no—
57C23×Dic61C2×C411yescharacteristic
58C23×Dic61C2×C412yes—
59C23×Dic61C2×C412yes—
60C23×Dic61D411yescharacteristic
61C23×Dic61D411yescharacteristic
62C23×Dic61D412yes—
63C23×Dic61D412yes—
64C23×Dic61D412yes—
65C23×Dic61C2312yes—
66#14519761—24no—
67#14519761—24no—
68#14519761—28no—
69#14519761—28no—
70#14519761—24no—
71#14519761—24no—
72#14519733—216no—
73#14519733—28no—
74#14519733—28no—
75C2×C4⋊Dic61—24no—
76C2×C4⋊Dic61—22no—
77C2×C4⋊Dic61—22no—
78C2×C4⋊Dic61C2×C418yescomplemented
79C2×#11758196—28no—
80C2×#11758196—24no—
81C2×C22⋊Dic61—22no—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—22no—
84C2×C22⋊Dic61—22no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61D414yes—
87C2×C22⋊Dic61C2312yes—
88C2×C22⋊Dic61C2312yes—
89C2×#11758198—24no—
90C2×#11758198—22no—
91C2×#11758198—22no—
92C2×#11758198C2×C418yescomplemented
93C2×C4×Dic61—28no—
94C2×C4×Dic61—24no—
95#14519691—28no—
96#14519691—28no—
97#14519684—28no—
98C25×C61C2311yescharacteristic
99C23×C4×C61—21no—
100C23×C4×C61—21no—
101C23×C4×C61C2×C412yes—
102C2×C22⋊C4×C61—21no—
103C2×C22⋊C4×C61—22no—
104C2×C22⋊C4×C61—21no—
105C2×C22⋊C4×C61—21no—
106C2×C22⋊C4×C61—21no—
107C2×C22⋊C4×C61—21no—
108C2×C22⋊C4×C61—22no—
109C2×C22⋊C4×C61—22no—
110C2×C22⋊C4×C61—21no—
111C2×C22⋊C4×C61C2×C412yes—
112C2×C22⋊C4×C61D414yes—
113C2×C22⋊C4×C61C2312yes—
114C2×C22⋊C4×C61C2312yes—
115C2×C22⋊C4×C61C2312yes—
116C24×C61—44no—
117C24×C61C22×C411yescharacteristic
118C24×C61C22×C411yescharacteristic
119C24×C61C2×D411yescharacteristic
120C24×C61C2×D411yescharacteristic
121C24×C61C2×D411yescharacteristic
122C24×C61C2×D411yescharacteristic
123C24×C61C2×D412yes—
124C24×C61C2×D412yes—
125C24×C61#4112yes—
126C24×C61#4112yes—
127C24×C61C2411yescharacteristic
128C23×D61—21no—
129C23×D61—21no—
130C23×D61—22no—
131C23×D61—22no—
132C23×D61—44no—
133C23×D61C22×C412yes—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—24no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—44no—
140C22×C4×C61—44no—
141C22×C4×C61—44no—
142C22×C4×C61—42no—
143C22×C4×C61C22×C414yes—
144C2×C22⋊D61—22no—
145C2×C22⋊D61—22no—
146C2×C22⋊D61—24no—
147C2×C22⋊D61—24no—
148C2×C22⋊D61—22no—
149C2×C22⋊D61—22no—
150C2×C22⋊D61—22no—
151C2×C22⋊D61—22no—
152C2×C22⋊D61—22no—
153C2×C22⋊D61—22no—
154C2×C22⋊D61—42no—
155C2×C22⋊D61—42no—
156C2×C22⋊D61—42no—
157C2×C22⋊D61—42no—
158C2×C22⋊D61—42no—
159C2×C22⋊D61—42no—
160C2×C22⋊D61—42no—
161C2×C22⋊D61—42no—
162C22×Dic61—24no—
163C22×Dic61—24no—
164C22×Dic61—24no—
165C22×Dic61—24no—
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—24no—
169C22×Dic61—24no—
170C22×Dic61—24no—
171C22×Dic61—24no—
172C22×Dic61—24no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—24no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—24no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—44no—
188C22×Dic61—44no—
189C22×Dic61—42no—
190C22×Dic61C22⋊C414yes—
191C22×Dic61C22⋊C412yes—
192C22×Dic61C22⋊C412yes—
193C22×Dic61C22⋊C412yes—
194C22×Dic61C22⋊C412yes—
195C22×Dic61C22⋊C414yes—
196C22×Dic61C22×C412yes—
197C22×Dic61C22×C414yes—
198C22×Dic61C2×D414yes—
199C22×Dic61C2×D412yes—
200C22×Dic61C2×D412yes—
201C22⋊C4×C61—22no—
202C22⋊C4×C61—22no—
203C22⋊C4×C61—24no—
204C22⋊C4×C61—22no—
205C22⋊C4×C61—22no—
206C22⋊C4×C61—22no—
207C22⋊C4×C61—22no—
208C22⋊C4×C61—22no—
209C22⋊C4×C61—42no—
210C22⋊C4×C61C2×D414yes—
211C22⋊Dic61—24no—
212C22⋊Dic61—22no—
213C22⋊Dic61—22no—
214C22⋊Dic61—22no—
215C22⋊Dic61—42no—
216C22⋊Dic61C2×D414yes—
217#11758198—28no—
218#11758198—28no—
219C4⋊Dic61—28no—
220C4⋊Dic61—28no—
221#11758196—216no—
222C4×Dic61—216no—
223C23×C61—24no—
224C23×C61—24no—
225C23×C61—24no—
226C23×C61—42no—
227C23×C61—42no—
228C23×C61—42no—
229C23×C61—44no—
230C23×C61—44no—
231C23×C61—44no—
232C23×C61—44no—
233C23×C61—42no—
234C23×C61C2×C22⋊C411yescharacteristic
235C23×C61C2×C22⋊C411yescharacteristic
236C23×C61C2×C22⋊C411yescharacteristic
237C23×C61C2×C22⋊C411yescharacteristic
238C23×C61C4×D412yes—
239C23×C61C4×D412yes—
240C23×C61C4×D412yes—
241C23×C61C4×D412yes—
242C23×C61#12012yes—
243C23×C61#12012yes—
244C23×C61#12112yes—
245C23×C61#12112yes—
246C23×C61#12112yes—
247C23×C61#12112yes—
248C23×C61#12312yes—
249C23×C61#12312yes—
250C23×C61C23×C411yescharacteristic
251C23×C61C22×D411yescharacteristic
252C23×C61C22×D411yescharacteristic
253C23×C61C22×D411yescharacteristic
254C23×C61C22×D411yescharacteristic
255C23×C61C2×#4111yescharacteristic
256C23×C61C2×#4111yescharacteristic
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—22no—
260C22×D61—44no—
261C22×D61—42no—
262C22×D61—42no—
263C22×D61—44no—
264C22×D61—44no—
265C22×D61—84no—
266C22×D61—84no—
267C2×C4×C61—24no—
268C2×C4×C61—24no—
269C2×C4×C61—44no—
270C2×C4×C61—48no—
271C2×C4×C61—44no—
272C2×C4×C61—44no—
273C2×C4×C61—44no—
274C2×C4×C61—44no—
275C2×C4×C61—42no—
276C2×C4×C61—84no—
277C22⋊D61—42no—
278C22⋊D61—42no—
279C22⋊D61—42no—
280C22⋊D61—42no—
281C22⋊D61—44no—
282C22⋊D61—44no—
283C2×Dic61—24no—
284C2×Dic61—24no—
285C2×Dic61—22no—
286C2×Dic61—22no—
287C2×Dic61—24no—
288C2×Dic61—24no—
289C2×Dic61—22no—
290C2×Dic61—22no—
291C2×Dic61—28no—
292C2×Dic61—24no—
293C2×Dic61—24no—
294C2×Dic61—28no—
295C2×Dic61—24no—
296C2×Dic61—24no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—24no—
301C2×Dic61—44no—
302C2×Dic61—48no—
303C2×Dic61—42no—
304C2×Dic61—42no—
305C2×Dic61—44no—
306C2×Dic61—42no—
307C2×Dic61—84no—
308C2×Dic61C2×C22⋊C414yes—
309C2×Dic61C2×C22⋊C414yes—
310C2×#1899—611nomaximal, Sylow
311C22×C61—22no—
312C22×C61—22no—
313C22×C61—22no—
314C22×C61—22no—
315C22×C61—22no—
316C22×C61—22no—
317C22×C61—24no—
318C22×C61—24no—
319C22×C61—24no—
320C22×C61—24no—
321C22×C61—24no—
322C22×C61—24no—
323C22×C61—42no—
324C22×C61—42no—
325C22×C61—42no—
326C22×C61—42no—
327C22×C61—42no—
328C22×C61—42no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61#38612yes—
334C22×C61#38612yes—
335C22×C61#38612yes—
336C22×C61#38612yes—
337C22×C61#41014yes—
338C22×C61C22×C22⋊C411yescharacteristic
339C22×C61C2×C4×D411yescharacteristic
340C22×C61C2×C4×D411yescharacteristic
341C22×C61C2×#12011yescharacteristic
342C22×C61C2×#12111yescharacteristic
343C22×C61C2×#12111yescharacteristic
344C22×C61C2×#12311yescharacteristic
345C2×D61—44no—
346C2×D61—42no—
347C2×D61—84no—
348C2×D61—84no—
349C2×D61—82no—
350C2×D61—82no—
351C4×C61—44no—
352C4×C61—44no—
353C4×C61—82no—
354Dic61—24no—
355Dic61—24no—
356Dic61—44no—
357Dic61—42no—
358Dic61—82no—
359C22×#123—611no—
360C22×#117—611no—
361C22×#99—611no—
362C22×#99—611no—
363C2×#381—611no—
364#1899—618no—
365C2×#342—611no—
366C2×#342D6111yescharacteristic, complemented
367C2×C61—21no—
368C2×C61—21no—
369C2×C61—21no—
370C2×C61—21no—
371C2×C61—21no—
372C2×C61—22no—
373C2×C61—21no—
374C2×C61—22no—
375C2×C61—22no—
376C2×C61#189914yescomplemented
377C2×C61C2×#38611yescharacteristic
378C2×C61C2×#41012yes—
379D61—82no—
380C23×D4—611no—
381C24×C4—611no—
382C2×#123—614no—
383C2×#123—614no—
384C2×#123—1221no—
385C2×#123—1222no—
386C2×#123—1222no—
387C2×#123—1222no—
388C2×#123—1221no—
389C2×#117—614no—
390C2×#117—1224no—
391C2×#117—1222no—
392C2×#117—1224no—
393C22×C4⋊C4—612no—
394C22×C4⋊C4—1221no—
395C22×C22⋊C4—611no—
396C22×C22⋊C4—612no—
397C22×C22⋊C4—611no—
398C22×C22⋊C4C2×D6111yescharacteristic
399C22×C22⋊C4C2×D6111yescharacteristic
400C22×C22⋊C4C2×D6111yescharacteristic
401C22×C42—1221no—
402C2×#99—614no—
403C2×#99—614no—
404C2×#99—1224no—
405C2×#99—1224no—
406#381—614no—
407#381—1222no—
408C2×#95—1222no—
409#342—614no—
410#342C2×D6114yescomplemented
411C61C2×#189911yescharacteristic, complemented, Sylow
412C25—611no—
413C25C22×D6111yescharacteristic
414C22×D4—612no—
415C22×D4—612no—
416C22×D4—1222no—
417C22×D4—1222no—
418C22×D4—1221no—
419C22×D4—1221no—
420C22×D4—1221no—
421C22×D4—1221no—
422C22×D4—1222no—
423C22×D4—1222no—
424C23×C4—21no—
425C23×C4—21no—
426C23×C4—612no—
427C23×C4—612no—
428C23×C4—611no—
429C23×C4—612no—
430C23×C4—612no—
431C23×C4—612no—
432C23×C4—611no—
433C23×C4—612no—
434C23×C4—611no—
435C23×C4—1222no—
436C23×C4—1222no—
437C23×C4—1222no—
438C23×C4—1222no—
439C23×C4—1221no—
440C23×C4—1221no—
441C23×C4C4×D6112yes—
442#123—1228no—
443#123—1224no—
444#123—1224no—
445#123—1224no—
446#123—1228no—
447#123—1224no—
448#117—1228no—
449#117—12216no—
450#117—1228no—
451C2×C4⋊C4—618no—
452C2×C4⋊C4—1224no—
453C2×C4⋊C4—1222no—
454C2×C4⋊C4—1222no—
455C2×C4⋊C4—1224no—
456C2×C4⋊C4—1228no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—614no—
467C2×C22⋊C4—612no—
468C2×C22⋊C4—618no—
469C2×C22⋊C4—612no—
470C2×C22⋊C4—1224no—
471C2×C22⋊C4—1222no—
472C2×C22⋊C4—1222no—
473C2×C22⋊C4—1222no—
474C2×C22⋊C4—1221no—
475C2×C22⋊C4—1222no—
476C2×C22⋊C4—1222no—
477C2×C22⋊C4—1221no—
478C2×C22⋊C4C4×D6112yes—
479C2×C22⋊C4D24414yes—
480C2×C22⋊C4C22×D6112yes—
481C2×C22⋊C4C22×D6112yes—
482C2×C22⋊C4C22×D6112yes—
483C2×C42—1224no—
484C2×C42—1228no—
485#99—1228no—
486#99—1228no—
487#95—1228no—
488C24—44no—
489C24—612no—
490C24—1222no—
491C24—1222no—
492C24—1221no—
493C24—1221no—
494C24—2444no—
495C24C2×C4×D6111yescharacteristic
496C24C2×C4×D6111yescharacteristic
497C24C2×D24412yes—
498C24#1175822212yes—
499C24D4×D6111yescharacteristic
500C24D4×D6111yescharacteristic
501C24D4×D6111yescharacteristic
502C24D4×D6111yescharacteristic
503C24D4×D6112yes—
504C24#1175822612yes—
505C24C23×D6111yescharacteristic
506C2×D4—1222no—
507C2×D4—1222no—
508C2×D4—1222no—
509C2×D4—1222no—
510C2×D4—1222no—
511C2×D4—1222no—
512C2×D4—1222no—
513C2×D4—1222no—
514C2×D4—1224no—
515C2×D4—1224no—
516C2×D4—2442no—
517C2×D4—2442no—
518C2×D4—2442no—
519C2×D4—2442no—
520C2×D4—2442no—
521C2×D4—2442no—
522C2×D4—2442no—
523C2×D4—2442no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—42no—
533C22×C4—614no—
534C22×C4—614no—
535C22×C4—612no—
536C22×C4—612no—
537C22×C4—614no—
538C22×C4—612no—
539C22×C4—614no—
540C22×C4—612no—
541C22×C4—612no—
542C22×C4—612no—
543C22×C4—612no—
544C22×C4—1222no—
545C22×C4—1222no—
546C22×C4—1222no—
547C22×C4—1222no—
548C22×C4—1224no—
549C22×C4—1224no—
550C22×C4—1224no—
551C22×C4—1224no—
552C22×C4—1222no—
553C22×C4—1222no—
554C22×C4—1224no—
555C22×C4—1224no—
556C22×C4—1224no—
557C22×C4—1224no—
558C22×C4—1224no—
559C22×C4—1222no—
560C22×C4—1222no—
561C22×C4—1224no—
562C22×C4—1222no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1224no—
568C22×C4—1222no—
569C22×C4—2444no—
570C22×C4—2442no—
571C22×C4—2444no—
572C22×C4C2×C4×D6114yes—
573C4⋊C4—1228no—
574C4⋊C4—1228no—
575C4⋊C4—12216no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—24no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—42no—
585C22⋊C4—614no—
586C22⋊C4—1228no—
587C22⋊C4—1228no—
588C22⋊C4—1222no—
589C22⋊C4—1224no—
590C22⋊C4—1222no—
591C22⋊C4—1222no—
592C22⋊C4—2442no—
593C22⋊C4C2×D24414yes—
594C42—12216no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—42no—
599C23—44no—
600C23—44no—
601C23—44no—
602C23—42no—
603C23—42no—
604C23—44no—
605C23—42no—
606C23—1222no—
607C23—1222no—
608C23—1222no—
609C23—4884no—
610C23—4884no—
611C23—2444no—
612C23—2444no—
613C23—2444no—
614C23—2442no—
615C23—2442no—
616C23C22⋊C4×D6111yescharacteristic
617C23C22⋊C4×D6111yescharacteristic
618C23C22⋊C4×D6111yescharacteristic
619C23C22⋊C4×D6111yescharacteristic
620C23#1451973912yes—
621C23#1451973912yes—
622C23C4×D24412yes—
623C23C4×D24412yes—
624C23#1451974712yes—
625C23#1451974712yes—
626C23#1451975012yes—
627C23#1451975012yes—
628C23#1451975212yes—
629C23#1451975212yes—
630C23#1451976212yes—
631C23#1451976212yes—
632C23C22×C4×D6111yescharacteristic
633C23C2×D4×D6111yescharacteristic
634C23C2×D4×D6111yescharacteristic
635C23C2×D4×D6111yescharacteristic
636C23C22×D24411yescharacteristic
637C23C2×#1175822211yescharacteristic
638C23C2×#1175822611yescharacteristic
639D4—2442no—
640D4—2442no—
641D4—2442no—
642D4—2442no—
643D4—2444no—
644D4—2444no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—48no—
648C2×C4—44no—
649C2×C4—44no—
650C2×C4—44no—
651C2×C4—44no—
652C2×C4—44no—
653C2×C4—42no—
654C2×C4—84no—
655C2×C4—614no—
656C2×C4—614no—
657C2×C4—1224no—
658C2×C4—1224no—
659C2×C4—1222no—
660C2×C4—1222no—
661C2×C4—1224no—
662C2×C4—1224no—
663C2×C4—1222no—
664C2×C4—1222no—
665C2×C4—1228no—
666C2×C4—1224no—
667C2×C4—1224no—
668C2×C4—1228no—
669C2×C4—1224no—
670C2×C4—1224no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1224no—
675C2×C4—4884no—
676C2×C4—2444no—
677C2×C4—2442no—
678C2×C4—2448no—
679C2×C4—2444no—
680C2×C4—2442no—
681C2×C4—2442no—
682C22—24no—
683C22—24no—
684C22—24no—
685C22—24no—
686C22—24no—
687C22—24no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—4882no—
705C22—4882no—
706C22—4884no—
707C22—4884no—
708C22—2442no—
709C22—2444no—
710C22#1683964012yes—
711C22#1683964012yes—
712C22#1683964012yes—
713C22#1683964012yes—
714C22#1683973414yes—
715C22C2×C22⋊C4×D6111yescharacteristic
716C22C2×#1451973911yescharacteristic
717C22C2×C4×D24411yescharacteristic
718C22C2×#1451974711yescharacteristic
719C22C2×#1451975011yescharacteristic
720C22C2×#1451975211yescharacteristic
721C22C2×#1451976211yescharacteristic
722C4—44no—
723C4—44no—
724C4—82no—
725C4—1224no—
726C4—1224no—
727C4—4882no—
728C4—2444no—
729C4—2442no—
730C2—21no—
731C2—21no—
732C2—21no—
733C2—21no—
734C2—21no—
735C2—22no—
736C2—21no—
737C2—22no—
738C2—22no—
739C2—4882no—
740C2#2144627614yesdirect product factor
741C2C2×#1683964011yescharacteristic
742C2C2×#1683973412yes—
subgroupG/H
centerC23C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC2×C61×#342C2
socleC23×C61C2×C22⋊C4
prime radicalC23×C22⋊D61C22
cosocleC24×C61C24
hypercenterC2×#342D61
hypocenterC61C2×#1899
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
2. C22×#14519733C2semidirect
5. C2×#16839623C2semidirect
6. #21446276C2direct (N × H)
7. C2×#16839529C2semidirect
8. C2×C61×#342C2semidirect
16. C2×#14519761C4semidirect
21. C2×#14519733C22semidirect
22. C22×C4⋊Dic61C4semidirect
26. C22×#11758198C4semidirect
33. #16839623C22semidirect
35. #16839529C22semidirect
39. C61×#342C22semidirect
78. C2×C4⋊Dic61C2×C4semidirect
92. C2×#11758198C2×C4semidirect
366. C2×#342D61semidirect
376. C2×C61#1899semidirect
410. #342C2×D61semidirect
411. C61C2×#1899semidirect
740. C2#21446276direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197612
C22×#145197332
C22×#145196912
C2×#168396232
#214462762
C2×#168395292
C2×C61×#3422
C2×#189961