Finite Group Databasebeta

← C2×#21461960 #30616251

Subgroups — C2×#21461960 #30616251

Order 15616.

2218 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519836C212yesmaximal, complemented
2C22×#14519835C212yesmaximal, complemented
3C2×#16840704C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊#6923C211yesmaximal, characteristic, complemented
5#21461960C218yesmaximal, direct product factor
6C22×#14519750C211yesmaximal, characteristic
7C22×C4⋊#6923—21no—
8C22×C22⋊#6923C2212yes—
9C22×C22⋊#6923C2212yes—
10C22×C4×#6923—21no—
11C2×#14519836—28no—
12C2×#14519836C2218yescomplemented
13C2×#14519835—28no—
14C2×#14519835C2218yescomplemented
15#16840704—22no—
16#16840704C2214yescomplemented
17C4×C22⋊#6923—22no—
18C4×C22⋊#6923C2214yescomplemented
19C2×(C2×#6923)⋊C4—21no—
20C2×(C2×#6923)⋊C4—21no—
21C23×D244C2211yescharacteristic
22C23×C22⋊D61C411yescharacteristic, complemented
23C23×C22⋊D61C2211yescharacteristic
24C23×C4×D61C2211yescharacteristic
25C2×#14519750—21no—
26C2×#14519750—21no—
27C2×#14519750—22no—
28C2×#14519750—21no—
29C2×#14519750—21no—
30C2×#14519750—22no—
31C2×#14519750C414yescomplemented
32C2×#14519750C2214yes—
33C22×#11758196C411yescharacteristic, complemented
34C22×#11758198C411yescharacteristic, complemented
35C22×C22⋊C4×C61C411yescharacteristic, complemented
36C23×#6923—22no—
37C23×#6923—22no—
38C2×C4⋊#6923—24no—
39C2×C4⋊#6923—44no—
40C2×C22⋊#6923—22no—
41C2×C22⋊#6923—24no—
42C2×C22⋊#6923—24no—
43C2×C22⋊#6923—24no—
44C2×C22⋊#6923—22no—
45C2×C22⋊#6923D418yescomplemented
46C2×C22⋊#6923C2314yes—
47C2×C22⋊#6923C2314yes—
48C2×C4×#6923—24no—
49C2×C4×#6923—44no—
50#14519836—216no—
51#14519835—216no—
52(C2×#6923)⋊C4—24no—
53(C2×#6923)⋊C4—24no—
54C24×D61C2×C411yescharacteristic
55C24×D61C2311yescharacteristic
56C22×D244—24no—
57C22×D244—21no—
58C22×D244—21no—
59C22×D244—21no—
60C22×D244—21no—
61C22×D244—24no—
62C22×D244C2×C412yes—
63C22×D244C2312yes—
64C22×C22⋊D61—24no—
65C22×C22⋊D61—21no—
66C22×C22⋊D61—21no—
67C22×C22⋊D61—21no—
68C22×C22⋊D61—21no—
69C22×C22⋊D61—24no—
70C22×C22⋊D61—22no—
71C22×C22⋊D61—21no—
72C22×C22⋊D61—21no—
73C22×C22⋊D61—44no—
74C22×C22⋊D61C2×C412yes—
75C22×C22⋊D61C2×C414yescomplemented
76C22×C22⋊D61C2312yes—
77C23×Dic61C2×C411yescharacteristic
78C23×Dic61C2×C411yescharacteristic
79C22×C4×D61—44no—
80C22×C4×D61C2×C412yes—
81C22×C4×D61D411yescharacteristic
82C22×C4×D61D411yescharacteristic
83C22×C4×D61D412yes—
84C22×C4×D61D411yescharacteristic
85C22×C4×D61D411yescharacteristic
86C22×C4×D61D412yes—
87C22×C4×D61C2312yes—
88#14519750—24no—
89#14519750—24no—
90#14519750—24no—
91#14519750—24no—
92#14519750—24no—
93#14519750—24no—
94#14519750—24no—
95#14519750—24no—
96C2×#11758196—22no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196C2×C414yescomplemented
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—22no—
103C2×#11758198C2×C414yescomplemented
104C25×C61C2×C411yescharacteristic
105C23×C4×C61C2×C411yescharacteristic
106C23×C4×C61C2×C411yescharacteristic
107C2×C22⋊C4×C61—21no—
108C2×C22⋊C4×C61—21no—
109C2×C22⋊C4×C61—22no—
110C2×C22⋊C4×C61C2×C414yescomplemented
111C24×C61—21no—
112C24×C61—21no—
113C24×C61—24no—
114C24×C61—42no—
115C24×C61—42no—
116C24×C61C22×C411yescharacteristic
117C24×C61C22×C412yes—
118C23×D61—21no—
119C23×D61—21no—
120C23×D61—24no—
121C23×D61—42no—
122C23×D61—42no—
123C23×D61—42no—
124C23×D61—42no—
125C23×D61C22×C412yes—
126C23×D61C22×C411yescharacteristic
127C23×D61C2×D411yescharacteristic
128C23×D61C2×D411yescharacteristic
129C23×D61C2×D411yescharacteristic
130C23×D61C2×D411yescharacteristic
131C23×D61C2×D414yes—
132C23×D61#4114yes—
133C23×D61C2411yescharacteristic
134C22×#6923—28no—
135C22×#6923—24no—
136C22×#6923—24no—
137C22×#6923—44no—
138C22×#6923—44no—
139C22×#6923—44no—
140C22×#6923—44no—
141C22×#6923—44no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—24no—
145C22×C4×C61—42no—
146C22×C4×C61C22⋊C411yescharacteristic
147C22×C4×C61C22⋊C411yescharacteristic
148C22×C4×C61C22⋊C412yes—
149C22×C4×C61C22×C412yes—
150C22×C4×C61C22×C412yes—
151C2×C22⋊D61—22no—
152C2×C22⋊D61—22no—
153C2×C22⋊D61—28no—
154C2×C22⋊D61—24no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61—22no—
157C2×C22⋊D61—24no—
158C2×C22⋊D61—24no—
159C2×C22⋊D61—24no—
160C2×C22⋊D61—44no—
161C2×C22⋊D61—48no—
162C2×C22⋊D61—48no—
163C2×C22⋊D61—44no—
164C2×C22⋊D61—44no—
165C2×C22⋊D61—42no—
166C2×C22⋊D61—42no—
167C2×C22⋊D61—42no—
168C2×C22⋊D61—42no—
169C2×C22⋊D61—44no—
170C22×Dic61—24no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—24no—
174C22×Dic61C22⋊C411yescharacteristic
175C22×Dic61C22⋊C412yes—
176C22×Dic61C22⋊C411yescharacteristic
177C22×Dic61C22×C412yes—
178C22×Dic61C22×C412yes—
179C2×D244—22no—
180C2×D244—22no—
181C2×D244—28no—
182C2×D244—24no—
183C2×D244—22no—
184C2×D244—22no—
185C2×D244—24no—
186C2×D244—44no—
187C2×D244—44no—
188C2×D244—42no—
189C2×D244—42no—
190C2×D244—42no—
191C2×D244—42no—
192C2×C4×D61—24no—
193C2×C4×D61—24no—
194C2×C4×D61—44no—
195C2×C4×D61—44no—
196C2×C4×D61—44no—
197C2×C4×D61—44no—
198C2×C4×D61—42no—
199C2×C4×D61—42no—
200C2×C4×D61C22⋊C412yes—
201C2×C4×D61C22⋊C412yes—
202C2×C4×D61C22⋊C412yes—
203C2×C4×D61C22⋊C412yes—
204C2×C4×D61C2×D412yes—
205C2×C4×D61C2×D412yes—
206C2×C4×D61C2×D412yes—
207C2×C4×D61C2×D412yes—
208C22⋊#6923—28no—
209C22⋊#6923—24no—
210C22⋊#6923—24no—
211C22⋊#6923—24no—
212C22⋊#6923—44no—
213C22⋊#6923C2×D418yescomplemented
214C4⋊#6923—48no—
215C4×#6923—48no—
216C22⋊C4×C61—24no—
217C22⋊C4×C61—24no—
218#11758198—24no—
219#11758198—24no—
220#11758196—24no—
221#11758196—24no—
222C23×C61—22no—
223C23×C61—22no—
224C23×C61—22no—
225C23×C61—24no—
226C23×C61—42no—
227C23×C61—42no—
228C23×C61—42no—
229C23×C61—42no—
230C23×C61—42no—
231C23×C61—42no—
232C23×C61—42no—
233C23×C61—42no—
234C23×C61—88no—
235C23×C61C2×C22⋊C411yescharacteristic
236C23×C61C2×C22⋊C411yescharacteristic
237C23×C61C4×D414yes—
238C23×C61C23×C411yescharacteristic
239C22×D61—22no—
240C22×D61—22no—
241C22×D61—22no—
242C22×D61—22no—
243C22×D61—22no—
244C22×D61—24no—
245C22×D61—41no—
246C22×D61—41no—
247C22×D61—41no—
248C22×D61—41no—
249C22×D61—41no—
250C22×D61—41no—
251C22×D61—41no—
252C22×D61—48no—
253C22×D61—48no—
254C22×D61—41no—
255C22×D61—42no—
256C22×D61—42no—
257C22×D61—42no—
258C22×D61—42no—
259C22×D61—42no—
260C22×D61—42no—
261C22×D61—42no—
262C22×D61—42no—
263C22×D61—88no—
264C22×D61C2×C22⋊C411yescharacteristic
265C22×D61C2×C22⋊C411yescharacteristic
266C22×D61C4×D414yes—
267C22×D61#12114yes—
268C22×D61#12114yes—
269C22×D61#12412yes—
270C22×D61#12412yes—
271C22×D61#12712yes—
272C22×D61#12712yes—
273C22×D61C22×D411yescharacteristic
274C22×D61C22×D411yescharacteristic
275C22×D61C22×D412yes—
276C22×D61C2×#4112yes—
277C2×#6923—28no—
278C2×#6923—44no—
279C2×#6923—44no—
280C2×#6923—416no—
281C2×#6923—44no—
282C2×#6923—44no—
283C2×#6923—44no—
284C2×#6923—88no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—24no—
289C2×C4×C61—42no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61—42no—
293C2×C4×C61C2×C22⋊C412yes—
294C2×C4×C61C2×C22⋊C412yes—
295C22⋊D61—48no—
296C22⋊D61—44no—
297C22⋊D61—42no—
298C22⋊D61—42no—
299C22⋊D61—44no—
300C22⋊D61—44no—
301C22⋊D61—48no—
302C2×Dic61—22no—
303C2×Dic61—24no—
304C2×Dic61—24no—
305C2×Dic61—22no—
306C2×Dic61—24no—
307C2×Dic61—42no—
308C2×Dic61—42no—
309C2×Dic61#9914yescomplemented
310C2×Dic61C2×C22⋊C412yes—
311C2×Dic61C2×C22⋊C412yes—
312D244—44no—
313D244—42no—
314D244—42no—
315D244—44no—
316D244—44no—
317C4×D61—24no—
318C4×D61—24no—
319C4×D61—24no—
320C4×D61—24no—
321C4×D61—42no—
322C4×D61—42no—
323C4×D61—42no—
324C4×D61—42no—
325C2×#1964—611nomaximal, Sylow
326C22×C61—21no—
327C22×C61—21no—
328C22×C61—21no—
329C22×C61—21no—
330C22×C61—28no—
331C22×C61—42no—
332C22×C61—42no—
333C22×C61—42no—
334C22×C61—84no—
335C22×C61—84no—
336C22×C61—84no—
337C22×C61#39012yes—
338C22×C61#39012yes—
339C22×C61C2×#9912yes—
340C22×C61#41012yes—
341C22×C61C22×C22⋊C411yescharacteristic
342C22×C61C2×C4×D412yes—
343C2×D61—21no—
344C2×D61—21no—
345C2×D61—21no—
346C2×D61—21no—
347C2×D61—21no—
348C2×D61—21no—
349C2×D61—21no—
350C2×D61—21no—
351C2×D61—28no—
352C2×D61—24no—
353C2×D61—24no—
354C2×D61—44no—
355C2×D61—44no—
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—42no—
363C2×D61—84no—
364C2×D61—84no—
365C2×D61—84no—
366C2×D61#39012yes—
367C2×D61#39012yes—
368C2×D61C2×#12112yes—
369C2×D61C2×#12411yescharacteristic
370C2×D61C2×#12711yescharacteristic
371#6923—48no—
372#6923—84no—
373C4×C61—22no—
374C4×C61—22no—
375C4×C61—42no—
376Dic61—22no—
377Dic61—42no—
378Dic61C2×#9914yescomplemented
379C22×#121—611no—
380C22×#99—612no—
381C22×#99—612no—
382C2×#380—611no—
383C2×C4×C22⋊C4—611no—
384#1964—618no—
385C2×C61—22no—
386C2×C61—22no—
387C2×C61—82no—
388C2×C61#196414yescomplemented
389C2×C61C2×#39011yescharacteristic
390C2×C61C22×#9911yescharacteristic
391C2×C61C2×#41011yescharacteristic
392D61—22no—
393D61—21no—
394D61—21no—
395D61—22no—
396D61—22no—
397D61—82no—
398C23×D4—611no—
399C23×D4—611no—
400C23×D4—611no—
401C24×C4—611no—
402C2×#121—614no—
403C2×#121—614no—
404C2×#121—1221no—
405C2×#121—1221no—
406C2×#121—1221no—
407C2×#121—1221no—
408C2×#121—1222no—
409C2×#121—1222no—
410C22×C4⋊C4—611no—
411C22×C4⋊C4—1221no—
412C22×C22⋊C4—612no—
413C22×C22⋊C4—611no—
414C22×C22⋊C4—612no—
415C22×C22⋊C4#692311yescharacteristic, complemented
416C22×C42—1221no—
417C2×#99—618no—
418C2×#99—618no—
419C2×#99—1228no—
420C2×#99—1228no—
421#380—614no—
422#380—1222no—
423C4×C22⋊C4—614no—
424C4×C22⋊C4—1222no—
425C2×#95—1221no—
426C2×#95—1221no—
427C61C2×#196411yescharacteristic, complemented, Sylow
428C25—611no—
429C25—611no—
430C25C2×#692311yescharacteristic
431C22×D4—612no—
432C22×D4—612no—
433C22×D4—614no—
434C22×D4—612no—
435C22×D4—612no—
436C22×D4—1221no—
437C22×D4—1221no—
438C22×D4—1221no—
439C22×D4—1221no—
440C22×D4—1224no—
441C22×D4—1224no—
442C22×D4—1221no—
443C22×D4—1222no—
444C22×D4—1221no—
445C22×D4—1221no—
446C22×D4—1221no—
447C22×D4—1221no—
448C22×D4—1221no—
449C22×D4—1224no—
450C22×D4—1224no—
451C22×D4—2444no—
452C23×C4—611no—
453C23×C4—611no—
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—611no—
457C23×C4—612no—
458C23×C4—612no—
459C23×C4—612no—
460C23×C4—612no—
461C23×C4—611no—
462C23×C4—1222no—
463C23×C4—1222no—
464C23×C4—2444no—
465C23×C4C2×#692311yescharacteristic
466C23×C4C2×#692311yescharacteristic
467#121—1224no—
468#121—1224no—
469#121—1224no—
470#121—1224no—
471#121—1224no—
472#121—1224no—
473#121—1224no—
474#121—1224no—
475C2×C4⋊C4—614no—
476C2×C4⋊C4—1222no—
477C2×C4⋊C4—1221no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—1224no—
480C2×C4⋊C4—2444no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—618no—
485C2×C22⋊C4—614no—
486C2×C22⋊C4—614no—
487C2×C22⋊C4—614no—
488C2×C22⋊C4—1224no—
489C2×C22⋊C4—1222no—
490C2×C22⋊C4—1222no—
491C2×C22⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1224no—
494C2×C22⋊C4—1224no—
495C2×C22⋊C4—1222no—
496C2×C22⋊C4C2×#692314yescomplemented
497C2×C42—1224no—
498C2×C42—2444no—
499#99—12216no—
500#99—12216no—
501#95—1224no—
502#95—1224no—
503C24—21no—
504C24—21no—
505C24—24no—
506C24—42no—
507C24—42no—
508C24—611no—
509C24—611no—
510C24—611no—
511C24—611no—
512C24—614no—
513C24—614no—
514C24—611no—
515C24—611no—
516C24—612no—
517C24—1224no—
518C24—1221no—
519C24—1221no—
520C24—2442no—
521C24—2442no—
522C24—2442no—
523C24—2442no—
524C24C22×#692311yescharacteristic
525C24C22×#692312yes—
526C2×D4—1224no—
527C2×D4—1222no—
528C2×D4—1222no—
529C2×D4—1222no—
530C2×D4—1222no—
531C2×D4—1228no—
532C2×D4—1224no—
533C2×D4—1224no—
534C2×D4—1224no—
535C2×D4—1224no—
536C2×D4—1222no—
537C2×D4—1222no—
538C2×D4—1222no—
539C2×D4—1222no—
540C2×D4—1228no—
541C2×D4—1224no—
542C2×D4—2444no—
543C2×D4—2442no—
544C2×D4—2442no—
545C2×D4—2444no—
546C2×D4—2442no—
547C2×D4—2442no—
548C2×D4—2444no—
549C2×D4—2448no—
550C2×D4—2444no—
551C2×D4—2448no—
552C2×D4—2444no—
553C2×D4—2442no—
554C2×D4—2442no—
555C2×D4—2444no—
556C2×D4—2442no—
557C2×D4—2442no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—24no—
561C22×C4—42no—
562C22×C4—611no—
563C22×C4—612no—
564C22×C4—611no—
565C22×C4—612no—
566C22×C4—612no—
567C22×C4—612no—
568C22×C4—612no—
569C22×C4—612no—
570C22×C4—612no—
571C22×C4—612no—
572C22×C4—612no—
573C22×C4—612no—
574C22×C4—612no—
575C22×C4—1224no—
576C22×C4—1224no—
577C22×C4—1224no—
578C22×C4—1224no—
579C22×C4—1228no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1224no—
583C22×C4—1224no—
584C22×C4—2442no—
585C22×C4—2442no—
586C22×C4—2444no—
587C22×C4—2444no—
588C22×C4—2444no—
589C22×C4—2444no—
590C22×C4—2444no—
591C22×C4—2444no—
592C22×C4—2444no—
593C22×C4—2444no—
594C22×C4—2444no—
595C22×C4C22⋊#692311yescharacteristic
596C22×C4C22⋊#692311yescharacteristic
597C22×C4C22⋊#692312yes—
598C22×C4C22×#692312yes—
599C22×C4C22×#692312yes—
600C4⋊C4—1224no—
601C4⋊C4—1224no—
602C4⋊C4—2448no—
603C22⋊C4—24no—
604C22⋊C4—24no—
605C22⋊C4—618no—
606C22⋊C4—1228no—
607C22⋊C4—1224no—
608C22⋊C4—1224no—
609C22⋊C4—1224no—
610C22⋊C4—1224no—
611C22⋊C4—1224no—
612C22⋊C4—2444no—
613C42—2448no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—24no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—88no—
627C23—614no—
628C23—612no—
629C23—612no—
630C23—611no—
631C23—611no—
632C23—611no—
633C23—611no—
634C23—614no—
635C23—612no—
636C23—612no—
637C23—614no—
638C23—612no—
639C23—612no—
640C23—1222no—
641C23—1222no—
642C23—1222no—
643C23—1222no—
644C23—1224no—
645C23—1222no—
646C23—4888no—
647C23—2441no—
648C23—2441no—
649C23—2441no—
650C23—2441no—
651C23—2441no—
652C23—2441no—
653C23—2441no—
654C23—2441no—
655C23—2448no—
656C23—2448no—
657C23—2442no—
658C23—2442no—
659C23—2442no—
660C23—2442no—
661C23—2442no—
662C23—2442no—
663C23—2442no—
664C23—2442no—
665C23C2×C22⋊#692311yescharacteristic
666C23C2×C22⋊#692311yescharacteristic
667C23D4×#692314yes—
668C23C23×#692311yescharacteristic
669D4—2444no—
670D4—2442no—
671D4—2442no—
672D4—2444no—
673D4—2444no—
674D4—2448no—
675D4—2448no—
676D4—2444no—
677D4—2442no—
678D4—2442no—
679D4—2444no—
680D4—2444no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—614no—
690C2×C4—612no—
691C2×C4—612no—
692C2×C4—1224no—
693C2×C4—1224no—
694C2×C4—1224no—
695C2×C4—1224no—
696C2×C4—1224no—
697C2×C4—1224no—
698C2×C4—1222no—
699C2×C4—1228no—
700C2×C4—1222no—
701C2×C4—1224no—
702C2×C4—4888no—
703C2×C4—2442no—
704C2×C4—2442no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2444no—
708C2×C4—2444no—
709C2×C4—2444no—
710C2×C4—2444no—
711C2×C4—2444no—
712C2×C4—24416no—
713C2×C4—2442no—
714C2×C4—2442no—
715C2×C4C2×C22⋊#692312yes—
716C2×C4C2×C22⋊#692312yes—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—28no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—84no—
727C22—84no—
728C22—612no—
729C22—611no—
730C22—611no—
731C22—612no—
732C22—612no—
733C22—1221no—
734C22—1221no—
735C22—1221no—
736C22—1221no—
737C22—1221no—
738C22—1221no—
739C22—1221no—
740C22—1221no—
741C22—1224no—
742C22—1228no—
743C22—1224no—
744C22—4884no—
745C22—4884no—
746C22—4884no—
747C22—2442no—
748C22—2444no—
749C22—2442no—
750C22—2442no—
751C22—2442no—
752C22—2444no—
753C22—2442no—
754C22—2442no—
755C22—2442no—
756C22#1684071412yes—
757C22#1684071412yes—
758C22D61⋊#9912yes—
759C22#1684074112yes—
760C22C22×C22⋊#692311yescharacteristic
761C22C2×D4×#692312yes—
762C4—22no—
763C4—22no—
764C4—42no—
765C4—614no—
766C4—1222no—
767C4—4884no—
768C4—2448no—
769C4—2442no—
770C2—22no—
771C2—22no—
772C2—82no—
773C2—1221no—
774C2—1222no—
775C2—1221no—
776C2—1222no—
777C2—1222no—
778C2—4882no—
779C2#2146196014yesdirect product factor
780C2C2×#1684071411yescharacteristic
781C2C2×D61⋊#9911yescharacteristic
782C2C2×#1684074111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C22⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC22×#14519750C2
cosocleC23×D61C24
hypercenterC22×C22⋊C4#6923
hypocenterC61C2×#1964
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#14519836C2semidirect
2. C22×#14519835C2semidirect
3. C2×#16840704C2semidirect
4. C2×C4×C22⋊#6923C2semidirect
5. #21461960C2direct (N × H)
12. C2×#14519836C22semidirect
14. C2×#14519835C22semidirect
16. #16840704C22semidirect
18. C4×C22⋊#6923C22semidirect
22. C23×C22⋊D61C4semidirect
31. C2×#14519750C4semidirect
33. C22×#11758196C4semidirect
34. C22×#11758198C4semidirect
35. C22×C22⋊C4×C61C4semidirect
45. C2×C22⋊#6923D4semidirect
75. C22×C22⋊D61C2×C4semidirect
99. C2×#11758196C2×C4semidirect
103. C2×#11758198C2×C4semidirect
110. C2×C22⋊C4×C61C2×C4semidirect
213. C22⋊#6923C2×D4semidirect
309. C2×Dic61#99semidirect
378. Dic61C2×#99semidirect
388. C2×C61#1964semidirect
415. C22×C22⋊C4#6923semidirect
427. C61C2×#1964semidirect
496. C2×C22⋊C4C2×#6923semidirect
779. C2#21461960direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198362
C22×#145198352
C2×#168407042
C2×C4×C22⋊#69232
#214619602
C22×#145197502
C2×#196461