Finite Group Databasebeta

← C2×#21446098 #29681092

Subgroups — C2×#21446098 #29681092

Order 15616.

1994 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840235C211yesmaximal, characteristic
2C22×#14519691C211yesmaximal, characteristic
3C2×#16839641C211yesmaximal, characteristic
4C2×#16839635C211yesmaximal, characteristic, complemented
5#21446098C218yesmaximal, direct product factor
6C2×#16839529C211yesmaximal, characteristic, complemented
7C2×#16839528C211yesmaximal, characteristic, complemented
8C2×C61×#385C211yesmaximal, characteristic, complemented
9C23×C22⋊D61C2211yescharacteristic
10#16840235—22no—
11#16840235—22no—
12#16840235—22no—
13#16840235C2214yes—
14C2×C4×C22⋊D61—21no—
15C2×C4×C22⋊D61—21no—
16C2×#14519737—21no—
17C2×#14519737—21no—
18C2×#14519733—21no—
19C22×#11758196—21no—
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×C22⋊Dic61C2211yescharacteristic
23C22×#11758198—21no—
24C2×C22⋊C4×D61—21no—
25C2×#14519691C418yescomplemented
26C2×#14519691C2214yes—
27#16839641—22no—
28#16839641C2214yes—
29#16839635—22no—
30#16839635C2214yescomplemented
31C2×#14519684—21no—
32C2×#14519684—21no—
33#16839529C2214yescomplemented
34#16839528C2214yescomplemented
35C24×C4×C61C2211yescharacteristic
36C22×C4⋊C4×C61—21no—
37C22×C22⋊C4×C61C2211yescharacteristic
38C22×C22⋊C4×C61C2211yescharacteristic
39C61×#385—22no—
40C61×#385C2214yescomplemented
41C2×#95×C61—21no—
42C24×D61D411yescharacteristic
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×C414yes—
50C22×C22⋊D61D412yes—
51C22×C22⋊D61Q814yes—
52C22×C22⋊D61C2312yes—
53C23×Dic61—21no—
54C23×Dic61—21no—
55C23×Dic61D411yescharacteristic
56C23×Dic61D411yescharacteristic
57C23×Dic61D411yescharacteristic
58C22×C4×D61—21no—
59C22×C4×D61—21no—
60C4×C22⋊D61—24no—
61C4×C22⋊D61—24no—
62C4×C22⋊D61—24no—
63C4×C22⋊D61—24no—
64#14519737—24no—
65#14519737—24no—
66#14519737—24no—
67#14519737—24no—
68#14519733—24no—
69#14519733—24no—
70C2×#11758196—21no—
71C2×#11758196—21no—
72C2×#11758196—24no—
73C2×#11758196—44no—
74C2×C22⋊Dic61—21no—
75C2×C22⋊Dic61—21no—
76C2×C22⋊Dic61—21no—
77C2×C22⋊Dic61—21no—
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61—22no—
80C2×C22⋊Dic61—22no—
81C2×C22⋊Dic61—22no—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61C2×C414yescomplemented
84C2×C22⋊Dic61D412yes—
85C2×C22⋊Dic61C2312yes—
86C2×C22⋊Dic61C2312yes—
87C2×C22⋊Dic61C2312yes—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—24no—
91C2×#11758198—44no—
92C22⋊C4×D61—24no—
93C22⋊C4×D61—24no—
94C2×C4×Dic61—21no—
95C2×C4×Dic61—21no—
96#14519691C2×C4116yescomplemented
97#14519684—24no—
98#14519684—24no—
99C25×C61C2311yescharacteristic
100C23×C4×C61—21no—
101C23×C4×C61—21no—
102C23×C4×C61—21no—
103C23×C4×C61—21no—
104C23×C4×C61—21no—
105C23×C4×C61—21no—
106C23×C4×C61—21no—
107C23×C4×C61—44no—
108C23×C4×C61D411yescharacteristic
109C23×C4×C61D411yescharacteristic
110C23×C4×C61C2312yes—
111C2×C4⋊C4×C61—24no—
112C2×C4⋊C4×C61—44no—
113C2×C22⋊C4×C61—21no—
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C22⋊C4×C61—21no—
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61—22no—
119C2×C22⋊C4×C61C2×C414yescomplemented
120C2×C22⋊C4×C61D412yes—
121C2×C22⋊C4×C61C2312yes—
122C2×C22⋊C4×C61C2312yes—
123#95×C61—24no—
124C24×C61—42no—
125C24×C61—42no—
126C24×C61C22×C412yes—
127C24×C61C2×D411yescharacteristic
128C24×C61C2×D411yescharacteristic
129C24×C61C2×D411yescharacteristic
130C24×C61C2×D411yescharacteristic
131C24×C61C2×D411yescharacteristic
132C24×C61C2×D411yescharacteristic
133C24×C61C2×Q812yes—
134C24×C61#4112yes—
135C24×C61#4112yes—
136C24×C61C2411yescharacteristic
137C23×D61—21no—
138C23×D61—21no—
139C23×D61—22no—
140C23×D61—42no—
141C23×D61—42no—
142C23×D61C4⋊C414yescomplemented
143C23×D61C2×D412yes—
144C22×C4×C61—24no—
145C22×C4×C61—24no—
146C22×C4×C61—24no—
147C22×C4×C61—24no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—44no—
157C22×C4×C61—44no—
158C22×C4×C61—44no—
159C22×C4×C61—44no—
160C22×C4×C61—42no—
161C22×C4×C61—42no—
162C22×C4×C61—42no—
163C22×C4×C61—42no—
164C22×C4×C61—42no—
165C22×C4×C61—41no—
166C22×C4×C61—41no—
167C22×C4×C61—41no—
168C22×C4×C61—41no—
169C22×C4×C61—42no—
170C22×C4×C61—42no—
171C22×C4×C61C2×D412yes—
172C22×C4×C61C2×D412yes—
173C2×C22⋊D61—24no—
174C2×C22⋊D61—24no—
175C2×C22⋊D61—24no—
176C2×C22⋊D61—24no—
177C2×C22⋊D61—22no—
178C2×C22⋊D61—22no—
179C2×C22⋊D61—24no—
180C2×C22⋊D61—24no—
181C2×C22⋊D61—24no—
182C2×C22⋊D61—24no—
183C2×C22⋊D61—24no—
184C2×C22⋊D61—22no—
185C2×C22⋊D61—22no—
186C2×C22⋊D61—22no—
187C2×C22⋊D61—22no—
188C2×C22⋊D61C4⋊C418yescomplemented
189C2×C22⋊D61C22×C414yes—
190C2×C22⋊D61C2×Q814yes—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—22no—
194C22×Dic61—24no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—22no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—22no—
201C22×Dic61—42no—
202C22×Dic61—42no—
203C22×Dic61—42no—
204C22×Dic61—42no—
205C22×Dic61—42no—
206C22×Dic61—42no—
207C22×Dic61—42no—
208C22×Dic61C4⋊C414yescomplemented
209C22×Dic61C2×D412yes—
210C22×Dic61C2×D412yes—
211C22×Dic61C2×D412yes—
212C2×C4×D61—24no—
213C2×C4×D61—24no—
214C2×C4×D61—82no—
215C2×C4×D61—82no—
216C4⋊C4×C61—48no—
217C22⋊C4×C61—24no—
218C22⋊C4×C61—22no—
219C22⋊C4×C61—22no—
220C22⋊C4×C61—22no—
221C22⋊C4×C61—22no—
222C22⋊C4×C61—22no—
223C22⋊C4×C61C22×C414yescomplemented
224C22⋊Dic61—24no—
225C22⋊Dic61—22no—
226C22⋊Dic61—22no—
227C22⋊Dic61—22no—
228C22⋊Dic61—22no—
229C22⋊Dic61—22no—
230C22⋊Dic61—22no—
231C22⋊Dic61—22no—
232C22⋊Dic61—42no—
233C22⋊Dic61C22×C414yescomplemented
234#11758198—24no—
235#11758198—24no—
236#11758198—48no—
237#11758196—24no—
238#11758196—24no—
239#11758196—48no—
240C4×Dic61—24no—
241C4×Dic61—24no—
242C23×C61—22no—
243C23×C61—22no—
244C23×C61—22no—
245C23×C61—22no—
246C23×C61—22no—
247C23×C61—22no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—44no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—44no—
257C23×C61—44no—
258C23×C61—44no—
259C23×C61—41no—
260C23×C61C2×C4⋊C412yes—
261C23×C61C2×C4⋊C412yes—
262C23×C61C4×D412yes—
263C23×C61C4×D412yes—
264C23×C61C4×D412yes—
265C23×C61C4×D412yes—
266C23×C61#12011yescharacteristic
267C23×C61#12011yescharacteristic
268C23×C61#12011yescharacteristic
269C23×C61#12011yescharacteristic
270C23×C61C22⋊Q812yes—
271C23×C61C22⋊Q812yes—
272C23×C61C22⋊Q812yes—
273C23×C61C22⋊Q812yes—
274C23×C61#12312yes—
275C23×C61#12312yes—
276C23×C61C23×C411yescharacteristic
277C23×C61C22×D411yescharacteristic
278C23×C61C22×D411yescharacteristic
279C23×C61C22×D411yescharacteristic
280C23×C61C22×Q811yescharacteristic
281C23×C61C2×#4111yescharacteristic
282C23×C61C2×#4111yescharacteristic
283C22×D61—22no—
284C22×D61—24no—
285C22×D61—22no—
286C22×D61—24no—
287C22×D61—42no—
288C22×D61—42no—
289C22×D61—42no—
290C22×D61—48no—
291C22×D61—42no—
292C22×D61—84no—
293C22×D61—81no—
294C22×D61—81no—
295C22×D61C2×C4⋊C414yescomplemented
296C2×C4×C61—24no—
297C2×C4×C61—24no—
298C2×C4×C61—24no—
299C2×C4×C61—24no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—42no—
303C2×C4×C61—48no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—44no—
308C2×C4×C61—42no—
309C2×C4×C61—44no—
310C2×C4×C61—44no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61—44no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—81no—
318C2×C4×C61—81no—
319C22⋊D61—24no—
320C22⋊D61—24no—
321C22⋊D61—24no—
322C22⋊D61—24no—
323C22⋊D61—28no—
324C22⋊D61—28no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—24no—
328C2×Dic61—24no—
329C2×Dic61—24no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—42no—
333C2×Dic61—48no—
334C2×Dic61—42no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61—42no—
342C2×Dic61—81no—
343C2×Dic61—81no—
344C2×Dic61—84no—
345C2×Dic61C2×C4⋊C414yescomplemented
346C4×D61—84no—
347C4×D61—84no—
348C2×#1867—611nomaximal, Sylow
349C22×C61—24no—
350C22×C61—24no—
351C22×C61—24no—
352C22×C61—24no—
353C22×C61—24no—
354C22×C61—24no—
355C22×C61—21no—
356C22×C61—21no—
357C22×C61—21no—
358C22×C61—21no—
359C22×C61—21no—
360C22×C61—21no—
361C22×C61—21no—
362C22×C61—21no—
363C22×C61—21no—
364C22×C61—21no—
365C22×C61—21no—
366C22×C61—21no—
367C22×C61—42no—
368C22×C61—42no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61#38512yes—
378C22×C61#38512yes—
379C22×C61#38512yes—
380C22×C61#38512yes—
381C22×C61B(4,𝔽2)12yes—
382C22×C61#45812yes—
383C22×C61C22×C4⋊C411yescharacteristic
384C22×C61C2×C4×D411yescharacteristic
385C22×C61C2×C4×D411yescharacteristic
386C22×C61C2×#12011yescharacteristic
387C22×C61C2×C22⋊Q811yescharacteristic
388C22×C61C2×C22⋊Q811yescharacteristic
389C22×C61C2×#12311yescharacteristic
390C2×D61—24no—
391C2×D61—48no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—44no—
395C2×D61—82no—
396C2×D61—84no—
397C4×C61—44no—
398C4×C61—42no—
399C4×C61—44no—
400C4×C61—42no—
401Dic61—24no—
402Dic61—44no—
403Dic61—42no—
404Dic61—42no—
405Dic61—82no—
406C2×#518—611no—
407C22×#99—611no—
408C2×#386—611no—
409C2×#385—611no—
410C2×#385D6111yescharacteristic, complemented
411#1867—618no—
412C2×#342—611no—
413C2×#342—611no—
414C2×C61—21no—
415C2×C61—21no—
416C2×C61—21no—
417C2×C61—21no—
418C2×C61—22no—
419C2×C61—21no—
420C2×C61—21no—
421C2×C61—22no—
422C2×C61—22no—
423C2×C61#186714yescomplemented
424C2×C61C2×#38511yescharacteristic
425C2×C61C2×B(4,𝔽2)11yescharacteristic
426C2×C61C2×#45811yescharacteristic
427D61—44no—
428C23×D4—611no—
429C24×C4C2×D6111yescharacteristic
430#518—614no—
431#518—1222no—
432#518—1222no—
433#518—1222no—
434C2×C4×D4—1221no—
435C2×C4×D4—1221no—
436C2×C4×D4—1221no—
437C2×C4×D4—1221no—
438C2×#117—1221no—
439C22×C4⋊C4—21no—
440C22×C4⋊C4—1221no—
441C22×C22⋊C4—611no—
442C22×C22⋊C4—611no—
443C22×C22⋊C4—611no—
444C22×C22⋊C4—1221no—
445C22×C22⋊C4—1221no—
446C22×C22⋊C4C2×D6111yescharacteristic
447C22×C22⋊C4C2×D6111yescharacteristic
448C2×#99—618no—
449C2×#99—614no—
450#386—614no—
451#386—1222no—
452#385—22no—
453#385—614no—
454#385—1222no—
455#385C2×D6114yescomplemented
456C2×#95—21no—
457C2×#95—1221no—
458C2×#95—1221no—
459#342—614no—
460#342—614no—
461C61C2×#186711yescharacteristic, complemented, Sylow
462C25—611no—
463C25C22×D6111yescharacteristic
464C22×D4—614no—
465C22×D4—612no—
466C22×D4—614no—
467C22×D4—612no—
468C22×D4—1222no—
469C22×D4—1221no—
470C22×D4—1221no—
471C22×D4—1222no—
472C22×D4—1221no—
473C22×D4—1221no—
474C23×C4—21no—
475C23×C4—21no—
476C23×C4—21no—
477C23×C4—21no—
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—44no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—1221no—
486C23×C4—1221no—
487C23×C4—1221no—
488C23×C4—1221no—
489C23×C4C22⋊D6111yescharacteristic
490C23×C4C22⋊D6111yescharacteristic
491C23×C4C22×D6112yes—
492C4×D4—1224no—
493C4×D4—1224no—
494C4×D4—1224no—
495C4×D4—1224no—
496C4×D4—1224no—
497C4×D4—1224no—
498C4×D4—1224no—
499C4×D4—1224no—
500#117—1224no—
501#117—1224no—
502C2×C4⋊C4—24no—
503C2×C4⋊C4—44no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1224no—
507C2×C4⋊C4—2444no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—614no—
515C2×C22⋊C4—612no—
516C2×C22⋊C4—612no—
517C2×C22⋊C4—612no—
518C2×C22⋊C4—612no—
519C2×C22⋊C4—1224no—
520C2×C22⋊C4—1224no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1222no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1222no—
530C2×C22⋊C4—1222no—
531C2×C22⋊C4—1224no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—2444no—
534C2×C22⋊C4C4×D6114yescomplemented
535C2×C22⋊C4C22⋊D6112yes—
536C2×C22⋊C4C22×D6112yes—
537C2×C22⋊C4C22×D6112yes—
538C2×C42—1221no—
539C2×C42—1221no—
540#99—6116no—
541#95—24no—
542#95—1224no—
543#95—1224no—
544C24—42no—
545C24—42no—
546C24—612no—
547C24—614no—
548C24—1221no—
549C24—1222no—
550C24—1221no—
551C24—2442no—
552C24—2442no—
553C24C2×C4×D6112yes—
554C24#1175822212yes—
555C24D4×D6111yescharacteristic
556C24D4×D6111yescharacteristic
557C24D4×D6111yescharacteristic
558C24D4×D6111yescharacteristic
559C24Q8×D6112yes—
560C24#1175822612yes—
561C24C2×C22⋊D6111yescharacteristic
562C24C2×C22⋊D6111yescharacteristic
563C24C23×D6111yescharacteristic
564C2×D4—614no—
565C2×D4—614no—
566C2×D4—618no—
567C2×D4—1222no—
568C2×D4—1222no—
569C2×D4—1222no—
570C2×D4—1222no—
571C2×D4—1224no—
572C2×D4—1224no—
573C2×D4—1224no—
574C2×D4—1224no—
575C2×D4—1222no—
576C2×D4—1222no—
577C2×D4—1224no—
578C2×D4—1224no—
579C2×D4—1224no—
580C2×D4—1224no—
581C2×D4—1224no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—612no—
610C22×C4—614no—
611C22×C4—612no—
612C22×C4—612no—
613C22×C4—1224no—
614C22×C4—1224no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—1222no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1222no—
621C22×C4—1224no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1222no—
625C22×C4—4882no—
626C22×C4—4882no—
627C22×C4—2442no—
628C22×C4—2442no—
629C22×C4—2442no—
630C22×C4—2442no—
631C22×C4—2442no—
632C22×C4—2442no—
633C22×C4—2442no—
634C22×C4C2×C22⋊D6112yes—
635C22×C4C2×C22⋊D6112yes—
636C4⋊C4—48no—
637C4⋊C4—1224no—
638C4⋊C4—1224no—
639C4⋊C4—2448no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—24no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—614no—
647C22⋊C4—1224no—
648C22⋊C4—1224no—
649C22⋊C4—1222no—
650C22⋊C4—1222no—
651C22⋊C4—1222no—
652C22⋊C4—1224no—
653C22⋊C4—1222no—
654C22⋊C4—1222no—
655C22⋊C4—1222no—
656C22⋊C4—1222no—
657C22⋊C4—2448no—
658C22⋊C4—2442no—
659C22⋊C4C2×C4×D6114yescomplemented
660C42—1224no—
661C42—1224no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—44no—
673C23—44no—
674C23—41no—
675C23—41no—
676C23—44no—
677C23—44no—
678C23—41no—
679C23—41no—
680C23—614no—
681C23—1222no—
682C23—1224no—
683C23—1222no—
684C23—1224no—
685C23—4881no—
686C23—4881no—
687C23—4884no—
688C23—2442no—
689C23—2442no—
690C23—2448no—
691C23—2442no—
692C23—2442no—
693C23C4⋊C4×D6112yes—
694C23C4⋊C4×D6112yes—
695C23C4×C22⋊D6112yes—
696C23C4×C22⋊D6112yes—
697C23#1451973912yes—
698C23#1451973912yes—
699C23#1451974511yescharacteristic
700C23#1451974511yescharacteristic
701C23#1451974511yescharacteristic
702C23#1451974511yescharacteristic
703C23#1451975312yes—
704C23#1451975312yes—
705C23#1451975512yes—
706C23#1451975512yes—
707C23#1451976212yes—
708C23#1451976212yes—
709C23C22×C4×D6111yescharacteristic
710C23C2×D4×D6111yescharacteristic
711C23C2×D4×D6111yescharacteristic
712C23C22×C22⋊D6111yescharacteristic
713C23C2×Q8×D6111yescharacteristic
714C23C2×#1175822211yescharacteristic
715C23C2×#1175822611yescharacteristic
716D4—1224no—
717D4—1224no—
718D4—1224no—
719D4—1224no—
720D4—1228no—
721D4—1228no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—48no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—614no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1224no—
749C2×C4—1224no—
750C2×C4—1224no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—4884no—
754C2×C4—4884no—
755C2×C4—4884no—
756C2×C4—4881no—
757C2×C4—4881no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4—2442no—
762C2×C4—2442no—
763C2×C4—2448no—
764C2×C4—2442no—
765C2×C4—2442no—
766C2×C4—2442no—
767C2×C4—2442no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—1224no—
797C22—4882no—
798C22—4884no—
799C22—2444no—
800C22—2442no—
801C22—2442no—
802C22—2448no—
803C22#1683963312yes—
804C22#1683963312yes—
805C22#1683963312yes—
806C22#1683963312yes—
807C22#1683994812yes—
808C22#1683995112yes—
809C22C2×C4⋊C4×D6111yescharacteristic
810C22C2×C4×C22⋊D6111yescharacteristic
811C22C2×#1451973911yescharacteristic
812C22C2×#1451974511yescharacteristic
813C22C2×#1451975311yescharacteristic
814C22C2×#1451975511yescharacteristic
815C22C2×#1451976211yescharacteristic
816C4—44no—
817C4—44no—
818C4—42no—
819C4—42no—
820C4—1224no—
821C4—4882no—
822C4—2444no—
823C4—2442no—
824C4—2442no—
825C2—21no—
826C2—21no—
827C2—21no—
828C2—22no—
829C2—21no—
830C2—21no—
831C2—21no—
832C2—22no—
833C2—22no—
834C2—2444no—
835C2#2144609814yesdirect product factor
836C2C2×#1683963311yescharacteristic
837C2C2×#1683994811yescharacteristic
838C2C2×#1683995111yescharacteristic
subgroupG/H
centerC23#14519745
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC2×C61×#385C2
socleC23×C61#120
prime radicalC23×C22⋊D61C22
cosocleC24×C61C24
hypercenterC2×#385D61
hypocenterC61C2×#1867
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C25 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C2×#16839635C2semidirect
5. #21446098C2direct (N × H)
6. C2×#16839529C2semidirect
7. C2×#16839528C2semidirect
8. C2×C61×#385C2semidirect
25. C2×#14519691C4semidirect
30. #16839635C22semidirect
33. #16839529C22semidirect
34. #16839528C22semidirect
40. C61×#385C22semidirect
83. C2×C22⋊Dic61C2×C4semidirect
96. #14519691C2×C4semidirect
119. C2×C22⋊C4×C61C2×C4semidirect
142. C23×D61C4⋊C4semidirect
188. C2×C22⋊D61C4⋊C4semidirect
208. C22×Dic61C4⋊C4semidirect
223. C22⋊C4×C61C22×C4semidirect
233. C22⋊Dic61C22×C4semidirect
295. C22×D61C2×C4⋊C4semidirect
345. C2×Dic61C2×C4⋊C4semidirect
410. C2×#385D61semidirect
423. C2×C61#1867semidirect
455. #385C2×D61semidirect
461. C61C2×#1867semidirect
534. C2×C22⋊C4C4×D61semidirect
659. C22⋊C4C2×C4×D61semidirect
835. C2#21446098direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402352
C22×#145196912
C2×#168396412
C2×#168396352
#214460982
C2×#168395292
C2×#168395282
C2×C61×#3852
C2×#186761