Finite Group Databasebeta

← #29685372

Subgroups — #29685372

Order 15616.

1162 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840356C211yesmaximal, characteristic
2#21448420C211yesmaximal, characteristic, complemented
3#21448175C211yesmaximal, characteristic, complemented
4#21446802C212yesmaximal, complemented
5#21446653C212yesmaximal
6#21446278C211yesmaximal, characteristic, complemented
7#21446277C211yesmaximal, characteristic, complemented
8#21446275C211yesmaximal, characteristic, complemented
9#99×Dic61C212yesmaximal, complemented
10#21445606C212yesmaximal, complemented
11C61×#1899C211yesmaximal, characteristic, complemented
12#16840356—22no—
13#16840356—22no—
14#16840356—22no—
15#16840356—22no—
16C2×#14519772C411yescharacteristic, complemented
17C2×#14519770C411yescharacteristic, complemented
18C2×#14519768C411yescharacteristic, complemented
19C2×#14519767C411yescharacteristic, complemented
20C2×#14519761C411yescharacteristic, complemented
21C2×#14519760C2211yescharacteristic
22C2×#14519759C411yescharacteristic, complemented
23C2×#14519757C411yescharacteristic, complemented
24C2×#14519754C411yescharacteristic, complemented
25C2×#14519754C2211yescharacteristic
26C2×#14519749C2211yescharacteristic
27C2×D4×Dic61C2211yescharacteristic
28C2×#14519737C2211yescharacteristic
29C2×#14519736C2211yescharacteristic
30C22×C4⋊Dic61C2211yescharacteristic
31C2×#14519692C2212yes—
32C2×#14519691C2212yes—
33C2×#14519691C2212yes—
34#16839647—22no—
35#16839645—22no—
36#16839625C2211yescharacteristic
37#16839620C2212yes—
38C4⋊C4×Dic61—22no—
39C4×C4⋊Dic61—22no—
40C22⋊C4×Dic61C2212yes—
41C22⋊C4×Dic61C2212yes—
42C22⋊C4×Dic61C2212yes—
43#16839529C2212yes—
44#16839528C2212yes—
45#16839528C2212yes—
46C2×#123×C61C2211yescharacteristic
47C2×#117×C61C2211yescharacteristic
48C2×#99×C61C2212yes—
49C61×#381C2211yescharacteristic
50C61×#342C2212yes—
51C22×Dic122C2×C411yescharacteristic
52C22×C22⋊D61C2×C411yescharacteristic
53C22×C22⋊D61C2311yescharacteristic
54C23×Dic61C2×C411yescharacteristic
55C23×Dic61C2311yescharacteristic
56C23×Dic61C2311yescharacteristic
57C22×C4×D61C2×C411yescharacteristic
58#14519772—22no—
59#14519772—22no—
60#14519770—22no—
61#14519770—22no—
62#14519768—22no—
63#14519768—22no—
64#14519767—22no—
65#14519767—22no—
66#14519761—22no—
67#14519761—22no—
68#14519760—21no—
69#14519760—21no—
70#14519760—21no—
71#14519760—21no—
72#14519759—22no—
73#14519759—22no—
74#14519757—22no—
75#14519757—22no—
76#14519754—22no—
77#14519754—22no—
78#14519754—22no—
79#14519754—22no—
80#14519749—22no—
81#14519749—22no—
82D4×Dic61—22no—
83D4×Dic61—22no—
84#14519737—22no—
85#14519737—22no—
86#14519736—24no—
87C2×C4⋊Dic61—21no—
88C2×C4⋊Dic61C2×C411yescharacteristic
89C2×C4⋊Dic61C2×C411yescharacteristic
90C2×C4⋊Dic61C2×C411yescharacteristic
91C2×C4⋊Dic61C2×C411yescharacteristic
92C2×C4⋊Dic61C2×C411yescharacteristic
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×C4⋊Dic61D412yes—
95C2×C4⋊Dic61D412yes—
96C2×C4⋊Dic61D412yes—
97C2×C4⋊Dic61D412yes—
98C2×#11758196—22no—
99C2×#11758196C2×C411yescharacteristic
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×#11758196C2×C411yescharacteristic
103C2×#11758196C2×C411yescharacteristic
104C2×#11758196C2×C411yescharacteristic
105C2×C22⋊Dic61C2×C411yescharacteristic
106C2×C22⋊Dic61C2×C411yescharacteristic
107C2×C22⋊Dic61C2312yes—
108C2×C22⋊Dic61C2311yescharacteristic
109C2×C22⋊Dic61C2312yes—
110C2×#11758198C2×C411yescharacteristic
111C2×#11758198C2×C411yescharacteristic
112C2×#11758198C2×C411yescharacteristic
113C2×#11758198C2×C411yescharacteristic
114C2×C4×Dic61—21no—
115C2×C4×Dic61—22no—
116C2×C4×Dic61—22no—
117C2×C4×Dic61—22no—
118C2×C4×Dic61C2×C411yescharacteristic
119C2×C4×Dic61C2×C411yescharacteristic
120#14519692—24no—
121#14519691—24no—
122#14519691—24no—
123#14519684—21no—
124#14519684—21no—
125#14519684—22no—
126#14519684—22no—
127#14519684—22no—
128#14519684—22no—
129C22×D4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131#123×C61—21no—
132#123×C61—21no—
133#123×C61—21no—
134#123×C61—21no—
135#117×C61—24no—
136C2×C4⋊C4×C61—21no—
137C2×C4⋊C4×C61C2×C411yescharacteristic
138C2×C4⋊C4×C61C2×C411yescharacteristic
139C2×C22⋊C4×C61C2×C411yescharacteristic
140C2×C22⋊C4×C61C2×C411yescharacteristic
141C2×C22⋊C4×C61C2312yes—
142C2×C22⋊C4×C61C2311yescharacteristic
143C2×C22⋊C4×C61C2312yes—
144C2×C42×C61—21no—
145#99×C61—24no—
146#95×C61—21no—
147#95×C61—21no—
148C24×C61C22×C411yescharacteristic
149C24×C61C2411yescharacteristic
150C23×D61C22×C411yescharacteristic
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—22no—
154C2×D4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C2×C22⋊D61—21no—
169C2×C22⋊D61—21no—
170C2×C22⋊D61—22no—
171C2×C22⋊D61—22no—
172C2×C22⋊D61—22no—
173C2×C22⋊D61—81no—
174C22×Dic61—22no—
175C22×Dic61—22no—
176C22×Dic61—22no—
177C22×Dic61—81no—
178C22×Dic61—81no—
179C22×Dic61—81no—
180C22×Dic61C22×C411yescharacteristic
181C22×Dic61C22×C411yescharacteristic
182C22×Dic61C22×C411yescharacteristic
183C22×Dic61C22×C411yescharacteristic
184C22×Dic61C22×C411yescharacteristic
185C22×Dic61C22×C411yescharacteristic
186C22×Dic61C22×C411yescharacteristic
187C22×Dic61C2×D412yes—
188C22×Dic61C2×D412yes—
189C22×Dic61C2×D412yes—
190C22×Dic61C2×D412yes—
191C2×C4×D61—22no—
192C2×C4×D61—81no—
193C2×Dic122—22no—
194C2×Dic122—81no—
195C4⋊C4×C61—24no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C22⋊C4×C61—21no—
201C22⋊C4×C61—21no—
202C22⋊C4×C61—22no—
203C22⋊C4×C61—21no—
204C22⋊C4×C61—21no—
205C22⋊C4×C61—21no—
206C22⋊C4×C61—21no—
207C22⋊C4×C61—22no—
208C22⋊C4×C61—22no—
209C22⋊C4×C61#4114yes—
210C42×C61—24no—
211C22⋊Dic61—21no—
212C22⋊Dic61—21no—
213C22⋊Dic61—22no—
214C22⋊Dic61—22no—
215C22⋊Dic61—22no—
216C22⋊Dic61—22no—
217C22⋊Dic61—22no—
218C22⋊Dic61#4114yes—
219#11758198—21no—
220#11758198—21no—
221#11758198—21no—
222#11758198—21no—
223#11758198—22no—
224#11758198—22no—
225C4⋊Dic61—24no—
226C4⋊Dic61—22no—
227C4⋊Dic61—22no—
228C4⋊Dic61C22⋊C412yes—
229C4⋊Dic61C22⋊C412yes—
230C4⋊Dic61C22⋊C412yes—
231C4⋊Dic61C22⋊C412yes—
232C4⋊Dic61C22⋊C412yes—
233C4⋊Dic61C22⋊C412yes—
234C4⋊Dic61C22⋊C412yes—
235C4⋊Dic61C22⋊C412yes—
236#11758196—21no—
237#11758196—21no—
238#11758196—21no—
239#11758196—21no—
240#11758196—22no—
241#11758196—22no—
242#11758196—22no—
243#11758196—22no—
244#11758196—82no—
245C4×Dic61—24no—
246C4×Dic61—22no—
247C4×Dic61—22no—
248C4×Dic61—82no—
249C4×Dic61—82no—
250C4×Dic61—82no—
251C23×C61—21no—
252C23×C61—22no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61C23×C411yescharacteristic
258C23×C61C22×D411yescharacteristic
259C23×C61C22×D411yescharacteristic
260C23×C61C2×#4112yes—
261C23×C61C2×#4112yes—
262C22×D61—21no—
263C22×D61—22no—
264C22×D61—41no—
265C22×D61—41no—
266D4×C61—41no—
267D4×C61—41no—
268D4×C61—42no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—22no—
281C2×C4×C61—24no—
282C2×C4×C61—42no—
283C2×C4×C61—42no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61C2×C22⋊C411yescharacteristic
290C2×C4×C61C2×C22⋊C411yescharacteristic
291C2×C4×C61C2×C22⋊C411yescharacteristic
292C2×C4×C61C2×C22⋊C411yescharacteristic
293C22⋊D61—41no—
294C22⋊D61—41no—
295C22⋊D61—42no—
296C22⋊D61—82no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—22no—
301C2×Dic61—24no—
302C2×Dic61—42no—
303C2×Dic61—42no—
304C2×Dic61—42no—
305C2×Dic61—42no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—42no—
311C2×Dic61—42no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—82no—
318C2×Dic61C2×C22⋊C412yes—
319C2×Dic61C2×C22⋊C412yes—
320C2×Dic61C2×C22⋊C412yes—
321C2×Dic61C2×C22⋊C412yes—
322C4×D61—82no—
323Dic122—82no—
324#21423—611nomaximal, Sylow
325C22×C61—21no—
326C22×C61—21no—
327C22×C61—21no—
328C22×C61—21no—
329C22×C61—21no—
330C22×C61—21no—
331C22×C61—42no—
332C22×C61—42no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—82no—
337C22×C61C22×C22⋊C411yescharacteristic
338C22×C61C4×#4112yes—
339C22×C61#52511yescharacteristic
340C22×C61#52511yescharacteristic
341C22×C61#53212yes—
342C2×D61—41no—
343C2×D61—41no—
344C2×D61—41no—
345C2×D61—82no—
346C4×C61—21no—
347C4×C61—21no—
348C4×C61—21no—
349C4×C61—21no—
350C4×C61—44no—
351C4×C61—41no—
352C4×C61—41no—
353C4×C61—41no—
354C4×C61—82no—
355Dic61—22no—
356Dic61—22no—
357Dic61—22no—
358Dic61—22no—
359Dic61—44no—
360Dic61—41no—
361Dic61—41no—
362Dic61—41no—
363Dic61—82no—
364C2×#539—611no—
365#2313—611no—
366#2274—611no—
367#1996—612no—
368#1964—612no—
369#1899—611no—
370#1899—611no—
371#1899—611no—
372#1899D6111yescharacteristic, complemented
373C4×#99—612no—
374C4×#99—612no—
375C2×C61—21no—
376C2×C61—22no—
377C2×C61—21no—
378C2×C61—22no—
379C2×C61—81no—
380C2×C61#229711yescharacteristic
381C2×C61#288311yescharacteristic
382C2×C61#288411yescharacteristic
383D61—81no—
384#539—1222no—
385#539—1222no—
386#539—1222no—
387#539—1222no—
388C2×#126—611no—
389C2×#126—611no—
390C2×#125—611no—
391C2×#125—611no—
392C2×#123—611no—
393C2×#123—611no—
394C2×#123—611no—
395C2×#123C2×D6111yescharacteristic
396C2×C22⋊Q8—611no—
397C2×C22⋊Q8—611no—
398C2×C22⋊Q8—611no—
399C2×#121—611no—
400C2×C4×D4—611no—
401C2×C4×D4—611no—
402C2×#117—611no—
403C2×#117C2×D6111yescharacteristic
404C22×C4⋊C4—611no—
405C2×#99—612no—
406C2×#99—612no—
407C2×#99—612no—
408C2×#99C2×D6112yes—
409#387—1222no—
410#387—1222no—
411#381—611no—
412#381C2×D6111yescharacteristic
413#380—612no—
414C4×C4⋊C4—1222no—
415C4×C4⋊C4—1222no—
416C4×C22⋊C4—612no—
417C4×C22⋊C4—612no—
418C4×C22⋊C4—612no—
419#342—612no—
420#342—612no—
421#342—612no—
422#342C2×D6112yes—
423C61#2142311yescharacteristic, complemented, Sylow
424C22×Q8—611no—
425C22×D4—611no—
426C22×D4—611no—
427C22×D4C22×D6111yescharacteristic
428C23×C4—611no—
429C23×C4—611no—
430C23×C4—611no—
431C23×C4—611no—
432C23×C4C22×D6111yescharacteristic
433#126—1222no—
434#126—1222no—
435#126—1222no—
436#126—1222no—
437#125—1222no—
438#125—1222no—
439#125—1222no—
440#125—1222no—
441#123—21no—
442#123—21no—
443#123—21no—
444#123—21no—
445#123—1222no—
446#123—1222no—
447#123—1222no—
448#123—1222no—
449#123—1221no—
450#123—1221no—
451#123—1221no—
452#123—1221no—
453C22⋊Q8—1222no—
454C22⋊Q8—1222no—
455C22⋊Q8—1222no—
456C22⋊Q8—1222no—
457C22⋊Q8—1222no—
458C22⋊Q8—1222no—
459#121—1222no—
460#121—1222no—
461C4×D4—1222no—
462C4×D4—1222no—
463C4×D4—1222no—
464C4×D4—1222no—
465#117—24no—
466#117—1224no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—612no—
473C2×C4⋊C4—612no—
474C2×C4⋊C4—612no—
475C2×C4⋊C4—612no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4—1222no—
486C2×C4⋊C4C4×D6111yescharacteristic
487C2×C4⋊C4C4×D6111yescharacteristic
488C2×C22⋊C4—612no—
489C2×C22⋊C4—611no—
490C2×C22⋊C4—611no—
491C2×C22⋊C4—611no—
492C2×C22⋊C4—611no—
493C2×C22⋊C4—611no—
494C2×C22⋊C4—611no—
495C2×C22⋊C4—611no—
496C2×C22⋊C4—612no—
497C2×C22⋊C4C4×D6111yescharacteristic
498C2×C22⋊C4C4×D6111yescharacteristic
499C2×C22⋊C4C22×D6112yes—
500C2×C22⋊C4C22×D6111yescharacteristic
501C2×C22⋊C4C22×D6112yes—
502C2×C42—21no—
503C2×C42—611no—
504C2×C42—611no—
505C2×C42—1221no—
506C2×C42—1222no—
507C2×C42—1222no—
508C2×C42—1222no—
509#99—24no—
510#99—1224no—
511#99—1224no—
512#99—1224no—
513#95—21no—
514#95—21no—
515#95—1222no—
516#95—1222no—
517#95—1222no—
518#95—1222no—
519#95—1221no—
520#95—1221no—
521C24—611no—
522C24C2×C4×D6111yescharacteristic
523C24C23×D6111yescharacteristic
524C2×Q8—1222no—
525C2×Q8—4881no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—1222no—
531C2×D4—1221no—
532C2×D4—1221no—
533C2×D4—1222no—
534C2×D4—1222no—
535C2×D4—4881no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—611no—
541C22×C4—611no—
542C22×C4—611no—
543C22×C4—611no—
544C22×C4—612no—
545C22×C4—612no—
546C22×C4—612no—
547C22×C4—612no—
548C22×C4—611no—
549C22×C4—611no—
550C22×C4—611no—
551C22×C4—1222no—
552C22×C4—1222no—
553C22×C4—1222no—
554C22×C4—1222no—
555C22×C4—4881no—
556C22×C4—4881no—
557C22×C4—4881no—
558C22×C4—4881no—
559C22×C4C2×C4×D6111yescharacteristic
560C22×C4C2×C4×D6111yescharacteristic
561C22×C4C2×C4×D6111yescharacteristic
562C22×C4C2×C4×D6111yescharacteristic
563C22×C4C2×C4×D6111yescharacteristic
564C22×C4D4×D6111yescharacteristic
565C22×C4D4×D6111yescharacteristic
566C22×C4D4×D6111yescharacteristic
567C22×C4D4×D6111yescharacteristic
568C4⋊C4—24no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—612no—
574C4⋊C4—612no—
575C4⋊C4—612no—
576C4⋊C4—612no—
577C4⋊C4—612no—
578C4⋊C4—612no—
579C4⋊C4—612no—
580C4⋊C4—612no—
581C4⋊C4—1222no—
582C4⋊C4—1222no—
583C4⋊C4—1222no—
584C4⋊C4—1222no—
585C4⋊C4—1222no—
586C4⋊C4—1222no—
587C4⋊C4—1224no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—4882no—
593C22⋊C4—21no—
594C22⋊C4—21no—
595C22⋊C4—22no—
596C22⋊C4—21no—
597C22⋊C4—21no—
598C22⋊C4—21no—
599C22⋊C4—21no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—614no—
603C22⋊C4—1222no—
604C22⋊C4—1222no—
605C22⋊C4—1222no—
606C22⋊C4—1222no—
607C22⋊C4—1221no—
608C22⋊C4—1221no—
609C22⋊C4—1222no—
610C22⋊C4—1221no—
611C22⋊C4—1221no—
612C22⋊C4—1221no—
613C22⋊C4—1221no—
614C22⋊C4—1222no—
615C22⋊C4—1222no—
616C22⋊C4#1175822414yes—
617C42—24no—
618C42—1222no—
619C42—1222no—
620C42—1224no—
621C42—4882no—
622C42—4882no—
623C42—4882no—
624C23—21no—
625C23—22no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—1222no—
631C23—1221no—
632C23—2441no—
633C23—2441no—
634C23C22×C4×D6111yescharacteristic
635C23C2×D4×D6111yescharacteristic
636C23C2×D4×D6111yescharacteristic
637C23#41×D6112yes—
638C23C2×#1175822412yes—
639Q8—4882no—
640D4—41no—
641D4—41no—
642D4—42no—
643D4—4882no—
644D4—2441no—
645D4—2441no—
646D4—2442no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—612no—
668C2×C4—612no—
669C2×C4—612no—
670C2×C4—612no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1222no—
675C2×C4—1224no—
676C2×C4—4882no—
677C2×C4—4882no—
678C2×C4—2442no—
679C2×C4—2442no—
680C2×C4—2442no—
681C2×C4—2442no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2442no—
687C2×C4—2442no—
688C2×C4—2442no—
689C2×C4—2442no—
690C2×C4—2442no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4C22⋊C4×D6111yescharacteristic
694C2×C4C22⋊C4×D6111yescharacteristic
695C2×C4C22⋊C4×D6111yescharacteristic
696C2×C4C22⋊C4×D6111yescharacteristic
697C22—21no—
698C22—21no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—42no—
704C22—42no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—82no—
709C22—4882no—
710C22—2441no—
711C22—2441no—
712C22—2441no—
713C22C2×C22⋊C4×D6111yescharacteristic
714C22C4×#1175822412yes—
715C22#1684026811yescharacteristic
716C22#1684027011yescharacteristic
717C22#1684030712yes—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—21no—
722C4—44no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—82no—
727C4—1222no—
728C4—1222no—
729C4—1222no—
730C4—1222no—
731C4—4882no—
732C4—2444no—
733C4—2441no—
734C4—2441no—
735C4—2441no—
736C2—21no—
737C2—22no—
738C2—21no—
739C2—22no—
740C2—81no—
741C2—4881no—
742C2#2144830411yescharacteristic
743C2#2145427811yescharacteristic
744C2#2145428111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1899C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519749C22
cosocleC24×C61C24
hypercenter#1899D61
hypocenterC61#21423
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1899

Complements

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

NH ≅ G/Ntype
2. #21448420C2semidirect
3. #21448175C2semidirect
4. #21446802C2semidirect
6. #21446278C2semidirect
7. #21446277C2semidirect
8. #21446275C2semidirect
9. #99×Dic61C2semidirect
10. #21445606C2semidirect
11. C61×#1899C2semidirect
16. C2×#14519772C4semidirect
17. C2×#14519770C4semidirect
18. C2×#14519768C4semidirect
19. C2×#14519767C4semidirect
20. C2×#14519761C4semidirect
22. C2×#14519759C4semidirect
23. C2×#14519757C4semidirect
24. C2×#14519754C4semidirect
372. #1899D61semidirect
423. C61#21423semidirect

Maximal subgroups

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

subgroupindex
C2×#168403562
#214484202
#214481752
#214468022
#214466532
#214462782
#214462772
#214462752
#99×Dic612
#214456062
C61×#18992
#2142361