Finite Group Databasebeta

← #29696764

Subgroups — #29696764

Order 15616.

1172 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
1C2×#16840460C211yesmaximal, characteristic
2#21448696C211yesmaximal, characteristic, complemented
3#21446655C211yesmaximal, characteristic, complemented
4#21446655C212yesmaximal, complemented
5#21446654C211yesmaximal, characteristic, complemented
6#21446654C212yesmaximal, complemented
7#21445804C211yesmaximal, characteristic, complemented
8#21445804C212yesmaximal, complemented
9C4×#14519691C211yesmaximal, characteristic, complemented
10C4×#14519691C212yesmaximal, complemented
11C61×#2345C211yesmaximal, characteristic, complemented
12#16840460—21no—
13#16840460—22no—
14#16840460—21no—
15#16840460—21no—
16#16840460—22no—
17#16840460—21no—
18C2×#14519772C412yescomplemented
19C2×#14519768C411yescharacteristic, complemented
20C2×#14519762C412yescomplemented
21C2×#14519752C411yescharacteristic, complemented
22C2×#14519751C2211yescharacteristic
23C2×#14519751C2212yes—
24C2×#14519739C411yescharacteristic, complemented
25C2×C4×C22⋊D61C2211yescharacteristic
26C2×C4×C22⋊D61C2212yes—
27C2×#14519735C411yescharacteristic, complemented
28C2×#14519691C2212yes—
29C2×#14519691C2211yescharacteristic
30C2×#14519691C2212yes—
31C2×#14519691C2211yescharacteristic
32C2×#14519691C2212yes—
33C2×#14519691C2212yes—
34C2×#14519691C2212yes—
35#16839661—21no—
36#16839648—22no—
37#16839622C2211yescharacteristic
38#16839622C2212yes—
39C4⋊C4×Dic61—21no—
40C4×C22⋊Dic61C2211yescharacteristic
41C4×C22⋊Dic61C2212yes—
42#16839528C2211yescharacteristic
43#16839528C2212yes—
44#16839528C2211yescharacteristic
45C22×C4⋊C4×C61C2211yescharacteristic
46C61×#389—21no—
47C61×#387—22no—
48C61×#380C2212yes—
49C61×#380C2211yescharacteristic
50C4×C4⋊C4×C61—21no—
51C4×C22⋊C4×C61C2211yescharacteristic
52C4×C22⋊C4×C61C2212yes—
53C22×D244C2×C411yescharacteristic
54C22×D244C2×C412yes—
55C22×C22⋊D61C2312yes—
56C22×C22⋊D61C2311yescharacteristic
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61C2×C412yes—
59#14519772—22no—
60#14519772—22no—
61#14519772—22no—
62#14519772—22no—
63#14519768—22no—
64#14519768—21no—
65#14519768—21no—
66#14519762—22no—
67#14519762—22no—
68#14519762—22no—
69#14519762—22no—
70#14519752—22no—
71#14519752—21no—
72#14519752—21no—
73#14519751—21no—
74#14519751—21no—
75#14519751—21no—
76#14519751—21no—
77#14519751—22no—
78#14519751—22no—
79#14519751—22no—
80#14519751—22no—
81#14519739—22no—
82#14519739—21no—
83#14519739—21no—
84C4×C22⋊D61—22no—
85C4×C22⋊D61—22no—
86C4×C22⋊D61—22no—
87C4×C22⋊D61—22no—
88C4×C22⋊D61—21no—
89C4×C22⋊D61—21no—
90C4×C22⋊D61—21no—
91C4×C22⋊D61—21no—
92#14519735—22no—
93#14519735—21no—
94#14519735—21no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61—22no—
97C2×C4⋊Dic61C2×C411yescharacteristic
98C2×C4⋊Dic61C2×C412yes—
99C2×#11758196C2×C412yes—
100C2×#11758196C2×C411yescharacteristic
101C2×C22⋊Dic61C2311yescharacteristic
102C2×C22⋊Dic61C2312yes—
103C2×C22⋊Dic61C2311yescharacteristic
104C2×C22⋊Dic61C2311yescharacteristic
105C2×#11758198C2×C412yes—
106C2×#11758198C2×C412yes—
107C2×#11758198C2×C411yescharacteristic
108C2×#11758198C2×C412yes—
109C2×#11758198C2×C412yes—
110C2×C4×Dic61—21no—
111C2×C4×Dic61—22no—
112C2×C4×Dic61C2×C412yes—
113C2×C4×Dic61C2×C411yescharacteristic
114#14519691—22no—
115#14519691—24no—
116#14519691—22no—
117#14519691—24no—
118#14519691—42no—
119#14519691—42no—
120#14519691—42no—
121#14519684—21no—
122#14519684—22no—
123#14519684—22no—
124#14519684—21no—
125C23×C4×C61C2311yescharacteristic
126C23×C4×C61C2312yes—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61—22no—
129C2×C4⋊C4×C61C2×C411yescharacteristic
130C2×C4⋊C4×C61C2×C411yescharacteristic
131C2×C4⋊C4×C61C2×C412yes—
132C2×C4⋊C4×C61D411yescharacteristic
133C2×C4⋊C4×C61D412yes—
134C2×C4⋊C4×C61D411yescharacteristic
135C2×C4⋊C4×C61D411yescharacteristic
136C2×C4⋊C4×C61D412yes—
137C2×C4⋊C4×C61D411yescharacteristic
138C2×C22⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61C2312yes—
140C2×C22⋊C4×C61C2311yescharacteristic
141C2×C42×C61—21no—
142C2×C42×C61—22no—
143#95×C61—21no—
144#95×C61—22no—
145#95×C61—22no—
146#95×C61—21no—
147C24×C61C2411yescharacteristic
148C23×D61C22×C411yescharacteristic
149C23×D61C22×C412yes—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—22no—
153C22×C4×C61—42no—
154C22×C4×C61—82no—
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C412yes—
157C22×C4×C61C22×C412yes—
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D412yes—
163C22×C4×C61C2×D412yes—
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D412yes—
166C22×C4×C61C2×D412yes—
167C2×C22⋊D61—22no—
168C2×C22⋊D61—21no—
169C2×C22⋊D61—22no—
170C2×C22⋊D61—21no—
171C2×C22⋊D61—22no—
172C2×C22⋊D61—21no—
173C2×C22⋊D61—22no—
174C2×C22⋊D61—21no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61—21no—
177C2×C22⋊D61—22no—
178C2×C22⋊D61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—22no—
182C22×Dic61C22×C412yes—
183C22×Dic61C22×C411yescharacteristic
184C22×Dic61C22×C411yescharacteristic
185C22×Dic61C22×C411yescharacteristic
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—22no—
189C2×D244—22no—
190C2×D244—42no—
191C2×D244—82no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—22no—
195C2×C4×D61—22no—
196C2×C4×D61—42no—
197C2×C4×D61—82no—
198C4⋊C4×C61—42no—
199C4⋊C4×C61—82no—
200C4⋊C4×C61C22⋊C412yes—
201C4⋊C4×C61C22⋊C411yescharacteristic
202C4⋊C4×C61C22⋊C411yescharacteristic
203C4⋊C4×C61C22⋊C412yes—
204C4⋊C4×C61C22⋊C411yescharacteristic
205C4⋊C4×C61C22⋊C411yescharacteristic
206C4⋊C4×C61C22⋊C412yes—
207C4⋊C4×C61C22⋊C412yes—
208C4⋊C4×C61C22⋊C412yes—
209C4⋊C4×C61C22⋊C412yes—
210C22⋊C4×C61—21no—
211C22⋊C4×C61—21no—
212C22⋊C4×C61—22no—
213C22⋊C4×C61—21no—
214C22⋊C4×C61—22no—
215C22⋊C4×C61#4112yes—
216C42×C61—42no—
217C42×C61—82no—
218C22⋊Dic61—21no—
219C22⋊Dic61—21no—
220C22⋊Dic61—21no—
221C22⋊Dic61—21no—
222C22⋊Dic61—22no—
223C22⋊Dic61—21no—
224C22⋊Dic61—22no—
225C22⋊Dic61#4112yes—
226#11758198—22no—
227#11758198—22no—
228#11758198—22no—
229#11758198—22no—
230#11758198—21no—
231#11758198—21no—
232#11758198—22no—
233#11758198—22no—
234#11758198—22no—
235#11758198—22no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—22no—
239C4⋊Dic61—22no—
240C4⋊Dic61—42no—
241C4⋊Dic61—82no—
242#11758196—22no—
243#11758196—22no—
244#11758196—21no—
245#11758196—21no—
246C4×Dic61—22no—
247C4×Dic61—22no—
248C4×Dic61—21no—
249C4×Dic61—21no—
250C4×Dic61—42no—
251C4×Dic61—82no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61C23×C411yescharacteristic
255C23×C61C22×D411yescharacteristic
256C23×C61C22×D411yescharacteristic
257C23×C61C2×#4111yescharacteristic
258C23×C61C2×#4111yescharacteristic
259C23×C61H(5,𝔽2)11yescharacteristic
260C23×C612−1+411yescharacteristic
261C22×D61—21no—
262C22×D61—22no—
263C22×D61—21no—
264C22×D61—22no—
265C22×D61—21no—
266C22×D61—22no—
267C22×D61—41no—
268C22×D61—42no—
269C22×D61—42no—
270C22×D61—41no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—42no—
276C2×C4×C61—42no—
277C2×C4×C61—42no—
278C2×C4×C61—42no—
279C2×C4×C61—42no—
280C2×C4×C61—42no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—42no—
292C2×C4×C61C2×C22⋊C411yescharacteristic
293C2×C4×C61C2×C22⋊C412yes—
294C2×C4×C61C2×C22⋊C412yes—
295C2×C4×C61C2×C22⋊C412yes—
296C2×C4×C61C2×C22⋊C412yes—
297C2×C4×C61C2×C22⋊C411yescharacteristic
298C2×C4×C61C2×C22⋊C411yescharacteristic
299C2×C4×C61C2×C22⋊C411yescharacteristic
300C22⋊D61—42no—
301C22⋊D61—41no—
302C22⋊D61—42no—
303C22⋊D61—41no—
304C22⋊D61—42no—
305C22⋊D61—41no—
306C22⋊D61—42no—
307C22⋊D61—41no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—22no—
311C2×Dic61—21no—
312C2×Dic61—22no—
313C2×Dic61—21no—
314C2×Dic61—22no—
315C2×Dic61—21no—
316C2×Dic61—22no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—42no—
327D244—42no—
328D244—42no—
329D244—82no—
330D244—82no—
331C4×D61—42no—
332C4×D61—42no—
333C4×D61—82no—
334C4×D61—82no—
335#22535—611nomaximal, Sylow
336C22×C61—21no—
337C22×C61—21no—
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—21no—
341C22×C61—21no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61C22×C22⋊C411yescharacteristic
347C22×C61C4×#4111yescharacteristic
348C22×C61#52011yescharacteristic
349C22×C61#54811yescharacteristic
350C22×C61#54811yescharacteristic
351C22×C61#55011yescharacteristic
352C22×C61#55011yescharacteristic
353C2×D61—41no—
354C2×D61—42no—
355C2×D61—41no—
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—41no—
359C2×D61—81no—
360C2×D61—82no—
361C2×D61—81no—
362C2×D61—82no—
363C4×C61—21no—
364C4×C61—21no—
365C4×C61—21no—
366C4×C61—22no—
367C4×C61—22no—
368C4×C61—22no—
369C4×C61—22no—
370C4×C61—42no—
371C4×C61—81no—
372C4×C61—82no—
373C4×C61#41012yes—
374Dic61—42no—
375Dic61—42no—
376Dic61—41no—
377Dic61—41no—
378Dic61—41no—
379Dic61—81no—
380Dic61—82no—
381C2×#553—611no—
382#2345—611no—
383#2345D6111yescharacteristic, complemented
384#1964—612no—
385#1964—611no—
386#1964—612no—
387#1964—611no—
388#1799—612no—
389#1799—611no—
390C4×#99—612no—
391C4×#99—611no—
392C2×C61—21no—
393C2×C61—21no—
394C2×C61—21no—
395C2×C61—21no—
396C2×C61—21no—
397C2×C61—21no—
398C2×C61#234111yescharacteristic
399C2×C61C2×#41011yescharacteristic
400C2×C61#288311yescharacteristic
401D61—81no—
402D61—82no—
403#553—1221no—
404#553—1222no—
405#553—1221no—
406#553—1221no—
407#553—1222no—
408#553—1221no—
409C2×#126—612no—
410C2×#125—611no—
411C2×#123—612no—
412C2×#121—612no—
413C2×#121—611no—
414C2×#121—611no—
415C2×C4×D4—612no—
416C2×C4×D4—611no—
417C2×C4×D4—611no—
418C2×#117—611no—
419C22×C4⋊C4C2×D6111yescharacteristic
420C2×#99—611no—
421C2×#99—612no—
422C2×#99—612no—
423C2×#99—611no—
424C2×#99—612no—
425C2×#99—612no—
426C2×#99—612no—
427#389—21no—
428#389—1221no—
429#387—22no—
430#387—1222no—
431#380—612no—
432#380—611no—
433#380C2×D6112yes—
434#380C2×D6111yescharacteristic
435C4×C4⋊C4—21no—
436C4×C4⋊C4—1221no—
437C4×C22⋊C4—611no—
438C4×C22⋊C4—612no—
439C4×C22⋊C4C2×D6111yescharacteristic
440C4×C22⋊C4C2×D6112yes—
441#342—612no—
442#342—611no—
443#342—611no—
444C61#2253511yescharacteristic, complemented, Sylow
445C22×D4—612no—
446C22×D4—611no—
447C22×D4—612no—
448C22×D4—611no—
449C23×C4—612no—
450C23×C4—611no—
451C23×C4C22×D6111yescharacteristic
452C23×C4C22×D6112yes—
453#126—1222no—
454#126—1222no—
455#126—1222no—
456#126—1222no—
457#125—1222no—
458#125—1221no—
459#125—1221no—
460#123—1222no—
461#123—1222no—
462#123—1222no—
463#123—1222no—
464#121—1222no—
465#121—1222no—
466#121—1221no—
467#121—1221no—
468#121—1222no—
469#121—1222no—
470#121—1221no—
471#121—1221no—
472#121—1222no—
473#121—1221no—
474#121—1221no—
475C4×D4—1222no—
476C4×D4—1222no—
477C4×D4—1221no—
478C4×D4—1221no—
479C4×D4—1222no—
480C4×D4—1222no—
481C4×D4—1221no—
482C4×D4—1221no—
483C4×D4—1222no—
484C4×D4—1221no—
485C4×D4—1221no—
486#117—1222no—
487#117—1221no—
488#117—1221no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—611no—
492C2×C4⋊C4—612no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—612no—
495C2×C4⋊C4—1222no—
496C2×C4⋊C4—1221no—
497C2×C4⋊C4C4×D6111yescharacteristic
498C2×C4⋊C4C4×D6111yescharacteristic
499C2×C4⋊C4C4×D6112yes—
500C2×C4⋊C4D24411yescharacteristic
501C2×C4⋊C4D24412yes—
502C2×C4⋊C4D24411yescharacteristic
503C2×C4⋊C4C22⋊D6111yescharacteristic
504C2×C4⋊C4C22⋊D6112yes—
505C2×C4⋊C4C22⋊D6111yescharacteristic
506C2×C22⋊C4—611no—
507C2×C22⋊C4—611no—
508C2×C22⋊C4—612no—
509C2×C22⋊C4—612no—
510C2×C22⋊C4—612no—
511C2×C22⋊C4—611no—
512C2×C22⋊C4—612no—
513C2×C22⋊C4—612no—
514C2×C22⋊C4—611no—
515C2×C22⋊C4C22×D6111yescharacteristic
516C2×C22⋊C4C22×D6112yes—
517C2×C22⋊C4C22×D6111yescharacteristic
518C2×C42—21no—
519C2×C42—22no—
520C2×C42—612no—
521C2×C42—611no—
522C2×C42—1222no—
523C2×C42—1221no—
524#99—1222no—
525#99—1224no—
526#99—1224no—
527#99—1222no—
528#99—2442no—
529#99—2442no—
530#99—2442no—
531#95—21no—
532#95—22no—
533#95—22no—
534#95—21no—
535#95—1221no—
536#95—1222no—
537#95—1222no—
538#95—1221no—
539C24—612no—
540C24—611no—
541C24C23×D6111yescharacteristic
542C2×D4—1222no—
543C2×D4—1221no—
544C2×D4—1222no—
545C2×D4—1221no—
546C2×D4—1222no—
547C2×D4—1221no—
548C2×D4—1222no—
549C2×D4—1221no—
550C2×D4—1222no—
551C2×D4—1221no—
552C2×D4—1222no—
553C2×D4—1221no—
554C2×D4—1222no—
555C2×D4—1222no—
556C2×D4—1221no—
557C2×D4—1221no—
558C2×D4—4882no—
559C2×D4—2442no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—42no—
564C22×C4—82no—
565C22×C4—612no—
566C22×C4—611no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—1221no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1222no—
575C22×C4—1221no—
576C22×C4—4882no—
577C22×C4—2442no—
578C22×C4C2×C4×D6111yescharacteristic
579C22×C4C2×C4×D6112yes—
580C22×C4C2×C4×D6111yescharacteristic
581C22×C4C2×C4×D6112yes—
582C22×C4C2×D24411yescharacteristic
583C22×C4C2×D24411yescharacteristic
584C22×C4C2×D24412yes—
585C22×C4C2×D24412yes—
586C22×C4C2×C22⋊D6111yescharacteristic
587C22×C4C2×C22⋊D6111yescharacteristic
588C22×C4C2×C22⋊D6112yes—
589C22×C4C2×C22⋊D6112yes—
590C4⋊C4—42no—
591C4⋊C4—82no—
592C4⋊C4—1222no—
593C4⋊C4—1222no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1222no—
599C4⋊C4—1222no—
600C4⋊C4—4882no—
601C4⋊C4—2442no—
602C4⋊C4#1175819812yes—
603C4⋊C4#1175819811yescharacteristic
604C4⋊C4#1175819811yescharacteristic
605C4⋊C4#1175819812yes—
606C4⋊C4#1175819811yescharacteristic
607C4⋊C4#1175819811yescharacteristic
608C4⋊C4#1175819812yes—
609C4⋊C4#1175819812yes—
610C4⋊C4#1175819812yes—
611C4⋊C4#1175819812yes—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—21no—
616C22⋊C4—22no—
617C22⋊C4—612no—
618C22⋊C4—1221no—
619C22⋊C4—1221no—
620C22⋊C4—1221no—
621C22⋊C4—1222no—
622C22⋊C4—1222no—
623C22⋊C4—1222no—
624C22⋊C4—1222no—
625C22⋊C4—1222no—
626C22⋊C4—1222no—
627C22⋊C4—1221no—
628C22⋊C4—1221no—
629C22⋊C4—1222no—
630C22⋊C4—1222no—
631C22⋊C4—1222no—
632C22⋊C4—1221no—
633C22⋊C4—1222no—
634C22⋊C4—1221no—
635C22⋊C4#1175822612yes—
636C42—42no—
637C42—82no—
638C42—1222no—
639C42—1222no—
640C42—1221no—
641C42—1221no—
642C42—4882no—
643C42—2442no—
644C23—41no—
645C23—41no—
646C23—1222no—
647C23—1221no—
648C23—1222no—
649C23—1221no—
650C23—1221no—
651C23—1222no—
652C23—2442no—
653C23—2441no—
654C23—2441no—
655C23—2442no—
656C23C22×C4×D6111yescharacteristic
657C23C22×C22⋊D6111yescharacteristic
658C23C22×D24411yescharacteristic
659C23#41×D6111yescharacteristic
660C23C2×#1175822611yescharacteristic
661C23#1451982311yescharacteristic
662C23#1451982511yescharacteristic
663D4—4882no—
664D4—4882no—
665D4—2442no—
666D4—2442no—
667D4—2441no—
668D4—2442no—
669D4—2441no—
670D4—2442no—
671D4—2441no—
672D4—2442no—
673D4—2441no—
674D4—2442no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—1221no—
697C2×C4—1222no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1222no—
701C2×C4—1221no—
702C2×C4—1222no—
703C2×C4—1221no—
704C2×C4—1222no—
705C2×C4—4882no—
706C2×C4—4882no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2442no—
712C2×C4—2442no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2442no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4C2×#1175819812yes—
720C2×C4C2×#1175819812yes—
721C2×C4C2×#1175819811yescharacteristic
722C2×C4C2×#1175819811yescharacteristic
723C2×C4C2×#1175819811yescharacteristic
724C2×C4C2×#1175819812yes—
725C2×C4C2×#1175819812yes—
726C2×C4C2×#1175819811yescharacteristic
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—4882no—
738C22—4881no—
739C22—4882no—
740C22—4881no—
741C22—2441no—
742C22—2442no—
743C22—2442no—
744C22—2441no—
745C22—2441no—
746C22—2442no—
747C22C22×#1175819811yescharacteristic
748C22C4×#1175822611yescharacteristic
749C22#1684024411yescharacteristic
750C22#1684042311yescharacteristic
751C22#1684042411yescharacteristic
752C22#1684043111yescharacteristic
753C22#1684043411yescharacteristic
754C4—21no—
755C4—21no—
756C4—21no—
757C4—22no—
758C4—22no—
759C4—22no—
760C4—22no—
761C4—42no—
762C4—81no—
763C4—82no—
764C4—4882no—
765C4—4881no—
766C4—2442no—
767C4—2441no—
768C4—2441no—
769C4—2442no—
770C4—2441no—
771C4#1683973512yes—
772C2—21no—
773C2—21no—
774C2—21no—
775C2—21no—
776C2—21no—
777C2—21no—
778C2—4881no—
779C2—4882no—
780C2#2144865711yescharacteristic
781C2C2×#1683973511yescharacteristic
782C2#2145427911yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#2345C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840460C2
cosocleC24×C61C24
hypercenter#2345D61
hypocenterC61#22535
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4⋊C4 ◁ #2345

Complements

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

NH ≅ G/Ntype
2. #21448696C2semidirect
3. #21446655C2semidirect
4. #21446655C2semidirect
5. #21446654C2semidirect
6. #21446654C2semidirect
7. #21445804C2semidirect
8. #21445804C2semidirect
9. C4×#14519691C2semidirect
10. C4×#14519691C2semidirect
11. C61×#2345C2semidirect
18. C2×#14519772C4semidirect
19. C2×#14519768C4semidirect
20. C2×#14519762C4semidirect
21. C2×#14519752C4semidirect
24. C2×#14519739C4semidirect
27. C2×#14519735C4semidirect
383. #2345D61semidirect
444. C61#22535semidirect

Maximal subgroups

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

subgroupindex
C2×#168404602
#214486962
#214466552
#214466542
#214458042
C4×#145196912
C61×#23452
#2253561