Finite Group Databasebeta

← #29696156

Subgroups — #29696156

Order 15616.

1294 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840438C211yesmaximal, characteristic
2#21448670C212yesmaximal, complemented
3#21446802C212yesmaximal, complemented
4#21446276C212yesmaximal, complemented
5#21446270C212yesmaximal
6#21445895C211yesmaximal, characteristic, complemented
7#21445806C211yesmaximal, characteristic, complemented
8#21445606C211yesmaximal, characteristic, complemented
9#21445550C211yesmaximal, characteristic, complemented
10C2×#16839529C211yesmaximal, characteristic, complemented
11C61×#1819C211yesmaximal, characteristic, complemented
12#16840438—22no—
13#16840438—22no—
14#16840438—22no—
15#16840438—22no—
16C2×#14519770C411yescharacteristic, complemented
17C2×#14519770C411yescharacteristic, complemented
18C2×#14519763C411yescharacteristic, complemented
19C2×#14519761C2211yescharacteristic
20C2×#14519760C411yescharacteristic, complemented
21C2×#14519759C411yescharacteristic, complemented
22C2×#14519756C411yescharacteristic, complemented
23C2×#14519754C2211yescharacteristic
24C2×#14519746C2211yescharacteristic
25C2×C4×C22⋊D61C411yescharacteristic, complemented
26C2×#14519737C2211yescharacteristic
27C2×#14519736C411yescharacteristic, complemented
28C2×#14519733C2212yes—
29C2×#14519733C2211yescharacteristic
30C22×C22⋊Dic61C2212yes—
31C22×C22⋊Dic61C2211yescharacteristic
32C2×#14519691C2212yes—
33C2×#14519691C2212yes—
34#16839656—22no—
35#16839650—22no—
36#16839634—22no—
37#16839623C2212yes—
38#16839620C2212yes—
39C22⋊C4×Dic61—22no—
40C22⋊C4×Dic61C2212yes—
41#16839529C2211yescharacteristic
42#16839529C2212yes—
43#16839529C2211yescharacteristic
44#16839528C2212yes—
45#16839528C2212yes—
46C22×C22⋊C4×C61C2211yescharacteristic
47C61×#379C2212yes—
48C61×#342C2211yescharacteristic
49C61×#342C2212yes—
50C61×#342C2211yescharacteristic
51C22×Dic122C2×C411yescharacteristic, complemented
52C22×C22⋊D61C2×C411yescharacteristic
53C22×C22⋊D61C2×C411yescharacteristic
54C22×C22⋊D61C2311yescharacteristic
55C23×Dic61—22no—
56C23×Dic61C2311yescharacteristic
57C23×Dic61C2311yescharacteristic
58C22×C4×D61C2×C411yescharacteristic, complemented
59#14519770—22no—
60#14519770—22no—
61#14519770—22no—
62#14519770—22no—
63#14519763—22no—
64#14519763—22no—
65#14519761—22no—
66#14519761—22no—
67#14519760—22no—
68#14519760—22no—
69#14519759—22no—
70#14519759—22no—
71#14519756—22no—
72#14519756—22no—
73#14519754—22no—
74#14519754—22no—
75#14519746—22no—
76#14519746—22no—
77C4×C22⋊D61—21no—
78C4×C22⋊D61—21no—
79C4×C22⋊D61—21no—
80C4×C22⋊D61—21no—
81#14519737—22no—
82#14519737—22no—
83#14519736—21no—
84#14519736—21no—
85#14519736—21no—
86#14519736—21no—
87#14519733—22no—
88#14519733—22no—
89#14519733—24no—
90#14519733—42no—
91C2×C4⋊Dic61C2×C411yescharacteristic, complemented
92C2×C4⋊Dic61C2×C411yescharacteristic, complemented
93C2×C4⋊Dic61C2×C411yescharacteristic, complemented
94C2×#11758196—22no—
95C2×#11758196—22no—
96C2×#11758196C2×C411yescharacteristic, complemented
97C2×#11758196C2×C411yescharacteristic, complemented
98C2×#11758196C2×C411yescharacteristic, complemented
99C2×#11758196C2×C411yescharacteristic, complemented
100C2×#11758196C2×C411yescharacteristic, complemented
101C2×C22⋊Dic61—24no—
102C2×C22⋊Dic61—22no—
103C2×C22⋊Dic61—42no—
104C2×C22⋊Dic61C2×C411yescharacteristic
105C2×C22⋊Dic61C2×C411yescharacteristic
106C2×C22⋊Dic61C2×C411yescharacteristic
107C2×C22⋊Dic61C2×C411yescharacteristic
108C2×C22⋊Dic61C2×C411yescharacteristic
109C2×C22⋊Dic61C2×C411yescharacteristic
110C2×C22⋊Dic61D412yes—
111C2×C22⋊Dic61D412yes—
112C2×C22⋊Dic61D412yes—
113C2×C22⋊Dic61D412yes—
114C2×C22⋊Dic61C2312yes—
115C2×C22⋊Dic61C2311yescharacteristic
116C2×C22⋊Dic61C2312yes—
117C2×#11758198C2×C411yescharacteristic, complemented
118C2×#11758198C2×C411yescharacteristic, complemented
119C2×#11758198C2×C411yescharacteristic, complemented
120C2×C4×Dic61—22no—
121C2×C4×Dic61—22no—
122C2×C4×Dic61C2×C411yescharacteristic, complemented
123C2×C4×Dic61C2×C411yescharacteristic, complemented
124C2×C4×Dic61C2×C411yescharacteristic, complemented
125#14519691—24no—
126#14519691—42no—
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—22no—
131C25×C61C2311yescharacteristic
132C23×C4×C61C2×C411yescharacteristic
133C23×C4×C61C2×C411yescharacteristic
134C2×C22⋊C4×C61—22no—
135C2×C22⋊C4×C61—22no—
136C2×C22⋊C4×C61—22no—
137C2×C22⋊C4×C61—22no—
138C2×C22⋊C4×C61C2×C411yescharacteristic
139C2×C22⋊C4×C61C2×C411yescharacteristic
140C2×C22⋊C4×C61C2312yes—
141C2×C22⋊C4×C61C2312yes—
142C2×C22⋊C4×C61C2311yescharacteristic
143C2×C22⋊C4×C61C2311yescharacteristic
144C24×C61—22no—
145C24×C61—21no—
146C24×C61—21no—
147C24×C61—42no—
148C24×C61—81no—
149C24×C61C22×C411yescharacteristic
150C24×C61C22×C411yescharacteristic
151C24×C61C2×D412yes—
152C24×C61C2×D412yes—
153C24×C61C2411yescharacteristic
154C23×D61C22×C411yescharacteristic
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—22no—
160C22×C4×C61—22no—
161C22×C4×C61—42no—
162C22×C4×C61—81no—
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C22×C411yescharacteristic
166C22×C4×C61C22×C411yescharacteristic
167C2×C22⋊D61—21no—
168C2×C22⋊D61—21no—
169C2×C22⋊D61—22no—
170C2×C22⋊D61—22no—
171C2×C22⋊D61—21no—
172C2×C22⋊D61—21no—
173C2×C22⋊D61—22no—
174C2×C22⋊D61—42no—
175C2×C22⋊D61—81no—
176C22×Dic61—22no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—44no—
182C22×Dic61—44no—
183C22×Dic61—81no—
184C22×Dic61—82no—
185C22×Dic61C22×C411yescharacteristic
186C22×Dic61C22×C411yescharacteristic
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C22×C411yescharacteristic
189C22×Dic61C22×C411yescharacteristic
190C22×Dic61C22×C411yescharacteristic
191C22×Dic61C22×C411yescharacteristic
192C22×Dic61C2×D412yes—
193C22×Dic61C2×D412yes—
194C22×Dic61C2×D412yes—
195C22×Dic61C2×D412yes—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—81no—
199C2×Dic122—22no—
200C2×Dic122—81no—
201C22⋊C4×C61—22no—
202C22⋊C4×C61—22no—
203C22⋊C4×C61—22no—
204C22⋊C4×C61—22no—
205C22⋊C4×C61—22no—
206C22⋊C4×C61—22no—
207C22⋊C4×C61—22no—
208C22⋊C4×C61—22no—
209C22⋊C4×C61—44no—
210C22⋊C4×C61—82no—
211C22⋊Dic61—21no—
212C22⋊Dic61—21no—
213C22⋊Dic61—22no—
214C22⋊Dic61—22no—
215C22⋊Dic61—22no—
216C22⋊Dic61—22no—
217C22⋊Dic61—22no—
218C22⋊Dic61—44no—
219C22⋊Dic61C22⋊C411yescharacteristic
220C22⋊Dic61C22⋊C411yescharacteristic
221C22⋊Dic61C22⋊C411yescharacteristic
222C22⋊Dic61C22⋊C411yescharacteristic
223C22⋊Dic61C22⋊C412yes—
224C22⋊Dic61C22⋊C412yes—
225C22⋊Dic61C22⋊C412yes—
226C22⋊Dic61C22⋊C412yes—
227C22⋊Dic61C22⋊C412yes—
228C22⋊Dic61C22⋊C412yes—
229C22⋊Dic61#4114yes—
230#11758198—22no—
231#11758198—21no—
232#11758198—21no—
233#11758198—22no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—22no—
239#11758196—22no—
240#11758196—22no—
241#11758196—22no—
242#11758196—21no—
243#11758196—21no—
244#11758196—22no—
245#11758196—44no—
246#11758196—82no—
247C4×Dic61—21no—
248C4×Dic61—21no—
249C4×Dic61—21no—
250C4×Dic61—21no—
251C4×Dic61—21no—
252C4×Dic61—21no—
253C4×Dic61—44no—
254C4×Dic61—82no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—24no—
260C23×C61—22no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—42no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—42no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—42no—
273C23×C61—84no—
274C23×C61—82no—
275C23×C61—82no—
276C23×C61C2×C22⋊C412yes—
277C23×C61C2×C22⋊C411yescharacteristic
278C23×C61C2×C22⋊C411yescharacteristic
279C23×C61C23×C411yescharacteristic
280C23×C61C22×D412yes—
281C23×C61C2×#4112yes—
282C23×C61H(5,𝔽2)11yescharacteristic
283C23×C612−1+411yescharacteristic
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—41no—
288C22×D61—41no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—42no—
294C2×C4×C61—42no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—42no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61—81no—
306C2×C4×C61—81no—
307C22⋊D61—42no—
308C22⋊D61—42no—
309C22⋊D61—42no—
310C22⋊D61—42no—
311C22⋊D61—82no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—24no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—42no—
331C2×Dic61—42no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—42no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—88no—
338C2×Dic61C2×C22⋊C411yescharacteristic
339C2×Dic61C2×C22⋊C411yescharacteristic
340C2×Dic61C2×C22⋊C411yescharacteristic
341C2×Dic61C2×C22⋊C411yescharacteristic
342C2×Dic61C2×C22⋊C412yes—
343C2×Dic61C2×C22⋊C412yes—
344C4×D61—81no—
345C4×D61—81no—
346Dic122—82no—
347#22477—611nomaximal, Sylow
348C22×C61—21no—
349C22×C61—22no—
350C22×C61—21no—
351C22×C61—22no—
352C22×C61—21no—
353C22×C61—21no—
354C22×C61—21no—
355C22×C61—22no—
356C22×C61—21no—
357C22×C61—22no—
358C22×C61—22no—
359C22×C61—21no—
360C22×C61—42no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—44no—
364C22×C61—44no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—82no—
368C22×C61—82no—
369C22×C61—81no—
370C22×C61—81no—
371C22×C61#41012yes—
372C22×C61C22×C22⋊C411yescharacteristic
373C22×C61C4×#4111yescharacteristic
374C22×C61#52011yescharacteristic
375C22×C61#54612yes—
376C22×C61#54712yes—
377C2×D61—41no—
378C2×D61—41no—
379C2×D61—41no—
380C2×D61—81no—
381C2×D61—81no—
382C4×C61—41no—
383C4×C61—41no—
384C4×C61—41no—
385C4×C61—41no—
386C4×C61—82no—
387C4×C61—82no—
388Dic61—21no—
389Dic61—22no—
390Dic61—21no—
391Dic61—22no—
392Dic61—21no—
393Dic61—21no—
394Dic61—44no—
395Dic61—41no—
396Dic61—41no—
397Dic61—41no—
398Dic61—82no—
399C2×#551—611no—
400#2342—612no—
401#1996—612no—
402#1899—612no—
403#1898—612no—
404#1820—611no—
405#1819D6111yescharacteristic, complemented
406#1799—611no—
407C4×#99—611no—
408#1740—611no—
409C2×#342—611no—
410C2×C61—22no—
411C2×C61—22no—
412C2×C61—21no—
413C2×C61—21no—
414C2×C61—22no—
415C2×C61—41no—
416C2×C61—42no—
417C2×C61#233911yescharacteristic
418C2×C61C2×#41011yescharacteristic
419C2×C61#288311yescharacteristic
420D61—81no—
421#551—1222no—
422#551—1222no—
423#551—1222no—
424#551—1222no—
425C2×#126—611no—
426C2×#126—611no—
427C2×#124—611no—
428C2×#123—611no—
429C2×#123—611no—
430C2×#123—611no—
431C2×C22⋊Q8—611no—
432C2×C22⋊Q8—611no—
433C2×#120—611no—
434C2×C4×D4—611no—
435C2×C4×D4—611no—
436C2×#117—611no—
437C2×#117—611no—
438C2×#117—612no—
439C22×C22⋊C4—611no—
440C22×C22⋊C4—612no—
441C22×C22⋊C4C2×D6111yescharacteristic
442C2×#99—612no—
443C2×#99—612no—
444#388—1222no—
445#388—1222no—
446#385—1222no—
447#381—612no—
448#380—612no—
449#379C2×D6112yes—
450C4×C22⋊C4—612no—
451C4×C22⋊C4—1222no—
452#342—611no—
453#342—612no—
454#342—612no—
455#342—612no—
456#342—611no—
457#342C2×D6111yescharacteristic
458#342C2×D6111yescharacteristic
459#342C2×D6112yes—
460C61#2247711yescharacteristic, complemented, Sylow
461C25C22×D6111yescharacteristic
462C22×Q8—611no—
463C22×D4—611no—
464C22×D4—611no—
465C22×D4—611no—
466C23×C4—611no—
467C23×C4—611no—
468C23×C4—611no—
469C23×C4—1222no—
470C23×C4C4×D6111yescharacteristic
471C23×C4C4×D6111yescharacteristic
472#126—1222no—
473#126—1222no—
474#126—1222no—
475#126—1222no—
476#124—1222no—
477#124—1222no—
478#123—1222no—
479#123—1222no—
480#123—1222no—
481#123—1222no—
482#123—1222no—
483#123—1222no—
484C22⋊Q8—1222no—
485C22⋊Q8—1222no—
486C22⋊Q8—1222no—
487C22⋊Q8—1222no—
488#120—1222no—
489#120—1222no—
490C4×D4—1222no—
491C4×D4—1222no—
492C4×D4—1221no—
493C4×D4—1221no—
494C4×D4—1221no—
495C4×D4—1221no—
496#117—1222no—
497#117—1222no—
498#117—1221no—
499#117—1221no—
500#117—1221no—
501#117—1221no—
502#117—1224no—
503#117—2442no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—1222no—
513C2×C4⋊C4—1222no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—611no—
519C2×C22⋊C4—611no—
520C2×C22⋊C4—611no—
521C2×C22⋊C4—611no—
522C2×C22⋊C4—612no—
523C2×C22⋊C4—612no—
524C2×C22⋊C4—612no—
525C2×C22⋊C4—612no—
526C2×C22⋊C4—612no—
527C2×C22⋊C4—611no—
528C2×C22⋊C4—611no—
529C2×C22⋊C4—611no—
530C2×C22⋊C4—611no—
531C2×C22⋊C4—611no—
532C2×C22⋊C4—611no—
533C2×C22⋊C4—612no—
534C2×C22⋊C4—1224no—
535C2×C22⋊C4—1222no—
536C2×C22⋊C4—2442no—
537C2×C22⋊C4C4×D6111yescharacteristic
538C2×C22⋊C4C4×D6111yescharacteristic
539C2×C22⋊C4C22×D6112yes—
540C2×C22⋊C4C22×D6112yes—
541C2×C22⋊C4C22×D6111yescharacteristic
542C2×C22⋊C4C22×D6111yescharacteristic
543C2×C42—611no—
544C2×C42—611no—
545C2×C42—611no—
546C2×C42—1222no—
547C2×C42—1222no—
548#99—1224no—
549#99—2442no—
550#95—1222no—
551#95—1222no—
552#95—1222no—
553#95—1222no—
554C24—22no—
555C24—21no—
556C24—21no—
557C24—42no—
558C24—81no—
559C24—611no—
560C24C2×C4×D6111yescharacteristic
561C24C2×C4×D6111yescharacteristic
562C24D4×D6112yes—
563C24D4×D6112yes—
564C24C23×D6111yescharacteristic
565C2×Q8—1222no—
566C2×Q8—4881no—
567C2×D4—1222no—
568C2×D4—1222no—
569C2×D4—1222no—
570C2×D4—1221no—
571C2×D4—1221no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4—4881no—
575C2×D4—2442no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—42no—
583C22×C4—81no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—612no—
587C22×C4—612no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—612no—
591C22×C4—612no—
592C22×C4—611no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1222no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—4881no—
603C22×C4—4882no—
604C22×C4—4881no—
605C22×C4—2444no—
606C22×C4—2444no—
607C22×C4C2×C4×D6111yescharacteristic
608C22×C4C2×C4×D6111yescharacteristic
609C22×C4C2×C4×D6111yescharacteristic
610C22×C4C2×C4×D6111yescharacteristic
611C4⋊C4—1222no—
612C4⋊C4—1222no—
613C4⋊C4—1222no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—1222no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1222no—
622C4⋊C4—4882no—
623C4⋊C4—2444no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—44no—
633C22⋊C4—82no—
634C22⋊C4—611no—
635C22⋊C4—611no—
636C22⋊C4—611no—
637C22⋊C4—611no—
638C22⋊C4—612no—
639C22⋊C4—612no—
640C22⋊C4—612no—
641C22⋊C4—612no—
642C22⋊C4—612no—
643C22⋊C4—612no—
644C22⋊C4—614no—
645C22⋊C4—1222no—
646C22⋊C4—1221no—
647C22⋊C4—1221no—
648C22⋊C4—1222no—
649C22⋊C4—1222no—
650C22⋊C4—1222no—
651C22⋊C4—1221no—
652C22⋊C4—1221no—
653C22⋊C4—1222no—
654C22⋊C4—1222no—
655C22⋊C4—1222no—
656C22⋊C4—2444no—
657C42—1221no—
658C42—1221no—
659C42—1221no—
660C42—1221no—
661C42—1221no—
662C42—1221no—
663C42—4882no—
664C42—2444no—
665C23—21no—
666C23—21no—
667C23—24no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—22no—
674C23—22no—
675C23—41no—
676C23—42no—
677C23—41no—
678C23—41no—
679C23—42no—
680C23—41no—
681C23—41no—
682C23—42no—
683C23—84no—
684C23—82no—
685C23—82no—
686C23—1221no—
687C23—1221no—
688C23—1221no—
689C23—2441no—
690C23—2441no—
691C23C22⋊C4×D6112yes—
692C23C22⋊C4×D6111yescharacteristic
693C23C22⋊C4×D6111yescharacteristic
694C23C22×C4×D6111yescharacteristic
695C23C2×D4×D6112yes—
696C23#41×D6112yes—
697C23#1451982311yescharacteristic
698C23#1451982411yescharacteristic
699Q8—4882no—
700D4—4882no—
701D4—2442no—
702D4—2442no—
703D4—2442no—
704D4—2442no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—611no—
724C2×C4—611no—
725C2×C4—611no—
726C2×C4—611no—
727C2×C4—612no—
728C2×C4—612no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—1221no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1221no—
738C2×C4—1221no—
739C2×C4—1221no—
740C2×C4—1221no—
741C2×C4—1221no—
742C2×C4—1224no—
743C2×C4—4881no—
744C2×C4—4881no—
745C2×C4—4888no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2442no—
751C2×C4—2442no—
752C2×C4—2442no—
753C2×C4—2442no—
754C2×C4—2442no—
755C2×C4—2441no—
756C2×C4—2441no—
757C22—22no—
758C22—21no—
759C22—21no—
760C22—22no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—22no—
765C22—21no—
766C22—22no—
767C22—21no—
768C22—22no—
769C22—42no—
770C22—41no—
771C22—41no—
772C22—44no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—82no—
777C22—82no—
778C22—81no—
779C22—81no—
780C22—4881no—
781C22—4881no—
782C22—2441no—
783C22—2441no—
784C22—2441no—
785C22#1683973412yes—
786C22C2×C22⋊C4×D6111yescharacteristic
787C22#1684023011yescharacteristic
788C22#1684024211yescharacteristic
789C22#1684040412yes—
790C22#1684041012yes—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—82no—
796C4—82no—
797C4—1221no—
798C4—1221no—
799C4—1222no—
800C4—1221no—
801C4—1221no—
802C4—1222no—
803C4—4882no—
804C4—2444no—
805C4—2441no—
806C4—2441no—
807C4—2441no—
808C2—22no—
809C2—22no—
810C2—22no—
811C2—21no—
812C2—21no—
813C2—41no—
814C2—42no—
815C2—4881no—
816C2#2144864311yescharacteristic
817C2C2×#1683973411yescharacteristic
818C2#2145427711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1819C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519746C22
cosocleC24×C61C24
hypercenter#1819D61
hypocenterC61#22477
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ #1819

Complements

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

NH ≅ G/Ntype
2. #21448670C2semidirect
3. #21446802C2semidirect
4. #21446276C2semidirect
6. #21445895C2semidirect
7. #21445806C2semidirect
8. #21445606C2semidirect
9. #21445550C2semidirect
10. C2×#16839529C2semidirect
11. C61×#1819C2semidirect
16. C2×#14519770C4semidirect
17. C2×#14519770C4semidirect
18. C2×#14519763C4semidirect
20. C2×#14519760C4semidirect
21. C2×#14519759C4semidirect
22. C2×#14519756C4semidirect
25. C2×C4×C22⋊D61C4semidirect
27. C2×#14519736C4semidirect
51. C22×Dic122C2×C4semidirect
58. C22×C4×D61C2×C4semidirect
91. C2×C4⋊Dic61C2×C4semidirect
92. C2×C4⋊Dic61C2×C4semidirect
93. C2×C4⋊Dic61C2×C4semidirect
96. C2×#11758196C2×C4semidirect
97. C2×#11758196C2×C4semidirect
98. C2×#11758196C2×C4semidirect
99. C2×#11758196C2×C4semidirect
100. C2×#11758196C2×C4semidirect
117. C2×#11758198C2×C4semidirect
118. C2×#11758198C2×C4semidirect
119. C2×#11758198C2×C4semidirect
122. C2×C4×Dic61C2×C4semidirect
123. C2×C4×Dic61C2×C4semidirect
124. C2×C4×Dic61C2×C4semidirect
405. #1819D61semidirect
460. C61#22477semidirect

Maximal subgroups

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

subgroupindex
C2×#168404382
#214486702
#214468022
#214462762
#214462702
#214458952
#214458062
#214456062
#214455502
C2×#168395292
C61×#18192
#2247761