Finite Group Databasebeta

← #29696155

Subgroups — #29696155

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×#16840436C211yesmaximal, characteristic
2#21448669C212yesmaximal, complemented
3#21446802C212yesmaximal, complemented
4#21446277C212yesmaximal, complemented
5#21446271C212yesmaximal
6#21445896C211yesmaximal, characteristic, complemented
7#21445892C211yesmaximal, characteristic, complemented
8#21445806C211yesmaximal, characteristic, complemented
9#21445606C211yesmaximal, characteristic, complemented
10#342×D61C211yesmaximal, characteristic, complemented
11C61×#1740C211yesmaximal, characteristic, complemented
12#16840436—22no—
13#16840436—22no—
14#16840436—22no—
15#16840436—22no—
16C2×#14519772C411yescharacteristic, complemented
17C2×#14519771C411yescharacteristic, complemented
18C2×#14519765C411yescharacteristic, complemented
19C2×#14519762C411yescharacteristic, complemented
20C2×#14519762C411yescharacteristic, complemented
21C2×#14519760C2211yescharacteristic
22C2×#14519755C411yescharacteristic, complemented
23C2×#14519754C2211yescharacteristic
24C2×#14519747C2211yescharacteristic
25C2×C4×D244C411yescharacteristic, complemented
26C2×#14519737C2211yescharacteristic
27C2×#14519734C411yescharacteristic, complemented
28C22×#11758198C2211yescharacteristic
29C2×C22⋊C4×D61C2212yes—
30C2×C22⋊C4×D61C2211yescharacteristic
31C2×#14519691C2212yes—
32C2×#14519691C2212yes—
33#16839653—22no—
34#16839652—22no—
35#16839633—22no—
36#16839625C2212yes—
37#16839620C2212yes—
38#16839617C2212yes—
39C22⋊C4×Dic61C2212yes—
40C4×#11758198—22no—
41#16839529C2211yescharacteristic
42#16839529C2212yes—
43#16839529C2211yescharacteristic
44#16839528C2212yes—
45#16839528C2212yes—
46C2×#117×C61C2212yes—
47C2×#117×C61C2211yescharacteristic
48C61×#342C2211yescharacteristic
49C61×#342C2212yes—
50C61×#342C2211yescharacteristic
51C24×D61C2311yescharacteristic
52C22×Dic122C2×C411yescharacteristic, complemented
53C22×D244C2×C411yescharacteristic
54C22×D244C2×C411yescharacteristic
55C22×C22⋊D61C2311yescharacteristic
56C23×Dic61C2311yescharacteristic
57C22×C4×D61—22no—
58C22×C4×D61C2×C411yescharacteristic
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61C2×C411yescharacteristic, complemented
61#14519772—22no—
62#14519772—22no—
63#14519771—22no—
64#14519771—22no—
65#14519765—22no—
66#14519765—22no—
67#14519762—22no—
68#14519762—22no—
69#14519762—22no—
70#14519762—22no—
71#14519760—22no—
72#14519760—22no—
73#14519755—22no—
74#14519755—22no—
75#14519754—22no—
76#14519754—22no—
77#14519747—22no—
78#14519747—22no—
79C4×D244—21no—
80C4×D244—21no—
81C4×D244—21no—
82C4×D244—21no—
83#14519737—22no—
84#14519737—22no—
85#14519734—21no—
86#14519734—21no—
87#14519734—21no—
88#14519734—21no—
89C2×C4⋊Dic61C2×C411yescharacteristic, complemented
90C2×#11758196—22no—
91C2×#11758196C2×C411yescharacteristic, complemented
92C2×#11758196C2×C411yescharacteristic, complemented
93C2×#11758196C2×C411yescharacteristic, complemented
94C2×#11758196C2×C411yescharacteristic, complemented
95C2×#11758196C2×C411yescharacteristic, complemented
96C2×C22⋊Dic61C2312yes—
97C2×C22⋊Dic61C2312yes—
98C2×C22⋊Dic61C2311yescharacteristic
99C2×#11758198—22no—
100C2×#11758198—22no—
101C2×#11758198—22no—
102C2×#11758198C2×C411yescharacteristic
103C2×#11758198C2×C411yescharacteristic
104C2×#11758198C2×C411yescharacteristic
105C2×#11758198C2×C411yescharacteristic
106C2×#11758198C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×#11758198C2×C411yescharacteristic
110C2×#11758198C2×C411yescharacteristic, complemented
111C2×#11758198C2×C411yescharacteristic, complemented
112C2×#11758198C2×C411yescharacteristic, complemented
113C2×#11758198D412yes—
114C2×#11758198D412yes—
115C2×#11758198D412yes—
116C2×#11758198D412yes—
117C22⋊C4×D61—22no—
118C22⋊C4×D61—22no—
119C22⋊C4×D61—24no—
120C22⋊C4×D61—42no—
121C2×C4×Dic61—22no—
122C2×C4×Dic61C2×C411yescharacteristic, complemented
123#14519691—24no—
124#14519691—42no—
125#14519684—22no—
126#14519684—22no—
127#14519684—22no—
128#14519684—22no—
129C23×C4×C61C2311yescharacteristic
130#117×C61—22no—
131#117×C61—22no—
132#117×C61—24no—
133#117×C61—42no—
134C2×C4⋊C4×C61—22no—
135C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
136C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
137C2×C22⋊C4×C61C2312yes—
138C2×C22⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61C2311yescharacteristic
140C2×C22⋊C4×C61C2312yes—
141C2×C42×C61—22no—
142C2×C42×C61C2×C411yescharacteristic, complemented
143C2×C42×C61C2×C411yescharacteristic, complemented
144C24×C61C2411yescharacteristic
145C23×D61—22no—
146C23×D61—21no—
147C23×D61—21no—
148C23×D61—42no—
149C23×D61—81no—
150C23×D61C22×C411yescharacteristic
151C23×D61C22×C411yescharacteristic
152C23×D61C22×C411yescharacteristic
153C23×D61C2×D412yes—
154C23×D61C2×D412yes—
155C22×C4×C61—22no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C22×C411yescharacteristic
166C22×C4×C61C2×D412yes—
167C22×C4×C61C2×D412yes—
168C2×C22⋊D61—22no—
169C2×C22⋊D61—22no—
170C2×C22⋊D61—21no—
171C2×C22⋊D61—21no—
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61—81no—
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C22×C411yescharacteristic
180C22×Dic61C2×D412yes—
181C22×Dic61C2×D412yes—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—22no—
185C2×D244—42no—
186C2×D244—81no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—42no—
194C2×C4×D61—44no—
195C2×C4×D61—44no—
196C2×C4×D61—82no—
197C2×C4×D61—81no—
198C2×C4×D61—81no—
199C2×Dic122—22no—
200C2×Dic122—81no—
201C4⋊C4×C61—22no—
202C4⋊C4×C61—22no—
203C4⋊C4×C61—44no—
204C22⋊C4×C61—22no—
205C22⋊C4×C61—22no—
206C22⋊C4×C61—22no—
207C22⋊C4×C61—22no—
208C22⋊C4×C61—22no—
209C22⋊C4×C61#4114yes—
210C42×C61—21no—
211C42×C61—21no—
212C42×C61—21no—
213C42×C61—21no—
214C42×C61—44no—
215C22⋊Dic61—22no—
216C22⋊Dic61—22no—
217C22⋊Dic61—22no—
218C22⋊Dic61—22no—
219C22⋊Dic61—22no—
220#11758198—22no—
221#11758198—22no—
222#11758198—21no—
223#11758198—21no—
224#11758198—22no—
225#11758198—21no—
226#11758198—21no—
227#11758198—22no—
228#11758198—22no—
229#11758198—44no—
230#11758198—44no—
231#11758198—82no—
232#11758198C22⋊C411yescharacteristic
233#11758198C22⋊C411yescharacteristic
234#11758198C22⋊C411yescharacteristic
235#11758198C22⋊C411yescharacteristic
236#11758198C22⋊C412yes—
237#11758198C22⋊C412yes—
238#11758198C22⋊C412yes—
239#11758198C22⋊C412yes—
240#11758198C22⋊C412yes—
241#11758198C22⋊C412yes—
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244#11758196—21no—
245#11758196—21no—
246#11758196—22no—
247#11758196—21no—
248#11758196—21no—
249#11758196—22no—
250#11758196—22no—
251#11758196—82no—
252C4×Dic61—21no—
253C4×Dic61—21no—
254C4×Dic61—82no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61C23×C411yescharacteristic
258C23×C61C22×D412yes—
259C23×C61C2×#4112yes—
260C23×C61H(5,𝔽2)11yescharacteristic
261C23×C612−1+411yescharacteristic
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—22no—
269C22×D61—22no—
270C22×D61—24no—
271C22×D61—22no—
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—41no—
276C22×D61—42no—
277C22×D61—42no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—42no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—82no—
284C22×D61—84no—
285C22×D61—82no—
286C22×D61C2×C22⋊C412yes—
287C22×D61C2×C22⋊C411yescharacteristic
288C22×D61C2×C22⋊C411yescharacteristic
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—24no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61—42no—
311C2×C4×C61C2×C22⋊C411yescharacteristic
312C2×C4×C61C2×C22⋊C411yescharacteristic
313C2×C4×C61C2×C22⋊C412yes—
314C22⋊D61—42no—
315C22⋊D61—42no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61C2×C22⋊C411yescharacteristic
334C2×Dic61C2×C22⋊C411yescharacteristic
335C2×Dic61C2×C22⋊C412yes—
336D244—42no—
337D244—42no—
338D244—82no—
339C4×D61—42no—
340C4×D61—42no—
341C4×D61—81no—
342C4×D61—81no—
343C4×D61—81no—
344C4×D61—81no—
345C4×D61—88no—
346Dic122—82no—
347#22477—611nomaximal, Sylow
348C22×C61—22no—
349C22×C61—21no—
350C22×C61—22no—
351C22×C61—21no—
352C22×C61—42no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61C22×C22⋊C411yescharacteristic
356C22×C61C4×#4111yescharacteristic
357C22×C61#52011yescharacteristic
358C22×C61#54612yes—
359C22×C61#54712yes—
360C2×D61—21no—
361C2×D61—21no—
362C2×D61—21no—
363C2×D61—22no—
364C2×D61—21no—
365C2×D61—22no—
366C2×D61—21no—
367C2×D61—22no—
368C2×D61—44no—
369C2×D61—44no—
370C2×D61—42no—
371C2×D61—42no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—41no—
375C2×D61—82no—
376C2×D61—82no—
377C2×D61—81no—
378C2×D61—81no—
379C2×D61—81no—
380C2×D61—81no—
381C2×D61#41012yes—
382C4×C61—21no—
383C4×C61—22no—
384C4×C61—21no—
385C4×C61—44no—
386C4×C61—41no—
387C4×C61—41no—
388C4×C61—41no—
389C4×C61—41no—
390C4×C61—82no—
391Dic61—22no—
392Dic61—21no—
393Dic61—21no—
394Dic61—41no—
395Dic61—41no—
396Dic61—41no—
397Dic61—82no—
398Dic61—82no—
399C2×#551—611no—
400#2342—612no—
401#1996—612no—
402#1899—612no—
403#1898—612no—
404#1820—611no—
405#1819—611no—
406#1799—611no—
407C4×#99—611no—
408#1740D6111yescharacteristic, complemented
409C2×#342—611no—
410C2×C61—22no—
411C2×C61—22no—
412C2×C61—21no—
413C2×C61—21no—
414C2×C61#233911yescharacteristic
415C2×C61C2×#41011yescharacteristic
416C2×C61#288311yescharacteristic
417D61—22no—
418D61—41no—
419D61—42no—
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×#117C2×D6112yes—
438C2×#117C2×D6111yescharacteristic
439C22×C22⋊C4—611no—
440C22×C22⋊C4—611no—
441C22×C22⋊C4—612no—
442C2×#99—612no—
443C2×#99—612no—
444#388—1222no—
445#388—1222no—
446#385—1222no—
447#381—612no—
448#380—612no—
449#379—612no—
450C4×C22⋊C4—612no—
451C4×C22⋊C4—1222no—
452#342—611no—
453#342—611no—
454#342—612no—
455#342—612no—
456#342—612no—
457#342C2×D6111yescharacteristic
458#342C2×D6112yes—
459#342C2×D6111yescharacteristic
460C61#2247711yescharacteristic, complemented, Sylow
461C25—611no—
462C22×Q8—611no—
463C22×D4—611no—
464C22×D4—611no—
465C22×D4—611no—
466C23×C4—611no—
467C23×C4—611no—
468C23×C4—611no—
469C23×C4—611no—
470C23×C4—1222no—
471C23×C4C22×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—1221no—
491C4×D4—1221no—
492C4×D4—1221no—
493C4×D4—1221no—
494C4×D4—1222no—
495C4×D4—1222no—
496#117—22no—
497#117—22no—
498#117—24no—
499#117—42no—
500#117—1221no—
501#117—1221no—
502#117—1221no—
503#117—1221no—
504C2×C4⋊C4—22no—
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—1222no—
512C2×C4⋊C4C4×D6111yescharacteristic, complemented
513C2×C4⋊C4C4×D6111yescharacteristic, complemented
514C2×C22⋊C4—611no—
515C2×C22⋊C4—611no—
516C2×C22⋊C4—611no—
517C2×C22⋊C4—611no—
518C2×C22⋊C4—612no—
519C2×C22⋊C4—612no—
520C2×C22⋊C4—612no—
521C2×C22⋊C4—612no—
522C2×C22⋊C4—611no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—611no—
525C2×C22⋊C4—611no—
526C2×C22⋊C4—611no—
527C2×C22⋊C4—611no—
528C2×C22⋊C4—611no—
529C2×C22⋊C4—611no—
530C2×C22⋊C4—612no—
531C2×C22⋊C4—612no—
532C2×C22⋊C4—1222no—
533C2×C22⋊C4—1222no—
534C2×C22⋊C4—1224no—
535C2×C22⋊C4—1222no—
536C2×C22⋊C4—1222no—
537C2×C22⋊C4—1222no—
538C2×C22⋊C4—2442no—
539C2×C22⋊C4C22×D6112yes—
540C2×C22⋊C4C22×D6111yescharacteristic
541C2×C22⋊C4C22×D6111yescharacteristic
542C2×C22⋊C4C22×D6112yes—
543C2×C42—22no—
544C2×C42—611no—
545C2×C42—1222no—
546C2×C42C4×D6111yescharacteristic, complemented
547C2×C42C4×D6111yescharacteristic, complemented
548#99—1224no—
549#99—2442no—
550#95—1222no—
551#95—1222no—
552#95—1222no—
553#95—1222no—
554C24—611no—
555C24—612no—
556C24—611no—
557C24—612no—
558C24—611no—
559C24—1222no—
560C24—1221no—
561C24—1221no—
562C24—4881no—
563C24—2442no—
564C24C23×D6111yescharacteristic
565C2×Q8—1222no—
566C2×Q8—4881no—
567C2×D4—1222no—
568C2×D4—1221no—
569C2×D4—1221no—
570C2×D4—1222no—
571C2×D4—1222no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4—4881no—
575C2×D4—2442no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—612no—
584C22×C4—612no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1222no—
595C22×C4—1222no—
596C22×C4—4882no—
597C22×C4—4881no—
598C22×C4—4881no—
599C22×C4—4881no—
600C22×C4—2444no—
601C22×C4—2444no—
602C22×C4—2442no—
603C22×C4C2×C4×D6111yescharacteristic
604C22×C4C2×C4×D6111yescharacteristic
605C22×C4C2×C4×D6111yescharacteristic
606C22×C4C2×C4×D6111yescharacteristic
607C22×C4C2×C4×D6111yescharacteristic
608C22×C4C2×C4×D6111yescharacteristic
609C22×C4D4×D6112yes—
610C22×C4D4×D6112yes—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—44no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—1222no—
617C4⋊C4—1222no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1222no—
623C4⋊C4—4882no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—611no—
630C22⋊C4—611no—
631C22⋊C4—611no—
632C22⋊C4—611no—
633C22⋊C4—612no—
634C22⋊C4—612no—
635C22⋊C4—612no—
636C22⋊C4—612no—
637C22⋊C4—612no—
638C22⋊C4—612no—
639C22⋊C4—1222no—
640C22⋊C4—1222no—
641C22⋊C4—1222no—
642C22⋊C4—1221no—
643C22⋊C4—1221no—
644C22⋊C4—1222no—
645C22⋊C4—1222no—
646C22⋊C4—1221no—
647C22⋊C4—1221no—
648C22⋊C4—1222no—
649C22⋊C4—1222no—
650C22⋊C4—1222no—
651C22⋊C4—1222no—
652C22⋊C4—1222no—
653C22⋊C4—4882no—
654C22⋊C4—2444no—
655C22⋊C4—2444no—
656C22⋊C4#1175822214yes—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—44no—
662C42—1221no—
663C42—1221no—
664C42—4882no—
665C23—41no—
666C23—41no—
667C23—611no—
668C23—612no—
669C23—611no—
670C23—1224no—
671C23—1222no—
672C23—1221no—
673C23—1221no—
674C23—1222no—
675C23—1222no—
676C23—1221no—
677C23—1221no—
678C23—1222no—
679C23—1222no—
680C23—1221no—
681C23—1221no—
682C23—1221no—
683C23—4884no—
684C23—4882no—
685C23—4882no—
686C23—2442no—
687C23—2441no—
688C23—2442no—
689C23—2441no—
690C23—2442no—
691C23—2441no—
692C23—2441no—
693C23—2441no—
694C23C22×C4×D6111yescharacteristic
695C23C2×D4×D6112yes—
696C23C2×#1175822212yes—
697C23#1451982211yescharacteristic
698C23#1451982511yescharacteristic
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—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—24no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—611no—
728C2×C4—611no—
729C2×C4—612no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—1221no—
733C2×C4—1221no—
734C2×C4—1221no—
735C2×C4—4881no—
736C2×C4—4881no—
737C2×C4—4888no—
738C2×C4—4881no—
739C2×C4—4881no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4—2442no—
743C2×C4—2442no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4—2442no—
749C2×C4—2442no—
750C2×C4—2442no—
751C2×C4—2442no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4C22⋊C4×D6111yescharacteristic
755C2×C4C22⋊C4×D6111yescharacteristic
756C2×C4C22⋊C4×D6112yes—
757C22—22no—
758C22—21no—
759C22—22no—
760C22—21no—
761C22—42no—
762C22—41no—
763C22—41no—
764C22—612no—
765C22—1221no—
766C22—1221no—
767C22—1221no—
768C22—1222no—
769C22—1222no—
770C22—1221no—
771C22—1221no—
772C22—1222no—
773C22—4881no—
774C22—4881no—
775C22—4882no—
776C22—4882no—
777C22—4881no—
778C22—4881no—
779C22—2444no—
780C22—2444no—
781C22—2442no—
782C22—2442no—
783C22—2441no—
784C22—2441no—
785C22—2441no—
786C22C2×C22⋊C4×D6111yescharacteristic
787C22C4×#1175822211yescharacteristic
788C22#1684024311yescharacteristic
789C22#1684040212yes—
790C22#1684041312yes—
791C4—21no—
792C4—22no—
793C4—21no—
794C4—44no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—41no—
799C4—82no—
800C4—1221no—
801C4—1221no—
802C4—1222no—
803C4—4882no—
804C4—4882no—
805C4—2441no—
806C4—2441no—
807C4—2441no—
808C2—22no—
809C2—22no—
810C2—21no—
811C2—21no—
812C2—1222no—
813C2—4881no—
814C2—2441no—
815C2—2442no—
816C2#2144864611yescharacteristic
817C2#410×D6111yescharacteristic
818C2#2145427811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1740C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519747C22
cosocleC24×C61C24
hypercenter#1740D61
hypocenterC61#22477
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1740

Complements

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

NH ≅ G/Ntype
2. #21448669C2semidirect
3. #21446802C2semidirect
4. #21446277C2semidirect
6. #21445896C2semidirect
7. #21445892C2semidirect
8. #21445806C2semidirect
9. #21445606C2semidirect
10. #342×D61C2semidirect
11. C61×#1740C2semidirect
16. C2×#14519772C4semidirect
17. C2×#14519771C4semidirect
18. C2×#14519765C4semidirect
19. C2×#14519762C4semidirect
20. C2×#14519762C4semidirect
22. C2×#14519755C4semidirect
25. C2×C4×D244C4semidirect
27. C2×#14519734C4semidirect
52. C22×Dic122C2×C4semidirect
60. C22×C4×D61C2×C4semidirect
89. C2×C4⋊Dic61C2×C4semidirect
91. C2×#11758196C2×C4semidirect
92. C2×#11758196C2×C4semidirect
93. C2×#11758196C2×C4semidirect
94. C2×#11758196C2×C4semidirect
95. C2×#11758196C2×C4semidirect
110. C2×#11758198C2×C4semidirect
111. C2×#11758198C2×C4semidirect
112. C2×#11758198C2×C4semidirect
122. C2×C4×Dic61C2×C4semidirect
135. C2×C4⋊C4×C61C2×C4semidirect
136. C2×C4⋊C4×C61C2×C4semidirect
142. C2×C42×C61C2×C4semidirect
143. C2×C42×C61C2×C4semidirect
408. #1740D61semidirect
460. C61#22477semidirect
512. C2×C4⋊C4C4×D61semidirect
513. C2×C4⋊C4C4×D61semidirect
546. C2×C42C4×D61semidirect
547. C2×C42C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404362
#214486692
#214468022
#214462772
#214462712
#214458962
#214458922
#214458062
#214456062
#342×D612
C61×#17402
#2247761