Finite Group Databasebeta

← #29689830

Subgroups — #29689830

Order 15616.

1254 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840345C211yesmaximal, characteristic
2#21448432C211yesmaximal, characteristic, complemented
3#21448416C211yesmaximal, characteristic, complemented
4#21446802C212yesmaximal, complemented
5#21446653C212yesmaximal, complemented
6#21446271C212yesmaximal, complemented
7#21446269C212yesmaximal, complemented
8#21445807C211yesmaximal, characteristic, complemented
9#21445804C211yesmaximal, characteristic, complemented
10#21445804C211yesmaximal, characteristic, complemented
11C61×#1799C211yesmaximal, characteristic, complemented
12#16840345—22no—
13#16840345—22no—
14#16840345—22no—
15#16840345—22no—
16C2×#14519772C411yescharacteristic, complemented
17C2×#14519771C411yescharacteristic, complemented
18C2×#14519765C411yescharacteristic, complemented
19C2×#14519763C411yescharacteristic, complemented
20C2×#14519762C411yescharacteristic, complemented
21C2×#14519760C411yescharacteristic, complemented
22C2×#14519754C2211yescharacteristic
23C2×#14519751C411yescharacteristic, complemented
24C2×#14519750C411yescharacteristic, complemented
25C2×#14519749C2211yescharacteristic
26C2×#14519747C2211yescharacteristic
27C2×#14519745C2211yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C2×C22⋊C4×D61C2212yes—
31C2×#14519692C2212yes—
32C2×#14519691C2212yes—
33C2×#14519691C2212yes—
34#16839654—22no—
35#16839652—22no—
36#16839636—22no—
37#16839633—22no—
38#16839622C2211yescharacteristic
39#16839622C2211yescharacteristic
40#16839620C2212yes—
41#16839617C2212yes—
42C22⋊C4×Dic61C2212yes—
43#16839529C2212yes—
44#16839528C2212yes—
45#16839528C2212yes—
46C2×C4×D4×C61C2211yescharacteristic
47C2×#99×C61C2212yes—
48C61×#380C2211yescharacteristic
49C61×#380C2211yescharacteristic
50C61×#342C2212yes—
51C24×D61C2311yescharacteristic
52C22×Dic122C2×C411yescharacteristic, complemented
53C22×D244C2×C411yescharacteristic
54C22×D244C2×C411yescharacteristic
55C22×C22⋊D61C2×C411yescharacteristic
56C22×C22⋊D61C2×C411yescharacteristic
57C22×C22⋊D61C2×C411yescharacteristic, complemented
58C22×C22⋊D61C2311yescharacteristic
59C23×Dic61C2311yescharacteristic
60C22×C4×D61—22no—
61C22×C4×D61C2×C411yescharacteristic, complemented
62#14519772—22no—
63#14519772—22no—
64#14519771—22no—
65#14519771—22no—
66#14519765—22no—
67#14519765—22no—
68#14519763—22no—
69#14519763—22no—
70#14519762—22no—
71#14519762—22no—
72#14519760—22no—
73#14519760—22no—
74#14519754—22no—
75#14519754—22no—
76#14519751—22no—
77#14519751—22no—
78#14519750—22no—
79#14519750—22no—
80#14519749—22no—
81#14519749—22no—
82#14519747—22no—
83#14519747—22no—
84#14519745—22no—
85#14519745—22no—
86C4×C22⋊D61—21no—
87C4×C22⋊D61—21no—
88C4×C22⋊D61—21no—
89C4×C22⋊D61—21no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61C2×C411yescharacteristic, complemented
93C2×#11758196—22no—
94C2×#11758196C2×C411yescharacteristic, complemented
95C2×#11758196C2×C411yescharacteristic, complemented
96C2×#11758196C2×C411yescharacteristic, complemented
97C2×#11758196C2×C411yescharacteristic, complemented
98C2×C22⋊Dic61C2×C411yescharacteristic, complemented
99C2×C22⋊Dic61C2312yes—
100C2×C22⋊Dic61C2312yes—
101C2×C22⋊Dic61C2311yescharacteristic
102C2×#11758198—22no—
103C2×#11758198—22no—
104C2×#11758198—22no—
105C2×#11758198C2×C411yescharacteristic
106C2×#11758198C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×#11758198C2×C411yescharacteristic
110C2×#11758198C2×C411yescharacteristic
111C2×#11758198C2×C411yescharacteristic
112C2×#11758198C2×C411yescharacteristic
113C2×#11758198C2×C411yescharacteristic, complemented
114C2×#11758198C2×C411yescharacteristic, complemented
115C2×#11758198D412yes—
116C2×#11758198D412yes—
117C2×#11758198D412yes—
118C2×#11758198D412yes—
119C22⋊C4×D61—42no—
120C22⋊C4×D61—42no—
121C2×C4×Dic61—22no—
122C2×C4×Dic61C2×C411yescharacteristic, complemented
123#14519692—42no—
124#14519691—42no—
125#14519691—42no—
126#14519684—21no—
127#14519684—21no—
128#14519684—22no—
129#14519684—22no—
130C22×D4×C61C2311yescharacteristic
131C23×C4×C61C2×C411yescharacteristic, complemented
132C23×C4×C61C2311yescharacteristic
133C4×D4×C61—21no—
134C4×D4×C61—21no—
135C4×D4×C61—21no—
136C4×D4×C61—21no—
137C2×C4⋊C4×C61—21no—
138C2×C4⋊C4×C61—21no—
139C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
140C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
141C2×C22⋊C4×C61C2312yes—
142C2×C22⋊C4×C61C2312yes—
143C2×C22⋊C4×C61C2311yescharacteristic
144C2×C42×C61C2×C411yescharacteristic, complemented
145#99×C61—42no—
146#95×C61—21no—
147#95×C61—21no—
148C24×C61C22×C411yescharacteristic
149C24×C61C2411yescharacteristic
150C23×D61—21no—
151C23×D61—21no—
152C23×D61—21no—
153C23×D61—21no—
154C23×D61—81no—
155C23×D61—81no—
156C23×D61C22×C411yescharacteristic
157C23×D61C22×C411yescharacteristic
158C23×D61C22×C411yescharacteristic
159C23×D61C2×D412yes—
160C23×D61C2×D412yes—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
171C22×C4×C61—81no—
172C22×C4×C61—81no—
173C22×C4×C61C22×C411yescharacteristic
174C22×C4×C61C22×C411yescharacteristic
175C22×C4×C61C22×C411yescharacteristic
176C22×C4×C61C22×C411yescharacteristic
177C22×C4×C61C22×C411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C2×C22⋊D61—21no—
183C2×C22⋊D61—21no—
184C2×C22⋊D61—21no—
185C2×C22⋊D61—21no—
186C2×C22⋊D61—21no—
187C2×C22⋊D61—21no—
188C2×C22⋊D61—22no—
189C2×C22⋊D61—22no—
190C2×C22⋊D61—22no—
191C2×C22⋊D61—81no—
192C2×C22⋊D61—81no—
193C2×C22⋊D61—81no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—81no—
197C22×Dic61C22×C411yescharacteristic
198C22×Dic61C22×C411yescharacteristic
199C22×Dic61C22×C411yescharacteristic
200C22×Dic61C22×C411yescharacteristic
201C22×Dic61C22×C411yescharacteristic
202C22×Dic61C2×D412yes—
203C22×Dic61C2×D412yes—
204C2×D244—22no—
205C2×D244—22no—
206C2×D244—81no—
207C2×D244—81no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—44no—
211C2×C4×D61—82no—
212C2×C4×D61—82no—
213C2×C4×D61—81no—
214C2×Dic122—22no—
215C2×Dic122—81no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—81no—
219C4⋊C4×C61—81no—
220C22⋊C4×C61—21no—
221C22⋊C4×C61—21no—
222C22⋊C4×C61—21no—
223C22⋊C4×C61—21no—
224C22⋊C4×C61—22no—
225C22⋊C4×C61—22no—
226C22⋊C4×C61—22no—
227C22⋊C4×C61—22no—
228C42×C61—21no—
229C42×C61—21no—
230C22⋊Dic61—21no—
231C22⋊Dic61—21no—
232C22⋊Dic61—22no—
233C22⋊Dic61—22no—
234C22⋊Dic61—22no—
235C22⋊Dic61—22no—
236C22⋊Dic61—22no—
237#11758198—22no—
238#11758198—22no—
239#11758198—22no—
240#11758198—22no—
241#11758198—21no—
242#11758198—21no—
243#11758198—22no—
244#11758198—44no—
245#11758198—82no—
246#11758198—82no—
247#11758198C22⋊C412yes—
248#11758198C22⋊C412yes—
249#11758198C22⋊C412yes—
250#11758198C22⋊C412yes—
251#11758198C22⋊C412yes—
252#11758198C22⋊C412yes—
253#11758198C22⋊C412yes—
254#11758198C22⋊C412yes—
255C4⋊Dic61—22no—
256C4⋊Dic61—81no—
257C4⋊Dic61—81no—
258#11758196—21no—
259#11758196—21no—
260#11758196—22no—
261#11758196—22no—
262#11758196—22no—
263#11758196—82no—
264C4×Dic61—21no—
265C4×Dic61—21no—
266C4×Dic61—82no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61C23×C411yescharacteristic
275C23×C61C22×D411yescharacteristic
276C23×C61C22×D411yescharacteristic
277C23×C61H(5,𝔽2)11yescharacteristic
278C23×C61H(5,𝔽2)11yescharacteristic
279C23×C612−1+411yescharacteristic
280C23×C612−1+411yescharacteristic
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—42no—
293C22×D61—42no—
294C22×D61—42no—
295C22×D61—42no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61—41no—
300C22×D61—41no—
301C22×D61—41no—
302C22×D61—82no—
303C22×D61—82no—
304C22×D61—82no—
305C22×D61—82no—
306C22×D61C2×C22⋊C412yes—
307C22×D61C2×C22⋊C412yes—
308D4×C61—41no—
309D4×C61—41no—
310D4×C61—41no—
311D4×C61—41no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—42no—
326C2×C4×C61—42no—
327C2×C4×C61—42no—
328C2×C4×C61—42no—
329C2×C4×C61—42no—
330C2×C4×C61—42no—
331C2×C4×C61—81no—
332C2×C4×C61—81no—
333C2×C4×C61C2×C22⋊C411yescharacteristic
334C2×C4×C61C2×C22⋊C411yescharacteristic
335C2×C4×C61C2×C22⋊C411yescharacteristic
336C2×C4×C61C2×C22⋊C411yescharacteristic
337C22⋊D61—41no—
338C22⋊D61—41no—
339C22⋊D61—41no—
340C22⋊D61—41no—
341C22⋊D61—82no—
342C22⋊D61—82no—
343C22⋊D61—82no—
344C2×Dic61—21no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—42no—
350C2×Dic61—42no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—42no—
356C2×Dic61—42no—
357C2×Dic61—42no—
358C2×Dic61—42no—
359C2×Dic61—42no—
360C2×Dic61—42no—
361C2×Dic61C2×C22⋊C412yes—
362C2×Dic61C2×C22⋊C412yes—
363D244—82no—
364D244—82no—
365C4×D61—81no—
366C4×D61—81no—
367C4×D61—88no—
368Dic122—82no—
369#21876—611nomaximal, Sylow
370C22×C61—21no—
371C22×C61—21no—
372C22×C61—21no—
373C22×C61—21no—
374C22×C61—21no—
375C22×C61—21no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—41no—
380C22×C61—41no—
381C22×C61—41no—
382C22×C61—41no—
383C22×C61—81no—
384C22×C61—81no—
385C22×C61C22×C22⋊C411yescharacteristic
386C22×C61#52011yescharacteristic
387C22×C61#52011yescharacteristic
388C22×C61#53511yescharacteristic
389C22×C61#53611yescharacteristic
390C22×C61#53711yescharacteristic
391C22×C61#53711yescharacteristic
392C2×D61—22no—
393C2×D61—22no—
394C2×D61—22no—
395C2×D61—22no—
396C2×D61—22no—
397C2×D61—22no—
398C2×D61—44no—
399C2×D61—44no—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—41no—
403C2×D61—82no—
404C2×D61—82no—
405C2×D61—81no—
406C2×D61—81no—
407C2×D61—81no—
408C2×D61—81no—
409C2×D61—81no—
410C2×D61—81no—
411C4×C61—21no—
412C4×C61—21no—
413C4×C61—21no—
414C4×C61—21no—
415C4×C61—41no—
416C4×C61—41no—
417C4×C61—41no—
418C4×C61—82no—
419C4×C61—82no—
420Dic61—22no—
421Dic61—22no—
422Dic61—41no—
423Dic61—41no—
424Dic61—41no—
425Dic61—82no—
426Dic61—82no—
427C2×#538—611no—
428#2315—611no—
429#2312—611no—
430#1996—612no—
431#1964—612no—
432#1898—612no—
433#1898—612no—
434#1799—611no—
435#1799—611no—
436#1799—611no—
437#1799D6111yescharacteristic, complemented
438C2×C61—21no—
439C2×C61—21no—
440C2×C61—21no—
441C2×C61—21no—
442C2×C61—21no—
443C2×C61—21no—
444C2×C61—81no—
445C2×C61#231111yescharacteristic
446C2×C61#288311yescharacteristic
447C2×C61#288311yescharacteristic
448D61—42no—
449D61—42no—
450D61—81no—
451#538—1222no—
452#538—1222no—
453#538—1222no—
454#538—1222no—
455C2×#126—611no—
456C2×#126—611no—
457C2×#124—611no—
458C2×#124—611no—
459C2×#123—611no—
460C2×#123—611no—
461C2×C22⋊Q8—611no—
462C2×#121—611no—
463C2×#121—611no—
464C2×#121—611no—
465C2×#120—611no—
466C2×#120—611no—
467C2×C4×D4—611no—
468C2×C4×D4C2×D6111yescharacteristic
469C22×C22⋊C4—611no—
470C22×C22⋊C4—612no—
471C2×#99—612no—
472C2×#99—612no—
473C2×#99—612no—
474C2×#99C2×D6112yes—
475#388—1222no—
476#388—1222no—
477#385—1222no—
478#385—1222no—
479#380—611no—
480#380—611no—
481#380—612no—
482#380C2×D6111yescharacteristic
483#380C2×D6111yescharacteristic
484#379—612no—
485C4×C22⋊C4—612no—
486#342—612no—
487#342—612no—
488#342—612no—
489#342C2×D6112yes—
490C61#2187611yescharacteristic, complemented, Sylow
491C25—611no—
492C22×Q8—611no—
493C22×D4—611no—
494C22×D4—611no—
495C22×D4—611no—
496C22×D4—611no—
497C22×D4—611no—
498C22×D4—611no—
499C22×D4C22×D6111yescharacteristic
500C23×C4—611no—
501C23×C4—611no—
502C23×C4—1222no—
503C23×C4C4×D6111yescharacteristic, complemented
504C23×C4C22×D6111yescharacteristic
505#126—1222no—
506#126—1222no—
507#126—1222no—
508#126—1222no—
509#124—1222no—
510#124—1222no—
511#124—1222no—
512#124—1222no—
513#123—1222no—
514#123—1222no—
515#123—1222no—
516#123—1222no—
517C22⋊Q8—1222no—
518C22⋊Q8—1222no—
519#121—1222no—
520#121—1222no—
521#121—1222no—
522#121—1222no—
523#121—1222no—
524#121—1222no—
525#120—1222no—
526#120—1222no—
527#120—1222no—
528#120—1222no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—21no—
533C4×D4—1221no—
534C4×D4—1221no—
535C4×D4—1221no—
536C4×D4—1221no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—611no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—611no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—611no—
544C2×C4⋊C4—1222no—
545C2×C4⋊C4—1221no—
546C2×C4⋊C4—1221no—
547C2×C4⋊C4C4×D6111yescharacteristic, complemented
548C2×C22⋊C4—611no—
549C2×C22⋊C4—611no—
550C2×C22⋊C4—611no—
551C2×C22⋊C4—611no—
552C2×C22⋊C4—612no—
553C2×C22⋊C4—612no—
554C2×C22⋊C4—612no—
555C2×C22⋊C4—612no—
556C2×C22⋊C4—611no—
557C2×C22⋊C4—611no—
558C2×C22⋊C4—611no—
559C2×C22⋊C4—611no—
560C2×C22⋊C4—611no—
561C2×C22⋊C4—611no—
562C2×C22⋊C4—611no—
563C2×C22⋊C4—611no—
564C2×C22⋊C4—612no—
565C2×C22⋊C4—612no—
566C2×C22⋊C4—1222no—
567C2×C22⋊C4—1222no—
568C2×C22⋊C4—1222no—
569C2×C22⋊C4—2442no—
570C2×C22⋊C4—2442no—
571C2×C22⋊C4C4×D6111yescharacteristic, complemented
572C2×C22⋊C4C22×D6112yes—
573C2×C22⋊C4C22×D6112yes—
574C2×C22⋊C4C22×D6111yescharacteristic
575C2×C42—611no—
576C2×C42—1222no—
577C2×C42C4×D6111yescharacteristic, complemented
578#99—42no—
579#99—2442no—
580#99—2442no—
581#99—2442no—
582#95—21no—
583#95—21no—
584#95—1222no—
585#95—1222no—
586#95—1221no—
587#95—1221no—
588C24—611no—
589C24—611no—
590C24—612no—
591C24—612no—
592C24—611no—
593C24—1221no—
594C24—1221no—
595C24—1221no—
596C24—1221no—
597C24—4881no—
598C24—4881no—
599C24C2×C4×D6111yescharacteristic
600C24C23×D6111yescharacteristic
601C2×Q8—1222no—
602C2×Q8—4881no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—1222no—
610C2×D4—1222no—
611C2×D4—1222no—
612C2×D4—1222no—
613C2×D4—1222no—
614C2×D4—1221no—
615C2×D4—1221no—
616C2×D4—1221no—
617C2×D4—1221no—
618C2×D4—1221no—
619C2×D4—1221no—
620C2×D4—4881no—
621C2×D4—4881no—
622C2×D4—4881no—
623C2×D4—4881no—
624C2×D4—4881no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—81no—
630C22×C4—81no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—612no—
634C22×C4—612no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—1222no—
641C22×C4—1222no—
642C22×C4—4882no—
643C22×C4—4882no—
644C22×C4—4881no—
645C22×C4—4881no—
646C22×C4—2444no—
647C22×C4C2×C4×D6111yescharacteristic
648C22×C4C2×C4×D6111yescharacteristic
649C22×C4C2×C4×D6111yescharacteristic
650C22×C4C2×C4×D6111yescharacteristic
651C22×C4C2×C4×D6111yescharacteristic
652C22×C4D4×D6111yescharacteristic
653C22×C4D4×D6111yescharacteristic
654C22×C4D4×D6111yescharacteristic
655C22×C4D4×D6111yescharacteristic
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—81no—
659C4⋊C4—81no—
660C4⋊C4—1222no—
661C4⋊C4—1222no—
662C4⋊C4—1222no—
663C4⋊C4—1222no—
664C4⋊C4—1221no—
665C4⋊C4—1221no—
666C4⋊C4—4882no—
667C4⋊C4—4881no—
668C4⋊C4—4881no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—612no—
678C22⋊C4—612no—
679C22⋊C4—612no—
680C22⋊C4—612no—
681C22⋊C4—612no—
682C22⋊C4—612no—
683C22⋊C4—612no—
684C22⋊C4—612no—
685C22⋊C4—1222no—
686C22⋊C4—1222no—
687C22⋊C4—1222no—
688C22⋊C4—1222no—
689C22⋊C4—1222no—
690C22⋊C4—1222no—
691C22⋊C4—1221no—
692C22⋊C4—1221no—
693C22⋊C4—1221no—
694C22⋊C4—1221no—
695C22⋊C4—1222no—
696C22⋊C4—1222no—
697C22⋊C4—1222no—
698C22⋊C4—1222no—
699C22⋊C4—4882no—
700C22⋊C4—4882no—
701C22⋊C4—2444no—
702C42—21no—
703C42—21no—
704C42—1221no—
705C42—1221no—
706C42—4882no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—612no—
715C23—612no—
716C23—1221no—
717C23—1221no—
718C23—1221no—
719C23—1221no—
720C23—1222no—
721C23—1222no—
722C23—1222no—
723C23—1222no—
724C23—1221no—
725C23—1221no—
726C23—1221no—
727C23—4882no—
728C23—4882no—
729C23—4882no—
730C23—4882no—
731C23—2442no—
732C23—2442no—
733C23—2441no—
734C23—2441no—
735C23—2441no—
736C23—2441no—
737C23—2442no—
738C23—2442no—
739C23—2441no—
740C23—2441no—
741C23C22×C4×D6111yescharacteristic
742C23C2×D4×D6111yescharacteristic
743C23C2×D4×D6111yescharacteristic
744C23#1451982211yescharacteristic
745C23#1451982311yescharacteristic
746C23#1451982411yescharacteristic
747C23#1451982511yescharacteristic
748Q8—4882no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—4882no—
754D4—4882no—
755D4—4882no—
756D4—4882no—
757D4—4882no—
758D4—2441no—
759D4—2441no—
760D4—2441no—
761D4—2441no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—612no—
784C2×C4—612no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—4881no—
791C2×C4—4881no—
792C2×C4—4888no—
793C2×C4—2442no—
794C2×C4—2442no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2442no—
798C2×C4—2442no—
799C2×C4—2442no—
800C2×C4—2442no—
801C2×C4—2442no—
802C2×C4—2442no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4C22⋊C4×D6111yescharacteristic
806C2×C4C22⋊C4×D6111yescharacteristic
807C2×C4C22⋊C4×D6111yescharacteristic
808C2×C4C22⋊C4×D6111yescharacteristic
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—81no—
823C22—81no—
824C22—1222no—
825C22—1222no—
826C22—1222no—
827C22—1222no—
828C22—1222no—
829C22—1222no—
830C22—4881no—
831C22—4881no—
832C22—4882no—
833C22—4882no—
834C22—4881no—
835C22—4881no—
836C22—4881no—
837C22—4881no—
838C22—2444no—
839C22—2444no—
840C22—2441no—
841C22—2441no—
842C22—2441no—
843C22C2×C22⋊C4×D6111yescharacteristic
844C22#1684024211yescharacteristic
845C22#1684024311yescharacteristic
846C22#1684032811yescharacteristic
847C22#1684033511yescharacteristic
848C22#1684034111yescharacteristic
849C22#1684034211yescharacteristic
850C4—21no—
851C4—21no—
852C4—21no—
853C4—21no—
854C4—41no—
855C4—41no—
856C4—41no—
857C4—82no—
858C4—82no—
859C4—1222no—
860C4—1222no—
861C4—4882no—
862C4—4882no—
863C4—2441no—
864C4—2441no—
865C4—2441no—
866C2—21no—
867C2—21no—
868C2—21no—
869C2—21no—
870C2—21no—
871C2—21no—
872C2—81no—
873C2—4881no—
874C2—2442no—
875C2—2442no—
876C2#2144840811yescharacteristic
877C2#2145427711yescharacteristic
878C2#2145427811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1799C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840345C2
cosocleC24×C61C24
hypercenter#1799D61
hypocenterC61#21876
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #21448432C2semidirect
3. #21448416C2semidirect
4. #21446802C2semidirect
5. #21446653C2semidirect
6. #21446271C2semidirect
7. #21446269C2semidirect
8. #21445807C2semidirect
9. #21445804C2semidirect
10. #21445804C2semidirect
11. C61×#1799C2semidirect
16. C2×#14519772C4semidirect
17. C2×#14519771C4semidirect
18. C2×#14519765C4semidirect
19. C2×#14519763C4semidirect
20. C2×#14519762C4semidirect
21. C2×#14519760C4semidirect
23. C2×#14519751C4semidirect
24. C2×#14519750C4semidirect
52. C22×Dic122C2×C4semidirect
57. C22×C22⋊D61C2×C4semidirect
61. C22×C4×D61C2×C4semidirect
92. C2×C4⋊Dic61C2×C4semidirect
94. C2×#11758196C2×C4semidirect
95. C2×#11758196C2×C4semidirect
96. C2×#11758196C2×C4semidirect
97. C2×#11758196C2×C4semidirect
98. C2×C22⋊Dic61C2×C4semidirect
113. C2×#11758198C2×C4semidirect
114. C2×#11758198C2×C4semidirect
122. C2×C4×Dic61C2×C4semidirect
131. C23×C4×C61C2×C4semidirect
139. C2×C4⋊C4×C61C2×C4semidirect
140. C2×C22⋊C4×C61C2×C4semidirect
144. C2×C42×C61C2×C4semidirect
437. #1799D61semidirect
490. C61#21876semidirect
503. C23×C4C4×D61semidirect
547. C2×C4⋊C4C4×D61semidirect
571. C2×C22⋊C4C4×D61semidirect
577. C2×C42C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403452
#214484322
#214484162
#214468022
#214466532
#214462712
#214462692
#214458072
#214458042
C61×#17992
#2187661