Finite Group Databasebeta

← #29696407

Subgroups — #29696407

Order 15616.

1186 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840460C211yesmaximal, characteristic
2C2×#16839831C211yesmaximal, characteristic, complemented
3#21448769C211yesmaximal, characteristic, complemented
4#21446786C211yesmaximal, characteristic, complemented
5#21446775C211yesmaximal, characteristic, complemented
6#21446257C211yesmaximal, characteristic, complemented
7#21446246C211yesmaximal, characteristic, complemented
8#21446141C211yesmaximal, characteristic, complemented
9#21446140C211yesmaximal, characteristic, complemented
10#21445913C211yesmaximal, characteristic, complemented
11#21445905C211yesmaximal, characteristic, complemented
12#21445818C211yesmaximal, characteristic, complemented
13#21445643C211yesmaximal, characteristic, complemented
14#21445534C211yesmaximal, characteristic, complemented
15C61×#1736C211yesmaximal, characteristic, complemented
16C22×C8×D61C2211yescharacteristic
17#16840460—24no—
18#16840460C418yescomplemented
19C2×#14519772—21no—
20C2×#14519768C2211yescharacteristic
21C2×#14519762—21no—
22C2×#14519752C2211yescharacteristic
23C2×#14519751—21no—
24C2×#14519751C2211yescharacteristic
25C2×#14519739C2211yescharacteristic
26C2×C4×C22⋊D61—21no—
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×#14519735C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30#16839831—24no—
31C2×#14519706C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37C2×#14519689C2211yescharacteristic
38C2×#14519687C2211yescharacteristic
39#16839662—21no—
40#16839653—21no—
41#16839650—21no—
42#16839631C2211yescharacteristic
43#16839622C2211yescharacteristic
44#16839619C2211yescharacteristic
45C4⋊C4×Dic61C2211yescharacteristic
46C4×#11758196—21no—
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C22×M16×C61C2211yescharacteristic
56C2×#117×C61C2211yescharacteristic
57C22×C4⋊C4×C61C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C22×D244—21no—
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61D411yescharacteristic
66C22×C4×D61—21no—
67C22×C4×D61C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C2×C8×D61—22no—
71C2×C8×D61—22no—
72C2×C8×D61—41no—
73#14519772—28no—
74#14519768—22no—
75#14519768C2×C414yes—
76#14519762—28no—
77#14519752—22no—
78#14519752C2×C414yes—
79#14519751—22no—
80#14519751—28no—
81#14519751C2×C414yes—
82#14519739—22no—
83#14519739C2×C414yes—
84C4×C22⋊D61—28no—
85C4×C22⋊D61C2×C414yes—
86C4×C22⋊D61D414yes—
87#14519735—22no—
88#14519735—22no—
89#14519735—41no—
90#14519735C2×C414yes—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196D411yescharacteristic
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61D411yescharacteristic
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198D411yescharacteristic
108C2×C4×Dic61—21no—
109C2×C4×Dic61—21no—
110C2×C4×Dic61—21no—
111C2×C4×Dic61C2311yescharacteristic
112#14519706—22no—
113#14519699—22no—
114#14519699—41no—
115#14519697—22no—
116#14519697—41no—
117C22⋊#92418—22no—
118#14519689—22no—
119#14519687—22no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123C23×C4×C61—21no—
124C23×C4×C61C2311yescharacteristic
125C2×M16×C61—22no—
126C2×M16×C61—22no—
127C2×M16×C61—41no—
128C22×C8×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130#117×C61—22no—
131#117×C61—41no—
132C2×C4⋊C4×C61—22no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61C2×C414yes—
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61—21no—
140C2×C42×C61—21no—
141C24×C61C2×D411yescharacteristic
142C23×D61—21no—
143C23×D61C2×D411yescharacteristic
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—24no—
152C22×C4×C61—21no—
153C22×C4×C61—81no—
154C22×C4×C61—81no—
155C22×C4×C61C22×C412yes—
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D412yes—
158C22×C4×C61C2411yescharacteristic
159C2×C22⋊D61—24no—
160C2×C22⋊D61—41no—
161C2×C22⋊D61—41no—
162C2×C22⋊D61—42no—
163C2×C22⋊D61—42no—
164C2×C22⋊D61C22⋊C414yes—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61C2×D411yescharacteristic
169C22×Dic61C2×D411yescharacteristic
170C22×Dic61C2×D411yescharacteristic
171C2×D244—21no—
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—24no—
177C2×D244—81no—
178C2×D244—81no—
179C2×D244C22×C412yes—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—24no—
185C2×C4×D61—81no—
186C2×C4×D61—81no—
187C2×C4×D61C22×C412yes—
188C2×C4×D61C2×D412yes—
189M16×C61—44no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61#4112yes—
196C4⋊C4×C61—24no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61C22×C412yes—
203C4⋊C4×C61C22×C412yes—
204C4⋊C4×C61#4112yes—
205C22⋊C4×C61—42no—
206C42×C61—42no—
207C22⋊Dic61—81no—
208C22⋊Dic61C22⋊C414yes—
209#11758198—24no—
210#11758198—24no—
211#11758198—24no—
212#11758198—24no—
213#11758198—42no—
214#11758198—81no—
215#11758198C22⋊C414yes—
216C4⋊Dic61—21no—
217C4⋊Dic61—24no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61C22×C412yes—
223#11758196—24no—
224#11758196—42no—
225#11758196—81no—
226#11758196C22⋊C414yes—
227C4×Dic61—24no—
228C4×Dic61—42no—
229C4×Dic61—42no—
230C4×Dic61C22×C412yes—
231C4×Dic61C2×D412yes—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C8×D61—44no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61C2×C22⋊C412yes—
246C23×C61C22×D411yescharacteristic
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—22no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61C2×C22⋊C412yes—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—84no—
280C2×C4×C61C2×C22⋊C412yes—
281C2×C4×C61C23×C411yescharacteristic
282C2×C4×C61C22×D411yescharacteristic
283C2×C4×C61C2×#4111yescharacteristic
284C2×C4×C61C2×#4111yescharacteristic
285C2×C4×C61H(5,𝔽2)11yescharacteristic
286C2×C4×C612−1+411yescharacteristic
287C22⋊D61—44no—
288C22⋊D61—48no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—22no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61C2×C22⋊C412yes—
305C2×Dic61C2×C22⋊C412yes—
306C2×Dic61C2×C22⋊C412yes—
307D244—22no—
308D244—22no—
309D244—41no—
310D244—41no—
311D244—84no—
312C4×D61—22no—
313C4×D61—22no—
314C4×D61—22no—
315C4×D61—22no—
316C4×D61—84no—
317C8×C61—22no—
318C8×C61—41no—
319#92418—41no—
320#92418—41no—
321#22498—611nomaximal, Sylow
322C22×C61—22no—
323C22×C61—22no—
324C22×C61—22no—
325C22×C61—41no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61C22×C22⋊C411yescharacteristic
330C22×C61#54611yescharacteristic
331C22×C61#54711yescharacteristic
332C22×C61#57511yescharacteristic
333C22×C61#57511yescharacteristic
334C22×C61#57611yescharacteristic
335C22×C61#57711yescharacteristic
336C2×D61—22no—
337C2×D61—22no—
338C2×D61—22no—
339C2×D61—41no—
340C2×D61—41no—
341C2×D61—41no—
342C2×D61—41no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—42no—
346C2×D61—81no—
347C2×D61—81no—
348C2×D61—81no—
349C2×D61—81no—
350C4×C61—22no—
351C4×C61—42no—
352C4×C61—42no—
353C4×C61—42no—
354C4×C61—81no—
355C4×C61C4×#4111yescharacteristic
356C4×C61#52011yescharacteristic
357C4×C61#54611yescharacteristic
358C4×C61#54711yescharacteristic
359Dic61—22no—
360Dic61—22no—
361Dic61—22no—
362Dic61—42no—
363Dic61—81no—
364Dic61—81no—
365C2×#553—611no—
366C2×#435—611no—
367#2354—611no—
368#1992—611no—
369#1989—611no—
370#1895—611no—
371#1893—611no—
372#1875—611no—
373#1875—611no—
374#1825—611no—
375#1823—611no—
376#1802—611no—
377#1762—611no—
378#1736D6111yescharacteristic, complemented
379#1735—611no—
380C2×C61—42no—
381C2×C61#233911yescharacteristic
382C2×C61#289611yescharacteristic
383C2×C61#289711yescharacteristic
384C2×C61#330711yescharacteristic
385C2×C61#330911yescharacteristic
386C2×C61#334711yescharacteristic
387C2×C61#335011yescharacteristic
388D61—42no—
389D61—82no—
390C22×M16C2×D6111yescharacteristic
391C23×C8—611no—
392#553—618no—
393#553—1224no—
394C2×#126—1221no—
395C2×#125—611no—
396C2×#123—1221no—
397C2×#121—611no—
398C2×#121—611no—
399C2×#121—1221no—
400C2×C4×D4—611no—
401C2×C4×D4—611no—
402C2×C4×D4—1221no—
403C2×#117—611no—
404C2×#117—611no—
405C2×#117C2×D6111yescharacteristic
406C22×C4⋊C4C2×D6111yescharacteristic
407#435—1224no—
408C2×C4⋊C8—611no—
409C2×#102—611no—
410C2×#102—611no—
411C2×#102—611no—
412C2×#102—611no—
413C2×C22⋊C8—611no—
414C2×C22⋊C8—611no—
415C2×#97—611no—
416#390—1221no—
417#388—1221no—
418#388—1221no—
419#384—611no—
420#380—611no—
421#380—611no—
422C4×C4⋊C4—611no—
423C4×C4⋊C4—1221no—
424#340—611no—
425#340—611no—
426#340—611no—
427#340—611no—
428#340—611no—
429#340—611no—
430#340—611no—
431#340—611no—
432#340C2×D6111yescharacteristic
433#340C2×D6111yescharacteristic
434#340C2×D6111yescharacteristic
435#340C2×D6111yescharacteristic
436C61#2249811yescharacteristic, complemented, Sylow
437C22×D4—611no—
438C22×D4—611no—
439C22×D4—1221no—
440C22×D4—1221no—
441C23×C4—21no—
442C23×C4—611no—
443C23×C4—1221no—
444C23×C4C22×D6111yescharacteristic
445C2×M16—22no—
446C2×M16—22no—
447C2×M16—41no—
448C22×C8—611no—
449C22×C8—611no—
450C22×C8—1222no—
451C22×C8—1222no—
452C22×C8—2441no—
453C22×C8C22×D6111yescharacteristic
454C22×C8C22×D6111yescharacteristic
455#126—1228no—
456#125—614no—
457#125—1222no—
458#123—1228no—
459#121—614no—
460#121—614no—
461#121—1222no—
462#121—1228no—
463#121—1222no—
464C4×D4—614no—
465C4×D4—614no—
466C4×D4—614no—
467C4×D4—1222no—
468C4×D4—1228no—
469#117—22no—
470#117—41no—
471#117—614no—
472#117—1222no—
473#117—1222no—
474#117—2441no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4C4×D6114yes—
486C2×C4⋊C4C22×D6111yescharacteristic
487C2×C4⋊C4C22×D6111yescharacteristic
488C2×C4⋊C4C22×D6111yescharacteristic
489C2×C4⋊C4C22×D6111yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—611no—
492C2×C22⋊C4—611no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C42—21no—
501C2×C42—611no—
502C2×C42—1221no—
503C2×C42—1221no—
504C2×C42—1221no—
505C4⋊C8—1222no—
506#102—1222no—
507#102—1222no—
508#102—2441no—
509#102—2441no—
510C22⋊C8—1222no—
511C22⋊C8—1222no—
512#97—1222no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516C24—611no—
517C24—1221no—
518C24D4×D6111yescharacteristic
519C2×D4—614no—
520C2×D4—612no—
521C2×D4—1224no—
522C2×D4—1224no—
523C2×D4—1221no—
524C2×D4—1221no—
525C2×D4—1221no—
526C2×D4—1221no—
527C2×D4—1221no—
528C2×D4—4881no—
529C2×D4—4881no—
530C2×D4—2441no—
531C2×D4—2441no—
532C2×D4—2442no—
533C2×D4—2442no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—24no—
542C22×C4—21no—
543C22×C4—81no—
544C22×C4—81no—
545C22×C4—611no—
546C22×C4—611no—
547C22×C4—611no—
548C22×C4—612no—
549C22×C4—612no—
550C22×C4—1224no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—4881no—
559C22×C4—4881no—
560C22×C4C2×C4×D6112yes—
561C22×C4D4×D6112yes—
562C22×C4D4×D6111yescharacteristic
563C22×C4C23×D6111yescharacteristic
564M16—44no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—1221no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8—2444no—
577C2×C8#1175822212yes—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—24no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—614no—
585C4⋊C4—612no—
586C4⋊C4—1224no—
587C4⋊C4—1224no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—1221no—
593C4⋊C4—4881no—
594C4⋊C4—2442no—
595C4⋊C4C2×C4×D6112yes—
596C4⋊C4C2×C4×D6112yes—
597C4⋊C4#1175822212yes—
598C22⋊C4—42no—
599C22⋊C4—614no—
600C22⋊C4—614no—
601C22⋊C4—1224no—
602C22⋊C4—1224no—
603C22⋊C4—1224no—
604C22⋊C4—1224no—
605C22⋊C4—4881no—
606C22⋊C4—4881no—
607C22⋊C4—2442no—
608C42—42no—
609C42—612no—
610C42—612no—
611C42—1224no—
612C42—2442no—
613C42—2442no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—612no—
621C23—1221no—
622C23—1221no—
623C23—1221no—
624C23—1221no—
625C23—1221no—
626C23—1221no—
627C23—1222no—
628C23—2441no—
629C23—2441no—
630C23—2441no—
631C23—2441no—
632C23—2441no—
633C23—2441no—
634C23C22⋊C4×D6112yes—
635C23C2×D4×D6111yescharacteristic
636D4—1222no—
637D4—1222no—
638D4—4884no—
639D4—2444no—
640D4—2448no—
641D4—2441no—
642D4—2441no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—84no—
662C2×C4—612no—
663C2×C4—612no—
664C2×C4—612no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—4884no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4C22⋊C4×D6112yes—
686C2×C4C22×C4×D6111yescharacteristic
687C2×C4C2×D4×D6111yescharacteristic
688C2×C4C2×#1175822211yescharacteristic
689C2×C4C2×#1175822211yescharacteristic
690C2×C4#1451982211yescharacteristic
691C2×C4#1451982511yescharacteristic
692C8—22no—
693C8—41no—
694C8—2441no—
695C8—2441no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—1222no—
704C22—1222no—
705C22—1222no—
706C22—4881no—
707C22—4881no—
708C22—4881no—
709C22—4881no—
710C22—2442no—
711C22—2442no—
712C22—2442no—
713C22—2441no—
714C22—2441no—
715C22—2441no—
716C22—2441no—
717C22C2×C22⋊C4×D6111yescharacteristic
718C22#1684040211yescharacteristic
719C22#1684041311yescharacteristic
720C22#1684056111yescharacteristic
721C22#1684056111yescharacteristic
722C22#1684056611yescharacteristic
723C22#1684057211yescharacteristic
724C4—22no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—81no—
729C4—1222no—
730C4—1222no—
731C4—1222no—
732C4—4881no—
733C4—4881no—
734C4—2442no—
735C4C4×#1175822211yescharacteristic
736C4#1684024311yescharacteristic
737C4#1684040211yescharacteristic
738C4#1684041311yescharacteristic
739C2—42no—
740C2—4882no—
741C2—2442no—
742C2#2144864611yescharacteristic
743C2#2145433711yescharacteristic
744C2#2145434411yescharacteristic
745C2#2145779611yescharacteristic
746C2#2145782611yescharacteristic
747C2#2145832011yescharacteristic
748C2#2145836511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1736C2
socleC23×C61C22×D4
prime radicalC2×#16840460C2
cosocleC22×C4×C61C24
hypercenter#1736D61
hypocenterC61#22498
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
2. C2×#16839831C2semidirect
3. #21448769C2semidirect
4. #21446786C2semidirect
5. #21446775C2semidirect
6. #21446257C2semidirect
7. #21446246C2semidirect
8. #21446141C2semidirect
9. #21446140C2semidirect
10. #21445913C2semidirect
11. #21445905C2semidirect
12. #21445818C2semidirect
13. #21445643C2semidirect
14. #21445534C2semidirect
15. C61×#1736C2semidirect
18. #16840460C4semidirect
378. #1736D61semidirect
436. C61#22498semidirect

Maximal subgroups

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

subgroupindex
C2×#168404602
C2×#168398312
#214487692
#214467862
#214467752
#214462572
#214462462
#214461412
#214461402
#214459132
#214459052
#214458182
#214456432
#214455342
C61×#17362
#2249861