Finite Group Databasebeta

← #29685153

Subgroups — #29685153

Order 15616.

1150 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840383C211yesmaximal, characteristic
2#21448175C211yesmaximal, characteristic, complemented
3#21446770C211yesmaximal, characteristic, complemented
4#21446766C211yesmaximal, characteristic, complemented
5#21446749C211yesmaximal, characteristic, complemented
6#21446749C211yesmaximal, characteristic, complemented
7#21446139C211yesmaximal, characteristic
8#21446134C211yesmaximal, characteristic
9#21446129C211yesmaximal, characteristic, complemented
10#21446124C211yesmaximal, characteristic, complemented
11#21445650C211yesmaximal, characteristic, complemented
12#21445645C211yesmaximal, characteristic, complemented
13C4×#14519702C211yesmaximal, characteristic, complemented
14C4×#14519699C211yesmaximal, characteristic, complemented
15C2×C61×#433C211yesmaximal, characteristic, complemented
16#16840383—24no—
17#16840383C418yescomplemented
18C2×#14519777C2211yescharacteristic
19C2×#14519772—21no—
20C2×#14519765C2211yescharacteristic
21C2×#14519763—21no—
22C2×#14519759—21no—
23C2×#14519756C2211yescharacteristic
24C2×#14519755—21no—
25C2×#14519751C2211yescharacteristic
26C2×C4×Dic122C2211yescharacteristic
27C2×C4×D244C2211yescharacteristic
28C2×#14519736C2211yescharacteristic
29C22×C4⋊Dic61C2211yescharacteristic
30C2×#14519702C2211yescharacteristic
31C2×#14519702C2211yescharacteristic
32C2×#14519702C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519699C2211yescharacteristic
38C4⋊C4×Dic61—21no—
39C4⋊C4×Dic61—21no—
40C4×C4⋊Dic61C2211yescharacteristic
41C4×C4⋊Dic61C2211yescharacteristic
42C4×C4⋊Dic61C2211yescharacteristic
43C4×C4⋊Dic61C2211yescharacteristic
44C22⋊C4×Dic61—21no—
45C22⋊C4×Dic61—21no—
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54C2×#117×C61C2211yescharacteristic
55C61×#433—24no—
56C2×C4⋊C8×C61C2211yescharacteristic
57C2×C4⋊C8×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×#97×C61C2211yescharacteristic
61C2×C4×C8×C61C2211yescharacteristic
62C22×Dic122—21no—
63C22×Dic122C2311yescharacteristic
64C22×D244C2311yescharacteristic
65C22×C22⋊D61—21no—
66C23×Dic61—21no—
67C22×C4×D61—21no—
68#14519777—22no—
69#14519777C2×C414yescomplemented
70#14519772—28no—
71#14519765—22no—
72#14519765C2×C414yescomplemented
73#14519763—28no—
74#14519759—28no—
75#14519756—22no—
76#14519756C2×C414yes—
77#14519755—28no—
78#14519751—22no—
79#14519751C2×C414yes—
80C4×Dic122—22no—
81C4×Dic122C2×C414yescomplemented
82C4×D244—22no—
83C4×D244C2×C414yescomplemented
84#14519736—22no—
85#14519736—22no—
86C2×C4⋊Dic61—21no—
87C2×C4⋊Dic61—21no—
88C2×C4⋊Dic61—22no—
89C2×C4⋊Dic61—22no—
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61—21no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—21no—
109C2×C4×Dic61—21no—
110#14519702—22no—
111#14519702—22no—
112#14519702—22no—
113#14519702—22no—
114#14519699—22no—
115#14519699—22no—
116#14519699—22no—
117#14519699—22no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122C23×C4×C61C2311yescharacteristic
123C22×C8×C61C2311yescharacteristic
124C22×C8×C61C2311yescharacteristic
125C22×C8×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127#117×C61C2×C414yes—
128#117×C61D414yes—
129C2×C4⋊C4×C61D411yescharacteristic
130C2×C4⋊C4×C61D411yescharacteristic
131C2×C22⋊C4×C61D411yescharacteristic
132C2×C22⋊C4×C61D411yescharacteristic
133C2×C42×C61C2311yescharacteristic
134C2×C42×C61C2311yescharacteristic
135C4⋊C8×C61—22no—
136C4⋊C8×C61—22no—
137C22⋊C8×C61—22no—
138C22⋊C8×C61—22no—
139#97×C61—22no—
140C4×C8×C61—22no—
141C24×C61C2×D411yescharacteristic
142C23×D61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61C22×C412yes—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D412yes—
154C22×C4×C61C2411yescharacteristic
155C2×C22⋊D61—24no—
156C2×C22⋊D61—81no—
157C2×C22⋊D61—81no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—24no—
166C22×Dic61—81no—
167C22×Dic61—81no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—21no—
173C2×D244C22×C412yes—
174C2×C4×D61—24no—
175C2×C4×D61—81no—
176C2×C4×D61—81no—
177C2×Dic122—21no—
178C2×Dic122—21no—
179C2×Dic122—21no—
180C2×Dic122—21no—
181C2×Dic122—21no—
182C2×Dic122—24no—
183C2×Dic122—81no—
184C2×Dic122—81no—
185C2×Dic122C22×C412yes—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C4⋊C4×C61C22⋊C414yes—
199C4⋊C4×C61C22⋊C414yes—
200C22⋊C4×C61C22⋊C414yes—
201C22⋊C4×C61C22⋊C414yes—
202C42×C61C22×C412yes—
203C42×C61C22×C412yes—
204C42×C61C2×D412yes—
205C42×C61C2×D412yes—
206C22⋊Dic61—24no—
207C22⋊Dic61—24no—
208#11758198—24no—
209#11758198—24no—
210#11758198—24no—
211#11758198—24no—
212C4⋊Dic61—24no—
213C4⋊Dic61—24no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61C22×C412yes—
221C4⋊Dic61C22×C412yes—
222C4⋊Dic61#4112yes—
223C4⋊Dic61#4112yes—
224C4⋊Dic61#4112yes—
225C4⋊Dic61#4112yes—
226#11758196—24no—
227#11758196—24no—
228C4×Dic61—24no—
229C4×Dic61—24no—
230C4×Dic61—81no—
231C4×Dic61—81no—
232C4×Dic61—81no—
233C4×Dic61—81no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61C2×C22⋊C412yes—
241C23×C61C22×D411yescharacteristic
242C22×D61—22no—
243C22×D61—41no—
244C22×D61—41no—
245C22×D61—41no—
246C22×D61—41no—
247C22×D61—41no—
248C22×D61—41no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—22no—
260C2×C4×C61—22no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61C2×C22⋊C412yes—
264C2×C4×C61C2×C22⋊C412yes—
265C2×C4×C61C2×C22⋊C412yes—
266C2×C4×C61C2×C22⋊C412yes—
267C2×C4×C61C2×C22⋊C412yes—
268C2×C4×C61C23×C411yescharacteristic
269C2×C4×C61C22×D411yescharacteristic
270C2×C4×C61C2×#4111yescharacteristic
271C2×C4×C61C2×#4111yescharacteristic
272C2×C4×C61C2×#4111yescharacteristic
273C2×C4×C61C2×#4111yescharacteristic
274C22⋊D61—84no—
275C2×Dic61—22no—
276C2×Dic61—22no—
277C2×Dic61—22no—
278C2×Dic61—22no—
279C2×Dic61—22no—
280C2×Dic61—22no—
281C2×Dic61—22no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289C2×Dic61—41no—
290C2×Dic61—41no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—84no—
297D244—22no—
298D244—22no—
299D244—41no—
300D244—41no—
301C4×D61—84no—
302Dic122—22no—
303Dic122—22no—
304Dic122—41no—
305Dic122—41no—
306Dic122—84no—
307C8×C61—41no—
308C8×C61—41no—
309C8×C61—41no—
310C8×C61—41no—
311#21397—611nomaximal, Sylow
312C22×C61—22no—
313C22×C61—22no—
314C22×C61—22no—
315C22×C61—41no—
316C22×C61—41no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61C22×C22⋊C411yescharacteristic
320C22×C61#52511yescharacteristic
321C22×C61#52511yescharacteristic
322C22×C61#57611yescharacteristic
323C22×C61#57711yescharacteristic
324C22×C61#57711yescharacteristic
325C22×C61#57811yescharacteristic
326C2×D61—42no—
327C2×D61—42no—
328C2×D61—42no—
329C2×D61—81no—
330C2×D61—81no—
331C2×D61—81no—
332C2×D61—81no—
333C4×C61—22no—
334C4×C61—22no—
335C4×C61—22no—
336C4×C61—22no—
337C4×C61—22no—
338C4×C61C4×#4111yescharacteristic
339C4×C61C4×#4111yescharacteristic
340C4×C61#53211yescharacteristic
341C4×C61#53211yescharacteristic
342Dic61—42no—
343Dic61—42no—
344Dic61—42no—
345Dic61—42no—
346Dic61—42no—
347Dic61—42no—
348Dic61—42no—
349C2×#542—611no—
350C2×#433D6111yescharacteristic, complemented
351#2274—611no—
352#1988—611no—
353#1987—611no—
354#1983—611no—
355#1983—611no—
356#1875—611no—
357#1874—611no—
358#1873—611no—
359#1872—611no—
360#1763—611no—
361#1762—611no—
362C4×#103—611no—
363C4×#102—611no—
364C2×C61—42no—
365C2×C61#229711yescharacteristic
366C2×C61#289711yescharacteristic
367C2×C61#289811yescharacteristic
368C2×C61#311811yescharacteristic
369C2×C61#312111yescharacteristic
370C2×C61#312411yescharacteristic
371C2×C61#312511yescharacteristic
372D61—82no—
373#542—618no—
374#542—1224no—
375C2×C4⋊Q8—611no—
376C2×#126—1221no—
377C2×#124—611no—
378C2×#124—1221no—
379C2×#123—1221no—
380C2×C22⋊Q8—611no—
381C2×C22⋊Q8—1221no—
382C2×#121—611no—
383C2×C4×Q8—611no—
384C2×C4×D4—611no—
385C2×#117—611no—
386C2×#117C2×D6111yescharacteristic
387C22×C4⋊C4—611no—
388#433—24no—
389C2×C4⋊C8C2×D6111yescharacteristic
390C2×C4⋊C8C2×D6111yescharacteristic
391C2×#103—611no—
392C2×#103—611no—
393C2×#103—611no—
394C2×#103—611no—
395C2×#102—611no—
396C2×#102—611no—
397C2×#102—611no—
398C2×#102—611no—
399C2×C22⋊C8C2×D6111yescharacteristic
400C2×C22⋊C8C2×D6111yescharacteristic
401C2×#97C2×D6111yescharacteristic
402C2×C4×C8C2×D6111yescharacteristic
403C4×C4⋊C4—611no—
404C4×C4⋊C4—611no—
405C4×C4⋊C4—611no—
406C4×C4⋊C4—611no—
407C4×C4⋊C4—1221no—
408C4×C4⋊C4—1221no—
409C4×C22⋊C4—1221no—
410C4×C22⋊C4—1221no—
411#340—611no—
412#340—611no—
413#340—611no—
414#340—611no—
415#340—611no—
416#340—611no—
417#340—611no—
418#340—611no—
419C61#2139711yescharacteristic, complemented, Sylow
420C22×Q8—611no—
421C22×Q8—1221no—
422C22×D4—611no—
423C22×D4—1221no—
424C23×C4—1221no—
425C23×C4—1221no—
426C23×C4C22×D6111yescharacteristic
427C22×C8C22×D6111yescharacteristic
428C22×C8C22×D6111yescharacteristic
429C22×C8C22×D6111yescharacteristic
430C22×C8C22×D6111yescharacteristic
431C4⋊Q8—614no—
432C4⋊Q8—1222no—
433#126—1228no—
434#124—614no—
435#124—1228no—
436#124—1222no—
437#123—1228no—
438C22⋊Q8—614no—
439C22⋊Q8—1222no—
440C22⋊Q8—1228no—
441#121—614no—
442#121—1222no—
443C4×Q8—614no—
444C4×Q8—1222no—
445C4×D4—614no—
446C4×D4—1222no—
447#117—1222no—
448#117—1222no—
449#117C4×D6114yes—
450#117C22⋊D6114yes—
451C2×C4⋊C4—611no—
452C2×C4⋊C4—611no—
453C2×C4⋊C4—611no—
454C2×C4⋊C4—611no—
455C2×C4⋊C4—611no—
456C2×C4⋊C4—611no—
457C2×C4⋊C4—1222no—
458C2×C4⋊C4—1222no—
459C2×C4⋊C4—1221no—
460C2×C4⋊C4—1221no—
461C2×C4⋊C4—1221no—
462C2×C4⋊C4—1221no—
463C2×C4⋊C4D24411yescharacteristic
464C2×C4⋊C4D24411yescharacteristic
465C2×C22⋊C4—1221no—
466C2×C22⋊C4—1221no—
467C2×C22⋊C4—1221no—
468C2×C22⋊C4—1221no—
469C2×C22⋊C4—1221no—
470C2×C22⋊C4—1221no—
471C2×C22⋊C4D24411yescharacteristic
472C2×C22⋊C4D24411yescharacteristic
473C2×C42—1221no—
474C2×C42—1221no—
475C2×C42—1221no—
476C2×C42—1221no—
477C2×C42—1221no—
478C2×C42—1221no—
479C2×C42C22×D6111yescharacteristic
480C2×C42C22×D6111yescharacteristic
481C4⋊C8—22no—
482C4⋊C8—22no—
483#103—1222no—
484#103—1222no—
485#103—1222no—
486#103—1222no—
487#102—1222no—
488#102—1222no—
489#102—1222no—
490#102—1222no—
491C22⋊C8—22no—
492C22⋊C8—22no—
493#97—22no—
494C4×C8—22no—
495#95—1221no—
496#95—1221no—
497#95—1221no—
498#95—1221no—
499C24—1221no—
500C24C2×D24411yescharacteristic
501C2×Q8—612no—
502C2×Q8—1221no—
503C2×Q8—1224no—
504C2×Q8—1221no—
505C2×Q8—1221no—
506C2×Q8—1221no—
507C2×Q8—1221no—
508C2×Q8—4881no—
509C2×Q8—4881no—
510C2×D4—612no—
511C2×D4—1224no—
512C2×D4—1221no—
513C2×D4—1221no—
514C2×D4—1221no—
515C2×D4—1221no—
516C2×D4—1221no—
517C2×D4—4881no—
518C2×D4—4881no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—1224no—
524C22×C4—1221no—
525C22×C4—1221no—
526C22×C4—1221no—
527C22×C4—1221no—
528C22×C4—1221no—
529C22×C4—1221no—
530C22×C4—1221no—
531C22×C4—1224no—
532C22×C4—4881no—
533C22×C4—4881no—
534C22×C4—4881no—
535C22×C4—4881no—
536C22×C4C2×C4×D6112yes—
537C22×C4C2×D24411yescharacteristic
538C22×C4C2×D24411yescharacteristic
539C22×C4C2×D24411yescharacteristic
540C22×C4C2×D24411yescharacteristic
541C22×C4C2×D24411yescharacteristic
542C22×C4C2×C22⋊D6112yes—
543C22×C4C23×D6111yescharacteristic
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C4⋊C4—612no—
557C4⋊C4—612no—
558C4⋊C4—612no—
559C4⋊C4—612no—
560C4⋊C4—612no—
561C4⋊C4—612no—
562C4⋊C4—1224no—
563C4⋊C4—1221no—
564C4⋊C4—1221no—
565C4⋊C4—1221no—
566C4⋊C4—1221no—
567C4⋊C4—1221no—
568C4⋊C4—1221no—
569C4⋊C4—1224no—
570C4⋊C4—1224no—
571C4⋊C4—1224no—
572C4⋊C4#1175819814yes—
573C4⋊C4#1175819814yes—
574C22⋊C4—1224no—
575C22⋊C4—1224no—
576C22⋊C4—1224no—
577C22⋊C4—1224no—
578C22⋊C4—1224no—
579C22⋊C4—1224no—
580C22⋊C4#1175819814yes—
581C22⋊C4#1175819814yes—
582C42—1224no—
583C42—1224no—
584C42—4881no—
585C42—4881no—
586C42—4881no—
587C42—4881no—
588C42C2×C4×D6112yes—
589C42C2×C4×D6112yes—
590C42C2×C22⋊D6112yes—
591C42C2×C22⋊D6112yes—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—1222no—
599C23—2441no—
600C23—2441no—
601C23—2441no—
602C23—2441no—
603C23—2441no—
604C23—2441no—
605C23C2×#1175819812yes—
606C23C22×D24411yescharacteristic
607Q8—1222no—
608Q8—1222no—
609Q8—4884no—
610Q8—2441no—
611Q8—2441no—
612D4—1222no—
613D4—1222no—
614D4—4884no—
615D4—2441no—
616D4—2441no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—1222no—
632C2×C4—1222no—
633C2×C4—1222no—
634C2×C4—1222no—
635C2×C4—1222no—
636C2×C4—1222no—
637C2×C4—1222no—
638C2×C4—4884no—
639C2×C4—4884no—
640C2×C4—2441no—
641C2×C4—2441no—
642C2×C4—2441no—
643C2×C4—2441no—
644C2×C4—2441no—
645C2×C4—2441no—
646C2×C4—2441no—
647C2×C4—2441no—
648C2×C4—2441no—
649C2×C4—2441no—
650C2×C4—2441no—
651C2×C4—2441no—
652C2×C4—2441no—
653C2×C4—2441no—
654C2×C4C2×#1175819812yes—
655C2×C4C2×#1175819812yes—
656C2×C4C2×#1175819812yes—
657C2×C4C2×#1175819812yes—
658C2×C4C2×#1175819812yes—
659C2×C4C22×C4×D6111yescharacteristic
660C2×C4C22×C22⋊D6111yescharacteristic
661C2×C4#41×D6111yescharacteristic
662C2×C4#41×D6111yescharacteristic
663C2×C4#41×D6111yescharacteristic
664C2×C4#41×D6111yescharacteristic
665C8—41no—
666C8—41no—
667C8—41no—
668C8—41no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—4881no—
677C22—4881no—
678C22—4881no—
679C22—4881no—
680C22—2442no—
681C22—2442no—
682C22—2442no—
683C22C22×#1175819811yescharacteristic
684C22#1684027411yescharacteristic
685C22#1684027411yescharacteristic
686C22#1684056711yescharacteristic
687C22#1684057411yescharacteristic
688C22#1684057411yescharacteristic
689C22#1684057911yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—2442no—
696C4—2442no—
697C4—2442no—
698C4—2442no—
699C4—2442no—
700C4—2442no—
701C4—2442no—
702C4#1684023011yescharacteristic
703C4#1684023011yescharacteristic
704C4#1684030811yescharacteristic
705C4#1684030811yescharacteristic
706C2—42no—
707C2—4882no—
708C2#2144830711yescharacteristic
709C2#2145434611yescharacteristic
710C2#2145435311yescharacteristic
711C2#2145600511yescharacteristic
712C2#2145605011yescharacteristic
713C2#2145608311yescharacteristic
714C2#2145609811yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#433C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
cosocleC22×C4×C61C24
hypercenterC2×#433D61
hypocenterC61#21397
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #21448175C2semidirect
3. #21446770C2semidirect
4. #21446766C2semidirect
5. #21446749C2semidirect
6. #21446749C2semidirect
9. #21446129C2semidirect
10. #21446124C2semidirect
11. #21445650C2semidirect
12. #21445645C2semidirect
13. C4×#14519702C2semidirect
14. C4×#14519699C2semidirect
15. C2×C61×#433C2semidirect
17. #16840383C4semidirect
69. #14519777C2×C4semidirect
72. #14519765C2×C4semidirect
81. C4×Dic122C2×C4semidirect
83. C4×D244C2×C4semidirect
350. C2×#433D61semidirect
419. C61#21397semidirect

Maximal subgroups

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

subgroupindex
C2×#168403832
#214481752
#214467702
#214467662
#214467492
#214461392
#214461342
#214461292
#214461242
#214456502
#214456452
C4×#145197022
C4×#145196992
C2×C61×#4332
#2139761