Finite Group Databasebeta

← #29690297

Subgroups — #29690297

Order 15616.

1090 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839724C211yesmaximal, characteristic
2#21448201C211yesmaximal, characteristic
3#21448198C211yesmaximal, characteristic
4#21446021C211yesmaximal, characteristic, complemented
5#21446020C211yesmaximal, characteristic, complemented
6#21446019C211yesmaximal, characteristic, complemented
7#21446018C211yesmaximal, characteristic, complemented
8#21446017C211yesmaximal, characteristic, complemented
9#21446016C211yesmaximal, characteristic, complemented
10#21446015C211yesmaximal, characteristic, complemented
11#21445853C211yesmaximal, characteristic, complemented
12#21445851C211yesmaximal, characteristic, complemented
13#21445851C211yesmaximal, characteristic, complemented
14#21445849C211yesmaximal, characteristic, complemented
15C61×#1854C211yesmaximal, characteristic, complemented
16C23×C4×D61C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20C2×#14519735C2211yescharacteristic
21C2×#14519735C2211yescharacteristic
22C2×#14519711C2211yescharacteristic, complemented
23C2×#14519710C2211yescharacteristic, complemented
24C2×#14519710C2211yescharacteristic, complemented
25C2×#14519709C2211yescharacteristic, complemented
26C2×#14519708C2211yescharacteristic, complemented
27C2×#14519708C2211yescharacteristic, complemented
28#16839724C418yescomplemented
29C2×C22⋊#92418C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32#16839624—21no—
33#16839623—21no—
34#16839622C2211yescharacteristic
35#16839619C2211yescharacteristic
36#16839619C2211yescharacteristic
37#16839619C2211yescharacteristic
38#16839619C2211yescharacteristic
39#16839619C2211yescharacteristic
40#16839619C2211yescharacteristic
41#16839617—21no—
42#16839617—21no—
43C22⋊C4×Dic61—21no—
44C4×#11758198—21no—
45C4×#11758198—21no—
46#16839609—21no—
47#16839525C2211yescharacteristic, complemented
48#16839525C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53C2×#117×C61C2211yescharacteristic
54C2×#107×C61C2211yescharacteristic, complemented
55C2×#106×C61C2211yescharacteristic, complemented
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#340C2211yescharacteristic, complemented
59C61×#340C2211yescharacteristic, complemented
60C24×D61D411yescharacteristic
61C23×Dic61D411yescharacteristic
62C22×C4×D61—41no—
63C22×C4×D61—41no—
64C22×C4×D61—41no—
65C22×C4×D61—41no—
66C22×C4×D61C2×C414yes—
67C22×C4×D61D411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61Q814yes—
70C22×C4×D61C2311yescharacteristic
71C22×C4×D61C2311yescharacteristic
72C2×#11758189—41no—
73C2×#11758189—41no—
74C2×#11758189—41no—
75C2×#11758189—41no—
76C2×#11758189C2×C414yes—
77C2×#11758189C2×C414yes—
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80#14519736—41no—
81#14519736—41no—
82#14519735—41no—
83#14519735—41no—
84#14519735—41no—
85#14519735—41no—
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×C4×Dic61—21no—
101C2×C4×Dic61—21no—
102C2×C4×Dic61—21no—
103#14519711—41no—
104#14519710—41no—
105#14519710—41no—
106#14519709—41no—
107#14519708—41no—
108#14519708—41no—
109C22⋊#92418C2×C414yes—
110#14519689C2×C414yes—
111#14519689C2×C414yes—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119C23×C4×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C22×C8×C61C2311yescharacteristic
122#117×C61—41no—
123#117×C61—41no—
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C42×C61—21no—
131#107×C61—41no—
132#106×C61—41no—
133C22⋊C8×C61C2×C414yes—
134#95×C61—21no—
135C24×C61C2×D411yescharacteristic
136C23×D61—41no—
137C23×D61—41no—
138C23×D61—41no—
139C23×D61—41no—
140C23×D61—41no—
141C23×D61—41no—
142C23×D61C4⋊C414yes—
143C23×D61C2×D411yescharacteristic
144C23×D61C2×D411yescharacteristic
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—21no—
152C22×C4×C61—21no—
153C22×C4×C61C22×C412yes—
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×Q812yes—
156C22×C4×C61C2411yescharacteristic
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—41no—
162C22×Dic61—41no—
163C22×Dic61C4⋊C414yes—
164C22×Dic61C2×D411yescharacteristic
165C22×Dic61C2×D411yescharacteristic
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61—44no—
175C2×C4×D61—44no—
176C2×C4×D61—44no—
177C2×C4×D61—44no—
178C2×C4×D61—41no—
179C2×C4×D61—41no—
180C2×C4×D61—41no—
181C2×C4×D61—41no—
182C2×C4×D61C4⋊C414yes—
183C2×C4×D61C4⋊C414yes—
184C2×C4×D61C22×C412yes—
185C2×C4×D61C22×C412yes—
186C2×C4×D61C2×Q812yes—
187C2×C4×D61C2×Q812yes—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61C22×C412yes—
193C2×C8×C61C22×C412yes—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C22⋊C4×C61—42no—
203C22⋊C4×C61—42no—
204C42×C61—42no—
205C22⋊Dic61—42no—
206C22⋊Dic61—42no—
207#11758198—42no—
208#11758198—42no—
209#11758198—42no—
210#11758198—42no—
211#11758198—42no—
212#11758198—42no—
213#11758198—42no—
214#11758198—42no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4×Dic61—42no—
224C4×Dic61—42no—
225C4×Dic61—42no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418C22×C412yes—
231C2×#92418C22×C412yes—
232#11758189—44no—
233#11758189—44no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61C2×C4⋊C412yes—
241C23×C61C22×D411yescharacteristic
242C22×D61—21no—
243C22×D61—21no—
244C22×D61—21no—
245C22×D61—21no—
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—44no—
255C22×D61—44no—
256C22×D61—44no—
257C22×D61—44no—
258C22×D61—44no—
259C22×D61—44no—
260C22×D61—44no—
261C22×D61C2×C4⋊C412yes—
262C22×D61C2×C4⋊C412yes—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—41no—
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—41no—
280C2×C4×C61—41no—
281C2×C4×C61C2×C4⋊C412yes—
282C2×C4×C61C23×C411yescharacteristic
283C2×C4×C61C22×Q811yescharacteristic
284C2×C4×C61H(5,𝔽2)11yescharacteristic
285C2×C4×C61H(5,𝔽2)11yescharacteristic
286C2×C4×C61H(5,𝔽2)11yescharacteristic
287C2×C4×C61H(5,𝔽2)11yescharacteristic
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—44no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
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×Dic61—41no—
305C2×Dic61C2×C4⋊C412yes—
306C2×Dic61C2×C4⋊C412yes—
307C4×D61—22no—
308C4×D61—22no—
309C4×D61—22no—
310C4×D61—22no—
311C4×D61—22no—
312C4×D61—22no—
313C4×D61—22no—
314C4×D61—22no—
315C4×D61—44no—
316C4×D61—44no—
317C8×C61—22no—
318C8×C61—22no—
319#92418—22no—
320#92418—22no—
321#21943—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×C4⋊C411yescharacteristic
330C22×C61#53411yescharacteristic
331C22×C61#53411yescharacteristic
332C22×C61#57511yescharacteristic
333C22×C61#57511yescharacteristic
334C22×C61#57511yescharacteristic
335C22×C61#57511yescharacteristic
336C2×D61—22no—
337C2×D61—22no—
338C2×D61—22no—
339C2×D61—22no—
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—416no—
343C2×D61—41no—
344C2×D61—41no—
345C2×D61—41no—
346C2×D61—41no—
347C2×D61—41no—
348C2×D61—41no—
349C2×D61—41no—
350C2×D61—41no—
351C4×C61—22no—
352C4×C61—81no—
353C4×C61—81no—
354C4×C61—81no—
355C4×C61—81no—
356C4×C61#51811yescharacteristic
357C4×C61#51811yescharacteristic
358C4×C61#54311yescharacteristic
359C4×C61#54311yescharacteristic
360Dic61—22no—
361Dic61—22no—
362Dic61—81no—
363Dic61—81no—
364Dic61—81no—
365Dic61—81no—
366C2×#407—611no—
367#2280—611no—
368#2280—611no—
369#1854—611no—
370#1854—611no—
371#1854—611no—
372#1854—611no—
373#1854—611no—
374#1854—611no—
375#1854—611no—
376#1854D6111yescharacteristic, complemented
377#1809—611no—
378#1809—611no—
379#1809—611no—
380#1809—611no—
381C2×C61—42no—
382C2×C61#231511yescharacteristic
383C2×C61#291111yescharacteristic
384C2×C61#291111yescharacteristic
385C2×C61#319711yescharacteristic
386C2×C61#319711yescharacteristic
387C2×C61#319711yescharacteristic
388C2×C61#319711yescharacteristic
389D61—42no—
390D61—42no—
391C24×C4—611no—
392C22×M16—611no—
393C22×M16—611no—
394C2×#117—611no—
395C2×#117—611no—
396C2×#117—611no—
397C2×#117C2×D6111yescharacteristic
398C2×#107—611no—
399C2×#107—611no—
400C2×#107—611no—
401C2×#107C2×D6111yescharacteristic, complemented
402C2×#106—611no—
403C2×#106—611no—
404C2×#106—611no—
405C2×#106C2×D6111yescharacteristic, complemented
406#407—618no—
407C2×C22⋊C8—611no—
408C2×C22⋊C8—611no—
409C2×C22⋊C8—611no—
410C2×C22⋊C8C2×D6111yescharacteristic
411#381—1221no—
412#381—1221no—
413#380—611no—
414#380—611no—
415#380—611no—
416#380—611no—
417#380—611no—
418#380—611no—
419#380—611no—
420#380C2×D6111yescharacteristic
421#379—1221no—
422#379—1221no—
423C4×C22⋊C4—1221no—
424C4×C22⋊C4—1221no—
425C4×C22⋊C4—1221no—
426C4×C22⋊C4—1221no—
427#340—611no—
428#340—611no—
429#340—611no—
430#340—611no—
431#340—611no—
432#340—611no—
433#340C2×D6111yescharacteristic, complemented
434#340C2×D6111yescharacteristic, complemented
435C61#2194311yescharacteristic, complemented, Sylow
436C25—611no—
437C23×C4—611no—
438C23×C4—611no—
439C23×C4—611no—
440C23×C4—614no—
441C23×C4—611no—
442C23×C4—611no—
443C23×C4—614no—
444C23×C4—2441no—
445C23×C4—2441no—
446C23×C4—2441no—
447C23×C4—2441no—
448C23×C4C22×D6111yescharacteristic
449C2×M16—614no—
450C2×M16—614no—
451C2×M16—2441no—
452C2×M16—2441no—
453C2×M16—2441no—
454C2×M16—2441no—
455C22×C8—611no—
456C22×C8—611no—
457C22×C8C22×D6111yescharacteristic
458C22×C8C22×D6111yescharacteristic
459#117—41no—
460#117—41no—
461#117—2441no—
462#117—2441no—
463#117—2441no—
464#117—2441no—
465#117—2441no—
466#117—2441no—
467C2×C4⋊C4—611no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4C22×D6111yescharacteristic
472C2×C4⋊C4C22×D6111yescharacteristic
473C2×C4⋊C4C22×D6111yescharacteristic
474C2×C4⋊C4C22×D6111yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—1221no—
478C2×C22⋊C4—1221no—
479C2×C22⋊C4—1221no—
480C2×C22⋊C4—1221no—
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
484C2×C22⋊C4—1221no—
485C2×C22⋊C4—1221no—
486C2×C22⋊C4—1221no—
487C2×C42—21no—
488C2×C42—1221no—
489C2×C42—1221no—
490C2×C42—1221no—
491#107—41no—
492#107—2441no—
493#107—2441no—
494#107—2441no—
495#106—41no—
496#106—2441no—
497#106—2441no—
498#106—2441no—
499C22⋊C8—614no—
500C22⋊C8—614no—
501C22⋊C8—614no—
502C22⋊C8C4×D6114yes—
503#95—21no—
504#95—1221no—
505#95—1221no—
506#95—1221no—
507#95—1221no—
508#95—1221no—
509#95—1221no—
510#95—1221no—
511C24—611no—
512C24—611no—
513C24—614no—
514C24—2441no—
515C24—2441no—
516C24—2441no—
517C24—2441no—
518C24—2441no—
519C24—2441no—
520C24D4×D6111yescharacteristic
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—611no—
530C22×C4—611no—
531C22×C4—614no—
532C22×C4—612no—
533C22×C4—612no—
534C22×C4—612no—
535C22×C4—612no—
536C22×C4—614no—
537C22×C4—614no—
538C22×C4—1221no—
539C22×C4—1221no—
540C22×C4—1221no—
541C22×C4—1221no—
542C22×C4—1221no—
543C22×C4—1221no—
544C22×C4—1221no—
545C22×C4—1221no—
546C22×C4—1221no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—2444no—
551C22×C4—2444no—
552C22×C4—2444no—
553C22×C4—2444no—
554C22×C4—2441no—
555C22×C4—2441no—
556C22×C4—2441no—
557C22×C4—2441no—
558C22×C4—2441no—
559C22×C4—2441no—
560C22×C4C2×C4×D6112yes—
561C22×C4D4×D6111yescharacteristic
562C22×C4Q8×D6112yes—
563C22×C4C23×D6111yescharacteristic
564M16—2444no—
565M16—2444no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—612no—
571C2×C8—612no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8C2×C4×D6112yes—
577C2×C8C2×C4×D6112yes—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—1221no—
587C4⋊C4—1221no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—1221no—
593C4⋊C4—1221no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—2442no—
597C22⋊C4—2442no—
598C22⋊C4—2442no—
599C22⋊C4—2442no—
600C22⋊C4—2442no—
601C22⋊C4—2442no—
602C22⋊C4—2442no—
603C22⋊C4—2442no—
604C22⋊C4—2442no—
605C22⋊C4—2442no—
606C42—42no—
607C42—2442no—
608C42—2442no—
609C42—2442no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—612no—
617C23—612no—
618C23—1221no—
619C23—1221no—
620C23—1221no—
621C23—1221no—
622C23—1221no—
623C23—1221no—
624C23—1221no—
625C23—1221no—
626C23—1221no—
627C23—1221no—
628C23—1221no—
629C23—1221no—
630C23—2444no—
631C23—2444no—
632C23—2444no—
633C23—2444no—
634C23—2444no—
635C23—2444no—
636C23—2444no—
637C23C4⋊C4×D6112yes—
638C23C2×D4×D6111yescharacteristic
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—612no—
658C2×C4—612no—
659C2×C4—1221no—
660C2×C4—1221no—
661C2×C4—1221no—
662C2×C4—1221no—
663C2×C4—1222no—
664C2×C4—1222no—
665C2×C4—1222no—
666C2×C4—1222no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—2444no—
672C2×C4—2444no—
673C2×C4—2444no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
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×C4—2441no—
686C2×C4C4⋊C4×D6112yes—
687C2×C4C22×C4×D6111yescharacteristic
688C2×C4C2×Q8×D6111yescharacteristic
689C2×C4#1451982211yescharacteristic
690C2×C4#1451982211yescharacteristic
691C2×C4#1451982311yescharacteristic
692C2×C4#1451982311yescharacteristic
693C8—22no—
694C8—22no—
695C8—1222no—
696C8—1222no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—1222no—
705C22—1222no—
706C22—1222no—
707C22—1222no—
708C22—1222no—
709C22—1222no—
710C22—24416no—
711C22—2441no—
712C22—2441no—
713C22—2441no—
714C22—2441no—
715C22—2441no—
716C22—2441no—
717C22—2441no—
718C22—2441no—
719C22C2×C4⋊C4×D6111yescharacteristic
720C22#1684032211yescharacteristic
721C22#1684032311yescharacteristic
722C22#1684055811yescharacteristic
723C22#1684055911yescharacteristic
724C22#1684055911yescharacteristic
725C22#1684056111yescharacteristic
726C4—22no—
727C4—81no—
728C4—81no—
729C4—81no—
730C4—81no—
731C4—1222no—
732C4—1222no—
733C4—4881no—
734C4—4881no—
735C4—4881no—
736C4—4881no—
737C4#1684023411yescharacteristic
738C4#1684023411yescharacteristic
739C4#1684038711yescharacteristic
740C4#1684038711yescharacteristic
741C2—42no—
742C2—2442no—
743C2—2442no—
744C2#2144843011yescharacteristic
745C2#2145440611yescharacteristic
746C2#2145440711yescharacteristic
747C2#2145665811yescharacteristic
748C2#2145665911yescharacteristic
749C2#2145666011yescharacteristic
750C2#2145666311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1854C2
socleC23×C61C22×D4
prime radicalC24×D61D4
cosocleC22×C4×C61C24
hypercenter#1854D61
hypocenterC61#21943
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
4. #21446021C2semidirect
5. #21446020C2semidirect
6. #21446019C2semidirect
7. #21446018C2semidirect
8. #21446017C2semidirect
9. #21446016C2semidirect
10. #21446015C2semidirect
11. #21445853C2semidirect
12. #21445851C2semidirect
13. #21445851C2semidirect
14. #21445849C2semidirect
15. C61×#1854C2semidirect
22. C2×#14519711C22semidirect
23. C2×#14519710C22semidirect
24. C2×#14519710C22semidirect
25. C2×#14519709C22semidirect
26. C2×#14519708C22semidirect
27. C2×#14519708C22semidirect
28. #16839724C4semidirect
47. #16839525C22semidirect
48. #16839525C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839524C22semidirect
54. C2×#107×C61C22semidirect
55. C2×#106×C61C22semidirect
58. C61×#340C22semidirect
59. C61×#340C22semidirect
376. #1854D61semidirect
401. C2×#107C2×D61semidirect
405. C2×#106C2×D61semidirect
433. #340C2×D61semidirect
434. #340C2×D61semidirect
435. C61#21943semidirect

Maximal subgroups

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

subgroupindex
C2×#168397242
#214482012
#214481982
#214460212
#214460202
#214460192
#214460182
#214460172
#214460162
#214460152
#214458532
#214458512
#214458492
C61×#18542
#2194361