Finite Group Databasebeta

← #29730698

Subgroups — #29730698

Order 15616.

980 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840157C211yesmaximal, characteristic
2C2×#16839981C211yesmaximal, characteristic
3C2×#16839972C211yesmaximal, characteristic, complemented
4C2×#16839967C211yesmaximal, characteristic
5#21450807C211yesmaximal, characteristic, complemented
6#21447141C211yesmaximal, characteristic, complemented
7#21447136C211yesmaximal, characteristic
8#21446918C211yesmaximal, characteristic, complemented
9#21446901C211yesmaximal, characteristic
10#21446742C211yesmaximal, characteristic, complemented
11#21446543C211yesmaximal, characteristic, complemented
12#21446160C211yesmaximal, characteristic, complemented
13#21446153C211yesmaximal, characteristic
14#21445652C211yesmaximal, characteristic, complemented
15C61×#2367C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C22×#11758202C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×#11758200C2211yescharacteristic
22C2×#14519777C2211yescharacteristic
23C2×#14519777C2211yescharacteristic
24C2×#14519777C2211yescharacteristic
25C2×C4×Dic122C2211yescharacteristic
26#16840157—24no—
27#16839981—24no—
28#16839972—24no—
29#16839967—24no—
30C2×C4⋊#92418C2211yescharacteristic
31C2×C4⋊#92418C2211yescharacteristic
32C2×C4⋊#92418C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×#14519688C2211yescharacteristic
42#16839694—21no—
43#16839694—21no—
44#16839668C2211yescharacteristic
45#16839668C2211yescharacteristic
46#16839661—21no—
47#16839661—21no—
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C2×#124×C61C2211yescharacteristic
53C2×C4×Q8×C61C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic
55C61×#391C2211yescharacteristic
56C61×#390C2211yescharacteristic
57C61×#388—21no—
58C61×#388—21no—
59C61×#385—21no—
60C4×C4⋊C4×C61C2211yescharacteristic
61C4×C4⋊C4×C61C2211yescharacteristic
62C4×C22⋊C4×C61—21no—
63C22×Dic122C2311yescharacteristic
64C22×Dic122C2311yescharacteristic
65C22×Dic122C2311yescharacteristic
66C2×#11758202—22no—
67C2×#11758202—22no—
68C2×#11758202—22no—
69C2×#11758202—22no—
70C2×#11758202—22no—
71C2×#11758202—22no—
72C2×#11758202—41no—
73C2×#11758202—41no—
74C2×#11758202—41no—
75C2×#11758200—22no—
76C2×#11758200—22no—
77C2×#11758200—22no—
78C2×#11758200—22no—
79C2×#11758200—22no—
80C2×#11758200—22no—
81C2×#11758200—41no—
82C2×#11758200—41no—
83C2×#11758200—41no—
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88#14519777—22no—
89#14519777—22no—
90#14519777—22no—
91#14519777—22no—
92#14519777—41no—
93#14519777—41no—
94C4×Dic122—22no—
95C4×Dic122—22no—
96C2×C4⋊Dic61—21no—
97C2×C4⋊Dic61—21no—
98C2×C4⋊Dic61—21no—
99C2×C4⋊Dic61—21no—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61—21no—
102C2×C4⋊Dic61C2311yescharacteristic
103C2×#11758196—21no—
104C2×C4×Dic61—21no—
105C4⋊#92418—22no—
106C4⋊#92418—22no—
107C4⋊#92418—22no—
108#14519701—22no—
109#14519700—22no—
110#14519700—22no—
111#14519700—22no—
112#14519700—41no—
113#14519700—41no—
114#14519700D414yes—
115#14519698—22no—
116#14519688—22no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121C22×Q8×C61C2311yescharacteristic
122C22×D4×C61C2311yescharacteristic
123C23×C4×C61—21no—
124#124×C61—22no—
125#124×C61D414yes—
126C4×Q8×C61—22no—
127C4×Q8×C61—41no—
128C4×D4×C61—22no—
129C4×D4×C61—41no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61D411yescharacteristic
132C2×C4⋊C4×C61D411yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C42×C61—21no—
141C2×C42×C61—21no—
142C2×C42×C61C2311yescharacteristic
143C2×C42×C61C2311yescharacteristic
144C2×C42×C61C2311yescharacteristic
145#95×C61—21no—
146#95×C61—21no—
147#95×C61—21no—
148#95×C61D411yescharacteristic
149#95×C61D411yescharacteristic
150C24×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61C2×D412yes—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61C2×D412yes—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—42no—
167C22×C4×C61—42no—
168C22×C4×C61—81no—
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2411yescharacteristic
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C2×Dic122—21no—
181C2×Dic122—21no—
182C2×Dic122—21no—
183C2×Dic122—21no—
184C2×Dic122—21no—
185C2×Dic122—21no—
186C2×Dic122—21no—
187C2×Dic122—21no—
188C2×Dic122—21no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122C2×D412yes—
198C4⋊C4×C61—22no—
199C4⋊C4×C61—22no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—42no—
204C4⋊C4×C61C2×D412yes—
205C22⋊C4×C61—24no—
206C22⋊C4×C61—24no—
207C22⋊C4×C61—42no—
208C22⋊C4×C61—42no—
209C22⋊C4×C61—81no—
210C42×C61—21no—
211C42×C61—21no—
212C42×C61—21no—
213C42×C61—21no—
214C42×C61—42no—
215C42×C61—81no—
216C42×C61C2×D412yes—
217C42×C61#4112yes—
218#11758202—44no—
219#11758202—44no—
220#11758202—44no—
221#11758200—44no—
222#11758200—44no—
223#11758200—44no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—42no—
227C4⋊Dic61—42no—
228C4⋊Dic61—42no—
229C4⋊Dic61—42no—
230C4⋊Dic61—42no—
231C4⋊Dic61—42no—
232#11758196—42no—
233C4×Dic61—42no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418C2×D412yes—
245C2×#92418#4112yes—
246C23×C61—22no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61C22×D411yescharacteristic
254Q8×C61—22no—
255Q8×C61—22no—
256Q8×C61—41no—
257Q8×C61—41no—
258D4×C61—22no—
259D4×C61—22no—
260D4×C61—41no—
261D4×C61—41no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—22no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—22no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—84no—
286C2×C4×C61#12112yes—
287C2×C4×C61#12112yes—
288C2×C4×C61#13712yes—
289C2×C4×C61#13712yes—
290C2×C4×C61C22×D411yescharacteristic
291C2×C4×C61C22×D411yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61H(5,𝔽2)11yescharacteristic
295C2×C4×C61H(5,𝔽2)11yescharacteristic
296C2×Dic61—22no—
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×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308Dic122—22no—
309Dic122—22no—
310Dic122—41no—
311Dic122—41no—
312Dic122—41no—
313Dic122—41no—
314Dic122—41no—
315Dic122—41no—
316Dic122—41no—
317Dic122—41no—
318Dic122—41no—
319Dic122—41no—
320#92418—22no—
321#92418—22no—
322#92418—41no—
323#92418—41no—
324#25382—611nomaximal, Sylow
325C22×C61—42no—
326C22×C61—42no—
327C22×C61—42no—
328C22×C61—81no—
329C22×C61—81no—
330C22×C61—81no—
331C22×C61—81no—
332C22×C61C2×#12111yescharacteristic
333C22×C61D4211yescharacteristic
334C22×C61#55011yescharacteristic
335C22×C61C2×#13711yescharacteristic
336C22×C61C2×#13711yescharacteristic
337C22×C61#57711yescharacteristic
338C22×C61#57811yescharacteristic
339C4×C61—22no—
340C4×C61—22no—
341C4×C61—22no—
342C4×C61—22no—
343C4×C61—42no—
344C4×C61—41no—
345C4×C61—42no—
346C4×C61—41no—
347C4×C61—81no—
348C4×C61#53211yescharacteristic
349C4×C61#54011yescharacteristic
350C4×C61D4211yescharacteristic
351C4×C61#54611yescharacteristic
352Dic61—42no—
353Dic61—81no—
354Dic61—81no—
355Dic61—81no—
356C2×#497—611no—
357C2×#464—611no—
358C2×#462—611no—
359C2×#461—611no—
360#2546—611no—
361#2367D6111yescharacteristic
362#2056—611no—
363#2055—611no—
364#2016—611no—
365#2013—611no—
366#1981—611no—
367#1940—611no—
368#1878—611no—
369#1877—611no—
370#1763—611no—
371C2×C61—82no—
372C2×C61#242811yescharacteristic
373C2×C61#303911yescharacteristic
374C2×C61#304611yescharacteristic
375C2×C61#326611yescharacteristic
376C2×C61#327011yescharacteristic
377C2×C61#339811yescharacteristic
378C2×C61#340011yescharacteristic
379C22×Q16—611no—
380C22×Q16—611no—
381C22×Q16—611no—
382C22×SD16—611no—
383C22×SD16—611no—
384C22×SD16—611no—
385C2×C4⋊Q8—611no—
386C2×C4⋊Q8—611no—
387C2×C4⋊Q8—611no—
388C2×#124C2×D6111yescharacteristic
389C2×C4×Q8—611no—
390C2×C4×Q8C2×D6111yescharacteristic
391C2×C4×D4C2×D6111yescharacteristic
392#497—1224no—
393#464—1224no—
394#462—1224no—
395#461—1224no—
396C2×C4⋊C8—611no—
397C2×C4⋊C8—611no—
398C2×C4⋊C8—611no—
399C2×#103—611no—
400C2×#103—611no—
401C2×#103—611no—
402C2×#103—611no—
403C2×#103—611no—
404C2×#103—611no—
405C2×#103—611no—
406C2×#102—611no—
407C2×#97—611no—
408#398—1221no—
409#398—1221no—
410#391—611no—
411#391—611no—
412#391C2×D6111yescharacteristic
413#390C2×D6111yescharacteristic
414#389—1221no—
415#389—1221no—
416#388—21no—
417#388—21no—
418#385—21no—
419C4×C4⋊C4C2×D6111yescharacteristic
420C4×C4⋊C4C2×D6111yescharacteristic
421C4×C22⋊C4—21no—
422#340—611no—
423#340—611no—
424#336—611no—
425#336—611no—
426C61#2538211yescharacteristic, complemented, Sylow
427C22×Q8—611no—
428C22×Q8—611no—
429C22×Q8—611no—
430C22×Q8C22×D6111yescharacteristic
431C22×D4C22×D6111yescharacteristic
432C23×C4—21no—
433C2×Q16—1222no—
434C2×Q16—1222no—
435C2×Q16—1222no—
436C2×Q16—1222no—
437C2×Q16—1222no—
438C2×Q16—1222no—
439C2×Q16—2441no—
440C2×Q16—2441no—
441C2×Q16—2441no—
442C2×SD16—1222no—
443C2×SD16—1222no—
444C2×SD16—1222no—
445C2×SD16—1222no—
446C2×SD16—1222no—
447C2×SD16—1222no—
448C2×SD16—2441no—
449C2×SD16—2441no—
450C2×SD16—2441no—
451C22×C8—611no—
452C22×C8—611no—
453C22×C8—611no—
454C22×C8—611no—
455C4⋊Q8—1222no—
456C4⋊Q8—1222no—
457C4⋊Q8—1222no—
458C4⋊Q8—1222no—
459C4⋊Q8—2441no—
460C4⋊Q8—2441no—
461#124—22no—
462#124D24414yes—
463C4×Q8—22no—
464C4×Q8—41no—
465C4×Q8—1222no—
466C4×Q8—1222no—
467C4×D4—22no—
468C4×D4—41no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—1221no—
472C2×C4⋊C4—1221no—
473C2×C4⋊C4—1221no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4—1221no—
477C2×C4⋊C4—1221no—
478C2×C4⋊C4C22⋊D6111yescharacteristic
479C2×C4⋊C4C22⋊D6111yescharacteristic
480C2×C4⋊C4C22×D6111yescharacteristic
481C2×C4⋊C4C22×D6111yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C42—21no—
488C2×C42—21no—
489C2×C42—1221no—
490C2×C42C22×D6111yescharacteristic
491C2×C42C22×D6111yescharacteristic
492C2×C42C22×D6111yescharacteristic
493C4⋊C8—1222no—
494C4⋊C8—1222no—
495C4⋊C8—1222no—
496#103—614no—
497#103—1222no—
498#103—1222no—
499#103—1222no—
500#103—1222no—
501#103—2441no—
502#103—2441no—
503#102—1222no—
504#97—1222no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—1221no—
509#95—1221no—
510#95—1221no—
511#95—1221no—
512#95C22⋊D6111yescharacteristic
513#95C22⋊D6111yescharacteristic
514C24—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—612no—
521C2×Q8—1221no—
522C2×Q8—1221no—
523C2×Q8—1221no—
524C2×Q8—1221no—
525C2×Q8—1221no—
526C2×Q8—1221no—
527C2×Q8—1221no—
528C2×Q8—1221no—
529C2×Q8—1221no—
530C2×Q8—1221no—
531C2×Q8—1221no—
532C2×Q8—1221no—
533C2×Q8—1221no—
534C2×Q8—1221no—
535C2×Q8—1221no—
536C2×Q8—1221no—
537C2×Q8—1221no—
538C2×Q8C2×D24412yes—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4C2×D24412yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—81no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4C2×C22⋊D6111yescharacteristic
556C22×C4C2×C22⋊D6111yescharacteristic
557C22×C4C2×C22⋊D6111yescharacteristic
558C22×C4C2×C22⋊D6111yescharacteristic
559C22×C4C2×C22⋊D6111yescharacteristic
560C22×C4C2×C22⋊D6111yescharacteristic
561C22×C4C23×D6111yescharacteristic
562Q16—2444no—
563Q16—2444no—
564Q16—2444no—
565SD16—2444no—
566SD16—2444no—
567SD16—2444no—
568C2×C8—612no—
569C2×C8—612no—
570C2×C8—1221no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C4⋊C4—21no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—42no—
586C4⋊C4—1221no—
587C4⋊C4—1221no—
588C4⋊C4—2442no—
589C4⋊C4—2442no—
590C4⋊C4—2442no—
591C4⋊C4—2442no—
592C4⋊C4—2442no—
593C4⋊C4—2442no—
594C4⋊C4—2442no—
595C4⋊C4D4×D6112yes—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—81no—
601C42—21no—
602C42—21no—
603C42—21no—
604C42—21no—
605C42—42no—
606C42—81no—
607C42—2442no—
608C42C2×D24412yes—
609C42#1175822212yes—
610C23—22no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23C22×C22⋊D6111yescharacteristic
618Q8—22no—
619Q8—22no—
620Q8—41no—
621Q8—41no—
622Q8—1222no—
623Q8—1222no—
624Q8—2441no—
625Q8—2441no—
626Q8—2441no—
627Q8—2441no—
628Q8—2441no—
629Q8—2441no—
630Q8—2441no—
631Q8—2441no—
632Q8—2441no—
633Q8—2441no—
634D4—22no—
635D4—22no—
636D4—41no—
637D4—41no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
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—1222no—
663C2×C4—2441no—
664C2×C4—2441no—
665C2×C4—2441no—
666C2×C4—2441no—
667C2×C4—2441no—
668C2×C4—2441no—
669C2×C4—2441no—
670C2×C4—2441no—
671C2×C4—2441no—
672C2×C4—2441no—
673C2×C4—2441no—
674C2×C4#1451975112yes—
675C2×C4#1451975112yes—
676C2×C4#1451980712yes—
677C2×C4#1451980712yes—
678C2×C4C2×D4×D6111yescharacteristic
679C2×C4C22×D24411yescharacteristic
680C2×C4#41×D6111yescharacteristic
681C2×C4C2×#1175822211yescharacteristic
682C2×C4#1451982211yescharacteristic
683C2×C4#1451982311yescharacteristic
684C8—1222no—
685C8—1222no—
686C8—2441no—
687C8—2441no—
688C22—42no—
689C22—42no—
690C22—42no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22C2×#1451975111yescharacteristic
696C22D4×C22⋊D6111yescharacteristic
697C22#1684043111yescharacteristic
698C22C2×#1451980711yescharacteristic
699C22C2×#1451980711yescharacteristic
700C22#1684057311yescharacteristic
701C22#1684057711yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—41no—
707C4—42no—
708C4—42no—
709C4—41no—
710C4—81no—
711C4—4881no—
712C4—4881no—
713C4—4881no—
714C4—2442no—
715C4#1684030911yescharacteristic
716C4#1684036311yescharacteristic
717C4D4×D24411yescharacteristic
718C4#1684040711yescharacteristic
719C2—82no—
720C2#2144940111yescharacteristic
721C2#2145530611yescharacteristic
722C2#2145536911yescharacteristic
723C2#2145732511yescharacteristic
724C2#2145738511yescharacteristic
725C2#2145885011yescharacteristic
726C2#2145887211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2367C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
hypercenter#2367D61
hypocenterC61#25382
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2367

Complements

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

NH ≅ G/Ntype
3. C2×#16839972C2semidirect
5. #21450807C2semidirect
6. #21447141C2semidirect
8. #21446918C2semidirect
10. #21446742C2semidirect
11. #21446543C2semidirect
12. #21446160C2semidirect
14. #21445652C2semidirect
426. C61#25382semidirect

Maximal subgroups

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

subgroupindex
C2×#168401572
C2×#168399812
C2×#168399722
C2×#168399672
#214508072
#214471412
#214471362
#214469182
#214469012
#214467422
#214465432
#214461602
#214461532
#214456522
C61×#23672
#2538261