Finite Group Databasebeta

← #29718815

Subgroups — #29718815

Order 15616.

986 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839905C211yesmaximal, characteristic
2C2×#16839823C211yesmaximal, characteristic, complemented
3#21448407C211yesmaximal, characteristic, complemented
4#21447211C211yesmaximal, characteristic, complemented
5#21447204C211yesmaximal, characteristic, complemented
6#21447136C211yesmaximal, characteristic, complemented
7#21447129C211yesmaximal, characteristic, complemented
8#21446699C211yesmaximal, characteristic, complemented
9#21446684C211yesmaximal, characteristic, complemented
10#21446515C211yesmaximal, characteristic, complemented
11#21446494C211yesmaximal, characteristic, complemented
12#21446137C211yesmaximal, characteristic, complemented
13#21446006C211yesmaximal, characteristic, complemented
14#21445757C211yesmaximal, characteristic, complemented
15C61×#2624C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20#16839905—24no—
21#16839823—24no—
22C2×#14519710C2211yescharacteristic
23C2×#14519710C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519700C2211yescharacteristic
27C2×#14519700C2211yescharacteristic
28C2×#14519700C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×#14519688C2211yescharacteristic
37C2×C4×#92418C2211yescharacteristic
38#16839668C2211yescharacteristic
39#16839668C2211yescharacteristic
40#16839664C2211yescharacteristic
41#16839664C2211yescharacteristic
42#16839639—21no—
43#16839639—21no—
44#16839619—21no—
45#16839619—21no—
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50C2×#121×C61C2211yescharacteristic
51C2×#117×C61C2211yescharacteristic
52C61×#399—21no—
53C61×#397—21no—
54C61×#394—21no—
55C61×#394—21no—
56C61×#390C2211yescharacteristic
57C61×#390C2211yescharacteristic
58C61×#389C2211yescharacteristic
59C61×#389C2211yescharacteristic
60C61×#380C2211yescharacteristic
61C2×#11758222—22no—
62C2×#11758222—22no—
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C22×Dic122C2311yescharacteristic
68C22×D244C2311yescharacteristic
69C22×C22⋊D61—21no—
70C23×Dic61—21no—
71C22×C4×D61—21no—
72C2×#11758200—22no—
73C2×#11758200—22no—
74C2×#11758200—41no—
75C2×#11758199—22no—
76C2×#11758199—22no—
77C2×#11758199—41no—
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61—41no—
84C2×C4⋊Dic61—41no—
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91#14519710—41no—
92#14519710—41no—
93C4⋊#92418—22no—
94C4⋊#92418—22no—
95#14519700—22no—
96#14519700—22no—
97#14519700—41no—
98#14519698—41no—
99#14519698—41no—
100#14519697—22no—
101#14519697—22no—
102#14519697—41no—
103C22⋊#92418—22no—
104C22⋊#92418D414yes—
105#14519688—22no—
106C4×#92418—22no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111C22×D4×C61—21no—
112C22×D4×C61C2311yescharacteristic
113C23×C4×C61C2311yescharacteristic
114#121×C61—22no—
115#121×C61—22no—
116#117×C61—22no—
117#117×C61—22no—
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61D411yescharacteristic
121C2×C4⋊C4×C61D411yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61D411yescharacteristic
132C2×C22⋊C4×C61D411yescharacteristic
133C2×C42×C61C2311yescharacteristic
134C2×C42×C61C2311yescharacteristic
135#95×C61—21no—
136#95×C61—21no—
137#95×C61—21no—
138C24×C61—21no—
139C24×C61C2×D411yescharacteristic
140C23×D61—21no—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—42no—
148C2×D4×C61—81no—
149C2×D4×C61—81no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D412yes—
163C22×C4×C61#4112yes—
164C22×C4×C61C2411yescharacteristic
165C2×C22⋊D61—24no—
166C2×C22⋊D61—42no—
167C2×C22⋊D61—42no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—42no—
172C22×Dic61—81no—
173C22×Dic61—81no—
174#11758222—44no—
175#11758222—44no—
176#11758222—44no—
177#11758222—44no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244#4112yes—
184C2×C4×D61—24no—
185C2×C4×D61—42no—
186C2×C4×D61—42no—
187C2×Dic122—21no—
188C2×Dic122—21no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122#4112yes—
193C4⋊C4×C61—22no—
194C4⋊C4×C61—22no—
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—81no—
202C4⋊C4×C61—81no—
203C22⋊C4×C61—22no—
204C22⋊C4×C61—22no—
205C22⋊C4×C61—42no—
206C22⋊C4×C61—81no—
207C22⋊C4×C61—81no—
208C22⋊C4×C61—81no—
209C22⋊C4×C61—81no—
210C22⋊C4×C61—81no—
211C42×C61—21no—
212C42×C61—21no—
213C42×C61—21no—
214C42×C61—21no—
215#11758200—44no—
216#11758199—44no—
217#11758198—81no—
218#11758198—81no—
219#11758198—81no—
220#11758198—81no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—42no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418C2×D412yes—
237C2×#92418C2×D412yes—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61#12112yes—
252C23×C61C22×D411yescharacteristic
253C22×D61—22no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260D4×C61—41no—
261D4×C61—41no—
262D4×C61—41no—
263D4×C61—41no—
264D4×C61—84no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61#12112yes—
293C2×C4×C61C22×D411yescharacteristic
294C2×C4×C61C2×#4111yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C2×C4×C61C2×#4111yescharacteristic
297C2×C4×C61H(5,𝔽2)11yescharacteristic
298C2×C4×C61H(5,𝔽2)11yescharacteristic
299C22⋊D61—48no—
300C2×Dic61—22no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—84no—
310D244—22no—
311D244—22no—
312D244—41no—
313D244—41no—
314C4×D61—48no—
315Dic122—22no—
316Dic122—22no—
317Dic122—41no—
318Dic122—41no—
319#92418—22no—
320#92418—22no—
321#92418—41no—
322#92418—41no—
323#24513—611nomaximal, Sylow
324C22×C61—22no—
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—81no—
332C22×C61—81no—
333C22×C61—81no—
334C22×C61—81no—
335C22×C61—81no—
336C22×C61—81no—
337C22×C61—81no—
338C22×C61C2×#12111yescharacteristic
339C22×C61#52511yescharacteristic
340C22×C61#53511yescharacteristic
341C22×C61#57611yescharacteristic
342C22×C61#57611yescharacteristic
343C22×C61#57711yescharacteristic
344C22×C61#57811yescharacteristic
345C2×D61—42no—
346C2×D61—42no—
347C2×D61—42no—
348C2×D61—81no—
349C2×D61—81no—
350C2×D61—81no—
351C2×D61—81no—
352C4×C61—22no—
353C4×C61—41no—
354C4×C61—41no—
355C4×C61—41no—
356C4×C61—41no—
357C4×C61—81no—
358C4×C61—81no—
359C4×C61—81no—
360C4×C61#54611yescharacteristic
361C4×C61#54611yescharacteristic
362C4×C61#55111yescharacteristic
363C4×C61#55111yescharacteristic
364Dic61—42no—
365Dic61—81no—
366Dic61—81no—
367C2×#449—611no—
368C2×#433—611no—
369#2624D6111yescharacteristic, complemented
370#2311—611no—
371#2068—611no—
372#2067—611no—
373#2055—611no—
374#2054—611no—
375#1973—611no—
376#1970—611no—
377#1936—611no—
378#1933—611no—
379#1874—611no—
380#1852—611no—
381#1788—611no—
382C2×C61—42no—
383C2×C61—161no—
384C2×C61#241111yescharacteristic
385C2×C61#306111yescharacteristic
386C2×C61#306211yescharacteristic
387C2×C61#311911yescharacteristic
388C2×C61#312411yescharacteristic
389C2×C61#322011yescharacteristic
390C2×C61#322511yescharacteristic
391D61—82no—
392C22×#41—611no—
393C22×SD16—611no—
394C22×D8—611no—
395C2×#121C2×D6111yescharacteristic
396C2×#117C2×D6111yescharacteristic
397C22×C4⋊C4—611no—
398#449—1224no—
399#433—1224no—
400C2×#107—611no—
401C2×#107—611no—
402C2×C4⋊C8—611no—
403C2×C4⋊C8—611no—
404C2×#103—611no—
405C2×#103—611no—
406C2×#103—611no—
407C2×#102—611no—
408C2×#102—611no—
409C2×#102—611no—
410C2×#102—611no—
411C2×#102—611no—
412C2×C22⋊C8—611no—
413C2×C22⋊C8—611no—
414C2×#97—611no—
415C2×C4×C8—611no—
416#399—21no—
417#397—21no—
418#394—21no—
419#394—21no—
420#391—611no—
421#391—611no—
422#390—611no—
423#390—611no—
424#390C2×D6111yescharacteristic
425#390C2×D6111yescharacteristic
426#389C2×D6111yescharacteristic
427#389C2×D6111yescharacteristic
428#386—1221no—
429#386—1221no—
430#380—1221no—
431#380—1221no—
432#380C2×D6111yescharacteristic
433#340—611no—
434#340—611no—
435#340—611no—
436#340—611no—
437C61#2451311yescharacteristic, complemented, Sylow
438C2×#41—1222no—
439C2×#41—1222no—
440C2×#41—1222no—
441C2×#41—1222no—
442C2×#41—2441no—
443C2×#41—2441no—
444C22×Q8—611no—
445C22×D4—21no—
446C22×D4—611no—
447C22×D4—1221no—
448C22×D4C22×D6111yescharacteristic
449C23×C4—1221no—
450C23×C4—1221no—
451C23×C4C22×D6111yescharacteristic
452C2×SD16—1222no—
453C2×SD16—1222no—
454C2×SD16—2441no—
455C2×D8—1222no—
456C2×D8—1222no—
457C2×D8—2441no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8—611no—
461C22×C8—611no—
462#121—22no—
463#121—22no—
464#117—22no—
465#117—22no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—1221no—
471C2×C4⋊C4—2441no—
472C2×C4⋊C4—2441no—
473C2×C4⋊C4C22⋊D6111yescharacteristic
474C2×C4⋊C4C22⋊D6111yescharacteristic
475C2×C4⋊C4C22×D6111yescharacteristic
476C2×C4⋊C4C22×D6111yescharacteristic
477C2×C4⋊C4C22×D6111yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—1221no—
485C2×C22⋊C4—1221no—
486C2×C22⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4C22⋊D6111yescharacteristic
489C2×C22⋊C4C22⋊D6111yescharacteristic
490C2×C42C22×D6111yescharacteristic
491C2×C42C22×D6111yescharacteristic
492#107—2441no—
493#107—2441no—
494C4⋊C8—1222no—
495C4⋊C8—1222no—
496#103—1222no—
497#103—1222no—
498#103—2441no—
499#102—1222no—
500#102—1222no—
501#102—2441no—
502#102—2441no—
503#102—2441no—
504C22⋊C8—614no—
505C22⋊C8—1222no—
506#97—1222no—
507C4×C8—1222no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—1221no—
512#95—1221no—
513#95—1221no—
514#95—1221no—
515C24—21no—
516C24—1221no—
517C24C2×C22⋊D6111yescharacteristic
518#41—2444no—
519#41—2444no—
520#41—2444no—
521#41—2444no—
522C2×Q8—612no—
523C2×Q8—1221no—
524C2×Q8—1221no—
525C2×Q8—1221no—
526C2×Q8—1221no—
527C2×Q8—1221no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—42no—
535C2×D4—81no—
536C2×D4—81no—
537C2×D4—612no—
538C2×D4—1224no—
539C2×D4—1221no—
540C2×D4—1221no—
541C2×D4—1221no—
542C2×D4—1221no—
543C2×D4—1221no—
544C2×D4—2442no—
545C2×D4—2442no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—1224no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—4881no—
558C22×C4—4881no—
559C22×C4—2442no—
560C22×C4—2442no—
561C22×C4—2442no—
562C22×C4D4×D6112yes—
563C22×C4#1175822412yes—
564C22×C4C2×C22⋊D6111yescharacteristic
565C22×C4C2×C22⋊D6111yescharacteristic
566C22×C4C2×C22⋊D6111yescharacteristic
567C22×C4C2×C22⋊D6111yescharacteristic
568C22×C4C2×C22⋊D6111yescharacteristic
569C22×C4C23×D6111yescharacteristic
570SD16—2444no—
571D8—2444no—
572C2×C8—612no—
573C2×C8—612no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—81no—
593C4⋊C4—81no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—2442no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—42no—
602C22⋊C4—81no—
603C22⋊C4—81no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C22⋊C4—4881no—
608C22⋊C4—4881no—
609C22⋊C4—4881no—
610C22⋊C4—4881no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—1222no—
629C23—2441no—
630C23—2441no—
631C23—2441no—
632C23—2441no—
633C23—2441no—
634C23—2441no—
635C23#1451974912yes—
636C23C22×C22⋊D6111yescharacteristic
637Q8—1222no—
638Q8—1222no—
639Q8—2441no—
640Q8—2441no—
641D4—41no—
642D4—41no—
643D4—41no—
644D4—41no—
645D4—84no—
646D4—1222no—
647D4—1222no—
648D4—2448no—
649D4—2441no—
650D4—2441no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—1222no—
679C2×C4—4884no—
680C2×C4—2448no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4#1451974912yes—
690C2×C4C2×D4×D6111yescharacteristic
691C2×C4#41×D6111yescharacteristic
692C2×C4#41×D6111yescharacteristic
693C2×C4C2×#1175822411yescharacteristic
694C2×C4#1451982311yescharacteristic
695C2×C4#1451982311yescharacteristic
696C8—1222no—
697C8—1222no—
698C8—2441no—
699C8—2441no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—4881no—
715C22—4881no—
716C22—4881no—
717C22—4881no—
718C22—2442no—
719C22—2442no—
720C22—2442no—
721C22C2×#1451974911yescharacteristic
722C22#1684026911yescharacteristic
723C22#1684032611yescharacteristic
724C22#1684056511yescharacteristic
725C22#1684056511yescharacteristic
726C22#1684057311yescharacteristic
727C22#1684057711yescharacteristic
728C4—22no—
729C4—41no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—81no—
734C4—81no—
735C4—81no—
736C4—4881no—
737C4—4881no—
738C4—2442no—
739C4#1684040411yescharacteristic
740C4#1684040411yescharacteristic
741C4#1684043511yescharacteristic
742C4#1684043511yescharacteristic
743C2—42no—
744C2—161no—
745C2—4882no—
746C2#2144920511yescharacteristic
747C2#2145548611yescharacteristic
748C2#2145549511yescharacteristic
749C2#2145601211yescharacteristic
750C2#2145607511yescharacteristic
751C2#2145686311yescharacteristic
752C2#2145692211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2624C2
socleC23×C61C22×D4
prime radicalC2×#16839905C2
hypercenter#2624D61
hypocenterC61#24513
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2624

Complements

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

NH ≅ G/Ntype
2. C2×#16839823C2semidirect
3. #21448407C2semidirect
4. #21447211C2semidirect
5. #21447204C2semidirect
6. #21447136C2semidirect
7. #21447129C2semidirect
8. #21446699C2semidirect
9. #21446684C2semidirect
10. #21446515C2semidirect
11. #21446494C2semidirect
12. #21446137C2semidirect
13. #21446006C2semidirect
14. #21445757C2semidirect
15. C61×#2624C2semidirect
369. #2624D61semidirect
437. C61#24513semidirect

Maximal subgroups

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

subgroupindex
C2×#168399052
C2×#168398232
#214484072
#214472112
#214472042
#214471362
#214471292
#214466992
#214466842
#214465152
#214464942
#214461372
#214460062
#214457572
C61×#26242
#2451361