Finite Group Databasebeta

← #29685766

Subgroups — #29685766

Order 15616.

1476 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840242C211yesmaximal, characteristic, complemented
2C2×#16839909C211yesmaximal, characteristic
3C2×#16839864C211yesmaximal, characteristic, complemented
4C2×C4×D488C211yesmaximal, characteristic, complemented
5#21448512C211yesmaximal, characteristic, complemented
6#21446173C211yesmaximal, characteristic, complemented
7#21446166C211yesmaximal, characteristic, complemented
8#21446134C211yesmaximal, characteristic, complemented
9#21446076C211yesmaximal, characteristic, complemented
10#21446069C211yesmaximal, characteristic, complemented
11#21446009C211yesmaximal, characteristic, complemented
12#21445760C211yesmaximal, characteristic, complemented
13#21445645C211yesmaximal, characteristic, complemented
14C4×#14519702C211yesmaximal, characteristic, complemented
15C61×#1750C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758190C2211yescharacteristic
18C22×D488C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20#16840242—24no—
21#16840242—24no—
22C2×C4×Dic122C2211yescharacteristic
23C2×C4×Dic122C2211yescharacteristic
24C2×C4×D244C2211yescharacteristic
25C2×C4×D244C2211yescharacteristic
26C2×C4×D244C2211yescharacteristic
27C2×#14519737—21no—
28C2×#14519737—21no—
29C2×#14519735—21no—
30C22×C4⋊Dic61C2211yescharacteristic
31C2×C4⋊C4×D61—21no—
32#16839909C418yescomplemented
33#16839864—24no—
34C4×D488—24no—
35C2×#14519711C2211yescharacteristic
36C2×#14519711C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519702C2211yescharacteristic
39C2×#14519702C2211yescharacteristic
40C2×#14519699C2211yescharacteristic
41C2×#14519699C2211yescharacteristic
42C2×#14519699C2211yescharacteristic
43C2×#14519699C2211yescharacteristic
44C2×#14519699C2211yescharacteristic
45#16839664C2211yescharacteristic
46#16839662—21no—
47#16839660C2211yescharacteristic
48#16839652—21no—
49#16839638—21no—
50#16839633—21no—
51#16839622C2211yescharacteristic
52C4×C4⋊Dic61C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839525C2211yescharacteristic
55#16839525C2211yescharacteristic
56#16839525C2211yescharacteristic
57C2×#117×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×#97×C61C2211yescharacteristic
61C2×C4×C8×C61C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C61×#336C2211yescharacteristic
64C2×#11758222—22no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—22no—
68C2×#11758222—22no—
69C2×#11758222C2×C414yescomplemented
70C22×Dic122C2311yescharacteristic
71C22×D244C2311yescharacteristic
72C22×D244C2311yescharacteristic
73C22×C22⋊D61—21no—
74C22×C22⋊D61—21no—
75C23×Dic61—21no—
76C22×C4×D61—21no—
77C22×C4×D61—21no—
78C22×C4×D61—21no—
79C22×C4×D61—21no—
80C2×#11758190—22no—
81C2×#11758190—22no—
82C2×#11758190C2×C414yescomplemented
83C2×D488—22no—
84C2×D488—22no—
85C2×D488C2×C414yescomplemented
86#14519751—22no—
87#14519751C2×C414yescomplemented
88C4×Dic122—22no—
89C4×Dic122—22no—
90C4×Dic122—22no—
91C4×Dic122D414yescomplemented
92C4×D244—22no—
93C4×D244—22no—
94C4×D244—22no—
95C4×D244—22no—
96C4×D244—22no—
97C4×D244D414yescomplemented
98#14519737—28no—
99#14519737—28no—
100#14519735—28no—
101C2×C4⋊Dic61—21no—
102C2×C4⋊Dic61—22no—
103C2×C4⋊Dic61—22no—
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×C4⋊Dic61C2311yescharacteristic
108C2×C4⋊Dic61C2311yescharacteristic
109C2×#11758196—21no—
110C2×#11758196—21no—
111C2×#11758196—21no—
112C4⋊C4×D61—28no—
113C2×C22⋊Dic61—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61—21no—
123#14519711—22no—
124#14519711—22no—
125#14519702—22no—
126#14519702—22no—
127#14519702C2×C414yescomplemented
128#14519699—22no—
129#14519699—22no—
130#14519699—22no—
131#14519699—22no—
132#14519699C2×C414yescomplemented
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136C23×C4×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138C22×C8×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141#117×C61—22no—
142#117×C61—22no—
143C2×C4⋊C4×C61D411yescharacteristic
144C2×C4⋊C4×C61D411yescharacteristic
145C2×C22⋊C4×C61D411yescharacteristic
146C2×C22⋊C4×C61D411yescharacteristic
147C2×C42×C61C2311yescharacteristic
148C2×C42×C61C2311yescharacteristic
149C22⋊C8×C61—22no—
150C22⋊C8×C61C2×C414yescomplemented
151#97×C61—22no—
152C4×C8×C61—22no—
153C24×C61C2×D411yescharacteristic
154C23×D61—21no—
155C23×D61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61C22×C412yes—
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61#4112yes—
167C22×C4×C61C2411yescharacteristic
168C2×C22⋊D61—24no—
169C2×C22⋊D61—24no—
170C2×C22⋊D61—24no—
171C2×C22⋊D61—24no—
172C2×C22⋊D61—81no—
173C2×C22⋊D61—81no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—24no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—81no—
182C22×Dic61—81no—
183#11758222—28no—
184#11758222—28no—
185#11758222—28no—
186#11758222—28no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244C22×C412yes—
196C2×D244C22×C412yes—
197C2×D244C2×D412yes—
198C2×D244#4112yes—
199C2×C4×D61—24no—
200C2×C4×D61—24no—
201C2×C4×D61—24no—
202C2×C4×D61—24no—
203C2×C4×D61—24no—
204C2×C4×D61—42no—
205C2×C4×D61—81no—
206C2×C4×D61—81no—
207C2×C4×D61—81no—
208C2×C4×D61—81no—
209C2×C4×D61—81no—
210C2×C4×D61—81no—
211C2×Dic122—21no—
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122C22×C412yes—
215C2×Dic122C2×D412yes—
216C2×Dic122#4112yes—
217C2×C8×C61—21no—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C2×C8×C61C22×C412yes—
228C2×C8×C61C22×C412yes—
229C4⋊C4×C61—22no—
230C4⋊C4×C61—22no—
231C22⋊C4×C61—22no—
232C22⋊C4×C61—22no—
233C42×C61—21no—
234C42×C61—21no—
235C42×C61C2×D412yes—
236C42×C61C2×D412yes—
237C22⋊Dic61—81no—
238#11758198—24no—
239#11758198—24no—
240#11758198—24no—
241#11758198—42no—
242#11758198—81no—
243#11758198—81no—
244C4⋊Dic61—24no—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61C22×C412yes—
253C4⋊Dic61C2×D412yes—
254C4⋊Dic61C2×D412yes—
255#11758196—24no—
256#11758196—24no—
257#11758196—81no—
258C4×Dic61—24no—
259C4×Dic61—24no—
260C4×Dic61—81no—
261D488—28no—
262#11758190—28no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61C4×D412yes—
270C23×C61C22×D411yescharacteristic
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61C4×D412yes—
302C2×C4×C61#12012yes—
303C2×C4×C61#12012yes—
304C2×C4×C61C23×C411yescharacteristic
305C2×C4×C61C22×D411yescharacteristic
306C2×C4×C61C22×D411yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C2×C4×C61C2×#4111yescharacteristic
309C2×C4×C61C2×#4111yescharacteristic
310C22⋊D61—216no—
311C22⋊D61—84no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—84no—
331D244—22no—
332D244—22no—
333D244—22no—
334D244—22no—
335D244—22no—
336D244—41no—
337D244—41no—
338D244C4×D414yes—
339C4×D61—216no—
340C4×D61—84no—
341C4×D61—84no—
342C4×D61—84no—
343Dic122—22no—
344Dic122—22no—
345Dic122—22no—
346Dic122C4×D414yes—
347C8×C61—22no—
348C8×C61—22no—
349C8×C61—41no—
350C8×C61—41no—
351#21460—611nomaximal, Sylow
352C22×C61—22no—
353C22×C61—22no—
354C22×C61—22no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61C2×C4×D411yescharacteristic
360C22×C61C2×#12011yescharacteristic
361C22×C61#52511yescharacteristic
362C22×C61#57611yescharacteristic
363C22×C61#57611yescharacteristic
364C22×C61#57711yescharacteristic
365C22×C61#57811yescharacteristic
366C2×D61—24no—
367C2×D61—42no—
368C2×D61—42no—
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—42no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—81no—
377C2×D61—81no—
378C2×D61—81no—
379C2×D61—81no—
380C4×C61—22no—
381C4×C61—22no—
382C4×C61—22no—
383C4×C61—41no—
384C4×C61—41no—
385C4×C61C2×C4×D411yescharacteristic
386C4×C61C2×C4×D411yescharacteristic
387C4×C61#52511yescharacteristic
388C4×C61#52511yescharacteristic
389Dic61—24no—
390Dic61—42no—
391Dic61—42no—
392Dic61—42no—
393Dic61—81no—
394Dic61—81no—
395C2×#520—611no—
396C2×#449—611no—
397C2×#440—611no—
398C2×C4×D8—611no—
399#2324—611no—
400#1880—611no—
401#1879—611no—
402#1874—611no—
403#1863—611no—
404#1862—611no—
405#1852—611no—
406#1788—611no—
407#1762—611no—
408C4×#103—611no—
409#1750D6111yescharacteristic, complemented
410C2×C61—42no—
411C2×C61C4×#12011yescharacteristic
412C2×C61#294611yescharacteristic
413C2×C61#295111yescharacteristic
414C2×C61#300811yescharacteristic
415C2×C61#301311yescharacteristic
416C2×C61#311911yescharacteristic
417C2×C61#312411yescharacteristic
418D61—44no—
419D61—82no—
420C22×#41—611no—
421C22×SD16—611no—
422C22×D8—611no—
423C2×#121—611no—
424#520—1224no—
425#520—1224no—
426C2×C4×Q8—611no—
427C2×C4×Q8—611no—
428C2×C4×D4—611no—
429C2×C4×D4—611no—
430C2×C4×D4—611no—
431C2×C4×D4—1221no—
432C2×C4×D4—1221no—
433C2×#117—1221no—
434C2×#117C2×D6111yescharacteristic
435C22×C4⋊C4—611no—
436C22×C4⋊C4—1221no—
437#449—618no—
438#440—1224no—
439C4×D8—1224no—
440C2×#107—611no—
441C2×#107—611no—
442C2×#103—611no—
443C2×#103—611no—
444C2×#103—611no—
445C2×#102—611no—
446C2×#102—611no—
447C2×#102—611no—
448C2×#102—611no—
449C2×#102—611no—
450C2×C22⋊C8C2×D6111yescharacteristic
451C2×C22⋊C8C2×D6111yescharacteristic
452C2×#97C2×D6111yescharacteristic
453C2×C4×C8C2×D6111yescharacteristic
454#390—611no—
455#390—1221no—
456#389—611no—
457#388—1221no—
458#386—1221no—
459#385—1221no—
460#380—611no—
461C4×C4⋊C4—611no—
462#340—611no—
463#340—611no—
464#340—611no—
465#340—611no—
466#336C2×D6111yescharacteristic
467#336C2×D6111yescharacteristic
468C61#2146011yescharacteristic, complemented, Sylow
469C2×#41—614no—
470C2×#41—1222no—
471C2×#41—1222no—
472C2×#41—1222no—
473C2×#41—1222no—
474C2×#41—1222no—
475C22×Q8—611no—
476C22×D4—611no—
477C22×D4—611no—
478C22×D4—1221no—
479C22×D4—1221no—
480C23×C4—1221no—
481C23×C4—1221no—
482C23×C4—1221no—
483C23×C4—1221no—
484C23×C4—1221no—
485C23×C4C22×D6111yescharacteristic
486C2×SD16—614no—
487C2×SD16—1222no—
488C2×SD16—1222no—
489C2×D8—614no—
490C2×D8—1222no—
491C2×D8—1222no—
492C22×C8C22×D6111yescharacteristic
493C22×C8C22×D6111yescharacteristic
494C22×C8C22×D6111yescharacteristic
495C22×C8C22×D6111yescharacteristic
496#121—614no—
497#121—1222no—
498C4×Q8—614no—
499C4×Q8—1222no—
500C4×Q8—1222no—
501C4×Q8—1222no—
502C4×D4—614no—
503C4×D4—1222no—
504C4×D4—1222no—
505C4×D4—1228no—
506C4×D4—1228no—
507C4×D4—1222no—
508C4×D4—1222no—
509C4×D4—1222no—
510#117—22no—
511#117—22no—
512#117—1228no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—1228no—
519C2×C4⋊C4—1222no—
520C2×C4⋊C4—1222no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4D24411yescharacteristic
526C2×C4⋊C4D24411yescharacteristic
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4D24411yescharacteristic
535C2×C22⋊C4D24411yescharacteristic
536C2×C42—1221no—
537C2×C42—1221no—
538C2×C42—1221no—
539C2×C42C22×D6111yescharacteristic
540C2×C42C22×D6111yescharacteristic
541#107—1222no—
542#107—1222no—
543#103—614no—
544#103—1222no—
545#103—1222no—
546#102—614no—
547#102—1222no—
548#102—1222no—
549#102—1222no—
550#102—1222no—
551C22⋊C8—22no—
552C22⋊C8C4×D6114yescomplemented
553#97—22no—
554C4×C8—22no—
555#95—1221no—
556#95—1221no—
557#95—1221no—
558C24—1221no—
559C24—1221no—
560C24C2×D24411yescharacteristic
561#41—1228no—
562#41—1228no—
563#41—1228no—
564#41—1228no—
565C2×Q8—612no—
566C2×Q8—612no—
567C2×Q8—612no—
568C2×Q8—1221no—
569C2×Q8—1221no—
570C2×Q8—1221no—
571C2×D4—612no—
572C2×D4—612no—
573C2×D4—612no—
574C2×D4—612no—
575C2×D4—1224no—
576C2×D4—1224no—
577C2×D4—1224no—
578C2×D4—1224no—
579C2×D4—1221no—
580C2×D4—1221no—
581C2×D4—1221no—
582C2×D4—1221no—
583C2×D4—1221no—
584C2×D4—1221no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—4881no—
588C2×D4—4881no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—1224no—
594C22×C4—1224no—
595C22×C4—1224no—
596C22×C4—1221no—
597C22×C4—1224no—
598C22×C4—1224no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1224no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—4881no—
606C22×C4—4881no—
607C22×C4—4881no—
608C22×C4—4881no—
609C22×C4—4881no—
610C22×C4—4881no—
611C22×C4—4881no—
612C22×C4—4881no—
613C22×C4—2442no—
614C22×C4C2×C4×D6112yes—
615C22×C4C2×D24411yescharacteristic
616C22×C4C2×D24411yescharacteristic
617C22×C4C2×D24411yescharacteristic
618C22×C4C2×D24411yescharacteristic
619C22×C4C2×D24411yescharacteristic
620C22×C4#1175822212yes—
621C22×C4C23×D6111yescharacteristic
622SD16—1228no—
623D8—1228no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8C2×C4×D6112yes—
635C2×C8C2×C4×D6112yes—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—612no—
639C4⋊C4—612no—
640C4⋊C4—612no—
641C4⋊C4—1224no—
642C4⋊C4—1224no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—1224no—
647C4⋊C4—1221no—
648C4⋊C4—1221no—
649C4⋊C4—1221no—
650C4⋊C4—1221no—
651C4⋊C4—4881no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—1224no—
655C22⋊C4—1224no—
656C22⋊C4—1224no—
657C22⋊C4—4881no—
658C22⋊C4—4881no—
659C22⋊C4—4881no—
660C22⋊C4—2442no—
661C42—21no—
662C42—21no—
663C42—1224no—
664C42—1224no—
665C42—4881no—
666C42D4×D6112yes—
667C42D4×D6112yes—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—1222no—
675C23—1222no—
676C23—1222no—
677C23—1222no—
678C23—2441no—
679C23—2441no—
680C23—2441no—
681C23—2441no—
682C23—2441no—
683C23—2441no—
684C23—2441no—
685C23—2441no—
686C23—2441no—
687C23—2441no—
688C23C4×D24412yes—
689C23C22×D24411yescharacteristic
690Q8—614no—
691Q8—1222no—
692Q8—1222no—
693Q8—1222no—
694D4—614no—
695D4—12216no—
696D4—1222no—
697D4—1222no—
698D4—1222no—
699D4—1222no—
700D4—1222no—
701D4—4884no—
702D4—2441no—
703D4—2441no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—12216no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—4884no—
728C2×C4—4884no—
729C2×C4—4884no—
730C2×C4—4884no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4C4×D24412yes—
744C2×C4#1451974712yes—
745C2×C4#1451974712yes—
746C2×C4C22×C4×D6111yescharacteristic
747C2×C4C2×D4×D6111yescharacteristic
748C2×C4C2×D4×D6111yescharacteristic
749C2×C4#41×D6111yescharacteristic
750C2×C4#41×D6111yescharacteristic
751C2×C4C2×#1175822211yescharacteristic
752C8—22no—
753C8—22no—
754C8—41no—
755C8—41no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—1224no—
764C22—4881no—
765C22—4881no—
766C22—4881no—
767C22—4881no—
768C22—2442no—
769C22—2442no—
770C22—2442no—
771C22—2442no—
772C22—2442no—
773C22—2442no—
774C22—2442no—
775C22—2442no—
776C22—2442no—
777C22C2×C4×D24411yescharacteristic
778C22C2×#1451974711yescharacteristic
779C22#1684027411yescharacteristic
780C22#1684056711yescharacteristic
781C22#1684056711yescharacteristic
782C22#1684057411yescharacteristic
783C22#1684057911yescharacteristic
784C4—22no—
785C4—22no—
786C4—22no—
787C4—41no—
788C4—41no—
789C4—1224no—
790C4—4881no—
791C4—4881no—
792C4—2442no—
793C4—2442no—
794C4—2442no—
795C4C4×D4×D6111yescharacteristic
796C4C4×D4×D6111yescharacteristic
797C4#1684027111yescharacteristic
798C4#1684027111yescharacteristic
799C2—42no—
800C2—4882no—
801C2—2444no—
802C2C4×#1451974711yescharacteristic
803C2#2145465311yescharacteristic
804C2#2145469611yescharacteristic
805C2#2145508911yescharacteristic
806C2#2145513711yescharacteristic
807C2#2145602011yescharacteristic
808C2#2145608311yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1750C2
socleC23×C61C22×D4
prime radicalC2×#16839909C2
cosocleC22×C4×C61C24
hypercenter#1750D61
hypocenterC61#21460
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ #1750

Complements

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

NH ≅ G/Ntype
1. C2×#16840242C2semidirect
3. C2×#16839864C2semidirect
4. C2×C4×D488C2semidirect
5. #21448512C2semidirect
6. #21446173C2semidirect
7. #21446166C2semidirect
8. #21446134C2semidirect
9. #21446076C2semidirect
10. #21446069C2semidirect
11. #21446009C2semidirect
12. #21445760C2semidirect
13. #21445645C2semidirect
14. C4×#14519702C2semidirect
15. C61×#1750C2semidirect
32. #16839909C4semidirect
69. C2×#11758222C2×C4semidirect
82. C2×#11758190C2×C4semidirect
85. C2×D488C2×C4semidirect
87. #14519751C2×C4semidirect
91. C4×Dic122D4semidirect
97. C4×D244D4semidirect
127. #14519702C2×C4semidirect
132. #14519699C2×C4semidirect
150. C22⋊C8×C61C2×C4semidirect
409. #1750D61semidirect
468. C61#21460semidirect
552. C22⋊C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402422
C2×#168399092
C2×#168398642
C2×C4×D4882
#214485122
#214461732
#214461662
#214461342
#214460762
#214460692
#214460092
#214457602
#214456452
C4×#145197022
C61×#17502
#2146061