Finite Group Databasebeta

← #29689127

Subgroups — #29689127

Order 15616.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840341C211yesmaximal, characteristic
2C2×#16839727C211yesmaximal, characteristic, complemented
3#21448412C211yesmaximal, characteristic, complemented
4#21446254C211yesmaximal, characteristic, complemented
5#21446251C211yesmaximal, characteristic, complemented
6#21446244C211yesmaximal, characteristic, complemented
7#21446241C211yesmaximal, characteristic, complemented
8#21446142C211yesmaximal, characteristic, complemented
9#21446129C211yesmaximal, characteristic, complemented
10#21446126C211yesmaximal, characteristic, complemented
11#21445908C211yesmaximal, characteristic, complemented
12#21445904C211yesmaximal, characteristic, complemented
13#21445756C211yesmaximal, characteristic, complemented
14#21445756C211yesmaximal, characteristic, complemented
15C61×#1874C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758224C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840341—24no—
21#16840341C418yescomplemented
22C2×#14519757C2211yescharacteristic
23C2×#14519756C2211yescharacteristic
24C2×#14519754—21no—
25C2×#14519750—21no—
26C2×#14519749—21no—
27C2×#14519748—21no—
28C2×#14519748C2211yescharacteristic
29C2×#14519736C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31C2×#14519702C2211yescharacteristic
32C2×#14519702C2211yescharacteristic
33C2×#14519700C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37#16839727—24no—
38C2×C22⋊#92418C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41#16839667—21no—
42#16839663—21no—
43#16839641—21no—
44#16839641—21no—
45#16839619C2211yescharacteristic
46#16839619C2211yescharacteristic
47#16839619C2211yescharacteristic
48#16839619C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C2×#121×C61C2211yescharacteristic
56C22×C4⋊C4×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C2×#11758222—41no—
63C2×#11758222—41no—
64C2×#11758222—41no—
65C2×#11758222—41no—
66C2×#11758222C2×C414yes—
67C2×#11758222D414yes—
68C2×#11758224—22no—
69C2×#11758224—41no—
70C2×#11758224—41no—
71C2×#11758224—41no—
72C2×#11758224—41no—
73C2×#11758224C2×C414yescomplemented
74C22×Dic122D411yescharacteristic
75C22×Dic122C2311yescharacteristic
76C22×D244D411yescharacteristic
77C22×C22⋊D61—21no—
78C22×C22⋊D61—21no—
79C22×C22⋊D61D411yescharacteristic
80C22×C22⋊D61D411yescharacteristic
81C23×Dic61—21no—
82C22×C4×D61—21no—
83C22×C4×D61C2311yescharacteristic
84C22×C4×D61C2311yescharacteristic
85C2×#11758189—22no—
86C2×#11758189—41no—
87C2×#11758189—41no—
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90C2×C8×D61—22no—
91C2×C8×D61—41no—
92C2×C8×D61—41no—
93#14519757—22no—
94#14519757C2×C414yescomplemented
95#14519756—22no—
96#14519756C2×C414yes—
97#14519754—28no—
98#14519750—28no—
99#14519749—28no—
100#14519748—28no—
101#14519748—22no—
102#14519748C2×C414yescomplemented
103#14519736—41no—
104#14519736—41no—
105C2×C4⋊Dic61—21no—
106C2×C4⋊Dic61C2311yescharacteristic
107C2×C4⋊Dic61C2311yescharacteristic
108C2×C4⋊Dic61C2311yescharacteristic
109C2×#11758196—21no—
110C2×#11758196—21no—
111C4⋊C4×D61—22no—
112C4⋊C4×D61C2×C414yescomplemented
113C2×C22⋊Dic61—21no—
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×C4×Dic61—21no—
122#14519702—41no—
123#14519702—41no—
124#14519700—41no—
125#14519700—41no—
126#14519698—41no—
127#14519698—41no—
128C22⋊#92418—22no—
129#14519689—22no—
130#14519689—22no—
131#14519684—21no—
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135C22×D4×C61—21no—
136C22×D4×C61C2311yescharacteristic
137C23×C4×C61—21no—
138C23×C4×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141#121×C61—22no—
142#121×C61C2×C414yes—
143C2×C4⋊C4×C61—21no—
144C2×C4⋊C4×C61—41no—
145C2×C4⋊C4×C61—41no—
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C22⋊C4×C61—21no—
150#102×C61—41no—
151#102×C61—41no—
152C22⋊C8×C61—22no—
153C24×C61—21no—
154C24×C61C2×D411yescharacteristic
155C23×D61C2×D411yescharacteristic
156C23×D61C2×D411yescharacteristic
157C2×D4×C61—24no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—81no—
164C2×D4×C61—81no—
165C2×D4×C61C22×C412yes—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—42no—
174C22×C4×C61—81no—
175C22×C4×C61—81no—
176C22×C4×C61C22×C412yes—
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D412yes—
179C22×C4×C61C2411yescharacteristic
180C2×C22⋊D61—24no—
181C2×C22⋊D61—24no—
182C2×C22⋊D61—41no—
183C2×C22⋊D61—41no—
184C2×C22⋊D61—41no—
185C2×C22⋊D61—41no—
186C2×C22⋊D61—42no—
187C2×C22⋊D61—42no—
188C2×C22⋊D61—81no—
189C2×C22⋊D61—81no—
190C2×C22⋊D61C22⋊C414yes—
191C2×C22⋊D61C22⋊C414yes—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—24no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—42no—
198C22×Dic61—42no—
199C22×Dic61C2×D411yescharacteristic
200C22×Dic61C2×D411yescharacteristic
201#11758224—44no—
202#11758224—44no—
203#11758224—44no—
204#11758224—44no—
205#11758222—44no—
206#11758222—44no—
207#11758222—44no—
208#11758222—44no—
209C2×D244—41no—
210C2×D244—41no—
211C2×D244C22⋊C414yes—
212C2×C4×D61—21no—
213C2×C4×D61—21no—
214C2×C4×D61—21no—
215C2×C4×D61—21no—
216C2×C4×D61—21no—
217C2×C4×D61—21no—
218C2×C4×D61—21no—
219C2×C4×D61—21no—
220C2×C4×D61—24no—
221C2×C4×D61—81no—
222C2×C4×D61—81no—
223C2×C4×D61C22×C412yes—
224C2×C4×D61C22×C412yes—
225C2×C4×D61C2×D412yes—
226C2×C4×D61C2×D412yes—
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122—21no—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122—41no—
233C2×Dic122—41no—
234C2×Dic122C22⋊C414yes—
235C2×Dic122C22×C412yes—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—42no—
248C4⋊C4×C61C22×C412yes—
249C22⋊C4×C61—24no—
250C22⋊Dic61—24no—
251C22⋊Dic61—24no—
252C22⋊Dic61—42no—
253#11758198—24no—
254#11758198—81no—
255#11758198—81no—
256#11758198—81no—
257#11758198—81no—
258C4⋊Dic61—21no—
259C4⋊Dic61—24no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61C22×C412yes—
265#11758196—24no—
266#11758196—24no—
267C4×Dic61—42no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418—21no—
274#11758189—44no—
275C8×D61—44no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—22no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61C2×C22⋊C412yes—
290C23×C61C22×D411yescharacteristic
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—21no—
294C22×D61—21no—
295C22×D61—21no—
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61—21no—
302C22×D61—21no—
303C22×D61C2×C22⋊C412yes—
304C22×D61C2×C22⋊C412yes—
305D4×C61—22no—
306D4×C61—22no—
307D4×C61—41no—
308D4×C61—41no—
309D4×C61—84no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—84no—
326C2×C4×C61C2×C22⋊C412yes—
327C2×C4×C61C23×C411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61H(5,𝔽2)11yescharacteristic
330C2×C4×C61H(5,𝔽2)11yescharacteristic
331C2×C4×C61H(5,𝔽2)11yescharacteristic
332C2×C4×C61H(5,𝔽2)11yescharacteristic
333C22⋊D61—44no—
334C22⋊D61—44no—
335C22⋊D61—48no—
336C22⋊D61—84no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—48no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61C2×C22⋊C412yes—
355C2×Dic61C2×C22⋊C412yes—
356D244—44no—
357C4×D61—22no—
358C4×D61—22no—
359C4×D61—22no—
360C4×D61—22no—
361C4×D61—22no—
362C4×D61—22no—
363C4×D61—22no—
364C4×D61—22no—
365C4×D61—84no—
366Dic122—22no—
367Dic122—22no—
368Dic122—44no—
369Dic122—41no—
370Dic122—41no—
371C8×C61—41no—
372C8×C61—41no—
373#92418—41no—
374#92418—41no—
375#21772—611nomaximal, Sylow
376C22×C61—22no—
377C22×C61—22no—
378C22×C61—22no—
379C22×C61—41no—
380C22×C61—41no—
381C22×C61—41no—
382C22×C61—41no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—81no—
387C22×C61—81no—
388C22×C61—81no—
389C22×C61—81no—
390C22×C61C22×C22⋊C411yescharacteristic
391C22×C61#53411yescharacteristic
392C22×C61#53411yescharacteristic
393C22×C61#57611yescharacteristic
394C22×C61#57711yescharacteristic
395C22×C61#57711yescharacteristic
396C22×C61#57811yescharacteristic
397C2×D61—22no—
398C2×D61—22no—
399C2×D61—22no—
400C2×D61—22no—
401C2×D61—22no—
402C2×D61—22no—
403C2×D61—41no—
404C2×D61—41no—
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—41no—
408C2×D61—41no—
409C2×D61—41no—
410C2×D61—41no—
411C4×C61—22no—
412C4×C61—42no—
413C4×C61—81no—
414C4×C61—81no—
415C4×C61#51811yescharacteristic
416C4×C61#51811yescharacteristic
417C4×C61#53411yescharacteristic
418C4×C61#53411yescharacteristic
419Dic61—22no—
420Dic61—22no—
421Dic61—42no—
422Dic61—42no—
423Dic61—81no—
424Dic61—81no—
425C2×#537—611no—
426C2×#408—611no—
427#2311—611no—
428#1895—611no—
429#1894—611no—
430#1893—611no—
431#1892—611no—
432#1875—611no—
433#1874D6111yescharacteristic, complemented
434#1873—611no—
435#1872—611no—
436#1824—611no—
437#1823—611no—
438#1788—611no—
439#1788—611no—
440C2×C61—42no—
441C2×C61—82no—
442C2×C61#230811yescharacteristic
443C2×C61#289711yescharacteristic
444C2×C61#289811yescharacteristic
445C2×C61#319811yescharacteristic
446C2×C61#320111yescharacteristic
447C2×C61#320311yescharacteristic
448C2×C61#320411yescharacteristic
449D61—42no—
450D61—42no—
451C22×#41—611no—
452C22×#41—611no—
453C22×M16—611no—
454C23×C8—611no—
455#537—618no—
456#537—1224no—
457C2×C22⋊Q8—611no—
458C2×C22⋊Q8—611no—
459C2×C22⋊Q8—1221no—
460C2×#121—611no—
461C2×#121—1221no—
462C2×#121—1221no—
463C2×#121—1221no—
464C2×#121C2×D6111yescharacteristic
465C2×#117—611no—
466C22×C4⋊C4—611no—
467C22×C4⋊C4C2×D6111yescharacteristic
468C2×#103—611no—
469C2×#103—611no—
470C2×#103—611no—
471C2×#103—611no—
472C2×#102—611no—
473C2×#102—611no—
474C2×#102C2×D6111yescharacteristic
475C2×#102C2×D6111yescharacteristic
476#408—1224no—
477C2×C22⋊C8—611no—
478C2×C22⋊C8—611no—
479C2×C22⋊C8—611no—
480C2×C22⋊C8C2×D6111yescharacteristic
481#391—1221no—
482#390—1221no—
483#386—1221no—
484#386—1221no—
485#380—611no—
486#380—611no—
487#380—611no—
488#380—611no—
489#340—611no—
490#340—611no—
491#340—611no—
492#340—611no—
493#340—611no—
494#340—611no—
495#340C2×D6111yescharacteristic
496#340C2×D6111yescharacteristic
497C61#2177211yescharacteristic, complemented, Sylow
498C2×#41—614no—
499C2×#41—614no—
500C2×#41—614no—
501C2×#41—1222no—
502C2×#41—2441no—
503C2×#41—2441no—
504C2×#41—2441no—
505C2×#41—2441no—
506C2×#41—2441no—
507C2×#41—2441no—
508C2×#41—2441no—
509C2×#41—2441no—
510C22×Q8—611no—
511C22×Q8—611no—
512C22×D4—21no—
513C22×D4—611no—
514C22×D4—611no—
515C22×D4—611no—
516C22×D4—1221no—
517C22×D4—1221no—
518C22×D4C22×D6111yescharacteristic
519C23×C4—21no—
520C23×C4—611no—
521C23×C4—611no—
522C23×C4—1221no—
523C23×C4—1221no—
524C23×C4C22×D6111yescharacteristic
525C2×M16—1222no—
526C2×M16—2441no—
527C2×M16—2441no—
528C22×C8—611no—
529C22×C8—611no—
530C22×C8—1222no—
531C22×C8—2441no—
532C22×C8—2441no—
533C22×C8C22×D6111yescharacteristic
534C22×C8C22×D6111yescharacteristic
535C22⋊Q8—614no—
536C22⋊Q8—614no—
537C22⋊Q8—1228no—
538C22⋊Q8—1222no—
539C22⋊Q8—1222no—
540#121—22no—
541#121—614no—
542#121—1228no—
543#121—1222no—
544#121—1228no—
545#121—1228no—
546#121C4×D6114yes—
547#117—2441no—
548#117—2441no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4—41no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—614no—
554C2×C4⋊C4—611no—
555C2×C4⋊C4—611no—
556C2×C4⋊C4—1222no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4C22×D6111yescharacteristic
561C2×C4⋊C4C22×D6111yescharacteristic
562C2×C4⋊C4C22×D6111yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C42—1221no—
573#103—2441no—
574#103—2441no—
575#103—2441no—
576#103—2441no—
577#102—41no—
578#102—41no—
579#102—2441no—
580#102—2441no—
581C22⋊C8—22no—
582C22⋊C8—1222no—
583C22⋊C8—1222no—
584C22⋊C8—1222no—
585#95—1221no—
586#95—1221no—
587#95—1221no—
588#95—1221no—
589C24—21no—
590C24—611no—
591C24—611no—
592C24D4×D6111yescharacteristic
593#41—2444no—
594#41—2444no—
595#41—2444no—
596#41—2444no—
597#41—2444no—
598#41—2444no—
599#41—2444no—
600#41—2444no—
601C2×Q8—614no—
602C2×Q8—612no—
603C2×Q8—1221no—
604C2×Q8—1221no—
605C2×Q8—1221no—
606C2×Q8—1221no—
607C2×Q8—1221no—
608C2×Q8—2441no—
609C2×Q8—2441no—
610C2×D4—24no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—614no—
619C2×D4—614no—
620C2×D4—614no—
621C2×D4—1224no—
622C2×D4—1224no—
623C2×D4—4881no—
624C2×D4—4881no—
625C2×D4—2441no—
626C2×D4—2441no—
627C2×D4—2441no—
628C2×D4—2441no—
629C2×D4—2441no—
630C2×D4—2441no—
631C2×D4—2442no—
632C2×D4—2442no—
633C2×D4C2×C4×D6112yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—42no—
642C22×C4—81no—
643C22×C4—81no—
644C22×C4—611no—
645C22×C4—611no—
646C22×C4—612no—
647C22×C4—612no—
648C22×C4—612no—
649C22×C4—612no—
650C22×C4—1224no—
651C22×C4—1224no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—4881no—
665C22×C4—4881no—
666C22×C4—2442no—
667C22×C4—2442no—
668C22×C4C2×C4×D6112yes—
669C22×C4D4×D6112yes—
670C22×C4D4×D6111yescharacteristic
671C22×C4C23×D6111yescharacteristic
672M16—2444no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—1221no—
680C2×C8—1221no—
681C2×C8—1221no—
682C2×C8—1221no—
683C2×C8—1221no—
684C2×C8—1221no—
685C2×C8—2444no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—42no—
692C4⋊C4—612no—
693C4⋊C4—1224no—
694C4⋊C4—1224no—
695C4⋊C4—1221no—
696C4⋊C4—1224no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4C2×C4×D6112yes—
702C22⋊C4—24no—
703C22⋊C4—1224no—
704C22⋊C4—1224no—
705C22⋊C4—1224no—
706C22⋊C4—4881no—
707C22⋊C4—4881no—
708C22⋊C4—4881no—
709C22⋊C4—4881no—
710C22⋊C4—2442no—
711C42—2442no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—22no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—612no—
726C23—612no—
727C23—1221no—
728C23—1221no—
729C23—1221no—
730C23—1221no—
731C23—1221no—
732C23—1221no—
733C23—1221no—
734C23—1221no—
735C23—1221no—
736C23—1221no—
737C23—1221no—
738C23—1221no—
739C23C22⋊C4×D6112yes—
740C23C2×D4×D6111yescharacteristic
741Q8—1222no—
742Q8—1222no—
743Q8—2444no—
744Q8—2441no—
745Q8—2441no—
746D4—22no—
747D4—22no—
748D4—41no—
749D4—41no—
750D4—84no—
751D4—4884no—
752D4—2444no—
753D4—2444no—
754D4—2444no—
755D4—2448no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—84no—
772C2×C4—612no—
773C2×C4—612no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—1222no—
782C2×C4—1222no—
783C2×C4—1222no—
784C2×C4—1222no—
785C2×C4—1222no—
786C2×C4—1222no—
787C2×C4—1222no—
788C2×C4—4884no—
789C2×C4—2448no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4C22⋊C4×D6112yes—
801C2×C4C22×C4×D6111yescharacteristic
802C2×C4C2×D4×D6111yescharacteristic
803C2×C4#1451982211yescharacteristic
804C2×C4#1451982211yescharacteristic
805C2×C4#1451982311yescharacteristic
806C2×C4#1451982311yescharacteristic
807C8—41no—
808C8—41no—
809C8—2441no—
810C8—2441no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—1222no—
826C22—1222no—
827C22—1222no—
828C22—1222no—
829C22—1222no—
830C22—1222no—
831C22—2441no—
832C22—2441no—
833C22—2441no—
834C22—2441no—
835C22—2441no—
836C22—2441no—
837C22—2441no—
838C22—2441no—
839C22C2×C22⋊C4×D6111yescharacteristic
840C22#1684032211yescharacteristic
841C22#1684032311yescharacteristic
842C22#1684056311yescharacteristic
843C22#1684056811yescharacteristic
844C22#1684057211yescharacteristic
845C22#1684057811yescharacteristic
846C4—22no—
847C4—42no—
848C4—81no—
849C4—81no—
850C4—1222no—
851C4—1222no—
852C4—4881no—
853C4—4881no—
854C4—2442no—
855C4—2442no—
856C4#1684023411yescharacteristic
857C4#1684023411yescharacteristic
858C4#1684032011yescharacteristic
859C4#1684032011yescharacteristic
860C2—42no—
861C2—82no—
862C2—2442no—
863C2—2442no—
864C2#2144839311yescharacteristic
865C2#2145434011yescharacteristic
866C2#2145435011yescharacteristic
867C2#2145666711yescharacteristic
868C2#2145669711yescharacteristic
869C2#2145671911yescharacteristic
870C2#2145673211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1874C2
socleC23×C61C22×D4
prime radicalC2×#16840341C2
cosocleC22×C4×C61C24
hypercenter#1874D61
hypocenterC61#21772
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. C2×#16839727C2semidirect
3. #21448412C2semidirect
4. #21446254C2semidirect
5. #21446251C2semidirect
6. #21446244C2semidirect
7. #21446241C2semidirect
8. #21446142C2semidirect
9. #21446129C2semidirect
10. #21446126C2semidirect
11. #21445908C2semidirect
12. #21445904C2semidirect
13. #21445756C2semidirect
14. #21445756C2semidirect
15. C61×#1874C2semidirect
21. #16840341C4semidirect
73. C2×#11758224C2×C4semidirect
94. #14519757C2×C4semidirect
102. #14519748C2×C4semidirect
112. C4⋊C4×D61C2×C4semidirect
433. #1874D61semidirect
497. C61#21772semidirect

Maximal subgroups

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

subgroupindex
C2×#168403412
C2×#168397272
#214484122
#214462542
#214462512
#214462442
#214462412
#214461422
#214461292
#214461262
#214459082
#214459042
#214457562
C61×#18742
#2177261