Finite Group Databasebeta

← #29689134

Subgroups — #29689134

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×#16840340C211yesmaximal, characteristic
2C2×#16839727C211yesmaximal, characteristic, complemented
3#21448408C211yesmaximal, characteristic, complemented
4#21446254C211yesmaximal, characteristic, complemented
5#21446249C211yesmaximal, characteristic, complemented
6#21446244C211yesmaximal, characteristic, complemented
7#21446239C211yesmaximal, characteristic, complemented
8#21446138C211yesmaximal, characteristic, complemented
9#21446133C211yesmaximal, characteristic, complemented
10#21446128C211yesmaximal, characteristic, complemented
11#21446123C211yesmaximal, characteristic, complemented
12#21445910C211yesmaximal, characteristic, complemented
13#21445903C211yesmaximal, characteristic, complemented
14#21445759C211yesmaximal, characteristic, complemented
15C61×#1788C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840340—24no—
20#16840340C418yescomplemented
21C2×#14519756—21no—
22C2×#14519753C2211yescharacteristic
23C2×#14519753C2211yescharacteristic
24C2×#14519751—21no—
25C2×#14519749—21no—
26C2×#14519749—21no—
27C2×#14519748C2211yescharacteristic
28C2×#14519748C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30C22×C4⋊Dic61C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36#16839727—24no—
37C2×C22⋊#92418C2211yescharacteristic
38C2×#14519689C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40#16839666—21no—
41#16839662—21no—
42#16839640—21no—
43#16839638—21no—
44#16839622C2211yescharacteristic
45#16839619C2211yescharacteristic
46#16839619C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C22×#41×C61C2211yescharacteristic
56C2×#103×C61C2211yescharacteristic
57C2×#103×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C2×#11758222—41no—
63C2×#11758222—41no—
64C2×#11758222—41no—
65C2×#11758222—41no—
66C2×#11758222C2×C414yes—
67C2×#11758222D414yes—
68C22×Dic122D411yescharacteristic
69C22×D244D411yescharacteristic
70C22×C22⋊D61—21no—
71C22×C22⋊D61—21no—
72C22×C22⋊D61D411yescharacteristic
73C22×C22⋊D61D411yescharacteristic
74C23×Dic61—21no—
75C22×C4×D61—21no—
76C22×C4×D61C2311yescharacteristic
77C22×C4×D61C2311yescharacteristic
78C2×#11758189—22no—
79C2×#11758189—41no—
80C2×#11758189—41no—
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C2×C8×D61—22no—
84C2×C8×D61—41no—
85C2×C8×D61—41no—
86#14519756—28no—
87#14519753—22no—
88#14519753—22no—
89#14519753C2×C414yes—
90#14519753C2×C414yescomplemented
91#14519751—28no—
92#14519749—28no—
93#14519749—28no—
94#14519748—22no—
95#14519748—22no—
96#14519748C2×C414yes—
97#14519748C2×C414yescomplemented
98#14519735—41no—
99#14519735—41no—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61—22no—
102C2×C4⋊Dic61C2×C414yescomplemented
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×#11758196—21no—
110C4⋊C4×D61—41no—
111C4⋊C4×D61—41no—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×C22⋊Dic61—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×C4×Dic61—21no—
121#14519701—41no—
122#14519701—41no—
123#14519698—41no—
124#14519698—41no—
125C22⋊#92418—22no—
126#14519689—22no—
127#14519689—22no—
128#14519684—21no—
129#14519684—21no—
130#14519684—21no—
131C2×#41×C61—22no—
132C2×#41×C61—41no—
133C2×#41×C61—41no—
134C2×#41×C61—41no—
135C2×#41×C61—41no—
136C2×#41×C61C2×C414yescomplemented
137C22×Q8×C61C2311yescharacteristic
138C22×D4×C61—21no—
139C22×D4×C61C2311yescharacteristic
140C23×C4×C61—21no—
141C23×C4×C61C2311yescharacteristic
142C22×C8×C61C2311yescharacteristic
143C22×C8×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61—21no—
147#103×C61—41no—
148#103×C61—41no—
149#102×C61—41no—
150#102×C61—41no—
151C22⋊C8×C61—22no—
152#95×C61—21no—
153C24×C61—21no—
154C24×C61C2×D411yescharacteristic
155C23×D61C2×D411yescharacteristic
156C23×D61C2×D411yescharacteristic
157#41×C61—44no—
158#41×C61—44no—
159#41×C61—44no—
160#41×C61—44no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61C22×C412yes—
167C2×D4×C61—24no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—42no—
174C2×D4×C61—42no—
175C2×D4×C61C22×C412yes—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—24no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—42no—
185C22×C4×C61—42no—
186C22×C4×C61C22×C412yes—
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D412yes—
189C22×C4×C61C2411yescharacteristic
190C2×C22⋊D61—24no—
191C2×C22⋊D61—24no—
192C2×C22⋊D61—41no—
193C2×C22⋊D61—41no—
194C2×C22⋊D61—41no—
195C2×C22⋊D61—41no—
196C2×C22⋊D61—81no—
197C2×C22⋊D61—81no—
198C2×C22⋊D61—81no—
199C2×C22⋊D61—81no—
200C2×C22⋊D61C22⋊C414yes—
201C2×C22⋊D61C22⋊C414yes—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—24no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—81no—
208C22×Dic61—81no—
209C22×Dic61C2×D411yescharacteristic
210C22×Dic61C2×D411yescharacteristic
211#11758222—44no—
212#11758222—44no—
213#11758222—44no—
214#11758222—44no—
215C2×D244—41no—
216C2×D244—41no—
217C2×D244C22⋊C414yes—
218C2×C4×D61—21no—
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—42no—
227C2×C4×D61—81no—
228C2×C4×D61—81no—
229C2×C4×D61C22×C412yes—
230C2×C4×D61C22×C412yes—
231C2×C4×D61C2×D412yes—
232C2×C4×D61C2×D412yes—
233C2×Dic122—41no—
234C2×Dic122—41no—
235C2×Dic122C22⋊C414yes—
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—
246C22⋊C4×C61—81no—
247C22⋊Dic61—24no—
248C22⋊Dic61—24no—
249C22⋊Dic61—81no—
250#11758198—24no—
251#11758198—24no—
252#11758198—42no—
253#11758198—81no—
254#11758198—81no—
255C4⋊Dic61—24no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61C22×C412yes—
263C4⋊Dic61C22×C412yes—
264#11758196—24no—
265#11758196—24no—
266#11758196—42no—
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—
305Q8×C61—22no—
306Q8×C61—22no—
307Q8×C61—41no—
308Q8×C61—41no—
309D4×C61—22no—
310D4×C61—22no—
311D4×C61—48no—
312D4×C61—41no—
313D4×C61—41no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—48no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61C2×C22⋊C412yes—
331C2×C4×C61C23×C411yescharacteristic
332C2×C4×C61C22×D411yescharacteristic
333C2×C4×C61H(5,𝔽2)11yescharacteristic
334C2×C4×C61H(5,𝔽2)11yescharacteristic
335C2×C4×C61H(5,𝔽2)11yescharacteristic
336C2×C4×C61H(5,𝔽2)11yescharacteristic
337C22⋊D61—44no—
338C22⋊D61—44no—
339C22⋊D61—84no—
340C22⋊D61—84no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—84no—
358C2×Dic61C2×C22⋊C412yes—
359C2×Dic61C2×C22⋊C412yes—
360D244—44no—
361C4×D61—22no—
362C4×D61—22no—
363C4×D61—22no—
364C4×D61—22no—
365C4×D61—22no—
366C4×D61—22no—
367C4×D61—22no—
368C4×D61—22no—
369C4×D61—84no—
370Dic122—44no—
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#1874—611no—
434#1873—611no—
435#1872—611no—
436#1824—611no—
437#1823—611no—
438#1788—611no—
439#1788D6111yescharacteristic, complemented
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×#41C2×D6111yescharacteristic
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—611no—
462C2×#121—1221no—
463C2×#121—1221no—
464C2×#121—1221no—
465C2×#117—611no—
466C22×C4⋊C4—611no—
467C22×C4⋊C4—611no—
468C2×#103—611no—
469C2×#103—611no—
470C2×#103C2×D6111yescharacteristic
471C2×#103C2×D6111yescharacteristic
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#380C2×D6111yescharacteristic
489#340—611no—
490#340—611no—
491#340—611no—
492#340—611no—
493#340—611no—
494#340—611no—
495#340—611no—
496#340—611no—
497C61#2177211yescharacteristic, complemented, Sylow
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—614no—
504C2×#41—614no—
505C2×#41—2441no—
506C2×#41—2441no—
507C2×#41—2441no—
508C2×#41—2441no—
509C2×#41C4×D6114yescomplemented
510C22×Q8—611no—
511C22×Q8C22×D6111yescharacteristic
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—614no—
541#121—614no—
542#121—1228no—
543#121—1222no—
544#121—1222no—
545#121—1228no—
546#121—1228no—
547#117—2441no—
548#117—2441no—
549C2×C4⋊C4—614no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1222no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—2441no—
560C2×C4⋊C4—2441no—
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—41no—
574#103—41no—
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—21no—
586#95—1221no—
587#95—1221no—
588#95—1221no—
589C24—21no—
590C24—611no—
591C24—611no—
592C24D4×D6111yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—2444no—
598#41—2444no—
599#41—2444no—
600#41—2444no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—614no—
607C2×Q8—2441no—
608C2×Q8—2441no—
609C2×Q8C2×C4×D6112yes—
610C2×D4—24no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—614no—
619C2×D4—614no—
620C2×D4—614no—
621C2×D4—1224no—
622C2×D4—1224no—
623C2×D4—4881no—
624C2×D4—4881no—
625C2×D4—4881no—
626C2×D4—4881no—
627C2×D4—2441no—
628C2×D4—2441no—
629C2×D4—2441no—
630C2×D4—2441no—
631C2×D4—2441no—
632C2×D4—2441no—
633C2×D4C2×C4×D6112yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—611no—
645C22×C4—611no—
646C22×C4—612no—
647C22×C4—612no—
648C22×C4—612no—
649C22×C4—612no—
650C22×C4—1221no—
651C22×C4—1221no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1224no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—4881no—
664C22×C4—4881no—
665C22×C4—4881no—
666C22×C4—4881no—
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—612no—
691C4⋊C4—612no—
692C4⋊C4—1224no—
693C4⋊C4—1224no—
694C4⋊C4—1221no—
695C4⋊C4—1221no—
696C4⋊C4—1224no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4—2442no—
702C22⋊C4—81no—
703C22⋊C4—1224no—
704C22⋊C4—1224no—
705C22⋊C4—1224no—
706C22⋊C4—1224no—
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—22no—
742Q8—22no—
743Q8—41no—
744Q8—41no—
745Q8—2444no—
746D4—22no—
747D4—22no—
748D4—48no—
749D4—41no—
750D4—41no—
751D4—4884no—
752D4—4884no—
753D4—2444no—
754D4—2444no—
755D4—2444no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—48no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
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—4884no—
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#1451982211yescharacteristic
806C2×C4#1451982211yescharacteristic
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#1684032211yescharacteristic
842C22#1684056611yescharacteristic
843C22#1684056911yescharacteristic
844C22#1684057111yescharacteristic
845C22#1684057611yescharacteristic
846C4—22no—
847C4—42no—
848C4—81no—
849C4—81no—
850C4—1222no—
851C4—1222no—
852C4—4881no—
853C4—4881no—
854C4—2442no—
855C4—2442no—
856C4#1684023511yescharacteristic
857C4#1684023511yescharacteristic
858C4#1684032211yescharacteristic
859C4#1684032211yescharacteristic
860C2—42no—
861C2—82no—
862C2—2442no—
863C2—2442no—
864C2#2144839511yescharacteristic
865C2#2145434311yescharacteristic
866C2#2145434811yescharacteristic
867C2#2145667011yescharacteristic
868C2#2145670011yescharacteristic
869C2#2145671811yescharacteristic
870C2#2145672711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1788C2
socleC23×C61C22×D4
prime radicalC2×#16840340C2
cosocleC22×C4×C61C24
hypercenter#1788D61
hypocenterC61#21772
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#16839727C2semidirect
3. #21448408C2semidirect
4. #21446254C2semidirect
5. #21446249C2semidirect
6. #21446244C2semidirect
7. #21446239C2semidirect
8. #21446138C2semidirect
9. #21446133C2semidirect
10. #21446128C2semidirect
11. #21446123C2semidirect
12. #21445910C2semidirect
13. #21445903C2semidirect
14. #21445759C2semidirect
15. C61×#1788C2semidirect
20. #16840340C4semidirect
90. #14519753C2×C4semidirect
97. #14519748C2×C4semidirect
102. C2×C4⋊Dic61C2×C4semidirect
136. C2×#41×C61C2×C4semidirect
439. #1788D61semidirect
497. C61#21772semidirect
509. C2×#41C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403402
C2×#168397272
#214484082
#214462542
#214462492
#214462442
#214462392
#214461382
#214461332
#214461282
#214461232
#214459102
#214459032
#214457592
C61×#17882
#2177261