Finite Group Databasebeta

← #29685725

Subgroups — #29685725

Order 15616.

1616 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840237C211yesmaximal, characteristic, complemented
2C2×#16839896C211yesmaximal, characteristic
3C2×#16839871C211yesmaximal, characteristic, complemented
4C2×#16839842C211yesmaximal, characteristic, complemented
5#21448508C211yesmaximal, characteristic, complemented
6#21446165C211yesmaximal, characteristic, complemented
7#21446165C211yesmaximal, characteristic, complemented
8#21446139C211yesmaximal, characteristic, complemented
9#21446078C211yesmaximal, characteristic, complemented
10#21446064C211yesmaximal, characteristic, complemented
11#21446016C211yesmaximal, characteristic, complemented
12#21445646C211yesmaximal, characteristic, complemented
13#102×Dic61C211yesmaximal, characteristic, complemented
14#21445587C211yesmaximal, characteristic, complemented
15C61×#1786C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19#16840237—24no—
20#16840237—24no—
21C2×D4×Dic61—21no—
22C2×D4×Dic61—21no—
23C2×D4×Dic61C2211yescharacteristic
24C2×D4×Dic61C2211yescharacteristic
25C2×D4×Dic61C2211yescharacteristic
26C2×D4×Dic61C2211yescharacteristic
27C2×#14519739C2211yescharacteristic, complemented
28C2×#14519736C2211yescharacteristic
29C2×#14519736C2211yescharacteristic
30C22×C22⋊Dic61—21no—
31C22×C22⋊Dic61—21no—
32#16839896C418yescomplemented
33#16839871—24no—
34#16839842—24no—
35C2×#14519710C2211yescharacteristic, complemented
36C2×#14519708C2211yescharacteristic, complemented
37C2×#14519699C2211yescharacteristic, complemented
38C2×#14519699C2211yescharacteristic, complemented
39C2×#14519698C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×#14519687C2211yescharacteristic, complemented
43C2×C8×Dic61C2211yescharacteristic, complemented
44#16839663C2211yescharacteristic, complemented
45#16839662—21no—
46#16839658C2211yescharacteristic, complemented
47#16839654—21no—
48#16839638—21no—
49#16839636—21no—
50C4⋊C4×Dic61C2211yescharacteristic, complemented
51#16839525C2211yescharacteristic, complemented
52#16839525C2211yescharacteristic, complemented
53#16839524C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839516C2211yescharacteristic, complemented
56#16839516C2211yescharacteristic, complemented
57C23×D4×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic
63C61×#380C2211yescharacteristic
64C22×D244C2311yescharacteristic
65C22×C22⋊D61—21no—
66C23×Dic61—21no—
67C23×Dic61—21no—
68C23×Dic61—21no—
69C23×Dic61—21no—
70C22×C4×D61—21no—
71C2×#11758199—22no—
72C2×#11758199—22no—
73C2×#11758199—22no—
74C2×#11758199—22no—
75C2×#11758199C2×C414yescomplemented
76C2×#11758199C2×C414yescomplemented
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79#14519751—22no—
80#14519751C2×C414yescomplemented
81D4×Dic61—28no—
82D4×Dic61—28no—
83D4×Dic61—22no—
84D4×Dic61—22no—
85D4×Dic61—22no—
86D4×Dic61—22no—
87D4×Dic61—22no—
88D4×Dic61—22no—
89D4×Dic61D414yescomplemented
90D4×Dic61D414yescomplemented
91#14519739—22no—
92#14519739—22no—
93#14519736—22no—
94#14519736—22no—
95#14519736—22no—
96#14519736—22no—
97C2×C4⋊Dic61D411yescharacteristic
98C2×C4⋊Dic61D411yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×C4⋊Dic61C2311yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×#11758196—21no—
103C2×C22⋊Dic61—28no—
104C2×C22⋊Dic61—28no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61—21no—
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61D411yescharacteristic
111C2×C22⋊Dic61D411yescharacteristic
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×C4×Dic61—21no—
117C2×C4×Dic61—21no—
118C2×C4×Dic61C2311yescharacteristic
119C2×C4×Dic61C2311yescharacteristic
120#14519710—22no—
121#14519708—22no—
122#14519699—22no—
123#14519699—22no—
124#14519698C2×C414yescomplemented
125#14519698C2×C414yescomplemented
126C22⋊#92418C2×C414yescomplemented
127#14519687—22no—
128C8×Dic61—22no—
129#14519684—21no—
130#14519684—21no—
131C25×C61—21no—
132C22×D4×C61—22no—
133C22×D4×C61—22no—
134C22×D4×C61—22no—
135C22×D4×C61—22no—
136C22×D4×C61—21no—
137C22×D4×C61—22no—
138C22×D4×C61C2×C414yescomplemented
139C22×D4×C61C2311yescharacteristic
140C22×D4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C22×C8×C61C2311yescharacteristic
143C22×C8×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61—21no—
147#102×C61—22no—
148#102×C61—22no—
149#102×C61—22no—
150#102×C61—22no—
151C22⋊C8×C61—22no—
152#95×C61—21no—
153C24×C61—24no—
154C24×C61—24no—
155C24×C61—21no—
156C24×C61—21no—
157C24×C61—24no—
158C24×C61—81no—
159C24×C61—81no—
160C24×C61—81no—
161C24×C61—81no—
162C24×C61C2×D411yescharacteristic
163C23×D61—21no—
164C2×D4×C61—24no—
165C2×D4×C61—28no—
166C2×D4×C61—28no—
167C2×D4×C61—24no—
168C2×D4×C61—28no—
169C2×D4×C61—28no—
170C2×D4×C61—24no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61C22×C412yes—
178C2×D4×C61C22×C412yes—
179C2×D4×C61C2×D412yes—
180C2×D4×C61C2×D412yes—
181C2×D4×C61#4112yes—
182C2×D4×C61#4112yes—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61C22×C412yes—
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61#4112yes—
192C22×C4×C61C2411yescharacteristic
193C2×C22⋊D61—24no—
194C2×C22⋊D61—81no—
195C2×C22⋊D61—81no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—24no—
200C22×Dic61—24no—
201C22×Dic61—24no—
202C22×Dic61—24no—
203C22×Dic61—81no—
204C22×Dic61—81no—
205C22×Dic61—81no—
206C22×Dic61—81no—
207C22×Dic61—81no—
208C22×Dic61—81no—
209C22×Dic61—81no—
210C22×Dic61—81no—
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213C22×Dic61C2×D411yescharacteristic
214C22×Dic61C2×D411yescharacteristic
215C2×D244—21no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244C22×C412yes—
221C2×C4×D61—42no—
222C2×C4×D61—81no—
223C2×C4×D61—81no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C22⋊C4×C61—81no—
235C22⋊Dic61—24no—
236C22⋊Dic61—24no—
237C22⋊Dic61—24no—
238C22⋊Dic61—22no—
239C22⋊Dic61—22no—
240C22⋊Dic61—24no—
241C22⋊Dic61—24no—
242#11758199—28no—
243#11758199—28no—
244#11758198—24no—
245#11758198—42no—
246#11758198—81no—
247#11758198—81no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—22no—
252C4⋊Dic61—22no—
253C4⋊Dic61C22×C412yes—
254C4⋊Dic61C2×D412yes—
255C4⋊Dic61C2×D412yes—
256#11758196—81no—
257C4×Dic61—24no—
258C4×Dic61—21no—
259C4×Dic61—21no—
260C4×Dic61—81no—
261C4×Dic61C2×D412yes—
262C4×Dic61C2×D412yes—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418C22×C412yes—
268C2×#92418C22×C412yes—
269C23×C61—216no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—21no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—21no—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—84no—
291C23×C61—84no—
292C23×C61—84no—
293C23×C61—84no—
294C23×C61—84no—
295C23×C61—84no—
296C23×C61C4×D412yes—
297C23×C61C22×D411yescharacteristic
298C22×D61—22no—
299C22×D61—41no—
300C22×D61—41no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61—41no—
305D4×C61—216no—
306D4×C61—22no—
307D4×C61—22no—
308D4×C61—22no—
309D4×C61—22no—
310D4×C61—22no—
311D4×C61—22no—
312D4×C61C4×D414yes—
313D4×C61C4×D414yes—
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—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61C4×D412yes—
327C2×C4×C61C23×C411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61C22×D411yescharacteristic
330C2×C4×C61C2×#4111yescharacteristic
331C2×C4×C61C2×#4111yescharacteristic
332C2×C4×C61C2×#4111yescharacteristic
333C22⋊D61—84no—
334C2×Dic61—21no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61—22no—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—84no—
354C2×Dic61—84no—
355C2×Dic61—84no—
356C2×Dic61—84no—
357C2×Dic61#12012yes—
358C2×Dic61#12012yes—
359D244—22no—
360D244—22no—
361D244—41no—
362D244—41no—
363C4×D61—84no—
364C8×C61—41no—
365C8×C61—41no—
366#92418—22no—
367#92418—22no—
368#21458—611nomaximal, Sylow
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—22no—
372C22×C61—24no—
373C22×C61—24no—
374C22×C61—41no—
375C22×C61—42no—
376C22×C61—42no—
377C22×C61—41no—
378C22×C61—42no—
379C22×C61—42no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—42no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—41no—
387C22×C61—42no—
388C22×C61—42no—
389C22×C61—41no—
390C22×C61—816no—
391C22×C61C2×C4×D411yescharacteristic
392C22×C61C2×#12011yescharacteristic
393C22×C61#52511yescharacteristic
394C22×C61#57611yescharacteristic
395C22×C61#57611yescharacteristic
396C22×C61#57611yescharacteristic
397C22×C61#57711yescharacteristic
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—42no—
401C2×D61—81no—
402C2×D61—81no—
403C2×D61—81no—
404C2×D61—81no—
405C4×C61—22no—
406C4×C61—81no—
407C4×C61—81no—
408C4×C61C2×C4×D411yescharacteristic
409C4×C61C2×C4×D411yescharacteristic
410C4×C61#52511yescharacteristic
411C4×C61#52511yescharacteristic
412Dic61—22no—
413Dic61—22no—
414Dic61—42no—
415Dic61—41no—
416Dic61—42no—
417Dic61—41no—
418Dic61—42no—
419C2×#518—611no—
420C2×#447—611no—
421C2×#442—611no—
422C2×C4×D8—611no—
423#2324—611no—
424#1879—611no—
425#1879—611no—
426#1875—611no—
427#1864—611no—
428#1862—611no—
429#1854—611no—
430#1786D6111yescharacteristic, complemented
431#1762—611no—
432C4×#102—611no—
433#1750—611no—
434C2×C61—42no—
435C2×C61—44no—
436C2×C61—44no—
437C2×C61C4×#12011yescharacteristic
438C2×C61#294611yescharacteristic
439C2×C61#294811yescharacteristic
440C2×C61#300811yescharacteristic
441C2×C61#301211yescharacteristic
442C2×C61#311811yescharacteristic
443C2×C61#312211yescharacteristic
444D61—82no—
445C23×D4C2×D6111yescharacteristic
446C22×D8—611no—
447C22×D8—611no—
448C2×#121—611no—
449#518—1224no—
450#518—1224no—
451C2×C4×D4—611no—
452C2×C4×D4—611no—
453C2×C4×D4—611no—
454C2×C4×D4—611no—
455C2×C4×D4—611no—
456C2×C4×D4—1221no—
457C2×C4×D4—1221no—
458C2×#117—611no—
459C2×#117—611no—
460C22×C22⋊C4—1221no—
461C22×C22⋊C4—1221no—
462#447—618no—
463#442—1224no—
464C4×D8—1224no—
465C2×#107—611no—
466C2×#106—611no—
467C2×#102—611no—
468C2×#102—611no—
469C2×#102—611no—
470C2×#102—611no—
471C2×#102C2×D6111yescharacteristic
472C2×#102C2×D6111yescharacteristic
473C2×#102C2×D6111yescharacteristic
474C2×#102C2×D6111yescharacteristic
475C2×C22⋊C8—611no—
476C2×C22⋊C8C2×D6111yescharacteristic
477C2×#97—611no—
478C2×C4×C8—611no—
479#390—611no—
480#390—1221no—
481#389—611no—
482#388—1221no—
483#386—1221no—
484#385—1221no—
485#380C2×D6111yescharacteristic
486C4×C4⋊C4—611no—
487#340—611no—
488#340—611no—
489#340—611no—
490#340—611no—
491#336—611no—
492#336—611no—
493C61#2145811yescharacteristic, complemented, Sylow
494C25—21no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—21no—
500C22×D4—22no—
501C22×D4—611no—
502C22×D4—1221no—
503C22×D4C4×D6114yescomplemented
504C22×D4C22×D6111yescharacteristic
505C22×D4C22×D6111yescharacteristic
506C23×C4—1221no—
507C23×C4—1221no—
508C23×C4—1221no—
509C23×C4—1221no—
510C23×C4—1221no—
511C23×C4C22×D6111yescharacteristic
512C2×D8—614no—
513C2×D8—614no—
514C2×D8—1222no—
515C2×D8—1222no—
516C2×D8—1222no—
517C2×D8—1222no—
518C22×C8—611no—
519C22×C8—611no—
520C22×C8C22×D6111yescharacteristic
521C22×C8C22×D6111yescharacteristic
522#121—614no—
523#121—1222no—
524C4×D4—614no—
525C4×D4—614no—
526C4×D4—1222no—
527C4×D4—1222no—
528C4×D4—1222no—
529C4×D4—1222no—
530C4×D4—1222no—
531C4×D4—1222no—
532C4×D4—1228no—
533C4×D4—1228no—
534C4×D4—1222no—
535C4×D4—1222no—
536#117—1222no—
537#117—1222no—
538#117—1222no—
539#117—1222no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—611no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—611no—
544C2×C4⋊C4—611no—
545C2×C4⋊C4—1221no—
546C2×C4⋊C4C22×D6111yescharacteristic
547C2×C4⋊C4C22×D6111yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—611no—
550C2×C22⋊C4—611no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1228no—
556C2×C22⋊C4—1228no—
557C2×C22⋊C4—1221no—
558C2×C22⋊C4—1221no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C42—611no—
563C2×C42—611no—
564C2×C42—1221no—
565C2×C42—1221no—
566#107—1222no—
567#106—1222no—
568#102—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102—614no—
573#102—614no—
574#102—1222no—
575#102—1222no—
576C22⋊C8—22no—
577C22⋊C8—614no—
578#97—1222no—
579C4×C8—1222no—
580#95—21no—
581#95—1221no—
582#95—1221no—
583C24—24no—
584C24—24no—
585C24—21no—
586C24—21no—
587C24—24no—
588C24—81no—
589C24—81no—
590C24—81no—
591C24—81no—
592C24—1221no—
593C24D4×D6111yescharacteristic
594C2×D4—24no—
595C2×D4—24no—
596C2×D4—28no—
597C2×D4—28no—
598C2×D4—28no—
599C2×D4—28no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—24no—
607C2×D4—612no—
608C2×D4—1224no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4—1221no—
613C2×D4—1221no—
614C2×D4—4881no—
615C2×D4—4881no—
616C2×D4C2×C4×D6112yes—
617C2×D4C2×C4×D6112yes—
618C2×D4D4×D6112yes—
619C2×D4D4×D6112yes—
620C2×D4#1175822412yes—
621C2×D4#1175822412yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—1224no—
633C22×C4—1224no—
634C22×C4—1224no—
635C22×C4—1224no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—4881no—
640C22×C4—4881no—
641C22×C4—4881no—
642C22×C4—4881no—
643C22×C4—4881no—
644C22×C4—4881no—
645C22×C4—4881no—
646C22×C4—4881no—
647C22×C4—4881no—
648C22×C4—4881no—
649C22×C4—2442no—
650C22×C4C2×C4×D6112yes—
651C22×C4D4×D6111yescharacteristic
652C22×C4#1175822412yes—
653C22×C4C23×D6111yescharacteristic
654D8—1228no—
655D8—1228no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—612no—
663C2×C8—612no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8—1221no—
667C2×C8—1221no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—612no—
673C4⋊C4—612no—
674C4⋊C4—612no—
675C4⋊C4—1222no—
676C4⋊C4—1222no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—4881no—
681C22⋊C4—81no—
682C22⋊C4—1222no—
683C22⋊C4—1222no—
684C22⋊C4—1224no—
685C22⋊C4—1224no—
686C22⋊C4—1224no—
687C22⋊C4—1224no—
688C22⋊C4—1224no—
689C22⋊C4—1224no—
690C22⋊C4—4881no—
691C22⋊C4—4881no—
692C22⋊C4—2442no—
693C42—612no—
694C42—612no—
695C42—1224no—
696C42—1221no—
697C42—1221no—
698C42—4881no—
699C23—216no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—21no—
706C23—22no—
707C23—22no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—84no—
721C23—84no—
722C23—84no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—1222no—
727C23—2441no—
728C23—2441no—
729C23—2441no—
730C23—2441no—
731C23—2441no—
732C23—2441no—
733C23#1451973712yes—
734C23C2×D4×D6111yescharacteristic
735D4—216no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—1222no—
743D4—1222no—
744D4—4884no—
745D4—2441no—
746D4—2441no—
747D4#1451973714yes—
748D4#1451973714yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—612no—
762C2×C4—612no—
763C2×C4—1221no—
764C2×C4—1221no—
765C2×C4—1221no—
766C2×C4—1221no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—1221no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—4884no—
777C2×C4—4884no—
778C2×C4—4884no—
779C2×C4—4884no—
780C2×C4—4884no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4#1451973712yes—
788C2×C4C22×C4×D6111yescharacteristic
789C2×C4C2×D4×D6111yescharacteristic
790C2×C4C2×D4×D6111yescharacteristic
791C2×C4C2×#1175822411yescharacteristic
792C2×C4C2×#1175822411yescharacteristic
793C2×C4C2×#1175822411yescharacteristic
794C8—41no—
795C8—41no—
796C8—1222no—
797C8—1222no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—24no—
802C22—24no—
803C22—42no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—41no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—41no—
819C22—816no—
820C22—4881no—
821C22—4881no—
822C22—4881no—
823C22—4881no—
824C22—2442no—
825C22—2442no—
826C22—2442no—
827C22C2×#1451973711yescharacteristic
828C22#120×D6111yescharacteristic
829C22#1684026811yescharacteristic
830C22#1684056311yescharacteristic
831C22#1684056611yescharacteristic
832C22#1684056611yescharacteristic
833C22#1684056811yescharacteristic
834C4—22no—
835C4—81no—
836C4—81no—
837C4—1222no—
838C4—1222no—
839C4—2441no—
840C4—2442no—
841C4—2442no—
842C4—2441no—
843C4—2442no—
844C4C2×#1451973711yescharacteristic
845C4C2×#1451973711yescharacteristic
846C4#1684026811yescharacteristic
847C4#1684026811yescharacteristic
848C2—42no—
849C2—44no—
850C2—44no—
851C2—4882no—
852C2#2144831811yescharacteristic
853C2#2145464511yescharacteristic
854C2#2145466711yescharacteristic
855C2#2145508211yescharacteristic
856C2#2145512411yescharacteristic
857C2#2145600411yescharacteristic
858C2#2145605611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1786C2
socleC23×C61C22×D4
prime radicalC2×#16839896C2
cosocleC22×C4×C61C24
hypercenter#1786D61
hypocenterC61#21458
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
1. C2×#16840237C2semidirect
3. C2×#16839871C2semidirect
4. C2×#16839842C2semidirect
5. #21448508C2semidirect
6. #21446165C2semidirect
7. #21446165C2semidirect
8. #21446139C2semidirect
9. #21446078C2semidirect
10. #21446064C2semidirect
11. #21446016C2semidirect
12. #21445646C2semidirect
13. #102×Dic61C2semidirect
14. #21445587C2semidirect
15. C61×#1786C2semidirect
27. C2×#14519739C22semidirect
32. #16839896C4semidirect
35. C2×#14519710C22semidirect
36. C2×#14519708C22semidirect
37. C2×#14519699C22semidirect
38. C2×#14519699C22semidirect
42. C2×#14519687C22semidirect
43. C2×C8×Dic61C22semidirect
44. #16839663C22semidirect
46. #16839658C22semidirect
50. C4⋊C4×Dic61C22semidirect
51. #16839525C22semidirect
52. #16839525C22semidirect
53. #16839524C22semidirect
54. #16839524C22semidirect
55. #16839516C22semidirect
56. #16839516C22semidirect
75. C2×#11758199C2×C4semidirect
76. C2×#11758199C2×C4semidirect
80. #14519751C2×C4semidirect
89. D4×Dic61D4semidirect
90. D4×Dic61D4semidirect
124. #14519698C2×C4semidirect
125. #14519698C2×C4semidirect
126. C22⋊#92418C2×C4semidirect
138. C22×D4×C61C2×C4semidirect
430. #1786D61semidirect
493. C61#21458semidirect
503. C22×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402372
C2×#168398962
C2×#168398712
C2×#168398422
#214485082
#214461652
#214461392
#214460782
#214460642
#214460162
#214456462
#102×Dic612
#214455872
C61×#17862
#2145861