Finite Group Databasebeta

← #29712801

Subgroups — #29712801

Order 15616.

1340 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840340C211yesmaximal, characteristic
2C2×#16840103C211yesmaximal, characteristic, complemented
3C2×#16840086C211yesmaximal, characteristic, complemented
4#21447022C211yesmaximal, characteristic, complemented
5#21447015C211yesmaximal, characteristic, complemented
6#21447008C211yesmaximal, characteristic, complemented
7#21447001C211yesmaximal, characteristic, complemented
8#21446136C211yesmaximal, characteristic, complemented
9#21446126C211yesmaximal, characteristic, complemented
10#21446011C211yesmaximal, characteristic, complemented
11#21446006C211yesmaximal, characteristic, complemented
12#21445757C211yesmaximal, characteristic, complemented
13#21445757C211yesmaximal, characteristic, complemented
14#21445731C211yesmaximal, characteristic, complemented
15C61×#2311C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17#16840340—24no—
18#16840340—24no—
19C2×#14519756C2211yescharacteristic
20C2×#14519756C2211yescharacteristic
21C2×#14519753—21no—
22C2×#14519751C2211yescharacteristic
23C2×#14519751C2211yescharacteristic
24C2×#14519749—21no—
25C2×#14519749—21no—
26C2×#14519748—21no—
27C22×C4⋊Dic61C2211yescharacteristic
28#16840103—24no—
29#16840086—24no—
30C2×#14519710C2211yescharacteristic
31C2×#14519710C2211yescharacteristic
32C2×#14519708C2211yescharacteristic
33C2×#14519708C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42C2×C22⋊#92418C2211yescharacteristic
43C2×C22⋊#92418C2211yescharacteristic
44C2×C22⋊#92418C2211yescharacteristic
45C2×C22⋊#92418C2211yescharacteristic
46C2×C22⋊#92418C2211yescharacteristic
47C2×C22⋊#92418C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52C22×#41×C61C2211yescharacteristic
53C2×#117×C61C2211yescharacteristic
54C22×C4⋊C4×C61C2211yescharacteristic
55C61×#391—21no—
56C61×#390—21no—
57C61×#386—21no—
58C61×#386—21no—
59C61×#380C2211yescharacteristic
60C61×#380C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C61×#380C2211yescharacteristic
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—41no—
68C2×#11758222—41no—
69C22×Dic122C2311yescharacteristic
70C22×D244C2311yescharacteristic
71C22×C22⋊D61—21no—
72C22×C22⋊D61—21no—
73C22×C22⋊D61—21no—
74C23×Dic61—21no—
75C22×C4×D61—21no—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80#14519756—22no—
81#14519756—22no—
82#14519756—22no—
83#14519756D414yes—
84#14519753—28no—
85#14519751—22no—
86#14519751—22no—
87#14519751—22no—
88#14519751D414yes—
89#14519749—28no—
90#14519749—28no—
91#14519748—28no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61—22no—
94C2×C4⋊Dic61—22no—
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103#14519710—22no—
104#14519710—22no—
105#14519708—22no—
106#14519708—22no—
107#14519700—22no—
108#14519700—22no—
109#14519700—41no—
110#14519700—41no—
111#14519697—22no—
112#14519697—22no—
113#14519697—41no—
114#14519697—41no—
115C22⋊#92418—22no—
116C22⋊#92418—22no—
117C22⋊#92418—22no—
118C22⋊#92418—22no—
119C22⋊#92418—41no—
120C22⋊#92418—41no—
121C2×#41×C61—22no—
122C2×#41×C61—22no—
123C2×#41×C61—22no—
124C2×#41×C61—22no—
125C2×#41×C61—41no—
126C2×#41×C61—41no—
127C22×Q8×C61D411yescharacteristic
128C22×D4×C61D411yescharacteristic
129C22×D4×C61D411yescharacteristic
130C22×D4×C61D411yescharacteristic
131C23×C4×C61—21no—
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135#117×C61—22no—
136#117×C61—22no—
137C2×C4⋊C4×C61—21no—
138C2×C4⋊C4×C61—41no—
139C2×C4⋊C4×C61—41no—
140C2×C4⋊C4×C61C2311yescharacteristic
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C22⋊C4×C61—21no—
145C2×C22⋊C4×C61—21no—
146C2×C22⋊C4×C61—21no—
147C2×C22⋊C4×C61—21no—
148C2×C22⋊C4×C61—21no—
149C2×C42×C61—21no—
150#95×C61—21no—
151#95×C61—21no—
152#95×C61—21no—
153#95×C61—21no—
154C24×C61C2×D411yescharacteristic
155C24×C61C2×D411yescharacteristic
156C24×C61C2×D411yescharacteristic
157C23×D61—21no—
158#41×C61—44no—
159#41×C61—44no—
160#41×C61—44no—
161#41×C61—44no—
162C2×Q8×C61—22no—
163C2×Q8×C61—22no—
164C2×Q8×C61—41no—
165C2×D4×C61—22no—
166C2×D4×C61—22no—
167C2×D4×C61—22no—
168C2×D4×C61—22no—
169C2×D4×C61—22no—
170C2×D4×C61—22no—
171C2×D4×C61—41no—
172C2×D4×C61—41no—
173C2×D4×C61—41no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
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×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—42no—
193C22×C4×C61—81no—
194C22×C4×C61—81no—
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D412yes—
198C22×C4×C61C2×D412yes—
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61#4112yes—
201C22×C4×C61#4112yes—
202C22×C4×C61C2411yescharacteristic
203C2×C22⋊D61—24no—
204C2×C22⋊D61—24no—
205C2×C22⋊D61—24no—
206C2×C22⋊D61—42no—
207C2×C22⋊D61—42no—
208C2×C22⋊D61—81no—
209C2×C22⋊D61—81no—
210C2×C22⋊D61—81no—
211C2×C22⋊D61—81no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—24no—
216C22×Dic61—81no—
217C22×Dic61—81no—
218#11758222—44no—
219#11758222—44no—
220#11758222—44no—
221#11758222—44no—
222C2×D244—21no—
223C2×D244—21no—
224C2×D244—21no—
225C2×D244—21no—
226C2×D244—21no—
227C2×D244C2×D412yes—
228C2×C4×D61—24no—
229C2×C4×D61—42no—
230C2×C4×D61—42no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122C2×D412yes—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—42no—
246C22⋊C4×C61—42no—
247C22⋊C4×C61—81no—
248C22⋊C4×C61—81no—
249C22⋊C4×C61—81no—
250C22⋊C4×C61—81no—
251C42×C61—42no—
252C22⋊Dic61—24no—
253C22⋊Dic61—24no—
254#11758198—24no—
255#11758198—24no—
256C4⋊Dic61—24no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61C2×D412yes—
260C4⋊Dic61C2×D412yes—
261#11758196—24no—
262#11758196—24no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418—21no—
274C2×#92418—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61#12012yes—
295C23×C61#12312yes—
296C23×C61C22×D411yescharacteristic
297C22×D61—22no—
298C22×D61—41no—
299C22×D61—41no—
300C22×D61—41no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61—41no—
304Q8×C61—44no—
305D4×C61—44no—
306D4×C61—44no—
307D4×C61—44no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
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—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
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×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—84no—
340C2×C4×C61#12012yes—
341C2×C4×C61#12312yes—
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C2×#4111yescharacteristic
345C2×C4×C61C2×#4111yescharacteristic
346C2×C4×C61H(5,𝔽2)11yescharacteristic
347C2×C4×C61H(5,𝔽2)11yescharacteristic
348C22⋊D61—48no—
349C22⋊D61—84no—
350C22⋊D61—84no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—84no—
361D244—22no—
362D244—22no—
363D244—41no—
364D244—41no—
365C4×D61—48no—
366Dic122—22no—
367Dic122—22no—
368Dic122—41no—
369Dic122—41no—
370#92418—41no—
371#92418—41no—
372#92418—41no—
373#92418—41no—
374#24017—611nomaximal, Sylow
375C22×C61—22no—
376C22×C61—22no—
377C22×C61—22no—
378C22×C61—22no—
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—41no—
382C22×C61—41no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61C2×#12011yescharacteristic
397C22×C61C2×#12311yescharacteristic
398C22×C61#53411yescharacteristic
399C22×C61#57611yescharacteristic
400C22×C61#57711yescharacteristic
401C22×C61#57711yescharacteristic
402C22×C61#57811yescharacteristic
403C2×D61—42no—
404C2×D61—42no—
405C2×D61—42no—
406C2×D61—81no—
407C2×D61—81no—
408C2×D61—81no—
409C2×D61—81no—
410C4×C61—22no—
411C4×C61—22no—
412C4×C61—41no—
413C4×C61—81no—
414C4×C61—81no—
415C4×C61—81no—
416C4×C61—81no—
417C4×C61#54611yescharacteristic
418C4×C61#54611yescharacteristic
419C4×C61#54611yescharacteristic
420C4×C61#54611yescharacteristic
421Dic61—42no—
422Dic61—42no—
423Dic61—42no—
424C2×#537—611no—
425C2×#485—611no—
426C2×#482—611no—
427#2311D6111yescharacteristic, complemented
428#2036—611no—
429#2035—611no—
430#2034—611no—
431#2033—611no—
432#1874—611no—
433#1872—611no—
434#1853—611no—
435#1852—611no—
436#1788—611no—
437#1788—611no—
438#1780—611no—
439C2×C61—42no—
440C2×C61—42no—
441C2×C61—81no—
442C2×C61#240511yescharacteristic
443C2×C61#301211yescharacteristic
444C2×C61#301311yescharacteristic
445C2×C61#309811yescharacteristic
446C2×C61#309911yescharacteristic
447C2×C61#319811yescharacteristic
448C2×C61#320111yescharacteristic
449D61—82no—
450C22×#41—611no—
451C22×#41C2×D6111yescharacteristic
452#537—1224no—
453#537—1224no—
454C2×C22⋊Q8—611no—
455C2×C22⋊Q8—611no—
456C2×C22⋊Q8—1221no—
457C2×#121—611no—
458C2×#121—611no—
459C2×#121—1221no—
460C2×#121—1221no—
461C2×#121—1221no—
462C2×#117C2×D6111yescharacteristic
463C22×C4⋊C4—611no—
464C22×C4⋊C4C2×D6111yescharacteristic
465#485—1224no—
466#482—1224no—
467C2×#107—611no—
468C2×#107—611no—
469C2×#106—611no—
470C2×#106—611no—
471C2×#103—611no—
472C2×#103—611no—
473C2×#103—611no—
474C2×#103—611no—
475C2×#102—611no—
476C2×#102—611no—
477C2×#102—611no—
478C2×#102—611no—
479C2×C22⋊C8—611no—
480C2×C22⋊C8—611no—
481C2×C22⋊C8—611no—
482C2×C22⋊C8—611no—
483C2×C22⋊C8—611no—
484C2×C22⋊C8—611no—
485#391—21no—
486#390—21no—
487#386—21no—
488#386—21no—
489#380C2×D6111yescharacteristic
490#380C2×D6111yescharacteristic
491#380C2×D6111yescharacteristic
492#380C2×D6111yescharacteristic
493#340—611no—
494#340—611no—
495#340—611no—
496#340—611no—
497C61#2401711yescharacteristic, complemented, Sylow
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—1222no—
505C2×#41—1222no—
506C2×#41—1222no—
507C2×#41—1222no—
508C2×#41—2441no—
509C2×#41—2441no—
510C22×Q8—611no—
511C22×Q8C22⋊D6111yescharacteristic
512C22×D4—611no—
513C22×D4—1221no—
514C22×D4—1221no—
515C22×D4—1221no—
516C22×D4C22⋊D6111yescharacteristic
517C22×D4C22⋊D6111yescharacteristic
518C22×D4C22⋊D6111yescharacteristic
519C23×C4—21no—
520C23×C4—1221no—
521C23×C4—1221no—
522C23×C4C22×D6111yescharacteristic
523C23×C4C22×D6111yescharacteristic
524C23×C4C22×D6111yescharacteristic
525C22×C8—611no—
526C22×C8—611no—
527C22×C8—611no—
528C22×C8—611no—
529C22⋊Q8—614no—
530C22⋊Q8—1222no—
531C22⋊Q8—1222no—
532C22⋊Q8—1228no—
533C22⋊Q8—1222no—
534#121—614no—
535#121—1222no—
536#121—1222no—
537#121—1228no—
538#121—1228no—
539#121—1228no—
540#121—1222no—
541#117—22no—
542#117—22no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—41no—
545C2×C4⋊C4—41no—
546C2×C4⋊C4—611no—
547C2×C4⋊C4—611no—
548C2×C4⋊C4—1222no—
549C2×C4⋊C4—1222no—
550C2×C4⋊C4—1221no—
551C2×C4⋊C4—1221no—
552C2×C4⋊C4—1221no—
553C2×C4⋊C4C22×D6111yescharacteristic
554C2×C4⋊C4C22×D6111yescharacteristic
555C2×C4⋊C4C22×D6111yescharacteristic
556C2×C4⋊C4C22×D6111yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4—1221no—
566C2×C42—21no—
567#107—1222no—
568#107—1222no—
569#106—1222no—
570#106—1222no—
571#103—1222no—
572#103—1222no—
573#103—2441no—
574#103—2441no—
575#102—1222no—
576#102—1222no—
577#102—2441no—
578#102—2441no—
579C22⋊C8—1222no—
580C22⋊C8—1222no—
581C22⋊C8—1222no—
582C22⋊C8—1222no—
583C22⋊C8—2441no—
584C22⋊C8—2441no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—1221no—
590C24C2×C22⋊D6111yescharacteristic
591C24C2×C22⋊D6111yescharacteristic
592C24C2×C22⋊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—22no—
602C2×Q8—22no—
603C2×Q8—41no—
604C2×Q8—612no—
605C2×Q8—1221no—
606C2×Q8—1221no—
607C2×Q8—1221no—
608C2×Q8—1221no—
609C2×Q8—1221no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—41no—
617C2×D4—41no—
618C2×D4—41no—
619C2×D4—612no—
620C2×D4—1224no—
621C2×D4—1224no—
622C2×D4—1224no—
623C2×D4—1221no—
624C2×D4—1221no—
625C2×D4—1221no—
626C2×D4—1221no—
627C2×D4—1221no—
628C2×D4—4881no—
629C2×D4—4881no—
630C2×D4—4881no—
631C2×D4—4881no—
632C2×D4—2442no—
633C2×D4—2442no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—42no—
653C22×C4—81no—
654C22×C4—81no—
655C22×C4—1224no—
656C22×C4—1224no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—4881no—
661C22×C4—4881no—
662C22×C4—2442no—
663C22×C4—2442no—
664C22×C4#1175822212yes—
665C22×C4#1175822212yes—
666C22×C4D4×D6112yes—
667C22×C4D4×D6112yes—
668C22×C4C2×C22⋊D6111yescharacteristic
669C22×C4C2×C22⋊D6111yescharacteristic
670C22×C4C2×C22⋊D6111yescharacteristic
671C22×C4C23×D6111yescharacteristic
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—1221no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8—1221no—
680C2×C8—1221no—
681C2×C8—1221no—
682C2×C8—1221no—
683C2×C8—1221no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—42no—
693C4⋊C4—612no—
694C4⋊C4—612no—
695C4⋊C4—1224no—
696C4⋊C4—1224no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1224no—
700C22⋊C4—42no—
701C22⋊C4—81no—
702C22⋊C4—81no—
703C22⋊C4—81no—
704C22⋊C4—81no—
705C22⋊C4—1224no—
706C22⋊C4—1224no—
707C22⋊C4—1224no—
708C22⋊C4—1224no—
709C42—42no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—1222no—
730C23—2441no—
731C23—2441no—
732C23—2441no—
733C23—2441no—
734C23—2441no—
735C23—2441no—
736C23#1451974512yes—
737C23#1451976012yes—
738C23C22×C22⋊D6111yescharacteristic
739Q8—44no—
740Q8—1222no—
741Q8—1222no—
742Q8—2441no—
743Q8—2441no—
744D4—44no—
745D4—44no—
746D4—44no—
747D4—1222no—
748D4—1222no—
749D4—4884no—
750D4—4884no—
751D4—2448no—
752D4—2441no—
753D4—2441no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—84no—
786C2×C4—1222no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—4884no—
790C2×C4—2448no—
791C2×C4—2441no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4#1451974512yes—
798C2×C4#1451976012yes—
799C2×C4C2×D4×D6111yescharacteristic
800C2×C4C2×D4×D6111yescharacteristic
801C2×C4C2×#1175822211yescharacteristic
802C2×C4C2×#1175822211yescharacteristic
803C2×C4#1451982211yescharacteristic
804C2×C4#1451982211yescharacteristic
805C8—2441no—
806C8—2441no—
807C8—2441no—
808C8—2441no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—4881no—
831C22—4881no—
832C22—4881no—
833C22—4881no—
834C22—2442no—
835C22—2442no—
836C22—2442no—
837C22C2×#1451974511yescharacteristic
838C22C2×#1451976011yescharacteristic
839C22#1684032111yescharacteristic
840C22#1684056511yescharacteristic
841C22#1684057011yescharacteristic
842C22#1684057311yescharacteristic
843C22#1684057711yescharacteristic
844C4—22no—
845C4—22no—
846C4—41no—
847C4—81no—
848C4—81no—
849C4—81no—
850C4—81no—
851C4—2442no—
852C4—2442no—
853C4—2442no—
854C4#1684040211yescharacteristic
855C4#1684040211yescharacteristic
856C4#1684040211yescharacteristic
857C4#1684040211yescharacteristic
858C2—42no—
859C2—42no—
860C2—81no—
861C2—4882no—
862C2#2144914611yescharacteristic
863C2#2145512011yescharacteristic
864C2#2145513111yescharacteristic
865C2#2145579711yescharacteristic
866C2#2145580811yescharacteristic
867C2#2145667111yescharacteristic
868C2#2145670111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2311C2
socleC23×C61C22×D4
prime radicalC2×#16840340C2
hypercenter#2311D61
hypocenterC61#24017
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×#41 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. C2×#16840103C2semidirect
3. C2×#16840086C2semidirect
4. #21447022C2semidirect
5. #21447015C2semidirect
6. #21447008C2semidirect
7. #21447001C2semidirect
8. #21446136C2semidirect
9. #21446126C2semidirect
10. #21446011C2semidirect
11. #21446006C2semidirect
12. #21445757C2semidirect
13. #21445757C2semidirect
14. #21445731C2semidirect
15. C61×#2311C2semidirect
427. #2311D61semidirect
497. C61#24017semidirect

Maximal subgroups

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

subgroupindex
C2×#168403402
C2×#168401032
C2×#168400862
#214470222
#214470152
#214470082
#214470012
#214461362
#214461262
#214460112
#214460062
#214457572
#214457312
C61×#23112
#2401761