Finite Group Databasebeta

← #29700787

Subgroups — #29700787

Order 15616.

1070 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455039C211yesmaximal, characteristic
2C2×#16839880C211yesmaximal, characteristic, complemented
3#21454543C211yesmaximal, characteristic, complemented
4C2×#104×D61C211yesmaximal, characteristic, complemented
5#21454267C211yesmaximal, characteristic, complemented
6#21446704C211yesmaximal, characteristic, complemented
7#21446469C211yesmaximal, characteristic, complemented
8#21446261C211yesmaximal, characteristic, complemented
9#21446149C211yesmaximal, characteristic, complemented
10#21446147C211yesmaximal, characteristic, complemented
11#21446093C211yesmaximal, characteristic, complemented
12#21446025C211yesmaximal, characteristic, complemented
13#21445653C211yesmaximal, characteristic, complemented
14C4×#14519689C211yesmaximal, characteristic, complemented
15C61×#1937C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×#14519799C2211yescharacteristic
18C2×#14519797C2211yescharacteristic
19C2×#14519785C2211yescharacteristic
20C2×#14519783C2211yescharacteristic
21C2×#14519783C2211yescharacteristic, complemented
22C2×M16×D61C2211yescharacteristic
23#16840274C2211yescharacteristic
24C2×C42×D61C2211yescharacteristic
25#16839927C411yescharacteristic, complemented
26#16839925C411yescharacteristic, complemented
27#16839919C411yescharacteristic, complemented
28#16839914C411yescharacteristic, complemented
29#16839910C411yescharacteristic, complemented
30#16839908C411yescharacteristic, complemented
31#16839902C411yescharacteristic, complemented
32#16839897C411yescharacteristic, complemented
33#16839880—24no—
34#16839839—21no—
35#16839832—21no—
36#16839832—21no—
37#16839827—21no—
38C2×#14519713C2211yescharacteristic, complemented
39C2×#14519712C2211yescharacteristic, complemented
40C2×#14519705C2211yescharacteristic
41C2×#14519705C2211yescharacteristic, complemented
42C2×#14519704C2211yescharacteristic
43C2×#14519703C2211yescharacteristic
44C2×#14519703C2211yescharacteristic, complemented
45#104×D61—24no—
46#16839756C2211yescharacteristic
47#16839730C2211yescharacteristic, complemented
48#16839729C2211yescharacteristic
49#16839727—21no—
50#16839727—21no—
51#16839725C2211yescharacteristic
52#16839724—21no—
53C2×#14519689C2211yescharacteristic
54C2×#14519689C2211yescharacteristic
55C22⋊C8×D61—21no—
56#16839718C2211yescharacteristic, complemented
57C2×C4×#92418C2211yescharacteristic, complemented
58#16839526C2211yescharacteristic, complemented
59#16839521C2211yescharacteristic, complemented
60#16839516C2211yescharacteristic, complemented
61#16839516C2211yescharacteristic, complemented
62C61×#424C2211yescharacteristic, complemented
63C2×#104×C61C2211yescharacteristic
64C61×#416C2211yescharacteristic
65C61×#408C2211yescharacteristic
66C2×C4×C8×C61C2211yescharacteristic, complemented
67C61×#341C2211yescharacteristic, complemented
68C61×#339C2211yescharacteristic, complemented
69C2×#11758226C2×C411yescharacteristic
70C2×#11758222—21no—
71C2×#11758222C2311yescharacteristic
72C2×#11758222C2311yescharacteristic
73C2×#11758224—21no—
74C2×#11758224C2×C411yescharacteristic
75#41×D61—22no—
76#41×D61—22no—
77#41×D61—41no—
78#41×D61—41no—
79C2×Q8×D61C2×C411yescharacteristic
80C2×D4×D61—21no—
81C2×D4×D61C2×C411yescharacteristic
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61C2311yescharacteristic
85#14519799—22no—
86#14519799—22no—
87#14519797—41no—
88#14519797—41no—
89C2×Dic244C2×C411yescharacteristic, complemented
90C2×#11758202C2×C411yescharacteristic, complemented
91C2×#11758190C2×C411yescharacteristic, complemented
92C2×#11758190C2×C411yescharacteristic, complemented
93C2×#11758200C2×C411yescharacteristic, complemented
94C2×#11758201C2×C411yescharacteristic, complemented
95C2×D488C2×C411yescharacteristic, complemented
96C2×#11758199C2×C411yescharacteristic, complemented
97#14519785—22no—
98#14519785—41no—
99#14519783—22no—
100#14519783—22no—
101#14519783—41no—
102#14519783—41no—
103C2×#11758194C2311yescharacteristic
104C2×#11758194C2311yescharacteristic
105C2×#11758189—21no—
106C2×#11758189—21no—
107C2×#11758189—21no—
108C2×#11758189—21no—
109M16×D61—22no—
110M16×D61—41no—
111C22×#92418C2311yescharacteristic
112C22×#92418C2311yescharacteristic
113C2×C8×D61—21no—
114C2×C8×D61—21no—
115C2×C8×D61—21no—
116C2×C8×D61—21no—
117#14519761—21no—
118#14519757C2×C411yescharacteristic
119#14519757C2×C411yescharacteristic
120#14519752C2×C411yescharacteristic
121#14519752C2×C411yescharacteristic
122#14519747—21no—
123C4×D244—21no—
124C4×D244—21no—
125C2×C4×Dic61—21no—
126C2×C4×Dic61C2311yescharacteristic
127C42×D61—22no—
128C42×D61—41no—
129#14519713—22no—
130#14519712—41no—
131#14519705—22no—
132#14519705D414yescomplemented
133#14519704—22no—
134#14519703—22no—
135#14519703—41no—
136#14519700C2×C411yescharacteristic, complemented
137#14519700C2×C411yescharacteristic, complemented
138#14519697C2×C411yescharacteristic, complemented
139#14519697C2×C411yescharacteristic, complemented
140C22⋊#92418—21no—
141C22⋊#92418—21no—
142#14519689—21no—
143#14519689—21no—
144#14519689—21no—
145#14519689—21no—
146#14519689C2×C411yescharacteristic
147#14519689C2×C411yescharacteristic
148#14519689C2×C411yescharacteristic
149#14519689C2×C411yescharacteristic
150#14519689D411yescharacteristic
151#14519689D411yescharacteristic
152#14519689D411yescharacteristic
153#14519689D411yescharacteristic
154#14519688—21no—
155C4×#92418—21no—
156C4×#92418—41no—
157C2×#41×C61C2311yescharacteristic
158C2×M16×C61C2311yescharacteristic
159C2×M16×C61C2311yescharacteristic
160C22×C8×C61C2311yescharacteristic
161C22×C8×C61C2311yescharacteristic
162#117×C61C2311yescharacteristic
163C2×C42×C61C2311yescharacteristic
164C4⋊C8×C61—21no—
165C4⋊C8×C61—21no—
166#104×C61—22no—
167#103×C61C2×C411yescharacteristic, complemented
168#103×C61C2×C411yescharacteristic, complemented
169#102×C61C2×C411yescharacteristic, complemented
170#102×C61C2×C411yescharacteristic, complemented
171C22⋊C8×C61—21no—
172C22⋊C8×C61—21no—
173C4×C8×C61—22no—
174C23×D61—21no—
175C23×D61#4111yescharacteristic
176#41×C61—21no—
177#41×C61—21no—
178#41×C61—21no—
179#41×C61—21no—
180C2×Q8×C61C22×C411yescharacteristic
181C2×D4×C61—21no—
182C2×D4×C61C22×C411yescharacteristic
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61C2411yescharacteristic
186C2×C22⋊D61—21no—
187C2×C22⋊D61—21no—
188C2×C22⋊D61—21no—
189C2×C22⋊D61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61#4111yescharacteristic
193#11758226—22no—
194#11758226—41no—
195Q8×D61—22no—
196Q8×D61—41no—
197#11758224—22no—
198#11758224—41no—
199#11758224—42no—
200#11758224—42no—
201D4×D61—22no—
202D4×D61—41no—
203D4×D61—42no—
204D4×D61—42no—
205#11758222—21no—
206#11758222—21no—
207#11758222—21no—
208#11758222—21no—
209#11758222—21no—
210#11758222—21no—
211#11758222—42no—
212#11758222—42no—
213#11758222C2×D412yes—
214#11758222#4112yes—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244C22×C411yescharacteristic
219C2×D244C22×C411yescharacteristic
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—24no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—42no—
230C2×C4×D61—42no—
231C2×C4×D61—42no—
232C2×C4×D61—42no—
233C2×C4×D61C22×C411yescharacteristic
234C2×C4×D61C22×C411yescharacteristic
235C2×C4×D61C2×D411yescharacteristic
236C2×C4×D61C2×D411yescharacteristic
237C2×Dic122—21no—
238C2×Dic122C22×C411yescharacteristic
239C2×Dic122C22×C411yescharacteristic
240M16×C61—21no—
241M16×C61—21no—
242M16×C61—21no—
243M16×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61C22×C411yescharacteristic
251C2×C8×C61C22×C411yescharacteristic
252C2×C8×C61C2×D411yescharacteristic
253C2×C8×C61C2×D411yescharacteristic
254C4⋊C4×C61C22×C411yescharacteristic
255C4⋊C4×C61C22×C411yescharacteristic
256C22⋊C4×C61—21no—
257C42×C61—21no—
258C42×C61—21no—
259C42×C61C2×D412yes—
260#11758202—41no—
261#11758201—41no—
262#11758200—41no—
263#11758199—41no—
264#11758198—21no—
265#11758198—21no—
266#11758198—21no—
267#11758198—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270C4×Dic61—21no—
271C4×Dic61—21no—
272C4×Dic61—42no—
273#11758194—21no—
274#11758194—21no—
275#11758194—21no—
276#11758194C2×D412yes—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418C22×C411yescharacteristic
284C2×#92418C22×C411yescharacteristic
285C2×#92418C2×D411yescharacteristic
286C2×#92418C2×D411yescharacteristic
287Dic244—22no—
288D488—22no—
289#11758190—22no—
290#11758190—22no—
291#11758189—42no—
292#11758189—42no—
293#11758189—42no—
294#11758189—42no—
295C8×D61—42no—
296C8×D61—42no—
297C8×D61—42no—
298C8×D61—42no—
299C23×C61—21no—
300C23×C61C2×#4111yescharacteristic
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—21no—
304C22×D61—22no—
305C22×D61—21no—
306C22×D61—41no—
307C22×D61—42no—
308C22×D61—42no—
309C22×D61—81no—
310C22×D61C4×D411yescharacteristic
311C22×D61C4×D411yescharacteristic
312Q8×C61—21no—
313Q8×C61—21no—
314D4×C61—21no—
315D4×C61—21no—
316D4×C61—41no—
317D4×C61—41no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61C23×C411yescharacteristic
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61C2×#4111yescharacteristic
330C2×C4×C61H(5,𝔽2)11yescharacteristic
331C2×C4×C61H(5,𝔽2)11yescharacteristic
332C22⋊D61—22no—
333C22⋊D61—22no—
334C22⋊D61—42no—
335C22⋊D61—42no—
336C22⋊D61—41no—
337C22⋊D61—41no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61—22no—
342C2×Dic61—21no—
343C2×Dic61—42no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61C4×D411yescharacteristic
347C2×Dic61C4×D411yescharacteristic
348D244—21no—
349D244—21no—
350D244—21no—
351D244—42no—
352D244—42no—
353D244—81no—
354D244C4×D412yes—
355C4×D61—21no—
356C4×D61—21no—
357C4×D61—21no—
358C4×D61—21no—
359C4×D61—21no—
360C4×D61—22no—
361C4×D61—21no—
362C4×D61—22no—
363C4×D61—21no—
364C4×D61—21no—
365C4×D61—42no—
366C4×D61—42no—
367C4×D61—48no—
368C4×D61—41no—
369C4×D61—41no—
370Dic122—21no—
371Dic122—21no—
372Dic122—21no—
373Dic122—42no—
374Dic122C4×D412yes—
375C8×C61—21no—
376C8×C61—21no—
377C8×C61—21no—
378C8×C61—21no—
379C8×C61—41no—
380C8×C61—41no—
381#92418—21no—
382#92418—21no—
383#92418—22no—
384#92418—21no—
385#92418—21no—
386#92418—41no—
387#22888—611nomaximal, Sylow
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61C2×C4×D411yescharacteristic
394C22×C61#54611yescharacteristic
395C22×C61#55111yescharacteristic
396C2×D61—21no—
397C2×D61—21no—
398C2×D61—21no—
399C2×D61—22no—
400C2×D61—21no—
401C2×D61—21no—
402C2×D61—42no—
403C2×D61—42no—
404C2×D61—41no—
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—41no—
408C2×D61—41no—
409C2×D61—84no—
410C2×D61#44312yescomplemented
411C4×C61—24no—
412C4×C61—41no—
413C4×C61—41no—
414C4×C61—41no—
415C4×C61C2×C4×D411yescharacteristic
416C4×C61#51811yescharacteristic
417C4×C61D4211yescharacteristic
418C4×C61#54611yescharacteristic
419Dic61—22no—
420Dic61—21no—
421Dic61—21no—
422Dic61—42no—
423Dic61—41no—
424#3002—611no—
425C2×#443—611no—
426#2933—611no—
427C22×#104—611no—
428#2880—611no—
429#1974—611no—
430#1937D6111yescharacteristic, complemented
431#1929—611no—
432#1896—611no—
433#1876—611no—
434#1876—611no—
435#1866—611no—
436#1855—611no—
437#1764—611no—
438C4×C22⋊C8—611no—
439C2×C61—21no—
440C2×C61—21no—
441C2×C61—81no—
442C2×C61#235811yescharacteristic
443C2×C61C2×#44311yescharacteristic
444C2×C61#295611yescharacteristic
445D61—22no—
446D61—41no—
447D61—42no—
448D61—81no—
449C22×#41—611no—
450C2×#135—611no—
451C2×#135—611no—
452C2×#131—611no—
453C2×#131—611no—
454C2×#131—611no—
455C22×M16—611no—
456#525—611no—
457C22×C42—611no—
458#452—611no—
459#452—611no—
460#451—611no—
461#450—611no—
462#449—611no—
463#449—611no—
464#448—611no—
465#447—611no—
466#443—1224no—
467#436—1221no—
468#435—1221no—
469#435—1221no—
470C8×D4—1221no—
471C2×#108—611no—
472C2×#108—611no—
473#424C2×D6111yescharacteristic, complemented
474C2×#104—611no—
475C2×#104—611no—
476C2×#104—611no—
477C2×#104—611no—
478C2×#104—611no—
479C2×#104—1224no—
480C2×#104C2×D6111yescharacteristic
481#416—611no—
482#416C2×D6111yescharacteristic
483#408—611no—
484#408—611no—
485#408—1221no—
486#408—1221no—
487#408C2×D6111yescharacteristic
488#407—611no—
489#407—1221no—
490C2×C22⋊C8—611no—
491C2×C22⋊C8—611no—
492C2×C22⋊C8—1221no—
493#405—611no—
494C2×C4×C8—611no—
495C2×C4×C8C2×D6111yescharacteristic, complemented
496#341—611no—
497#341C2×D6111yescharacteristic, complemented
498#339—611no—
499#339C2×D6111yescharacteristic, complemented
500#336—611no—
501#336—611no—
502C61#2288811yescharacteristic, complemented, Sylow
503C2×#41—611no—
504C2×#41—611no—
505C2×#41—611no—
506C2×#41—611no—
507C2×#41—1221no—
508C2×#41—1221no—
509C2×#41—1222no—
510C2×#41—1222no—
511C2×#41—2441no—
512C2×#41—2441no—
513C2×#41C22×D6111yescharacteristic
514C22×Q8—611no—
515C22×D4—611no—
516C22×D4—1221no—
517C23×C4—611no—
518C23×C4—1221no—
519C23×C4—1221no—
520#135—1222no—
521#135—1222no—
522#135—2441no—
523#135—2441no—
524C2×Q16—611no—
525C2×Q16—611no—
526C2×SD16—611no—
527C2×SD16—611no—
528C2×SD16—611no—
529C2×SD16—611no—
530C2×D8—611no—
531C2×D8—611no—
532#131—1222no—
533#131—1222no—
534#131—1222no—
535#131—2441no—
536#131—2441no—
537#131—2441no—
538C2×M16—611no—
539C2×M16—611no—
540C2×M16—1221no—
541C2×M16—1221no—
542C2×M16—1221no—
543C2×M16—1221no—
544C2×M16—1222no—
545C2×M16—2441no—
546C2×M16C22×D6111yescharacteristic
547C2×M16C22×D6111yescharacteristic
548C22×C8—611no—
549C22×C8—611no—
550C22×C8—1221no—
551C22×C8—1221no—
552C22×C8—1221no—
553C22×C8—1221no—
554C22×C8C22×D6111yescharacteristic
555C22×C8C22×D6111yescharacteristic
556#123—1221no—
557C22⋊Q8—611no—
558C22⋊Q8—611no—
559#121—611no—
560#121—611no—
561#120—1221no—
562C4×D4—1221no—
563C4×D4—1221no—
564#117C22×D6111yescharacteristic
565C2×C42—611no—
566C2×C42—1222no—
567C2×C42—1221no—
568C2×C42—2441no—
569C2×C42C22×D6111yescharacteristic
570#108—1222no—
571#108—2441no—
572C4⋊C8—21no—
573C4⋊C8—21no—
574#104—22no—
575#104—614no—
576#104—1222no—
577#104—1222no—
578#104—1222no—
579#104—2441no—
580#103—611no—
581#103—611no—
582#103C4×D6111yescharacteristic, complemented
583#103C4×D6111yescharacteristic, complemented
584#102—611no—
585#102—611no—
586#102C4×D6111yescharacteristic, complemented
587#102C4×D6111yescharacteristic, complemented
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—611no—
591C22⋊C8—611no—
592C22⋊C8—611no—
593C22⋊C8—611no—
594C22⋊C8—611no—
595C22⋊C8—611no—
596C22⋊C8—611no—
597C22⋊C8—611no—
598C22⋊C8—1221no—
599C22⋊C8—1221no—
600C22⋊C8—1221no—
601C22⋊C8—1221no—
602C22⋊C8—1221no—
603C22⋊C8—1221no—
604#97—1221no—
605C4×C8—22no—
606C4×C8—1221no—
607C4×C8—2441no—
608C24—611no—
609C24—1221no—
610#41—21no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—612no—
615#41—612no—
616#41—1221no—
617#41—1221no—
618#41—1222no—
619#41—1222no—
620#41—1221no—
621#41—1221no—
622#41—1221no—
623#41—1221no—
624#41—2442no—
625#41—2442no—
626#41—2441no—
627#41—2442no—
628#41—2442no—
629#41—2441no—
630C2×Q8—611no—
631C2×Q8—611no—
632C2×Q8—1221no—
633C2×Q8—1222no—
634C2×Q8—2441no—
635C2×Q8C2×C4×D6111yescharacteristic
636C2×D4—21no—
637C2×D4—611no—
638C2×D4—611no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—1222no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—2441no—
648C2×D4—2442no—
649C2×D4—2442no—
650C2×D4C2×C4×D6111yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—611no—
654C22×C4—611no—
655C22×C4—611no—
656C22×C4—611no—
657C22×C4—611no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1224no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—2442no—
670C22×C4—2442no—
671C22×C4—2442no—
672C22×C4—2442no—
673C22×C4C23×D6111yescharacteristic
674Q16—1222no—
675Q16—2441no—
676SD16—1222no—
677SD16—1222no—
678SD16—2441no—
679SD16—2441no—
680D8—1222no—
681D8—2441no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—21no—
686M16—612no—
687M16—1221no—
688M16—1221no—
689M16—1221no—
690M16—2442no—
691M16—2442no—
692M16—2442no—
693M16—2442no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—611no—
701C2×C8—611no—
702C2×C8—611no—
703C2×C8—611no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—2442no—
711C2×C8—2442no—
712C2×C8—2442no—
713C2×C8—2442no—
714C2×C8C2×C4×D6111yescharacteristic
715C2×C8C2×C4×D6111yescharacteristic
716C2×C8D4×D6111yescharacteristic
717C2×C8D4×D6111yescharacteristic
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4C2×C4×D6111yescharacteristic
721C4⋊C4C2×C4×D6111yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—1221no—
724C22⋊C4—1221no—
725C22⋊C4—1221no—
726C22⋊C4—1221no—
727C42—21no—
728C42—21no—
729C42—1221no—
730C42—1221no—
731C42—2442no—
732C42D4×D6112yes—
733C23—21no—
734C23—611no—
735C23—611no—
736C23—1222no—
737C23—1221no—
738C23—1221no—
739C23—1221no—
740C23—1221no—
741C23—4881no—
742C23—2441no—
743C23—2442no—
744C23—2442no—
745C23#41×D6111yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—612no—
749Q8—1221no—
750Q8—1221no—
751Q8—1221no—
752Q8—2442no—
753D4—21no—
754D4—21no—
755D4—41no—
756D4—41no—
757D4—612no—
758D4—1222no—
759D4—1222no—
760D4—1221no—
761D4—1221no—
762D4—1221no—
763D4—4881no—
764D4—2442no—
765D4—2442no—
766D4—2442no—
767D4—2442no—
768D4—2441no—
769D4—2441no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—611no—
779C2×C4—611no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1222no—
789C2×C4—1221no—
790C2×C4—1222no—
791C2×C4—1221no—
792C2×C4—1221no—
793C2×C4—1222no—
794C2×C4—1221no—
795C2×C4—2448no—
796C2×C4—2442no—
797C2×C4—2442no—
798C2×C4—2442no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4C22×C4×D6111yescharacteristic
804C2×C4C2×D4×D6111yescharacteristic
805C2×C4C2×D4×D6111yescharacteristic
806C2×C4#41×D6111yescharacteristic
807C2×C4#1451982311yescharacteristic
808C2×C4#1451982311yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—41no—
814C8—41no—
815C8—1221no—
816C8—1221no—
817C8—1222no—
818C8—1221no—
819C8—1221no—
820C8—2441no—
821C22—21no—
822C22—21no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—612no—
827C22—1221no—
828C22—1221no—
829C22—1221no—
830C22—1222no—
831C22—1221no—
832C22—1221no—
833C22—4884no—
834C22—2442no—
835C22—2442no—
836C22—2441no—
837C22—2441no—
838C22—2441no—
839C22—2441no—
840C22—2441no—
841C22C4×D4×D6111yescharacteristic
842C22#1684040411yescharacteristic
843C22#1684043711yescharacteristic
844C4—24no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—1221no—
849C4—1221no—
850C4—1222no—
851C4—2442no—
852C4—2441no—
853C4C4×D4×D6111yescharacteristic
854C4#1684023611yescharacteristic
855C4#1684039611yescharacteristic
856C4#1684040511yescharacteristic
857C2—21no—
858C2—21no—
859C2—81no—
860C2—1222no—
861C2—4881no—
862C2—2441no—
863C2—2442no—
864C2#2144879711yescharacteristic
865C2#443×D6111yescharacteristic
866C2#2145472411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1937C2
socleC22×C61C2×C4×D4
prime radical#21455039C2
cosocleC22×C4×C61C24
hypercenter#1937D61
hypocenterC61#22888
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1937

Complements

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

NH ≅ G/Ntype
2. C2×#16839880C2semidirect
3. #21454543C2semidirect
4. C2×#104×D61C2semidirect
5. #21454267C2semidirect
6. #21446704C2semidirect
7. #21446469C2semidirect
8. #21446261C2semidirect
9. #21446149C2semidirect
10. #21446147C2semidirect
11. #21446093C2semidirect
12. #21446025C2semidirect
13. #21445653C2semidirect
14. C4×#14519689C2semidirect
15. C61×#1937C2semidirect
21. C2×#14519783C22semidirect
25. #16839927C4semidirect
26. #16839925C4semidirect
27. #16839919C4semidirect
28. #16839914C4semidirect
29. #16839910C4semidirect
30. #16839908C4semidirect
31. #16839902C4semidirect
32. #16839897C4semidirect
38. C2×#14519713C22semidirect
39. C2×#14519712C22semidirect
41. C2×#14519705C22semidirect
44. C2×#14519703C22semidirect
47. #16839730C22semidirect
56. #16839718C22semidirect
57. C2×C4×#92418C22semidirect
58. #16839526C22semidirect
59. #16839521C22semidirect
60. #16839516C22semidirect
61. #16839516C22semidirect
62. C61×#424C22semidirect
66. C2×C4×C8×C61C22semidirect
67. C61×#341C22semidirect
68. C61×#339C22semidirect
89. C2×Dic244C2×C4semidirect
90. C2×#11758202C2×C4semidirect
91. C2×#11758190C2×C4semidirect
92. C2×#11758190C2×C4semidirect
93. C2×#11758200C2×C4semidirect
94. C2×#11758201C2×C4semidirect
95. C2×D488C2×C4semidirect
96. C2×#11758199C2×C4semidirect
132. #14519705D4semidirect
136. #14519700C2×C4semidirect
137. #14519700C2×C4semidirect
138. #14519697C2×C4semidirect
139. #14519697C2×C4semidirect
167. #103×C61C2×C4semidirect
168. #103×C61C2×C4semidirect
169. #102×C61C2×C4semidirect
170. #102×C61C2×C4semidirect
410. C2×D61#443semidirect
430. #1937D61semidirect
473. #424C2×D61semidirect
495. C2×C4×C8C2×D61semidirect
497. #341C2×D61semidirect
499. #339C2×D61semidirect
502. C61#22888semidirect
582. #103C4×D61semidirect
583. #103C4×D61semidirect
586. #102C4×D61semidirect
587. #102C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214550392
C2×#168398802
#214545432
C2×#104×D612
#214542672
#214467042
#214464692
#214462612
#214461492
#214461472
#214460932
#214460252
#214456532
C4×#145196892
C61×#19372
#2288861