Finite Group Databasebeta

← #29700778

Subgroups — #29700778

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×#16839877C211yesmaximal, characteristic, complemented
3#21454543C211yesmaximal, characteristic, complemented
4C2×#104×D61C211yesmaximal, characteristic, complemented
5#21454266C211yesmaximal, characteristic, complemented
6#21446705C211yesmaximal, characteristic, complemented
7#21446522C211yesmaximal, characteristic, complemented
8#21446465C211yesmaximal, characteristic, complemented
9#21446261C211yesmaximal, characteristic, complemented
10#21446145C211yesmaximal, characteristic, complemented
11#21446144C211yesmaximal, characteristic, complemented
12#21446022C211yesmaximal, characteristic, complemented
13#21445659C211yesmaximal, characteristic, complemented
14#21445576C211yesmaximal, characteristic, complemented
15C61×#1866C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×#14519799C2211yescharacteristic
18C2×#14519797C2211yescharacteristic
19C2×#14519784C2211yescharacteristic
20C2×#14519783C2211yescharacteristic, complemented
21C2×M16×D61C2211yescharacteristic
22#16840274C2211yescharacteristic
23C2×C42×D61C2211yescharacteristic
24#16839927C411yescharacteristic, complemented
25#16839925C411yescharacteristic, complemented
26#16839919C411yescharacteristic, complemented
27#16839914C411yescharacteristic, complemented
28#16839910C411yescharacteristic, complemented
29#16839908C411yescharacteristic, complemented
30#16839902C411yescharacteristic, complemented
31#16839897C411yescharacteristic, complemented
32#16839877—24no—
33#16839839—21no—
34#16839832—21no—
35#16839832—21no—
36#16839827—21no—
37C2×#14519712C2211yescharacteristic, complemented
38C2×#14519705C2211yescharacteristic
39C2×#14519705C2211yescharacteristic, complemented
40C2×#14519704C2211yescharacteristic
41C2×#14519703C2211yescharacteristic
42C2×#14519703C2211yescharacteristic, complemented
43#104×D61—24no—
44#16839756C2211yescharacteristic
45#16839730—21no—
46#16839730C2211yescharacteristic
47#16839730C2211yescharacteristic, complemented
48#16839728—21no—
49#16839728C2211yescharacteristic
50#16839725—21no—
51#16839725C2211yescharacteristic
52C2×#14519689—21no—
53C2×#14519689C2211yescharacteristic
54C2×#14519689C2211yescharacteristic
55#16839718C2211yescharacteristic, complemented
56C2×C8×Dic61C2211yescharacteristic, complemented
57C2×C8×Dic61C2211yescharacteristic, complemented
58#16839527C2211yescharacteristic, complemented
59#16839526C2211yescharacteristic, complemented
60#16839521C2211yescharacteristic, complemented
61#16839517C2211yescharacteristic, complemented
62C2×#131×C61C2211yescharacteristic
63C2×#108×C61C2211yescharacteristic, complemented
64C61×#424C2211yescharacteristic, complemented
65C2×#104×C61C2211yescharacteristic
66C61×#416C2211yescharacteristic
67C61×#339C2211yescharacteristic, complemented
68C61×#336C2211yescharacteristic, 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—41no—
86#14519799—41no—
87#14519797—22no—
88#14519797—22no—
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#14519784—22no—
98#14519784—41no—
99#14519783—22no—
100#14519783—41no—
101C2×#11758194—21no—
102C2×#11758194C2311yescharacteristic
103C2×#11758194C2311yescharacteristic
104C2×#11758189—21no—
105C2×#11758189—21no—
106M16×D61—22no—
107M16×D61—41no—
108C22×#92418—21no—
109C22×#92418C2311yescharacteristic
110C22×#92418C2311yescharacteristic
111C2×C8×D61—21no—
112C2×C8×D61—21no—
113#14519761—21no—
114#14519757C2×C411yescharacteristic
115#14519757C2×C411yescharacteristic
116#14519752C2×C411yescharacteristic
117#14519752C2×C411yescharacteristic
118#14519747—21no—
119C4×D244—21no—
120C4×D244—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61C2311yescharacteristic
123C42×D61—22no—
124C42×D61—41no—
125#14519712—22no—
126#14519705—22no—
127#14519705—41no—
128#14519704D414yescomplemented
129#14519703—22no—
130#14519703—22no—
131#14519700C2×C411yescharacteristic, complemented
132#14519700C2×C411yescharacteristic, complemented
133#14519697C2×C411yescharacteristic, complemented
134#14519697C2×C411yescharacteristic, complemented
135#14519689—21no—
136#14519689—21no—
137#14519689—21no—
138#14519689—21no—
139#14519689—21no—
140#14519689—21no—
141#14519689—21no—
142#14519689—21no—
143#14519689C2×C411yescharacteristic
144#14519689C2×C411yescharacteristic
145#14519689C2×C411yescharacteristic
146#14519689C2×C411yescharacteristic
147#14519689D411yescharacteristic
148#14519689D411yescharacteristic
149#14519689D411yescharacteristic
150#14519689D411yescharacteristic
151#14519688—21no—
152C4×#92418—21no—
153C8×Dic61—22no—
154C8×Dic61—41no—
155C2×#41×C61C2311yescharacteristic
156#131×C61—22no—
157#131×C61—41no—
158C2×M16×C61—21no—
159C2×M16×C61C2311yescharacteristic
160C2×M16×C61C2311yescharacteristic
161C22×C8×C61—21no—
162C22×C8×C61C2311yescharacteristic
163C22×C8×C61C2311yescharacteristic
164#117×C61C2311yescharacteristic
165C2×C42×C61C2311yescharacteristic
166#108×C61—41no—
167C4⋊C8×C61—21no—
168C4⋊C8×C61—21no—
169#104×C61—22no—
170#103×C61C2×C411yescharacteristic, complemented
171#103×C61C2×C411yescharacteristic, complemented
172#102×C61C2×C411yescharacteristic, complemented
173#102×C61C2×C411yescharacteristic, complemented
174C23×D61—21no—
175C23×D61#4111yescharacteristic
176#41×C61—21no—
177#41×C61—21no—
178#41×C61C2×D412yes—
179#41×C61#4112yes—
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—21no—
212#11758222—21no—
213#11758222—42no—
214#11758222—42no—
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—24no—
225C2×C4×D61—21no—
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—
244M16×C61—42no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61—42no—
252C2×C8×C61C22×C411yescharacteristic
253C2×C8×C61C22×C411yescharacteristic
254C2×C8×C61C2×D411yescharacteristic
255C2×C8×C61C2×D411yescharacteristic
256C4⋊C4×C61C22×C411yescharacteristic
257C4⋊C4×C61C22×C411yescharacteristic
258C22⋊C4×C61—21no—
259C42×C61—21no—
260C42×C61—21no—
261C42×C61—21no—
262#11758202—22no—
263#11758201—22no—
264#11758200—22no—
265#11758199—22no—
266#11758198—21no—
267#11758198—21no—
268#11758198—21no—
269#11758198—21no—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4×Dic61—21no—
273C4×Dic61—42no—
274C4×Dic61C2×D412yes—
275#11758194—21no—
276#11758194—21no—
277#11758194—21no—
278#11758194—42no—
279#11758194C2×D412yes—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—42no—
287C2×#92418C22×C411yescharacteristic
288C2×#92418C22×C411yescharacteristic
289C2×#92418C2×D411yescharacteristic
290C2×#92418C2×D411yescharacteristic
291Dic244—41no—
292D488—41no—
293#11758190—41no—
294#11758190—41no—
295#11758189—42no—
296#11758189—42no—
297C8×D61—42no—
298C8×D61—42no—
299C23×C61—21no—
300C23×C61C2×#4111yescharacteristic
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—22no—
304C22×D61—21no—
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×C61C4×D412yes—
314D4×C61—22no—
315D4×C61—22no—
316D4×C61—21no—
317D4×C61C4×D412yes—
318C2×C4×C61—21no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
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—42no—
333C22⋊D61—42no—
334C22⋊D61—41no—
335C22⋊D61—41no—
336C22⋊D61—41no—
337C22⋊D61—41no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—42no—
346C2×Dic61C4×D411yescharacteristic
347C2×Dic61C4×D411yescharacteristic
348D244—21no—
349D244—21no—
350D244—21no—
351D244—21no—
352D244—42no—
353D244—42no—
354D244—81no—
355C4×D61—21no—
356C4×D61—21no—
357C4×D61—21no—
358C4×D61—21no—
359C4×D61—21no—
360C4×D61—21no—
361C4×D61—21no—
362C4×D61—21no—
363C4×D61—42no—
364C4×D61—48no—
365C4×D61—42no—
366C4×D61—41no—
367C4×D61—41no—
368C4×D61—41no—
369C4×D61—41no—
370Dic122—21no—
371Dic122—21no—
372Dic122—21no—
373Dic122—21no—
374Dic122—42no—
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—22no—
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—21no—
400C2×D61—21no—
401C2×D61—42no—
402C2×D61—42no—
403C2×D61—41no—
404C2×D61—41no—
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—41no—
408C2×D61—41no—
409C2×D61—84no—
410C2×D61#44312yescomplemented
411C4×C61—22no—
412C4×C61—42no—
413C4×C61—41no—
414C4×C61—41no—
415C4×C61C2×C4×D411yescharacteristic
416C4×C61#51811yescharacteristic
417C4×C61D4211yescharacteristic
418C4×C61#54611yescharacteristic
419Dic61—24no—
420Dic61—21no—
421Dic61—21no—
422Dic61—41no—
423Dic61—41no—
424#3002—611no—
425C2×#443—611no—
426#2933—611no—
427C22×#104—611no—
428#2880—611no—
429#1974—611no—
430#1937—611no—
431#1929—611no—
432#1896—611no—
433#1876—611no—
434#1876—611no—
435#1866D6111yescharacteristic, complemented
436#1855—611no—
437#1764—611no—
438C4×C22⋊C8—611no—
439C2×C61—21no—
440C2×C61—21no—
441C2×C61—42no—
442C2×C61#235811yescharacteristic
443C2×C61C2×#44311yescharacteristic
444C2×C61#295611yescharacteristic
445D61—22no—
446D61—41no—
447D61—81no—
448D61—81no—
449C22×#41—611no—
450C2×#135—611no—
451C2×#135—611no—
452C2×#131—611no—
453C2×#131—611no—
454C2×#131C2×D6111yescharacteristic
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×#108C2×D6111yescharacteristic, complemented
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—611no—
486#408—1221no—
487#408—1221no—
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×C8—611no—
496#341—611no—
497#341—611no—
498#339—611no—
499#339C2×D6111yescharacteristic, complemented
500#336—611no—
501#336C2×D6111yescharacteristic, complemented
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—22no—
533#131—41no—
534#131—1222no—
535#131—1222no—
536#131—2441no—
537#131—2441no—
538C2×M16—21no—
539C2×M16—611no—
540C2×M16—611no—
541C2×M16—1221no—
542C2×M16—1221no—
543C2×M16—1221no—
544C2×M16—1222no—
545C2×M16—2441no—
546C2×M16C22×D6111yescharacteristic
547C2×M16C22×D6111yescharacteristic
548C22×C8—21no—
549C22×C8—611no—
550C22×C8—611no—
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—41no—
571#108—1222no—
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—611no—
589C22⋊C8—611no—
590C22⋊C8—611no—
591C22⋊C8—611no—
592C22⋊C8—611no—
593C22⋊C8—611no—
594C22⋊C8—611no—
595C22⋊C8—611no—
596C22⋊C8—1221no—
597C22⋊C8—1221no—
598C22⋊C8—1221no—
599C22⋊C8—1221no—
600C22⋊C8—1221no—
601C22⋊C8—1221no—
602C22⋊C8—1221no—
603C22⋊C8—1221no—
604#97—1221no—
605C4×C8—1221no—
606C4×C8—1222no—
607C4×C8—2441no—
608C24—611no—
609C24—1221no—
610#41—21no—
611#41—21no—
612#41—1222no—
613#41—1222no—
614#41—1221no—
615#41—1221no—
616#41—1221no—
617#41—1221no—
618#41—1221no—
619#41—1221no—
620#41—1221no—
621#41—1221no—
622#41—2442no—
623#41—2442no—
624#41—2441no—
625#41—2442no—
626#41—2442no—
627#41—2441no—
628#41D4×D6112yes—
629#41#1175822612yes—
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—42no—
687M16—612no—
688M16—1221no—
689M16—1221no—
690M16—1221no—
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—42no—
701C2×C8—611no—
702C2×C8—611no—
703C2×C8—611no—
704C2×C8—611no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—1221no—
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—21no—
730C42—612no—
731C42—1221no—
732C42—2442no—
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—1221no—
748Q8—1221no—
749Q8—1221no—
750Q8—1221no—
751Q8—2442no—
752Q8#1451973912yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—1221no—
757D4—1221no—
758D4—1221no—
759D4—1221no—
760D4—4881no—
761D4—2442no—
762D4—2442no—
763D4—2442no—
764D4—2442no—
765D4—2441no—
766D4—2441no—
767D4—2441no—
768D4—2441no—
769D4#1451973912yes—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—611no—
779C2×C4—611no—
780C2×C4—1222no—
781C2×C4—1222no—
782C2×C4—1222no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1221no—
793C2×C4—1221no—
794C2×C4—1221no—
795C2×C4—2442no—
796C2×C4—2442no—
797C2×C4—2448no—
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×C4C2×#1175822611yescharacteristic
807C2×C4#1451982211yescharacteristic
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—22no—
824C22—41no—
825C22—41no—
826C22—612no—
827C22—1221no—
828C22—1221no—
829C22—1221no—
830C22—1221no—
831C22—1221no—
832C22—4884no—
833C22—2442no—
834C22—2442no—
835C22—2441no—
836C22—2441no—
837C22—2441no—
838C22—2441no—
839C22—2441no—
840C22—2441no—
841C22C4×D4×D6111yescharacteristic
842C22#1684040411yescharacteristic
843C22#1684043911yescharacteristic
844C4—22no—
845C4—42no—
846C4—41no—
847C4—41no—
848C4—1224no—
849C4—1221no—
850C4—1221no—
851C4—2441no—
852C4—2441no—
853C4C2×#1451973911yescharacteristic
854C4#1684023411yescharacteristic
855C4#1684039411yescharacteristic
856C4#1684040311yescharacteristic
857C2—21no—
858C2—21no—
859C2—42no—
860C2—1222no—
861C2—4881no—
862C2—4881no—
863C2—2441no—
864C2#2144879511yescharacteristic
865C2#443×D6111yescharacteristic
866C2#2145472711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1866C2
socleC22×C61C2×C4×D4
prime radical#21455039C2
cosocleC22×C4×C61C24
hypercenter#1866D61
hypocenterC61#22888
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1866

Complements

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

NH ≅ G/Ntype
2. C2×#16839877C2semidirect
3. #21454543C2semidirect
4. C2×#104×D61C2semidirect
5. #21454266C2semidirect
6. #21446705C2semidirect
7. #21446522C2semidirect
8. #21446465C2semidirect
9. #21446261C2semidirect
10. #21446145C2semidirect
11. #21446144C2semidirect
12. #21446022C2semidirect
13. #21445659C2semidirect
14. #21445576C2semidirect
15. C61×#1866C2semidirect
20. C2×#14519783C22semidirect
24. #16839927C4semidirect
25. #16839925C4semidirect
26. #16839919C4semidirect
27. #16839914C4semidirect
28. #16839910C4semidirect
29. #16839908C4semidirect
30. #16839902C4semidirect
31. #16839897C4semidirect
37. C2×#14519712C22semidirect
39. C2×#14519705C22semidirect
42. C2×#14519703C22semidirect
47. #16839730C22semidirect
55. #16839718C22semidirect
56. C2×C8×Dic61C22semidirect
57. C2×C8×Dic61C22semidirect
58. #16839527C22semidirect
59. #16839526C22semidirect
60. #16839521C22semidirect
61. #16839517C22semidirect
63. C2×#108×C61C22semidirect
64. C61×#424C22semidirect
67. C61×#339C22semidirect
68. C61×#336C22semidirect
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
128. #14519704D4semidirect
131. #14519700C2×C4semidirect
132. #14519700C2×C4semidirect
133. #14519697C2×C4semidirect
134. #14519697C2×C4semidirect
170. #103×C61C2×C4semidirect
171. #103×C61C2×C4semidirect
172. #102×C61C2×C4semidirect
173. #102×C61C2×C4semidirect
410. C2×D61#443semidirect
435. #1866D61semidirect
472. C2×#108C2×D61semidirect
473. #424C2×D61semidirect
499. #339C2×D61semidirect
501. #336C2×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×#168398772
#214545432
C2×#104×D612
#214542662
#214467052
#214465222
#214464652
#214462612
#214461452
#214461442
#214460222
#214456592
#214455762
C61×#18662
#2288861