Finite Group Databasebeta

← #29700752

Subgroups — #29700752

Order 15616.

1058 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×#16839881C211yesmaximal, characteristic, complemented
3#21454547C211yesmaximal, characteristic, complemented
4C2×#104×D61C211yesmaximal, characteristic, complemented
5#21454266C211yesmaximal, characteristic, complemented
6#21446712C211yesmaximal, characteristic, complemented
7#21446531C211yesmaximal, characteristic, complemented
8#21446467C211yesmaximal, characteristic, complemented
9#21446261C211yesmaximal, characteristic, complemented
10#21446147C211yesmaximal, characteristic, complemented
11#21446146C211yesmaximal, characteristic, complemented
12#21446096C211yesmaximal, characteristic, complemented
13#21446025C211yesmaximal, characteristic, complemented
14#21445582C211yesmaximal, characteristic, complemented
15C61×#1765C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×#14519799C2211yescharacteristic
18C2×#14519797C2211yescharacteristic
19C2×#14519785C2211yescharacteristic, complemented
20C2×#14519784C2211yescharacteristic
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#16839881—24no—
33#16839841—21no—
34#16839835—21no—
35#16839835—21no—
36C8×D244—21no—
37C2×#14519713C2211yescharacteristic, complemented
38C2×#14519712C2211yescharacteristic, complemented
39#16839789C2211yescharacteristic, complemented
40C2×#14519705C2211yescharacteristic
41C2×#14519705C2211yescharacteristic, complemented
42C2×#14519704C2211yescharacteristic
43C2×#14519703C2211yescharacteristic
44C2×#14519703C2211yescharacteristic, complemented
45#104×D61—24no—
46#16839756C2211yescharacteristic
47#16839730—21no—
48#16839730C2211yescharacteristic
49#16839728—21no—
50#16839728C2211yescharacteristic
51#16839728C2211yescharacteristic, complemented
52#16839725—21no—
53#16839725C2211yescharacteristic
54C2×#14519689—21no—
55C2×#14519689C2211yescharacteristic
56C2×#14519689C2211yescharacteristic
57C2×#14519688C2211yescharacteristic, complemented
58#16839526C2211yescharacteristic, complemented
59#16839521C2211yescharacteristic, complemented
60#16839516C2211yescharacteristic, complemented
61#16839516C2211yescharacteristic, complemented
62C2×#131×C61C2211yescharacteristic
63C2×#104×C61C2211yescharacteristic
64C61×#416C2211yescharacteristic
65C61×#405C2211yescharacteristic, complemented
66C2×#97×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—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#14519785—22no—
98#14519785—41no—
99#14519784—22no—
100#14519784—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#14519713—41no—
126#14519712—22no—
127C4⋊#92418—21no—
128C4⋊#92418—21no—
129#14519705—22no—
130#14519705—22no—
131#14519704—22no—
132#14519703—22no—
133#14519703—41no—
134#14519700C2×C411yescharacteristic, complemented
135#14519700C2×C411yescharacteristic, complemented
136#14519697C2×C411yescharacteristic, complemented
137#14519697C2×C411yescharacteristic, complemented
138#14519689—21no—
139#14519689—21no—
140#14519689—21no—
141#14519689—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—22no—
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#104×C61D414yescomplemented
167#103×C61C2×C411yescharacteristic, complemented
168#103×C61C2×C411yescharacteristic, complemented
169#102×C61C2×C411yescharacteristic, complemented
170#102×C61C2×C411yescharacteristic, complemented
171#97×C61—21no—
172#97×C61—41no—
173C4×C8×C61—21no—
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—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—42no—
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—42no—
244M16×C61C2×D412yes—
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×C61C2×D412yes—
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—21no—
274C4×Dic61—42no—
275#11758194—21no—
276#11758194—21no—
277#11758194—21no—
278#11758194—21no—
279#11758194—42no—
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—21no—
322C2×C4×C61—21no—
323C2×C4×C61—22no—
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—21no—
339C2×Dic61—21no—
340C2×Dic61—22no—
341C2×Dic61—21no—
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—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—42no—
365C4×D61—48no—
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—22no—
378C8×C61—21no—
379C8×C61—21no—
380C8×C61—41no—
381#92418—21no—
382#92418—21no—
383#92418—21no—
384#92418—21no—
385#92418—41no—
386#92418—41no—
387#22886—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#44412yescomplemented
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—21no—
420Dic61—21no—
421Dic61—42no—
422Dic61—41no—
423Dic61—41no—
424#3002—611no—
425C2×#444—611no—
426#2933—611no—
427C22×#104—611no—
428#2880—611no—
429#1975—611no—
430#1938—611no—
431#1929—611no—
432#1896—611no—
433#1876—611no—
434#1876—611no—
435#1866—611no—
436#1855—611no—
437#1765D6111yescharacteristic, complemented
438#1749—611no—
439C2×C61—21no—
440C2×C61—21no—
441C2×C61—42no—
442C2×C61#235811yescharacteristic
443C2×C61C2×#44411yescharacteristic
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#444—1224no—
467#436—1221no—
468#435—1221no—
469#435—1221no—
470C8×D4—1221no—
471C2×#108—611no—
472C2×#108—611no—
473#424—611no—
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#405C2×D6111yescharacteristic, complemented
494C2×#97—611no—
495C2×#97C2×D6111yescharacteristic, complemented
496#341—611no—
497#341C2×D6111yescharacteristic, complemented
498#339—611no—
499#339C2×D6111yescharacteristic, complemented
500#336—611no—
501#336—611no—
502C61#2288611yescharacteristic, 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—1222no—
571#108—2441no—
572C4⋊C8—1221no—
573C4⋊C8—1221no—
574#104—1222no—
575#104—1222no—
576#104—1222no—
577#104—1222no—
578#104—2441no—
579#104D24414yescomplemented
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—21no—
605#97—41no—
606#97—1222no—
607C4×C8—21no—
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#41C2×D24412yes—
629#41#1175822212yes—
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—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—2442no—
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—42no—
686M16—1221no—
687M16—1221no—
688M16—1221no—
689M16—1221no—
690M16—2442no—
691M16—2442no—
692M16—2442no—
693M16C2×D24412yes—
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—1221no—
730C42—1221no—
731C42—2442no—
732C42C2×D24412yes—
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—
752Q8C4×D24412yes—
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—
769D4C4×D24412yes—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—22no—
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—1221no—
789C2×C4—1221no—
790C2×C4—1222no—
791C2×C4—1221no—
792C2×C4—1221no—
793C2×C4—2442no—
794C2×C4—2442no—
795C2×C4—2448no—
796C2×C4—2442no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4C22×C4×D6111yescharacteristic
804C2×C4C2×D4×D6111yescharacteristic
805C2×C4C22×D24411yescharacteristic
806C2×C4C2×#1175822211yescharacteristic
807C2×C4#1451982211yescharacteristic
808C2×C4#1451982311yescharacteristic
809C8—21no—
810C8—21no—
811C8—22no—
812C8—21no—
813C8—21no—
814C8—41no—
815C8—1221no—
816C8—1221no—
817C8—1221no—
818C8—1221no—
819C8—2441no—
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#1684040711yescharacteristic
843C22#1684043611yescharacteristic
844C4—22no—
845C4—42no—
846C4—41no—
847C4—41no—
848C4—1221no—
849C4—1221no—
850C4—2442no—
851C4—2441no—
852C4—2441no—
853C4C2×C4×D24411yescharacteristic
854C4#1684023411yescharacteristic
855C4D4×D24411yescharacteristic
856C4#1684040211yescharacteristic
857C2—21no—
858C2—21no—
859C2—42no—
860C2—1222no—
861C2—4881no—
862C2—4881no—
863C2—2441no—
864C2#2144880111yescharacteristic
865C2#444×D6111yescharacteristic
866C2#2145472711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1765C2
socleC22×C61C2×C4×D4
prime radical#21455039C2
cosocleC22×C4×C61C24
hypercenter#1765D61
hypocenterC61#22886
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1765

Complements

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

NH ≅ G/Ntype
2. C2×#16839881C2semidirect
3. #21454547C2semidirect
4. C2×#104×D61C2semidirect
5. #21454266C2semidirect
6. #21446712C2semidirect
7. #21446531C2semidirect
8. #21446467C2semidirect
9. #21446261C2semidirect
10. #21446147C2semidirect
11. #21446146C2semidirect
12. #21446096C2semidirect
13. #21446025C2semidirect
14. #21445582C2semidirect
15. C61×#1765C2semidirect
19. C2×#14519785C22semidirect
24. #16839927C4semidirect
25. #16839925C4semidirect
26. #16839919C4semidirect
27. #16839914C4semidirect
28. #16839910C4semidirect
29. #16839908C4semidirect
30. #16839902C4semidirect
31. #16839897C4semidirect
37. C2×#14519713C22semidirect
38. C2×#14519712C22semidirect
39. #16839789C22semidirect
41. C2×#14519705C22semidirect
44. C2×#14519703C22semidirect
51. #16839728C22semidirect
57. C2×#14519688C22semidirect
58. #16839526C22semidirect
59. #16839521C22semidirect
60. #16839516C22semidirect
61. #16839516C22semidirect
65. C61×#405C22semidirect
66. C2×#97×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
134. #14519700C2×C4semidirect
135. #14519700C2×C4semidirect
136. #14519697C2×C4semidirect
137. #14519697C2×C4semidirect
166. #104×C61D4semidirect
167. #103×C61C2×C4semidirect
168. #103×C61C2×C4semidirect
169. #102×C61C2×C4semidirect
170. #102×C61C2×C4semidirect
410. C2×D61#444semidirect
437. #1765D61semidirect
493. #405C2×D61semidirect
495. C2×#97C2×D61semidirect
497. #341C2×D61semidirect
499. #339C2×D61semidirect
502. C61#22886semidirect
579. #104D244semidirect
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×#168398812
#214545472
C2×#104×D612
#214542662
#214467122
#214465312
#214464672
#214462612
#214461472
#214461462
#214460962
#214460252
#214455822
C61×#17652
#2288661