Finite Group Databasebeta

← #29700796

Subgroups — #29700796

Order 15616.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455035C211yesmaximal, characteristic
2C2×#16839877C211yesmaximal, characteristic, complemented
3C2×#16839778C211yesmaximal, characteristic, complemented
4#21454265C211yesmaximal, characteristic, complemented
5#21446711C211yesmaximal, characteristic, complemented
6#21446522C211yesmaximal, characteristic, complemented
7#21446467C211yesmaximal, characteristic, complemented
8#21446268C211yesmaximal, characteristic, complemented
9#21446149C211yesmaximal, characteristic, complemented
10#21446146C211yesmaximal, characteristic, complemented
11#21446093C211yesmaximal, characteristic, complemented
12#21446024C211yesmaximal, characteristic, complemented
13#21445665C211yesmaximal, characteristic, complemented
14#21445587C211yesmaximal, characteristic, complemented
15C61×#2933C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#14519797C2211yescharacteristic
18C2×#14519797C2211yescharacteristic
19C2×#14519783C2211yescharacteristic
20C2×#14519783C2211yescharacteristic
21C2×#14519736C2211yescharacteristic
22#16839922C411yescharacteristic, complemented
23#16839922C411yescharacteristic, complemented
24#16839917C411yescharacteristic, complemented
25#16839912C411yescharacteristic, complemented
26#16839905C411yescharacteristic, complemented
27#16839905C411yescharacteristic, complemented
28#16839900C411yescharacteristic, complemented
29#16839895C411yescharacteristic, complemented
30#16839877—24no—
31C2×#14519712C2211yescharacteristic, complemented
32C2×#14519712C2211yescharacteristic, complemented
33#16839778—24no—
34C2×#14519704C2211yescharacteristic, complemented
35C2×#14519704C2211yescharacteristic, complemented
36C2×#14519703C2211yescharacteristic
37C2×#14519703C2211yescharacteristic
38C2×#14519703C2211yescharacteristic
39C2×#14519703C2211yescharacteristic
40#16839756C2211yescharacteristic
41#16839756C2211yescharacteristic
42#16839728C2211yescharacteristic
43#16839728C2211yescharacteristic
44#16839727—21no—
45#16839727—21no—
46#16839726C2211yescharacteristic
47#16839724—21no—
48C2×C22⋊#92418C2211yescharacteristic
49C22⋊C8×D61—21no—
50C2×#14519687C2211yescharacteristic, complemented
51C2×C8×Dic61C2211yescharacteristic, complemented
52#16839526C2211yescharacteristic, complemented
53#16839526C2211yescharacteristic, complemented
54#16839521C2211yescharacteristic, complemented
55#16839521C2211yescharacteristic, complemented
56#16839516C2211yescharacteristic, complemented
57#16839516C2211yescharacteristic, complemented
58C2×#131×C61C2211yescharacteristic, complemented
59C22×M16×C61C2211yescharacteristic
60C61×#525C2211yescharacteristic
61C61×#436—21no—
62C61×#435—21no—
63C61×#435—21no—
64C8×D4×C61—21no—
65C61×#424C2211yescharacteristic, complemented
66C61×#408C2211yescharacteristic, complemented
67C2×C22⋊C8×C61C2211yescharacteristic
68C61×#405C2211yescharacteristic, complemented
69C2×#11758222—21no—
70C2×#11758222—21no—
71C2×#11758222—22no—
72C2×#11758222—22no—
73C2×#11758222—41no—
74C2×#11758222—41no—
75C2×#11758222C2×C411yescharacteristic
76C2×#11758222C2×C411yescharacteristic
77C2×#11758222C2311yescharacteristic
78C2×#11758222C2311yescharacteristic
79C22×Dic122C2×C411yescharacteristic
80C22×D244C2×C411yescharacteristic
81C22×C22⋊D61—21no—
82C22×C4×D61—21no—
83#14519797—22no—
84#14519797—22no—
85#14519797—41no—
86#14519797—41no—
87C2×#11758202C2×C411yescharacteristic
88C2×#11758202C2×C411yescharacteristic
89C2×#11758200C2×C411yescharacteristic
90C2×#11758200C2×C411yescharacteristic
91C2×#11758201C2×C411yescharacteristic
92C2×#11758201C2×C411yescharacteristic
93C2×#11758199C2×C411yescharacteristic
94C2×#11758199C2×C411yescharacteristic
95#14519783—22no—
96#14519783—22no—
97#14519783—41no—
98#14519783—41no—
99C2×#11758194C2311yescharacteristic
100C2×#11758194C2311yescharacteristic
101C2×#11758189—21no—
102C2×#11758189—21no—
103C22×#92418C2311yescharacteristic
104C22×#92418C2311yescharacteristic
105C2×C8×D61—21no—
106C2×C8×D61—21no—
107#14519736—22no—
108#14519736—41no—
109C2×C4⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×C4×Dic61C2311yescharacteristic
112C2×C4×Dic61C2311yescharacteristic
113#14519712—22no—
114#14519712—41no—
115#14519704—22no—
116#14519704—41no—
117#14519703—22no—
118#14519703—22no—
119#14519703—22no—
120#14519703D414yescomplemented
121#14519700C2×C411yescharacteristic
122#14519700C2×C411yescharacteristic
123#14519700C2×C411yescharacteristic
124#14519700C2×C411yescharacteristic
125#14519697C2×C411yescharacteristic
126#14519697C2×C411yescharacteristic
127#14519697C2×C411yescharacteristic
128#14519697C2×C411yescharacteristic
129C22⋊#92418—21no—
130C22⋊#92418—21no—
131C22⋊#92418C2×C411yescharacteristic
132C22⋊#92418C2×C411yescharacteristic
133C22⋊#92418C2×C411yescharacteristic
134C22⋊#92418C2×C411yescharacteristic
135#14519689—21no—
136#14519689—21no—
137#14519689—21no—
138#14519689—21no—
139#14519687—41no—
140C8×Dic61—22no—
141C2×#41×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143#131×C61—22no—
144#131×C61—41no—
145C2×M16×C61—21no—
146C2×M16×C61—21no—
147C2×M16×C61—22no—
148C2×M16×C61—41no—
149C2×M16×C61C2311yescharacteristic
150C2×M16×C61C2311yescharacteristic
151C22×C8×C61—21no—
152C22×C8×C61—21no—
153C22×C8×C61C2311yescharacteristic
154C22×C8×C61C2311yescharacteristic
155#123×C61—21no—
156C22⋊Q8×C61C2×C411yescharacteristic
157C22⋊Q8×C61C2×C411yescharacteristic
158#121×C61C2×C411yescharacteristic
159#121×C61C2×C411yescharacteristic
160#120×C61—21no—
161C4×D4×C61—21no—
162C4×D4×C61—21no—
163#117×C61C2311yescharacteristic
164C4⋊C8×C61—21no—
165C4⋊C8×C61—21no—
166C22⋊C8×C61—21no—
167C22⋊C8×C61—21no—
168C22⋊C8×C61D411yescharacteristic
169C22⋊C8×C61D411yescharacteristic
170C22⋊C8×C61D411yescharacteristic
171C22⋊C8×C61D411yescharacteristic
172#97×C61—21no—
173C4×C8×C61—21no—
174C24×C61#4111yescharacteristic
175C23×D61—21no—
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×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61C22×C411yescharacteristic
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61C22×C411yescharacteristic
191C22×C4×C61C22×C411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61#4111yescharacteristic
195C22×C4×C61C2411yescharacteristic
196C2×C22⋊D61—21no—
197C2×C22⋊D61—21no—
198C2×C22⋊D61—21no—
199C2×C22⋊D61—21no—
200C2×C22⋊D61—42no—
201C2×C22⋊D61—42no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205#11758222—21no—
206#11758222—21no—
207#11758222—21no—
208#11758222—21no—
209#11758222—21no—
210#11758222—21no—
211#11758222—22no—
212#11758222—22no—
213#11758222—41no—
214#11758222—41no—
215#11758222—42no—
216#11758222—42no—
217#11758222—42no—
218#11758222—42no—
219#11758222C2×D412yes—
220#11758222#4112yes—
221C2×D244—22no—
222C2×D244—21no—
223C2×D244—41no—
224C2×D244C22×C411yescharacteristic
225C2×D244C22×C411yescharacteristic
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—42no—
231C2×C4×D61—42no—
232C2×Dic122—22no—
233C2×Dic122—21no—
234C2×Dic122—41no—
235C2×Dic122C22×C411yescharacteristic
236C2×Dic122C22×C411yescharacteristic
237M16×C61—21no—
238M16×C61—21no—
239M16×C61—21no—
240M16×C61—42no—
241M16×C61—42no—
242M16×C61C2×D412yes—
243C2×C8×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—42no—
250C2×C8×C61—42no—
251C2×C8×C61C2×D411yescharacteristic
252C2×C8×C61C2×D411yescharacteristic
253C2×C8×C61C2×D411yescharacteristic
254C2×C8×C61C2×D411yescharacteristic
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61C22×C411yescharacteristic
258C4⋊C4×C61C22×C411yescharacteristic
259C22⋊C4×C61—21no—
260C22⋊C4×C61—21no—
261C22⋊C4×C61—21no—
262C22⋊C4×C61—21no—
263C22⋊C4×C61—21no—
264C42×C61—21no—
265C22⋊Dic61—42no—
266#11758202—22no—
267#11758202—41no—
268#11758201—22no—
269#11758201—41no—
270#11758200—22no—
271#11758200—41no—
272#11758199—22no—
273#11758199—41no—
274C4⋊Dic61—42no—
275C4×Dic61—21no—
276C4×Dic61—21no—
277C4×Dic61—21no—
278C4×Dic61C2×D412yes—
279#11758194—21no—
280#11758194—21no—
281#11758194—21no—
282#11758194—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418C22×C411yescharacteristic
290C2×#92418C22×C411yescharacteristic
291C2×#92418C22×C411yescharacteristic
292C2×#92418C22×C411yescharacteristic
293#11758189—42no—
294#11758189—42no—
295C8×D61—42no—
296C8×D61—42no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61C4×D411yescharacteristic
303C23×C61C4×D411yescharacteristic
304C23×C61C2×#4111yescharacteristic
305C22×D61—21no—
306C22×D61—21no—
307C22×D61—42no—
308C22×D61—42no—
309C22×D61—81no—
310Q8×C61—21no—
311Q8×C61—21no—
312D4×C61—21no—
313D4×C61—21no—
314D4×C61—42no—
315D4×C61—41no—
316D4×C61—41no—
317D4×C61—81no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61C4×D411yescharacteristic
334C2×C4×C61C4×D411yescharacteristic
335C2×C4×C61C23×C411yescharacteristic
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61C2×#4111yescharacteristic
339C2×C4×C61H(5,𝔽2)11yescharacteristic
340C2×C4×C61H(5,𝔽2)11yescharacteristic
341C22⋊D61—22no—
342C22⋊D61—22no—
343C22⋊D61—42no—
344C22⋊D61—42no—
345C22⋊D61—41no—
346C22⋊D61—41no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—22no—
350C2×Dic61—42no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356D244—21no—
357D244—21no—
358D244—21no—
359D244—42no—
360D244C4×D412yes—
361C4×D61—22no—
362C4×D61—22no—
363C4×D61—42no—
364C4×D61—42no—
365C4×D61—41no—
366C4×D61—41no—
367Dic122—21no—
368Dic122—21no—
369Dic122—21no—
370Dic122—42no—
371Dic122C4×D412yes—
372C8×C61—21no—
373C8×C61—21no—
374C8×C61—22no—
375C8×C61—21no—
376C8×C61—21no—
377C8×C61—41no—
378#92418—21no—
379#92418—21no—
380#92418—21no—
381#92418—21no—
382#92418—41no—
383#92418—41no—
384#22889—611nomaximal, Sylow
385C22×C61—21no—
386C22×C61—21no—
387C22×C61—21no—
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—21no—
391C22×C61—21no—
392C22×C61—21no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—81no—
397C22×C61—81no—
398C22×C61C2×C4×D411yescharacteristic
399C22×C61#54611yescharacteristic
400C22×C61#55111yescharacteristic
401C2×D61—22no—
402C2×D61—41no—
403C2×D61—41no—
404C2×D61—41no—
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—84no—
408C4×C61—21no—
409C4×C61—21no—
410C4×C61—41no—
411C4×C61—41no—
412C4×C61—41no—
413C4×C61C2×C4×D411yescharacteristic
414C4×C61#51811yescharacteristic
415C4×C61D4211yescharacteristic
416C4×C61#54611yescharacteristic
417Dic61—22no—
418Dic61—42no—
419Dic61—41no—
420Dic61—81no—
421#3002—611no—
422C2×#443—611no—
423#2933D6111yescharacteristic, complemented
424C2×#421—611no—
425#2880—611no—
426#1975—611no—
427#1937—611no—
428#1929—611no—
429#1897—611no—
430#1876—611no—
431#1876—611no—
432#1866—611no—
433#1855—611no—
434#1765—611no—
435#1750—611no—
436C2×C61—21no—
437C2×C61—21no—
438C2×C61—41no—
439C2×C61—41no—
440C2×C61—81no—
441C2×C61#235811yescharacteristic
442C2×C61#295511yescharacteristic
443C2×C61#295711yescharacteristic
444D61—42no—
445D61—81no—
446C22×#41—611no—
447C2×#135—611no—
448C2×#135—611no—
449C2×#131—611no—
450C2×#131—611no—
451C2×#131C2×D6111yescharacteristic, complemented
452C22×M16C2×D6111yescharacteristic
453#525C2×D6111yescharacteristic
454C2×#117—611no—
455#452—611no—
456#452—611no—
457#451—611no—
458#450—611no—
459#449—611no—
460#449—611no—
461#448—611no—
462#447—611no—
463#443—1224no—
464#436—21no—
465#435—21no—
466#435—21no—
467C8×D4—21no—
468C2×#108—611no—
469C2×#108—611no—
470#424C2×D6111yescharacteristic, complemented
471#421—1224no—
472C2×#104—611no—
473C2×#104—611no—
474C2×#104—611no—
475C2×#104—611no—
476C2×#104—611no—
477C2×#104—611no—
478#416—611no—
479#416—611no—
480#408—611no—
481#408—611no—
482#408—1221no—
483#408—1221no—
484#408C2×D6111yescharacteristic, complemented
485#407—611no—
486#407—1221no—
487C2×C22⋊C8—611no—
488C2×C22⋊C8—1221no—
489C2×C22⋊C8C2×D6111yescharacteristic
490#405C2×D6111yescharacteristic, complemented
491C2×#97—611no—
492C2×C4×C8—611no—
493#341—611no—
494#341—611no—
495#339—611no—
496#339—611no—
497#336—611no—
498#336—611no—
499C61#2288911yescharacteristic, complemented, Sylow
500C2×#41—611no—
501C2×#41—611no—
502C2×#41—611no—
503C2×#41—611no—
504C2×#41—1222no—
505C2×#41—1222no—
506C2×#41—1221no—
507C2×#41—1221no—
508C2×#41—2441no—
509C2×#41—2441no—
510C2×#41C22×D6111yescharacteristic
511C22×Q8—611no—
512C22×D4—611no—
513C22×D4—1221no—
514C23×C4—1221no—
515C23×C4C22×D6111yescharacteristic
516#135—1222no—
517#135—1222no—
518#135—2441no—
519#135—2441no—
520C2×Q16—611no—
521C2×Q16—611no—
522C2×SD16—611no—
523C2×SD16—611no—
524C2×SD16—611no—
525C2×SD16—611no—
526C2×D8—611no—
527C2×D8—611no—
528#131—22no—
529#131—41no—
530#131—1222no—
531#131—1222no—
532#131—2441no—
533#131—2441no—
534C2×M16—21no—
535C2×M16—21no—
536C2×M16—22no—
537C2×M16—41no—
538C2×M16—611no—
539C2×M16—611no—
540C2×M16—1221no—
541C2×M16—1221no—
542C2×M16C22×D6111yescharacteristic
543C2×M16C22×D6111yescharacteristic
544C22×C8—21no—
545C22×C8—21no—
546C22×C8—611no—
547C22×C8—611no—
548C22×C8—1221no—
549C22×C8—1221no—
550C22×C8C22×D6111yescharacteristic
551C22×C8C22×D6111yescharacteristic
552#123—21no—
553C22⋊Q8C4×D6111yescharacteristic
554C22⋊Q8C4×D6111yescharacteristic
555#121C4×D6111yescharacteristic
556#121C4×D6111yescharacteristic
557#120—21no—
558C4×D4—21no—
559C4×D4—21no—
560#117—1222no—
561#117—2441no—
562#117C22×D6111yescharacteristic
563C2×C4⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C42—611no—
566C2×C42—611no—
567#108—1222no—
568#108—2441no—
569C4⋊C8—21no—
570C4⋊C8—21no—
571#104—614no—
572#104—1222no—
573#104—1222no—
574#104—1222no—
575#104—1222no—
576#104—2441no—
577#103—611no—
578#103—611no—
579#103—611no—
580#103—611no—
581#102—611no—
582#102—611no—
583#102—611no—
584#102—611no—
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—611no—
588C22⋊C8—611no—
589C22⋊C8—611no—
590C22⋊C8—611no—
591C22⋊C8—1221no—
592C22⋊C8—1221no—
593C22⋊C8—1221no—
594C22⋊C8—1221no—
595C22⋊C8—1221no—
596C22⋊C8—1221no—
597C22⋊C8C22⋊D6111yescharacteristic
598C22⋊C8C22⋊D6111yescharacteristic
599C22⋊C8C22⋊D6111yescharacteristic
600C22⋊C8C22⋊D6111yescharacteristic
601#97—21no—
602#97—2441no—
603C4×C8—21no—
604C4×C8—1222no—
605C24—1221no—
606C24#1175822211yescharacteristic
607#41—21no—
608#41—21no—
609#41—21no—
610#41—21no—
611#41—612no—
612#41—612no—
613#41—1222no—
614#41—1222no—
615#41—1221no—
616#41—1221no—
617#41—1221no—
618#41—1221no—
619#41—1221no—
620#41—1221no—
621#41—2442no—
622#41—2442no—
623#41—2441no—
624#41—2441no—
625#41—2442no—
626#41—2442no—
627C2×Q8—611no—
628C2×Q8—611no—
629C2×Q8—1222no—
630C2×Q8—1221no—
631C2×Q8—2441no—
632C2×Q8C2×C4×D6111yescharacteristic
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—611no—
637C2×D4—611no—
638C2×D4—1222no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—1221no—
644C2×D4—2441no—
645C2×D4—2442no—
646C2×D4—2442no—
647C2×D4C2×C4×D6111yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—1221no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—2442no—
661C22×C4—2442no—
662C22×C4C2×C4×D6111yescharacteristic
663C22×C4C2×C4×D6111yescharacteristic
664C22×C4#1175822211yescharacteristic
665C22×C4C2×C22⋊D6111yescharacteristic
666C22×C4C2×C22⋊D6111yescharacteristic
667C22×C4C23×D6111yescharacteristic
668Q16—1222no—
669Q16—2441no—
670SD16—1222no—
671SD16—1222no—
672SD16—2441no—
673SD16—2441no—
674D8—1222no—
675D8—2441no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—42no—
680M16—42no—
681M16—1221no—
682M16—1221no—
683M16—1221no—
684M16—1221no—
685M16—2442no—
686M16—2442no—
687M16D4×D6112yes—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—42no—
695C2×C8—42no—
696C2×C8—611no—
697C2×C8—611no—
698C2×C8—611no—
699C2×C8—611no—
700C2×C8—1221no—
701C2×C8—1221no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—2442no—
707C2×C8—2442no—
708C2×C8C2×C22⋊D6111yescharacteristic
709C2×C8C2×C22⋊D6111yescharacteristic
710C2×C8C2×C22⋊D6111yescharacteristic
711C2×C8C2×C22⋊D6111yescharacteristic
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—2442no—
715C4⋊C4C2×C4×D6111yescharacteristic
716C4⋊C4C2×C4×D6111yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—2442no—
723C42—21no—
724C42—612no—
725C42—1221no—
726C42—1221no—
727C42—1221no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—41no—
732C23—41no—
733C23—1221no—
734C23—1221no—
735C23—4881no—
736C23—2442no—
737C23—2442no—
738C23C4×C22⋊D6111yescharacteristic
739C23C4×C22⋊D6111yescharacteristic
740C23C2×#1175822211yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—612no—
744Q8—1221no—
745Q8—1221no—
746Q8—1221no—
747Q8—2442no—
748D4—21no—
749D4—21no—
750D4—42no—
751D4—41no—
752D4—41no—
753D4—81no—
754D4—612no—
755D4—1222no—
756D4—1222no—
757D4—1221no—
758D4—1221no—
759D4—1221no—
760D4—2442no—
761D4—2442no—
762D4—2442no—
763D4—2441no—
764D4—2441no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—1221no—
781C2×C4—1222no—
782C2×C4—1222no—
783C2×C4—1221no—
784C2×C4—1222no—
785C2×C4—2442no—
786C2×C4—2442no—
787C2×C4—2442no—
788C2×C4—2441no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4C4×C22⋊D6111yescharacteristic
796C2×C4C4×C22⋊D6111yescharacteristic
797C2×C4C22×C4×D6111yescharacteristic
798C2×C4C2×D4×D6111yescharacteristic
799C2×C4C22×C22⋊D6111yescharacteristic
800C2×C4#41×D6111yescharacteristic
801C2×C4#1451982211yescharacteristic
802C2×C4#1451982311yescharacteristic
803C8—21no—
804C8—21no—
805C8—22no—
806C8—21no—
807C8—21no—
808C8—41no—
809C8—1221no—
810C8—1221no—
811C8—1221no—
812C8—1221no—
813C8—2441no—
814C8—2441no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—81no—
827C22—81no—
828C22—1222no—
829C22—4884no—
830C22—2441no—
831C22—2441no—
832C22—2441no—
833C22—2441no—
834C22—2441no—
835C22C2×C4×C22⋊D6111yescharacteristic
836C22#1684040811yescharacteristic
837C22#1684044111yescharacteristic
838C4—21no—
839C4—21no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—1222no—
844C4—4881no—
845C4—2442no—
846C4—2441no—
847C4C4×D4×D6111yescharacteristic
848C4#1684023411yescharacteristic
849C4D4×C22⋊D6111yescharacteristic
850C4#1684040011yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—81no—
856C2—4881no—
857C2—2442no—
858C2#2144879611yescharacteristic
859C2#2145472011yescharacteristic
860C2#2145473411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2933C2
socleC22×C61C2×C4×D4
prime radical#21455035C2
cosocleC22×C4×C61C24
hypercenter#2933D61
hypocenterC61#22889
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2933

Complements

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

NH ≅ G/Ntype
2. C2×#16839877C2semidirect
3. C2×#16839778C2semidirect
4. #21454265C2semidirect
5. #21446711C2semidirect
6. #21446522C2semidirect
7. #21446467C2semidirect
8. #21446268C2semidirect
9. #21446149C2semidirect
10. #21446146C2semidirect
11. #21446093C2semidirect
12. #21446024C2semidirect
13. #21445665C2semidirect
14. #21445587C2semidirect
15. C61×#2933C2semidirect
22. #16839922C4semidirect
23. #16839922C4semidirect
24. #16839917C4semidirect
25. #16839912C4semidirect
26. #16839905C4semidirect
27. #16839905C4semidirect
28. #16839900C4semidirect
29. #16839895C4semidirect
31. C2×#14519712C22semidirect
32. C2×#14519712C22semidirect
34. C2×#14519704C22semidirect
35. C2×#14519704C22semidirect
50. C2×#14519687C22semidirect
51. C2×C8×Dic61C22semidirect
52. #16839526C22semidirect
53. #16839526C22semidirect
54. #16839521C22semidirect
55. #16839521C22semidirect
56. #16839516C22semidirect
57. #16839516C22semidirect
58. C2×#131×C61C22semidirect
65. C61×#424C22semidirect
66. C61×#408C22semidirect
68. C61×#405C22semidirect
120. #14519703D4semidirect
423. #2933D61semidirect
451. C2×#131C2×D61semidirect
470. #424C2×D61semidirect
484. #408C2×D61semidirect
490. #405C2×D61semidirect
499. C61#22889semidirect

Maximal subgroups

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

subgroupindex
#214550352
C2×#168398772
C2×#168397782
#214542652
#214467112
#214465222
#214464672
#214462682
#214461492
#214461462
#214460932
#214460242
#214456652
#214455872
C61×#29332
#2288961