Finite Group Databasebeta

← #28610330

Subgroups — #28610330

Order 15104.

768 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432823C211yesmaximal, characteristic
2#21432754C211yesmaximal, characteristic, complemented
3#21424850C211yesmaximal, characteristic, complemented
4#21424809C211yesmaximal, characteristic, complemented
5#21424746C211yesmaximal, characteristic, complemented
6#21424697C211yesmaximal, characteristic, complemented
7#21424697C211yesmaximal, characteristic, complemented
8#21424540C211yesmaximal, characteristic
9#21424373C211yesmaximal, characteristic, complemented
10#21424303C211yesmaximal, characteristic, complemented
11#21423982C211yesmaximal, characteristic, complemented
12#21423943C211yesmaximal, characteristic, complemented
13#21423860C211yesmaximal, characteristic, complemented
14C2×#16837161C211yesmaximal, characteristic, complemented
15C59×#3091C211yesmaximal, characteristic
16C2×#14273734C2211yescharacteristic
17C22×#11745664C2211yescharacteristic
18C22×C4×Dic59C2211yescharacteristic
19#16837480—21no—
20#16837474—21no—
21#16837474—21no—
22D4×C59⋊C8—21no—
23#16837463—21no—
24#16837463—21no—
25#16837459—21no—
26#16837455—21no—
27C2×#14273663C2211yescharacteristic
28C2×#14273663C2211yescharacteristic
29#16837429C2211yescharacteristic
30#16837429C2211yescharacteristic
31#16837429C2211yescharacteristic
32C2×#14273654C2211yescharacteristic
33C2×#14273654C2211yescharacteristic
34#16837369C2211yescharacteristic
35#16837366C2211yescharacteristic
36C2×C22⋊(C59⋊C8)C2211yescharacteristic
37#16837358C2211yescharacteristic
38#16837358C2211yescharacteristic
39#16837358C2211yescharacteristic
40C2×#14273637C2211yescharacteristic
41C2×#14273637C2211yescharacteristic
42#16837167C2211yescharacteristic
43#16837167C2211yescharacteristic
44#16837161C2211yescharacteristic
45#16837161C2211yescharacteristic
46#16837161C2211yescharacteristic
47#16837161C2211yescharacteristic
48#16837161C2211yescharacteristic
49#16837161C2211yescharacteristic
50#16837156C2211yescharacteristic
51#16837156C2211yescharacteristic
52C59×#525C2211yescharacteristic
53C2×#117×C59C2211yescharacteristic
54C59×#485C411yescharacteristic, complemented
55C59×#485C411yescharacteristic, complemented
56C59×#484C411yescharacteristic, complemented
57C59×#483C411yescharacteristic, complemented
58C59×#482C411yescharacteristic, complemented
59C59×#482C411yescharacteristic, complemented
60C59×#481C411yescharacteristic, complemented
61C59×#480C411yescharacteristic, complemented
62C59×#427C2211yescharacteristic
63C59×#427C2211yescharacteristic
64C59×#416C2211yescharacteristic
65C59×#416C2211yescharacteristic
66C2×C22⋊C8×C59C2211yescharacteristic
67C23×Dic59—21no—
68#14273734—22no—
69#14273734—41no—
70C2×#11745664—21no—
71C2×#11745664—21no—
72C2×#11745664—22no—
73C2×#11745664—41no—
74C2×#11745664C2311yescharacteristic
75C2×#11745664C2311yescharacteristic
76C2×#11745664C2311yescharacteristic
77C2×#11745664C2311yescharacteristic
78C22×C59⋊C8—21no—
79C22×C59⋊C8—21no—
80C22×C59⋊C8C2311yescharacteristic
81C22×C59⋊C8C2311yescharacteristic
82C2×C4×Dic59—22no—
83C2×C4×Dic59—21no—
84C2×C4×Dic59—41no—
85C2×C4×Dic59C2311yescharacteristic
86C2×C4×Dic59C2311yescharacteristic
87#14273663—22no—
88#14273663—41no—
89C4⋊(C59⋊C8)—21no—
90C4⋊(C59⋊C8)—21no—
91C4⋊(C59⋊C8)—21no—
92C4⋊(C59⋊C8)—21no—
93C4⋊(C59⋊C8)—21no—
94C4⋊(C59⋊C8)—21no—
95#14273654—22no—
96#14273654—41no—
97C22⋊(C59⋊C8)—21no—
98C22⋊(C59⋊C8)—21no—
99C22⋊(C59⋊C8)—21no—
100C22⋊(C59⋊C8)—21no—
101C22⋊(C59⋊C8)D411yescharacteristic
102C22⋊(C59⋊C8)D411yescharacteristic
103C22⋊(C59⋊C8)D411yescharacteristic
104C22⋊(C59⋊C8)D411yescharacteristic
105#14273638—21no—
106#14273638—21no—
107#14273638—21no—
108#14273637—22no—
109#14273637—41no—
110C4×C59⋊C8—21no—
111C4×C59⋊C8—21no—
112C4×C59⋊C8—21no—
113C2×#41×C59C2311yescharacteristic
114C23×C4×C59C2311yescharacteristic
115C22×C8×C59C2311yescharacteristic
116C22×C8×C59C2311yescharacteristic
117#123×C59—21no—
118C22⋊Q8×C59C2×C411yescharacteristic
119C22⋊Q8×C59C2×C411yescharacteristic
120#121×C59C2×C411yescharacteristic
121#121×C59C2×C411yescharacteristic
122#120×C59—21no—
123C4×D4×C59—21no—
124C4×D4×C59—21no—
125#117×C59—21no—
126#117×C59—21no—
127#117×C59C2×C411yescharacteristic
128#117×C59C2×C411yescharacteristic
129#117×C59C2311yescharacteristic
130#117×C59C2311yescharacteristic
131#117×C59C2311yescharacteristic
132C2×C4⋊C4×C59C2×C411yescharacteristic
133C2×C4⋊C4×C59C2×C411yescharacteristic
134C2×C22⋊C4×C59—21no—
135C2×C42×C59—21no—
136#107×C59C2×C411yescharacteristic, complemented
137#107×C59C2×C411yescharacteristic, complemented
138#107×C59C2×C411yescharacteristic, complemented
139#107×C59C2×C411yescharacteristic, complemented
140#106×C59C2×C411yescharacteristic, complemented
141#106×C59C2×C411yescharacteristic, complemented
142#106×C59C2×C411yescharacteristic, complemented
143#106×C59C2×C411yescharacteristic, complemented
144#103×C59C2×C411yescharacteristic, complemented
145#103×C59C2×C411yescharacteristic, complemented
146#103×C59C2×C411yescharacteristic, complemented
147#103×C59C2×C411yescharacteristic, complemented
148#102×C59C2×C411yescharacteristic, complemented
149#102×C59C2×C411yescharacteristic, complemented
150#102×C59C2×C411yescharacteristic, complemented
151#102×C59C2×C411yescharacteristic, complemented
152C22⋊C8×C59C2×C411yescharacteristic
153C22⋊C8×C59C2×C411yescharacteristic
154C22⋊C8×C59C2×C411yescharacteristic
155C22⋊C8×C59C2×C411yescharacteristic
156C24×C59#4111yescharacteristic
157#41×C59—21no—
158#41×C59—21no—
159#41×C59—21no—
160#41×C59—21no—
161C2×Q8×C59C22×C411yescharacteristic
162C2×D4×C59—21no—
163C2×D4×C59—21no—
164C2×D4×C59—21no—
165C2×D4×C59C22×C411yescharacteristic
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59C22×C411yescharacteristic
174C22×C4×C59C22×C411yescharacteristic
175C22×C4×C59C2×D411yescharacteristic
176C22×C4×C59C2×D411yescharacteristic
177C22×C4×C59#4111yescharacteristic
178C22×C4×C59C2411yescharacteristic
179C22×Dic59—21no—
180C22×Dic59—21no—
181C22×Dic59—42no—
182C22×Dic59—42no—
183C22×Dic59—42no—
184C2×C8×C59—21no—
185C2×C8×C59—21no—
186C2×C8×C59—21no—
187C2×C8×C59—21no—
188C2×C8×C59C22×C411yescharacteristic
189C2×C8×C59C22×C411yescharacteristic
190C2×C8×C59C22×C411yescharacteristic
191C2×C8×C59C22×C411yescharacteristic
192C4⋊C4×C59—21no—
193C4⋊C4×C59—21no—
194C4⋊C4×C59—21no—
195C4⋊C4×C59—21no—
196C4⋊C4×C59C22×C411yescharacteristic
197C4⋊C4×C59C22×C411yescharacteristic
198C4⋊C4×C59C22×C411yescharacteristic
199C4⋊C4×C59C22×C411yescharacteristic
200C4⋊C4×C59C22×C411yescharacteristic
201C4⋊C4×C59C22×C411yescharacteristic
202C22⋊C4×C59—21no—
203C22⋊C4×C59—21no—
204C22⋊C4×C59—21no—
205C22⋊C4×C59—21no—
206C22⋊C4×C59—21no—
207C22⋊C4×C59—21no—
208C22⋊C4×C59—21no—
209C22⋊C4×C59—21no—
210C22⋊C4×C59—21no—
211C42×C59—21no—
212C42×C59—21no—
213C42×C59—21no—
214C42×C59—21no—
215C42×C59—21no—
216C4×Dic59—21no—
217C4×Dic59—21no—
218C4×Dic59—21no—
219C4×Dic59—42no—
220C4×Dic59#4112yes—
221#11745664—21no—
222#11745664—21no—
223#11745664—21no—
224#11745664—21no—
225#11745664—21no—
226#11745664—21no—
227#11745664—21no—
228#11745664—42no—
229#11745664—42no—
230#11745664#4112yes—
231C2×C59⋊C8—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8—21no—
236C2×C59⋊C8—21no—
237C2×C59⋊C8—21no—
238C2×C59⋊C8—21no—
239C2×C59⋊C8—42no—
240C2×C59⋊C8—42no—
241C2×C59⋊C8C2×D411yescharacteristic
242C2×C59⋊C8C2×D411yescharacteristic
243C2×C59⋊C8C2×D411yescharacteristic
244C2×C59⋊C8C2×D411yescharacteristic
245C23×C59—21no—
246C23×C59—21no—
247C23×C59—22no—
248C23×C59—21no—
249C23×C59—41no—
250C23×C59C4×D411yescharacteristic
251C23×C59C4×D411yescharacteristic
252C23×C59C2×#4111yescharacteristic
253Q8×C59—21no—
254Q8×C59—21no—
255D4×C59—21no—
256D4×C59—21no—
257D4×C59—41no—
258D4×C59—41no—
259D4×C59—42no—
260D4×C59—81no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—21no—
264C2×C4×C59—21no—
265C2×C4×C59—21no—
266C2×C4×C59—21no—
267C2×C4×C59—21no—
268C2×C4×C59—21no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59—21no—
272C2×C4×C59—21no—
273C2×C4×C59—21no—
274C2×C4×C59—21no—
275C2×C4×C59—21no—
276C2×C4×C59—21no—
277C2×C4×C59—21no—
278C2×C4×C59—42no—
279C2×C4×C59—41no—
280C2×C4×C59—41no—
281C2×C4×C59—81no—
282C2×C4×C59C4×D411yescharacteristic
283C2×C4×C59C4×D411yescharacteristic
284C2×C4×C59C23×C411yescharacteristic
285C2×C4×C59C22×D411yescharacteristic
286C2×C4×C59C2×#4111yescharacteristic
287C2×C4×C59C2×#4111yescharacteristic
288C2×C4×C59H(5,𝔽2)11yescharacteristic
289C2×C4×C592−1+411yescharacteristic
290C2×Dic59—22no—
291C2×Dic59—22no—
292C2×Dic59—41no—
293C2×Dic59—41no—
294C2×Dic59—41no—
295C2×Dic59—48no—
296C2×Dic59—41no—
297C8×C59—21no—
298C8×C59—21no—
299C8×C59—21no—
300C8×C59—21no—
301C59⋊C8—21no—
302C59⋊C8—21no—
303C59⋊C8—22no—
304C59⋊C8—21no—
305C59⋊C8—21no—
306C59⋊C8—41no—
307C59⋊C8—41no—
308C59⋊C8—41no—
309#22950—591nomaximal, Sylow
310C22×C59—21no—
311C22×C59—21no—
312C22×C59—21no—
313C22×C59—21no—
314C22×C59—21no—
315C22×C59—21no—
316C22×C59—21no—
317C22×C59—42no—
318C22×C59—42no—
319C22×C59—41no—
320C22×C59—41no—
321C22×C59—41no—
322C22×C59#44412yes—
323C22×C59C2×C4×D411yescharacteristic
324C22×C59#55111yescharacteristic
325C22×C59#55211yescharacteristic
326C4×C59—21no—
327C4×C59—21no—
328C4×C59—41no—
329C4×C59—41no—
330C4×C59—41no—
331C4×C59—41no—
332C4×C59—41no—
333C4×C59—41no—
334C4×C59—41no—
335C4×C59C4×#4111yescharacteristic
336C4×C59#52011yescharacteristic
337C4×C59#54611yescharacteristic
338C4×C59#54711yescharacteristic
339Dic59—42no—
340Dic59—42no—
341#3091D5911yescharacteristic
342#2933—591no—
343#2924—591no—
344#1946—591no—
345#1938—591no—
346#1929—591no—
347#1922—591no—
348#1922—591no—
349#1896—591no—
350#1866—591no—
351#1855—591no—
352#1773—591no—
353#1765—591no—
354#1749—591no—
355C2×#339—591no—
356C2×C59—21no—
357C2×C59—21no—
358C2×C59—22no—
359C2×C59—41no—
360C2×C59—81no—
361C2×C59#235911yescharacteristic
362C2×C59C2×#44411yescharacteristic
363C2×C59#295611yescharacteristic
364C2×#131—591no—
365C22×M16—591no—
366#525C2×D5911yescharacteristic
367C2×#117C2×D5911yescharacteristic
368C22×C42—591no—
369#485Dic5911yescharacteristic, complemented
370#485Dic5911yescharacteristic, complemented
371#484Dic5911yescharacteristic, complemented
372#483Dic5911yescharacteristic, complemented
373#482Dic5911yescharacteristic, complemented
374#482Dic5911yescharacteristic, complemented
375#481Dic5911yescharacteristic, complemented
376#480Dic5911yescharacteristic, complemented
377#436—1181no—
378#435—1181no—
379#435—1181no—
380C8×D4—1181no—
381#433—1181no—
382#433—1181no—
383#432—1181no—
384#431—1181no—
385C2×#108—591no—
386C2×#108—591no—
387#427C2×D5911yescharacteristic
388#427C2×D5911yescharacteristic
389#424—591no—
390#424—591no—
391#424—591no—
392C2×#104—591no—
393C2×#104—591no—
394#416C2×D5911yescharacteristic
395#416C2×D5911yescharacteristic
396#408—591no—
397#407—591no—
398C2×C22⋊C8—591no—
399C2×C22⋊C8C2×D5911yescharacteristic
400#405—591no—
401#405—591no—
402#405—591no—
403C2×#97—591no—
404C2×#97—591no—
405#341—591no—
406#341—591no—
407#339—591no—
408#339—591no—
409#339—591no—
410#339—591no—
411#339—591no—
412#339—591no—
413#336—591no—
414#336—591no—
415C59#2295011yescharacteristic, complemented, Sylow
416C2×#41C22×D5911yescharacteristic
417C23×C4—1181no—
418C23×C4C22×D5911yescharacteristic
419#131—1182no—
420#131—2361no—
421C2×M16—591no—
422C2×M16—591no—
423C2×M16—591no—
424C2×M16—591no—
425C2×M16—1181no—
426C2×M16—1181no—
427C2×M16—1182no—
428C2×M16—2361no—
429C22×C8—591no—
430C22×C8—591no—
431C22×C8—1181no—
432C22×C8—1181no—
433C22×C8C22×D5911yescharacteristic
434C22×C8C22×D5911yescharacteristic
435#123—21no—
436C22⋊Q8C2×Dic5911yescharacteristic
437C22⋊Q8C2×Dic5911yescharacteristic
438#121C2×Dic5911yescharacteristic
439#121C2×Dic5911yescharacteristic
440#120—21no—
441C4×D4—21no—
442C4×D4—21no—
443#117—21no—
444#117—21no—
445#117C2×Dic5911yescharacteristic
446#117C2×Dic5911yescharacteristic
447#117C22×D5911yescharacteristic
448#117C22×D5911yescharacteristic
449#117C22×D5911yescharacteristic
450C2×C4⋊C4C2×Dic5911yescharacteristic
451C2×C4⋊C4C2×Dic5911yescharacteristic
452C2×C22⋊C4—21no—
453C2×C42—21no—
454C2×C42—591no—
455C2×C42—591no—
456C2×C42—1182no—
457C2×C42—1181no—
458C2×C42—2361no—
459#108—1182no—
460#108—2361no—
461#107C2×Dic5911yescharacteristic, complemented
462#107C2×Dic5911yescharacteristic, complemented
463#107C2×Dic5911yescharacteristic, complemented
464#107C2×Dic5911yescharacteristic, complemented
465#106C2×Dic5911yescharacteristic, complemented
466#106C2×Dic5911yescharacteristic, complemented
467#106C2×Dic5911yescharacteristic, complemented
468#106C2×Dic5911yescharacteristic, complemented
469C4⋊C8—1181no—
470C4⋊C8—1181no—
471C4⋊C8—1181no—
472C4⋊C8—1181no—
473C4⋊C8—1181no—
474C4⋊C8—1181no—
475#104—1182no—
476#104—2361no—
477#103C2×Dic5911yescharacteristic, complemented
478#103C2×Dic5911yescharacteristic, complemented
479#103C2×Dic5911yescharacteristic, complemented
480#103C2×Dic5911yescharacteristic, complemented
481#102C2×Dic5911yescharacteristic, complemented
482#102C2×Dic5911yescharacteristic, complemented
483#102C2×Dic5911yescharacteristic, complemented
484#102C2×Dic5911yescharacteristic, complemented
485C22⋊C8—591no—
486C22⋊C8—591no—
487C22⋊C8—591no—
488C22⋊C8—591no—
489C22⋊C8—1181no—
490C22⋊C8—1181no—
491C22⋊C8—1181no—
492C22⋊C8—1181no—
493C22⋊C8C2×Dic5911yescharacteristic
494C22⋊C8C2×Dic5911yescharacteristic
495C22⋊C8C2×Dic5911yescharacteristic
496C22⋊C8C2×Dic5911yescharacteristic
497#97—1181no—
498#97—1181no—
499#97—1181no—
500#97—1182no—
501#97—2361no—
502C4×C8—1181no—
503C4×C8—1181no—
504C4×C8—1181no—
505C24#1174568711yescharacteristic
506#41—21no—
507#41—21no—
508#41—21no—
509#41—21no—
510C2×Q8C22×Dic5911yescharacteristic
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4C22×Dic5911yescharacteristic
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—1181no—
523C22×C4—1181no—
524C22×C4—2362no—
525C22×C4—2362no—
526C22×C4—2362no—
527C22×C4D4×D5911yescharacteristic
528C22×C4D4×D5911yescharacteristic
529C22×C4#1174568711yescharacteristic
530C22×C4C22×Dic5911yescharacteristic
531C22×C4C22×Dic5911yescharacteristic
532C22×C4C23×D5911yescharacteristic
533M16—592no—
534M16—1181no—
535M16—1181no—
536M16—1181no—
537M16—1181no—
538M16—1181no—
539M16—1181no—
540M16—1181no—
541M16—2362no—
542M16—2362no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—591no—
548C2×C8—591no—
549C2×C8—591no—
550C2×C8—591no—
551C2×C8—1181no—
552C2×C8—1181no—
553C2×C8—1181no—
554C2×C8—1181no—
555C2×C8—1181no—
556C2×C8—1181no—
557C2×C8—1181no—
558C2×C8—1181no—
559C2×C8—2362no—
560C2×C8—2362no—
561C2×C8C22×Dic5911yescharacteristic
562C2×C8C22×Dic5911yescharacteristic
563C2×C8C22×Dic5911yescharacteristic
564C2×C8C22×Dic5911yescharacteristic
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4C22×Dic5911yescharacteristic
570C4⋊C4C22×Dic5911yescharacteristic
571C4⋊C4C22×Dic5911yescharacteristic
572C4⋊C4C22×Dic5911yescharacteristic
573C4⋊C4C22×Dic5911yescharacteristic
574C4⋊C4C22×Dic5911yescharacteristic
575C22⋊C4—21no—
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—21no—
579C22⋊C4—21no—
580C22⋊C4—21no—
581C22⋊C4—21no—
582C22⋊C4—21no—
583C22⋊C4—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—592no—
590C42—1181no—
591C42—1181no—
592C42—1181no—
593C42—2362no—
594C23—22no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—41no—
599C23D4×Dic5911yescharacteristic
600C23D4×Dic5911yescharacteristic
601C23C2×#1174568711yescharacteristic
602Q8—21no—
603Q8—21no—
604D4—21no—
605D4—21no—
606D4—42no—
607D4—41no—
608D4—41no—
609D4—81no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—42no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—81no—
631C2×C4—1182no—
632C2×C4—1182no—
633C2×C4—2361no—
634C2×C4—2361no—
635C2×C4—2361no—
636C2×C4—2368no—
637C2×C4—2361no—
638C2×C4D4×Dic5911yescharacteristic
639C2×C4D4×Dic5911yescharacteristic
640C2×C4C23×Dic5911yescharacteristic
641C2×C4C2×D4×D5911yescharacteristic
642C2×C4#41×D5911yescharacteristic
643C2×C4#41×D5911yescharacteristic
644C2×C4#1427377311yescharacteristic
645C2×C4#1427377411yescharacteristic
646C8—21no—
647C8—21no—
648C8—21no—
649C8—21no—
650C8—1181no—
651C8—1181no—
652C8—1182no—
653C8—1181no—
654C8—1181no—
655C8—2361no—
656C8—2361no—
657C8—2361no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—42no—
666C22—42no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22#1683752412yes—
671C22C2×D4×Dic5911yescharacteristic
672C22#1683807511yescharacteristic
673C22#1683808911yescharacteristic
674C4—21no—
675C4—21no—
676C4—41no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—41no—
681C4—41no—
682C4—41no—
683C4—2362no—
684C4—2362no—
685C4#41×Dic5911yescharacteristic
686C4#1683788511yescharacteristic
687C4#1683804411yescharacteristic
688C4#1683805011yescharacteristic
689C2—21no—
690C2—22no—
691C2—21no—
692C2—41no—
693C2—81no—
694C2#2142709211yescharacteristic
695C2C2×#1683752411yescharacteristic
696C2#2143300611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#3091C2
socleC22×C59C2×C4×D4
prime radicalC59×#525C22
cosocleC22×C4×C59C24
hypercenter#3091D59
hypocenterC59#22950
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3091

Complements

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

NH ≅ G/Ntype
2. #21432754C2semidirect
3. #21424850C2semidirect
4. #21424809C2semidirect
5. #21424746C2semidirect
6. #21424697C2semidirect
7. #21424697C2semidirect
9. #21424373C2semidirect
10. #21424303C2semidirect
11. #21423982C2semidirect
12. #21423943C2semidirect
13. #21423860C2semidirect
14. C2×#16837161C2semidirect
54. C59×#485C4semidirect
55. C59×#485C4semidirect
56. C59×#484C4semidirect
57. C59×#483C4semidirect
58. C59×#482C4semidirect
59. C59×#482C4semidirect
60. C59×#481C4semidirect
61. C59×#480C4semidirect
136. #107×C59C2×C4semidirect
137. #107×C59C2×C4semidirect
138. #107×C59C2×C4semidirect
139. #107×C59C2×C4semidirect
140. #106×C59C2×C4semidirect
141. #106×C59C2×C4semidirect
142. #106×C59C2×C4semidirect
143. #106×C59C2×C4semidirect
144. #103×C59C2×C4semidirect
145. #103×C59C2×C4semidirect
146. #103×C59C2×C4semidirect
147. #103×C59C2×C4semidirect
148. #102×C59C2×C4semidirect
149. #102×C59C2×C4semidirect
150. #102×C59C2×C4semidirect
151. #102×C59C2×C4semidirect
369. #485Dic59semidirect
370. #485Dic59semidirect
371. #484Dic59semidirect
372. #483Dic59semidirect
373. #482Dic59semidirect
374. #482Dic59semidirect
375. #481Dic59semidirect
376. #480Dic59semidirect
415. C59#22950semidirect
461. #107C2×Dic59semidirect
462. #107C2×Dic59semidirect
463. #107C2×Dic59semidirect
464. #107C2×Dic59semidirect
465. #106C2×Dic59semidirect
466. #106C2×Dic59semidirect
467. #106C2×Dic59semidirect
468. #106C2×Dic59semidirect
477. #103C2×Dic59semidirect
478. #103C2×Dic59semidirect
479. #103C2×Dic59semidirect
480. #103C2×Dic59semidirect
481. #102C2×Dic59semidirect
482. #102C2×Dic59semidirect
483. #102C2×Dic59semidirect
484. #102C2×Dic59semidirect

Maximal subgroups

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

subgroupindex
#214328232
#214327542
#214248502
#214248092
#214247462
#214246972
#214245402
#214243732
#214243032
#214239822
#214239432
#214238602
C2×#168371612
C59×#30912
#2295059