Finite Group Databasebeta

← C2×#21436916 #29468447

Subgroups — C2×#21436916 #29468447

Order 15104.

1886 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838126C211yesmaximal, characteristic, complemented
2C2×#16838111C211yesmaximal, characteristic, complemented
3#21436916C2116yesmaximal, direct product factor
4C2×#16837770C211yesmaximal, characteristic, complemented
5C2×#16837763C211yesmaximal, characteristic, complemented
6C2×#16837758C211yesmaximal, characteristic, complemented
7C2×#16837711C211yesmaximal, characteristic, complemented
8C2×#16837685C211yesmaximal, characteristic, complemented
9C2×#16837703C211yesmaximal, characteristic, complemented
10C2×#16837619C211yesmaximal, characteristic
11C2×#16837619C211yesmaximal, characteristic
12C2×#16837531C211yesmaximal, characteristic, complemented
13C2×#16837512C211yesmaximal, characteristic
14C2×#16837503C211yesmaximal, characteristic, complemented
15C2×SD16×Dic59C211yesmaximal, characteristic, complemented
16C2×C59×#461C211yesmaximal, characteristic, complemented
17C22×#11745669C2211yescharacteristic
18#16838126—24no—
19#16838126C2218yescomplemented
20#16838111—24no—
21#16838111C2218yescomplemented
22C2×#14273726C2211yescharacteristic
23C2×#14273722—21no—
24C2×#14273722—21no—
25C2×#14273719C2211yescharacteristic
26C2×#14273718C2211yescharacteristic
27C2×#14273716C2211yescharacteristic
28C2×#14273716C2211yescharacteristic
29C2×#14273707—21no—
30C2×#14273706—21no—
31C2×#14273704—21no—
32C2×#14273704—21no—
33C2×Q8×Dic59C2211yescharacteristic
34C2×Q8×Dic59C2211yescharacteristic
35C2×C4×Dic118C2211yescharacteristic
36C2×C4×D236C2211yescharacteristic
37C2×D4×Dic59C2211yescharacteristic
38C2×D4×Dic59C2211yescharacteristic
39C2×#14273685—21no—
40C22×Dic59⋊C4—21no—
41#16837770C2218yescomplemented
42#16837763C2218yescomplemented
43#16837758C2218yescomplemented
44#16837711C2218yescomplemented
45#16837703C2218yescomplemented
46#16837685C2218yescomplemented
47#16837619C2218yes—
48#16837619C2218yes—
49#16837531C2218yescomplemented
50#16837512C2218yes—
51#16837503C2218yescomplemented
52SD16×Dic59C2218yescomplemented
53C2×#14273661C2211yescharacteristic
54C2×#14273659C2211yescharacteristic
55C2×#14273658C2211yescharacteristic
56C2×Dic59⋊C8C2211yescharacteristic
57C2×Dic59⋊C8C2211yescharacteristic
58C2×#14273651C2211yescharacteristic
59C2×#14273651C2211yescharacteristic
60C2×#14273651C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273649C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×#14273638C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C22×SD16×C59C2211yescharacteristic
70C22×SD16×C59C2211yescharacteristic
71C2×C4⋊Q8×C59C2211yescharacteristic
72C2×C4×D4×C59C2211yescharacteristic
73C59×#461C2218yescomplemented
74C2×C4⋊C8×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#103×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118D411yescharacteristic
79C22×D236C2311yescharacteristic
80C23×Dic59—21no—
81C23×Dic59—21no—
82C22×C4×D59—21no—
83C2×#11745669—24no—
84C2×#11745669C2314yes—
85C22×C59⋊C8C2311yescharacteristic
86C22×C59⋊C8C2311yescharacteristic
87#14273726—22no—
88#14273726C2314yes—
89#14273722—28no—
90#14273722—28no—
91#14273719—22no—
92#14273719C2314yes—
93#14273718—22no—
94#14273718C2314yes—
95#14273716—22no—
96#14273716—22no—
97#14273716C2314yes—
98#14273716C2314yes—
99#14273707—28no—
100#14273706—28no—
101#14273704—28no—
102#14273704—28no—
103Q8×Dic59—22no—
104Q8×Dic59—22no—
105Q8×Dic59C2314yes—
106Q8×Dic59C2314yes—
107C4×Dic118D414yes—
108C4×Dic118C2314yes—
109C4×D236—22no—
110C4×D236C2314yes—
111D4×Dic59—22no—
112D4×Dic59—22no—
113D4×Dic59C2314yes—
114D4×Dic59C2314yes—
115#14273685—28no—
116C2×C4⋊Dic59—21no—
117C2×C4⋊Dic59—21no—
118C2×C4⋊Dic59—21no—
119C2×C4⋊Dic59D411yescharacteristic
120C2×C4⋊Dic59C2311yescharacteristic
121C2×C4⋊Dic59C2311yescharacteristic
122C2×C4⋊Dic59C2311yescharacteristic
123C2×Dic59⋊C4—21no—
124C2×Dic59⋊C4—21no—
125C2×Dic59⋊C4—21no—
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—28no—
128C2×Dic59⋊C4D411yescharacteristic
129C2×Dic59⋊C4D411yescharacteristic
130C2×C22⋊Dic59—21no—
131C2×C22⋊Dic59—21no—
132C2×(C2×D59)⋊C4—21no—
133C2×(C2×D59)⋊C4—21no—
134C2×(C2×D59)⋊C4—21no—
135C2×(C2×D59)⋊C4—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×C4×Dic59—21no—
138C2×C4×Dic59—21no—
139C2×C4×Dic59C2311yescharacteristic
140C2×C4×Dic59C2311yescharacteristic
141#14273661C2314yes—
142#14273659C2314yes—
143#14273658C2314yes—
144Dic59⋊C8C2314yes—
145Dic59⋊C8C2314yes—
146#14273651C2314yes—
147#14273651C2314yes—
148#14273651C2314yes—
149#14273651C2314yes—
150#14273649C2314yes—
151#14273649C2314yes—
152#14273648C2314yes—
153#14273647C2314yes—
154#14273638C2314yes—
155#14273637C2314yes—
156C8×Dic59C2314yes—
157C22×Q8×C59C2311yescharacteristic
158C22×Q8×C59C2311yescharacteristic
159C22×D4×C59C2311yescharacteristic
160C23×C4×C59—21no—
161C2×SD16×C59—24no—
162C2×SD16×C59—24no—
163C2×SD16×C59C2314yes—
164C2×SD16×C59C2314yes—
165C22×C8×C59C2311yescharacteristic
166C22×C8×C59C2311yescharacteristic
167C4⋊Q8×C59—22no—
168C4⋊Q8×C59C2314yes—
169C4×D4×C59—22no—
170C4×D4×C59C2314yes—
171C2×C4⋊C4×C59—21no—
172C2×C4⋊C4×C59—21no—
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C22⋊C4×C59—21no—
175C2×C42×C59C2311yescharacteristic
176C4⋊C8×C59C2314yes—
177#103×C59C2314yes—
178#103×C59C2314yes—
179C24×C59—21no—
180C23×D59—21no—
181C2×Q8×C59—21no—
182C2×Q8×C59—21no—
183C2×Q8×C59—22no—
184C2×Q8×C59—22no—
185C2×Q8×C59—22no—
186C2×Q8×C59—22no—
187C2×Q8×C59C2412yes—
188C2×Q8×C59C2412yes—
189C2×D4×C59—21no—
190C2×D4×C59—22no—
191C2×D4×C59#4114yes—
192C2×D4×C59C2412yes—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—24no—
197C22×C4×C59—82no—
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2411yescharacteristic
201C22×Dic59—21no—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59—24no—
205C22×Dic59—24no—
206C22×Dic59—44no—
207C22×Dic59—82no—
208C22×Dic59C2×D411yescharacteristic
209C22×Dic59C2×D411yescharacteristic
210C22×Dic59C2×D411yescharacteristic
211C22×Dic59C2×D411yescharacteristic
212C2×D236—22no—
213C2×D236—22no—
214C2×D236—21no—
215C2×D236C2412yes—
216C2×C4×D59—24no—
217C2×C4×D59—44no—
218C2×Dic118—24no—
219C2×Dic118—42no—
220C2×Dic118—82no—
221C2×Dic118C2×D414yes—
222SD16×C59—28no—
223SD16×C59—28no—
224C2×C8×C59—22no—
225C2×C8×C59—22no—
226C2×C8×C59C2412yes—
227C2×C8×C59C2412yes—
228C4⋊C4×C59—24no—
229C4⋊C4×C59—24no—
230C4⋊C4×C59—21no—
231C4⋊C4×C59C2412yes—
232C22⋊C4×C59—24no—
233C42×C59C2×D412yes—
234C42×C59C2412yes—
235C22⋊Dic59—24no—
236C22⋊Dic59—24no—
237#11745669—28no—
238(C2×D59)⋊C4—24no—
239(C2×D59)⋊C4—24no—
240(C2×D59)⋊C4—24no—
241(C2×D59)⋊C4—24no—
242(C2×D59)⋊C4—24no—
243C4⋊Dic59—21no—
244C4⋊Dic59—21no—
245C4⋊Dic59—21no—
246C4⋊Dic59—24no—
247C4⋊Dic59—24no—
248C4⋊Dic59—24no—
249C4⋊Dic59C2×D414yes—
250C4⋊Dic59C2412yes—
251C4⋊Dic59C2412yes—
252C4⋊Dic59C2412yes—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256Dic59⋊C4—24no—
257Dic59⋊C4C2×D414yes—
258Dic59⋊C4C2×D414yes—
259C4×Dic59—24no—
260C4×Dic59—24no—
261C4×Dic59C2×D412yes—
262C4×Dic59C2×D412yes—
263C4×Dic59C2412yes—
264C4×Dic59C2412yes—
265C2×C59⋊C8—22no—
266C2×C59⋊C8—22no—
267C2×C59⋊C8C2412yes—
268C2×C59⋊C8C2412yes—
269C23×C59—24no—
270C23×C59—22no—
271C23×C59—42no—
272C23×C59—42no—
273C23×C59C22×D411yescharacteristic
274C22×D59—22no—
275C22×D59—42no—
276C22×D59—42no—
277C22×D59—42no—
278Q8×C59—22no—
279Q8×C59—22no—
280Q8×C59—22no—
281Q8×C59—22no—
282Q8×C59—42no—
283Q8×C59—42no—
284D4×C59—24no—
285D4×C59—22no—
286D4×C59C2×#4114yes—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—42no—
293C2×C4×C59—42no—
294C2×C4×C59—42no—
295C2×C4×C59—84no—
296C2×C4×C59C22×D412yes—
297C2×C4×C59C22×D412yes—
298C2×C4×C59C22×D411yescharacteristic
299C2×C4×C59C2×#4112yes—
300C2×C4×C592−1+412yes—
301C2×C4×C59C2511yescharacteristic
302C2×Dic59—22no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—48no—
310C2×Dic59—42no—
311C2×Dic59—42no—
312C2×Dic59—42no—
313C2×Dic59—84no—
314C2×Dic59C22×D412yes—
315C2×Dic59C22×D412yes—
316C2×Dic59C22×D412yes—
317C2×Dic59C22×D412yes—
318D236—22no—
319D236—22no—
320D236—42no—
321C4×D59—48no—
322Dic118—44no—
323Dic118—84no—
324C8×C59—22no—
325C8×C59—22no—
326C59⋊C8—22no—
327C59⋊C8—22no—
328C2×#3376—591nomaximal, Sylow
329C22×C59—24no—
330C22×C59—48no—
331C22×C59—42no—
332C22×C59—42no—
333C22×C59#54812yes—
334C22×C59#57512yes—
335C22×C59#57712yes—
336C22×C59C23×D411yescharacteristic
337C2×D59—42no—
338C2×D59—42no—
339C2×D59—42no—
340C2×D59—84no—
341C4×C59—22no—
342C4×C59—22no—
343C4×C59—42no—
344C4×C59—42no—
345C4×C59—42no—
346C4×C59#54812yes—
347C4×C59C22×#4111yescharacteristic
348C4×C59C2×2−1+411yescharacteristic
349Dic59—22no—
350Dic59—22no—
351Dic59—22no—
352Dic59—22no—
353Dic59—42no—
354Dic59—42no—
355Dic59—42no—
356C2×#556—591no—
357C2×#554—591no—
358#3376—5916no—
359C2×#491—591no—
360C2×#489—591no—
361C2×#488—591no—
362C2×#479—591no—
363C2×#475—591no—
364C2×#478—591no—
365C2×#463—591no—
366C2×#463—591no—
367C2×#461D5911yescharacteristic, complemented
368C2×#446—591no—
369C2×#442—591no—
370C2×#440—591no—
371C2×C4×SD16—591no—
372C2×C59—44no—
373C2×C59#337614yescomplemented
374C2×C59C2×#54811yescharacteristic
375C2×C59C2×#57511yescharacteristic
376C2×C59C2×#57711yescharacteristic
377D59—82no—
378C22×SD16C2×D5911yescharacteristic
379C22×SD16C2×D5911yescharacteristic
380C22×D8—591no—
381#556—598no—
382#556—1184no—
383#554—598no—
384#554—1184no—
385C2×C4⋊Q8—591no—
386C2×C4⋊Q8C2×D5911yescharacteristic
387C2×#126—1181no—
388C2×#126—1181no—
389C2×#125—591no—
390C2×#125—591no—
391C2×#124—591no—
392C2×#124—591no—
393C2×C22⋊Q8—1181no—
394C2×C22⋊Q8—1181no—
395C2×C22⋊Q8—1181no—
396C2×C22⋊Q8—1181no—
397C2×C4×Q8—591no—
398C2×C4×Q8—591no—
399C2×C4×Q8—591no—
400C2×C4×D4—591no—
401C2×C4×D4—591no—
402C2×C4×D4—591no—
403C2×C4×D4C2×D5911yescharacteristic
404C2×#117—1181no—
405C22×C4⋊C4—1181no—
406#491—598no—
407#489—598no—
408#488—598no—
409#479—598no—
410#478—598no—
411#475—598no—
412#463—598no—
413#463—598no—
414#461C2×D5918yescomplemented
415#446—598no—
416#442—598no—
417#440—598no—
418C4×SD16—598no—
419C2×#107—591no—
420C2×#106—591no—
421C2×#106—591no—
422C2×C4⋊C8—591no—
423C2×C4⋊C8—591no—
424C2×C4⋊C8C2×D5911yescharacteristic
425C2×#103—591no—
426C2×#103—591no—
427C2×#103—591no—
428C2×#103—591no—
429C2×#103C2×D5911yescharacteristic
430C2×#103C2×D5911yescharacteristic
431C2×#102—591no—
432C2×#102—591no—
433C2×#102—591no—
434C2×#102—591no—
435C2×#97—591no—
436C2×#97—591no—
437C2×C4×C8—591no—
438C59C2×#337611yescharacteristic, complemented, Sylow
439C22×Q8—591no—
440C22×Q8—1181no—
441C22×Q8C22×D5911yescharacteristic
442C22×Q8C22×D5911yescharacteristic
443C22×D4—591no—
444C22×D4C22×D5911yescharacteristic
445C23×C4—21no—
446C23×C4—1181no—
447C23×C4—1181no—
448C23×C4—1181no—
449C2×SD16—24no—
450C2×SD16—24no—
451C2×SD16C22×D5914yes—
452C2×SD16C22×D5914yes—
453C2×D8—594no—
454C2×D8—1184no—
455C22×C8—591no—
456C22×C8—591no—
457C22×C8C22×D5911yescharacteristic
458C22×C8C22×D5911yescharacteristic
459C4⋊Q8—22no—
460C4⋊Q8—594no—
461C4⋊Q8—1182no—
462C4⋊Q8C22×D5914yes—
463#126—1188no—
464#126—1188no—
465#125—594no—
466#125—594no—
467#125—1182no—
468#125—1182no—
469#124—594no—
470#124—594no—
471#124—1182no—
472#124—1182no—
473C22⋊Q8—1188no—
474C22⋊Q8—1188no—
475C22⋊Q8—1188no—
476C22⋊Q8—1188no—
477C4×Q8—594no—
478C4×Q8—594no—
479C4×Q8—594no—
480C4×Q8—594no—
481C4×Q8—1182no—
482C4×Q8—1182no—
483C4×D4—22no—
484C4×D4—594no—
485C4×D4—594no—
486C4×D4—594no—
487C4×D4—1182no—
488C4×D4—1182no—
489C4×D4—1182no—
490C4×D4C22×D5914yes—
491#117—1188no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—591no—
495C2×C4⋊C4—591no—
496C2×C4⋊C4—591no—
497C2×C4⋊C4—591no—
498C2×C4⋊C4—591no—
499C2×C4⋊C4—591no—
500C2×C4⋊C4—1188no—
501C2×C4⋊C4—1181no—
502C2×C4⋊C4—1181no—
503C2×C4⋊C4—1181no—
504C2×C4⋊C4—1181no—
505C2×C4⋊C4—1181no—
506C2×C4⋊C4—1181no—
507C2×C4⋊C4—1181no—
508C2×C4⋊C4C22×D5911yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—1181no—
511C2×C22⋊C4—1181no—
512C2×C22⋊C4—1181no—
513C2×C22⋊C4—1181no—
514C2×C22⋊C4—1181no—
515C2×C22⋊C4—1181no—
516C2×C22⋊C4—1181no—
517C2×C42—591no—
518C2×C42—591no—
519C2×C42—1181no—
520C2×C42—1181no—
521C2×C42C22×D5911yescharacteristic
522#107—594no—
523#106—594no—
524#106—594no—
525C4⋊C8—594no—
526C4⋊C8—594no—
527C4⋊C8C22×D5914yes—
528#103—594no—
529#103—594no—
530#103—594no—
531#103—594no—
532#103C22×D5914yes—
533#103C22×D5914yes—
534#102—594no—
535#102—594no—
536#102—594no—
537#102—594no—
538#97—594no—
539#97—594no—
540C4×C8—594no—
541C24—21no—
542C24—1181no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—594no—
550C2×Q8—1184no—
551C2×Q8—4722no—
552C2×Q8—2362no—
553C2×Q8C23×D5912yes—
554C2×Q8C23×D5912yes—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—592no—
558C2×D4—1181no—
559C2×D4—1182no—
560C2×D4—1182no—
561C2×D4#1174568714yes—
562C2×D4C23×D5912yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—82no—
568C22×C4—591no—
569C22×C4—591no—
570C22×C4—591no—
571C22×C4—591no—
572C22×C4—1184no—
573C22×C4—1184no—
574C22×C4—1181no—
575C22×C4—1181no—
576C22×C4—1181no—
577C22×C4—1184no—
578C22×C4—4722no—
579C22×C4—2364no—
580C22×C4—2364no—
581C22×C4D4×D5911yescharacteristic
582C22×C4D4×D5911yescharacteristic
583C22×C4C23×D5911yescharacteristic
584SD16—28no—
585SD16—28no—
586D8—1188no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—592no—
590C2×C8—592no—
591C2×C8—1182no—
592C2×C8—1182no—
593C2×C8C23×D5912yes—
594C2×C8C23×D5912yes—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—21no—
598C4⋊C4—594no—
599C4⋊C4—594no—
600C4⋊C4—594no—
601C4⋊C4—592no—
602C4⋊C4—592no—
603C4⋊C4—592no—
604C4⋊C4—1184no—
605C4⋊C4—1184no—
606C4⋊C4—1184no—
607C4⋊C4—1184no—
608C4⋊C4—1184no—
609C4⋊C4—1181no—
610C4⋊C4—1181no—
611C4⋊C4—1181no—
612C4⋊C4—1184no—
613C4⋊C4—1184no—
614C4⋊C4C23×D5912yes—
615C22⋊C4—24no—
616C22⋊C4—1184no—
617C22⋊C4—1184no—
618C22⋊C4—1184no—
619C22⋊C4—1184no—
620C22⋊C4—1184no—
621C22⋊C4—1184no—
622C22⋊C4—1184no—
623C42—592no—
624C42—592no—
625C42—592no—
626C42—592no—
627C42—1184no—
628C42—1184no—
629C42D4×D5912yes—
630C42C23×D5912yes—
631C23—22no—
632C23—24no—
633C23—42no—
634C23—42no—
635C23—1182no—
636C23—2362no—
637C23—2362no—
638C23—2362no—
639C23C2×D4×D5911yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—22no—
644Q8—42no—
645Q8—42no—
646Q8—4724no—
647Q8—2364no—
648D4—22no—
649D4—24no—
650D4—1182no—
651D4—1182no—
652D4—2362no—
653D4C2×#1174568714yes—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—84no—
663C2×C4—592no—
664C2×C4—592no—
665C2×C4—592no—
666C2×C4—592no—
667C2×C4—1182no—
668C2×C4—1182no—
669C2×C4—1182no—
670C2×C4—1182no—
671C2×C4—1182no—
672C2×C4—1182no—
673C2×C4—1182no—
674C2×C4—4724no—
675C2×C4—2368no—
676C2×C4—2368no—
677C2×C4—2362no—
678C2×C4—2362no—
679C2×C4—2362no—
680C2×C4C2×D4×D5912yes—
681C2×C4C2×D4×D5912yes—
682C2×C4C2×D4×D5911yescharacteristic
683C2×C4C2×#1174568712yes—
684C2×C4#1427377412yes—
685C2×C4C24×D5911yescharacteristic
686C8—22no—
687C8—22no—
688C8—1182no—
689C8—1182no—
690C22—24no—
691C22—42no—
692C22—42no—
693C22—48no—
694C22—4724no—
695C22—2362no—
696C22—2362no—
697C22—2362no—
698C22#1683805812yes—
699C22#1683820112yes—
700C22#1683820812yes—
701C22C22×D4×D5911yescharacteristic
702C4—22no—
703C4—22no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—1182no—
708C4—1182no—
709C4—1182no—
710C4—1182no—
711C4—2362no—
712C4—2362no—
713C4—2362no—
714C4#1683805812yes—
715C4C22×#1174568711yescharacteristic
716C4C2×#1427377411yescharacteristic
717C2—44no—
718C2—4722no—
719C2#2143691614yesdirect product factor
720C2C2×#1683805811yescharacteristic
721C2C2×#1683820111yescharacteristic
722C2C2×#1683820811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#461C2
socleC23×C59C22×D4
prime radicalC22×#11745669C22
hypercenterC2×#461D59
hypocenterC59C2×#3376
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#16838126C2semidirect
2. C2×#16838111C2semidirect
3. #21436916C2direct (N × H)
4. C2×#16837770C2semidirect
5. C2×#16837763C2semidirect
6. C2×#16837758C2semidirect
7. C2×#16837711C2semidirect
8. C2×#16837685C2semidirect
9. C2×#16837703C2semidirect
12. C2×#16837531C2semidirect
14. C2×#16837503C2semidirect
15. C2×SD16×Dic59C2semidirect
16. C2×C59×#461C2semidirect
19. #16838126C22semidirect
21. #16838111C22semidirect
41. #16837770C22semidirect
42. #16837763C22semidirect
43. #16837758C22semidirect
44. #16837711C22semidirect
45. #16837703C22semidirect
46. #16837685C22semidirect
49. #16837531C22semidirect
51. #16837503C22semidirect
52. SD16×Dic59C22semidirect
73. C59×#461C22semidirect
367. C2×#461D59semidirect
373. C2×C59#3376semidirect
414. #461C2×D59semidirect
438. C59C2×#3376semidirect
719. C2#21436916direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381262
C2×#168381112
#214369162
C2×#168377702
C2×#168377632
C2×#168377582
C2×#168377112
C2×#168376852
C2×#168377032
C2×#168376192
C2×#168375312
C2×#168375122
C2×#168375032
C2×SD16×Dic592
C2×C59×#4612
C2×#337659