Finite Group Databasebeta

← C2×#21436858 #29468464

Subgroups — C2×#21436858 #29468464

Order 15104.

1874 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×#16838130C211yesmaximal, characteristic, complemented
2#21436858C2116yesmaximal, direct product factor
3C2×#16837766C211yesmaximal, characteristic
4C2×#16837761C211yesmaximal, characteristic, complemented
5C2×#16837756C211yesmaximal, characteristic, complemented
6C2×#16837709C211yesmaximal, characteristic, complemented
7C2×#16837702C211yesmaximal, characteristic, complemented
8C2×#16837692C211yesmaximal, characteristic, complemented
9C2×#16837621C211yesmaximal, characteristic, complemented
10C2×#16837621C211yesmaximal, characteristic, complemented
11C2×#16837599C211yesmaximal, characteristic
12C2×#16837533C211yesmaximal, characteristic, complemented
13C2×#16837507C211yesmaximal, characteristic, complemented
14C2×#16837502C211yesmaximal, characteristic, complemented
15C2×C4×#11745670C211yesmaximal, characteristic, complemented
16C2×C59×#559C211yesmaximal, characteristic
17C22×#11745672C2211yescharacteristic
18C22×#11745670C2211yescharacteristic
19C22×#11745670C2211yescharacteristic
20#16838130—24no—
21#16838130C2218yescomplemented
22C2×#14273727C2211yescharacteristic
23C2×#14273725—21no—
24C2×#14273719C2211yescharacteristic
25C2×#14273719C2211yescharacteristic
26C2×#14273717—21no—
27C2×#14273717—21no—
28C2×C4×Dic118C2211yescharacteristic
29C2×C4×Dic118C2211yescharacteristic
30C2×C4×Dic118C2211yescharacteristic
31C2×#14273692—21no—
32#16837766C2218yes—
33#16837761C2218yescomplemented
34#16837756C2218yescomplemented
35#16837709C2218yescomplemented
36#16837702C2218yescomplemented
37#16837692C2218yescomplemented
38#16837621C2218yescomplemented
39#16837621C2218yescomplemented
40#16837599C2218yes—
41#16837533C2218yescomplemented
42#16837507C2218yescomplemented
43#16837502C2218yescomplemented
44C4×#11745670C2218yescomplemented
45C2×#14273660C2211yescharacteristic
46C2×#14273658C2211yescharacteristic
47C2×#14273658C2211yescharacteristic
48C2×C4⋊(C59⋊C8)C2211yescharacteristic
49C2×C4⋊(C59⋊C8)C2211yescharacteristic
50C2×C4⋊(C59⋊C8)C2211yescharacteristic
51C2×#14273651C2211yescharacteristic
52C2×#14273651C2211yescharacteristic
53C2×#14273651C2211yescharacteristic
54C2×#14273650C2211yescharacteristic
55C2×#14273648C2211yescharacteristic
56C2×#14273648C2211yescharacteristic
57C2×#14273648C2211yescharacteristic
58C2×#14273648C2211yescharacteristic
59C2×#14273648C2211yescharacteristic
60C2×#14273648C2211yescharacteristic
61C2×#14273638C2211yescharacteristic
62C2×#14273638C2211yescharacteristic
63C2×C4×C59⋊C8C2211yescharacteristic
64C59×#559—24no—
65C59×#559C2218yes—
66C2×#127×C59C2211yescharacteristic
67C2×#124×C59—21no—
68C2×#124×C59C2211yescharacteristic
69C2×#124×C59C2211yescharacteristic
70C2×#123×C59—21no—
71C2×#123×C59—21no—
72C2×C4×Q8×C59C2211yescharacteristic
73C2×C4×Q8×C59C2211yescharacteristic
74C2×C4×D4×C59—21no—
75C2×C4×D4×C59C2211yescharacteristic
76C2×C4×D4×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C2×#11745672—24no—
80C2×#11745672C2314yes—
81C2×#11745670—24no—
82C2×#11745670—24no—
83C2×#11745670C2314yes—
84C2×#11745670C2314yes—
85C22×C59⋊C8C2311yescharacteristic
86C22×C59⋊C8C2311yescharacteristic
87C22×C59⋊C8C2311yescharacteristic
88C22×C59⋊C8C2311yescharacteristic
89#14273727—22no—
90#14273727C2314yes—
91#14273725—28no—
92#14273719—22no—
93#14273719—22no—
94#14273719C2314yes—
95#14273719C2314yes—
96#14273717—28no—
97#14273717—28no—
98C4×Dic118—22no—
99C4×Dic118—22no—
100C4×Dic118—22no—
101C4×Dic118C2314yes—
102C4×Dic118C2314yes—
103C4×Dic118C2314yes—
104#14273692—28no—
105C2×C4⋊Dic59—21no—
106C2×C4⋊Dic59C2311yescharacteristic
107C2×C4⋊Dic59C2311yescharacteristic
108C2×C4⋊Dic59C2311yescharacteristic
109C2×Dic59⋊C4—21no—
110C2×Dic59⋊C4—21no—
111C2×Dic59⋊C4—21no—
112C2×Dic59⋊C4—21no—
113C2×Dic59⋊C4—21no—
114C2×Dic59⋊C4—21no—
115C2×Dic59⋊C4—21no—
116C2×C4×Dic59—21no—
117C2×C4×Dic59—21no—
118C2×C4×Dic59—21no—
119#14273660C2314yes—
120#14273658C2314yes—
121#14273658C2314yes—
122C4⋊(C59⋊C8)C2314yes—
123C4⋊(C59⋊C8)C2314yes—
124C4⋊(C59⋊C8)C2314yes—
125#14273651C2314yes—
126#14273651C2314yes—
127#14273651C2314yes—
128#14273650C2314yes—
129#14273648C2314yes—
130#14273648C2314yes—
131#14273648C2314yes—
132#14273648C2314yes—
133#14273648C2314yes—
134#14273648C2314yes—
135#14273638C2314yes—
136#14273638C2314yes—
137C4×C59⋊C8C2314yes—
138C22×Q8×C59D411yescharacteristic
139C22×Q8×C59C2311yescharacteristic
140C22×D4×C59—21no—
141C22×D4×C59—21no—
142C22×D4×C59C2311yescharacteristic
143C22×D4×C59C2311yescharacteristic
144C23×C4×C59—21no—
145C23×C4×C59—21no—
146#127×C59—22no—
147#127×C59C2314yes—
148#124×C59—28no—
149#124×C59—22no—
150#124×C59—22no—
151#124×C59C2314yes—
152#124×C59C2314yes—
153#123×C59—28no—
154#123×C59—28no—
155C4×Q8×C59—22no—
156C4×Q8×C59D414yes—
157C4×Q8×C59C2314yes—
158C4×Q8×C59C2314yes—
159C4×D4×C59—28no—
160C4×D4×C59—22no—
161C4×D4×C59—22no—
162C4×D4×C59C2314yes—
163C4×D4×C59C2314yes—
164C2×C4⋊C4×C59—21no—
165C2×C4⋊C4×C59D411yescharacteristic
166C2×C4⋊C4×C59D411yescharacteristic
167C2×C4⋊C4×C59D411yescharacteristic
168C2×C4⋊C4×C59C2311yescharacteristic
169C2×C22⋊C4×C59—21no—
170C2×C22⋊C4×C59—21no—
171C2×C22⋊C4×C59—21no—
172C2×C22⋊C4×C59—21no—
173C2×C22⋊C4×C59—21no—
174C2×C22⋊C4×C59—21no—
175C2×C42×C59—21no—
176C2×C42×C59C2311yescharacteristic
177C2×C42×C59C2311yescharacteristic
178C2×C42×C59C2311yescharacteristic
179C24×C59—21no—
180C24×C59—21no—
181C2×Q8×C59—21no—
182C2×Q8×C59—22no—
183C2×Q8×C59—22no—
184C2×Q8×C59—42no—
185C2×Q8×C59C2×D414yes—
186C2×Q8×C59C2412yes—
187C2×D4×C59—21no—
188C2×D4×C59—21no—
189C2×D4×C59—24no—
190C2×D4×C59—24no—
191C2×D4×C59—22no—
192C2×D4×C59—22no—
193C2×D4×C59—22no—
194C2×D4×C59—22no—
195C2×D4×C59—44no—
196C2×D4×C59—82no—
197C2×D4×C59C2412yes—
198C2×D4×C59C2412yes—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—24no—
202C22×C4×C59—24no—
203C22×C4×C59—82no—
204C22×C4×C59—82no—
205C22×C4×C59C2×D411yescharacteristic
206C22×C4×C59C2×D411yescharacteristic
207C22×C4×C59C2×D411yescharacteristic
208C22×C4×C59C2×D411yescharacteristic
209C22×C4×C59C2×D411yescharacteristic
210C22×C4×C59C2×D411yescharacteristic
211C22×C4×C59C2411yescharacteristic
212C22×Dic59—21no—
213C22×Dic59—21no—
214C22×Dic59—21no—
215C22×Dic59—21no—
216C2×Dic118—21no—
217C2×Dic118—22no—
218C2×Dic118—24no—
219C2×Dic118—44no—
220C2×Dic118#4114yes—
221C2×Dic118C2412yes—
222C4⋊C4×C59—24no—
223C4⋊C4×C59—21no—
224C4⋊C4×C59C2×D414yes—
225C4⋊C4×C59C2×D414yes—
226C4⋊C4×C59C2×D414yes—
227C4⋊C4×C59C2412yes—
228C22⋊C4×C59—24no—
229C22⋊C4×C59—24no—
230C22⋊C4×C59—24no—
231C22⋊C4×C59—24no—
232C22⋊C4×C59—24no—
233C22⋊C4×C59—24no—
234C42×C59—24no—
235C42×C59C2×D412yes—
236C42×C59C2×D412yes—
237C42×C59C2×D412yes—
238C42×C59C2412yes—
239C42×C59C2412yes—
240C42×C59C2412yes—
241#11745672—28no—
242#11745670—28no—
243#11745670—28no—
244C4⋊Dic59—24no—
245C4⋊Dic59—21no—
246C4⋊Dic59—21no—
247C4⋊Dic59—21no—
248C4⋊Dic59C2412yes—
249C4⋊Dic59C2412yes—
250C4⋊Dic59C2412yes—
251Dic59⋊C4—24no—
252Dic59⋊C4—24no—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258C4×Dic59—24no—
259C4×Dic59—24no—
260C4×Dic59—24no—
261C2×C59⋊C8—22no—
262C2×C59⋊C8—22no—
263C2×C59⋊C8—22no—
264C2×C59⋊C8—22no—
265C2×C59⋊C8C2412yes—
266C2×C59⋊C8C2412yes—
267C2×C59⋊C8C2412yes—
268C2×C59⋊C8C2412yes—
269C23×C59—22no—
270C23×C59—22no—
271C23×C59—42no—
272C23×C59—42no—
273C23×C59—42no—
274C23×C59—42no—
275C23×C59—42no—
276C23×C59—42no—
277C23×C59C22×D411yescharacteristic
278Q8×C59—22no—
279Q8×C59—22no—
280Q8×C59—44no—
281Q8×C59—42no—
282D4×C59—22no—
283D4×C59—22no—
284D4×C59—22no—
285D4×C59—22no—
286D4×C59—48no—
287D4×C59—42no—
288D4×C59—42no—
289D4×C59—84no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—42no—
299C2×C4×C59—42no—
300C2×C4×C59—84no—
301C2×C4×C59—84no—
302C2×C4×C59C22×D412yes—
303C2×C4×C59C22×D412yes—
304C2×C4×C59C22×D412yes—
305C2×C4×C59C22×D412yes—
306C2×C4×C59C22×D412yes—
307C2×C4×C59C22×D412yes—
308C2×C4×C59C22×D411yescharacteristic
309C2×C4×C59C2×#4112yes—
310C2×C4×C592−1+412yes—
311C2×C4×C59C2511yescharacteristic
312C2×Dic59—24no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—42no—
318C2×Dic59—42no—
319C2×Dic59—42no—
320Dic118—24no—
321Dic118—22no—
322Dic118—48no—
323Dic118C2×#4114yes—
324C59⋊C8—22no—
325C59⋊C8—22no—
326C59⋊C8—22no—
327C59⋊C8—22no—
328C2×#3371—591nomaximal, Sylow
329C22×C59—42no—
330C22×C59—42no—
331C22×C59—42no—
332C22×C59—42no—
333C22×C59—42no—
334C22×C59—42no—
335C22×C59—84no—
336C22×C59—84no—
337C22×C59#54812yes—
338C22×C59#57512yes—
339C22×C59#57712yes—
340C22×C59C23×D411yescharacteristic
341C4×C59—22no—
342C4×C59—22no—
343C4×C59—22no—
344C4×C59—22no—
345C4×C59—22no—
346C4×C59—22no—
347C4×C59—42no—
348C4×C59—42no—
349C4×C59#54812yes—
350C4×C59C22×#4111yescharacteristic
351C4×C59C2×2−1+411yescharacteristic
352Dic59—24no—
353Dic59—42no—
354Dic59—42no—
355Dic59—42no—
356C2×#559D5911yescharacteristic
357C2×#557—591no—
358#3371—5916no—
359C2×#490—591no—
360C2×#489—591no—
361C2×#488—591no—
362C2×#479—591no—
363C2×#478—591no—
364C2×#476—591no—
365C2×#464—591no—
366C2×#464—591no—
367C2×#460—591no—
368C2×#446—591no—
369C2×#441—591no—
370C2×#440—591no—
371C2×C4×SD16—591no—
372C2×C59—82no—
373C2×C59—82no—
374C2×C59#337114yescomplemented
375C2×C59C2×#54811yescharacteristic
376C2×C59C2×#57511yescharacteristic
377C2×C59C2×#57711yescharacteristic
378C22×Q16—591no—
379C22×SD16—591no—
380C22×SD16—591no—
381#559—24no—
382#559C2×D5918yes—
383#557—598no—
384#557—1184no—
385C2×C4⋊Q8—591no—
386C2×C4⋊Q8—1181no—
387C2×#127C2×D5911yescharacteristic
388C2×#125—591no—
389C2×#125—591no—
390C2×#125—1181no—
391C2×#125—1181no—
392C2×#124—21no—
393C2×#124C2×D5911yescharacteristic
394C2×#124C2×D5911yescharacteristic
395C2×#123—21no—
396C2×#123—21no—
397C2×C4×Q8—591no—
398C2×C4×Q8—591no—
399C2×C4×Q8—591no—
400C2×C4×Q8—1181no—
401C2×C4×Q8C2×D5911yescharacteristic
402C2×C4×Q8C2×D5911yescharacteristic
403C2×C4×D4—21no—
404C2×C4×D4C2×D5911yescharacteristic
405C2×C4×D4C2×D5911yescharacteristic
406#490—598no—
407#489—598no—
408#488—598no—
409#479—598no—
410#478—598no—
411#476—598no—
412#464—598no—
413#464—598no—
414#460—598no—
415#446—598no—
416#441—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⋊C8—591no—
425C2×#103—591no—
426C2×#103—591no—
427C2×#103—591no—
428C2×#103—591no—
429C2×#102—591no—
430C2×#102—591no—
431C2×#102—591no—
432C2×#102—591no—
433C2×#102—591no—
434C2×#102—591no—
435C2×#97—591no—
436C2×#97—591no—
437C2×C4×C8—591no—
438C59C2×#337111yescharacteristic, complemented, Sylow
439C22×Q8—591no—
440C22×Q8—1181no—
441C22×Q8C22⋊D5911yescharacteristic
442C22×Q8C22×D5911yescharacteristic
443C22×D4—21no—
444C22×D4—21no—
445C22×D4C22×D5911yescharacteristic
446C22×D4C22×D5911yescharacteristic
447C23×C4—21no—
448C23×C4—21no—
449C2×Q16—594no—
450C2×Q16—1184no—
451C2×SD16—594no—
452C2×SD16—594no—
453C2×SD16—1184no—
454C2×SD16—1184no—
455C22×C8—591no—
456C22×C8—591no—
457C22×C8—591no—
458C22×C8—591no—
459C4⋊Q8—594no—
460C4⋊Q8—1188no—
461C4⋊Q8—1182no—
462#127—22no—
463#127C22×D5914yes—
464#125—594no—
465#125—594no—
466#125—1188no—
467#125—1188no—
468#125—1182no—
469#125—1182no—
470#124—28no—
471#124—22no—
472#124—22no—
473#124C22×D5914yes—
474#124C22×D5914yes—
475#123—28no—
476#123—28no—
477C4×Q8—22no—
478C4×Q8—594no—
479C4×Q8—594no—
480C4×Q8—594no—
481C4×Q8—1188no—
482C4×Q8—1182no—
483C4×Q8—1182no—
484C4×Q8—1182no—
485C4×Q8C22⋊D5914yes—
486C4×Q8C22×D5914yes—
487C4×Q8C22×D5914yes—
488C4×D4—28no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4C22×D5914yes—
492C4×D4C22×D5914yes—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—591no—
495C2×C4⋊C4—591no—
496C2×C4⋊C4—591no—
497C2×C4⋊C4—1181no—
498C2×C4⋊C4—1181no—
499C2×C4⋊C4—1181no—
500C2×C4⋊C4—1181no—
501C2×C4⋊C4—1181no—
502C2×C4⋊C4—1181no—
503C2×C4⋊C4—1181no—
504C2×C4⋊C4—1181no—
505C2×C4⋊C4C22⋊D5911yescharacteristic
506C2×C4⋊C4C22⋊D5911yescharacteristic
507C2×C4⋊C4C22⋊D5911yescharacteristic
508C2×C4⋊C4C22×D5911yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C42—21no—
516C2×C42—1181no—
517C2×C42—1181no—
518C2×C42—1181no—
519C2×C42C22×D5911yescharacteristic
520C2×C42C22×D5911yescharacteristic
521C2×C42C22×D5911yescharacteristic
522#107—594no—
523#106—594no—
524#106—594no—
525C4⋊C8—594no—
526C4⋊C8—594no—
527C4⋊C8—594no—
528#103—594no—
529#103—594no—
530#103—594no—
531#103—594no—
532#102—594no—
533#102—594no—
534#102—594no—
535#102—594no—
536#102—594no—
537#102—594no—
538#97—594no—
539#97—594no—
540C4×C8—594no—
541C24—21no—
542C24—21no—
543C2×Q8—21no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—42no—
547C2×Q8—594no—
548C2×Q8—592no—
549C2×Q8—1181no—
550C2×Q8—1184no—
551C2×Q8—1182no—
552C2×Q8—2364no—
553C2×Q8C2×C22⋊D5914yes—
554C2×Q8C23×D5912yes—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—24no—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—44no—
564C2×D4—82no—
565C2×D4C23×D5912yes—
566C2×D4C23×D5912yes—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—82no—
572C22×C4—82no—
573C22×C4—1181no—
574C22×C4—1181no—
575C22×C4—1181no—
576C22×C4—1181no—
577C22×C4C2×C22⋊D5911yescharacteristic
578C22×C4C2×C22⋊D5911yescharacteristic
579C22×C4C2×C22⋊D5911yescharacteristic
580C22×C4C2×C22⋊D5911yescharacteristic
581C22×C4C2×C22⋊D5911yescharacteristic
582C22×C4C2×C22⋊D5911yescharacteristic
583C22×C4C23×D5911yescharacteristic
584Q16—1188no—
585SD16—1188no—
586SD16—1188no—
587C2×C8—592no—
588C2×C8—592no—
589C2×C8—592no—
590C2×C8—592no—
591C2×C8—1182no—
592C2×C8—1182no—
593C2×C8—1182no—
594C2×C8—1182no—
595C4⋊C4—24no—
596C4⋊C4—21no—
597C4⋊C4—592no—
598C4⋊C4—592no—
599C4⋊C4—592no—
600C4⋊C4—1181no—
601C4⋊C4—1181no—
602C4⋊C4—1181no—
603C4⋊C4—1184no—
604C4⋊C4—1184no—
605C4⋊C4—1184no—
606C4⋊C4—1184no—
607C4⋊C4—1184no—
608C4⋊C4—1184no—
609C4⋊C4—1184no—
610C4⋊C4—1184no—
611C4⋊C4C2×C22⋊D5914yes—
612C4⋊C4C2×C22⋊D5914yes—
613C4⋊C4C2×C22⋊D5914yes—
614C4⋊C4C23×D5912yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—24no—
619C22⋊C4—24no—
620C22⋊C4—24no—
621C42—24no—
622C42—1184no—
623C42—1184no—
624C42—1184no—
625C42C2×C22⋊D5912yes—
626C42C2×C22⋊D5912yes—
627C42C2×C22⋊D5912yes—
628C42C23×D5912yes—
629C42C23×D5912yes—
630C42C23×D5912yes—
631C23—22no—
632C23—22no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23C22×C22⋊D5911yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—44no—
643Q8—42no—
644Q8—594no—
645Q8—1182no—
646Q8—1184no—
647Q8—2368no—
648D4—22no—
649D4—22no—
650D4—22no—
651D4—22no—
652D4—48no—
653D4—42no—
654D4—42no—
655D4—84no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—84no—
667C2×C4—84no—
668C2×C4—1182no—
669C2×C4—1184no—
670C2×C4—1182no—
671C2×C4—1182no—
672C2×C4—1182no—
673C2×C4—2362no—
674C2×C4—2362no—
675C2×C4—2362no—
676C2×C4C22×C22⋊D5912yes—
677C2×C4C22×C22⋊D5912yes—
678C2×C4C22×C22⋊D5912yes—
679C2×C4C22×C22⋊D5912yes—
680C2×C4C22×C22⋊D5912yes—
681C2×C4C22×C22⋊D5912yes—
682C2×C4C22×C22⋊D5911yescharacteristic
683C2×C4#41×D5912yes—
684C2×C4#1427377412yes—
685C2×C4C24×D5911yescharacteristic
686C8—1182no—
687C8—1182no—
688C8—1182no—
689C8—1182no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—84no—
697C22—84no—
698C22#1683805912yes—
699C22#1683820012yes—
700C22#1683821312yes—
701C22C23×C22⋊D5911yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—42no—
709C4—42no—
710C4—1184no—
711C4—2362no—
712C4—2362no—
713C4—2362no—
714C4#1683805912yes—
715C4C2×#41×D5911yescharacteristic
716C4C2×#1427377411yescharacteristic
717C2—82no—
718C2—82no—
719C2#2143685814yesdirect product factor
720C2C2×#1683805911yescharacteristic
721C2C2×#1683820011yescharacteristic
722C2C2×#1683821311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#559C2
socleC23×C59C22×D4
prime radicalC2×#127×C59C22
hypercenterC2×#559D59
hypocenterC59C2×#3371
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#16838130C2semidirect
2. #21436858C2direct (N × H)
4. C2×#16837761C2semidirect
5. C2×#16837756C2semidirect
6. C2×#16837709C2semidirect
7. C2×#16837702C2semidirect
8. C2×#16837692C2semidirect
9. C2×#16837621C2semidirect
10. C2×#16837621C2semidirect
12. C2×#16837533C2semidirect
13. C2×#16837507C2semidirect
14. C2×#16837502C2semidirect
15. C2×C4×#11745670C2semidirect
21. #16838130C22semidirect
33. #16837761C22semidirect
34. #16837756C22semidirect
35. #16837709C22semidirect
36. #16837702C22semidirect
37. #16837692C22semidirect
38. #16837621C22semidirect
39. #16837621C22semidirect
41. #16837533C22semidirect
42. #16837507C22semidirect
43. #16837502C22semidirect
44. C4×#11745670C22semidirect
374. C2×C59#3371semidirect
438. C59C2×#3371semidirect
719. C2#21436858direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381302
#214368582
C2×#168377662
C2×#168377612
C2×#168377562
C2×#168377092
C2×#168377022
C2×#168376922
C2×#168376212
C2×#168375992
C2×#168375332
C2×#168375072
C2×#168375022
C2×C4×#117456702
C2×C59×#5592
C2×#337159