Finite Group Databasebeta

← C2×#21435523 #29461616

Subgroups — C2×#21435523 #29461616

Order 15104.

1818 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838019C211yesmaximal, characteristic
2C2×#16838012C211yesmaximal, characteristic, complemented
3#21435523C2116yesmaximal, direct product factor
4C2×#16837708C211yesmaximal, characteristic, complemented
5C2×#16837696C211yesmaximal, characteristic, complemented
6C2×#16837685C211yesmaximal, characteristic, complemented
7C2×#16837704C211yesmaximal, characteristic, complemented
8C2×#16837660C211yesmaximal, characteristic, complemented
9C2×#16837641C211yesmaximal, characteristic, complemented
10C2×#16837629C211yesmaximal, characteristic
11C2×#16837623C211yesmaximal, characteristic, complemented
12C2×#16837622C211yesmaximal, characteristic, complemented
13C2×#16837611C211yesmaximal, characteristic, complemented
14C2×#16837605C211yesmaximal, characteristic, complemented
15C2×#16837430C211yesmaximal, characteristic, complemented
16C2×C59×#468C211yesmaximal, characteristic
17C22×Dic236C2211yescharacteristic
18C22×#11745672C2211yescharacteristic
19C22×#11745670C2211yescharacteristic
20C23×C59⋊C8C2211yescharacteristic
21#16838019—24no—
22#16838019C2218yes—
23#16838012—24no—
24#16838012C2218yescomplemented
25C2×#14273726C2211yescharacteristic
26C2×#14273725C2211yescharacteristic
27C2×#14273720—21no—
28C2×#14273720—21no—
29C2×#14273720—21no—
30C2×#14273718—21no—
31C2×#14273718C2211yescharacteristic
32C2×#14273717—21no—
33C2×#14273714—21no—
34C2×#14273714C2211yescharacteristic
35C2×#14273708—21no—
36C2×#14273706C2211yescharacteristic
37C2×#14273706C2211yescharacteristic
38C2×#14273704—21no—
39C2×Q8×Dic59C2211yescharacteristic
40C2×#14273692C2211yescharacteristic
41C2×#14273692C2211yescharacteristic
42C2×D4×Dic59C2211yescharacteristic
43C2×#14273686C2211yescharacteristic
44#16837708C2218yescomplemented
45#16837704C2218yescomplemented
46#16837696C2218yescomplemented
47#16837685C2218yescomplemented
48#16837660C2218yescomplemented
49#16837641C2218yescomplemented
50#16837629C2218yes—
51#16837623C2218yescomplemented
52#16837622C2218yescomplemented
53#16837611C2218yescomplemented
54#16837605C2218yescomplemented
55C2×#14273660C2211yescharacteristic
56C2×#14273659C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58#16837430C2218yescomplemented
59C2×Dic59⋊C8C2211yescharacteristic
60C2×Dic59⋊C8C2211yescharacteristic
61C2×Dic59⋊C8C2211yescharacteristic
62C2×Dic59⋊C8C2211yescharacteristic
63C2×#14273652C2211yescharacteristic
64C2×#14273652C2211yescharacteristic
65C2×#14273651C2211yescharacteristic
66C2×#14273650C2211yescharacteristic
67C2×#14273650C2211yescharacteristic
68C2×#14273648C2211yescharacteristic
69C22×SD16×C59C2211yescharacteristic
70C22×M16×C59C2211yescharacteristic
71C2×C22⋊Q8×C59C2211yescharacteristic
72C2×#121×C59C2211yescharacteristic
73C59×#468C2218yes—
74C2×#107×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C22×Dic118C2311yescharacteristic
80C23×Dic59—21no—
81C2×Dic236—42no—
82C2×Dic236C2314yes—
83C2×#11745672—42no—
84C2×#11745672C2314yes—
85C2×#11745670—42no—
86C2×#11745670C2314yes—
87C22×C59⋊C8—42no—
88C22×C59⋊C8C2311yescharacteristic
89C22×C59⋊C8C2311yescharacteristic
90C22×C59⋊C8C2314yes—
91#14273726—22no—
92#14273726C2314yes—
93#14273725—22no—
94#14273725C2314yes—
95#14273720—28no—
96#14273720—28no—
97#14273720—28no—
98#14273718—28no—
99#14273718—22no—
100#14273718C2314yes—
101#14273717—28no—
102#14273714—28no—
103#14273714—22no—
104#14273714C2314yes—
105#14273708—28no—
106#14273706—22no—
107#14273706—22no—
108#14273706C2314yes—
109#14273706C2314yes—
110#14273704—28no—
111Q8×Dic59—22no—
112Q8×Dic59C2314yes—
113#14273692—22no—
114#14273692—22no—
115#14273692C2314yes—
116#14273692C2314yes—
117D4×Dic59—22no—
118D4×Dic59C2314yes—
119#14273686D414yes—
120#14273686C2314yes—
121C2×C4⋊Dic59—21no—
122C2×C4⋊Dic59—21no—
123C2×C4⋊Dic59D411yescharacteristic
124C2×C4⋊Dic59D411yescharacteristic
125C2×C4⋊Dic59C2311yescharacteristic
126C2×C4⋊Dic59C2311yescharacteristic
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4—21no—
135C2×C22⋊Dic59—21no—
136C2×C22⋊Dic59—21no—
137C2×C22⋊Dic59—21no—
138C2×C22⋊Dic59—21no—
139C2×C22⋊Dic59—21no—
140C2×C22⋊Dic59D411yescharacteristic
141C2×C22⋊Dic59D411yescharacteristic
142C2×C4×Dic59—21no—
143C2×C4×Dic59—21no—
144C2×C4×Dic59—21no—
145C2×C4×Dic59C2311yescharacteristic
146C2×C4×Dic59C2311yescharacteristic
147#14273660C2314yes—
148#14273659C2314yes—
149#14273658C2314yes—
150Dic59⋊C8C2314yes—
151Dic59⋊C8C2314yes—
152Dic59⋊C8C2314yes—
153Dic59⋊C8C2314yes—
154#14273652C2314yes—
155#14273652C2314yes—
156#14273651C2314yes—
157#14273650C2314yes—
158#14273650C2314yes—
159#14273648C2314yes—
160C22×Q8×C59C2311yescharacteristic
161C22×D4×C59—21no—
162C22×D4×C59C2311yescharacteristic
163C23×C4×C59C2311yescharacteristic
164C2×SD16×C59—42no—
165C2×SD16×C59C2314yes—
166C2×M16×C59—42no—
167C2×M16×C59C2314yes—
168C22×C8×C59C2311yescharacteristic
169C22×C8×C59C2311yescharacteristic
170C22⋊Q8×C59—22no—
171C22⋊Q8×C59C2314yes—
172#121×C59—22no—
173#121×C59C2314yes—
174C2×C4⋊C4×C59—21no—
175C2×C4⋊C4×C59C2311yescharacteristic
176C2×C4⋊C4×C59C2311yescharacteristic
177C2×C22⋊C4×C59—21no—
178C2×C22⋊C4×C59—21no—
179#107×C59C2314yes—
180#103×C59C2314yes—
181#102×C59C2314yes—
182C24×C59—21no—
183C24×C59C2×D411yescharacteristic
184C2×Q8×C59—21no—
185C2×Q8×C59—22no—
186C2×Q8×C59—22no—
187C2×Q8×C59C2412yes—
188C2×D4×C59—24no—
189C2×D4×C59—21no—
190C2×D4×C59—22no—
191C2×D4×C59—22no—
192C2×D4×C59—82no—
193C2×D4×C59C2412yes—
194C22×C4×C59—22no—
195C22×C4×C59—22no—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2×D412yes—
201C22×C4×C59C2412yes—
202C22×C4×C59C2411yescharacteristic
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59—21no—
207C22×Dic59—24no—
208C22×Dic59—82no—
209C22×Dic59C2×D411yescharacteristic
210C22×Dic59C2×D411yescharacteristic
211C22×Dic59C2×D411yescharacteristic
212C22×Dic59C2×D411yescharacteristic
213C2×Dic118—22no—
214C2×Dic118—22no—
215C2×Dic118—22no—
216C2×Dic118—22no—
217C2×Dic118—21no—
218C2×Dic118—21no—
219C2×Dic118—24no—
220C2×Dic118—82no—
221C2×Dic118C2412yes—
222C2×Dic118C2412yes—
223SD16×C59—44no—
224M16×C59—44no—
225C2×C8×C59—22no—
226C2×C8×C59—22no—
227C2×C8×C59C2412yes—
228C2×C8×C59C2412yes—
229C4⋊C4×C59—24no—
230C4⋊C4×C59—21no—
231C4⋊C4×C59—21no—
232C4⋊C4×C59C2412yes—
233C4⋊C4×C59C2412yes—
234C22⋊C4×C59—24no—
235C22⋊C4×C59—24no—
236C22⋊Dic59—24no—
237C22⋊Dic59—24no—
238C22⋊Dic59—24no—
239C22⋊Dic59—24no—
240C22⋊Dic59—24no—
241C22⋊Dic59C2×D414yes—
242C22⋊Dic59C2×D414yes—
243#11745672—44no—
244#11745670—44no—
245C4⋊Dic59—21no—
246C4⋊Dic59—21no—
247C4⋊Dic59—24no—
248C4⋊Dic59—24no—
249C4⋊Dic59C2×D414yes—
250C4⋊Dic59C2×D414yes—
251C4⋊Dic59C2412yes—
252C4⋊Dic59C2412yes—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261C4×Dic59—24no—
262C4×Dic59—24no—
263C4×Dic59—24no—
264C4×Dic59C2×D412yes—
265C4×Dic59C2×D412yes—
266C4×Dic59C2412yes—
267C4×Dic59C2412yes—
268C2×C59⋊C8—22no—
269C2×C59⋊C8—22no—
270C2×C59⋊C8—44no—
271C2×C59⋊C8C2412yes—
272C2×C59⋊C8C2412yes—
273Dic236—44no—
274C23×C59—22no—
275C23×C59—22no—
276C23×C59—22no—
277C23×C59—22no—
278C23×C59—42no—
279C23×C59—42no—
280C23×C59—42no—
281C23×C59C22×D412yes—
282C23×C59C22×D411yescharacteristic
283Q8×C59—22no—
284Q8×C59—22no—
285Q8×C59—42no—
286D4×C59—22no—
287D4×C59—22no—
288D4×C59—42no—
289D4×C59—84no—
290C2×C4×C59—22no—
291C2×C4×C59—24no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—42no—
298C2×C4×C59—42no—
299C2×C4×C59—42no—
300C2×C4×C59C22×D412yes—
301C2×C4×C59C22×D411yescharacteristic
302C2×C4×C59H(5,𝔽2)12yes—
303C2×C4×C592−1+412yes—
304C2×C4×C59C2511yescharacteristic
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—42no—
314C2×Dic59—42no—
315C2×Dic59—42no—
316C2×Dic59—42no—
317C2×Dic59—84no—
318C2×Dic59C22×D412yes—
319C2×Dic59C22×D412yes—
320C2×Dic59C22×D412yes—
321C2×Dic59C22×D412yes—
322Dic118—22no—
323Dic118—22no—
324Dic118—22no—
325Dic118—22no—
326Dic118—42no—
327Dic118—42no—
328Dic118—84no—
329C8×C59—22no—
330C8×C59—22no—
331C59⋊C8—22no—
332C59⋊C8—22no—
333C2×#3258—591nomaximal, Sylow
334C22×C59—22no—
335C22×C59—22no—
336C22×C59—22no—
337C22×C59—44no—
338C22×C59—42no—
339C22×C59—42no—
340C22×C59—42no—
341C22×C59—84no—
342C22×C59#53712yes—
343C22×C59#57712yes—
344C22×C59#57812yes—
345C22×C59C23×D411yescharacteristic
346C4×C59—22no—
347C4×C59—42no—
348C4×C59—42no—
349C4×C59—42no—
350C4×C59#53712yes—
351C4×C59C2×H(5,𝔽2)11yescharacteristic
352C4×C59C2×2−1+411yescharacteristic
353Dic59—22no—
354Dic59—22no—
355Dic59—22no—
356Dic59—22no—
357Dic59—42no—
358Dic59—42no—
359Dic59—42no—
360Dic59—42no—
361C2×#542—591no—
362C2×#541—591no—
363#3258—5916no—
364C2×#479—591no—
365C2×#477—591no—
366C2×#475—591no—
367C2×#478—591no—
368C2×#470—591no—
369C2×#468D5911yescharacteristic
370C2×#467—591no—
371C2×#465—591no—
372C2×#464—591no—
373C2×#464—591no—
374C2×#462—591no—
375C2×#461—591no—
376C2×#424—591no—
377C2×C59—42no—
378C2×C59—82no—
379C2×C59#325814yescomplemented
380C2×C59C2×#53711yescharacteristic
381C2×C59C2×#57711yescharacteristic
382C2×C59C2×#57811yescharacteristic
383C22×Q16—591no—
384C22×Q16—591no—
385C22×SD16—591no—
386C22×SD16C2×D5911yescharacteristic
387C22×M16C2×D5911yescharacteristic
388C23×C8—591no—
389#542—598no—
390#542—1184no—
391#541—598no—
392#541—1184no—
393C2×C4⋊Q8—591no—
394C2×C4⋊Q8—591no—
395C2×#126—1181no—
396C2×#126—1181no—
397C2×#126—1181no—
398C2×#125—591no—
399C2×#125—1181no—
400C2×#125—1181no—
401C2×#124—591no—
402C2×#124—1181no—
403C2×#123—1181no—
404C2×C22⋊Q8—591no—
405C2×C22⋊Q8—591no—
406C2×C22⋊Q8—1181no—
407C2×C22⋊Q8C2×D5911yescharacteristic
408C2×#121C2×D5911yescharacteristic
409C2×C4×Q8—591no—
410C2×C4×Q8—591no—
411C2×C4×Q8—591no—
412C2×C4×D4—591no—
413C2×#117—591no—
414#479—598no—
415#478—598no—
416#477—598no—
417#475—598no—
418#470—598no—
419#468C2×D5918yes—
420#467—598no—
421#465—598no—
422#464—598no—
423#464—598no—
424#462—598no—
425#461—598no—
426C2×#107—591no—
427C2×#107C2×D5911yescharacteristic
428C2×#106—591no—
429C2×#106—591no—
430#424—598no—
431C2×C4⋊C8—591no—
432C2×C4⋊C8—591no—
433C2×C4⋊C8—591no—
434C2×C4⋊C8—591no—
435C2×#103—591no—
436C2×#103—591no—
437C2×#103—591no—
438C2×#103—591no—
439C2×#103—591no—
440C2×#103C2×D5911yescharacteristic
441C2×#102—591no—
442C2×#102C2×D5911yescharacteristic
443C59C2×#325811yescharacteristic, complemented, Sylow
444C22×Q8—591no—
445C22×Q8—591no—
446C22×Q8—1181no—
447C22×Q8C22×D5911yescharacteristic
448C22×D4—21no—
449C22×D4C22×D5911yescharacteristic
450C23×C4—1181no—
451C23×C4C22×D5911yescharacteristic
452C2×Q16—594no—
453C2×Q16—594no—
454C2×Q16—2362no—
455C2×Q16—2362no—
456C2×SD16—42no—
457C2×SD16—594no—
458C2×SD16—2362no—
459C2×SD16C22×D5914yes—
460C2×M16—42no—
461C2×M16C22×D5914yes—
462C22×C8—591no—
463C22×C8—591no—
464C22×C8—594no—
465C22×C8—2362no—
466C22×C8C22×D5911yescharacteristic
467C22×C8C22×D5911yescharacteristic
468C4⋊Q8—594no—
469C4⋊Q8—594no—
470C4⋊Q8—1182no—
471C4⋊Q8—1182no—
472#126—1188no—
473#126—1188no—
474#126—1188no—
475#125—594no—
476#125—1182no—
477#125—1188no—
478#125—1188no—
479#124—594no—
480#124—1182no—
481#124—1188no—
482#123—1188no—
483C22⋊Q8—22no—
484C22⋊Q8—594no—
485C22⋊Q8—594no—
486C22⋊Q8—1188no—
487C22⋊Q8—1182no—
488C22⋊Q8—1182no—
489C22⋊Q8C22×D5914yes—
490#121—22no—
491#121C22×D5914yes—
492C4×Q8—594no—
493C4×Q8—594no—
494C4×Q8—594no—
495C4×Q8—1182no—
496C4×Q8—1182no—
497C4×Q8—1182no—
498C4×D4—594no—
499C4×D4—1182no—
500#117—594no—
501#117—594no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—591no—
504C2×C4⋊C4—591no—
505C2×C4⋊C4—591no—
506C2×C4⋊C4—591no—
507C2×C4⋊C4—1181no—
508C2×C4⋊C4—1181no—
509C2×C4⋊C4—1181no—
510C2×C4⋊C4—1181no—
511C2×C4⋊C4—1181no—
512C2×C4⋊C4—1181no—
513C2×C4⋊C4—1181no—
514C2×C4⋊C4—1181no—
515C2×C4⋊C4—1181no—
516C2×C4⋊C4—1181no—
517C2×C4⋊C4C22×D5911yescharacteristic
518C2×C4⋊C4C22×D5911yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—591no—
522C2×C22⋊C4—591no—
523C2×C22⋊C4—1181no—
524C2×C22⋊C4—1181no—
525C2×C22⋊C4—1181no—
526C2×C22⋊C4—1181no—
527C2×C22⋊C4—1181no—
528C2×C42—591no—
529C2×C42—591no—
530C2×C42—1181no—
531C2×C42—1181no—
532C2×C42—1181no—
533#107—594no—
534#107C22×D5914yes—
535#106—594no—
536#106—594no—
537C4⋊C8—594no—
538C4⋊C8—594no—
539C4⋊C8—594no—
540C4⋊C8—594no—
541#103—594no—
542#103—594no—
543#103—594no—
544#103—594no—
545#103—594no—
546#103C22×D5914yes—
547#102—594no—
548#102C22×D5914yes—
549C24—21no—
550C24D4×D5911yescharacteristic
551C2×Q8—21no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—592no—
555C2×Q8—592no—
556C2×Q8—1184no—
557C2×Q8—1181no—
558C2×Q8—1181no—
559C2×Q8—1182no—
560C2×Q8—1182no—
561C2×Q8—1182no—
562C2×Q8—1182no—
563C2×Q8—4722no—
564C2×Q8C23×D5912yes—
565C2×D4—24no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—82no—
570C2×D4C23×D5912yes—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—591no—
577C22×C4—591no—
578C22×C4—591no—
579C22×C4—591no—
580C22×C4—1184no—
581C22×C4—1181no—
582C22×C4—1181no—
583C22×C4—1181no—
584C22×C4—1181no—
585C22×C4—4722no—
586C22×C4D4×D5912yes—
587C22×C4D4×D5911yescharacteristic
588C22×C4C23×D5912yes—
589C22×C4C23×D5911yescharacteristic
590Q16—2364no—
591Q16—2364no—
592SD16—44no—
593SD16—2364no—
594M16—44no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—592no—
598C2×C8—592no—
599C2×C8—1182no—
600C2×C8—1182no—
601C2×C8—2364no—
602C2×C8C23×D5912yes—
603C2×C8C23×D5912yes—
604C4⋊C4—24no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—594no—
608C4⋊C4—594no—
609C4⋊C4—592no—
610C4⋊C4—592no—
611C4⋊C4—1184no—
612C4⋊C4—1184no—
613C4⋊C4—1184no—
614C4⋊C4—1184no—
615C4⋊C4—1184no—
616C4⋊C4—1184no—
617C4⋊C4—1184no—
618C4⋊C4—1184no—
619C4⋊C4—1181no—
620C4⋊C4—1181no—
621C4⋊C4—1184no—
622C4⋊C4—1184no—
623C4⋊C4C23×D5912yes—
624C4⋊C4C23×D5912yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—594no—
628C22⋊C4—594no—
629C22⋊C4—1184no—
630C22⋊C4—1184no—
631C22⋊C4—1184no—
632C22⋊C4—1184no—
633C22⋊C4—1184no—
634C42—592no—
635C42—592no—
636C42—592no—
637C42—592no—
638C42—1184no—
639C42—1184no—
640C42—1184no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23C2×D4×D5912yes—
649C23C2×D4×D5911yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—1182no—
654Q8—1182no—
655Q8—1182no—
656Q8—1182no—
657Q8—4724no—
658Q8—2362no—
659Q8—2362no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—84no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—592no—
675C2×C4—592no—
676C2×C4—592no—
677C2×C4—592no—
678C2×C4—1182no—
679C2×C4—1182no—
680C2×C4—1182no—
681C2×C4—1182no—
682C2×C4—1182no—
683C2×C4—1182no—
684C2×C4—1182no—
685C2×C4—1182no—
686C2×C4—4724no—
687C2×C4—2362no—
688C2×C4—2362no—
689C2×C4—2362no—
690C2×C4—2362no—
691C2×C4C2×D4×D5912yes—
692C2×C4C2×D4×D5911yescharacteristic
693C2×C4#1427377212yes—
694C2×C4#1427377412yes—
695C2×C4C24×D5911yescharacteristic
696C8—22no—
697C8—22no—
698C8—1182no—
699C8—1182no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—84no—
708C22#1683797912yes—
709C22#1683821212yes—
710C22#1683821812yes—
711C22C22×D4×D5911yescharacteristic
712C4—22no—
713C4—42no—
714C4—42no—
715C4—42no—
716C4—1182no—
717C4—1182no—
718C4—1182no—
719C4—1182no—
720C4—2362no—
721C4—2362no—
722C4—2362no—
723C4—2362no—
724C4#1683797912yes—
725C4C2×#1427377211yescharacteristic
726C4C2×#1427377411yescharacteristic
727C2—42no—
728C2—82no—
729C2#2143552314yesdirect product factor
730C2C2×#1683797911yescharacteristic
731C2C2×#1683821211yescharacteristic
732C2C2×#1683821811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#468C2
socleC23×C59C22×D4
prime radicalC2×#121×C59C22
hypercenterC2×#468D59
hypocenterC59C2×#3258
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
2. C2×#16838012C2semidirect
3. #21435523C2direct (N × H)
4. C2×#16837708C2semidirect
5. C2×#16837696C2semidirect
6. C2×#16837685C2semidirect
7. C2×#16837704C2semidirect
8. C2×#16837660C2semidirect
9. C2×#16837641C2semidirect
11. C2×#16837623C2semidirect
12. C2×#16837622C2semidirect
13. C2×#16837611C2semidirect
14. C2×#16837605C2semidirect
15. C2×#16837430C2semidirect
24. #16838012C22semidirect
44. #16837708C22semidirect
45. #16837704C22semidirect
46. #16837696C22semidirect
47. #16837685C22semidirect
48. #16837660C22semidirect
49. #16837641C22semidirect
51. #16837623C22semidirect
52. #16837622C22semidirect
53. #16837611C22semidirect
54. #16837605C22semidirect
58. #16837430C22semidirect
379. C2×C59#3258semidirect
443. C59C2×#3258semidirect
729. C2#21435523direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380192
C2×#168380122
#214355232
C2×#168377082
C2×#168376962
C2×#168376852
C2×#168377042
C2×#168376602
C2×#168376412
C2×#168376292
C2×#168376232
C2×#168376222
C2×#168376112
C2×#168376052
C2×#168374302
C2×C59×#4682
C2×#325859