Finite Group Databasebeta

← C2×#21434768 #29458561

Subgroups — C2×#21434768 #29458561

Order 15104.

1906 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×#16838024C211yesmaximal, characteristic
2C2×#16838010C211yesmaximal, characteristic, complemented
3#21434768C2116yesmaximal, direct product factor
4C2×#16837810C211yesmaximal, characteristic, complemented
5C2×#16837795C211yesmaximal, characteristic, complemented
6C2×#16837758C211yesmaximal, characteristic, complemented
7C2×#16837751C211yesmaximal, characteristic, complemented
8C2×#16837657C211yesmaximal, characteristic, complemented
9C2×#16837649C211yesmaximal, characteristic
10C2×#16837642C211yesmaximal, characteristic, complemented
11C2×#16837634C211yesmaximal, characteristic
12C2×#16837507C211yesmaximal, characteristic, complemented
13C2×#16837500C211yesmaximal, characteristic, complemented
14C2×C4×#11745660C211yesmaximal, characteristic, complemented
15C2×#16837356C211yesmaximal, characteristic, complemented
16C2×C4×Q16×C59C211yesmaximal, characteristic, complemented
17C22×#11745672C2211yescharacteristic
18C22×#11745660C2211yescharacteristic
19C22×#11745671C2211yescharacteristic
20C22×#11745659C2211yescharacteristic
21C22×C8×D59C2211yescharacteristic
22#16838024—24no—
23#16838024C2218yes—
24#16838010—24no—
25#16838010C2218yescomplemented
26C2×#14273726C2211yescharacteristic
27C2×#14273725C2211yescharacteristic
28C2×#14273722—21no—
29C2×#14273721—21no—
30C2×#14273721—21no—
31C2×#14273719—21no—
32C2×#14273718C2211yescharacteristic
33C2×#14273717—21no—
34C2×#14273716C2211yescharacteristic
35C2×#14273715—21no—
36C2×#14273712—21no—
37C2×#14273707C2211yescharacteristic
38C2×#14273705—21no—
39C2×#14273703C2211yescharacteristic
40C2×#14273703C2211yescharacteristic
41C2×#14273702C2211yescharacteristic
42C2×C4×Dic118C2211yescharacteristic
43C2×C4×D236C2211yescharacteristic
44C2×#14273684C2211yescharacteristic
45#16837810C2218yescomplemented
46#16837795C2218yescomplemented
47#16837758C2218yescomplemented
48#16837751C2218yescomplemented
49#16837657C2218yescomplemented
50#16837649C2218yes—
51#16837642C2218yescomplemented
52#16837634C2218yes—
53#16837507C2218yescomplemented
54#16837500C2218yescomplemented
55C4×#11745660C2218yescomplemented
56C2×#14273660C2211yescharacteristic
57C2×#14273659C2211yescharacteristic
58C2×#14273658C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273651C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65#16837356C2218yescomplemented
66C2×#14273638C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C22×Q16×C59C2211yescharacteristic
70C2×C4×Q8×C59C2211yescharacteristic
71C2×C4×Q8×C59C2211yescharacteristic
72C4×Q16×C59C2218yescomplemented
73C2×#107×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×C4×C8×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C22×D236—21no—
80C22×D236C2311yescharacteristic
81C22×C4×D59—21no—
82C22×C4×D59C2311yescharacteristic
83C2×#11745672—24no—
84C2×#11745672C2314yes—
85C2×#11745660—24no—
86C2×#11745660C2314yes—
87C2×#11745671—24no—
88C2×#11745671C2314yes—
89C2×#11745659—24no—
90C2×#11745659C2314yes—
91C22×C59⋊C8C2311yescharacteristic
92C22×C59⋊C8C2311yescharacteristic
93C2×C8×D59—24no—
94C2×C8×D59C2314yes—
95#14273726—22no—
96#14273726C2314yes—
97#14273725—22no—
98#14273725C2314yes—
99#14273722—28no—
100#14273721—28no—
101#14273721—28no—
102#14273719—28no—
103#14273718—22no—
104#14273718C2314yes—
105#14273717—28no—
106#14273716—22no—
107#14273716C2314yes—
108#14273715—28no—
109#14273712—28no—
110#14273707—22no—
111#14273707C2314yes—
112#14273705—28no—
113#14273703—22no—
114#14273703—22no—
115#14273703C2314yes—
116#14273703C2314yes—
117#14273702—22no—
118#14273702C2314yes—
119C4×Dic118—22no—
120C4×Dic118C2314yes—
121C4×D236—22no—
122C4×D236C2314yes—
123#14273684D414yes—
124#14273684C2314yes—
125C2×C4⋊Dic59—21no—
126C2×C4⋊Dic59—21no—
127C2×C4⋊Dic59C2311yescharacteristic
128C2×C4⋊Dic59C2311yescharacteristic
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×Dic59⋊C4—21no—
136C2×Dic59⋊C4D411yescharacteristic
137C2×Dic59⋊C4D411yescharacteristic
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4—21no—
142C2×(C2×D59)⋊C4—21no—
143C2×(C2×D59)⋊C4—21no—
144C2×(C2×D59)⋊C4—21no—
145C2×(C2×D59)⋊C4D411yescharacteristic
146C2×(C2×D59)⋊C4D411yescharacteristic
147C2×C4×Dic59—21no—
148C2×C4×Dic59C2311yescharacteristic
149#14273660C2314yes—
150#14273659C2314yes—
151#14273658C2314yes—
152#14273652C2314yes—
153#14273651C2314yes—
154#14273651C2314yes—
155#14273650C2314yes—
156#14273649C2314yes—
157#14273647C2314yes—
158#14273638C2314yes—
159#14273637C2314yes—
160C8×Dic59C2314yes—
161C22×Q8×C59C2311yescharacteristic
162C22×Q8×C59C2311yescharacteristic
163C2×Q16×C59—24no—
164C2×Q16×C59C2314yes—
165C22×C8×C59C2311yescharacteristic
166C22×C8×C59C2311yescharacteristic
167C4×Q8×C59—22no—
168C4×Q8×C59—22no—
169C4×Q8×C59C2314yes—
170C4×Q8×C59C2314yes—
171C2×C4⋊C4×C59—21no—
172C2×C4⋊C4×C59—21no—
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C4⋊C4×C59C2311yescharacteristic
175C2×C42×C59—21no—
176C2×C42×C59—21no—
177C2×C42×C59C2311yescharacteristic
178#107×C59C2314yes—
179#103×C59C2314yes—
180#103×C59C2314yes—
181C4×C8×C59C2314yes—
182C23×D59—21no—
183C23×D59C2×D411yescharacteristic
184C2×Q8×C59—21no—
185C2×Q8×C59—21no—
186C2×Q8×C59—22no—
187C2×Q8×C59—22no—
188C2×Q8×C59—22no—
189C2×Q8×C59—22no—
190C2×Q8×C59C2412yes—
191C2×Q8×C59C2412yes—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2411yescharacteristic
199C22×Dic59—21no—
200C22×Dic59—21no—
201C22×Dic59—21no—
202C22×Dic59C2×D411yescharacteristic
203C22×Dic59C2×D411yescharacteristic
204C22×Dic59C2×D411yescharacteristic
205C2×D236—22no—
206C2×D236—22no—
207C2×D236—21no—
208C2×D236—24no—
209C2×D236—82no—
210C2×D236C2412yes—
211C2×C4×D59—22no—
212C2×C4×D59—22no—
213C2×C4×D59—24no—
214C2×C4×D59—82no—
215C2×C4×D59C2×D412yes—
216C2×C4×D59C2412yes—
217C2×Dic118—22no—
218C2×Dic118—22no—
219C2×Dic118—21no—
220C2×Dic118—24no—
221C2×Dic118—82no—
222C2×Dic118C2412yes—
223Q16×C59—28no—
224C2×C8×C59—22no—
225C2×C8×C59#4114yes—
226C2×C8×C59C2412yes—
227C2×C8×C59C2412yes—
228C4⋊C4×C59—24no—
229C4⋊C4×C59—24no—
230C4⋊C4×C59—21no—
231C4⋊C4×C59—21no—
232C4⋊C4×C59C2412yes—
233C4⋊C4×C59C2412yes—
234C42×C59—24no—
235C42×C59—24no—
236C42×C59C2×D412yes—
237C42×C59C2412yes—
238#11745672—28no—
239#11745671—28no—
240(C2×D59)⋊C4—24no—
241(C2×D59)⋊C4—24no—
242(C2×D59)⋊C4—24no—
243(C2×D59)⋊C4—24no—
244(C2×D59)⋊C4—24no—
245(C2×D59)⋊C4—24no—
246(C2×D59)⋊C4—24no—
247(C2×D59)⋊C4C2×D414yes—
248(C2×D59)⋊C4C2×D414yes—
249C4⋊Dic59—21no—
250C4⋊Dic59—21no—
251C4⋊Dic59—24no—
252C4⋊Dic59—24no—
253C4⋊Dic59C2412yes—
254C4⋊Dic59C2412yes—
255Dic59⋊C4—24no—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4—24no—
262Dic59⋊C4C2×D414yes—
263Dic59⋊C4C2×D414yes—
264C4×Dic59—24no—
265C4×Dic59C2×D412yes—
266C4×Dic59C2412yes—
267C2×C59⋊C8—22no—
268C2×C59⋊C8#4114yes—
269C2×C59⋊C8C2412yes—
270C2×C59⋊C8C2412yes—
271#11745660—28no—
272#11745659—28no—
273C8×D59—28no—
274C23×C59C22×D411yescharacteristic
275C22×D59—22no—
276C22×D59—22no—
277C22×D59—22no—
278C22×D59—22no—
279C22×D59—42no—
280C22×D59—42no—
281C22×D59—42no—
282C22×D59C22×D412yes—
283Q8×C59—22no—
284Q8×C59—22no—
285Q8×C59—22no—
286Q8×C59—22no—
287Q8×C59—42no—
288Q8×C59—42no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—42no—
296C2×C4×C59—42no—
297C2×C4×C59—42no—
298C2×C4×C59—42no—
299C2×C4×C59C22×D412yes—
300C2×C4×C59C22×D412yes—
301C2×C4×C59C22×D411yescharacteristic
302C2×C4×C59C2×#4112yes—
303C2×C4×C59C2×#4112yes—
304C2×C4×C59C2511yescharacteristic
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—42no—
312C2×Dic59—42no—
313C2×Dic59—42no—
314C2×Dic59C22×D412yes—
315C2×Dic59C22×D412yes—
316C2×Dic59C22×D412yes—
317D236—22no—
318D236—22no—
319D236—42no—
320D236—84no—
321C4×D59—24no—
322C4×D59—22no—
323C4×D59—22no—
324C4×D59—84no—
325Dic118—22no—
326Dic118—22no—
327Dic118—42no—
328Dic118—84no—
329C8×C59—22no—
330C8×C59C2×#4114yes—
331C59⋊C8—22no—
332C59⋊C8C2×#4114yes—
333C2×#3178—591nomaximal, Sylow
334C22×C59#53212yes—
335C22×C59#57712yes—
336C22×C59#57812yes—
337C22×C59C23×D411yescharacteristic
338C2×D59—22no—
339C2×D59—22no—
340C2×D59—22no—
341C2×D59—44no—
342C2×D59—42no—
343C2×D59—42no—
344C2×D59—42no—
345C2×D59—84no—
346C4×C59—22no—
347C4×C59—22no—
348C4×C59—42no—
349C4×C59—42no—
350C4×C59—42no—
351C4×C59—42no—
352C4×C59#53212yes—
353C4×C59C22×#4111yescharacteristic
354C4×C59C22×#4111yescharacteristic
355Dic59—22no—
356Dic59—22no—
357Dic59—22no—
358Dic59—42no—
359Dic59—42no—
360Dic59—42no—
361C2×#542—591no—
362C2×#541—591no—
363#3178—5916no—
364C2×#501—591no—
365C2×#497—591no—
366C2×#488—591no—
367C2×#487—591no—
368C2×#470—591no—
369C2×#468—591no—
370C2×#467—591no—
371C2×#465—591no—
372C2×#441—591no—
373C2×#440—591no—
374C2×C4×Q16D5911yescharacteristic, complemented
375C2×C4×SD16—591no—
376C2×#405—591no—
377C2×C59#317814yescomplemented
378C2×C59C2×#53211yescharacteristic
379C2×C59C2×#57711yescharacteristic
380C2×C59C2×#57811yescharacteristic
381D59—42no—
382D59—82no—
383C22×Q16—591no—
384C22×Q16C2×D5911yescharacteristic
385C22×SD16—591no—
386C22×SD16—591no—
387C22×M16—591no—
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—591no—
407C2×C22⋊Q8—1181no—
408C2×#121—591no—
409C2×C4×Q8—591no—
410C2×C4×Q8C2×D5911yescharacteristic
411C2×C4×Q8C2×D5911yescharacteristic
412C2×C4×D4—591no—
413C2×#117—591no—
414#501—598no—
415#497—598no—
416#488—598no—
417#487—598no—
418#470—598no—
419#468—598no—
420#467—598no—
421#465—598no—
422#441—598no—
423#440—598no—
424C4×Q16C2×D5918yescomplemented
425C4×SD16—598no—
426C2×#107—591no—
427C2×#107C2×D5911yescharacteristic
428C2×#106—591no—
429C2×#106—591no—
430C2×#103—591no—
431C2×#103—591no—
432C2×#103—591no—
433C2×#103—591no—
434C2×#103C2×D5911yescharacteristic
435C2×#103C2×D5911yescharacteristic
436C2×#102—591no—
437C2×#102—591no—
438#405—598no—
439C2×#97—591no—
440C2×#97—591no—
441C2×C4×C8—591no—
442C2×C4×C8C2×D5911yescharacteristic
443C59C2×#317811yescharacteristic, complemented, Sylow
444C22×Q8—591no—
445C22×Q8—1181no—
446C22×Q8C22×D5911yescharacteristic
447C22×Q8C22×D5911yescharacteristic
448C22×D4—591no—
449C22×D4—1181no—
450C23×C4—591no—
451C23×C4—1181no—
452C2×Q16—24no—
453C2×Q16—594no—
454C2×Q16—1184no—
455C2×Q16C22×D5914yes—
456C2×SD16—594no—
457C2×SD16—594no—
458C2×SD16—1184no—
459C2×SD16—1184no—
460C2×M16—594no—
461C2×M16—1184no—
462C22×C8—591no—
463C22×C8—591no—
464C22×C8—594no—
465C22×C8—1184no—
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—1188no—
477#125—1182no—
478#125—1188no—
479#124—594no—
480#124—1188no—
481#124—1182no—
482#123—1188no—
483C22⋊Q8—594no—
484C22⋊Q8—594no—
485C22⋊Q8—594no—
486C22⋊Q8—1188no—
487C22⋊Q8—1182no—
488C22⋊Q8—1182no—
489C22⋊Q8—1182no—
490#121—594no—
491#121—1182no—
492C4×Q8—22no—
493C4×Q8—22no—
494C4×Q8—594no—
495C4×Q8—1182no—
496C4×Q8C22×D5914yes—
497C4×Q8C22×D5914yes—
498C4×D4—594no—
499C4×D4—1182no—
500#117—594no—
501#117—594no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—591no—
505C2×C4⋊C4—591no—
506C2×C4⋊C4—591no—
507C2×C4⋊C4—591no—
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—591no—
520C2×C22⋊C4—591no—
521C2×C22⋊C4—1181no—
522C2×C22⋊C4—1181no—
523C2×C22⋊C4—1181no—
524C2×C22⋊C4—1181no—
525C2×C22⋊C4—1181no—
526C2×C22⋊C4—1181no—
527C2×C22⋊C4—1181no—
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—591no—
531C2×C42—1181no—
532C2×C42C22×D5911yescharacteristic
533#107—594no—
534#107C22×D5914yes—
535#106—594no—
536#106—594no—
537#103—594no—
538#103—594no—
539#103—594no—
540#103—594no—
541#103C22×D5914yes—
542#103C22×D5914yes—
543#102—594no—
544#102—594no—
545#97—594no—
546#97—594no—
547C4×C8—594no—
548C4×C8C22×D5914yes—
549C24—591no—
550C24—1181no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—592no—
558C2×Q8—1184no—
559C2×Q8—1181no—
560C2×Q8—1182no—
561C2×Q8—1182no—
562C2×Q8—4722no—
563C2×Q8C23×D5912yes—
564C2×Q8C23×D5912yes—
565C2×D4—592no—
566C2×D4—1184no—
567C2×D4—1181no—
568C2×D4—1182no—
569C2×D4—1182no—
570C2×D4—4722no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—591no—
576C22×C4—591no—
577C22×C4—591no—
578C22×C4—592no—
579C22×C4—592no—
580C22×C4—1182no—
581C22×C4—1182no—
582C22×C4—1181no—
583C22×C4—1181no—
584C22×C4—1181no—
585C22×C4—1184no—
586C22×C4—4722no—
587C22×C4D4×D5911yescharacteristic
588C22×C4D4×D5911yescharacteristic
589C22×C4C23×D5911yescharacteristic
590Q16—28no—
591Q16—1188no—
592SD16—1188no—
593SD16—1188no—
594M16—1188no—
595C2×C8—22no—
596C2×C8—594no—
597C2×C8—592no—
598C2×C8—592no—
599C2×C8—1188no—
600C2×C8—1182no—
601C2×C8#1174568514yes—
602C2×C8C23×D5912yes—
603C2×C8C23×D5912yes—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—594no—
609C4⋊C4—594no—
610C4⋊C4—592no—
611C4⋊C4—592no—
612C4⋊C4—1184no—
613C4⋊C4—1184no—
614C4⋊C4—1184no—
615C4⋊C4—1184no—
616C4⋊C4—1184no—
617C4⋊C4—1184no—
618C4⋊C4—1184no—
619C4⋊C4—1184no—
620C4⋊C4—1181no—
621C4⋊C4—1181no—
622C4⋊C4—1184no—
623C4⋊C4C23×D5912yes—
624C4⋊C4C23×D5912yes—
625C22⋊C4—594no—
626C22⋊C4—594no—
627C22⋊C4—1184no—
628C22⋊C4—1184no—
629C22⋊C4—1184no—
630C22⋊C4—1184no—
631C22⋊C4—1184no—
632C22⋊C4—1184no—
633C22⋊C4—1184no—
634C42—24no—
635C42—24no—
636C42—592no—
637C42—592no—
638C42—1184no—
639C42D4×D5912yes—
640C42C23×D5912yes—
641C23—592no—
642C23—1182no—
643C23—1182no—
644C23—1182no—
645C23—1182no—
646C23—2362no—
647C23—2362no—
648C23—2362no—
649C23C2×D4×D5911yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—42no—
655Q8—42no—
656Q8—1182no—
657Q8—1182no—
658Q8—4724no—
659Q8—2362no—
660D4—1182no—
661D4—1182no—
662D4—4724no—
663D4—2362no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—592no—
675C2×C4—592no—
676C2×C4—592no—
677C2×C4—1182no—
678C2×C4—1182no—
679C2×C4—1182no—
680C2×C4—1184no—
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×C4C2×D4×D5912yes—
691C2×C4C2×D4×D5912yes—
692C2×C4C2×D4×D5911yescharacteristic
693C2×C4#41×D5912yes—
694C2×C4C2×#1174568512yes—
695C2×C4C24×D5911yescharacteristic
696C8—22no—
697C8—594no—
698C8—1182no—
699C8C2×#1174568514yes—
700C22—1182no—
701C22—1182no—
702C22—1182no—
703C22—4724no—
704C22—2362no—
705C22—2362no—
706C22—2362no—
707C22—2364no—
708C22#1683794912yes—
709C22#1683820912yes—
710C22#1683821512yes—
711C22C22×D4×D5911yescharacteristic
712C4—22no—
713C4—22no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—1182no—
719C4—1182no—
720C4—1182no—
721C4—2362no—
722C4—2362no—
723C4—2362no—
724C4#1683794912yes—
725C4C2×#41×D5911yescharacteristic
726C4C22×#1174568511yescharacteristic
727C2—4722no—
728C2—2362no—
729C2#2143476814yesdirect product factor
730C2C2×#1683794911yescharacteristic
731C2C2×#1683820911yescharacteristic
732C2C2×#1683821511yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C4×Q16×C59C2
socleC23×C59C22×D4
prime radicalC2×#14273702C22
hypercenterC2×C4×Q16D59
hypocenterC59C2×#3178
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
2. C2×#16838010C2semidirect
3. #21434768C2direct (N × H)
4. C2×#16837810C2semidirect
5. C2×#16837795C2semidirect
6. C2×#16837758C2semidirect
7. C2×#16837751C2semidirect
8. C2×#16837657C2semidirect
10. C2×#16837642C2semidirect
12. C2×#16837507C2semidirect
13. C2×#16837500C2semidirect
14. C2×C4×#11745660C2semidirect
15. C2×#16837356C2semidirect
16. C2×C4×Q16×C59C2semidirect
25. #16838010C22semidirect
45. #16837810C22semidirect
46. #16837795C22semidirect
47. #16837758C22semidirect
48. #16837751C22semidirect
49. #16837657C22semidirect
51. #16837642C22semidirect
53. #16837507C22semidirect
54. #16837500C22semidirect
55. C4×#11745660C22semidirect
65. #16837356C22semidirect
72. C4×Q16×C59C22semidirect
374. C2×C4×Q16D59semidirect
377. C2×C59#3178semidirect
424. C4×Q16C2×D59semidirect
443. C59C2×#3178semidirect
729. C2#21434768direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380242
C2×#168380102
#214347682
C2×#168378102
C2×#168377952
C2×#168377582
C2×#168377512
C2×#168376572
C2×#168376492
C2×#168376422
C2×#168376342
C2×#168375072
C2×#168375002
C2×C4×#117456602
C2×#168373562
C2×C4×Q16×C592
C2×#317859