Finite Group Databasebeta

← C2×#21434764 #29458557

Subgroups — C2×#21434764 #29458557

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×#16838023C211yesmaximal, characteristic
2C2×#16838014C211yesmaximal, characteristic, complemented
3#21434764C2116yesmaximal, direct product factor
4C2×#16837811C211yesmaximal, characteristic, complemented
5C2×#16837796C211yesmaximal, characteristic, complemented
6C2×#16837757C211yesmaximal, characteristic, complemented
7C2×#16837753C211yesmaximal, characteristic, complemented
8C2×#16837660C211yesmaximal, characteristic, complemented
9C2×#16837648C211yesmaximal, characteristic
10C2×#16837643C211yesmaximal, characteristic, complemented
11C2×#16837631C211yesmaximal, characteristic
12C2×#16837510C211yesmaximal, characteristic, complemented
13C2×#16837504C211yesmaximal, characteristic, complemented
14C2×C4×Dic236C211yesmaximal, characteristic, complemented
15C2×C4×#11745660C211yesmaximal, characteristic, complemented
16C2×C59×#405C211yesmaximal, characteristic, complemented
17C22×Dic236C2211yescharacteristic
18C22×Dic236C2211yescharacteristic
19C22×#11745660C2211yescharacteristic
20C22×#11745660C2211yescharacteristic
21#16838023—24no—
22#16838023C2218yes—
23#16838014—24no—
24#16838014C2218yescomplemented
25C2×#14273727C2211yescharacteristic
26C2×#14273727C2211yescharacteristic
27C2×#14273722—21no—
28C2×#14273720—21no—
29C2×#14273720—21no—
30C2×#14273719C2211yescharacteristic
31C2×#14273717—21no—
32C2×#14273717—21no—
33C2×#14273715C2211yescharacteristic
34C2×#14273713—21no—
35C2×#14273709—21no—
36C2×#14273706C2211yescharacteristic
37C2×#14273706C2211yescharacteristic
38C2×#14273706C2211yescharacteristic
39C2×#14273705—21no—
40C2×#14273701C2211yescharacteristic
41C2×C4×Dic118C2211yescharacteristic
42C2×C4×Dic118C2211yescharacteristic
43C2×C4×Dic118C2211yescharacteristic
44C2×C4×D236C2211yescharacteristic
45#16837811C2218yescomplemented
46#16837796C2218yescomplemented
47#16837757C2218yescomplemented
48#16837753C2218yescomplemented
49#16837660C2218yescomplemented
50#16837648C2218yes—
51#16837643C2218yescomplemented
52#16837631C2218yes—
53#16837510C2218yescomplemented
54#16837504C2218yescomplemented
55C4×Dic236C2218yescomplemented
56C4×#11745660C2218yescomplemented
57C2×#14273661C2211yescharacteristic
58C2×#14273661C2211yescharacteristic
59C2×#14273659C2211yescharacteristic
60C2×#14273659C2211yescharacteristic
61C2×#14273652C2211yescharacteristic
62C2×#14273652C2211yescharacteristic
63C2×#14273652C2211yescharacteristic
64C2×#14273652C2211yescharacteristic
65C2×#14273652C2211yescharacteristic
66C2×#14273652C2211yescharacteristic
67C2×#14273649C2211yescharacteristic
68C2×#14273649C2211yescharacteristic
69C22×M16×C59C2211yescharacteristic
70C23×C8×C59C2211yescharacteristic
71C2×#117×C59C2211yescharacteristic
72C59×#405C2218yescomplemented
73C2×#97×C59C2211yescharacteristic
74C2×#97×C59C2211yescharacteristic
75C2×C4×C8×C59C2211yescharacteristic
76C2×C4×C8×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C22×Dic118C2311yescharacteristic
80C22×Dic118C2311yescharacteristic
81C22×D236C2311yescharacteristic
82C22×C22⋊D59—21no—
83C22×C4×D59—21no—
84C2×Dic236—24no—
85C2×Dic236—24no—
86C2×Dic236C2314yes—
87C2×Dic236C2314yes—
88C2×#11745660—24no—
89C2×#11745660—24no—
90C2×#11745660C2314yes—
91C2×#11745660C2314yes—
92#14273727—22no—
93#14273727—22no—
94#14273727C2314yes—
95#14273727C2314yes—
96#14273722—28no—
97#14273720—28no—
98#14273720—28no—
99#14273719—22no—
100#14273719C2314yes—
101#14273717—28no—
102#14273717—28no—
103#14273715—22no—
104#14273715C2314yes—
105#14273713—28no—
106#14273709—28no—
107#14273706—22no—
108#14273706—22no—
109#14273706—22no—
110#14273706C2314yes—
111#14273706C2314yes—
112#14273706C2314yes—
113#14273705—28no—
114#14273701—22no—
115#14273701C2314yes—
116C4×Dic118—22no—
117C4×Dic118—22no—
118C4×Dic118—22no—
119C4×Dic118C2314yes—
120C4×Dic118C2314yes—
121C4×Dic118C2314yes—
122C4×D236—22no—
123C4×D236C2314yes—
124C2×C4⋊Dic59—21no—
125C2×C4⋊Dic59—21no—
126C2×C4⋊Dic59—21no—
127C2×C4⋊Dic59C2311yescharacteristic
128C2×C4⋊Dic59C2311yescharacteristic
129C2×C4⋊Dic59C2311yescharacteristic
130C2×C4⋊Dic59C2311yescharacteristic
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4—21no—
137C2×Dic59⋊C4—21no—
138C2×Dic59⋊C4—21no—
139C2×C22⋊Dic59—21no—
140C2×C22⋊Dic59—21no—
141C2×C22⋊Dic59—21no—
142C2×(C2×D59)⋊C4—21no—
143C2×(C2×D59)⋊C4—21no—
144C2×(C2×D59)⋊C4—21no—
145C2×(C2×D59)⋊C4—21no—
146C2×C4×Dic59—21no—
147C2×C4×Dic59—21no—
148C2×C4×Dic59—21no—
149#14273661C2314yes—
150#14273661C2314yes—
151#14273659C2314yes—
152#14273659C2314yes—
153#14273652C2314yes—
154#14273652C2314yes—
155#14273652C2314yes—
156#14273652C2314yes—
157#14273652C2314yes—
158#14273652C2314yes—
159#14273649C2314yes—
160#14273649C2314yes—
161C23×C4×C59C2311yescharacteristic
162C2×M16×C59—24no—
163C2×M16×C59C2314yes—
164C22×C8×C59—24no—
165C22×C8×C59C2314yes—
166C22×C8×C59C2311yescharacteristic
167C22×C8×C59C2311yescharacteristic
168C22×C8×C59C2311yescharacteristic
169C22×C8×C59C2311yescharacteristic
170#117×C59D414yes—
171#117×C59C2314yes—
172C2×C4⋊C4×C59D411yescharacteristic
173C2×C4⋊C4×C59D411yescharacteristic
174C2×C22⋊C4×C59D411yescharacteristic
175C2×C22⋊C4×C59D411yescharacteristic
176C2×C42×C59C2311yescharacteristic
177C2×C42×C59C2311yescharacteristic
178#97×C59C2314yes—
179#97×C59C2314yes—
180C4×C8×C59C2314yes—
181C4×C8×C59C2314yes—
182C24×C59C2×D411yescharacteristic
183C23×D59—21no—
184C22×C4×C59—22no—
185C22×C4×C59—22no—
186C22×C4×C59C2×D411yescharacteristic
187C22×C4×C59C2×D411yescharacteristic
188C22×C4×C59C2×D411yescharacteristic
189C22×C4×C59C2×D411yescharacteristic
190C22×C4×C59C2×D411yescharacteristic
191C22×C4×C59C2×D412yes—
192C22×C4×C59C2412yes—
193C22×C4×C59C2411yescharacteristic
194C2×C22⋊D59—24no—
195C2×C22⋊D59—82no—
196C22×Dic59—21no—
197C22×Dic59—21no—
198C22×Dic59—21no—
199C22×Dic59—21no—
200C22×Dic59—21no—
201C22×Dic59—21no—
202C22×Dic59—21no—
203C2×D236—22no—
204C2×D236—22no—
205C2×D236—21no—
206C2×D236C2412yes—
207C2×C4×D59—24no—
208C2×C4×D59—82no—
209C2×Dic118—22no—
210C2×Dic118—22no—
211C2×Dic118—22no—
212C2×Dic118—22no—
213C2×Dic118—22no—
214C2×Dic118—22no—
215C2×Dic118—21no—
216C2×Dic118—21no—
217C2×Dic118—21no—
218C2×Dic118—24no—
219C2×Dic118—82no—
220C2×Dic118C2412yes—
221C2×Dic118C2412yes—
222C2×Dic118C2412yes—
223M16×C59—28no—
224C2×C8×C59—22no—
225C2×C8×C59—22no—
226C2×C8×C59—28no—
227C2×C8×C59#4114yes—
228C2×C8×C59#4114yes—
229C2×C8×C59C2412yes—
230C2×C8×C59C2412yes—
231C2×C8×C59C2412yes—
232C2×C8×C59C2412yes—
233C4⋊C4×C59C2×D414yes—
234C4⋊C4×C59C2×D414yes—
235C22⋊C4×C59C2×D414yes—
236C22⋊C4×C59C2×D414yes—
237C42×C59C2×D412yes—
238C42×C59C2×D412yes—
239C42×C59C2412yes—
240C42×C59C2412yes—
241C22⋊Dic59—24no—
242C22⋊Dic59—24no—
243C22⋊Dic59—24no—
244(C2×D59)⋊C4—24no—
245(C2×D59)⋊C4—24no—
246(C2×D59)⋊C4—24no—
247(C2×D59)⋊C4—24no—
248C4⋊Dic59—24no—
249C4⋊Dic59—24no—
250C4⋊Dic59—24no—
251C4⋊Dic59—21no—
252C4⋊Dic59—21no—
253C4⋊Dic59—21no—
254C4⋊Dic59—21no—
255C4⋊Dic59C2412yes—
256C4⋊Dic59C2412yes—
257C4⋊Dic59C2412yes—
258C4⋊Dic59C2412yes—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4—24no—
262Dic59⋊C4—24no—
263Dic59⋊C4—24no—
264Dic59⋊C4—24no—
265Dic59⋊C4—24no—
266Dic59⋊C4—24no—
267C4×Dic59—24no—
268C4×Dic59—24no—
269C4×Dic59—24no—
270Dic236—28no—
271Dic236—28no—
272#11745660—28no—
273#11745660—28no—
274C23×C59—22no—
275C23×C59—22no—
276C23×C59—22no—
277C23×C59C22×D412yes—
278C23×C59C22×D411yescharacteristic
279C22×D59—22no—
280C22×D59—42no—
281C22×D59—42no—
282C22×D59—42no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—24no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59C22×D412yes—
292C2×C4×C59C22×D412yes—
293C2×C4×C59C22×D412yes—
294C2×C4×C59C22×D412yes—
295C2×C4×C59C22×D412yes—
296C2×C4×C59C22×D411yescharacteristic
297C2×C4×C59C2×#4112yes—
298C2×C4×C59C2×#4112yes—
299C2×C4×C59C2511yescharacteristic
300C22⋊D59—84no—
301C2×Dic59—22no—
302C2×Dic59—22no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—22no—
308C2×Dic59—42no—
309C2×Dic59—42no—
310C2×Dic59—42no—
311C2×Dic59—42no—
312C2×Dic59—42no—
313C2×Dic59—42no—
314C2×Dic59—42no—
315D236—22no—
316D236—22no—
317D236—42no—
318C4×D59—84no—
319Dic118—22no—
320Dic118—22no—
321Dic118—22no—
322Dic118—22no—
323Dic118—22no—
324Dic118—22no—
325Dic118—42no—
326Dic118—42no—
327Dic118—42no—
328Dic118—84no—
329C8×C59—22no—
330C8×C59—22no—
331C8×C59C2×#4114yes—
332C8×C59C2×#4114yes—
333C2×#3178—591nomaximal, Sylow
334C22×C59—22no—
335C22×C59—22no—
336C22×C59—22no—
337C22×C59—44no—
338C22×C59#53212yes—
339C22×C59#57712yes—
340C22×C59#57812yes—
341C22×C59C23×D411yescharacteristic
342C2×D59—42no—
343C2×D59—42no—
344C2×D59—42no—
345C2×D59—84no—
346C4×C59—22no—
347C4×C59—22no—
348C4×C59—22no—
349C4×C59—22no—
350C4×C59—22no—
351C4×C59#53212yes—
352C4×C59C22×#4111yescharacteristic
353C4×C59C22×#4111yescharacteristic
354Dic59—42no—
355Dic59—42no—
356Dic59—42no—
357Dic59—42no—
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×Q16—591no—
375C2×C4×SD16—591no—
376C2×#405D5911yescharacteristic, complemented
377C2×C59—42no—
378C2×C59#317814yescomplemented
379C2×C59C2×#53211yescharacteristic
380C2×C59C2×#57711yescharacteristic
381C2×C59C2×#57811yescharacteristic
382D59—82no—
383C22×Q16—591no—
384C22×Q16—591no—
385C22×SD16—591no—
386C22×SD16—591no—
387C22×M16C2×D5911yescharacteristic
388C23×C8C2×D5911yescharacteristic
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×Q8—591no—
411C2×C4×Q8—591no—
412C2×C4×D4—591no—
413C2×#117C2×D5911yescharacteristic
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×Q16—598no—
425C4×SD16—598no—
426C2×#107—591no—
427C2×#107—591no—
428C2×#106—591no—
429C2×#106—591no—
430C2×#103—591no—
431C2×#103—591no—
432C2×#103—591no—
433C2×#103—591no—
434C2×#103—591no—
435C2×#103—591no—
436C2×#102—591no—
437C2×#102—591no—
438#405C2×D5918yescomplemented
439C2×#97C2×D5911yescharacteristic
440C2×#97C2×D5911yescharacteristic
441C2×C4×C8C2×D5911yescharacteristic
442C2×C4×C8C2×D5911yescharacteristic
443C59C2×#317811yescharacteristic, complemented, Sylow
444C22×Q8—591no—
445C22×Q8—591no—
446C22×Q8—591no—
447C22×Q8—1181no—
448C22×D4—591no—
449C22×D4—1181no—
450C23×C4—1181no—
451C23×C4C22×D5911yescharacteristic
452C2×Q16—594no—
453C2×Q16—594no—
454C2×Q16—1184no—
455C2×Q16—1184no—
456C2×SD16—594no—
457C2×SD16—594no—
458C2×SD16—1184no—
459C2×SD16—1184no—
460C2×M16—24no—
461C2×M16C22×D5914yes—
462C22×C8—24no—
463C22×C8C22×D5911yescharacteristic
464C22×C8C22×D5914yes—
465C22×C8C22×D5911yescharacteristic
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—1188no—
478#125—1182no—
479#124—594no—
480#124—1188no—
481#124—1182no—
482#123—1188no—
483C22⋊Q8—594no—
484C22⋊Q8—594no—
485C22⋊Q8—594no—
486C22⋊Q8—1182no—
487C22⋊Q8—1182no—
488C22⋊Q8—1182no—
489C22⋊Q8—1188no—
490#121—594no—
491#121—1182no—
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#117D23614yes—
501#117C22×D5914yes—
502C2×C4⋊C4—591no—
503C2×C4⋊C4—591no—
504C2×C4⋊C4—591no—
505C2×C4⋊C4—591no—
506C2×C4⋊C4—1181no—
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⋊C4D23611yescharacteristic
518C2×C4⋊C4D23611yescharacteristic
519C2×C22⋊C4—1181no—
520C2×C22⋊C4—1181no—
521C2×C22⋊C4—1181no—
522C2×C22⋊C4—1181no—
523C2×C22⋊C4—1181no—
524C2×C22⋊C4—1181no—
525C2×C22⋊C4—1181no—
526C2×C22⋊C4D23611yescharacteristic
527C2×C22⋊C4D23611yescharacteristic
528C2×C42—1181no—
529C2×C42—1181no—
530C2×C42—1181no—
531C2×C42C22×D5911yescharacteristic
532C2×C42C22×D5911yescharacteristic
533#107—594no—
534#107—594no—
535#106—594no—
536#106—594no—
537#103—594no—
538#103—594no—
539#103—594no—
540#103—594no—
541#103—594no—
542#103—594no—
543#102—594no—
544#102—594no—
545#97C22×D5914yes—
546#97C22×D5914yes—
547C4×C8C22×D5914yes—
548C4×C8C22×D5914yes—
549C24—1181no—
550C24C2×D23611yescharacteristic
551C2×Q8—592no—
552C2×Q8—592no—
553C2×Q8—592no—
554C2×Q8—1184no—
555C2×Q8—1181no—
556C2×Q8—1181no—
557C2×Q8—1181no—
558C2×Q8—1182no—
559C2×Q8—1182no—
560C2×Q8—1182no—
561C2×Q8—1182no—
562C2×Q8—1182no—
563C2×Q8—1182no—
564C2×Q8—4722no—
565C2×D4—592no—
566C2×D4—1184no—
567C2×D4—1181no—
568C2×D4—1182no—
569C2×D4—1182no—
570C2×D4—4722no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—1181no—
574C22×C4—1181no—
575C22×C4—1181no—
576C22×C4—1181no—
577C22×C4—1181no—
578C22×C4—1181no—
579C22×C4—1181no—
580C22×C4—1184no—
581C22×C4—4722no—
582C22×C4C2×D23612yes—
583C22×C4C2×D23611yescharacteristic
584C22×C4C2×D23611yescharacteristic
585C22×C4C2×D23611yescharacteristic
586C22×C4C2×D23611yescharacteristic
587C22×C4C2×D23611yescharacteristic
588C22×C4C23×D5912yes—
589C22×C4C23×D5911yescharacteristic
590Q16—1188no—
591Q16—1188no—
592SD16—1188no—
593SD16—1188no—
594M16—28no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—28no—
598C2×C8#1174568514yes—
599C2×C8#1174568514yes—
600C2×C8C23×D5912yes—
601C2×C8C23×D5912yes—
602C2×C8C23×D5912yes—
603C2×C8C23×D5912yes—
604C4⋊C4—592no—
605C4⋊C4—592no—
606C4⋊C4—592no—
607C4⋊C4—592no—
608C4⋊C4—1181no—
609C4⋊C4—1181no—
610C4⋊C4—1181no—
611C4⋊C4—1181no—
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—1184no—
621C4⋊C4—1184no—
622C4⋊C4—1184no—
623C4⋊C4C2×D23614yes—
624C4⋊C4C2×D23614yes—
625C22⋊C4—1184no—
626C22⋊C4—1184no—
627C22⋊C4—1184no—
628C22⋊C4—1184no—
629C22⋊C4—1184no—
630C22⋊C4—1184no—
631C22⋊C4—1184no—
632C22⋊C4C2×D23614yes—
633C22⋊C4C2×D23614yes—
634C42—1184no—
635C42—1184no—
636C42—1184no—
637C42C2×D23612yes—
638C42C2×D23612yes—
639C42C23×D5912yes—
640C42C23×D5912yes—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—1182no—
645C23—2362no—
646C23—2362no—
647C23—2362no—
648C23C22×D23612yes—
649C23C22×D23611yescharacteristic
650Q8—1182no—
651Q8—1182no—
652Q8—1182no—
653Q8—1182no—
654Q8—1182no—
655Q8—1182no—
656Q8—4724no—
657Q8—2362no—
658Q8—2362no—
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—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—1182no—
673C2×C4—1182no—
674C2×C4—1182no—
675C2×C4—1182no—
676C2×C4—1182no—
677C2×C4—1182no—
678C2×C4—1182no—
679C2×C4—4724no—
680C2×C4—2362no—
681C2×C4—2362no—
682C2×C4—2362no—
683C2×C4—2362no—
684C2×C4—2362no—
685C2×C4—2362no—
686C2×C4—2362no—
687C2×C4C22×D23612yes—
688C2×C4C22×D23612yes—
689C2×C4C22×D23612yes—
690C2×C4C22×D23612yes—
691C2×C4C22×D23612yes—
692C2×C4C22×D23611yescharacteristic
693C2×C4C2×#1174568512yes—
694C2×C4C2×#1174568512yes—
695C2×C4C24×D5911yescharacteristic
696C8—22no—
697C8—22no—
698C8C2×#1174568514yes—
699C8C2×#1174568514yes—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—4724no—
705C22—2362no—
706C22—2362no—
707C22—2362no—
708C22#1683795212yes—
709C22#1683821412yes—
710C22#1683821912yes—
711C22C23×D23611yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—2362no—
718C4—2362no—
719C4—2362no—
720C4—2362no—
721C4—2362no—
722C4—2362no—
723C4—2362no—
724C4#1683795212yes—
725C4C22×#1174568511yescharacteristic
726C4C22×#1174568511yescharacteristic
727C2—42no—
728C2—4722no—
729C2#2143476414yesdirect product factor
730C2C2×#1683795211yescharacteristic
731C2C2×#1683821411yescharacteristic
732C2C2×#1683821911yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#405C2
socleC23×C59C22×D4
prime radicalC2×#14273701C22
hypercenterC2×#405D59
hypocenterC59C2×#3178
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
2. C2×#16838014C2semidirect
3. #21434764C2direct (N × H)
4. C2×#16837811C2semidirect
5. C2×#16837796C2semidirect
6. C2×#16837757C2semidirect
7. C2×#16837753C2semidirect
8. C2×#16837660C2semidirect
10. C2×#16837643C2semidirect
12. C2×#16837510C2semidirect
13. C2×#16837504C2semidirect
14. C2×C4×Dic236C2semidirect
15. C2×C4×#11745660C2semidirect
16. C2×C59×#405C2semidirect
24. #16838014C22semidirect
45. #16837811C22semidirect
46. #16837796C22semidirect
47. #16837757C22semidirect
48. #16837753C22semidirect
49. #16837660C22semidirect
51. #16837643C22semidirect
53. #16837510C22semidirect
54. #16837504C22semidirect
55. C4×Dic236C22semidirect
56. C4×#11745660C22semidirect
72. C59×#405C22semidirect
376. C2×#405D59semidirect
378. C2×C59#3178semidirect
438. #405C2×D59semidirect
443. C59C2×#3178semidirect
729. C2#21434764direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380232
C2×#168380142
#214347642
C2×#168378112
C2×#168377962
C2×#168377572
C2×#168377532
C2×#168376602
C2×#168376482
C2×#168376432
C2×#168376312
C2×#168375102
C2×#168375042
C2×C4×Dic2362
C2×C4×#117456602
C2×C59×#4052
C2×#317859