Finite Group Databasebeta

← C2×#21434312 #29456954

Subgroups — C2×#21434312 #29456954

Order 15104.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838014C211yesmaximal, characteristic, complemented
2C2×#16837882C211yesmaximal, characteristic
3#21434312C2116yesmaximal, direct product factor
4C2×#16837738C211yesmaximal, characteristic, complemented
5C2×#16837733C211yesmaximal, characteristic, complemented
6C2×#16837710C211yesmaximal, characteristic, complemented
7C2×#16837703C211yesmaximal, characteristic, complemented
8C2×#16837613C211yesmaximal, characteristic, complemented
9C2×#16837608C211yesmaximal, characteristic, complemented
10C2×#16837566C211yesmaximal, characteristic
11C2×#16837566C211yesmaximal, characteristic
12C2×#16837510C211yesmaximal, characteristic, complemented
13C2×#16837504C211yesmaximal, characteristic, complemented
14C2×C4×Dic236C211yesmaximal, characteristic, complemented
15C2×C4×#11745660C211yesmaximal, characteristic, complemented
16C2×C59×#433C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C22×Dic236C2211yescharacteristic
19C22×Dic236C2211yescharacteristic
20C22×#11745660C2211yescharacteristic
21C22×#11745660C2211yescharacteristic
22#16838014—24no—
23#16838014C2218yescomplemented
24C2×#14273727C2211yescharacteristic
25C2×#14273720—21no—
26C2×#14273720—21no—
27C2×#14273719C2211yescharacteristic
28C2×#14273717—21no—
29C2×#14273717—21no—
30C2×#14273706C2211yescharacteristic
31C2×#14273706C2211yescharacteristic
32#16837882—24no—
33#16837882C2218yes—
34C2×C4×Dic118C2211yescharacteristic
35C2×C4×Dic118C2211yescharacteristic
36C2×C4×Dic118C2211yescharacteristic
37C2×C4×Dic118C2211yescharacteristic
38C2×C4×D236C2211yescharacteristic
39C2×C4×D236C2211yescharacteristic
40C2×(C22⋊D59)⋊C4—21no—
41C2×(C22⋊D59)⋊C4—21no—
42C2×#14273685—21no—
43C22×C4⋊Dic59C2211yescharacteristic
44C2×C4⋊C4×D59—21no—
45#16837738C2218yescomplemented
46#16837733C2218yescomplemented
47#16837710C2218yescomplemented
48#16837703C2218yescomplemented
49#16837613C2218yescomplemented
50#16837608C2218yescomplemented
51#16837566C2218yes—
52#16837566C2218yes—
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
69C2×#117×C59C2211yescharacteristic
70C59×#433C2218yescomplemented
71C2×C4⋊C8×C59C2211yescharacteristic
72C2×C4⋊C8×C59C2211yescharacteristic
73C2×C22⋊C8×C59C2211yescharacteristic
74C2×C22⋊C8×C59C2211yescharacteristic
75C2×#97×C59C2211yescharacteristic
76C2×C4×C8×C59C2211yescharacteristic
77C2×#11745685—22no—
78C2×#11745685—24no—
79C2×#11745685—24no—
80C2×#11745685C2314yes—
81C22×Dic118C2311yescharacteristic
82C22×Dic118C2311yescharacteristic
83C22×Dic118C2311yescharacteristic
84C22×D236C2311yescharacteristic
85C22×C22⋊D59—21no—
86C23×Dic59—21no—
87C22×C4×D59—21no—
88C22×C4×D59—21no—
89C22×C4×D59—21no—
90C2×Dic236—24no—
91C2×Dic236—24no—
92C2×Dic236C2314yes—
93C2×Dic236C2314yes—
94C2×#11745660—24no—
95C2×#11745660—24no—
96C2×#11745660C2314yes—
97C2×#11745660C2314yes—
98#14273727—22no—
99#14273727C2314yes—
100#14273720—28no—
101#14273720—28no—
102#14273719—22no—
103#14273719C2314yes—
104#14273717—28no—
105#14273717—28no—
106#14273706—22no—
107#14273706—22no—
108#14273706C2314yes—
109#14273706C2314yes—
110C4×Dic118—22no—
111C4×Dic118—22no—
112C4×Dic118—22no—
113C4×Dic118—22no—
114C4×Dic118C2314yes—
115C4×Dic118C2314yes—
116C4×Dic118C2314yes—
117C4×Dic118C2314yes—
118C4×D236—22no—
119C4×D236—22no—
120C4×D236C2314yes—
121C4×D236C2314yes—
122(C22⋊D59)⋊C4—28no—
123(C22⋊D59)⋊C4—28no—
124#14273685—28no—
125C2×C4⋊Dic59—21no—
126C2×C4⋊Dic59—21no—
127C2×C4⋊Dic59—21no—
128C2×C4⋊Dic59—22no—
129C2×C4⋊Dic59C2311yescharacteristic
130C2×C4⋊Dic59C2311yescharacteristic
131C2×C4⋊Dic59C2311yescharacteristic
132C2×C4⋊Dic59C2311yescharacteristic
133C2×C4⋊Dic59C2314yes—
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4—21no—
137C2×Dic59⋊C4—21no—
138C2×Dic59⋊C4—21no—
139C2×Dic59⋊C4—21no—
140C2×Dic59⋊C4—21no—
141C2×Dic59⋊C4—21no—
142C4⋊C4×D59—28no—
143C2×C22⋊Dic59—21no—
144C2×C22⋊Dic59—21no—
145C2×(C2×D59)⋊C4—21no—
146C2×(C2×D59)⋊C4—21no—
147C2×C4×Dic59—21no—
148C2×C4×Dic59—21no—
149C2×C4×Dic59—21no—
150C2×C4×Dic59—21no—
151#14273661C2314yes—
152#14273661C2314yes—
153#14273659C2314yes—
154#14273659C2314yes—
155#14273652C2314yes—
156#14273652C2314yes—
157#14273652C2314yes—
158#14273652C2314yes—
159#14273652C2314yes—
160#14273652C2314yes—
161#14273649C2314yes—
162#14273649C2314yes—
163C23×C4×C59C2311yescharacteristic
164C22×C8×C59C2311yescharacteristic
165C22×C8×C59C2311yescharacteristic
166C22×C8×C59C2311yescharacteristic
167C22×C8×C59C2311yescharacteristic
168#117×C59D414yes—
169#117×C59C2314yes—
170C2×C4⋊C4×C59D411yescharacteristic
171C2×C4⋊C4×C59D411yescharacteristic
172C2×C22⋊C4×C59D411yescharacteristic
173C2×C22⋊C4×C59D411yescharacteristic
174C2×C42×C59C2311yescharacteristic
175C2×C42×C59C2311yescharacteristic
176C4⋊C8×C59C2314yes—
177C4⋊C8×C59C2314yes—
178C22⋊C8×C59C2314yes—
179C22⋊C8×C59C2314yes—
180#97×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—28no—
195C2×C22⋊D59—24no—
196C22×Dic59—21no—
197C22×Dic59—21no—
198C22×Dic59—21no—
199C22×Dic59—21no—
200C22×Dic59—21no—
201C22×Dic59—21no—
202C22×Dic59—21no—
203C22×Dic59—24no—
204C22×Dic59—82no—
205#11745685—216no—
206#11745685—28no—
207#11745685—28no—
208C2×D236—21no—
209C2×D236—22no—
210C2×D236#4114yes—
211C2×D236C2412yes—
212C2×C4×D59—28no—
213C2×C4×D59—24no—
214C2×C4×D59—24no—
215C2×C4×D59—24no—
216C2×C4×D59—82no—
217C2×C4×D59—82no—
218C2×Dic118—21no—
219C2×Dic118—22no—
220C2×Dic118—22no—
221C2×Dic118—22no—
222C2×Dic118—22no—
223C2×Dic118—22no—
224C2×Dic118—21no—
225C2×Dic118—21no—
226C2×Dic118#4114yes—
227C2×Dic118C2412yes—
228C2×Dic118C2412yes—
229C2×Dic118C2412yes—
230C2×C8×C59—22no—
231C2×C8×C59—22no—
232C2×C8×C59—22no—
233C2×C8×C59—22no—
234C2×C8×C59C2412yes—
235C2×C8×C59C2412yes—
236C2×C8×C59C2412yes—
237C2×C8×C59C2412yes—
238C4⋊C4×C59C2×D414yes—
239C4⋊C4×C59C2×D414yes—
240C22⋊C4×C59C2×D414yes—
241C22⋊C4×C59C2×D414yes—
242C42×C59C2×D412yes—
243C42×C59C2×D412yes—
244C42×C59C2412yes—
245C42×C59C2412yes—
246C22⋊Dic59—24no—
247C22⋊Dic59—24no—
248(C2×D59)⋊C4—24no—
249(C2×D59)⋊C4—24no—
250C4⋊Dic59—24no—
251C4⋊Dic59—21no—
252C4⋊Dic59—21no—
253C4⋊Dic59—24no—
254C4⋊Dic59—24no—
255C4⋊Dic59—21no—
256C4⋊Dic59—21no—
257C4⋊Dic59C2412yes—
258C4⋊Dic59C2412yes—
259C4⋊Dic59C2412yes—
260C4⋊Dic59C2412yes—
261Dic59⋊C4—24no—
262Dic59⋊C4—24no—
263Dic59⋊C4—24no—
264Dic59⋊C4—24no—
265Dic59⋊C4—24no—
266Dic59⋊C4—24no—
267Dic59⋊C4—24no—
268Dic59⋊C4—24no—
269C4×Dic59—24no—
270C4×Dic59—24no—
271C4×Dic59—24no—
272C4×Dic59—24no—
273Dic236—28no—
274Dic236—28no—
275#11745660—28no—
276#11745660—28no—
277C23×C59—22no—
278C23×C59—22no—
279C23×C59—22no—
280C23×C59C22×D412yes—
281C23×C59C22×D411yescharacteristic
282C22×D59—24no—
283C22×D59—22no—
284C22×D59—42no—
285C22×D59—42no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—24no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59C22×D412yes—
295C2×C4×C59C22×D412yes—
296C2×C4×C59C22×D412yes—
297C2×C4×C59C22×D412yes—
298C2×C4×C59C22×D412yes—
299C2×C4×C59C22×D411yescharacteristic
300C2×C4×C59C2×#4112yes—
301C2×C4×C59C2×#4112yes—
302C2×C4×C59C2511yescharacteristic
303C22⋊D59—216no—
304C2×Dic59—24no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—42no—
313C2×Dic59—42no—
314C2×Dic59—42no—
315C2×Dic59—42no—
316C2×Dic59—42no—
317C2×Dic59—42no—
318C2×Dic59—84no—
319D236—24no—
320D236—22no—
321D236C2×#4114yes—
322C4×D59—216no—
323C4×D59—84no—
324C4×D59—84no—
325Dic118—24no—
326Dic118—22no—
327Dic118—22no—
328Dic118—22no—
329Dic118—22no—
330Dic118—22no—
331Dic118—42no—
332Dic118—42no—
333Dic118C2×#4114yes—
334C8×C59—22no—
335C8×C59—22no—
336C8×C59—22no—
337C8×C59—22no—
338C2×#3120—591nomaximal, Sylow
339C22×C59—22no—
340C22×C59—22no—
341C22×C59—22no—
342C22×C59—44no—
343C22×C59#52512yes—
344C22×C59#57712yes—
345C22×C59#57812yes—
346C22×C59C23×D411yescharacteristic
347C2×D59—24no—
348C2×D59—48no—
349C2×D59—42no—
350C2×D59—42no—
351C4×C59—22no—
352C4×C59—22no—
353C4×C59—22no—
354C4×C59—22no—
355C4×C59—22no—
356C4×C59#52512yes—
357C4×C59C22×#4111yescharacteristic
358C4×C59C22×#4111yescharacteristic
359Dic59—24no—
360Dic59—42no—
361Dic59—42no—
362Dic59—42no—
363Dic59—42no—
364Dic59—42no—
365Dic59—42no—
366C2×#541—591no—
367C2×#520—591no—
368#3120—5916no—
369C2×#484—591no—
370C2×#483—591no—
371C2×#479—591no—
372C2×#478—591no—
373C2×#462—591no—
374C2×#461—591no—
375C2×#452—591no—
376C2×#452—591no—
377C2×#441—591no—
378C2×#440—591no—
379C2×C4×Q16—591no—
380C2×C4×SD16—591no—
381C2×#433D5911yescharacteristic, complemented
382C2×C59—42no—
383C2×C59#312014yescomplemented
384C2×C59C2×#52511yescharacteristic
385C2×C59C2×#57711yescharacteristic
386C2×C59C2×#57811yescharacteristic
387D59—44no—
388C22×#41—591no—
389C22×Q16—591no—
390C22×Q16—591no—
391C22×SD16—591no—
392C22×SD16—591no—
393#541—598no—
394#541—1184no—
395C2×C4⋊Q8—591no—
396C2×#126—1181no—
397C2×#126—1181no—
398C2×#125—591no—
399C2×#125—1181no—
400C2×#125—1181no—
401C2×C22⋊Q8—591no—
402C2×C22⋊Q8—591no—
403#520—598no—
404#520—1184no—
405C2×C4×Q8—591no—
406C2×C4×Q8—591no—
407C2×C4×Q8—591no—
408C2×C4×Q8—591no—
409C2×C4×D4—591no—
410C2×C4×D4—591no—
411C2×C4×D4—1181no—
412C2×C4×D4—1181no—
413C2×#117—1181no—
414C2×#117C2×D5911yescharacteristic
415C22×C4⋊C4—591no—
416C22×C4⋊C4—1181no—
417#484—598no—
418#483—598no—
419#479—598no—
420#478—598no—
421#462—598no—
422#461—598no—
423#452—598no—
424#452—598no—
425#441—598no—
426#440—598no—
427C4×Q16—598no—
428C4×SD16—598no—
429#433C2×D5918yescomplemented
430C2×#107—591no—
431C2×#107—591no—
432C2×#106—591no—
433C2×#106—591no—
434C2×C4⋊C8C2×D5911yescharacteristic
435C2×C4⋊C8C2×D5911yescharacteristic
436C2×#103—591no—
437C2×#103—591no—
438C2×#103—591no—
439C2×#103—591no—
440C2×#103—591no—
441C2×#103—591no—
442C2×#102—591no—
443C2×#102—591no—
444C2×C22⋊C8C2×D5911yescharacteristic
445C2×C22⋊C8C2×D5911yescharacteristic
446C2×#97C2×D5911yescharacteristic
447C2×C4×C8C2×D5911yescharacteristic
448C59C2×#312011yescharacteristic, complemented, Sylow
449C2×#41—594no—
450C2×#41—1184no—
451C2×#41—1184no—
452C2×#41—1182no—
453C22×Q8—591no—
454C22×Q8—591no—
455C22×Q8—591no—
456C22×D4—591no—
457C22×D4—1181no—
458C23×C4—1181no—
459C23×C4—1181no—
460C23×C4—1181no—
461C23×C4—1181no—
462C23×C4C22×D5911yescharacteristic
463C2×Q16—594no—
464C2×Q16—594no—
465C2×Q16—1184no—
466C2×Q16—1184no—
467C2×SD16—594no—
468C2×SD16—594no—
469C2×SD16—1184no—
470C2×SD16—1184no—
471C22×C8C22×D5911yescharacteristic
472C22×C8C22×D5911yescharacteristic
473C22×C8C22×D5911yescharacteristic
474C22×C8C22×D5911yescharacteristic
475C4⋊Q8—594no—
476C4⋊Q8—1182no—
477#126—1188no—
478#126—1188no—
479#125—594no—
480#125—1188no—
481#125—1188no—
482#125—1182no—
483C22⋊Q8—594no—
484C22⋊Q8—594no—
485C22⋊Q8—1182no—
486C22⋊Q8—1182no—
487C4×Q8—594no—
488C4×Q8—594no—
489C4×Q8—594no—
490C4×Q8—594no—
491C4×Q8—1182no—
492C4×Q8—1182no—
493C4×Q8—1182no—
494C4×Q8—1182no—
495C4×D4—594no—
496C4×D4—594no—
497C4×D4—1188no—
498C4×D4—1188no—
499C4×D4—1182no—
500C4×D4—1182no—
501#117—1188no—
502#117D23614yes—
503#117C22×D5914yes—
504C2×C4⋊C4—591no—
505C2×C4⋊C4—591no—
506C2×C4⋊C4—594no—
507C2×C4⋊C4—591no—
508C2×C4⋊C4—591no—
509C2×C4⋊C4—1181no—
510C2×C4⋊C4—1182no—
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⋊C4—1181no—
518C2×C4⋊C4—1181no—
519C2×C4⋊C4—1181no—
520C2×C4⋊C4—1181no—
521C2×C4⋊C4—1188no—
522C2×C4⋊C4D23611yescharacteristic
523C2×C4⋊C4D23611yescharacteristic
524C2×C22⋊C4—1181no—
525C2×C22⋊C4—1181no—
526C2×C22⋊C4—1181no—
527C2×C22⋊C4—1181no—
528C2×C22⋊C4D23611yescharacteristic
529C2×C22⋊C4D23611yescharacteristic
530C2×C42—1181no—
531C2×C42—1181no—
532C2×C42—1181no—
533C2×C42—1181no—
534C2×C42C22×D5911yescharacteristic
535C2×C42C22×D5911yescharacteristic
536#107—594no—
537#107—594no—
538#106—594no—
539#106—594no—
540C4⋊C8C22×D5914yes—
541C4⋊C8C22×D5914yes—
542#103—594no—
543#103—594no—
544#103—594no—
545#103—594no—
546#103—594no—
547#103—594no—
548#102—594no—
549#102—594no—
550C22⋊C8C22×D5914yes—
551C22⋊C8C22×D5914yes—
552#97C22×D5914yes—
553C4×C8C22×D5914yes—
554C24—1181no—
555C24C2×D23611yescharacteristic
556#41—1188no—
557#41—1188no—
558#41—11816no—
559C2×Q8—594no—
560C2×Q8—592no—
561C2×Q8—592no—
562C2×Q8—592no—
563C2×Q8—1181no—
564C2×Q8—1181no—
565C2×Q8—1181no—
566C2×Q8—1182no—
567C2×Q8—1182no—
568C2×Q8—1182no—
569C2×Q8—1182no—
570C2×Q8—1182no—
571C2×D4—594no—
572C2×D4—592no—
573C2×D4—1188no—
574C2×D4—1184no—
575C2×D4—1181no—
576C2×D4—1182no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—1188no—
580C22×C4—1181no—
581C22×C4—1184no—
582C22×C4—1184no—
583C22×C4—1181no—
584C22×C4—1181no—
585C22×C4—1181no—
586C22×C4—1181no—
587C22×C4—1181no—
588C22×C4—1181no—
589C22×C4—1184no—
590C22×C4—1184no—
591C22×C4—4722no—
592C22×C4—4722no—
593C22×C4—4722no—
594C22×C4C2×D23612yes—
595C22×C4C2×D23611yescharacteristic
596C22×C4C2×D23611yescharacteristic
597C22×C4C2×D23611yescharacteristic
598C22×C4C2×D23611yescharacteristic
599C22×C4C2×D23611yescharacteristic
600C22×C4C23×D5912yes—
601C22×C4C23×D5911yescharacteristic
602Q16—1188no—
603Q16—1188no—
604SD16—1188no—
605SD16—1188no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8C23×D5912yes—
611C2×C8C23×D5912yes—
612C2×C8C23×D5912yes—
613C2×C8C23×D5912yes—
614C4⋊C4—592no—
615C4⋊C4—592no—
616C4⋊C4—592no—
617C4⋊C4—592no—
618C4⋊C4—1184no—
619C4⋊C4—1181no—
620C4⋊C4—1181no—
621C4⋊C4—1181no—
622C4⋊C4—1181no—
623C4⋊C4—1184no—
624C4⋊C4—1184no—
625C4⋊C4—1184no—
626C4⋊C4—1184no—
627C4⋊C4—1184no—
628C4⋊C4—1184no—
629C4⋊C4—1184no—
630C4⋊C4—1184no—
631C4⋊C4—1184no—
632C4⋊C4—1184no—
633C4⋊C4C2×D23614yes—
634C4⋊C4C2×D23614yes—
635C22⋊C4—1184no—
636C22⋊C4—1184no—
637C22⋊C4—1184no—
638C22⋊C4—1184no—
639C22⋊C4C2×D23614yes—
640C22⋊C4C2×D23614yes—
641C42—1184no—
642C42—1184no—
643C42—1184no—
644C42—1184no—
645C42C2×D23612yes—
646C42C2×D23612yes—
647C42C23×D5912yes—
648C42C23×D5912yes—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—1184no—
653C23—1182no—
654C23—2362no—
655C23—2362no—
656C23C22×D23612yes—
657C23C22×D23611yescharacteristic
658Q8—594no—
659Q8—1184no—
660Q8—1182no—
661Q8—1182no—
662Q8—1182no—
663Q8—1182no—
664Q8—1182no—
665Q8—2362no—
666Q8—2362no—
667D4—594no—
668D4—11816no—
669D4—1184no—
670D4—1182no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—11816no—
680C2×C4—1184no—
681C2×C4—1182no—
682C2×C4—1182no—
683C2×C4—1182no—
684C2×C4—1182no—
685C2×C4—1182no—
686C2×C4—1182no—
687C2×C4—1182no—
688C2×C4—4724no—
689C2×C4—4724no—
690C2×C4—4724no—
691C2×C4—2362no—
692C2×C4—2362no—
693C2×C4—2362no—
694C2×C4—2362no—
695C2×C4—2362no—
696C2×C4—2362no—
697C2×C4C22×D23612yes—
698C2×C4C22×D23612yes—
699C2×C4C22×D23612yes—
700C2×C4C22×D23612yes—
701C2×C4C22×D23612yes—
702C2×C4C22×D23611yescharacteristic
703C2×C4#41×D5912yes—
704C2×C4#41×D5912yes—
705C2×C4C24×D5911yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—1184no—
715C22—2362no—
716C22—2362no—
717C22—2368no—
718C22#1683791412yes—
719C22#1683821412yes—
720C22#1683821912yes—
721C22C23×D23611yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—1184no—
728C4—2362no—
729C4—2362no—
730C4—2362no—
731C4—2362no—
732C4—2362no—
733C4—2362no—
734C4#1683791412yes—
735C4C2×#41×D5911yescharacteristic
736C4C2×#41×D5911yescharacteristic
737C2—42no—
738C2—2364no—
739C2#2143431214yesdirect product factor
740C2C2×#1683791411yescharacteristic
741C2C2×#1683821411yescharacteristic
742C2C2×#1683821911yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#433C2
socleC23×C59C22×D4
prime radicalC22×#11745685C22
hypercenterC2×#433D59
hypocenterC59C2×#3120
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#16838014C2semidirect
3. #21434312C2direct (N × H)
4. C2×#16837738C2semidirect
5. C2×#16837733C2semidirect
6. C2×#16837710C2semidirect
7. C2×#16837703C2semidirect
8. C2×#16837613C2semidirect
9. C2×#16837608C2semidirect
12. C2×#16837510C2semidirect
13. C2×#16837504C2semidirect
14. C2×C4×Dic236C2semidirect
15. C2×C4×#11745660C2semidirect
16. C2×C59×#433C2semidirect
23. #16838014C22semidirect
45. #16837738C22semidirect
46. #16837733C22semidirect
47. #16837710C22semidirect
48. #16837703C22semidirect
49. #16837613C22semidirect
50. #16837608C22semidirect
53. #16837510C22semidirect
54. #16837504C22semidirect
55. C4×Dic236C22semidirect
56. C4×#11745660C22semidirect
70. C59×#433C22semidirect
381. C2×#433D59semidirect
383. C2×C59#3120semidirect
429. #433C2×D59semidirect
448. C59C2×#3120semidirect
739. C2#21434312direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380142
C2×#168378822
#214343122
C2×#168377382
C2×#168377332
C2×#168377102
C2×#168377032
C2×#168376132
C2×#168376082
C2×#168375662
C2×#168375102
C2×#168375042
C2×C4×Dic2362
C2×C4×#117456602
C2×C59×#4332
C2×#312059