Finite Group Databasebeta

← C2×#21434765 #29458558

Subgroups — C2×#21434765 #29458558

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×#16838025C211yesmaximal, characteristic
2C2×#16838012C211yesmaximal, characteristic, complemented
3#21434765C2116yesmaximal, direct product factor
4C2×#16837809C211yesmaximal, characteristic, complemented
5C2×#16837795C211yesmaximal, characteristic, complemented
6C2×#16837758C211yesmaximal, characteristic, complemented
7C2×#16837751C211yesmaximal, characteristic, complemented
8C2×#16837648C211yesmaximal, characteristic
9C2×#16837641C211yesmaximal, characteristic, complemented
10C2×#16837633C211yesmaximal, characteristic
11C2×#16837506C211yesmaximal, characteristic, complemented
12C2×#16837505C211yesmaximal, characteristic, complemented
13C2×Q16×Dic59C211yesmaximal, characteristic, complemented
14C2×#16837489C211yesmaximal, characteristic, complemented
15C2×#16837360C211yesmaximal, characteristic, complemented
16C2×C59×#470C211yesmaximal, characteristic, complemented
17C22×#11745672C2211yescharacteristic
18C22×#11745660C2211yescharacteristic
19C22×#11745671C2211yescharacteristic
20C23×C59⋊C8C2211yescharacteristic
21#16838025—24no—
22#16838025C2218yes—
23#16838012—24no—
24#16838012C2218yescomplemented
25C2×#14273726C2211yescharacteristic
26C2×#14273725C2211yescharacteristic
27C2×#14273722—21no—
28C2×#14273720—21no—
29C2×#14273720—21no—
30C2×#14273718—21no—
31C2×#14273718C2211yescharacteristic
32C2×#14273717—21no—
33C2×#14273716C2211yescharacteristic
34C2×#14273713—21no—
35C2×#14273709—21no—
36C2×#14273707—21no—
37C2×#14273706C2211yescharacteristic
38C2×#14273701C2211yescharacteristic
39C2×Q8×Dic59C2211yescharacteristic
40C2×Q8×Dic59C2211yescharacteristic
41C2×#14273692C2211yescharacteristic
42C2×#14273689C2211yescharacteristic
43C2×#14273686C2211yescharacteristic
44#16837809C2218yescomplemented
45#16837795C2218yescomplemented
46#16837758C2218yescomplemented
47#16837751C2218yescomplemented
48#16837648C2218yes—
49#16837641C2218yescomplemented
50#16837633C2218yes—
51#16837506C2218yescomplemented
52#16837505C2218yescomplemented
53Q16×Dic59C2218yescomplemented
54#16837489C2218yescomplemented
55C2×#14273661C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×#14273652C2211yescharacteristic
59C2×#14273651C2211yescharacteristic
60C2×#14273651C2211yescharacteristic
61C2×#14273650C2211yescharacteristic
62C2×#14273649C2211yescharacteristic
63C2×#14273647C2211yescharacteristic
64#16837360C2218yescomplemented
65C2×#14273637C2211yescharacteristic
66C2×#14273637C2211yescharacteristic
67C2×C8×Dic59C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C22×Q16×C59C2211yescharacteristic
70C22×M16×C59C2211yescharacteristic
71C2×C22⋊Q8×C59C2211yescharacteristic
72C2×C22⋊Q8×C59C2211yescharacteristic
73C59×#470C2218yescomplemented
74C2×#106×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#103×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C22×D236C2311yescharacteristic
80C22×C22⋊D59—21no—
81C22×C4×D59—21no—
82C2×#11745672—24no—
83C2×#11745672C2314yes—
84C2×#11745660—24no—
85C2×#11745660C2314yes—
86C2×#11745671—24no—
87C2×#11745671C2314yes—
88C22×C59⋊C8—24no—
89C22×C59⋊C8C2314yes—
90C22×C59⋊C8C2311yescharacteristic
91C22×C59⋊C8C2311yescharacteristic
92#14273726—22no—
93#14273726C2314yes—
94#14273725—22no—
95#14273725C2314yes—
96#14273722—28no—
97#14273720—28no—
98#14273720—28no—
99#14273718—28no—
100#14273718—22no—
101#14273718C2314yes—
102#14273717—28no—
103#14273716—22no—
104#14273716C2314yes—
105#14273713—28no—
106#14273709—28no—
107#14273707—28no—
108#14273706—22no—
109#14273706C2314yes—
110#14273701—22no—
111#14273701C2314yes—
112Q8×Dic59—22no—
113Q8×Dic59—22no—
114Q8×Dic59C2314yes—
115Q8×Dic59C2314yes—
116#14273692—22no—
117#14273692C2314yes—
118#14273689—22no—
119#14273689C2314yes—
120#14273686D414yes—
121#14273686C2314yes—
122C2×C4⋊Dic59—21no—
123C2×C4⋊Dic59—21no—
124C2×C4⋊Dic59—21no—
125C2×C4⋊Dic59D411yescharacteristic
126C2×C4⋊Dic59D411yescharacteristic
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×C22⋊Dic59—21no—
136C2×C22⋊Dic59D411yescharacteristic
137C2×C22⋊Dic59D411yescharacteristic
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4—21no—
142C2×C4×Dic59—21no—
143C2×C4×Dic59—21no—
144C2×C4×Dic59—21no—
145C2×C4×Dic59C2311yescharacteristic
146C2×C4×Dic59C2311yescharacteristic
147#14273661C2314yes—
148#14273660C2314yes—
149#14273658C2314yes—
150#14273652C2314yes—
151#14273651C2314yes—
152#14273651C2314yes—
153#14273650C2314yes—
154#14273649C2314yes—
155#14273647C2314yes—
156#14273637C2314yes—
157#14273637C2314yes—
158C8×Dic59C2314yes—
159C8×Dic59C2314yes—
160C22×Q8×C59C2311yescharacteristic
161C22×Q8×C59C2311yescharacteristic
162C23×C4×C59C2311yescharacteristic
163C2×Q16×C59—24no—
164C2×Q16×C59C2314yes—
165C2×M16×C59—24no—
166C2×M16×C59C2314yes—
167C22×C8×C59C2311yescharacteristic
168C22×C8×C59C2311yescharacteristic
169C22⋊Q8×C59—22no—
170C22⋊Q8×C59—22no—
171C22⋊Q8×C59C2314yes—
172C22⋊Q8×C59C2314yes—
173C2×C4⋊C4×C59—21no—
174C2×C4⋊C4×C59—21no—
175C2×C4⋊C4×C59C2311yescharacteristic
176C2×C4⋊C4×C59C2311yescharacteristic
177C2×C22⋊C4×C59—21no—
178C2×C22⋊C4×C59—21no—
179#106×C59C2314yes—
180#103×C59C2314yes—
181#103×C59C2314yes—
182C24×C59C2×D411yescharacteristic
183C23×D59—21no—
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—22no—
193C22×C4×C59—22no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2×D412yes—
200C22×C4×C59C2412yes—
201C22×C4×C59C2411yescharacteristic
202C2×C22⋊D59—24no—
203C2×C22⋊D59—82no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59—21no—
207C22×Dic59C2×D411yescharacteristic
208C22×Dic59C2×D411yescharacteristic
209C22×Dic59C2×D411yescharacteristic
210C22×Dic59C2×D411yescharacteristic
211C2×D236—22no—
212C2×D236—22no—
213C2×D236—21no—
214C2×D236C2412yes—
215C2×C4×D59—24no—
216C2×C4×D59—82no—
217C2×Dic118—22no—
218C2×Dic118—22no—
219C2×Dic118—21no—
220C2×Dic118—24no—
221C2×Dic118—82no—
222C2×Dic118C2412yes—
223Q16×C59—28no—
224M16×C59—28no—
225C2×C8×C59—22no—
226C2×C8×C59#4114yes—
227C2×C8×C59C2412yes—
228C2×C8×C59C2412yes—
229C4⋊C4×C59—24no—
230C4⋊C4×C59—24no—
231C4⋊C4×C59—21no—
232C4⋊C4×C59—21no—
233C4⋊C4×C59C2412yes—
234C4⋊C4×C59C2412yes—
235C22⋊C4×C59—24no—
236C22⋊C4×C59—24no—
237C22⋊Dic59—24no—
238C22⋊Dic59C2×D414yes—
239C22⋊Dic59C2×D414yes—
240#11745672—28no—
241#11745671—28no—
242(C2×D59)⋊C4—24no—
243(C2×D59)⋊C4—24no—
244(C2×D59)⋊C4—24no—
245(C2×D59)⋊C4—24no—
246C4⋊Dic59—21no—
247C4⋊Dic59—21no—
248C4⋊Dic59—24no—
249C4⋊Dic59—24no—
250C4⋊Dic59—24no—
251C4⋊Dic59C2×D414yes—
252C4⋊Dic59C2×D414yes—
253C4⋊Dic59C2412yes—
254C4⋊Dic59C2412yes—
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—28no—
270C2×C59⋊C8#4114yes—
271C2×C59⋊C8C2412yes—
272C2×C59⋊C8C2412yes—
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—
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—24no—
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—42no—
298C2×C4×C59—42no—
299C2×C4×C59—42no—
300C2×C4×C59—42no—
301C2×C4×C59C22×D412yes—
302C2×C4×C59C22×D411yescharacteristic
303C2×C4×C59C2×#4112yes—
304C2×C4×C59C2×#4112yes—
305C2×C4×C59C2511yescharacteristic
306C22⋊D59—84no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—42no—
315C2×Dic59—42no—
316C2×Dic59—42no—
317C2×Dic59C22×D412yes—
318C2×Dic59C22×D412yes—
319C2×Dic59C22×D412yes—
320C2×Dic59C22×D412yes—
321D236—22no—
322D236—22no—
323D236—42no—
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—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—42no—
348C4×C59—42no—
349C4×C59—42no—
350C4×C59—42no—
351C4×C59#53212yes—
352C4×C59C22×#4111yescharacteristic
353C4×C59C22×#4111yescharacteristic
354Dic59—22no—
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×#470D5911yescharacteristic, complemented
369C2×#468—591no—
370C2×#467—591no—
371C2×#465—591no—
372C2×#441—591no—
373C2×#440—591no—
374C2×C4×Q16—591no—
375C2×C4×SD16—591no—
376C2×#405—591no—
377C2×C59—42no—
378C2×C59#317814yescomplemented
379C2×C59C2×#53211yescharacteristic
380C2×C59C2×#57711yescharacteristic
381C2×C59C2×#57811yescharacteristic
382D59—82no—
383C22×Q16—591no—
384C22×Q16C2×D5911yescharacteristic
385C22×SD16—591no—
386C22×SD16—591no—
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—1181no—
406C2×C22⋊Q8C2×D5911yescharacteristic
407C2×C22⋊Q8C2×D5911yescharacteristic
408C2×#121—591no—
409C2×C4×Q8—591no—
410C2×C4×Q8—591no—
411C2×C4×Q8—591no—
412C2×C4×D4—591no—
413C2×#117—591no—
414#501—598no—
415#497—598no—
416#488—598no—
417#487—598no—
418#470C2×D5918yescomplemented
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×#106C2×D5911yescharacteristic
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×C8—591no—
443C59C2×#317811yescharacteristic, complemented, Sylow
444C22×Q8—591no—
445C22×Q8—1181no—
446C22×Q8C22×D5911yescharacteristic
447C22×Q8C22×D5911yescharacteristic
448C22×D4—591no—
449C22×D4—1181no—
450C23×C4—1181no—
451C23×C4C22×D5911yescharacteristic
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—24no—
461C2×M16C22×D5914yes—
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—1182no—
477#125—1188no—
478#125—1188no—
479#124—594no—
480#124—1182no—
481#124—1188no—
482#123—1188no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8—594no—
486C22⋊Q8—1188no—
487C22⋊Q8—1182no—
488C22⋊Q8C22×D5914yes—
489C22⋊Q8C22×D5914yes—
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#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—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#107—594no—
535#106—594no—
536#106C22×D5914yes—
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×C8—594no—
549C24—1181no—
550C24D4×D5911yescharacteristic
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—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—591no—
578C22×C4—591no—
579C22×C4—591no—
580C22×C4—591no—
581C22×C4—1184no—
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—28no—
591Q16—1188no—
592SD16—1188no—
593SD16—1188no—
594M16—28no—
595C2×C8—22no—
596C2×C8—594no—
597C2×C8—592no—
598C2×C8—592no—
599C2×C8—1188no—
600C2×C8—1182no—
601C2×C8#1174568714yes—
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—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—1182no—
645C23—2362no—
646C23—2362no—
647C23—2362no—
648C23C2×D4×D5912yes—
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—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—592no—
677C2×C4—592no—
678C2×C4—592no—
679C2×C4—592no—
680C2×C4—1182no—
681C2×C4—1182no—
682C2×C4—1182no—
683C2×C4—1182no—
684C2×C4—1182no—
685C2×C4—1182no—
686C2×C4—1182no—
687C2×C4—4724no—
688C2×C4—2362no—
689C2×C4—2362no—
690C2×C4—2362no—
691C2×C4C2×D4×D5912yes—
692C2×C4C2×D4×D5911yescharacteristic
693C2×C4#41×D5912yes—
694C2×C4C2×#1174568712yes—
695C2×C4C24×D5911yescharacteristic
696C8—22no—
697C8—594no—
698C8—1182no—
699C8C2×#1174568714yes—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—4724no—
705C22—2362no—
706C22—2362no—
707C22—2362no—
708C22#1683794712yes—
709C22#1683821112yes—
710C22#1683821812yes—
711C22C22×D4×D5911yescharacteristic
712C4—22no—
713C4—42no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—1182no—
718C4—1182no—
719C4—1182no—
720C4—1182no—
721C4—2362no—
722C4—2362no—
723C4—2362no—
724C4#1683794712yes—
725C4C2×#41×D5911yescharacteristic
726C4C22×#1174568711yescharacteristic
727C2—42no—
728C2—4722no—
729C2#2143476514yesdirect product factor
730C2C2×#1683794711yescharacteristic
731C2C2×#1683821111yescharacteristic
732C2C2×#1683821811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#470C2
socleC23×C59C22×D4
prime radicalC2×#14273701C22
hypercenterC2×#470D59
hypocenterC59C2×#3178
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
2. C2×#16838012C2semidirect
3. #21434765C2direct (N × H)
4. C2×#16837809C2semidirect
5. C2×#16837795C2semidirect
6. C2×#16837758C2semidirect
7. C2×#16837751C2semidirect
9. C2×#16837641C2semidirect
11. C2×#16837506C2semidirect
12. C2×#16837505C2semidirect
13. C2×Q16×Dic59C2semidirect
14. C2×#16837489C2semidirect
15. C2×#16837360C2semidirect
16. C2×C59×#470C2semidirect
24. #16838012C22semidirect
44. #16837809C22semidirect
45. #16837795C22semidirect
46. #16837758C22semidirect
47. #16837751C22semidirect
49. #16837641C22semidirect
51. #16837506C22semidirect
52. #16837505C22semidirect
53. Q16×Dic59C22semidirect
54. #16837489C22semidirect
64. #16837360C22semidirect
73. C59×#470C22semidirect
368. C2×#470D59semidirect
378. C2×C59#3178semidirect
418. #470C2×D59semidirect
443. C59C2×#3178semidirect
729. C2#21434765direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380252
C2×#168380122
#214347652
C2×#168378092
C2×#168377952
C2×#168377582
C2×#168377512
C2×#168376482
C2×#168376412
C2×#168376332
C2×#168375062
C2×#168375052
C2×Q16×Dic592
C2×#168374892
C2×#168373602
C2×C59×#4702
C2×#317859