Finite Group Databasebeta

← C2×#21437172 #29469706

Subgroups — C2×#21437172 #29469706

Order 15104.

1938 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838126C211yesmaximal, characteristic, complemented
2C2×#16838121C211yesmaximal, characteristic, complemented
3#21437172C2116yesmaximal, direct product factor
4C2×#16837795C211yesmaximal, characteristic, complemented
5C2×#16837783C211yesmaximal, characteristic
6C2×#16837626C211yesmaximal, characteristic, complemented
7C2×#16837622C211yesmaximal, characteristic, complemented
8C2×#16837610C211yesmaximal, characteristic, complemented
9C2×#16837609C211yesmaximal, characteristic, complemented
10C2×#16837619C211yesmaximal, characteristic
11C2×#16837614C211yesmaximal, characteristic
12C2×#16837530C211yesmaximal, characteristic, complemented
13C2×#16837504C211yesmaximal, characteristic, complemented
14C2×#16837503C211yesmaximal, characteristic, complemented
15C2×Q16×Dic59C211yesmaximal, characteristic, complemented
16C2×C59×#497C211yesmaximal, characteristic, complemented
17C22×#11745672C2211yescharacteristic
18C22×#11745672C2211yescharacteristic
19C22×#11745660C2211yescharacteristic
20C22×#11745671C2211yescharacteristic
21C22×#11745669C2211yescharacteristic
22#16838126—24no—
23#16838126C2218yescomplemented
24#16838121—24no—
25#16838121C2218yescomplemented
26C2×#14273725C2211yescharacteristic
27C2×#14273722—21no—
28C2×#14273722—21no—
29C2×#14273720—21no—
30C2×#14273720—21no—
31C2×#14273716C2211yescharacteristic
32C2×#14273716C2211yescharacteristic
33C2×#14273714C2211yescharacteristic
34C2×#14273707—21no—
35C2×#14273704—21no—
36C2×Q8×Dic59C2211yescharacteristic
37C2×Q8×Dic59C2211yescharacteristic
38C2×Q8×Dic59C2211yescharacteristic
39C2×C4×Dic118C2211yescharacteristic
40C2×C4×Dic118C2211yescharacteristic
41C2×C4×D236C2211yescharacteristic
42C2×D4×Dic59C2211yescharacteristic
43C2×#14273685—21no—
44C2×#14273683—21no—
45#16837795C2218yescomplemented
46#16837783C2218yes—
47#16837626C2218yescomplemented
48#16837622C2218yescomplemented
49#16837619C2218yes—
50#16837614C2218yes—
51#16837610C2218yescomplemented
52#16837609C2218yescomplemented
53#16837530C2218yescomplemented
54#16837504C2218yescomplemented
55#16837503C2218yescomplemented
56Q16×Dic59C2218yescomplemented
57C2×#14273661C2211yescharacteristic
58C2×C4⋊(C59⋊C8)C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×Dic59⋊C8C2211yescharacteristic
61C2×#14273652C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273651C2211yescharacteristic
64C2×#14273651C2211yescharacteristic
65C2×#14273649C2211yescharacteristic
66C2×#14273648C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C22×Q16×C59C2211yescharacteristic
70C22×Q16×C59C2211yescharacteristic
71C22×SD16×C59C2211yescharacteristic
72C22×SD16×C59C2211yescharacteristic
73C2×C4⋊Q8×C59C2211yescharacteristic
74C2×#124×C59C2211yescharacteristic
75C59×#497C2218yescomplemented
76C2×#97×C59C2211yescharacteristic
77C22×Dic118D411yescharacteristic
78C22×Dic118C2311yescharacteristic
79C22×D236C2311yescharacteristic
80C23×Dic59—21no—
81C22×C4×D59—21no—
82C2×#11745672—42no—
83C2×#11745672—42no—
84C2×#11745672C2314yes—
85C2×#11745672C2314yes—
86C2×#11745660—24no—
87C2×#11745660C2314yes—
88C2×#11745671—42no—
89C2×#11745671C2314yes—
90C2×#11745669—42no—
91C2×#11745669C2314yes—
92C22×C59⋊C8C2311yescharacteristic
93C22×C59⋊C8C2311yescharacteristic
94#14273725—22no—
95#14273725C2314yes—
96#14273722—28no—
97#14273722—28no—
98#14273720—28no—
99#14273720—28no—
100#14273716—22no—
101#14273716—22no—
102#14273716C2314yes—
103#14273716C2314yes—
104#14273714—22no—
105#14273714C2314yes—
106#14273707—28no—
107#14273704—28no—
108Q8×Dic59—22no—
109Q8×Dic59—22no—
110Q8×Dic59—22no—
111Q8×Dic59C2314yes—
112Q8×Dic59C2314yes—
113Q8×Dic59C2314yes—
114C4×Dic118—22no—
115C4×Dic118D414yes—
116C4×Dic118C2314yes—
117C4×Dic118C2314yes—
118C4×D236—22no—
119C4×D236C2314yes—
120D4×Dic59—22no—
121D4×Dic59C2314yes—
122#14273685—28no—
123#14273683—28no—
124C2×C4⋊Dic59—21no—
125C2×C4⋊Dic59—21no—
126C2×C4⋊Dic59—21no—
127C2×C4⋊Dic59D411yescharacteristic
128C2×C4⋊Dic59C2311yescharacteristic
129C2×C4⋊Dic59C2311yescharacteristic
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4D411yescharacteristic
134C2×Dic59⋊C4D411yescharacteristic
135C2×C22⋊Dic59—21no—
136C2×C22⋊Dic59—21no—
137C2×C22⋊Dic59—21no—
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×C4×Dic59—21no—
144C2×C4×Dic59—21no—
145C2×C4×Dic59—21no—
146C2×C4×Dic59—21no—
147C2×C4×Dic59C2311yescharacteristic
148C2×C4×Dic59C2311yescharacteristic
149#14273661C2314yes—
150C4⋊(C59⋊C8)C2314yes—
151Dic59⋊C8C2314yes—
152Dic59⋊C8C2314yes—
153#14273652C2314yes—
154#14273651C2314yes—
155#14273651C2314yes—
156#14273651C2314yes—
157#14273649C2314yes—
158#14273648C2314yes—
159#14273637C2314yes—
160C8×Dic59C2314yes—
161C22×Q8×C59C2311yescharacteristic
162C22×Q8×C59C2311yescharacteristic
163C22×Q8×C59C2311yescharacteristic
164C22×D4×C59C2311yescharacteristic
165C2×Q16×C59—24no—
166C2×Q16×C59—42no—
167C2×Q16×C59C2314yes—
168C2×Q16×C59C2314yes—
169C2×SD16×C59—24no—
170C2×SD16×C59—42no—
171C2×SD16×C59C2314yes—
172C2×SD16×C59C2314yes—
173C22×C8×C59C2311yescharacteristic
174C22×C8×C59C2311yescharacteristic
175C4⋊Q8×C59—22no—
176C4⋊Q8×C59C2314yes—
177#124×C59—22no—
178#124×C59C2314yes—
179C2×C4⋊C4×C59—21no—
180C2×C4⋊C4×C59—21no—
181C2×C22⋊C4×C59—21no—
182C2×C22⋊C4×C59—21no—
183C2×C42×C59C2311yescharacteristic
184#97×C59C2314yes—
185C24×C59—21no—
186C23×D59—21no—
187C2×Q8×C59—21no—
188C2×Q8×C59—21no—
189C2×Q8×C59—21no—
190C2×Q8×C59—22no—
191C2×Q8×C59—22no—
192C2×Q8×C59—22no—
193C2×Q8×C59—22no—
194C2×Q8×C59—22no—
195C2×Q8×C59—22no—
196C2×Q8×C59C2412yes—
197C2×Q8×C59C2412yes—
198C2×Q8×C59C2412yes—
199C2×D4×C59—21no—
200C2×D4×C59—22no—
201C2×D4×C59—22no—
202C2×D4×C59C2412yes—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59C2×D411yescharacteristic
207C22×C4×C59C2×D411yescharacteristic
208C22×C4×C59C2411yescharacteristic
209C22×Dic59—21no—
210C22×Dic59—21no—
211C22×Dic59—21no—
212C22×Dic59—24no—
213C22×Dic59—44no—
214C22×Dic59C2×D411yescharacteristic
215C22×Dic59C2×D411yescharacteristic
216C22×Dic59C2×D411yescharacteristic
217C22×Dic59C2×D411yescharacteristic
218C2×D236—22no—
219C2×D236—22no—
220C2×D236—21no—
221C2×D236C2412yes—
222C2×C4×D59—24no—
223C2×C4×D59—44no—
224C2×Dic118—22no—
225C2×Dic118—22no—
226C2×Dic118—21no—
227C2×Dic118—42no—
228C2×Dic118C2×D414yes—
229C2×Dic118C2412yes—
230Q16×C59—28no—
231Q16×C59—44no—
232SD16×C59—28no—
233SD16×C59—44no—
234C2×C8×C59—22no—
235C2×C8×C59#4114yes—
236C2×C8×C59C2412yes—
237C2×C8×C59C2412yes—
238C4⋊C4×C59—24no—
239C4⋊C4×C59—24no—
240C22⋊C4×C59—24no—
241C22⋊C4×C59—24no—
242C42×C59C2×D412yes—
243C42×C59C2412yes—
244C22⋊Dic59—24no—
245C22⋊Dic59—24no—
246C22⋊Dic59—24no—
247#11745672—44no—
248#11745672—44no—
249#11745671—44no—
250#11745669—44no—
251(C2×D59)⋊C4—24no—
252(C2×D59)⋊C4—24no—
253(C2×D59)⋊C4—24no—
254(C2×D59)⋊C4—24no—
255(C2×D59)⋊C4—24no—
256C4⋊Dic59—21no—
257C4⋊Dic59—21no—
258C4⋊Dic59—24no—
259C4⋊Dic59—24no—
260C4⋊Dic59—24no—
261C4⋊Dic59C2×D414yes—
262C4⋊Dic59C2412yes—
263C4⋊Dic59C2412yes—
264Dic59⋊C4—24no—
265Dic59⋊C4—24no—
266Dic59⋊C4—24no—
267Dic59⋊C4C2×D414yes—
268Dic59⋊C4C2×D414yes—
269C4×Dic59—24no—
270C4×Dic59—24no—
271C4×Dic59—24no—
272C4×Dic59—24no—
273C4×Dic59C2×D412yes—
274C4×Dic59C2×D412yes—
275C4×Dic59C2412yes—
276C4×Dic59C2412yes—
277C2×C59⋊C8—22no—
278C2×C59⋊C8—22no—
279C2×C59⋊C8C2412yes—
280C2×C59⋊C8C2412yes—
281#11745660—28no—
282C23×C59—22no—
283C23×C59—42no—
284C23×C59—42no—
285C23×C59—42no—
286C23×C59C22×D411yescharacteristic
287C22×D59—22no—
288C22×D59—42no—
289C22×D59—42no—
290C22×D59—42no—
291Q8×C59—22no—
292Q8×C59—22no—
293Q8×C59—22no—
294Q8×C59—22no—
295Q8×C59—22no—
296Q8×C59—22no—
297Q8×C59—42no—
298Q8×C59—42no—
299Q8×C59—42no—
300D4×C59—22no—
301D4×C59—22no—
302D4×C59—42no—
303C2×C4×C59—22no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—22no—
307C2×C4×C59—22no—
308C2×C4×C59—42no—
309C2×C4×C59—42no—
310C2×C4×C59—42no—
311C2×C4×C59C22×D412yes—
312C2×C4×C59C22×D412yes—
313C2×C4×C59C22×D411yescharacteristic
314C2×C4×C59C2×#4112yes—
315C2×C4×C59H(5,𝔽2)12yes—
316C2×C4×C59C2511yescharacteristic
317C2×Dic59—22no—
318C2×Dic59—22no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—48no—
325C2×Dic59—42no—
326C2×Dic59—42no—
327C2×Dic59—42no—
328C2×Dic59C22×D412yes—
329C2×Dic59C22×D412yes—
330C2×Dic59C22×D412yes—
331C2×Dic59C22×D412yes—
332D236—22no—
333D236—22no—
334D236—42no—
335C4×D59—48no—
336Dic118—22no—
337Dic118—22no—
338Dic118—44no—
339Dic118—42no—
340C8×C59—22no—
341C8×C59C2×#4114yes—
342C59⋊C8—22no—
343C59⋊C8—22no—
344C2×#3402—591nomaximal, Sylow
345C22×C59—42no—
346C22×C59—42no—
347C22×C59—42no—
348C22×C59—84no—
349C22×C59#55012yes—
350C22×C59#57512yes—
351C22×C59#57812yes—
352C22×C59C23×D411yescharacteristic
353C2×D59—42no—
354C2×D59—42no—
355C2×D59—42no—
356C2×D59—84no—
357C4×C59—22no—
358C4×C59—22no—
359C4×C59—42no—
360C4×C59—42no—
361C4×C59—42no—
362C4×C59#55012yes—
363C4×C59C22×#4111yescharacteristic
364C4×C59C2×H(5,𝔽2)11yescharacteristic
365Dic59—22no—
366Dic59—22no—
367Dic59—22no—
368Dic59—22no—
369Dic59—42no—
370Dic59—42no—
371Dic59—42no—
372C2×#556—591no—
373C2×#556—591no—
374#3402—5916no—
375C2×#497—591no—
376C2×#497D5911yescharacteristic, complemented
377C2×#495—591no—
378C2×#464—591no—
379C2×#464—591no—
380C2×#462—591no—
381C2×#462—591no—
382C2×#463—591no—
383C2×#463—591no—
384C2×#446—591no—
385C2×#440—591no—
386C2×#440—591no—
387C2×C4×Q16—591no—
388C2×C59—82no—
389C2×C59#340214yescomplemented
390C2×C59C2×#55011yescharacteristic
391C2×C59C2×#57511yescharacteristic
392C2×C59C2×#57811yescharacteristic
393D59—82no—
394C22×Q16—591no—
395C22×Q16—591no—
396C22×Q16C2×D5911yescharacteristic
397C22×Q16C2×D5911yescharacteristic
398C22×SD16—591no—
399C22×SD16—591no—
400C22×SD16C2×D5911yescharacteristic
401C22×SD16C2×D5911yescharacteristic
402C22×D8—591no—
403#556—598no—
404#556—598no—
405#556—1184no—
406#556—1184no—
407C2×C4⋊Q8—591no—
408C2×C4⋊Q8C2×D5911yescharacteristic
409C2×#126—1181no—
410C2×#126—1181no—
411C2×#126—1181no—
412C2×#126—1181no—
413C2×#124—591no—
414C2×#124—591no—
415C2×#124—591no—
416C2×#124C2×D5911yescharacteristic
417C2×C22⋊Q8—1181no—
418C2×C22⋊Q8—1181no—
419C2×C4×Q8—591no—
420C2×C4×Q8—591no—
421C2×C4×Q8—591no—
422C2×C4×Q8—591no—
423C2×C4×Q8—591no—
424C2×C4×D4—591no—
425C2×C4×D4—591no—
426C2×#117—1181no—
427C2×#117—1181no—
428#497—598no—
429#497C2×D5918yescomplemented
430#495—598no—
431#464—598no—
432#464—598no—
433#463—598no—
434#463—598no—
435#462—598no—
436#462—598no—
437#446—598no—
438#440—598no—
439#440—598no—
440C4×Q16—598no—
441C2×#107—591no—
442C2×C4⋊C8—591no—
443C2×C4⋊C8—591no—
444C2×C4⋊C8—591no—
445C2×#103—591no—
446C2×#103—591no—
447C2×#103—591no—
448C2×#103—591no—
449C2×#102—591no—
450C2×#102—591no—
451C2×#97—591no—
452C2×#97C2×D5911yescharacteristic
453C2×C4×C8—591no—
454C59C2×#340211yescharacteristic, complemented, Sylow
455C22×Q8—591no—
456C22×Q8—591no—
457C22×Q8C22×D5911yescharacteristic
458C22×Q8C22×D5911yescharacteristic
459C22×Q8C22×D5911yescharacteristic
460C22×D4—591no—
461C22×D4C22×D5911yescharacteristic
462C23×C4—1181no—
463C23×C4—1181no—
464C2×Q16—24no—
465C2×Q16—42no—
466C2×Q16—594no—
467C2×Q16—594no—
468C2×Q16—2362no—
469C2×Q16—2362no—
470C2×Q16C22×D5914yes—
471C2×Q16C22×D5914yes—
472C2×SD16—24no—
473C2×SD16—42no—
474C2×SD16—594no—
475C2×SD16—594no—
476C2×SD16—1184no—
477C2×SD16—2362no—
478C2×SD16C22×D5914yes—
479C2×SD16C22×D5914yes—
480C2×D8—594no—
481C2×D8—2362no—
482C22×C8—591no—
483C22×C8—591no—
484C22×C8C22×D5911yescharacteristic
485C22×C8C22×D5911yescharacteristic
486C4⋊Q8—22no—
487C4⋊Q8—594no—
488C4⋊Q8—1182no—
489C4⋊Q8C22×D5914yes—
490#126—1188no—
491#126—1188no—
492#126—1188no—
493#126—1188no—
494#124—22no—
495#124—594no—
496#124—594no—
497#124—594no—
498#124—1182no—
499#124—1182no—
500#124—1182no—
501#124C22×D5914yes—
502C22⋊Q8—1188no—
503C22⋊Q8—1188no—
504C4×Q8—594no—
505C4×Q8—594no—
506C4×Q8—594no—
507C4×Q8—594no—
508C4×Q8—594no—
509C4×Q8—594no—
510C4×Q8—1182no—
511C4×Q8—1182no—
512C4×Q8—1182no—
513C4×Q8—1182no—
514C4×D4—594no—
515C4×D4—594no—
516C4×D4—1182no—
517C4×D4—1182no—
518#117—1188no—
519#117—1188no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—591no—
523C2×C4⋊C4—591no—
524C2×C4⋊C4—591no—
525C2×C4⋊C4—591no—
526C2×C4⋊C4—591no—
527C2×C4⋊C4—1181no—
528C2×C4⋊C4—1181no—
529C2×C4⋊C4—1181no—
530C2×C4⋊C4—1181no—
531C2×C4⋊C4—1181no—
532C2×C4⋊C4—1181no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—1181no—
536C2×C22⋊C4—1181no—
537C2×C22⋊C4—1181no—
538C2×C22⋊C4—1181no—
539C2×C22⋊C4—1181no—
540C2×C22⋊C4—1181no—
541C2×C22⋊C4—1181no—
542C2×C22⋊C4—1181no—
543C2×C42—591no—
544C2×C42—591no—
545C2×C42—1181no—
546C2×C42—1181no—
547C2×C42—1181no—
548C2×C42—1181no—
549C2×C42C22×D5911yescharacteristic
550#107—594no—
551C4⋊C8—594no—
552C4⋊C8—594no—
553C4⋊C8—594no—
554#103—594no—
555#103—594no—
556#103—594no—
557#103—594no—
558#102—594no—
559#102—594no—
560#97—594no—
561#97C22×D5914yes—
562C4×C8—594no—
563C24—21no—
564C24—1181no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—594no—
575C2×Q8—592no—
576C2×Q8—1181no—
577C2×Q8—1182no—
578C2×Q8—1182no—
579C2×Q8—2362no—
580C2×Q8C23×D5912yes—
581C2×Q8C23×D5912yes—
582C2×Q8C23×D5912yes—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—592no—
587C2×D4—1181no—
588C2×D4—1182no—
589C2×D4—1182no—
590C2×D4C23×D5912yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—591no—
595C22×C4—591no—
596C22×C4—591no—
597C22×C4—591no—
598C22×C4—1184no—
599C22×C4—1181no—
600C22×C4—1181no—
601C22×C4—1181no—
602C22×C4—1184no—
603C22×C4—2364no—
604C22×C4—2364no—
605C22×C4D4×D5911yescharacteristic
606C22×C4D4×D5911yescharacteristic
607C22×C4C23×D5911yescharacteristic
608Q16—28no—
609Q16—44no—
610Q16—2364no—
611Q16—2364no—
612SD16—28no—
613SD16—44no—
614SD16—1188no—
615SD16—2364no—
616D8—2364no—
617C2×C8—22no—
618C2×C8—592no—
619C2×C8—592no—
620C2×C8—1182no—
621C2×C8—1182no—
622C2×C8#1174568714yes—
623C2×C8C23×D5912yes—
624C2×C8C23×D5912yes—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—594no—
628C4⋊C4—594no—
629C4⋊C4—594no—
630C4⋊C4—592no—
631C4⋊C4—592no—
632C4⋊C4—1184no—
633C4⋊C4—1184no—
634C4⋊C4—1184no—
635C4⋊C4—1184no—
636C4⋊C4—1184no—
637C4⋊C4—1181no—
638C4⋊C4—1181no—
639C4⋊C4—1184no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—1184no—
643C22⋊C4—1184no—
644C22⋊C4—1184no—
645C22⋊C4—1184no—
646C22⋊C4—1184no—
647C22⋊C4—1184no—
648C22⋊C4—1184no—
649C22⋊C4—1184no—
650C42—592no—
651C42—592no—
652C42—592no—
653C42—592no—
654C42—1184no—
655C42—1184no—
656C42—1184no—
657C42—1184no—
658C42D4×D5912yes—
659C42C23×D5912yes—
660C23—22no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—1182no—
665C23—2362no—
666C23—2362no—
667C23—2362no—
668C23C2×D4×D5911yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—22no—
673Q8—22no—
674Q8—22no—
675Q8—42no—
676Q8—42no—
677Q8—42no—
678Q8—1182no—
679Q8—1182no—
680Q8—2364no—
681Q8—2362no—
682D4—22no—
683D4—22no—
684D4—42no—
685D4—1182no—
686D4—1182no—
687D4—2362no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—592no—
697C2×C4—592no—
698C2×C4—592no—
699C2×C4—592no—
700C2×C4—1182no—
701C2×C4—1182no—
702C2×C4—1182no—
703C2×C4—1182no—
704C2×C4—1182no—
705C2×C4—1182no—
706C2×C4—1182no—
707C2×C4—2368no—
708C2×C4—2368no—
709C2×C4—2362no—
710C2×C4—2362no—
711C2×C4—2362no—
712C2×C4C2×D4×D5912yes—
713C2×C4C2×D4×D5912yes—
714C2×C4C2×D4×D5911yescharacteristic
715C2×C4C2×#1174568712yes—
716C2×C4#1427377212yes—
717C2×C4C24×D5911yescharacteristic
718C8—22no—
719C8—1182no—
720C8—1182no—
721C8C2×#1174568714yes—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—4724no—
727C22—2362no—
728C22—2362no—
729C22—2362no—
730C22#1683807212yes—
731C22#1683820112yes—
732C22#1683821812yes—
733C22C22×D4×D5911yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—1182no—
740C4—1182no—
741C4—1182no—
742C4—1182no—
743C4—2362no—
744C4—2362no—
745C4—2362no—
746C4#1683807212yes—
747C4C22×#1174568711yescharacteristic
748C4C2×#1427377211yescharacteristic
749C2—82no—
750C2—4722no—
751C2#2143717214yesdirect product factor
752C2C2×#1683807211yescharacteristic
753C2C2×#1683820111yescharacteristic
754C2C2×#1683821811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#497C2
socleC23×C59C22×D4
prime radicalC22×#11745669C22
hypercenterC2×#497D59
hypocenterC59C2×#3402
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. C2×#16838126C2semidirect
2. C2×#16838121C2semidirect
3. #21437172C2direct (N × H)
4. C2×#16837795C2semidirect
6. C2×#16837626C2semidirect
7. C2×#16837622C2semidirect
8. C2×#16837610C2semidirect
9. C2×#16837609C2semidirect
12. C2×#16837530C2semidirect
13. C2×#16837504C2semidirect
14. C2×#16837503C2semidirect
15. C2×Q16×Dic59C2semidirect
16. C2×C59×#497C2semidirect
23. #16838126C22semidirect
25. #16838121C22semidirect
45. #16837795C22semidirect
47. #16837626C22semidirect
48. #16837622C22semidirect
51. #16837610C22semidirect
52. #16837609C22semidirect
53. #16837530C22semidirect
54. #16837504C22semidirect
55. #16837503C22semidirect
56. Q16×Dic59C22semidirect
75. C59×#497C22semidirect
376. C2×#497D59semidirect
389. C2×C59#3402semidirect
429. #497C2×D59semidirect
454. C59C2×#3402semidirect
751. C2#21437172direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381262
C2×#168381212
#214371722
C2×#168377952
C2×#168377832
C2×#168376262
C2×#168376222
C2×#168376102
C2×#168376092
C2×#168376192
C2×#168376142
C2×#168375302
C2×#168375042
C2×#168375032
C2×Q16×Dic592
C2×C59×#4972
C2×#340259