Finite Group Databasebeta

← C2×#21436567 #29467253

Subgroups — C2×#21436567 #29467253

Order 15104.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838096C211yesmaximal, characteristic, complemented
2C2×#16838053C211yesmaximal, characteristic, complemented
3#21436567C2116yesmaximal, direct product factor
4C2×#16837810C211yesmaximal, characteristic, complemented
5C2×#16837722C211yesmaximal, characteristic, complemented
6C2×#16837720C211yesmaximal, characteristic, complemented
7C2×#16837726C211yesmaximal, characteristic, complemented
8C2×#16837717C211yesmaximal, characteristic, complemented
9C2×#16837705C211yesmaximal, characteristic, complemented
10C2×#16837691C211yesmaximal, characteristic, complemented
11C2×#16837655C211yesmaximal, characteristic, complemented
12C2×#16837639C211yesmaximal, characteristic, complemented
13C2×#16837513C211yesmaximal, characteristic, complemented
14C2×#16837471C211yesmaximal, characteristic, complemented
15C2×#106×D59C211yesmaximal, characteristic, complemented
16C2×C59×#428C211yesmaximal, characteristic, complemented
17C22×#11745685—21no—
18C22×D472C2211yescharacteristic
19C22×C8×D59C2211yescharacteristic
20#16838096—24no—
21#16838096C2218yescomplemented
22#16838053—24no—
23#16838053C2218yescomplemented
24C2×#14273726C2211yescharacteristic
25C2×#14273721—21no—
26C2×#14273718C2211yescharacteristic
27C2×#14273712—21no—
28C2×#14273710—21no—
29C2×#14273709—21no—
30C2×#14273705—21no—
31C2×#14273702C2211yescharacteristic
32C2×#14273702C2211yescharacteristic
33C2×#14273701C2211yescharacteristic
34C2×#14273701C2211yescharacteristic
35C2×#14273700—21no—
36C2×C4×D236—21no—
37C2×#14273689C2211yescharacteristic
38C2×#14273689C2211yescharacteristic
39C2×C4×C22⋊D59C2211yescharacteristic
40C2×C4⋊C4×D59C2211yescharacteristic
41C2×C4⋊C4×D59C2211yescharacteristic
42#16837810C2218yescomplemented
43#16837726C2218yescomplemented
44#16837722C2218yescomplemented
45#16837720C2218yescomplemented
46#16837717C2218yescomplemented
47#16837705C2218yescomplemented
48#16837691C2218yescomplemented
49#16837655C2218yescomplemented
50#16837639C2218yescomplemented
51#16837513C2218yescomplemented
52#16837471C2218yescomplemented
53C2×#14273660C2211yescharacteristic
54C2×#14273659C2211yescharacteristic
55C2×#14273658C2211yescharacteristic
56C2×#14273658C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58#106×D59C2218yescomplemented
59C2×Dic59⋊C8C2211yescharacteristic
60C2×#14273649C2211yescharacteristic
61C2×#14273649C2211yescharacteristic
62C2×#14273647C2211yescharacteristic
63C2×#14273647C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×#14273637C2211yescharacteristic
69C22×M16×C59C2211yescharacteristic
70C2×#117×C59C2211yescharacteristic
71C22×C4⋊C4×C59C2211yescharacteristic
72C59×#428C2218yescomplemented
73C2×#107×C59C2211yescharacteristic
74C2×#107×C59C2211yescharacteristic
75C2×#106×C59C2211yescharacteristic
76C2×#106×C59C2211yescharacteristic
77C2×#11745685—28no—
78C2×#11745685—48no—
79C22×Dic118—21no—
80C22×D236—21no—
81C22×D236—21no—
82C22×D236C2311yescharacteristic
83C22×D236C2311yescharacteristic
84C22×C22⋊D59—21no—
85C22×C22⋊D59—21no—
86C22×C22⋊D59D411yescharacteristic
87C22×C4×D59—21no—
88C22×C4×D59—21no—
89C22×C4×D59—21no—
90C22×C4×D59—21no—
91C22×C4×D59C2311yescharacteristic
92C2×D472—24no—
93C2×D472C2314yes—
94C22×C59⋊C8C2311yescharacteristic
95C22×C59⋊C8C2311yescharacteristic
96C2×C8×D59—24no—
97C2×C8×D59C2314yes—
98#14273726—22no—
99#14273726C2314yes—
100#14273721—28no—
101#14273718—22no—
102#14273718C2314yes—
103#14273712—28no—
104#14273710—28no—
105#14273709—28no—
106#14273705—28no—
107#14273702—22no—
108#14273702—22no—
109#14273702C2314yes—
110#14273702C2314yes—
111#14273701—22no—
112#14273701—22no—
113#14273701C2314yes—
114#14273701C2314yes—
115#14273700—28no—
116C4×D236—28no—
117#14273689—22no—
118#14273689—22no—
119#14273689C2314yes—
120#14273689C2314yes—
121C4×C22⋊D59D414yes—
122C4×C22⋊D59C2314yes—
123C2×C4⋊Dic59—21no—
124C2×C4⋊Dic59C2311yescharacteristic
125C2×C4⋊Dic59C2311yescharacteristic
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4D411yescharacteristic
131C4⋊C4×D59—22no—
132C4⋊C4×D59—22no—
133C4⋊C4×D59C2314yes—
134C4⋊C4×D59C2314yes—
135C2×C22⋊Dic59D411yescharacteristic
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4—21no—
142C2×(C2×D59)⋊C4D411yescharacteristic
143C2×C4×Dic59C2311yescharacteristic
144#14273660C2314yes—
145#14273659C2314yes—
146#14273658C2314yes—
147#14273658C2314yes—
148#14273658C2314yes—
149Dic59⋊C8C2314yes—
150#14273649C2314yes—
151#14273649C2314yes—
152#14273647C2314yes—
153#14273647C2314yes—
154#14273647C2314yes—
155#14273647C2314yes—
156C22⋊(C59⋊C8)C2314yes—
157(C2×D59)⋊C8C2314yes—
158#14273637C2314yes—
159C23×C4×C59—21no—
160C23×C4×C59C2311yescharacteristic
161C2×M16×C59—24no—
162C2×M16×C59C2314yes—
163C22×C8×C59C2311yescharacteristic
164C22×C8×C59C2311yescharacteristic
165#117×C59—22no—
166#117×C59C2314yes—
167C2×C4⋊C4×C59—21no—
168C2×C4⋊C4×C59—22no—
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C4⋊C4×C59C2314yes—
174C2×C22⋊C4×C59—21no—
175C2×C42×C59—21no—
176#107×C59C2314yes—
177#107×C59C2314yes—
178#106×C59C2314yes—
179#106×C59C2314yes—
180C24×C59C2×D411yescharacteristic
181C23×D59—21no—
182C23×D59—21no—
183C23×D59C2×D411yescharacteristic
184C22×C4×C59—22no—
185C22×C4×C59—22no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—24no—
191C22×C4×C59—44no—
192C22×C4×C59C2×D411yescharacteristic
193C22×C4×C59C2×D412yes—
194C22×C4×C59C2412yes—
195C22×C4×C59C2411yescharacteristic
196C2×C22⋊D59—24no—
197C2×C22⋊D59—24no—
198C2×C22⋊D59—24no—
199C2×C22⋊D59—44no—
200C2×C22⋊D59—82no—
201C2×C22⋊D59C2×D414yes—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59C2×D411yescharacteristic
205C22×Dic59C2×D411yescharacteristic
206C22×Dic59C2×D411yescharacteristic
207#11745685—432no—
208C2×D236—22no—
209C2×D236—22no—
210C2×D236—22no—
211C2×D236—22no—
212C2×D236—24no—
213C2×D236—24no—
214C2×D236—21no—
215C2×D236—21no—
216C2×D236—44no—
217C2×D236—44no—
218C2×D236C2412yes—
219C2×D236C2412yes—
220C2×C4×D59—22no—
221C2×C4×D59—22no—
222C2×C4×D59—24no—
223C2×C4×D59—24no—
224C2×C4×D59—24no—
225C2×C4×D59—24no—
226C2×C4×D59—44no—
227C2×C4×D59—44no—
228C2×C4×D59—82no—
229C2×C4×D59—82no—
230C2×C4×D59C2×D412yes—
231C2×C4×D59C2412yes—
232C2×Dic118—24no—
233C2×Dic118—44no—
234M16×C59—28no—
235C2×C8×C59—22no—
236C2×C8×C59#4114yescomplemented
237C2×C8×C59C2412yes—
238C2×C8×C59C2412yes—
239C4⋊C4×C59—21no—
240C4⋊C4×C59—21no—
241C4⋊C4×C59—24no—
242C4⋊C4×C59—21no—
243C4⋊C4×C59—21no—
244C4⋊C4×C59C2412yes—
245C4⋊C4×C59C2412yes—
246C4⋊C4×C59C2412yes—
247C4⋊C4×C59C2412yes—
248C22⋊C4×C59—24no—
249C42×C59—24no—
250C22⋊Dic59C2×D414yes—
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—
256(C2×D59)⋊C4—24no—
257(C2×D59)⋊C4C2×D414yes—
258C4⋊Dic59—21no—
259C4⋊Dic59—21no—
260C4⋊Dic59—24no—
261C4⋊Dic59C2412yes—
262C4⋊Dic59C2412yes—
263Dic59⋊C4—24no—
264Dic59⋊C4—24no—
265Dic59⋊C4—24no—
266Dic59⋊C4—24no—
267Dic59⋊C4C2×D414yes—
268C4×Dic59C2×D412yes—
269C4×Dic59C2412yes—
270C2×C59⋊C8—22no—
271C2×C59⋊C8—22no—
272C2×C59⋊C8C2412yes—
273C2×C59⋊C8C2412yes—
274D472—28no—
275C8×D59—28no—
276C23×C59—22no—
277C23×C59—22no—
278C23×C59—22no—
279C23×C59C22×D412yes—
280C23×C59C22×D411yescharacteristic
281C22×D59—22no—
282C22×D59—22no—
283C22×D59—22no—
284C22×D59—22no—
285C22×D59—42no—
286C22×D59—42no—
287C22×D59—42no—
288C22×D59—42no—
289C22×D59—42no—
290C22×D59—42no—
291C22×D59AGL(1,ℤ/8)14yes—
292C22×D59C22×D412yes—
293C2×C4×C59—22no—
294C2×C4×C59—24no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—48no—
302C2×C4×C59—42no—
303C2×C4×C59—42no—
304C2×C4×C59—42no—
305C2×C4×C59—42no—
306C2×C4×C59C22×D412yes—
307C2×C4×C59C22×D411yescharacteristic
308C2×C4×C59C2×#4112yes—
309C2×C4×C592−1+412yes—
310C2×C4×C59C2511yescharacteristic
311C22⋊D59—28no—
312C22⋊D59—48no—
313C22⋊D59—84no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—22no—
318C2×Dic59—22no—
319C2×Dic59—42no—
320C2×Dic59—42no—
321C2×Dic59C22×D412yes—
322C2×Dic59C22×D412yes—
323C2×Dic59C22×D412yes—
324D236—22no—
325D236—22no—
326D236—22no—
327D236—22no—
328D236—48no—
329D236—48no—
330D236—42no—
331D236—42no—
332C4×D59—24no—
333C4×D59—22no—
334C4×D59—22no—
335C4×D59—48no—
336C4×D59—48no—
337C4×D59—84no—
338C4×D59—84no—
339Dic118—48no—
340C8×C59—22no—
341C8×C59C2×#4114yescomplemented
342C59⋊C8—22no—
343C59⋊C8—22no—
344C2×#3345—591nomaximal, Sylow
345C22×C59—22no—
346C22×C59—22no—
347C22×C59—22no—
348C22×C59—44no—
349C22×C59#54712yes—
350C22×C59C2×AGL(1,ℤ/8)12yes—
351C22×C59#57712yes—
352C22×C59C23×D411yescharacteristic
353C2×D59—28no—
354C2×D59—22no—
355C2×D59—22no—
356C2×D59—42no—
357C2×D59—42no—
358C2×D59—42no—
359C2×D59—42no—
360C2×D59—42no—
361C2×D59—42no—
362C2×D59—84no—
363C2×D59—84no—
364C2×D59C2×AGL(1,ℤ/8)14yes—
365C4×C59—22no—
366C4×C59—42no—
367C4×C59—42no—
368C4×C59—42no—
369C4×C59—42no—
370C4×C59#54712yes—
371C4×C59C22×#4111yescharacteristic
372C4×C59C2×2−1+411yescharacteristic
373Dic59—22no—
374Dic59—22no—
375Dic59—22no—
376Dic59—42no—
377Dic59—42no—
378C2×#553—591no—
379C2×#547—591no—
380#3345—5916no—
381C2×#501—591no—
382C2×#481—591no—
383C2×#481—591no—
384C2×#482—591no—
385C2×#480—591no—
386C2×#478—591no—
387C2×#476—591no—
388C2×#469—591no—
389C2×#466—591no—
390C2×#442—591no—
391C2×#435—591no—
392C2×#428D5911yescharacteristic, complemented
393C22×#106—591no—
394C2×C59—42no—
395C2×C59#334514yescomplemented
396C2×C59C2×#54711yescharacteristic
397C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
398C2×C59C2×#57711yescharacteristic
399D59—24no—
400D59—82no—
401D59—82no—
402C22×#41—1181no—
403C22×D8—591no—
404C22×M16C2×D5911yescharacteristic
405C23×C8—591no—
406#553—598no—
407#553—1184no—
408#547—598no—
409#547—1184no—
410C2×C4⋊Q8—591no—
411C2×#126—1181no—
412C2×#125—591no—
413C2×#123—1181no—
414C2×#123—1181no—
415C2×#123—1181no—
416C2×C22⋊Q8—1181no—
417C2×#121—591no—
418C2×#121—591no—
419C2×#121—591no—
420C2×#121—591no—
421C2×#121—1181no—
422C2×C4×D4—591no—
423C2×C4×D4—591no—
424C2×C4×D4—591no—
425C2×C4×D4—1181no—
426C2×#117C2×D5911yescharacteristic
427C22×C4⋊C4—591no—
428C22×C4⋊C4—591no—
429C22×C4⋊C4C2×D5911yescharacteristic
430#501—598no—
431#482—598no—
432#481—598no—
433#481—598no—
434#480—598no—
435#478—598no—
436#476—598no—
437#469—598no—
438#466—598no—
439#442—598no—
440#435—598no—
441#428C2×D5918yescomplemented
442C2×#107—591no—
443C2×#107C2×D5911yescharacteristic
444C2×#107C2×D5911yescharacteristic
445C2×#106—591no—
446C2×#106—591no—
447C2×#106—591no—
448C2×#106—591no—
449C2×#106—598no—
450C2×#106C2×D5911yescharacteristic
451C2×#106C2×D5911yescharacteristic
452C2×C4⋊C8—591no—
453C2×#102—591no—
454C2×#102—591no—
455C2×#102—591no—
456C2×#102—591no—
457C2×#102—591no—
458C2×#102—591no—
459C2×C22⋊C8—591no—
460C2×C22⋊C8—591no—
461C2×#97—591no—
462C59C2×#334511yescharacteristic, complemented, Sylow
463C2×#41—1188no—
464C2×#41—2368no—
465C22×Q8—1181no—
466C22×D4—591no—
467C22×D4—591no—
468C22×D4—591no—
469C22×D4—1181no—
470C22×D4—1181no—
471C22×D4—1181no—
472C22×D4—1181no—
473C23×C4—21no—
474C23×C4—591no—
475C23×C4—1181no—
476C23×C4—1181no—
477C23×C4—1181no—
478C23×C4—1181no—
479C23×C4C22×D5911yescharacteristic
480C2×D8—594no—
481C2×D8—1184no—
482C2×M16—24no—
483C2×M16C22×D5914yes—
484C22×C8—591no—
485C22×C8—591no—
486C22×C8—594no—
487C22×C8—1184no—
488C22×C8C22×D5911yescharacteristic
489C22×C8C22×D5911yescharacteristic
490C4⋊Q8—594no—
491C4⋊Q8—1182no—
492#126—1188no—
493#125—594no—
494#125—1182no—
495#123—1188no—
496#123—1188no—
497#123—1188no—
498C22⋊Q8—1188no—
499#121—594no—
500#121—594no—
501#121—594no—
502#121—594no—
503#121—1188no—
504#121—1182no—
505#121—1182no—
506#121—1182no—
507#121—1182no—
508C4×D4—594no—
509C4×D4—594no—
510C4×D4—594no—
511C4×D4—594no—
512C4×D4—1188no—
513C4×D4—1182no—
514C4×D4—1182no—
515#117—22no—
516#117C22×D5914yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—591no—
520C2×C4⋊C4—591no—
521C2×C4⋊C4—591no—
522C2×C4⋊C4—594no—
523C2×C4⋊C4—594no—
524C2×C4⋊C4—1182no—
525C2×C4⋊C4—1182no—
526C2×C4⋊C4—1181no—
527C2×C4⋊C4—1181no—
528C2×C4⋊C4—1181no—
529C2×C4⋊C4—1181no—
530C2×C4⋊C4—1181no—
531C2×C4⋊C4C22×D5911yescharacteristic
532C2×C4⋊C4C22×D5911yescharacteristic
533C2×C4⋊C4C22×D5911yescharacteristic
534C2×C4⋊C4C22×D5914yes—
535C2×C4⋊C4C22×D5911yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—591no—
538C2×C22⋊C4—591no—
539C2×C22⋊C4—1181no—
540C2×C22⋊C4—1181no—
541C2×C22⋊C4—1181no—
542C2×C22⋊C4—1181no—
543C2×C22⋊C4—1181no—
544C2×C22⋊C4—1181no—
545C2×C42—21no—
546C2×C42—591no—
547#107—594no—
548#107C22×D5914yes—
549#107C22×D5914yes—
550#106—594no—
551#106—594no—
552#106—594no—
553#106—594no—
554#106C22×D5914yes—
555#106C22×D5914yes—
556C4⋊C8—594no—
557#102—594no—
558#102—594no—
559#102—594no—
560#102—594no—
561#102—594no—
562#102—594no—
563C22⋊C8—594no—
564C22⋊C8—594no—
565#97—594no—
566C24—591no—
567C24—1181no—
568C24—1181no—
569C24D4×D5911yescharacteristic
570#41—23632no—
571C2×Q8—1184no—
572C2×Q8—2364no—
573C2×D4—594no—
574C2×D4—592no—
575C2×D4—592no—
576C2×D4—1184no—
577C2×D4—1184no—
578C2×D4—1184no—
579C2×D4—1184no—
580C2×D4—1184no—
581C2×D4—1181no—
582C2×D4—1181no—
583C2×D4—1182no—
584C2×D4—1182no—
585C2×D4—1182no—
586C2×D4—1182no—
587C2×D4—4722no—
588C2×D4—2364no—
589C2×D4—2364no—
590C2×D4—2364no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—24no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—44no—
599C22×C4—591no—
600C22×C4—591no—
601C22×C4—591no—
602C22×C4—592no—
603C22×C4—592no—
604C22×C4—1184no—
605C22×C4—1184no—
606C22×C4—1184no—
607C22×C4—1184no—
608C22×C4—1182no—
609C22×C4—1182no—
610C22×C4—1181no—
611C22×C4—1181no—
612C22×C4—4722no—
613C22×C4—4722no—
614C22×C4—2364no—
615C22×C4—2364no—
616C22×C4D4×D5912yes—
617C22×C4D4×D5911yescharacteristic
618C22×C4C23×D5912yes—
619C22×C4C23×D5911yescharacteristic
620D8—1188no—
621M16—28no—
622C2×C8—22no—
623C2×C8—592no—
624C2×C8—592no—
625C2×C8—1182no—
626C2×C8—1182no—
627C2×C8—1188no—
628C2×C8#1174568514yescomplemented
629C2×C8C23×D5912yes—
630C2×C8C23×D5912yes—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—594no—
637C4⋊C4—592no—
638C4⋊C4—592no—
639C4⋊C4—1184no—
640C4⋊C4—1184no—
641C4⋊C4—1184no—
642C4⋊C4—1184no—
643C4⋊C4—1184no—
644C4⋊C4—1181no—
645C4⋊C4—1181no—
646C4⋊C4C23×D5912yes—
647C4⋊C4C23×D5912yes—
648C4⋊C4C23×D5912yes—
649C4⋊C4C23×D5912yes—
650C22⋊C4—24no—
651C22⋊C4—594no—
652C22⋊C4—594no—
653C22⋊C4—1184no—
654C22⋊C4—1184no—
655C22⋊C4—1184no—
656C22⋊C4—1184no—
657C22⋊C4—1184no—
658C22⋊C4—1184no—
659C42—24no—
660C42—592no—
661C42—592no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—594no—
666C23—592no—
667C23—1182no—
668C23—1182no—
669C23—1182no—
670C23—1182no—
671C23—2362no—
672C23—2362no—
673C23—2362no—
674C23—2362no—
675C23—2362no—
676C23—2362no—
677C23C2×D4×D5912yes—
678C23C2×D4×D5911yescharacteristic
679Q8—2368no—
680D4—1188no—
681D4—1182no—
682D4—1182no—
683D4—1182no—
684D4—1182no—
685D4—4724no—
686D4—2368no—
687D4—2368no—
688D4—2368no—
689D4—2362no—
690D4—2362no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—48no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—592no—
705C2×C4—592no—
706C2×C4—592no—
707C2×C4—1182no—
708C2×C4—1182no—
709C2×C4—1182no—
710C2×C4—1182no—
711C2×C4—1182no—
712C2×C4—1184no—
713C2×C4—1182no—
714C2×C4—1182no—
715C2×C4—4724no—
716C2×C4—4724no—
717C2×C4—2368no—
718C2×C4—2368no—
719C2×C4—2362no—
720C2×C4—2362no—
721C2×C4C2×D4×D5912yes—
722C2×C4C2×D4×D5911yescharacteristic
723C2×C4C2×#1174568512yes—
724C2×C4#1427377512yes—
725C2×C4C24×D5911yescharacteristic
726C8—22no—
727C8—1182no—
728C8—1182no—
729C8C2×#1174568514yescomplemented
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—594no—
735C22—1182no—
736C22—1182no—
737C22—1188no—
738C22—4724no—
739C22—4724no—
740C22—2362no—
741C22—2362no—
742C22—2362no—
743C22—2362no—
744C22—2362no—
745C22—2362no—
746C22#1683805312yes—
747C22AGL(1,ℤ/8)×D5912yes—
748C22#1683821112yes—
749C22C22×D4×D5911yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—1182no—
756C4—1182no—
757C4—1182no—
758C4—2362no—
759C4—2362no—
760C4#1683805312yes—
761C4C22×#1174568511yescharacteristic
762C4C2×#1427377511yescharacteristic
763C2—42no—
764C2—1184no—
765C2—4722no—
766C2—4722no—
767C2#2143656714yesdirect product factor
768C2C2×#1683805311yescharacteristic
769C2C2×AGL(1,ℤ/8)×D5911yescharacteristic
770C2C2×#1683821111yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#428C2
socleC23×C59C22×D4
hypercenterC2×#428D59
hypocenterC59C2×#3345
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#16838096C2semidirect
2. C2×#16838053C2semidirect
3. #21436567C2direct (N × H)
4. C2×#16837810C2semidirect
5. C2×#16837722C2semidirect
6. C2×#16837720C2semidirect
7. C2×#16837726C2semidirect
8. C2×#16837717C2semidirect
9. C2×#16837705C2semidirect
10. C2×#16837691C2semidirect
11. C2×#16837655C2semidirect
12. C2×#16837639C2semidirect
13. C2×#16837513C2semidirect
14. C2×#16837471C2semidirect
15. C2×#106×D59C2semidirect
16. C2×C59×#428C2semidirect
21. #16838096C22semidirect
23. #16838053C22semidirect
42. #16837810C22semidirect
43. #16837726C22semidirect
44. #16837722C22semidirect
45. #16837720C22semidirect
46. #16837717C22semidirect
47. #16837705C22semidirect
48. #16837691C22semidirect
49. #16837655C22semidirect
50. #16837639C22semidirect
51. #16837513C22semidirect
52. #16837471C22semidirect
58. #106×D59C22semidirect
72. C59×#428C22semidirect
236. C2×C8×C59#41semidirect
341. C8×C59C2×#41semidirect
392. C2×#428D59semidirect
395. C2×C59#3345semidirect
441. #428C2×D59semidirect
462. C59C2×#3345semidirect
628. C2×C8#11745685semidirect
729. C8C2×#11745685semidirect
767. C2#21436567direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380962
C2×#168380532
#214365672
C2×#168378102
C2×#168377222
C2×#168377202
C2×#168377262
C2×#168377172
C2×#168377052
C2×#168376912
C2×#168376552
C2×#168376392
C2×#168375132
C2×#168374712
C2×#106×D592
C2×C59×#4282
C2×#334559