Finite Group Databasebeta

← C2×#21436537 #29467221

Subgroups — C2×#21436537 #29467221

Order 15104.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838091C211yesmaximal, characteristic, complemented
2C2×#16838053C211yesmaximal, characteristic
3#21436537C2116yesmaximal, direct product factor
4C2×#16837809C211yesmaximal, characteristic, complemented
5C2×#16837737C211yesmaximal, characteristic, complemented
6C2×#16837726C211yesmaximal, characteristic, complemented
7C2×#16837734C211yesmaximal, characteristic, complemented
8C2×#16837717C211yesmaximal, characteristic, complemented
9C2×#16837696C211yesmaximal, characteristic, complemented
10C2×#16837701C211yesmaximal, characteristic, complemented
11C2×#16837648C211yesmaximal, characteristic, complemented
12C2×#16837632C211yesmaximal, characteristic, complemented
13C2×#16837501C211yesmaximal, characteristic, complemented
14C2×#16837471C211yesmaximal, characteristic, complemented
15C2×#107×D59C211yesmaximal, characteristic, complemented
16C2×C59×#428C211yesmaximal, characteristic, complemented
17C22×#11745685—21no—
18C22×#11745660C2211yescharacteristic
19C22×C8×D59C2211yescharacteristic
20#16838091—24no—
21#16838091C2218yescomplemented
22#16838053—24no—
23#16838053C2218yes—
24C2×#14273726C2211yescharacteristic
25C2×#14273720—21no—
26C2×#14273719—21no—
27C2×#14273718C2211yescharacteristic
28C2×#14273712—21no—
29C2×#14273710—21no—
30C2×#14273709—21no—
31C2×#14273707C2211yescharacteristic
32C2×#14273706C2211yescharacteristic
33C2×#14273705—21no—
34C2×#14273702C2211yescharacteristic
35C2×#14273701C2211yescharacteristic
36C2×#14273692C2211yescharacteristic
37C2×#14273689C2211yescharacteristic
38C2×C4×C22⋊D59C2211yescharacteristic
39C2×#14273684—21no—
40C2×C4⋊C4×D59C2211yescharacteristic
41C2×C4⋊C4×D59C2211yescharacteristic
42#16837809C2218yescomplemented
43#16837737C2218yescomplemented
44#16837734C2218yescomplemented
45#16837726C2218yescomplemented
46#16837717C2218yescomplemented
47#16837701C2218yescomplemented
48#16837696C2218yescomplemented
49#16837648C2218yescomplemented
50#16837632C2218yescomplemented
51#16837501C2218yescomplemented
52#16837471C2218yescomplemented
53C2×#14273661C2211yescharacteristic
54C2×#14273660C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57#107×D59C2218yescomplemented
58C2×#14273658C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273650C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
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×Dic118C2311yescharacteristic
81C22×D236—21no—
82C22×D236C2311yescharacteristic
83C22×C22⋊D59—21no—
84C22×C22⋊D59D411yescharacteristic
85C22×C4×D59—21no—
86C22×C4×D59—21no—
87C22×C4×D59—21no—
88C22×C4×D59C2311yescharacteristic
89C2×#11745660—24no—
90C2×#11745660C2314yes—
91C22×C59⋊C8C2311yescharacteristic
92C22×C59⋊C8C2311yescharacteristic
93C2×C8×D59—24no—
94C2×C8×D59C2314yes—
95#14273726—22no—
96#14273726C2314yes—
97#14273720—28no—
98#14273719—28no—
99#14273718—22no—
100#14273718C2314yes—
101#14273712—28no—
102#14273710—28no—
103#14273709—28no—
104#14273707—22no—
105#14273707C2314yes—
106#14273706—22no—
107#14273706C2314yes—
108#14273705—28no—
109#14273702—22no—
110#14273702C2314yes—
111#14273701—22no—
112#14273701C2314yes—
113#14273692—22no—
114#14273692C2314yes—
115#14273689—22no—
116#14273689C2314yes—
117C4×C22⋊D59D414yes—
118C4×C22⋊D59C2314yes—
119#14273684—28no—
120C2×C4⋊Dic59—21no—
121C2×C4⋊Dic59—21no—
122C2×C4⋊Dic59C2311yescharacteristic
123C2×C4⋊Dic59C2311yescharacteristic
124C2×Dic59⋊C4—21no—
125C2×Dic59⋊C4—21no—
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⋊Dic59—21no—
136C2×C22⋊Dic59D411yescharacteristic
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4D411yescharacteristic
142C2×C4×Dic59—21no—
143C2×C4×Dic59C2311yescharacteristic
144#14273661C2314yes—
145#14273660C2314yes—
146#14273660C2314yes—
147#14273660C2314yes—
148#14273658C2314yes—
149Dic59⋊C8C2314yes—
150#14273652C2314yes—
151#14273650C2314yes—
152#14273650C2314yes—
153#14273649C2314yes—
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×D59C2×D411yescharacteristic
183C22×C4×C59—22no—
184C22×C4×C59—22no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—24no—
190C22×C4×C59—44no—
191C22×C4×C59C2×D411yescharacteristic
192C22×C4×C59C2×D412yes—
193C22×C4×C59C2412yes—
194C22×C4×C59C2411yescharacteristic
195C2×C22⋊D59—24no—
196C2×C22⋊D59—24no—
197C2×C22⋊D59—44no—
198C2×C22⋊D59C2×D414yes—
199C22×Dic59—21no—
200C22×Dic59—21no—
201C22×Dic59—21no—
202C22×Dic59C2×D411yescharacteristic
203C22×Dic59C2×D411yescharacteristic
204C22×Dic59C2×D411yescharacteristic
205#11745685—432no—
206C2×D236—22no—
207C2×D236—22no—
208C2×D236—24no—
209C2×D236—21no—
210C2×D236—44no—
211C2×D236C2412yes—
212C2×C4×D59—22no—
213C2×C4×D59—22no—
214C2×C4×D59—24no—
215C2×C4×D59—24no—
216C2×C4×D59—24no—
217C2×C4×D59—44no—
218C2×C4×D59—44no—
219C2×C4×D59—44no—
220C2×C4×D59C2×D412yes—
221C2×C4×D59C2412yes—
222C2×Dic118—22no—
223C2×Dic118—22no—
224C2×Dic118—21no—
225C2×Dic118—24no—
226C2×Dic118—44no—
227C2×Dic118C2412yes—
228M16×C59—28no—
229C2×C8×C59—22no—
230C2×C8×C59#4114yescomplemented
231C2×C8×C59C2412yes—
232C2×C8×C59C2412yes—
233C4⋊C4×C59—21no—
234C4⋊C4×C59—21no—
235C4⋊C4×C59—24no—
236C4⋊C4×C59—21no—
237C4⋊C4×C59—21no—
238C4⋊C4×C59C2412yes—
239C4⋊C4×C59C2412yes—
240C4⋊C4×C59C2412yes—
241C4⋊C4×C59C2412yes—
242C22⋊C4×C59—24no—
243C42×C59—24no—
244C22⋊Dic59—24no—
245C22⋊Dic59C2×D414yes—
246(C2×D59)⋊C4—24no—
247(C2×D59)⋊C4—24no—
248(C2×D59)⋊C4—24no—
249(C2×D59)⋊C4—24no—
250(C2×D59)⋊C4C2×D414yes—
251C4⋊Dic59—21no—
252C4⋊Dic59—21no—
253C4⋊Dic59—24no—
254C4⋊Dic59—24no—
255C4⋊Dic59C2412yes—
256C4⋊Dic59C2412yes—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4—24no—
262Dic59⋊C4—24no—
263Dic59⋊C4C2×D414yes—
264C4×Dic59—24no—
265C4×Dic59C2×D412yes—
266C4×Dic59C2412yes—
267C2×C59⋊C8—22no—
268C2×C59⋊C8—22no—
269C2×C59⋊C8C2412yes—
270C2×C59⋊C8C2412yes—
271#11745660—28no—
272C8×D59—28no—
273C23×C59—22no—
274C23×C59—22no—
275C23×C59—22no—
276C23×C59C22×D412yes—
277C23×C59C22×D411yescharacteristic
278C22×D59—22no—
279C22×D59—22no—
280C22×D59—22no—
281C22×D59—42no—
282C22×D59—42no—
283C22×D59—42no—
284C22×D59AGL(1,ℤ/8)14yes—
285C22×D59C22×D412yes—
286C2×C4×C59—22no—
287C2×C4×C59—24no—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—48no—
295C2×C4×C59—42no—
296C2×C4×C59—42no—
297C2×C4×C59—42no—
298C2×C4×C59—42no—
299C2×C4×C59C22×D412yes—
300C2×C4×C59C22×D411yescharacteristic
301C2×C4×C59C2×#4112yes—
302C2×C4×C592−1+412yes—
303C2×C4×C59C2511yescharacteristic
304C22⋊D59—28no—
305C22⋊D59—48no—
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×Dic59C22×D412yes—
316C2×Dic59C22×D412yes—
317C2×Dic59C22×D412yes—
318D236—22no—
319D236—22no—
320D236—48no—
321D236—42no—
322C4×D59—24no—
323C4×D59—22no—
324C4×D59—22no—
325C4×D59—48no—
326C4×D59—48no—
327C4×D59—48no—
328Dic118—22no—
329Dic118—22no—
330Dic118—48no—
331Dic118—42no—
332C8×C59—22no—
333C8×C59C2×#4114yescomplemented
334C59⋊C8—22no—
335C59⋊C8—22no—
336C2×#3343—591nomaximal, Sylow
337C22×C59—22no—
338C22×C59—22no—
339C22×C59—22no—
340C22×C59—44no—
341C22×C59#54712yes—
342C22×C59C2×AGL(1,ℤ/8)12yes—
343C22×C59#57812yes—
344C22×C59C23×D411yescharacteristic
345C2×D59—28no—
346C2×D59—22no—
347C2×D59—22no—
348C2×D59—42no—
349C2×D59—42no—
350C2×D59—42no—
351C2×D59—84no—
352C2×D59C2×AGL(1,ℤ/8)14yes—
353C4×C59—22no—
354C4×C59—42no—
355C4×C59—42no—
356C4×C59—42no—
357C4×C59—42no—
358C4×C59#54712yes—
359C4×C59C22×#4111yescharacteristic
360C4×C59C2×2−1+411yescharacteristic
361Dic59—22no—
362Dic59—22no—
363Dic59—22no—
364Dic59—42no—
365Dic59—42no—
366Dic59—42no—
367C2×#552—591no—
368C2×#547—591no—
369#3343—5916no—
370C2×#501—591no—
371C2×#484—591no—
372C2×#482—591no—
373C2×#483—591no—
374C2×#480—591no—
375C2×#477—591no—
376C2×#478—591no—
377C2×#468—591no—
378C2×#465—591no—
379C2×#440—591no—
380C2×#435—591no—
381C2×#428D5911yescharacteristic, complemented
382C22×#107—591no—
383C2×C59—42no—
384C2×C59#334314yescomplemented
385C2×C59C2×#54711yescharacteristic
386C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
387C2×C59C2×#57811yescharacteristic
388D59—24no—
389D59—82no—
390C22×#41—1181no—
391C22×SD16—591no—
392C22×M16C2×D5911yescharacteristic
393C23×C8—591no—
394#552—598no—
395#552—1184no—
396#547—598no—
397#547—1184no—
398C2×C4⋊Q8—591no—
399C2×#126—1181no—
400C2×#125—591no—
401C2×#125—1181no—
402C2×#123—1181no—
403C2×#123—1181no—
404C2×#123—1181no—
405C2×C22⋊Q8—591no—
406C2×C22⋊Q8—591no—
407C2×C22⋊Q8—1181no—
408C2×#121—591no—
409C2×#121—591no—
410C2×C4×Q8—591no—
411C2×C4×D4—591no—
412C2×C4×D4—591no—
413C2×#117—1181no—
414C2×#117C2×D5911yescharacteristic
415C22×C4⋊C4—591no—
416C22×C4⋊C4—591no—
417C22×C4⋊C4C2×D5911yescharacteristic
418#501—598no—
419#484—598no—
420#483—598no—
421#482—598no—
422#480—598no—
423#478—598no—
424#477—598no—
425#468—598no—
426#465—598no—
427#440—598no—
428#435—598no—
429#428C2×D5918yescomplemented
430C2×#107—591no—
431C2×#107—591no—
432C2×#107—591no—
433C2×#107—591no—
434C2×#107—598no—
435C2×#107C2×D5911yescharacteristic
436C2×#107C2×D5911yescharacteristic
437C2×#106—591no—
438C2×#106C2×D5911yescharacteristic
439C2×#106C2×D5911yescharacteristic
440C2×C4⋊C8—591no—
441C2×#103—591no—
442C2×#103—591no—
443C2×#103—591no—
444C2×#102—591no—
445C2×#102—591no—
446C2×#102—591no—
447C2×C22⋊C8—591no—
448C2×C22⋊C8—591no—
449C2×#97—591no—
450C59C2×#334311yescharacteristic, complemented, Sylow
451C2×#41—1188no—
452C2×#41—2368no—
453C22×Q8—591no—
454C22×Q8—1181no—
455C22×D4—591no—
456C22×D4—591no—
457C22×D4—1181no—
458C22×D4—1181no—
459C23×C4—21no—
460C23×C4—591no—
461C23×C4—1181no—
462C23×C4—1181no—
463C23×C4—1181no—
464C23×C4C22×D5911yescharacteristic
465C2×SD16—594no—
466C2×SD16—1184no—
467C2×M16—24no—
468C2×M16C22×D5914yes—
469C22×C8—591no—
470C22×C8—591no—
471C22×C8—594no—
472C22×C8—1184no—
473C22×C8C22×D5911yescharacteristic
474C22×C8C22×D5911yescharacteristic
475C4⋊Q8—594no—
476C4⋊Q8—1182no—
477#126—1188no—
478#125—594no—
479#125—1188no—
480#125—1182no—
481#123—1188no—
482#123—1188no—
483#123—1188no—
484C22⋊Q8—594no—
485C22⋊Q8—594no—
486C22⋊Q8—1188no—
487C22⋊Q8—1182no—
488C22⋊Q8—1182no—
489#121—594no—
490#121—594no—
491#121—1182no—
492#121—1182no—
493C4×Q8—594no—
494C4×Q8—1182no—
495C4×D4—594no—
496C4×D4—594no—
497C4×D4—594no—
498C4×D4—1182no—
499#117—22no—
500#117—1188no—
501#117C22×D5914yes—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—591no—
505C2×C4⋊C4—591no—
506C2×C4⋊C4—591no—
507C2×C4⋊C4—594no—
508C2×C4⋊C4—594no—
509C2×C4⋊C4—1182no—
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⋊C4C22×D5911yescharacteristic
520C2×C4⋊C4C22×D5911yescharacteristic
521C2×C4⋊C4C22×D5911yescharacteristic
522C2×C4⋊C4C22×D5914yes—
523C2×C4⋊C4C22×D5911yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—591no—
526C2×C22⋊C4—591no—
527C2×C22⋊C4—1181no—
528C2×C22⋊C4—1181no—
529C2×C22⋊C4—1181no—
530C2×C22⋊C4—1181no—
531C2×C22⋊C4—1181no—
532C2×C42—21no—
533C2×C42—591no—
534C2×C42—1181no—
535#107—594no—
536#107—594no—
537#107—594no—
538#107—594no—
539#107C22×D5914yes—
540#107C22×D5914yes—
541#106—594no—
542#106C22×D5914yes—
543#106C22×D5914yes—
544C4⋊C8—594no—
545#103—594no—
546#103—594no—
547#103—594no—
548#102—594no—
549#102—594no—
550#102—594no—
551C22⋊C8—594no—
552C22⋊C8—594no—
553#97—594no—
554C24—591no—
555C24—1181no—
556C24D4×D5911yescharacteristic
557#41—23632no—
558C2×Q8—592no—
559C2×Q8—1184no—
560C2×Q8—1181no—
561C2×Q8—1182no—
562C2×Q8—1182no—
563C2×Q8—2364no—
564C2×D4—594no—
565C2×D4—592no—
566C2×D4—1184no—
567C2×D4—1184no—
568C2×D4—1184no—
569C2×D4—1181no—
570C2×D4—1182no—
571C2×D4—1182no—
572C2×D4—2364no—
573C2×D4—2364no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—44no—
582C22×C4—591no—
583C22×C4—591no—
584C22×C4—591no—
585C22×C4—592no—
586C22×C4—592no—
587C22×C4—1184no—
588C22×C4—1184no—
589C22×C4—1184no—
590C22×C4—1182no—
591C22×C4—1182no—
592C22×C4—1181no—
593C22×C4—1181no—
594C22×C4—1181no—
595C22×C4—2364no—
596C22×C4—2364no—
597C22×C4—2364no—
598C22×C4D4×D5912yes—
599C22×C4D4×D5911yescharacteristic
600C22×C4C23×D5912yes—
601C22×C4C23×D5911yescharacteristic
602SD16—1188no—
603M16—28no—
604C2×C8—22no—
605C2×C8—592no—
606C2×C8—592no—
607C2×C8—1182no—
608C2×C8—1182no—
609C2×C8—1188no—
610C2×C8#1174568514yescomplemented
611C2×C8C23×D5912yes—
612C2×C8C23×D5912yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—594no—
619C4⋊C4—592no—
620C4⋊C4—592no—
621C4⋊C4—1184no—
622C4⋊C4—1184no—
623C4⋊C4—1184no—
624C4⋊C4—1184no—
625C4⋊C4—1184no—
626C4⋊C4—1184no—
627C4⋊C4—1184no—
628C4⋊C4—1181no—
629C4⋊C4—1181no—
630C4⋊C4—1184no—
631C4⋊C4C23×D5912yes—
632C4⋊C4C23×D5912yes—
633C4⋊C4C23×D5912yes—
634C4⋊C4C23×D5912yes—
635C22⋊C4—24no—
636C22⋊C4—594no—
637C22⋊C4—594no—
638C22⋊C4—1184no—
639C22⋊C4—1184no—
640C22⋊C4—1184no—
641C22⋊C4—1184no—
642C22⋊C4—1184no—
643C42—24no—
644C42—592no—
645C42—592no—
646C42—1184no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—594no—
651C23—592no—
652C23—1182no—
653C23—1182no—
654C23—1182no—
655C23—2362no—
656C23—2362no—
657C23—2362no—
658C23C2×D4×D5912yes—
659C23C2×D4×D5911yescharacteristic
660Q8—1182no—
661Q8—1182no—
662Q8—2368no—
663Q8—2362no—
664D4—1188no—
665D4—1182no—
666D4—1182no—
667D4—2368no—
668D4—2368no—
669D4—2362no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—48no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—592no—
684C2×C4—592no—
685C2×C4—592no—
686C2×C4—1182no—
687C2×C4—1182no—
688C2×C4—1182no—
689C2×C4—1182no—
690C2×C4—1182no—
691C2×C4—1184no—
692C2×C4—1182no—
693C2×C4—1182no—
694C2×C4—1182no—
695C2×C4—2368no—
696C2×C4—2368no—
697C2×C4—2368no—
698C2×C4—2362no—
699C2×C4—2362no—
700C2×C4—2362no—
701C2×C4C2×D4×D5912yes—
702C2×C4C2×D4×D5911yescharacteristic
703C2×C4C2×#1174568512yes—
704C2×C4#1427377512yes—
705C2×C4C24×D5911yescharacteristic
706C8—22no—
707C8—1182no—
708C8—1182no—
709C8C2×#1174568514yescomplemented
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—594no—
715C22—1182no—
716C22—1188no—
717C22—1182no—
718C22—4724no—
719C22—2362no—
720C22—2362no—
721C22—2362no—
722C22#1683805312yes—
723C22AGL(1,ℤ/8)×D5912yes—
724C22#1683821812yes—
725C22C22×D4×D5911yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—1182no—
732C4—1182no—
733C4—1182no—
734C4—2362no—
735C4—2362no—
736C4—2362no—
737C4#1683805312yes—
738C4C22×#1174568511yescharacteristic
739C4C2×#1427377511yescharacteristic
740C2—42no—
741C2—1184no—
742C2—4722no—
743C2#2143653714yesdirect product factor
744C2C2×#1683805311yescharacteristic
745C2C2×AGL(1,ℤ/8)×D5911yescharacteristic
746C2C2×#1683821811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#428C2
socleC23×C59C22×D4
prime radicalC2×#16838053C2
hypercenterC2×#428D59
hypocenterC59C2×#3343
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×#16838091C2semidirect
3. #21436537C2direct (N × H)
4. C2×#16837809C2semidirect
5. C2×#16837737C2semidirect
6. C2×#16837726C2semidirect
7. C2×#16837734C2semidirect
8. C2×#16837717C2semidirect
9. C2×#16837696C2semidirect
10. C2×#16837701C2semidirect
11. C2×#16837648C2semidirect
12. C2×#16837632C2semidirect
13. C2×#16837501C2semidirect
14. C2×#16837471C2semidirect
15. C2×#107×D59C2semidirect
16. C2×C59×#428C2semidirect
21. #16838091C22semidirect
42. #16837809C22semidirect
43. #16837737C22semidirect
44. #16837734C22semidirect
45. #16837726C22semidirect
46. #16837717C22semidirect
47. #16837701C22semidirect
48. #16837696C22semidirect
49. #16837648C22semidirect
50. #16837632C22semidirect
51. #16837501C22semidirect
52. #16837471C22semidirect
57. #107×D59C22semidirect
72. C59×#428C22semidirect
230. C2×C8×C59#41semidirect
333. C8×C59C2×#41semidirect
381. C2×#428D59semidirect
384. C2×C59#3343semidirect
429. #428C2×D59semidirect
450. C59C2×#3343semidirect
610. C2×C8#11745685semidirect
709. C8C2×#11745685semidirect
743. C2#21436537direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380912
C2×#168380532
#214365372
C2×#168378092
C2×#168377372
C2×#168377262
C2×#168377342
C2×#168377172
C2×#168376962
C2×#168377012
C2×#168376482
C2×#168376322
C2×#168375012
C2×#168374712
C2×#107×D592
C2×C59×#4282
C2×#334359