Finite Group Databasebeta

← C2×#21436583 #29467270

Subgroups — C2×#21436583 #29467270

Order 15104.

1942 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×#16838109C211yesmaximal, characteristic, complemented
2C2×#16838098C211yesmaximal, characteristic
3#21436583C2116yesmaximal, direct product factor
4C2×#16837811C211yesmaximal, characteristic, complemented
5C2×#16837738C211yesmaximal, characteristic, complemented
6C2×#16837721C211yesmaximal, characteristic, complemented
7C2×#16837744C211yesmaximal, characteristic, complemented
8C2×#16837716C211yesmaximal, characteristic, complemented
9C2×#16837710C211yesmaximal, characteristic, complemented
10C2×#16837683C211yesmaximal, characteristic, complemented
11C2×#16837648C211yesmaximal, characteristic, complemented
12C2×#16837631C211yesmaximal, characteristic, complemented
13C2×#16837504C211yesmaximal, characteristic, complemented
14C2×#16837444C211yesmaximal, characteristic, complemented
15C22×#14273661C211yesmaximal, characteristic, complemented
16C2×C59×#435C211yesmaximal, characteristic, complemented
17C22×#11745660C2211yescharacteristic
18#16838109—24no—
19#16838109C2218yescomplemented
20#16838098—24no—
21#16838098C2218yes—
22C2×#14273727C2211yescharacteristic
23C2×#14273722—21no—
24C2×#14273719C2211yescharacteristic
25C2×#14273718—21no—
26C2×#14273709—21no—
27C2×#14273706C2211yescharacteristic
28C2×#14273706C2211yescharacteristic
29C2×#14273704—21no—
30C2×#14273704—21no—
31C2×#14273701C2211yescharacteristic
32C2×#14273701C2211yescharacteristic
33C2×#14273699—21no—
34C2×C4×Dic118C2211yescharacteristic
35C2×C4×D236C2211yescharacteristic
36C2×D4×Dic59—21no—
37C2×(C22⋊D59)⋊C4—21no—
38C2×#14273686C2211yescharacteristic
39C22×C4⋊Dic59C2211yescharacteristic
40C22×C4⋊Dic59C2211yescharacteristic
41C22×C4⋊Dic59C2211yescharacteristic
42#16837811C2218yescomplemented
43#16837744C2218yescomplemented
44#16837738C2218yescomplemented
45#16837721C2218yescomplemented
46#16837716C2218yescomplemented
47#16837710C2218yescomplemented
48#16837683C2218yescomplemented
49#16837648C2218yescomplemented
50#16837631C2218yescomplemented
51#16837504C2218yescomplemented
52#16837444C2218yescomplemented
53C2×#14273661C2211yescharacteristic
54C2×#14273661C2211yescharacteristic
55C2×#14273661C2211yescharacteristic
56C2×#14273661C2211yescharacteristic
57C2×#14273661C2211yescharacteristic
58C2×#14273661C2211yescharacteristic
59C2×#14273661C2218yescomplemented
60C2×#14273659C2211yescharacteristic
61C2×#14273659C2211yescharacteristic
62C2×#14273659C2211yescharacteristic
63C2×#14273652C2211yescharacteristic
64C2×#14273652C2211yescharacteristic
65C2×#14273652C2211yescharacteristic
66C2×#14273649C2211yescharacteristic
67C2×#14273649C2211yescharacteristic
68C2×#14273649C2211yescharacteristic
69C22×M16×C59C2211yescharacteristic
70C23×C8×C59C2211yescharacteristic
71C2×C4×D4×C59C2211yescharacteristic
72C59×#435C2218yescomplemented
73C2×C4⋊C8×C59C2211yescharacteristic
74C2×C22⋊C8×C59C2211yescharacteristic
75C2×C22⋊C8×C59C2211yescharacteristic
76C2×#97×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C22×D236C2311yescharacteristic
80C22×C22⋊D59—21no—
81C22×C22⋊D59—21no—
82C23×Dic59—21no—
83C23×Dic59—21no—
84C23×Dic59—21no—
85C22×C4×D59—21no—
86C2×#11745660—24no—
87C2×#11745660C2314yes—
88#14273727—22no—
89#14273727C2314yes—
90#14273722—28no—
91#14273719—22no—
92#14273719C2314yes—
93#14273718—28no—
94#14273709—28no—
95#14273706—22no—
96#14273706—22no—
97#14273706C2314yes—
98#14273706C2314yes—
99#14273704—28no—
100#14273704—28no—
101#14273701—22no—
102#14273701—22no—
103#14273701C2314yes—
104#14273701C2314yes—
105#14273699—28no—
106C4×Dic118—22no—
107C4×Dic118C2314yes—
108C4×D236—22no—
109C4×D236C2314yes—
110D4×Dic59—28no—
111(C22⋊D59)⋊C4—28no—
112#14273686—22no—
113#14273686C2314yes—
114C2×C4⋊Dic59—21no—
115C2×C4⋊Dic59—21no—
116C2×C4⋊Dic59—21no—
117C2×C4⋊Dic59—21no—
118C2×C4⋊Dic59—22no—
119C2×C4⋊Dic59—22no—
120C2×C4⋊Dic59—22no—
121C2×C4⋊Dic59C2311yescharacteristic
122C2×C4⋊Dic59C2311yescharacteristic
123C2×C4⋊Dic59C2311yescharacteristic
124C2×C4⋊Dic59C2311yescharacteristic
125C2×C4⋊Dic59C2311yescharacteristic
126C2×C4⋊Dic59C2311yescharacteristic
127C2×C4⋊Dic59C2314yes—
128C2×C4⋊Dic59C2314yes—
129C2×C4⋊Dic59C2314yes—
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⋊Dic59—21no—
137C2×C22⋊Dic59—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×C4×Dic59—21no—
142C2×C4×Dic59—21no—
143#14273661C2314yes—
144#14273661C2314yes—
145#14273661C2314yes—
146#14273661C2314yes—
147#14273661C2314yes—
148#14273661C2314yes—
149#14273659C2314yes—
150#14273659C2314yes—
151#14273659C2314yes—
152#14273652C2314yes—
153#14273652C2314yes—
154#14273652C2314yes—
155#14273649C2314yes—
156#14273649C2314yes—
157#14273649C2314yes—
158C22×D4×C59D411yescharacteristic
159C23×C4×C59C2311yescharacteristic
160C23×C4×C59C2311yescharacteristic
161C2×M16×C59—24no—
162C2×M16×C59C2314yes—
163C22×C8×C59—24no—
164C22×C8×C59C2311yescharacteristic
165C22×C8×C59C2311yescharacteristic
166C22×C8×C59C2311yescharacteristic
167C22×C8×C59C2314yes—
168C22×C8×C59C2311yescharacteristic
169C4×D4×C59D414yes—
170C4×D4×C59C2314yes—
171C2×C4⋊C4×C59D411yescharacteristic
172C2×C22⋊C4×C59D411yescharacteristic
173C2×C22⋊C4×C59D411yescharacteristic
174C2×C42×C59C2311yescharacteristic
175C4⋊C8×C59C2314yes—
176C22⋊C8×C59C2314yes—
177C22⋊C8×C59C2314yes—
178#97×C59C2314yes—
179C24×C59C2×D411yescharacteristic
180C24×C59C2×D411yescharacteristic
181C23×D59—21no—
182C2×D4×C59—24no—
183C2×D4×C59C2×D414yes—
184C22×C4×C59—22no—
185C22×C4×C59—22no—
186C22×C4×C59—22no—
187C22×C4×C59—22no—
188C22×C4×C59C2×D411yescharacteristic
189C22×C4×C59C2×D411yescharacteristic
190C22×C4×C59C2×D411yescharacteristic
191C22×C4×C59C2×D411yescharacteristic
192C22×C4×C59C2×D412yes—
193C22×C4×C59C2×D412yes—
194C22×C4×C59C2412yes—
195C22×C4×C59C2412yes—
196C22×C4×C59C2411yescharacteristic
197C2×C22⋊D59—24no—
198C2×C22⋊D59—24no—
199C2×C22⋊D59—44no—
200C2×C22⋊D59—82no—
201C22×Dic59—21no—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59—21no—
207C22×Dic59—21no—
208C22×Dic59—24no—
209C22×Dic59—24no—
210C22×Dic59—24no—
211C22×Dic59—82no—
212C22×Dic59—82no—
213C22×Dic59—82no—
214C2×D236—22no—
215C2×D236—22no—
216C2×D236—21no—
217C2×D236C2412yes—
218C2×C4×D59—24no—
219C2×C4×D59—82no—
220C2×Dic118—22no—
221C2×Dic118—22no—
222C2×Dic118—21no—
223C2×Dic118—24no—
224C2×Dic118—82no—
225C2×Dic118C2412yes—
226M16×C59—28no—
227C2×C8×C59—22no—
228C2×C8×C59—22no—
229C2×C8×C59—22no—
230C2×C8×C59—28no—
231C2×C8×C59#4114yes—
232C2×C8×C59C2412yes—
233C2×C8×C59C2412yes—
234C2×C8×C59C2412yes—
235C2×C8×C59C2412yes—
236C4⋊C4×C59C2×D414yes—
237C22⋊C4×C59C2×D414yes—
238C22⋊C4×C59C2×D414yes—
239C42×C59C2×D412yes—
240C42×C59C2412yes—
241C22⋊Dic59—24no—
242C22⋊Dic59—24no—
243C22⋊Dic59—24no—
244(C2×D59)⋊C4—24no—
245(C2×D59)⋊C4—24no—
246(C2×D59)⋊C4—24no—
247C4⋊Dic59—21no—
248C4⋊Dic59—21no—
249C4⋊Dic59—21no—
250C4⋊Dic59—24no—
251C4⋊Dic59—24no—
252C4⋊Dic59—21no—
253C4⋊Dic59—21no—
254C4⋊Dic59—24no—
255C4⋊Dic59—24no—
256C4⋊Dic59—21no—
257C4⋊Dic59C2412yes—
258C4⋊Dic59C2412yes—
259C4⋊Dic59C2412yes—
260C4⋊Dic59C2412yes—
261C4⋊Dic59C2412yes—
262C4⋊Dic59C2412yes—
263Dic59⋊C4—24no—
264Dic59⋊C4—24no—
265Dic59⋊C4—24no—
266Dic59⋊C4—24no—
267Dic59⋊C4—24no—
268C4×Dic59—24no—
269C4×Dic59—24no—
270#11745660—28no—
271C23×C59—22no—
272C23×C59—22no—
273C23×C59—22no—
274C23×C59—22no—
275C23×C59—22no—
276C23×C59#13714yes—
277C23×C59C22×D412yes—
278C23×C59C22×D412yes—
279C23×C59C22×D411yescharacteristic
280C22×D59—22no—
281C22×D59—42no—
282C22×D59—42no—
283C22×D59—42no—
284D4×C59—28no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—24no—
290C2×C4×C59—24no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
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×C592−1+412yes—
302C2×C4×C59C2511yescharacteristic
303C22⋊D59—48no—
304C22⋊D59—84no—
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—42no—
319C2×Dic59—84no—
320C2×Dic59—84no—
321C2×Dic59—84no—
322D236—22no—
323D236—22no—
324D236—42no—
325C4×D59—84no—
326Dic118—22no—
327Dic118—22no—
328Dic118—42no—
329Dic118—84no—
330C8×C59—22no—
331C8×C59—22no—
332C8×C59—22no—
333C8×C59C2×#4114yes—
334C2×#3346—591nomaximal, Sylow
335C22×C59—28no—
336C22×C59—22no—
337C22×C59—22no—
338C22×C59—22no—
339C22×C59—22no—
340C22×C59—22no—
341C22×C59—44no—
342C22×C59#54712yes—
343C22×C59C2×#13714yes—
344C22×C59C2×#13712yes—
345C22×C59#57612yes—
346C22×C59C23×D411yescharacteristic
347C2×D59—42no—
348C2×D59—42no—
349C2×D59—42no—
350C2×D59—84no—
351C4×C59—22no—
352C4×C59—22no—
353C4×C59—22no—
354C4×C59—22no—
355C4×C59#54712yes—
356C4×C59C22×#4111yescharacteristic
357C4×C59C2×2−1+411yescharacteristic
358Dic59—42no—
359Dic59—42no—
360Dic59—42no—
361Dic59—42no—
362Dic59—42no—
363Dic59—42no—
364Dic59—42no—
365C2×#554—591no—
366C2×#553—591no—
367#3346—5916no—
368C2×#501—591no—
369C2×#484—591no—
370C2×#481—591no—
371C2×#485—591no—
372C2×#480—591no—
373C2×#479—591no—
374C2×#474—591no—
375C2×#468—591no—
376C2×#465—591no—
377C2×#440—591no—
378C2×#435D5911yescharacteristic, complemented
379C2×#428—591no—
380C22×#107—591no—
381C2×C59—24no—
382C2×C59—42no—
383C2×C59#334614yescomplemented
384C2×C59C2×#54711yescharacteristic
385C2×C59C22×#13711yescharacteristic
386C2×C59C2×#57611yescharacteristic
387D59—82no—
388C22×SD16—591no—
389C22×M16C2×D5911yescharacteristic
390C23×C8C2×D5911yescharacteristic
391#554—598no—
392#554—1184no—
393#553—598no—
394#553—1184no—
395C2×C4⋊Q8—591no—
396C2×#126—1181no—
397C2×#125—591no—
398C2×#125—1181no—
399C2×#123—1181no—
400C2×C22⋊Q8—591no—
401C2×C22⋊Q8—591no—
402C2×C22⋊Q8—1181no—
403C2×C22⋊Q8—1181no—
404C2×#121—591no—
405C2×#121—591no—
406C2×#121—1181no—
407C2×C4×Q8—591no—
408C2×C4×D4—591no—
409C2×C4×D4—1181no—
410C2×C4×D4—1181no—
411C2×C4×D4C2×D5911yescharacteristic
412C2×#117—591no—
413C22×C4⋊C4—591no—
414C22×C4⋊C4—591no—
415C22×C4⋊C4—591no—
416#501—598no—
417#485—598no—
418#484—598no—
419#481—598no—
420#480—598no—
421#479—598no—
422#474—598no—
423#468—598no—
424#465—598no—
425#440—598no—
426#435C2×D5918yescomplemented
427#428—598no—
428C2×#107—591no—
429C2×#107—591no—
430C2×#107—591no—
431C2×#107—591no—
432C2×#107—598no—
433C2×#107—591no—
434C2×#107—591no—
435C2×#106—591no—
436C2×#106—591no—
437C2×#106—591no—
438C2×C4⋊C8C2×D5911yescharacteristic
439C2×#103—591no—
440C2×#103—591no—
441C2×#103—591no—
442C2×#102—591no—
443C2×#102—591no—
444C2×#102—591no—
445C2×C22⋊C8C2×D5911yescharacteristic
446C2×C22⋊C8C2×D5911yescharacteristic
447C2×#97C2×D5911yescharacteristic
448C59C2×#334611yescharacteristic, complemented, Sylow
449C22×Q8—591no—
450C22×Q8—1181no—
451C22×D4—591no—
452C22×D4—1181no—
453C22×D4—1181no—
454C22×D4D23611yescharacteristic
455C23×C4—1181no—
456C23×C4—1181no—
457C23×C4—1181no—
458C23×C4—1181no—
459C23×C4C22×D5911yescharacteristic
460C23×C4C22×D5911yescharacteristic
461C2×SD16—594no—
462C2×SD16—1184no—
463C2×M16—24no—
464C2×M16C22×D5914yes—
465C22×C8—24no—
466C22×C8C22×D5911yescharacteristic
467C22×C8C22×D5914yes—
468C22×C8C22×D5911yescharacteristic
469C22×C8C22×D5911yescharacteristic
470C22×C8C22×D5911yescharacteristic
471C4⋊Q8—594no—
472C4⋊Q8—1182no—
473#126—1188no—
474#125—594no—
475#125—1188no—
476#125—1182no—
477#123—1188no—
478C22⋊Q8—594no—
479C22⋊Q8—594no—
480C22⋊Q8—1182no—
481C22⋊Q8—1182no—
482C22⋊Q8—1188no—
483C22⋊Q8—1188no—
484#121—594no—
485#121—594no—
486#121—1188no—
487#121—1182no—
488#121—1182no—
489C4×Q8—594no—
490C4×Q8—1182no—
491C4×D4—594no—
492C4×D4—1188no—
493C4×D4—1188no—
494C4×D4—1182no—
495C4×D4D23614yes—
496C4×D4C22×D5914yes—
497#117—594no—
498#117—1182no—
499C2×C4⋊C4—591no—
500C2×C4⋊C4—591no—
501C2×C4⋊C4—591no—
502C2×C4⋊C4—591no—
503C2×C4⋊C4—591no—
504C2×C4⋊C4—594no—
505C2×C4⋊C4—594no—
506C2×C4⋊C4—594no—
507C2×C4⋊C4—591no—
508C2×C4⋊C4—1181no—
509C2×C4⋊C4—1181no—
510C2×C4⋊C4—1181no—
511C2×C4⋊C4—1182no—
512C2×C4⋊C4—1182no—
513C2×C4⋊C4—1182no—
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⋊C4D23611yescharacteristic
521C2×C22⋊C4—1181no—
522C2×C22⋊C4—1181no—
523C2×C22⋊C4—1181no—
524C2×C22⋊C4—1181no—
525C2×C22⋊C4—1181no—
526C2×C22⋊C4—1181no—
527C2×C22⋊C4D23611yescharacteristic
528C2×C22⋊C4D23611yescharacteristic
529C2×C42—1181no—
530C2×C42—1181no—
531C2×C42C22×D5911yescharacteristic
532#107—594no—
533#107—594no—
534#107—594no—
535#107—594no—
536#107—594no—
537#107—594no—
538#106—594no—
539#106—594no—
540#106—594no—
541C4⋊C8C22×D5914yes—
542#103—594no—
543#103—594no—
544#103—594no—
545#102—594no—
546#102—594no—
547#102—594no—
548C22⋊C8C22×D5914yes—
549C22⋊C8C22×D5914yes—
550#97C22×D5914yes—
551C24—1181no—
552C24C2×D23611yescharacteristic
553C24C2×D23611yescharacteristic
554C2×Q8—592no—
555C2×Q8—1184no—
556C2×Q8—1181no—
557C2×Q8—1182no—
558C2×Q8—1182no—
559C2×Q8—4722no—
560C2×D4—24no—
561C2×D4—592no—
562C2×D4—1184no—
563C2×D4—1184no—
564C2×D4—1181no—
565C2×D4—1182no—
566C2×D4—1182no—
567C2×D4—4722no—
568C2×D4—2364no—
569C2×D4C2×D23614yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—1184no—
575C22×C4—1184no—
576C22×C4—1184no—
577C22×C4—1181no—
578C22×C4—1181no—
579C22×C4—1181no—
580C22×C4—1181no—
581C22×C4—1181no—
582C22×C4—1181no—
583C22×C4—1181no—
584C22×C4—1184no—
585C22×C4—4722no—
586C22×C4—4722no—
587C22×C4—4722no—
588C22×C4—4722no—
589C22×C4C2×D23612yes—
590C22×C4C2×D23612yes—
591C22×C4C2×D23611yescharacteristic
592C22×C4C2×D23611yescharacteristic
593C22×C4C2×D23611yescharacteristic
594C22×C4C2×D23611yescharacteristic
595C22×C4C23×D5912yes—
596C22×C4C23×D5912yes—
597C22×C4C23×D5911yescharacteristic
598SD16—1188no—
599M16—28no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—28no—
604C2×C8#1174568714yes—
605C2×C8C23×D5912yes—
606C2×C8C23×D5912yes—
607C2×C8C23×D5912yes—
608C2×C8C23×D5912yes—
609C4⋊C4—592no—
610C4⋊C4—592no—
611C4⋊C4—592no—
612C4⋊C4—592no—
613C4⋊C4—592no—
614C4⋊C4—592no—
615C4⋊C4—1181no—
616C4⋊C4—1181no—
617C4⋊C4—1181no—
618C4⋊C4—1184no—
619C4⋊C4—1184no—
620C4⋊C4—1181no—
621C4⋊C4—1181no—
622C4⋊C4—1184no—
623C4⋊C4—1181no—
624C4⋊C4—1184no—
625C4⋊C4—1184no—
626C4⋊C4—1184no—
627C4⋊C4—1184no—
628C4⋊C4—1184no—
629C4⋊C4—1184no—
630C4⋊C4C2×D23614yes—
631C22⋊C4—1184no—
632C22⋊C4—1184no—
633C22⋊C4—1184no—
634C22⋊C4—1184no—
635C22⋊C4—1184no—
636C22⋊C4—1184no—
637C22⋊C4C2×D23614yes—
638C22⋊C4C2×D23614yes—
639C42—1184no—
640C42—1184no—
641C42C2×D23612yes—
642C42C23×D5912yes—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—1182no—
649C23—2362no—
650C23—2362no—
651C23—2362no—
652C23#1427376014yes—
653C23C22×D23612yes—
654C23C22×D23612yes—
655C23C22×D23611yescharacteristic
656Q8—1182no—
657Q8—1182no—
658Q8—4724no—
659Q8—2362no—
660D4—28no—
661D4—1182no—
662D4—1182no—
663D4—4724no—
664D4—2368no—
665D4—2362no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—1182no—
677C2×C4—1182no—
678C2×C4—1182no—
679C2×C4—1182no—
680C2×C4—1182no—
681C2×C4—1182no—
682C2×C4—1182no—
683C2×C4—4724no—
684C2×C4—4724no—
685C2×C4—4724no—
686C2×C4—4724no—
687C2×C4—2362no—
688C2×C4—2362no—
689C2×C4—2362no—
690C2×C4—2362no—
691C2×C4—2362no—
692C2×C4—2362no—
693C2×C4—2362no—
694C2×C4C22×D23612yes—
695C2×C4C22×D23612yes—
696C2×C4C22×D23612yes—
697C2×C4C22×D23612yes—
698C2×C4C22×D23611yescharacteristic
699C2×C4C2×#1174568712yes—
700C2×C4#1427377412yes—
701C2×C4C24×D5911yescharacteristic
702C8—22no—
703C8—22no—
704C8—22no—
705C8C2×#1174568714yes—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—4724no—
714C22—2362no—
715C22—2362no—
716C22—2362no—
717C22#1683805612yes—
718C22C2×#1427376014yes—
719C22C2×#1427376012yes—
720C22#1683820712yes—
721C22C23×D23611yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—2362no—
727C4—2362no—
728C4—2362no—
729C4—2362no—
730C4—2362no—
731C4—2362no—
732C4—2362no—
733C4#1683805612yes—
734C4C22×#1174568711yescharacteristic
735C4C2×#1427377411yescharacteristic
736C2—24no—
737C2—42no—
738C2—4722no—
739C2#2143658314yesdirect product factor
740C2C2×#1683805611yescharacteristic
741C2C22×#1427376011yescharacteristic
742C2C2×#1683820711yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#435C2
socleC23×C59C22×D4
prime radicalC2×#16838098C2
hypercenterC2×#435D59
hypocenterC59C2×#3346
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#16838109C2semidirect
3. #21436583C2direct (N × H)
4. C2×#16837811C2semidirect
5. C2×#16837738C2semidirect
6. C2×#16837721C2semidirect
7. C2×#16837744C2semidirect
8. C2×#16837716C2semidirect
9. C2×#16837710C2semidirect
10. C2×#16837683C2semidirect
11. C2×#16837648C2semidirect
12. C2×#16837631C2semidirect
13. C2×#16837504C2semidirect
14. C2×#16837444C2semidirect
15. C22×#14273661C2semidirect
16. C2×C59×#435C2semidirect
19. #16838109C22semidirect
42. #16837811C22semidirect
43. #16837744C22semidirect
44. #16837738C22semidirect
45. #16837721C22semidirect
46. #16837716C22semidirect
47. #16837710C22semidirect
48. #16837683C22semidirect
49. #16837648C22semidirect
50. #16837631C22semidirect
51. #16837504C22semidirect
52. #16837444C22semidirect
59. C2×#14273661C22semidirect
72. C59×#435C22semidirect
378. C2×#435D59semidirect
383. C2×C59#3346semidirect
426. #435C2×D59semidirect
448. C59C2×#3346semidirect
739. C2#21436583direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381092
C2×#168380982
#214365832
C2×#168378112
C2×#168377382
C2×#168377212
C2×#168377442
C2×#168377162
C2×#168377102
C2×#168376832
C2×#168376482
C2×#168376312
C2×#168375042
C2×#168374442
C22×#142736612
C2×C59×#4352
C2×#334659