Finite Group Databasebeta

← C2×#21434980 #29459377

Subgroups — C2×#21434980 #29459377

Order 15104.

2186 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837980C211yesmaximal, characteristic
2C2×#16837973C211yesmaximal, characteristic, complemented
3#21434980C2116yesmaximal, direct product factor
4C2×#16837738C211yesmaximal, characteristic, complemented
5C2×#16837744C211yesmaximal, characteristic, complemented
6C2×#16837727C211yesmaximal, characteristic, complemented
7C2×#16837733C211yesmaximal, characteristic, complemented
8C2×#16837660C211yesmaximal, characteristic, complemented
9C2×#16837648C211yesmaximal, characteristic, complemented
10C2×#16837643C211yesmaximal, characteristic, complemented
11C2×#16837631C211yesmaximal, characteristic, complemented
12C2×#16837566C211yesmaximal, characteristic, complemented
13C2×#16837566C211yesmaximal, characteristic, complemented
14C2×#16837560C211yesmaximal, characteristic, complemented
15C2×#16837543C211yesmaximal, characteristic, complemented
16C2×C59×#408C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C23×Dic118C2211yescharacteristic
19C22×Dic236C2211yescharacteristic
20C22×Dic236C2211yescharacteristic
21C22×#11745660C2211yescharacteristic
22C22×#11745660C2211yescharacteristic
23#16837980—24no—
24#16837980C2218yes—
25#16837973—24no—
26#16837973C2218yescomplemented
27C2×#14273725—21no—
28C2×#14273714—21no—
29C2×#14273708—21no—
30C2×#14273708—21no—
31C2×#14273706C2211yescharacteristic
32C2×#14273706C2211yescharacteristic
33C2×#14273706C2211yescharacteristic
34C2×#14273706C2211yescharacteristic
35C2×#14273706C2211yescharacteristic
36C2×#14273706C2211yescharacteristic
37C2×#14273703—21no—
38C2×#14273701C2211yescharacteristic
39C2×#14273701C2211yescharacteristic
40C2×#14273699—21no—
41C2×#14273699—21no—
42C2×#14273698—21no—
43C2×#14273686C2211yescharacteristic
44C22×C4⋊Dic59C2211yescharacteristic
45#16837744C2218yescomplemented
46#16837738C2218yescomplemented
47#16837733C2218yescomplemented
48#16837727C2218yescomplemented
49#16837660C2218yescomplemented
50#16837648C2218yescomplemented
51#16837643C2218yescomplemented
52#16837631C2218yescomplemented
53#16837566C2218yescomplemented
54#16837566C2218yescomplemented
55#16837560C2218yescomplemented
56#16837543C2218yescomplemented
57C2×#14273661C2211yescharacteristic
58C2×#14273661C2211yescharacteristic
59C2×#14273659C2211yescharacteristic
60C2×#14273659C2211yescharacteristic
61C2×#14273652C2211yescharacteristic
62C2×#14273652C2211yescharacteristic
63C2×#14273652C2211yescharacteristic
64C2×#14273652C2211yescharacteristic
65C2×#14273652C2211yescharacteristic
66C2×#14273652C2211yescharacteristic
67C2×#14273649C2211yescharacteristic
68C2×#14273649C2211yescharacteristic
69C22×#41×C59C2211yescharacteristic
70C22×M16×C59C2211yescharacteristic
71C23×C8×C59C2211yescharacteristic
72C59×#408C2218yescomplemented
73C2×C22⋊C8×C59C2211yescharacteristic
74C2×C22⋊C8×C59C2211yescharacteristic
75C2×C22⋊C8×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C2×#11745685—22no—
78C2×#11745685—42no—
79C2×#11745685—42no—
80C2×#11745685C2314yes—
81C22×Dic118—21no—
82C22×Dic118—22no—
83C22×Dic118—42no—
84C22×Dic118—42no—
85C22×Dic118C2311yescharacteristic
86C22×Dic118C2311yescharacteristic
87C22×Dic118C2311yescharacteristic
88C22×Dic118C2314yes—
89C22×D236C2311yescharacteristic
90C22×C22⋊D59—21no—
91C22×C22⋊D59—21no—
92C22×C22⋊D59—21no—
93C23×Dic59—21no—
94C23×Dic59—21no—
95C22×C4×D59—21no—
96C2×Dic236—42no—
97C2×Dic236—42no—
98C2×Dic236C2314yes—
99C2×Dic236C2314yes—
100C2×#11745660—42no—
101C2×#11745660—42no—
102C2×#11745660C2314yes—
103C2×#11745660C2314yes—
104#14273725—28no—
105#14273714—28no—
106#14273708—28no—
107#14273708—28no—
108#14273706—22no—
109#14273706—22no—
110#14273706—22no—
111#14273706—22no—
112#14273706—22no—
113#14273706—22no—
114#14273706C2314yes—
115#14273706C2314yes—
116#14273706C2314yes—
117#14273706C2314yes—
118#14273706C2314yes—
119#14273706C2314yes—
120#14273703—28no—
121#14273701—22no—
122#14273701—22no—
123#14273701C2314yes—
124#14273701C2314yes—
125#14273699—28no—
126#14273699—28no—
127#14273698—28no—
128#14273686—22no—
129#14273686C2314yes—
130C2×C4⋊Dic59—21no—
131C2×C4⋊Dic59—22no—
132C2×C4⋊Dic59C2311yescharacteristic
133C2×C4⋊Dic59C2311yescharacteristic
134C2×C4⋊Dic59C2311yescharacteristic
135C2×C4⋊Dic59C2311yescharacteristic
136C2×C4⋊Dic59C2314yes—
137C2×Dic59⋊C4—21no—
138C2×Dic59⋊C4—21no—
139C2×Dic59⋊C4—21no—
140C2×Dic59⋊C4—21no—
141C2×Dic59⋊C4—21no—
142C2×Dic59⋊C4—21no—
143C2×C22⋊Dic59—21no—
144C2×C22⋊Dic59—21no—
145C2×C22⋊Dic59—21no—
146C2×C22⋊Dic59—21no—
147C2×C22⋊Dic59—21no—
148C2×C22⋊Dic59—21no—
149C2×C22⋊Dic59—21no—
150C2×(C2×D59)⋊C4—21no—
151C2×(C2×D59)⋊C4—21no—
152C2×C4×Dic59—21no—
153#14273661C2314yes—
154#14273661C2314yes—
155#14273659C2314yes—
156#14273659C2314yes—
157#14273652C2314yes—
158#14273652C2314yes—
159#14273652C2314yes—
160#14273652C2314yes—
161#14273652C2314yes—
162#14273652C2314yes—
163#14273649C2314yes—
164#14273649C2314yes—
165C2×#41×C59—42no—
166C2×#41×C59—42no—
167C2×#41×C59D414yes—
168C2×#41×C59C2314yes—
169C22×Q8×C59D411yescharacteristic
170C22×D4×C59D411yescharacteristic
171C22×D4×C59D411yescharacteristic
172C22×D4×C59D411yescharacteristic
173C23×C4×C59C2311yescharacteristic
174C23×C4×C59C2311yescharacteristic
175C23×C4×C59C2311yescharacteristic
176C2×M16×C59—42no—
177C2×M16×C59C2314yes—
178C22×C8×C59—42no—
179C22×C8×C59C2311yescharacteristic
180C22×C8×C59C2311yescharacteristic
181C22×C8×C59C2311yescharacteristic
182C22×C8×C59C2311yescharacteristic
183C22×C8×C59C2314yes—
184C22⋊C8×C59C2314yes—
185C22⋊C8×C59C2314yes—
186C22⋊C8×C59C2314yes—
187C22⋊C8×C59C2314yes—
188C24×C59C2×D411yescharacteristic
189C24×C59C2×D411yescharacteristic
190C24×C59C2×D411yescharacteristic
191C23×D59—21no—
192#41×C59—48no—
193#41×C59—44no—
194#41×C59—44no—
195C2×Q8×C59—42no—
196C2×Q8×C59C2×D414yes—
197C2×D4×C59—42no—
198C2×D4×C59—42no—
199C2×D4×C59—42no—
200C2×D4×C59C2×D414yes—
201C2×D4×C59C2×D414yes—
202C2×D4×C59C2×D414yes—
203C22×C4×C59—22no—
204C22×C4×C59—22no—
205C22×C4×C59—22no—
206C22×C4×C59—22no—
207C22×C4×C59—22no—
208C22×C4×C59—22no—
209C22×C4×C59C2×D411yescharacteristic
210C22×C4×C59C2×D411yescharacteristic
211C22×C4×C59C2×D411yescharacteristic
212C22×C4×C59C2×D412yes—
213C22×C4×C59C2×D412yes—
214C22×C4×C59C2×D412yes—
215C22×C4×C59C2412yes—
216C22×C4×C59C2412yes—
217C22×C4×C59C2412yes—
218C22×C4×C59C2411yescharacteristic
219C2×C22⋊D59—24no—
220C2×C22⋊D59—24no—
221C2×C22⋊D59—24no—
222C2×C22⋊D59—44no—
223C2×C22⋊D59—82no—
224C2×C22⋊D59—82no—
225C22×Dic59—21no—
226C22×Dic59—21no—
227C22×Dic59—21no—
228C22×Dic59—21no—
229C22×Dic59—21no—
230C22×Dic59—21no—
231C22×Dic59—21no—
232C22×Dic59—24no—
233C22×Dic59—24no—
234C22×Dic59—44no—
235C22×Dic59—82no—
236#11745685—44no—
237#11745685—44no—
238#11745685—48no—
239C2×D236—22no—
240C2×D236—22no—
241C2×D236—21no—
242C2×D236C2412yes—
243C2×C4×D59—24no—
244C2×C4×D59—44no—
245C2×Dic118—22no—
246C2×Dic118—22no—
247C2×Dic118—22no—
248C2×Dic118—22no—
249C2×Dic118—22no—
250C2×Dic118—22no—
251C2×Dic118—21no—
252C2×Dic118—21no—
253C2×Dic118—21no—
254C2×Dic118—24no—
255C2×Dic118—44no—
256C2×Dic118—44no—
257C2×Dic118—44no—
258C2×Dic118—48no—
259C2×Dic118C2412yes—
260C2×Dic118C2412yes—
261C2×Dic118C2412yes—
262M16×C59—44no—
263C2×C8×C59—22no—
264C2×C8×C59—22no—
265C2×C8×C59—22no—
266C2×C8×C59—22no—
267C2×C8×C59—44no—
268C2×C8×C59C2412yes—
269C2×C8×C59C2412yes—
270C2×C8×C59C2412yes—
271C2×C8×C59C2412yes—
272C22⋊Dic59—24no—
273C22⋊Dic59—24no—
274C22⋊Dic59—24no—
275C22⋊Dic59—24no—
276C22⋊Dic59—24no—
277C22⋊Dic59—24no—
278C22⋊Dic59—24no—
279(C2×D59)⋊C4—24no—
280(C2×D59)⋊C4—24no—
281C4⋊Dic59—24no—
282C4⋊Dic59—21no—
283C4⋊Dic59—21no—
284C4⋊Dic59—21no—
285C4⋊Dic59—21no—
286C4⋊Dic59C2412yes—
287C4⋊Dic59C2412yes—
288C4⋊Dic59C2412yes—
289C4⋊Dic59C2412yes—
290Dic59⋊C4—24no—
291Dic59⋊C4—24no—
292Dic59⋊C4—24no—
293Dic59⋊C4—24no—
294Dic59⋊C4—24no—
295Dic59⋊C4—24no—
296C4×Dic59—24no—
297Dic236—44no—
298Dic236—44no—
299#11745660—44no—
300#11745660—44no—
301C23×C59—22no—
302C23×C59—22no—
303C23×C59—22no—
304C23×C59—22no—
305C23×C59—22no—
306C23×C59—22no—
307C23×C59—22no—
308C23×C59—22no—
309C23×C59—22no—
310C23×C59C22×D412yes—
311C23×C59C22×D412yes—
312C23×C59C22×D412yes—
313C23×C59C22×D411yescharacteristic
314C22×D59—22no—
315C22×D59—42no—
316C22×D59—42no—
317C22×D59—42no—
318Q8×C59—44no—
319D4×C59—44no—
320D4×C59—44no—
321D4×C59—44no—
322C2×C4×C59—22no—
323C2×C4×C59—22no—
324C2×C4×C59—22no—
325C2×C4×C59—24no—
326C2×C4×C59—24no—
327C2×C4×C59—24no—
328C2×C4×C59—22no—
329C2×C4×C59—22no—
330C2×C4×C59—22no—
331C2×C4×C59—22no—
332C2×C4×C59—22no—
333C2×C4×C59—22no—
334C2×C4×C59C22×D412yes—
335C2×C4×C59C22×D412yes—
336C2×C4×C59C22×D412yes—
337C2×C4×C59C22×D411yescharacteristic
338C2×C4×C59H(5,𝔽2)12yes—
339C2×C4×C59H(5,𝔽2)12yes—
340C2×C4×C59C2511yescharacteristic
341C22⋊D59—48no—
342C22⋊D59—84no—
343C22⋊D59—84no—
344C2×Dic59—22no—
345C2×Dic59—22no—
346C2×Dic59—22no—
347C2×Dic59—22no—
348C2×Dic59—22no—
349C2×Dic59—22no—
350C2×Dic59—22no—
351C2×Dic59—48no—
352C2×Dic59—42no—
353C2×Dic59—42no—
354C2×Dic59—42no—
355C2×Dic59—42no—
356C2×Dic59—42no—
357C2×Dic59—42no—
358C2×Dic59—42no—
359C2×Dic59—84no—
360D236—22no—
361D236—22no—
362D236—42no—
363C4×D59—48no—
364Dic118—22no—
365Dic118—22no—
366Dic118—22no—
367Dic118—22no—
368Dic118—22no—
369Dic118—22no—
370Dic118—48no—
371Dic118—42no—
372Dic118—42no—
373Dic118—42no—
374C8×C59—22no—
375C8×C59—22no—
376C8×C59—22no—
377C8×C59—22no—
378C2×#3201—591nomaximal, Sylow
379C22×C59—22no—
380C22×C59—22no—
381C22×C59—22no—
382C22×C59—22no—
383C22×C59—22no—
384C22×C59—22no—
385C22×C59—22no—
386C22×C59—22no—
387C22×C59—22no—
388C22×C59—44no—
389C22×C59—44no—
390C22×C59—44no—
391C22×C59#53412yes—
392C22×C59#57712yes—
393C22×C59#57812yes—
394C22×C59C23×D411yescharacteristic
395C2×D59—42no—
396C2×D59—42no—
397C2×D59—42no—
398C2×D59—84no—
399C4×C59—22no—
400C4×C59—22no—
401C4×C59—22no—
402C4×C59#53412yes—
403C4×C59C2×H(5,𝔽2)11yescharacteristic
404C4×C59C2×H(5,𝔽2)11yescharacteristic
405Dic59—42no—
406Dic59—42no—
407Dic59—42no—
408Dic59—42no—
409Dic59—42no—
410Dic59—42no—
411Dic59—42no—
412C2×#537—591no—
413C2×#536—591no—
414#3201—5916no—
415C2×#484—591no—
416C2×#485—591no—
417C2×#482—591no—
418C2×#483—591no—
419C2×#470—591no—
420C2×#468—591no—
421C2×#467—591no—
422C2×#465—591no—
423C2×#452—591no—
424C2×#452—591no—
425C2×#451—591no—
426C2×#448—591no—
427C2×#408D5911yescharacteristic, complemented
428C2×C59—42no—
429C2×C59—42no—
430C2×C59—42no—
431C2×C59#320114yescomplemented
432C2×C59C2×#53411yescharacteristic
433C2×C59C2×#57711yescharacteristic
434C2×C59C2×#57811yescharacteristic
435D59—82no—
436C22×#41—591no—
437C22×#41C2×D5911yescharacteristic
438C23×Q8—591no—
439C22×Q16—591no—
440C22×Q16—591no—
441C22×SD16—591no—
442C22×SD16—591no—
443C22×M16C2×D5911yescharacteristic
444C23×C8C2×D5911yescharacteristic
445#537—598no—
446#537—1184no—
447#536—598no—
448#536—1184no—
449C2×C4⋊Q8—1181no—
450C2×#124—1181no—
451C2×#123—1181no—
452C2×#123—1181no—
453C2×C22⋊Q8—591no—
454C2×C22⋊Q8—591no—
455C2×C22⋊Q8—591no—
456C2×C22⋊Q8—591no—
457C2×C22⋊Q8—591no—
458C2×C22⋊Q8—591no—
459C2×C22⋊Q8—1181no—
460C2×#121—591no—
461C2×#121—591no—
462C2×#121—1181no—
463C2×#121—1181no—
464C2×#121—1181no—
465C2×#117—591no—
466C22×C4⋊C4—591no—
467#485—598no—
468#484—598no—
469#483—598no—
470#482—598no—
471#470—598no—
472#468—598no—
473#467—598no—
474#465—598no—
475#452—598no—
476#452—598no—
477#451—598no—
478#448—598no—
479C2×#107—591no—
480C2×#107—591no—
481C2×#106—591no—
482C2×#106—591no—
483C2×#103—591no—
484C2×#103—591no—
485C2×#103—591no—
486C2×#103—591no—
487C2×#103—591no—
488C2×#103—591no—
489C2×#102—591no—
490C2×#102—591no—
491#408C2×D5918yescomplemented
492C2×C22⋊C8C2×D5911yescharacteristic
493C2×C22⋊C8C2×D5911yescharacteristic
494C2×C22⋊C8C2×D5911yescharacteristic
495C2×C22⋊C8C2×D5911yescharacteristic
496C59C2×#320111yescharacteristic, complemented, Sylow
497C2×#41—42no—
498C2×#41—42no—
499C2×#41—594no—
500C2×#41—1182no—
501C2×#41—2362no—
502C2×#41—2362no—
503C2×#41D23614yes—
504C2×#41C22×D5914yes—
505C22×Q8—591no—
506C22×Q8—591no—
507C22×Q8—591no—
508C22×Q8—594no—
509C22×Q8—1181no—
510C22×Q8—1182no—
511C22×Q8—2362no—
512C22×Q8—2362no—
513C22×Q8D23611yescharacteristic
514C22×D4—591no—
515C22×D4—1181no—
516C22×D4—1181no—
517C22×D4—1181no—
518C22×D4D23611yescharacteristic
519C22×D4D23611yescharacteristic
520C22×D4D23611yescharacteristic
521C23×C4—1181no—
522C23×C4—1181no—
523C23×C4—1181no—
524C23×C4C22×D5911yescharacteristic
525C23×C4C22×D5911yescharacteristic
526C23×C4C22×D5911yescharacteristic
527C2×Q16—594no—
528C2×Q16—594no—
529C2×Q16—2362no—
530C2×Q16—2362no—
531C2×SD16—594no—
532C2×SD16—594no—
533C2×SD16—2362no—
534C2×SD16—2362no—
535C2×M16—42no—
536C2×M16C22×D5914yes—
537C22×C8—42no—
538C22×C8C22×D5911yescharacteristic
539C22×C8C22×D5911yescharacteristic
540C22×C8C22×D5911yescharacteristic
541C22×C8C22×D5911yescharacteristic
542C22×C8C22×D5914yes—
543C4⋊Q8—1188no—
544#124—1188no—
545#123—1188no—
546#123—1188no—
547C22⋊Q8—594no—
548C22⋊Q8—594no—
549C22⋊Q8—594no—
550C22⋊Q8—594no—
551C22⋊Q8—594no—
552C22⋊Q8—594no—
553C22⋊Q8—1188no—
554C22⋊Q8—1182no—
555C22⋊Q8—1182no—
556C22⋊Q8—1182no—
557C22⋊Q8—1182no—
558C22⋊Q8—1182no—
559C22⋊Q8—1182no—
560#121—594no—
561#121—594no—
562#121—1188no—
563#121—1188no—
564#121—1188no—
565#121—1182no—
566#121—1182no—
567#117—594no—
568#117—1182no—
569C2×C4⋊C4—591no—
570C2×C4⋊C4—591no—
571C2×C4⋊C4—594no—
572C2×C4⋊C4—591no—
573C2×C4⋊C4—591no—
574C2×C4⋊C4—1181no—
575C2×C4⋊C4—1182no—
576C2×C4⋊C4—1181no—
577C2×C4⋊C4—1181no—
578C2×C4⋊C4—1181no—
579C2×C4⋊C4—1181no—
580C2×C4⋊C4—1181no—
581C2×C4⋊C4—1181no—
582C2×C22⋊C4—1181no—
583C2×C22⋊C4—1181no—
584C2×C22⋊C4—1181no—
585C2×C22⋊C4—1181no—
586C2×C22⋊C4—1181no—
587C2×C22⋊C4—1181no—
588C2×C22⋊C4—1181no—
589C2×C22⋊C4—1181no—
590C2×C22⋊C4—1181no—
591C2×C42—1181no—
592#107—594no—
593#107—594no—
594#106—594no—
595#106—594no—
596#103—594no—
597#103—594no—
598#103—594no—
599#103—594no—
600#103—594no—
601#103—594no—
602#102—594no—
603#102—594no—
604C22⋊C8C22×D5914yes—
605C22⋊C8C22×D5914yes—
606C22⋊C8C22×D5914yes—
607C22⋊C8C22×D5914yes—
608C24—1181no—
609C24C2×D23611yescharacteristic
610C24C2×D23611yescharacteristic
611C24C2×D23611yescharacteristic
612#41—48no—
613#41—44no—
614#41—44no—
615#41—2364no—
616#41—2364no—
617#41—2368no—
618C2×Q8—42no—
619C2×Q8—592no—
620C2×Q8—592no—
621C2×Q8—592no—
622C2×Q8—1181no—
623C2×Q8—1181no—
624C2×Q8—1181no—
625C2×Q8—1184no—
626C2×Q8—1182no—
627C2×Q8—1182no—
628C2×Q8—1182no—
629C2×Q8—1182no—
630C2×Q8—1182no—
631C2×Q8—1182no—
632C2×Q8—2364no—
633C2×Q8—2364no—
634C2×Q8—2364no—
635C2×Q8—2368no—
636C2×Q8C2×D23614yes—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—592no—
641C2×D4—1184no—
642C2×D4—1184no—
643C2×D4—1184no—
644C2×D4—1181no—
645C2×D4—1182no—
646C2×D4—1182no—
647C2×D4—4722no—
648C2×D4—4722no—
649C2×D4—2364no—
650C2×D4C2×D23614yes—
651C2×D4C2×D23614yes—
652C2×D4C2×D23614yes—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—1184no—
660C22×C4—1184no—
661C22×C4—1181no—
662C22×C4—1181no—
663C22×C4—1181no—
664C22×C4—1181no—
665C22×C4—1181no—
666C22×C4—1181no—
667C22×C4—1181no—
668C22×C4—1184no—
669C22×C4—4722no—
670C22×C4—2364no—
671C22×C4—2364no—
672C22×C4C2×D23612yes—
673C22×C4C2×D23612yes—
674C22×C4C2×D23612yes—
675C22×C4C2×D23611yescharacteristic
676C22×C4C2×D23611yescharacteristic
677C22×C4C2×D23611yescharacteristic
678C22×C4C23×D5912yes—
679C22×C4C23×D5912yes—
680C22×C4C23×D5912yes—
681C22×C4C23×D5911yescharacteristic
682Q16—2364no—
683Q16—2364no—
684SD16—2364no—
685SD16—2364no—
686M16—44no—
687C2×C8—22no—
688C2×C8—22no—
689C2×C8—22no—
690C2×C8—22no—
691C2×C8—44no—
692C2×C8C23×D5912yes—
693C2×C8C23×D5912yes—
694C2×C8C23×D5912yes—
695C2×C8C23×D5912yes—
696C4⋊C4—592no—
697C4⋊C4—592no—
698C4⋊C4—592no—
699C4⋊C4—592no—
700C4⋊C4—1184no—
701C4⋊C4—1181no—
702C4⋊C4—1181no—
703C4⋊C4—1181no—
704C4⋊C4—1181no—
705C4⋊C4—1184no—
706C4⋊C4—1184no—
707C4⋊C4—1184no—
708C4⋊C4—1184no—
709C4⋊C4—1184no—
710C4⋊C4—1184no—
711C22⋊C4—1184no—
712C22⋊C4—1184no—
713C22⋊C4—1184no—
714C22⋊C4—1184no—
715C22⋊C4—1184no—
716C22⋊C4—1184no—
717C22⋊C4—1184no—
718C22⋊C4—1184no—
719C22⋊C4—1184no—
720C42—1184no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—1182no—
731C23—2362no—
732C23—2362no—
733C23—2362no—
734C23C22×D23612yes—
735C23C22×D23612yes—
736C23C22×D23612yes—
737C23C22×D23611yescharacteristic
738Q8—44no—
739Q8—1182no—
740Q8—1182no—
741Q8—1182no—
742Q8—1182no—
743Q8—1182no—
744Q8—1182no—
745Q8—2368no—
746Q8—2362no—
747Q8—2362no—
748Q8—2362no—
749D4—44no—
750D4—44no—
751D4—44no—
752D4—1182no—
753D4—1182no—
754D4—4724no—
755D4—4724no—
756D4—2368no—
757D4—2362no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—1182no—
771C2×C4—1182no—
772C2×C4—1182no—
773C2×C4—1182no—
774C2×C4—1182no—
775C2×C4—1182no—
776C2×C4—1182no—
777C2×C4—4724no—
778C2×C4—2368no—
779C2×C4—2368no—
780C2×C4—2362no—
781C2×C4—2362no—
782C2×C4—2362no—
783C2×C4—2362no—
784C2×C4—2362no—
785C2×C4—2362no—
786C2×C4—2362no—
787C2×C4C22×D23612yes—
788C2×C4C22×D23612yes—
789C2×C4C22×D23612yes—
790C2×C4C22×D23611yescharacteristic
791C2×C4#1427377212yes—
792C2×C4#1427377212yes—
793C2×C4C24×D5911yescharacteristic
794C8—22no—
795C8—22no—
796C8—22no—
797C8—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—44no—
808C22—44no—
809C22—44no—
810C22—4724no—
811C22—2362no—
812C22—2362no—
813C22—2362no—
814C22#1683796412yes—
815C22#1683821412yes—
816C22#1683821912yes—
817C22C23×D23611yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—2362no—
822C4—2362no—
823C4—2362no—
824C4—2362no—
825C4—2362no—
826C4—2362no—
827C4—2362no—
828C4#1683796412yes—
829C4C2×#1427377211yescharacteristic
830C4C2×#1427377211yescharacteristic
831C2—42no—
832C2—42no—
833C2—42no—
834C2—4722no—
835C2#2143498014yesdirect product factor
836C2C2×#1683796411yescharacteristic
837C2C2×#1683821411yescharacteristic
838C2C2×#1683821911yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#408C2
socleC23×C59C22×D4
prime radicalC2×#16837980C2
hypercenterC2×#408D59
hypocenterC59C2×#3201
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
2. C2×#16837973C2semidirect
3. #21434980C2direct (N × H)
4. C2×#16837738C2semidirect
5. C2×#16837744C2semidirect
6. C2×#16837727C2semidirect
7. C2×#16837733C2semidirect
8. C2×#16837660C2semidirect
9. C2×#16837648C2semidirect
10. C2×#16837643C2semidirect
11. C2×#16837631C2semidirect
12. C2×#16837566C2semidirect
13. C2×#16837566C2semidirect
14. C2×#16837560C2semidirect
15. C2×#16837543C2semidirect
16. C2×C59×#408C2semidirect
26. #16837973C22semidirect
45. #16837744C22semidirect
46. #16837738C22semidirect
47. #16837733C22semidirect
48. #16837727C22semidirect
49. #16837660C22semidirect
50. #16837648C22semidirect
51. #16837643C22semidirect
52. #16837631C22semidirect
53. #16837566C22semidirect
54. #16837566C22semidirect
55. #16837560C22semidirect
56. #16837543C22semidirect
72. C59×#408C22semidirect
427. C2×#408D59semidirect
431. C2×C59#3201semidirect
491. #408C2×D59semidirect
496. C59C2×#3201semidirect
835. C2#21434980direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379802
C2×#168379732
#214349802
C2×#168377382
C2×#168377442
C2×#168377272
C2×#168377332
C2×#168376602
C2×#168376482
C2×#168376432
C2×#168376312
C2×#168375662
C2×#168375602
C2×#168375432
C2×C59×#4082
C2×#320159