Finite Group Databasebeta

← C2×#21434950 #29459344

Subgroups — C2×#21434950 #29459344

Order 15104.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837980C211yesmaximal, characteristic, complemented
2C2×#16837966C211yesmaximal, characteristic, complemented
3#21434950C2116yesmaximal, direct product factor
4C2×#16837721C211yesmaximal, characteristic, complemented
5C2×#16837744C211yesmaximal, characteristic, complemented
6C2×#16837727C211yesmaximal, characteristic, complemented
7C2×#16837716C211yesmaximal, characteristic, complemented
8C2×#16837655C211yesmaximal, characteristic, complemented
9C2×#16837648C211yesmaximal, characteristic, complemented
10C2×#16837638C211yesmaximal, characteristic, complemented
11C2×#16837631C211yesmaximal, characteristic, complemented
12C2×#16837549C211yesmaximal, characteristic, complemented
13C2×#16837549C211yesmaximal, characteristic, complemented
14C2×#16837555C211yesmaximal, characteristic, complemented
15C2×#16837538C211yesmaximal, characteristic, complemented
16C2×C59×#408C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic, complemented
18C23×D236C2211yescharacteristic
19C22×#11745660C2211yescharacteristic
20C22×#11745660C2211yescharacteristic
21C22×D472C2211yescharacteristic
22C22×D472C2211yescharacteristic
23#16837980—24no—
24#16837980C2218yescomplemented
25#16837966—24no—
26#16837966C2218yescomplemented
27C2×#14273723—21no—
28C2×#14273716—21no—
29C2×#14273706C2211yescharacteristic
30C2×#14273706C2211yescharacteristic, complemented
31C2×#14273703—21no—
32C2×#14273701C2211yescharacteristic
33C2×#14273701C2211yescharacteristic
34C2×#14273701C2211yescharacteristic
35C2×#14273701C2211yescharacteristic
36C2×#14273701C2211yescharacteristic
37C2×#14273701C2211yescharacteristic, complemented
38C2×#14273699—21no—
39C2×#14273699—21no—
40C2×#14273698—21no—
41C2×#14273695—21no—
42C2×#14273695—21no—
43C2×#14273686C2211yescharacteristic
44C22×C4⋊Dic59C2211yescharacteristic, complemented
45#16837744C2218yescomplemented
46#16837727C2218yescomplemented
47#16837721C2218yescomplemented
48#16837716C2218yescomplemented
49#16837655C2218yescomplemented
50#16837648C2218yescomplemented
51#16837638C2218yescomplemented
52#16837631C2218yescomplemented
53#16837555C2218yescomplemented
54#16837549C2218yescomplemented
55#16837549C2218yescomplemented
56#16837538C2218yescomplemented
57C2×#14273661C2211yescharacteristic, complemented
58C2×#14273661C2211yescharacteristic, complemented
59C2×#14273659C2211yescharacteristic, complemented
60C2×#14273659C2211yescharacteristic, complemented
61C2×#14273652C2211yescharacteristic, complemented
62C2×#14273652C2211yescharacteristic, complemented
63C2×#14273649C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273649C2211yescharacteristic
66C2×#14273649C2211yescharacteristic
67C2×#14273649C2211yescharacteristic, complemented
68C2×#14273649C2211yescharacteristic, complemented
69C22×#41×C59C2211yescharacteristic
70C22×M16×C59C2211yescharacteristic, complemented
71C23×C8×C59C2211yescharacteristic, complemented
72C59×#408C2218yescomplemented
73C2×C22⋊C8×C59C2211yescharacteristic
74C2×C22⋊C8×C59C2211yescharacteristic
75C2×C22⋊C8×C59C2211yescharacteristic, complemented
76C2×C22⋊C8×C59C2211yescharacteristic, complemented
77C24×D59—21no—
78C2×#11745685—22no—
79C2×#11745685—42no—
80C2×#11745685—42no—
81C2×#11745685C2314yescomplemented
82C22×Dic118C2311yescharacteristic
83C22×D236—21no—
84C22×D236—22no—
85C22×D236—42no—
86C22×D236—42no—
87C22×D236C2311yescharacteristic
88C22×D236C2311yescharacteristic
89C22×D236C2311yescharacteristic
90C22×D236C2314yes—
91C22×C22⋊D59—21no—
92C22×C22⋊D59—21no—
93C22×C22⋊D59—21no—
94C22×C22⋊D59—21no—
95C22×C22⋊D59—21no—
96C22×C22⋊D59—21no—
97C22×C22⋊D59—21no—
98C23×Dic59—21no—
99C22×C4×D59—21no—
100C2×#11745660—42no—
101C2×#11745660—42no—
102C2×#11745660C2314yes—
103C2×#11745660C2314yes—
104C2×D472—42no—
105C2×D472—42no—
106C2×D472C2314yes—
107C2×D472C2314yes—
108#14273723—28no—
109#14273716—28no—
110#14273706—22no—
111#14273706—22no—
112#14273706C2314yes—
113#14273706C2314yescomplemented
114#14273703—28no—
115#14273701—22no—
116#14273701—22no—
117#14273701—22no—
118#14273701—22no—
119#14273701—22no—
120#14273701—22no—
121#14273701C2314yes—
122#14273701C2314yes—
123#14273701C2314yes—
124#14273701C2314yes—
125#14273701C2314yes—
126#14273701C2314yescomplemented
127#14273699—28no—
128#14273699—28no—
129#14273698—28no—
130#14273695—28no—
131#14273695—28no—
132#14273686—22no—
133#14273686C2314yes—
134C2×C4⋊Dic59—21no—
135C2×C4⋊Dic59—22no—
136C2×C4⋊Dic59C2311yescharacteristic
137C2×C4⋊Dic59C2311yescharacteristic
138C2×C4⋊Dic59C2311yescharacteristic
139C2×C4⋊Dic59C2311yescharacteristic
140C2×C4⋊Dic59C2314yescomplemented
141C2×Dic59⋊C4—21no—
142C2×Dic59⋊C4—21no—
143C2×C22⋊Dic59—21no—
144C2×C22⋊Dic59—21no—
145C2×C22⋊Dic59—21no—
146C2×(C2×D59)⋊C4—21no—
147C2×(C2×D59)⋊C4—21no—
148C2×(C2×D59)⋊C4—21no—
149C2×(C2×D59)⋊C4—21no—
150C2×(C2×D59)⋊C4—21no—
151C2×(C2×D59)⋊C4—21no—
152C2×C4×Dic59—21no—
153#14273661C2314yescomplemented
154#14273661C2314yescomplemented
155#14273659C2314yescomplemented
156#14273659C2314yescomplemented
157#14273652C2314yescomplemented
158#14273652C2314yescomplemented
159#14273649C2314yes—
160#14273649C2314yes—
161#14273649C2314yes—
162#14273649C2314yes—
163#14273649C2314yescomplemented
164#14273649C2314yescomplemented
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×C59C2314yescomplemented
178C22×C8×C59—42no—
179C22×C8×C59C2311yescharacteristic
180C22×C8×C59C2311yescharacteristic
181C22×C8×C59C2311yescharacteristic
182C22×C8×C59C2311yescharacteristic
183C22×C8×C59C2314yescomplemented
184C22⋊C8×C59C2314yes—
185C22⋊C8×C59C2314yes—
186C22⋊C8×C59C2314yescomplemented
187C22⋊C8×C59C2314yescomplemented
188C24×C59C2×D411yescharacteristic
189C24×C59C2×D411yescharacteristic
190C24×C59C2×D411yescharacteristic
191C23×D59—21no—
192C23×D59—21no—
193C23×D59—21no—
194C23×D59—24no—
195C23×D59—44no—
196C23×D59—82no—
197C23×D59—82no—
198#41×C59—48no—
199#41×C59—44no—
200#41×C59—44no—
201C2×Q8×C59—42no—
202C2×Q8×C59C2×D414yes—
203C2×D4×C59—42no—
204C2×D4×C59—42no—
205C2×D4×C59—42no—
206C2×D4×C59C2×D414yes—
207C2×D4×C59C2×D414yes—
208C2×D4×C59C2×D414yes—
209C22×C4×C59—22no—
210C22×C4×C59—22no—
211C22×C4×C59—22no—
212C22×C4×C59—22no—
213C22×C4×C59—22no—
214C22×C4×C59—22no—
215C22×C4×C59C2×D411yescharacteristic
216C22×C4×C59C2×D411yescharacteristic
217C22×C4×C59C2×D411yescharacteristic
218C22×C4×C59C2×D412yes—
219C22×C4×C59C2×D412yes—
220C22×C4×C59C2×D412yes—
221C22×C4×C59C2412yes—
222C22×C4×C59C2412yes—
223C22×C4×C59C2412yes—
224C22×C4×C59C2411yescharacteristic
225C2×C22⋊D59—24no—
226C2×C22⋊D59—24no—
227C2×C22⋊D59—24no—
228C2×C22⋊D59—24no—
229C2×C22⋊D59—24no—
230C2×C22⋊D59—24no—
231C2×C22⋊D59—24no—
232C2×C22⋊D59—44no—
233C2×C22⋊D59—82no—
234C2×C22⋊D59—82no—
235C2×C22⋊D59—82no—
236C2×C22⋊D59—82no—
237C2×C22⋊D59—82no—
238C2×C22⋊D59—82no—
239C22×Dic59—21no—
240C22×Dic59—21no—
241C22×Dic59—21no—
242C22×Dic59—21no—
243C22×Dic59—21no—
244C22×Dic59—24no—
245C22×Dic59—82no—
246#11745685—44no—
247#11745685—44no—
248#11745685—48no—
249C2×D236—22no—
250C2×D236—22no—
251C2×D236—22no—
252C2×D236—22no—
253C2×D236—22no—
254C2×D236—22no—
255C2×D236—21no—
256C2×D236—21no—
257C2×D236—21no—
258C2×D236—24no—
259C2×D236—44no—
260C2×D236—44no—
261C2×D236—44no—
262C2×D236—48no—
263C2×D236C2412yes—
264C2×D236C2412yes—
265C2×D236C2412yes—
266C2×C4×D59—24no—
267C2×C4×D59—44no—
268C2×Dic118—22no—
269C2×Dic118—22no—
270C2×Dic118—21no—
271C2×Dic118C2412yes—
272M16×C59—44no—
273C2×C8×C59—22no—
274C2×C8×C59—22no—
275C2×C8×C59—22no—
276C2×C8×C59—22no—
277C2×C8×C59—44no—
278C2×C8×C59C2412yes—
279C2×C8×C59C2412yes—
280C2×C8×C59C2412yes—
281C2×C8×C59C2412yes—
282C22⋊Dic59—24no—
283C22⋊Dic59—24no—
284C22⋊Dic59—24no—
285(C2×D59)⋊C4—24no—
286(C2×D59)⋊C4—24no—
287(C2×D59)⋊C4—24no—
288(C2×D59)⋊C4—24no—
289(C2×D59)⋊C4—24no—
290(C2×D59)⋊C4—24no—
291C4⋊Dic59—21no—
292C4⋊Dic59—21no—
293C4⋊Dic59—24no—
294C4⋊Dic59—21no—
295C4⋊Dic59—21no—
296C4⋊Dic59C2412yes—
297C4⋊Dic59C2412yes—
298C4⋊Dic59C2412yes—
299C4⋊Dic59C2412yes—
300Dic59⋊C4—24no—
301Dic59⋊C4—24no—
302C4×Dic59—24no—
303D472—44no—
304D472—44no—
305#11745660—44no—
306#11745660—44no—
307C23×C59—22no—
308C23×C59—22no—
309C23×C59—22no—
310C23×C59—22no—
311C23×C59—22no—
312C23×C59—22no—
313C23×C59—22no—
314C23×C59—22no—
315C23×C59—22no—
316C23×C59C22×D412yes—
317C23×C59C22×D412yes—
318C23×C59C22×D412yes—
319C23×C59C22×D411yescharacteristic
320C22×D59—22no—
321C22×D59—22no—
322C22×D59—22no—
323C22×D59—48no—
324C22×D59—42no—
325C22×D59—42no—
326C22×D59—42no—
327C22×D59—42no—
328C22×D59—42no—
329C22×D59—42no—
330C22×D59—42no—
331C22×D59—42no—
332C22×D59—42no—
333C22×D59—84no—
334C22×D59—84no—
335C22×D59—816no—
336Q8×C59—44no—
337D4×C59—44no—
338D4×C59—44no—
339D4×C59—44no—
340C2×C4×C59—22no—
341C2×C4×C59—22no—
342C2×C4×C59—22no—
343C2×C4×C59—24no—
344C2×C4×C59—24no—
345C2×C4×C59—24no—
346C2×C4×C59—22no—
347C2×C4×C59—22no—
348C2×C4×C59—22no—
349C2×C4×C59—22no—
350C2×C4×C59—22no—
351C2×C4×C59—22no—
352C2×C4×C59C22×D412yes—
353C2×C4×C59C22×D412yes—
354C2×C4×C59C22×D412yes—
355C2×C4×C59C22×D411yescharacteristic
356C2×C4×C59H(5,𝔽2)12yes—
357C2×C4×C59H(5,𝔽2)12yes—
358C2×C4×C59C2511yescharacteristic
359C22⋊D59—48no—
360C22⋊D59—84no—
361C22⋊D59—84no—
362C22⋊D59—84no—
363C22⋊D59—84no—
364C22⋊D59—84no—
365C22⋊D59—84no—
366C2×Dic59—22no—
367C2×Dic59—22no—
368C2×Dic59—22no—
369C2×Dic59—22no—
370C2×Dic59—22no—
371C2×Dic59—42no—
372C2×Dic59—42no—
373C2×Dic59—42no—
374C2×Dic59—42no—
375C2×Dic59—42no—
376C2×Dic59—84no—
377D236—22no—
378D236—22no—
379D236—22no—
380D236—22no—
381D236—22no—
382D236—22no—
383D236—48no—
384D236—42no—
385D236—42no—
386D236—42no—
387C4×D59—48no—
388Dic118—22no—
389Dic118—22no—
390Dic118—42no—
391C8×C59—22no—
392C8×C59—22no—
393C8×C59—22no—
394C8×C59—22no—
395C2×#3198—591nomaximal, Sylow
396C22×C59—22no—
397C22×C59—22no—
398C22×C59—22no—
399C22×C59—22no—
400C22×C59—22no—
401C22×C59—22no—
402C22×C59—22no—
403C22×C59—22no—
404C22×C59—22no—
405C22×C59—44no—
406C22×C59—44no—
407C22×C59—44no—
408C22×C59#53412yes—
409C22×C59#57612yes—
410C22×C59#57712yes—
411C22×C59C23×D411yescharacteristic
412C2×D59—42no—
413C2×D59—42no—
414C2×D59—42no—
415C2×D59—42no—
416C2×D59—42no—
417C2×D59—42no—
418C2×D59—42no—
419C2×D59—42no—
420C2×D59—42no—
421C2×D59—816no—
422C2×D59—84no—
423C2×D59—84no—
424C2×D59—84no—
425C4×C59—22no—
426C4×C59—22no—
427C4×C59—22no—
428C4×C59#53412yes—
429C4×C59C2×H(5,𝔽2)11yescharacteristic
430C4×C59C2×H(5,𝔽2)11yescharacteristic
431Dic59—42no—
432Dic59—42no—
433Dic59—42no—
434Dic59—42no—
435Dic59—42no—
436C2×#537—591no—
437C2×#535—591no—
438#3198—5916no—
439C2×#481—591no—
440C2×#485—591no—
441C2×#482—591no—
442C2×#480—591no—
443C2×#469—591no—
444C2×#468—591no—
445C2×#466—591no—
446C2×#465—591no—
447C2×#449—591no—
448C2×#449—591no—
449C2×#450—591no—
450C2×#447—591no—
451C2×#408D5911yescharacteristic, complemented
452C2×C59—42no—
453C2×C59—42no—
454C2×C59—42no—
455C2×C59#319814yescomplemented
456C2×C59C2×#53411yescharacteristic
457C2×C59C2×#57611yescharacteristic
458C2×C59C2×#57711yescharacteristic
459D59—82no—
460D59—82no—
461D59—82no—
462C22×#41—591no—
463C22×#41C2×D5911yescharacteristic
464C23×D4—591no—
465C22×SD16—591no—
466C22×SD16—591no—
467C22×D8—591no—
468C22×D8—591no—
469C22×M16C2×D5911yescharacteristic, complemented
470C23×C8C2×D5911yescharacteristic, complemented
471#537—598no—
472#537—1184no—
473#535—598no—
474#535—1184no—
475C2×#127—1181no—
476C2×#124—1181no—
477C2×C22⋊Q8—591no—
478C2×C22⋊Q8—591no—
479C2×C22⋊Q8—1181no—
480C2×#121—591no—
481C2×#121—591no—
482C2×#121—591no—
483C2×#121—591no—
484C2×#121—591no—
485C2×#121—591no—
486C2×#121—1181no—
487C2×#121—1181no—
488C2×#121—1181no—
489C2×#120—1181no—
490C2×#120—1181no—
491C2×#117—591no—
492C22×C4⋊C4—591no—
493#485—598no—
494#482—598no—
495#481—598no—
496#480—598no—
497#469—598no—
498#468—598no—
499#466—598no—
500#465—598no—
501#450—598no—
502#449—598no—
503#449—598no—
504#447—598no—
505C2×#107—591no—
506C2×#107—591no—
507C2×#106—591no—
508C2×#106—591no—
509C2×#103—591no—
510C2×#103—591no—
511C2×#102—591no—
512C2×#102—591no—
513C2×#102—591no—
514C2×#102—591no—
515C2×#102—591no—
516C2×#102—591no—
517#408C2×D5918yescomplemented
518C2×C22⋊C8C2×D5911yescharacteristic
519C2×C22⋊C8C2×D5911yescharacteristic
520C2×C22⋊C8C2×D5911yescharacteristic, complemented
521C2×C22⋊C8C2×D5911yescharacteristic, complemented
522C59C2×#319811yescharacteristic, complemented, Sylow
523C25—1181no—
524C2×#41—42no—
525C2×#41—42no—
526C2×#41—594no—
527C2×#41—1182no—
528C2×#41—2362no—
529C2×#41—2362no—
530C2×#41D23614yes—
531C2×#41C22×D5914yes—
532C22×Q8—591no—
533C22×Q8D23611yescharacteristic
534C22×D4—591no—
535C22×D4—591no—
536C22×D4—591no—
537C22×D4—594no—
538C22×D4—1181no—
539C22×D4—1181no—
540C22×D4—1181no—
541C22×D4—1181no—
542C22×D4—1181no—
543C22×D4—1181no—
544C22×D4—1181no—
545C22×D4—1181no—
546C22×D4—1182no—
547C22×D4—2362no—
548C22×D4—2362no—
549C22×D4D23611yescharacteristic
550C22×D4D23611yescharacteristic
551C22×D4D23611yescharacteristic
552C23×C4—1181no—
553C23×C4—1181no—
554C23×C4C22×D5911yescharacteristic
555C23×C4C22×D5911yescharacteristic
556C23×C4C22×D5911yescharacteristic
557C2×SD16—594no—
558C2×SD16—594no—
559C2×SD16—2362no—
560C2×SD16—2362no—
561C2×D8—594no—
562C2×D8—594no—
563C2×D8—2362no—
564C2×D8—2362no—
565C2×M16—42no—
566C2×M16C22×D5914yescomplemented
567C22×C8—42no—
568C22×C8C22×D5911yescharacteristic
569C22×C8C22×D5911yescharacteristic
570C22×C8C22×D5911yescharacteristic
571C22×C8C22×D5911yescharacteristic
572C22×C8C22×D5914yescomplemented
573#127—1188no—
574#124—1188no—
575C22⋊Q8—594no—
576C22⋊Q8—594no—
577C22⋊Q8—1188no—
578C22⋊Q8—1182no—
579C22⋊Q8—1182no—
580#121—594no—
581#121—594no—
582#121—594no—
583#121—594no—
584#121—594no—
585#121—594no—
586#121—1188no—
587#121—1188no—
588#121—1188no—
589#121—1182no—
590#121—1182no—
591#121—1182no—
592#121—1182no—
593#121—1182no—
594#121—1182no—
595#120—1188no—
596#120—1188no—
597#117—594no—
598#117—1182no—
599C2×C4⋊C4—591no—
600C2×C4⋊C4—591no—
601C2×C4⋊C4—594no—
602C2×C4⋊C4—591no—
603C2×C4⋊C4—591no—
604C2×C4⋊C4—1181no—
605C2×C4⋊C4—1182no—
606C2×C4⋊C4—1181no—
607C2×C4⋊C4—1181no—
608C2×C22⋊C4—1181no—
609C2×C22⋊C4—1181no—
610C2×C22⋊C4—1181no—
611C2×C22⋊C4—1181no—
612C2×C22⋊C4—1181no—
613C2×C22⋊C4—1181no—
614C2×C22⋊C4—1181no—
615C2×C22⋊C4—1181no—
616C2×C22⋊C4—1181no—
617C2×C42—1181no—
618#107—594no—
619#107—594no—
620#106—594no—
621#106—594no—
622#103—594no—
623#103—594no—
624#102—594no—
625#102—594no—
626#102—594no—
627#102—594no—
628#102—594no—
629#102—594no—
630C22⋊C8C22×D5914yes—
631C22⋊C8C22×D5914yes—
632C22⋊C8C22×D5914yescomplemented
633C22⋊C8C22×D5914yescomplemented
634C24—1184no—
635C24—1181no—
636C24—1181no—
637C24—1181no—
638C24—4722no—
639C24—4722no—
640C24—2364no—
641C24C2×D23611yescharacteristic
642C24C2×D23611yescharacteristic
643C24C2×D23611yescharacteristic
644#41—48no—
645#41—44no—
646#41—44no—
647#41—2364no—
648#41—2364no—
649#41—2368no—
650C2×Q8—42no—
651C2×Q8—592no—
652C2×Q8—1181no—
653C2×Q8—1182no—
654C2×Q8—1182no—
655C2×Q8C2×D23614yes—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—592no—
660C2×D4—592no—
661C2×D4—592no—
662C2×D4—1184no—
663C2×D4—1184no—
664C2×D4—1184no—
665C2×D4—1184no—
666C2×D4—1184no—
667C2×D4—1184no—
668C2×D4—1184no—
669C2×D4—1181no—
670C2×D4—1181no—
671C2×D4—1181no—
672C2×D4—1184no—
673C2×D4—1182no—
674C2×D4—1182no—
675C2×D4—1182no—
676C2×D4—1182no—
677C2×D4—1182no—
678C2×D4—1182no—
679C2×D4—4722no—
680C2×D4—4722no—
681C2×D4—4722no—
682C2×D4—4722no—
683C2×D4—4722no—
684C2×D4—4722no—
685C2×D4—2364no—
686C2×D4—2364no—
687C2×D4—2364no—
688C2×D4—2368no—
689C2×D4—2364no—
690C2×D4C2×D23614yes—
691C2×D4C2×D23614yes—
692C2×D4C2×D23614yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—1184no—
700C22×C4—1181no—
701C22×C4—1181no—
702C22×C4—1181no—
703C22×C4—1181no—
704C22×C4—1181no—
705C22×C4—1184no—
706C22×C4—4722no—
707C22×C4—2364no—
708C22×C4C2×D23612yes—
709C22×C4C2×D23612yes—
710C22×C4C2×D23612yes—
711C22×C4C2×D23611yescharacteristic
712C22×C4C2×D23611yescharacteristic
713C22×C4C2×D23611yescharacteristic
714C22×C4C23×D5912yes—
715C22×C4C23×D5912yes—
716C22×C4C23×D5912yes—
717C22×C4C23×D5911yescharacteristic
718SD16—2364no—
719SD16—2364no—
720D8—2364no—
721D8—2364no—
722M16—44no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—22no—
726C2×C8—22no—
727C2×C8—44no—
728C2×C8C23×D5912yes—
729C2×C8C23×D5912yes—
730C2×C8C23×D5912yes—
731C2×C8C23×D5912yes—
732C4⋊C4—592no—
733C4⋊C4—592no—
734C4⋊C4—592no—
735C4⋊C4—592no—
736C4⋊C4—1184no—
737C4⋊C4—1181no—
738C4⋊C4—1181no—
739C4⋊C4—1181no—
740C4⋊C4—1181no—
741C4⋊C4—1184no—
742C4⋊C4—1184no—
743C22⋊C4—1184no—
744C22⋊C4—1184no—
745C22⋊C4—1184no—
746C22⋊C4—1184no—
747C22⋊C4—1184no—
748C22⋊C4—1184no—
749C22⋊C4—1184no—
750C22⋊C4—1184no—
751C22⋊C4—1184no—
752C42—1184no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—1182no—
763C23—1182no—
764C23—1182no—
765C23—4724no—
766C23—4724no—
767C23—47216no—
768C23—2368no—
769C23—2362no—
770C23—2362no—
771C23—2362no—
772C23—2362no—
773C23—2362no—
774C23—2362no—
775C23—2362no—
776C23—2362no—
777C23—2362no—
778C23C22×D23612yes—
779C23C22×D23612yes—
780C23C22×D23612yes—
781C23C22×D23611yescharacteristic
782Q8—44no—
783Q8—1182no—
784Q8—1182no—
785Q8—2362no—
786D4—44no—
787D4—44no—
788D4—44no—
789D4—1182no—
790D4—1182no—
791D4—1182no—
792D4—1182no—
793D4—1182no—
794D4—1182no—
795D4—4724no—
796D4—4724no—
797D4—4724no—
798D4—4724no—
799D4—4724no—
800D4—4724no—
801D4—2368no—
802D4—2368no—
803D4—2362no—
804D4—2362no—
805D4—2362no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—1182no—
819C2×C4—1182no—
820C2×C4—1182no—
821C2×C4—1182no—
822C2×C4—1182no—
823C2×C4—4724no—
824C2×C4—2368no—
825C2×C4—2362no—
826C2×C4—2362no—
827C2×C4—2362no—
828C2×C4—2362no—
829C2×C4—2362no—
830C2×C4C22×D23612yes—
831C2×C4C22×D23612yes—
832C2×C4C22×D23612yes—
833C2×C4C22×D23611yescharacteristic
834C2×C4#1427377212yes—
835C2×C4#1427377212yes—
836C2×C4C24×D5911yescharacteristic
837C8—22no—
838C8—22no—
839C8—22no—
840C8—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—47216no—
854C22—4724no—
855C22—4724no—
856C22—4724no—
857C22—2362no—
858C22—2362no—
859C22—2362no—
860C22—2362no—
861C22—2362no—
862C22—2362no—
863C22—2362no—
864C22—2362no—
865C22—2362no—
866C22#1683796412yes—
867C22#1683820712yes—
868C22#1683821412yes—
869C22C23×D23611yescharacteristic
870C4—22no—
871C4—22no—
872C4—22no—
873C4—2362no—
874C4—2362no—
875C4—2362no—
876C4—2362no—
877C4—2362no—
878C4#1683796412yes—
879C4C2×#1427377211yescharacteristic
880C4C2×#1427377211yescharacteristic
881C2—42no—
882C2—42no—
883C2—42no—
884C2—4722no—
885C2—4722no—
886C2—4722no—
887C2#2143495014yesdirect product factor
888C2C2×#1683796411yescharacteristic
889C2C2×#1683820711yescharacteristic
890C2C2×#1683821411yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#408C2
socleC23×C59C22×D4
hypercenterC2×#408D59
hypocenterC59C2×#3198
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
1. C2×#16837980C2semidirect
2. C2×#16837966C2semidirect
3. #21434950C2direct (N × H)
4. C2×#16837721C2semidirect
5. C2×#16837744C2semidirect
6. C2×#16837727C2semidirect
7. C2×#16837716C2semidirect
8. C2×#16837655C2semidirect
9. C2×#16837648C2semidirect
10. C2×#16837638C2semidirect
11. C2×#16837631C2semidirect
12. C2×#16837549C2semidirect
13. C2×#16837549C2semidirect
14. C2×#16837555C2semidirect
15. C2×#16837538C2semidirect
16. C2×C59×#408C2semidirect
17. C22×#11745685C22semidirect
24. #16837980C22semidirect
26. #16837966C22semidirect
30. C2×#14273706C22semidirect
37. C2×#14273701C22semidirect
44. C22×C4⋊Dic59C22semidirect
45. #16837744C22semidirect
46. #16837727C22semidirect
47. #16837721C22semidirect
48. #16837716C22semidirect
49. #16837655C22semidirect
50. #16837648C22semidirect
51. #16837638C22semidirect
52. #16837631C22semidirect
53. #16837555C22semidirect
54. #16837549C22semidirect
55. #16837549C22semidirect
56. #16837538C22semidirect
57. C2×#14273661C22semidirect
58. C2×#14273661C22semidirect
59. C2×#14273659C22semidirect
60. C2×#14273659C22semidirect
61. C2×#14273652C22semidirect
62. C2×#14273652C22semidirect
67. C2×#14273649C22semidirect
68. C2×#14273649C22semidirect
70. C22×M16×C59C22semidirect
71. C23×C8×C59C22semidirect
72. C59×#408C22semidirect
75. C2×C22⋊C8×C59C22semidirect
76. C2×C22⋊C8×C59C22semidirect
81. C2×#11745685C23semidirect
113. #14273706C23semidirect
126. #14273701C23semidirect
140. C2×C4⋊Dic59C23semidirect
153. #14273661C23semidirect
154. #14273661C23semidirect
155. #14273659C23semidirect
156. #14273659C23semidirect
157. #14273652C23semidirect
158. #14273652C23semidirect
163. #14273649C23semidirect
164. #14273649C23semidirect
177. C2×M16×C59C23semidirect
183. C22×C8×C59C23semidirect
186. C22⋊C8×C59C23semidirect
187. C22⋊C8×C59C23semidirect
451. C2×#408D59semidirect
455. C2×C59#3198semidirect
469. C22×M16C2×D59semidirect
470. C23×C8C2×D59semidirect
517. #408C2×D59semidirect
520. C2×C22⋊C8C2×D59semidirect
521. C2×C22⋊C8C2×D59semidirect
522. C59C2×#3198semidirect
566. C2×M16C22×D59semidirect
572. C22×C8C22×D59semidirect
632. C22⋊C8C22×D59semidirect
633. C22⋊C8C22×D59semidirect
887. C2#21434950direct (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×#168379662
#214349502
C2×#168377212
C2×#168377442
C2×#168377272
C2×#168377162
C2×#168376552
C2×#168376482
C2×#168376382
C2×#168376312
C2×#168375492
C2×#168375552
C2×#168375382
C2×C59×#4082
C2×#319859