Finite Group Databasebeta

← C2×#21433920 #29456241

Subgroups — C2×#21433920 #29456241

Order 15104.

2234 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838029C211yesmaximal, characteristic, complemented
2C2×#16837874C211yesmaximal, characteristic
3#21433920C2116yesmaximal, direct product factor
4C2×#16837705C211yesmaximal, characteristic, complemented
5C2×#16837703C211yesmaximal, characteristic, complemented
6C2×#16837702C211yesmaximal, characteristic, complemented
7C2×#16837700C211yesmaximal, characteristic, complemented
8C2×#16837690C211yesmaximal, characteristic, complemented
9C2×#16837689C211yesmaximal, characteristic, complemented
10C2×#16837681C211yesmaximal, characteristic, complemented
11C2×#16837443C211yesmaximal, characteristic, complemented
12C2×#16837439C211yesmaximal, characteristic, complemented
13C2×#16837427C211yesmaximal, characteristic, complemented
14C2×#16837405C211yesmaximal, characteristic
15C2×#102×D59C211yesmaximal, characteristic
16C2×C59×#474C211yesmaximal, characteristic, complemented
17C22×D4×D59C2211yescharacteristic
18C22×#11745659C2211yescharacteristic
19C22×C8×D59C2211yescharacteristic
20#16838029—24no—
21#16838029C2218yescomplemented
22C2×#14273726C2211yescharacteristic, complemented
23C2×#14273725—21no—
24C2×#14273719C2211yescharacteristic, complemented
25C2×#14273718C2211yescharacteristic, complemented
26C2×#14273717—21no—
27C2×#14273705—21no—
28C2×#14273703—21no—
29#16837874—24no—
30#16837874C2218yes—
31C2×C4×D236C2211yescharacteristic
32C2×D4×Dic59C2211yescharacteristic
33C2×#14273689C2211yescharacteristic
34C2×C4×C22⋊D59—21no—
35C2×(C22⋊D59)⋊C4—21no—
36C2×#14273685C2211yescharacteristic
37C2×#14273685C2211yescharacteristic
38C2×#14273684C2211yescharacteristic
39C2×C4⋊C4×D59C2211yescharacteristic
40C22×(C2×D59)⋊C4—21no—
41C2×C22⋊C4×D59—21no—
42#16837705C2218yescomplemented
43#16837703C2218yescomplemented
44#16837702C2218yescomplemented
45#16837700C2218yescomplemented
46#16837690C2218yescomplemented
47#16837689C2218yescomplemented
48#16837681C2218yescomplemented
49#16837443C2218yescomplemented
50#16837439C2218yescomplemented
51C2×#14273661C2211yescharacteristic, complemented
52C2×#14273660C2211yescharacteristic, complemented
53C2×#14273659C2211yescharacteristic, complemented
54C2×#14273658C2211yescharacteristic, complemented
55C2×#14273658C2211yescharacteristic, complemented
56C2×#14273658C2211yescharacteristic, complemented
57#16837427C2218yescomplemented
58C2×C4⋊(C59⋊C8)C2211yescharacteristic, complemented
59C2×Dic59⋊C8C2211yescharacteristic, complemented
60C2×Dic59⋊C8C2211yescharacteristic, complemented
61#16837405C2218yes—
62C2×#14273649C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×#14273647C2211yescharacteristic
67C2×#14273647C2211yescharacteristic
68#102×D59C2218yes—
69C2×C4⋊Q8×C59C2211yescharacteristic, complemented
70C2×C4×D4×C59C2211yescharacteristic
71C59×#474C2218yescomplemented
72C2×#107×C59C2211yescharacteristic, complemented
73C2×#107×C59C2211yescharacteristic, complemented
74C2×C4⋊C8×C59C2211yescharacteristic, complemented
75C2×#102×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C24×D59—21no—
78C22×Dic118—21no—
79C22×D236C2311yescharacteristic
80C22×C22⋊D59—21no—
81C2×D4×D59—22no—
82C2×D4×D59—24no—
83C2×D4×D59Q818yescomplemented
84C2×D4×D59C2314yes—
85C23×Dic59—21no—
86C22×C4×D59—21no—
87C22×C4×D59—21no—
88C22×C4×D59—21no—
89C22×C4×D59C2311yescharacteristic
90C2×#11745659—24no—
91C2×#11745659C2314yes—
92C22×C59⋊C8C2311yescharacteristic
93C22×C59⋊C8C2311yescharacteristic
94C2×C8×D59—24no—
95C2×C8×D59C2314yes—
96#14273726—22no—
97#14273726C2314yescomplemented
98#14273725—28no—
99#14273719—22no—
100#14273719C2314yescomplemented
101#14273718—22no—
102#14273718C2314yescomplemented
103#14273717—28no—
104#14273705—28no—
105#14273703—28no—
106C4×D236—22no—
107C4×D236C2314yes—
108D4×Dic59—22no—
109D4×Dic59C2314yes—
110#14273689—22no—
111#14273689C2314yes—
112C4×C22⋊D59—28no—
113(C22⋊D59)⋊C4—28no—
114#14273685—22no—
115#14273685—22no—
116#14273685C2314yes—
117#14273685C2314yes—
118#14273684D414yes—
119#14273684C2314yes—
120C2×C4⋊Dic59—21no—
121C2×C4⋊Dic59C2311yescharacteristic
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⋊C4D411yescharacteristic
130C2×Dic59⋊C4D411yescharacteristic
131C4⋊C4×D59—22no—
132C4⋊C4×D59C2314yes—
133C2×C22⋊Dic59—21no—
134C2×(C2×D59)⋊C4—21no—
135C2×(C2×D59)⋊C4—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—28no—
139C2×(C2×D59)⋊C4D411yescharacteristic
140C2×(C2×D59)⋊C4D411yescharacteristic
141C22⋊C4×D59—28no—
142C2×C4×Dic59—21no—
143C2×C4×Dic59—21no—
144C2×C4×Dic59C2311yescharacteristic
145#14273661C2314yescomplemented
146#14273660C2314yescomplemented
147#14273659C2314yescomplemented
148#14273658C2314yescomplemented
149#14273658C2314yescomplemented
150#14273658C2314yescomplemented
151C4⋊(C59⋊C8)C2314yescomplemented
152Dic59⋊C8C2314yescomplemented
153Dic59⋊C8C2314yescomplemented
154#14273649C2314yes—
155#14273649C2314yes—
156#14273648C2314yes—
157#14273648C2314yes—
158#14273647C2314yes—
159#14273647C2314yes—
160C22×Q8×C59—21no—
161C22×D4×C59C2311yescharacteristic
162C23×C4×C59—21no—
163C22×C8×C59C2311yescharacteristic
164C22×C8×C59C2311yescharacteristic
165C4⋊Q8×C59—22no—
166C4⋊Q8×C59C2314yescomplemented
167C4×D4×C59—22no—
168C4×D4×C59C2314yes—
169C2×C4⋊C4×C59—21no—
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C22⋊C4×C59—21no—
174C2×C42×C59C2311yescharacteristic
175#107×C59C2314yescomplemented
176#107×C59C2314yescomplemented
177C4⋊C8×C59C2314yescomplemented
178#102×C59C2314yes—
179#102×C59C2314yes—
180C24×C59—21no—
181C23×D59—21no—
182C23×D59—28no—
183C23×D59—24no—
184C23×D59—82no—
185C23×D59—82no—
186C23×D59C2×D411yescharacteristic
187C2×Q8×C59—24no—
188C2×Q8×C59—82no—
189C2×D4×C59—21no—
190C2×D4×C59—22no—
191C2×D4×C59C2×Q814yes—
192C2×D4×C59C2412yes—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—24no—
197C22×C4×C59—82no—
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2411yescharacteristic
201C2×C22⋊D59—28no—
202C2×C22⋊D59—24no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59—24no—
207C22×Dic59—82no—
208C22×Dic59C2×D411yescharacteristic
209C22×Dic59C2×D411yescharacteristic
210C22×Dic59C2×D411yescharacteristic
211D4×D59—216no—
212D4×D59—28no—
213D4×D59C2×Q8116yescomplemented
214C2×D236—21no—
215C2×D236—22no—
216C2×D236C2×Q814yes—
217C2×D236C2412yes—
218C2×C4×D59—24no—
219C2×C4×D59—24no—
220C2×C4×D59—24no—
221C2×C4×D59—82no—
222C2×C4×D59—82no—
223C2×C4×D59—82no—
224C2×C4×D59C2×D412yes—
225C2×C4×D59C2×Q814yes—
226C2×C4×D59#4114yes—
227C2×C4×D59C2412yes—
228C2×Dic118—24no—
229C2×Dic118—82no—
230C2×C8×C59—22no—
231C2×C8×C59—22no—
232C2×C8×C59C2412yes—
233C2×C8×C59C2412yes—
234C4⋊C4×C59—24no—
235C4⋊C4×C59—21no—
236C4⋊C4×C59—21no—
237C4⋊C4×C59—21no—
238C4⋊C4×C59C2412yes—
239C4⋊C4×C59C2412yes—
240C4⋊C4×C59C2412yes—
241C22⋊C4×C59—24no—
242C42×C59C2×D412yes—
243C42×C59C2412yes—
244C22⋊Dic59—24no—
245(C2×D59)⋊C4—24no—
246(C2×D59)⋊C4—24no—
247(C2×D59)⋊C4—24no—
248(C2×D59)⋊C4—24no—
249(C2×D59)⋊C4C2×D414yes—
250(C2×D59)⋊C4C2×D414yes—
251C4⋊Dic59—21no—
252C4⋊Dic59—21no—
253C4⋊Dic59—21no—
254C4⋊Dic59—24no—
255C4⋊Dic59C2412yes—
256C4⋊Dic59C2412yes—
257C4⋊Dic59C2412yes—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4—24no—
262Dic59⋊C4—24no—
263Dic59⋊C4C2×D414yes—
264Dic59⋊C4C2×D414yes—
265C4×Dic59—24no—
266C4×Dic59—24no—
267C4×Dic59C2×D412yes—
268C4×Dic59C2412yes—
269C2×C59⋊C8—22no—
270C2×C59⋊C8—22no—
271C2×C59⋊C8C2412yes—
272C2×C59⋊C8C2412yes—
273#11745659—28no—
274C8×D59—28no—
275C23×C59—24no—
276C23×C59—22no—
277C23×C59—42no—
278C23×C59—42no—
279C23×C59C22×D411yescharacteristic
280C22×D59—22no—
281C22×D59—22no—
282C22×D59—24no—
283C22×D59—22no—
284C22×D59—216no—
285C22×D59—42no—
286C22×D59—42no—
287C22×D59—816no—
288C22×D59—84no—
289C22×D59—84no—
290C22×D59C22⋊Q814yes—
291C22×D59C22×D412yes—
292Q8×C59—84no—
293D4×C59—24no—
294D4×C59—22no—
295D4×C59C22×Q814yes—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—42no—
302C2×C4×C59—42no—
303C2×C4×C59—42no—
304C2×C4×C59—84no—
305C2×C4×C59C22×D412yes—
306C2×C4×C59C22×D412yes—
307C2×C4×C59C22×D411yescharacteristic
308C2×C4×C59C22×Q812yes—
309C2×C4×C59C2×#4112yes—
310C2×C4×C59C2511yescharacteristic
311C22⋊D59—216no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—42no—
318C2×Dic59—42no—
319C2×Dic59—42no—
320C2×Dic59—84no—
321C2×Dic59C22⋊Q814yes—
322C2×Dic59C22×D412yes—
323C2×Dic59C22×D412yes—
324C2×Dic59C22×D412yes—
325D236—24no—
326D236—22no—
327D236C22×Q814yes—
328C4×D59—84no—
329C4×D59—84no—
330C4×D59—84no—
331C4×D59C22⋊Q818yes—
332C4×D59C22×Q814yes—
333C4×D59C2×#4114yes—
334Dic118—84no—
335C8×C59—22no—
336C8×C59—22no—
337C59⋊C8—22no—
338C59⋊C8—22no—
339C2×#3081—591nomaximal, Sylow
340C22×C59—24no—
341C22×C59—48no—
342C22×C59—42no—
343C22×C59—42no—
344C22×C59C2×C22⋊Q812yes—
345C22×C59#57612yes—
346C22×C59#57712yes—
347C22×C59C23×D411yescharacteristic
348C2×D59—28no—
349C2×D59—22no—
350C2×D59—22no—
351C2×D59—24no—
352C2×D59—48no—
353C2×D59—42no—
354C2×D59—42no—
355C2×D59—816no—
356C2×D59C2×C22⋊Q814yes—
357C4×C59—22no—
358C4×C59—22no—
359C4×C59—42no—
360C4×C59—42no—
361C4×C59—42no—
362C4×C59C2×C22⋊Q812yes—
363C4×C59C23×Q811yescharacteristic
364C4×C59C22×#4111yescharacteristic
365Dic59—22no—
366Dic59—22no—
367Dic59—42no—
368Dic59—42no—
369Dic59—42no—
370Dic59C2×C22⋊Q814yes—
371C2×#544—591no—
372C2×#518—591no—
373#3081—5916no—
374C2×#478—591no—
375C2×#478—591no—
376C2×#478—591no—
377C2×#478—591no—
378C2×#476—591no—
379C2×#476—591no—
380C2×#474—591no—
381C2×#474D5911yescharacteristic, complemented
382C2×#428—591no—
383C2×#427—591no—
384C2×#424—591no—
385C2×#418—591no—
386C22×#102—591no—
387C2×C59—44no—
388C2×C59#308114yescomplemented
389C2×C59C22×C22⋊Q811yescharacteristic
390C2×C59C2×#57611yescharacteristic
391C2×C59C2×#57711yescharacteristic
392D59—24no—
393D59—44no—
394C23×D4—591no—
395C22×M16—591no—
396C23×C8—591no—
397#544—598no—
398#544—1184no—
399C2×C4⋊Q8—591no—
400C2×C4⋊Q8—1181no—
401C2×C4⋊Q8C2×D5911yescharacteristic, complemented
402C2×#125—591no—
403C2×#125—591no—
404C2×#125—1181no—
405C2×C22⋊Q8—1181no—
406C2×C22⋊Q8—1181no—
407#518—598no—
408#518—1184no—
409C2×C4×D4—591no—
410C2×C4×D4—591no—
411C2×C4×D4—591no—
412C2×C4×D4—1181no—
413C2×C4×D4—1181no—
414C2×C4×D4C2×D5911yescharacteristic
415C2×#117—591no—
416C2×#117—591no—
417C2×#117—591no—
418C22×C4⋊C4—591no—
419C22×C22⋊C4—1181no—
420C22×C22⋊C4—1181no—
421#478—598no—
422#478—598no—
423#478—598no—
424#478—598no—
425#476—598no—
426#476—598no—
427#474—598no—
428#474C2×D5918yescomplemented
429#428—598no—
430#427—598no—
431C2×#107—591no—
432C2×#107—591no—
433C2×#107C2×D5911yescharacteristic, complemented
434C2×#107C2×D5911yescharacteristic, complemented
435C2×#106—591no—
436C2×#106—591no—
437C2×#106—591no—
438C2×#106—591no—
439#424—598no—
440C2×C4⋊C8—591no—
441C2×C4⋊C8—591no—
442C2×C4⋊C8—591no—
443C2×C4⋊C8C2×D5911yescharacteristic, complemented
444#418—598no—
445C2×#102—591no—
446C2×#102—591no—
447C2×#102—591no—
448C2×#102—591no—
449C2×#102—591no—
450C2×#102—591no—
451C2×#102—598no—
452C2×#102C2×D5911yescharacteristic
453C2×#102C2×D5911yescharacteristic
454C59C2×#308111yescharacteristic, complemented, Sylow
455C25—1181no—
456C22×Q8—21no—
457C22×Q8—1181no—
458C22×D4—598no—
459C22×D4—594no—
460C22×D4—591no—
461C22×D4—1182no—
462C22×D4—1184no—
463C22×D4—1181no—
464C22×D4C22×D5911yescharacteristic
465C23×C4—21no—
466C23×C4—591no—
467C23×C4—1181no—
468C23×C4—1181no—
469C23×C4—1181no—
470C23×C4—1181no—
471C2×M16—594no—
472C2×M16—1184no—
473C22×C8—591no—
474C22×C8—591no—
475C22×C8—594no—
476C22×C8—1184no—
477C22×C8C22×D5911yescharacteristic
478C22×C8C22×D5911yescharacteristic
479C4⋊Q8—22no—
480C4⋊Q8—594no—
481C4⋊Q8—1182no—
482C4⋊Q8—1188no—
483C4⋊Q8C22×D5914yescomplemented
484#125—594no—
485#125—594no—
486#125—1182no—
487#125—1188no—
488#125—1182no—
489C22⋊Q8—1188no—
490C22⋊Q8—1188no—
491C4×D4—22no—
492C4×D4—594no—
493C4×D4—594no—
494C4×D4—594no—
495C4×D4—1182no—
496C4×D4—1182no—
497C4×D4—1188no—
498C4×D4—1188no—
499C4×D4—1182no—
500C4×D4C22×D5914yes—
501#117—594no—
502#117—594no—
503#117—594no—
504#117—594no—
505#117—1182no—
506#117—1182no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—591no—
509C2×C4⋊C4—591no—
510C2×C4⋊C4—591no—
511C2×C4⋊C4—591no—
512C2×C4⋊C4—591no—
513C2×C4⋊C4—594no—
514C2×C4⋊C4—1182no—
515C2×C4⋊C4—1181no—
516C2×C4⋊C4—1181no—
517C2×C4⋊C4—1181no—
518C2×C4⋊C4—1181no—
519C2×C4⋊C4—1181no—
520C2×C4⋊C4—1181no—
521C2×C4⋊C4C22×D5911yescharacteristic
522C2×C4⋊C4C22×D5911yescharacteristic
523C2×C4⋊C4C22×D5911yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—591no—
526C2×C22⋊C4—591no—
527C2×C22⋊C4—1188no—
528C2×C22⋊C4—1188no—
529C2×C22⋊C4—1181no—
530C2×C22⋊C4—1181no—
531C2×C22⋊C4—1181no—
532C2×C22⋊C4—1181no—
533C2×C22⋊C4—1181no—
534C2×C42—591no—
535C2×C42—1181no—
536C2×C42—1181no—
537C2×C42C22×D5911yescharacteristic
538#107—594no—
539#107—594no—
540#107C22×D5914yescomplemented
541#107C22×D5914yescomplemented
542#106—594no—
543#106—594no—
544#106—594no—
545#106—594no—
546C4⋊C8—594no—
547C4⋊C8—594no—
548C4⋊C8—594no—
549C4⋊C8C22×D5914yescomplemented
550#102—594no—
551#102—594no—
552#102—594no—
553#102—594no—
554#102—594no—
555#102—594no—
556#102C22×D5914yes—
557#102C22×D5914yes—
558C24—21no—
559C24—591no—
560C24—1184no—
561C24—1188no—
562C24—1181no—
563C24—4722no—
564C24—4722no—
565C2×Q8—24no—
566C2×Q8—82no—
567C2×Q8—1184no—
568C2×Q8—4722no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—5916no—
572C2×D4—594no—
573C2×D4—592no—
574C2×D4—11816no—
575C2×D4—1188no—
576C2×D4—1184no—
577C2×D4—1188no—
578C2×D4—1181no—
579C2×D4—1182no—
580C2×D4Q8×D5914yes—
581C2×D4C23×D5912yes—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—24no—
586C22×C4—82no—
587C22×C4—591no—
588C22×C4—592no—
589C22×C4—594no—
590C22×C4—594no—
591C22×C4—592no—
592C22×C4—591no—
593C22×C4—591no—
594C22×C4—1184no—
595C22×C4—1184no—
596C22×C4—1184no—
597C22×C4—1181no—
598C22×C4—1181no—
599C22×C4—1181no—
600C22×C4—1184no—
601C22×C4—4722no—
602C22×C4—4722no—
603C22×C4—4722no—
604C22×C4—4722no—
605C22×C4D4×D5911yescharacteristic
606C22×C4D4×D5911yescharacteristic
607C22×C4C23×D5911yescharacteristic
608M16—1188no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—592no—
612C2×C8—592no—
613C2×C8—1188no—
614C2×C8—1182no—
615C2×C8—1182no—
616C2×C8C23×D5912yes—
617C2×C8C23×D5912yes—
618C4⋊C4—24no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—594no—
623C4⋊C4—594no—
624C4⋊C4—592no—
625C4⋊C4—592no—
626C4⋊C4—592no—
627C4⋊C4—1184no—
628C4⋊C4—1184no—
629C4⋊C4—1184no—
630C4⋊C4—1184no—
631C4⋊C4—1181no—
632C4⋊C4—1181no—
633C4⋊C4—1181no—
634C4⋊C4—1184no—
635C4⋊C4—1184no—
636C4⋊C4C23×D5912yes—
637C4⋊C4C23×D5912yes—
638C4⋊C4C23×D5912yes—
639C22⋊C4—24no—
640C22⋊C4—594no—
641C22⋊C4—594no—
642C22⋊C4—1184no—
643C22⋊C4—1184no—
644C22⋊C4—1184no—
645C22⋊C4—1184no—
646C22⋊C4—1184no—
647C42—592no—
648C42—592no—
649C42—1184no—
650C42—1184no—
651C42D4×D5912yes—
652C42C23×D5912yes—
653C23—24no—
654C23—22no—
655C23—42no—
656C23—42no—
657C23—594no—
658C23—592no—
659C23—11816no—
660C23—1182no—
661C23—1182no—
662C23—1184no—
663C23—1182no—
664C23—47216no—
665C23—4724no—
666C23—4724no—
667C23—2362no—
668C23—2362no—
669C23C2×D4×D5911yescharacteristic
670Q8—84no—
671Q8—4724no—
672D4—24no—
673D4—22no—
674D4—594no—
675D4—11816no—
676D4—1184no—
677D4—1182no—
678D4C2×Q8×D5914yes—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—84no—
688C2×C4—594no—
689C2×C4—592no—
690C2×C4—598no—
691C2×C4—594no—
692C2×C4—594no—
693C2×C4—592no—
694C2×C4—592no—
695C2×C4—1182no—
696C2×C4—1182no—
697C2×C4—1182no—
698C2×C4—1182no—
699C2×C4—1182no—
700C2×C4—4724no—
701C2×C4—4724no—
702C2×C4—4724no—
703C2×C4—4724no—
704C2×C4—2362no—
705C2×C4—2362no—
706C2×C4—2362no—
707C2×C4C2×D4×D5912yes—
708C2×C4C2×D4×D5912yes—
709C2×C4C2×D4×D5911yescharacteristic
710C2×C4C2×Q8×D5912yes—
711C2×C4#41×D5912yes—
712C2×C4C24×D5911yescharacteristic
713C8—22no—
714C8—22no—
715C8—1182no—
716C8—1182no—
717C22—24no—
718C22—48no—
719C22—42no—
720C22—42no—
721C22—594no—
722C22—1188no—
723C22—1182no—
724C22—1182no—
725C22—1184no—
726C22—47216no—
727C22—2368no—
728C22—2362no—
729C22—2362no—
730C22C22⋊Q8×D5912yes—
731C22#1683820312yes—
732C22#1683821112yes—
733C22C22×D4×D5911yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—594no—
740C4—1182no—
741C4—1182no—
742C4—2362no—
743C4—2362no—
744C4—2362no—
745C4C22⋊Q8×D5912yes—
746C4C22×Q8×D5911yescharacteristic
747C4C2×#41×D5911yescharacteristic
748C2—44no—
749C2—1184no—
750C2—2364no—
751C2#2143392014yesdirect product factor
752C2C2×C22⋊Q8×D5911yescharacteristic
753C2C2×#1683820311yescharacteristic
754C2C2×#1683821111yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#474C2
socleC23×C59C22×D4
prime radicalC22×D4×D59C22
hypercenterC2×#474D59
hypocenterC59C2×#3081
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#16838029C2semidirect
3. #21433920C2direct (N × H)
4. C2×#16837705C2semidirect
5. C2×#16837703C2semidirect
6. C2×#16837702C2semidirect
7. C2×#16837700C2semidirect
8. C2×#16837690C2semidirect
9. C2×#16837689C2semidirect
10. C2×#16837681C2semidirect
11. C2×#16837443C2semidirect
12. C2×#16837439C2semidirect
13. C2×#16837427C2semidirect
16. C2×C59×#474C2semidirect
21. #16838029C22semidirect
22. C2×#14273726C22semidirect
24. C2×#14273719C22semidirect
25. C2×#14273718C22semidirect
42. #16837705C22semidirect
43. #16837703C22semidirect
44. #16837702C22semidirect
45. #16837700C22semidirect
46. #16837690C22semidirect
47. #16837689C22semidirect
48. #16837681C22semidirect
49. #16837443C22semidirect
50. #16837439C22semidirect
51. C2×#14273661C22semidirect
52. C2×#14273660C22semidirect
53. C2×#14273659C22semidirect
54. C2×#14273658C22semidirect
55. C2×#14273658C22semidirect
56. C2×#14273658C22semidirect
57. #16837427C22semidirect
58. C2×C4⋊(C59⋊C8)C22semidirect
59. C2×Dic59⋊C8C22semidirect
60. C2×Dic59⋊C8C22semidirect
69. C2×C4⋊Q8×C59C22semidirect
71. C59×#474C22semidirect
72. C2×#107×C59C22semidirect
73. C2×#107×C59C22semidirect
74. C2×C4⋊C8×C59C22semidirect
83. C2×D4×D59Q8semidirect
97. #14273726C23semidirect
100. #14273719C23semidirect
102. #14273718C23semidirect
145. #14273661C23semidirect
146. #14273660C23semidirect
147. #14273659C23semidirect
148. #14273658C23semidirect
149. #14273658C23semidirect
150. #14273658C23semidirect
151. C4⋊(C59⋊C8)C23semidirect
152. Dic59⋊C8C23semidirect
153. Dic59⋊C8C23semidirect
166. C4⋊Q8×C59C23semidirect
175. #107×C59C23semidirect
176. #107×C59C23semidirect
177. C4⋊C8×C59C23semidirect
213. D4×D59C2×Q8semidirect
381. C2×#474D59semidirect
388. C2×C59#3081semidirect
401. C2×C4⋊Q8C2×D59semidirect
428. #474C2×D59semidirect
433. C2×#107C2×D59semidirect
434. C2×#107C2×D59semidirect
443. C2×C4⋊C8C2×D59semidirect
454. C59C2×#3081semidirect
483. C4⋊Q8C22×D59semidirect
540. #107C22×D59semidirect
541. #107C22×D59semidirect
549. C4⋊C8C22×D59semidirect
751. C2#21433920direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380292
C2×#168378742
#214339202
C2×#168377052
C2×#168377032
C2×#168377022
C2×#168377002
C2×#168376902
C2×#168376892
C2×#168376812
C2×#168374432
C2×#168374392
C2×#168374272
C2×#168374052
C2×#102×D592
C2×C59×#4742
C2×#308159