Finite Group Databasebeta

← C2×#21434631 #29458318

Subgroups — C2×#21434631 #29458318

Order 15104.

1854 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838032C211yesmaximal, characteristic
2C2×#16838029C211yesmaximal, characteristic
3#21434631C2116yesmaximal, direct product factor
4C2×#16837811C211yesmaximal, characteristic, complemented
5C2×#16837810C211yesmaximal, characteristic, complemented
6C2×#16837809C211yesmaximal, characteristic, complemented
7C2×#16837806C211yesmaximal, characteristic, complemented
8C2×#16837805C211yesmaximal, characteristic, complemented
9C2×#16837802C211yesmaximal, characteristic, complemented
10C2×#16837801C211yesmaximal, characteristic, complemented
11C2×#16837443C211yesmaximal, characteristic
12C2×#16837441C211yesmaximal, characteristic
13C2×#16837437C211yesmaximal, characteristic
14C2×#107×D59C211yesmaximal, characteristic
15C2×#16837359C211yesmaximal, characteristic
16C2×C59×#501C211yesmaximal, characteristic, complemented
17C22×#11745659C2211yescharacteristic
18C22×C8×D59C2211yescharacteristic
19#16838032—24no—
20#16838032C2218yes—
21#16838029—24no—
22#16838029C2218yes—
23C2×#14273727C2211yescharacteristic
24C2×#14273726—21no—
25C2×#14273726C2211yescharacteristic
26C2×#14273726C2211yescharacteristic
27C2×#14273725—21no—
28C2×#14273719C2211yescharacteristic
29C2×#14273718C2211yescharacteristic
30C2×#14273718C2211yescharacteristic
31C2×#14273717—21no—
32C2×#14273717—21no—
33C2×#14273707—21no—
34C2×#14273705—21no—
35C2×#14273705—21no—
36C2×#14273703—21no—
37C2×#14273685C2211yescharacteristic
38C2×#14273685C2211yescharacteristic
39C2×#14273684C2211yescharacteristic
40C2×C4⋊C4×D59C2211yescharacteristic
41C2×C4⋊C4×D59C2211yescharacteristic
42#16837811C2218yescomplemented
43#16837810C2218yescomplemented
44#16837809C2218yescomplemented
45#16837806C2218yescomplemented
46#16837805C2218yescomplemented
47#16837802C2218yescomplemented
48#16837801C2218yescomplemented
49#16837443C2218yes—
50#16837441C2218yes—
51#16837437C2218yes—
52C2×#14273661C2211yescharacteristic
53C2×#14273661C2211yescharacteristic
54C2×#14273660C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273660C2211yescharacteristic
58C2×#14273660C2211yescharacteristic
59C2×#14273660C2211yescharacteristic
60#107×D59C2218yes—
61C2×#14273659C2211yescharacteristic
62C2×#14273659C2211yescharacteristic
63C2×#14273658C2211yescharacteristic
64C2×#14273658C2211yescharacteristic
65#16837359C2218yes—
66C2×#14273637C2211yescharacteristic
67C2×C4×C59⋊C8C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C2×C4⋊Q8×C59C2211yescharacteristic
70C2×#125×C59C2211yescharacteristic
71C59×#501C2218yescomplemented
72C2×#107×C59C2211yescharacteristic
73C2×#107×C59C2211yescharacteristic
74C2×#106×C59C2211yescharacteristic
75C2×#106×C59C2211yescharacteristic
76C2×#97×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×Dic118—21no—
80C22×C4×D59—21no—
81C22×C4×D59—21no—
82C22×C4×D59C2311yescharacteristic
83C2×#11745659Q818yescomplemented
84C2×#11745659C2314yes—
85C22×C59⋊C8C2311yescharacteristic
86C22×C59⋊C8C2311yescharacteristic
87C2×C8×D59Q818yescomplemented
88C2×C8×D59C2314yes—
89#14273727—22no—
90#14273727C2314yes—
91#14273726—28no—
92#14273726—22no—
93#14273726—22no—
94#14273726C2314yes—
95#14273726C2314yes—
96#14273725—28no—
97#14273719—22no—
98#14273719C2314yes—
99#14273718—22no—
100#14273718—22no—
101#14273718C2314yes—
102#14273718C2314yes—
103#14273717—28no—
104#14273717—28no—
105#14273707—28no—
106#14273705—28no—
107#14273705—28no—
108#14273703—28no—
109#14273685—22no—
110#14273685—22no—
111#14273685C2314yes—
112#14273685C2314yes—
113#14273684D414yes—
114#14273684C2314yes—
115C2×C4⋊Dic59—21no—
116C2×C4⋊Dic59—21no—
117C2×C4⋊Dic59—21no—
118C2×C4⋊Dic59C2311yescharacteristic
119C2×C4⋊Dic59C2311yescharacteristic
120C2×C4⋊Dic59C2311yescharacteristic
121C2×C4⋊Dic59C2311yescharacteristic
122C2×Dic59⋊C4—21no—
123C2×Dic59⋊C4—21no—
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
131C2×Dic59⋊C4D411yescharacteristic
132C4⋊C4×D59—22no—
133C4⋊C4×D59—22no—
134C4⋊C4×D59C2314yes—
135C4⋊C4×D59C2314yes—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4D411yescharacteristic
139C2×(C2×D59)⋊C4D411yescharacteristic
140C2×C4×Dic59—21no—
141C2×C4×Dic59—21no—
142C2×C4×Dic59C2311yescharacteristic
143#14273661C2314yes—
144#14273661C2314yes—
145#14273660C2314yes—
146#14273660C2314yes—
147#14273660C2314yes—
148#14273660C2314yes—
149#14273660C2314yes—
150#14273660C2314yes—
151#14273659C2314yes—
152#14273659C2314yes—
153#14273658C2314yes—
154#14273658C2314yes—
155#14273637C2314yes—
156C4×C59⋊C8C2314yes—
157C8×Dic59C2314yes—
158C22×Q8×C59—21no—
159C22×C8×C59C2311yescharacteristic
160C22×C8×C59C2311yescharacteristic
161C4⋊Q8×C59—22no—
162C4⋊Q8×C59C2314yes—
163#125×C59—22no—
164#125×C59C2314yes—
165C2×C4⋊C4×C59—21no—
166C2×C4⋊C4×C59—21no—
167C2×C4⋊C4×C59—21no—
168C2×C4⋊C4×C59C2311yescharacteristic
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C42×C59C2311yescharacteristic
173#107×C59C2314yes—
174#107×C59C2314yes—
175#106×C59C2314yes—
176#106×C59C2314yes—
177#97×C59C2314yes—
178C23×D59C2×D411yescharacteristic
179C2×Q8×C59—24no—
180C2×Q8×C59—82no—
181C22×C4×C59—21no—
182C22×C4×C59—21no—
183C22×C4×C59—21no—
184C22×C4×C59—21no—
185C22×C4×C59C2×D411yescharacteristic
186C22×C4×C59C2×D411yescharacteristic
187C22×C4×C59C2411yescharacteristic
188C22×Dic59—21no—
189C22×Dic59—21no—
190C22×Dic59—21no—
191C22×Dic59—21no—
192C22×Dic59C2×D411yescharacteristic
193C22×Dic59C2×D411yescharacteristic
194C22×Dic59C2×D411yescharacteristic
195C2×C4×D59—24no—
196C2×C4×D59—24no—
197C2×C4×D59—82no—
198C2×C4×D59—82no—
199C2×C4×D59C2×D412yes—
200C2×C4×D59C2×Q814yes—
201C2×C4×D59C2×Q814yes—
202C2×C4×D59C2412yes—
203C2×Dic118—24no—
204C2×Dic118—24no—
205C2×Dic118—24no—
206C2×Dic118—82no—
207C2×Dic118—82no—
208C2×Dic118—82no—
209C2×C8×C59C2×Q814yes—
210C2×C8×C59C2×Q814yes—
211C2×C8×C59C2412yes—
212C2×C8×C59C2412yes—
213C4⋊C4×C59—24no—
214C4⋊C4×C59—24no—
215C4⋊C4×C59—24no—
216C4⋊C4×C59—21no—
217C4⋊C4×C59—21no—
218C4⋊C4×C59—21no—
219C4⋊C4×C59—21no—
220C4⋊C4×C59C2412yes—
221C4⋊C4×C59C2412yes—
222C4⋊C4×C59C2412yes—
223C4⋊C4×C59C2412yes—
224C42×C59C2×D412yes—
225C42×C59C2412yes—
226(C2×D59)⋊C4—24no—
227(C2×D59)⋊C4—24no—
228(C2×D59)⋊C4C2×D414yes—
229(C2×D59)⋊C4C2×D414yes—
230C4⋊Dic59—21no—
231C4⋊Dic59—21no—
232C4⋊Dic59—24no—
233C4⋊Dic59—21no—
234C4⋊Dic59—21no—
235C4⋊Dic59—24no—
236C4⋊Dic59—24no—
237C4⋊Dic59C2412yes—
238C4⋊Dic59C2412yes—
239C4⋊Dic59C2412yes—
240C4⋊Dic59C2412yes—
241Dic59⋊C4—24no—
242Dic59⋊C4—24no—
243Dic59⋊C4—24no—
244Dic59⋊C4—24no—
245Dic59⋊C4—24no—
246Dic59⋊C4—24no—
247Dic59⋊C4—24no—
248Dic59⋊C4—24no—
249Dic59⋊C4C2×D414yes—
250Dic59⋊C4C2×D414yes—
251C4×Dic59—24no—
252C4×Dic59—24no—
253C4×Dic59C2×D412yes—
254C4×Dic59C2412yes—
255C2×C59⋊C8C2×Q814yes—
256C2×C59⋊C8C2×Q814yes—
257C2×C59⋊C8C2412yes—
258C2×C59⋊C8C2412yes—
259#11745659C2×Q8116yescomplemented
260C8×D59C2×Q8116yescomplemented
261C23×C59C22×D411yescharacteristic
262C22×D59—22no—
263C22×D59—22no—
264C22×D59C4⋊Q814yes—
265C22×D59C22×D412yes—
266Q8×C59—84no—
267C2×C4×C59—22no—
268C2×C4×C59—22no—
269C2×C4×C59—22no—
270C2×C4×C59—22no—
271C2×C4×C59—22no—
272C2×C4×C59—22no—
273C2×C4×C59—42no—
274C2×C4×C59—42no—
275C2×C4×C59—42no—
276C2×C4×C59—42no—
277C2×C4×C59C22×D412yes—
278C2×C4×C59C22×D412yes—
279C2×C4×C59C22×D411yescharacteristic
280C2×C4×C59C22×Q812yes—
281C2×C4×C59C22×Q812yes—
282C2×C4×C59C2511yescharacteristic
283C2×Dic59—22no—
284C2×Dic59—22no—
285C2×Dic59—22no—
286C2×Dic59—22no—
287C2×Dic59—22no—
288C2×Dic59—22no—
289C2×Dic59—42no—
290C2×Dic59—42no—
291C2×Dic59—42no—
292C2×Dic59—42no—
293C2×Dic59C4⋊Q814yes—
294C2×Dic59C22×D412yes—
295C2×Dic59C22×D412yes—
296C2×Dic59C22×D412yes—
297C4×D59—84no—
298C4×D59—84no—
299C4×D59C4⋊Q818yes—
300C4×D59C22×Q814yes—
301C4×D59C22×Q814yes—
302Dic118—84no—
303Dic118—84no—
304Dic118—84no—
305C8×C59C22×Q814yes—
306C8×C59C22×Q814yes—
307C59⋊C8C22×Q814yes—
308C59⋊C8C22×Q814yes—
309C2×#3164—591nomaximal, Sylow
310C22×C59C2×C4⋊Q812yes—
311C22×C59#57612yes—
312C22×C59#57812yes—
313C22×C59C23×D411yescharacteristic
314C2×D59—28no—
315C2×D59—22no—
316C2×D59—22no—
317C2×D59C2×C4⋊Q814yes—
318C4×C59—22no—
319C4×C59—22no—
320C4×C59—42no—
321C4×C59—42no—
322C4×C59—42no—
323C4×C59—42no—
324C4×C59C2×C4⋊Q812yes—
325C4×C59C23×Q811yescharacteristic
326C4×C59C23×Q811yescharacteristic
327Dic59—22no—
328Dic59—22no—
329Dic59—42no—
330Dic59—42no—
331Dic59—42no—
332Dic59—42no—
333Dic59C2×C4⋊Q814yes—
334C2×#544—591no—
335C2×#544—591no—
336#3164—5916no—
337C2×#501—591no—
338C2×#501—591no—
339C2×#501—591no—
340C2×#501D5911yescharacteristic, complemented
341C2×#500—591no—
342C2×#500—591no—
343C2×#499—591no—
344C2×#499—591no—
345C2×#428—591no—
346C2×#428—591no—
347C2×#427—591no—
348C22×#107—591no—
349C2×#405—591no—
350C2×C59#316414yescomplemented
351C2×C59C22×C4⋊Q811yescharacteristic
352C2×C59C2×#57611yescharacteristic
353C2×C59C2×#57811yescharacteristic
354D59—24no—
355C22×M16—591no—
356C23×C8—591no—
357#544—598no—
358#544—598no—
359#544—1184no—
360#544—1184no—
361C2×C4⋊Q8—591no—
362C2×C4⋊Q8—591no—
363C2×C4⋊Q8—591no—
364C2×C4⋊Q8—1181no—
365C2×C4⋊Q8—1181no—
366C2×C4⋊Q8C2×D5911yescharacteristic
367C2×#125—591no—
368C2×#125—591no—
369C2×#125—591no—
370C2×#125—1181no—
371C2×#125—1181no—
372C2×#125C2×D5911yescharacteristic
373C2×C22⋊Q8—1181no—
374C2×C22⋊Q8—1181no—
375C2×C22⋊Q8—1181no—
376C2×C22⋊Q8—1181no—
377C2×#117—591no—
378C2×#117—591no—
379C2×#117—591no—
380C22×C4⋊C4—591no—
381C22×C4⋊C4—591no—
382#501—598no—
383#501—598no—
384#501—598no—
385#501C2×D5918yescomplemented
386#500—598no—
387#500—598no—
388#499—598no—
389#499—598no—
390#428—598no—
391#428—598no—
392#427—598no—
393C2×#107—591no—
394C2×#107—591no—
395C2×#107—591no—
396C2×#107—591no—
397C2×#107—591no—
398C2×#107—591no—
399C2×#107—591no—
400C2×#107—591no—
401C2×#107—598no—
402C2×#107C2×D5911yescharacteristic
403C2×#107C2×D5911yescharacteristic
404C2×#106—591no—
405C2×#106—591no—
406C2×#106—591no—
407C2×#106—591no—
408C2×#106C2×D5911yescharacteristic
409C2×#106C2×D5911yescharacteristic
410#405—598no—
411C2×#97—591no—
412C2×#97C2×D5911yescharacteristic
413C2×C4×C8—591no—
414C2×C4×C8—591no—
415C59C2×#316411yescharacteristic, complemented, Sylow
416C22×Q8—21no—
417C22×Q8—1181no—
418C22×Q8—1181no—
419C22×Q8—1181no—
420C23×C4—591no—
421C23×C4—1181no—
422C23×C4—1181no—
423C2×M16—598no—
424C2×M16—594no—
425C22×C8—591no—
426C22×C8—591no—
427C22×C8—598no—
428C22×C8—594no—
429C22×C8C22×D5911yescharacteristic
430C22×C8C22×D5911yescharacteristic
431C4⋊Q8—22no—
432C4⋊Q8—594no—
433C4⋊Q8—594no—
434C4⋊Q8—594no—
435C4⋊Q8—1182no—
436C4⋊Q8—1182no—
437C4⋊Q8—1188no—
438C4⋊Q8—1188no—
439C4⋊Q8—1182no—
440C4⋊Q8C22×D5914yes—
441#125—22no—
442#125—594no—
443#125—594no—
444#125—594no—
445#125—1182no—
446#125—1182no—
447#125—1188no—
448#125—1188no—
449#125—1182no—
450#125C22×D5914yes—
451C22⋊Q8—1188no—
452C22⋊Q8—1188no—
453C22⋊Q8—1188no—
454C22⋊Q8—1188no—
455#117—594no—
456#117—594no—
457#117—594no—
458#117—594no—
459#117—1182no—
460#117—1182no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—591no—
465C2×C4⋊C4—591no—
466C2×C4⋊C4—591no—
467C2×C4⋊C4—591no—
468C2×C4⋊C4—591no—
469C2×C4⋊C4—591no—
470C2×C4⋊C4—594no—
471C2×C4⋊C4—594no—
472C2×C4⋊C4—1182no—
473C2×C4⋊C4—1182no—
474C2×C4⋊C4—1181no—
475C2×C4⋊C4—1181no—
476C2×C4⋊C4—1181no—
477C2×C4⋊C4—1181no—
478C2×C4⋊C4—1181no—
479C2×C4⋊C4—1181no—
480C2×C4⋊C4—1181no—
481C2×C4⋊C4—1181no—
482C2×C4⋊C4—1181no—
483C2×C4⋊C4—1181no—
484C2×C4⋊C4—1181no—
485C2×C4⋊C4C22×D5911yescharacteristic
486C2×C4⋊C4C22×D5911yescharacteristic
487C2×C4⋊C4C22×D5911yescharacteristic
488C2×C4⋊C4C22×D5911yescharacteristic
489C2×C22⋊C4—591no—
490C2×C22⋊C4—591no—
491C2×C22⋊C4—1181no—
492C2×C22⋊C4—1181no—
493C2×C42—591no—
494C2×C42—1181no—
495C2×C42—1181no—
496C2×C42C22×D5911yescharacteristic
497#107—594no—
498#107—594no—
499#107—594no—
500#107—594no—
501#107—594no—
502#107—594no—
503#107—594no—
504#107—594no—
505#107C22×D5914yes—
506#107C22×D5914yes—
507#106—594no—
508#106—594no—
509#106—594no—
510#106—594no—
511#106C22×D5914yes—
512#106C22×D5914yes—
513#97—594no—
514#97C22×D5914yes—
515C4×C8—594no—
516C4×C8—594no—
517C24—591no—
518C2×Q8—24no—
519C2×Q8—82no—
520C2×Q8—1184no—
521C2×Q8—1184no—
522C2×Q8—1184no—
523C2×Q8—4722no—
524C2×Q8—4722no—
525C2×Q8—4722no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—591no—
531C22×C4—592no—
532C22×C4—594no—
533C22×C4—594no—
534C22×C4—592no—
535C22×C4—591no—
536C22×C4—591no—
537C22×C4—1184no—
538C22×C4—1184no—
539C22×C4—1181no—
540C22×C4—1181no—
541C22×C4—1181no—
542C22×C4—1181no—
543C22×C4—4722no—
544C22×C4—4722no—
545C22×C4D4×D5911yescharacteristic
546C22×C4D4×D5911yescharacteristic
547C22×C4C23×D5911yescharacteristic
548M16—5916no—
549C2×C8—594no—
550C2×C8—594no—
551C2×C8—592no—
552C2×C8—592no—
553C2×C8—5916no—
554C2×C8Q8×D5914yes—
555C2×C8Q8×D5914yes—
556C2×C8C23×D5912yes—
557C2×C8C23×D5912yes—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—594no—
566C4⋊C4—594no—
567C4⋊C4—592no—
568C4⋊C4—592no—
569C4⋊C4—592no—
570C4⋊C4—592no—
571C4⋊C4—1184no—
572C4⋊C4—1184no—
573C4⋊C4—1184no—
574C4⋊C4—1184no—
575C4⋊C4—1184no—
576C4⋊C4—1184no—
577C4⋊C4—1184no—
578C4⋊C4—1184no—
579C4⋊C4—1181no—
580C4⋊C4—1181no—
581C4⋊C4—1181no—
582C4⋊C4—1181no—
583C4⋊C4—1184no—
584C4⋊C4—1184no—
585C4⋊C4—1184no—
586C4⋊C4C23×D5912yes—
587C4⋊C4C23×D5912yes—
588C4⋊C4C23×D5912yes—
589C4⋊C4C23×D5912yes—
590C22⋊C4—594no—
591C22⋊C4—594no—
592C22⋊C4—1184no—
593C22⋊C4—1184no—
594C42—592no—
595C42—592no—
596C42—1184no—
597C42—1184no—
598C42D4×D5912yes—
599C42C23×D5912yes—
600C23—594no—
601C23—592no—
602C23—1182no—
603C23—1182no—
604C23C2×D4×D5911yescharacteristic
605Q8—84no—
606Q8—4724no—
607Q8—4724no—
608Q8—4724no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—594no—
620C2×C4—592no—
621C2×C4—598no—
622C2×C4—594no—
623C2×C4—594no—
624C2×C4—592no—
625C2×C4—592no—
626C2×C4—1182no—
627C2×C4—1182no—
628C2×C4—1182no—
629C2×C4—1182no—
630C2×C4—1182no—
631C2×C4—1182no—
632C2×C4—4724no—
633C2×C4—4724no—
634C2×C4—2362no—
635C2×C4—2362no—
636C2×C4—2362no—
637C2×C4—2362no—
638C2×C4C2×D4×D5912yes—
639C2×C4C2×D4×D5912yes—
640C2×C4C2×D4×D5911yescharacteristic
641C2×C4C2×Q8×D5912yes—
642C2×C4C2×Q8×D5912yes—
643C2×C4C24×D5911yescharacteristic
644C8—594no—
645C8—594no—
646C8C2×Q8×D5914yes—
647C8C2×Q8×D5914yes—
648C22—594no—
649C22—1188no—
650C22—1182no—
651C22—1182no—
652C22C4⋊Q8×D5912yes—
653C22#1683820612yes—
654C22#1683821812yes—
655C22C22×D4×D5911yescharacteristic
656C4—22no—
657C4—22no—
658C4—42no—
659C4—42no—
660C4—42no—
661C4—42no—
662C4—594no—
663C4—1182no—
664C4—1182no—
665C4—2362no—
666C4—2362no—
667C4—2362no—
668C4—2362no—
669C4C4⋊Q8×D5912yes—
670C4C22×Q8×D5911yescharacteristic
671C4C22×Q8×D5911yescharacteristic
672C2—1184no—
673C2#2143463114yesdirect product factor
674C2C2×C4⋊Q8×D5911yescharacteristic
675C2C2×#1683820611yescharacteristic
676C2C2×#1683821811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#501C2
socleC23×C59C22×D4
prime radicalC23×D59C2×D4
hypercenterC2×#501D59
hypocenterC59C2×#3164
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
3. #21434631C2direct (N × H)
4. C2×#16837811C2semidirect
5. C2×#16837810C2semidirect
6. C2×#16837809C2semidirect
7. C2×#16837806C2semidirect
8. C2×#16837805C2semidirect
9. C2×#16837802C2semidirect
10. C2×#16837801C2semidirect
16. C2×C59×#501C2semidirect
42. #16837811C22semidirect
43. #16837810C22semidirect
44. #16837809C22semidirect
45. #16837806C22semidirect
46. #16837805C22semidirect
47. #16837802C22semidirect
48. #16837801C22semidirect
71. C59×#501C22semidirect
83. C2×#11745659Q8semidirect
87. C2×C8×D59Q8semidirect
259. #11745659C2×Q8semidirect
260. C8×D59C2×Q8semidirect
340. C2×#501D59semidirect
350. C2×C59#3164semidirect
385. #501C2×D59semidirect
415. C59C2×#3164semidirect
673. C2#21434631direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380322
C2×#168380292
#214346312
C2×#168378112
C2×#168378102
C2×#168378092
C2×#168378062
C2×#168378052
C2×#168378022
C2×#168378012
C2×#168374432
C2×#168374412
C2×#168374372
C2×#107×D592
C2×#168373592
C2×C59×#5012
C2×#316459