Finite Group Databasebeta

← C2×#21437003 #29469175

Subgroups — C2×#21437003 #29469175

Order 15104.

1854 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838132C211yesmaximal, characteristic, complemented
2C2×#16838108C211yesmaximal, characteristic
3#21437003C2116yesmaximal, direct product factor
4C2×#16837809C211yesmaximal, characteristic, complemented
5C2×#16837806C211yesmaximal, characteristic, complemented
6C2×#16837712C211yesmaximal, characteristic, complemented
7C2×#16837706C211yesmaximal, characteristic, complemented
8C2×#16837696C211yesmaximal, characteristic, complemented
9C2×#16837691C211yesmaximal, characteristic
10C2×#16837681C211yesmaximal, characteristic
11C2×#16837679C211yesmaximal, characteristic
12C2×#16837530C211yesmaximal, characteristic, complemented
13C2×#16837504C211yesmaximal, characteristic
14C2×#16837501C211yesmaximal, characteristic
15C2×#16837489C211yesmaximal, characteristic
16C2×C59×#501C211yesmaximal, characteristic, complemented
17C22×#11745660C2211yescharacteristic
18#16838132—24no—
19#16838132C2218yescomplemented
20#16838108—24no—
21#16838108C2218yes—
22C2×#14273726—21no—
23C2×#14273726C2211yescharacteristic
24C2×#14273726C2211yescharacteristic
25C2×#14273726C2211yescharacteristic
26C2×#14273725—21no—
27C2×#14273725—21no—
28C2×#14273718C2211yescharacteristic
29C2×#14273707—21no—
30C2×#14273705—21no—
31C2×#14273705—21no—
32C2×C4×Dic118C2211yescharacteristic
33C2×C4×Dic118C2211yescharacteristic
34C2×#14273692—21no—
35C2×#14273692C2211yescharacteristic
36C2×#14273692C2211yescharacteristic
37C2×C4×D236C2211yescharacteristic
38C2×#14273689C2211yescharacteristic
39C2×#14273689C2211yescharacteristic
40C2×C4⋊C4×D59—21no—
41#16837809C2218yescomplemented
42#16837806C2218yescomplemented
43#16837712C2218yescomplemented
44#16837706C2218yescomplemented
45#16837696C2218yescomplemented
46#16837691C2218yes—
47#16837681C2218yes—
48#16837679C2218yes—
49#16837530C2218yescomplemented
50#16837504C2218yes—
51#16837501C2218yes—
52#16837489C2218yes—
53C2×#14273661C2211yescharacteristic
54C2×#14273660C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×C4⋊(C59⋊C8)C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×Dic59⋊C8C2211yescharacteristic
61C2×#14273652C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×#14273647C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
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×Dic118D411yescharacteristic
81C22×Dic118C2311yescharacteristic
82C22×D236C2311yescharacteristic
83C22×C4×D59—21no—
84C22×C4×D59—21no—
85C22×C4×D59—21no—
86C2×#11745660Q818yescomplemented
87C2×#11745660C2314yes—
88C22×C59⋊C8C2311yescharacteristic
89C22×C59⋊C8C2311yescharacteristic
90#14273726—28no—
91#14273726—22no—
92#14273726—22no—
93#14273726—22no—
94#14273726C2314yes—
95#14273726C2314yes—
96#14273726C2314yes—
97#14273725—28no—
98#14273725—28no—
99#14273718—22no—
100#14273718C2314yes—
101#14273707—28no—
102#14273705—28no—
103#14273705—28no—
104C4×Dic118—22no—
105C4×Dic118D414yes—
106C4×Dic118C2314yes—
107C4×Dic118C2314yes—
108#14273692—28no—
109#14273692—22no—
110#14273692—22no—
111#14273692C2314yes—
112#14273692C2314yes—
113C4×D236—22no—
114C4×D236C2314yes—
115#14273689—22no—
116#14273689—22no—
117#14273689C2314yes—
118#14273689C2314yes—
119C2×C4⋊Dic59—21no—
120C2×C4⋊Dic59D411yescharacteristic
121C2×C4⋊Dic59C2311yescharacteristic
122C2×C4⋊Dic59C2311yescharacteristic
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—28no—
133C2×(C2×D59)⋊C4—21no—
134C2×(C2×D59)⋊C4—21no—
135C2×(C2×D59)⋊C4—21no—
136C2×C4×Dic59—21no—
137C2×C4×Dic59—21no—
138C2×C4×Dic59—21no—
139C2×C4×Dic59C2311yescharacteristic
140C2×C4×Dic59C2311yescharacteristic
141#14273661C2314yes—
142#14273660C2314yes—
143#14273660C2314yes—
144#14273660C2314yes—
145#14273658C2314yes—
146C4⋊(C59⋊C8)C2314yes—
147Dic59⋊C8C2314yes—
148Dic59⋊C8C2314yes—
149#14273652C2314yes—
150#14273650C2314yes—
151#14273650C2314yes—
152#14273649C2314yes—
153#14273647C2314yes—
154#14273647C2314yes—
155#14273637C2314yes—
156C8×Dic59C2314yes—
157C22×Q8×C59—21no—
158C22×C8×C59C2311yescharacteristic
159C22×C8×C59C2311yescharacteristic
160C4⋊Q8×C59—22no—
161C4⋊Q8×C59C2314yes—
162#125×C59—22no—
163#125×C59C2314yes—
164C2×C4⋊C4×C59—21no—
165C2×C4⋊C4×C59—21no—
166C2×C4⋊C4×C59—21no—
167C2×C4⋊C4×C59C2311yescharacteristic
168C2×C4⋊C4×C59C2311yescharacteristic
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C42×C59C2311yescharacteristic
172#107×C59C2314yes—
173#107×C59C2314yes—
174#106×C59C2314yes—
175#106×C59C2314yes—
176#97×C59C2314yes—
177C23×D59—21no—
178C2×Q8×C59—24no—
179C2×Q8×C59—82no—
180C22×C4×C59—21no—
181C22×C4×C59—21no—
182C22×C4×C59—21no—
183C22×C4×C59—21no—
184C22×C4×C59C2×D411yescharacteristic
185C22×C4×C59C2×D411yescharacteristic
186C22×C4×C59C2411yescharacteristic
187C22×Dic59—21no—
188C22×Dic59—21no—
189C22×Dic59—21no—
190C22×Dic59C2×D411yescharacteristic
191C22×Dic59C2×D411yescharacteristic
192C22×Dic59C2×D411yescharacteristic
193C22×Dic59C2×D411yescharacteristic
194C2×D236—21no—
195C2×D236—22no—
196C2×D236C2×Q814yes—
197C2×D236C2412yes—
198C2×C4×D59—24no—
199C2×C4×D59—24no—
200C2×C4×D59—24no—
201C2×C4×D59—44no—
202C2×C4×D59—82no—
203C2×C4×D59—82no—
204C2×Dic118—21no—
205C2×Dic118—22no—
206C2×Dic118—24no—
207C2×Dic118—24no—
208C2×Dic118—24no—
209C2×Dic118—24no—
210C2×Dic118—82no—
211C2×Dic118—82no—
212C2×Dic118—82no—
213C2×Dic118C2×D414yes—
214C2×Dic118C2×Q814yes—
215C2×Dic118C2412yes—
216C2×C8×C59—22no—
217C2×C8×C59C2×Q814yes—
218C2×C8×C59C2412yes—
219C2×C8×C59C2412yes—
220C4⋊C4×C59—24no—
221C4⋊C4×C59—24no—
222C4⋊C4×C59—24no—
223C4⋊C4×C59—21no—
224C4⋊C4×C59—21no—
225C4⋊C4×C59—21no—
226C4⋊C4×C59—21no—
227C4⋊C4×C59C2412yes—
228C4⋊C4×C59C2412yes—
229C4⋊C4×C59C2412yes—
230C4⋊C4×C59C2412yes—
231C42×C59C2×D412yes—
232C42×C59C2412yes—
233(C2×D59)⋊C4—24no—
234(C2×D59)⋊C4—24no—
235(C2×D59)⋊C4—24no—
236C4⋊Dic59—21no—
237C4⋊Dic59—21no—
238C4⋊Dic59—24no—
239C4⋊Dic59C2×D414yes—
240C4⋊Dic59C2412yes—
241C4⋊Dic59C2412yes—
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×Dic59—24no—
254C4×Dic59C2×D412yes—
255C4×Dic59C2×D412yes—
256C4×Dic59C2412yes—
257C4×Dic59C2412yes—
258C2×C59⋊C8—22no—
259C2×C59⋊C8—22no—
260C2×C59⋊C8C2412yes—
261C2×C59⋊C8C2412yes—
262#11745660C2×Q8116yescomplemented
263C23×C59C22×D411yescharacteristic
264C22×D59—24no—
265C22×D59—22no—
266C22×D59—42no—
267C22×D59—42no—
268Q8×C59—84no—
269C2×C4×C59—22no—
270C2×C4×C59—22no—
271C2×C4×C59—22no—
272C2×C4×C59—22no—
273C2×C4×C59—22no—
274C2×C4×C59—22no—
275C2×C4×C59—42no—
276C2×C4×C59—42no—
277C2×C4×C59—42no—
278C2×C4×C59—42no—
279C2×C4×C59C22×D412yes—
280C2×C4×C59C22×D412yes—
281C2×C4×C59C22×D411yescharacteristic
282C2×C4×C59C22×Q812yes—
283C2×C4×C592−1+412yes—
284C2×C4×C59C2511yescharacteristic
285C2×Dic59—24no—
286C2×Dic59—22no—
287C2×Dic59—22no—
288C2×Dic59—22no—
289C2×Dic59—22no—
290C2×Dic59—22no—
291C2×Dic59—22no—
292C2×Dic59—42no—
293C2×Dic59—42no—
294C2×Dic59#13714yes—
295C2×Dic59C22×D412yes—
296C2×Dic59C22×D412yes—
297C2×Dic59C22×D412yes—
298C2×Dic59C22×D412yes—
299D236—24no—
300D236—22no—
301D236C22×Q814yes—
302C4×D59—48no—
303C4×D59—84no—
304C4×D59—84no—
305Dic118—24no—
306Dic118—22no—
307Dic118—28no—
308Dic118—84no—
309Dic118—84no—
310Dic118—84no—
311Dic118C22×Q814yes—
312C8×C59—22no—
313C8×C59C22×Q814yes—
314C59⋊C8—22no—
315C59⋊C8—22no—
316C2×#3385—591nomaximal, Sylow
317C22×C59D4×Q812yes—
318C22×C59C2×#13712yes—
319C22×C59#57612yes—
320C22×C59C23×D411yescharacteristic
321C2×D59—24no—
322C2×D59—48no—
323C2×D59—42no—
324C2×D59—42no—
325C4×C59—22no—
326C4×C59—22no—
327C4×C59—42no—
328C4×C59—42no—
329C4×C59—42no—
330C4×C59—42no—
331C4×C59D4×Q812yes—
332C4×C59C23×Q811yescharacteristic
333C4×C59C2×2−1+411yescharacteristic
334Dic59—24no—
335Dic59—22no—
336Dic59—22no—
337Dic59—22no—
338Dic59—42no—
339Dic59—42no—
340Dic59C2×#13714yes—
341C2×Q82—591no—
342C2×#554—591no—
343#3385—5916no—
344C2×#501—591no—
345C2×#501D5911yescharacteristic, complemented
346C2×#500—591no—
347C2×#479—591no—
348C2×#479—591no—
349C2×#477—591no—
350C2×#476—591no—
351C2×#474—591no—
352C2×#474—591no—
353C2×#446—591no—
354C2×#440—591no—
355C2×#440—591no—
356C2×C4×SD16—591no—
357C2×C59#338514yescomplemented
358C2×C59C2×D4×Q811yescharacteristic
359C2×C59C22×#13711yescharacteristic
360C2×C59C2×#57611yescharacteristic
361D59—44no—
362C22×SD16—591no—
363Q82—598no—
364Q82—1184no—
365#554—598no—
366#554—1184no—
367C2×C4⋊Q8—591no—
368C2×C4⋊Q8—591no—
369C2×C4⋊Q8—591no—
370C2×C4⋊Q8—1181no—
371C2×C4⋊Q8—1181no—
372C2×C4⋊Q8—1181no—
373C2×C4⋊Q8C2×D5911yescharacteristic
374C2×#125—591no—
375C2×#125C2×D5911yescharacteristic
376C2×C22⋊Q8—1181no—
377C2×C22⋊Q8—1181no—
378C2×C22⋊Q8—1181no—
379C2×C4×Q8—591no—
380C2×C4×Q8—591no—
381C2×C4×Q8—591no—
382C2×C4×Q8—591no—
383C2×C4×Q8—1181no—
384C2×C4×D4—591no—
385C2×C4×D4—591no—
386C2×C4×D4—591no—
387C22×C4⋊C4—1181no—
388#501—598no—
389#501C2×D5918yescomplemented
390#500—598no—
391#479—598no—
392#479—598no—
393#477—598no—
394#476—598no—
395#474—598no—
396#474—598no—
397#446—598no—
398#440—598no—
399#440—598no—
400C4×SD16—598no—
401C2×#107—591no—
402C2×#107—591no—
403C2×#107—591no—
404C2×#107—591no—
405C2×#107C2×D5911yescharacteristic
406C2×#107C2×D5911yescharacteristic
407C2×#106—591no—
408C2×#106C2×D5911yescharacteristic
409C2×#106C2×D5911yescharacteristic
410C2×C4⋊C8—591no—
411C2×C4⋊C8—591no—
412C2×C4⋊C8—591no—
413C2×#103—591no—
414C2×#103—591no—
415C2×#103—591no—
416C2×#102—591no—
417C2×#102—591no—
418C2×#102—591no—
419C2×#97—591no—
420C2×#97C2×D5911yescharacteristic
421C2×C4×C8—591no—
422C59C2×#338511yescharacteristic, complemented, Sylow
423C22×Q8—21no—
424C22×Q8—591no—
425C22×Q8—591no—
426C22×Q8—1181no—
427C22×Q8—1181no—
428C22×Q8—1181no—
429C22×D4—591no—
430C23×C4—1181no—
431C23×C4—1181no—
432C23×C4—1181no—
433C2×SD16—598no—
434C2×SD16—594no—
435C22×C8—591no—
436C22×C8—591no—
437C22×C8C22×D5911yescharacteristic
438C22×C8C22×D5911yescharacteristic
439C4⋊Q8—22no—
440C4⋊Q8—594no—
441C4⋊Q8—594no—
442C4⋊Q8—594no—
443C4⋊Q8—1182no—
444C4⋊Q8—1182no—
445C4⋊Q8—1182no—
446C4⋊Q8—1188no—
447C4⋊Q8—1188no—
448C4⋊Q8—1188no—
449C4⋊Q8C22×D5914yes—
450#125—22no—
451#125—594no—
452#125—1182no—
453#125C22×D5914yes—
454C22⋊Q8—1188no—
455C22⋊Q8—1188no—
456C22⋊Q8—1188no—
457C4×Q8—594no—
458C4×Q8—594no—
459C4×Q8—594no—
460C4×Q8—594no—
461C4×Q8—594no—
462C4×Q8—1182no—
463C4×Q8—1182no—
464C4×Q8—1188no—
465C4×Q8—1182no—
466C4×D4—594no—
467C4×D4—594no—
468C4×D4—594no—
469C4×D4—1182no—
470C4×D4—1182no—
471C4×D4—1182no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—591no—
476C2×C4⋊C4—591no—
477C2×C4⋊C4—591no—
478C2×C4⋊C4—591no—
479C2×C4⋊C4—591no—
480C2×C4⋊C4—1188no—
481C2×C4⋊C4—1181no—
482C2×C4⋊C4—1181no—
483C2×C4⋊C4—1181no—
484C2×C4⋊C4—1181no—
485C2×C4⋊C4—1181no—
486C2×C4⋊C4—1181no—
487C2×C4⋊C4—1181no—
488C2×C4⋊C4—1181no—
489C2×C4⋊C4C22×D5911yescharacteristic
490C2×C4⋊C4C22×D5911yescharacteristic
491C2×C4⋊C4C22×D5911yescharacteristic
492C2×C4⋊C4C22×D5911yescharacteristic
493C2×C22⋊C4—1181no—
494C2×C22⋊C4—1181no—
495C2×C22⋊C4—1181no—
496C2×C42—591no—
497C2×C42—591no—
498C2×C42—1181no—
499C2×C42—1181no—
500C2×C42—1181no—
501C2×C42C22×D5911yescharacteristic
502#107—594no—
503#107—594no—
504#107—594no—
505#107—594no—
506#107C22×D5914yes—
507#107C22×D5914yes—
508#106—594no—
509#106C22×D5914yes—
510#106C22×D5914yes—
511C4⋊C8—594no—
512C4⋊C8—594no—
513C4⋊C8—594no—
514#103—594no—
515#103—594no—
516#103—594no—
517#102—594no—
518#102—594no—
519#102—594no—
520#97—594no—
521#97C22×D5914yes—
522C4×C8—594no—
523C24—1181no—
524C2×Q8—24no—
525C2×Q8—82no—
526C2×Q8—594no—
527C2×Q8—594no—
528C2×Q8—592no—
529C2×Q8—1184no—
530C2×Q8—1184no—
531C2×Q8—1184no—
532C2×Q8—1184no—
533C2×Q8—1181no—
534C2×Q8—1182no—
535C2×Q8—4722no—
536C2×Q8—4722no—
537C2×Q8—4722no—
538C2×D4—594no—
539C2×D4—592no—
540C2×D4—1181no—
541C2×D4—1182no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—591no—
547C22×C4—591no—
548C22×C4—591no—
549C22×C4—591no—
550C22×C4—1184no—
551C22×C4—1184no—
552C22×C4—1181no—
553C22×C4—1181no—
554C22×C4—1181no—
555C22×C4—1184no—
556C22×C4—4722no—
557C22×C4—4722no—
558C22×C4—2364no—
559C22×C4D4×D5911yescharacteristic
560C22×C4D4×D5911yescharacteristic
561C22×C4C23×D5911yescharacteristic
562SD16—5916no—
563C2×C8—22no—
564C2×C8—592no—
565C2×C8—592no—
566C2×C8—1182no—
567C2×C8—1182no—
568C2×C8Q8×D5914yes—
569C2×C8C23×D5912yes—
570C2×C8C23×D5912yes—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—594no—
579C4⋊C4—594no—
580C4⋊C4—594no—
581C4⋊C4—592no—
582C4⋊C4—592no—
583C4⋊C4—1184no—
584C4⋊C4—1184no—
585C4⋊C4—1184no—
586C4⋊C4—1184no—
587C4⋊C4—1184no—
588C4⋊C4—1184no—
589C4⋊C4—1184no—
590C4⋊C4—1181no—
591C4⋊C4—1181no—
592C4⋊C4—1184no—
593C4⋊C4C23×D5912yes—
594C4⋊C4C23×D5912yes—
595C4⋊C4C23×D5912yes—
596C4⋊C4C23×D5912yes—
597C22⋊C4—1184no—
598C22⋊C4—1184no—
599C22⋊C4—1184no—
600C42—592no—
601C42—592no—
602C42—592no—
603C42—592no—
604C42—1184no—
605C42—1184no—
606C42—1184no—
607C42D4×D5912yes—
608C42C23×D5912yes—
609C23—1182no—
610C23—1184no—
611C23—2362no—
612C23—2362no—
613C23C2×D4×D5911yescharacteristic
614Q8—84no—
615Q8—594no—
616Q8—1188no—
617Q8—1182no—
618Q8—1184no—
619Q8—4724no—
620Q8—4724no—
621Q8—4724no—
622D4—594no—
623D4—1182no—
624D4—1184no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—594no—
636C2×C4—592no—
637C2×C4—592no—
638C2×C4—592no—
639C2×C4—592no—
640C2×C4—1182no—
641C2×C4—1182no—
642C2×C4—1182no—
643C2×C4—1182no—
644C2×C4—1184no—
645C2×C4—1182no—
646C2×C4—1182no—
647C2×C4—4724no—
648C2×C4—4724no—
649C2×C4—2368no—
650C2×C4—2362no—
651C2×C4—2362no—
652C2×C4C2×D4×D5912yes—
653C2×C4C2×D4×D5912yes—
654C2×C4C2×D4×D5911yescharacteristic
655C2×C4C2×Q8×D5912yes—
656C2×C4#1427377512yes—
657C2×C4C24×D5911yescharacteristic
658C8—22no—
659C8—1182no—
660C8—1182no—
661C8C2×Q8×D5914yes—
662C22—1184no—
663C22—2368no—
664C22—2362no—
665C22—2362no—
666C22#1683806712yes—
667C22#137×D5912yes—
668C22#1683820612yes—
669C22C22×D4×D5911yescharacteristic
670C4—22no—
671C4—22no—
672C4—42no—
673C4—42no—
674C4—42no—
675C4—42no—
676C4—594no—
677C4—1182no—
678C4—1182no—
679C4—1182no—
680C4—1184no—
681C4—2362no—
682C4—2362no—
683C4#1683806712yes—
684C4C22×Q8×D5911yescharacteristic
685C4C2×#1427377511yescharacteristic
686C2—2364no—
687C2#2143700314yesdirect product factor
688C2C2×#1683806711yescharacteristic
689C2C2×#137×D5911yescharacteristic
690C2C2×#1683820611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#501C2
socleC23×C59C22×D4
prime radicalC22×D236C23
hypercenterC2×#501D59
hypocenterC59C2×#3385
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
1. C2×#16838132C2semidirect
3. #21437003C2direct (N × H)
4. C2×#16837809C2semidirect
5. C2×#16837806C2semidirect
6. C2×#16837712C2semidirect
7. C2×#16837706C2semidirect
8. C2×#16837696C2semidirect
12. C2×#16837530C2semidirect
16. C2×C59×#501C2semidirect
19. #16838132C22semidirect
41. #16837809C22semidirect
42. #16837806C22semidirect
43. #16837712C22semidirect
44. #16837706C22semidirect
45. #16837696C22semidirect
49. #16837530C22semidirect
71. C59×#501C22semidirect
86. C2×#11745660Q8semidirect
262. #11745660C2×Q8semidirect
345. C2×#501D59semidirect
357. C2×C59#3385semidirect
389. #501C2×D59semidirect
422. C59C2×#3385semidirect
687. C2#21437003direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381322
C2×#168381082
#214370032
C2×#168378092
C2×#168378062
C2×#168377122
C2×#168377062
C2×#168376962
C2×#168376912
C2×#168376812
C2×#168376792
C2×#168375302
C2×#168375042
C2×#168375012
C2×#168374892
C2×C59×#5012
C2×#338559