Finite Group Databasebeta

← C2×#21436934 #29468482

Subgroups — C2×#21436934 #29468482

Order 15104.

1810 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838128C211yesmaximal, characteristic, complemented
2C2×#16838124C211yesmaximal, characteristic
3#21436934C2116yesmaximal, direct product factor
4C2×#16837769C211yesmaximal, characteristic, complemented
5C2×#16837763C211yesmaximal, characteristic
6C2×#16837757C211yesmaximal, characteristic
7C2×#16837709C211yesmaximal, characteristic, complemented
8C2×#16837696C211yesmaximal, characteristic, complemented
9C2×#16837705C211yesmaximal, characteristic
10C2×#16837626C211yesmaximal, characteristic
11C2×#16837624C211yesmaximal, characteristic
12C2×#16837610C211yesmaximal, characteristic, complemented
13C2×#16837532C211yesmaximal, characteristic, complemented
14C2×#16837506C211yesmaximal, characteristic, complemented
15C2×#16837505C211yesmaximal, characteristic
16C2×C4×Q16×C59C211yesmaximal, characteristic, complemented
17C22×#11745672C2211yescharacteristic
18C22×#11745671C2211yescharacteristic
19#16838128—24no—
20#16838128C2218yescomplemented
21#16838124—24no—
22#16838124C2218yes—
23C2×#14273726—21no—
24C2×#14273726C2211yescharacteristic
25C2×#14273725C2211yescharacteristic
26C2×#14273722—21no—
27C2×#14273721—21no—
28C2×#14273719—21no—
29C2×#14273719C2211yescharacteristic
30C2×#14273718—21no—
31C2×#14273718C2211yescharacteristic
32C2×#14273716C2211yescharacteristic
33C2×#14273715C2211yescharacteristic
34C2×#14273705—21no—
35C2×Q8×Dic59C2211yescharacteristic
36C2×Q8×Dic59C2211yescharacteristic
37C2×C4×Dic118—21no—
38C2×C4×Dic118C2211yescharacteristic
39C2×#14273692C2211yescharacteristic
40C2×#14273689C2211yescharacteristic
41C2×#14273684—21no—
42#16837769C2218yescomplemented
43#16837763C2218yes—
44#16837757C2218yes—
45#16837709C2218yescomplemented
46#16837705C2218yes—
47#16837696C2218yescomplemented
48#16837626C2218yes—
49#16837624C2218yes—
50#16837610C2218yescomplemented
51#16837532C2218yescomplemented
52#16837506C2218yescomplemented
53#16837505C2218yes—
54C2×#14273660C2211yescharacteristic
55C2×#14273658C2211yescharacteristic
56C2×C4⋊(C59⋊C8)C2211yescharacteristic
57C2×Dic59⋊C8C2211yescharacteristic
58C2×Dic59⋊C8C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273649C2211yescharacteristic
66C2×#14273647C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C2×#14273637C2211yescharacteristic
69C22×Q16×C59C2211yescharacteristic
70C2×C4×Q8×C59C2211yescharacteristic
71C2×C4×Q8×C59C2211yescharacteristic
72C4×Q16×C59C2218yescomplemented
73C2×#107×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×C4×C8×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118D411yescharacteristic
79C22×Dic118C2311yescharacteristic
80C22×D236C2311yescharacteristic
81C22×C4×D59—21no—
82C2×#11745672—24no—
83C2×#11745672C2314yes—
84C2×#11745671—24no—
85C2×#11745671C2314yes—
86C22×C59⋊C8C2311yescharacteristic
87C22×C59⋊C8C2311yescharacteristic
88#14273726—28no—
89#14273726—22no—
90#14273726C2314yes—
91#14273725—22no—
92#14273725C2314yes—
93#14273722—28no—
94#14273721—28no—
95#14273719—22no—
96#14273719—28no—
97#14273719C2314yes—
98#14273718—28no—
99#14273718—22no—
100#14273718C2314yes—
101#14273716—22no—
102#14273716C2314yes—
103#14273715—22no—
104#14273715C2314yes—
105#14273705—28no—
106Q8×Dic59—22no—
107Q8×Dic59—22no—
108Q8×Dic59C2314yes—
109Q8×Dic59C2314yes—
110C4×Dic118—28no—
111C4×Dic118D414yes—
112C4×Dic118C2314yes—
113#14273692—22no—
114#14273692C2314yes—
115#14273689—22no—
116#14273689C2314yes—
117#14273684—28no—
118C2×C4⋊Dic59—21no—
119C2×C4⋊Dic59—21no—
120C2×C4⋊Dic59—21no—
121C2×C4⋊Dic59D411yescharacteristic
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⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4D411yescharacteristic
132C2×Dic59⋊C4D411yescharacteristic
133C2×(C2×D59)⋊C4—21no—
134C2×(C2×D59)⋊C4—21no—
135C2×(C2×D59)⋊C4—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×C4×Dic59—21no—
139C2×C4×Dic59—21no—
140C2×C4×Dic59—21no—
141C2×C4×Dic59C2311yescharacteristic
142C2×C4×Dic59C2311yescharacteristic
143#14273660C2314yes—
144#14273658C2314yes—
145C4⋊(C59⋊C8)C2314yes—
146Dic59⋊C8C2314yes—
147Dic59⋊C8C2314yes—
148#14273652C2314yes—
149#14273652C2314yes—
150#14273651C2314yes—
151#14273651C2314yes—
152#14273650C2314yes—
153#14273649C2314yes—
154#14273649C2314yes—
155#14273647C2314yes—
156#14273637C2314yes—
157#14273637C2314yes—
158C22×Q8×C59C2311yescharacteristic
159C22×Q8×C59C2311yescharacteristic
160C2×Q16×C59—24no—
161C2×Q16×C59C2314yes—
162C22×C8×C59C2311yescharacteristic
163C22×C8×C59C2311yescharacteristic
164C4×Q8×C59—22no—
165C4×Q8×C59—22no—
166C4×Q8×C59C2314yes—
167C4×Q8×C59C2314yes—
168C2×C4⋊C4×C59—21no—
169C2×C4⋊C4×C59—21no—
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C42×C59—21no—
173C2×C42×C59—21no—
174C2×C42×C59C2311yescharacteristic
175#107×C59C2314yes—
176#103×C59C2314yes—
177#103×C59C2314yes—
178C4×C8×C59C2314yes—
179C23×D59—21no—
180C2×Q8×C59—21no—
181C2×Q8×C59—21no—
182C2×Q8×C59—22no—
183C2×Q8×C59—22no—
184C2×Q8×C59—22no—
185C2×Q8×C59#4114yes—
186C2×Q8×C59C2412yes—
187C2×Q8×C59C2412yes—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—21no—
191C22×C4×C59—21no—
192C22×C4×C59C2×D411yescharacteristic
193C22×C4×C59C2×D411yescharacteristic
194C22×C4×C59C2411yescharacteristic
195C22×Dic59—21no—
196C22×Dic59—21no—
197C22×Dic59—21no—
198C22×Dic59C2×D411yescharacteristic
199C22×Dic59C2×D411yescharacteristic
200C22×Dic59C2×D411yescharacteristic
201C22×Dic59C2×D411yescharacteristic
202C2×D236—22no—
203C2×D236—22no—
204C2×D236—21no—
205C2×D236C2412yes—
206C2×C4×D59—24no—
207C2×C4×D59—44no—
208C2×Dic118—22no—
209C2×Dic118—22no—
210C2×Dic118—21no—
211C2×Dic118—24no—
212C2×Dic118—42no—
213C2×Dic118—44no—
214C2×Dic118C2×D414yes—
215C2×Dic118C2412yes—
216Q16×C59—28no—
217C2×C8×C59—22no—
218C2×C8×C59—22no—
219C2×C8×C59C2412yes—
220C2×C8×C59C2412yes—
221C4⋊C4×C59—24no—
222C4⋊C4×C59—24no—
223C4⋊C4×C59—21no—
224C4⋊C4×C59—21no—
225C4⋊C4×C59C2412yes—
226C4⋊C4×C59C2412yes—
227C42×C59—24no—
228C42×C59—24no—
229C42×C59C2×D412yes—
230C42×C59C2412yes—
231#11745672—28no—
232#11745671—28no—
233(C2×D59)⋊C4—24no—
234(C2×D59)⋊C4—24no—
235(C2×D59)⋊C4—24no—
236(C2×D59)⋊C4—24no—
237(C2×D59)⋊C4—24no—
238C4⋊Dic59—21no—
239C4⋊Dic59—21no—
240C4⋊Dic59—24no—
241C4⋊Dic59—24no—
242C4⋊Dic59—24no—
243C4⋊Dic59C2×D414yes—
244C4⋊Dic59C2412yes—
245C4⋊Dic59C2412yes—
246Dic59⋊C4—24no—
247Dic59⋊C4—24no—
248Dic59⋊C4—24no—
249Dic59⋊C4—24no—
250Dic59⋊C4—24no—
251Dic59⋊C4—24no—
252Dic59⋊C4—24no—
253Dic59⋊C4C2×D414yes—
254Dic59⋊C4C2×D414yes—
255C4×Dic59—24no—
256C4×Dic59—24no—
257C4×Dic59—24no—
258C4×Dic59C2×D412yes—
259C4×Dic59C2×D412yes—
260C4×Dic59C2412yes—
261C4×Dic59C2412yes—
262C2×C59⋊C8—22no—
263C2×C59⋊C8—22no—
264C2×C59⋊C8C2412yes—
265C2×C59⋊C8C2412yes—
266C23×C59C22×D411yescharacteristic
267C22×D59—22no—
268C22×D59—42no—
269C22×D59—42no—
270C22×D59—42no—
271Q8×C59—24no—
272Q8×C59—22no—
273Q8×C59—22no—
274Q8×C59—22no—
275Q8×C59—42no—
276Q8×C59C2×#4114yes—
277C2×C4×C59—24no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—42no—
285C2×C4×C59—42no—
286C2×C4×C59—42no—
287C2×C4×C59C22×D412yes—
288C2×C4×C59C22×D412yes—
289C2×C4×C59C22×D411yescharacteristic
290C2×C4×C59C2×#4112yes—
291C2×C4×C592−1+412yes—
292C2×C4×C59C2511yescharacteristic
293C2×Dic59—22no—
294C2×Dic59—22no—
295C2×Dic59—22no—
296C2×Dic59—22no—
297C2×Dic59—22no—
298C2×Dic59—22no—
299C2×Dic59—22no—
300C2×Dic59—42no—
301C2×Dic59—42no—
302C2×Dic59—42no—
303C2×Dic59C22×D412yes—
304C2×Dic59C22×D412yes—
305C2×Dic59C22×D412yes—
306C2×Dic59C22×D412yes—
307D236—22no—
308D236—22no—
309D236—42no—
310C4×D59—48no—
311Dic118—22no—
312Dic118—22no—
313Dic118—44no—
314Dic118—48no—
315Dic118—42no—
316C8×C59—22no—
317C8×C59—22no—
318C59⋊C8—22no—
319C59⋊C8—22no—
320C2×#3377—591nomaximal, Sylow
321C22×C59#54812yes—
322C22×C59#57512yes—
323C22×C59#57812yes—
324C22×C59C23×D411yescharacteristic
325C2×D59—42no—
326C2×D59—42no—
327C2×D59—42no—
328C2×D59—84no—
329C4×C59—24no—
330C4×C59—22no—
331C4×C59—22no—
332C4×C59—42no—
333C4×C59—42no—
334C4×C59—42no—
335C4×C59#54812yes—
336C4×C59C22×#4111yescharacteristic
337C4×C59C2×2−1+411yescharacteristic
338Dic59—22no—
339Dic59—22no—
340Dic59—22no—
341Dic59—22no—
342Dic59—42no—
343Dic59—42no—
344Dic59—42no—
345C2×#557—591no—
346C2×#556—591no—
347#3377—5916no—
348C2×#491—591no—
349C2×#489—591no—
350C2×#488—591no—
351C2×#479—591no—
352C2×#477—591no—
353C2×#478—591no—
354C2×#464—591no—
355C2×#464—591no—
356C2×#462—591no—
357C2×#446—591no—
358C2×#441—591no—
359C2×#440—591no—
360C2×C4×Q16D5911yescharacteristic, complemented
361C2×C59#337714yescomplemented
362C2×C59C2×#54811yescharacteristic
363C2×C59C2×#57511yescharacteristic
364C2×C59C2×#57811yescharacteristic
365D59—82no—
366C22×Q16—591no—
367C22×Q16C2×D5911yescharacteristic
368C22×SD16—591no—
369#557—598no—
370#557—1184no—
371#556—598no—
372#556—1184no—
373C2×C4⋊Q8—591no—
374C2×C4⋊Q8—591no—
375C2×C4⋊Q8—1181no—
376C2×#126—1181no—
377C2×#126—1181no—
378C2×#125—591no—
379C2×#125—591no—
380C2×#125—1181no—
381C2×#125—1181no—
382C2×#124—591no—
383C2×#124—591no—
384C2×C22⋊Q8—1181no—
385C2×C4×Q8—591no—
386C2×C4×Q8—591no—
387C2×C4×Q8—591no—
388C2×C4×Q8—591no—
389C2×C4×Q8—1181no—
390C2×C4×Q8C2×D5911yescharacteristic
391C2×C4×Q8C2×D5911yescharacteristic
392C2×C4×D4—591no—
393C2×#117—1181no—
394#491—598no—
395#489—598no—
396#488—598no—
397#479—598no—
398#478—598no—
399#477—598no—
400#464—598no—
401#464—598no—
402#462—598no—
403#446—598no—
404#441—598no—
405#440—598no—
406C4×Q16C2×D5918yescomplemented
407C2×#107—591no—
408C2×#107C2×D5911yescharacteristic
409C2×#106—591no—
410C2×C4⋊C8—591no—
411C2×C4⋊C8—591no—
412C2×C4⋊C8—591no—
413C2×#103—591no—
414C2×#103—591no—
415C2×#103—591no—
416C2×#103—591no—
417C2×#103—591no—
418C2×#103C2×D5911yescharacteristic
419C2×#103C2×D5911yescharacteristic
420C2×#102—591no—
421C2×#102—591no—
422C2×#102—591no—
423C2×#97—591no—
424C2×#97—591no—
425C2×C4×C8C2×D5911yescharacteristic
426C59C2×#337711yescharacteristic, complemented, Sylow
427C22×Q8—591no—
428C22×Q8—591no—
429C22×Q8—1181no—
430C22×Q8C22×D5911yescharacteristic
431C22×Q8C22×D5911yescharacteristic
432C22×D4—591no—
433C23×C4—1181no—
434C2×Q16—24no—
435C2×Q16—594no—
436C2×Q16—1184no—
437C2×Q16C22×D5914yes—
438C2×SD16—594no—
439C2×SD16—1184no—
440C22×C8—591no—
441C22×C8—591no—
442C22×C8C22×D5911yescharacteristic
443C22×C8C22×D5911yescharacteristic
444C4⋊Q8—594no—
445C4⋊Q8—594no—
446C4⋊Q8—1182no—
447C4⋊Q8—1182no—
448C4⋊Q8—1188no—
449#126—1188no—
450#126—1188no—
451#125—594no—
452#125—594no—
453#125—1188no—
454#125—1182no—
455#125—1188no—
456#125—1182no—
457#124—594no—
458#124—594no—
459#124—1182no—
460#124—1182no—
461C22⋊Q8—1188no—
462C4×Q8—22no—
463C4×Q8—22no—
464C4×Q8—594no—
465C4×Q8—594no—
466C4×Q8—594no—
467C4×Q8—594no—
468C4×Q8—594no—
469C4×Q8—1188no—
470C4×Q8—1182no—
471C4×Q8—1182no—
472C4×Q8—1182no—
473C4×Q8C22×D5914yes—
474C4×Q8C22×D5914yes—
475C4×D4—594no—
476C4×D4—1182no—
477#117—1188no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—591no—
481C2×C4⋊C4—591no—
482C2×C4⋊C4—591no—
483C2×C4⋊C4—591no—
484C2×C4⋊C4—591no—
485C2×C4⋊C4—1181no—
486C2×C4⋊C4—1181no—
487C2×C4⋊C4—1181no—
488C2×C4⋊C4—1181no—
489C2×C4⋊C4—1181no—
490C2×C4⋊C4—1181no—
491C2×C4⋊C4—1181no—
492C2×C4⋊C4—1181no—
493C2×C4⋊C4—1181no—
494C2×C4⋊C4—1181no—
495C2×C4⋊C4C22×D5911yescharacteristic
496C2×C4⋊C4C22×D5911yescharacteristic
497C2×C22⋊C4—1181no—
498C2×C22⋊C4—1181no—
499C2×C22⋊C4—1181no—
500C2×C22⋊C4—1181no—
501C2×C22⋊C4—1181no—
502C2×C42—21no—
503C2×C42—21no—
504C2×C42—591no—
505C2×C42—591no—
506C2×C42—1181no—
507C2×C42—1181no—
508C2×C42—1181no—
509C2×C42C22×D5911yescharacteristic
510#107—594no—
511#107C22×D5914yes—
512#106—594no—
513C4⋊C8—594no—
514C4⋊C8—594no—
515C4⋊C8—594no—
516#103—594no—
517#103—594no—
518#103—594no—
519#103—594no—
520#103—594no—
521#103C22×D5914yes—
522#103C22×D5914yes—
523#102—594no—
524#102—594no—
525#102—594no—
526#97—594no—
527#97—594no—
528C4×C8C22×D5914yes—
529C24—1181no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—594no—
536C2×Q8—592no—
537C2×Q8—1184no—
538C2×Q8—1181no—
539C2×Q8—1182no—
540C2×Q8—1182no—
541C2×Q8—2362no—
542C2×Q8—2364no—
543C2×Q8#1174568514yes—
544C2×Q8C23×D5912yes—
545C2×Q8C23×D5912yes—
546C2×D4—592no—
547C2×D4—1181no—
548C2×D4—1182no—
549C2×D4—1182no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—591no—
555C22×C4—591no—
556C22×C4—591no—
557C22×C4—591no—
558C22×C4—1184no—
559C22×C4—1181no—
560C22×C4—1181no—
561C22×C4—1181no—
562C22×C4—2364no—
563C22×C4D4×D5911yescharacteristic
564C22×C4D4×D5911yescharacteristic
565C22×C4C23×D5911yescharacteristic
566Q16—28no—
567Q16—1188no—
568SD16—1188no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—592no—
572C2×C8—592no—
573C2×C8—1182no—
574C2×C8—1182no—
575C2×C8C23×D5912yes—
576C2×C8C23×D5912yes—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—594no—
582C4⋊C4—594no—
583C4⋊C4—594no—
584C4⋊C4—592no—
585C4⋊C4—592no—
586C4⋊C4—1184no—
587C4⋊C4—1184no—
588C4⋊C4—1184no—
589C4⋊C4—1184no—
590C4⋊C4—1184no—
591C4⋊C4—1184no—
592C4⋊C4—1184no—
593C4⋊C4—1184no—
594C4⋊C4—1181no—
595C4⋊C4—1181no—
596C4⋊C4—1184no—
597C4⋊C4—1184no—
598C4⋊C4C23×D5912yes—
599C4⋊C4C23×D5912yes—
600C22⋊C4—1184no—
601C22⋊C4—1184no—
602C22⋊C4—1184no—
603C22⋊C4—1184no—
604C22⋊C4—1184no—
605C42—24no—
606C42—24no—
607C42—592no—
608C42—592no—
609C42—592no—
610C42—592no—
611C42—1184no—
612C42—1184no—
613C42—1184no—
614C42D4×D5912yes—
615C42C23×D5912yes—
616C23—1182no—
617C23—2362no—
618C23—2362no—
619C23—2362no—
620C23C2×D4×D5911yescharacteristic
621Q8—22no—
622Q8—24no—
623Q8—22no—
624Q8—22no—
625Q8—42no—
626Q8—1182no—
627Q8—1182no—
628Q8—2364no—
629Q8—2368no—
630Q8—2362no—
631Q8C2×#1174568514yes—
632D4—1182no—
633D4—1182no—
634D4—2362no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—24no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—592no—
646C2×C4—592no—
647C2×C4—592no—
648C2×C4—592no—
649C2×C4—1182no—
650C2×C4—1182no—
651C2×C4—1182no—
652C2×C4—1182no—
653C2×C4—1182no—
654C2×C4—1182no—
655C2×C4—1182no—
656C2×C4—2368no—
657C2×C4—2362no—
658C2×C4—2362no—
659C2×C4—2362no—
660C2×C4C2×D4×D5912yes—
661C2×C4C2×D4×D5912yes—
662C2×C4C2×D4×D5911yescharacteristic
663C2×C4C2×#1174568512yes—
664C2×C4#1427377412yes—
665C2×C4C24×D5911yescharacteristic
666C8—22no—
667C8—22no—
668C8—1182no—
669C8—1182no—
670C22—4724no—
671C22—2362no—
672C22—2362no—
673C22—2362no—
674C22#1683806112yes—
675C22#1683819912yes—
676C22#1683821512yes—
677C22C22×D4×D5911yescharacteristic
678C4—22no—
679C4—24no—
680C4—22no—
681C4—42no—
682C4—42no—
683C4—42no—
684C4—1182no—
685C4—1182no—
686C4—1182no—
687C4—1182no—
688C4—2362no—
689C4—2362no—
690C4—2362no—
691C4#1683806112yes—
692C4C22×#1174568511yescharacteristic
693C4C2×#1427377411yescharacteristic
694C2—4722no—
695C2#2143693414yesdirect product factor
696C2C2×#1683806111yescharacteristic
697C2C2×#1683819911yescharacteristic
698C2C2×#1683821511yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C4×Q16×C59C2
socleC23×C59C22×D4
prime radicalC22×D236C23
hypercenterC2×C4×Q16D59
hypocenterC59C2×#3377
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#16838128C2semidirect
3. #21436934C2direct (N × H)
4. C2×#16837769C2semidirect
7. C2×#16837709C2semidirect
8. C2×#16837696C2semidirect
12. C2×#16837610C2semidirect
13. C2×#16837532C2semidirect
14. C2×#16837506C2semidirect
16. C2×C4×Q16×C59C2semidirect
20. #16838128C22semidirect
42. #16837769C22semidirect
45. #16837709C22semidirect
47. #16837696C22semidirect
50. #16837610C22semidirect
51. #16837532C22semidirect
52. #16837506C22semidirect
72. C4×Q16×C59C22semidirect
360. C2×C4×Q16D59semidirect
361. C2×C59#3377semidirect
406. C4×Q16C2×D59semidirect
426. C59C2×#3377semidirect
695. C2#21436934direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381282
C2×#168381242
#214369342
C2×#168377692
C2×#168377632
C2×#168377572
C2×#168377092
C2×#168376962
C2×#168377052
C2×#168376262
C2×#168376242
C2×#168376102
C2×#168375322
C2×#168375062
C2×#168375052
C2×C4×Q16×C592
C2×#337759