Finite Group Databasebeta

← C2×#21437001 #29469173

Subgroups — C2×#21437001 #29469173

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×#16838111C211yesmaximal, characteristic
3#21437001C2116yesmaximal, direct product factor
4C2×#16837810C211yesmaximal, characteristic, complemented
5C2×#16837808C211yesmaximal, characteristic, complemented
6C2×#16837806C211yesmaximal, characteristic, complemented
7C2×#16837710C211yesmaximal, characteristic, complemented
8C2×#16837708C211yesmaximal, characteristic, complemented
9C2×#16837696C211yesmaximal, characteristic, complemented
10C2×#16837690C211yesmaximal, characteristic
11C2×#16837680C211yesmaximal, characteristic
12C2×#16837531C211yesmaximal, characteristic, complemented
13C2×#16837502C211yesmaximal, characteristic
14C2×#16837499C211yesmaximal, characteristic
15C2×#16837493C211yesmaximal, characteristic
16C2×C59×#474C211yesmaximal, characteristic
17C22×#11745670C2211yescharacteristic
18#16838132—24no—
19#16838132C2218yescomplemented
20#16838111—24no—
21#16838111C2218yes—
22C2×#14273726—21no—
23C2×#14273726C2211yescharacteristic
24C2×#14273726C2211yescharacteristic
25C2×#14273726C2211yescharacteristic
26C2×#14273725—21no—
27C2×#14273725—21no—
28C2×#14273719C2211yescharacteristic
29C2×#14273718C2211yescharacteristic
30C2×#14273706—21no—
31C2×#14273704—21no—
32C2×#14273704—21no—
33C2×C4×Dic118C2211yescharacteristic
34C2×C4×Dic118C2211yescharacteristic
35C2×#14273692—21no—
36C2×#14273692C2211yescharacteristic
37C2×#14273692C2211yescharacteristic
38C2×D4×Dic59C2211yescharacteristic
39C2×D4×Dic59C2211yescharacteristic
40C22×Dic59⋊C4—21no—
41#16837810C2218yescomplemented
42#16837808C2218yescomplemented
43#16837806C2218yescomplemented
44#16837710C2218yescomplemented
45#16837708C2218yescomplemented
46#16837696C2218yescomplemented
47#16837690C2218yes—
48#16837680C2218yes—
49#16837531C2218yescomplemented
50#16837502C2218yes—
51#16837499C2218yes—
52#16837493C2218yes—
53C2×#14273661C2211yescharacteristic
54C2×#14273660C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273659C2211yescharacteristic
58C2×#14273658C2211yescharacteristic
59C2×#14273658C2211yescharacteristic
60C2×Dic59⋊C8C2211yescharacteristic
61C2×Dic59⋊C8C2211yescharacteristic
62C2×#14273652C2211yescharacteristic
63C2×#14273652C2211yescharacteristic
64C2×#14273650C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×#14273638C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C2×C4⋊Q8×C59C2211yescharacteristic
70C2×C4×D4×C59C2211yescharacteristic
71C59×#474C2218yes—
72C2×#107×C59C2211yescharacteristic
73C2×#107×C59C2211yescharacteristic
74C2×C4⋊C8×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×Dic118—21no—
80C22×Dic118D411yescharacteristic
81C22×Dic118C2311yescharacteristic
82C23×Dic59—21no—
83C23×Dic59—21no—
84C2×#11745670Q818yescomplemented
85C2×#11745670C2314yes—
86C22×C59⋊C8C2311yescharacteristic
87C22×C59⋊C8C2311yescharacteristic
88#14273726—28no—
89#14273726—22no—
90#14273726—22no—
91#14273726—22no—
92#14273726C2314yes—
93#14273726C2314yes—
94#14273726C2314yes—
95#14273725—28no—
96#14273725—28no—
97#14273719—22no—
98#14273719C2314yes—
99#14273718—22no—
100#14273718C2314yes—
101#14273706—28no—
102#14273704—28no—
103#14273704—28no—
104C4×Dic118—22no—
105C4×Dic118D414yes—
106C4×Dic118C2314yes—
107C4×Dic118C2314yes—
108#14273692—28no—
109#14273692—22no—
110#14273692—22no—
111#14273692C2314yes—
112#14273692C2314yes—
113D4×Dic59—22no—
114D4×Dic59—22no—
115D4×Dic59C2314yes—
116D4×Dic59C2314yes—
117C2×C4⋊Dic59—21no—
118C2×C4⋊Dic59D411yescharacteristic
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⋊C4—21no—
131C2×Dic59⋊C4—28no—
132C2×Dic59⋊C4D411yescharacteristic
133C2×Dic59⋊C4D411yescharacteristic
134C2×C22⋊Dic59—21no—
135C2×C22⋊Dic59—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#14273659C2314yes—
146#14273658C2314yes—
147#14273658C2314yes—
148Dic59⋊C8C2314yes—
149Dic59⋊C8C2314yes—
150#14273652C2314yes—
151#14273652C2314yes—
152#14273650C2314yes—
153#14273648C2314yes—
154#14273638C2314yes—
155#14273637C2314yes—
156C8×Dic59C2314yes—
157C22×Q8×C59—21no—
158C22×D4×C59C2311yescharacteristic
159C23×C4×C59—21no—
160C22×C8×C59C2311yescharacteristic
161C22×C8×C59C2311yescharacteristic
162C4⋊Q8×C59—22no—
163C4⋊Q8×C59C2314yes—
164C4×D4×C59—22no—
165C4×D4×C59C2314yes—
166C2×C4⋊C4×C59—21no—
167C2×C4⋊C4×C59C2311yescharacteristic
168C2×C4⋊C4×C59C2311yescharacteristic
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C22⋊C4×C59—21no—
171C2×C42×C59C2311yescharacteristic
172#107×C59C2314yes—
173#107×C59C2314yes—
174C4⋊C8×C59C2314yes—
175#102×C59C2314yes—
176#102×C59C2314yes—
177C24×C59—21no—
178C2×Q8×C59—24no—
179C2×Q8×C59—82no—
180C2×D4×C59—21no—
181C2×D4×C59—22no—
182C2×D4×C59C2×Q814yes—
183C2×D4×C59C2412yes—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—24no—
188C22×C4×C59—82no—
189C22×C4×C59C2×D411yescharacteristic
190C22×C4×C59C2×D411yescharacteristic
191C22×C4×C59C2411yescharacteristic
192C22×Dic59—21no—
193C22×Dic59—21no—
194C22×Dic59—21no—
195C22×Dic59—21no—
196C22×Dic59—24no—
197C22×Dic59—24no—
198C22×Dic59—44no—
199C22×Dic59—82no—
200C22×Dic59C2×D411yescharacteristic
201C22×Dic59C2×D411yescharacteristic
202C22×Dic59C2×D411yescharacteristic
203C22×Dic59C2×D411yescharacteristic
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×C59—22no—
218C2×C8×C59C2412yes—
219C2×C8×C59C2412yes—
220C4⋊C4×C59—24no—
221C4⋊C4×C59—21no—
222C4⋊C4×C59—21no—
223C4⋊C4×C59—21no—
224C4⋊C4×C59C2412yes—
225C4⋊C4×C59C2412yes—
226C4⋊C4×C59C2412yes—
227C22⋊C4×C59—24no—
228C42×C59C2×D412yes—
229C42×C59C2412yes—
230C22⋊Dic59—24no—
231C22⋊Dic59—24no—
232#11745670C2×Q8116yescomplemented
233C4⋊Dic59—21no—
234C4⋊Dic59—21no—
235C4⋊Dic59—21no—
236C4⋊Dic59—24no—
237C4⋊Dic59C2×D414yes—
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⋊C4—24no—
250Dic59⋊C4C2×D414yes—
251Dic59⋊C4C2×D414yes—
252C4×Dic59—24no—
253C4×Dic59—24no—
254C4×Dic59—24no—
255C4×Dic59C2×D412yes—
256C4×Dic59C2×D412yes—
257C4×Dic59C2412yes—
258C4×Dic59C2412yes—
259C2×C59⋊C8—22no—
260C2×C59⋊C8C2×Q814yes—
261C2×C59⋊C8C2412yes—
262C2×C59⋊C8C2412yes—
263C23×C59—24no—
264C23×C59—22no—
265C23×C59—42no—
266C23×C59—42no—
267C23×C59C22×D411yescharacteristic
268Q8×C59—84no—
269D4×C59—24no—
270D4×C59—22no—
271D4×C59C22×Q814yes—
272C2×C4×C59—22no—
273C2×C4×C59—22no—
274C2×C4×C59—22no—
275C2×C4×C59—22no—
276C2×C4×C59—22no—
277C2×C4×C59—42no—
278C2×C4×C59—42no—
279C2×C4×C59—42no—
280C2×C4×C59—84no—
281C2×C4×C59C22×D412yes—
282C2×C4×C59C22×D412yes—
283C2×C4×C59C22×D411yescharacteristic
284C2×C4×C59C22×Q812yes—
285C2×C4×C592−1+412yes—
286C2×C4×C59C2511yescharacteristic
287C2×Dic59—24no—
288C2×Dic59—22no—
289C2×Dic59—22no—
290C2×Dic59—22no—
291C2×Dic59—22no—
292C2×Dic59—22no—
293C2×Dic59—22no—
294C2×Dic59—22no—
295C2×Dic59—42no—
296C2×Dic59—42no—
297C2×Dic59—42no—
298C2×Dic59—48no—
299C2×Dic59—84no—
300C2×Dic59#13714yes—
301C2×Dic59C22×D412yes—
302C2×Dic59C22×D412yes—
303C2×Dic59C22×D412yes—
304C2×Dic59C22×D412yes—
305Dic118—24no—
306Dic118—22no—
307Dic118—28no—
308Dic118—84no—
309Dic118—84no—
310Dic118—84no—
311Dic118C22×Q814yes—
312C8×C59—22no—
313C8×C59—22no—
314C59⋊C8—22no—
315C59⋊C8C22×Q814yes—
316C2×#3385—591nomaximal, Sylow
317C22×C59—24no—
318C22×C59—48no—
319C22×C59—42no—
320C22×C59—42no—
321C22×C59D4×Q812yes—
322C22×C59C2×#13712yes—
323C22×C59#57612yes—
324C22×C59C23×D411yescharacteristic
325C4×C59—22no—
326C4×C59—22no—
327C4×C59—42no—
328C4×C59—42no—
329C4×C59—42no—
330C4×C59D4×Q812yes—
331C4×C59C23×Q811yescharacteristic
332C4×C59C2×2−1+411yescharacteristic
333Dic59—24no—
334Dic59—22no—
335Dic59—22no—
336Dic59—22no—
337Dic59—42no—
338Dic59—42no—
339Dic59—42no—
340Dic59C2×#13714yes—
341C2×Q82—591no—
342C2×#554—591no—
343#3385—5916no—
344C2×#501—591no—
345C2×#501—591no—
346C2×#500—591no—
347C2×#479—591no—
348C2×#479—591no—
349C2×#477—591no—
350C2×#476—591no—
351C2×#474—591no—
352C2×#474D5911yescharacteristic
353C2×#446—591no—
354C2×#440—591no—
355C2×#440—591no—
356C2×C4×SD16—591no—
357C2×C59—44no—
358C2×C59#338514yescomplemented
359C2×C59C2×D4×Q811yescharacteristic
360C2×C59C22×#13711yescharacteristic
361C2×C59C2×#57611yescharacteristic
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×#125—591no—
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×D4C2×D5911yescharacteristic
387C22×C4⋊C4—1181no—
388#501—598no—
389#501—598no—
390#500—598no—
391#479—598no—
392#479—598no—
393#477—598no—
394#476—598no—
395#474—598no—
396#474C2×D5918yes—
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×#106—591no—
409C2×#106—591no—
410C2×C4⋊C8—591no—
411C2×C4⋊C8—591no—
412C2×C4⋊C8C2×D5911yescharacteristic
413C2×#103—591no—
414C2×#103—591no—
415C2×#103—591no—
416C2×#102—591no—
417C2×#102C2×D5911yescharacteristic
418C2×#102C2×D5911yescharacteristic
419C2×#97—591no—
420C2×#97—591no—
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×D4C22×D5911yescharacteristic
430C23×C4—21no—
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—594no—
451#125—594no—
452#125—1182no—
453#125—1182no—
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—22no—
467C4×D4—594no—
468C4×D4—594no—
469C4×D4—1182no—
470C4×D4—1182no—
471C4×D4C22×D5914yes—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—591no—
474C2×C4⋊C4—591no—
475C2×C4⋊C4—591no—
476C2×C4⋊C4—591no—
477C2×C4⋊C4—591no—
478C2×C4⋊C4—591no—
479C2×C4⋊C4—1188no—
480C2×C4⋊C4—1181no—
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⋊C4—1181no—
490C2×C4⋊C4C22×D5911yescharacteristic
491C2×C4⋊C4C22×D5911yescharacteristic
492C2×C4⋊C4C22×D5911yescharacteristic
493C2×C22⋊C4—21no—
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#106—594no—
510#106—594no—
511C4⋊C8—594no—
512C4⋊C8—594no—
513C4⋊C8C22×D5914yes—
514#103—594no—
515#103—594no—
516#103—594no—
517#102—594no—
518#102C22×D5914yes—
519#102C22×D5914yes—
520#97—594no—
521#97—594no—
522C4×C8—594no—
523C24—21no—
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—21no—
539C2×D4—22no—
540C2×D4Q8×D5914yes—
541C2×D4C23×D5912yes—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—24no—
546C22×C4—82no—
547C22×C4—591no—
548C22×C4—591no—
549C22×C4—591no—
550C22×C4—591no—
551C22×C4—1184no—
552C22×C4—1184no—
553C22×C4—1181no—
554C22×C4—1181no—
555C22×C4—1181no—
556C22×C4—1181no—
557C22×C4—4722no—
558C22×C4—2364no—
559C22×C4D4×D5911yescharacteristic
560C22×C4D4×D5911yescharacteristic
561C22×C4C23×D5911yescharacteristic
562SD16—5916no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—594no—
566C2×C8—592no—
567C2×C8—592no—
568C2×C8—1182no—
569C2×C8C23×D5912yes—
570C2×C8C23×D5912yes—
571C4⋊C4—24no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—594no—
576C4⋊C4—594no—
577C4⋊C4—594no—
578C4⋊C4—592no—
579C4⋊C4—592no—
580C4⋊C4—592no—
581C4⋊C4—1184no—
582C4⋊C4—1184no—
583C4⋊C4—1184no—
584C4⋊C4—1184no—
585C4⋊C4—1184no—
586C4⋊C4—1184no—
587C4⋊C4—1184no—
588C4⋊C4—1181no—
589C4⋊C4—1181no—
590C4⋊C4—1181no—
591C4⋊C4—1184no—
592C4⋊C4—1184no—
593C4⋊C4—1184no—
594C4⋊C4C23×D5912yes—
595C4⋊C4C23×D5912yes—
596C4⋊C4C23×D5912yes—
597C22⋊C4—24no—
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—22no—
610C23—24no—
611C23—42no—
612C23—42no—
613C23C2×D4×D5911yescharacteristic
614Q8—84no—
615Q8—594no—
616Q8—1188no—
617Q8—1182no—
618Q8—1184no—
619Q8—4724no—
620Q8—4724no—
621Q8—4724no—
622D4—22no—
623D4—24no—
624D4C2×Q8×D5914yes—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—84no—
634C2×C4—594no—
635C2×C4—592no—
636C2×C4—592no—
637C2×C4—592no—
638C2×C4—592no—
639C2×C4—1182no—
640C2×C4—1182no—
641C2×C4—1182no—
642C2×C4—1182no—
643C2×C4—1184no—
644C2×C4—1182no—
645C2×C4—1182no—
646C2×C4—1182no—
647C2×C4—4724no—
648C2×C4—2368no—
649C2×C4—2362no—
650C2×C4—2362no—
651C2×C4—2362no—
652C2×C4C2×D4×D5912yes—
653C2×C4C2×D4×D5912yes—
654C2×C4C2×D4×D5911yescharacteristic
655C2×C4C2×Q8×D5912yes—
656C2×C4#1427377412yes—
657C2×C4C24×D5911yescharacteristic
658C8—22no—
659C8—22no—
660C8—594no—
661C8—1182no—
662C22—24no—
663C22—48no—
664C22—42no—
665C22—42no—
666C22#1683806512yes—
667C22#137×D5912yes—
668C22#1683820312yes—
669C22C22×D4×D5911yescharacteristic
670C4—22no—
671C4—22no—
672C4—42no—
673C4—42no—
674C4—42no—
675C4—594no—
676C4—1182no—
677C4—1182no—
678C4—1182no—
679C4—1184no—
680C4—2362no—
681C4—2362no—
682C4—2362no—
683C4#1683806512yes—
684C4C22×Q8×D5911yescharacteristic
685C4C2×#1427377411yescharacteristic
686C2—44no—
687C2#2143700114yesdirect product factor
688C2C2×#1683806511yescharacteristic
689C2C2×#137×D5911yescharacteristic
690C2C2×#1683820311yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#474C2
socleC23×C59C22×D4
prime radicalC22×D4×C59C23
hypercenterC2×#474D59
hypocenterC59C2×#3385
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×#16838132C2semidirect
3. #21437001C2direct (N × H)
4. C2×#16837810C2semidirect
5. C2×#16837808C2semidirect
6. C2×#16837806C2semidirect
7. C2×#16837710C2semidirect
8. C2×#16837708C2semidirect
9. C2×#16837696C2semidirect
12. C2×#16837531C2semidirect
19. #16838132C22semidirect
41. #16837810C22semidirect
42. #16837808C22semidirect
43. #16837806C22semidirect
44. #16837710C22semidirect
45. #16837708C22semidirect
46. #16837696C22semidirect
49. #16837531C22semidirect
84. C2×#11745670Q8semidirect
232. #11745670C2×Q8semidirect
358. C2×C59#3385semidirect
422. C59C2×#3385semidirect
687. C2#21437001direct (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×#168381112
#214370012
C2×#168378102
C2×#168378082
C2×#168378062
C2×#168377102
C2×#168377082
C2×#168376962
C2×#168376902
C2×#168376802
C2×#168375312
C2×#168375022
C2×#168374992
C2×#168374932
C2×C59×#4742
C2×#338559