Finite Group Databasebeta

← C2×#23776082 #35167878

Subgroups — C2×#23776082 #35167878

Order 20224.

1830 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×#19099290C211yesmaximal, characteristic, complemented
2C2×#19099282C211yesmaximal, characteristic
3#23776082C2116yesmaximal, direct product factor
4C2×#19098916C211yesmaximal, characteristic
5C2×#19098912C211yesmaximal, characteristic, complemented
6C2×#19098872C211yesmaximal, characteristic, complemented
7C2×#19098867C211yesmaximal, characteristic, complemented
8C2×#19098841C211yesmaximal, characteristic
9C2×#19098784C211yesmaximal, characteristic
10C2×#19098782C211yesmaximal, characteristic
11C2×#19098772C211yesmaximal, characteristic, complemented
12C2×C8×Dic158C211yesmaximal, characteristic, complemented
13C2×C4×Dic316C211yesmaximal, characteristic, complemented
14C2×#19098655C211yesmaximal, characteristic, complemented
15C2×#19098654C211yesmaximal, characteristic
16C2×#488×C79C211yesmaximal, characteristic
17C22×Dic316C2211yescharacteristic
18C22×#11929614C2211yescharacteristic
19C22×#11929612C2211yescharacteristic
20#19099290—24no—
21#19099290C2218yescomplemented
22#19099282—24no—
23#19099282C2218yes—
24C2×#14579160—21no—
25C2×#14579160C2211yescharacteristic
26C2×#14579159C2211yescharacteristic
27C2×#14579154—21no—
28C2×#14579154—21no—
29C2×#14579152C2211yescharacteristic
30C2×#14579151—21no—
31C2×#14579151—21no—
32C2×#14579148C2211yescharacteristic
33C2×#14579138—21no—
34C2×Q8×Dic79C2211yescharacteristic
35C2×C4×Dic158C2211yescharacteristic
36C2×C4×Dic158C2211yescharacteristic
37C2×C4×Dic158C2211yescharacteristic
38C2×#14579126—21no—
39C2×#14579126C2211yescharacteristic
40C2×#14579126C2211yescharacteristic
41C2×D4×Dic79C2211yescharacteristic
42C2×#14579117—21no—
43#19098916C2218yes—
44#19098912C2218yescomplemented
45#19098872C2218yescomplemented
46#19098867C2218yescomplemented
47#19098841C2218yes—
48#19098784C2218yes—
49#19098782C2218yes—
50#19098772C2218yescomplemented
51C8×Dic158C2218yescomplemented
52C4×Dic316C2218yescomplemented
53#19098655C2218yescomplemented
54#19098654C2218yes—
55C2×#14579095C2211yescharacteristic
56C2×#14579094C2211yescharacteristic
57C2×#14579092C2211yescharacteristic
58C2×C4⋊(C79⋊C8)C2211yescharacteristic
59C2×Dic79⋊C8C2211yescharacteristic
60C2×Dic79⋊C8C2211yescharacteristic
61C2×#14579086C2211yescharacteristic
62C2×#14579086C2211yescharacteristic
63C2×#14579085C2211yescharacteristic
64C2×#14579084C2211yescharacteristic
65C2×#14579084C2211yescharacteristic
66C2×#14579082C2211yescharacteristic
67C2×C8×Dic79C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C2×#125×C79C2211yescharacteristic
70C2×#124×C79C2211yescharacteristic
71#488×C79C2218yes—
72C2×#103×C79C2211yescharacteristic
73C2×#103×C79C2211yescharacteristic
74C2×#102×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic
76C2×C4×C8×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158D411yescharacteristic
79C22×Dic158C2311yescharacteristic
80C22×Dic158C2311yescharacteristic
81C23×Dic79—21no—
82C2×Dic316—24no—
83C2×Dic316C2314yes—
84C2×#11929614—24no—
85C2×#11929614C2314yes—
86C2×#11929612—24no—
87C2×#11929612C2314yes—
88C22×C79⋊C8C2311yescharacteristic
89C22×C79⋊C8C2311yescharacteristic
90#14579160—28no—
91#14579160—22no—
92#14579160C2314yes—
93#14579159—22no—
94#14579159C2314yes—
95#14579154—28no—
96#14579154—28no—
97#14579152—22no—
98#14579152C2314yes—
99#14579151—28no—
100#14579151—28no—
101#14579148—22no—
102#14579148C2314yes—
103#14579138—28no—
104Q8×Dic79—22no—
105Q8×Dic79C2314yes—
106C4×Dic158—22no—
107C4×Dic158—22no—
108C4×Dic158D414yes—
109C4×Dic158C2314yes—
110C4×Dic158C2314yes—
111C4×Dic158C2314yes—
112#14579126—28no—
113#14579126—22no—
114#14579126—22no—
115#14579126C2314yes—
116#14579126C2314yes—
117D4×Dic79—22no—
118D4×Dic79C2314yes—
119#14579117—28no—
120C2×C4⋊Dic79—21no—
121C2×C4⋊Dic79—21no—
122C2×C4⋊Dic79D411yescharacteristic
123C2×C4⋊Dic79C2311yescharacteristic
124C2×C4⋊Dic79C2311yescharacteristic
125C2×Dic79⋊C4—21no—
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4—21no—
132C2×Dic79⋊C4—21no—
133C2×Dic79⋊C4D411yescharacteristic
134C2×Dic79⋊C4D411yescharacteristic
135C2×C22⋊Dic79—21no—
136C2×C22⋊Dic79—21no—
137C2×C22⋊Dic79—21no—
138C2×C4×Dic79—21no—
139C2×C4×Dic79—21no—
140C2×C4×Dic79—21no—
141C2×C4×Dic79—21no—
142C2×C4×Dic79—21no—
143C2×C4×Dic79C2311yescharacteristic
144C2×C4×Dic79C2311yescharacteristic
145#14579095C2314yes—
146#14579094C2314yes—
147#14579092C2314yes—
148C4⋊(C79⋊C8)C2314yes—
149Dic79⋊C8C2314yes—
150Dic79⋊C8C2314yes—
151#14579086C2314yes—
152#14579086C2314yes—
153#14579085C2314yes—
154#14579084C2314yes—
155#14579084C2314yes—
156#14579082C2314yes—
157C8×Dic79C2314yes—
158C8×Dic79C2314yes—
159C22×Q8×C79C2311yescharacteristic
160C22×D4×C79C2311yescharacteristic
161C22×C8×C79C2311yescharacteristic
162C22×C8×C79C2311yescharacteristic
163#125×C79—22no—
164#125×C79C2314yes—
165#124×C79—22no—
166#124×C79C2314yes—
167C2×C4⋊C4×C79—21no—
168C2×C4⋊C4×C79—21no—
169C2×C4⋊C4×C79C2311yescharacteristic
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C22⋊C4×C79—21no—
172C2×C22⋊C4×C79—21no—
173C2×C42×C79C2311yescharacteristic
174#103×C79C2314yes—
175#103×C79C2314yes—
176#102×C79C2314yes—
177#102×C79C2314yes—
178C4×C8×C79C2314yes—
179C2×Dic158—24no—
180C2×Dic158—24no—
181C2×Dic158—21no—
182C2×Dic158—21no—
183C2×Dic158—22no—
184C2×Dic158—22no—
185C2×Dic158—22no—
186C2×Dic158—44no—
187C2×Dic158C2×D414yes—
188C2×Dic158#4114yes—
189C2×Dic158C2412yes—
190C2×Dic158C2412yes—
191C22×Dic79—24no—
192C22×Dic79—21no—
193C22×Dic79—21no—
194C22×Dic79—21no—
195C22×Dic79—21no—
196C22×Dic79—44no—
197C22×Dic79C2×D411yescharacteristic
198C22×Dic79C2×D411yescharacteristic
199C22×Dic79C2×D411yescharacteristic
200C22×Dic79C2×D411yescharacteristic
201Dic316—28no—
202#11929614—28no—
203#11929612—28no—
204C2×C79⋊C8—22no—
205C2×C79⋊C8—22no—
206C2×C79⋊C8C2412yes—
207C2×C79⋊C8C2412yes—
208C4⋊Dic79—24no—
209C4⋊Dic79—24no—
210C4⋊Dic79—21no—
211C4⋊Dic79—21no—
212C4⋊Dic79C2×D414yes—
213C4⋊Dic79C2412yes—
214C4⋊Dic79C2412yes—
215Dic79⋊C4—24no—
216Dic79⋊C4—24no—
217Dic79⋊C4—24no—
218Dic79⋊C4—24no—
219Dic79⋊C4—24no—
220Dic79⋊C4—24no—
221Dic79⋊C4—24no—
222Dic79⋊C4—24no—
223Dic79⋊C4C2×D414yes—
224Dic79⋊C4C2×D414yes—
225C22⋊Dic79—24no—
226C22⋊Dic79—24no—
227C22⋊Dic79—24no—
228C4×Dic79—24no—
229C4×Dic79—24no—
230C4×Dic79—24no—
231C4×Dic79—24no—
232C4×Dic79—24no—
233C4×Dic79C2×D412yes—
234C4×Dic79C2×D412yes—
235C4×Dic79C2412yes—
236C4×Dic79C2412yes—
237C24×C79—21no—
238C2×Q8×C79—21no—
239C2×Q8×C79—22no—
240C2×Q8×C79—22no—
241C2×Q8×C79C2412yes—
242C2×D4×C79—21no—
243C2×D4×C79—22no—
244C2×D4×C79—22no—
245C2×D4×C79C2412yes—
246C22×C4×C79—21no—
247C22×C4×C79—21no—
248C22×C4×C79—21no—
249C22×C4×C79C2×D411yescharacteristic
250C22×C4×C79C2×D411yescharacteristic
251C22×C4×C79C2411yescharacteristic
252C2×C8×C79—22no—
253C2×C8×C79—22no—
254C2×C8×C79C2412yes—
255C2×C8×C79C2412yes—
256C4⋊C4×C79—24no—
257C4⋊C4×C79—24no—
258C4⋊C4×C79—21no—
259C4⋊C4×C79—21no—
260C4⋊C4×C79C2412yes—
261C4⋊C4×C79C2412yes—
262C22⋊C4×C79—24no—
263C22⋊C4×C79—24no—
264C42×C79C2×D412yes—
265C42×C79C2412yes—
266C23×C79—22no—
267C23×C79—42no—
268C23×C79—42no—
269C23×C79—42no—
270C23×C79C22×D411yescharacteristic
271Q8×C79—22no—
272Q8×C79—22no—
273Q8×C79—42no—
274D4×C79—22no—
275D4×C79—22no—
276D4×C79—42no—
277C2×C4×C79—22no—
278C2×C4×C79—22no—
279C2×C4×C79—22no—
280C2×C4×C79—22no—
281C2×C4×C79—22no—
282C2×C4×C79—42no—
283C2×C4×C79—42no—
284C2×C4×C79—42no—
285C2×C4×C79C22×D412yes—
286C2×C4×C79C22×D412yes—
287C2×C4×C79C22×D411yescharacteristic
288C2×C4×C79C2×#4112yes—
289C2×C4×C792−1+412yes—
290C2×C4×C79C2511yescharacteristic
291C2×Dic79—24no—
292C2×Dic79—22no—
293C2×Dic79—22no—
294C2×Dic79—22no—
295C2×Dic79—22no—
296C2×Dic79—22no—
297C2×Dic79—22no—
298C2×Dic79—22no—
299C2×Dic79—42no—
300C2×Dic79—42no—
301C2×Dic79—42no—
302C2×Dic79—48no—
303C2×Dic79#13514yes—
304C2×Dic79C22×D412yes—
305C2×Dic79C22×D412yes—
306C2×Dic79C22×D412yes—
307C2×Dic79C22×D412yes—
308Dic158—24no—
309Dic158—22no—
310Dic158—28no—
311Dic158—22no—
312Dic158—22no—
313Dic158—42no—
314Dic158—48no—
315Dic158C2×#4114yes—
316C8×C79—22no—
317C8×C79—22no—
318C79⋊C8—22no—
319C79⋊C8—22no—
320C22×C79—42no—
321C22×C79—42no—
322C22×C79—42no—
323C22×C79—84no—
324C22×C79#54812yes—
325C22×C79C2×#13512yes—
326C22×C79#57812yes—
327C22×C79C23×D411yescharacteristic
328C4×C79—22no—
329C4×C79—22no—
330C4×C79—42no—
331C4×C79—42no—
332C4×C79—42no—
333C4×C79#54812yes—
334C4×C79C22×#4111yescharacteristic
335C4×C79C2×2−1+411yescharacteristic
336Dic79—24no—
337Dic79—22no—
338Dic79—22no—
339Dic79—22no—
340Dic79—42no—
341Dic79—42no—
342Dic79—42no—
343Dic79C2×#13514yes—
344C2×#3364—791nomaximal, Sylow
345C2×C79—82no—
346C2×C79#336414yescomplemented
347C2×C79C2×#54811yescharacteristic
348C2×C79C22×#13511yescharacteristic
349C2×C79C2×#57811yescharacteristic
350C2×#557—791no—
351C2×#556—791no—
352#3364—7916no—
353C2×#488—791no—
354C2×#488D7911yescharacteristic
355C2×#487—791no—
356C2×#479—791no—
357C2×#479—791no—
358C2×#474—791no—
359C2×#464—791no—
360C2×#464—791no—
361C2×#462—791no—
362C2×C8×Q8—791no—
363C2×C4×Q16—791no—
364C2×C4×Q16—791no—
365C2×C4×SD16—791no—
366C79C2×#336411yescharacteristic, complemented, Sylow
367C22×Q16—791no—
368C22×Q16—791no—
369C22×SD16—791no—
370#557—798no—
371#557—1584no—
372#556—798no—
373#556—1584no—
374C2×C4⋊Q8—791no—
375C2×C4⋊Q8—791no—
376C2×C4⋊Q8—1581no—
377C2×#126—1581no—
378C2×#126—1581no—
379C2×#125—791no—
380C2×#125—1581no—
381C2×#125—1581no—
382C2×#125C2×D7911yescharacteristic
383C2×#124—791no—
384C2×#124C2×D7911yescharacteristic
385C2×C22⋊Q8—1581no—
386C2×C4×Q8—791no—
387C2×C4×Q8—791no—
388C2×C4×Q8—791no—
389C2×C4×Q8—791no—
390C2×C4×Q8—791no—
391C2×C4×Q8—791no—
392C2×C4×Q8—1581no—
393C2×C4×D4—791no—
394C2×#117—1581no—
395#488—798no—
396#488C2×D7918yes—
397#487—798no—
398#479—798no—
399#479—798no—
400#474—798no—
401#464—798no—
402#464—798no—
403#462—798no—
404C8×Q8—798no—
405C4×Q16—798no—
406C4×Q16—798no—
407C4×SD16—798no—
408C2×#107—791no—
409C2×#107—791no—
410C2×#106—791no—
411C2×C4⋊C8—791no—
412C2×C4⋊C8—791no—
413C2×C4⋊C8—791no—
414C2×#103—791no—
415C2×#103—791no—
416C2×#103—791no—
417C2×#103—791no—
418C2×#103—791no—
419C2×#103C2×D7911yescharacteristic
420C2×#103C2×D7911yescharacteristic
421C2×#102—791no—
422C2×#102C2×D7911yescharacteristic
423C2×#102C2×D7911yescharacteristic
424C2×C4×C8—791no—
425C2×C4×C8—791no—
426C2×C4×C8C2×D7911yescharacteristic
427C22×Q8—791no—
428C22×Q8—791no—
429C22×Q8—791no—
430C22×Q8—1581no—
431C22×Q8C22×D7911yescharacteristic
432C22×D4C22×D7911yescharacteristic
433C23×C4—1581no—
434C2×Q16—794no—
435C2×Q16—794no—
436C2×Q16—1584no—
437C2×Q16—1584no—
438C2×SD16—794no—
439C2×SD16—1584no—
440C22×C8—791no—
441C22×C8—791no—
442C22×C8C22×D7911yescharacteristic
443C22×C8C22×D7911yescharacteristic
444C4⋊Q8—794no—
445C4⋊Q8—794no—
446C4⋊Q8—1582no—
447C4⋊Q8—1582no—
448C4⋊Q8—1588no—
449#126—1588no—
450#126—1588no—
451#125—22no—
452#125—794no—
453#125—1582no—
454#125—1588no—
455#125—1588no—
456#125C22×D7914yes—
457#124—22no—
458#124—794no—
459#124—1582no—
460#124C22×D7914yes—
461C22⋊Q8—1588no—
462C4×Q8—794no—
463C4×Q8—794no—
464C4×Q8—794no—
465C4×Q8—794no—
466C4×Q8—794no—
467C4×Q8—794no—
468C4×Q8—794no—
469C4×Q8—1582no—
470C4×Q8—1582no—
471C4×Q8—1582no—
472C4×Q8—1588no—
473C4×Q8—1582no—
474C4×Q8—1582no—
475C4×D4—794no—
476C4×D4—1582no—
477#117—1588no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—791no—
481C2×C4⋊C4—791no—
482C2×C4⋊C4—791no—
483C2×C4⋊C4—791no—
484C2×C4⋊C4—791no—
485C2×C4⋊C4—1581no—
486C2×C4⋊C4—1581no—
487C2×C4⋊C4—1581no—
488C2×C4⋊C4—1581no—
489C2×C4⋊C4—1581no—
490C2×C4⋊C4—1581no—
491C2×C4⋊C4—1581no—
492C2×C4⋊C4—1581no—
493C2×C4⋊C4—1581no—
494C2×C4⋊C4—1581no—
495C2×C4⋊C4C22×D7911yescharacteristic
496C2×C4⋊C4C22×D7911yescharacteristic
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—1581no—
500C2×C22⋊C4—1581no—
501C2×C22⋊C4—1581no—
502C2×C42—791no—
503C2×C42—791no—
504C2×C42—1581no—
505C2×C42—1581no—
506C2×C42—1581no—
507C2×C42—1581no—
508C2×C42—1581no—
509C2×C42C22×D7911yescharacteristic
510#107—794no—
511#107—794no—
512#106—794no—
513C4⋊C8—794no—
514C4⋊C8—794no—
515C4⋊C8—794no—
516#103—794no—
517#103—794no—
518#103—794no—
519#103—794no—
520#103—794no—
521#103C22×D7914yes—
522#103C22×D7914yes—
523#102—794no—
524#102C22×D7914yes—
525#102C22×D7914yes—
526C4×C8—794no—
527C4×C8—794no—
528C4×C8C22×D7914yes—
529C24—21no—
530C2×Q8—21no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—3164no—
534C2×Q8—794no—
535C2×Q8—794no—
536C2×Q8—792no—
537C2×Q8—792no—
538C2×Q8—1584no—
539C2×Q8—1584no—
540C2×Q8—1582no—
541C2×Q8—1582no—
542C2×Q8—1582no—
543C2×Q8—1581no—
544C2×Q8—1581no—
545C2×Q8C23×D7912yes—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4C23×D7912yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—3164no—
554C22×C4—791no—
555C22×C4—791no—
556C22×C4—791no—
557C22×C4—791no—
558C22×C4—1584no—
559C22×C4—1581no—
560C22×C4—1581no—
561C22×C4—1581no—
562C22×C4—1581no—
563C22×C4D4×D7911yescharacteristic
564C22×C4D4×D7911yescharacteristic
565C22×C4C23×D7911yescharacteristic
566Q16—1588no—
567Q16—1588no—
568SD16—1588no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—792no—
572C2×C8—792no—
573C2×C8—1582no—
574C2×C8—1582no—
575C2×C8C23×D7912yes—
576C2×C8C23×D7912yes—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—794no—
582C4⋊C4—794no—
583C4⋊C4—794no—
584C4⋊C4—792no—
585C4⋊C4—792no—
586C4⋊C4—1584no—
587C4⋊C4—1584no—
588C4⋊C4—1584no—
589C4⋊C4—1584no—
590C4⋊C4—1584no—
591C4⋊C4—1584no—
592C4⋊C4—1584no—
593C4⋊C4—1584no—
594C4⋊C4—1584no—
595C4⋊C4—1584no—
596C4⋊C4—1581no—
597C4⋊C4—1581no—
598C4⋊C4C23×D7912yes—
599C4⋊C4C23×D7912yes—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—1584no—
603C22⋊C4—1584no—
604C22⋊C4—1584no—
605C42—792no—
606C42—792no—
607C42—792no—
608C42—792no—
609C42—1584no—
610C42—1584no—
611C42—1584no—
612C42—1584no—
613C42—1584no—
614C42D4×D7912yes—
615C42C23×D7912yes—
616C23—22no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23C2×D4×D7911yescharacteristic
621Q8—22no—
622Q8—22no—
623Q8—42no—
624Q8—3168no—
625Q8—3162no—
626Q8—794no—
627Q8—1588no—
628Q8—1582no—
629Q8—1582no—
630Q8—1582no—
631Q8—1584no—
632D4—22no—
633D4—22no—
634D4—42no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—3162no—
644C2×C4—3162no—
645C2×C4—3162no—
646C2×C4—3168no—
647C2×C4—794no—
648C2×C4—792no—
649C2×C4—792no—
650C2×C4—792no—
651C2×C4—792no—
652C2×C4—1582no—
653C2×C4—1582no—
654C2×C4—1582no—
655C2×C4—1584no—
656C2×C4—1582no—
657C2×C4—1582no—
658C2×C4—1582no—
659C2×C4—1582no—
660C2×C4C2×D4×D7912yes—
661C2×C4C2×D4×D7912yes—
662C2×C4C2×D4×D7911yescharacteristic
663C2×C4#41×D7912yes—
664C2×C4#1457920812yes—
665C2×C4C24×D7911yescharacteristic
666C8—22no—
667C8—22no—
668C8—1582no—
669C8—1582no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—84no—
674C22#1909922112yes—
675C22#135×D7912yes—
676C22#1909937712yes—
677C22C22×D4×D7911yescharacteristic
678C4—22no—
679C4—22no—
680C4—42no—
681C4—42no—
682C4—42no—
683C4—3162no—
684C4—3162no—
685C4—3162no—
686C4—794no—
687C4—1582no—
688C4—1584no—
689C4—1582no—
690C4—1582no—
691C4#1909922112yes—
692C4C2×#41×D7911yescharacteristic
693C4C2×#1457920811yescharacteristic
694C2—82no—
695C2#2377608214yesdirect product factor
696C2C2×#1909922111yescharacteristic
697C2C2×#135×D7911yescharacteristic
698C2C2×#1909937711yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#488×C79C2
socleC23×C79C22×D4
prime radicalC22×D4×C79C23
hypercenterC2×#488D79
hypocenterC79C2×#3364
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. C2×#19099290C2semidirect
3. #23776082C2direct (N × H)
5. C2×#19098912C2semidirect
6. C2×#19098872C2semidirect
7. C2×#19098867C2semidirect
11. C2×#19098772C2semidirect
12. C2×C8×Dic158C2semidirect
13. C2×C4×Dic316C2semidirect
14. C2×#19098655C2semidirect
21. #19099290C22semidirect
44. #19098912C22semidirect
45. #19098872C22semidirect
46. #19098867C22semidirect
50. #19098772C22semidirect
51. C8×Dic158C22semidirect
52. C4×Dic316C22semidirect
53. #19098655C22semidirect
346. C2×C79#3364semidirect
366. C79C2×#3364semidirect
695. C2#23776082direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992902
C2×#190992822
#237760822
C2×#190989162
C2×#190989122
C2×#190988722
C2×#190988672
C2×#190988412
C2×#190987842
C2×#190987822
C2×#190987722
C2×C8×Dic1582
C2×C4×Dic3162
C2×#190986552
C2×#190986542
C2×#488×C792
C2×#336479