Finite Group Databasebeta

← C2×#19140130 #25267145

Subgroups — C2×#19140130 #25267145

Order 11008.

2074 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140130C2116yesmaximal, direct product factor
2C2×#14582840C211yesmaximal, characteristic, complemented
3C2×#14582838C211yesmaximal, characteristic, complemented
4C2×#14582835C211yesmaximal, characteristic
5C2×#14582824C211yesmaximal, characteristic
6C2×#14582798C211yesmaximal, characteristic, complemented
7C2×#14582793C211yesmaximal, characteristic
8C2×#14582792C211yesmaximal, characteristic
9C2×#14582792C211yesmaximal, characteristic
10C2×#14582787C211yesmaximal, characteristic
11C2×#14582784C211yesmaximal, characteristic, complemented
12C2×#14582783C211yesmaximal, characteristic, complemented
13C2×#14582782C211yesmaximal, characteristic, complemented
14C2×C4×C4⋊Dic43C211yesmaximal, characteristic, complemented
15C2×#14582750C211yesmaximal, characteristic, complemented
16C2×C43×#388C211yesmaximal, characteristic
17C22×C4⋊Dic43C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C22×C22⋊Dic43C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C22×C22⋊Dic43C2211yescharacteristic
29C22×C4×Dic43C2211yescharacteristic
30C22×C4×Dic43C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33#14582840C2218yescomplemented
34#14582838C2218yescomplemented
35#14582835C2218yes—
36#14582824C2218yes—
37#14582798C2218yescomplemented
38#14582793C2218yes—
39#14582792C2218yes—
40#14582792C2218yes—
41#14582787C2218yes—
42#14582784C2218yescomplemented
43#14582783C2218yescomplemented
44#14582782C2218yescomplemented
45C4×C4⋊Dic43C2218yescomplemented
46#14582750C2218yescomplemented
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C22×C4⋊C4×C43C2211yescharacteristic
60C22×C22⋊C4×C43C2211yescharacteristic
61C22×C22⋊C4×C43C2211yescharacteristic
62C22×C22⋊C4×C43C2211yescharacteristic
63C22×C42×C43C2211yescharacteristic
64C43×#388C2218yes—
65C2×#95×C43C2211yescharacteristic
66C2×#95×C43C2211yescharacteristic
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C2×C4⋊Dic43—24no—
76C2×C4⋊Dic43—24no—
77C2×C4⋊Dic43—24no—
78C2×C4⋊Dic43—24no—
79C2×C4⋊Dic43C2314yes—
80C2×C4⋊Dic43C2314yes—
81C2×C4⋊Dic43C2314yes—
82C2×C4⋊Dic43C2314yes—
83C2×Dic43⋊C4—24no—
84C2×Dic43⋊C4—24no—
85C2×Dic43⋊C4—24no—
86C2×Dic43⋊C4—42no—
87C2×Dic43⋊C4C2314yes—
88C2×Dic43⋊C4C2314yes—
89C2×Dic43⋊C4C2314yes—
90C2×Dic43⋊C4C2314yes—
91C2×C22⋊Dic43—24no—
92C2×C22⋊Dic43—24no—
93C2×C22⋊Dic43—42no—
94C2×C22⋊Dic43—42no—
95C2×C22⋊Dic43C2314yes—
96C2×C22⋊Dic43C2314yes—
97C2×C22⋊Dic43C2314yes—
98C2×C22⋊Dic43C2314yes—
99C2×C4×Dic43—24no—
100C2×C4×Dic43—42no—
101C2×C4×Dic43—42no—
102C2×C4×Dic43—42no—
103C2×C4×Dic43C2314yes—
104C2×C4×Dic43C2314yes—
105C2×C4×Dic43C2314yes—
106C2×C4×Dic43C2314yes—
107C43⋊#95C2314yes—
108C43⋊#95C2314yes—
109C43⋊#95C2314yes—
110C43⋊#95C2314yes—
111C43⋊#95C2314yes—
112C43⋊#95C2314yes—
113C43⋊#95C2314yes—
114C43⋊#95C2314yes—
115C43⋊#95C2314yes—
116C43⋊#95C2314yes—
117C43⋊#95C2314yes—
118C43⋊#95C2314yes—
119C25×C43C2311yescharacteristic
120C23×C4×C43C2311yescharacteristic
121C23×C4×C43C2311yescharacteristic
122C23×C4×C43C2311yescharacteristic
123C23×C4×C43C2311yescharacteristic
124C23×C4×C43C2311yescharacteristic
125C23×C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43—24no—
127C2×C4⋊C4×C43C2314yes—
128C2×C22⋊C4×C43—24no—
129C2×C22⋊C4×C43—24no—
130C2×C22⋊C4×C43—24no—
131C2×C22⋊C4×C43C2314yes—
132C2×C22⋊C4×C43C2314yes—
133C2×C22⋊C4×C43C2314yes—
134C2×C42×C43—24no—
135C2×C42×C43C2314yes—
136#95×C43C2314yes—
137#95×C43C2314yes—
138C24×C43—22no—
139C24×C43—22no—
140C24×C43—22no—
141C24×C43—22no—
142C24×C43—22no—
143C24×C43—22no—
144C24×C43—22no—
145C24×C43C2412yes—
146C24×C43C2411yescharacteristic
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—22no—
162C22×C4×C43#4114yes—
163C22×C4×C43#4114yes—
164C22×C4×C43#4114yes—
165C22×C4×C43C2412yes—
166C22×C4×C43C2412yes—
167C22×C4×C43C2412yes—
168C22×C4×C43C2412yes—
169C22×C4×C43C2412yes—
170C22×C4×C43C2412yes—
171C22×Dic43—22no—
172C22×Dic43—22no—
173C22×Dic43—22no—
174C22×Dic43—22no—
175C22×Dic43—22no—
176C22×Dic43—22no—
177C22×Dic43—22no—
178C22×Dic43—22no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—22no—
186C22×Dic43—22no—
187C22×Dic43—22no—
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43#4114yes—
194C22×Dic43#4114yes—
195C22×Dic43C2412yes—
196C22×Dic43C2412yes—
197C22×Dic43C2412yes—
198C22×Dic43C2412yes—
199C22×Dic43C2412yes—
200C22×Dic43C2412yes—
201C22×Dic43C2412yes—
202C22×Dic43C2412yes—
203C4⋊C4×C43—28no—
204C22⋊C4×C43—28no—
205C22⋊C4×C43—28no—
206C22⋊C4×C43—28no—
207C42×C43—28no—
208C22⋊Dic43—28no—
209C22⋊Dic43—28no—
210C22⋊Dic43—44no—
211C22⋊Dic43—44no—
212C4⋊Dic43—28no—
213C4⋊Dic43—28no—
214C4⋊Dic43—28no—
215C4⋊Dic43—28no—
216Dic43⋊C4—28no—
217Dic43⋊C4—28no—
218Dic43⋊C4—28no—
219Dic43⋊C4—44no—
220C4×Dic43—28no—
221C4×Dic43—44no—
222C4×Dic43—44no—
223C4×Dic43—44no—
224C23×C43—22no—
225C23×C43—22no—
226C23×C43—22no—
227C23×C43—22no—
228C23×C43—22no—
229C23×C43—22no—
230C23×C43—22no—
231C23×C43—44no—
232C23×C43—44no—
233C23×C43—44no—
234C23×C43—44no—
235C23×C43—44no—
236C23×C43—44no—
237C23×C43—44no—
238C23×C43C2×#4112yes—
239C23×C43C2×#4112yes—
240C23×C43C2×#4112yes—
241C23×C43C2×#4112yes—
242C23×C43C2×#4112yes—
243C23×C43H(5,𝔽2)12yes—
244C23×C432−1+412yes—
245C23×C43C2511yescharacteristic
246C2×C4×C43—28no—
247C2×C4×C43—28no—
248C2×C4×C43—28no—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—22no—
254C2×C4×C43—22no—
255C2×C4×C43—22no—
256C2×C4×C43—22no—
257C2×C4×C43—22no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—22no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—44no—
265C2×C4×C43—44no—
266C2×C4×C43—44no—
267C2×C4×C43C2×#4114yes—
268C2×C4×C43C2×#4114yes—
269C2×C4×C43C2×#4114yes—
270C2×Dic43—28no—
271C2×Dic43—28no—
272C2×Dic43—22no—
273C2×Dic43—22no—
274C2×Dic43—22no—
275C2×Dic43—22no—
276C2×Dic43—22no—
277C2×Dic43—22no—
278C2×Dic43—22no—
279C2×Dic43—22no—
280C2×Dic43—22no—
281C2×Dic43—22no—
282C2×Dic43—22no—
283C2×Dic43—22no—
284C2×Dic43—22no—
285C2×Dic43—22no—
286C2×Dic43—22no—
287C2×Dic43—22no—
288C2×Dic43—22no—
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—22no—
292C2×Dic43—22no—
293C2×Dic43—22no—
294C2×Dic43—44no—
295C2×Dic43—44no—
296C2×Dic43—44no—
297C2×Dic43—44no—
298C2×Dic43—44no—
299C2×Dic43—44no—
300C2×Dic43C2×#4114yes—
301C2×Dic43C2×#4114yes—
302C2×#2596—431nomaximal, Sylow
303C22×C43—42no—
304C22×C43—42no—
305C22×C43—42no—
306C22×C43—42no—
307C22×C43—42no—
308C22×C43—42no—
309C22×C43—42no—
310C22×C43—88no—
311C22×C43#52914yes—
312C22×C43#52914yes—
313C22×C43#53914yes—
314C22×C43#55214yes—
315C22×C43#55314yes—
316C22×C43#55614yes—
317C22×C43#55914yes—
318C22×C43C22×#4111yescharacteristic
319C22×C43C22×#4111yescharacteristic
320C22×C43C22×#4111yescharacteristic
321C22×C43C22×#4111yescharacteristic
322C22×C43C22×#4111yescharacteristic
323C22×C43C2×H(5,𝔽2)11yescharacteristic
324C22×C43C2×2−1+411yescharacteristic
325C4×C43—24no—
326C4×C43—24no—
327C4×C43—24no—
328C4×C43—42no—
329C4×C43—42no—
330C4×C43—42no—
331Dic43—24no—
332Dic43—24no—
333Dic43—42no—
334Dic43—42no—
335Dic43—42no—
336Dic43—42no—
337Dic43—42no—
338Dic43—42no—
339#2596—4316no—
340C2×#400—431no—
341C2×#400—431no—
342C2×#399—431no—
343C2×#397—431no—
344C2×#389—431no—
345C2×#388—431no—
346C2×#388—431no—
347C2×#388—431no—
348C2×#388—431no—
349C2×#388D4311yescharacteristic
350C2×#387—431no—
351C2×#387—431no—
352C2×#387—431no—
353C2×C4×C4⋊C4—431no—
354C2×C4×C4⋊C4—431no—
355C2×C43—82no—
356C2×C43#259618yescomplemented
357C2×C43C2×#52911yescharacteristic
358C2×C43C2×#52911yescharacteristic
359C2×C43C2×#53911yescharacteristic
360C2×C43C2×#55211yescharacteristic
361C2×C43C2×#55311yescharacteristic
362C2×C43C2×#55611yescharacteristic
363C2×C43C2×#55911yescharacteristic
364C22×C4⋊C4—431no—
365C22×C4⋊C4—431no—
366C22×C4⋊C4—431no—
367C22×C4⋊C4—431no—
368C22×C4⋊C4—431no—
369C22×C4⋊C4—431no—
370C22×C4⋊C4—431no—
371C22×C4⋊C4—431no—
372C22×C4⋊C4C2×D4311yescharacteristic
373C22×C22⋊C4—431no—
374C22×C22⋊C4—431no—
375C22×C22⋊C4—431no—
376C22×C22⋊C4—431no—
377C22×C22⋊C4C2×D4311yescharacteristic
378C22×C22⋊C4C2×D4311yescharacteristic
379C22×C22⋊C4C2×D4311yescharacteristic
380C22×C42—431no—
381C22×C42—431no—
382C22×C42—431no—
383C22×C42—431no—
384C22×C42C2×D4311yescharacteristic
385#400—438no—
386#400—438no—
387#399—438no—
388#397—438no—
389#389—438no—
390#388—438no—
391#388—438no—
392#388—438no—
393#388—438no—
394#388C2×D4318yes—
395#387—438no—
396#387—438no—
397#387—438no—
398C4×C4⋊C4—438no—
399C4×C4⋊C4—438no—
400C2×#95—431no—
401C2×#95—431no—
402C2×#95—431no—
403C2×#95—431no—
404C2×#95—431no—
405C2×#95—431no—
406C2×#95—431no—
407C2×#95—431no—
408C2×#95—431no—
409C2×#95—431no—
410C2×#95—431no—
411C2×#95—431no—
412C2×#95C2×D4311yescharacteristic
413C2×#95C2×D4311yescharacteristic
414C43C2×#259611yescharacteristic, complemented, Sylow
415C25C22×D4311yescharacteristic
416C23×C4—431no—
417C23×C4—431no—
418C23×C4—431no—
419C23×C4—431no—
420C23×C4—431no—
421C23×C4—431no—
422C23×C4—431no—
423C23×C4—431no—
424C23×C4C22×D4311yescharacteristic
425C23×C4C22×D4311yescharacteristic
426C23×C4C22×D4311yescharacteristic
427C23×C4C22×D4311yescharacteristic
428C23×C4C22×D4311yescharacteristic
429C23×C4C22×D4311yescharacteristic
430C2×C4⋊C4—24no—
431C2×C4⋊C4—434no—
432C2×C4⋊C4—434no—
433C2×C4⋊C4—434no—
434C2×C4⋊C4—434no—
435C2×C4⋊C4—434no—
436C2×C4⋊C4—434no—
437C2×C4⋊C4—434no—
438C2×C4⋊C4—434no—
439C2×C4⋊C4—864no—
440C2×C4⋊C4—864no—
441C2×C4⋊C4—864no—
442C2×C4⋊C4—864no—
443C2×C4⋊C4—864no—
444C2×C4⋊C4—864no—
445C2×C4⋊C4—864no—
446C2×C4⋊C4—1722no—
447C2×C4⋊C4C22×D4314yes—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—434no—
452C2×C22⋊C4—434no—
453C2×C22⋊C4—434no—
454C2×C22⋊C4—434no—
455C2×C22⋊C4—864no—
456C2×C22⋊C4—864no—
457C2×C22⋊C4—1722no—
458C2×C22⋊C4—1722no—
459C2×C22⋊C4C22×D4314yes—
460C2×C22⋊C4C22×D4314yes—
461C2×C22⋊C4C22×D4314yes—
462C2×C42—24no—
463C2×C42—434no—
464C2×C42—434no—
465C2×C42—434no—
466C2×C42—434no—
467C2×C42—864no—
468C2×C42—1722no—
469C2×C42—1722no—
470C2×C42—1722no—
471C2×C42C22×D4314yes—
472#95—434no—
473#95—434no—
474#95—434no—
475#95—434no—
476#95—434no—
477#95—434no—
478#95—434no—
479#95—434no—
480#95—434no—
481#95—434no—
482#95—434no—
483#95—434no—
484#95C22×D4314yes—
485#95C22×D4314yes—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24C23×D4312yes—
494C24C23×D4311yescharacteristic
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—434no—
511C22×C4—434no—
512C22×C4—432no—
513C22×C4—432no—
514C22×C4—432no—
515C22×C4—432no—
516C22×C4—432no—
517C22×C4—432no—
518C22×C4—432no—
519C22×C4—432no—
520C22×C4—862no—
521C22×C4—862no—
522C22×C4—862no—
523C22×C4—862no—
524C22×C4—862no—
525C22×C4—862no—
526C22×C4—862no—
527C22×C4—862no—
528C22×C4—862no—
529C22×C4—862no—
530C22×C4—862no—
531C22×C4—862no—
532C22×C4—862no—
533C22×C4—862no—
534C22×C4—862no—
535C22×C4—862no—
536C22×C4—862no—
537C22×C4—862no—
538C22×C4—862no—
539C22×C4—862no—
540C22×C4—862no—
541C22×C4—862no—
542C22×C4#1062189814yes—
543C22×C4#1062190014yes—
544C22×C4#1062190014yes—
545C22×C4C23×D4312yes—
546C22×C4C23×D4312yes—
547C22×C4C23×D4312yes—
548C22×C4C23×D4312yes—
549C22×C4C23×D4312yes—
550C22×C4C23×D4312yes—
551C4⋊C4—28no—
552C4⋊C4—868no—
553C4⋊C4—868no—
554C4⋊C4—868no—
555C4⋊C4—868no—
556C4⋊C4—868no—
557C4⋊C4—868no—
558C4⋊C4—868no—
559C4⋊C4—1724no—
560C22⋊C4—28no—
561C22⋊C4—28no—
562C22⋊C4—28no—
563C22⋊C4—868no—
564C22⋊C4—868no—
565C22⋊C4—1724no—
566C22⋊C4—1724no—
567C42—28no—
568C42—868no—
569C42—1724no—
570C42—1724no—
571C42—1724no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—44no—
580C23—44no—
581C23—44no—
582C23—44no—
583C23—44no—
584C23—44no—
585C23—44no—
586C23#41×D4312yes—
587C23#41×D4312yes—
588C23C2×#1062190012yes—
589C23C2×#1062190012yes—
590C23C2×#1062189812yes—
591C23#1306337112yes—
592C23#1306337212yes—
593C23C24×D4311yescharacteristic
594C2×C4—28no—
595C2×C4—28no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—28no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—44no—
613C2×C4—44no—
614C2×C4—44no—
615C2×C4—434no—
616C2×C4—434no—
617C2×C4—868no—
618C2×C4—868no—
619C2×C4—862no—
620C2×C4—862no—
621C2×C4—862no—
622C2×C4—862no—
623C2×C4—862no—
624C2×C4—862no—
625C2×C4—862no—
626C2×C4—862no—
627C2×C4—862no—
628C2×C4—862no—
629C2×C4—862no—
630C2×C4—862no—
631C2×C4—862no—
632C2×C4—862no—
633C2×C4—862no—
634C2×C4—862no—
635C2×C4—862no—
636C2×C4—862no—
637C2×C4—862no—
638C2×C4—862no—
639C2×C4—862no—
640C2×C4—862no—
641C2×C4—1724no—
642C2×C4—1724no—
643C2×C4—1724no—
644C2×C4—1724no—
645C2×C4—1724no—
646C2×C4—1724no—
647C2×C4C2×#1062190014yes—
648C2×C4C2×#1062190014yes—
649C2×C4C2×#1062189814yes—
650C22—42no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—88no—
658C22#1458343014yes—
659C22#1458343114yes—
660C22#1458349314yes—
661C22#1458358914yes—
662C22#1458359314yes—
663C22#1458361614yes—
664C22#1458363114yes—
665C22C2×#41×D4311yescharacteristic
666C22C2×#41×D4311yescharacteristic
667C22C22×#1062190011yescharacteristic
668C22C22×#1062190011yescharacteristic
669C22C22×#1062189811yescharacteristic
670C22C2×#1306337111yescharacteristic
671C22C2×#1306337211yescharacteristic
672C4—24no—
673C4—24no—
674C4—24no—
675C4—42no—
676C4—42no—
677C4—42no—
678C4—864no—
679C4—864no—
680C4—1722no—
681C4—1722no—
682C4—1722no—
683C4—1722no—
684C4—1722no—
685C4—1722no—
686C2—82no—
687C2#1914013018yesdirect product factor
688C2C2×#1458343011yescharacteristic
689C2C2×#1458343111yescharacteristic
690C2C2×#1458349311yescharacteristic
691C2C2×#1458358911yescharacteristic
692C2C2×#1458359311yescharacteristic
693C2C2×#1458361611yescharacteristic
694C2C2×#1458363111yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#388C2
socleC24×C43C24
prime radicalC25×C43C23
hypercenterC2×#388D43
hypocenterC43C2×#2596
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. #19140130C2direct (N × H)
2. C2×#14582840C2semidirect
3. C2×#14582838C2semidirect
6. C2×#14582798C2semidirect
11. C2×#14582784C2semidirect
12. C2×#14582783C2semidirect
13. C2×#14582782C2semidirect
14. C2×C4×C4⋊Dic43C2semidirect
15. C2×#14582750C2semidirect
33. #14582840C22semidirect
34. #14582838C22semidirect
37. #14582798C22semidirect
42. #14582784C22semidirect
43. #14582783C22semidirect
44. #14582782C22semidirect
45. C4×C4⋊Dic43C22semidirect
46. #14582750C22semidirect
356. C2×C43#2596semidirect
414. C43C2×#2596semidirect
687. C2#19140130direct (N × H)

Maximal subgroups

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

subgroupindex
#191401302
C2×#145828402
C2×#145828382
C2×#145828352
C2×#145828242
C2×#145827982
C2×#145827932
C2×#145827922
C2×#145827872
C2×#145827842
C2×#145827832
C2×#145827822
C2×C4×C4⋊Dic432
C2×#145827502
C2×C43×#3882
C2×#259643