Finite Group Databasebeta

← C2×#22622666 #33965702

Subgroups — C2×#22622666 #33965702

Order 18688.

1842 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×Dic146C211yesmaximal, characteristic, complemented
2C2×#17989306C211yesmaximal, characteristic
3#22622666C2116yesmaximal, direct product factor
4C2×#17988946C211yesmaximal, characteristic
5C2×#17988945C211yesmaximal, characteristic
6C2×#17988936C211yesmaximal, characteristic, complemented
7C2×#17988873C211yesmaximal, characteristic, complemented
8C2×#17988870C211yesmaximal, characteristic, complemented
9C2×#17988875C211yesmaximal, characteristic
10C2×#17988807C211yesmaximal, characteristic
11C2×#17988795C211yesmaximal, characteristic, complemented
12C2×#17988716C211yesmaximal, characteristic, complemented
13C2×#17988694C211yesmaximal, characteristic, complemented
14C2×#17988692C211yesmaximal, characteristic, complemented
15C2×SD16×Dic73C211yesmaximal, characteristic
16C2×#464×C73C211yesmaximal, characteristic
17C22×#11924018C2211yescharacteristic
18Q8×Dic146—24no—
19Q8×Dic146C2218yescomplemented
20#17989306—24no—
21#17989306C2218yes—
22C2×#14556591—21no—
23C2×#14556591C2211yescharacteristic
24C2×#14556590—21no—
25C2×#14556590—21no—
26C2×#14556590C2211yescharacteristic
27C2×#14556590C2211yescharacteristic
28C2×#14556589C2211yescharacteristic
29C2×#14556584—21no—
30C2×#14556584—21no—
31C2×#14556578C2211yescharacteristic
32C2×#14556568—21no—
33C2×Q8×Dic73C2211yescharacteristic
34C2×Q8×Dic73C2211yescharacteristic
35C2×Q8×Dic73C2211yescharacteristic
36C2×C4×Dic146—21no—
37C2×C4×Dic146C2211yescharacteristic
38C2×C4×Dic146C2211yescharacteristic
39C2×D4×Dic73C2211yescharacteristic
40C2×#14556547—21no—
41#17988946C2218yes—
42#17988945C2218yes—
43#17988936C2218yescomplemented
44#17988875C2218yes—
45#17988873C2218yescomplemented
46#17988870C2218yescomplemented
47#17988807C2218yes—
48#17988795C2218yescomplemented
49#17988716C2218yescomplemented
50#17988694C2218yescomplemented
51#17988692C2218yescomplemented
52SD16×Dic73C2218yes—
53C2×#14556523C2211yescharacteristic
54C2×#14556523C2211yescharacteristic
55C2×#14556522C2211yescharacteristic
56C2×#14556520C2211yescharacteristic
57C2×#14556520C2211yescharacteristic
58C2×#14556516C2211yescharacteristic
59C2×#14556516C2211yescharacteristic
60C2×#14556515C2211yescharacteristic
61C2×#14556515C2211yescharacteristic
62C2×#14556515C2211yescharacteristic
63C2×#14556514C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65C2×#14556512C2211yescharacteristic
66C2×#14556502C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×Q16×C73C2211yescharacteristic
70C22×SD16×C73C2211yescharacteristic
71C2×#124×C73C2211yescharacteristic
72C2×C4×Q8×C73C2211yescharacteristic
73#464×C73C2218yes—
74C2×C4⋊C8×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#102×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146—21no—
79C22×Dic146—21no—
80C22×Dic146D411yescharacteristic
81C22×Dic146C2311yescharacteristic
82C23×Dic73—21no—
83C2×#11924018—24no—
84C2×#11924018C2314yes—
85C22×#10596831C2311yescharacteristic
86C22×#10596831C2311yescharacteristic
87#14556591—28no—
88#14556591—22no—
89#14556591C2314yes—
90#14556590—28no—
91#14556590—28no—
92#14556590—22no—
93#14556590—22no—
94#14556590C2314yes—
95#14556590C2314yes—
96#14556589—22no—
97#14556589C2314yes—
98#14556584—28no—
99#14556584—28no—
100#14556578—22no—
101#14556578C2314yes—
102#14556568—28no—
103Q8×Dic73—22no—
104Q8×Dic73—22no—
105Q8×Dic73—22no—
106Q8×Dic73C2314yes—
107Q8×Dic73C2314yes—
108Q8×Dic73C2314yes—
109C4×Dic146—28no—
110C4×Dic146—22no—
111C4×Dic146D414yes—
112C4×Dic146C2314yes—
113C4×Dic146C2314yes—
114D4×Dic73—22no—
115D4×Dic73C2314yes—
116#14556547—28no—
117C2×C4⋊Dic73—21no—
118C2×C4⋊Dic73—21no—
119C2×C4⋊Dic73—21no—
120C2×C4⋊Dic73—21no—
121C2×C4⋊Dic73D411yescharacteristic
122C2×C4⋊Dic73C2311yescharacteristic
123C2×C4⋊Dic73C2311yescharacteristic
124C2×C4⋊Dic73C2311yescharacteristic
125C2×#11924007—21no—
126C2×#11924007—21no—
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007D411yescharacteristic
131C2×#11924007D411yescharacteristic
132C2×C22⋊Dic73—21no—
133C2×C22⋊Dic73—21no—
134C2×C22⋊Dic73—21no—
135C2×C4×Dic73—21no—
136C2×C4×Dic73—21no—
137C2×C4×Dic73—21no—
138C2×C4×Dic73—21no—
139C2×C4×Dic73C2311yescharacteristic
140C2×C4×Dic73C2311yescharacteristic
141#14556523C2314yes—
142#14556523C2314yes—
143#14556522C2314yes—
144#14556520C2314yes—
145#14556520C2314yes—
146#14556516C2314yes—
147#14556516C2314yes—
148#14556515C2314yes—
149#14556515C2314yes—
150#14556515C2314yes—
151#14556514C2314yes—
152#14556512C2314yes—
153#14556512C2314yes—
154#14556502C2314yes—
155#14556501C2314yes—
156C8×Dic73C2314yes—
157C22×Q8×C73C2311yescharacteristic
158C22×Q8×C73C2311yescharacteristic
159C22×D4×C73C2311yescharacteristic
160C2×Q16×C73—24no—
161C2×Q16×C73C2314yes—
162C2×SD16×C73—24no—
163C2×SD16×C73C2314yes—
164C22×C8×C73C2311yescharacteristic
165C22×C8×C73C2311yescharacteristic
166#124×C73—22no—
167#124×C73C2314yes—
168C4×Q8×C73—22no—
169C4×Q8×C73C2314yes—
170C2×C4⋊C4×C73—21no—
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C22⋊C4×C73—21no—
173C2×C22⋊C4×C73—21no—
174C2×C42×C73—21no—
175C2×C42×C73C2311yescharacteristic
176C4⋊C8×C73C2314yes—
177#103×C73C2314yes—
178#102×C73C2314yes—
179C2×Dic146—24no—
180C2×Dic146—22no—
181C2×Dic146—22no—
182C2×Dic146—21no—
183C2×Dic146—24no—
184C2×Dic146—24no—
185C2×Dic146—24no—
186C2×Dic146—82no—
187C2×Dic146—82no—
188C2×Dic146—82no—
189C2×Dic146C2×D414yes—
190C2×Dic146C2412yes—
191C22×Dic73—21no—
192C22×Dic73—21no—
193C22×Dic73—21no—
194C22×Dic73—21no—
195C22×Dic73—24no—
196C22×Dic73—44no—
197C22×Dic73C2×D411yescharacteristic
198C22×Dic73C2×D411yescharacteristic
199C22×Dic73C2×D411yescharacteristic
200C22×Dic73C2×D411yescharacteristic
201#11924018—28no—
202C2×#10596831—22no—
203C2×#10596831—22no—
204C2×#10596831C2412yes—
205C2×#10596831C2412yes—
206C4⋊Dic73—24no—
207C4⋊Dic73—21no—
208C4⋊Dic73—21no—
209C4⋊Dic73—21no—
210C4⋊Dic73—24no—
211C4⋊Dic73—24no—
212C4⋊Dic73—24no—
213C4⋊Dic73C2×D414yes—
214C4⋊Dic73C2412yes—
215C4⋊Dic73C2412yes—
216C4⋊Dic73C2412yes—
217#11924007—24no—
218#11924007—24no—
219#11924007—24no—
220#11924007—24no—
221#11924007—24no—
222#11924007C2×D414yes—
223#11924007C2×D414yes—
224C22⋊Dic73—24no—
225C22⋊Dic73—24no—
226C22⋊Dic73—24no—
227C4×Dic73—24no—
228C4×Dic73—24no—
229C4×Dic73—24no—
230C4×Dic73—24no—
231C4×Dic73C2×D412yes—
232C4×Dic73C2×D412yes—
233C4×Dic73C2412yes—
234C4×Dic73C2412yes—
235C24×C73—21no—
236C2×Q8×C73—21no—
237C2×Q8×C73—21no—
238C2×Q8×C73—22no—
239C2×Q8×C73—22no—
240C2×Q8×C73—22no—
241C2×Q8×C73#4114yes—
242C2×Q8×C73C2412yes—
243C2×Q8×C73C2412yes—
244C2×D4×C73—21no—
245C2×D4×C73—22no—
246C2×D4×C73—22no—
247C2×D4×C73C2412yes—
248C22×C4×C73—21no—
249C22×C4×C73—21no—
250C22×C4×C73—21no—
251C22×C4×C73C2×D411yescharacteristic
252C22×C4×C73C2×D411yescharacteristic
253C22×C4×C73C2411yescharacteristic
254Q16×C73—28no—
255SD16×C73—28no—
256C2×C8×C73—22no—
257C2×C8×C73—22no—
258C2×C8×C73C2412yes—
259C2×C8×C73C2412yes—
260C4⋊C4×C73—24no—
261C4⋊C4×C73—21no—
262C4⋊C4×C73C2412yes—
263C22⋊C4×C73—24no—
264C22⋊C4×C73—24no—
265C42×C73—24no—
266C42×C73C2×D412yes—
267C42×C73C2412yes—
268C23×C73—22no—
269C23×C73—42no—
270C23×C73—42no—
271C23×C73—42no—
272C23×C73C22×D411yescharacteristic
273Q8×C73—24no—
274Q8×C73—22no—
275Q8×C73—22no—
276Q8×C73—22no—
277Q8×C73—42no—
278Q8×C73C2×#4114yes—
279D4×C73—22no—
280D4×C73—22no—
281D4×C73—42no—
282C2×C4×C73—24no—
283C2×C4×C73—22no—
284C2×C4×C73—22no—
285C2×C4×C73—22no—
286C2×C4×C73—22no—
287C2×C4×C73—22no—
288C2×C4×C73—42no—
289C2×C4×C73—42no—
290C2×C4×C73C22×D412yes—
291C2×C4×C73C22×D412yes—
292C2×C4×C73C22×D411yescharacteristic
293C2×C4×C73C2×#4112yes—
294C2×C4×C732−1+412yes—
295C2×C4×C73C2511yescharacteristic
296C2×Dic73—22no—
297C2×Dic73—22no—
298C2×Dic73—22no—
299C2×Dic73—22no—
300C2×Dic73—22no—
301C2×Dic73—22no—
302C2×Dic73—22no—
303C2×Dic73—42no—
304C2×Dic73—42no—
305C2×Dic73—42no—
306C2×Dic73—42no—
307C2×Dic73—48no—
308C2×Dic73#13714yes—
309C2×Dic73C22×D412yes—
310C2×Dic73C22×D412yes—
311C2×Dic73C22×D412yes—
312C2×Dic73C22×D412yes—
313Dic146—28no—
314Dic146—22no—
315Dic146—22no—
316Dic146—42no—
317Dic146—84no—
318Dic146—84no—
319Dic146—84no—
320C8×C73—22no—
321C8×C73—22no—
322#10596831—22no—
323#10596831—22no—
324C22×C73—42no—
325C22×C73—42no—
326C22×C73—42no—
327C22×C73—84no—
328C22×C73#54812yes—
329C22×C73C2×#13712yes—
330C22×C73#57712yes—
331C22×C73C23×D411yescharacteristic
332C4×C73—24no—
333C4×C73—22no—
334C4×C73—22no—
335C4×C73—42no—
336C4×C73—42no—
337C4×C73#54812yes—
338C4×C73C22×#4111yescharacteristic
339C4×C73C2×2−1+411yescharacteristic
340Dic73—22no—
341Dic73—22no—
342Dic73—22no—
343Dic73—42no—
344Dic73—42no—
345Dic73—42no—
346Dic73—42no—
347Dic73C2×#13714yes—
348C2×#3369—731nomaximal, Sylow
349C2×C73—82no—
350C2×C73#336914yescomplemented
351C2×C73C2×#54811yescharacteristic
352C2×C73C22×#13711yescharacteristic
353C2×C73C2×#57711yescharacteristic
354C2×Q82—731no—
355C2×#556—731no—
356#3369—7316no—
357C2×#489—731no—
358C2×#489—731no—
359C2×#487—731no—
360C2×#475—731no—
361C2×#475—731no—
362C2×#476—731no—
363C2×#464—731no—
364C2×#464D7311yescharacteristic
365C2×#462—731no—
366C2×#446—731no—
367C2×#441—731no—
368C2×#441—731no—
369C2×C4×SD16—731no—
370C73C2×#336911yescharacteristic, complemented, Sylow
371C22×Q16—731no—
372C22×Q16C2×D7311yescharacteristic
373C22×SD16C2×D7311yescharacteristic
374Q82—738no—
375Q82—1464no—
376#556—738no—
377#556—1464no—
378C2×C4⋊Q8—731no—
379C2×C4⋊Q8—731no—
380C2×C4⋊Q8—731no—
381C2×C4⋊Q8—731no—
382C2×C4⋊Q8—1461no—
383C2×C4⋊Q8—1461no—
384C2×C4⋊Q8—1461no—
385C2×#126—1461no—
386C2×#126—1461no—
387C2×#124—731no—
388C2×#124C2×D7311yescharacteristic
389C2×C22⋊Q8—1461no—
390C2×C4×Q8—731no—
391C2×C4×Q8—731no—
392C2×C4×Q8—731no—
393C2×C4×Q8—731no—
394C2×C4×Q8—731no—
395C2×C4×Q8—1461no—
396C2×C4×Q8C2×D7311yescharacteristic
397C2×C4×D4—731no—
398C2×#117—1461no—
399#489—738no—
400#489—738no—
401#487—738no—
402#476—738no—
403#475—738no—
404#475—738no—
405#464—738no—
406#464C2×D7318yes—
407#462—738no—
408#446—738no—
409#441—738no—
410#441—738no—
411C4×SD16—738no—
412C2×#106—731no—
413C2×#106—731no—
414C2×#106—731no—
415C2×C4⋊C8—731no—
416C2×C4⋊C8—731no—
417C2×C4⋊C8C2×D7311yescharacteristic
418C2×#103—731no—
419C2×#103—731no—
420C2×#103—731no—
421C2×#103—731no—
422C2×#103—731no—
423C2×#103—731no—
424C2×#103C2×D7311yescharacteristic
425C2×#102—731no—
426C2×#102—731no—
427C2×#102C2×D7311yescharacteristic
428C2×#97—731no—
429C2×#97—731no—
430C2×C4×C8—731no—
431C22×Q8—731no—
432C22×Q8—731no—
433C22×Q8—1461no—
434C22×Q8—1461no—
435C22×Q8—1461no—
436C22×Q8C22×D7311yescharacteristic
437C22×Q8C22×D7311yescharacteristic
438C22×D4C22×D7311yescharacteristic
439C23×C4—1461no—
440C2×Q16—24no—
441C2×Q16—734no—
442C2×Q16—1464no—
443C2×Q16C22×D7314yes—
444C2×SD16—24no—
445C2×SD16C22×D7314yes—
446C22×C8—731no—
447C22×C8—731no—
448C22×C8C22×D7311yescharacteristic
449C22×C8C22×D7311yescharacteristic
450C4⋊Q8—734no—
451C4⋊Q8—734no—
452C4⋊Q8—734no—
453C4⋊Q8—734no—
454C4⋊Q8—1468no—
455C4⋊Q8—1462no—
456C4⋊Q8—1462no—
457C4⋊Q8—1462no—
458C4⋊Q8—1468no—
459C4⋊Q8—1468no—
460C4⋊Q8—1462no—
461#126—1468no—
462#126—1468no—
463#124—22no—
464#124—734no—
465#124—1462no—
466#124C22×D7314yes—
467C22⋊Q8—1468no—
468C4×Q8—22no—
469C4×Q8—734no—
470C4×Q8—734no—
471C4×Q8—734no—
472C4×Q8—734no—
473C4×Q8—734no—
474C4×Q8—734no—
475C4×Q8—1468no—
476C4×Q8—1462no—
477C4×Q8—1462no—
478C4×Q8—1462no—
479C4×Q8—1462no—
480C4×Q8C22×D7314yes—
481C4×D4—734no—
482C4×D4—1462no—
483#117—1468no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—731no—
486C2×C4⋊C4—731no—
487C2×C4⋊C4—731no—
488C2×C4⋊C4—731no—
489C2×C4⋊C4—731no—
490C2×C4⋊C4—731no—
491C2×C4⋊C4—1461no—
492C2×C4⋊C4—1461no—
493C2×C4⋊C4—1461no—
494C2×C4⋊C4—1461no—
495C2×C4⋊C4—1461no—
496C2×C4⋊C4—1461no—
497C2×C4⋊C4—1461no—
498C2×C4⋊C4—1461no—
499C2×C4⋊C4—1461no—
500C2×C4⋊C4C22×D7311yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—1461no—
504C2×C22⋊C4—1461no—
505C2×C22⋊C4—1461no—
506C2×C42—21no—
507C2×C42—731no—
508C2×C42—731no—
509C2×C42—1461no—
510C2×C42—1461no—
511C2×C42—1461no—
512C2×C42—1461no—
513C2×C42C22×D7311yescharacteristic
514#106—734no—
515#106—734no—
516#106—734no—
517C4⋊C8—734no—
518C4⋊C8—734no—
519C4⋊C8C22×D7314yes—
520#103—734no—
521#103—734no—
522#103—734no—
523#103—734no—
524#103—734no—
525#103—734no—
526#103C22×D7314yes—
527#102—734no—
528#102—734no—
529#102C22×D7314yes—
530#97—734no—
531#97—734no—
532C4×C8—734no—
533C24—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—5842no—
540C2×Q8—5842no—
541C2×Q8—5842no—
542C2×Q8—734no—
543C2×Q8—732no—
544C2×Q8—1464no—
545C2×Q8—1464no—
546C2×Q8—1464no—
547C2×Q8—1462no—
548C2×Q8—1462no—
549C2×Q8—1461no—
550C2×Q8—1464no—
551C2×Q8#1192402714yes—
552C2×Q8C23×D7312yes—
553C2×Q8C23×D7312yes—
554C2×D4—21no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4C23×D7312yes—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—2924no—
562C22×C4—731no—
563C22×C4—731no—
564C22×C4—731no—
565C22×C4—731no—
566C22×C4—1464no—
567C22×C4—1461no—
568C22×C4—1461no—
569C22×C4—1461no—
570C22×C4—1461no—
571C22×C4D4×D7311yescharacteristic
572C22×C4D4×D7311yescharacteristic
573C22×C4C23×D7311yescharacteristic
574Q16—28no—
575Q16—1468no—
576SD16—28no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—732no—
580C2×C8—732no—
581C2×C8—1462no—
582C2×C8—1462no—
583C2×C8C23×D7312yes—
584C2×C8C23×D7312yes—
585C4⋊C4—24no—
586C4⋊C4—21no—
587C4⋊C4—734no—
588C4⋊C4—734no—
589C4⋊C4—734no—
590C4⋊C4—732no—
591C4⋊C4—732no—
592C4⋊C4—732no—
593C4⋊C4—1464no—
594C4⋊C4—1464no—
595C4⋊C4—1464no—
596C4⋊C4—1464no—
597C4⋊C4—1464no—
598C4⋊C4—1464no—
599C4⋊C4—1464no—
600C4⋊C4—1464no—
601C4⋊C4—1461no—
602C4⋊C4—1461no—
603C4⋊C4—1461no—
604C4⋊C4—1464no—
605C4⋊C4C23×D7312yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—1464no—
609C22⋊C4—1464no—
610C22⋊C4—1464no—
611C42—24no—
612C42—732no—
613C42—732no—
614C42—732no—
615C42—732no—
616C42—1464no—
617C42—1464no—
618C42—1464no—
619C42—1464no—
620C42D4×D7312yes—
621C42C23×D7312yes—
622C23—22no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23C2×D4×D7311yescharacteristic
627Q8—22no—
628Q8—24no—
629Q8—22no—
630Q8—22no—
631Q8—42no—
632Q8—2922no—
633Q8—5844no—
634Q8—5844no—
635Q8—5844no—
636Q8—1468no—
637Q8—1462no—
638Q8—1462no—
639Q8C2×#1192402714yes—
640D4—22no—
641D4—22no—
642D4—42no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—2922no—
652C2×C4—2922no—
653C2×C4—2922no—
654C2×C4—2922no—
655C2×C4—2928no—
656C2×C4—734no—
657C2×C4—732no—
658C2×C4—732no—
659C2×C4—732no—
660C2×C4—732no—
661C2×C4—1462no—
662C2×C4—1462no—
663C2×C4—1462no—
664C2×C4—1462no—
665C2×C4—1462no—
666C2×C4—1462no—
667C2×C4—1462no—
668C2×C4C2×D4×D7312yes—
669C2×C4C2×D4×D7312yes—
670C2×C4C2×D4×D7311yescharacteristic
671C2×C4C2×#1192402712yes—
672C2×C4#1455663812yes—
673C2×C4C24×D7311yescharacteristic
674C8—22no—
675C8—22no—
676C8—1462no—
677C8—1462no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—84no—
682C22#1798924312yes—
683C22#137×D7312yes—
684C22#1798939412yes—
685C22C22×D4×D7311yescharacteristic
686C4—22no—
687C4—24no—
688C4—22no—
689C4—42no—
690C4—42no—
691C4—2922no—
692C4—2922no—
693C4—2922no—
694C4—2922no—
695C4—734no—
696C4—1462no—
697C4—1462no—
698C4—1462no—
699C4#1798924312yes—
700C4C22×#1192402711yescharacteristic
701C4C2×#1455663811yescharacteristic
702C2—82no—
703C2#2262266614yesdirect product factor
704C2C2×#1798924311yescharacteristic
705C2C2×#137×D7311yescharacteristic
706C2C2×#1798939411yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#464×C73C2
socleC23×C73C22×D4
prime radicalC22×D4×C73C23
hypercenterC2×#464D73
hypocenterC73C2×#3369
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic146C2semidirect
3. #22622666C2direct (N × H)
6. C2×#17988936C2semidirect
7. C2×#17988873C2semidirect
8. C2×#17988870C2semidirect
11. C2×#17988795C2semidirect
12. C2×#17988716C2semidirect
13. C2×#17988694C2semidirect
14. C2×#17988692C2semidirect
19. Q8×Dic146C22semidirect
43. #17988936C22semidirect
45. #17988873C22semidirect
46. #17988870C22semidirect
48. #17988795C22semidirect
49. #17988716C22semidirect
50. #17988694C22semidirect
51. #17988692C22semidirect
350. C2×C73#3369semidirect
370. C73C2×#3369semidirect
703. C2#22622666direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×Dic1462
C2×#179893062
#226226662
C2×#179889462
C2×#179889452
C2×#179889362
C2×#179888732
C2×#179888702
C2×#179888752
C2×#179888072
C2×#179887952
C2×#179887162
C2×#179886942
C2×#179886922
C2×SD16×Dic732
C2×#464×C732
C2×#336973