Finite Group Databasebeta

← C2×#20254754 #27089127

Subgroups — C2×#20254754 #27089127

Order 12032.

1898 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689675C211yesmaximal, characteristic, complemented
2C2×#15689654C211yesmaximal, characteristic
3#20254754C2116yesmaximal, direct product factor
4C2×#15689429C211yesmaximal, characteristic, complemented
5C2×#15689428C211yesmaximal, characteristic, complemented
6C2×#15689417C211yesmaximal, characteristic, complemented
7C2×#15689411C211yesmaximal, characteristic, complemented
8C2×#15689381C211yesmaximal, characteristic, complemented
9C2×#15689379C211yesmaximal, characteristic, complemented
10C2×#15689367C211yesmaximal, characteristic
11C2×#15689344C211yesmaximal, characteristic, complemented
12C2×#15689343C211yesmaximal, characteristic, complemented
13C2×#15689332C211yesmaximal, characteristic, complemented
14C2×#15689326C211yesmaximal, characteristic, complemented
15C2×#15689146C211yesmaximal, characteristic, complemented
16C2×C47×#468C211yesmaximal, characteristic
17C22×Dic188C2211yescharacteristic
18C22×#10625337C2211yescharacteristic
19C22×#10625335C2211yescharacteristic
20C22×#10625329C2211yescharacteristic
21#15689675—24no—
22#15689675C2218yescomplemented
23C2×#13094023C2211yescharacteristic
24C2×#13094022C2211yescharacteristic
25#15689654—24no—
26#15689654C2218yes—
27C2×#13094017—21no—
28C2×#13094015C2211yescharacteristic
29C2×#13094014—21no—
30C2×#13094011C2211yescharacteristic
31C2×#13094005—21no—
32C2×#13094003C2211yescharacteristic
33C2×#13094003C2211yescharacteristic
34C2×#13094001—21no—
35C2×Q8×Dic47C2211yescharacteristic
36C2×#13093989—21no—
37C2×#13093989C2211yescharacteristic
38C2×#13093989C2211yescharacteristic
39C2×D4×Dic47—21no—
40C2×D4×Dic47C2211yescharacteristic
41C2×#13093980—21no—
42C2×#13093980—21no—
43C22×C4×Dic47C2211yescharacteristic
44#15689429C2218yescomplemented
45#15689428C2218yescomplemented
46#15689417C2218yescomplemented
47#15689411C2218yescomplemented
48#15689381C2218yescomplemented
49#15689379C2218yescomplemented
50#15689367C2218yes—
51#15689344C2218yescomplemented
52#15689343C2218yescomplemented
53#15689332C2218yescomplemented
54#15689326C2218yescomplemented
55C2×#13093957C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58#15689146C2218yescomplemented
59C2×Dic47⋊C8C2211yescharacteristic
60C2×Dic47⋊C8C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×Dic47⋊C8C2211yescharacteristic
63C2×#13093949C2211yescharacteristic
64C2×#13093949C2211yescharacteristic
65C2×#13093948C2211yescharacteristic
66C2×#13093947C2211yescharacteristic
67C2×#13093947C2211yescharacteristic
68C2×#13093945C2211yescharacteristic
69C22×SD16×C47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic
71C2×C22⋊Q8×C47C2211yescharacteristic
72C2×#121×C47C2211yescharacteristic
73C47×#468C2218yes—
74C2×#107×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C22×Dic94C2311yescharacteristic
80C23×Dic47—21no—
81C23×Dic47D411yescharacteristic
82C23×Dic47D411yescharacteristic
83C2×Dic188—42no—
84C2×Dic188C2314yes—
85C2×#10625337—42no—
86C2×#10625337C2314yes—
87C2×#10625335—42no—
88C2×#10625335C2314yes—
89C2×#10625329—42no—
90C2×#10625329C2314yes—
91C22×C47⋊C8C2311yescharacteristic
92C22×C47⋊C8C2311yescharacteristic
93#13094023—22no—
94#13094023C2314yes—
95#13094022—22no—
96#13094022C2314yes—
97#13094017—28no—
98#13094015—22no—
99#13094015C2314yes—
100#13094014—28no—
101#13094011—22no—
102#13094011C2314yes—
103#13094005—28no—
104#13094003—22no—
105#13094003—22no—
106#13094003C2314yes—
107#13094003C2314yes—
108#13094001—28no—
109Q8×Dic47—22no—
110Q8×Dic47C2314yes—
111#13093989—28no—
112#13093989—22no—
113#13093989—22no—
114#13093989C2314yes—
115#13093989C2314yes—
116D4×Dic47—28no—
117D4×Dic47—22no—
118D4×Dic47C2314yes—
119#13093980—28no—
120#13093980—28no—
121C2×C4⋊Dic47—21no—
122C2×C4⋊Dic47—21no—
123C2×C4⋊Dic47C2311yescharacteristic
124C2×C4⋊Dic47C2311yescharacteristic
125C2×Dic47⋊C4—21no—
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×C22⋊Dic47—21no—
134C2×C22⋊Dic47—21no—
135C2×C22⋊Dic47—21no—
136C2×C22⋊Dic47—21no—
137C2×C22⋊Dic47—21no—
138C2×C4×Dic47—21no—
139C2×C4×Dic47—21no—
140C2×C4×Dic47—21no—
141C2×C4×Dic47D411yescharacteristic
142C2×C4×Dic47D411yescharacteristic
143C2×C4×Dic47D414yes—
144C2×C4×Dic47C2311yescharacteristic
145C2×C4×Dic47C2311yescharacteristic
146C2×C4×Dic47C2314yes—
147#13093957C2314yes—
148#13093956C2314yes—
149#13093955C2314yes—
150Dic47⋊C8C2314yes—
151Dic47⋊C8C2314yes—
152Dic47⋊C8C2314yes—
153Dic47⋊C8C2314yes—
154#13093949C2314yes—
155#13093949C2314yes—
156#13093948C2314yes—
157#13093947C2314yes—
158#13093947C2314yes—
159#13093945C2314yes—
160C22×Q8×C47C2311yescharacteristic
161C22×D4×C47—21no—
162C22×D4×C47C2311yescharacteristic
163C23×C4×C47C2311yescharacteristic
164C2×SD16×C47—42no—
165C2×SD16×C47C2314yes—
166C2×M16×C47—42no—
167C2×M16×C47C2314yes—
168C22×C8×C47C2311yescharacteristic
169C22×C8×C47C2311yescharacteristic
170C22⋊Q8×C47—22no—
171C22⋊Q8×C47C2314yes—
172#121×C47—22no—
173#121×C47C2314yes—
174C2×C4⋊C4×C47—21no—
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C22⋊C4×C47—21no—
178C2×C22⋊C4×C47—21no—
179#107×C47C2314yes—
180#103×C47C2314yes—
181#102×C47C2314yes—
182C24×C47—21no—
183C24×C47C2×D411yescharacteristic
184C2×Q8×C47—21no—
185C2×Q8×C47—22no—
186C2×Q8×C47—22no—
187C2×Q8×C47C2412yes—
188C2×D4×C47—24no—
189C2×D4×C47—21no—
190C2×D4×C47—22no—
191C2×D4×C47—22no—
192C2×D4×C47—44no—
193C2×D4×C47C2412yes—
194C22×C4×C47—22no—
195C22×C4×C47—22no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D412yes—
201C22×C4×C47C2412yes—
202C22×C4×C47C2411yescharacteristic
203C22×Dic47—24no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—24no—
209C22×Dic47—42no—
210C22×Dic47—44no—
211C22×Dic47C2×D411yescharacteristic
212C22×Dic47C2×D411yescharacteristic
213C22×Dic47C2×D411yescharacteristic
214C22×Dic47C2×D414yes—
215C22×Dic47C2×D414yes—
216C22×Dic47C2×D411yescharacteristic
217C2×Dic94—22no—
218C2×Dic94—22no—
219C2×Dic94—22no—
220C2×Dic94—22no—
221C2×Dic94—21no—
222C2×Dic94—21no—
223C2×Dic94—24no—
224C2×Dic94—44no—
225C2×Dic94C2412yes—
226C2×Dic94C2412yes—
227SD16×C47—44no—
228M16×C47—44no—
229C2×C8×C47—22no—
230C2×C8×C47—22no—
231C2×C8×C47C2412yes—
232C2×C8×C47C2412yes—
233C4⋊C4×C47—24no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47C2412yes—
237C4⋊C4×C47C2412yes—
238C22⋊C4×C47—24no—
239C22⋊C4×C47—24no—
240C22⋊Dic47—24no—
241C22⋊Dic47—24no—
242C22⋊Dic47—24no—
243C22⋊Dic47—24no—
244C22⋊Dic47—24no—
245#10625337—44no—
246#10625335—44no—
247C4⋊Dic47—21no—
248C4⋊Dic47—21no—
249C4⋊Dic47—24no—
250C4⋊Dic47—24no—
251C4⋊Dic47C2412yes—
252C4⋊Dic47C2412yes—
253Dic47⋊C4—24no—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260Dic47⋊C4—24no—
261C4×Dic47—24no—
262C4×Dic47—24no—
263C4×Dic47—24no—
264C4×Dic47C2×D414yes—
265C4×Dic47C2×D412yes—
266C4×Dic47C2×D414yes—
267C4×Dic47C2×D412yes—
268C4×Dic47C2412yes—
269C4×Dic47C2412yes—
270#10625329—44no—
271C2×C47⋊C8—22no—
272C2×C47⋊C8—22no—
273C2×C47⋊C8C2412yes—
274C2×C47⋊C8C2412yes—
275Dic188—44no—
276C23×C47—22no—
277C23×C47—22no—
278C23×C47—22no—
279C23×C47—22no—
280C23×C47—42no—
281C23×C47—42no—
282C23×C47—42no—
283C23×C47C22×D412yes—
284C23×C47C22×D411yescharacteristic
285Q8×C47—22no—
286Q8×C47—22no—
287Q8×C47—42no—
288D4×C47—22no—
289D4×C47—22no—
290D4×C47—48no—
291D4×C47—42no—
292C2×C4×C47—22no—
293C2×C4×C47—24no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—42no—
300C2×C4×C47—42no—
301C2×C4×C47—42no—
302C2×C4×C47C22×D412yes—
303C2×C4×C47C22×D411yescharacteristic
304C2×C4×C47H(5,𝔽2)12yes—
305C2×C4×C472−1+412yes—
306C2×C4×C47C2511yescharacteristic
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—28no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—44no—
316C2×Dic47—42no—
317C2×Dic47—42no—
318C2×Dic47—42no—
319C2×Dic47—42no—
320C2×Dic47—48no—
321C2×Dic47#13714yes—
322C2×Dic47C22×D412yes—
323C2×Dic47C22×D412yes—
324C2×Dic47C22×D412yes—
325C2×Dic47C22×D412yes—
326Dic94—22no—
327Dic94—22no—
328Dic94—22no—
329Dic94—22no—
330Dic94—48no—
331Dic94—42no—
332Dic94—42no—
333C8×C47—22no—
334C8×C47—22no—
335C47⋊C8—22no—
336C47⋊C8—22no—
337C2×#3252—471nomaximal, Sylow
338C22×C47—22no—
339C22×C47—22no—
340C22×C47—22no—
341C22×C47—44no—
342C22×C47—42no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—84no—
346C22×C47#53712yes—
347C22×C47C2×#13712yes—
348C22×C47#57512yes—
349C22×C47C23×D411yescharacteristic
350C4×C47—22no—
351C4×C47—42no—
352C4×C47—42no—
353C4×C47—42no—
354C4×C47#53712yes—
355C4×C47C2×H(5,𝔽2)11yescharacteristic
356C4×C47C2×2−1+411yescharacteristic
357Dic47—22no—
358Dic47—22no—
359Dic47—22no—
360Dic47—42no—
361Dic47—42no—
362Dic47—42no—
363Dic47—42no—
364Dic47C2×#13714yes—
365C2×#533—471no—
366C2×#529—471no—
367#3252—4716no—
368C2×#479—471no—
369C2×#479—471no—
370C2×#477—471no—
371C2×#476—471no—
372C2×#470—471no—
373C2×#470—471no—
374C2×#468—471no—
375C2×#468D4711yescharacteristic
376C2×#464—471no—
377C2×#464—471no—
378C2×#462—471no—
379C2×#461—471no—
380C2×#423—471no—
381C2×C47—42no—
382C2×C47—82no—
383C2×C47#325214yescomplemented
384C2×C47C2×#53711yescharacteristic
385C2×C47C22×#13711yescharacteristic
386C2×C47C2×#57511yescharacteristic
387C22×Q16—471no—
388C22×Q16—471no—
389C22×SD16—471no—
390C22×SD16C2×D4711yescharacteristic
391C22×M16—471no—
392C22×M16C2×D4711yescharacteristic
393#533—478no—
394#533—944no—
395C2×C4⋊Q8—471no—
396C2×C4⋊Q8—471no—
397#529—478no—
398#529—944no—
399C2×#126—941no—
400C2×#125—471no—
401C2×#125—941no—
402C2×#124—471no—
403C2×#123—941no—
404C2×C22⋊Q8—471no—
405C2×C22⋊Q8—471no—
406C2×C22⋊Q8—941no—
407C2×C22⋊Q8C2×D4711yescharacteristic
408C2×#121C2×D4711yescharacteristic
409C2×C4×Q8—471no—
410C2×C4×Q8—471no—
411C2×C4×Q8—471no—
412C2×C4×Q8—941no—
413C2×C4×D4—471no—
414C2×C4×D4—941no—
415C2×#117—941no—
416C2×#117—941no—
417C22×C42—471no—
418#479—478no—
419#479—478no—
420#477—478no—
421#476—478no—
422#470—478no—
423#470—478no—
424#468—478no—
425#468C2×D4718yes—
426#464—478no—
427#464—478no—
428#462—478no—
429#461—478no—
430C2×#107—471no—
431C2×#107C2×D4711yescharacteristic
432C2×#106—471no—
433C2×#106—471no—
434#423—478no—
435C2×C4⋊C8—471no—
436C2×C4⋊C8—471no—
437C2×C4⋊C8—471no—
438C2×C4⋊C8—471no—
439C2×#103—471no—
440C2×#103—471no—
441C2×#103—471no—
442C2×#103—471no—
443C2×#103—471no—
444C2×#103C2×D4711yescharacteristic
445C2×#102—471no—
446C2×#102C2×D4711yescharacteristic
447C47C2×#325211yescharacteristic, complemented, Sylow
448C22×Q8—471no—
449C22×Q8—471no—
450C22×Q8—941no—
451C22×Q8C22×D4711yescharacteristic
452C22×D4—21no—
453C22×D4C22×D4711yescharacteristic
454C23×C4—471no—
455C23×C4—471no—
456C23×C4—941no—
457C23×C4C22×D4711yescharacteristic
458C2×Q16—474no—
459C2×Q16—474no—
460C2×Q16—1882no—
461C2×Q16—1882no—
462C2×SD16—42no—
463C2×SD16—474no—
464C2×SD16—1882no—
465C2×SD16C22×D4714yes—
466C2×M16—42no—
467C2×M16—474no—
468C2×M16—1882no—
469C2×M16C22×D4714yes—
470C22×C8—471no—
471C22×C8—471no—
472C22×C8C22×D4711yescharacteristic
473C22×C8C22×D4711yescharacteristic
474C4⋊Q8—474no—
475C4⋊Q8—474no—
476C4⋊Q8—942no—
477C4⋊Q8—942no—
478#126—948no—
479#125—474no—
480#125—942no—
481#125—948no—
482#124—474no—
483#124—942no—
484#123—948no—
485C22⋊Q8—22no—
486C22⋊Q8—474no—
487C22⋊Q8—474no—
488C22⋊Q8—948no—
489C22⋊Q8—942no—
490C22⋊Q8—942no—
491C22⋊Q8C22×D4714yes—
492#121—22no—
493#121C22×D4714yes—
494C4×Q8—474no—
495C4×Q8—474no—
496C4×Q8—474no—
497C4×Q8—942no—
498C4×Q8—942no—
499C4×Q8—948no—
500C4×Q8—942no—
501C4×D4—474no—
502C4×D4—942no—
503C4×D4—948no—
504#117—948no—
505#117—948no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—471no—
508C2×C4⋊C4—471no—
509C2×C4⋊C4—941no—
510C2×C4⋊C4—941no—
511C2×C4⋊C4—941no—
512C2×C4⋊C4—941no—
513C2×C4⋊C4—941no—
514C2×C4⋊C4—941no—
515C2×C4⋊C4—941no—
516C2×C4⋊C4—941no—
517C2×C4⋊C4—941no—
518C2×C4⋊C4—941no—
519C2×C4⋊C4C22×D4711yescharacteristic
520C2×C4⋊C4C22×D4711yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—941no—
524C2×C22⋊C4—941no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—941no—
528C2×C42—471no—
529C2×C42—471no—
530C2×C42—474no—
531C2×C42—471no—
532C2×C42—471no—
533C2×C42—474no—
534C2×C42—941no—
535C2×C42—941no—
536C2×C42—941no—
537#107—474no—
538#107C22×D4714yes—
539#106—474no—
540#106—474no—
541C4⋊C8—474no—
542C4⋊C8—474no—
543C4⋊C8—474no—
544C4⋊C8—474no—
545#103—474no—
546#103—474no—
547#103—474no—
548#103—474no—
549#103—474no—
550#103C22×D4714yes—
551#102—474no—
552#102C22×D4714yes—
553C24—21no—
554C24D4×D4711yescharacteristic
555C2×Q8—21no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—472no—
559C2×Q8—472no—
560C2×Q8—944no—
561C2×Q8—941no—
562C2×Q8—941no—
563C2×Q8—942no—
564C2×Q8—942no—
565C2×Q8—942no—
566C2×Q8—942no—
567C2×Q8—1884no—
568C2×Q8C23×D4712yes—
569C2×D4—24no—
570C2×D4—21no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—44no—
574C2×D4C23×D4712yes—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—471no—
581C22×C4—474no—
582C22×C4—471no—
583C22×C4—471no—
584C22×C4—471no—
585C22×C4—474no—
586C22×C4—944no—
587C22×C4—944no—
588C22×C4—941no—
589C22×C4—941no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—1884no—
593C22×C4—1882no—
594C22×C4D4×D4712yes—
595C22×C4D4×D4711yescharacteristic
596C22×C4C23×D4712yes—
597C22×C4C23×D4711yescharacteristic
598Q16—1884no—
599Q16—1884no—
600SD16—44no—
601SD16—1884no—
602M16—44no—
603M16—1884no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—472no—
607C2×C8—472no—
608C2×C8—942no—
609C2×C8—942no—
610C2×C8C23×D4712yes—
611C2×C8C23×D4712yes—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—472no—
616C4⋊C4—472no—
617C4⋊C4—944no—
618C4⋊C4—944no—
619C4⋊C4—944no—
620C4⋊C4—944no—
621C4⋊C4—944no—
622C4⋊C4—944no—
623C4⋊C4—944no—
624C4⋊C4—944no—
625C4⋊C4—944no—
626C4⋊C4—944no—
627C4⋊C4—941no—
628C4⋊C4—941no—
629C4⋊C4C23×D4712yes—
630C4⋊C4C23×D4712yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—944no—
634C22⋊C4—944no—
635C22⋊C4—944no—
636C22⋊C4—944no—
637C22⋊C4—944no—
638C42—474no—
639C42—472no—
640C42—472no—
641C42—474no—
642C42—472no—
643C42—472no—
644C42—944no—
645C42—944no—
646C42—944no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23C2×D4×D4712yes—
655C23C2×D4×D4711yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—942no—
660Q8—942no—
661Q8—942no—
662Q8—942no—
663Q8—1888no—
664Q8—1882no—
665Q8—1882no—
666D4—22no—
667D4—22no—
668D4—48no—
669D4—42no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—474no—
681C2×C4—472no—
682C2×C4—472no—
683C2×C4—472no—
684C2×C4—472no—
685C2×C4—948no—
686C2×C4—942no—
687C2×C4—942no—
688C2×C4—942no—
689C2×C4—942no—
690C2×C4—942no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—1888no—
694C2×C4—1884no—
695C2×C4—1882no—
696C2×C4—1882no—
697C2×C4—1882no—
698C2×C4—1882no—
699C2×C4C2×D4×D4712yes—
700C2×C4C2×D4×D4711yescharacteristic
701C2×C4#1309406912yes—
702C2×C4#1309407112yes—
703C2×C4C24×D4711yescharacteristic
704C8—22no—
705C8—22no—
706C8—942no—
707C8—942no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—44no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—84no—
716C22#1568970012yes—
717C22#137×D4712yes—
718C22#1568991912yes—
719C22C22×D4×D4711yescharacteristic
720C4—22no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—474no—
725C4—942no—
726C4—942no—
727C4—942no—
728C4—1882no—
729C4—1882no—
730C4—1882no—
731C4—1882no—
732C4#1568970012yes—
733C4C2×#1309406911yescharacteristic
734C4C2×#1309407111yescharacteristic
735C2—42no—
736C2—82no—
737C2#2025475414yesdirect product factor
738C2C2×#1568970011yescharacteristic
739C2C2×#137×D4711yescharacteristic
740C2C2×#1568991911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#468C2
socleC23×C47C22×D4
prime radicalC2×#121×C47C22
hypercenterC2×#468D47
hypocenterC47C2×#3252
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#15689675C2semidirect
3. #20254754C2direct (N × H)
4. C2×#15689429C2semidirect
5. C2×#15689428C2semidirect
6. C2×#15689417C2semidirect
7. C2×#15689411C2semidirect
8. C2×#15689381C2semidirect
9. C2×#15689379C2semidirect
11. C2×#15689344C2semidirect
12. C2×#15689343C2semidirect
13. C2×#15689332C2semidirect
14. C2×#15689326C2semidirect
15. C2×#15689146C2semidirect
22. #15689675C22semidirect
44. #15689429C22semidirect
45. #15689428C22semidirect
46. #15689417C22semidirect
47. #15689411C22semidirect
48. #15689381C22semidirect
49. #15689379C22semidirect
51. #15689344C22semidirect
52. #15689343C22semidirect
53. #15689332C22semidirect
54. #15689326C22semidirect
58. #15689146C22semidirect
383. C2×C47#3252semidirect
447. C47C2×#3252semidirect
737. C2#20254754direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896752
C2×#156896542
#202547542
C2×#156894292
C2×#156894282
C2×#156894172
C2×#156894112
C2×#156893812
C2×#156893792
C2×#156893672
C2×#156893442
C2×#156893432
C2×#156893322
C2×#156893262
C2×#156891462
C2×C47×#4682
C2×#325247