Finite Group Databasebeta

← C2×#20253214 #27083832

Subgroups — C2×#20253214 #27083832

Order 12032.

2234 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689750C211yesmaximal, characteristic, complemented
2C2×#15689595C211yesmaximal, characteristic
3#20253214C2116yesmaximal, direct product factor
4C2×#15689425C211yesmaximal, characteristic, complemented
5C2×#15689424C211yesmaximal, characteristic, complemented
6C2×#15689423C211yesmaximal, characteristic, complemented
7C2×#15689422C211yesmaximal, characteristic, complemented
8C2×#15689412C211yesmaximal, characteristic, complemented
9C2×#15689401C211yesmaximal, characteristic, complemented
10C2×#15689400C211yesmaximal, characteristic, complemented
11C2×#15689162C211yesmaximal, characteristic, complemented
12C2×#15689158C211yesmaximal, characteristic, complemented
13C2×#15689148C211yesmaximal, characteristic, complemented
14C2×#15689126C211yesmaximal, characteristic
15C2×#102×D47C211yesmaximal, characteristic
16C2×C47×#476C211yesmaximal, characteristic, complemented
17C22×D4×D47C2211yescharacteristic
18C22×#10625324C2211yescharacteristic
19C22×C8×D47C2211yescharacteristic
20#15689750—24no—
21#15689750C2218yescomplemented
22C2×#13094023C2211yescharacteristic, complemented
23C2×#13094022—21no—
24C2×#13094016C2211yescharacteristic, complemented
25C2×#13094015C2211yescharacteristic, complemented
26C2×#13094014—21no—
27C2×#13094002—21no—
28C2×#13094000—21no—
29#15689595—24no—
30#15689595C2218yes—
31C2×C4×D188C2211yescharacteristic
32C2×D4×Dic47C2211yescharacteristic
33C2×#13093986C2211yescharacteristic
34C2×C4×C22⋊D47—21no—
35C2×(C22⋊D47)⋊C4—21no—
36C2×#13093982C2211yescharacteristic
37C2×#13093982C2211yescharacteristic
38C2×#13093981C2211yescharacteristic
39C2×C4⋊C4×D47C2211yescharacteristic
40C22×(C2×D47)⋊C4—21no—
41C2×C22⋊C4×D47—21no—
42#15689425C2218yescomplemented
43#15689424C2218yescomplemented
44#15689423C2218yescomplemented
45#15689422C2218yescomplemented
46#15689412C2218yescomplemented
47#15689401C2218yescomplemented
48#15689400C2218yescomplemented
49#15689162C2218yescomplemented
50#15689158C2218yescomplemented
51C2×#13093958C2211yescharacteristic, complemented
52C2×#13093957C2211yescharacteristic, complemented
53C2×#13093957C2211yescharacteristic, complemented
54C2×#13093957C2211yescharacteristic, complemented
55C2×#13093956C2211yescharacteristic, complemented
56C2×#13093955C2211yescharacteristic, complemented
57#15689148C2218yescomplemented
58C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
59C2×Dic47⋊C8C2211yescharacteristic, complemented
60C2×Dic47⋊C8C2211yescharacteristic, complemented
61#15689126C2218yes—
62C2×#13093946C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×#13093945C2211yescharacteristic
66C2×#13093944C2211yescharacteristic
67C2×#13093944C2211yescharacteristic
68#102×D47C2218yes—
69C2×C4⋊Q8×C47C2211yescharacteristic, complemented
70C2×C4×D4×C47C2211yescharacteristic
71C47×#476C2218yescomplemented
72C2×#106×C47C2211yescharacteristic, complemented
73C2×#106×C47C2211yescharacteristic, complemented
74C2×C4⋊C8×C47C2211yescharacteristic, complemented
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C24×D47—21no—
78C22×Dic94—21no—
79C22×D188C2311yescharacteristic
80C22×C22⋊D47—21no—
81C2×D4×D47—22no—
82C2×D4×D47—24no—
83C2×D4×D47Q818yescomplemented
84C2×D4×D47C2314yes—
85C23×Dic47—21no—
86C22×C4×D47—21no—
87C22×C4×D47—21no—
88C22×C4×D47—21no—
89C22×C4×D47C2311yescharacteristic
90C2×#10625324—24no—
91C2×#10625324C2314yes—
92C22×C47⋊C8C2311yescharacteristic
93C22×C47⋊C8C2311yescharacteristic
94C2×C8×D47—24no—
95C2×C8×D47C2314yes—
96#13094023—22no—
97#13094023C2314yescomplemented
98#13094022—28no—
99#13094016—22no—
100#13094016C2314yescomplemented
101#13094015—22no—
102#13094015C2314yescomplemented
103#13094014—28no—
104#13094002—28no—
105#13094000—28no—
106C4×D188—22no—
107C4×D188C2314yes—
108D4×Dic47—22no—
109D4×Dic47C2314yes—
110#13093986—22no—
111#13093986C2314yes—
112C4×C22⋊D47—28no—
113(C22⋊D47)⋊C4—28no—
114#13093982—22no—
115#13093982—22no—
116#13093982C2314yes—
117#13093982C2314yes—
118#13093981D414yes—
119#13093981C2314yes—
120C2×C4⋊Dic47—21no—
121C2×C4⋊Dic47C2311yescharacteristic
122C2×C4⋊Dic47C2311yescharacteristic
123C2×C4⋊Dic47C2311yescharacteristic
124C2×Dic47⋊C4—21no—
125C2×Dic47⋊C4—21no—
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4D411yescharacteristic
130C2×Dic47⋊C4D411yescharacteristic
131C4⋊C4×D47—22no—
132C4⋊C4×D47C2314yes—
133C2×C22⋊Dic47—21no—
134C2×(C2×D47)⋊C4—21no—
135C2×(C2×D47)⋊C4—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—28no—
139C2×(C2×D47)⋊C4D411yescharacteristic
140C2×(C2×D47)⋊C4D411yescharacteristic
141C22⋊C4×D47—28no—
142C2×C4×Dic47—21no—
143C2×C4×Dic47—21no—
144C2×C4×Dic47C2311yescharacteristic
145#13093958C2314yescomplemented
146#13093957C2314yescomplemented
147#13093957C2314yescomplemented
148#13093957C2314yescomplemented
149#13093956C2314yescomplemented
150#13093955C2314yescomplemented
151C4⋊(C47⋊C8)C2314yescomplemented
152Dic47⋊C8C2314yescomplemented
153Dic47⋊C8C2314yescomplemented
154#13093946C2314yes—
155#13093946C2314yes—
156#13093945C2314yes—
157#13093945C2314yes—
158#13093944C2314yes—
159#13093944C2314yes—
160C22×Q8×C47—21no—
161C22×D4×C47C2311yescharacteristic
162C23×C4×C47—21no—
163C22×C8×C47C2311yescharacteristic
164C22×C8×C47C2311yescharacteristic
165C4⋊Q8×C47—22no—
166C4⋊Q8×C47C2314yescomplemented
167C4×D4×C47—22no—
168C4×D4×C47C2314yes—
169C2×C4⋊C4×C47—21no—
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C22⋊C4×C47—21no—
174C2×C42×C47C2311yescharacteristic
175#106×C47C2314yescomplemented
176#106×C47C2314yescomplemented
177C4⋊C8×C47C2314yescomplemented
178#102×C47C2314yes—
179#102×C47C2314yes—
180C24×C47—21no—
181C23×D47—21no—
182C23×D47—28no—
183C23×D47—24no—
184C23×D47—82no—
185C23×D47—82no—
186C23×D47C2×D411yescharacteristic
187C2×Q8×C47—24no—
188C2×Q8×C47—82no—
189C2×D4×C47—21no—
190C2×D4×C47—22no—
191C2×D4×C47C2×Q814yes—
192C2×D4×C47C2412yes—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—24no—
197C22×C4×C47—82no—
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2411yescharacteristic
201C2×C22⋊D47—28no—
202C2×C22⋊D47—24no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—24no—
207C22×Dic47—82no—
208C22×Dic47C2×D411yescharacteristic
209C22×Dic47C2×D411yescharacteristic
210C22×Dic47C2×D411yescharacteristic
211D4×D47—216no—
212D4×D47—28no—
213D4×D47C2×Q8116yescomplemented
214C2×D188—21no—
215C2×D188—22no—
216C2×D188C2×Q814yes—
217C2×D188C2412yes—
218C2×C4×D47—24no—
219C2×C4×D47—24no—
220C2×C4×D47—24no—
221C2×C4×D47—82no—
222C2×C4×D47—82no—
223C2×C4×D47—82no—
224C2×C4×D47C2×D412yes—
225C2×C4×D47C2×Q814yes—
226C2×C4×D47#4114yes—
227C2×C4×D47C2412yes—
228C2×Dic94—24no—
229C2×Dic94—82no—
230C2×C8×C47—22no—
231C2×C8×C47—22no—
232C2×C8×C47C2412yes—
233C2×C8×C47C2412yes—
234C4⋊C4×C47—24no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—21no—
238C4⋊C4×C47C2412yes—
239C4⋊C4×C47C2412yes—
240C4⋊C4×C47C2412yes—
241C22⋊C4×C47—24no—
242C42×C47C2×D412yes—
243C42×C47C2412yes—
244C22⋊Dic47—24no—
245(C2×D47)⋊C4—24no—
246(C2×D47)⋊C4—24no—
247(C2×D47)⋊C4—24no—
248(C2×D47)⋊C4—24no—
249(C2×D47)⋊C4C2×D414yes—
250(C2×D47)⋊C4C2×D414yes—
251C4⋊Dic47—21no—
252C4⋊Dic47—21no—
253C4⋊Dic47—21no—
254C4⋊Dic47—24no—
255C4⋊Dic47C2412yes—
256C4⋊Dic47C2412yes—
257C4⋊Dic47C2412yes—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260Dic47⋊C4—24no—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263Dic47⋊C4C2×D414yes—
264Dic47⋊C4C2×D414yes—
265C4×Dic47—24no—
266C4×Dic47—24no—
267C4×Dic47C2×D412yes—
268C4×Dic47C2412yes—
269C2×C47⋊C8—22no—
270C2×C47⋊C8—22no—
271C2×C47⋊C8C2412yes—
272C2×C47⋊C8C2412yes—
273#10625324—28no—
274C8×D47—28no—
275C23×C47—24no—
276C23×C47—22no—
277C23×C47—42no—
278C23×C47—42no—
279C23×C47C22×D411yescharacteristic
280C22×D47—22no—
281C22×D47—22no—
282C22×D47—24no—
283C22×D47—22no—
284C22×D47—216no—
285C22×D47—42no—
286C22×D47—42no—
287C22×D47—816no—
288C22×D47—84no—
289C22×D47—84no—
290C22×D47C22⋊Q814yes—
291C22×D47C22×D412yes—
292Q8×C47—84no—
293D4×C47—24no—
294D4×C47—22no—
295D4×C47C22×Q814yes—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—42no—
302C2×C4×C47—42no—
303C2×C4×C47—42no—
304C2×C4×C47—84no—
305C2×C4×C47C22×D412yes—
306C2×C4×C47C22×D412yes—
307C2×C4×C47C22×D411yescharacteristic
308C2×C4×C47C22×Q812yes—
309C2×C4×C47C2×#4112yes—
310C2×C4×C47C2511yescharacteristic
311C22⋊D47—216no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—42no—
318C2×Dic47—42no—
319C2×Dic47—42no—
320C2×Dic47—84no—
321C2×Dic47C22⋊Q814yes—
322C2×Dic47C22×D412yes—
323C2×Dic47C22×D412yes—
324C2×Dic47C22×D412yes—
325D188—24no—
326D188—22no—
327D188C22×Q814yes—
328C4×D47—84no—
329C4×D47—84no—
330C4×D47—84no—
331C4×D47C22⋊Q818yes—
332C4×D47C22×Q814yes—
333C4×D47C2×#4114yes—
334Dic94—84no—
335C8×C47—22no—
336C8×C47—22no—
337C47⋊C8—22no—
338C47⋊C8—22no—
339C2×#3081—471nomaximal, Sylow
340C22×C47—24no—
341C22×C47—48no—
342C22×C47—42no—
343C22×C47—42no—
344C22×C47C2×C22⋊Q812yes—
345C22×C47#57612yes—
346C22×C47#57712yes—
347C22×C47C23×D411yescharacteristic
348C2×D47—28no—
349C2×D47—22no—
350C2×D47—22no—
351C2×D47—24no—
352C2×D47—48no—
353C2×D47—42no—
354C2×D47—42no—
355C2×D47—816no—
356C2×D47C2×C22⋊Q814yes—
357C4×C47—22no—
358C4×C47—22no—
359C4×C47—42no—
360C4×C47—42no—
361C4×C47—42no—
362C4×C47C2×C22⋊Q812yes—
363C4×C47C23×Q811yescharacteristic
364C4×C47C22×#4111yescharacteristic
365Dic47—22no—
366Dic47—22no—
367Dic47—42no—
368Dic47—42no—
369Dic47—42no—
370Dic47C2×C22⋊Q814yes—
371C2×#544—471no—
372C2×#518—471no—
373#3081—4716no—
374C2×#478—471no—
375C2×#478—471no—
376C2×#478—471no—
377C2×#478—471no—
378C2×#476—471no—
379C2×#476D4711yescharacteristic, complemented
380C2×#474—471no—
381C2×#474—471no—
382C2×#428—471no—
383C2×#427—471no—
384C2×#424—471no—
385C2×#418—471no—
386C22×#102—471no—
387C2×C47—44no—
388C2×C47#308114yescomplemented
389C2×C47C22×C22⋊Q811yescharacteristic
390C2×C47C2×#57611yescharacteristic
391C2×C47C2×#57711yescharacteristic
392D47—24no—
393D47—44no—
394C23×D4—471no—
395C22×M16—471no—
396C23×C8—471no—
397#544—478no—
398#544—944no—
399C2×C4⋊Q8—471no—
400C2×C4⋊Q8—941no—
401C2×C4⋊Q8C2×D4711yescharacteristic, complemented
402C2×#125—471no—
403C2×#125—471no—
404C2×#125—941no—
405C2×C22⋊Q8—941no—
406C2×C22⋊Q8—941no—
407#518—478no—
408#518—944no—
409C2×C4×D4—471no—
410C2×C4×D4—471no—
411C2×C4×D4—471no—
412C2×C4×D4—941no—
413C2×C4×D4—941no—
414C2×C4×D4C2×D4711yescharacteristic
415C2×#117—471no—
416C2×#117—471no—
417C2×#117—471no—
418C22×C4⋊C4—471no—
419C22×C22⋊C4—941no—
420C22×C22⋊C4—941no—
421#478—478no—
422#478—478no—
423#478—478no—
424#478—478no—
425#476—478no—
426#476C2×D4718yescomplemented
427#474—478no—
428#474—478no—
429#428—478no—
430#427—478no—
431C2×#107—471no—
432C2×#107—471no—
433C2×#107—471no—
434C2×#107—471no—
435C2×#106—471no—
436C2×#106—471no—
437C2×#106C2×D4711yescharacteristic, complemented
438C2×#106C2×D4711yescharacteristic, complemented
439#424—478no—
440C2×C4⋊C8—471no—
441C2×C4⋊C8—471no—
442C2×C4⋊C8—471no—
443C2×C4⋊C8C2×D4711yescharacteristic, complemented
444#418—478no—
445C2×#102—471no—
446C2×#102—471no—
447C2×#102—471no—
448C2×#102—471no—
449C2×#102—471no—
450C2×#102—471no—
451C2×#102—478no—
452C2×#102C2×D4711yescharacteristic
453C2×#102C2×D4711yescharacteristic
454C47C2×#308111yescharacteristic, complemented, Sylow
455C25—941no—
456C22×Q8—21no—
457C22×Q8—941no—
458C22×D4—478no—
459C22×D4—474no—
460C22×D4—471no—
461C22×D4—942no—
462C22×D4—944no—
463C22×D4—941no—
464C22×D4C22×D4711yescharacteristic
465C23×C4—21no—
466C23×C4—471no—
467C23×C4—941no—
468C23×C4—941no—
469C23×C4—941no—
470C23×C4—941no—
471C2×M16—474no—
472C2×M16—944no—
473C22×C8—471no—
474C22×C8—471no—
475C22×C8—474no—
476C22×C8—944no—
477C22×C8C22×D4711yescharacteristic
478C22×C8C22×D4711yescharacteristic
479C4⋊Q8—22no—
480C4⋊Q8—474no—
481C4⋊Q8—942no—
482C4⋊Q8—948no—
483C4⋊Q8C22×D4714yescomplemented
484#125—474no—
485#125—474no—
486#125—942no—
487#125—948no—
488#125—942no—
489C22⋊Q8—948no—
490C22⋊Q8—948no—
491C4×D4—22no—
492C4×D4—474no—
493C4×D4—474no—
494C4×D4—474no—
495C4×D4—942no—
496C4×D4—942no—
497C4×D4—948no—
498C4×D4—948no—
499C4×D4—942no—
500C4×D4C22×D4714yes—
501#117—474no—
502#117—474no—
503#117—474no—
504#117—474no—
505#117—942no—
506#117—942no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—471no—
509C2×C4⋊C4—471no—
510C2×C4⋊C4—471no—
511C2×C4⋊C4—471no—
512C2×C4⋊C4—471no—
513C2×C4⋊C4—474no—
514C2×C4⋊C4—942no—
515C2×C4⋊C4—941no—
516C2×C4⋊C4—941no—
517C2×C4⋊C4—941no—
518C2×C4⋊C4—941no—
519C2×C4⋊C4—941no—
520C2×C4⋊C4—941no—
521C2×C4⋊C4C22×D4711yescharacteristic
522C2×C4⋊C4C22×D4711yescharacteristic
523C2×C4⋊C4C22×D4711yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—471no—
526C2×C22⋊C4—471no—
527C2×C22⋊C4—948no—
528C2×C22⋊C4—948no—
529C2×C22⋊C4—941no—
530C2×C22⋊C4—941no—
531C2×C22⋊C4—941no—
532C2×C22⋊C4—941no—
533C2×C22⋊C4—941no—
534C2×C42—471no—
535C2×C42—941no—
536C2×C42—941no—
537C2×C42C22×D4711yescharacteristic
538#107—474no—
539#107—474no—
540#107—474no—
541#107—474no—
542#106—474no—
543#106—474no—
544#106C22×D4714yescomplemented
545#106C22×D4714yescomplemented
546C4⋊C8—474no—
547C4⋊C8—474no—
548C4⋊C8—474no—
549C4⋊C8C22×D4714yescomplemented
550#102—474no—
551#102—474no—
552#102—474no—
553#102—474no—
554#102—474no—
555#102—474no—
556#102C22×D4714yes—
557#102C22×D4714yes—
558C24—21no—
559C24—471no—
560C24—944no—
561C24—948no—
562C24—941no—
563C24—3762no—
564C24—3762no—
565C2×Q8—24no—
566C2×Q8—82no—
567C2×Q8—944no—
568C2×Q8—3762no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—4716no—
572C2×D4—474no—
573C2×D4—472no—
574C2×D4—9416no—
575C2×D4—948no—
576C2×D4—944no—
577C2×D4—948no—
578C2×D4—941no—
579C2×D4—942no—
580C2×D4Q8×D4714yes—
581C2×D4C23×D4712yes—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—24no—
586C22×C4—82no—
587C22×C4—471no—
588C22×C4—472no—
589C22×C4—474no—
590C22×C4—474no—
591C22×C4—472no—
592C22×C4—471no—
593C22×C4—471no—
594C22×C4—944no—
595C22×C4—944no—
596C22×C4—944no—
597C22×C4—941no—
598C22×C4—941no—
599C22×C4—941no—
600C22×C4—944no—
601C22×C4—3762no—
602C22×C4—3762no—
603C22×C4—3762no—
604C22×C4—3762no—
605C22×C4D4×D4711yescharacteristic
606C22×C4D4×D4711yescharacteristic
607C22×C4C23×D4711yescharacteristic
608M16—948no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—472no—
612C2×C8—472no—
613C2×C8—948no—
614C2×C8—942no—
615C2×C8—942no—
616C2×C8C23×D4712yes—
617C2×C8C23×D4712yes—
618C4⋊C4—24no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—474no—
623C4⋊C4—474no—
624C4⋊C4—472no—
625C4⋊C4—472no—
626C4⋊C4—472no—
627C4⋊C4—944no—
628C4⋊C4—944no—
629C4⋊C4—944no—
630C4⋊C4—944no—
631C4⋊C4—944no—
632C4⋊C4—944no—
633C4⋊C4—941no—
634C4⋊C4—941no—
635C4⋊C4—941no—
636C4⋊C4C23×D4712yes—
637C4⋊C4C23×D4712yes—
638C4⋊C4C23×D4712yes—
639C22⋊C4—24no—
640C22⋊C4—474no—
641C22⋊C4—474no—
642C22⋊C4—944no—
643C22⋊C4—944no—
644C22⋊C4—944no—
645C22⋊C4—944no—
646C22⋊C4—944no—
647C42—472no—
648C42—472no—
649C42—944no—
650C42—944no—
651C42D4×D4712yes—
652C42C23×D4712yes—
653C23—24no—
654C23—22no—
655C23—42no—
656C23—42no—
657C23—474no—
658C23—472no—
659C23—9416no—
660C23—942no—
661C23—942no—
662C23—944no—
663C23—942no—
664C23—37616no—
665C23—3764no—
666C23—3764no—
667C23—1882no—
668C23—1882no—
669C23C2×D4×D4711yescharacteristic
670Q8—84no—
671Q8—3764no—
672D4—24no—
673D4—22no—
674D4—474no—
675D4—9416no—
676D4—944no—
677D4—942no—
678D4C2×Q8×D4714yes—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—84no—
688C2×C4—474no—
689C2×C4—472no—
690C2×C4—478no—
691C2×C4—474no—
692C2×C4—474no—
693C2×C4—472no—
694C2×C4—472no—
695C2×C4—942no—
696C2×C4—942no—
697C2×C4—942no—
698C2×C4—942no—
699C2×C4—942no—
700C2×C4—3764no—
701C2×C4—3764no—
702C2×C4—3764no—
703C2×C4—3764no—
704C2×C4—1882no—
705C2×C4—1882no—
706C2×C4—1882no—
707C2×C4C2×D4×D4712yes—
708C2×C4C2×D4×D4712yes—
709C2×C4C2×D4×D4711yescharacteristic
710C2×C4C2×Q8×D4712yes—
711C2×C4#41×D4712yes—
712C2×C4C24×D4711yescharacteristic
713C8—22no—
714C8—22no—
715C8—942no—
716C8—942no—
717C22—24no—
718C22—48no—
719C22—42no—
720C22—42no—
721C22—474no—
722C22—948no—
723C22—942no—
724C22—942no—
725C22—944no—
726C22—37616no—
727C22—1888no—
728C22—1882no—
729C22—1882no—
730C22C22⋊Q8×D4712yes—
731C22#1568992712yes—
732C22#1568992912yes—
733C22C22×D4×D4711yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—474no—
740C4—942no—
741C4—942no—
742C4—1882no—
743C4—1882no—
744C4—1882no—
745C4C22⋊Q8×D4712yes—
746C4C22×Q8×D4711yescharacteristic
747C4C2×#41×D4711yescharacteristic
748C2—44no—
749C2—944no—
750C2—1884no—
751C2#2025321414yesdirect product factor
752C2C2×C22⋊Q8×D4711yescharacteristic
753C2C2×#1568992711yescharacteristic
754C2C2×#1568992911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#476C2
socleC23×C47C22×D4
prime radicalC22×D4×D47C22
hypercenterC2×#476D47
hypocenterC47C2×#3081
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#15689750C2semidirect
3. #20253214C2direct (N × H)
4. C2×#15689425C2semidirect
5. C2×#15689424C2semidirect
6. C2×#15689423C2semidirect
7. C2×#15689422C2semidirect
8. C2×#15689412C2semidirect
9. C2×#15689401C2semidirect
10. C2×#15689400C2semidirect
11. C2×#15689162C2semidirect
12. C2×#15689158C2semidirect
13. C2×#15689148C2semidirect
16. C2×C47×#476C2semidirect
21. #15689750C22semidirect
22. C2×#13094023C22semidirect
24. C2×#13094016C22semidirect
25. C2×#13094015C22semidirect
42. #15689425C22semidirect
43. #15689424C22semidirect
44. #15689423C22semidirect
45. #15689422C22semidirect
46. #15689412C22semidirect
47. #15689401C22semidirect
48. #15689400C22semidirect
49. #15689162C22semidirect
50. #15689158C22semidirect
51. C2×#13093958C22semidirect
52. C2×#13093957C22semidirect
53. C2×#13093957C22semidirect
54. C2×#13093957C22semidirect
55. C2×#13093956C22semidirect
56. C2×#13093955C22semidirect
57. #15689148C22semidirect
58. C2×C4⋊(C47⋊C8)C22semidirect
59. C2×Dic47⋊C8C22semidirect
60. C2×Dic47⋊C8C22semidirect
69. C2×C4⋊Q8×C47C22semidirect
71. C47×#476C22semidirect
72. C2×#106×C47C22semidirect
73. C2×#106×C47C22semidirect
74. C2×C4⋊C8×C47C22semidirect
83. C2×D4×D47Q8semidirect
97. #13094023C23semidirect
100. #13094016C23semidirect
102. #13094015C23semidirect
145. #13093958C23semidirect
146. #13093957C23semidirect
147. #13093957C23semidirect
148. #13093957C23semidirect
149. #13093956C23semidirect
150. #13093955C23semidirect
151. C4⋊(C47⋊C8)C23semidirect
152. Dic47⋊C8C23semidirect
153. Dic47⋊C8C23semidirect
166. C4⋊Q8×C47C23semidirect
175. #106×C47C23semidirect
176. #106×C47C23semidirect
177. C4⋊C8×C47C23semidirect
213. D4×D47C2×Q8semidirect
379. C2×#476D47semidirect
388. C2×C47#3081semidirect
401. C2×C4⋊Q8C2×D47semidirect
426. #476C2×D47semidirect
437. C2×#106C2×D47semidirect
438. C2×#106C2×D47semidirect
443. C2×C4⋊C8C2×D47semidirect
454. C47C2×#3081semidirect
483. C4⋊Q8C22×D47semidirect
544. #106C22×D47semidirect
545. #106C22×D47semidirect
549. C4⋊C8C22×D47semidirect
751. C2#20253214direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897502
C2×#156895952
#202532142
C2×#156894252
C2×#156894242
C2×#156894232
C2×#156894222
C2×#156894122
C2×#156894012
C2×#156894002
C2×#156891622
C2×#156891582
C2×#156891482
C2×#156891262
C2×#102×D472
C2×C47×#4762
C2×#308147