Finite Group Databasebeta

← C22⋊C4×#10625350 #26375480

Subgroups — C22⋊C4×#10625350 #26375480

Order 12032.

5646 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#10625350C211yesmaximal, characteristic
2C2×C4×#10625350C212yesmaximal, complemented
3#20246228C212yesmaximal, complemented
4C22⋊C4×Dic94C212yesmaximal, complemented
5#20246219C212yesmaximal, complemented
6#20246215C214yesmaximal, complemented
7C22⋊C4×D188C212yesmaximal, complemented
8C22⋊C4×C22⋊D47C214yesmaximal, complemented
9#20245878C212yesmaximal, complemented
10#20245874C214yesmaximal, complemented
11#20245771C211yesmaximal, characteristic, complemented
12#20245769C212yesmaximal, complemented
13C4×C22⋊C4×D47C212yesmaximal, complemented
14C2×C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
15C22×#10625350—216no—
16C22×#10625350C4116yescomplemented
17C22×#10625350C2212yes—
18C22×#10625350C2211yescharacteristic
19C22×#10625350C2212yes—
20C22×#10625350C2211yescharacteristic
21C22×#10625350C2211yescharacteristic
22C22×#10625350C2211yescharacteristic
23C23×Dic94C2211yescharacteristic
24C23×D188C2211yescharacteristic
25C23×C22⋊D47C2212yes—
26C23×C4×D47C2212yes—
27C4×#10625350—216no—
28C2×C4×Dic94C2214yescomplemented
29C2×C4×D188C2214yescomplemented
30C2×C4×C22⋊D47C2218yescomplemented
31C2×#13093983C2212yescomplemented
32C2×#13093981C2214yescomplemented
33C2×C22⋊C4×D47C2214yes—
34C2×C42×D47C2214yescomplemented
35#15689029C2214yescomplemented
36#15689027C2218yescomplemented
37#15689025C2214yescomplemented
38#15689023C2218yescomplemented
39#15689002C2218yescomplemented
40#15689001C2218yescomplemented
41#15688999C2218yescomplemented
42#15688986C2212yescomplemented
43#15688985C2214yescomplemented
44#15688983C2212yes—
45#15688983C2212yescomplemented
46#15688982C2214yescomplemented
47#15688981C2214yes—
48#15688979C2212yes—
49#15688978C2214yes—
50C22⋊C4×Dic47C2214yes—
51C4×(C2×D47)⋊C4C2214yescomplemented
52C4×(C2×D47)⋊C4C2214yescomplemented
53C4×C22⋊Dic47C2212yes—
54C4×C22⋊Dic47C2212yescomplemented
55#15688970C2214yescomplemented
56#95×D47C2214yescomplemented
57C24×C4×C47C2211yescharacteristic
58C22×C22⋊C4×C47C2212yes—
59C22×C42×C47C2212yescomplemented
60C4×C22⋊C4×C47C2211yescharacteristic
61C4×C22⋊C4×C47C2212yes—
62C4×C22⋊C4×C47C2211yescharacteristic
63C4×C22⋊C4×C47C2212yescomplemented
64C4×C22⋊C4×C47C2212yescomplemented
65C2×#95×C47C2212yescomplemented
66C24×D47C2312yes—
67C2×#10625350—28no—
68C2×#10625350—216no—
69C2×#10625350—2128no—
70C2×#10625350—28no—
71C2×#10625350—216no—
72C2×#10625350—28no—
73C2×#10625350C2×C418yes—
74C2×#10625350C2×C418yescomplemented
75C2×#10625350C2×C4116yescomplemented
76C2×#10625350C2×C418yescomplemented
77C2×#10625350C2×C4116yescomplemented
78C2×#10625350C2×C418yescomplemented
79C2×#10625350D4116yes—
80C22×Dic94—28no—
81C22×Dic94C2×C418yescomplemented
82C22×Dic94C2312yes—
83C22×Dic94C2311yescharacteristic
84C22×Dic94C2311yescharacteristic
85C22×D188—28no—
86C22×D188C2×C418yescomplemented
87C22×D188C2312yes—
88C22×D188C2311yescharacteristic
89C22×D188C2311yescharacteristic
90C22×C22⋊D47—216no—
91C22×C22⋊D47C2×C4116yescomplemented
92C22×C22⋊D47C2312yes—
93C22×C22⋊D47C2312yes—
94C22×C22⋊D47C2312yes—
95C22×C22⋊D47C2312yes—
96C23×Dic47C2312yes—
97C22×C4×D47—216no—
98C22×C4×D47C2×C4116yescomplemented
99C22×C4×D47C2318yes—
100C22×C4×D47C2312yes—
101C22×C4×D47C2312yes—
102C22×C4×D47C2312yes—
103C22×C4×D47C2312yes—
104C4×Dic94—216no—
105C4×D188—216no—
106C4×C22⋊D47—232no—
107#13093983—28no—
108#13093981—216no—
109C2×C4⋊Dic47C2314yes—
110C2×Dic47⋊C4C2318yes—
111C2×C22⋊Dic47C2314yes—
112C2×C22⋊Dic47C2314yes—
113C2×C22⋊Dic47C2314yes—
114C2×(C2×D47)⋊C4C2318yes—
115C2×(C2×D47)⋊C4C2318yes—
116C2×(C2×D47)⋊C4C2318yes—
117C22⋊C4×D47—216no—
118C2×C4×Dic47C2318yes—
119C2×C4×Dic47C2314yes—
120C42×D47—216no—
121C47⋊#95C2314yes—
122C47⋊#95C2318yes—
123C47⋊#95C2314yes—
124C47⋊#95C2318yes—
125C25×C47C2311yescharacteristic
126C23×C4×C47—28no—
127C23×C4×C47C2×C418yescomplemented
128C23×C4×C47C2314yes—
129C23×C4×C47C2311yescharacteristic
130C23×C4×C47C2311yescharacteristic
131C23×C4×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C2×C22⋊C4×C47—28no—
136C2×C22⋊C4×C47C2312yes—
137C2×C22⋊C4×C47C2314yes—
138C2×C22⋊C4×C47C2312yes—
139C2×C42×C47—28no—
140C2×C42×C47C2312yes—
141C2×C42×C47C2312yes—
142C2×C42×C47C2314yes—
143#95×C47C2312yes—
144#95×C47C2312yes—
145#95×C47C2314yes—
146C24×C47—24no—
147C24×C47—24no—
148C24×C47—42no—
149C24×C47C22×C414yes—
150C24×C47C2411yescharacteristic
151C24×C47C2411yescharacteristic
152C24×C47C2411yescharacteristic
153C23×D47—28no—
154C23×D47—28no—
155C23×D47—44no—
156C23×D47C22×C418yes—
157C23×D47C2412yes—
158C23×D47C2412yes—
159C22×C4×C47—24no—
160C22×C4×C47—232no—
161C22×C4×C47—24no—
162C22×C4×C47—24no—
163C22×C4×C47—24no—
164C22×C4×C47—24no—
165C22×C4×C47—28no—
166C22×C4×C47—28no—
167C22×C4×C47—44no—
168C22×C4×C47C22×C414yes—
169C22×C4×C47C22×C414yes—
170C22×C4×C47C22×C414yes—
171C22×C4×C47C22×C414yes—
172C22×C4×C47C22×C414yes—
173C22×C4×C47C22×C414yes—
174C22×C4×C47C2×D418yes—
175C22×C4×C47C2414yes—
176C22×C4×C47C2411yescharacteristic
177C22×C4×C47C2411yescharacteristic
178C22×C4×C47C2414yes—
179C22×C4×C47C2411yescharacteristic
180C22×C4×C47C2411yescharacteristic
181C2×C22⋊D47—28no—
182C2×C22⋊D47—28no—
183C2×C22⋊D47—264no—
184C2×C22⋊D47—28no—
185C2×C22⋊D47C22×C418yes—
186C2×C22⋊D47C22×C418yes—
187C2×C22⋊D47C22×C418yes—
188C2×C22⋊D47C22×C418yes—
189C2×C22⋊D47C2×D4116yes—
190C22×Dic47—28no—
191C22×Dic47C22×C418yes—
192C22×Dic47C2418yes—
193C22×Dic47C2412yes—
194C22×Dic47C2412yes—
195#10625350—232no—
196#10625350—264no—
197#10625350—232no—
198#10625350—264no—
199#10625350—232no—
200#10625350C22⋊C4164yesdirect product factor
201C2×D188—28no—
202C2×D188—24no—
203C2×D188—232no—
204C2×D188C22×C418yes—
205C2×D188C22×C414yes—
206C2×D188C22×C414yes—
207C2×D188C2×D418yes—
208C2×C4×D47—28no—
209C2×C4×D47—28no—
210C2×C4×D47—28no—
211C2×C4×D47—264no—
212C2×C4×D47—216no—
213C2×C4×D47—216no—
214C2×C4×D47—48no—
215C2×C4×D47C22×C418yes—
216C2×C4×D47C22×C418yes—
217C2×C4×D47C22×C418yes—
218C2×C4×D47C22×C418yes—
219C2×C4×D47C2×D4116yes—
220C2×Dic94—24no—
221C2×Dic94—28no—
222C2×Dic94—232no—
223C2×Dic94C22×C414yes—
224C2×Dic94C22×C418yes—
225C2×Dic94C22×C414yes—
226C2×Dic94C2×D418yes—
227C22⋊C4×C47—24no—
228C22⋊C4×C47—28no—
229C22⋊C4×C47#4118yescomplemented
230C42×C47—24no—
231C42×C47—24no—
232C42×C47—28no—
233C22⋊Dic47—28no—
234C22⋊Dic47—28no—
235C22⋊Dic47—44no—
236(C2×D47)⋊C4—216no—
237(C2×D47)⋊C4—216no—
238(C2×D47)⋊C4—48no—
239C4⋊Dic47—28no—
240Dic47⋊C4—216no—
241C4×Dic47—28no—
242C4×Dic47—216no—
243C23×C47—22no—
244C23×C47—22no—
245C23×C47—22no—
246C23×C47—22no—
247C23×C47—28no—
248C23×C47—28no—
249C23×C47—22no—
250C23×C47—22no—
251C23×C47—22no—
252C23×C47—44no—
253C23×C47—416no—
254C23×C47C23×C412yes—
255C23×C47C23×C412yes—
256C23×C47C23×C412yes—
257C23×C47C22×D414yes—
258C23×C47C2×#4114yes—
259C23×C47C2511yescharacteristic
260C22×D47—24no—
261C22×D47—24no—
262C22×D47—216no—
263C22×D47—24no—
264C22×D47—24no—
265C22×D47—24no—
266C22×D47—216no—
267C22×D47—48no—
268C22×D47—432no—
269C22×D47C23×C414yes—
270C22×D47C23×C414yes—
271C22×D47C22×D418yes—
272C2×C4×C47—28no—
273C2×C4×C47—24no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—24no—
277C2×C4×C47—28no—
278C2×C4×C47—28no—
279C2×C4×C47—28no—
280C2×C4×C47—28no—
281C2×C4×C47—24no—
282C2×C4×C47—24no—
283C2×C4×C47—24no—
284C2×C4×C47—416no—
285C2×C4×C47C2×C22⋊C4116yescomplemented
286C2×C4×C47C23×C412yes—
287C2×C4×C47C23×C412yes—
288C2×C4×C47C23×C412yes—
289C2×C4×C47C23×C412yes—
290C2×C4×C47C22×D414yes—
291C2×C4×C47C22×D414yes—
292C2×C4×C47C2×#4118yescomplemented
293C22⋊D47—216no—
294C22⋊D47—216no—
295C22⋊D47—216no—
296C22⋊D47C2×C22⋊C4132yescomplemented
297C2×Dic47—24no—
298C2×Dic47—216no—
299C2×Dic47—28no—
300C2×Dic47—28no—
301C2×Dic47—28no—
302C2×Dic47C23×C414yes—
303C2×Dic47C23×C414yes—
304C2×Dic47C22×D418yes—
305D188—216no—
306D188—28no—
307D188C2×C22⋊C4116yescomplemented
308C4×D47—216no—
309C4×D47—216no—
310C4×D47—216no—
311C4×D47—432no—
312C4×D47C2×C22⋊C4132yescomplemented
313Dic94—28no—
314Dic94—216no—
315Dic94C2×C22⋊C4116yescomplemented
316C22⋊C4×#41—471nomaximal, Sylow
317C22×C47—22no—
318C22×C47—22no—
319C22×C47—22no—
320C22×C47—22no—
321C22×C47—28no—
322C22×C47—28no—
323C22×C47—22no—
324C22×C47—22no—
325C22×C47—22no—
326C22×C47—416no—
327C22×C47—44no—
328C22×C47C22×C22⋊C414yes—
329C22×C47C4×#4114yescomplemented
330C22×C47C24×C411yescharacteristic
331C22×C47C23×D412yes—
332C22×C47C22×#4112yes—
333C22×C47#58512yes—
334C2×D47—24no—
335C2×D47—24no—
336C2×D47—216no—
337C2×D47—24no—
338C2×D47—24no—
339C2×D47—24no—
340C2×D47—432no—
341C2×D47—48no—
342C2×D47C22×C22⋊C418yes—
343C4×C47—22no—
344C4×C47—22no—
345C4×C47—28no—
346C4×C47—44no—
347C4×C47C22×C22⋊C414yes—
348C4×C47C22×C22⋊C414yes—
349Dic47—24no—
350Dic47—48no—
351Dic47C22×C22⋊C418yes—
352C23×#41—471no—
353C2×C4×#41—472no—
354#2341—472no—
355Q8×C22⋊C4—472no—
356#2339—472no—
357#2339—474no—
358D4×C22⋊C4—472no—
359D4×C22⋊C4—474no—
360#2297—472no—
361#2297—474no—
362#2280—472no—
363#2280—471no—
364C2×C4×C22⋊C4—472no—
365C2×C4×C22⋊C4D4711yescharacteristic, complemented
366C2×C47—24no—
367C2×C47—24no—
368C2×C47—42no—
369C2×C47C23×C22⋊C411yescharacteristic
370C2×C47C2×C4×#4111yescharacteristic
371C2×C47#342811yescharacteristic
372C2×C47D4×#4114yes—
373D47—28no—
374D47—44no—
375C22×#41—4716no—
376C22×#41—471no—
377C22×#41—471no—
378C22×#41—472no—
379C22×#41—471no—
380C22×#41—472no—
381C22×#41—471no—
382C22×#41—9416no—
383C23×Q8—471no—
384C23×D4—472no—
385C23×D4—471no—
386C24×C4—472no—
387C24×C4C2×D4711yescharacteristic
388C4×#41—9416no—
389C2×C4×Q8—474no—
390C2×C4×D4—478no—
391C2×C4×D4—474no—
392C2×#117—472no—
393C2×#117—474no—
394C22×C22⋊C4—474no—
395C22×C22⋊C4C2×D4712yes—
396C22×C42—474no—
397C22×C42C2×D4712yescomplemented
398#391—474no—
399#391—478no—
400#390—478no—
401#390—474no—
402#386—478no—
403#386—478no—
404#386—478no—
405#381—472no—
406#381—474no—
407#380—472no—
408#380—472no—
409#380—474no—
410#380—474no—
411#379—472no—
412#379—474no—
413C4×C22⋊C4—472no—
414C4×C22⋊C4—472no—
415C4×C22⋊C4—474no—
416C4×C22⋊C4—474no—
417C4×C22⋊C4—474no—
418C4×C22⋊C4—474no—
419C4×C22⋊C4C2×D4712yes—
420C4×C22⋊C4C2×D4711yescharacteristic
421C4×C22⋊C4C2×D4711yescharacteristic
422C4×C22⋊C4C2×D4712yescomplemented
423C4×C22⋊C4C2×D4712yescomplemented
424C2×#95—474no—
425C2×#95C2×D4712yescomplemented
426C47C22⋊C4×#4111yescharacteristic, complemented, Sylow
427C25—472no—
428C25C22×D4711yescharacteristic
429C2×#41—478no—
430C2×#41—4716no—
431C2×#41—4716no—
432C2×#41—478no—
433C2×#41—478no—
434C2×#41—478no—
435C2×#41—4716no—
436C2×#41—9416no—
437C2×#41—9416no—
438C2×#41—948no—
439C2×#41—948no—
440C2×#41—94128no—
441C2×#41—948no—
442C22×Q8—478no—
443C22×Q8—471no—
444C22×Q8—472no—
445C22×Q8—471no—
446C22×Q8—948no—
447C22×D4—472no—
448C22×D4—4716no—
449C22×D4—472no—
450C22×D4—472no—
451C22×D4—472no—
452C22×D4—478no—
453C22×D4—471no—
454C22×D4—472no—
455C22×D4—471no—
456C22×D4—948no—
457C22×D4—9416no—
458C23×C4—28no—
459C23×C4—472no—
460C23×C4—472no—
461C23×C4—4716no—
462C23×C4—472no—
463C23×C4—472no—
464C23×C4—472no—
465C23×C4—478no—
466C23×C4—9416no—
467C23×C4C4×D4718yescomplemented
468C23×C4C22×D4714yes—
469C23×C4C22×D4711yescharacteristic
470C23×C4C22×D4711yescharacteristic
471C23×C4C22×D4711yescharacteristic
472C23×C4C22×D4711yescharacteristic
473C23×C4C22×D4711yescharacteristic
474C23×C4C22×D4711yescharacteristic
475C4×Q8—9416no—
476C4×D4—9416no—
477C4×D4—9432no—
478#117—9416no—
479#117—948no—
480C2×C4⋊C4—478no—
481C2×C4⋊C4—474no—
482C2×C22⋊C4—28no—
483C2×C22⋊C4—474no—
484C2×C22⋊C4—474no—
485C2×C22⋊C4—478no—
486C2×C22⋊C4—478no—
487C2×C22⋊C4—474no—
488C2×C22⋊C4—478no—
489C2×C22⋊C4—9416no—
490C2×C22⋊C4C22×D4712yes—
491C2×C22⋊C4C22×D4714yes—
492C2×C22⋊C4C22×D4712yes—
493C2×C42—28no—
494C2×C42—478no—
495C2×C42—474no—
496C2×C42—9416no—
497C2×C42C22×D4714yes—
498C2×C42C22×D4712yes—
499C2×C42C22×D4712yes—
500#95—474no—
501#95—478no—
502#95—478no—
503#95—474no—
504#95C22×D4712yes—
505#95C22×D4712yes—
506#95C22×D4714yes—
507C24—24no—
508C24—24no—
509C24—42no—
510C24—472no—
511C24—472no—
512C24—478no—
513C24—948no—
514C24—948no—
515C24—1884no—
516C24C2×C4×D4714yes—
517C24C23×D4711yescharacteristic
518C24C23×D4711yescharacteristic
519C24C23×D4711yescharacteristic
520#41—4764no—
521#41—9464no—
522#41—9464no—
523#41—9432no—
524#41—9432no—
525#41—9432no—
526C2×Q8—474no—
527C2×Q8—478no—
528C2×Q8—474no—
529C2×Q8—478no—
530C2×Q8—948no—
531C2×Q8—9432no—
532C2×Q8—944no—
533C2×D4—478no—
534C2×D4—4716no—
535C2×D4—478no—
536C2×D4—478no—
537C2×D4—478no—
538C2×D4—474no—
539C2×D4—478no—
540C2×D4—474no—
541C2×D4—478no—
542C2×D4—9432no—
543C2×D4—948no—
544C2×D4—948no—
545C2×D4—9464no—
546C2×D4—948no—
547C2×D4—948no—
548C2×D4—944no—
549C22×C4—24no—
550C22×C4—232no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—44no—
558C22×C4—472no—
559C22×C4—478no—
560C22×C4—4716no—
561C22×C4—478no—
562C22×C4—472no—
563C22×C4—478no—
564C22×C4—478no—
565C22×C4—478no—
566C22×C4—478no—
567C22×C4—948no—
568C22×C4—9464no—
569C22×C4—948no—
570C22×C4—9416no—
571C22×C4—948no—
572C22×C4—948no—
573C22×C4—9416no—
574C22×C4—1888no—
575C22×C4C2×C4×D4714yes—
576C22×C4C2×C4×D4714yes—
577C22×C4C2×C4×D4714yes—
578C22×C4C2×C4×D4714yes—
579C22×C4C2×C4×D4714yes—
580C22×C4C2×C4×D4714yes—
581C22×C4D4×D4718yes—
582C22×C4C23×D4714yes—
583C22×C4C23×D4711yescharacteristic
584C22×C4C23×D4711yescharacteristic
585C22×C4C23×D4714yes—
586C22×C4C23×D4711yescharacteristic
587C22×C4C23×D4711yescharacteristic
588C4⋊C4—9416no—
589C4⋊C4—948no—
590C22⋊C4—24no—
591C22⋊C4—28no—
592C22⋊C4—9416no—
593C22⋊C4—948no—
594C22⋊C4—948no—
595C22⋊C4—9416no—
596C22⋊C4—1888no—
597C22⋊C4—1884no—
598C22⋊C4#1062535018yesdirect product factor
599C42—24no—
600C42—24no—
601C42—28no—
602C42—9416no—
603C42—948no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—28no—
609C23—28no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—44no—
614C23—416no—
615C23—474no—
616C23—478no—
617C23—474no—
618C23—9416no—
619C23—944no—
620C23—944no—
621C23—9416no—
622C23—944no—
623C23—944no—
624C23—944no—
625C23—1888no—
626C23—18832no—
627C23C22×C4×D4712yes—
628C23C22×C4×D4712yes—
629C23C22×C4×D4712yes—
630C23C2×D4×D4714yes—
631C23C2×#1062535014yes—
632C23C24×D4711yescharacteristic
633Q8—4716no—
634Q8—9416no—
635Q8—948no—
636D4—4732no—
637D4—4716no—
638D4—9416no—
639D4—9416no—
640D4—9416no—
641D4—9416no—
642D4—948no—
643C2×C4—28no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—28no—
649C2×C4—28no—
650C2×C4—28no—
651C2×C4—28no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—416no—
656C2×C4—474no—
657C2×C4—478no—
658C2×C4—4732no—
659C2×C4—474no—
660C2×C4—9416no—
661C2×C4—9416no—
662C2×C4—9416no—
663C2×C4—944no—
664C2×C4—9416no—
665C2×C4—948no—
666C2×C4—948no—
667C2×C4—948no—
668C2×C4—18832no—
669C2×C4C22⋊C4×D47116yescomplemented
670C2×C4C22×C4×D4712yes—
671C2×C4C22×C4×D4712yes—
672C2×C4C22×C4×D4712yes—
673C2×C4C22×C4×D4712yes—
674C2×C4C2×D4×D4714yes—
675C2×C4C2×D4×D4714yes—
676C2×C4C2×#1062535018yescomplemented
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—28no—
682C22—28no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—416no—
687C22—44no—
688C22—478no—
689C22—944no—
690C22—944no—
691C22—9416no—
692C22—944no—
693C22—944no—
694C22—944no—
695C22—18832no—
696C22—1888no—
697C22C2×C22⋊C4×D4714yes—
698C22C4×#1062535014yescomplemented
699C22C23×C4×D4711yescharacteristic
700C22C22×D4×D4712yes—
701C22C22×#1062535012yes—
702C22#1568995912yes—
703C4—22no—
704C4—22no—
705C4—28no—
706C4—44no—
707C4—478no—
708C4—944no—
709C4—1888no—
710C4C2×C22⋊C4×D4714yes—
711C4C2×C22⋊C4×D4714yes—
712C2—24no—
713C2—24no—
714C2—42no—
715C2—948no—
716C2—1884no—
717C2C22×C22⋊C4×D4711yescharacteristic
718C2C2×C4×#1062535011yescharacteristic
719C2#2025658911yescharacteristic
720C2D4×#1062535014yes—
subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C4×C22⋊C4×C47C2
socle, cosocleC23×C47C25
prime radicalC23×#10625350C2
hypercenterC2×C4×C22⋊C4D47
hypocenterC47C22⋊C4×#41
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10625350C2semidirect
3. #20246228C2semidirect
4. C22⋊C4×Dic94C2semidirect
5. #20246219C2semidirect
6. #20246215C2semidirect
7. C22⋊C4×D188C2semidirect
8. C22⋊C4×C22⋊D47C2semidirect
9. #20245878C2semidirect
10. #20245874C2semidirect
11. #20245771C2semidirect
12. #20245769C2semidirect
13. C4×C22⋊C4×D47C2semidirect
14. C2×C4×C22⋊C4×C47C2semidirect
16. C22×#10625350C4semidirect
28. C2×C4×Dic94C22semidirect
29. C2×C4×D188C22semidirect
30. C2×C4×C22⋊D47C22semidirect
31. C2×#13093983C22semidirect
32. C2×#13093981C22semidirect
34. C2×C42×D47C22semidirect
35. #15689029C22semidirect
36. #15689027C22semidirect
37. #15689025C22semidirect
38. #15689023C22semidirect
39. #15689002C22semidirect
40. #15689001C22semidirect
41. #15688999C22semidirect
42. #15688986C22semidirect
43. #15688985C22semidirect
45. #15688983C22semidirect
46. #15688982C22semidirect
51. C4×(C2×D47)⋊C4C22semidirect
52. C4×(C2×D47)⋊C4C22semidirect
54. C4×C22⋊Dic47C22semidirect
55. #15688970C22semidirect
56. #95×D47C22semidirect
59. C22×C42×C47C22semidirect
63. C4×C22⋊C4×C47C22semidirect
64. C4×C22⋊C4×C47C22semidirect
65. C2×#95×C47C22semidirect
74. C2×#10625350C2×C4semidirect
75. C2×#10625350C2×C4semidirect
76. C2×#10625350C2×C4semidirect
77. C2×#10625350C2×C4semidirect
78. C2×#10625350C2×C4semidirect
81. C22×Dic94C2×C4semidirect
86. C22×D188C2×C4semidirect
91. C22×C22⋊D47C2×C4semidirect
98. C22×C4×D47C2×C4semidirect
127. C23×C4×C47C2×C4semidirect
200. #10625350C22⋊C4direct (N × H)
229. C22⋊C4×C47#41semidirect
285. C2×C4×C47C2×C22⋊C4semidirect
292. C2×C4×C47C2×#41semidirect
296. C22⋊D47C2×C22⋊C4semidirect
307. D188C2×C22⋊C4semidirect
312. C4×D47C2×C22⋊C4semidirect
315. Dic94C2×C22⋊C4semidirect
329. C22×C47C4×#41semidirect
365. C2×C4×C22⋊C4D47semidirect
397. C22×C42C2×D47semidirect
422. C4×C22⋊C4C2×D47semidirect
423. C4×C22⋊C4C2×D47semidirect
425. C2×#95C2×D47semidirect
426. C47C22⋊C4×#41semidirect
467. C23×C4C4×D47semidirect
598. C22⋊C4#10625350direct (N × H)
669. C2×C4C22⋊C4×D47semidirect
676. C2×C4C2×#10625350semidirect
698. C22C4×#10625350semidirect

Maximal subgroups

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

subgroupindex
C23×#106253502
C2×C4×#106253502
#202462282
C22⋊C4×Dic942
#202462192
#202462152
C22⋊C4×D1882
C22⋊C4×C22⋊D472
#202458782
#202458742
#202457712
#202457692
C4×C22⋊C4×D472
C2×C4×C22⋊C4×C472
C22⋊C4×#4147