Finite Group Databasebeta

← C47×#17604 #26057302

Subgroups — C47×#17604 #26057302

Order 12032.

1004 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3494C211yesmaximal, characteristic
2C47×#2924C211yesmaximal, characteristic, complemented
3C47×#2343C211yesmaximal, characteristic, complemented
4C47×#1521C211yesmaximal, characteristic, complemented
5C47×#1517C211yesmaximal, characteristic, complemented
6C47×#1516C211yesmaximal, characteristic, complemented
7C47×#1514C211yesmaximal, characteristic, complemented
8C47×#1512C211yesmaximal, characteristic, complemented
9C47×#1510C211yesmaximal, characteristic, complemented
10C47×#1509C211yesmaximal, characteristic, complemented
11C47×#1505C211yesmaximal, characteristic, complemented
12C47×#1504C211yesmaximal, characteristic, complemented
13C47×#1502C211yesmaximal, characteristic, complemented
14C47×#1500C211yesmaximal, characteristic, complemented
15C2×C47×#327C211yesmaximal, characteristic, complemented
16C47×#555—21no—
17C47×#553—21no—
18C47×#553—21no—
19C47×#551—21no—
20C47×#551—21no—
21C47×#547—21no—
22C47×#546—21no—
23C47×#546—21no—
24C47×#544C411yescharacteristic, complemented
25C47×#542C411yescharacteristic, complemented
26C47×#542C411yescharacteristic, complemented
27C47×#540C411yescharacteristic, complemented
28C47×#540C411yescharacteristic, complemented
29C47×#535C411yescharacteristic, complemented
30C47×#532C2211yescharacteristic
31C47×#532C2211yescharacteristic
32C47×#529C2211yescharacteristic
33C47×#529C2211yescharacteristic
34C47×#525C2211yescharacteristic
35C2×#121×C47C2211yescharacteristic
36C47×#520C411yescharacteristic, complemented
37C47×#518C411yescharacteristic, complemented
38C2×#117×C47C2211yescharacteristic
39C47×#433—21no—
40C47×#433—21no—
41C47×#432C2211yescharacteristic, complemented
42C47×#432C2211yescharacteristic, complemented
43C47×#431C2211yescharacteristic, complemented
44C47×#431C2211yescharacteristic, complemented
45C47×#424—21no—
46C47×#407C2211yescharacteristic
47C2×C22⋊C8×C47C2211yescharacteristic
48C47×#405—21no—
49C47×#387—21no—
50C47×#387—21no—
51C47×#385—21no—
52C47×#383C2211yescharacteristic, complemented
53C47×#382C2211yescharacteristic, complemented
54C47×#381C2211yescharacteristic
55C4×C4⋊C4×C47C2211yescharacteristic, complemented
56C4×C22⋊C4×C47—21no—
57C47×#376C2211yescharacteristic, complemented
58C2×#95×C47C2211yescharacteristic
59C47×#328C2211yescharacteristic, complemented
60C47×#328C2211yescharacteristic, complemented
61C47×#328C2211yescharacteristic, complemented
62C47×#328C2211yescharacteristic, complemented
63C47×#327C2211yescharacteristic
64C47×#327C2211yescharacteristic
65C47×#327C2211yescharacteristic
66C47×#327C2211yescharacteristic
67C47×#327C2211yescharacteristic
68C47×#327C2211yescharacteristic
69C47×#327C2211yescharacteristic
70C47×#327C2211yescharacteristic
71C47×#327C2211yescharacteristic, complemented
72C47×#327C2211yescharacteristic, complemented
73C47×#327C2211yescharacteristic, complemented
74C47×#327C2211yescharacteristic, complemented
75C2×#41×C47—21no—
76C2×#41×C47—21no—
77C2×#41×C47C2×C411yescharacteristic
78C22×D4×C47—21no—
79C22×D4×C47C2×C411yescharacteristic
80C23×C4×C47—21no—
81C23×C4×C47C2311yescharacteristic
82C2×M16×C47—21no—
83C22×C8×C47—21no—
84C4⋊Q8×C47—21no—
85C4⋊Q8×C47C2×C411yescharacteristic, complemented
86C4⋊Q8×C47C2×C411yescharacteristic, complemented
87#127×C47C2×C411yescharacteristic, complemented
88#127×C47C2×C411yescharacteristic, complemented
89#126×C47—21no—
90#126×C47—21no—
91#126×C47—21no—
92#126×C47—21no—
93#125×C47—21no—
94#125×C47C2×C411yescharacteristic, complemented
95#125×C47C2×C411yescharacteristic, complemented
96#124×C47—21no—
97#124×C47—21no—
98#124×C47—21no—
99#124×C47—21no—
100#124×C47C2×C411yescharacteristic, complemented
101#124×C47C2×C411yescharacteristic, complemented
102#123×C47—21no—
103#123×C47—21no—
104#123×C47—21no—
105#123×C47—21no—
106#123×C47—21no—
107#123×C47—21no—
108#123×C47—21no—
109#123×C47—21no—
110#123×C47—21no—
111C22⋊Q8×C47—21no—
112C22⋊Q8×C47—21no—
113C22⋊Q8×C47—21no—
114C22⋊Q8×C47—21no—
115C22⋊Q8×C47C2×C411yescharacteristic
116C22⋊Q8×C47C2311yescharacteristic
117#121×C47—21no—
118#121×C47—21no—
119#121×C47—21no—
120#121×C47—21no—
121#121×C47—21no—
122#121×C47—21no—
123#121×C47—21no—
124#121×C47—21no—
125#121×C47—21no—
126#121×C47—21no—
127#121×C47C2×C411yescharacteristic
128#121×C47C2×C411yescharacteristic
129#121×C47C2×C411yescharacteristic
130#121×C47C2311yescharacteristic
131#121×C47C2311yescharacteristic
132#121×C47C2311yescharacteristic
133#120×C47—21no—
134#120×C47—21no—
135#120×C47—21no—
136C4×Q8×C47C2×C411yescharacteristic, complemented
137C4×Q8×C47C2×C411yescharacteristic, complemented
138C4×D4×C47—21no—
139C4×D4×C47—21no—
140C4×D4×C47—21no—
141C4×D4×C47—21no—
142C4×D4×C47—21no—
143C4×D4×C47—21no—
144C4×D4×C47—21no—
145C4×D4×C47—21no—
146C4×D4×C47—21no—
147C4×D4×C47—21no—
148C4×D4×C47C2×C411yescharacteristic, complemented
149C4×D4×C47C2×C411yescharacteristic, complemented
150C4×D4×C47C2×C411yescharacteristic, complemented
151C4×D4×C47C2×C411yescharacteristic, complemented
152C4×D4×C47C2×C411yescharacteristic, complemented
153C4×D4×C47C2×C411yescharacteristic, complemented
154#117×C47—21no—
155#117×C47—21no—
156#117×C47—21no—
157#117×C47C2×C411yescharacteristic
158#117×C47C2×C411yescharacteristic
159#117×C47C2×C411yescharacteristic
160#117×C47C2×C411yescharacteristic
161#117×C47C2×C411yescharacteristic
162#117×C47D411yescharacteristic
163#117×C47D411yescharacteristic
164#117×C47D411yescharacteristic
165#117×C47D411yescharacteristic
166C2×C4⋊C4×C47—21no—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47—21no—
169C2×C4⋊C4×C47C2×C411yescharacteristic
170C2×C4⋊C4×C47D411yescharacteristic
171C2×C4⋊C4×C47D411yescharacteristic
172C2×C22⋊C4×C47—21no—
173C2×C22⋊C4×C47—21no—
174C2×C22⋊C4×C47—21no—
175C2×C22⋊C4×C47—21no—
176C2×C22⋊C4×C47D411yescharacteristic
177C2×C22⋊C4×C47D411yescharacteristic
178C2×C42×C47—21no—
179C2×C42×C47—21no—
180C2×C42×C47C2311yescharacteristic
181C2×C42×C47C2311yescharacteristic
182C4⋊C8×C47—21no—
183C4⋊C8×C47—21no—
184C4⋊C8×C47—21no—
185C4⋊C8×C47—21no—
186C22⋊C8×C47—21no—
187C22⋊C8×C47—21no—
188C22⋊C8×C47C2311yescharacteristic
189C22⋊C8×C47C2311yescharacteristic
190C22⋊C8×C47C2311yescharacteristic
191C22⋊C8×C47C2311yescharacteristic
192#97×C47—21no—
193#97×C47—21no—
194C4×C8×C47—21no—
195C4×C8×C47—21no—
196#95×C47—21no—
197#95×C47—21no—
198#95×C47—21no—
199#95×C47—21no—
200#95×C47—21no—
201#95×C47—21no—
202#95×C47C2311yescharacteristic
203#95×C47C2311yescharacteristic
204#95×C47C2311yescharacteristic
205#95×C47C2311yescharacteristic
206C24×C47—21no—
207C24×C47C2×D411yescharacteristic
208#41×C47—42no—
209#41×C47—81no—
210#41×C47—81no—
211#41×C47—81no—
212#41×C47—81no—
213C2×Q8×C47—21no—
214C2×Q8×C47—21no—
215C2×Q8×C47C22×C411yescharacteristic
216C2×D4×C47—21no—
217C2×D4×C47—21no—
218C2×D4×C47—21no—
219C2×D4×C47—21no—
220C2×D4×C47—21no—
221C2×D4×C47—21no—
222C2×D4×C47—21no—
223C2×D4×C47—21no—
224C2×D4×C47—21no—
225C2×D4×C47—21no—
226C2×D4×C47—21no—
227C2×D4×C47—21no—
228C2×D4×C47—42no—
229C2×D4×C47—81no—
230C2×D4×C47—81no—
231C2×D4×C47C22×C411yescharacteristic
232C2×D4×C47C22×C411yescharacteristic
233C2×D4×C47C22×C411yescharacteristic
234C22×C4×C47—21no—
235C22×C4×C47—21no—
236C22×C4×C47—21no—
237C22×C4×C47—21no—
238C22×C4×C47—21no—
239C22×C4×C47—21no—
240C22×C4×C47—21no—
241C22×C4×C47—21no—
242C22×C4×C47—21no—
243C22×C4×C47—21no—
244C22×C4×C47—21no—
245C22×C4×C47—21no—
246C22×C4×C47—42no—
247C22×C4×C47—42no—
248C22×C4×C47—42no—
249C22×C4×C47—81no—
250C22×C4×C47C22×C411yescharacteristic
251C22×C4×C47C22×C411yescharacteristic
252C22×C4×C47C2×D411yescharacteristic
253C22×C4×C47C2×D411yescharacteristic
254C22×C4×C47C2×D411yescharacteristic
255C22×C4×C47C2×D411yescharacteristic
256C22×C4×C47C2×D411yescharacteristic
257C22×C4×C47C2×D411yescharacteristic
258C22×C4×C47C2×D411yescharacteristic
259C22×C4×C47C2411yescharacteristic
260M16×C47—42no—
261C2×C8×C47—21no—
262C2×C8×C47—21no—
263C2×C8×C47—21no—
264C2×C8×C47—21no—
265C2×C8×C47—42no—
266C4⋊C4×C47—21no—
267C4⋊C4×C47—21no—
268C4⋊C4×C47—21no—
269C4⋊C4×C47—21no—
270C4⋊C4×C47—21no—
271C4⋊C4×C47—21no—
272C4⋊C4×C47—21no—
273C4⋊C4×C47—21no—
274C4⋊C4×C47—21no—
275C4⋊C4×C47—21no—
276C4⋊C4×C47—21no—
277C4⋊C4×C47—42no—
278C4⋊C4×C47—81no—
279C4⋊C4×C47C22⋊C411yescharacteristic
280C4⋊C4×C47C22⋊C411yescharacteristic
281C4⋊C4×C47C22⋊C411yescharacteristic
282C4⋊C4×C47C22⋊C411yescharacteristic
283C4⋊C4×C47C22⋊C411yescharacteristic
284C4⋊C4×C47C22⋊C411yescharacteristic
285C4⋊C4×C47C22⋊C411yescharacteristic
286C4⋊C4×C47C22⋊C411yescharacteristic
287C4⋊C4×C47C22×C411yescharacteristic
288C4⋊C4×C47C22×C411yescharacteristic
289C4⋊C4×C47C22×C411yescharacteristic
290C4⋊C4×C47C22×C411yescharacteristic
291C22⋊C4×C47—21no—
292C22⋊C4×C47—21no—
293C22⋊C4×C47—21no—
294C22⋊C4×C47—21no—
295C22⋊C4×C47—21no—
296C22⋊C4×C47—21no—
297C22⋊C4×C47—21no—
298C22⋊C4×C47—21no—
299C22⋊C4×C47—21no—
300C22⋊C4×C47—21no—
301C22⋊C4×C47—21no—
302C22⋊C4×C47—21no—
303C22⋊C4×C47—21no—
304C22⋊C4×C47—21no—
305C22⋊C4×C47—21no—
306C22⋊C4×C47—21no—
307C22⋊C4×C47—21no—
308C22⋊C4×C47—21no—
309C22⋊C4×C47—21no—
310C22⋊C4×C47—42no—
311C22⋊C4×C47C22⋊C411yescharacteristic
312C22⋊C4×C47C22⋊C411yescharacteristic
313C22⋊C4×C47C22⋊C411yescharacteristic
314C22⋊C4×C47C22⋊C411yescharacteristic
315C22⋊C4×C47C22⋊C411yescharacteristic
316C22⋊C4×C47C22⋊C411yescharacteristic
317C22⋊C4×C47C22⋊C411yescharacteristic
318C22⋊C4×C47C22⋊C411yescharacteristic
319C42×C47—21no—
320C42×C47—21no—
321C42×C47—21no—
322C42×C47—42no—
323C42×C47—81no—
324C42×C47C22×C411yescharacteristic
325C42×C47C22×C411yescharacteristic
326C42×C47C22×C411yescharacteristic
327C42×C47C22×C411yescharacteristic
328C42×C47C2×D411yescharacteristic
329C42×C47C2×D411yescharacteristic
330C42×C47C2×D411yescharacteristic
331C42×C47C2×D411yescharacteristic
332C23×C47—21no—
333C23×C47—21no—
334C23×C47—22no—
335C23×C47—21no—
336C23×C47—21no—
337C23×C47—21no—
338C23×C47—41no—
339C23×C47—42no—
340C23×C47—81no—
341C23×C47—81no—
342C23×C47C2×C22⋊C411yescharacteristic
343C23×C47C2×C22⋊C411yescharacteristic
344C23×C47C22×D411yescharacteristic
345Q8×C47—41no—
346Q8×C47—81no—
347Q8×C47—81no—
348D4×C47—41no—
349D4×C47—41no—
350D4×C47—41no—
351D4×C47—42no—
352D4×C47—41no—
353D4×C47—41no—
354D4×C47—41no—
355D4×C47—41no—
356D4×C47—41no—
357D4×C47—41no—
358D4×C47—42no—
359D4×C47—81no—
360D4×C47—81no—
361D4×C47—81no—
362D4×C47—81no—
363D4×C47—81no—
364D4×C47—81no—
365D4×C47—81no—
366C2×C4×C47—21no—
367C2×C4×C47—21no—
368C2×C4×C47—21no—
369C2×C4×C47—21no—
370C2×C4×C47—22no—
371C2×C4×C47—22no—
372C2×C4×C47—22no—
373C2×C4×C47—21no—
374C2×C4×C47—21no—
375C2×C4×C47—21no—
376C2×C4×C47—21no—
377C2×C4×C47—21no—
378C2×C4×C47—41no—
379C2×C4×C47—41no—
380C2×C4×C47—41no—
381C2×C4×C47—41no—
382C2×C4×C47—41no—
383C2×C4×C47—41no—
384C2×C4×C47—42no—
385C2×C4×C47—41no—
386C2×C4×C47—41no—
387C2×C4×C47—41no—
388C2×C4×C47—41no—
389C2×C4×C47—41no—
390C2×C4×C47—41no—
391C2×C4×C47—41no—
392C2×C4×C47—41no—
393C2×C4×C47—41no—
394C2×C4×C47—41no—
395C2×C4×C47—41no—
396C2×C4×C47—81no—
397C2×C4×C47—81no—
398C2×C4×C47—81no—
399C2×C4×C47—81no—
400C2×C4×C47—81no—
401C2×C4×C47—81no—
402C2×C4×C47—81no—
403C2×C4×C47—84no—
404C2×C4×C47C2×C22⋊C411yescharacteristic
405C2×C4×C47C2×C22⋊C411yescharacteristic
406C2×C4×C47C2×C22⋊C411yescharacteristic
407C2×C4×C47C2×C22⋊C411yescharacteristic
408C2×C4×C47C2×C22⋊C411yescharacteristic
409C2×C4×C47C2×C22⋊C411yescharacteristic
410C2×C4×C47C2×C22⋊C411yescharacteristic
411C2×C4×C47C2×C22⋊C411yescharacteristic
412C2×C4×C47C2×C22⋊C411yescharacteristic
413C2×C4×C47C2×C22⋊C411yescharacteristic
414C2×C4×C47C23×C411yescharacteristic
415C2×C4×C47C22×D411yescharacteristic
416C8×C47—41no—
417C8×C47—41no—
418C8×C47—41no—
419C8×C47—41no—
420#17604C4711yesmaximal, characteristic, direct product factor, Sylow
421C22×C47—21no—
422C22×C47—21no—
423C22×C47—21no—
424C22×C47—21no—
425C22×C47—21no—
426C22×C47—21no—
427C22×C47—21no—
428C22×C47—42no—
429C22×C47—42no—
430C22×C47—41no—
431C22×C47—41no—
432C22×C47—41no—
433C22×C47—41no—
434C22×C47—41no—
435C22×C47—41no—
436C22×C47—41no—
437C22×C47—41no—
438C22×C47—41no—
439C22×C47—162no—
440C22×C47#41012yes—
441C22×C47C22×C22⋊C411yescharacteristic
442C22×C47#57611yescharacteristic
443C22×C47#57711yescharacteristic
444C4×C47—21no—
445C4×C47—21no—
446C4×C47—21no—
447C4×C47—21no—
448C4×C47—21no—
449C4×C47—21no—
450C4×C47—21no—
451C4×C47—21no—
452C4×C47—21no—
453C4×C47—21no—
454C4×C47—21no—
455C4×C47—21no—
456C4×C47—42no—
457C4×C47—41no—
458C4×C47—41no—
459C4×C47—41no—
460C4×C47—41no—
461C4×C47—41no—
462C4×C47—81no—
463C4×C47—81no—
464C4×C47—81no—
465#3494C2×C4711yescharacteristic
466#2924C2×C4711yescharacteristic, complemented
467#2343C2×C4711yescharacteristic, complemented
468#1521C2×C4711yescharacteristic, complemented
469#1517C2×C4711yescharacteristic, complemented
470#1516C2×C4711yescharacteristic, complemented
471#1514C2×C4711yescharacteristic, complemented
472#1512C2×C4711yescharacteristic, complemented
473#1510C2×C4711yescharacteristic, complemented
474#1509C2×C4711yescharacteristic, complemented
475#1505C2×C4711yescharacteristic, complemented
476#1504C2×C4711yescharacteristic, complemented
477#1502C2×C4711yescharacteristic, complemented
478#1500C2×C4711yescharacteristic, complemented
479C2×#327C2×C4711yescharacteristic, complemented
480C2×C47—21no—
481C2×C47—21no—
482C2×C47—22no—
483C2×C47—41no—
484C2×C47—81no—
485C2×C47—81no—
486C2×C47—81no—
487C2×C47C2×#41011yescharacteristic
488C2×C47#289711yescharacteristic
489C2×C47#290111yescharacteristic
490#555—21no—
491#553—21no—
492#553—21no—
493#551—21no—
494#551—21no—
495#547—21no—
496#546—21no—
497#546—21no—
498#544C4×C4711yescharacteristic, complemented
499#542C4×C4711yescharacteristic, complemented
500#542C4×C4711yescharacteristic, complemented
501#540C4×C4711yescharacteristic, complemented
502#540C4×C4711yescharacteristic, complemented
503#535C4×C4711yescharacteristic, complemented
504#532C22×C4711yescharacteristic
505#532C22×C4711yescharacteristic
506#529C22×C4711yescharacteristic
507#529C22×C4711yescharacteristic
508#525C22×C4711yescharacteristic
509C2×#121C22×C4711yescharacteristic
510#520C4×C4711yescharacteristic, complemented
511#518C4×C4711yescharacteristic, complemented
512C2×#117C22×C4711yescharacteristic
513#433—21no—
514#433—21no—
515#432C22×C4711yescharacteristic, complemented
516#432C22×C4711yescharacteristic, complemented
517#431C22×C4711yescharacteristic, complemented
518#431C22×C4711yescharacteristic, complemented
519#424—21no—
520#407C22×C4711yescharacteristic
521C2×C22⋊C8C22×C4711yescharacteristic
522#405—21no—
523#387—21no—
524#387—21no—
525#385—21no—
526#383C22×C4711yescharacteristic, complemented
527#382C22×C4711yescharacteristic, complemented
528#381C22×C4711yescharacteristic
529C4×C4⋊C4C22×C4711yescharacteristic, complemented
530C4×C22⋊C4—21no—
531#376C22×C4711yescharacteristic, complemented
532C2×#95C22×C4711yescharacteristic
533#328C22×C4711yescharacteristic, complemented
534#328C22×C4711yescharacteristic, complemented
535#328C22×C4711yescharacteristic, complemented
536#328C22×C4711yescharacteristic, complemented
537#327C22×C4711yescharacteristic
538#327C22×C4711yescharacteristic
539#327C22×C4711yescharacteristic
540#327C22×C4711yescharacteristic
541#327C22×C4711yescharacteristic
542#327C22×C4711yescharacteristic
543#327C22×C4711yescharacteristic
544#327C22×C4711yescharacteristic
545#327C22×C4711yescharacteristic, complemented
546#327C22×C4711yescharacteristic, complemented
547#327C22×C4711yescharacteristic, complemented
548#327C22×C4711yescharacteristic, complemented
549C47#1760411yescharacteristic, direct product factor, Sylow
550C2×#41—21no—
551C2×#41—21no—
552C2×#41C2×C4×C4711yescharacteristic
553C22×D4—21no—
554C22×D4C2×C4×C4711yescharacteristic
555C23×C4—21no—
556C23×C4C23×C4711yescharacteristic
557C2×M16—21no—
558C22×C8—21no—
559C4⋊Q8—21no—
560C4⋊Q8C2×C4×C4711yescharacteristic, complemented
561C4⋊Q8C2×C4×C4711yescharacteristic, complemented
562#127C2×C4×C4711yescharacteristic, complemented
563#127C2×C4×C4711yescharacteristic, complemented
564#126—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#125—21no—
569#125C2×C4×C4711yescharacteristic, complemented
570#125C2×C4×C4711yescharacteristic, complemented
571#124—21no—
572#124—21no—
573#124—21no—
574#124—21no—
575#124C2×C4×C4711yescharacteristic, complemented
576#124C2×C4×C4711yescharacteristic, complemented
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586C22⋊Q8—21no—
587C22⋊Q8—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8C2×C4×C4711yescharacteristic
591C22⋊Q8C23×C4711yescharacteristic
592#121—21no—
593#121—21no—
594#121—21no—
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121C2×C4×C4711yescharacteristic
603#121C2×C4×C4711yescharacteristic
604#121C2×C4×C4711yescharacteristic
605#121C23×C4711yescharacteristic
606#121C23×C4711yescharacteristic
607#121C23×C4711yescharacteristic
608#120—21no—
609#120—21no—
610#120—21no—
611C4×Q8C2×C4×C4711yescharacteristic, complemented
612C4×Q8C2×C4×C4711yescharacteristic, complemented
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4—21no—
619C4×D4—21no—
620C4×D4—21no—
621C4×D4—21no—
622C4×D4—21no—
623C4×D4C2×C4×C4711yescharacteristic, complemented
624C4×D4C2×C4×C4711yescharacteristic, complemented
625C4×D4C2×C4×C4711yescharacteristic, complemented
626C4×D4C2×C4×C4711yescharacteristic, complemented
627C4×D4C2×C4×C4711yescharacteristic, complemented
628C4×D4C2×C4×C4711yescharacteristic, complemented
629#117—21no—
630#117—21no—
631#117—21no—
632#117C2×C4×C4711yescharacteristic
633#117C2×C4×C4711yescharacteristic
634#117C2×C4×C4711yescharacteristic
635#117C2×C4×C4711yescharacteristic
636#117C2×C4×C4711yescharacteristic
637#117D4×C4711yescharacteristic
638#117D4×C4711yescharacteristic
639#117D4×C4711yescharacteristic
640#117D4×C4711yescharacteristic
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4C2×C4×C4711yescharacteristic
645C2×C4⋊C4D4×C4711yescharacteristic
646C2×C4⋊C4D4×C4711yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4D4×C4711yescharacteristic
652C2×C22⋊C4D4×C4711yescharacteristic
653C2×C42—21no—
654C2×C42—21no—
655C2×C42C23×C4711yescharacteristic
656C2×C42C23×C4711yescharacteristic
657C4⋊C8—21no—
658C4⋊C8—21no—
659C4⋊C8—21no—
660C4⋊C8—21no—
661C22⋊C8—21no—
662C22⋊C8—21no—
663C22⋊C8C23×C4711yescharacteristic
664C22⋊C8C23×C4711yescharacteristic
665C22⋊C8C23×C4711yescharacteristic
666C22⋊C8C23×C4711yescharacteristic
667#97—21no—
668#97—21no—
669C4×C8—21no—
670C4×C8—21no—
671#95—21no—
672#95—21no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95C23×C4711yescharacteristic
678#95C23×C4711yescharacteristic
679#95C23×C4711yescharacteristic
680#95C23×C4711yescharacteristic
681C24—21no—
682C24C2×D4×C4711yescharacteristic
683#41—42no—
684#41—81no—
685#41—81no—
686#41—81no—
687#41—81no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8C22×C4×C4711yescharacteristic
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—42no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4C22×C4×C4711yescharacteristic
707C2×D4C22×C4×C4711yescharacteristic
708C2×D4C22×C4×C4711yescharacteristic
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—81no—
725C22×C4C22×C4×C4711yescharacteristic
726C22×C4C22×C4×C4711yescharacteristic
727C22×C4C2×D4×C4711yescharacteristic
728C22×C4C2×D4×C4711yescharacteristic
729C22×C4C2×D4×C4711yescharacteristic
730C22×C4C2×D4×C4711yescharacteristic
731C22×C4C2×D4×C4711yescharacteristic
732C22×C4C2×D4×C4711yescharacteristic
733C22×C4C2×D4×C4711yescharacteristic
734C22×C4C24×C4711yescharacteristic
735M16—42no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—42no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—42no—
753C4⋊C4—81no—
754C4⋊C4C22⋊C4×C4711yescharacteristic
755C4⋊C4C22⋊C4×C4711yescharacteristic
756C4⋊C4C22⋊C4×C4711yescharacteristic
757C4⋊C4C22⋊C4×C4711yescharacteristic
758C4⋊C4C22⋊C4×C4711yescharacteristic
759C4⋊C4C22⋊C4×C4711yescharacteristic
760C4⋊C4C22⋊C4×C4711yescharacteristic
761C4⋊C4C22⋊C4×C4711yescharacteristic
762C4⋊C4C22×C4×C4711yescharacteristic
763C4⋊C4C22×C4×C4711yescharacteristic
764C4⋊C4C22×C4×C4711yescharacteristic
765C4⋊C4C22×C4×C4711yescharacteristic
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—42no—
786C22⋊C4C22⋊C4×C4711yescharacteristic
787C22⋊C4C22⋊C4×C4711yescharacteristic
788C22⋊C4C22⋊C4×C4711yescharacteristic
789C22⋊C4C22⋊C4×C4711yescharacteristic
790C22⋊C4C22⋊C4×C4711yescharacteristic
791C22⋊C4C22⋊C4×C4711yescharacteristic
792C22⋊C4C22⋊C4×C4711yescharacteristic
793C22⋊C4C22⋊C4×C4711yescharacteristic
794C42—21no—
795C42—21no—
796C42—21no—
797C42—42no—
798C42—81no—
799C42C22×C4×C4711yescharacteristic
800C42C22×C4×C4711yescharacteristic
801C42C22×C4×C4711yescharacteristic
802C42C22×C4×C4711yescharacteristic
803C42C2×D4×C4711yescharacteristic
804C42C2×D4×C4711yescharacteristic
805C42C2×D4×C4711yescharacteristic
806C42C2×D4×C4711yescharacteristic
807C23—21no—
808C23—21no—
809C23—22no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—41no—
814C23—42no—
815C23—81no—
816C23—81no—
817C23C2×C22⋊C4×C4711yescharacteristic
818C23C2×C22⋊C4×C4711yescharacteristic
819C23C22×D4×C4711yescharacteristic
820Q8—41no—
821Q8—81no—
822Q8—81no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—42no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—42no—
834D4—81no—
835D4—81no—
836D4—81no—
837D4—81no—
838D4—81no—
839D4—81no—
840D4—81no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—81no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—81no—
875C2×C4—81no—
876C2×C4—81no—
877C2×C4—81no—
878C2×C4—84no—
879C2×C4C2×C22⋊C4×C4711yescharacteristic
880C2×C4C2×C22⋊C4×C4711yescharacteristic
881C2×C4C2×C22⋊C4×C4711yescharacteristic
882C2×C4C2×C22⋊C4×C4711yescharacteristic
883C2×C4C2×C22⋊C4×C4711yescharacteristic
884C2×C4C2×C22⋊C4×C4711yescharacteristic
885C2×C4C2×C22⋊C4×C4711yescharacteristic
886C2×C4C2×C22⋊C4×C4711yescharacteristic
887C2×C4C2×C22⋊C4×C4711yescharacteristic
888C2×C4C2×C22⋊C4×C4711yescharacteristic
889C2×C4C23×C4×C4711yescharacteristic
890C2×C4C22×D4×C4711yescharacteristic
891C8—41no—
892C8—41no—
893C8—41no—
894C8—41no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—42no—
903C22—42no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—162no—
914C22C47×#41012yes—
915C22C22×C22⋊C4×C4711yescharacteristic
916C22C47×#57611yescharacteristic
917C22C47×#57711yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—42no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—81no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—22no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—81no—
946C2C2×C47×#41011yescharacteristic
947C2C47×#289711yescharacteristic
948C2C47×#290111yescharacteristic
subgroupG/H
center, socleC22×C47C22×C22⋊C4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC22×C4C24×C47
prime radicalC47×#3494C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×#117×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2924C2semidirect
3. C47×#2343C2semidirect
4. C47×#1521C2semidirect
5. C47×#1517C2semidirect
6. C47×#1516C2semidirect
7. C47×#1514C2semidirect
8. C47×#1512C2semidirect
9. C47×#1510C2semidirect
10. C47×#1509C2semidirect
11. C47×#1505C2semidirect
12. C47×#1504C2semidirect
13. C47×#1502C2semidirect
14. C47×#1500C2semidirect
15. C2×C47×#327C2semidirect
24. C47×#544C4semidirect
25. C47×#542C4semidirect
26. C47×#542C4semidirect
27. C47×#540C4semidirect
28. C47×#540C4semidirect
29. C47×#535C4semidirect
36. C47×#520C4semidirect
37. C47×#518C4semidirect
41. C47×#432C22semidirect
42. C47×#432C22semidirect
43. C47×#431C22semidirect
44. C47×#431C22semidirect
52. C47×#383C22semidirect
53. C47×#382C22semidirect
55. C4×C4⋊C4×C47C22semidirect
57. C47×#376C22semidirect
59. C47×#328C22semidirect
60. C47×#328C22semidirect
61. C47×#328C22semidirect
62. C47×#328C22semidirect
71. C47×#327C22semidirect
72. C47×#327C22semidirect
73. C47×#327C22semidirect
74. C47×#327C22semidirect
85. C4⋊Q8×C47C2×C4semidirect
86. C4⋊Q8×C47C2×C4semidirect
87. #127×C47C2×C4semidirect
88. #127×C47C2×C4semidirect
94. #125×C47C2×C4semidirect
95. #125×C47C2×C4semidirect
100. #124×C47C2×C4semidirect
101. #124×C47C2×C4semidirect
136. C4×Q8×C47C2×C4semidirect
137. C4×Q8×C47C2×C4semidirect
148. C4×D4×C47C2×C4semidirect
149. C4×D4×C47C2×C4semidirect
150. C4×D4×C47C2×C4semidirect
151. C4×D4×C47C2×C4semidirect
152. C4×D4×C47C2×C4semidirect
153. C4×D4×C47C2×C4semidirect
420. #17604C47direct (N × H)
466. #2924C2×C47semidirect
467. #2343C2×C47semidirect
468. #1521C2×C47semidirect
469. #1517C2×C47semidirect
470. #1516C2×C47semidirect
471. #1514C2×C47semidirect
472. #1512C2×C47semidirect
473. #1510C2×C47semidirect
474. #1509C2×C47semidirect
475. #1505C2×C47semidirect
476. #1504C2×C47semidirect
477. #1502C2×C47semidirect
478. #1500C2×C47semidirect
479. C2×#327C2×C47semidirect
498. #544C4×C47semidirect
499. #542C4×C47semidirect
500. #542C4×C47semidirect
501. #540C4×C47semidirect
502. #540C4×C47semidirect
503. #535C4×C47semidirect
510. #520C4×C47semidirect
511. #518C4×C47semidirect
515. #432C22×C47semidirect
516. #432C22×C47semidirect
517. #431C22×C47semidirect
518. #431C22×C47semidirect
526. #383C22×C47semidirect
527. #382C22×C47semidirect
529. C4×C4⋊C4C22×C47semidirect
531. #376C22×C47semidirect
533. #328C22×C47semidirect
534. #328C22×C47semidirect
535. #328C22×C47semidirect
536. #328C22×C47semidirect
545. #327C22×C47semidirect
546. #327C22×C47semidirect
547. #327C22×C47semidirect
548. #327C22×C47semidirect
549. C47#17604direct (N × H)
560. C4⋊Q8C2×C4×C47semidirect
561. C4⋊Q8C2×C4×C47semidirect
562. #127C2×C4×C47semidirect
563. #127C2×C4×C47semidirect
569. #125C2×C4×C47semidirect
570. #125C2×C4×C47semidirect
575. #124C2×C4×C47semidirect
576. #124C2×C4×C47semidirect
611. C4×Q8C2×C4×C47semidirect
612. C4×Q8C2×C4×C47semidirect
623. C4×D4C2×C4×C47semidirect
624. C4×D4C2×C4×C47semidirect
625. C4×D4C2×C4×C47semidirect
626. C4×D4C2×C4×C47semidirect
627. C4×D4C2×C4×C47semidirect
628. C4×D4C2×C4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#34942
C47×#29242
C47×#23432
C47×#15212
C47×#15172
C47×#15162
C47×#15142
C47×#15122
C47×#15102
C47×#15092
C47×#15052
C47×#15042
C47×#15022
C47×#15002
C2×C47×#3272
#1760447