Finite Group Databasebeta

← C2×C47×#3242 #26100554

Subgroups — C2×C47×#3242 #26100554

Order 12032.

1678 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#544C211yesmaximal, characteristic
2C2×C47×#541C211yesmaximal, characteristic
3C47×#3242C2116yesmaximal, direct product factor
4C2×C47×#501C211yesmaximal, characteristic, complemented
5C2×C47×#499C211yesmaximal, characteristic, complemented
6C2×C47×#491C211yesmaximal, characteristic, complemented
7C2×C47×#487C211yesmaximal, characteristic, complemented
8C2×C47×#484C211yesmaximal, characteristic
9C2×C47×#485C211yesmaximal, characteristic
10C2×C47×#485C211yesmaximal, characteristic
11C2×C47×#483C211yesmaximal, characteristic
12C2×C47×#479C211yesmaximal, characteristic, complemented
13C2×C47×#479C211yesmaximal, characteristic, complemented
14C2×C47×#477C211yesmaximal, characteristic, complemented
15C2×C47×#475C211yesmaximal, characteristic, complemented
16C2×C47×#433C211yesmaximal, characteristic
17C47×#544—24no—
18C47×#544C2218yes—
19C47×#541—24no—
20C47×#541C2218yes—
21C2×C4⋊Q8×C47—21no—
22C2×C4⋊Q8×C47C2211yescharacteristic
23C2×C4⋊Q8×C47C2211yescharacteristic
24C2×C4⋊Q8×C47C2211yescharacteristic
25C2×#126×C47—21no—
26C2×#126×C47—21no—
27C2×#125×C47—21no—
28C2×#125×C47—21no—
29C2×#125×C47—21no—
30C2×#125×C47C2211yescharacteristic
31C2×#125×C47C2211yescharacteristic
32C2×#125×C47C2211yescharacteristic
33C2×C22⋊Q8×C47—21no—
34C2×C22⋊Q8×C47—21no—
35C2×C22⋊Q8×C47C2211yescharacteristic
36C2×C22⋊Q8×C47C2211yescharacteristic
37C2×C4×Q8×C47C2211yescharacteristic
38C2×C4×Q8×C47C2211yescharacteristic
39C2×#117×C47C2211yescharacteristic
40C2×#117×C47C2211yescharacteristic
41C22×C4⋊C4×C47C2211yescharacteristic
42C47×#501C2218yescomplemented
43C47×#499C2218yescomplemented
44C47×#491C2218yescomplemented
45C47×#487C2218yescomplemented
46C47×#485C2218yes—
47C47×#485C2218yes—
48C47×#484C2218yes—
49C47×#483C2218yes—
50C47×#479C2218yescomplemented
51C47×#479C2218yescomplemented
52C47×#477C2218yescomplemented
53C47×#475C2218yescomplemented
54C47×#433C2218yes—
55C2×#107×C47C2211yescharacteristic
56C2×#107×C47C2211yescharacteristic
57C2×#107×C47C2211yescharacteristic
58C2×#107×C47C2211yescharacteristic
59C2×#106×C47C2211yescharacteristic
60C2×#106×C47C2211yescharacteristic
61C2×#106×C47C2211yescharacteristic
62C2×#106×C47C2211yescharacteristic
63C2×C4⋊C8×C47C2211yescharacteristic
64C2×C4⋊C8×C47C2211yescharacteristic
65C2×#103×C47C2211yescharacteristic
66C2×#103×C47C2211yescharacteristic
67C2×#103×C47C2211yescharacteristic
68C2×#103×C47C2211yescharacteristic
69C2×#103×C47C2211yescharacteristic
70C2×#103×C47C2211yescharacteristic
71C2×#103×C47C2211yescharacteristic
72C2×#103×C47C2211yescharacteristic
73C2×C22⋊C8×C47C2211yescharacteristic
74C2×C22⋊C8×C47C2211yescharacteristic
75C2×#97×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C22×Q8×C47—21no—
78C22×Q8×C47—21no—
79C22×Q8×C47C2311yescharacteristic
80C22×Q8×C47C2311yescharacteristic
81C23×C4×C47—21no—
82C23×C4×C47C2311yescharacteristic
83C22×C8×C47C2311yescharacteristic
84C22×C8×C47C2311yescharacteristic
85C22×C8×C47C2311yescharacteristic
86C22×C8×C47C2311yescharacteristic
87C4⋊Q8×C47—28no—
88C4⋊Q8×C47—22no—
89C4⋊Q8×C47—22no—
90C4⋊Q8×C47—22no—
91C4⋊Q8×C47C2314yes—
92C4⋊Q8×C47C2314yes—
93C4⋊Q8×C47C2314yes—
94#126×C47—28no—
95#126×C47—28no—
96#125×C47—28no—
97#125×C47—28no—
98#125×C47—28no—
99#125×C47—22no—
100#125×C47—22no—
101#125×C47—22no—
102#125×C47C2314yes—
103#125×C47C2314yes—
104#125×C47C2314yes—
105C22⋊Q8×C47—22no—
106C22⋊Q8×C47—22no—
107C22⋊Q8×C47—28no—
108C22⋊Q8×C47—28no—
109C22⋊Q8×C47C2314yes—
110C22⋊Q8×C47C2314yes—
111C4×Q8×C47—22no—
112C4×Q8×C47—22no—
113C4×Q8×C47C2314yes—
114C4×Q8×C47C2314yes—
115#117×C47—22no—
116#117×C47D414yes—
117#117×C47C2314yes—
118#117×C47C2314yes—
119C2×C4⋊C4×C47—21no—
120C2×C4⋊C4×C47—22no—
121C2×C4⋊C4×C47—21no—
122C2×C4⋊C4×C47—21no—
123C2×C4⋊C4×C47—21no—
124C2×C4⋊C4×C47—21no—
125C2×C4⋊C4×C47—21no—
126C2×C4⋊C4×C47—21no—
127C2×C4⋊C4×C47—21no—
128C2×C4⋊C4×C47—21no—
129C2×C4⋊C4×C47—21no—
130C2×C4⋊C4×C47—21no—
131C2×C4⋊C4×C47—21no—
132C2×C4⋊C4×C47—21no—
133C2×C4⋊C4×C47—21no—
134C2×C4⋊C4×C47—21no—
135C2×C4⋊C4×C47D411yescharacteristic
136C2×C4⋊C4×C47D411yescharacteristic
137C2×C4⋊C4×C47C2314yes—
138C2×C4⋊C4×C47C2311yescharacteristic
139C2×C4⋊C4×C47C2311yescharacteristic
140C2×C4⋊C4×C47C2311yescharacteristic
141C2×C4⋊C4×C47C2311yescharacteristic
142C2×C4⋊C4×C47C2311yescharacteristic
143C2×C4⋊C4×C47C2311yescharacteristic
144C2×C22⋊C4×C47—21no—
145C2×C22⋊C4×C47—21no—
146C2×C22⋊C4×C47—21no—
147C2×C22⋊C4×C47D411yescharacteristic
148C2×C22⋊C4×C47D411yescharacteristic
149C2×C42×C47—21no—
150C2×C42×C47—21no—
151C2×C42×C47—21no—
152C2×C42×C47C2311yescharacteristic
153C2×C42×C47C2311yescharacteristic
154#107×C47C2314yes—
155#107×C47C2314yes—
156#107×C47C2314yes—
157#107×C47C2314yes—
158#106×C47C2314yes—
159#106×C47C2314yes—
160#106×C47C2314yes—
161#106×C47C2314yes—
162C4⋊C8×C47C2314yes—
163C4⋊C8×C47C2314yes—
164#103×C47C2314yes—
165#103×C47C2314yes—
166#103×C47C2314yes—
167#103×C47C2314yes—
168#103×C47C2314yes—
169#103×C47C2314yes—
170#103×C47C2314yes—
171#103×C47C2314yes—
172C22⋊C8×C47C2314yes—
173C22⋊C8×C47C2314yes—
174#97×C47C2314yes—
175C4×C8×C47C2314yes—
176C24×C47C2×D411yescharacteristic
177C2×Q8×C47—21no—
178C2×Q8×C47—21no—
179C2×Q8×C47—24no—
180C2×Q8×C47—24no—
181C2×Q8×C47—22no—
182C2×Q8×C47—22no—
183C2×Q8×C47—22no—
184C2×Q8×C47—22no—
185C2×Q8×C47—82no—
186C2×Q8×C47—82no—
187C2×Q8×C47C2412yes—
188C2×Q8×C47C2412yes—
189C22×C4×C47—22no—
190C22×C4×C47—22no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—24no—
200C22×C4×C47—82no—
201C22×C4×C47C2×D412yes—
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2412yes—
208C22×C4×C47C2411yescharacteristic
209C2×C8×C47—22no—
210C2×C8×C47—22no—
211C2×C8×C47—22no—
212C2×C8×C47—22no—
213C2×C8×C47C2412yes—
214C2×C8×C47C2412yes—
215C2×C8×C47C2412yes—
216C2×C8×C47C2412yes—
217C4⋊C4×C47—24no—
218C4⋊C4×C47—21no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—24no—
221C4⋊C4×C47—24no—
222C4⋊C4×C47—24no—
223C4⋊C4×C47—24no—
224C4⋊C4×C47—24no—
225C4⋊C4×C47—24no—
226C4⋊C4×C47—24no—
227C4⋊C4×C47—24no—
228C4⋊C4×C47—24no—
229C4⋊C4×C47—24no—
230C4⋊C4×C47—24no—
231C4⋊C4×C47—24no—
232C4⋊C4×C47—24no—
233C4⋊C4×C47—24no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—21no—
238C4⋊C4×C47C2×D414yes—
239C4⋊C4×C47C2×D414yes—
240C4⋊C4×C47C2412yes—
241C4⋊C4×C47C2412yes—
242C4⋊C4×C47C2412yes—
243C4⋊C4×C47C2412yes—
244C4⋊C4×C47C2412yes—
245C4⋊C4×C47C2412yes—
246C22⋊C4×C47—24no—
247C22⋊C4×C47—24no—
248C22⋊C4×C47—24no—
249C22⋊C4×C47C2×D414yes—
250C22⋊C4×C47C2×D414yes—
251C42×C47—24no—
252C42×C47—24no—
253C42×C47—24no—
254C42×C47C2×D412yes—
255C42×C47C2×D412yes—
256C42×C47C2412yes—
257C42×C47C2412yes—
258C23×C47—22no—
259C23×C47—22no—
260C23×C47—22no—
261C23×C47C22×D412yes—
262C23×C47C22×D411yescharacteristic
263Q8×C47—22no—
264Q8×C47—22no—
265Q8×C47—22no—
266Q8×C47—22no—
267Q8×C47—42no—
268Q8×C47—42no—
269Q8×C47—84no—
270Q8×C47—84no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—24no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—42no—
288C2×C4×C47—42no—
289C2×C4×C47—42no—
290C2×C4×C47—42no—
291C2×C4×C47—42no—
292C2×C4×C47—42no—
293C2×C4×C47—42no—
294C2×C4×C47—42no—
295C2×C4×C47—84no—
296C2×C4×C47C22×D412yes—
297C2×C4×C47C22×D412yes—
298C2×C4×C47C22×D412yes—
299C2×C4×C47C22×D412yes—
300C2×C4×C47C22×D412yes—
301C2×C4×C47C22×D411yescharacteristic
302C2×C4×C472−1+412yes—
303C2×C4×C472−1+412yes—
304C2×C4×C47C2511yescharacteristic
305C8×C47—22no—
306C8×C47—22no—
307C8×C47—22no—
308C8×C47—22no—
309C2×#3242C4711yesmaximal, characteristic, direct product factor, Sylow
310C22×C47—22no—
311C22×C47—22no—
312C22×C47—22no—
313C22×C47—44no—
314C22×C47#53612yes—
315C22×C47#57712yes—
316C22×C47#57812yes—
317C22×C47C23×D411yescharacteristic
318C4×C47—22no—
319C4×C47—22no—
320C4×C47—22no—
321C4×C47—22no—
322C4×C47—22no—
323C4×C47—42no—
324C4×C47—42no—
325C4×C47—42no—
326C4×C47—42no—
327C4×C47—42no—
328C4×C47—42no—
329C4×C47—42no—
330C4×C47—42no—
331C4×C47#53612yes—
332C4×C47C2×2−1+411yescharacteristic
333C4×C47C2×2−1+411yescharacteristic
334C2×#544C2×C4711yescharacteristic
335C2×#541C2×C4711yescharacteristic
336#3242C2×C47116yesdirect product factor
337C2×#501C2×C4711yescharacteristic, complemented
338C2×#499C2×C4711yescharacteristic, complemented
339C2×#491C2×C4711yescharacteristic, complemented
340C2×#487C2×C4711yescharacteristic, complemented
341C2×#484C2×C4711yescharacteristic
342C2×#485C2×C4711yescharacteristic
343C2×#485C2×C4711yescharacteristic
344C2×#483C2×C4711yescharacteristic
345C2×#479C2×C4711yescharacteristic, complemented
346C2×#479C2×C4711yescharacteristic, complemented
347C2×#477C2×C4711yescharacteristic, complemented
348C2×#475C2×C4711yescharacteristic, complemented
349C2×#433C2×C4711yescharacteristic
350C2×C47—42no—
351C2×C47#324214yesdirect product factor
352C2×C47C2×#53611yescharacteristic
353C2×C47C2×#57711yescharacteristic
354C2×C47C2×#57811yescharacteristic
355#544—24no—
356#544C22×C4718yes—
357#541—24no—
358#541C22×C4718yes—
359C2×C4⋊Q8—21no—
360C2×C4⋊Q8C22×C4711yescharacteristic
361C2×C4⋊Q8C22×C4711yescharacteristic
362C2×C4⋊Q8C22×C4711yescharacteristic
363C2×#126—21no—
364C2×#126—21no—
365C2×#125—21no—
366C2×#125—21no—
367C2×#125—21no—
368C2×#125C22×C4711yescharacteristic
369C2×#125C22×C4711yescharacteristic
370C2×#125C22×C4711yescharacteristic
371C2×C22⋊Q8—21no—
372C2×C22⋊Q8—21no—
373C2×C22⋊Q8C22×C4711yescharacteristic
374C2×C22⋊Q8C22×C4711yescharacteristic
375C2×C4×Q8C22×C4711yescharacteristic
376C2×C4×Q8C22×C4711yescharacteristic
377C2×#117C22×C4711yescharacteristic
378C2×#117C22×C4711yescharacteristic
379C22×C4⋊C4C22×C4711yescharacteristic
380#501C22×C4718yescomplemented
381#499C22×C4718yescomplemented
382#491C22×C4718yescomplemented
383#487C22×C4718yescomplemented
384#485C22×C4718yes—
385#485C22×C4718yes—
386#484C22×C4718yes—
387#483C22×C4718yes—
388#479C22×C4718yescomplemented
389#479C22×C4718yescomplemented
390#477C22×C4718yescomplemented
391#475C22×C4718yescomplemented
392#433C22×C4718yes—
393C2×#107C22×C4711yescharacteristic
394C2×#107C22×C4711yescharacteristic
395C2×#107C22×C4711yescharacteristic
396C2×#107C22×C4711yescharacteristic
397C2×#106C22×C4711yescharacteristic
398C2×#106C22×C4711yescharacteristic
399C2×#106C22×C4711yescharacteristic
400C2×#106C22×C4711yescharacteristic
401C2×C4⋊C8C22×C4711yescharacteristic
402C2×C4⋊C8C22×C4711yescharacteristic
403C2×#103C22×C4711yescharacteristic
404C2×#103C22×C4711yescharacteristic
405C2×#103C22×C4711yescharacteristic
406C2×#103C22×C4711yescharacteristic
407C2×#103C22×C4711yescharacteristic
408C2×#103C22×C4711yescharacteristic
409C2×#103C22×C4711yescharacteristic
410C2×#103C22×C4711yescharacteristic
411C2×C22⋊C8C22×C4711yescharacteristic
412C2×C22⋊C8C22×C4711yescharacteristic
413C2×#97C22×C4711yescharacteristic
414C2×C4×C8C22×C4711yescharacteristic
415C47C2×#324211yescharacteristic, direct product factor, Sylow
416C22×Q8—21no—
417C22×Q8—21no—
418C22×Q8C23×C4711yescharacteristic
419C22×Q8C23×C4711yescharacteristic
420C23×C4—21no—
421C23×C4C23×C4711yescharacteristic
422C22×C8C23×C4711yescharacteristic
423C22×C8C23×C4711yescharacteristic
424C22×C8C23×C4711yescharacteristic
425C22×C8C23×C4711yescharacteristic
426C4⋊Q8—28no—
427C4⋊Q8—22no—
428C4⋊Q8—22no—
429C4⋊Q8—22no—
430C4⋊Q8C23×C4714yes—
431C4⋊Q8C23×C4714yes—
432C4⋊Q8C23×C4714yes—
433#126—28no—
434#126—28no—
435#125—28no—
436#125—28no—
437#125—28no—
438#125—22no—
439#125—22no—
440#125—22no—
441#125C23×C4714yes—
442#125C23×C4714yes—
443#125C23×C4714yes—
444C22⋊Q8—22no—
445C22⋊Q8—22no—
446C22⋊Q8—28no—
447C22⋊Q8—28no—
448C22⋊Q8C23×C4714yes—
449C22⋊Q8C23×C4714yes—
450C4×Q8—22no—
451C4×Q8—22no—
452C4×Q8C23×C4714yes—
453C4×Q8C23×C4714yes—
454#117—22no—
455#117D4×C4714yes—
456#117C23×C4714yes—
457#117C23×C4714yes—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4D4×C4711yescharacteristic
475C2×C4⋊C4D4×C4711yescharacteristic
476C2×C4⋊C4C23×C4711yescharacteristic
477C2×C4⋊C4C23×C4711yescharacteristic
478C2×C4⋊C4C23×C4714yes—
479C2×C4⋊C4C23×C4711yescharacteristic
480C2×C4⋊C4C23×C4711yescharacteristic
481C2×C4⋊C4C23×C4711yescharacteristic
482C2×C4⋊C4C23×C4711yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4D4×C4711yescharacteristic
487C2×C22⋊C4D4×C4711yescharacteristic
488C2×C42—21no—
489C2×C42—21no—
490C2×C42—21no—
491C2×C42C23×C4711yescharacteristic
492C2×C42C23×C4711yescharacteristic
493#107C23×C4714yes—
494#107C23×C4714yes—
495#107C23×C4714yes—
496#107C23×C4714yes—
497#106C23×C4714yes—
498#106C23×C4714yes—
499#106C23×C4714yes—
500#106C23×C4714yes—
501C4⋊C8C23×C4714yes—
502C4⋊C8C23×C4714yes—
503#103C23×C4714yes—
504#103C23×C4714yes—
505#103C23×C4714yes—
506#103C23×C4714yes—
507#103C23×C4714yes—
508#103C23×C4714yes—
509#103C23×C4714yes—
510#103C23×C4714yes—
511C22⋊C8C23×C4714yes—
512C22⋊C8C23×C4714yes—
513#97C23×C4714yes—
514C4×C8C23×C4714yes—
515C24C2×D4×C4711yescharacteristic
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—24no—
519C2×Q8—24no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—82no—
525C2×Q8—82no—
526C2×Q8C24×C4712yes—
527C2×Q8C24×C4712yes—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—24no—
539C22×C4—82no—
540C22×C4C2×D4×C4711yescharacteristic
541C22×C4C2×D4×C4711yescharacteristic
542C22×C4C2×D4×C4711yescharacteristic
543C22×C4C2×D4×C4711yescharacteristic
544C22×C4C2×D4×C4711yescharacteristic
545C22×C4C2×D4×C4712yes—
546C22×C4C24×C4712yes—
547C22×C4C24×C4711yescharacteristic
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8C24×C4712yes—
553C2×C8C24×C4712yes—
554C2×C8C24×C4712yes—
555C2×C8C24×C4712yes—
556C4⋊C4—24no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4C2×D4×C4714yes—
578C4⋊C4C2×D4×C4714yes—
579C4⋊C4C24×C4712yes—
580C4⋊C4C24×C4712yes—
581C4⋊C4C24×C4712yes—
582C4⋊C4C24×C4712yes—
583C4⋊C4C24×C4712yes—
584C4⋊C4C24×C4712yes—
585C22⋊C4—24no—
586C22⋊C4—24no—
587C22⋊C4—24no—
588C22⋊C4C2×D4×C4714yes—
589C22⋊C4C2×D4×C4714yes—
590C42—24no—
591C42—24no—
592C42—24no—
593C42C2×D4×C4712yes—
594C42C2×D4×C4712yes—
595C42C24×C4712yes—
596C42C24×C4712yes—
597C23—22no—
598C23—22no—
599C23—22no—
600C23C22×D4×C4712yes—
601C23C22×D4×C4711yescharacteristic
602Q8—22no—
603Q8—22no—
604Q8—22no—
605Q8—22no—
606Q8—42no—
607Q8—42no—
608Q8—84no—
609Q8—84no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—84no—
635C2×C4C22×D4×C4712yes—
636C2×C4C22×D4×C4712yes—
637C2×C4C22×D4×C4712yes—
638C2×C4C22×D4×C4712yes—
639C2×C4C22×D4×C4712yes—
640C2×C4C22×D4×C4711yescharacteristic
641C2×C42−1+4×C4712yes—
642C2×C42−1+4×C4712yes—
643C2×C4C25×C4711yescharacteristic
644C8—22no—
645C8—22no—
646C8—22no—
647C8—22no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—44no—
652C22C47×#53612yes—
653C22C47×#57712yes—
654C22C47×#57812yes—
655C22C23×D4×C4711yescharacteristic
656C4—22no—
657C4—22no—
658C4—22no—
659C4—22no—
660C4—22no—
661C4—42no—
662C4—42no—
663C4—42no—
664C4—42no—
665C4—42no—
666C4—42no—
667C4—42no—
668C4—42no—
669C4C47×#53612yes—
670C4C2×2−1+4×C4711yescharacteristic
671C4C2×2−1+4×C4711yescharacteristic
672C2—42no—
673C2C47×#324214yesdirect product factor
674C2C2×C47×#53611yescharacteristic
675C2C2×C47×#57711yescharacteristic
676C2C2×C47×#57811yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC2×C4C25×C47
prime radicalC24×C47C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×#117×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#3242C2direct (N × H)
4. C2×C47×#501C2semidirect
5. C2×C47×#499C2semidirect
6. C2×C47×#491C2semidirect
7. C2×C47×#487C2semidirect
12. C2×C47×#479C2semidirect
13. C2×C47×#479C2semidirect
14. C2×C47×#477C2semidirect
15. C2×C47×#475C2semidirect
42. C47×#501C22semidirect
43. C47×#499C22semidirect
44. C47×#491C22semidirect
45. C47×#487C22semidirect
50. C47×#479C22semidirect
51. C47×#479C22semidirect
52. C47×#477C22semidirect
53. C47×#475C22semidirect
309. C2×#3242C47direct (N × H)
336. #3242C2×C47direct (N × H)
337. C2×#501C2×C47semidirect
338. C2×#499C2×C47semidirect
339. C2×#491C2×C47semidirect
340. C2×#487C2×C47semidirect
345. C2×#479C2×C47semidirect
346. C2×#479C2×C47semidirect
347. C2×#477C2×C47semidirect
348. C2×#475C2×C47semidirect
351. C2×C47#3242direct (N × H)
380. #501C22×C47semidirect
381. #499C22×C47semidirect
382. #491C22×C47semidirect
383. #487C22×C47semidirect
388. #479C22×C47semidirect
389. #479C22×C47semidirect
390. #477C22×C47semidirect
391. #475C22×C47semidirect
415. C47C2×#3242direct (N × H)
673. C2C47×#3242direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#5442
C2×C47×#5412
C47×#32422
C2×C47×#5012
C2×C47×#4992
C2×C47×#4912
C2×C47×#4872
C2×C47×#4842
C2×C47×#4852
C2×C47×#4832
C2×C47×#4792
C2×C47×#4772
C2×C47×#4752
C2×C47×#4332
C2×#324247