Finite Group Databasebeta

← C2×C4×#13094006 #26374712

Subgroups — C2×C4×#13094006 #26374712

Order 12032.

4070 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094006C211yesmaximal, characteristic
2C22×C4×C22⋊D47C211yesmaximal, characteristic
3C22×C42×D47C211yesmaximal, characteristic, complemented
4C4×#13094006C2116yesmaximal, direct product factor
5C2×#15689017C211yesmaximal, characteristic, complemented
6C2×#15689016C211yesmaximal, characteristic, complemented
7C2×#15689006C211yesmaximal, characteristic, complemented
8C2×#15689005C211yesmaximal, characteristic, complemented
9C2×#15688999C211yesmaximal, characteristic
10C2×#15688997C211yesmaximal, characteristic, complemented
11C2×#15688985C211yesmaximal, characteristic, complemented
12C2×C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
13C2×C4×C4⋊Dic47C211yesmaximal, characteristic, complemented
14C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
17C23×C22⋊D47C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C2×#13094006C4116yesdirect product factor
22C2×#13094006C2218yes—
23C2×C4×C22⋊D47—28no—
24C2×C4×C22⋊D47C2218yes—
25C22×C4⋊Dic47C2211yescharacteristic
26C22×C4⋊Dic47C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×C22⋊Dic47C2211yescharacteristic
31C22×C22⋊Dic47C2211yescharacteristic
32C22×C22⋊Dic47C2211yescharacteristic
33C22×(C2×D47)⋊C4C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×(C2×D47)⋊C4C2211yescharacteristic
36C22×C4×Dic47C2211yescharacteristic
37C22×C4×Dic47C2211yescharacteristic
38C22×C4×Dic47C2211yescharacteristic
39C22×C4×Dic47C2211yescharacteristic
40C22×C4×Dic47C2211yescharacteristic
41C2×C42×D47—28no—
42C2×C42×D47C2218yescomplemented
43#15689017C2218yescomplemented
44#15689016C2218yescomplemented
45#15689006C2218yescomplemented
46#15689005C2218yescomplemented
47#15688999C2218yes—
48#15688997C2218yescomplemented
49#15688985C2218yescomplemented
50C4×Dic47⋊C4C2218yescomplemented
51C4×C4⋊Dic47C2218yescomplemented
52C4×(C2×D47)⋊C4C2218yescomplemented
53C4×C22⋊Dic47C2218yescomplemented
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C24×C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C42×C47C2211yescharacteristic
66C22×C42×C47C2211yescharacteristic
67C4×C22⋊C4×C47C2218yescomplemented
68C2×#95×C47C2211yescharacteristic
69C2×#95×C47C2211yescharacteristic
70C24×D47C2311yescharacteristic
71C22×C22⋊D47—24no—
72C22×C22⋊D47—24no—
73C22×C22⋊D47C2×C418yes—
74C22×C22⋊D47C2314yes—
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C22×C4×D47—24no—
83C22×C4×D47—24no—
84C22×C4×D47—24no—
85C22×C4×D47—24no—
86C22×C4×D47—24no—
87C22×C4×D47—24no—
88C22×C4×D47—24no—
89C22×C4×D47C2×C418yescomplemented
90C22×C4×D47D418yes—
91C22×C4×D47C2314yes—
92C22×C4×D47C2314yes—
93C22×C4×D47C2314yes—
94#13094006C2×C4164yesdirect product factor
95C4×C22⋊D47—232no—
96C2×C4⋊Dic47—24no—
97C2×C4⋊Dic47C2×C418yescomplemented
98C2×C4⋊Dic47C2314yes—
99C2×C4⋊Dic47C2314yes—
100C2×Dic47⋊C4—24no—
101C2×Dic47⋊C4—24no—
102C2×Dic47⋊C4C2×C418yescomplemented
103C2×Dic47⋊C4C2314yes—
104C2×Dic47⋊C4C2314yes—
105C2×Dic47⋊C4C2314yes—
106C2×C22⋊Dic47—24no—
107C2×C22⋊Dic47—24no—
108C2×C22⋊Dic47C2×C418yescomplemented
109C2×C22⋊Dic47C2314yes—
110C2×C22⋊Dic47C2314yes—
111C2×C22⋊Dic47C2314yes—
112C2×(C2×D47)⋊C4—24no—
113C2×(C2×D47)⋊C4—24no—
114C2×(C2×D47)⋊C4C2×C418yescomplemented
115C2×(C2×D47)⋊C4C2314yes—
116C2×(C2×D47)⋊C4C2314yes—
117C2×(C2×D47)⋊C4C2314yes—
118C2×C4×Dic47—24no—
119C2×C4×Dic47—24no—
120C2×C4×Dic47—24no—
121C2×C4×Dic47—24no—
122C2×C4×Dic47—24no—
123C2×C4×Dic47C2314yes—
124C2×C4×Dic47C2314yes—
125C2×C4×Dic47C2314yes—
126C2×C4×Dic47C2314yes—
127C2×C4×Dic47C2314yes—
128C42×D47—232no—
129C47⋊#95C2314yes—
130C47⋊#95C2314yes—
131C47⋊#95C2314yes—
132C47⋊#95C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
135C47⋊#95C2314yes—
136C47⋊#95C2314yes—
137C25×C47C2311yescharacteristic
138C23×C4×C47—24no—
139C23×C4×C47—24no—
140C23×C4×C47—24no—
141C23×C4×C47C2311yescharacteristic
142C23×C4×C47C2311yescharacteristic
143C23×C4×C47C2314yes—
144C23×C4×C47C2311yescharacteristic
145C23×C4×C47C2311yescharacteristic
146C23×C4×C47C2311yescharacteristic
147C23×C4×C47C2311yescharacteristic
148C2×C22⋊C4×C47—24no—
149C2×C22⋊C4×C47C2×C418yescomplemented
150C2×C22⋊C4×C47C2314yes—
151C2×C22⋊C4×C47C2314yes—
152C2×C42×C47—24no—
153C2×C42×C47—24no—
154C2×C42×C47C2314yes—
155C2×C42×C47C2314yes—
156#95×C47C2314yes—
157#95×C47C2314yes—
158C24×C47—22no—
159C24×C47—22no—
160C24×C47—22no—
161C24×C47—22no—
162C24×C47—22no—
163C24×C47—22no—
164C24×C47C22×C414yes—
165C24×C47C2412yes—
166C24×C47C2411yescharacteristic
167C23×D47—22no—
168C23×D47—22no—
169C23×D47—22no—
170C23×D47—22no—
171C23×D47C22×C414yes—
172C23×D47C2×D414yes—
173C23×D47#4114yes—
174C23×D47C2412yes—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—22no—
179C22×C4×C47—22no—
180C22×C4×C47—22no—
181C22×C4×C47—22no—
182C22×C4×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—28no—
188C22×C4×C47—28no—
189C22×C4×C47—28no—
190C22×C4×C47—416no—
191C22×C4×C47C22×C414yes—
192C22×C4×C47C22×C414yes—
193C22×C4×C47C2×D414yes—
194C22×C4×C47#4114yes—
195C22×C4×C47#4114yes—
196C22×C4×C47#4114yes—
197C22×C4×C47C2412yes—
198C22×C4×C47C2412yes—
199C22×C4×C47C2412yes—
200C22×C4×C47C2412yes—
201C22×C4×C47C2412yes—
202C22×C4×C47C2412yes—
203C2×C22⋊D47—232no—
204C2×C22⋊D47—28no—
205C2×C22⋊D47—28no—
206C2×C22⋊D47C22×C4116yes—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47—22no—
212C22×Dic47—22no—
213C22×Dic47—22no—
214C22×Dic47—22no—
215C22×Dic47—22no—
216C22×Dic47—22no—
217C22×Dic47—22no—
218C22×Dic47—22no—
219C22×Dic47—22no—
220C22×Dic47—22no—
221C22×Dic47—22no—
222C22×Dic47—22no—
223C22×Dic47C22×C414yes—
224C22×Dic47C22×C414yes—
225C22×Dic47C22×C414yes—
226C22×Dic47C2×D414yes—
227C22×Dic47#4114yes—
228C22×Dic47C2412yes—
229C22×Dic47C2412yes—
230C22×Dic47C2412yes—
231C22×Dic47C2412yes—
232C22×Dic47C2412yes—
233C22×Dic47C2412yes—
234C22×Dic47C2412yes—
235C2×C4×D47—232no—
236C2×C4×D47—232no—
237C2×C4×D47—28no—
238C2×C4×D47—28no—
239C2×C4×D47—28no—
240C2×C4×D47—232no—
241C2×C4×D47—28no—
242C2×C4×D47—28no—
243C2×C4×D47—28no—
244C2×C4×D47—28no—
245C2×C4×D47C22×C4116yescomplemented
246C2×C4×D47C2×D4116yes—
247C22⋊C4×C47—28no—
248C22⋊C4×C47C22×C4116yescomplemented
249C42×C47—28no—
250C42×C47—28no—
251C22⋊Dic47—28no—
252C22⋊Dic47—28no—
253C22⋊Dic47C22×C4116yescomplemented
254(C2×D47)⋊C4—28no—
255(C2×D47)⋊C4—28no—
256(C2×D47)⋊C4C22×C4116yescomplemented
257C4⋊Dic47—28no—
258C4⋊Dic47C22×C4116yescomplemented
259Dic47⋊C4—28no—
260Dic47⋊C4—28no—
261Dic47⋊C4C22×C4116yescomplemented
262C4×Dic47—28no—
263C4×Dic47—28no—
264C4×Dic47—28no—
265C4×Dic47—28no—
266C4×Dic47—28no—
267C23×C47—28no—
268C23×C47—28no—
269C23×C47—28no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—44no—
277C23×C47—44no—
278C23×C47—44no—
279C23×C47—44no—
280C23×C47C23×C414yes—
281C23×C47C23×C412yes—
282C23×C47C22×D412yes—
283C23×C47C2×#4112yes—
284C23×C47C2×#4112yes—
285C23×C47C2×#4112yes—
286C23×C47C2×#4112yes—
287C23×C47C2×#4112yes—
288C23×C47C2511yescharacteristic
289C22×D47—28no—
290C22×D47—28no—
291C22×D47—28no—
292C22×D47—28no—
293C22×D47—28no—
294C22×D47—28no—
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—22no—
299C22×D47C4×D4116yes—
300C22×D47C23×C414yes—
301C22×D47C22×D414yes—
302C22×D47C2×#4114yes—
303C2×C4×C47—28no—
304C2×C4×C47—28no—
305C2×C4×C47—28no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—44no—
319C2×C4×C47—44no—
320C2×C4×C47—416no—
321C2×C4×C47#123116yescomplemented
322C2×C4×C47C23×C414yes—
323C2×C4×C47C23×C414yes—
324C2×C4×C47C22×D414yes—
325C2×C4×C47C2×#4114yes—
326C2×C4×C47C2×#4114yes—
327C2×C4×C47C2×#4114yes—
328C22⋊D47—232no—
329C2×Dic47—28no—
330C2×Dic47—28no—
331C2×Dic47—28no—
332C2×Dic47—28no—
333C2×Dic47—28no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—22no—
347C2×Dic47—22no—
348C2×Dic47—22no—
349C2×Dic47—22no—
350C2×Dic47—44no—
351C2×Dic47—44no—
352C2×Dic47C23×C414yes—
353C2×Dic47C23×C414yes—
354C2×Dic47C23×C414yes—
355C2×Dic47C22×D414yes—
356C2×Dic47C2×#4114yes—
357C4×D47—232no—
358C4×D47—232no—
359C4×D47—232no—
360C2×C4×#123—471nomaximal, Sylow
361C22×C47—24no—
362C22×C47—24no—
363C22×C47—24no—
364C22×C47—42no—
365C22×C47—42no—
366C22×C47—42no—
367C22×C47—42no—
368C22×C47—416no—
369C22×C47C2×C4×D414yes—
370C22×C47C4×#4114yes—
371C22×C47C4×#4114yes—
372C22×C47C2×#12314yes—
373C22×C47#52514yes—
374C22×C47#52914yes—
375C22×C47#52914yes—
376C22×C47C24×C411yescharacteristic
377C22×C47C23×D411yescharacteristic
378C22×C47C22×#4111yescharacteristic
379C22×C47C22×#4111yescharacteristic
380C22×C47C22×#4111yescharacteristic
381C22×C47C22×#4111yescharacteristic
382C22×C47C22×#4111yescharacteristic
383C2×D47—24no—
384C2×D47—24no—
385C2×D47—24no—
386C2×D47—24no—
387C2×D47—24no—
388C2×D47—24no—
389C2×D47—232no—
390C2×D47C2×C4×D418yes—
391C4×C47—24no—
392C4×C47—24no—
393C4×C47—24no—
394C4×C47—42no—
395C4×C47—42no—
396C4×C47C2×#12318yescomplemented
397Dic47—24no—
398Dic47—24no—
399Dic47—24no—
400Dic47—24no—
401Dic47—24no—
402Dic47—42no—
403Dic47—42no—
404C22×#123—471no—
405C22×C4×D4—471no—
406C23×C42—471no—
407C4×#123—4716no—
408C2×#388—471no—
409C2×#388—471no—
410C2×#387—471no—
411C2×#387—471no—
412C2×#386—471no—
413C2×#385—471no—
414C2×#381—471no—
415C2×C4×C4⋊C4—471no—
416C2×C4×C4⋊C4—471no—
417C2×C4×C22⋊C4—471no—
418C2×C4×C22⋊C4—471no—
419C2×C4×C22⋊C4D4711yescharacteristic, complemented
420C2×C47—44no—
421C2×C47C4×#12318yescomplemented
422C2×C47C22×C4×D411yescharacteristic
423C2×C47C2×C4×#4111yescharacteristic
424C2×C47C2×C4×#4111yescharacteristic
425C2×C47C22×#12311yescharacteristic
426C2×C47C2×#52511yescharacteristic
427C2×C47C2×#52911yescharacteristic
428C2×C47C2×#52911yescharacteristic
429D47—28no—
430C23×D4—471no—
431C24×C4—471no—
432C24×C4—471no—
433C24×C4—471no—
434C24×C4C2×D4711yescharacteristic
435C2×#123—4716no—
436C2×#123—478no—
437C2×C4×D4—478no—
438C2×C4×D4—948no—
439C22×C4⋊C4—471no—
440C22×C4⋊C4—471no—
441C22×C4⋊C4—471no—
442C22×C4⋊C4—471no—
443C22×C4⋊C4—471no—
444C22×C22⋊C4—471no—
445C22×C22⋊C4—471no—
446C22×C22⋊C4—471no—
447C22×C22⋊C4—471no—
448C22×C22⋊C4—471no—
449C22×C22⋊C4—471no—
450C22×C22⋊C4C2×D4711yescharacteristic
451C22×C22⋊C4C2×D4711yescharacteristic
452C22×C42—471no—
453C22×C42—471no—
454C22×C42—471no—
455C22×C42—471no—
456C22×C42—471no—
457C22×C42—478no—
458C22×C42—948no—
459C22×C42C2×D4711yescharacteristic
460C22×C42C2×D4711yescharacteristic
461#388—478no—
462#388—478no—
463#387—478no—
464#387—478no—
465#386—478no—
466#385—478no—
467#381—478no—
468C4×C4⋊C4—478no—
469C4×C4⋊C4—478no—
470C4×C22⋊C4—478no—
471C4×C22⋊C4—478no—
472C4×C22⋊C4C2×D4718yescomplemented
473C2×#95—471no—
474C2×#95—471no—
475C2×#95—471no—
476C2×#95—471no—
477C2×#95—471no—
478C2×#95—471no—
479C2×#95—471no—
480C2×#95—471no—
481C2×#95C2×D4711yescharacteristic
482C2×#95C2×D4711yescharacteristic
483C47C2×C4×#12311yescharacteristic, complemented, Sylow
484C25—471no—
485C25C22×D4711yescharacteristic
486C22×D4—478no—
487C22×D4—474no—
488C22×D4—944no—
489C22×D4—944no—
490C23×C4—24no—
491C23×C4—24no—
492C23×C4—24no—
493C23×C4—471no—
494C23×C4—471no—
495C23×C4—471no—
496C23×C4—471no—
497C23×C4—471no—
498C23×C4—478no—
499C23×C4—478no—
500C23×C4—474no—
501C23×C4—474no—
502C23×C4—471no—
503C23×C4—471no—
504C23×C4—474no—
505C23×C4—944no—
506C23×C4—944no—
507C23×C4—944no—
508C23×C4—944no—
509C23×C4—944no—
510C23×C4—944no—
511C23×C4—944no—
512C23×C4C22×D4711yescharacteristic
513C23×C4C22×D4711yescharacteristic
514C23×C4C22×D4714yes—
515C23×C4C22×D4711yescharacteristic
516C23×C4C22×D4711yescharacteristic
517C23×C4C22×D4711yescharacteristic
518C23×C4C22×D4711yescharacteristic
519#123—4764no—
520C4×D4—9432no—
521C2×C4⋊C4—478no—
522C2×C4⋊C4—478no—
523C2×C4⋊C4—474no—
524C2×C4⋊C4—474no—
525C2×C4⋊C4—474no—
526C2×C4⋊C4—474no—
527C2×C4⋊C4—474no—
528C2×C4⋊C4—944no—
529C2×C4⋊C4—944no—
530C2×C4⋊C4—944no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—478no—
533C2×C22⋊C4—474no—
534C2×C22⋊C4—478no—
535C2×C22⋊C4—474no—
536C2×C22⋊C4—474no—
537C2×C22⋊C4—474no—
538C2×C22⋊C4—474no—
539C2×C22⋊C4—474no—
540C2×C22⋊C4—944no—
541C2×C22⋊C4—944no—
542C2×C22⋊C4—944no—
543C2×C22⋊C4—944no—
544C2×C22⋊C4C4×D4718yescomplemented
545C2×C22⋊C4C22×D4714yes—
546C2×C22⋊C4C22×D4714yes—
547C2×C42—24no—
548C2×C42—24no—
549C2×C42—474no—
550C2×C42—474no—
551C2×C42—474no—
552C2×C42—474no—
553C2×C42—474no—
554C2×C42—9432no—
555C2×C42—944no—
556C2×C42—944no—
557C2×C42—944no—
558C2×C42—944no—
559C2×C42—944no—
560C2×C42C22×D4714yes—
561C2×C42C22×D4714yes—
562#95—474no—
563#95—474no—
564#95—474no—
565#95—474no—
566#95—474no—
567#95—474no—
568#95—474no—
569#95—474no—
570#95C22×D4714yes—
571#95C22×D4714yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—474no—
579C24—474no—
580C24—474no—
581C24—472no—
582C24—942no—
583C24—942no—
584C24—942no—
585C24—942no—
586C24C2×C4×D4714yes—
587C24C23×D4712yes—
588C24C23×D4711yescharacteristic
589C2×D4—4716no—
590C2×D4—948no—
591C2×D4—9432no—
592C2×D4—948no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—28no—
606C22×C4—28no—
607C22×C4—28no—
608C22×C4—416no—
609C22×C4—474no—
610C22×C4—474no—
611C22×C4—474no—
612C22×C4—474no—
613C22×C4—474no—
614C22×C4—472no—
615C22×C4—472no—
616C22×C4—472no—
617C22×C4—472no—
618C22×C4—472no—
619C22×C4—4716no—
620C22×C4—4716no—
621C22×C4—472no—
622C22×C4—472no—
623C22×C4—948no—
624C22×C4—948no—
625C22×C4—948no—
626C22×C4—9432no—
627C22×C4—948no—
628C22×C4—9432no—
629C22×C4—942no—
630C22×C4—942no—
631C22×C4—942no—
632C22×C4—942no—
633C22×C4—942no—
634C22×C4—942no—
635C22×C4—942no—
636C22×C4—942no—
637C22×C4—942no—
638C22×C4—942no—
639C22×C4—9432no—
640C22×C4—948no—
641C22×C4—948no—
642C22×C4—948no—
643C22×C4—942no—
644C22×C4—942no—
645C22×C4—942no—
646C22×C4—942no—
647C22×C4—942no—
648C22×C4—942no—
649C22×C4C2×C4×D4714yes—
650C22×C4C2×C4×D4714yes—
651C22×C4#1062535014yes—
652C22×C4#1062535014yes—
653C22×C4D4×D4714yes—
654C22×C4#1062535214yes—
655C22×C4C23×D4712yes—
656C22×C4C23×D4712yes—
657C22×C4C23×D4712yes—
658C22×C4C23×D4712yes—
659C22×C4C23×D4712yes—
660C22×C4C23×D4712yes—
661C4⋊C4—4716no—
662C4⋊C4—4716no—
663C4⋊C4—948no—
664C4⋊C4—948no—
665C4⋊C4—948no—
666C22⋊C4—28no—
667C22⋊C4—4716no—
668C22⋊C4—4716no—
669C22⋊C4—948no—
670C22⋊C4—948no—
671C22⋊C4—948no—
672C22⋊C4—948no—
673C22⋊C4C2×C4×D47116yescomplemented
674C42—28no—
675C42—28no—
676C42—948no—
677C42—948no—
678C42—948no—
679C42—948no—
680C42—948no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—4716no—
695C23—474no—
696C23—474no—
697C23—474no—
698C23—948no—
699C23—948no—
700C23—948no—
701C23—948no—
702C23—948no—
703C23—948no—
704C23—942no—
705C23—942no—
706C23—942no—
707C23—942no—
708C23C22×C4×D4714yes—
709C23C22×C4×D4712yes—
710C23C2×D4×D4712yes—
711C23#41×D4712yes—
712C23#41×D4712yes—
713C23C2×#1062535212yes—
714C23C2×#1062535012yes—
715C23C2×#1062535012yes—
716C23C24×D4711yescharacteristic
717D4—9432no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—416no—
736C2×C4—474no—
737C2×C4—474no—
738C2×C4—474no—
739C2×C4—474no—
740C2×C4—474no—
741C2×C4—9432no—
742C2×C4—9432no—
743C2×C4—948no—
744C2×C4—948no—
745C2×C4—948no—
746C2×C4—948no—
747C2×C4—948no—
748C2×C4—942no—
749C2×C4—942no—
750C2×C4—942no—
751C2×C4—942no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—942no—
755C2×C4—942no—
756C2×C4—942no—
757C2×C4—942no—
758C2×C4—9432no—
759C2×C4—942no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—942no—
764C2×C4—942no—
765C2×C4—1884no—
766C2×C4—1884no—
767C2×C4#13094006116yesdirect product factor
768C2×C4C22×C4×D4714yes—
769C2×C4C22×C4×D4714yes—
770C2×C4C2×D4×D4714yes—
771C2×C4C2×#1062535214yes—
772C2×C4C2×#1062535014yes—
773C2×C4C2×#1062535014yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—416no—
782C22—478no—
783C22—944no—
784C22—944no—
785C22—944no—
786C22—944no—
787C22—944no—
788C22—944no—
789C22—9432no—
790C22C4×D4×D4714yes—
791C22C4×#1062535214yes—
792C22C4×#1062535014yes—
793C22C2×#1309400614yes—
794C22#1568963214yes—
795C22#1568965114yes—
796C22#1568965514yes—
797C22C23×C4×D4711yescharacteristic
798C22C22×D4×D4711yescharacteristic
799C22C2×#41×D4711yescharacteristic
800C22C2×#41×D4711yescharacteristic
801C22C22×#1062535211yescharacteristic
802C22C22×#1062535011yescharacteristic
803C22C22×#1062535011yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—944no—
810C4—944no—
811C4—944no—
812C4—944no—
813C4—944no—
814C4—1882no—
815C4—1882no—
816C4C2×#1309400618yesdirect product factor
817C2—44no—
818C2—948no—
819C2C4×#1309400618yesdirect product factor
820C2C2×C4×D4×D4711yescharacteristic
821C2C2×C4×#1062535211yescharacteristic
822C2C2×C4×#1062535011yescharacteristic
823C2C22×#1309400611yescharacteristic
824C2C2×#1568963211yescharacteristic
825C2C2×#1568965111yescharacteristic
826C2C2×#1568965511yescharacteristic
subgroupG/H
centerC23×C4C22×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C4×C22⋊C4×C47C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
cosocleC23×C47C25
hypercenterC2×C4×C22⋊C4D47
hypocenterC47C2×C4×#123
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×C42×D47C2semidirect
4. C4×#13094006C2direct (N × H)
5. C2×#15689017C2semidirect
6. C2×#15689016C2semidirect
7. C2×#15689006C2semidirect
8. C2×#15689005C2semidirect
10. C2×#15688997C2semidirect
11. C2×#15688985C2semidirect
12. C2×C4×Dic47⋊C4C2semidirect
13. C2×C4×C4⋊Dic47C2semidirect
14. C2×C4×(C2×D47)⋊C4C2semidirect
15. C2×C4×C22⋊Dic47C2semidirect
16. C2×C4×C22⋊C4×C47C2semidirect
21. C2×#13094006C4direct (N × H)
42. C2×C42×D47C22semidirect
43. #15689017C22semidirect
44. #15689016C22semidirect
45. #15689006C22semidirect
46. #15689005C22semidirect
48. #15688997C22semidirect
49. #15688985C22semidirect
50. C4×Dic47⋊C4C22semidirect
51. C4×C4⋊Dic47C22semidirect
52. C4×(C2×D47)⋊C4C22semidirect
53. C4×C22⋊Dic47C22semidirect
67. C4×C22⋊C4×C47C22semidirect
89. C22×C4×D47C2×C4semidirect
94. #13094006C2×C4direct (N × H)
97. C2×C4⋊Dic47C2×C4semidirect
102. C2×Dic47⋊C4C2×C4semidirect
108. C2×C22⋊Dic47C2×C4semidirect
114. C2×(C2×D47)⋊C4C2×C4semidirect
149. C2×C22⋊C4×C47C2×C4semidirect
245. C2×C4×D47C22×C4semidirect
248. C22⋊C4×C47C22×C4semidirect
253. C22⋊Dic47C22×C4semidirect
256. (C2×D47)⋊C4C22×C4semidirect
258. C4⋊Dic47C22×C4semidirect
261. Dic47⋊C4C22×C4semidirect
321. C2×C4×C47#123semidirect
396. C4×C47C2×#123semidirect
419. C2×C4×C22⋊C4D47semidirect
421. C2×C47C4×#123semidirect
472. C4×C22⋊C4C2×D47semidirect
483. C47C2×C4×#123semidirect
544. C2×C22⋊C4C4×D47semidirect
673. C22⋊C4C2×C4×D47semidirect
767. C2×C4#13094006direct (N × H)
816. C4C2×#13094006direct (N × H)
819. C2C4×#13094006direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940062
C22×C4×C22⋊D472
C22×C42×D472
C4×#130940062
C2×#156890172
C2×#156890162
C2×#156890062
C2×#156890052
C2×#156889992
C2×#156889972
C2×#156889852
C2×C4×Dic47⋊C42
C2×C4×C4⋊Dic472
C2×C4×(C2×D47)⋊C42
C2×C4×C22⋊Dic472
C2×C4×C22⋊C4×C472
C2×C4×#12347