Finite Group Databasebeta

← C2×#20252413 #27081002

Subgroups — C2×#20252413 #27081002

Order 12032.

2610 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D47C211yesmaximal, characteristic
2#20252413C2116yesmaximal, direct product factor
3C2×#15689197C211yesmaximal, characteristic, complemented
4C2×#15689196C211yesmaximal, characteristic, complemented
5C2×#15689195C211yesmaximal, characteristic, complemented
6C2×#15689194C211yesmaximal, characteristic, complemented
7C2×#15689193C211yesmaximal, characteristic, complemented
8C2×#15689192C211yesmaximal, characteristic, complemented
9C2×#15689191C211yesmaximal, characteristic, complemented
10C2×#15689179C211yesmaximal, characteristic, complemented
11C2×#15689178C211yesmaximal, characteristic, complemented
12C2×#15689086C211yesmaximal, characteristic, complemented
13C2×#15689085C211yesmaximal, characteristic, complemented
14C22×(C2×D47)⋊C8C211yesmaximal, characteristic, complemented
15C2×C22⋊C8×D47C211yesmaximal, characteristic, complemented
16C2×C47×#435C211yesmaximal, characteristic, complemented
17C22×D4×D47C411yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C22×#10625329C2211yescharacteristic, complemented
21C22×#10625324C2211yescharacteristic, complemented
22C22×#10625324C2211yescharacteristic, complemented
23C23×C47⋊C8C2211yescharacteristic, complemented
24C22×C8×D47C2211yescharacteristic, complemented
25C22×C8×D47C2211yescharacteristic, complemented
26C2×C4×D188C2211yescharacteristic
27C2×D4×Dic47C411yescharacteristic
28C2×#13093986C411yescharacteristic
29C2×C4×C22⋊D47C2211yescharacteristic
30C2×C4×C22⋊D47C2211yescharacteristic
31C2×(C22⋊D47)⋊C4C411yescharacteristic
32C2×(C22⋊D47)⋊C4C411yescharacteristic
33C4×D4×D47C418yes—
34C4×D4×D47C2218yes—
35C2×C4⋊C4×D47C411yescharacteristic
36C2×C22⋊C4×D47C411yescharacteristic
37C2×C22⋊C4×D47C411yescharacteristic
38C2×C42×D47C2211yescharacteristic
39#15689197C2218yescomplemented
40#15689196C2218yescomplemented
41#15689195C2218yescomplemented
42#15689194C2218yescomplemented
43#15689193C2218yescomplemented
44#15689192C2218yescomplemented
45#15689191C2218yescomplemented
46#15689179C2218yescomplemented
47#15689178C2218yescomplemented
48C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
49C2×Dic47⋊C8C2211yescharacteristic, complemented
50C2×Dic47⋊C8C2211yescharacteristic, complemented
51#15689086C2218yescomplemented
52#15689085C2218yescomplemented
53C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
54C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
55C2×(C2×D47)⋊C8C2211yescharacteristic
56C2×(C2×D47)⋊C8C2211yescharacteristic
57C2×(C2×D47)⋊C8C2211yescharacteristic
58C2×(C2×D47)⋊C8C2211yescharacteristic
59C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
60C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
61C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
62C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
63C2×(C2×D47)⋊C8C2218yescomplemented
64C22⋊C8×D47C2218yescomplemented
65C2×#13093935C2211yescharacteristic, complemented
66C2×#13093934C2211yescharacteristic, complemented
67C2×#13093934C2211yescharacteristic, complemented
68C22×M16×C47C2211yescharacteristic, complemented
69C23×C8×C47C2211yescharacteristic, complemented
70C2×C4×D4×C47C2211yescharacteristic
71C47×#435C2218yescomplemented
72C2×C4⋊C8×C47C2211yescharacteristic, complemented
73C2×C22⋊C8×C47C2211yescharacteristic, complemented
74C2×C22⋊C8×C47C2211yescharacteristic, complemented
75C2×#97×C47C2211yescharacteristic, complemented
76C24×D47C2×C411yescharacteristic
77C24×D47C2×C411yescharacteristic
78C22×D188C2×C411yescharacteristic
79C22×C22⋊D47C2×C411yescharacteristic
80C22×C22⋊D47C2×C411yescharacteristic
81C2×D4×D47—28no—
82C2×D4×D47C2×C418yes—
83C23×Dic47C2×C411yescharacteristic
84C23×Dic47C2×C411yescharacteristic
85C22×C4×D47—42no—
86C22×C4×D47—42no—
87C22×C4×D47—42no—
88C22×C4×D47—42no—
89C22×C4×D47C2×C411yescharacteristic
90C22×C4×D47C2×C411yescharacteristic
91C22×C4×D47C2×C411yescharacteristic
92C22×C4×D47C2×C411yescharacteristic
93C22×C4×D47C2×C414yes—
94C22×C4×D47C2×C414yes—
95C22×C4×D47C2×C411yescharacteristic
96C22×C4×D47C2×C411yescharacteristic
97C22×C4×D47C2311yescharacteristic
98C22×C4×D47C2311yescharacteristic
99C22×C4×D47C2311yescharacteristic
100C22×C4×D47C2314yes—
101C22×C4×D47C2314yes—
102C2×#10625329—42no—
103C2×#10625329C2314yescomplemented
104C2×#10625324—42no—
105C2×#10625324—42no—
106C2×#10625324C2314yescomplemented
107C2×#10625324C2314yescomplemented
108C22×C47⋊C8—42no—
109C22×C47⋊C8C2311yescharacteristic
110C22×C47⋊C8C2311yescharacteristic
111C22×C47⋊C8C2311yescharacteristic
112C22×C47⋊C8C2311yescharacteristic
113C22×C47⋊C8C2314yescomplemented
114C2×C8×D47—42no—
115C2×C8×D47—42no—
116C2×C8×D47C2314yescomplemented
117C2×C8×D47C2314yescomplemented
118C4×D188C2×C414yes—
119C4×D188C2314yes—
120D4×Dic47C2×C418yes—
121#13093986C2×C418yes—
122C4×C22⋊D47C2×C414yes—
123C4×C22⋊D47C2×C414yes—
124C4×C22⋊D47C2314yes—
125C4×C22⋊D47C2314yes—
126(C22⋊D47)⋊C4C2×C418yes—
127(C22⋊D47)⋊C4C2×C418yes—
128C2×C4⋊Dic47C2×C411yescharacteristic
129C2×Dic47⋊C4C2×C411yescharacteristic
130C2×Dic47⋊C4C2×C411yescharacteristic
131C4⋊C4×D47C2×C418yes—
132C2×C22⋊Dic47C2×C411yescharacteristic
133C2×C22⋊Dic47C2×C411yescharacteristic
134C2×(C2×D47)⋊C4C2×C411yescharacteristic
135C2×(C2×D47)⋊C4C2×C411yescharacteristic
136C2×(C2×D47)⋊C4C2×C411yescharacteristic
137C2×(C2×D47)⋊C4C2×C411yescharacteristic
138C22⋊C4×D47C2×C418yes—
139C22⋊C4×D47C2×C418yes—
140C2×C4×Dic47C2×C411yescharacteristic
141C2×C4×Dic47C2×C411yescharacteristic
142C2×C4×Dic47C2311yescharacteristic
143C42×D47C2×C414yes—
144C42×D47C2314yes—
145C4⋊(C47⋊C8)C2314yescomplemented
146Dic47⋊C8C2314yescomplemented
147Dic47⋊C8C2314yescomplemented
148C22⋊(C47⋊C8)C2314yescomplemented
149C22⋊(C47⋊C8)C2314yescomplemented
150(C2×D47)⋊C8C2314yes—
151(C2×D47)⋊C8C2314yes—
152(C2×D47)⋊C8C2314yes—
153(C2×D47)⋊C8C2314yes—
154(C2×D47)⋊C8C2314yescomplemented
155(C2×D47)⋊C8C2314yescomplemented
156(C2×D47)⋊C8C2314yescomplemented
157(C2×D47)⋊C8C2314yescomplemented
158#13093935C2314yescomplemented
159#13093934C2314yescomplemented
160#13093934C2314yescomplemented
161C22×D4×C47C2×C411yescharacteristic
162C23×C4×C47C2311yescharacteristic
163C23×C4×C47C2311yescharacteristic
164C2×M16×C47—42no—
165C2×M16×C47C2314yescomplemented
166C22×C8×C47—42no—
167C22×C8×C47C2311yescharacteristic
168C22×C8×C47C2311yescharacteristic
169C22×C8×C47C2311yescharacteristic
170C22×C8×C47C2311yescharacteristic
171C22×C8×C47C2314yescomplemented
172C4×D4×C47C2×C414yes—
173C4×D4×C47C2314yes—
174C2×C4⋊C4×C47C2×C411yescharacteristic
175C2×C22⋊C4×C47C2×C411yescharacteristic
176C2×C22⋊C4×C47C2×C411yescharacteristic
177C2×C42×C47C2311yescharacteristic
178C4⋊C8×C47C2314yescomplemented
179C22⋊C8×C47C2314yescomplemented
180C22⋊C8×C47C2314yescomplemented
181#97×C47C2314yescomplemented
182C24×C47C22×C411yescharacteristic
183C24×C47C22×C411yescharacteristic
184C23×D47—24no—
185C23×D47—42no—
186C23×D47—42no—
187C23×D47—42no—
188C23×D47—42no—
189C23×D47M1618yescomplemented
190C23×D47C22×C411yescharacteristic
191C23×D47C22×C411yescharacteristic
192C23×D47C22×C411yescharacteristic
193C23×D47C22×C414yes—
194C23×D47C22×C414yes—
195C2×D4×C47—24no—
196C2×D4×C47C22×C414yes—
197C22×C4×C47—22no—
198C22×C4×C47—22no—
199C22×C4×C47—22no—
200C22×C4×C47—22no—
201C22×C4×C47C22×C411yescharacteristic
202C22×C4×C47C22×C411yescharacteristic
203C22×C4×C47C22×C411yescharacteristic
204C22×C4×C47C22×C411yescharacteristic
205C22×C4×C47C22×C412yes—
206C22×C4×C47C22×C412yes—
207C22×C4×C47C2412yes—
208C22×C4×C47C2412yes—
209C22×C4×C47C2411yescharacteristic
210C2×C22⋊D47—24no—
211C2×C22⋊D47—24no—
212C2×C22⋊D47C22×C414yes—
213C2×C22⋊D47C22×C414yes—
214C22×Dic47—42no—
215C22×Dic47—42no—
216C22×Dic47C22×C411yescharacteristic
217C22×Dic47C22×C411yescharacteristic
218C22×Dic47C22×C411yescharacteristic
219C22×Dic47C22×C411yescharacteristic
220C22×Dic47C22×C411yescharacteristic
221C22×Dic47C22×C414yes—
222C22×Dic47C22×C414yes—
223D4×D47—232no—
224C2×D188—24no—
225C2×D188C22×C414yes—
226C2×C4×D47—24no—
227C2×C4×D47—22no—
228C2×C4×D47—22no—
229C2×C4×D47—22no—
230C2×C4×D47—22no—
231C2×C4×D47—22no—
232C2×C4×D47—22no—
233C2×C4×D47—48no—
234C2×C4×D47—48no—
235C2×C4×D47—44no—
236C2×C4×D47—44no—
237C2×C4×D47—44no—
238C2×C4×D47—44no—
239C2×C4×D47—42no—
240C2×C4×D47—42no—
241C2×C4×D47—42no—
242C2×C4×D47—42no—
243C2×C4×D47—42no—
244C2×C4×D47C22×C412yes—
245C2×C4×D47C22×C414yes—
246C2×C4×D47C22×C412yes—
247C2×C4×D47C22×C412yes—
248C2×C4×D47C22×C414yes—
249C2×C4×D47C22×C414yes—
250C2×C4×D47C22×C414yes—
251C2×C4×D47C22×C414yes—
252C2×C4×D47C22×C414yes—
253C2×C4×D47C2412yes—
254C2×C4×D47C2412yes—
255C2×C4×D47C2412yes—
256M16×C47—44no—
257C2×C8×C47—22no—
258C2×C8×C47—22no—
259C2×C8×C47—22no—
260C2×C8×C47—22no—
261C2×C8×C47—44no—
262C2×C8×C47C2412yes—
263C2×C8×C47C2412yes—
264C2×C8×C47C2412yes—
265C2×C8×C47C2412yes—
266C4⋊C4×C47C22×C414yes—
267C22⋊C4×C47C22×C414yes—
268C22⋊C4×C47C22×C414yes—
269C42×C47C22×C412yes—
270C42×C47C2412yes—
271C22⋊Dic47C22×C414yes—
272C22⋊Dic47C22×C414yes—
273(C2×D47)⋊C4C22×C414yes—
274(C2×D47)⋊C4C22×C414yes—
275(C2×D47)⋊C4C22×C414yes—
276(C2×D47)⋊C4C22×C414yes—
277C4⋊Dic47C22×C414yes—
278Dic47⋊C4C22×C414yes—
279Dic47⋊C4C22×C414yes—
280C4×Dic47C22×C412yes—
281C4×Dic47C22×C414yes—
282C4×Dic47C22×C414yes—
283C4×Dic47C2412yes—
284#10625329—44no—
285C2×C47⋊C8—22no—
286C2×C47⋊C8—22no—
287C2×C47⋊C8—22no—
288C2×C47⋊C8—22no—
289C2×C47⋊C8—44no—
290C2×C47⋊C8C2412yes—
291C2×C47⋊C8C2412yes—
292C2×C47⋊C8C2412yes—
293C2×C47⋊C8C2412yes—
294#10625324—44no—
295#10625324—44no—
296C8×D47—44no—
297C8×D47—44no—
298C23×C47—22no—
299C23×C47—22no—
300C23×C47—22no—
301C23×C47—22no—
302C23×C47—22no—
303C23×C47C2×M1614yes—
304C23×C47C23×C412yes—
305C23×C47C23×C412yes—
306C23×C47C23×C411yescharacteristic
307C22×D47—22no—
308C22×D47—22no—
309C22×D47—22no—
310C22×D47—22no—
311C22×D47—22no—
312C22×D47—22no—
313C22×D47—22no—
314C22×D47—28no—
315C22×D47—44no—
316C22×D47—44no—
317C22×D47—416no—
318C22×D47—44no—
319C22×D47—44no—
320C22×D47—416no—
321C22×D47C2×M1614yes—
322C22×D47C2×M1614yes—
323C22×D47C2×M16116yescomplemented
324C22×D47C23×C412yes—
325C22×D47C23×C412yes—
326C22×D47C23×C412yes—
327D4×C47—28no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—24no—
333C2×C4×C47—24no—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47C23×C412yes—
339C2×C4×C47C23×C412yes—
340C2×C4×C47C23×C412yes—
341C2×C4×C47C23×C412yes—
342C2×C4×C47C23×C411yescharacteristic
343C2×C4×C47H(5,𝔽2)12yes—
344C2×C4×C47H(5,𝔽2)12yes—
345C2×C4×C47C2511yescharacteristic
346C22⋊D47—28no—
347C22⋊D47—28no—
348C2×Dic47—22no—
349C2×Dic47—22no—
350C2×Dic47—22no—
351C2×Dic47—22no—
352C2×Dic47—22no—
353C2×Dic47—44no—
354C2×Dic47—44no—
355C2×Dic47C23×C412yes—
356C2×Dic47C23×C412yes—
357C2×Dic47C23×C412yes—
358C2×Dic47C23×C412yes—
359C2×Dic47C23×C412yes—
360D188—28no—
361C4×D47—28no—
362C4×D47—24no—
363C4×D47—24no—
364C4×D47—24no—
365C4×D47—22no—
366C4×D47—22no—
367C4×D47—22no—
368C4×D47—22no—
369C4×D47—22no—
370C4×D47—22no—
371C4×D47—44no—
372C4×D47—44no—
373C4×D47—44no—
374C4×D47—44no—
375C4×D47—44no—
376C8×C47—22no—
377C8×C47—22no—
378C8×C47—22no—
379C8×C47—22no—
380C47⋊C8—22no—
381C47⋊C8—22no—
382C47⋊C8—22no—
383C47⋊C8—22no—
384C2×#2973—471nomaximal, Sylow
385C22×C47—22no—
386C22×C47—28no—
387C22×C47—22no—
388C22×C47—22no—
389C22×C47—22no—
390C22×C47—22no—
391C22×C47—44no—
392C22×C47#51812yes—
393C22×C47C22×M1614yes—
394C22×C47C22×M1612yes—
395C22×C47#56812yes—
396C22×C47C24×C411yescharacteristic
397C2×D47—22no—
398C2×D47—22no—
399C2×D47—28no—
400C2×D47—28no—
401C2×D47—22no—
402C2×D47—22no—
403C2×D47—22no—
404C2×D47—22no—
405C2×D47—22no—
406C2×D47—416no—
407C2×D47—416no—
408C2×D47—44no—
409C2×D47C22×M1614yes—
410C2×D47C22×M1614yes—
411C4×C47—22no—
412C4×C47—22no—
413C4×C47—22no—
414C4×C47—22no—
415C4×C47#51812yes—
416C4×C47C2×H(5,𝔽2)11yescharacteristic
417C4×C47C2×H(5,𝔽2)11yescharacteristic
418Dic47—22no—
419Dic47—22no—
420Dic47—22no—
421Dic47—22no—
422Dic47—22no—
423C22×C4×D4—471no—
424#2973—4716no—
425C2×#435—471no—
426C2×#435—471no—
427C2×#435—471no—
428C2×#435—471no—
429C2×#435—471no—
430C2×#435—471no—
431C2×#435—471no—
432C2×#435D4711yescharacteristic, complemented
433C2×#432—471no—
434C2×#432—471no—
435C2×#407—471no—
436C2×#407—471no—
437C22×C22⋊C8—471no—
438C22×C22⋊C8—471no—
439C2×C47—24no—
440C2×C47—42no—
441C2×C47#297314yescomplemented
442C2×C47C2×#51811yescharacteristic
443C2×C47C23×M1611yescharacteristic
444C2×C47C2×#56811yescharacteristic
445D47—24no—
446D47—24no—
447D47—42no—
448C23×D4—471no—
449C24×C4—471no—
450C24×C4—471no—
451C22×M16—471no—
452C22×M16—471no—
453C22×M16—471no—
454C22×M16C2×D4711yescharacteristic, complemented
455C23×C8—471no—
456C23×C8—471no—
457C23×C8—471no—
458C23×C8C2×D4711yescharacteristic, complemented
459C2×C4×D4—471no—
460C2×C4×D4—471no—
461C2×C4×D4—471no—
462C2×C4×D4—478no—
463C2×C4×D4—478no—
464C2×C4×D4—471no—
465C2×C4×D4—471no—
466C2×C4×D4—471no—
467C2×C4×D4—471no—
468C2×C4×D4C2×D4711yescharacteristic
469C22×C4⋊C4—471no—
470C22×C22⋊C4—471no—
471C22×C22⋊C4—471no—
472C22×C42—471no—
473#435—478no—
474#435—478no—
475#435—478no—
476#435—478no—
477#435—478no—
478#435—478no—
479#435—478no—
480#435C2×D4718yescomplemented
481#432—478no—
482#432—478no—
483C2×C4⋊C8—471no—
484C2×C4⋊C8—471no—
485C2×C4⋊C8—471no—
486C2×C4⋊C8C2×D4711yescharacteristic, complemented
487#407—478no—
488#407—478no—
489C2×C22⋊C8—471no—
490C2×C22⋊C8—471no—
491C2×C22⋊C8—471no—
492C2×C22⋊C8—471no—
493C2×C22⋊C8—471no—
494C2×C22⋊C8—471no—
495C2×C22⋊C8—471no—
496C2×C22⋊C8—471no—
497C2×C22⋊C8—471no—
498C2×C22⋊C8—471no—
499C2×C22⋊C8—478no—
500C2×C22⋊C8—478no—
501C2×C22⋊C8C2×D4711yescharacteristic, complemented
502C2×C22⋊C8C2×D4711yescharacteristic, complemented
503C2×#97—471no—
504C2×#97—471no—
505C2×#97—471no—
506C2×#97C2×D4711yescharacteristic, complemented
507C47C2×#297311yescharacteristic, complemented, Sylow
508C25—471no—
509C25—471no—
510C22×D4—471no—
511C22×D4—471no—
512C22×D4—478no—
513C22×D4—471no—
514C22×D4—948no—
515C22×D4C4×D4711yescharacteristic
516C23×C4—471no—
517C23×C4—471no—
518C23×C4—471no—
519C23×C4—471no—
520C23×C4—471no—
521C23×C4—471no—
522C23×C4—471no—
523C23×C4—471no—
524C23×C4—471no—
525C23×C4—471no—
526C23×C4—471no—
527C23×C4—474no—
528C23×C4—474no—
529C23×C4—474no—
530C23×C4—474no—
531C23×C4—1882no—
532C23×C4—1882no—
533C23×C4—1882no—
534C23×C4—1882no—
535C23×C4C22×D4711yescharacteristic
536C23×C4C22×D4711yescharacteristic
537C2×M16—42no—
538C2×M16—474no—
539C2×M16—474no—
540C2×M16—474no—
541C2×M16—1882no—
542C2×M16—1882no—
543C2×M16—1882no—
544C2×M16C22×D4714yescomplemented
545C22×C8—42no—
546C22×C8—471no—
547C22×C8—471no—
548C22×C8—471no—
549C22×C8—471no—
550C22×C8—474no—
551C22×C8—474no—
552C22×C8—474no—
553C22×C8—1882no—
554C22×C8—1882no—
555C22×C8—1882no—
556C22×C8C22×D4711yescharacteristic
557C22×C8C22×D4711yescharacteristic
558C22×C8C22×D4711yescharacteristic
559C22×C8C22×D4711yescharacteristic
560C22×C8C22×D4714yescomplemented
561C4×D4—478no—
562C4×D4—474no—
563C4×D4—474no—
564C4×D4—474no—
565C4×D4—474no—
566C4×D4—478no—
567C4×D4—478no—
568C4×D4—478no—
569C4×D4—474no—
570C4×D4—474no—
571C4×D4C4×D4714yes—
572C4×D4C22×D4714yes—
573C2×C4⋊C4—471no—
574C2×C4⋊C4—471no—
575C2×C4⋊C4—471no—
576C2×C4⋊C4—478no—
577C2×C4⋊C4C4×D4711yescharacteristic
578C2×C22⋊C4—471no—
579C2×C22⋊C4—471no—
580C2×C22⋊C4—471no—
581C2×C22⋊C4—471no—
582C2×C22⋊C4—471no—
583C2×C22⋊C4—471no—
584C2×C22⋊C4—478no—
585C2×C22⋊C4—478no—
586C2×C22⋊C4C4×D4711yescharacteristic
587C2×C22⋊C4C4×D4711yescharacteristic
588C2×C42—471no—
589C2×C42—471no—
590C2×C42—471no—
591C2×C42—474no—
592C2×C42—474no—
593C2×C42C22×D4711yescharacteristic
594C4⋊C8—474no—
595C4⋊C8—474no—
596C4⋊C8—474no—
597C4⋊C8C22×D4714yescomplemented
598C22⋊C8—474no—
599C22⋊C8—474no—
600C22⋊C8—474no—
601C22⋊C8—474no—
602C22⋊C8—474no—
603C22⋊C8—474no—
604C22⋊C8—474no—
605C22⋊C8—474no—
606C22⋊C8—474no—
607C22⋊C8—474no—
608C22⋊C8C22×D4714yescomplemented
609C22⋊C8C22×D4714yescomplemented
610#97—474no—
611#97—474no—
612#97—474no—
613#97C22×D4714yescomplemented
614C24—471no—
615C24—471no—
616C24—478no—
617C24—474no—
618C24—471no—
619C24—474no—
620C24—944no—
621C24—1882no—
622C24—1882no—
623C24—1882no—
624C24—1882no—
625C24C2×C4×D4711yescharacteristic
626C24C2×C4×D4711yescharacteristic
627C2×D4—24no—
628C2×D4—474no—
629C2×D4—474no—
630C2×D4—474no—
631C2×D4—944no—
632C2×D4—9432no—
633C2×D4—944no—
634C2×D4—944no—
635C2×D4C2×C4×D4714yes—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—471no—
641C22×C4—471no—
642C22×C4—471no—
643C22×C4—471no—
644C22×C4—471no—
645C22×C4—474no—
646C22×C4—474no—
647C22×C4—474no—
648C22×C4—472no—
649C22×C4—472no—
650C22×C4—472no—
651C22×C4—472no—
652C22×C4—472no—
653C22×C4—472no—
654C22×C4—474no—
655C22×C4—474no—
656C22×C4—474no—
657C22×C4—474no—
658C22×C4—474no—
659C22×C4—944no—
660C22×C4—942no—
661C22×C4—942no—
662C22×C4—942no—
663C22×C4—942no—
664C22×C4—942no—
665C22×C4—942no—
666C22×C4—1888no—
667C22×C4—1888no—
668C22×C4—1884no—
669C22×C4—1884no—
670C22×C4—1884no—
671C22×C4—1884no—
672C22×C4—1882no—
673C22×C4—1882no—
674C22×C4—1882no—
675C22×C4—1882no—
676C22×C4—1882no—
677C22×C4—1882no—
678C22×C4—1882no—
679C22×C4C2×C4×D4711yescharacteristic
680C22×C4C2×C4×D4711yescharacteristic
681C22×C4C2×C4×D4711yescharacteristic
682C22×C4C2×C4×D4711yescharacteristic
683C22×C4C2×C4×D4712yes—
684C22×C4C2×C4×D4712yes—
685C22×C4C23×D4712yes—
686C22×C4C23×D4712yes—
687C22×C4C23×D4711yescharacteristic
688M16—44no—
689M16—1884no—
690M16—1884no—
691M16—1884no—
692C2×C8—22no—
693C2×C8—22no—
694C2×C8—22no—
695C2×C8—22no—
696C2×C8—44no—
697C2×C8—472no—
698C2×C8—472no—
699C2×C8—472no—
700C2×C8—472no—
701C2×C8—942no—
702C2×C8—942no—
703C2×C8—942no—
704C2×C8—942no—
705C2×C8—1884no—
706C2×C8—1884no—
707C2×C8—1884no—
708C2×C8C23×D4712yes—
709C2×C8C23×D4712yes—
710C2×C8C23×D4712yes—
711C2×C8C23×D4712yes—
712C4⋊C4—474no—
713C4⋊C4—474no—
714C4⋊C4—474no—
715C4⋊C4C2×C4×D4714yes—
716C22⋊C4—474no—
717C22⋊C4—474no—
718C22⋊C4—474no—
719C22⋊C4—474no—
720C22⋊C4—474no—
721C22⋊C4—474no—
722C22⋊C4C2×C4×D4714yes—
723C22⋊C4C2×C4×D4714yes—
724C42—472no—
725C42—474no—
726C42—474no—
727C42—472no—
728C42C2×C4×D4712yes—
729C42C23×D4712yes—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—474no—
736C23—474no—
737C23—472no—
738C23—472no—
739C23—4716no—
740C23—472no—
741C23—948no—
742C23—942no—
743C23—942no—
744C23—942no—
745C23—942no—
746C23—942no—
747C23—942no—
748C23—942no—
749C23—1884no—
750C23—1884no—
751C23—1884no—
752C23—18816no—
753C23—1884no—
754C23—18816no—
755C23M16×D4714yes—
756C23C22×C4×D4712yes—
757C23C22×C4×D4712yes—
758C23C22×C4×D4711yescharacteristic
759D4—28no—
760D4—948no—
761D4—948no—
762D4—948no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—472no—
774C2×C4—472no—
775C2×C4—472no—
776C2×C4—472no—
777C2×C4—472no—
778C2×C4—948no—
779C2×C4—942no—
780C2×C4—942no—
781C2×C4—942no—
782C2×C4—942no—
783C2×C4—942no—
784C2×C4—944no—
785C2×C4—944no—
786C2×C4—944no—
787C2×C4—942no—
788C2×C4—942no—
789C2×C4—942no—
790C2×C4—942no—
791C2×C4—942no—
792C2×C4—942no—
793C2×C4—1884no—
794C2×C4—1884no—
795C2×C4—1884no—
796C2×C4—1884no—
797C2×C4—1884no—
798C2×C4—1884no—
799C2×C4—1884no—
800C2×C4C22×C4×D4712yes—
801C2×C4C22×C4×D4712yes—
802C2×C4C22×C4×D4712yes—
803C2×C4C22×C4×D4712yes—
804C2×C4C22×C4×D4711yescharacteristic
805C2×C4#1309406912yes—
806C2×C4#1309407012yes—
807C2×C4C24×D4711yescharacteristic
808C8—22no—
809C8—22no—
810C8—22no—
811C8—22no—
812C8—942no—
813C8—942no—
814C8—942no—
815C8—942no—
816C22—22no—
817C22—22no—
818C22—28no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—44no—
823C22—474no—
824C22—474no—
825C22—942no—
826C22—942no—
827C22—942no—
828C22—942no—
829C22—948no—
830C22—948no—
831C22—942no—
832C22—942no—
833C22—942no—
834C22—18816no—
835C22—18816no—
836C22—1884no—
837C22#1568959512yes—
838C22C2×M16×D4714yes—
839C22C2×M16×D4712yes—
840C22#1568988812yes—
841C22C23×C4×D4711yescharacteristic
842C4—22no—
843C4—22no—
844C4—22no—
845C4—22no—
846C4—942no—
847C4—942no—
848C4—942no—
849C4—942no—
850C4—942no—
851C4#1568959512yes—
852C4C2×#1309406911yescharacteristic
853C4C2×#1309407011yescharacteristic
854C2—24no—
855C2—42no—
856C2—944no—
857C2—944no—
858C2—1882no—
859C2#2025241314yesdirect product factor
860C2C2×#1568959511yescharacteristic
861C2C22×M16×D4711yescharacteristic
862C2C2×#1568988811yescharacteristic
subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC2×C4C24×D47
FittingC2×C47×#435C2
socleC23×C47C23×C4
prime radicalC22×D4×D47C4
cosocleC2×C4×C47C25
hypercenterC2×#435D47
hypocenterC47C2×#2973
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #20252413C2direct (N × H)
3. C2×#15689197C2semidirect
4. C2×#15689196C2semidirect
5. C2×#15689195C2semidirect
6. C2×#15689194C2semidirect
7. C2×#15689193C2semidirect
8. C2×#15689192C2semidirect
9. C2×#15689191C2semidirect
10. C2×#15689179C2semidirect
11. C2×#15689178C2semidirect
12. C2×#15689086C2semidirect
13. C2×#15689085C2semidirect
14. C22×(C2×D47)⋊C8C2semidirect
15. C2×C22⋊C8×D47C2semidirect
16. C2×C47×#435C2semidirect
20. C22×#10625329C22semidirect
21. C22×#10625324C22semidirect
22. C22×#10625324C22semidirect
23. C23×C47⋊C8C22semidirect
24. C22×C8×D47C22semidirect
25. C22×C8×D47C22semidirect
39. #15689197C22semidirect
40. #15689196C22semidirect
41. #15689195C22semidirect
42. #15689194C22semidirect
43. #15689193C22semidirect
44. #15689192C22semidirect
45. #15689191C22semidirect
46. #15689179C22semidirect
47. #15689178C22semidirect
48. C2×C4⋊(C47⋊C8)C22semidirect
49. C2×Dic47⋊C8C22semidirect
50. C2×Dic47⋊C8C22semidirect
51. #15689086C22semidirect
52. #15689085C22semidirect
53. C2×C22⋊(C47⋊C8)C22semidirect
54. C2×C22⋊(C47⋊C8)C22semidirect
59. C2×(C2×D47)⋊C8C22semidirect
60. C2×(C2×D47)⋊C8C22semidirect
61. C2×(C2×D47)⋊C8C22semidirect
62. C2×(C2×D47)⋊C8C22semidirect
63. C2×(C2×D47)⋊C8C22semidirect
64. C22⋊C8×D47C22semidirect
65. C2×#13093935C22semidirect
66. C2×#13093934C22semidirect
67. C2×#13093934C22semidirect
68. C22×M16×C47C22semidirect
69. C23×C8×C47C22semidirect
71. C47×#435C22semidirect
72. C2×C4⋊C8×C47C22semidirect
73. C2×C22⋊C8×C47C22semidirect
74. C2×C22⋊C8×C47C22semidirect
75. C2×#97×C47C22semidirect
103. C2×#10625329C23semidirect
106. C2×#10625324C23semidirect
107. C2×#10625324C23semidirect
113. C22×C47⋊C8C23semidirect
116. C2×C8×D47C23semidirect
117. C2×C8×D47C23semidirect
145. C4⋊(C47⋊C8)C23semidirect
146. Dic47⋊C8C23semidirect
147. Dic47⋊C8C23semidirect
148. C22⋊(C47⋊C8)C23semidirect
149. C22⋊(C47⋊C8)C23semidirect
154. (C2×D47)⋊C8C23semidirect
155. (C2×D47)⋊C8C23semidirect
156. (C2×D47)⋊C8C23semidirect
157. (C2×D47)⋊C8C23semidirect
158. #13093935C23semidirect
159. #13093934C23semidirect
160. #13093934C23semidirect
165. C2×M16×C47C23semidirect
171. C22×C8×C47C23semidirect
178. C4⋊C8×C47C23semidirect
179. C22⋊C8×C47C23semidirect
180. C22⋊C8×C47C23semidirect
181. #97×C47C23semidirect
189. C23×D47M16semidirect
323. C22×D47C2×M16semidirect
432. C2×#435D47semidirect
441. C2×C47#2973semidirect
454. C22×M16C2×D47semidirect
458. C23×C8C2×D47semidirect
480. #435C2×D47semidirect
486. C2×C4⋊C8C2×D47semidirect
501. C2×C22⋊C8C2×D47semidirect
502. C2×C22⋊C8C2×D47semidirect
506. C2×#97C2×D47semidirect
507. C47C2×#2973semidirect
544. C2×M16C22×D47semidirect
560. C22×C8C22×D47semidirect
597. C4⋊C8C22×D47semidirect
608. C22⋊C8C22×D47semidirect
609. C22⋊C8C22×D47semidirect
613. #97C22×D47semidirect
859. C2#20252413direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D4×D472
#202524132
C2×#156891972
C2×#156891962
C2×#156891952
C2×#156891942
C2×#156891932
C2×#156891922
C2×#156891912
C2×#156891792
C2×#156891782
C2×#156890862
C2×#156890852
C22×(C2×D47)⋊C82
C2×C22⋊C8×D472
C2×C47×#4352
C2×#297347