Finite Group Databasebeta

← C2×#20252432 #27081024

Subgroups — C2×#20252432 #27081024

Order 12032.

2306 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689632C211yesmaximal, characteristic
2#20252432C2116yesmaximal, direct product factor
3C2×#15689199C211yesmaximal, characteristic, complemented
4C2×#15689197C211yesmaximal, characteristic, complemented
5C2×#15689195C211yesmaximal, characteristic, complemented
6C2×#15689193C211yesmaximal, characteristic, complemented
7C2×#15689192C211yesmaximal, characteristic, complemented
8C2×C8×D188C211yesmaximal, characteristic, complemented
9C2×(C22⋊D47)⋊C8C211yesmaximal, characteristic, complemented
10C2×#15689183C211yesmaximal, characteristic, complemented
11C2×#15689182C211yesmaximal, characteristic, complemented
12C2×#15689091C211yesmaximal, characteristic, complemented
13C2×#15689088C211yesmaximal, characteristic, complemented
14C2×#15689086C211yesmaximal, characteristic, complemented
15C2×C22⋊C8×D47C211yesmaximal, characteristic, complemented
16C2×C47×#436C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C22×#10625329C2211yescharacteristic
20C22×#10625324C2211yescharacteristic, complemented
21C23×C47⋊C8C2211yescharacteristic, complemented
22C22×C8×D47C2211yescharacteristic
23C22×C8×D47C2211yescharacteristic
24C22×C8×D47C2211yescharacteristic, complemented
25#15689632C418yes—
26#15689632C2218yes—
27C2×#13094009C411yescharacteristic
28C2×#13094006C411yescharacteristic
29C2×#13094002C411yescharacteristic
30C2×#13094001C411yescharacteristic
31C2×#13093997C411yescharacteristic
32C2×#13093996C411yescharacteristic
33C2×#13093994C411yescharacteristic
34C2×#13093992C411yescharacteristic
35C2×C4×D188C2211yescharacteristic
36C2×C4×C22⋊D47C2211yescharacteristic
37C2×C4×C22⋊D47C2211yescharacteristic
38C2×#13093981C2211yescharacteristic
39#15689199C2218yescomplemented
40#15689197C2218yescomplemented
41#15689195C2218yescomplemented
42#15689193C2218yescomplemented
43#15689192C2218yescomplemented
44C8×D188C2218yescomplemented
45(C22⋊D47)⋊C8C2218yescomplemented
46#15689183C2218yescomplemented
47#15689182C2218yescomplemented
48C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
49C2×Dic47⋊C8C2211yescharacteristic, complemented
50C2×Dic47⋊C8C2211yescharacteristic, complemented
51#15689091C2218yescomplemented
52#15689088C2218yescomplemented
53#15689086C2218yescomplemented
54C2×C22⋊(C47⋊C8)C2211yescharacteristic
55C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
56C2×(C2×D47)⋊C8C2211yescharacteristic
57C2×(C2×D47)⋊C8C2211yescharacteristic
58C2×(C2×D47)⋊C8C2211yescharacteristic
59C2×(C2×D47)⋊C8C2211yescharacteristic
60C2×(C2×D47)⋊C8C2211yescharacteristic
61C2×(C2×D47)⋊C8C2211yescharacteristic
62C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
63C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
64C22⋊C8×D47C2218yescomplemented
65C2×#13093935C2211yescharacteristic, complemented
66C2×#13093934C2211yescharacteristic, complemented
67C2×C8×Dic47C2211yescharacteristic, complemented
68C22×M16×C47C2211yescharacteristic
69C22×M16×C47C2211yescharacteristic, complemented
70C2×C4×D4×C47C2211yescharacteristic
71C47×#436C2218yescomplemented
72C2×C4⋊C8×C47C2211yescharacteristic, complemented
73C2×C22⋊C8×C47C2211yescharacteristic
74C2×C22⋊C8×C47C2211yescharacteristic, complemented
75C2×C4×C8×C47C2211yescharacteristic, complemented
76C24×D47C2×C411yescharacteristic
77C2×#10625350—42no—
78C2×#10625350—42no—
79C2×#10625350C2×C414yes—
80C2×#10625350C2314yes—
81C22×Dic94C2×C411yescharacteristic
82C22×D188C2×C411yescharacteristic
83C22×D188C2×C411yescharacteristic
84C22×C22⋊D47C2×C411yescharacteristic
85C22×C22⋊D47C2×C411yescharacteristic
86C22×C22⋊D47C2×C411yescharacteristic
87C22×C22⋊D47C2×C411yescharacteristic
88C23×Dic47C2×C411yescharacteristic
89C22×C4×D47—42no—
90C22×C4×D47—42no—
91C22×C4×D47C2×C411yescharacteristic
92C22×C4×D47C2×C411yescharacteristic
93C22×C4×D47C2×C414yes—
94C22×C4×D47C2311yescharacteristic
95C22×C4×D47C2311yescharacteristic
96C22×C4×D47C2311yescharacteristic
97C22×C4×D47C2314yes—
98C2×#10625329—42no—
99C2×#10625329C2314yes—
100C2×#10625324—42no—
101C2×#10625324C2314yescomplemented
102C22×C47⋊C8—42no—
103C22×C47⋊C8C2311yescharacteristic
104C22×C47⋊C8C2311yescharacteristic
105C22×C47⋊C8C2311yescharacteristic
106C22×C47⋊C8C2311yescharacteristic
107C22×C47⋊C8C2314yescomplemented
108C2×C8×D47—42no—
109C2×C8×D47—42no—
110C2×C8×D47—42no—
111C2×C8×D47C2314yes—
112C2×C8×D47C2314yes—
113C2×C8×D47C2314yescomplemented
114#13094009C2×C418yes—
115#13094006C2×C418yes—
116#13094002C2×C418yes—
117#13094001C2×C418yes—
118#13093997C2×C418yes—
119#13093996C2×C418yes—
120#13093994C2×C418yes—
121#13093992C2×C418yes—
122C4×D188C2×C414yes—
123C4×D188C2314yes—
124C4×C22⋊D47C2×C414yes—
125C4×C22⋊D47C2×C414yes—
126C4×C22⋊D47C2314yes—
127C4×C22⋊D47C2314yes—
128#13093981C2×C414yes—
129#13093981C2314yes—
130C2×C4⋊Dic47C2×C411yescharacteristic
131C2×Dic47⋊C4C2×C411yescharacteristic
132C2×Dic47⋊C4C2×C411yescharacteristic
133C2×Dic47⋊C4C2×C411yescharacteristic
134C2×Dic47⋊C4C2×C411yescharacteristic
135C2×C22⋊Dic47C2×C411yescharacteristic
136C2×C22⋊Dic47C2×C411yescharacteristic
137C2×(C2×D47)⋊C4C2×C411yescharacteristic
138C2×(C2×D47)⋊C4C2×C411yescharacteristic
139C2×(C2×D47)⋊C4C2×C411yescharacteristic
140C2×(C2×D47)⋊C4C2×C411yescharacteristic
141C2×(C2×D47)⋊C4C2×C411yescharacteristic
142C2×(C2×D47)⋊C4C2×C411yescharacteristic
143C2×C4×Dic47C2311yescharacteristic
144C4⋊(C47⋊C8)C2314yescomplemented
145Dic47⋊C8C2314yescomplemented
146Dic47⋊C8C2314yescomplemented
147C22⋊(C47⋊C8)C2314yes—
148C22⋊(C47⋊C8)C2314yescomplemented
149(C2×D47)⋊C8C2314yes—
150(C2×D47)⋊C8C2314yes—
151(C2×D47)⋊C8C2314yes—
152(C2×D47)⋊C8C2314yes—
153(C2×D47)⋊C8C2314yes—
154(C2×D47)⋊C8C2314yes—
155(C2×D47)⋊C8C2314yescomplemented
156(C2×D47)⋊C8C2314yescomplemented
157#13093935C2314yescomplemented
158#13093934C2314yescomplemented
159C8×Dic47C2314yescomplemented
160C22×D4×C47C2×C411yescharacteristic
161C23×C4×C47C2311yescharacteristic
162C23×C4×C47C2311yescharacteristic
163C2×M16×C47—42no—
164C2×M16×C47—42no—
165C2×M16×C47C2314yes—
166C2×M16×C47C2314yescomplemented
167C22×C8×C47C2311yescharacteristic
168C22×C8×C47C2311yescharacteristic
169C22×C8×C47C2311yescharacteristic
170C22×C8×C47C2311yescharacteristic
171C4×D4×C47C2×C414yes—
172C4×D4×C47C2314yes—
173C2×C4⋊C4×C47C2×C411yescharacteristic
174C2×C22⋊C4×C47C2×C411yescharacteristic
175C2×C22⋊C4×C47C2×C411yescharacteristic
176C2×C42×C47C2311yescharacteristic
177C4⋊C8×C47C2314yescomplemented
178C22⋊C8×C47C2314yes—
179C22⋊C8×C47C2314yescomplemented
180C4×C8×C47C2314yescomplemented
181C24×C47C22×C411yescharacteristic
182C24×C47C22×C411yescharacteristic
183C23×D47—24no—
184C23×D47—42no—
185C23×D47—42no—
186C23×D47C22×C411yescharacteristic
187C23×D47C22×C411yescharacteristic
188C23×D47C22×C411yescharacteristic
189C23×D47C22×C414yes—
190C2×D4×C47—42no—
191C2×D4×C47C22×C414yes—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47—22no—
195C22×C4×C47—22no—
196C22×C4×C47C22×C411yescharacteristic
197C22×C4×C47C22×C411yescharacteristic
198C22×C4×C47C22×C411yescharacteristic
199C22×C4×C47C22×C411yescharacteristic
200C22×C4×C47C22×C412yes—
201C22×C4×C47C22×C412yes—
202C22×C4×C47C2412yes—
203C22×C4×C47C2412yes—
204C22×C4×C47C2411yescharacteristic
205C2×C22⋊D47—24no—
206C2×C22⋊D47—42no—
207C2×C22⋊D47—42no—
208C2×C22⋊D47—42no—
209C2×C22⋊D47C22×C414yes—
210C2×C22⋊D47C22×C414yes—
211C2×C22⋊D47C22×C414yes—
212C2×C22⋊D47C22×C414yes—
213C22×Dic47—42no—
214C22×Dic47C22×C411yescharacteristic
215C22×Dic47C22×C411yescharacteristic
216C22×Dic47C22×C411yescharacteristic
217C22×Dic47C22×C411yescharacteristic
218C22×Dic47C22×C411yescharacteristic
219C22×Dic47C22×C414yes—
220#10625350—48no—
221#10625350—44no—
222#10625350—44no—
223C2×D188—24no—
224C2×D188—42no—
225C2×D188C22×C414yes—
226C2×D188C22×C414yes—
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—44no—
235C2×C4×D47—44no—
236C2×C4×D47—42no—
237C2×C4×D47—42no—
238C2×C4×D47C22×C412yes—
239C2×C4×D47C22×C412yes—
240C2×C4×D47C22×C412yes—
241C2×C4×D47C22×C414yes—
242C2×C4×D47C22×C414yes—
243C2×C4×D47C2412yes—
244C2×C4×D47C2412yes—
245C2×C4×D47C2412yes—
246C2×Dic94—42no—
247C2×Dic94C22×C414yes—
248M16×C47—44no—
249M16×C47—44no—
250C2×C8×C47—22no—
251C2×C8×C47—22no—
252C2×C8×C47—22no—
253C2×C8×C47—22no—
254C2×C8×C47C2412yes—
255C2×C8×C47C2412yes—
256C2×C8×C47C2412yes—
257C2×C8×C47C2412yes—
258C4⋊C4×C47C22×C414yes—
259C22⋊C4×C47C22×C414yes—
260C22⋊C4×C47C22×C414yes—
261C42×C47C22×C412yes—
262C42×C47C2412yes—
263C22⋊Dic47C22×C414yes—
264C22⋊Dic47C22×C414yes—
265(C2×D47)⋊C4C22×C414yes—
266(C2×D47)⋊C4C22×C414yes—
267(C2×D47)⋊C4C22×C414yes—
268(C2×D47)⋊C4C22×C414yes—
269(C2×D47)⋊C4C22×C414yes—
270(C2×D47)⋊C4C22×C414yes—
271C4⋊Dic47C22×C414yes—
272Dic47⋊C4C22×C414yes—
273Dic47⋊C4C22×C414yes—
274Dic47⋊C4C22×C414yes—
275Dic47⋊C4C22×C414yes—
276C4×Dic47C22×C412yes—
277C4×Dic47C2412yes—
278#10625329—44no—
279C2×C47⋊C8—22no—
280C2×C47⋊C8—22no—
281C2×C47⋊C8—22no—
282C2×C47⋊C8—22no—
283C2×C47⋊C8—44no—
284C2×C47⋊C8C2412yes—
285C2×C47⋊C8C2412yes—
286C2×C47⋊C8C2412yes—
287C2×C47⋊C8C2412yes—
288#10625324—44no—
289C8×D47—44no—
290C8×D47—44no—
291C8×D47—44no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47C23×C412yes—
299C23×C47C23×C412yes—
300C23×C47C23×C411yescharacteristic
301C22×D47—22no—
302C22×D47—22no—
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—22no—
307C22×D47—22no—
308C22×D47—22no—
309C22×D47—28no—
310C22×D47—44no—
311C22×D47—44no—
312C22×D47—416no—
313C22×D47#13114yes—
314C22×D47C23×C412yes—
315C22×D47C23×C412yes—
316C22×D47C23×C412yes—
317D4×C47—44no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—24no—
323C2×C4×C47—24no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47C23×C412yes—
329C2×C4×C47C23×C412yes—
330C2×C4×C47C23×C412yes—
331C2×C4×C47C23×C412yes—
332C2×C4×C47C23×C411yescharacteristic
333C2×C4×C47H(5,𝔽2)12yes—
334C2×C4×C47H(5,𝔽2)12yes—
335C2×C4×C47C2511yescharacteristic
336C22⋊D47—28no—
337C22⋊D47—44no—
338C22⋊D47—44no—
339C22⋊D47—44no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—44no—
346C2×Dic47C23×C412yes—
347C2×Dic47C23×C412yes—
348C2×Dic47C23×C412yes—
349C2×Dic47C23×C412yes—
350C2×Dic47C23×C412yes—
351D188—28no—
352D188—44no—
353C4×D47—24no—
354C4×D47—24no—
355C4×D47—24no—
356C4×D47—22no—
357C4×D47—22no—
358C4×D47—22no—
359C4×D47—22no—
360C4×D47—22no—
361C4×D47—22no—
362C4×D47—44no—
363C4×D47—44no—
364Dic94—44no—
365C8×C47—22no—
366C8×C47—22no—
367C8×C47—22no—
368C8×C47—22no—
369C47⋊C8—22no—
370C47⋊C8—22no—
371C47⋊C8—22no—
372C47⋊C8—22no—
373C2×#2976—471nomaximal, Sylow
374C22×C47—22no—
375C22×C47—22no—
376C22×C47—22no—
377C22×C47—22no—
378C22×C47—22no—
379C22×C47—22no—
380C22×C47—44no—
381C22×C47—44no—
382C22×C47#51812yes—
383C22×C47C2×#13112yes—
384C22×C47#56812yes—
385C22×C47C24×C411yescharacteristic
386C2×D47—22no—
387C2×D47—28no—
388C2×D47—22no—
389C2×D47—22no—
390C2×D47—22no—
391C2×D47—22no—
392C2×D47—22no—
393C2×D47—22no—
394C2×D47—22no—
395C2×D47—416no—
396C2×D47—44no—
397C2×D47—44no—
398C2×D47C2×#13114yes—
399C4×C47—22no—
400C4×C47—22no—
401C4×C47—22no—
402C4×C47—22no—
403C4×C47#51812yes—
404C4×C47C2×H(5,𝔽2)11yescharacteristic
405C4×C47C2×H(5,𝔽2)11yescharacteristic
406Dic47—22no—
407Dic47—22no—
408Dic47—22no—
409Dic47—22no—
410Dic47—22no—
411C2×#525—471no—
412#2976—4716no—
413C2×#436—471no—
414C2×#436D4711yescharacteristic, complemented
415C2×#435—471no—
416C2×#435—471no—
417C2×#435—471no—
418C2×#435—471no—
419C2×C8×D4—471no—
420C2×C8×D4—471no—
421C2×#433—471no—
422C2×#433—471no—
423C2×#408—471no—
424C2×#408—471no—
425C2×#407—471no—
426C22×C22⋊C8—471no—
427C2×C47—42no—
428C2×C47—42no—
429C2×C47#297614yescomplemented
430C2×C47C2×#51811yescharacteristic
431C2×C47C22×#13111yescharacteristic
432C2×C47C2×#56811yescharacteristic
433D47—24no—
434D47—42no—
435D47—42no—
436C22×#41—471no—
437C24×C4—471no—
438C22×M16—471no—
439C22×M16—471no—
440C22×M16C2×D4711yescharacteristic
441C22×M16C2×D4711yescharacteristic, complemented
442C23×C8—471no—
443C23×C8—471no—
444C23×C8—471no—
445C23×C8—471no—
446#525—478no—
447#525—478no—
448C2×#123—471no—
449C2×#123—471no—
450C2×C22⋊Q8—471no—
451C2×C22⋊Q8—471no—
452C2×#121—471no—
453C2×#121—471no—
454C2×#120—471no—
455C2×#120—471no—
456C2×C4×D4—471no—
457C2×C4×D4—471no—
458C2×C4×D4—471no—
459C2×C4×D4C2×D4711yescharacteristic
460C2×#117—471no—
461#436—478no—
462#436C2×D4718yescomplemented
463#435—478no—
464#435—478no—
465#435—478no—
466#435—478no—
467C8×D4—478no—
468C8×D4—478no—
469#433—478no—
470#433—478no—
471C2×C4⋊C8—471no—
472C2×C4⋊C8—471no—
473C2×C4⋊C8—471no—
474C2×C4⋊C8C2×D4711yescharacteristic, complemented
475#408—478no—
476#408—478no—
477#407—478no—
478C2×C22⋊C8—471no—
479C2×C22⋊C8—471no—
480C2×C22⋊C8—471no—
481C2×C22⋊C8—471no—
482C2×C22⋊C8—471no—
483C2×C22⋊C8—471no—
484C2×C22⋊C8—471no—
485C2×C22⋊C8—471no—
486C2×C22⋊C8—471no—
487C2×C22⋊C8—471no—
488C2×C22⋊C8—478no—
489C2×C22⋊C8C2×D4711yescharacteristic
490C2×C22⋊C8C2×D4711yescharacteristic, complemented
491C2×#97—471no—
492C2×#97—471no—
493C2×C4×C8—471no—
494C2×C4×C8C2×D4711yescharacteristic, complemented
495C47C2×#297611yescharacteristic, complemented, Sylow
496C25—471no—
497C2×#41—474no—
498C2×#41—474no—
499C2×#41—1882no—
500C2×#41—1882no—
501C22×Q8—471no—
502C22×D4—471no—
503C22×D4—471no—
504C22×D4—471no—
505C22×D4—471no—
506C22×D4—471no—
507C22×D4—471no—
508C22×D4C4×D4711yescharacteristic
509C23×C4—471no—
510C23×C4—471no—
511C23×C4—471no—
512C23×C4—471no—
513C23×C4—471no—
514C23×C4—471no—
515C23×C4—474no—
516C23×C4—474no—
517C23×C4—1882no—
518C23×C4—1882no—
519C23×C4C22×D4711yescharacteristic
520C23×C4C22×D4711yescharacteristic
521C2×M16—42no—
522C2×M16—42no—
523C2×M16—474no—
524C2×M16—474no—
525C2×M16—1882no—
526C2×M16—1882no—
527C2×M16C22×D4714yes—
528C2×M16C22×D4714yescomplemented
529C22×C8—471no—
530C22×C8—471no—
531C22×C8—471no—
532C22×C8—471no—
533C22×C8—474no—
534C22×C8—474no—
535C22×C8—474no—
536C22×C8—474no—
537C22×C8—1882no—
538C22×C8—1882no—
539C22×C8—1882no—
540C22×C8—1882no—
541C22×C8C22×D4711yescharacteristic
542C22×C8C22×D4711yescharacteristic
543C22×C8C22×D4711yescharacteristic
544C22×C8C22×D4711yescharacteristic
545#123—478no—
546#123—478no—
547C22⋊Q8—478no—
548C22⋊Q8—478no—
549#121—478no—
550#121—478no—
551#120—478no—
552#120—478no—
553C4×D4—474no—
554C4×D4—474no—
555C4×D4—474no—
556C4×D4—474no—
557C4×D4—474no—
558C4×D4—474no—
559C4×D4C4×D4714yes—
560C4×D4C22×D4714yes—
561#117—474no—
562#117—474no—
563C2×C4⋊C4—471no—
564C2×C4⋊C4—471no—
565C2×C4⋊C4—471no—
566C2×C4⋊C4—471no—
567C2×C4⋊C4—471no—
568C2×C4⋊C4C4×D4711yescharacteristic
569C2×C22⋊C4—471no—
570C2×C22⋊C4—471no—
571C2×C22⋊C4—471no—
572C2×C22⋊C4—471no—
573C2×C22⋊C4—471no—
574C2×C22⋊C4—471no—
575C2×C22⋊C4—471no—
576C2×C22⋊C4—471no—
577C2×C22⋊C4C4×D4711yescharacteristic
578C2×C22⋊C4C4×D4711yescharacteristic
579C2×C42—471no—
580C2×C42C22×D4711yescharacteristic
581C4⋊C8—474no—
582C4⋊C8—474no—
583C4⋊C8—474no—
584C4⋊C8C22×D4714yescomplemented
585C22⋊C8—474no—
586C22⋊C8—474no—
587C22⋊C8—474no—
588C22⋊C8—474no—
589C22⋊C8—474no—
590C22⋊C8—474no—
591C22⋊C8—474no—
592C22⋊C8—474no—
593C22⋊C8—474no—
594C22⋊C8—474no—
595C22⋊C8C22×D4714yes—
596C22⋊C8C22×D4714yescomplemented
597#97—474no—
598#97—474no—
599C4×C8—474no—
600C4×C8C22×D4714yescomplemented
601C24—471no—
602C24—471no—
603C24—471no—
604C24—474no—
605C24—944no—
606C24—1882no—
607C24—1882no—
608C24C2×C4×D4711yescharacteristic
609C24C2×C4×D4711yescharacteristic
610#41—1888no—
611#41—1884no—
612#41—1884no—
613C2×Q8—474no—
614C2×Q8—1882no—
615C2×D4—42no—
616C2×D4—474no—
617C2×D4—474no—
618C2×D4—474no—
619C2×D4—474no—
620C2×D4—474no—
621C2×D4—474no—
622C2×D4—944no—
623C2×D4—944no—
624C2×D4—1882no—
625C2×D4—1882no—
626C2×D4—1882no—
627C2×D4—1882no—
628C2×D4C2×C4×D4714yes—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—471no—
634C22×C4—471no—
635C22×C4—471no—
636C22×C4—471no—
637C22×C4—471no—
638C22×C4—474no—
639C22×C4—472no—
640C22×C4—472no—
641C22×C4—472no—
642C22×C4—472no—
643C22×C4—472no—
644C22×C4—472no—
645C22×C4—474no—
646C22×C4—474no—
647C22×C4—942no—
648C22×C4—942no—
649C22×C4—942no—
650C22×C4—942no—
651C22×C4—942no—
652C22×C4—942no—
653C22×C4—1888no—
654C22×C4—1884no—
655C22×C4—1884no—
656C22×C4—1882no—
657C22×C4—1882no—
658C22×C4—1882no—
659C22×C4C2×C4×D4711yescharacteristic
660C22×C4C2×C4×D4711yescharacteristic
661C22×C4C2×C4×D4711yescharacteristic
662C22×C4C2×C4×D4711yescharacteristic
663C22×C4C2×C4×D4712yes—
664C22×C4C2×C4×D4712yes—
665C22×C4C23×D4712yes—
666C22×C4C23×D4712yes—
667C22×C4C23×D4711yescharacteristic
668M16—44no—
669M16—44no—
670M16—1884no—
671M16—1884no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—22no—
676C2×C8—472no—
677C2×C8—472no—
678C2×C8—472no—
679C2×C8—472no—
680C2×C8—942no—
681C2×C8—942no—
682C2×C8—942no—
683C2×C8—942no—
684C2×C8—1884no—
685C2×C8—1884no—
686C2×C8—1884no—
687C2×C8—1884no—
688C2×C8C23×D4712yes—
689C2×C8C23×D4712yes—
690C2×C8C23×D4712yes—
691C2×C8C23×D4712yes—
692C4⋊C4—474no—
693C4⋊C4—474no—
694C4⋊C4—474no—
695C4⋊C4—474no—
696C4⋊C4—474no—
697C4⋊C4C2×C4×D4714yes—
698C22⋊C4—474no—
699C22⋊C4—474no—
700C22⋊C4—474no—
701C22⋊C4—474no—
702C22⋊C4—474no—
703C22⋊C4—474no—
704C22⋊C4—474no—
705C22⋊C4—474no—
706C22⋊C4C2×C4×D4714yes—
707C22⋊C4C2×C4×D4714yes—
708C42—472no—
709C42—472no—
710C42C2×C4×D4712yes—
711C42C23×D4712yes—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—474no—
719C23—472no—
720C23—472no—
721C23—472no—
722C23—948no—
723C23—942no—
724C23—942no—
725C23—942no—
726C23—942no—
727C23—942no—
728C23—942no—
729C23—942no—
730C23—942no—
731C23—1884no—
732C23—1884no—
733C23—18816no—
734C23C22×C4×D4712yes—
735C23C22×C4×D4712yes—
736C23C22×C4×D4711yescharacteristic
737Q8—1884no—
738D4—44no—
739D4—948no—
740D4—948no—
741D4—1884no—
742D4—1884no—
743D4—1884no—
744D4—1884no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—472no—
756C2×C4—472no—
757C2×C4—472no—
758C2×C4—472no—
759C2×C4—472no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—942no—
764C2×C4—942no—
765C2×C4—944no—
766C2×C4—944no—
767C2×C4—944no—
768C2×C4—942no—
769C2×C4—942no—
770C2×C4—942no—
771C2×C4—942no—
772C2×C4—942no—
773C2×C4—942no—
774C2×C4—1884no—
775C2×C4—1884no—
776C2×C4—1884no—
777C2×C4C22×C4×D4712yes—
778C2×C4C22×C4×D4712yes—
779C2×C4C22×C4×D4712yes—
780C2×C4C22×C4×D4712yes—
781C2×C4C22×C4×D4711yescharacteristic
782C2×C4#1309406912yes—
783C2×C4#1309407012yes—
784C2×C4C24×D4711yescharacteristic
785C8—22no—
786C8—22no—
787C8—22no—
788C8—22no—
789C8—942no—
790C8—942no—
791C8—942no—
792C8—942no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—44no—
800C22—44no—
801C22—474no—
802C22—948no—
803C22—942no—
804C22—942no—
805C22—942no—
806C22—942no—
807C22—942no—
808C22—942no—
809C22—942no—
810C22—942no—
811C22—18816no—
812C22—1884no—
813C22—1884no—
814C22#1568959512yes—
815C22#131×D4712yes—
816C22#1568988912yes—
817C22C23×C4×D4711yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—942no—
823C4—942no—
824C4—942no—
825C4—942no—
826C4—942no—
827C4#1568959512yes—
828C4C2×#1309406911yescharacteristic
829C4C2×#1309407011yescharacteristic
830C2—42no—
831C2—42no—
832C2—944no—
833C2—1882no—
834C2—1882no—
835C2#2025243214yesdirect product factor
836C2C2×#1568959511yescharacteristic
837C2C2×#131×D4711yescharacteristic
838C2C2×#1568988911yescharacteristic
subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC2×C4C24×D47
FittingC2×C47×#436C2
socleC23×C47C23×C4
prime radicalC2×#15689632C2
cosocleC2×C4×C47C25
hypercenterC2×#436D47
hypocenterC47C2×#2976
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
2. #20252432C2direct (N × H)
3. C2×#15689199C2semidirect
4. C2×#15689197C2semidirect
5. C2×#15689195C2semidirect
6. C2×#15689193C2semidirect
7. C2×#15689192C2semidirect
8. C2×C8×D188C2semidirect
9. C2×(C22⋊D47)⋊C8C2semidirect
10. C2×#15689183C2semidirect
11. C2×#15689182C2semidirect
12. C2×#15689091C2semidirect
13. C2×#15689088C2semidirect
14. C2×#15689086C2semidirect
15. C2×C22⋊C8×D47C2semidirect
16. C2×C47×#436C2semidirect
20. C22×#10625324C22semidirect
21. C23×C47⋊C8C22semidirect
24. C22×C8×D47C22semidirect
39. #15689199C22semidirect
40. #15689197C22semidirect
41. #15689195C22semidirect
42. #15689193C22semidirect
43. #15689192C22semidirect
44. C8×D188C22semidirect
45. (C22⋊D47)⋊C8C22semidirect
46. #15689183C22semidirect
47. #15689182C22semidirect
48. C2×C4⋊(C47⋊C8)C22semidirect
49. C2×Dic47⋊C8C22semidirect
50. C2×Dic47⋊C8C22semidirect
51. #15689091C22semidirect
52. #15689088C22semidirect
53. #15689086C22semidirect
55. C2×C22⋊(C47⋊C8)C22semidirect
62. C2×(C2×D47)⋊C8C22semidirect
63. C2×(C2×D47)⋊C8C22semidirect
64. C22⋊C8×D47C22semidirect
65. C2×#13093935C22semidirect
66. C2×#13093934C22semidirect
67. C2×C8×Dic47C22semidirect
69. C22×M16×C47C22semidirect
71. C47×#436C22semidirect
72. C2×C4⋊C8×C47C22semidirect
74. C2×C22⋊C8×C47C22semidirect
75. C2×C4×C8×C47C22semidirect
101. C2×#10625324C23semidirect
107. C22×C47⋊C8C23semidirect
113. C2×C8×D47C23semidirect
144. C4⋊(C47⋊C8)C23semidirect
145. Dic47⋊C8C23semidirect
146. Dic47⋊C8C23semidirect
148. C22⋊(C47⋊C8)C23semidirect
155. (C2×D47)⋊C8C23semidirect
156. (C2×D47)⋊C8C23semidirect
157. #13093935C23semidirect
158. #13093934C23semidirect
159. C8×Dic47C23semidirect
166. C2×M16×C47C23semidirect
177. C4⋊C8×C47C23semidirect
179. C22⋊C8×C47C23semidirect
180. C4×C8×C47C23semidirect
414. C2×#436D47semidirect
429. C2×C47#2976semidirect
441. C22×M16C2×D47semidirect
462. #436C2×D47semidirect
474. C2×C4⋊C8C2×D47semidirect
490. C2×C22⋊C8C2×D47semidirect
494. C2×C4×C8C2×D47semidirect
495. C47C2×#2976semidirect
528. C2×M16C22×D47semidirect
584. C4⋊C8C22×D47semidirect
596. C22⋊C8C22×D47semidirect
600. C4×C8C22×D47semidirect
835. C2#20252432direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896322
#202524322
C2×#156891992
C2×#156891972
C2×#156891952
C2×#156891932
C2×#156891922
C2×C8×D1882
C2×(C22⋊D47)⋊C82
C2×#156891832
C2×#156891822
C2×#156890912
C2×#156890882
C2×#156890862
C2×C22⋊C8×D472
C2×C47×#4362
C2×#297647