Finite Group Databasebeta

← C2×#20249162 #26382632

Subgroups — C2×#20249162 #26382632

Order 12032.

4378 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093994C211yesmaximal, characteristic
2C22×C22⋊C4×D47C211yesmaximal, characteristic, complemented
3#20249162C2116yesmaximal, direct product factor
4C2×#15689052C211yesmaximal, characteristic, complemented
5C2×#15689051C211yesmaximal, characteristic, complemented
6C2×#15689050C211yesmaximal, characteristic, complemented
7C2×#15689041C211yesmaximal, characteristic, complemented
8C2×#15689040C211yesmaximal, characteristic, complemented
9C2×#15689039C211yesmaximal, characteristic, complemented
10C2×#15689038C211yesmaximal, characteristic, complemented
11C2×#15689001C211yesmaximal, characteristic, complemented
12C2×#15689001C211yesmaximal, characteristic, complemented
13C2×#15688997C211yesmaximal, characteristic, complemented
14C2×#15688994C211yesmaximal, characteristic, complemented
15C2×#15688978C211yesmaximal, characteristic, complemented
16C2×C47×#397C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C23×D188C2211yescharacteristic
20C23×C22⋊D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C23×C4×D47C2211yescharacteristic
23C2×#13093994—28no—
24C2×#13093994C2218yes—
25C22×C4⋊Dic47C2211yescharacteristic, complemented
26C22×Dic47⋊C4C2211yescharacteristic, complemented
27C22×Dic47⋊C4C2211yescharacteristic, complemented
28C22×C22⋊Dic47C2211yescharacteristic
29C22×C22⋊Dic47C2211yescharacteristic
30C22×(C2×D47)⋊C4C2211yescharacteristic
31C22×(C2×D47)⋊C4C2211yescharacteristic
32C22×(C2×D47)⋊C4C2211yescharacteristic
33C22×(C2×D47)⋊C4C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×(C2×D47)⋊C4C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
39C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
40C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
41C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
42C2×C22⋊C4×D47—28no—
43C2×C22⋊C4×D47C2218yescomplemented
44#15689052C2218yescomplemented
45#15689051C2218yescomplemented
46#15689050C2218yescomplemented
47#15689041C2218yescomplemented
48#15689040C2218yescomplemented
49#15689039C2218yescomplemented
50#15689038C2218yescomplemented
51#15689001C2218yescomplemented
52#15689001C2218yescomplemented
53#15688997C2218yescomplemented
54#15688994C2218yescomplemented
55#15688978C2218yescomplemented
56C2×C47⋊#95C2211yescharacteristic, complemented
57C2×C47⋊#95C2211yescharacteristic, complemented
58C2×C47⋊#95C2211yescharacteristic, complemented
59C2×C47⋊#95C2211yescharacteristic, complemented
60C2×C47⋊#95C2211yescharacteristic, complemented
61C22×C4⋊C4×C47C2211yescharacteristic, complemented
62C22×C22⋊C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C47×#397C2218yescomplemented
66C2×#95×C47C2211yescharacteristic, complemented
67C2×#95×C47C2211yescharacteristic, complemented
68C2×#95×C47C2211yescharacteristic, complemented
69C24×D47—24no—
70C24×D47—24no—
71C24×D47—42no—
72C24×D47—42no—
73C24×D47—42no—
74C24×D47—42no—
75C24×D47D418yes—
76C24×D47C2311yescharacteristic
77C24×D47C2311yescharacteristic
78C24×D47C2311yescharacteristic
79C24×D47C2314yes—
80C22×D188—24no—
81C22×D188—24no—
82C22×D188—24no—
83C22×D188—24no—
84C22×D188—42no—
85C22×D188—42no—
86C22×D188C2314yes—
87C22×D188C2314yes—
88C22×C22⋊D47—24no—
89C22×C22⋊D47—42no—
90C22×C22⋊D47—42no—
91C22×C22⋊D47C2314yes—
92C23×Dic47C2311yescharacteristic
93C23×Dic47C2311yescharacteristic
94C23×Dic47C2311yescharacteristic
95C23×Dic47C2311yescharacteristic
96C23×Dic47C2311yescharacteristic
97C22×C4×D47—24no—
98C22×C4×D47—24no—
99C22×C4×D47—42no—
100C22×C4×D47—42no—
101C22×C4×D47—42no—
102C22×C4×D47—42no—
103C22×C4×D47C2314yes—
104C22×C4×D47C2314yes—
105#13093994—232no—
106C2×C4⋊Dic47—42no—
107C2×C4⋊Dic47C2314yescomplemented
108C2×Dic47⋊C4—42no—
109C2×Dic47⋊C4—42no—
110C2×Dic47⋊C4C2314yescomplemented
111C2×Dic47⋊C4C2314yescomplemented
112C2×C22⋊Dic47—24no—
113C2×C22⋊Dic47—42no—
114C2×C22⋊Dic47C2314yes—
115C2×C22⋊Dic47C2314yes—
116C2×(C2×D47)⋊C4—24no—
117C2×(C2×D47)⋊C4—24no—
118C2×(C2×D47)⋊C4—24no—
119C2×(C2×D47)⋊C4—24no—
120C2×(C2×D47)⋊C4—24no—
121C2×(C2×D47)⋊C4—24no—
122C2×(C2×D47)⋊C4—42no—
123C2×(C2×D47)⋊C4—42no—
124C2×(C2×D47)⋊C4—42no—
125C2×(C2×D47)⋊C4—42no—
126C2×(C2×D47)⋊C4—42no—
127C2×(C2×D47)⋊C4—42no—
128C2×(C2×D47)⋊C4C2314yes—
129C2×(C2×D47)⋊C4C2314yes—
130C2×(C2×D47)⋊C4C2314yes—
131C2×(C2×D47)⋊C4C2314yes—
132C2×(C2×D47)⋊C4C2314yes—
133C2×(C2×D47)⋊C4C2314yes—
134C2×(C2×D47)⋊C4C2314yes—
135C2×(C2×D47)⋊C4C2314yes—
136C2×(C2×D47)⋊C4C2314yescomplemented
137C2×(C2×D47)⋊C4C2314yescomplemented
138C2×(C2×D47)⋊C4C2314yescomplemented
139C2×(C2×D47)⋊C4C2314yescomplemented
140C22⋊C4×D47—232no—
141C47⋊#95C2314yescomplemented
142C47⋊#95C2314yescomplemented
143C47⋊#95C2314yescomplemented
144C47⋊#95C2314yescomplemented
145C47⋊#95C2314yescomplemented
146C25×C47C2311yescharacteristic
147C23×C4×C47C2311yescharacteristic
148C23×C4×C47C2311yescharacteristic
149C23×C4×C47C2311yescharacteristic
150C23×C4×C47C2311yescharacteristic
151C23×C4×C47C2311yescharacteristic
152C23×C4×C47C2311yescharacteristic
153C2×C4⋊C4×C47—42no—
154C2×C4⋊C4×C47C2314yescomplemented
155C2×C22⋊C4×C47—24no—
156C2×C22⋊C4×C47—24no—
157C2×C22⋊C4×C47—42no—
158C2×C22⋊C4×C47C2314yes—
159C2×C22⋊C4×C47C2314yes—
160C2×C22⋊C4×C47C2314yes—
161#95×C47C2314yescomplemented
162#95×C47C2314yescomplemented
163#95×C47C2314yescomplemented
164C24×C47—22no—
165C24×C47—22no—
166C24×C47—22no—
167C24×C47—22no—
168C24×C47—22no—
169C24×C47—22no—
170C24×C47C2×D414yes—
171C24×C47C2412yes—
172C24×C47C2411yescharacteristic
173C23×D47—22no—
174C23×D47—22no—
175C23×D47—22no—
176C23×D47—22no—
177C23×D47—22no—
178C23×D47—22no—
179C23×D47—22no—
180C23×D47—22no—
181C23×D47—22no—
182C23×D47—22no—
183C23×D47—232no—
184C23×D47—28no—
185C23×D47—28no—
186C23×D47—22no—
187C23×D47—22no—
188C23×D47—22no—
189C23×D47—22no—
190C23×D47—22no—
191C23×D47—22no—
192C23×D47—22no—
193C23×D47—416no—
194C23×D47—416no—
195C23×D47—44no—
196C23×D47—44no—
197C23×D47—44no—
198C23×D47—44no—
199C23×D47—416no—
200C23×D47—416no—
201C23×D47—416no—
202C23×D47—416no—
203C23×D47C2×D414yes—
204C23×D47C2×D414yes—
205C23×D47C2×D4116yes—
206C23×D47#4114yes—
207C23×D47#4114yes—
208C23×D47C2412yes—
209C23×D47C2412yes—
210C23×D47C2412yes—
211C22×C4×C47—22no—
212C22×C4×C47—22no—
213C22×C4×C47—22no—
214C22×C4×C47—22no—
215C22×C4×C47—22no—
216C22×C4×C47—22no—
217C22×C4×C47—22no—
218C22×C4×C47—22no—
219C22×C4×C47—22no—
220C22×C4×C47—22no—
221C22×C4×C47—22no—
222C22×C4×C47—22no—
223C22×C4×C47—22no—
224C22×C4×C47—22no—
225C22×C4×C47—22no—
226C22×C4×C47—22no—
227C22×C4×C47—22no—
228C22×C4×C47—22no—
229C22×C4×C47C2412yes—
230C22×C4×C47C2412yes—
231C22×C4×C47C2412yes—
232C22×C4×C47C2412yes—
233C22×C4×C47C2412yes—
234C22×C4×C47C2412yes—
235C2×C22⋊D47—28no—
236C2×C22⋊D47—44no—
237C2×C22⋊D47—44no—
238C2×C22⋊D47—416no—
239C22×Dic47—22no—
240C22×Dic47—22no—
241C22×Dic47—22no—
242C22×Dic47—22no—
243C22×Dic47—22no—
244C22×Dic47—22no—
245C22×Dic47—22no—
246C22×Dic47—22no—
247C22×Dic47—22no—
248C22×Dic47—22no—
249C22×Dic47—22no—
250C22×Dic47—22no—
251C22×Dic47—22no—
252C22×Dic47—22no—
253C22×Dic47—22no—
254C22×Dic47C2412yes—
255C22×Dic47C2412yes—
256C22×Dic47C2412yes—
257C22×Dic47C2412yes—
258C22×Dic47C2412yes—
259C2×D188—28no—
260C2×D188—28no—
261C2×D188—28no—
262C2×D188—28no—
263C2×D188—44no—
264C2×D188—44no—
265C2×D188—416no—
266C2×D188—416no—
267C2×C4×D47—28no—
268C2×C4×D47—28no—
269C2×C4×D47—44no—
270C2×C4×D47—44no—
271C2×C4×D47—44no—
272C2×C4×D47—44no—
273C2×C4×D47—416no—
274C2×C4×D47—416no—
275C4⋊C4×C47—44no—
276C22⋊C4×C47—28no—
277C22⋊C4×C47—28no—
278C22⋊C4×C47—44no—
279C22⋊Dic47—28no—
280C22⋊Dic47—44no—
281(C2×D47)⋊C4—28no—
282(C2×D47)⋊C4—28no—
283(C2×D47)⋊C4—28no—
284(C2×D47)⋊C4—28no—
285(C2×D47)⋊C4—28no—
286(C2×D47)⋊C4—28no—
287(C2×D47)⋊C4—44no—
288(C2×D47)⋊C4—44no—
289(C2×D47)⋊C4—44no—
290(C2×D47)⋊C4—44no—
291(C2×D47)⋊C4—44no—
292(C2×D47)⋊C4—44no—
293C4⋊Dic47—44no—
294Dic47⋊C4—44no—
295Dic47⋊C4—44no—
296C23×C47—28no—
297C23×C47—28no—
298C23×C47—28no—
299C23×C47—22no—
300C23×C47—22no—
301C23×C47—22no—
302C23×C47—22no—
303C23×C47—22no—
304C23×C47—22no—
305C23×C47—44no—
306C23×C47—44no—
307C23×C47—44no—
308C23×C47—44no—
309C23×C47C22×D414yes—
310C23×C47C22×D412yes—
311C23×C47C2×#4112yes—
312C23×C47C2×#4112yes—
313C23×C47H(5,𝔽2)12yes—
314C23×C47H(5,𝔽2)12yes—
315C23×C47H(5,𝔽2)12yes—
316C23×C47H(5,𝔽2)12yes—
317C23×C47C2511yescharacteristic
318C22×D47—28no—
319C22×D47—28no—
320C22×D47—28no—
321C22×D47—28no—
322C22×D47—28no—
323C22×D47—28no—
324C22×D47—22no—
325C22×D47—22no—
326C22×D47—22no—
327C22×D47—22no—
328C22×D47—28no—
329C22×D47—28no—
330C22×D47—28no—
331C22×D47—22no—
332C22×D47—22no—
333C22×D47—22no—
334C22×D47—22no—
335C22×D47—22no—
336C22×D47—22no—
337C22×D47—232no—
338C22×D47—22no—
339C22×D47—22no—
340C22×D47—22no—
341C22×D47—22no—
342C22×D47—22no—
343C22×D47—22no—
344C22×D47—22no—
345C22×D47—416no—
346C22×D47—416no—
347C22×D47—4128no—
348C22×D47—416no—
349C22×D47—416no—
350C22×D47—416no—
351C22×D47—416no—
352C22×D47—44no—
353C22×D47—44no—
354C22×D47—44no—
355C22×D47—44no—
356C22×D47—44no—
357C22×D47—44no—
358C22×D47—44no—
359C22×D47—44no—
360C22×D47—44no—
361C22×D47—44no—
362C22×D47—44no—
363C22×D47#123116yes—
364C22×D47C22×D414yes—
365C22×D47C22×D414yes—
366C22×D47C2×#4114yes—
367C22×D47C2×#4114yes—
368C2×C4×C47—22no—
369C2×C4×C47—22no—
370C2×C4×C47—22no—
371C2×C4×C47—22no—
372C2×C4×C47—22no—
373C2×C4×C47—22no—
374C2×C4×C47—22no—
375C2×C4×C47—22no—
376C2×C4×C47—22no—
377C2×C4×C47—22no—
378C2×C4×C47—22no—
379C2×C4×C47—22no—
380C2×C4×C47—22no—
381C2×C4×C47—22no—
382C2×C4×C47—22no—
383C2×C4×C47—22no—
384C2×C4×C47—22no—
385C2×C4×C47—22no—
386C2×C4×C47—44no—
387C2×C4×C47—44no—
388C2×C4×C47—44no—
389C2×C4×C47—44no—
390C2×C4×C47—44no—
391C2×C4×C47—44no—
392C22⋊D47—416no—
393C2×Dic47—22no—
394C2×Dic47—22no—
395C2×Dic47—22no—
396C2×Dic47—22no—
397C2×Dic47—22no—
398C2×Dic47—22no—
399C2×Dic47—22no—
400C2×Dic47—22no—
401C2×Dic47—22no—
402C2×Dic47—22no—
403C2×Dic47—22no—
404C2×Dic47—22no—
405C2×Dic47—22no—
406C2×Dic47—22no—
407C2×Dic47—22no—
408C2×Dic47—44no—
409C2×Dic47—44no—
410C2×Dic47—44no—
411C2×Dic47—44no—
412C2×Dic47—44no—
413D188—416no—
414D188—416no—
415C4×D47—416no—
416C4×D47—416no—
417C2×#2622—471nomaximal, Sylow
418C22×C47—24no—
419C22×C47—24no—
420C22×C47—24no—
421C22×C47—416no—
422C22×C47—42no—
423C22×C47—42no—
424C22×C47—42no—
425C22×C47—42no—
426C22×C47C2×#12314yes—
427C22×C47#53414yes—
428C22×C47#53414yes—
429C22×C47#53814yes—
430C22×C47#53814yes—
431C22×C47#53814yes—
432C22×C47#53814yes—
433C22×C47C23×D411yescharacteristic
434C22×C47C22×#4111yescharacteristic
435C22×C47C22×#4111yescharacteristic
436C22×C47C2×H(5,𝔽2)11yescharacteristic
437C22×C47C2×H(5,𝔽2)11yescharacteristic
438C22×C47C2×H(5,𝔽2)11yescharacteristic
439C22×C47C2×H(5,𝔽2)11yescharacteristic
440C2×D47—232no—
441C2×D47—24no—
442C2×D47—24no—
443C2×D47—24no—
444C2×D47—24no—
445C2×D47—24no—
446C2×D47—24no—
447C2×D47—24no—
448C2×D47—24no—
449C2×D47—24no—
450C2×D47—464no—
451C2×D47—416no—
452C2×D47—42no—
453C2×D47—42no—
454C2×D47—42no—
455C2×D47—42no—
456C2×D47—42no—
457C2×D47—42no—
458C2×D47—42no—
459C2×D47—42no—
460C2×D47—42no—
461C2×D47—42no—
462C2×D47—42no—
463C2×D47—88no—
464C2×D47C2×#12318yes—
465C4×C47—42no—
466C4×C47—42no—
467C4×C47—42no—
468C4×C47—42no—
469C4×C47—42no—
470C4×C47—42no—
471Dic47—42no—
472Dic47—42no—
473Dic47—42no—
474Dic47—42no—
475Dic47—42no—
476C22×#120—471no—
477C23×C22⋊C4—471no—
478#2622—4716no—
479C2×#397—471no—
480C2×#397—471no—
481C2×#397—471no—
482C2×#397D4711yescharacteristic, complemented
483C2×#394—471no—
484C2×#394—471no—
485C2×#394—471no—
486C2×#394—471no—
487C2×#386—471no—
488C2×#386—471no—
489C2×#385—471no—
490C2×#385—471no—
491C2×#379—471no—
492C2×C47—44no—
493C2×C47#262218yescomplemented
494C2×C47C22×#12311yescharacteristic
495C2×C47C2×#53411yescharacteristic
496C2×C47C2×#53411yescharacteristic
497C2×C47C2×#53811yescharacteristic
498C2×C47C2×#53811yescharacteristic
499C2×C47C2×#53811yescharacteristic
500C2×C47C2×#53811yescharacteristic
501D47—28no—
502D47—44no—
503D47—82no—
504C26—471no—
505C23×D4—471no—
506C23×D4—471no—
507C23×D4—471no—
508C24×C4—471no—
509C24×C4—471no—
510C2×#120—478no—
511C2×#120—948no—
512C22×C4⋊C4—471no—
513C22×C4⋊C4—471no—
514C22×C4⋊C4—471no—
515C22×C4⋊C4C2×D4711yescharacteristic, complemented
516C22×C22⋊C4—471no—
517C22×C22⋊C4—471no—
518C22×C22⋊C4—471no—
519C22×C22⋊C4—471no—
520C22×C22⋊C4—471no—
521C22×C22⋊C4—471no—
522C22×C22⋊C4—471no—
523C22×C22⋊C4—471no—
524C22×C22⋊C4—471no—
525C22×C22⋊C4—471no—
526C22×C22⋊C4—471no—
527C22×C22⋊C4—471no—
528C22×C22⋊C4—471no—
529C22×C22⋊C4—471no—
530C22×C22⋊C4—478no—
531C22×C22⋊C4—948no—
532C22×C22⋊C4C2×D4711yescharacteristic
533C22×C22⋊C4C2×D4711yescharacteristic
534C22×C22⋊C4C2×D4711yescharacteristic
535#397—478no—
536#397—478no—
537#397—478no—
538#397C2×D4718yescomplemented
539#394—478no—
540#394—478no—
541#394—478no—
542#394—478no—
543#386—478no—
544#386—478no—
545#385—478no—
546#385—478no—
547#379—478no—
548C2×#95—471no—
549C2×#95—471no—
550C2×#95—471no—
551C2×#95—471no—
552C2×#95—471no—
553C2×#95C2×D4711yescharacteristic, complemented
554C2×#95C2×D4711yescharacteristic, complemented
555C2×#95C2×D4711yescharacteristic, complemented
556C47C2×#262211yescharacteristic, complemented, Sylow
557C25—471no—
558C25—471no—
559C25—478no—
560C25—474no—
561C25—471no—
562C25—944no—
563C25—944no—
564C25—1882no—
565C25—1882no—
566C25—1882no—
567C25—1882no—
568C25C22×D4711yescharacteristic
569C22×D4—474no—
570C22×D4—474no—
571C22×D4—474no—
572C22×D4—944no—
573C22×D4—944no—
574C22×D4—944no—
575C22×D4—944no—
576C22×D4—944no—
577C22×D4—1882no—
578C22×D4—1882no—
579C22×D4—1882no—
580C22×D4—1882no—
581C23×C4—471no—
582C23×C4—471no—
583C23×C4—471no—
584C23×C4—471no—
585C23×C4—471no—
586C23×C4—474no—
587C23×C4—474no—
588C23×C4—944no—
589C23×C4—944no—
590C23×C4—1882no—
591C23×C4—1882no—
592C23×C4—1882no—
593C23×C4—1882no—
594C23×C4C22×D4711yescharacteristic
595C23×C4C22×D4711yescharacteristic
596C23×C4C22×D4711yescharacteristic
597C23×C4C22×D4711yescharacteristic
598C23×C4C22×D4711yescharacteristic
599C23×C4C22×D4711yescharacteristic
600#120—9432no—
601C2×C4⋊C4—42no—
602C2×C4⋊C4—474no—
603C2×C4⋊C4—474no—
604C2×C4⋊C4—474no—
605C2×C4⋊C4—1882no—
606C2×C4⋊C4—1882no—
607C2×C4⋊C4—1882no—
608C2×C4⋊C4C22×D4714yescomplemented
609C2×C22⋊C4—24no—
610C2×C22⋊C4—24no—
611C2×C22⋊C4—42no—
612C2×C22⋊C4—474no—
613C2×C22⋊C4—474no—
614C2×C22⋊C4—474no—
615C2×C22⋊C4—474no—
616C2×C22⋊C4—474no—
617C2×C22⋊C4—474no—
618C2×C22⋊C4—474no—
619C2×C22⋊C4—474no—
620C2×C22⋊C4—474no—
621C2×C22⋊C4—474no—
622C2×C22⋊C4—474no—
623C2×C22⋊C4—474no—
624C2×C22⋊C4—474no—
625C2×C22⋊C4—474no—
626C2×C22⋊C4—9432no—
627C2×C22⋊C4—944no—
628C2×C22⋊C4—944no—
629C2×C22⋊C4—944no—
630C2×C22⋊C4—944no—
631C2×C22⋊C4—944no—
632C2×C22⋊C4—944no—
633C2×C22⋊C4—944no—
634C2×C22⋊C4—1882no—
635C2×C22⋊C4—1882no—
636C2×C22⋊C4—1882no—
637C2×C22⋊C4—1882no—
638C2×C22⋊C4—1882no—
639C2×C22⋊C4—1882no—
640C2×C22⋊C4—1882no—
641C2×C22⋊C4C22×D4714yes—
642C2×C22⋊C4C22×D4714yes—
643C2×C22⋊C4C22×D4714yes—
644#95—474no—
645#95—474no—
646#95—474no—
647#95—474no—
648#95—474no—
649#95C22×D4714yescomplemented
650#95C22×D4714yescomplemented
651#95C22×D4714yescomplemented
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—474no—
659C24—474no—
660C24—474no—
661C24—472no—
662C24—474no—
663C24—472no—
664C24—4716no—
665C24—472no—
666C24—9432no—
667C24—948no—
668C24—948no—
669C24—942no—
670C24—942no—
671C24—942no—
672C24—942no—
673C24—942no—
674C24—942no—
675C24—942no—
676C24—942no—
677C24—942no—
678C24—942no—
679C24—942no—
680C24—942no—
681C24—942no—
682C24—942no—
683C24—942no—
684C24—942no—
685C24—942no—
686C24—18816no—
687C24—18816no—
688C24—1884no—
689C24—1884no—
690C24—1884no—
691C24—1884no—
692C24—18816no—
693C24—18816no—
694C24—18816no—
695C24—18816no—
696C24D4×D4714yes—
697C24C23×D4712yes—
698C24C23×D4711yescharacteristic
699C2×D4—948no—
700C2×D4—948no—
701C2×D4—948no—
702C2×D4—948no—
703C2×D4—948no—
704C2×D4—1884no—
705C2×D4—1884no—
706C2×D4—18816no—
707C2×D4—18816no—
708C2×D4—1884no—
709C2×D4—1884no—
710C2×D4—18816no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—472no—
730C22×C4—472no—
731C22×C4—472no—
732C22×C4—472no—
733C22×C4—472no—
734C22×C4—948no—
735C22×C4—948no—
736C22×C4—942no—
737C22×C4—942no—
738C22×C4—942no—
739C22×C4—942no—
740C22×C4—942no—
741C22×C4—942no—
742C22×C4—942no—
743C22×C4—942no—
744C22×C4—942no—
745C22×C4—942no—
746C22×C4—942no—
747C22×C4—942no—
748C22×C4—942no—
749C22×C4—942no—
750C22×C4—942no—
751C22×C4—1884no—
752C22×C4—1884no—
753C22×C4—1884no—
754C22×C4—1884no—
755C22×C4—18816no—
756C22×C4—18816no—
757C22×C4C23×D4712yes—
758C22×C4C23×D4712yes—
759C22×C4C23×D4712yes—
760C22×C4C23×D4712yes—
761C22×C4C23×D4712yes—
762C22×C4C23×D4712yes—
763C4⋊C4—44no—
764C4⋊C4—1884no—
765C4⋊C4—1884no—
766C4⋊C4—1884no—
767C22⋊C4—28no—
768C22⋊C4—28no—
769C22⋊C4—44no—
770C22⋊C4—948no—
771C22⋊C4—948no—
772C22⋊C4—948no—
773C22⋊C4—948no—
774C22⋊C4—948no—
775C22⋊C4—948no—
776C22⋊C4—948no—
777C22⋊C4—1884no—
778C22⋊C4—1884no—
779C22⋊C4—1884no—
780C22⋊C4—1884no—
781C22⋊C4—1884no—
782C22⋊C4—1884no—
783C22⋊C4—1884no—
784C23—28no—
785C23—28no—
786C23—28no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—4716no—
798C23—474no—
799C23—474no—
800C23—474no—
801C23—474no—
802C23—9432no—
803C23—948no—
804C23—948no—
805C23—942no—
806C23—942no—
807C23—942no—
808C23—942no—
809C23—948no—
810C23—948no—
811C23—948no—
812C23—948no—
813C23—948no—
814C23—948no—
815C23—948no—
816C23—942no—
817C23—942no—
818C23—942no—
819C23—942no—
820C23—942no—
821C23—942no—
822C23—942no—
823C23—942no—
824C23—942no—
825C23—942no—
826C23—942no—
827C23—942no—
828C23—942no—
829C23—18816no—
830C23—18816no—
831C23—188128no—
832C23—18816no—
833C23—18816no—
834C23—18816no—
835C23—18816no—
836C23—1884no—
837C23—1884no—
838C23—1884no—
839C23—1884no—
840C23—1884no—
841C23—1884no—
842C23—1884no—
843C23—1884no—
844C23—1884no—
845C23—1884no—
846C23—1884no—
847C23C2×D4×D4714yes—
848C23C2×D4×D4712yes—
849C23#41×D4712yes—
850C23#41×D4712yes—
851C23#1309406912yes—
852C23#1309407012yes—
853C23#1309407012yes—
854C23#1309407012yes—
855C23C24×D4711yescharacteristic
856D4—18816no—
857D4—18816no—
858D4—18816no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—44no—
878C2×C4—44no—
879C2×C4—44no—
880C2×C4—44no—
881C2×C4—44no—
882C2×C4—44no—
883C2×C4—942no—
884C2×C4—942no—
885C2×C4—942no—
886C2×C4—942no—
887C2×C4—942no—
888C2×C4—942no—
889C2×C4—942no—
890C2×C4—942no—
891C2×C4—942no—
892C2×C4—942no—
893C2×C4—942no—
894C2×C4—942no—
895C2×C4—942no—
896C2×C4—942no—
897C2×C4—942no—
898C2×C4—18816no—
899C2×C4—18816no—
900C2×C4—1884no—
901C2×C4—1884no—
902C2×C4—1884no—
903C2×C4—1884no—
904C2×C4—1884no—
905C22—24no—
906C22—24no—
907C22—24no—
908C22—416no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—478no—
914C22—9432no—
915C22—944no—
916C22—944no—
917C22—944no—
918C22—944no—
919C22—944no—
920C22—944no—
921C22—944no—
922C22—944no—
923C22—944no—
924C22—3768no—
925C22—18864no—
926C22—1882no—
927C22—1882no—
928C22—1882no—
929C22—1882no—
930C22—1882no—
931C22—1882no—
932C22—1882no—
933C22—18816no—
934C22—1882no—
935C22—1882no—
936C22—1882no—
937C22—1882no—
938C22#123×D4714yes—
939C22#1568968114yes—
940C22#1568968414yes—
941C22#1568970714yes—
942C22#1568970914yes—
943C22#1568971214yes—
944C22#1568971214yes—
945C22C22×D4×D4711yescharacteristic
946C22C2×#41×D4711yescharacteristic
947C22C2×#41×D4711yescharacteristic
948C22C2×#1309406911yescharacteristic
949C22C2×#1309407011yescharacteristic
950C22C2×#1309407011yescharacteristic
951C22C2×#1309407011yescharacteristic
952C4—42no—
953C4—42no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—1882no—
959C4—1882no—
960C4—1882no—
961C4—1882no—
962C4—1882no—
963C2—44no—
964C2—948no—
965C2—3762no—
966C2—1884no—
967C2#2024916218yesdirect product factor
968C2C2×#123×D4711yescharacteristic
969C2C2×#1568968111yescharacteristic
970C2C2×#1568968411yescharacteristic
971C2C2×#1568970711yescharacteristic
972C2C2×#1568970911yescharacteristic
973C2C2×#1568971211yescharacteristic
974C2C2×#1568971211yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#397C2
socleC24×C47C24
prime radicalC22×#13093994C2
hypercenterC2×#397D47
hypocenterC47C2×#2622
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊C4×D47C2semidirect
3. #20249162C2direct (N × H)
4. C2×#15689052C2semidirect
5. C2×#15689051C2semidirect
6. C2×#15689050C2semidirect
7. C2×#15689041C2semidirect
8. C2×#15689040C2semidirect
9. C2×#15689039C2semidirect
10. C2×#15689038C2semidirect
11. C2×#15689001C2semidirect
12. C2×#15689001C2semidirect
13. C2×#15688997C2semidirect
14. C2×#15688994C2semidirect
15. C2×#15688978C2semidirect
16. C2×C47×#397C2semidirect
25. C22×C4⋊Dic47C22semidirect
26. C22×Dic47⋊C4C22semidirect
27. C22×Dic47⋊C4C22semidirect
38. C22×(C2×D47)⋊C4C22semidirect
39. C22×(C2×D47)⋊C4C22semidirect
40. C22×(C2×D47)⋊C4C22semidirect
41. C22×(C2×D47)⋊C4C22semidirect
43. C2×C22⋊C4×D47C22semidirect
44. #15689052C22semidirect
45. #15689051C22semidirect
46. #15689050C22semidirect
47. #15689041C22semidirect
48. #15689040C22semidirect
49. #15689039C22semidirect
50. #15689038C22semidirect
51. #15689001C22semidirect
52. #15689001C22semidirect
53. #15688997C22semidirect
54. #15688994C22semidirect
55. #15688978C22semidirect
56. C2×C47⋊#95C22semidirect
57. C2×C47⋊#95C22semidirect
58. C2×C47⋊#95C22semidirect
59. C2×C47⋊#95C22semidirect
60. C2×C47⋊#95C22semidirect
61. C22×C4⋊C4×C47C22semidirect
65. C47×#397C22semidirect
66. C2×#95×C47C22semidirect
67. C2×#95×C47C22semidirect
68. C2×#95×C47C22semidirect
107. C2×C4⋊Dic47C23semidirect
110. C2×Dic47⋊C4C23semidirect
111. C2×Dic47⋊C4C23semidirect
136. C2×(C2×D47)⋊C4C23semidirect
137. C2×(C2×D47)⋊C4C23semidirect
138. C2×(C2×D47)⋊C4C23semidirect
139. C2×(C2×D47)⋊C4C23semidirect
141. C47⋊#95C23semidirect
142. C47⋊#95C23semidirect
143. C47⋊#95C23semidirect
144. C47⋊#95C23semidirect
145. C47⋊#95C23semidirect
154. C2×C4⋊C4×C47C23semidirect
161. #95×C47C23semidirect
162. #95×C47C23semidirect
163. #95×C47C23semidirect
482. C2×#397D47semidirect
493. C2×C47#2622semidirect
515. C22×C4⋊C4C2×D47semidirect
538. #397C2×D47semidirect
553. C2×#95C2×D47semidirect
554. C2×#95C2×D47semidirect
555. C2×#95C2×D47semidirect
556. C47C2×#2622semidirect
608. C2×C4⋊C4C22×D47semidirect
649. #95C22×D47semidirect
650. #95C22×D47semidirect
651. #95C22×D47semidirect
967. C2#20249162direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939942
C22×C22⋊C4×D472
#202491622
C2×#156890522
C2×#156890512
C2×#156890502
C2×#156890412
C2×#156890402
C2×#156890392
C2×#156890382
C2×#156890012
C2×#156889972
C2×#156889942
C2×#156889782
C2×C47×#3972
C2×#262247