Finite Group Databasebeta

← C2×#19138536 #25264242

Subgroups — C2×#19138536 #25264242

Order 11008.

3394 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063313C211yesmaximal, characteristic, complemented
2C22×#13063287C211yesmaximal, characteristic, complemented
3#19138536C2116yesmaximal, direct product factor
4C2×#14582817C211yesmaximal, characteristic, complemented
5C2×#14582816C211yesmaximal, characteristic, complemented
6C2×#14582812C211yesmaximal, characteristic, complemented
7C2×#14582809C211yesmaximal, characteristic
8C2×#14582803C211yesmaximal, characteristic, complemented
9C2×#14582789C211yesmaximal, characteristic, complemented
10C2×#14582789C211yesmaximal, characteristic, complemented
11C2×#14582788C211yesmaximal, characteristic, complemented
12C2×#14582777C211yesmaximal, characteristic, complemented
13C2×#14582777C211yesmaximal, characteristic, complemented
14C2×#14582761C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
16C2×C43×#387C211yesmaximal, characteristic, complemented
17C23×Dic86C2211yescharacteristic
18C23×D172C2211yescharacteristic
19C23×D172C2211yescharacteristic
20C23×D172C2211yescharacteristic
21C23×C4×D43C2211yescharacteristic
22C23×C4×D43C2211yescharacteristic
23C2×#13063313—28no—
24C2×#13063313C2218yescomplemented
25C2×#13063287—28no—
26C2×#13063287C2218yescomplemented
27C22×Dic43⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×(C2×D43)⋊C4C2211yescharacteristic
39C22×(C2×D43)⋊C4C2211yescharacteristic
40C22×(C2×D43)⋊C4C2211yescharacteristic
41C22×C4×Dic43C2211yescharacteristic
42C22×C4×Dic43C2211yescharacteristic
43#14582817C2218yescomplemented
44#14582816C2218yescomplemented
45#14582812C2218yescomplemented
46#14582809C2218yes—
47#14582803C2218yescomplemented
48#14582789C2218yescomplemented
49#14582789C2218yescomplemented
50#14582788C2218yescomplemented
51#14582777C2218yescomplemented
52#14582777C2218yescomplemented
53#14582761C2218yescomplemented
54C4×(C2×D43)⋊C4C2218yescomplemented
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C22×C4⋊C4×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×C42×C43C2211yescharacteristic
64C43×#387C2218yescomplemented
65C2×#95×C43C2211yescharacteristic
66C2×#95×C43C2211yescharacteristic
67C2×#95×C43C2211yescharacteristic
68C2×#95×C43C2211yescharacteristic
69C24×D43C2311yescharacteristic
70C24×D43C2311yescharacteristic
71C24×D43C2311yescharacteristic
72C22×Dic86—24no—
73C22×Dic86—24no—
74C22×Dic86—42no—
75C22×Dic86C2314yes—
76C22×D172—24no—
77C22×D172—24no—
78C22×D172—24no—
79C22×D172—24no—
80C22×D172—24no—
81C22×D172—24no—
82C22×D172—42no—
83C22×D172—42no—
84C22×D172—42no—
85C22×D172C2314yes—
86C22×D172C2314yes—
87C22×D172C2314yes—
88C23×Dic43C2311yescharacteristic
89C23×Dic43C2311yescharacteristic
90C23×Dic43C2311yescharacteristic
91C23×Dic43C2311yescharacteristic
92C23×Dic43C2311yescharacteristic
93C22×C4×D43—24no—
94C22×C4×D43—24no—
95C22×C4×D43—24no—
96C22×C4×D43—24no—
97C22×C4×D43—42no—
98C22×C4×D43—42no—
99C22×C4×D43C2314yes—
100C22×C4×D43C2314yes—
101#13063313—232no—
102#13063287—232no—
103C2×Dic43⋊C4—42no—
104C2×Dic43⋊C4C2314yes—
105C2×(C2×D43)⋊C4—24no—
106C2×(C2×D43)⋊C4—24no—
107C2×(C2×D43)⋊C4—24no—
108C2×(C2×D43)⋊C4—24no—
109C2×(C2×D43)⋊C4—24no—
110C2×(C2×D43)⋊C4—24no—
111C2×(C2×D43)⋊C4—24no—
112C2×(C2×D43)⋊C4—24no—
113C2×(C2×D43)⋊C4—42no—
114C2×(C2×D43)⋊C4—42no—
115C2×(C2×D43)⋊C4—42no—
116C2×(C2×D43)⋊C4—42no—
117C2×(C2×D43)⋊C4D418yescomplemented
118C2×(C2×D43)⋊C4C2314yes—
119C2×(C2×D43)⋊C4C2314yes—
120C2×(C2×D43)⋊C4C2314yes—
121C2×(C2×D43)⋊C4C2314yes—
122C2×(C2×D43)⋊C4C2314yes—
123C2×(C2×D43)⋊C4C2314yes—
124C2×(C2×D43)⋊C4C2314yes—
125C2×(C2×D43)⋊C4C2314yes—
126C2×(C2×D43)⋊C4C2314yes—
127C2×(C2×D43)⋊C4C2314yes—
128C2×(C2×D43)⋊C4C2314yes—
129C2×(C2×D43)⋊C4C2314yes—
130C2×(C2×D43)⋊C4C2314yes—
131C2×C4×Dic43—24no—
132C2×C4×Dic43—42no—
133C2×C4×Dic43C2314yes—
134C2×C4×Dic43C2314yes—
135C43⋊#95C2314yes—
136C43⋊#95C2314yes—
137C43⋊#95C2314yes—
138C43⋊#95C2314yes—
139C43⋊#95C2314yes—
140C43⋊#95C2314yes—
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C2×C4⋊C4×C43—24no—
149C2×C4⋊C4×C43—24no—
150C2×C4⋊C4×C43C2314yes—
151C2×C4⋊C4×C43C2314yes—
152C2×C42×C43—24no—
153C2×C42×C43C2314yes—
154#95×C43C2314yes—
155#95×C43C2314yes—
156#95×C43C2314yes—
157#95×C43C2314yes—
158C24×C43C2411yescharacteristic
159C23×D43—22no—
160C23×D43—22no—
161C23×D43—22no—
162C23×D43—22no—
163C23×D43—22no—
164C23×D43—22no—
165C23×D43—22no—
166C23×D43—22no—
167C23×D43—22no—
168C23×D43—22no—
169C23×D43—22no—
170C23×D43—22no—
171C23×D43—22no—
172C23×D43—22no—
173C23×D43—22no—
174C23×D43—22no—
175C23×D43—22no—
176C23×D43—22no—
177C23×D43—22no—
178C23×D43C2×D414yes—
179C23×D43#4114yes—
180C23×D43C2412yes—
181C23×D43C2412yes—
182C23×D43C2412yes—
183C22×C4×C43—22no—
184C22×C4×C43—22no—
185C22×C4×C43—22no—
186C22×C4×C43—22no—
187C22×C4×C43—22no—
188C22×C4×C43—22no—
189C22×C4×C43—22no—
190C22×C4×C43—22no—
191C22×C4×C43—22no—
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43—22no—
195C22×C4×C43—22no—
196C22×C4×C43—22no—
197C22×C4×C43—22no—
198C22×C4×C43—22no—
199C22×C4×C43—22no—
200C22×C4×C43—22no—
201C22×C4×C43C2×D414yes—
202C22×C4×C43#4114yes—
203C22×C4×C43#4114yes—
204C22×C4×C43C2412yes—
205C22×C4×C43C2412yes—
206C22×C4×C43C2412yes—
207C22×C4×C43C2412yes—
208C22×C4×C43C2412yes—
209C22×C4×C43C2412yes—
210C22×C4×C43C2412yes—
211C22×Dic43—22no—
212C22×Dic43—22no—
213C22×Dic43—22no—
214C22×Dic43—22no—
215C22×Dic43—22no—
216C22×Dic43—22no—
217C22×Dic43—22no—
218C22×Dic43—22no—
219C22×Dic43—22no—
220C22×Dic43—22no—
221C22×Dic43—22no—
222C22×Dic43—22no—
223C22×Dic43—22no—
224C22×Dic43C2×D414yes—
225C22×Dic43#4114yes—
226C22×Dic43C2412yes—
227C22×Dic43C2412yes—
228C22×Dic43C2412yes—
229C22×Dic43C2412yes—
230C22×Dic43C2412yes—
231C2×D172—232no—
232C2×D172—28no—
233C2×D172—28no—
234C2×D172—28no—
235C2×D172—28no—
236C2×D172—28no—
237C2×D172—28no—
238C2×D172—44no—
239C2×D172—44no—
240C2×D172—44no—
241C2×D172—416no—
242C2×D172—416no—
243C2×C4×D43—28no—
244C2×C4×D43—28no—
245C2×C4×D43—28no—
246C2×C4×D43—28no—
247C2×C4×D43—44no—
248C2×C4×D43—44no—
249C2×C4×D43—416no—
250C2×C4×D43—416no—
251C2×Dic86—28no—
252C2×Dic86—28no—
253C2×Dic86—44no—
254C2×Dic86—416no—
255C4⋊C4×C43—28no—
256C4⋊C4×C43—28no—
257C42×C43—28no—
258(C2×D43)⋊C4—28no—
259(C2×D43)⋊C4—28no—
260(C2×D43)⋊C4—28no—
261(C2×D43)⋊C4—28no—
262(C2×D43)⋊C4—28no—
263(C2×D43)⋊C4—28no—
264(C2×D43)⋊C4—28no—
265(C2×D43)⋊C4—28no—
266(C2×D43)⋊C4—44no—
267(C2×D43)⋊C4—44no—
268(C2×D43)⋊C4—44no—
269(C2×D43)⋊C4—44no—
270(C2×D43)⋊C4C2×D4116yescomplemented
271Dic43⋊C4—44no—
272C4×Dic43—28no—
273C4×Dic43—44no—
274C23×C43C22×D412yes—
275C23×C43C2×#4112yes—
276C23×C43C2×#4112yes—
277C23×C43C2×#4112yes—
278C23×C43C2×#4112yes—
279C23×C43H(5,𝔽2)12yes—
280C23×C43H(5,𝔽2)12yes—
281C23×C43C2511yescharacteristic
282C22×D43—28no—
283C22×D43—28no—
284C22×D43—28no—
285C22×D43—28no—
286C22×D43—28no—
287C22×D43—28no—
288C22×D43—22no—
289C22×D43—22no—
290C22×D43—22no—
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—44no—
308C22×D43—44no—
309C22×D43—44no—
310C22×D43—44no—
311C22×D43—44no—
312C22×D43—44no—
313C22×D43—44no—
314C22×D43—44no—
315C22×D43—44no—
316C22×D43—44no—
317C22×D43—44no—
318C22×D43—44no—
319C22×D43—44no—
320C22×D43—44no—
321C22×D43—44no—
322C22×D43C22×D414yes—
323C22×D43C2×#4114yes—
324C2×C4×C43—28no—
325C2×C4×C43—28no—
326C2×C4×C43—28no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—44no—
346C2×C4×C43—44no—
347C2×C4×C43—44no—
348C2×C4×C43—44no—
349C2×C4×C43C22×D414yes—
350C2×C4×C43C2×#4114yes—
351C2×C4×C43C2×#4114yes—
352C2×Dic43—28no—
353C2×Dic43—28no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—22no—
357C2×Dic43—22no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—22no—
362C2×Dic43—22no—
363C2×Dic43—22no—
364C2×Dic43—22no—
365C2×Dic43—22no—
366C2×Dic43—22no—
367C2×Dic43—44no—
368C2×Dic43—44no—
369C2×Dic43—44no—
370C2×Dic43C22×D414yes—
371C2×Dic43C2×#4114yes—
372D172—232no—
373D172—416no—
374D172—416no—
375C4×D43—416no—
376C4×D43—416no—
377Dic86—416no—
378C2×#2459—431nomaximal, Sylow
379C22×C43#52514yes—
380C22×C43#52914yes—
381C22×C43#53814yes—
382C22×C43#54614yes—
383C22×C43#54614yes—
384C22×C43#55514yes—
385C22×C43#55914yes—
386C22×C43C23×D411yescharacteristic
387C22×C43C22×#4111yescharacteristic
388C22×C43C22×#4111yescharacteristic
389C22×C43C22×#4111yescharacteristic
390C22×C43C22×#4111yescharacteristic
391C22×C43C2×H(5,𝔽2)11yescharacteristic
392C22×C43C2×H(5,𝔽2)11yescharacteristic
393C2×D43—24no—
394C2×D43—24no—
395C2×D43—24no—
396C2×D43—24no—
397C2×D43—24no—
398C2×D43—24no—
399C2×D43—42no—
400C2×D43—42no—
401C2×D43—42no—
402C2×D43—42no—
403C2×D43—42no—
404C2×D43—42no—
405C2×D43—42no—
406C2×D43—42no—
407C2×D43—416no—
408C2×D43—416no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—42no—
412C2×D43—42no—
413C2×D43—42no—
414C2×D43—42no—
415C2×D43—42no—
416C2×D43—88no—
417C4×C43—24no—
418C4×C43—24no—
419C4×C43—24no—
420C4×C43—42no—
421C4×C43—42no—
422C4×C43—42no—
423C4×C43—42no—
424Dic43—24no—
425Dic43—24no—
426Dic43—42no—
427Dic43—42no—
428Dic43—42no—
429C22×#124—431no—
430C22×C4×D4—431no—
431#2459—4316no—
432C2×#394—431no—
433C2×#394—431no—
434C2×#393—431no—
435C2×#392—431no—
436C2×#391—431no—
437C2×#388—431no—
438C2×#388—431no—
439C2×#388—431no—
440C2×#387D4311yescharacteristic, complemented
441C2×#386—431no—
442C2×#386—431no—
443C2×#381—431no—
444C2×C4×C22⋊C4—431no—
445C2×C43#245918yescomplemented
446C2×C43C2×#52511yescharacteristic
447C2×C43C2×#52911yescharacteristic
448C2×C43C2×#53811yescharacteristic
449C2×C43C2×#54611yescharacteristic
450C2×C43C2×#54611yescharacteristic
451C2×C43C2×#55511yescharacteristic
452C2×C43C2×#55911yescharacteristic
453D43—44no—
454D43—44no—
455D43—82no—
456C23×Q8—431no—
457C23×D4—431no—
458C23×D4—431no—
459C23×D4—431no—
460C24×C4—431no—
461C24×C4—431no—
462C2×#124—438no—
463C2×#124—868no—
464C2×C4×D4—438no—
465C2×C4×D4—868no—
466C22×C4⋊C4—431no—
467C22×C4⋊C4C2×D4311yescharacteristic
468C22×C4⋊C4C2×D4311yescharacteristic
469C22×C22⋊C4—431no—
470C22×C22⋊C4—431no—
471C22×C22⋊C4—431no—
472C22×C22⋊C4—431no—
473C22×C22⋊C4—431no—
474C22×C22⋊C4—431no—
475C22×C22⋊C4—431no—
476C22×C22⋊C4—431no—
477C22×C22⋊C4—431no—
478C22×C22⋊C4—431no—
479C22×C22⋊C4—431no—
480C22×C22⋊C4—431no—
481C22×C22⋊C4—431no—
482C22×C42—431no—
483C22×C42—431no—
484C22×C42C2×D4311yescharacteristic
485#394—438no—
486#394—438no—
487#393—438no—
488#392—438no—
489#391—438no—
490#388—438no—
491#388—438no—
492#388—438no—
493#387C2×D4318yescomplemented
494#386—438no—
495#386—438no—
496#381—438no—
497C4×C22⋊C4—438no—
498C2×#95—431no—
499C2×#95—431no—
500C2×#95—431no—
501C2×#95—431no—
502C2×#95—431no—
503C2×#95—431no—
504C2×#95C2×D4311yescharacteristic
505C2×#95C2×D4311yescharacteristic
506C2×#95C2×D4311yescharacteristic
507C2×#95C2×D4311yescharacteristic
508C43C2×#245911yescharacteristic, complemented, Sylow
509C25—431no—
510C25—431no—
511C25—431no—
512C22×Q8—434no—
513C22×Q8—864no—
514C22×Q8—864no—
515C22×Q8—1722no—
516C22×D4—434no—
517C22×D4—434no—
518C22×D4—434no—
519C22×D4—864no—
520C22×D4—864no—
521C22×D4—864no—
522C22×D4—864no—
523C22×D4—864no—
524C22×D4—864no—
525C22×D4—1722no—
526C22×D4—1722no—
527C22×D4—1722no—
528C23×C4—431no—
529C23×C4—431no—
530C23×C4—431no—
531C23×C4—431no—
532C23×C4—431no—
533C23×C4—434no—
534C23×C4—434no—
535C23×C4—864no—
536C23×C4—864no—
537C23×C4—864no—
538C23×C4—864no—
539C23×C4—1722no—
540C23×C4—1722no—
541C23×C4C22×D4311yescharacteristic
542C23×C4C22×D4311yescharacteristic
543C23×C4C22×D4311yescharacteristic
544C23×C4C22×D4311yescharacteristic
545C23×C4C22×D4311yescharacteristic
546C23×C4C22×D4311yescharacteristic
547C23×C4C22×D4311yescharacteristic
548#124—8632no—
549C4×D4—8632no—
550C2×C4⋊C4—24no—
551C2×C4⋊C4—24no—
552C2×C4⋊C4—434no—
553C2×C4⋊C4—1722no—
554C2×C4⋊C4C22×D4314yes—
555C2×C4⋊C4C22×D4314yes—
556C2×C22⋊C4—438no—
557C2×C22⋊C4—434no—
558C2×C22⋊C4—434no—
559C2×C22⋊C4—434no—
560C2×C22⋊C4—434no—
561C2×C22⋊C4—434no—
562C2×C22⋊C4—434no—
563C2×C22⋊C4—434no—
564C2×C22⋊C4—434no—
565C2×C22⋊C4—434no—
566C2×C22⋊C4—434no—
567C2×C22⋊C4—434no—
568C2×C22⋊C4—434no—
569C2×C22⋊C4—434no—
570C2×C22⋊C4—864no—
571C2×C22⋊C4—864no—
572C2×C22⋊C4—864no—
573C2×C22⋊C4—864no—
574C2×C22⋊C4—864no—
575C2×C22⋊C4—864no—
576C2×C22⋊C4—864no—
577C2×C22⋊C4—864no—
578C2×C22⋊C4—1722no—
579C2×C22⋊C4—1722no—
580C2×C22⋊C4—1722no—
581C2×C22⋊C4—1722no—
582C2×C42—24no—
583C2×C42—434no—
584C2×C42—434no—
585C2×C42—864no—
586C2×C42—1722no—
587C2×C42C22×D4314yes—
588#95—434no—
589#95—434no—
590#95—434no—
591#95—434no—
592#95—434no—
593#95—434no—
594#95C22×D4314yes—
595#95C22×D4314yes—
596#95C22×D4314yes—
597#95C22×D4314yes—
598C24—434no—
599C24—434no—
600C24—432no—
601C24—432no—
602C24—432no—
603C24—862no—
604C24—862no—
605C24—862no—
606C24—862no—
607C24—862no—
608C24—862no—
609C24—862no—
610C24—862no—
611C24—862no—
612C24—862no—
613C24—862no—
614C24—862no—
615C24—862no—
616C24—862no—
617C24—862no—
618C24—862no—
619C24—862no—
620C24—862no—
621C24—862no—
622C24C23×D4311yescharacteristic
623C2×Q8—868no—
624C2×Q8—868no—
625C2×Q8—1724no—
626C2×Q8—17216no—
627C2×D4—868no—
628C2×D4—868no—
629C2×D4—8632no—
630C2×D4—868no—
631C2×D4—868no—
632C2×D4—868no—
633C2×D4—868no—
634C2×D4—1724no—
635C2×D4—1724no—
636C2×D4—1724no—
637C2×D4—17216no—
638C2×D4—17216no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—434no—
658C22×C4—434no—
659C22×C4—432no—
660C22×C4—432no—
661C22×C4—432no—
662C22×C4—432no—
663C22×C4—432no—
664C22×C4—868no—
665C22×C4—868no—
666C22×C4—868no—
667C22×C4—862no—
668C22×C4—862no—
669C22×C4—862no—
670C22×C4—862no—
671C22×C4—862no—
672C22×C4—862no—
673C22×C4—862no—
674C22×C4—862no—
675C22×C4—862no—
676C22×C4—862no—
677C22×C4—862no—
678C22×C4—862no—
679C22×C4—862no—
680C22×C4—868no—
681C22×C4—1724no—
682C22×C4—1724no—
683C22×C4—17216no—
684C22×C4—17216no—
685C22×C4#1062189814yes—
686C22×C4D4×D4314yes—
687C22×C4#1062190214yes—
688C22×C4C23×D4312yes—
689C22×C4C23×D4312yes—
690C22×C4C23×D4312yes—
691C22×C4C23×D4312yes—
692C22×C4C23×D4312yes—
693C22×C4C23×D4312yes—
694C22×C4C23×D4312yes—
695C4⋊C4—28no—
696C4⋊C4—28no—
697C4⋊C4—1724no—
698C22⋊C4—4316no—
699C22⋊C4—868no—
700C22⋊C4—868no—
701C22⋊C4—868no—
702C22⋊C4—868no—
703C22⋊C4—868no—
704C22⋊C4—868no—
705C22⋊C4—868no—
706C22⋊C4—868no—
707C22⋊C4—1724no—
708C22⋊C4—1724no—
709C22⋊C4—1724no—
710C22⋊C4—1724no—
711C42—28no—
712C42—868no—
713C42—1724no—
714C23—434no—
715C23—434no—
716C23—868no—
717C23—868no—
718C23—868no—
719C23—862no—
720C23—862no—
721C23—862no—
722C23—862no—
723C23—862no—
724C23—862no—
725C23—862no—
726C23—862no—
727C23—862no—
728C23—862no—
729C23—862no—
730C23—862no—
731C23—868no—
732C23—868no—
733C23—868no—
734C23—862no—
735C23—862no—
736C23—862no—
737C23—862no—
738C23—862no—
739C23—862no—
740C23—862no—
741C23—1724no—
742C23—1724no—
743C23—1724no—
744C23—1724no—
745C23—1724no—
746C23—1724no—
747C23—1724no—
748C23—1724no—
749C23—1724no—
750C23—1724no—
751C23—1724no—
752C23—1724no—
753C23—1724no—
754C23—1724no—
755C23—1724no—
756C23C2×D4×D4312yes—
757C23#41×D4312yes—
758C23#41×D4312yes—
759C23C2×#1062189812yes—
760C23C2×#1062190212yes—
761C23#1306337112yes—
762C23#1306337112yes—
763C23C24×D4311yescharacteristic
764Q8—17216no—
765D4—8632no—
766D4—17216no—
767D4—17216no—
768C2×C4—28no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—28no—
776C2×C4—28no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—434no—
794C2×C4—434no—
795C2×C4—862no—
796C2×C4—862no—
797C2×C4—862no—
798C2×C4—862no—
799C2×C4—868no—
800C2×C4—868no—
801C2×C4—862no—
802C2×C4—862no—
803C2×C4—862no—
804C2×C4—862no—
805C2×C4—862no—
806C2×C4—862no—
807C2×C4—862no—
808C2×C4—862no—
809C2×C4—862no—
810C2×C4—17216no—
811C2×C4—17216no—
812C2×C4—1724no—
813C2×C4—1724no—
814C2×C4—1724no—
815C2×C4C2×D4×D4314yes—
816C2×C4C2×#1062189814yes—
817C2×C4C2×#1062190214yes—
818C22—864no—
819C22—864no—
820C22—864no—
821C22—864no—
822C22—864no—
823C22—864no—
824C22—3448no—
825C22—1722no—
826C22—1722no—
827C22—1722no—
828C22—1722no—
829C22—1722no—
830C22—1722no—
831C22—1722no—
832C22—1722no—
833C22—1722no—
834C22—1722no—
835C22—1722no—
836C22—1722no—
837C22—1722no—
838C22—1722no—
839C22—1722no—
840C22—17216no—
841C22—17216no—
842C22#1458340814yes—
843C22#1458343414yes—
844C22#1458348814yes—
845C22#1458354014yes—
846C22#1458354114yes—
847C22#1458361214yes—
848C22#1458363414yes—
849C22C22×D4×D4311yescharacteristic
850C22C2×#41×D4311yescharacteristic
851C22C2×#41×D4311yescharacteristic
852C22C22×#1062189811yescharacteristic
853C22C22×#1062190211yescharacteristic
854C22C2×#1306337111yescharacteristic
855C22C2×#1306337111yescharacteristic
856C4—24no—
857C4—24no—
858C4—24no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—864no—
864C4—864no—
865C4—1722no—
866C4—1722no—
867C4—1722no—
868C2—3442no—
869C2—1724no—
870C2—1724no—
871C2#1913853618yesdirect product factor
872C2C2×#1458340811yescharacteristic
873C2C2×#1458343411yescharacteristic
874C2C2×#1458348811yescharacteristic
875C2C2×#1458354011yescharacteristic
876C2C2×#1458354111yescharacteristic
877C2C2×#1458361211yescharacteristic
878C2C2×#1458363411yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#387C2
socleC24×C43C24
prime radicalC2×#14582809C2
hypercenterC2×#387D43
hypocenterC43C2×#2459
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#13063313C2semidirect
2. C22×#13063287C2semidirect
3. #19138536C2direct (N × H)
4. C2×#14582817C2semidirect
5. C2×#14582816C2semidirect
6. C2×#14582812C2semidirect
8. C2×#14582803C2semidirect
9. C2×#14582789C2semidirect
10. C2×#14582789C2semidirect
11. C2×#14582788C2semidirect
12. C2×#14582777C2semidirect
13. C2×#14582777C2semidirect
14. C2×#14582761C2semidirect
15. C2×C4×(C2×D43)⋊C4C2semidirect
16. C2×C43×#387C2semidirect
24. C2×#13063313C22semidirect
26. C2×#13063287C22semidirect
43. #14582817C22semidirect
44. #14582816C22semidirect
45. #14582812C22semidirect
47. #14582803C22semidirect
48. #14582789C22semidirect
49. #14582789C22semidirect
50. #14582788C22semidirect
51. #14582777C22semidirect
52. #14582777C22semidirect
53. #14582761C22semidirect
54. C4×(C2×D43)⋊C4C22semidirect
64. C43×#387C22semidirect
117. C2×(C2×D43)⋊C4D4semidirect
270. (C2×D43)⋊C4C2×D4semidirect
440. C2×#387D43semidirect
445. C2×C43#2459semidirect
493. #387C2×D43semidirect
508. C43C2×#2459semidirect
871. C2#19138536direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633132
C22×#130632872
#191385362
C2×#145828172
C2×#145828162
C2×#145828122
C2×#145828092
C2×#145828032
C2×#145827892
C2×#145827882
C2×#145827772
C2×#145827612
C2×C4×(C2×D43)⋊C42
C2×C43×#3872
C2×#245943