Finite Group Databasebeta

← C2×#19137453 #25255821

Subgroups — C2×#19137453 #25255821

Order 11008.

3006 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063281C211yesmaximal, characteristic
2#19137453C2116yesmaximal, direct product factor
3C2×#14582786C211yesmaximal, characteristic, complemented
4C2×#14582786C211yesmaximal, characteristic, complemented
5C2×#14582780C211yesmaximal, characteristic, complemented
6C2×#14582780C211yesmaximal, characteristic, complemented
7C2×#14582774C211yesmaximal, characteristic
8C2×#14582766C211yesmaximal, characteristic, complemented
9C2×#14582764C211yesmaximal, characteristic, complemented
10C2×#14582760C211yesmaximal, characteristic
11C2×C4⋊C4×Dic43C211yesmaximal, characteristic, complemented
12C2×C22⋊C4×Dic43C211yesmaximal, characteristic
13C2×C4×C22⋊Dic43C211yesmaximal, characteristic
14C2×#14582744C211yesmaximal, characteristic, complemented
15C22×C43⋊#95C211yesmaximal, characteristic
16C2×C43×#385C211yesmaximal, characteristic
17C24×Dic43C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C2×#13063281C4116yescomplemented
20C2×#13063281C2218yes—
21C22×C4⋊Dic43C2211yescharacteristic
22C22×C4⋊Dic43C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C22×C22⋊Dic43C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×C4×Dic43C2211yescharacteristic
28C22×C4×Dic43C2211yescharacteristic
29C22×C4×Dic43C2211yescharacteristic
30C22×C4×Dic43C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33#14582786C2218yescomplemented
34#14582786C2218yescomplemented
35#14582780C2218yescomplemented
36#14582780C2218yescomplemented
37#14582774C2218yes—
38#14582766C2218yescomplemented
39#14582764C2218yescomplemented
40#14582760C2218yes—
41C4⋊C4×Dic43C2218yescomplemented
42C22⋊C4×Dic43C2218yes—
43C4×C22⋊Dic43C2218yes—
44#14582744C2218yescomplemented
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2218yes—
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C24×C4×C43C2211yescharacteristic
61C22×C4⋊C4×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×C22⋊C4×C43C2211yescharacteristic
64C22×C22⋊C4×C43C2211yescharacteristic
65C43×#385C2218yes—
66C2×#95×C43C2211yescharacteristic
67C2×#95×C43C2211yescharacteristic
68C23×Dic43—24no—
69C23×Dic43—24no—
70C23×Dic43—24no—
71C23×Dic43—24no—
72C23×Dic43—42no—
73C23×Dic43C2×C418yes—
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2314yes—
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2314yes—
83C23×Dic43C2311yescharacteristic
84#13063281C2×C4164yescomplemented
85C2×C4⋊Dic43—24no—
86C2×C4⋊Dic43—42no—
87C2×C4⋊Dic43C2314yes—
88C2×C4⋊Dic43C2314yes—
89C2×Dic43⋊C4C2×C418yescomplemented
90C2×Dic43⋊C4C2×C418yescomplemented
91C2×Dic43⋊C4C2314yes—
92C2×Dic43⋊C4C2314yes—
93C2×C22⋊Dic43—24no—
94C2×C22⋊Dic43C2×C418yes—
95C2×C22⋊Dic43C2314yes—
96C2×C22⋊Dic43C2314yes—
97C2×C4×Dic43—24no—
98C2×C4×Dic43—24no—
99C2×C4×Dic43—42no—
100C2×C4×Dic43—42no—
101C2×C4×Dic43C2×C418yescomplemented
102C2×C4×Dic43C2×C418yescomplemented
103C2×C4×Dic43C2314yes—
104C2×C4×Dic43C2314yes—
105C2×C4×Dic43C2314yes—
106C2×C4×Dic43C2314yes—
107C2×C4×Dic43C2314yes—
108C2×C4×Dic43C2314yes—
109C43⋊#95C2314yes—
110C43⋊#95C2314yes—
111C43⋊#95C2314yes—
112C43⋊#95C2314yes—
113C43⋊#95C2314yes—
114C43⋊#95C2314yes—
115C43⋊#95C2314yes—
116C43⋊#95C2314yes—
117C43⋊#95C2314yes—
118C43⋊#95C2314yes—
119C43⋊#95C2314yes—
120C43⋊#95C2314yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C25×C43C2311yescharacteristic
124C23×C4×C43—24no—
125C23×C4×C43—24no—
126C23×C4×C43—42no—
127C23×C4×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C23×C4×C43C2314yes—
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43—24no—
135C2×C4⋊C4×C43—42no—
136C2×C4⋊C4×C43C2314yes—
137C2×C4⋊C4×C43C2314yes—
138C2×C22⋊C4×C43—24no—
139C2×C22⋊C4×C43C2×C418yes—
140C2×C22⋊C4×C43C2314yes—
141C2×C22⋊C4×C43C2314yes—
142#95×C43C2314yes—
143#95×C43C2314yes—
144C24×C43—22no—
145C24×C43—22no—
146C24×C43—22no—
147C24×C43—22no—
148C24×C43C22×C414yes—
149C24×C43#4114yes—
150C24×C43#4114yes—
151C24×C43C2412yes—
152C24×C43C2411yescharacteristic
153C22×C4×C43—28no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—28no—
161C22×C4×C43—22no—
162C22×C4×C43—22no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43—44no—
171C22×C4×C43—416no—
172C22×C4×C43C22×C414yes—
173C22×C4×C43C22×C414yes—
174C22×C4×C43#4114yes—
175C22×C4×C43C2412yes—
176C22×C4×C43C2412yes—
177C22×C4×C43C2412yes—
178C22×C4×C43C2412yes—
179C22×C4×C43C2412yes—
180C22×C4×C43C2412yes—
181C22×Dic43—28no—
182C22×Dic43—232no—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—28no—
186C22×Dic43—22no—
187C22×Dic43—22no—
188C22×Dic43—28no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43—22no—
197C22×Dic43—28no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43—22no—
203C22×Dic43—22no—
204C22×Dic43—22no—
205C22×Dic43—44no—
206C22×Dic43—416no—
207C22×Dic43C22×C414yes—
208C22×Dic43C22×C414yes—
209C22×Dic43C22×C414yes—
210C22×Dic43C22×C414yes—
211C22×Dic43C22×C4116yes—
212C22×Dic43#4114yes—
213C22×Dic43C2412yes—
214C22×Dic43C2412yes—
215C22×Dic43C2412yes—
216C22×Dic43C2412yes—
217C22×Dic43C2412yes—
218C22×Dic43C2412yes—
219C22×Dic43C2412yes—
220C22×Dic43C2412yes—
221C4⋊C4×C43—28no—
222C4⋊C4×C43—44no—
223C22⋊C4×C43—28no—
224C22⋊C4×C43C22×C4116yes—
225C22⋊Dic43—28no—
226C22⋊Dic43C22×C4116yes—
227C4⋊Dic43—28no—
228C4⋊Dic43—44no—
229Dic43⋊C4C22×C4116yescomplemented
230Dic43⋊C4C22×C4116yescomplemented
231C4×Dic43—28no—
232C4×Dic43—28no—
233C4×Dic43—44no—
234C4×Dic43—44no—
235C4×Dic43C22×C4116yescomplemented
236C4×Dic43C22×C4116yescomplemented
237C23×C43—28no—
238C23×C43—28no—
239C23×C43—28no—
240C23×C43—28no—
241C23×C43—28no—
242C23×C43—28no—
243C23×C43—22no—
244C23×C43—22no—
245C23×C43—22no—
246C23×C43—22no—
247C23×C43#117116yes—
248C23×C43C23×C414yes—
249C23×C43C23×C412yes—
250C23×C43C2×#4112yes—
251C23×C43C2×#4114yes—
252C23×C43C2×#4112yes—
253C23×C43C2×#4112yes—
254C23×C43C2×#4114yes—
255C23×C43C2×#4112yes—
256C23×C43H(5,𝔽2)12yes—
257C23×C432−1+412yes—
258C23×C43C2511yescharacteristic
259C2×C4×C43—28no—
260C2×C4×C43—28no—
261C2×C4×C43—28no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—416no—
278C2×C4×C43—44no—
279C2×C4×C43—44no—
280C2×C4×C43—44no—
281C2×C4×C43C23×C414yes—
282C2×C4×C43C23×C414yes—
283C2×C4×C43C2×#4114yes—
284C2×Dic43—232no—
285C2×Dic43—28no—
286C2×Dic43—28no—
287C2×Dic43—28no—
288C2×Dic43—28no—
289C2×Dic43—28no—
290C2×Dic43—22no—
291C2×Dic43—22no—
292C2×Dic43—22no—
293C2×Dic43—22no—
294C2×Dic43—22no—
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—416no—
310C2×Dic43—44no—
311C2×Dic43—44no—
312C2×Dic43—44no—
313C2×Dic43C23×C414yes—
314C2×Dic43C23×C414yes—
315C2×Dic43C23×C414yes—
316C2×Dic43C23×C414yes—
317C2×Dic43C2×#4114yes—
318C2×#2343—431nomaximal, Sylow
319C22×C43—232no—
320C22×C43—24no—
321C22×C43—24no—
322C22×C43—24no—
323C22×C43—24no—
324C22×C43—24no—
325C22×C43—24no—
326C22×C43C2×#11718yes—
327C22×C43C2×#11714yes—
328C22×C43C4×#4114yes—
329C22×C43#52014yes—
330C22×C43#55114yes—
331C22×C43#55114yes—
332C22×C43#55214yes—
333C22×C43#55214yes—
334C22×C43C24×C411yescharacteristic
335C22×C43C22×#4111yescharacteristic
336C22×C43C22×#4111yescharacteristic
337C22×C43C22×#4111yescharacteristic
338C22×C43C22×#4111yescharacteristic
339C22×C43C2×H(5,𝔽2)11yescharacteristic
340C22×C43C2×2−1+411yescharacteristic
341C4×C43—24no—
342C4×C43—24no—
343C4×C43—24no—
344C4×C43—42no—
345C4×C43—42no—
346C4×C43—42no—
347Dic43—24no—
348Dic43—24no—
349Dic43—24no—
350Dic43—24no—
351Dic43—24no—
352Dic43—42no—
353Dic43—42no—
354Dic43—42no—
355C22×#117—431no—
356#2343—4316no—
357C2×#387—431no—
358C2×#387—431no—
359C2×#387—431no—
360C2×#387—431no—
361C2×#385—431no—
362C2×#385D4311yescharacteristic
363C2×#383—431no—
364C2×#382—431no—
365C2×#381—431no—
366C2×C4×C4⋊C4—431no—
367C2×C4×C22⋊C4—431no—
368C2×C4×C22⋊C4—431no—
369C2×#376—431no—
370C22×#95—431no—
371C2×C43—28no—
372C2×C43#234318yescomplemented
373C2×C43C22×#11711yescharacteristic
374C2×C43C2×C4×#4111yescharacteristic
375C2×C43C2×#52011yescharacteristic
376C2×C43C2×#55111yescharacteristic
377C2×C43C2×#55111yescharacteristic
378C2×C43C2×#55211yescharacteristic
379C2×C43C2×#55211yescharacteristic
380C24×C4—431no—
381C24×C4—431no—
382C24×C4C2×D4311yescharacteristic
383C2×#117—438no—
384C2×#117—4316no—
385C22×C4⋊C4—431no—
386C22×C4⋊C4—431no—
387C22×C4⋊C4—431no—
388C22×C4⋊C4—431no—
389C22×C4⋊C4C2×D4311yescharacteristic
390C22×C4⋊C4C2×D4311yescharacteristic
391C22×C22⋊C4—431no—
392C22×C22⋊C4—431no—
393C22×C22⋊C4C2×D4311yescharacteristic
394C22×C22⋊C4C2×D4311yescharacteristic
395C22×C42—431no—
396C22×C42—431no—
397C22×C42—431no—
398C22×C42—431no—
399C22×C42—431no—
400C22×C42—431no—
401#387—438no—
402#387—438no—
403#387—438no—
404#387—438no—
405#385—438no—
406#385C2×D4318yes—
407#383—438no—
408#382—438no—
409#381—438no—
410C4×C4⋊C4—438no—
411C4×C22⋊C4—438no—
412C4×C22⋊C4—438no—
413#376—438no—
414C2×#95—438no—
415C2×#95—431no—
416C2×#95—431no—
417C2×#95—431no—
418C2×#95—431no—
419C2×#95—431no—
420C2×#95—431no—
421C2×#95—431no—
422C2×#95—431no—
423C2×#95—431no—
424C2×#95—431no—
425C2×#95—431no—
426C2×#95—431no—
427C2×#95—431no—
428C2×#95—431no—
429C2×#95C2×D4311yescharacteristic
430C2×#95C2×D4311yescharacteristic
431C43C2×#234311yescharacteristic, complemented, Sylow
432C25C22×D4311yescharacteristic
433C23×C4—24no—
434C23×C4—24no—
435C23×C4—42no—
436C23×C4—438no—
437C23×C4—434no—
438C23×C4—431no—
439C23×C4—431no—
440C23×C4—431no—
441C23×C4—431no—
442C23×C4—431no—
443C23×C4—431no—
444C23×C4—431no—
445C23×C4—431no—
446C23×C4—434no—
447C23×C4—864no—
448C23×C4—864no—
449C23×C4—864no—
450C23×C4—864no—
451C23×C4—1722no—
452C23×C4C22×D4311yescharacteristic
453C23×C4C22×D4311yescharacteristic
454C23×C4C22×D4311yescharacteristic
455C23×C4C22×D4314yes—
456C23×C4C22×D4311yescharacteristic
457C23×C4C22×D4311yescharacteristic
458C23×C4C22×D4311yescharacteristic
459#117—4364no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—438no—
463C2×C4⋊C4—438no—
464C2×C4⋊C4—434no—
465C2×C4⋊C4—434no—
466C2×C4⋊C4—434no—
467C2×C4⋊C4—434no—
468C2×C4⋊C4—864no—
469C2×C4⋊C4—1722no—
470C2×C4⋊C4C22×D4314yes—
471C2×C4⋊C4C22×D4314yes—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—438no—
474C2×C22⋊C4—434no—
475C2×C22⋊C4—434no—
476C2×C22⋊C4—864no—
477C2×C22⋊C4C4×D4318yes—
478C2×C22⋊C4C22×D4314yes—
479C2×C22⋊C4C22×D4314yes—
480C2×C42—438no—
481C2×C42—438no—
482C2×C42—434no—
483C2×C42—434no—
484C2×C42—434no—
485C2×C42—434no—
486C2×C42—434no—
487C2×C42—434no—
488C2×C42—864no—
489C2×C42—864no—
490C2×C42—1722no—
491C2×C42—1722no—
492#95—434no—
493#95—434no—
494#95—434no—
495#95—434no—
496#95—434no—
497#95—434no—
498#95—434no—
499#95—434no—
500#95—434no—
501#95—434no—
502#95—434no—
503#95—434no—
504#95—434no—
505#95—434no—
506#95C22×D4314yes—
507#95C22×D4314yes—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24C2×C4×D4314yes—
513C24#1062190014yes—
514C24#1062190214yes—
515C24C23×D4312yes—
516C24C23×D4311yescharacteristic
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—28no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—28no—
534C22×C4—44no—
535C22×C4—416no—
536C22×C4—434no—
537C22×C4—434no—
538C22×C4—434no—
539C22×C4—434no—
540C22×C4—4316no—
541C22×C4—434no—
542C22×C4—432no—
543C22×C4—432no—
544C22×C4—432no—
545C22×C4—432no—
546C22×C4—432no—
547C22×C4—432no—
548C22×C4—432no—
549C22×C4—432no—
550C22×C4—868no—
551C22×C4—8632no—
552C22×C4—862no—
553C22×C4—862no—
554C22×C4—868no—
555C22×C4—862no—
556C22×C4—862no—
557C22×C4—862no—
558C22×C4—868no—
559C22×C4—862no—
560C22×C4—862no—
561C22×C4—862no—
562C22×C4—862no—
563C22×C4—862no—
564C22×C4—862no—
565C22×C4—862no—
566C22×C4—862no—
567C22×C4—862no—
568C22×C4—862no—
569C22×C4—868no—
570C22×C4—862no—
571C22×C4—862no—
572C22×C4—862no—
573C22×C4—862no—
574C22×C4—1724no—
575C22×C4—17216no—
576C22×C4C2×C4×D4314yes—
577C22×C4C2×C4×D4314yes—
578C22×C4#1062190014yes—
579C22×C4C23×D4312yes—
580C22×C4C23×D4312yes—
581C22×C4C23×D4312yes—
582C22×C4C23×D4312yes—
583C22×C4C23×D4312yes—
584C22×C4C23×D4312yes—
585C4⋊C4—28no—
586C4⋊C4—44no—
587C4⋊C4—4316no—
588C4⋊C4—4316no—
589C4⋊C4—868no—
590C4⋊C4—1724no—
591C22⋊C4—28no—
592C22⋊C4—4316no—
593C22⋊C4—868no—
594C22⋊C4C2×C4×D43116yes—
595C42—4316no—
596C42—4316no—
597C42—868no—
598C42—868no—
599C42—1724no—
600C42—1724no—
601C23—28no—
602C23—28no—
603C23—28no—
604C23—28no—
605C23—28no—
606C23—28no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23#13063283116yes—
612C23C22×C4×D4314yes—
613C23C22×C4×D4312yes—
614C23#41×D4312yes—
615C23C2×#1062190014yes—
616C23C2×#1062190012yes—
617C23C2×#1062190012yes—
618C23C2×#1062190214yes—
619C23C2×#1062190212yes—
620C23#1306337012yes—
621C23#1306337212yes—
622C23C24×D4311yescharacteristic
623C2×C4—28no—
624C2×C4—28no—
625C2×C4—28no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—416no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—434no—
646C2×C4—434no—
647C2×C4—434no—
648C2×C4—434no—
649C2×C4—434no—
650C2×C4—868no—
651C2×C4—8632no—
652C2×C4—868no—
653C2×C4—868no—
654C2×C4—868no—
655C2×C4—868no—
656C2×C4—862no—
657C2×C4—862no—
658C2×C4—862no—
659C2×C4—862no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—862no—
664C2×C4—862no—
665C2×C4—862no—
666C2×C4—862no—
667C2×C4—862no—
668C2×C4—862no—
669C2×C4—862no—
670C2×C4—862no—
671C2×C4—862no—
672C2×C4—862no—
673C2×C4—862no—
674C2×C4—862no—
675C2×C4—17216no—
676C2×C4—1724no—
677C2×C4—1724no—
678C2×C4—1724no—
679C2×C4C22×C4×D4314yes—
680C2×C4C22×C4×D4314yes—
681C2×C4C2×#1062190014yes—
682C22—24no—
683C22—24no—
684C22—24no—
685C22—24no—
686C22—24no—
687C22—232no—
688C22—24no—
689C22C2×#1306328318yes—
690C22C2×#1306328314yes—
691C22C4×#1062190014yes—
692C22#1458337814yes—
693C22#1458357614yes—
694C22#1458358014yes—
695C22#1458358614yes—
696C22#1458359114yes—
697C22C23×C4×D4311yescharacteristic
698C22C2×#41×D4311yescharacteristic
699C22C22×#1062190011yescharacteristic
700C22C22×#1062190011yescharacteristic
701C22C22×#1062190211yescharacteristic
702C22C2×#1306337011yescharacteristic
703C22C2×#1306337211yescharacteristic
704C4—24no—
705C4—24no—
706C4—24no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—864no—
711C4—864no—
712C4—864no—
713C4—864no—
714C4—864no—
715C4—1722no—
716C4—1722no—
717C4—1722no—
718C2—28no—
719C2#1913745318yesdirect product factor
720C2C22×#1306328311yescharacteristic
721C2C2×C4×#1062190011yescharacteristic
722C2C2×#1458337811yescharacteristic
723C2C2×#1458357611yescharacteristic
724C2C2×#1458358011yescharacteristic
725C2C2×#1458358611yescharacteristic
726C2C2×#1458359111yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#385C2
socleC24×C43C24
prime radicalC25×C43C23
cosocleC23×C43C25
hypercenterC2×#385D43
hypocenterC43C2×#2343
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. #19137453C2direct (N × H)
3. C2×#14582786C2semidirect
4. C2×#14582786C2semidirect
5. C2×#14582780C2semidirect
6. C2×#14582780C2semidirect
8. C2×#14582766C2semidirect
9. C2×#14582764C2semidirect
11. C2×C4⋊C4×Dic43C2semidirect
14. C2×#14582744C2semidirect
19. C2×#13063281C4semidirect
33. #14582786C22semidirect
34. #14582786C22semidirect
35. #14582780C22semidirect
36. #14582780C22semidirect
38. #14582766C22semidirect
39. #14582764C22semidirect
41. C4⋊C4×Dic43C22semidirect
44. #14582744C22semidirect
84. #13063281C2×C4semidirect
89. C2×Dic43⋊C4C2×C4semidirect
90. C2×Dic43⋊C4C2×C4semidirect
101. C2×C4×Dic43C2×C4semidirect
102. C2×C4×Dic43C2×C4semidirect
229. Dic43⋊C4C22×C4semidirect
230. Dic43⋊C4C22×C4semidirect
235. C4×Dic43C22×C4semidirect
236. C4×Dic43C22×C4semidirect
372. C2×C43#2343semidirect
431. C43C2×#2343semidirect
719. C2#19137453direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130632812
#191374532
C2×#145827862
C2×#145827802
C2×#145827742
C2×#145827662
C2×#145827642
C2×#145827602
C2×C4⋊C4×Dic432
C2×C22⋊C4×Dic432
C2×C4×C22⋊Dic432
C2×#145827442
C22×C43⋊#952
C2×C43×#3852
C2×#234343