Finite Group Databasebeta

← C2×#19146340 #25971867

Subgroups — C2×#19146340 #25971867

Order 11008.

2742 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#10621885C211yesmaximal, characteristic, complemented
2C22×Q16×D43C211yesmaximal, characteristic, complemented
3C2×Q8×C22⋊D43C211yesmaximal, characteristic
4C2×#14583562C211yesmaximal, characteristic
5#19146340C2116yesmaximal, direct product factor
6C2×#14583277C211yesmaximal, characteristic, complemented
7C2×#14583139C211yesmaximal, characteristic, complemented
8C2×#14583138C211yesmaximal, characteristic, complemented
9C2×#14583108C211yesmaximal, characteristic, complemented
10C2×#14583107C211yesmaximal, characteristic, complemented
11C2×#14583057C211yesmaximal, characteristic, complemented
12C2×#14583056C211yesmaximal, characteristic, complemented
13C2×#14583053C211yesmaximal, characteristic, complemented
14C2×#14582991C211yesmaximal, characteristic, complemented
15C2×(C22⋊D43)⋊C8C211yesmaximal, characteristic
16C2×C43×#451C211yesmaximal, characteristic, complemented
17C23×Dic86C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19C22×Q8×D43C2211yescharacteristic
20C22×Dic172C2211yescharacteristic
21C22×Dic172C2211yescharacteristic
22C22×#10621885—28no—
23C22×#10621885C2211yescharacteristic
24C22×#10621885C2211yescharacteristic
25C22×#10621885C2211yescharacteristic
26C22×#10621885C2211yescharacteristic
27C22×#10621885C2211yescharacteristic
28C22×#10621885C2218yescomplemented
29C2×Q16×D43—28no—
30C2×Q16×D43C2218yescomplemented
31C23×C43⋊C8C2211yescharacteristic
32C22×C8×D43C2211yescharacteristic
33Q8×C22⋊D43—24no—
34Q8×C22⋊D43C2218yes—
35#14583562—24no—
36#14583562C2218yes—
37C2×#13063324—21no—
38C2×#13063323—21no—
39C2×#13063323C2211yescharacteristic
40C2×#13063323C2211yescharacteristic
41C2×#13063305C2211yescharacteristic
42C2×#13063304—21no—
43C2×#13063304C2211yescharacteristic
44C2×#13063303—21no—
45C2×#13063302—21no—
46C2×#13063301—21no—
47C2×#13063301C2211yescharacteristic
48C2×Q8×Dic43C2211yescharacteristic
49C2×#13063290C2211yescharacteristic
50C2×C4×C22⋊D43—21no—
51C2×C4×C22⋊D43C2211yescharacteristic
52C2×(C22⋊D43)⋊C4—21no—
53#14583277C2218yescomplemented
54#14583139C2218yescomplemented
55#14583138C2218yescomplemented
56#14583108C2218yescomplemented
57#14583107C2218yescomplemented
58#14583057C2218yescomplemented
59#14583056C2218yescomplemented
60#14583053C2218yescomplemented
61#14582991C2218yescomplemented
62(C22⋊D43)⋊C8C2218yes—
63C2×#13063258C2211yescharacteristic
64C2×Dic43⋊C8C2211yescharacteristic
65C2×#13063250C2211yescharacteristic
66C2×#13063250C2211yescharacteristic
67C2×#13063249C2211yescharacteristic
68C2×#13063248C2211yescharacteristic
69C2×(C2×D43)⋊C8C2211yescharacteristic
70C2×C8×Dic43C2211yescharacteristic
71C23×Q8×C43C2211yescharacteristic
72C22×Q16×C43C2211yescharacteristic
73C22×Q16×C43C2211yescharacteristic
74C2×C22⋊Q8×C43C2211yescharacteristic
75C43×#451C2218yescomplemented
76C2×#103×C43C2211yescharacteristic
77C2×#103×C43C2211yescharacteristic
78C2×C22⋊C8×C43C2211yescharacteristic
79C22×Dic86—24no—
80C22×Dic86—22no—
81C22×Dic86—21no—
82C22×Dic86—21no—
83C22×Dic86—21no—
84C22×Dic86—42no—
85C22×Dic86C2311yescharacteristic
86C22×Dic86C2311yescharacteristic
87C22×Dic86C2314yes—
88C22×Dic86C2311yescharacteristic
89C2×Q8×D43—22no—
90C2×Q8×D43—22no—
91C2×Q8×D43—24no—
92C2×Q8×D43—24no—
93C2×Q8×D43—42no—
94C2×Q8×D43—42no—
95C2×Q8×D43C2314yes—
96C2×Q8×D43C2314yes—
97C22×C22⋊D43D411yescharacteristic
98C23×Dic43—21no—
99C22×C4×D43—21no—
100C22×C4×D43—21no—
101C22×C4×D43C2311yescharacteristic
102C2×Dic172—24no—
103C2×Dic172—42no—
104C2×Dic172C2314yes—
105C2×Dic172C2314yes—
106C2×#10621885—24no—
107C2×#10621885—24no—
108C2×#10621885—232no—
109C2×#10621885—24no—
110C2×#10621885—24no—
111C2×#10621885D418yescomplemented
112C2×#10621885C2314yes—
113C2×#10621885C2314yes—
114C2×#10621885C2314yes—
115C2×#10621885C2314yes—
116C2×#10621885C2314yes—
117Q16×D43—232no—
118C22×C43⋊C8—24no—
119C22×C43⋊C8C2311yescharacteristic
120C22×C43⋊C8C2314yes—
121C22×C43⋊C8C2311yescharacteristic
122C2×C8×D43—24no—
123C2×C8×D43C2314yes—
124#13063324—28no—
125#13063323—28no—
126#13063323—22no—
127#13063323—22no—
128#13063323C2314yes—
129#13063323C2314yes—
130#13063305—22no—
131#13063305C2314yes—
132#13063304—22no—
133#13063304—28no—
134#13063304C2314yes—
135#13063303—28no—
136#13063302—28no—
137#13063301—22no—
138#13063301—28no—
139#13063301C2314yes—
140Q8×Dic43—22no—
141Q8×Dic43C2314yes—
142#13063290—22no—
143#13063290C2314yes—
144C4×C22⋊D43—28no—
145C4×C22⋊D43D414yes—
146C4×C22⋊D43C2314yes—
147(C22⋊D43)⋊C4—28no—
148C2×C4⋊Dic43—21no—
149C2×C4⋊Dic43—21no—
150C2×C4⋊Dic43C2311yescharacteristic
151C2×Dic43⋊C4—21no—
152C2×Dic43⋊C4—21no—
153C2×Dic43⋊C4—21no—
154C2×Dic43⋊C4—21no—
155C2×Dic43⋊C4—21no—
156C2×Dic43⋊C4—21no—
157C2×Dic43⋊C4—21no—
158C2×Dic43⋊C4D411yescharacteristic
159C2×C22⋊Dic43—21no—
160C2×C22⋊Dic43D411yescharacteristic
161C2×(C2×D43)⋊C4—21no—
162C2×(C2×D43)⋊C4—21no—
163C2×(C2×D43)⋊C4D411yescharacteristic
164C2×C4×Dic43—21no—
165C2×C4×Dic43—21no—
166C2×C4×Dic43C2311yescharacteristic
167#13063258C2314yes—
168Dic43⋊C8C2314yes—
169#13063250C2314yes—
170#13063250C2314yes—
171#13063249C2314yes—
172#13063248C2314yes—
173(C2×D43)⋊C8C2314yes—
174C8×Dic43C2314yes—
175C22×Q8×C43—22no—
176C22×Q8×C43—21no—
177C22×Q8×C43—24no—
178C22×Q8×C43—42no—
179C22×Q8×C43C2311yescharacteristic
180C22×Q8×C43C2311yescharacteristic
181C22×Q8×C43C2314yes—
182C22×Q8×C43C2311yescharacteristic
183C23×C4×C43—21no—
184C23×C4×C43C2311yescharacteristic
185C2×Q16×C43—24no—
186C2×Q16×C43—42no—
187C2×Q16×C43C2314yes—
188C2×Q16×C43C2314yes—
189C22×C8×C43C2311yescharacteristic
190C22×C8×C43C2311yescharacteristic
191C22⋊Q8×C43—22no—
192C22⋊Q8×C43C2314yes—
193C2×C4⋊C4×C43—21no—
194C2×C4⋊C4×C43C2311yescharacteristic
195C2×C22⋊C4×C43—21no—
196#103×C43C2314yes—
197#103×C43C2314yes—
198C22⋊C8×C43C2314yes—
199C24×C43C2×D411yescharacteristic
200C23×D43C2×D411yescharacteristic
201C2×Q8×C43—21no—
202C2×Q8×C43—21no—
203C2×Q8×C43—24no—
204C2×Q8×C43—21no—
205C2×Q8×C43—22no—
206C2×Q8×C43—28no—
207C2×Q8×C43—22no—
208C2×Q8×C43—22no—
209C2×Q8×C43—22no—
210C2×Q8×C43—22no—
211C2×Q8×C43—44no—
212C2×Q8×C43—44no—
213C2×Q8×C43—48no—
214C2×Q8×C43C2×D414yes—
215C2×Q8×C43C2412yes—
216C2×Q8×C43C2412yes—
217C2×Q8×C43C2412yes—
218C22×C4×C43—22no—
219C22×C4×C43—22no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—24no—
225C22×C4×C43—44no—
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D412yes—
228C22×C4×C43C2412yes—
229C22×C4×C43C2411yescharacteristic
230C2×C22⋊D43Q1618yescomplemented
231C2×C22⋊D43C2×D414yes—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—24no—
237C22×Dic43—44no—
238C22×Dic43C2×D411yescharacteristic
239C22×Dic43C2×D411yescharacteristic
240C22×Dic43C2×D411yescharacteristic
241Q8×D43—28no—
242Q8×D43—28no—
243Q8×D43—44no—
244Q8×D43—44no—
245Q8×D43—48no—
246Q8×D43—48no—
247C2×C4×D43—22no—
248C2×C4×D43—22no—
249C2×C4×D43—24no—
250C2×C4×D43—24no—
251C2×C4×D43—44no—
252C2×C4×D43—44no—
253C2×C4×D43C2×D412yes—
254C2×C4×D43C2412yes—
255C2×Dic86—21no—
256C2×Dic86—22no—
257C2×Dic86—22no—
258C2×Dic86—22no—
259C2×Dic86—22no—
260C2×Dic86—22no—
261C2×Dic86—28no—
262C2×Dic86—24no—
263C2×Dic86—21no—
264C2×Dic86—21no—
265C2×Dic86—24no—
266C2×Dic86—24no—
267C2×Dic86—44no—
268C2×Dic86—48no—
269C2×Dic86—44no—
270C2×Dic86—44no—
271C2×Dic86—44no—
272C2×Dic86C2×D414yes—
273C2×Dic86C2412yes—
274C2×Dic86C2412yes—
275C2×Dic86C2412yes—
276Q16×C43—28no—
277Q16×C43—44no—
278C2×C8×C43—22no—
279C2×C8×C43—22no—
280C2×C8×C43C2412yes—
281C2×C8×C43C2412yes—
282C4⋊C4×C43—24no—
283C4⋊C4×C43—21no—
284C4⋊C4×C43C2412yes—
285C22⋊C4×C43—24no—
286C22⋊Dic43—24no—
287C22⋊Dic43C2×D414yes—
288#10621885—28no—
289#10621885—28no—
290#10621885—28no—
291#10621885—28no—
292#10621885C2×D4116yescomplemented
293(C2×D43)⋊C4—24no—
294(C2×D43)⋊C4—24no—
295(C2×D43)⋊C4C2×D414yes—
296C4⋊Dic43—21no—
297C4⋊Dic43—24no—
298C4⋊Dic43—24no—
299C4⋊Dic43C2412yes—
300Dic43⋊C4—24no—
301Dic43⋊C4—24no—
302Dic43⋊C4—24no—
303Dic43⋊C4—24no—
304Dic43⋊C4—24no—
305Dic43⋊C4—24no—
306Dic43⋊C4—24no—
307Dic43⋊C4C2×D414yes—
308C4×Dic43—24no—
309C4×Dic43—24no—
310C4×Dic43C2×D412yes—
311C4×Dic43C2412yes—
312C2×C43⋊C8—22no—
313C2×C43⋊C8—28no—
314C2×C43⋊C8C2×D414yes—
315C2×C43⋊C8C2412yes—
316C2×C43⋊C8C2412yes—
317Dic172—28no—
318Dic172—44no—
319C8×D43—28no—
320C23×C43—22no—
321C23×C43—22no—
322C23×C43C2×Q1614yescomplemented
323C23×C43C22×D412yes—
324C23×C43C22×D411yescharacteristic
325C22×D43—22no—
326C22×D43—22no—
327C22×D43C2×Q1614yescomplemented
328C22×D43C22×D412yes—
329Q8×C43—24no—
330Q8×C43—22no—
331Q8×C43—22no—
332Q8×C43—22no—
333Q8×C43—22no—
334Q8×C43—22no—
335Q8×C43—48no—
336Q8×C43—42no—
337Q8×C43—42no—
338Q8×C43C22×D414yes—
339C2×C4×C43—22no—
340C2×C4×C43—24no—
341C2×C4×C43—22no—
342C2×C4×C43—24no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—48no—
349C2×C4×C43—42no—
350C2×C4×C43—42no—
351C2×C4×C43—42no—
352C2×C4×C43C22×D412yes—
353C2×C4×C43C22×D411yescharacteristic
354C2×C4×C43C22×D412yes—
355C2×C4×C43H(5,𝔽2)12yes—
356C2×C4×C43C2511yescharacteristic
357C22⋊D43C2×Q16116yescomplemented
358C2×Dic43—24no—
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—22no—
362C2×Dic43—22no—
363C2×Dic43—22no—
364C2×Dic43—22no—
365C2×Dic43—48no—
366C2×Dic43—42no—
367C2×Dic43—42no—
368C2×Dic43—42no—
369C2×Dic43C2×Q1614yescomplemented
370C2×Dic43C22×D412yes—
371C2×Dic43C22×D412yes—
372C2×Dic43C22×D412yes—
373C4×D43—24no—
374C4×D43—22no—
375C4×D43—22no—
376C4×D43—48no—
377C4×D43—48no—
378Dic86—24no—
379Dic86—22no—
380Dic86—22no—
381Dic86—22no—
382Dic86—22no—
383Dic86—22no—
384Dic86—48no—
385Dic86—48no—
386Dic86—48no—
387Dic86—42no—
388Dic86—42no—
389Dic86C22×D414yes—
390C8×C43—22no—
391C8×C43—22no—
392C43⋊C8—22no—
393C43⋊C8C22×D414yes—
394C2×D4×Q16—431nomaximal, Sylow
395C22×C43—22no—
396C22×C43—28no—
397C22×C43—22no—
398C22×C43D4212yes—
399C22×C43C22×Q1612yes—
400C22×C43C22×Q1614yescomplemented
401C22×C43#57812yes—
402C22×C43C23×D411yescharacteristic
403C2×D43—22no—
404C2×D43—28no—
405C2×D43—22no—
406C2×D43C22×Q1614yescomplemented
407C4×C43—22no—
408C4×C43—24no—
409C4×C43—42no—
410C4×C43—42no—
411C4×C43—42no—
412C4×C43D4212yes—
413C4×C43C23×D411yescharacteristic
414C4×C43C2×H(5,𝔽2)11yescharacteristic
415Dic43—24no—
416Dic43—22no—
417Dic43—22no—
418Dic43—42no—
419Dic43—42no—
420Dic43—42no—
421Dic43C22×Q1614yescomplemented
422C23×Q16—431no—
423C23×Q16—431no—
424C2×D4×Q8—431no—
425C2×D4×Q8—431no—
426D4×Q16—4316no—
427C2×#494—431no—
428C2×#467—431no—
429C2×#467—431no—
430C2×#462—431no—
431C2×#462—431no—
432C2×#451—431no—
433C2×#451—431no—
434C2×#451—431no—
435C2×#451D4311yescharacteristic, complemented
436C2×C4×Q16—431no—
437C2×C8×D4—431no—
438C2×C43—24no—
439C2×C43D4×Q1614yescomplemented
440C2×C43C2×D4211yescharacteristic
441C2×C43C23×Q1611yescharacteristic
442C2×C43C2×#57811yescharacteristic
443D43—24no—
444C23×Q8—431no—
445C23×Q8—431no—
446C23×Q8—431no—
447C23×Q8C2×D4311yescharacteristic
448C22×Q16—431no—
449C22×Q16—431no—
450C22×Q16—431no—
451C22×Q16—431no—
452C22×Q16—431no—
453C22×Q16—438no—
454C22×Q16—438no—
455C22×Q16—431no—
456C22×Q16—431no—
457C22×Q16—868no—
458C22×Q16—868no—
459C22×Q16C2×D4311yescharacteristic
460C22×Q16C2×D4311yescharacteristic
461C23×C8—431no—
462C23×C8—431no—
463D4×Q8—438no—
464D4×Q8—438no—
465D4×Q8—864no—
466D4×Q8—864no—
467C2×C4⋊Q8—431no—
468C2×C4⋊Q8—431no—
469C2×C4⋊Q8—861no—
470C2×C4⋊Q8—861no—
471C2×C22⋊Q8—431no—
472C2×C22⋊Q8—431no—
473C2×C22⋊Q8—431no—
474C2×C22⋊Q8—861no—
475C2×C22⋊Q8—861no—
476C2×C22⋊Q8—861no—
477C2×C22⋊Q8—861no—
478C2×C22⋊Q8C2×D4311yescharacteristic
479C2×C4×Q8—431no—
480C2×C4×Q8—431no—
481C2×C4×D4—431no—
482C2×C4×D4—861no—
483C2×C4×D4—861no—
484#494—438no—
485#467—438no—
486#467—438no—
487#462—438no—
488#462—438no—
489#451—438no—
490#451—438no—
491#451—438no—
492#451C2×D4318yescomplemented
493C4×Q16—438no—
494C8×D4—438no—
495C2×#107—431no—
496C2×C4⋊C8—431no—
497C2×#103—431no—
498C2×#103—431no—
499C2×#103—431no—
500C2×#103—431no—
501C2×#103C2×D4311yescharacteristic
502C2×#103C2×D4311yescharacteristic
503C2×C22⋊C8—431no—
504C2×C22⋊C8C2×D4311yescharacteristic
505C2×C4×C8—431no—
506C43C2×D4×Q1611yescharacteristic, complemented, Sylow
507C22×Q8—21no—
508C22×Q8—22no—
509C22×Q8—24no—
510C22×Q8—42no—
511C22×Q8—434no—
512C22×Q8—434no—
513C22×Q8—431no—
514C22×Q8—431no—
515C22×Q8—431no—
516C22×Q8—434no—
517C22×Q8—861no—
518C22×Q8—861no—
519C22×Q8—864no—
520C22×Q8—862no—
521C22×Q8—862no—
522C22×Q8—861no—
523C22×Q8—862no—
524C22×Q8—864no—
525C22×Q8—864no—
526C22×Q8—1722no—
527C22×Q8—1722no—
528C22×Q8—1722no—
529C22×Q8C22×D4311yescharacteristic
530C22×Q8C22×D4311yescharacteristic
531C22×Q8C22×D4314yes—
532C22×Q8C22×D4311yescharacteristic
533C22×D4—431no—
534C23×C4—21no—
535C23×C4—431no—
536C23×C4—861no—
537C23×C4—861no—
538C23×C4—861no—
539C23×C4C22×D4311yescharacteristic
540C2×Q16—24no—
541C2×Q16—42no—
542C2×Q16—438no—
543C2×Q16—434no—
544C2×Q16—434no—
545C2×Q16—434no—
546C2×Q16—434no—
547C2×Q16—434no—
548C2×Q16—434no—
549C2×Q16—434no—
550C2×Q16—864no—
551C2×Q16—864no—
552C2×Q16—864no—
553C2×Q16—8632no—
554C2×Q16—8632no—
555C2×Q16—864no—
556C2×Q16—864no—
557C2×Q16—1722no—
558C2×Q16C22×D4314yes—
559C2×Q16C22×D4314yes—
560C22×C8—431no—
561C22×C8—431no—
562C22×C8—434no—
563C22×C8—434no—
564C22×C8—864no—
565C22×C8—864no—
566C22×C8C22×D4311yescharacteristic
567C22×C8C22×D4311yescharacteristic
568C4⋊Q8—434no—
569C4⋊Q8—434no—
570C4⋊Q8—862no—
571C4⋊Q8—862no—
572C4⋊Q8—868no—
573C4⋊Q8—868no—
574C22⋊Q8—22no—
575C22⋊Q8—434no—
576C22⋊Q8—434no—
577C22⋊Q8—434no—
578C22⋊Q8—868no—
579C22⋊Q8—868no—
580C22⋊Q8—868no—
581C22⋊Q8—868no—
582C22⋊Q8—862no—
583C22⋊Q8—862no—
584C22⋊Q8—862no—
585C22⋊Q8C22×D4314yes—
586C4×Q8—434no—
587C4×Q8—434no—
588C4×Q8—862no—
589C4×Q8—862no—
590C4×D4—434no—
591C4×D4—434no—
592C4×D4—868no—
593C4×D4—868no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—431no—
596C2×C4⋊C4—431no—
597C2×C4⋊C4—861no—
598C2×C4⋊C4—861no—
599C2×C4⋊C4—861no—
600C2×C4⋊C4—861no—
601C2×C4⋊C4—861no—
602C2×C4⋊C4—861no—
603C2×C4⋊C4—861no—
604C2×C4⋊C4—861no—
605C2×C4⋊C4—861no—
606C2×C4⋊C4C22×D4311yescharacteristic
607C2×C22⋊C4—21no—
608C2×C22⋊C4—431no—
609C2×C22⋊C4—431no—
610C2×C22⋊C4—861no—
611C2×C22⋊C4—861no—
612C2×C22⋊C4—861no—
613C2×C42—431no—
614C2×C42—861no—
615C2×C42—861no—
616#107—434no—
617C4⋊C8—434no—
618#103—434no—
619#103—434no—
620#103—434no—
621#103—434no—
622#103C22×D4314yes—
623#103C22×D4314yes—
624C22⋊C8—434no—
625C22⋊C8C22×D4314yes—
626C4×C8—434no—
627C24—431no—
628C24D4×D4311yescharacteristic
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—24no—
632C2×Q8—21no—
633C2×Q8—22no—
634C2×Q8—28no—
635C2×Q8—22no—
636C2×Q8—22no—
637C2×Q8—22no—
638C2×Q8—22no—
639C2×Q8—44no—
640C2×Q8—44no—
641C2×Q8—48no—
642C2×Q8—434no—
643C2×Q8—432no—
644C2×Q8—432no—
645C2×Q8—432no—
646C2×Q8—864no—
647C2×Q8—864no—
648C2×Q8—868no—
649C2×Q8—861no—
650C2×Q8—864no—
651C2×Q8—861no—
652C2×Q8—861no—
653C2×Q8—862no—
654C2×Q8—868no—
655C2×Q8—868no—
656C2×Q8—862no—
657C2×Q8—862no—
658C2×Q8—862no—
659C2×Q8—862no—
660C2×Q8—1724no—
661C2×Q8—1724no—
662C2×Q8—1724no—
663C2×Q8—1728no—
664C2×Q8—1724no—
665C2×Q8—1724no—
666C2×Q8—1724no—
667C2×Q8—1728no—
668C2×Q8—1728no—
669C2×Q8D4×D4314yes—
670C2×Q8C23×D4312yes—
671C2×Q8C23×D4312yes—
672C2×Q8C23×D4312yes—
673C2×D4—438no—
674C2×D4—434no—
675C22×C4—21no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—24no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—44no—
683C22×C4—431no—
684C22×C4—431no—
685C22×C4—431no—
686C22×C4—432no—
687C22×C4—432no—
688C22×C4—864no—
689C22×C4—864no—
690C22×C4—861no—
691C22×C4—862no—
692C22×C4—862no—
693C22×C4—864no—
694C22×C4—861no—
695C22×C4—861no—
696C22×C4—861no—
697C22×C4—1724no—
698C22×C4—1724no—
699C22×C4—1724no—
700C22×C4D4×D4312yes—
701C22×C4D4×D4311yescharacteristic
702C22×C4C23×D4312yes—
703C22×C4C23×D4311yescharacteristic
704Q16—28no—
705Q16—44no—
706Q16—4316no—
707Q16—868no—
708Q16—868no—
709Q16—868no—
710Q16—868no—
711Q16—868no—
712Q16—1724no—
713C2×C8—22no—
714C2×C8—22no—
715C2×C8—434no—
716C2×C8—432no—
717C2×C8—432no—
718C2×C8—868no—
719C2×C8—868no—
720C2×C8—862no—
721C2×C8C23×D4312yes—
722C2×C8C23×D4312yes—
723C4⋊C4—24no—
724C4⋊C4—21no—
725C4⋊C4—434no—
726C4⋊C4—432no—
727C4⋊C4—864no—
728C4⋊C4—864no—
729C4⋊C4—864no—
730C4⋊C4—864no—
731C4⋊C4—864no—
732C4⋊C4—864no—
733C4⋊C4—864no—
734C4⋊C4—864no—
735C4⋊C4—861no—
736C4⋊C4—864no—
737C4⋊C4C23×D4312yes—
738C22⋊C4—24no—
739C22⋊C4—434no—
740C22⋊C4—434no—
741C22⋊C4—864no—
742C22⋊C4—864no—
743C22⋊C4—864no—
744C42—432no—
745C42—432no—
746C42—864no—
747C42—864no—
748C23—22no—
749C23—22no—
750C23—434no—
751C23—432no—
752C23—862no—
753C23—862no—
754C23Q16×D4314yescomplemented
755C23C2×D4×D4312yes—
756C23C2×D4×D4311yescharacteristic
757Q8—22no—
758Q8—24no—
759Q8—22no—
760Q8—22no—
761Q8—22no—
762Q8—22no—
763Q8—48no—
764Q8—42no—
765Q8—42no—
766Q8—434no—
767Q8—862no—
768Q8—864no—
769Q8—862no—
770Q8—862no—
771Q8—862no—
772Q8—862no—
773Q8—1728no—
774Q8—1728no—
775Q8—1728no—
776Q8—1722no—
777Q8—1722no—
778Q8C2×D4×D4314yes—
779D4—4316no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—24no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—48no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—434no—
794C2×C4—432no—
795C2×C4—432no—
796C2×C4—432no—
797C2×C4—862no—
798C2×C4—862no—
799C2×C4—862no—
800C2×C4—864no—
801C2×C4—862no—
802C2×C4—862no—
803C2×C4—864no—
804C2×C4—862no—
805C2×C4—862no—
806C2×C4—862no—
807C2×C4—1728no—
808C2×C4—1728no—
809C2×C4—1728no—
810C2×C4—1722no—
811C2×C4—1722no—
812C2×C4—1722no—
813C2×C4C2×D4×D4312yes—
814C2×C4C2×D4×D4312yes—
815C2×C4C2×D4×D4311yescharacteristic
816C2×C4#1306337012yes—
817C2×C4C24×D4311yescharacteristic
818C8—22no—
819C8—22no—
820C8—434no—
821C8—862no—
822C22—22no—
823C22—28no—
824C22—22no—
825C22—434no—
826C22—862no—
827C22—868no—
828C22—862no—
829C22#1458353112yes—
830C22C2×Q16×D4312yes—
831C22C2×Q16×D4314yescomplemented
832C22#1458371512yes—
833C22C22×D4×D4311yescharacteristic
834C4—22no—
835C4—24no—
836C4—42no—
837C4—42no—
838C4—42no—
839C4—434no—
840C4—862no—
841C4—862no—
842C4—864no—
843C4—1722no—
844C4—1722no—
845C4—1722no—
846C4#1458353112yes—
847C4C22×D4×D4311yescharacteristic
848C4C2×#1306337011yescharacteristic
849C2—24no—
850C2—864no—
851C2#1914634014yesdirect product factor
852C2C2×#1458353111yescharacteristic
853C2C22×Q16×D4311yescharacteristic
854C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#451C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenterC2×#451D43
hypocenterC43C2×D4×Q16
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C23×#10621885C2semidirect
2. C22×Q16×D43C2semidirect
5. #19146340C2direct (N × H)
6. C2×#14583277C2semidirect
7. C2×#14583139C2semidirect
8. C2×#14583138C2semidirect
9. C2×#14583108C2semidirect
10. C2×#14583107C2semidirect
11. C2×#14583057C2semidirect
12. C2×#14583056C2semidirect
13. C2×#14583053C2semidirect
14. C2×#14582991C2semidirect
16. C2×C43×#451C2semidirect
28. C22×#10621885C22semidirect
30. C2×Q16×D43C22semidirect
53. #14583277C22semidirect
54. #14583139C22semidirect
55. #14583138C22semidirect
56. #14583108C22semidirect
57. #14583107C22semidirect
58. #14583057C22semidirect
59. #14583056C22semidirect
60. #14583053C22semidirect
61. #14582991C22semidirect
75. C43×#451C22semidirect
111. C2×#10621885D4semidirect
230. C2×C22⋊D43Q16semidirect
292. #10621885C2×D4semidirect
322. C23×C43C2×Q16semidirect
327. C22×D43C2×Q16semidirect
357. C22⋊D43C2×Q16semidirect
369. C2×Dic43C2×Q16semidirect
400. C22×C43C22×Q16semidirect
406. C2×D43C22×Q16semidirect
421. Dic43C22×Q16semidirect
435. C2×#451D43semidirect
439. C2×C43D4×Q16semidirect
492. #451C2×D43semidirect
506. C43C2×D4×Q16semidirect
754. C23Q16×D43semidirect
831. C22C2×Q16×D43semidirect
851. C2#19146340direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#106218852
C22×Q16×D432
C2×Q8×C22⋊D432
C2×#145835622
#191463402
C2×#145832772
C2×#145831392
C2×#145831382
C2×#145831082
C2×#145831072
C2×#145830572
C2×#145830562
C2×#145830532
C2×#145829912
C2×(C22⋊D43)⋊C82
C2×C43×#4512
C2×D4×Q1643