Finite Group Databasebeta

← C2×#19148263 #26004909

Subgroups — C2×#19148263 #26004909

Order 11008.

12366 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063371C211yesmaximal, characteristic, complemented
2C22×#41×D43C211yesmaximal, characteristic, complemented
3#19148263C2132yesmaximal, direct product factor
4C2×#14583568C211yesmaximal, characteristic, complemented
5C2×#14583561C211yesmaximal, characteristic, complemented
6C2×#14583556C211yesmaximal, characteristic, complemented
7C2×#14583546C213yesmaximal, complemented
8C2×#14583545C213yesmaximal, complemented
9C2×#14583534C213yesmaximal, complemented
10C2×#14583533C213yesmaximal, complemented
11C2×#14583478C213yesmaximal, complemented
12C2×#14583462C213yesmaximal, complemented
13C2×#14583408C213yesmaximal, complemented
14C2×#121×D43C213yesmaximal, complemented
15C2×#14583381C211yesmaximal, characteristic, complemented
16C2×C43×#550C211yesmaximal, characteristic, complemented
17C2×#13063371—216no—
18C2×#13063371C22116yescomplemented
19C22×#10621902C2211yescharacteristic
20C22×#10621902C2211yescharacteristic, complemented
21C22×#10621898C2213yescomplemented
22C22×#10621898C2213yescomplemented
23C22×#10621900C2213yescomplemented
24C2×#41×D43—216no—
25C2×#41×D43C22116yescomplemented
26C22×Q8×D43C2211yescharacteristic, complemented
27C23×D172C2213yescomplemented
28C22×D4×D43C2213yescomplemented
29C22×D4×D43C2213yescomplemented
30C22×D4×D43C2213yescomplemented
31C22×D4×D43C2216yescomplemented
32C23×C4×D43C2213yescomplemented
33#14583568C22116yescomplemented
34#14583561C22116yescomplemented
35#14583556C22116yescomplemented
36#14583546C22148yescomplemented
37#14583545C22148yescomplemented
38#14583534C22148yescomplemented
39#14583533C22148yescomplemented
40#14583478C22148yescomplemented
41#14583462C22148yescomplemented
42C2×#13063321C2213yescomplemented
43C2×#13063313C2213yescomplemented
44C2×#13063312C2213yescomplemented
45#14583408C22148yescomplemented
46C2×#13063310C2213yescomplemented
47C2×#13063307C2213yescomplemented
48C2×#13063305C2213yescomplemented
49C2×#13063304C2213yescomplemented
50C2×#13063303C2211yescharacteristic, complemented
51C2×#13063302C2213yescomplemented
52C2×#13063300C2213yescomplemented
53C2×#13063299C2213yescomplemented
54C2×#13063298C2216yescomplemented
55C2×#13063298C2213yescomplemented
56C2×#13063297C2216yescomplemented
57C2×#13063297C2213yescomplemented
58C2×#13063296C2216yescomplemented
59C2×#13063296C2213yescomplemented
60C2×#13063296C2213yescomplemented
61#121×D43C22148yescomplemented
62C2×#13063295C2213yescomplemented
63C2×#13063293C2216yescomplemented
64C2×#13063293C2213yescomplemented
65C2×#13063293C2216yescomplemented
66#14583381C22116yescomplemented
67C2×Q8×Dic43C2211yescharacteristic, complemented
68C2×C4×D172C2213yescomplemented
69C2×C4×D172C2213yescomplemented
70C2×#13063287C2213yescomplemented
71C2×C4×C22⋊D43C2213yescomplemented
72C2×C4×C22⋊D43C2213yescomplemented
73C2×#13063282C2213yescomplemented
74C2×C4⋊C4×D43C2213yescomplemented
75C2×C22⋊C4×D43C2216yescomplemented
76C22×#41×C43C2211yescharacteristic, complemented
77C22×#41×C43C2211yescharacteristic, complemented
78C43×#550C22116yescomplemented
79C2×#127×C43C2213yescomplemented
80C2×#121×C43C2213yescomplemented
81C2×#121×C43C2213yescomplemented
82C2×C4×Q8×C43C2211yescharacteristic, complemented
83C2×C4×D4×C43C2213yescomplemented
84C24×D43C2313yes—
85C24×D43C2316yes—
86#13063371—2128no—
87C2×#10621902—28no—
88C2×#10621902D4116yescomplemented
89C2×#10621902C2318yes—
90C2×#10621902C2318yescomplemented
91C2×#10621898—224no—
92C2×#10621898—224no—
93C2×#10621898C23124yescomplemented
94C2×#10621898C23124yescomplemented
95C2×#10621900—224no—
96C2×#10621900C23124yescomplemented
97#41×D43—2128no—
98C22×Dic86C2311yescharacteristic
99C22×Dic86C2313yes—
100C2×Q8×D43—28no—
101C2×Q8×D43C2318yescomplemented
102C22×D172—224no—
103C22×D172C2313yes—
104C22×D172C2313yes—
105C22×D172C2313yes—
106C22×D172C2313yes—
107C22×D172C23124yescomplemented
108C22×C22⋊D43C2313yes—
109C22×C22⋊D43C2316yes—
110C22×C22⋊D43C2313yes—
111C22×C22⋊D43C2313yes—
112C22×C22⋊D43C2313yes—
113C22×C22⋊D43C2316yes—
114C2×D4×D43—224no—
115C2×D4×D43—224no—
116C2×D4×D43—224no—
117C2×D4×D43—424no—
118C2×D4×D43C23124yescomplemented
119C2×D4×D43C23124yescomplemented
120C2×D4×D43C23124yescomplemented
121C2×D4×D43C23148yescomplemented
122C23×Dic43C2313yes—
123C22×C4×D43—224no—
124C22×C4×D43C2313yes—
125C22×C4×D43C2313yes—
126C22×C4×D43C2313yes—
127C22×C4×D43C2311yescharacteristic
128C22×C4×D43C2316yes—
129C22×C4×D43C2313yes—
130C22×C4×D43C23124yescomplemented
131#13063321C23124yescomplemented
132#13063313C23124yescomplemented
133#13063312C23124yescomplemented
134#13063310C23124yescomplemented
135#13063307C23124yescomplemented
136#13063305C23124yescomplemented
137#13063304C23124yescomplemented
138#13063303C2318yescomplemented
139#13063302C23124yescomplemented
140#13063300C23124yescomplemented
141#13063299C23124yescomplemented
142#13063298C23124yescomplemented
143#13063298C23148yescomplemented
144#13063297C23148yescomplemented
145#13063297C23124yescomplemented
146#13063296C23124yescomplemented
147#13063296C23124yescomplemented
148#13063296C23148yescomplemented
149#13063295C23124yescomplemented
150#13063293C23124yescomplemented
151#13063293C23148yescomplemented
152#13063293C23148yescomplemented
153Q8×Dic43C2318yescomplemented
154C4×D172C23124yescomplemented
155C4×D172C23124yescomplemented
156#13063287C23124yescomplemented
157C4×C22⋊D43C23124yescomplemented
158C4×C22⋊D43C23124yescomplemented
159#13063282C23124yescomplemented
160C2×C4⋊Dic43C2313yes—
161C2×C4⋊Dic43C2313yes—
162C2×Dic43⋊C4C2313yes—
163C2×Dic43⋊C4C2311yescharacteristic
164C2×Dic43⋊C4C2311yescharacteristic
165C2×Dic43⋊C4C2313yes—
166C4⋊C4×D43C23124yescomplemented
167C2×C22⋊Dic43C2316yes—
168C2×C22⋊Dic43C2313yes—
169C2×C22⋊Dic43C2313yes—
170C2×(C2×D43)⋊C4C2313yes—
171C2×(C2×D43)⋊C4C2316yes—
172C2×(C2×D43)⋊C4C2313yes—
173C2×(C2×D43)⋊C4C2313yes—
174C2×(C2×D43)⋊C4C2311yescharacteristic
175C2×(C2×D43)⋊C4C2311yescharacteristic
176C2×(C2×D43)⋊C4C2313yes—
177C22⋊C4×D43C23148yescomplemented
178C2×C4×Dic43C2313yes—
179C2×#41×C43—28no—
180C2×#41×C43—28no—
181C2×#41×C43C2318yescomplemented
182C2×#41×C43C2318yescomplemented
183C22×Q8×C43C2311yescharacteristic
184C22×D4×C43C2313yes—
185C22×D4×C43C2313yes—
186C22×D4×C43C2313yes—
187C22×D4×C43C2316yes—
188C23×C4×C43C2313yes—
189C23×C4×C43C2313yes—
190#127×C43C23124yescomplemented
191#121×C43C23124yescomplemented
192#121×C43C23124yescomplemented
193C4×Q8×C43C2318yescomplemented
194C4×D4×C43C23124yescomplemented
195C2×C4⋊C4×C43C2311yescharacteristic
196C2×C4⋊C4×C43C2313yes—
197C2×C22⋊C4×C43C2313yes—
198C2×C22⋊C4×C43C2313yes—
199C2×C42×C43C2313yes—
200C24×C43C2413yes—
201C24×C43C2413yes—
202C23×D43—212no—
203C23×D43—212no—
204C23×D43—224no—
205C23×D43—46no—
206C23×D43—412no—
207C23×D43—412no—
208C23×D43C2413yes—
209C23×D43C24112yes—
210C23×D43C2413yes—
211C23×D43C2411yescharacteristic
212C23×D43C24124yes—
213#41×C43—232no—
214#41×C43—232no—
215C2×Q8×C43C2×D418yescomplemented
216C2×Q8×C43C2414yes—
217C2×D4×C43—212no—
218C2×D4×C43—212no—
219C2×D4×C43—46no—
220C2×D4×C43—412no—
221C2×D4×C43C24112yes—
222C2×D4×C43C24112yes—
223C2×D4×C43C24112yes—
224C2×D4×C43C24124yes—
225C22×C4×C43—212no—
226C22×C4×C43—212no—
227C22×C4×C43C2411yescharacteristic
228C22×C4×C43C2413yes—
229C22×C4×C43C2411yescharacteristic
230C22×C4×C43C2411yescharacteristic
231C22×C4×C43C24112yes—
232C22×C4×C43C24112yes—
233C22×C4×C43C2413yes—
234C2×C22⋊D43—212no—
235C2×C22⋊D43—212no—
236C2×C22⋊D43—224no—
237C2×C22⋊D43—212no—
238C2×C22⋊D43—412no—
239C2×C22⋊D43—46no—
240C2×C22⋊D43C24112yes—
241C2×C22⋊D43C24124yes—
242C2×C22⋊D43C24112yes—
243C2×C22⋊D43C24112yes—
244C2×C22⋊D43C24112yes—
245C2×C22⋊D43C24124yes—
246C22×Dic43—212no—
247C22×Dic43C2411yescharacteristic
248C22×Dic43C2413yes—
249C22×Dic43C2413yes—
250C22×Dic43C2411yescharacteristic
251C22×Dic43C24112yes—
252C22×Dic43C2411yescharacteristic
253#10621902—232no—
254#10621902C2×D4164yescomplemented
255Q8×D43—232no—
256#10621900—296no—
257D4×D43—296no—
258D4×D43—296no—
259D4×D43—296no—
260D4×D43—496no—
261#10621898—296no—
262#10621898—296no—
263C2×D172—212no—
264C2×D172—296no—
265C2×D172—212no—
266C2×D172—212no—
267C2×D172C2×D4124yescomplemented
268C2×D172C24112yes—
269C2×D172C24112yes—
270C2×D172C24112yes—
271C2×D172C24112yes—
272C2×C4×D43—212no—
273C2×C4×D43—212no—
274C2×C4×D43—24no—
275C2×C4×D43—296no—
276C2×C4×D43—212no—
277C2×C4×D43—412no—
278C2×C4×D43C2×D4124yescomplemented
279C2×C4×D43C24112yes—
280C2×C4×D43C24112yes—
281C2×C4×D43C24112yes—
282C2×C4×D43C2414yes—
283C2×C4×D43C24124yes—
284C2×C4×D43C24112yes—
285C2×Dic86—212no—
286C2×Dic86—24no—
287C2×Dic86C2414yes—
288C2×Dic86C24112yes—
289C4⋊C4×C43C2414yes—
290C4⋊C4×C43C24112yes—
291C22⋊C4×C43C24112yes—
292C22⋊C4×C43C24112yes—
293C42×C43C24112yes—
294C22⋊Dic43C24124yes—
295C22⋊Dic43C24112yes—
296C22⋊Dic43C24112yes—
297(C2×D43)⋊C4C24112yes—
298(C2×D43)⋊C4C24124yes—
299(C2×D43)⋊C4C24112yes—
300(C2×D43)⋊C4C24112yes—
301(C2×D43)⋊C4C2414yes—
302(C2×D43)⋊C4C2414yes—
303(C2×D43)⋊C4C24112yes—
304C4⋊Dic43C24112yes—
305C4⋊Dic43C24112yes—
306Dic43⋊C4C24112yes—
307Dic43⋊C4C2414yes—
308Dic43⋊C4C2414yes—
309Dic43⋊C4C24112yes—
310C4×Dic43C24112yes—
311C23×C43—26no—
312C23×C43—26no—
313C23×C43—26no—
314C23×C43—26no—
315C23×C43—26no—
316C23×C43—26no—
317C23×C43C2516yes—
318C23×C43C2516yes—
319C23×C43C2511yescharacteristic
320C22×D43—22no—
321C22×D43—26no—
322C22×D43—22no—
323C22×D43—26no—
324C22×D43—26no—
325C22×D43—26no—
326C22×D43—26no—
327C22×D43—224no—
328C22×D43—224no—
329C22×D43—248no—
330C22×D43—412no—
331C22×D43—448no—
332C22×D43—424no—
333C22×D43—424no—
334C22×D43—848no—
335C22×D43C22×D4112yes—
336C22×D43H(5,𝔽2)14yescomplemented
337C22×D43C2516yes—
338C22×D43C2516yes—
339C22×D43C2512yes—
340Q8×C43C22×D4116yescomplemented
341D4×C43—224no—
342D4×C43—224no—
343D4×C43—424no—
344D4×C43—412no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—26no—
348C2×C4×C43—22no—
349C2×C4×C43—224no—
350C2×C4×C43—224no—
351C2×C4×C43C22×D4112yes—
352C2×C4×C43C2512yes—
353C2×C4×C43C2516yes—
354C2×C4×C43C2512yes—
355C2×C4×C43C2512yes—
356C2×C4×C43C2516yes—
357C22⋊D43—224no—
358C22⋊D43—248no—
359C22⋊D43—224no—
360C22⋊D43—224no—
361C22⋊D43—424no—
362C22⋊D43—412no—
363C2×Dic43—26no—
364C2×Dic43—22no—
365C2×Dic43—26no—
366C2×Dic43—22no—
367C2×Dic43—224no—
368C2×Dic43C22×D414yes—
369C2×Dic43C2512yes—
370C2×Dic43C2516yes—
371C2×Dic43C2512yes—
372C2×Dic43C2516yes—
373C2×Dic43C2512yes—
374D172—224no—
375D172—224no—
376D172—224no—
377D172C22×D4148yescomplemented
378C4×D43—224no—
379C4×D43—224no—
380C4×D43—224no—
381C4×D43—28no—
382C4×D43—424no—
383C4×D43C22×D4148yescomplemented
384Dic86—224no—
385Dic86—28no—
386C2×#3488—431nomaximal, Sylow
387C22×C43—26no—
388C22×C43—26no—
389C22×C43—26no—
390C22×C43—26no—
391C22×C43—26no—
392C22×C43—26no—
393C22×C43—412no—
394C22×C43—412no—
395C22×C43C23×D412yes—
396C22×C43C2×H(5,𝔽2)12yes—
397C22×C43#58512yes—
398C22×C43C2611yescharacteristic
399C2×D43—22no—
400C2×D43—26no—
401C2×D43—22no—
402C2×D43—26no—
403C2×D43—28no—
404C2×D43—224no—
405C2×D43—26no—
406C2×D43—26no—
407C2×D43—26no—
408C2×D43—448no—
409C2×D43—412no—
410C2×D43—848no—
411C2×D43C23×D4112yes—
412C2×D43C2×H(5,𝔽2)14yescomplemented
413C4×C43—22no—
414C4×C43—22no—
415C4×C43—26no—
416C4×C43—22no—
417C4×C43C23×D4112yes—
418Dic43—26no—
419Dic43—22no—
420Dic43—26no—
421Dic43—22no—
422Dic43C23×D414yes—
423C22×H(5,𝔽2)—431no—
424C23×#41—431no—
425#3488—4332no—
426C2×#550—431no—
427C2×#550D4311yescharacteristic, complemented
428C2×#548—431no—
429C2×#548—431no—
430C2×#546—433no—
431C2×#546—433no—
432C2×D42—433no—
433C2×D42—433no—
434C2×#537—433no—
435C2×#535—433no—
436C2×#525—433no—
437C22×#121—433no—
438C2×#520—431no—
439C2×C43—46no—
440C2×C43—46no—
441C2×C43#348814yescomplemented
442C2×C43C24×D411yescharacteristic
443C2×C43C22×H(5,𝔽2)11yescharacteristic
444C2×C43C2×#58511yescharacteristic
445D43—24no—
446D43—212no—
447D43—46no—
448C2×H(5,𝔽2)—4316no—
449C2×H(5,𝔽2)—8616no—
450C22×#41—4316no—
451C22×#41—431no—
452C22×#41—431no—
453C22×#41—433no—
454C22×#41—433no—
455C22×#41—433no—
456C22×#41—8616no—
457C22×#41C2×D4311yescharacteristic, complemented
458C22×#41C2×D4311yescharacteristic, complemented
459C23×Q8—431no—
460C23×D4—433no—
461C23×D4—433no—
462C23×D4—433no—
463C23×D4—436no—
464C23×D4—433no—
465C24×C4—433no—
466#550—4316no—
467#550C2×D43116yescomplemented
468#548—4316no—
469#548—4316no—
470#546—4348no—
471#546—4348no—
472D42—4348no—
473D42—4348no—
474#537—4348no—
475#535—4348no—
476C2×#127—433no—
477C2×#127C2×D4313yescomplemented
478C2×#124—433no—
479C2×#124—433no—
480#525—4348no—
481C2×#123—433no—
482C2×#123—433no—
483C2×C22⋊Q8—433no—
484C2×C22⋊Q8—431no—
485C2×C22⋊Q8—433no—
486C2×C22⋊Q8—433no—
487C2×#121—433no—
488C2×#121—436no—
489C2×#121—433no—
490C2×#121—436no—
491C2×#121—433no—
492C2×#121—433no—
493C2×#121—4348no—
494C2×#121—433no—
495C2×#121—433no—
496C2×#121—436no—
497C2×#121C2×D4313yescomplemented
498C2×#121C2×D4313yescomplemented
499C2×#120—433no—
500C2×#120—436no—
501C2×#120—436no—
502C2×#120—433no—
503#520—4316no—
504C2×C4×Q8—431no—
505C2×C4×Q8C2×D4311yescharacteristic, complemented
506C2×C4×D4—433no—
507C2×C4×D4—433no—
508C2×C4×D4—433no—
509C2×C4×D4—433no—
510C2×C4×D4—433no—
511C2×C4×D4C2×D4313yescomplemented
512C2×#117—433no—
513C22×C4⋊C4—433no—
514C22×C22⋊C4—436no—
515C43C2×#348811yescharacteristic, complemented, Sylow
516C25—433no—
517C25—436no—
518H(5,𝔽2)—86128no—
519C2×#41—28no—
520C2×#41—28no—
521C2×#41—4316no—
522C2×#41—438no—
523C2×#41—438no—
524C2×#41—4324no—
525C2×#41—4324no—
526C2×#41—4324no—
527C2×#41—8624no—
528C2×#41—8624no—
529C2×#41—8624no—
530C2×#41—86128no—
531C2×#41—868no—
532C2×#41C22×D4318yescomplemented
533C2×#41C22×D4318yescomplemented
534C22×Q8—438no—
535C22×Q8—431no—
536C22×Q8—433no—
537C22×Q8—868no—
538C22×Q8C22×D4311yescharacteristic
539C22×D4—433no—
540C22×D4—436no—
541C22×D4—433no—
542C22×D4—433no—
543C22×D4—433no—
544C22×D4—436no—
545C22×D4—4324no—
546C22×D4—4324no—
547C22×D4—4324no—
548C22×D4—4348no—
549C22×D4—433no—
550C22×D4—433no—
551C22×D4—433no—
552C22×D4—433no—
553C22×D4—4324no—
554C22×D4—8624no—
555C22×D4—8624no—
556C22×D4—8624no—
557C22×D4—8624no—
558C22×D4—17224no—
559C22×D4C22×D4313yes—
560C22×D4C22×D4313yes—
561C22×D4C22×D4313yes—
562C22×D4C22×D4316yes—
563C23×C4—433no—
564C23×C4—433no—
565C23×C4—433no—
566C23×C4—433no—
567C23×C4—433no—
568C23×C4—431no—
569C23×C4—4324no—
570C23×C4—436no—
571C23×C4—8624no—
572C23×C4C22×D4313yes—
573C23×C4C22×D4313yes—
574#127—4324no—
575#127C22×D43124yescomplemented
576#124—4324no—
577#124—4324no—
578#123—4324no—
579#123—4324no—
580C22⋊Q8—4324no—
581C22⋊Q8—438no—
582C22⋊Q8—4324no—
583C22⋊Q8—4324no—
584#121—4348no—
585#121—4324no—
586#121—4324no—
587#121—4348no—
588#121—4324no—
589#121—4324no—
590#121—4324no—
591#121—4324no—
592#121—4348no—
593#121C22×D43124yescomplemented
594#121C22×D43124yescomplemented
595#120—4324no—
596#120—4348no—
597#120—4348no—
598#120—4324no—
599C4×Q8—438no—
600C4×Q8C22×D4318yescomplemented
601C4×D4—4324no—
602C4×D4—4324no—
603C4×D4—4324no—
604C4×D4—4324no—
605C4×D4—4324no—
606C4×D4C22×D43124yescomplemented
607#117—4324no—
608C2×C4⋊C4—433no—
609C2×C4⋊C4—433no—
610C2×C4⋊C4—431no—
611C2×C4⋊C4—431no—
612C2×C4⋊C4—433no—
613C2×C4⋊C4—433no—
614C2×C4⋊C4—4324no—
615C2×C4⋊C4C22×D4313yes—
616C2×C4⋊C4C22×D4311yescharacteristic
617C2×C22⋊C4—436no—
618C2×C22⋊C4—433no—
619C2×C22⋊C4—433no—
620C2×C22⋊C4—433no—
621C2×C22⋊C4—436no—
622C2×C22⋊C4—433no—
623C2×C22⋊C4—433no—
624C2×C22⋊C4—431no—
625C2×C22⋊C4—431no—
626C2×C22⋊C4—433no—
627C2×C22⋊C4—4348no—
628C2×C22⋊C4C22×D4313yes—
629C2×C22⋊C4C22×D4313yes—
630C2×C42—433no—
631C2×C42C22×D4313yes—
632C24—433no—
633C24—431no—
634C24—433no—
635C24—4312no—
636C24—4324no—
637C24—8624no—
638C24—8612no—
639C24—8612no—
640C24—17212no—
641C24—17212no—
642C24—1726no—
643C24C23×D4313yes—
644C24C23×D4313yes—
645#41—232no—
646#41—232no—
647#41—4364no—
648#41—8696no—
649#41—8696no—
650#41—8696no—
651#41—8632no—
652C2×Q8—434no—
653C2×Q8—4312no—
654C2×Q8—864no—
655C2×Q8—8632no—
656C2×Q8—8612no—
657C2×Q8D4×D4318yescomplemented
658C2×Q8C23×D4314yes—
659C2×D4—212no—
660C2×D4—212no—
661C2×D4—412no—
662C2×D4—46no—
663C2×D4—4312no—
664C2×D4—4324no—
665C2×D4—4312no—
666C2×D4—4312no—
667C2×D4—4312no—
668C2×D4—4324no—
669C2×D4—4324no—
670C2×D4—4312no—
671C2×D4—4312no—
672C2×D4—4312no—
673C2×D4—4312no—
674C2×D4—8696no—
675C2×D4—8612no—
676C2×D4—8612no—
677C2×D4—8696no—
678C2×D4—8612no—
679C2×D4—8696no—
680C2×D4—8696no—
681C2×D4—8612no—
682C2×D4—8624no—
683C2×D4—8612no—
684C2×D4—8612no—
685C2×D4—17212no—
686C2×D4—1726no—
687C2×D4—17296no—
688C2×D4C23×D43112yes—
689C2×D4C23×D43112yes—
690C2×D4C23×D43112yes—
691C2×D4C23×D43124yes—
692C22×C4—212no—
693C22×C4—212no—
694C22×C4—431no—
695C22×C4—4324no—
696C22×C4—4312no—
697C22×C4—4312no—
698C22×C4—431no—
699C22×C4—433no—
700C22×C4—433no—
701C22×C4—431no—
702C22×C4—4312no—
703C22×C4—4312no—
704C22×C4—4312no—
705C22×C4—434no—
706C22×C4—4324no—
707C22×C4—864no—
708C22×C4—8696no—
709C22×C4—8612no—
710C22×C4—8612no—
711C22×C4—8612no—
712C22×C4—8612no—
713C22×C4—17212no—
714C22×C4C23×D43112yes—
715C22×C4C23×D43112yes—
716C22×C4C23×D4311yescharacteristic
717C22×C4C23×D4313yes—
718C22×C4C23×D4311yescharacteristic
719C22×C4C23×D4311yescharacteristic
720C22×C4C23×D4313yes—
721C4⋊C4—4312no—
722C4⋊C4—4312no—
723C4⋊C4—434no—
724C4⋊C4—434no—
725C4⋊C4—4312no—
726C4⋊C4—4312no—
727C4⋊C4C23×D43112yes—
728C4⋊C4C23×D4314yes—
729C22⋊C4—4324no—
730C22⋊C4—4312no—
731C22⋊C4—4312no—
732C22⋊C4—4312no—
733C22⋊C4—4324no—
734C22⋊C4—4312no—
735C22⋊C4—4312no—
736C22⋊C4—434no—
737C22⋊C4—434no—
738C22⋊C4—4312no—
739C22⋊C4C23×D43112yes—
740C22⋊C4C23×D43112yes—
741C42—4312no—
742C42C23×D43112yes—
743C23—26no—
744C23—26no—
745C23—26no—
746C23—26no—
747C23—26no—
748C23—26no—
749C23—4312no—
750C23—434no—
751C23—436no—
752C23—432no—
753C23—436no—
754C23—8648no—
755C23—8624no—
756C23—8624no—
757C23—862no—
758C23—866no—
759C23—866no—
760C23—862no—
761C23—866no—
762C23—866no—
763C23—866no—
764C23—34448no—
765C23—17224no—
766C23—17224no—
767C23—17212no—
768C23—17248no—
769C23C24×D4316yes—
770C23C24×D4316yes—
771C23C24×D4311yescharacteristic
772Q8—868no—
773Q8—8624no—
774Q8C2×D4×D43116yescomplemented
775D4—224no—
776D4—224no—
777D4—424no—
778D4—412no—
779D4—4348no—
780D4—8624no—
781D4—8624no—
782D4—8624no—
783D4—8624no—
784D4—8648no—
785D4—8624no—
786D4—8624no—
787D4—17224no—
788D4—17212no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—26no—
792C2×C4—22no—
793C2×C4—224no—
794C2×C4—224no—
795C2×C4—434no—
796C2×C4—432no—
797C2×C4—4348no—
798C2×C4—432no—
799C2×C4—436no—
800C2×C4—436no—
801C2×C4—432no—
802C2×C4—868no—
803C2×C4—8624no—
804C2×C4—8624no—
805C2×C4—862no—
806C2×C4—866no—
807C2×C4—866no—
808C2×C4—862no—
809C2×C4—8624no—
810C2×C4—8624no—
811C2×C4—17224no—
812C2×C4C2×D4×D43112yes—
813C2×C4C24×D4312yes—
814C2×C4C24×D4316yes—
815C2×C4C24×D4312yes—
816C2×C4C24×D4312yes—
817C2×C4C24×D4316yes—
818C22—26no—
819C22—26no—
820C22—26no—
821C22—26no—
822C22—26no—
823C22—26no—
824C22—412no—
825C22—412no—
826C22—4312no—
827C22—434no—
828C22—862no—
829C22—866no—
830C22—866no—
831C22—862no—
832C22—8624no—
833C22—868no—
834C22—866no—
835C22—866no—
836C22—866no—
837C22—34448no—
838C22—17248no—
839C22—17212no—
840C22C22×D4×D4312yes—
841C22H(5,𝔽2)×D4312yes—
842C22#1458373512yes—
843C22C25×D4311yescharacteristic
844C4—22no—
845C4—22no—
846C4—26no—
847C4—22no—
848C4—434no—
849C4—862no—
850C4—866no—
851C4—866no—
852C4—862no—
853C4C22×D4×D43112yes—
854C2—46no—
855C2—46no—
856C2—8612no—
857C2—864no—
858C2—1726no—
859C2#1914826314yesdirect product factor
860C2C23×D4×D4311yescharacteristic
861C2C2×H(5,𝔽2)×D4311yescharacteristic
862C2C2×#1458373511yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#550C2
socleC23×C43C25
hypercenterC2×#550D43
hypocenterC43C2×#3488
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C22×#13063371C2semidirect
2. C22×#41×D43C2semidirect
3. #19148263C2direct (N × H)
4. C2×#14583568C2semidirect
5. C2×#14583561C2semidirect
6. C2×#14583556C2semidirect
7. C2×#14583546C2semidirect
8. C2×#14583545C2semidirect
9. C2×#14583534C2semidirect
10. C2×#14583533C2semidirect
11. C2×#14583478C2semidirect
12. C2×#14583462C2semidirect
13. C2×#14583408C2semidirect
14. C2×#121×D43C2semidirect
15. C2×#14583381C2semidirect
16. C2×C43×#550C2semidirect
18. C2×#13063371C22semidirect
20. C22×#10621902C22semidirect
21. C22×#10621898C22semidirect
22. C22×#10621898C22semidirect
23. C22×#10621900C22semidirect
25. C2×#41×D43C22semidirect
26. C22×Q8×D43C22semidirect
27. C23×D172C22semidirect
28. C22×D4×D43C22semidirect
29. C22×D4×D43C22semidirect
30. C22×D4×D43C22semidirect
31. C22×D4×D43C22semidirect
32. C23×C4×D43C22semidirect
33. #14583568C22semidirect
34. #14583561C22semidirect
35. #14583556C22semidirect
36. #14583546C22semidirect
37. #14583545C22semidirect
38. #14583534C22semidirect
39. #14583533C22semidirect
40. #14583478C22semidirect
41. #14583462C22semidirect
42. C2×#13063321C22semidirect
43. C2×#13063313C22semidirect
44. C2×#13063312C22semidirect
45. #14583408C22semidirect
46. C2×#13063310C22semidirect
47. C2×#13063307C22semidirect
48. C2×#13063305C22semidirect
49. C2×#13063304C22semidirect
50. C2×#13063303C22semidirect
51. C2×#13063302C22semidirect
52. C2×#13063300C22semidirect
53. C2×#13063299C22semidirect
54. C2×#13063298C22semidirect
55. C2×#13063298C22semidirect
56. C2×#13063297C22semidirect
57. C2×#13063297C22semidirect
58. C2×#13063296C22semidirect
59. C2×#13063296C22semidirect
60. C2×#13063296C22semidirect
61. #121×D43C22semidirect
62. C2×#13063295C22semidirect
63. C2×#13063293C22semidirect
64. C2×#13063293C22semidirect
65. C2×#13063293C22semidirect
66. #14583381C22semidirect
67. C2×Q8×Dic43C22semidirect
68. C2×C4×D172C22semidirect
69. C2×C4×D172C22semidirect
70. C2×#13063287C22semidirect
71. C2×C4×C22⋊D43C22semidirect
72. C2×C4×C22⋊D43C22semidirect
73. C2×#13063282C22semidirect
74. C2×C4⋊C4×D43C22semidirect
75. C2×C22⋊C4×D43C22semidirect
76. C22×#41×C43C22semidirect
77. C22×#41×C43C22semidirect
78. C43×#550C22semidirect
79. C2×#127×C43C22semidirect
80. C2×#121×C43C22semidirect
81. C2×#121×C43C22semidirect
82. C2×C4×Q8×C43C22semidirect
83. C2×C4×D4×C43C22semidirect
88. C2×#10621902D4semidirect
90. C2×#10621902C23semidirect
93. C2×#10621898C23semidirect
94. C2×#10621898C23semidirect
96. C2×#10621900C23semidirect
101. C2×Q8×D43C23semidirect
107. C22×D172C23semidirect
118. C2×D4×D43C23semidirect
119. C2×D4×D43C23semidirect
120. C2×D4×D43C23semidirect
121. C2×D4×D43C23semidirect
130. C22×C4×D43C23semidirect
131. #13063321C23semidirect
132. #13063313C23semidirect
133. #13063312C23semidirect
134. #13063310C23semidirect
135. #13063307C23semidirect
136. #13063305C23semidirect
137. #13063304C23semidirect
138. #13063303C23semidirect
139. #13063302C23semidirect
140. #13063300C23semidirect
141. #13063299C23semidirect
142. #13063298C23semidirect
143. #13063298C23semidirect
144. #13063297C23semidirect
145. #13063297C23semidirect
146. #13063296C23semidirect
147. #13063296C23semidirect
148. #13063296C23semidirect
149. #13063295C23semidirect
150. #13063293C23semidirect
151. #13063293C23semidirect
152. #13063293C23semidirect
153. Q8×Dic43C23semidirect
154. C4×D172C23semidirect
155. C4×D172C23semidirect
156. #13063287C23semidirect
157. C4×C22⋊D43C23semidirect
158. C4×C22⋊D43C23semidirect
159. #13063282C23semidirect
166. C4⋊C4×D43C23semidirect
177. C22⋊C4×D43C23semidirect
181. C2×#41×C43C23semidirect
182. C2×#41×C43C23semidirect
190. #127×C43C23semidirect
191. #121×C43C23semidirect
192. #121×C43C23semidirect
193. C4×Q8×C43C23semidirect
194. C4×D4×C43C23semidirect
215. C2×Q8×C43C2×D4semidirect
254. #10621902C2×D4semidirect
267. C2×D172C2×D4semidirect
278. C2×C4×D43C2×D4semidirect
336. C22×D43H(5,𝔽2)semidirect
340. Q8×C43C22×D4semidirect
377. D172C22×D4semidirect
383. C4×D43C22×D4semidirect
412. C2×D43C2×H(5,𝔽2)semidirect
427. C2×#550D43semidirect
441. C2×C43#3488semidirect
457. C22×#41C2×D43semidirect
458. C22×#41C2×D43semidirect
467. #550C2×D43semidirect
477. C2×#127C2×D43semidirect
497. C2×#121C2×D43semidirect
498. C2×#121C2×D43semidirect
505. C2×C4×Q8C2×D43semidirect
511. C2×C4×D4C2×D43semidirect
515. C43C2×#3488semidirect
532. C2×#41C22×D43semidirect
533. C2×#41C22×D43semidirect
575. #127C22×D43semidirect
593. #121C22×D43semidirect
594. #121C22×D43semidirect
600. C4×Q8C22×D43semidirect
606. C4×D4C22×D43semidirect
657. C2×Q8D4×D43semidirect
774. Q8C2×D4×D43semidirect
859. C2#19148263direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633712
C22×#41×D432
#191482632
C2×#145835682
C2×#145835612
C2×#145835562
C2×#145835462
C2×#145835452
C2×#145835342
C2×#145835332
C2×#145834782
C2×#145834622
C2×#145834082
C2×#121×D432
C2×#145833812
C2×C43×#5502
C2×#348843