Finite Group Databasebeta

← C2×#19148386 #26005065

Subgroups — C2×#19148386 #26005065

Order 11008.

11534 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063373C211yesmaximal, characteristic, complemented
2C22×#13063371C211yesmaximal, characteristic, complemented
3#19148386C2132yesmaximal, direct product factor
4C2×#14583561C211yesmaximal, characteristic, complemented
5C2×#14583560C211yesmaximal, characteristic, complemented
6C2×#14583556C211yesmaximal, characteristic, complemented
7C2×#14583546C213yesmaximal, complemented
8C2×#14583545C213yesmaximal, complemented
9C2×#14583542C213yesmaximal, complemented
10C2×#14583540C213yesmaximal, complemented
11C2×#14583472C213yesmaximal, complemented
12C2×#14583465C213yesmaximal, complemented
13C2×#14583446C213yesmaximal, complemented
14C2×#124×D43C213yesmaximal, complemented
15C2×C4×#10621902C211yesmaximal, characteristic, complemented
16C2×C43×#548C211yesmaximal, characteristic, complemented
17C2×#13063373—216no—
18C2×#13063373C22116yescomplemented
19C2×#13063371—216no—
20C2×#13063371C22116yescomplemented
21C22×#10621902C2211yescharacteristic
22C22×#10621902C2211yescharacteristic
23C22×#10621902C2213yescomplemented
24C22×#10621898C2213yes—
25C22×#10621898C2213yescomplemented
26C22×#10621898C2213yescomplemented
27C22×Q8×D43C2211yescharacteristic, complemented
28C22×Q8×D43C2213yescomplemented
29C23×D172C2213yes—
30C22×D4×D43C2213yes—
31C22×D4×D43C2213yes—
32#14583561C22116yescomplemented
33#14583560C22116yescomplemented
34#14583556C22116yescomplemented
35#14583546C22148yescomplemented
36#14583545C22148yescomplemented
37#14583542C22148yescomplemented
38#14583540C22148yescomplemented
39#14583472C22148yescomplemented
40#14583465C22148yescomplemented
41#14583446C22148yescomplemented
42C2×#13063324C2213yescomplemented
43C2×#13063321C2213yescomplemented
44C2×#13063314C2213yescomplemented
45C2×#13063313C2213yescomplemented
46C2×#13063312C2213yescomplemented
47C2×#13063311C2213yescomplemented
48C2×#13063311C2216yescomplemented
49C2×#13063311C2211yescharacteristic, complemented
50#124×D43C22148yescomplemented
51C2×#13063310C2216yescomplemented
52C2×#13063307C2216yescomplemented
53C2×#13063305C2213yescomplemented
54C2×#13063304C2213yescomplemented
55C2×#13063301C2213yescomplemented
56C2×#13063300C2213yescomplemented
57C2×#13063300C2213yescomplemented
58C2×#13063299C2213yescomplemented
59C2×#13063298C2213yescomplemented
60C2×#13063298C2213yescomplemented
61C2×#13063296C2213yescomplemented
62C2×#13063296C2213yescomplemented
63C2×#13063295C2216yescomplemented
64C2×#13063293C2216yescomplemented
65C4×#10621902C22116yescomplemented
66C2×Q8×Dic43C2211yescharacteristic, complemented
67C2×C4×D172C2213yescomplemented
68C2×C4×D172C2213yescomplemented
69C2×#13063287C2213yescomplemented
70C2×C4×C22⋊D43C2213yescomplemented
71C2×C4×C22⋊D43C2213yescomplemented
72C2×#13063283C2213yescomplemented
73C2×C22⋊C4×D43C2216yescomplemented
74C2×C22⋊C4×D43C2216yescomplemented
75C2×C42×D43C2213yescomplemented
76C22×#41×C43C2211yescharacteristic
77C23×Q8×C43C2211yescharacteristic, complemented
78C43×#548C22116yescomplemented
79C2×#124×C43C2213yescomplemented
80C2×C22⋊Q8×C43C2213yescomplemented
81C2×#121×C43C2213yescomplemented
82C2×C4×Q8×C43C2211yescharacteristic, complemented
83C2×C4×D4×C43C2213yescomplemented
84C24×D43C2316yes—
85#13063373—2128no—
86#13063371—2128no—
87C2×#10621902—28no—
88C2×#10621902—224no—
89C2×#10621902D4116yescomplemented
90C2×#10621902C2318yes—
91C2×#10621902C2318yes—
92C2×#10621902C23124yescomplemented
93C2×#10621898—224no—
94C2×#10621898—224no—
95C2×#10621898—224no—
96C2×#10621898C23124yes—
97C2×#10621898C23124yescomplemented
98C2×#10621898C23124yescomplemented
99C22×Dic86C2313yes—
100C22×Dic86C2313yes—
101C22×Dic86C2311yescharacteristic
102C2×Q8×D43—28no—
103C2×Q8×D43—224no—
104C2×Q8×D43C2318yescomplemented
105C2×Q8×D43C23124yescomplemented
106C22×D172—224no—
107C22×D172C2313yes—
108C22×D172C2313yes—
109C22×D172C2313yes—
110C22×D172C23124yes—
111C22×D172C2313yes—
112C22×D172C2313yes—
113C22×C22⋊D43C2313yes—
114C22×C22⋊D43C2313yes—
115C22×C22⋊D43C2313yes—
116C22×C22⋊D43C2311yescharacteristic
117C22×C22⋊D43C2313yes—
118C22×C22⋊D43C2313yes—
119C2×D4×D43—224no—
120C2×D4×D43—224no—
121C2×D4×D43C23124yes—
122C2×D4×D43C23124yes—
123C22×C4×D43C2316yes—
124C22×C4×D43C2313yes—
125C22×C4×D43C2313yes—
126C22×C4×D43C2313yes—
127C22×C4×D43C2313yes—
128C22×C4×D43C2313yes—
129#13063324C23124yescomplemented
130#13063321C23124yescomplemented
131#13063314C23124yescomplemented
132#13063313C23124yescomplemented
133#13063312C23124yescomplemented
134#13063311C23124yescomplemented
135#13063311C23148yescomplemented
136#13063311C2318yescomplemented
137#13063310C23148yescomplemented
138#13063307C23148yescomplemented
139#13063305C23124yescomplemented
140#13063304C23124yescomplemented
141#13063301C23124yescomplemented
142#13063300C23124yescomplemented
143#13063300C23124yescomplemented
144#13063299C23124yescomplemented
145#13063298C23124yescomplemented
146#13063298C23124yescomplemented
147#13063296C23124yescomplemented
148#13063296C23124yescomplemented
149#13063295C23148yescomplemented
150#13063293C23148yescomplemented
151Q8×Dic43C2318yescomplemented
152C4×D172C23124yescomplemented
153C4×D172C23124yescomplemented
154#13063287C23124yescomplemented
155C4×C22⋊D43C23124yescomplemented
156C4×C22⋊D43C23124yescomplemented
157#13063283C23124yescomplemented
158C2×C4⋊Dic43C2313yes—
159C2×C4⋊Dic43C2313yes—
160C2×Dic43⋊C4C2313yes—
161C2×Dic43⋊C4C2313yes—
162C2×C22⋊Dic43C2313yes—
163C2×C22⋊Dic43C2316yes—
164C2×C22⋊Dic43C2311yescharacteristic
165C2×(C2×D43)⋊C4C2313yes—
166C2×(C2×D43)⋊C4C2313yes—
167C2×(C2×D43)⋊C4C2316yes—
168C2×(C2×D43)⋊C4C2316yes—
169C2×(C2×D43)⋊C4C2316yes—
170C2×(C2×D43)⋊C4C2311yescharacteristic
171C2×(C2×D43)⋊C4C2311yescharacteristic
172C22⋊C4×D43C23148yescomplemented
173C22⋊C4×D43C23148yescomplemented
174C2×C4×Dic43C2311yescharacteristic
175C2×C4×Dic43C2313yes—
176C2×C4×Dic43C2313yes—
177C42×D43C23124yescomplemented
178C2×#41×C43—28no—
179C2×#41×C43C2318yes—
180C22×Q8×C43—28no—
181C22×Q8×C43C2313yes—
182C22×Q8×C43C2311yescharacteristic
183C22×Q8×C43C2318yescomplemented
184C22×D4×C43C2313yes—
185C22×D4×C43C2313yes—
186C23×C4×C43C2313yes—
187C23×C4×C43C2313yes—
188#124×C43C23124yescomplemented
189C22⋊Q8×C43C23124yescomplemented
190#121×C43C23124yescomplemented
191C4×Q8×C43C2318yescomplemented
192C4×D4×C43C23124yescomplemented
193C2×C4⋊C4×C43C2313yes—
194C2×C4⋊C4×C43C2313yes—
195C2×C22⋊C4×C43C2311yescharacteristic
196C2×C22⋊C4×C43C2313yes—
197C2×C22⋊C4×C43C2316yes—
198C2×C42×C43C2313yes—
199C24×C43C2413yes—
200C24×C43C2411yescharacteristic
201C23×D43—224no—
202C23×D43—412no—
203C23×D43—412no—
204C23×D43C2413yes—
205C23×D43C2411yescharacteristic
206C23×D43C2413yes—
207C23×D43C24124yes—
208#41×C43—232no—
209C2×Q8×C43—232no—
210C2×Q8×C43—212no—
211C2×Q8×C43C2×D418yes—
212C2×Q8×C43C24112yes—
213C2×Q8×C43C2414yes—
214C2×D4×C43—212no—
215C2×D4×C43—46no—
216C2×D4×C43C24112yes—
217C2×D4×C43C24112yes—
218C22×C4×C43—212no—
219C22×C4×C43—212no—
220C22×C4×C43C2411yescharacteristic
221C22×C4×C43C2413yes—
222C22×C4×C43C2413yes—
223C22×C4×C43C2411yescharacteristic
224C22×C4×C43C24112yes—
225C22×C4×C43C24112yes—
226C22×C4×C43C2413yes—
227C2×C22⋊D43—212no—
228C2×C22⋊D43—24no—
229C2×C22⋊D43—212no—
230C2×C22⋊D43—212no—
231C2×C22⋊D43—46no—
232C2×C22⋊D43—46no—
233C2×C22⋊D43C24112yes—
234C2×C22⋊D43C24112yes—
235C2×C22⋊D43C24112yes—
236C2×C22⋊D43C2414yes—
237C2×C22⋊D43C24112yes—
238C2×C22⋊D43C24112yes—
239C22×Dic43C2411yescharacteristic
240C22×Dic43C2413yes—
241C22×Dic43C2413yes—
242C22×Dic43C2411yescharacteristic
243C22×Dic43C2411yescharacteristic
244#10621902—232no—
245#10621902—296no—
246#10621902C2×D4164yescomplemented
247Q8×D43—232no—
248Q8×D43—296no—
249D4×D43—296no—
250D4×D43—296no—
251#10621898—296no—
252#10621898—296no—
253#10621898—296no—
254C2×D172—212no—
255C2×D172—296no—
256C2×D172—212no—
257C2×D172—212no—
258C2×D172—46no—
259C2×D172C2×D4124yes—
260C2×D172C24112yes—
261C2×D172C24112yes—
262C2×D172C24112yes—
263C2×D172C24112yes—
264C2×D172C24112yes—
265C2×C4×D43—212no—
266C2×C4×D43—212no—
267C2×C4×D43—224no—
268C2×C4×D43—46no—
269C2×C4×D43—46no—
270C2×C4×D43C2×D4124yes—
271C2×C4×D43C24124yes—
272C2×C4×D43C24112yes—
273C2×C4×D43C24112yes—
274C2×C4×D43C24112yes—
275C2×C4×D43C24112yes—
276C2×C4×D43C24112yes—
277C2×Dic86—212no—
278C2×Dic86—212no—
279C2×Dic86—24no—
280C2×Dic86C24112yes—
281C2×Dic86C24112yes—
282C2×Dic86C2414yes—
283C4⋊C4×C43C24112yes—
284C4⋊C4×C43C24112yes—
285C22⋊C4×C43C2414yes—
286C22⋊C4×C43C24112yes—
287C22⋊C4×C43C24124yes—
288C42×C43C24112yes—
289C22⋊Dic43C24112yes—
290C22⋊Dic43C24124yes—
291C22⋊Dic43C2414yes—
292(C2×D43)⋊C4C24112yes—
293(C2×D43)⋊C4C24112yes—
294(C2×D43)⋊C4C24124yes—
295(C2×D43)⋊C4C24124yes—
296(C2×D43)⋊C4C24124yes—
297(C2×D43)⋊C4C2414yes—
298(C2×D43)⋊C4C2414yes—
299C4⋊Dic43C24112yes—
300C4⋊Dic43C24112yes—
301Dic43⋊C4C24112yes—
302Dic43⋊C4C24112yes—
303C4×Dic43C2414yes—
304C4×Dic43C24112yes—
305C4×Dic43C24112yes—
306C23×C43—22no—
307C23×C43—26no—
308C23×C43—22no—
309C23×C43—26no—
310C23×C43—22no—
311C23×C43—26no—
312C23×C43C2516yes—
313C23×C43C2512yes—
314C23×C43C2511yescharacteristic
315C22×D43—26no—
316C22×D43—26no—
317C22×D43—22no—
318C22×D43—26no—
319C22×D43—22no—
320C22×D43—26no—
321C22×D43—22no—
322C22×D43—26no—
323C22×D43—248no—
324C22×D43—424no—
325C22×D43—424no—
326C22×D43—848no—
327C22×D43C22×D4112yes—
328C22×D43C2516yes—
329C22×D43C2512yes—
330C22×D43C2516yes—
331Q8×C43—224no—
332Q8×C43C22×D4116yes—
333D4×C43—224no—
334D4×C43—412no—
335C2×C4×C43—26no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—26no—
339C2×C4×C43—224no—
340C2×C4×C43—224no—
341C2×C4×C43C22×D4112yes—
342C2×C4×C43C2516yes—
343C2×C4×C43C2512yes—
344C2×C4×C43C2512yes—
345C2×C4×C43C2516yes—
346C2×C4×C43C2516yes—
347C22⋊D43—224no—
348C22⋊D43—224no—
349C22⋊D43—28no—
350C22⋊D43—224no—
351C22⋊D43—412no—
352C22⋊D43—412no—
353C2×Dic43—26no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—26no—
357C2×Dic43C22×D414yes—
358C2×Dic43C2512yes—
359C2×Dic43C2516yes—
360C2×Dic43C2512yes—
361C2×Dic43C2516yes—
362C2×Dic43C2512yes—
363D172—224no—
364D172—224no—
365D172—224no—
366D172—412no—
367D172C22×D4148yes—
368C4×D43—248no—
369C4×D43—224no—
370C4×D43—224no—
371C4×D43—412no—
372C4×D43—412no—
373C4×D43C22×D4148yes—
374Dic86—224no—
375Dic86—28no—
376Dic86—224no—
377C2×#3500—431nomaximal, Sylow
378C22×C43—26no—
379C22×C43—22no—
380C22×C43—26no—
381C22×C43—26no—
382C22×C43—22no—
383C22×C43—22no—
384C22×C43—412no—
385C22×C43—44no—
386C22×C43C23×D412yes—
387C22×C43#58512yes—
388C22×C43#58512yes—
389C22×C43C2611yescharacteristic
390C2×D43—26no—
391C2×D43—26no—
392C2×D43—224no—
393C2×D43—26no—
394C2×D43—22no—
395C2×D43—26no—
396C2×D43—26no—
397C2×D43—22no—
398C2×D43—22no—
399C2×D43—44no—
400C2×D43—412no—
401C2×D43—848no—
402C2×D43C23×D4112yes—
403C4×C43—26no—
404C4×C43—22no—
405C4×C43—22no—
406C4×C43—26no—
407C4×C43C23×D4112yes—
408Dic43—26no—
409Dic43—22no—
410Dic43—22no—
411Dic43—26no—
412Dic43C23×D414yes—
413C22×2−1+4—431no—
414C22×H(5,𝔽2)—431no—
415#3500—4332no—
416C2×#548—431no—
417C2×#548—431no—
418C2×#548—431no—
419C2×#548D4311yescharacteristic, complemented
420C2×#546—433no—
421C2×#546—433no—
422C2×#546—433no—
423C2×#546—433no—
424C2×#536—433no—
425C2×#535—433no—
426C2×#532—433no—
427C22×#124—433no—
428C2×C4×#41—431no—
429C2×C43—46no—
430C2×C43—42no—
431C2×C43#350014yescomplemented
432C2×C43C24×D411yescharacteristic
433C2×C43C2×#58511yescharacteristic
434C2×C43C2×#58511yescharacteristic
435D43—212no—
436D43—42no—
437D43—46no—
438C2×2−1+4—4316no—
439C2×2−1+4—8616no—
440C2×H(5,𝔽2)—4316no—
441C2×H(5,𝔽2)—8616no—
442C22×#41—431no—
443C22×#41—431no—
444C22×#41—433no—
445C22×#41—433no—
446C22×#41—433no—
447C22×#41—433no—
448C22×#41C2×D4311yescharacteristic
449C23×Q8—433no—
450C23×Q8—431no—
451C23×Q8C2×D4311yescharacteristic, complemented
452C23×D4—433no—
453C23×D4—433no—
454C23×D4—433no—
455#548—4316no—
456#548—4316no—
457#548—4316no—
458#548C2×D43116yescomplemented
459#546—4348no—
460#546—4348no—
461#546—4348no—
462#546—4348no—
463#536—4348no—
464#535—4348no—
465#532—4348no—
466C2×C4⋊Q8—433no—
467C2×#127—433no—
468C2×#124—433no—
469C2×#124—433no—
470C2×#124—4348no—
471C2×#124—433no—
472C2×#124—436no—
473C2×#124—431no—
474C2×#124—433no—
475C2×#124C2×D4313yescomplemented
476C2×#123—436no—
477C2×#123—436no—
478C2×C22⋊Q8—433no—
479C2×C22⋊Q8—433no—
480C2×C22⋊Q8—433no—
481C2×C22⋊Q8C2×D4313yescomplemented
482C2×#121—433no—
483C2×#121—433no—
484C2×#121—433no—
485C2×#121—433no—
486C2×#121—433no—
487C2×#121—433no—
488C2×#121—433no—
489C2×#121C2×D4313yescomplemented
490C2×#120—436no—
491C2×#120—436no—
492C4×#41—4316no—
493C2×C4×Q8—431no—
494C2×C4×Q8C2×D4311yescharacteristic, complemented
495C2×C4×D4—433no—
496C2×C4×D4—433no—
497C2×C4×D4—433no—
498C2×C4×D4—433no—
499C2×C4×D4—433no—
500C2×C4×D4C2×D4313yescomplemented
501C2×#117—433no—
502C22×C22⋊C4—436no—
503C22×C22⋊C4—436no—
504C22×C42—433no—
505C43C2×#350011yescharacteristic, complemented, Sylow
506C25—436no—
5072−1+4—86128no—
508H(5,𝔽2)—86128no—
509C2×#41—28no—
510C2×#41—4316no—
511C2×#41—438no—
512C2×#41—4324no—
513C2×#41—438no—
514C2×#41—4324no—
515C2×#41—4324no—
516C2×#41—4324no—
517C2×#41—8624no—
518C2×#41—8624no—
519C2×#41—8624no—
520C2×#41—8624no—
521C2×#41—868no—
522C2×#41C22×D4318yes—
523C22×Q8—28no—
524C22×Q8—4324no—
525C22×Q8—438no—
526C22×Q8—433no—
527C22×Q8—433no—
528C22×Q8—431no—
529C22×Q8—8624no—
530C22×Q8—868no—
531C22×Q8C22×D4313yes—
532C22×Q8C22×D4311yescharacteristic
533C22×Q8C22×D4318yescomplemented
534C22×D4—433no—
535C22×D4—433no—
536C22×D4—433no—
537C22×D4—431no—
538C22×D4—433no—
539C22×D4—433no—
540C22×D4—4324no—
541C22×D4—4324no—
542C22×D4—433no—
543C22×D4—433no—
544C22×D4—433no—
545C22×D4—433no—
546C22×D4—4324no—
547C22×D4—433no—
548C22×D4—8624no—
549C22×D4—8624no—
550C22×D4—8624no—
551C22×D4C22×D4313yes—
552C22×D4C22×D4313yes—
553C23×C4—433no—
554C23×C4—436no—
555C23×C4—433no—
556C23×C4—433no—
557C23×C4—433no—
558C23×C4—433no—
559C23×C4C22×D4313yes—
560C23×C4C22×D4313yes—
561C4⋊Q8—4324no—
562#127—4324no—
563#124—4324no—
564#124—4324no—
565#124—4324no—
566#124—4348no—
567#124—438no—
568#124—4324no—
569#124C22×D43124yescomplemented
570#123—4348no—
571#123—4348no—
572C22⋊Q8—4324no—
573C22⋊Q8—4324no—
574C22⋊Q8—4324no—
575C22⋊Q8C22×D43124yescomplemented
576#121—4324no—
577#121—4324no—
578#121—4324no—
579#121—4324no—
580#121—4324no—
581#121—4324no—
582#121—4324no—
583#121C22×D43124yescomplemented
584#120—4348no—
585#120—4348no—
586C4×Q8—438no—
587C4×Q8C22×D4318yescomplemented
588C4×D4—4324no—
589C4×D4—4324no—
590C4×D4—4324no—
591C4×D4—4324no—
592C4×D4—4324no—
593C4×D4C22×D43124yescomplemented
594#117—4324no—
595C2×C4⋊C4—433no—
596C2×C4⋊C4—433no—
597C2×C4⋊C4—433no—
598C2×C4⋊C4—433no—
599C2×C4⋊C4C22×D4313yes—
600C2×C4⋊C4C22×D4313yes—
601C2×C22⋊C4—433no—
602C2×C22⋊C4—436no—
603C2×C22⋊C4—431no—
604C2×C22⋊C4—433no—
605C2×C22⋊C4—433no—
606C2×C22⋊C4—436no—
607C2×C22⋊C4—436no—
608C2×C22⋊C4—436no—
609C2×C22⋊C4—431no—
610C2×C22⋊C4—431no—
611C2×C22⋊C4—4348no—
612C2×C22⋊C4—4348no—
613C2×C22⋊C4C22×D4313yes—
614C2×C22⋊C4C22×D4316yes—
615C2×C22⋊C4C22×D4311yescharacteristic
616C2×C42—433no—
617C2×C42—433no—
618C2×C42—431no—
619C2×C42—4324no—
620C2×C42C22×D4313yes—
621C24—433no—
622C24—433no—
623C24—431no—
624C24—4324no—
625C24—8624no—
626C24—17212no—
627C24—17212no—
628C24C23×D4313yes—
629C24C23×D4311yescharacteristic
630#41—232no—
631#41—4364no—
632#41—8696no—
633#41—8696no—
634#41—8696no—
635#41—8696no—
636#41—8632no—
637C2×Q8—232no—
638C2×Q8—212no—
639C2×Q8—4312no—
640C2×Q8—4312no—
641C2×Q8—434no—
642C2×Q8—8612no—
643C2×Q8—864no—
644C2×Q8—8696no—
645C2×Q8—8632no—
646C2×Q8—8612no—
647C2×Q8D4×D4318yes—
648C2×Q8C23×D43112yes—
649C2×Q8C23×D4314yes—
650C2×D4—212no—
651C2×D4—46no—
652C2×D4—4312no—
653C2×D4—4312no—
654C2×D4—4312no—
655C2×D4—434no—
656C2×D4—4312no—
657C2×D4—4312no—
658C2×D4—4324no—
659C2×D4—4312no—
660C2×D4—4312no—
661C2×D4—4312no—
662C2×D4—4312no—
663C2×D4—4312no—
664C2×D4—8696no—
665C2×D4—8612no—
666C2×D4—8612no—
667C2×D4—8696no—
668C2×D4—8612no—
669C2×D4—864no—
670C2×D4—8696no—
671C2×D4—8612no—
672C2×D4—8612no—
673C2×D4—8612no—
674C2×D4—1726no—
675C2×D4—1726no—
676C2×D4—1726no—
677C2×D4C23×D43112yes—
678C2×D4C23×D43112yes—
679C22×C4—212no—
680C22×C4—212no—
681C22×C4—431no—
682C22×C4—4324no—
683C22×C4—4312no—
684C22×C4—431no—
685C22×C4—433no—
686C22×C4—433no—
687C22×C4—431no—
688C22×C4—4324no—
689C22×C4—4312no—
690C22×C4—4312no—
691C22×C4—4312no—
692C22×C4—4312no—
693C22×C4—8624no—
694C22×C4—8612no—
695C22×C4—8612no—
696C22×C4—1726no—
697C22×C4—1726no—
698C22×C4C23×D43112yes—
699C22×C4C23×D43112yes—
700C22×C4C23×D4311yescharacteristic
701C22×C4C23×D4313yes—
702C22×C4C23×D4313yes—
703C22×C4C23×D4311yescharacteristic
704C22×C4C23×D4313yes—
705C4⋊C4—4312no—
706C4⋊C4—4312no—
707C4⋊C4—4312no—
708C4⋊C4—4312no—
709C4⋊C4C23×D43112yes—
710C4⋊C4C23×D43112yes—
711C22⋊C4—4312no—
712C22⋊C4—4324no—
713C22⋊C4—434no—
714C22⋊C4—4312no—
715C22⋊C4—4312no—
716C22⋊C4—4324no—
717C22⋊C4—4324no—
718C22⋊C4—4324no—
719C22⋊C4—434no—
720C22⋊C4—434no—
721C22⋊C4C23×D43112yes—
722C22⋊C4C23×D43124yes—
723C22⋊C4C23×D4314yes—
724C42—434no—
725C42—4312no—
726C42—4312no—
727C42C23×D43112yes—
728C23—22no—
729C23—26no—
730C23—22no—
731C23—26no—
732C23—22no—
733C23—26no—
734C23—4312no—
735C23—436no—
736C23—436no—
737C23—432no—
738C23—8648no—
739C23—866no—
740C23—866no—
741C23—862no—
742C23—866no—
743C23—862no—
744C23—866no—
745C23—862no—
746C23—866no—
747C23—34448no—
748C23—17224no—
749C23—17224no—
750C23C24×D4316yes—
751C23C24×D4312yes—
752C23C24×D4311yescharacteristic
753Q8—224no—
754Q8—8624no—
755Q8—868no—
756Q8—8624no—
757Q8C2×D4×D43116yes—
758D4—224no—
759D4—412no—
760D4—4348no—
761D4—8624no—
762D4—8624no—
763D4—8624no—
764D4—868no—
765D4—8624no—
766D4—8624no—
767D4—8624no—
768D4—17212no—
769D4—17212no—
770D4—17212no—
771C2×C4—22no—
772C2×C4—26no—
773C2×C4—26no—
774C2×C4—22no—
775C2×C4—224no—
776C2×C4—224no—
777C2×C4—434no—
778C2×C4—432no—
779C2×C4—4348no—
780C2×C4—432no—
781C2×C4—436no—
782C2×C4—436no—
783C2×C4—432no—
784C2×C4—8648no—
785C2×C4—862no—
786C2×C4—866no—
787C2×C4—862no—
788C2×C4—866no—
789C2×C4—8624no—
790C2×C4—8624no—
791C2×C4—17212no—
792C2×C4—17212no—
793C2×C4C2×D4×D43112yes—
794C2×C4C24×D4312yes—
795C2×C4C24×D4316yes—
796C2×C4C24×D4316yes—
797C2×C4C24×D4312yes—
798C2×C4C24×D4316yes—
799C22—22no—
800C22—26no—
801C22—22no—
802C22—26no—
803C22—22no—
804C22—26no—
805C22—412no—
806C22—44no—
807C22—4312no—
808C22—866no—
809C22—866no—
810C22—8624no—
811C22—862no—
812C22—866no—
813C22—862no—
814C22—866no—
815C22—862no—
816C22—866no—
817C22—34448no—
818C22—17212no—
819C22—1724no—
820C22C22×D4×D4312yes—
821C22#1458373512yes—
822C22#1458373612yes—
823C22C25×D4311yescharacteristic
824C4—22no—
825C4—26no—
826C4—26no—
827C4—22no—
828C4—434no—
829C4—862no—
830C4—866no—
831C4—862no—
832C4—866no—
833C4C22×D4×D43112yes—
834C2—46no—
835C2—42no—
836C2—8612no—
837C2—1726no—
838C2—1722no—
839C2#1914838614yesdirect product factor
840C2C23×D4×D4311yescharacteristic
841C2C2×#1458373511yescharacteristic
842C2C2×#1458373611yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#548C2
socleC23×C43C25
hypercenterC2×#548D43
hypocenterC43C2×#3500
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#13063373C2semidirect
2. C22×#13063371C2semidirect
3. #19148386C2direct (N × H)
4. C2×#14583561C2semidirect
5. C2×#14583560C2semidirect
6. C2×#14583556C2semidirect
7. C2×#14583546C2semidirect
8. C2×#14583545C2semidirect
9. C2×#14583542C2semidirect
10. C2×#14583540C2semidirect
11. C2×#14583472C2semidirect
12. C2×#14583465C2semidirect
13. C2×#14583446C2semidirect
14. C2×#124×D43C2semidirect
15. C2×C4×#10621902C2semidirect
16. C2×C43×#548C2semidirect
18. C2×#13063373C22semidirect
20. C2×#13063371C22semidirect
23. C22×#10621902C22semidirect
25. C22×#10621898C22semidirect
26. C22×#10621898C22semidirect
27. C22×Q8×D43C22semidirect
28. C22×Q8×D43C22semidirect
32. #14583561C22semidirect
33. #14583560C22semidirect
34. #14583556C22semidirect
35. #14583546C22semidirect
36. #14583545C22semidirect
37. #14583542C22semidirect
38. #14583540C22semidirect
39. #14583472C22semidirect
40. #14583465C22semidirect
41. #14583446C22semidirect
42. C2×#13063324C22semidirect
43. C2×#13063321C22semidirect
44. C2×#13063314C22semidirect
45. C2×#13063313C22semidirect
46. C2×#13063312C22semidirect
47. C2×#13063311C22semidirect
48. C2×#13063311C22semidirect
49. C2×#13063311C22semidirect
50. #124×D43C22semidirect
51. C2×#13063310C22semidirect
52. C2×#13063307C22semidirect
53. C2×#13063305C22semidirect
54. C2×#13063304C22semidirect
55. C2×#13063301C22semidirect
56. C2×#13063300C22semidirect
57. C2×#13063300C22semidirect
58. C2×#13063299C22semidirect
59. C2×#13063298C22semidirect
60. C2×#13063298C22semidirect
61. C2×#13063296C22semidirect
62. C2×#13063296C22semidirect
63. C2×#13063295C22semidirect
64. C2×#13063293C22semidirect
65. C4×#10621902C22semidirect
66. C2×Q8×Dic43C22semidirect
67. C2×C4×D172C22semidirect
68. C2×C4×D172C22semidirect
69. C2×#13063287C22semidirect
70. C2×C4×C22⋊D43C22semidirect
71. C2×C4×C22⋊D43C22semidirect
72. C2×#13063283C22semidirect
73. C2×C22⋊C4×D43C22semidirect
74. C2×C22⋊C4×D43C22semidirect
75. C2×C42×D43C22semidirect
77. C23×Q8×C43C22semidirect
78. C43×#548C22semidirect
79. C2×#124×C43C22semidirect
80. C2×C22⋊Q8×C43C22semidirect
81. C2×#121×C43C22semidirect
82. C2×C4×Q8×C43C22semidirect
83. C2×C4×D4×C43C22semidirect
89. C2×#10621902D4semidirect
92. C2×#10621902C23semidirect
97. C2×#10621898C23semidirect
98. C2×#10621898C23semidirect
104. C2×Q8×D43C23semidirect
105. C2×Q8×D43C23semidirect
129. #13063324C23semidirect
130. #13063321C23semidirect
131. #13063314C23semidirect
132. #13063313C23semidirect
133. #13063312C23semidirect
134. #13063311C23semidirect
135. #13063311C23semidirect
136. #13063311C23semidirect
137. #13063310C23semidirect
138. #13063307C23semidirect
139. #13063305C23semidirect
140. #13063304C23semidirect
141. #13063301C23semidirect
142. #13063300C23semidirect
143. #13063300C23semidirect
144. #13063299C23semidirect
145. #13063298C23semidirect
146. #13063298C23semidirect
147. #13063296C23semidirect
148. #13063296C23semidirect
149. #13063295C23semidirect
150. #13063293C23semidirect
151. Q8×Dic43C23semidirect
152. C4×D172C23semidirect
153. C4×D172C23semidirect
154. #13063287C23semidirect
155. C4×C22⋊D43C23semidirect
156. C4×C22⋊D43C23semidirect
157. #13063283C23semidirect
172. C22⋊C4×D43C23semidirect
173. C22⋊C4×D43C23semidirect
177. C42×D43C23semidirect
183. C22×Q8×C43C23semidirect
188. #124×C43C23semidirect
189. C22⋊Q8×C43C23semidirect
190. #121×C43C23semidirect
191. C4×Q8×C43C23semidirect
192. C4×D4×C43C23semidirect
246. #10621902C2×D4semidirect
419. C2×#548D43semidirect
431. C2×C43#3500semidirect
451. C23×Q8C2×D43semidirect
458. #548C2×D43semidirect
475. C2×#124C2×D43semidirect
481. C2×C22⋊Q8C2×D43semidirect
489. C2×#121C2×D43semidirect
494. C2×C4×Q8C2×D43semidirect
500. C2×C4×D4C2×D43semidirect
505. C43C2×#3500semidirect
533. C22×Q8C22×D43semidirect
569. #124C22×D43semidirect
575. C22⋊Q8C22×D43semidirect
583. #121C22×D43semidirect
587. C4×Q8C22×D43semidirect
593. C4×D4C22×D43semidirect
839. C2#19148386direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633732
C22×#130633712
#191483862
C2×#145835612
C2×#145835602
C2×#145835562
C2×#145835462
C2×#145835452
C2×#145835422
C2×#145835402
C2×#145834722
C2×#145834652
C2×#145834462
C2×#124×D432
C2×C4×#106219022
C2×C43×#5482
C2×#350043