Finite Group Databasebeta

← C2×#19148363 #26004771

Subgroups — C2×#19148363 #26004771

Order 11008.

11210 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063373C211yesmaximal, characteristic, complemented
2C22×#13063372C211yesmaximal, characteristic, complemented
3#19148363C2132yesmaximal, direct product factor
4C2×#14583568C211yesmaximal, characteristic, complemented
5C2×#14583567C213yesmaximal, complemented
6C2×Q8×C22⋊D43C211yesmaximal, characteristic, complemented
7C2×#14583562C213yesmaximal, complemented
8C2×#14583561C211yesmaximal, characteristic, complemented
9C2×#14583558C213yesmaximal, complemented
10C2×#14583557C213yesmaximal, complemented
11C2×#14583479C213yesmaximal, complemented
12C2×#14583478C213yesmaximal, complemented
13C2×#14583448C213yesmaximal, complemented
14C2×#14583446C213yesmaximal, complemented
15C2×C4×Q8×D43C211yesmaximal, characteristic, complemented
16C2×C43×#548C211yesmaximal, characteristic, complemented
17C2×#13063373—216no—
18C2×#13063373C22116yescomplemented
19C2×#13063372—216no—
20C2×#13063372C22116yescomplemented
21C22×#10621902C2211yescharacteristic
22C22×#10621902C2213yes—
23C22×#10621898C2213yes—
24C22×#10621898C2213yes—
25C22×#10621898C2213yes—
26C22×#10621900C2213yes—
27C22×#10621900C2213yes—
28C23×Dic86C2213yes—
29C22×Q8×D43C2213yes—
30C22×Q8×D43C2211yescharacteristic
31C22×Q8×D43C2211yescharacteristic
32#14583568C22116yescomplemented
33#14583567C22148yescomplemented
34Q8×C22⋊D43C22116yescomplemented
35#14583562C22148yescomplemented
36#14583561C22116yescomplemented
37#14583558C22148yescomplemented
38#14583557C22148yescomplemented
39#14583479C22148yescomplemented
40#14583478C22148yescomplemented
41#14583448C22148yescomplemented
42#14583446C22148yescomplemented
43C2×#13063324C2213yes—
44C2×#13063323C2213yes—
45C2×#13063321C2213yes—
46C2×#13063321C2213yes—
47C2×#13063313C2213yes—
48C2×#13063311C2213yes—
49C2×#13063311C2213yes—
50C2×#13063305C2213yes—
51C2×#13063304C2213yes—
52C2×#13063303C2216yes—
53C2×#13063302C2216yes—
54C2×#13063301C2213yes—
55C2×#13063300C2213yes—
56C2×#13063300C2213yes—
57C2×#13063299C2213yes—
58C2×#13063298C2216yes—
59C2×#13063298C2211yescharacteristic
60C2×#13063298C2213yes—
61C2×#13063298C2216yes—
62C2×#13063297C2216yes—
63C2×#13063296C2213yes—
64C2×#13063296C2213yes—
65C2×Q8×Dic43C2211yescharacteristic
66C2×C4×Dic86C2213yes—
67C2×#13063290C2213yes—
68C4×Q8×D43C22116yescomplemented
69C2×C4×D172C2213yes—
70C2×C4×C22⋊D43C2213yes—
71C2×C4×C22⋊D43C2213yes—
72C2×(C22⋊D43)⋊C4C2216yes—
73C2×(C22⋊D43)⋊C4C2216yes—
74C2×C4⋊C4×D43C2213yes—
75C2×C42×D43C2213yes—
76C22×#41×C43C2211yescharacteristic
77C23×Q8×C43C2211yescharacteristic
78C43×#548C22116yescomplemented
79C2×#124×C43C2213yes—
80C2×C22⋊Q8×C43C2213yes—
81C2×#121×C43C2213yes—
82C2×C4×Q8×C43C2211yescharacteristic
83C2×C4×D4×C43C2213yes—
84#13063373—2128no—
85#13063372—2128no—
86C2×#10621902—28no—
87C2×#10621902—224no—
88C2×#10621902C2318yes—
89C2×#10621902C23124yes—
90C2×#10621898—224no—
91C2×#10621898—224no—
92C2×#10621898—224no—
93C2×#10621898C23124yes—
94C2×#10621898C23124yes—
95C2×#10621898C23124yes—
96C2×#10621900—224no—
97C2×#10621900—224no—
98C2×#10621900C23124yes—
99C2×#10621900C23124yes—
100C22×Dic86—224no—
101C22×Dic86C23124yes—
102C22×Dic86C2313yes—
103C22×Dic86C2313yes—
104C22×Dic86C2313yes—
105C22×Dic86C2313yes—
106C2×Q8×D43—28no—
107C2×Q8×D43—224no—
108C2×Q8×D43D4116yescomplemented
109C2×Q8×D43C23124yes—
110C2×Q8×D43C2318yes—
111C2×Q8×D43C2318yes—
112C22×D172C2313yes—
113C22×D172C2311yescharacteristic
114C22×D172C2313yes—
115C22×D172C2313yes—
116C22×C22⋊D43C2313yes—
117C22×C22⋊D43C2311yescharacteristic
118C22×C22⋊D43C2311yescharacteristic
119C22×C22⋊D43C2313yes—
120C22×C22⋊D43C2313yes—
121C22×C22⋊D43C2313yes—
122C22×C22⋊D43C2316yes—
123C23×Dic43C2316yes—
124C22×C4×D43C2311yescharacteristic
125C22×C4×D43C2316yes—
126C22×C4×D43C2313yes—
127C22×C4×D43C2313yes—
128C22×C4×D43C2313yes—
129C22×C4×D43C2313yes—
130#13063324C23124yes—
131#13063323C23124yes—
132#13063321C23124yes—
133#13063321C23124yes—
134#13063313C23124yes—
135#13063311C23124yes—
136#13063311C23124yes—
137#13063305C23124yes—
138#13063304C23124yes—
139#13063303C23148yes—
140#13063302C23148yes—
141#13063301C23124yes—
142#13063300C23124yes—
143#13063300C23124yes—
144#13063299C23124yes—
145#13063298C23148yes—
146#13063298C2318yes—
147#13063298C23124yes—
148#13063298C23148yes—
149#13063297C23148yes—
150#13063296C23124yes—
151#13063296C23124yes—
152Q8×Dic43C2318yes—
153C4×Dic86C23124yes—
154#13063290C23124yes—
155C4×D172C23124yes—
156C4×C22⋊D43C23124yes—
157C4×C22⋊D43C23124yes—
158(C22⋊D43)⋊C4C23148yes—
159(C22⋊D43)⋊C4C23148yes—
160C2×C4⋊Dic43C2313yes—
161C2×C4⋊Dic43C2313yes—
162C2×Dic43⋊C4C2316yes—
163C2×Dic43⋊C4C2313yes—
164C2×Dic43⋊C4C2316yes—
165C2×Dic43⋊C4C2311yescharacteristic
166C4⋊C4×D43C23124yes—
167C2×C22⋊Dic43C2313yes—
168C2×C22⋊Dic43C2313yes—
169C2×(C2×D43)⋊C4C2313yes—
170C2×(C2×D43)⋊C4C2316yes—
171C2×(C2×D43)⋊C4C2313yes—
172C2×(C2×D43)⋊C4C2313yes—
173C2×(C2×D43)⋊C4C2311yescharacteristic
174C2×C4×Dic43C2313yes—
175C2×C4×Dic43C2313yes—
176C2×C4×Dic43C2313yes—
177C42×D43C23124yes—
178C2×#41×C43—28no—
179C2×#41×C43C2318yes—
180C22×Q8×C43—28no—
181C22×Q8×C43C2318yes—
182C22×Q8×C43C2313yes—
183C22×Q8×C43C2311yescharacteristic
184C22×D4×C43C2313yes—
185C22×D4×C43C2313yes—
186C23×C4×C43C2313yes—
187C23×C4×C43C2313yes—
188#124×C43C23124yes—
189C22⋊Q8×C43C23124yes—
190#121×C43C23124yes—
191C4×Q8×C43C2318yes—
192C4×D4×C43C23124yes—
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×D43C2413yes—
202C23×D43C2411yescharacteristic
203C23×D43C2411yescharacteristic
204#41×C43—232no—
205C2×Q8×C43—232no—
206C2×Q8×C43—212no—
207C2×Q8×C43C2×D418yes—
208C2×Q8×C43C24112yes—
209C2×Q8×C43C2414yes—
210C2×D4×C43—212no—
211C2×D4×C43—46no—
212C2×D4×C43C24112yes—
213C2×D4×C43C24112yes—
214C22×C4×C43—212no—
215C22×C4×C43—212no—
216C22×C4×C43C2411yescharacteristic
217C22×C4×C43C2413yes—
218C22×C4×C43C2413yes—
219C22×C4×C43C2411yescharacteristic
220C22×C4×C43C24112yes—
221C22×C4×C43C24112yes—
222C22×C4×C43C2413yes—
223C2×C22⋊D43—212no—
224C2×C22⋊D43—212no—
225C2×C22⋊D43—212no—
226C2×C22⋊D43—24no—
227C2×C22⋊D43—212no—
228C2×C22⋊D43—24no—
229C2×C22⋊D43—412no—
230C2×C22⋊D43C24112yes—
231C2×C22⋊D43C2414yes—
232C2×C22⋊D43C2414yes—
233C2×C22⋊D43C24112yes—
234C2×C22⋊D43C24112yes—
235C2×C22⋊D43C24112yes—
236C2×C22⋊D43C24124yes—
237C22×Dic43—224no—
238C22×Dic43C2413yes—
239C22×Dic43C2413yes—
240C22×Dic43C2411yescharacteristic
241C22×Dic43C24124yes—
242C22×Dic43C2413yes—
243C22×Dic43C2411yescharacteristic
244#10621902—232no—
245#10621902—296no—
246Q8×D43—232no—
247Q8×D43—296no—
248Q8×D43C2×D4164yescomplemented
249#10621900—296no—
250#10621900—296no—
251#10621898—296no—
252#10621898—296no—
253#10621898—296no—
254C2×D172—212no—
255C2×D172—24no—
256C2×D172—212no—
257C2×D172—46no—
258C2×D172C24112yes—
259C2×D172C2414yes—
260C2×D172C24112yes—
261C2×D172C24112yes—
262C2×C4×D43—212no—
263C2×C4×D43—212no—
264C2×C4×D43—224no—
265C2×C4×D43—24no—
266C2×C4×D43—46no—
267C2×C4×D43C2×D4124yes—
268C2×C4×D43C2414yes—
269C2×C4×D43C24124yes—
270C2×C4×D43C24112yes—
271C2×C4×D43C24112yes—
272C2×C4×D43C24112yes—
273C2×C4×D43C24112yes—
274C2×Dic86—212no—
275C2×Dic86—212no—
276C2×Dic86—212no—
277C2×Dic86—296no—
278C2×Dic86C2×D4124yes—
279C2×Dic86C24112yes—
280C2×Dic86C24112yes—
281C2×Dic86C24112yes—
282C2×Dic86C24112yes—
283C4⋊C4×C43C24112yes—
284C4⋊C4×C43C24112yes—
285C22⋊C4×C43C2414yes—
286C22⋊C4×C43C24112yes—
287C22⋊C4×C43C24124yes—
288C42×C43C24112yes—
289C22⋊Dic43C24112yes—
290C22⋊Dic43C24112yes—
291(C2×D43)⋊C4C24112yes—
292(C2×D43)⋊C4C24124yes—
293(C2×D43)⋊C4C24112yes—
294(C2×D43)⋊C4C24112yes—
295(C2×D43)⋊C4C2414yes—
296C4⋊Dic43C24112yes—
297C4⋊Dic43C24112yes—
298Dic43⋊C4C24124yes—
299Dic43⋊C4C24112yes—
300Dic43⋊C4C24124yes—
301Dic43⋊C4C2414yes—
302C4×Dic43C24112yes—
303C4×Dic43C24112yes—
304C4×Dic43C24112yes—
305C23×C43—26no—
306C23×C43—22no—
307C23×C43—26no—
308C23×C43—22no—
309C23×C43—26no—
310C23×C43—22no—
311C23×C43C2512yes—
312C23×C43C2516yes—
313C23×C43C2511yescharacteristic
314C22×D43—22no—
315C22×D43—22no—
316C22×D43—26no—
317C22×D43—22no—
318C22×D43—26no—
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—26no—
322C22×D43C22×D414yes—
323C22×D43C2516yes—
324C22×D43C2512yes—
325C22×D43C2512yes—
326Q8×C43—224no—
327Q8×C43C22×D4116yes—
328D4×C43—224no—
329D4×C43—412no—
330C2×C4×C43—22no—
331C2×C4×C43—26no—
332C2×C4×C43—22no—
333C2×C4×C43—26no—
334C2×C4×C43—224no—
335C2×C4×C43—224no—
336C2×C4×C43C22×D4112yes—
337C2×C4×C43C2512yes—
338C2×C4×C43C2516yes—
339C2×C4×C43C2516yes—
340C2×C4×C43C2512yes—
341C2×C4×C43C2516yes—
342C22⋊D43—28no—
343C22⋊D43—224no—
344C22⋊D43—224no—
345C22⋊D43—224no—
346C22⋊D43—224no—
347C22⋊D43—28no—
348C22⋊D43—424no—
349C2×Dic43—22no—
350C2×Dic43—26no—
351C2×Dic43—26no—
352C2×Dic43—248no—
353C2×Dic43C22×D4112yes—
354C2×Dic432−1+414yescomplemented
355C2×Dic43C2516yes—
356C2×Dic43C2516yes—
357C2×Dic43C2512yes—
358C2×Dic43C2516yes—
359C2×Dic43C2512yes—
360D172—28no—
361D172—224no—
362D172—224no—
363D172—412no—
364C4×D43—224no—
365C4×D43—224no—
366C4×D43—248no—
367C4×D43—28no—
368C4×D43—412no—
369C4×D43C22×D4148yes—
370Dic86—224no—
371Dic86—224no—
372Dic86—224no—
373Dic86C22×D4148yes—
374C2×#3497—431nomaximal, Sylow
375C22×C43—26no—
376C22×C43—22no—
377C22×C43—22no—
378C22×C43—26no—
379C22×C43—26no—
380C22×C43—22no—
381C22×C43—412no—
382C22×C43—44no—
383C22×C43C23×D412yes—
384C22×C43C2×2−1+412yes—
385C22×C43#58512yes—
386C22×C43C2611yescharacteristic
387C2×D43—22no—
388C2×D43—22no—
389C2×D43—28no—
390C2×D43—26no—
391C2×D43—22no—
392C2×D43—26no—
393C2×D43—22no—
394C2×D43—22no—
395C2×D43—26no—
396C2×D43—412no—
397C2×D43—44no—
398C2×D43C23×D414yes—
399C4×C43—22no—
400C4×C43—26no—
401C4×C43—22no—
402C4×C43—26no—
403C4×C43C23×D4112yes—
404Dic43—22no—
405Dic43—26no—
406Dic43—26no—
407Dic43C23×D4112yes—
408Dic43C2×2−1+414yescomplemented
409C22×2−1+4—431no—
410C22×2−1+4—431no—
411#3497—4332no—
412C2×#550—431no—
413C2×#550—433no—
414C2×D4×Q8—431no—
415C2×D4×Q8—433no—
416C2×#548—433no—
417C2×#548—431no—
418C2×#548—433no—
419C2×#548D4311yescharacteristic, complemented
420C2×#537—433no—
421C2×#537—433no—
422C2×#532—433no—
423C2×#532—433no—
424C22×C4×Q8—431no—
425C2×C43—46no—
426C2×C43—42no—
427C2×C43#349714yescomplemented
428C2×C43C24×D411yescharacteristic
429C2×C43C22×2−1+411yescharacteristic
430C2×C43C2×#58511yescharacteristic
431D43—24no—
432D43—46no—
433D43—42no—
434C2×2−1+4—4316no—
435C2×2−1+4—4316no—
436C2×2−1+4—8616no—
437C2×2−1+4—8616no—
438C22×#41—433no—
439C22×#41—431no—
440C22×#41—433no—
441C22×#41—433no—
442C22×#41—433no—
443C22×#41—433no—
444C22×#41—433no—
445C22×#41C2×D4311yescharacteristic
446C23×Q8—431no—
447C23×Q8—433no—
448C23×Q8—431no—
449C23×Q8—433no—
450C23×Q8C2×D4311yescharacteristic
451#550—4316no—
452#550—4348no—
453D4×Q8—4316no—
454D4×Q8—4348no—
455#548—4348no—
456#548—4316no—
457#548—4348no—
458#548C2×D43116yescomplemented
459#537—4348no—
460#537—4348no—
461#532—4348no—
462#532—4348no—
463C2×C4⋊Q8—433no—
464C2×C4⋊Q8—433no—
465C2×#127—433no—
466C2×#127—433no—
467C2×#124—433no—
468C2×#124—433no—
469C2×#124—433no—
470C2×#124C2×D4313yes—
471C2×C22⋊Q8—433no—
472C2×C22⋊Q8—433no—
473C2×C22⋊Q8—436no—
474C2×C22⋊Q8—433no—
475C2×C22⋊Q8—436no—
476C2×C22⋊Q8C2×D4313yes—
477C2×#121—433no—
478C2×#121—433no—
479C2×#121—436no—
480C2×#121—433no—
481C2×#121—433no—
482C2×#121—433no—
483C2×#121—433no—
484C2×#121—431no—
485C2×#121—436no—
486C2×#121—436no—
487C2×#121C2×D4313yes—
488C2×C4×Q8—431no—
489C2×C4×Q8—4316no—
490C2×C4×Q8—433no—
491C2×C4×Q8—433no—
492C2×C4×Q8C2×D4311yescharacteristic
493C2×C4×D4—433no—
494C2×C4×D4—433no—
495C2×C4×D4—436no—
496C2×C4×D4—436no—
497C2×C4×D4—433no—
498C2×C4×D4C2×D4313yes—
499C22×C4⋊C4—433no—
500C22×C42—433no—
501C43C2×#349711yescharacteristic, complemented, Sylow
5022−1+4—86128no—
5032−1+4—86128no—
504C2×#41—28no—
505C2×#41—4324no—
506C2×#41—438no—
507C2×#41—4324no—
508C2×#41—4324no—
509C2×#41—4324no—
510C2×#41—4324no—
511C2×#41—4324no—
512C2×#41—8624no—
513C2×#41—8624no—
514C2×#41—8624no—
515C2×#41—8624no—
516C2×#41—8624no—
517C2×#41—8624no—
518C2×#41—868no—
519C2×#41C22×D4318yes—
520C22×Q8—28no—
521C22×Q8—4316no—
522C22×Q8—438no—
523C22×Q8—4324no—
524C22×Q8—438no—
525C22×Q8—433no—
526C22×Q8—433no—
527C22×Q8—433no—
528C22×Q8—433no—
529C22×Q8—4324no—
530C22×Q8—8624no—
531C22×Q8—8624no—
532C22×Q8—868no—
533C22×Q8C22×D4313yes—
534C22×Q8C22×D4318yes—
535C22×Q8C22×D4311yescharacteristic
536C22×D4—431no—
537C22×D4—433no—
538C22×D4—431no—
539C22×D4—433no—
540C22×D4—433no—
541C22×D4—433no—
542C22×D4—436no—
543C22×D4—431no—
544C22×D4—433no—
545C22×D4—433no—
546C22×D4—433no—
547C22×D4C22×D4313yes—
548C22×D4C22×D4313yes—
549C23×C4—433no—
550C23×C4—436no—
551C23×C4—436no—
552C23×C4—433no—
553C23×C4—433no—
554C23×C4—431no—
555C23×C4—433no—
556C23×C4C22×D4313yes—
557C23×C4C22×D4313yes—
558C4⋊Q8—4324no—
559C4⋊Q8—4324no—
560#127—4324no—
561#127—4324no—
562#124—4324no—
563#124—4324no—
564#124—4324no—
565#124C22×D43124yes—
566C22⋊Q8—4324no—
567C22⋊Q8—4324no—
568C22⋊Q8—4348no—
569C22⋊Q8—4324no—
570C22⋊Q8—4348no—
571C22⋊Q8C22×D43124yes—
572#121—4324no—
573#121—4324no—
574#121—4348no—
575#121—4324no—
576#121—4324no—
577#121—4324no—
578#121—4324no—
579#121—438no—
580#121—4348no—
581#121—4348no—
582#121C22×D43124yes—
583C4×Q8—438no—
584C4×Q8—4324no—
585C4×Q8—4324no—
586C4×Q8C22×D4318yes—
587C4×D4—4324no—
588C4×D4—4324no—
589C4×D4—4348no—
590C4×D4—4348no—
591C4×D4—4324no—
592C4×D4C22×D43124yes—
593C2×C4⋊C4—436no—
594C2×C4⋊C4—433no—
595C2×C4⋊C4—431no—
596C2×C4⋊C4—433no—
597C2×C4⋊C4—436no—
598C2×C4⋊C4—433no—
599C2×C4⋊C4—4324no—
600C2×C4⋊C4C22×D4313yes—
601C2×C4⋊C4C22×D4313yes—
602C2×C22⋊C4—433no—
603C2×C22⋊C4—433no—
604C2×C22⋊C4—433no—
605C2×C22⋊C4—431no—
606C2×C22⋊C4—433no—
607C2×C22⋊C4—433no—
608C2×C22⋊C4—436no—
609C2×C22⋊C4C22×D4313yes—
610C2×C22⋊C4C22×D4316yes—
611C2×C22⋊C4C22×D4311yescharacteristic
612C2×C42—433no—
613C2×C42—433no—
614C2×C42—433no—
615C2×C42—4324no—
616C2×C42C22×D4313yes—
617C24—431no—
618C24—431no—
619C24—433no—
620C24C23×D4311yescharacteristic
621C24C23×D4313yes—
622#41—232no—
623#41—8696no—
624#41—8696no—
625#41—8696no—
626#41—8696no—
627#41—8696no—
628#41—8696no—
629#41—8632no—
630C2×Q8—232no—
631C2×Q8—212no—
632C2×Q8—4364no—
633C2×Q8—4324no—
634C2×Q8—4312no—
635C2×Q8—4312no—
636C2×Q8—4312no—
637C2×Q8—4312no—
638C2×Q8—8612no—
639C2×Q8—8612no—
640C2×Q8—8696no—
641C2×Q8—8696no—
642C2×Q8—8632no—
643C2×Q8—8612no—
644C2×Q8D4×D4318yes—
645C2×Q8C23×D43112yes—
646C2×Q8C23×D4314yes—
647C2×D4—212no—
648C2×D4—46no—
649C2×D4—434no—
650C2×D4—4312no—
651C2×D4—434no—
652C2×D4—4312no—
653C2×D4—4312no—
654C2×D4—4312no—
655C2×D4—4324no—
656C2×D4—434no—
657C2×D4—4312no—
658C2×D4—4312no—
659C2×D4—4312no—
660C2×D4—864no—
661C2×D4—8612no—
662C2×D4—8612no—
663C2×D4—8612no—
664C2×D4—864no—
665C2×D4—8612no—
666C2×D4—864no—
667C2×D4—8612no—
668C2×D4—8612no—
669C2×D4—1726no—
670C2×D4—17212no—
671C2×D4C23×D43112yes—
672C2×D4C23×D43112yes—
673C22×C4—212no—
674C22×C4—212no—
675C22×C4—431no—
676C22×C4—433no—
677C22×C4—4324no—
678C22×C4—4312no—
679C22×C4—4324no—
680C22×C4—433no—
681C22×C4—431no—
682C22×C4—433no—
683C22×C4—434no—
684C22×C4—4324no—
685C22×C4—4312no—
686C22×C4—4312no—
687C22×C4—4312no—
688C22×C4—8624no—
689C22×C4—864no—
690C22×C4—8624no—
691C22×C4—8612no—
692C22×C4—8612no—
693C22×C4—1726no—
694C22×C4C23×D43112yes—
695C22×C4C23×D43112yes—
696C22×C4C23×D4311yescharacteristic
697C22×C4C23×D4313yes—
698C22×C4C23×D4311yescharacteristic
699C22×C4C23×D4313yes—
700C22×C4C23×D4313yes—
701C4⋊C4—4324no—
702C4⋊C4—4312no—
703C4⋊C4—434no—
704C4⋊C4—4312no—
705C4⋊C4—4324no—
706C4⋊C4—4312no—
707C4⋊C4C23×D43112yes—
708C4⋊C4C23×D43112yes—
709C22⋊C4—4312no—
710C22⋊C4—4312no—
711C22⋊C4—4312no—
712C22⋊C4—434no—
713C22⋊C4—4312no—
714C22⋊C4—4312no—
715C22⋊C4—4324no—
716C22⋊C4C23×D43112yes—
717C22⋊C4C23×D43124yes—
718C22⋊C4C23×D4314yes—
719C42—4312no—
720C42—4312no—
721C42—4312no—
722C42C23×D43112yes—
723C23—22no—
724C23—26no—
725C23—22no—
726C23—26no—
727C23—22no—
728C23—26no—
729C23—434no—
730C23—432no—
731C23—432no—
732C23—436no—
733C23—862no—
734C23—862no—
735C23—866no—
736C23—862no—
737C23—862no—
738C23—866no—
739C23—862no—
740C23—866no—
741C23C24×D4312yes—
742C23C24×D4316yes—
743C23C24×D4311yescharacteristic
744Q8—224no—
745Q8—4348no—
746Q8—8624no—
747Q8—8624no—
748Q8—8624no—
749Q8C2×D4×D43116yes—
750D4—224no—
751D4—412no—
752D4—868no—
753D4—8624no—
754D4—8624no—
755D4—8624no—
756D4—868no—
757D4—8624no—
758D4—868no—
759D4—8624no—
760D4—8624no—
761D4—17212no—
762D4—17224no—
763C2×C4—22no—
764C2×C4—26no—
765C2×C4—22no—
766C2×C4—26no—
767C2×C4—224no—
768C2×C4—224no—
769C2×C4—4312no—
770C2×C4—434no—
771C2×C4—432no—
772C2×C4—436no—
773C2×C4—4348no—
774C2×C4—436no—
775C2×C4—432no—
776C2×C4—436no—
777C2×C4—8648no—
778C2×C4—868no—
779C2×C4—8648no—
780C2×C4—866no—
781C2×C4—862no—
782C2×C4—866no—
783C2×C4—8624no—
784C2×C4—8624no—
785C2×C4—17212no—
786C2×C4C2×D4×D43112yes—
787C2×C4C24×D4312yes—
788C2×C4C24×D4316yes—
789C2×C4C24×D4312yes—
790C2×C4C24×D4316yes—
791C2×C4C24×D4316yes—
792C22—22no—
793C22—26no—
794C22—22no—
795C22—26no—
796C22—22no—
797C22—26no—
798C22—44no—
799C22—412no—
800C22—434no—
801C22—868no—
802C22—862no—
803C22—862no—
804C22—866no—
805C22—862no—
806C22—862no—
807C22—866no—
808C22—862no—
809C22—866no—
810C22—17212no—
811C22—1724no—
812C22C22×D4×D4312yes—
813C222−1+4×D4312yes—
814C22#1458373512yes—
815C22C25×D4311yescharacteristic
816C4—22no—
817C4—26no—
818C4—22no—
819C4—26no—
820C4—4312no—
821C4—434no—
822C4—866no—
823C4—862no—
824C4—866no—
825C4C22×D4×D43112yes—
826C2—42no—
827C2—46no—
828C2—864no—
829C2—1726no—
830C2—1722no—
831C2#1914836314yesdirect product factor
832C2C23×D4×D4311yescharacteristic
833C2C2×2−1+4×D4311yescharacteristic
834C2C2×#1458373511yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#548C2
socleC23×C43C25
hypercenterC2×#548D43
hypocenterC43C2×#3497
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×#13063372C2semidirect
3. #19148363C2direct (N × H)
4. C2×#14583568C2semidirect
5. C2×#14583567C2semidirect
6. C2×Q8×C22⋊D43C2semidirect
7. C2×#14583562C2semidirect
8. C2×#14583561C2semidirect
9. C2×#14583558C2semidirect
10. C2×#14583557C2semidirect
11. C2×#14583479C2semidirect
12. C2×#14583478C2semidirect
13. C2×#14583448C2semidirect
14. C2×#14583446C2semidirect
15. C2×C4×Q8×D43C2semidirect
16. C2×C43×#548C2semidirect
18. C2×#13063373C22semidirect
20. C2×#13063372C22semidirect
32. #14583568C22semidirect
33. #14583567C22semidirect
34. Q8×C22⋊D43C22semidirect
35. #14583562C22semidirect
36. #14583561C22semidirect
37. #14583558C22semidirect
38. #14583557C22semidirect
39. #14583479C22semidirect
40. #14583478C22semidirect
41. #14583448C22semidirect
42. #14583446C22semidirect
68. C4×Q8×D43C22semidirect
78. C43×#548C22semidirect
108. C2×Q8×D43D4semidirect
248. Q8×D43C2×D4semidirect
354. C2×Dic432−1+4semidirect
408. Dic43C2×2−1+4semidirect
419. C2×#548D43semidirect
427. C2×C43#3497semidirect
458. #548C2×D43semidirect
501. C43C2×#3497semidirect
831. C2#19148363direct (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×#130633722
#191483632
C2×#145835682
C2×#145835672
C2×Q8×C22⋊D432
C2×#145835622
C2×#145835612
C2×#145835582
C2×#145835572
C2×#145834792
C2×#145834782
C2×#145834482
C2×#145834462
C2×C4×Q8×D432
C2×C43×#5482
C2×#349743