Finite Group Databasebeta

← C2×#19148274 #26005002

Subgroups — C2×#19148274 #26005002

Order 11008.

11438 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063373C211yesmaximal, characteristic, complemented
2C22×#41×D43C211yesmaximal, characteristic, complemented
3#19148274C2132yesmaximal, direct product factor
4C2×Q8×D172C211yesmaximal, characteristic, complemented
5C2×Q8×C22⋊D43C211yesmaximal, characteristic, complemented
6C2×#14583556C211yesmaximal, characteristic, complemented
7C2×#14583554C213yesmaximal, complemented
8C2×#14583551C213yesmaximal, complemented
9C2×#14583546C213yesmaximal, complemented
10C2×#14583542C213yesmaximal, complemented
11C2×#14583478C213yesmaximal, complemented
12C2×#14583469C213yesmaximal, complemented
13C2×#14583408C213yesmaximal, complemented
14C2×C22⋊Q8×D43C213yesmaximal, complemented
15C2×#14583381C211yesmaximal, characteristic, complemented
16C2×C43×#548C211yesmaximal, characteristic, complemented
17C2×#13063373—216no—
18C2×#13063373C22116yescomplemented
19C22×#10621902C2211yescharacteristic
20C22×#10621902C2213yescomplemented
21C22×#10621898C2213yes—
22C22×#10621898C2213yescomplemented
23C22×#10621898C2213yescomplemented
24C22×#10621900C2213yes—
25C2×#41×D43—216no—
26C2×#41×D43C22116yescomplemented
27C22×Q8×D43C2211yescharacteristic
28C22×Q8×D43C2211yescharacteristic, complemented
29C22×Q8×D43C2213yescomplemented
30C22×D4×D43C2213yes—
31C23×C4×D43C2213yes—
32Q8×D172C22116yescomplemented
33Q8×C22⋊D43C22116yescomplemented
34#14583556C22116yescomplemented
35#14583554C22148yescomplemented
36#14583551C22148yescomplemented
37#14583546C22148yescomplemented
38#14583542C22148yescomplemented
39#14583478C22148yescomplemented
40#14583469C22148yescomplemented
41C2×#13063325C2213yescomplemented
42C2×#13063323C2213yescomplemented
43C2×#13063312C2213yescomplemented
44#14583408C22148yescomplemented
45C2×#13063310C2213yescomplemented
46C2×#13063307C2216yescomplemented
47C2×#13063307C2216yescomplemented
48C2×#13063307C2213yescomplemented
49C2×#13063305C2213yes—
50C2×#13063305C2213yescomplemented
51C2×#13063304C2213yescomplemented
52C2×#13063304C2213yescomplemented
53C2×#13063303C2213yes—
54C2×#13063302C2216yescomplemented
55C2×#13063302C2213yescomplemented
56C2×#13063301C2213yes—
57C22⋊Q8×D43C22148yescomplemented
58C2×#13063298C2211yescharacteristic
59C2×#13063298C2216yescomplemented
60C2×#13063297C2213yescomplemented
61C2×#13063296C2213yescomplemented
62C2×#13063296C2216yescomplemented
63C2×#13063295C2213yes—
64C2×#13063293C2213yes—
65#14583381C22116yescomplemented
66C2×Q8×Dic43C2211yescharacteristic, complemented
67C2×C4×D172C2213yes—
68C2×C4×D172C2213yescomplemented
69C2×#13063287C2213yescomplemented
70C2×C4×C22⋊D43C2213yes—
71C2×C4×C22⋊D43C2213yescomplemented
72C2×#13063282C2213yescomplemented
73C2×C4⋊C4×D43C2213yescomplemented
74C2×C4⋊C4×D43C2216yescomplemented
75C2×C22⋊C4×D43C2216yes—
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×D43C2313yes—
85#13063373—2128no—
86C2×#10621902—224no—
87C2×#10621902D4116yescomplemented
88C2×#10621902C2318yes—
89C2×#10621902C23124yescomplemented
90C2×#10621898—224no—
91C2×#10621898—224no—
92C2×#10621898—224no—
93C2×#10621898C23124yes—
94C2×#10621898C23124yescomplemented
95C2×#10621898C23124yescomplemented
96C2×#10621900—224no—
97C2×#10621900C23124yes—
98#41×D43—2128no—
99C22×Dic86C2313yes—
100C22×Dic86C2313yes—
101C22×Dic86C2313yes—
102C2×Q8×D43—28no—
103C2×Q8×D43—28no—
104C2×Q8×D43—224no—
105C2×Q8×D43C2318yes—
106C2×Q8×D43C2318yescomplemented
107C2×Q8×D43C23124yescomplemented
108C22×D172C2311yescharacteristic
109C22×D172C2313yes—
110C22×D172C2313yes—
111C22×C22⋊D43C2311yescharacteristic
112C22×C22⋊D43C2313yes—
113C22×C22⋊D43C2316yes—
114C22×C22⋊D43C2311yescharacteristic
115C22×C22⋊D43C2313yes—
116C2×D4×D43—224no—
117C2×D4×D43C23124yes—
118C23×Dic43C2313yes—
119C22×C4×D43—224no—
120C22×C4×D43C2316yes—
121C22×C4×D43C2313yes—
122C22×C4×D43C2313yes—
123C22×C4×D43C2313yes—
124C22×C4×D43C2311yescharacteristic
125C22×C4×D43C23124yes—
126C22×C4×D43C2316yes—
127C22×C4×D43C2313yes—
128#13063325C23124yescomplemented
129#13063323C23124yescomplemented
130#13063312C23124yescomplemented
131#13063310C23124yescomplemented
132#13063307C23124yescomplemented
133#13063307C23148yescomplemented
134#13063307C23148yescomplemented
135#13063305C23124yes—
136#13063305C23124yescomplemented
137#13063304C23124yescomplemented
138#13063304C23124yescomplemented
139#13063303C23124yes—
140#13063302C23148yescomplemented
141#13063302C23124yescomplemented
142#13063301C23124yes—
143#13063298C2318yes—
144#13063298C23148yescomplemented
145#13063297C23124yescomplemented
146#13063296C23148yescomplemented
147#13063296C23124yescomplemented
148#13063295C23124yes—
149#13063293C23124yes—
150Q8×Dic43C2318yescomplemented
151C4×D172C23124yes—
152C4×D172C23124yescomplemented
153#13063287C23124yescomplemented
154C4×C22⋊D43C23124yes—
155C4×C22⋊D43C23124yescomplemented
156#13063282C23124yescomplemented
157C2×C4⋊Dic43C2313yes—
158C2×C4⋊Dic43C2316yes—
159C2×C4⋊Dic43C2313yes—
160C2×Dic43⋊C4C2313yes—
161C2×Dic43⋊C4C2313yes—
162C2×Dic43⋊C4C2316yes—
163C2×Dic43⋊C4C2311yescharacteristic
164C2×Dic43⋊C4C2313yes—
165C4⋊C4×D43C23148yescomplemented
166C4⋊C4×D43C23124yescomplemented
167C2×C22⋊Dic43C2316yes—
168C2×C22⋊Dic43C2313yes—
169C2×C22⋊Dic43C2313yes—
170C2×(C2×D43)⋊C4C2313yes—
171C2×(C2×D43)⋊C4C2313yes—
172C2×(C2×D43)⋊C4C2313yes—
173C2×(C2×D43)⋊C4C2313yes—
174C2×(C2×D43)⋊C4C2311yescharacteristic
175C2×(C2×D43)⋊C4C2313yes—
176C22⋊C4×D43C23148yes—
177C2×C4×Dic43C2313yes—
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—212no—
202C23×D43—212no—
203C23×D43—46no—
204C23×D43C2411yescharacteristic
205C23×D43C24112yes—
206C23×D43C2413yes—
207C23×D43C2411yescharacteristic
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—24no—
228C2×C22⋊D43—224no—
229C2×C22⋊D43—212no—
230C2×C22⋊D43—24no—
231C2×C22⋊D43—46no—
232C2×C22⋊D43C2414yes—
233C2×C22⋊D43C24112yes—
234C2×C22⋊D43C24124yes—
235C2×C22⋊D43C2414yes—
236C2×C22⋊D43C24112yes—
237C22×Dic43—212no—
238C22×Dic43C2411yescharacteristic
239C22×Dic43C2413yes—
240C22×Dic43C2413yes—
241C22×Dic43C2413yes—
242C22×Dic43C24112yes—
243C22×Dic43C2411yescharacteristic
244#10621902—296no—
245#10621902C2×D4164yescomplemented
246Q8×D43—232no—
247Q8×D43—232no—
248Q8×D43—296no—
249#10621900—296no—
250D4×D43—296no—
251#10621898—296no—
252#10621898—296no—
253#10621898—296no—
254C2×D172—212no—
255C2×D172—24no—
256C2×D172C2×D4124yes—
257C2×D172C2414yes—
258C2×D172C24112yes—
259C2×D172C24112yes—
260C2×C4×D43—212no—
261C2×C4×D43—212no—
262C2×C4×D43—24no—
263C2×C4×D43—296no—
264C2×C4×D43—212no—
265C2×C4×D43—224no—
266C2×C4×D43—412no—
267C2×C4×D43C2×D4124yes—
268C2×C4×D43C24124yes—
269C2×C4×D43C24112yes—
270C2×C4×D43C24112yes—
271C2×C4×D43C24112yes—
272C2×C4×D43C2414yes—
273C2×C4×D43C24124yes—
274C2×C4×D43C24112yes—
275C2×Dic86—212no—
276C2×Dic86—212no—
277C2×Dic86—212no—
278C2×Dic86C24112yes—
279C2×Dic86C24112yes—
280C2×Dic86C24112yes—
281C4⋊C4×C43C24112yes—
282C4⋊C4×C43C24112yes—
283C22⋊C4×C43C2414yes—
284C22⋊C4×C43C24112yes—
285C22⋊C4×C43C24124yes—
286C42×C43C24112yes—
287C22⋊Dic43C24124yes—
288C22⋊Dic43C24112yes—
289C22⋊Dic43C24112yes—
290(C2×D43)⋊C4C24112yes—
291(C2×D43)⋊C4C24112yes—
292(C2×D43)⋊C4C24112yes—
293(C2×D43)⋊C4C24112yes—
294(C2×D43)⋊C4C2414yes—
295(C2×D43)⋊C4C24112yes—
296C4⋊Dic43C24112yes—
297C4⋊Dic43C24124yes—
298C4⋊Dic43C24112yes—
299Dic43⋊C4C24112yes—
300Dic43⋊C4C24112yes—
301Dic43⋊C4C24124yes—
302Dic43⋊C4C2414yes—
303Dic43⋊C4C24112yes—
304C4×Dic43C24112yes—
305C23×C43—26no—
306C23×C43—22no—
307C23×C43—22no—
308C23×C43—26no—
309C23×C43—26no—
310C23×C43—22no—
311C23×C43C2516yes—
312C23×C43C2512yes—
313C23×C43C2511yescharacteristic
314C22×D43—22no—
315C22×D43—26no—
316C22×D43—26no—
317C22×D43—22no—
318C22×D43—22no—
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—224no—
322C22×D43—224no—
323C22×D43—412no—
324C22×D43—448no—
325C22×D43C22×D4112yes—
326C22×D432−1+414yescomplemented
327C22×D43C2512yes—
328C22×D43C2516yes—
329C22×D43C2512yes—
330Q8×C43—224no—
331Q8×C43C22×D4116yes—
332D4×C43—224no—
333D4×C43—412no—
334C2×C4×C43—26no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—26no—
338C2×C4×C43—224no—
339C2×C4×C43—224no—
340C2×C4×C43C22×D4112yes—
341C2×C4×C43C2516yes—
342C2×C4×C43C2512yes—
343C2×C4×C43C2512yes—
344C2×C4×C43C2516yes—
345C2×C4×C43C2516yes—
346C22⋊D43—224no—
347C22⋊D43—248no—
348C22⋊D43—28no—
349C22⋊D43—28no—
350C22⋊D43—412no—
351C2×Dic43—26no—
352C2×Dic43—26no—
353C2×Dic43—22no—
354C2×Dic43—26no—
355C2×Dic43—224no—
356C2×Dic43C22×D414yes—
357C2×Dic43C2512yes—
358C2×Dic43C2516yes—
359C2×Dic43C2516yes—
360C2×Dic43C2516yes—
361C2×Dic43C2512yes—
362D172—224no—
363D172—28no—
364D172C22×D4148yes—
365C4×D43—224no—
366C4×D43—248no—
367C4×D43—224no—
368C4×D43—224no—
369C4×D43—28no—
370C4×D43—424no—
371C4×D43C22×D4148yes—
372Dic86—224no—
373Dic86—224no—
374Dic86—224no—
375C2×#3489—431nomaximal, Sylow
376C22×C43—26no—
377C22×C43—22no—
378C22×C43—26no—
379C22×C43—22no—
380C22×C43—26no—
381C22×C43—22no—
382C22×C43—412no—
383C22×C43—44no—
384C22×C43C23×D412yes—
385C22×C43C2×2−1+412yes—
386C22×C43#58512yes—
387C22×C43C2611yescharacteristic
388C2×D43—22no—
389C2×D43—26no—
390C2×D43—22no—
391C2×D43—26no—
392C2×D43—28no—
393C2×D43—224no—
394C2×D43—22no—
395C2×D43—22no—
396C2×D43—22no—
397C2×D43—448no—
398C2×D43—44no—
399C2×D43C23×D4112yes—
400C2×D43C2×2−1+414yescomplemented
401C4×C43—26no—
402C4×C43—22no—
403C4×C43—22no—
404C4×C43—26no—
405C4×C43C23×D4112yes—
406Dic43—26no—
407Dic43—26no—
408Dic43—22no—
409Dic43—26no—
410Dic43C23×D414yes—
411C22×2−1+4—431no—
412C23×#41—431no—
413#3489—4332no—
414C2×D4×Q8—431no—
415C2×D4×Q8—431no—
416C2×#548—431no—
417C2×#548D4311yescharacteristic, complemented
418C2×#547—433no—
419C2×#547—433no—
420C2×#546—433no—
421C2×#546—433no—
422C2×#537—433no—
423C2×#536—433no—
424C2×#525—433no—
425C22×C22⋊Q8—433no—
426C2×#520—431no—
427C2×C43—46no—
428C2×C43—42no—
429C2×C43#348914yescomplemented
430C2×C43C24×D411yescharacteristic
431C2×C43C22×2−1+411yescharacteristic
432C2×C43C2×#58511yescharacteristic
433D43—24no—
434D43—212no—
435D43—42no—
436C2×2−1+4—4316no—
437C2×2−1+4—8616no—
438C22×#41—4316no—
439C22×#41—431no—
440C22×#41—433no—
441C22×#41—433no—
442C22×#41—433no—
443C22×#41—433no—
444C22×#41—433no—
445C22×#41—8616no—
446C22×#41C2×D4311yescharacteristic
447C23×Q8—431no—
448C23×Q8—433no—
449C23×Q8—431no—
450C23×Q8C2×D4311yescharacteristic, complemented
451C23×D4—433no—
452C24×C4—433no—
453D4×Q8—4316no—
454D4×Q8—4316no—
455#548—4316no—
456#548C2×D43116yescomplemented
457#547—4348no—
458#547—4348no—
459#546—4348no—
460#546—4348no—
461#537—4348no—
462#536—4348no—
463C2×C4⋊Q8—433no—
464C2×C4⋊Q8—433no—
465C2×#124—433no—
466C2×#124C2×D4313yescomplemented
467#525—4348no—
468C2×#123—433no—
469C2×#123—433no—
470C2×#123—436no—
471C2×#123—436no—
472C2×C22⋊Q8—433no—
473C2×C22⋊Q8—433no—
474C2×C22⋊Q8—433no—
475C2×C22⋊Q8—4348no—
476C2×C22⋊Q8—433no—
477C2×C22⋊Q8—433no—
478C2×C22⋊Q8—433no—
479C2×C22⋊Q8—436no—
480C2×C22⋊Q8—433no—
481C2×C22⋊Q8C2×D4313yescomplemented
482C2×#121—436no—
483C2×#121—433no—
484C2×#121—433no—
485C2×#121—431no—
486C2×#121—436no—
487C2×#121C2×D4313yescomplemented
488C2×#120—433no—
489C2×#120—433no—
490#520—4316no—
491C2×C4×Q8—431no—
492C2×C4×Q8C2×D4311yescharacteristic, complemented
493C2×C4×D4—433no—
494C2×C4×D4—433no—
495C2×C4×D4—433no—
496C2×C4×D4—433no—
497C2×C4×D4—433no—
498C2×C4×D4C2×D4313yescomplemented
499C2×#117—433no—
500C22×C4⋊C4—433no—
501C22×C4⋊C4—436no—
502C22×C22⋊C4—436no—
503C43C2×#348911yescharacteristic, complemented, Sylow
504C25—433no—
5052−1+4—86128no—
506C2×#41—28no—
507C2×#41—4316no—
508C2×#41—438no—
509C2×#41—4324no—
510C2×#41—4324no—
511C2×#41—4324no—
512C2×#41—4324no—
513C2×#41—4324no—
514C2×#41—8624no—
515C2×#41—8624no—
516C2×#41—8624no—
517C2×#41—8624no—
518C2×#41—8624no—
519C2×#41—86128no—
520C2×#41C22×D4318yes—
521C22×Q8—28no—
522C22×Q8—4324no—
523C22×Q8—438no—
524C22×Q8—438no—
525C22×Q8—433no—
526C22×Q8—433no—
527C22×Q8—433no—
528C22×Q8—8624no—
529C22×Q8—868no—
530C22×Q8—868no—
531C22×Q8C22×D4313yes—
532C22×Q8C22×D4311yescharacteristic
533C22×Q8C22×D4318yescomplemented
534C22×D4—431no—
535C22×D4—433no—
536C22×D4—431no—
537C22×D4—436no—
538C22×D4—433no—
539C22×D4—4324no—
540C22×D4—433no—
541C22×D4—431no—
542C22×D4—433no—
543C22×D4—8624no—
544C22×D4C22×D4313yes—
545C22×D4C22×D4313yes—
546C23×C4—433no—
547C23×C4—433no—
548C23×C4—436no—
549C23×C4—433no—
550C23×C4—433no—
551C23×C4—433no—
552C23×C4—431no—
553C23×C4—4324no—
554C23×C4—436no—
555C23×C4—8624no—
556C23×C4C22×D4313yes—
557C23×C4C22×D4313yes—
558C4⋊Q8—4324no—
559C4⋊Q8—4324no—
560#124—4324no—
561#124C22×D43124yescomplemented
562#123—4324no—
563#123—4324no—
564#123—4348no—
565#123—4348no—
566C22⋊Q8—4324no—
567C22⋊Q8—4324no—
568C22⋊Q8—4324no—
569C22⋊Q8—4324no—
570C22⋊Q8—4324no—
571C22⋊Q8—4324no—
572C22⋊Q8—4348no—
573C22⋊Q8—4324no—
574C22⋊Q8C22×D43124yescomplemented
575#121—4324no—
576#121—4348no—
577#121—4324no—
578#121—438no—
579#121—4348no—
580#121C22×D43124yescomplemented
581#120—4324no—
582#120—4324no—
583C4×Q8—438no—
584C4×Q8C22×D4318yescomplemented
585C4×D4—4324no—
586C4×D4—4324no—
587C4×D4—4324no—
588C4×D4—4324no—
589C4×D4—4324no—
590C4×D4C22×D43124yescomplemented
591#117—4324no—
592C2×C4⋊C4—433no—
593C2×C4⋊C4—433no—
594C2×C4⋊C4—433no—
595C2×C4⋊C4—436no—
596C2×C4⋊C4—436no—
597C2×C4⋊C4—431no—
598C2×C4⋊C4—433no—
599C2×C4⋊C4—433no—
600C2×C4⋊C4—4324no—
601C2×C4⋊C4—4348no—
602C2×C4⋊C4C22×D4313yes—
603C2×C4⋊C4C22×D4313yes—
604C2×C22⋊C4—436no—
605C2×C22⋊C4—433no—
606C2×C22⋊C4—433no—
607C2×C22⋊C4—433no—
608C2×C22⋊C4—433no—
609C2×C22⋊C4—433no—
610C2×C22⋊C4—433no—
611C2×C22⋊C4—431no—
612C2×C22⋊C4—433no—
613C2×C22⋊C4—4348no—
614C2×C22⋊C4C22×D4316yes—
615C2×C22⋊C4C22×D4311yescharacteristic
616C2×C22⋊C4C22×D4313yes—
617C2×C42—433no—
618C2×C42C22×D4313yes—
619C24—431no—
620C24—433no—
621C24—431no—
622C24—4312no—
623C24—8612no—
624C24—8612no—
625C24—1726no—
626C24C23×D4313yes—
627C24C23×D4311yescharacteristic
628#41—232no—
629#41—4364no—
630#41—8696no—
631#41—8696no—
632#41—8696no—
633#41—8696no—
634#41—8696no—
635C2×Q8—232no—
636C2×Q8—212no—
637C2×Q8—4312no—
638C2×Q8—4312no—
639C2×Q8—4312no—
640C2×Q8—8612no—
641C2×Q8—8696no—
642C2×Q8—8632no—
643C2×Q8—8632no—
644C2×Q8—8612no—
645C2×Q8—8612no—
646C2×Q8D4×D4318yes—
647C2×Q8C23×D43112yes—
648C2×Q8C23×D4314yes—
649C2×D4—212no—
650C2×D4—46no—
651C2×D4—434no—
652C2×D4—4312no—
653C2×D4—434no—
654C2×D4—4324no—
655C2×D4—4312no—
656C2×D4—4324no—
657C2×D4—4312no—
658C2×D4—434no—
659C2×D4—4312no—
660C2×D4—8612no—
661C2×D4—864no—
662C2×D4—864no—
663C2×D4—8696no—
664C2×D4—8624no—
665C2×D4—8612no—
666C2×D4—864no—
667C2×D4—1726no—
668C2×D4C23×D43112yes—
669C2×D4C23×D43112yes—
670C22×C4—212no—
671C22×C4—212no—
672C22×C4—431no—
673C22×C4—4324no—
674C22×C4—4312no—
675C22×C4—4312no—
676C22×C4—431no—
677C22×C4—433no—
678C22×C4—433no—
679C22×C4—433no—
680C22×C4—4324no—
681C22×C4—4312no—
682C22×C4—4312no—
683C22×C4—4312no—
684C22×C4—434no—
685C22×C4—4324no—
686C22×C4—864no—
687C22×C4—8696no—
688C22×C4—8612no—
689C22×C4—8624no—
690C22×C4—8612no—
691C22×C4—8612no—
692C22×C4—8612no—
693C22×C4—17212no—
694C22×C4C23×D43112yes—
695C22×C4C23×D43112yes—
696C22×C4C23×D4311yescharacteristic
697C22×C4C23×D4313yes—
698C22×C4C23×D4313yes—
699C22×C4C23×D4311yescharacteristic
700C22×C4C23×D4313yes—
701C4⋊C4—4312no—
702C4⋊C4—4312no—
703C4⋊C4—4312no—
704C4⋊C4—4324no—
705C4⋊C4—4324no—
706C4⋊C4—434no—
707C4⋊C4—4312no—
708C4⋊C4—4312no—
709C4⋊C4C23×D43112yes—
710C4⋊C4C23×D43112yes—
711C22⋊C4—4324no—
712C22⋊C4—4312no—
713C22⋊C4—4312no—
714C22⋊C4—4312no—
715C22⋊C4—4312no—
716C22⋊C4—4312no—
717C22⋊C4—4312no—
718C22⋊C4—434no—
719C22⋊C4—4312no—
720C22⋊C4C23×D43124yes—
721C22⋊C4C23×D4314yes—
722C22⋊C4C23×D43112yes—
723C42—4312no—
724C42C23×D43112yes—
725C23—22no—
726C23—26no—
727C23—22no—
728C23—26no—
729C23—22no—
730C23—26no—
731C23—4312no—
732C23—434no—
733C23—432no—
734C23—436no—
735C23—432no—
736C23—8624no—
737C23—8624no—
738C23—862no—
739C23—866no—
740C23—866no—
741C23—862no—
742C23—862no—
743C23—862no—
744C23—862no—
745C23—17212no—
746C23—17248no—
747C23C24×D4316yes—
748C23C24×D4312yes—
749C23C24×D4311yescharacteristic
750Q8—224no—
751Q8—8624no—
752Q8—8624no—
753Q8—8624no—
754Q8C2×D4×D43116yes—
755D4—224no—
756D4—412no—
757D4—4348no—
758D4—8624no—
759D4—868no—
760D4—868no—
761D4—8648no—
762D4—8624no—
763D4—868no—
764D4—17212no—
765C2×C4—22no—
766C2×C4—26no—
767C2×C4—22no—
768C2×C4—26no—
769C2×C4—224no—
770C2×C4—224no—
771C2×C4—434no—
772C2×C4—432no—
773C2×C4—4348no—
774C2×C4—432no—
775C2×C4—436no—
776C2×C4—436no—
777C2×C4—436no—
778C2×C4—868no—
779C2×C4—8624no—
780C2×C4—8648no—
781C2×C4—8624no—
782C2×C4—866no—
783C2×C4—866no—
784C2×C4—862no—
785C2×C4—866no—
786C2×C4—8624no—
787C2×C4—8624no—
788C2×C4—17224no—
789C2×C4C2×D4×D43112yes—
790C2×C4C24×D4312yes—
791C2×C4C24×D4316yes—
792C2×C4C24×D4316yes—
793C2×C4C24×D4312yes—
794C2×C4C24×D4316yes—
795C22—22no—
796C22—26no—
797C22—22no—
798C22—26no—
799C22—22no—
800C22—26no—
801C22—412no—
802C22—44no—
803C22—4312no—
804C22—434no—
805C22—862no—
806C22—866no—
807C22—866no—
808C22—862no—
809C22—868no—
810C22—8624no—
811C22—862no—
812C22—862no—
813C22—862no—
814C22—17248no—
815C22—1724no—
816C22C22×D4×D4312yes—
817C222−1+4×D4312yes—
818C22#1458373512yes—
819C22C25×D4311yescharacteristic
820C4—22no—
821C4—26no—
822C4—22no—
823C4—26no—
824C4—434no—
825C4—866no—
826C4—866no—
827C4—862no—
828C4—866no—
829C4C22×D4×D43112yes—
830C2—46no—
831C2—42no—
832C2—864no—
833C2—8612no—
834C2—1722no—
835C2#1914827414yesdirect product factor
836C2C23×D4×D4311yescharacteristic
837C2C2×2−1+4×D4311yescharacteristic
838C2C2×#1458373511yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#548C2
socleC23×C43C25
hypercenterC2×#548D43
hypocenterC43C2×#3489
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×#41×D43C2semidirect
3. #19148274C2direct (N × H)
4. C2×Q8×D172C2semidirect
5. C2×Q8×C22⋊D43C2semidirect
6. C2×#14583556C2semidirect
7. C2×#14583554C2semidirect
8. C2×#14583551C2semidirect
9. C2×#14583546C2semidirect
10. C2×#14583542C2semidirect
11. C2×#14583478C2semidirect
12. C2×#14583469C2semidirect
13. C2×#14583408C2semidirect
14. C2×C22⋊Q8×D43C2semidirect
15. C2×#14583381C2semidirect
16. C2×C43×#548C2semidirect
18. C2×#13063373C22semidirect
20. C22×#10621902C22semidirect
22. C22×#10621898C22semidirect
23. C22×#10621898C22semidirect
26. C2×#41×D43C22semidirect
28. C22×Q8×D43C22semidirect
29. C22×Q8×D43C22semidirect
32. Q8×D172C22semidirect
33. Q8×C22⋊D43C22semidirect
34. #14583556C22semidirect
35. #14583554C22semidirect
36. #14583551C22semidirect
37. #14583546C22semidirect
38. #14583542C22semidirect
39. #14583478C22semidirect
40. #14583469C22semidirect
41. C2×#13063325C22semidirect
42. C2×#13063323C22semidirect
43. C2×#13063312C22semidirect
44. #14583408C22semidirect
45. C2×#13063310C22semidirect
46. C2×#13063307C22semidirect
47. C2×#13063307C22semidirect
48. C2×#13063307C22semidirect
50. C2×#13063305C22semidirect
51. C2×#13063304C22semidirect
52. C2×#13063304C22semidirect
54. C2×#13063302C22semidirect
55. C2×#13063302C22semidirect
57. C22⋊Q8×D43C22semidirect
59. C2×#13063298C22semidirect
60. C2×#13063297C22semidirect
61. C2×#13063296C22semidirect
62. C2×#13063296C22semidirect
65. #14583381C22semidirect
66. C2×Q8×Dic43C22semidirect
68. C2×C4×D172C22semidirect
69. C2×#13063287C22semidirect
71. C2×C4×C22⋊D43C22semidirect
72. C2×#13063282C22semidirect
73. C2×C4⋊C4×D43C22semidirect
74. C2×C4⋊C4×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
87. C2×#10621902D4semidirect
89. C2×#10621902C23semidirect
94. C2×#10621898C23semidirect
95. C2×#10621898C23semidirect
106. C2×Q8×D43C23semidirect
107. C2×Q8×D43C23semidirect
128. #13063325C23semidirect
129. #13063323C23semidirect
130. #13063312C23semidirect
131. #13063310C23semidirect
132. #13063307C23semidirect
133. #13063307C23semidirect
134. #13063307C23semidirect
136. #13063305C23semidirect
137. #13063304C23semidirect
138. #13063304C23semidirect
140. #13063302C23semidirect
141. #13063302C23semidirect
144. #13063298C23semidirect
145. #13063297C23semidirect
146. #13063296C23semidirect
147. #13063296C23semidirect
150. Q8×Dic43C23semidirect
152. C4×D172C23semidirect
153. #13063287C23semidirect
155. C4×C22⋊D43C23semidirect
156. #13063282C23semidirect
165. C4⋊C4×D43C23semidirect
166. C4⋊C4×D43C23semidirect
183. C22×Q8×C43C23semidirect
188. #124×C43C23semidirect
189. C22⋊Q8×C43C23semidirect
190. #121×C43C23semidirect
191. C4×Q8×C43C23semidirect
192. C4×D4×C43C23semidirect
245. #10621902C2×D4semidirect
326. C22×D432−1+4semidirect
400. C2×D43C2×2−1+4semidirect
417. C2×#548D43semidirect
429. C2×C43#3489semidirect
450. C23×Q8C2×D43semidirect
456. #548C2×D43semidirect
466. C2×#124C2×D43semidirect
481. C2×C22⋊Q8C2×D43semidirect
487. C2×#121C2×D43semidirect
492. C2×C4×Q8C2×D43semidirect
498. C2×C4×D4C2×D43semidirect
503. C43C2×#3489semidirect
533. C22×Q8C22×D43semidirect
561. #124C22×D43semidirect
574. C22⋊Q8C22×D43semidirect
580. #121C22×D43semidirect
584. C4×Q8C22×D43semidirect
590. C4×D4C22×D43semidirect
835. C2#19148274direct (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×#41×D432
#191482742
C2×Q8×D1722
C2×Q8×C22⋊D432
C2×#145835562
C2×#145835542
C2×#145835512
C2×#145835462
C2×#145835422
C2×#145834782
C2×#145834692
C2×#145834082
C2×C22⋊Q8×D432
C2×#145833812
C2×C43×#5482
C2×#348943