Finite Group Databasebeta

← C2×#19148348 #26005029

Subgroups — C2×#19148348 #26005029

Order 11008.

7206 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148348C2132yesmaximal, direct product factor
2C2×#14583617C212yesmaximal, complemented
3C2×#14583604C212yesmaximal, complemented
4C2×#14583589C214yesmaximal, complemented
5C2×#14583588C212yesmaximal, complemented
6C2×#14583584C212yesmaximal, complemented
7C2×#14583578C214yesmaximal, complemented
8C2×#14583530C211yesmaximal, characteristic, complemented
9C2×#14583514C212yesmaximal, complemented
10C2×#14583507C212yesmaximal, complemented
11C2×#14583470C211yesmaximal, characteristic, complemented
12C2×#14583453C212yesmaximal, complemented
13C2×#14583431C212yesmaximal, complemented
14C2×#14583406C211yesmaximal, characteristic
15C22×#13063305C211yesmaximal, characteristic, complemented
16C2×#14583376C211yesmaximal, characteristic, complemented
17C2×#117×D43C211yesmaximal, characteristic, complemented
18C2×C43×#520C211yesmaximal, characteristic, complemented
19C23×Dic86C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21#14583617C22132yescomplemented
22#14583604C22132yescomplemented
23#14583589C22164yescomplemented
24#14583588C22132yescomplemented
25#14583584C22132yescomplemented
26#14583578C22164yescomplemented
27#14583530C22116yescomplemented
28#14583514C22132yescomplemented
29#14583507C22132yescomplemented
30#14583470C22116yescomplemented
31#14583453C22132yescomplemented
32C2×#13063324C2212yescomplemented
33C2×#13063324C2212yescomplemented
34C2×#13063323C2212yescomplemented
35#14583431C22132yescomplemented
36C2×#13063320C2214yes—
37C2×#13063319C2214yes—
38C2×#13063318C2214yescomplemented
39C2×#13063318C2214yescomplemented
40C2×#13063317C2214yescomplemented
41C2×#13063316C2212yescomplemented
42C2×#13063316C2212yescomplemented
43C2×#13063315C2214yescomplemented
44C2×#13063315C2214yescomplemented
45C2×#13063312C2212yescomplemented
46C2×#13063311C2214yes—
47#14583406C22116yes—
48C2×#13063308C2214yes—
49C2×#13063307C2214yes—
50C2×#13063306C2212yes—
51C2×#13063306C2214yes—
52C2×#13063305C2212yes—
53C2×#13063305C2212yes—
54C2×#13063305C2212yes—
55C2×#13063305C2212yes—
56C2×#13063305C22116yescomplemented
57C2×#13063304C2214yes—
58C2×#13063304C2212yescomplemented
59C2×#13063304C2214yescomplemented
60C2×#13063304C2212yescomplemented
61C2×#13063303C2214yes—
62C2×#13063301C2211yescharacteristic
63C2×#13063301C2211yescharacteristic
64C2×#13063296C2211yescharacteristic
65C2×#13063296C2211yescharacteristic
66C2×#13063293C2212yes—
67#14583376C22116yescomplemented
68C2×C4×Dic86C2212yescomplemented
69C2×C4×Dic86C2212yescomplemented
70C2×C4×Dic86C2214yescomplemented
71C2×#13063290C2212yescomplemented
72C2×#13063290C2212yescomplemented
73C2×C4×C22⋊D43C2212yes—
74C2×C4×C22⋊D43C2212yes—
75C2×C4×C22⋊D43C2214yes—
76C2×#13063284C2211yescharacteristic
77C2×#13063284C2211yescharacteristic
78C2×#13063284C2214yescomplemented
79C2×#13063283C2211yescharacteristic
80C2×#13063283C2211yescharacteristic
81C2×#13063282C2214yes—
82C2×#13063282C2212yes—
83C2×#13063281C2214yes—
84C2×#13063281C2212yes—
85#117×D43C22116yescomplemented
86C22×C4⋊Dic43C2212yes—
87C2×C4⋊C4×D43C2211yescharacteristic
88C2×C4⋊C4×D43C2211yescharacteristic
89C22×(C2×D43)⋊C4C2212yes—
90C2×C22⋊C4×D43C2212yes—
91C2×C42×D43C2212yes—
92C22×#41×C43C2211yescharacteristic
93C43×#520C22116yescomplemented
94C2×C4×Q8×C43C2212yescomplemented
95C2×C4×D4×C43C2214yes—
96C2×C4×D4×C43C2212yescomplemented
97C2×#117×C43C2211yescharacteristic
98C2×#117×C43C2212yescomplemented
99C22×C4⋊C4×C43C2211yescharacteristic
100C22×C4⋊C4×C43C2212yescomplemented
101C24×D43C2311yescharacteristic
102C22×Dic86—28no—
103C22×Dic86C2312yes—
104C22×Dic86C2312yes—
105C22×Dic86C2318yes—
106C22×Dic86C2314yes—
107C22×C22⋊D43C2312yes—
108C22×C22⋊D43C2312yes—
109C23×Dic43C2312yes—
110C23×Dic43C2311yescharacteristic
111C22×C4×D43—28no—
112C22×C4×D43C2311yescharacteristic
113C22×C4×D43C2312yes—
114C22×C4×D43C2311yescharacteristic
115C22×C4×D43C2318yes—
116C22×C4×D43C2311yescharacteristic
117C22×C4×D43C2311yescharacteristic
118C22×C4×D43C2312yes—
119#13063324C23116yescomplemented
120#13063324C23116yescomplemented
121#13063323C23116yescomplemented
122#13063320C23132yes—
123#13063319C23132yes—
124#13063318C23132yescomplemented
125#13063318C23132yescomplemented
126#13063317C23132yescomplemented
127#13063316C23116yescomplemented
128#13063316C23116yescomplemented
129#13063315C23132yescomplemented
130#13063315C23132yescomplemented
131#13063312C23116yescomplemented
132#13063311C23132yes—
133#13063308C23132yes—
134#13063307C23132yes—
135#13063306C23132yes—
136#13063306C23116yes—
137#13063305C23116yes—
138#13063305C23116yes—
139#13063305C23116yes—
140#13063305C23116yes—
141#13063304C23132yes—
142#13063304C23116yescomplemented
143#13063304C23132yescomplemented
144#13063304C23116yescomplemented
145#13063303C23132yes—
146#13063301C2318yes—
147#13063301C2318yes—
148#13063296C2318yes—
149#13063296C2318yes—
150#13063293C23116yes—
151C4×Dic86C23132yescomplemented
152C4×Dic86C23116yescomplemented
153C4×Dic86C23116yescomplemented
154#13063290C23116yescomplemented
155#13063290C23116yescomplemented
156C4×C22⋊D43C23132yes—
157C4×C22⋊D43C23116yes—
158C4×C22⋊D43C23116yes—
159#13063284C2318yes—
160#13063284C2318yes—
161#13063284C23132yescomplemented
162#13063283C2318yes—
163#13063283C2318yes—
164#13063282C23132yes—
165#13063282C23116yes—
166#13063281C23132yes—
167#13063281C23116yes—
168C2×C4⋊Dic43C23116yes—
169C2×C4⋊Dic43C2311yescharacteristic
170C2×C4⋊Dic43C2311yescharacteristic
171C2×C4⋊Dic43C2314yes—
172C2×C4⋊Dic43C2314yes—
173C2×C4⋊Dic43C2311yescharacteristic
174C2×C4⋊Dic43C2311yescharacteristic
175C2×C4⋊Dic43C2314yes—
176C2×Dic43⋊C4C2312yes—
177C2×Dic43⋊C4C2312yes—
178C2×Dic43⋊C4C2314yes—
179C2×Dic43⋊C4C2314yes—
180C2×Dic43⋊C4C2314yes—
181C2×Dic43⋊C4C2314yes—
182C2×Dic43⋊C4C2312yes—
183C2×Dic43⋊C4C2312yes—
184C2×Dic43⋊C4C2314yes—
185C2×Dic43⋊C4C2314yes—
186C4⋊C4×D43C2318yes—
187C4⋊C4×D43C2318yes—
188C2×C22⋊Dic43C2312yes—
189C2×C22⋊Dic43C2312yes—
190C2×C22⋊Dic43C2312yes—
191C2×C22⋊Dic43C2314yes—
192C2×C22⋊Dic43C2312yes—
193C2×C22⋊Dic43C2314yes—
194C2×(C2×D43)⋊C4C23116yes—
195C2×(C2×D43)⋊C4C2312yes—
196C2×(C2×D43)⋊C4C2312yes—
197C2×(C2×D43)⋊C4C2314yes—
198C2×(C2×D43)⋊C4C2314yes—
199C2×(C2×D43)⋊C4C2312yes—
200C2×(C2×D43)⋊C4C2312yes—
201C22⋊C4×D43C23116yes—
202C2×C4×Dic43C2312yes—
203C2×C4×Dic43C2312yes—
204C2×C4×Dic43C2312yes—
205C2×C4×Dic43C2314yes—
206C2×C4×Dic43C2314yes—
207C2×C4×Dic43C2312yes—
208C42×D43C23116yes—
209C2×#41×C43—28no—
210C2×#41×C43C2318yes—
211C22×Q8×C43C2311yescharacteristic
212C22×D4×C43C2312yes—
213C22×D4×C43C2311yescharacteristic
214C23×C4×C43C2312yes—
215C23×C4×C43C2312yes—
216C23×C4×C43C2314yes—
217C23×C4×C43C2311yescharacteristic
218C4×Q8×C43C23116yescomplemented
219C4×D4×C43C23132yes—
220C4×D4×C43C23116yescomplemented
221#117×C43C2318yes—
222#117×C43C23116yescomplemented
223C2×C4⋊C4×C43C2312yes—
224C2×C4⋊C4×C43C2312yes—
225C2×C4⋊C4×C43C2318yes—
226C2×C4⋊C4×C43C2311yescharacteristic
227C2×C4⋊C4×C43C2314yes—
228C2×C4⋊C4×C43C2311yescharacteristic
229C2×C4⋊C4×C43C23116yescomplemented
230C2×C22⋊C4×C43C2312yes—
231C2×C22⋊C4×C43C2314yes—
232C2×C42×C43C2312yes—
233C2×C42×C43C2314yes—
234C24×C43C2412yes—
235C24×C43C2411yescharacteristic
236C23×D43—24no—
237C23×D43—24no—
238C23×D43—42no—
239C23×D43C2411yescharacteristic
240C23×D43C2414yes—
241C23×D43C2411yescharacteristic
242#41×C43—232no—
243C2×Q8×C43—24no—
244C2×Q8×C43C2414yes—
245C2×D4×C43—24no—
246C2×D4×C43—28no—
247C2×D4×C43C2418yes—
248C2×D4×C43C2414yes—
249C22×C4×C43—28no—
250C22×C4×C43—44no—
251C22×C4×C43—48no—
252C22×C4×C43#4118yes—
253C22×C4×C43C2412yes—
254C22×C4×C43C2412yes—
255C22×C4×C43C2412yes—
256C22×C4×C43C2414yes—
257C22×C4×C43C2418yes—
258C22×C4×C43C2418yes—
259C22×C4×C43C24116yes—
260C22×C4×C43C2411yescharacteristic
261C22×C4×C43C2411yescharacteristic
262C22×C4×C43C2414yes—
263C2×C22⋊D43—28no—
264C2×C22⋊D43—44no—
265C2×C22⋊D43C2418yes—
266C2×C22⋊D43C2418yes—
267C22×Dic43—24no—
268C22×Dic43—28no—
269C22×Dic43C2411yescharacteristic
270C22×Dic43C2412yes—
271C22×Dic43C2412yes—
272C22×Dic43C2414yes—
273C22×Dic43C2412yes—
274C22×Dic43C2412yes—
275C22×Dic43C2418yes—
276C22×Dic43C2411yescharacteristic
277C22×Dic43C2414yes—
278C2×C4×D43—24no—
279C2×C4×D43—24no—
280C2×C4×D43—24no—
281C2×C4×D43—24no—
282C2×C4×D43—232no—
283C2×C4×D43—28no—
284C2×C4×D43—44no—
285C2×C4×D43C2414yes—
286C2×C4×D43C2418yes—
287C2×C4×D43C2414yes—
288C2×C4×D43C2414yes—
289C2×C4×D43C2414yes—
290C2×C4×D43C2418yes—
291C2×Dic86—28no—
292C2×Dic86—28no—
293C2×Dic86—232no—
294C2×Dic86—48no—
295C2×Dic86C2418yes—
296C2×Dic86C2418yes—
297C2×Dic86C24116yes—
298C4⋊C4×C43C2418yes—
299C4⋊C4×C43C2418yes—
300C4⋊C4×C43C2414yes—
301C4⋊C4×C43C24116yes—
302C4⋊C4×C43C2414yes—
303C22⋊C4×C43C2418yes—
304C22⋊C4×C43C24116yes—
305C42×C43C2418yes—
306C42×C43C24116yes—
307C22⋊Dic43C2418yes—
308C22⋊Dic43C2418yes—
309C22⋊Dic43C2418yes—
310C22⋊Dic43C24116yes—
311C22⋊Dic43C2418yes—
312C22⋊Dic43C24116yes—
313(C2×D43)⋊C4C2418yes—
314(C2×D43)⋊C4C2418yes—
315(C2×D43)⋊C4C24116yes—
316(C2×D43)⋊C4C24116yes—
317(C2×D43)⋊C4C2418yes—
318(C2×D43)⋊C4C2418yes—
319C4⋊Dic43C2414yes—
320C4⋊Dic43C2414yes—
321C4⋊Dic43C24116yes—
322C4⋊Dic43C24116yes—
323C4⋊Dic43C2414yes—
324C4⋊Dic43C2414yes—
325C4⋊Dic43C24116yes—
326Dic43⋊C4C2418yes—
327Dic43⋊C4C2418yes—
328Dic43⋊C4C24116yes—
329Dic43⋊C4C24116yes—
330Dic43⋊C4C24116yes—
331Dic43⋊C4C24116yes—
332Dic43⋊C4C2418yes—
333Dic43⋊C4C2418yes—
334Dic43⋊C4C24116yes—
335Dic43⋊C4C24116yes—
336C4×Dic43C2418yes—
337C4×Dic43C2418yes—
338C4×Dic43C2418yes—
339C4×Dic43C24116yes—
340C4×Dic43C24116yes—
341C4×Dic43C2418yes—
342C23×C43—22no—
343C23×C43—22no—
344C23×C43—24no—
345C23×C43—24no—
346C23×C43—24no—
347C23×C43C2×#4114yes—
348C23×C43C2514yes—
349C23×C43C2512yes—
350C23×C43C2511yescharacteristic
351C22×D43—22no—
352C22×D43—22no—
353C22×D43—28no—
354C22×D43—22no—
355C22×D43—22no—
356C22×D43—22no—
357C22×D43—28no—
358C22×D43—44no—
359C22×D43—416no—
360C22×D432−1+414yes—
361C22×D43C2512yes—
362C22×D43C2512yes—
363Q8×C43—28no—
364D4×C43—216no—
365D4×C43—28no—
366C2×C4×C43—24no—
367C2×C4×C43—24no—
368C2×C4×C43—28no—
369C2×C4×C43—24no—
370C2×C4×C43—216no—
371C2×C4×C43—48no—
372C2×C4×C43—416no—
373C2×C4×C43C2×#4114yes—
374C2×C4×C43C2×#4114yes—
375C2×C4×C43C2×#41116yes—
376C2×C4×C43C2514yes—
377C2×C4×C43C2514yes—
378C2×C4×C43C2514yes—
379C2×C4×C43C2518yes—
380C2×C4×C43C2512yes—
381C2×C4×C43C2512yes—
382C22⋊D43—216no—
383C22⋊D43—48no—
384C2×Dic43—216no—
385C2×Dic43—28no—
386C2×Dic43—28no—
387C2×Dic43—22no—
388C2×Dic43—22no—
389C2×Dic43—24no—
390C2×Dic43—24no—
391C2×Dic43—24no—
392C2×Dic43—24no—
393C2×Dic43C2512yes—
394C2×Dic43C2514yes—
395C2×Dic43C2514yes—
396C2×Dic43C2514yes—
397C2×Dic43C2514yes—
398C2×Dic43C2518yes—
399C2×Dic43C2512yes—
400C4×D43—216no—
401C4×D43—28no—
402C4×D43—28no—
403C4×D43—28no—
404C4×D43—28no—
405C4×D43—48no—
406Dic86—216no—
407Dic86—216no—
408Dic86—416no—
409C2×#3495—431nomaximal, Sylow
410C22×C43—22no—
411C22×C43—22no—
412C22×C43—28no—
413C22×C43—24no—
414C22×C43—24no—
415C22×C43—24no—
416C22×C43—48no—
417C22×C43C22×#4114yes—
418C22×C43C22×#4112yes—
419C22×C43C2×2−1+412yes—
420C22×C43#58512yes—
421C22×C43C2611yescharacteristic
422C2×D43—22no—
423C2×D43—22no—
424C2×D43—28no—
425C2×D43—22no—
426C2×D43—22no—
427C2×D43—22no—
428C2×D43—416no—
429C2×D43—44no—
430C2×D43C2×2−1+414yes—
431C4×C43—24no—
432C4×C43—24no—
433C4×C43—28no—
434C4×C43—24no—
435C4×C43C22×#4114yes—
436C4×C43C22×#4114yes—
437Dic43—28no—
438Dic43—22no—
439Dic43—22no—
440Dic43—24no—
441Dic43—24no—
442Dic43—24no—
443Dic43—24no—
444#3495—4332no—
445C2×#556—432no—
446C2×#554—432no—
447C2×#552—434no—
448C2×#552—432no—
449C2×#552—432no—
450C2×#551—434no—
451C2×#544—431no—
452C2×#542—432no—
453C2×#541—432no—
454C2×#536—431no—
455C2×#533—432no—
456C2×#529—432no—
457C2×#525—431no—
458C22×C22⋊Q8—431no—
459C2×#520D4311yescharacteristic, complemented
460C2×#519—431no—
461C22×#117—431no—
462C2×C43—24no—
463C2×C43—44no—
464C2×C43#349514yescomplemented
465C2×C43C23×#4111yescharacteristic
466C2×C43C22×2−1+411yescharacteristic
467C2×C43C2×#58511yescharacteristic
468D43—24no—
469D43—42no—
470C22×#41C2×D4311yescharacteristic
471C23×Q8—431no—
472C24×C4—431no—
473#556—4332no—
474#554—4332no—
475#552—4364no—
476#552—4332no—
477#552—4332no—
478#551—4364no—
479#544—4316no—
480#542—4332no—
481#541—4332no—
482#536—4316no—
483#533—4332no—
484C2×C4⋊Q8—432no—
485C2×C4⋊Q8—432no—
486C2×C4⋊Q8—432no—
487#529—4332no—
488C2×#126—434no—
489C2×#126—434no—
490C2×#126—434no—
491C2×#126—434no—
492C2×#125—432no—
493C2×#125—434no—
494C2×#125—434no—
495C2×#125—432no—
496C2×#125—434no—
497C2×#124—432no—
498C2×#124—434no—
499#525—4316no—
500C2×#123—432no—
501C2×#123—434no—
502C2×#123—434no—
503C2×#123—434no—
504C2×C22⋊Q8—431no—
505C2×C22⋊Q8—431no—
506C2×C22⋊Q8—434no—
507C2×C22⋊Q8—432no—
508C2×C22⋊Q8—432no—
509C2×C22⋊Q8—434no—
510C2×C22⋊Q8—434no—
511C2×C22⋊Q8—432no—
512C2×C22⋊Q8—432no—
513C2×C22⋊Q8—432no—
514C2×C22⋊Q8—432no—
515C2×C22⋊Q8—4316no—
516C2×#121—431no—
517C2×#121—431no—
518C2×#120—432no—
519#520C2×D43116yescomplemented
520#519—4316no—
521C2×C4×Q8—432no—
522C2×C4×Q8—432no—
523C2×C4×Q8—432no—
524C2×C4×Q8—432no—
525C2×C4×Q8—434no—
526C2×C4×Q8C2×D4312yescomplemented
527C2×C4×D4—432no—
528C2×C4×D4—432no—
529C2×C4×D4—434no—
530C2×C4×D4C2×D4314yes—
531C2×C4×D4C2×D4312yescomplemented
532C2×#117—431no—
533C2×#117—431no—
534C2×#117—434no—
535C2×#117—4316no—
536C2×#117—431no—
537C2×#117—431no—
538C2×#117—432no—
539C2×#117—434no—
540C2×#117—432no—
541C2×#117—434no—
542C2×#117C2×D4311yescharacteristic
543C2×#117C2×D4312yescomplemented
544C22×C4⋊C4—432no—
545C22×C4⋊C4—431no—
546C22×C4⋊C4—431no—
547C22×C4⋊C4C2×D4311yescharacteristic
548C22×C4⋊C4C2×D4312yescomplemented
549C22×C22⋊C4—432no—
550C22×C22⋊C4—432no—
551C22×C42—432no—
552C43C2×#349511yescharacteristic, complemented, Sylow
553C25—431no—
554C2×#41—28no—
555C2×#41C22×D4318yes—
556C22×Q8—432no—
557C22×Q8—432no—
558C22×Q8—438no—
559C22×Q8—434no—
560C22×Q8—868no—
561C22×Q8C22×D4311yescharacteristic
562C22×D4—432no—
563C22×D4—432no—
564C22×D4C22×D4312yes—
565C22×D4C22×D4311yescharacteristic
566C23×C4—432no—
567C23×C4—431no—
568C23×C4—432no—
569C23×C4—431no—
570C23×C4—431no—
571C23×C4—431no—
572C23×C4—438no—
573C23×C4—431no—
574C23×C4—432no—
575C23×C4—868no—
576C23×C4C22×D4312yes—
577C23×C4C22×D4312yes—
578C23×C4C22×D4314yes—
579C23×C4C22×D4311yescharacteristic
580C4⋊Q8—4316no—
581C4⋊Q8—4316no—
582C4⋊Q8—4316no—
583#126—4332no—
584#126—4332no—
585#126—4332no—
586#126—4332no—
587#125—4316no—
588#125—4332no—
589#125—4332no—
590#125—4316no—
591#125—4332no—
592#124—4316no—
593#124—4332no—
594#123—4316no—
595#123—4332no—
596#123—4332no—
597#123—4332no—
598C22⋊Q8—438no—
599C22⋊Q8—438no—
600C22⋊Q8—4316no—
601C22⋊Q8—4316no—
602C22⋊Q8—4332no—
603C22⋊Q8—4332no—
604C22⋊Q8—4316no—
605C22⋊Q8—4316no—
606C22⋊Q8—4316no—
607C22⋊Q8—4316no—
608C22⋊Q8—4332no—
609#121—438no—
610#121—438no—
611#120—4316no—
612C4×Q8—4316no—
613C4×Q8—4316no—
614C4×Q8—4316no—
615C4×Q8—4316no—
616C4×Q8—4332no—
617C4×Q8C22×D43116yescomplemented
618C4×D4—4316no—
619C4×D4—4316no—
620C4×D4—4332no—
621C4×D4C22×D43132yes—
622C4×D4C22×D43116yescomplemented
623#117—438no—
624#117—438no—
625#117—4332no—
626#117—438no—
627#117—438no—
628#117—4316no—
629#117—4332no—
630#117—4316no—
631#117—4332no—
632#117C22×D4318yes—
633#117C22×D43116yescomplemented
634C2×C4⋊C4—432no—
635C2×C4⋊C4—431no—
636C2×C4⋊C4—431no—
637C2×C4⋊C4—432no—
638C2×C4⋊C4—434no—
639C2×C4⋊C4—434no—
640C2×C4⋊C4—4316no—
641C2×C4⋊C4—431no—
642C2×C4⋊C4—431no—
643C2×C4⋊C4—434no—
644C2×C4⋊C4—434no—
645C2×C4⋊C4—434no—
646C2×C4⋊C4—434no—
647C2×C4⋊C4—434no—
648C2×C4⋊C4—432no—
649C2×C4⋊C4—432no—
650C2×C4⋊C4—434no—
651C2×C4⋊C4—434no—
652C2×C4⋊C4—438no—
653C2×C4⋊C4—438no—
654C2×C4⋊C4C22×D4311yescharacteristic
655C2×C4⋊C4C22×D4311yescharacteristic
656C2×C4⋊C4C22×D4312yes—
657C2×C4⋊C4C22×D4312yes—
658C2×C4⋊C4C22×D4318yes—
659C2×C4⋊C4C22×D4314yes—
660C2×C4⋊C4C22×D43116yescomplemented
661C2×C22⋊C4—432no—
662C2×C22⋊C4—432no—
663C2×C22⋊C4—432no—
664C2×C22⋊C4—434no—
665C2×C22⋊C4—432no—
666C2×C22⋊C4—434no—
667C2×C22⋊C4—432no—
668C2×C22⋊C4—432no—
669C2×C22⋊C4—434no—
670C2×C22⋊C4—434no—
671C2×C22⋊C4—4316no—
672C2×C22⋊C4—432no—
673C2×C22⋊C4—432no—
674C2×C22⋊C4—4316no—
675C2×C22⋊C4C22×D4312yes—
676C2×C22⋊C4C22×D4314yes—
677C2×C42—432no—
678C2×C42—434no—
679C2×C42—434no—
680C2×C42—432no—
681C2×C42—432no—
682C2×C42—432no—
683C2×C42—4316no—
684C2×C42C22×D4312yes—
685C2×C42C22×D4314yes—
686C24—431no—
687C24—431no—
688C24—434no—
689C24—864no—
690C24—864no—
691C24—1722no—
692C24C23×D4312yes—
693C24C23×D4311yescharacteristic
694#41—232no—
695C2×Q8—24no—
696C2×Q8—438no—
697C2×Q8—438no—
698C2×Q8—4316no—
699C2×Q8—868no—
700C2×Q8—868no—
701C2×Q8—8632no—
702C2×Q8—1728no—
703C2×Q8C23×D4314yes—
704C2×D4—28no—
705C2×D4—24no—
706C2×D4—438no—
707C2×D4—438no—
708C2×D4—868no—
709C2×D4—1724no—
710C2×D4C23×D4318yes—
711C2×D4C23×D4314yes—
712C22×C4—28no—
713C22×C4—48no—
714C22×C4—44no—
715C22×C4—438no—
716C22×C4—434no—
717C22×C4—431no—
718C22×C4—432no—
719C22×C4—432no—
720C22×C4—432no—
721C22×C4—434no—
722C22×C4—432no—
723C22×C4—431no—
724C22×C4—434no—
725C22×C4—438no—
726C22×C4—434no—
727C22×C4—434no—
728C22×C4—434no—
729C22×C4—438no—
730C22×C4—868no—
731C22×C4—864no—
732C22×C4—868no—
733C22×C4—864no—
734C22×C4—864no—
735C22×C4—864no—
736C22×C4—864no—
737C22×C4—8632no—
738C22×C4—1724no—
739C22×C4#1062189818yes—
740C22×C4C23×D4318yes—
741C22×C4C23×D4312yes—
742C22×C4C23×D4312yes—
743C22×C4C23×D4312yes—
744C22×C4C23×D4314yes—
745C22×C4C23×D4318yes—
746C22×C4C23×D43116yes—
747C22×C4C23×D4314yes—
748C22×C4C23×D4311yescharacteristic
749C22×C4C23×D4311yescharacteristic
750C4⋊C4—438no—
751C4⋊C4—434no—
752C4⋊C4—434no—
753C4⋊C4—438no—
754C4⋊C4—4316no—
755C4⋊C4—4316no—
756C4⋊C4—434no—
757C4⋊C4—434no—
758C4⋊C4—4316no—
759C4⋊C4—4316no—
760C4⋊C4—4316no—
761C4⋊C4—4316no—
762C4⋊C4—4316no—
763C4⋊C4—438no—
764C4⋊C4—438no—
765C4⋊C4—4316no—
766C4⋊C4—4316no—
767C4⋊C4C23×D4314yes—
768C4⋊C4C23×D4314yes—
769C4⋊C4C23×D4318yes—
770C4⋊C4C23×D4318yes—
771C4⋊C4C23×D43116yes—
772C22⋊C4—438no—
773C22⋊C4—438no—
774C22⋊C4—438no—
775C22⋊C4—4316no—
776C22⋊C4—438no—
777C22⋊C4—4316no—
778C22⋊C4—438no—
779C22⋊C4—438no—
780C22⋊C4—4316no—
781C22⋊C4—4316no—
782C22⋊C4—438no—
783C22⋊C4—438no—
784C22⋊C4C23×D4318yes—
785C22⋊C4C23×D43116yes—
786C42—438no—
787C42—438no—
788C42—438no—
789C42—4316no—
790C42—4316no—
791C42—438no—
792C42C23×D4318yes—
793C42C23×D43116yes—
794C23—22no—
795C23—22no—
796C23—24no—
797C23—24no—
798C23—24no—
799C23—434no—
800C23—432no—
801C23—432no—
802C23—868no—
803C23—862no—
804C23—862no—
805C23—868no—
806C23—862no—
807C23—862no—
808C23—862no—
809C23—1724no—
810C23—17216no—
811C23C2×#1062189814yes—
812C23C24×D4314yes—
813C23C24×D4312yes—
814C23C24×D4311yescharacteristic
815Q8—28no—
816Q8—8616no—
817Q8—8616no—
818Q8—17216no—
819D4—216no—
820D4—28no—
821D4—8616no—
822D4—1728no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—28no—
827C2×C4—216no—
828C2×C4—416no—
829C2×C4—48no—
830C2×C4—432no—
831C2×C4—434no—
832C2×C4—434no—
833C2×C4—434no—
834C2×C4—438no—
835C2×C4—434no—
836C2×C4—432no—
837C2×C4—8616no—
838C2×C4—868no—
839C2×C4—862no—
840C2×C4—862no—
841C2×C4—8616no—
842C2×C4—868no—
843C2×C4—864no—
844C2×C4—864no—
845C2×C4—864no—
846C2×C4—864no—
847C2×C4—868no—
848C2×C4—868no—
849C2×C4—868no—
850C2×C4—868no—
851C2×C4—1728no—
852C2×C4C2×#1062189814yes—
853C2×C4C2×#1062189814yes—
854C2×C4C2×#10621898116yes—
855C2×C4C24×D4314yes—
856C2×C4C24×D4314yes—
857C2×C4C24×D4314yes—
858C2×C4C24×D4318yes—
859C2×C4C24×D4312yes—
860C2×C4C24×D4312yes—
861C22—28no—
862C22—22no—
863C22—22no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—48no—
868C22—434no—
869C22—868no—
870C22—862no—
871C22—862no—
872C22—862no—
873C22—862no—
874C22—862no—
875C22—17216no—
876C22—1724no—
877C22C22×#1062189814yes—
878C22C22×#1062189812yes—
879C222−1+4×D4312yes—
880C22#1458373412yes—
881C22C25×D4311yescharacteristic
882C4—24no—
883C4—24no—
884C4—24no—
885C4—28no—
886C4—862no—
887C4—862no—
888C4—868no—
889C4—864no—
890C4—864no—
891C4—864no—
892C4—864no—
893C4C22×#1062189814yes—
894C4C22×#1062189814yes—
895C2—24no—
896C2—44no—
897C2—864no—
898C2—1722no—
899C2#1914834814yesdirect product factor
900C2C23×#1062189811yescharacteristic
901C2C2×2−1+4×D4311yescharacteristic
902C2C2×#1458373411yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#520C2
socleC23×C43C25
prime radicalC2×#14583406C2
hypercenterC2×#520D43
hypocenterC43C2×#3495
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #19148348C2direct (N × H)
2. C2×#14583617C2semidirect
3. C2×#14583604C2semidirect
4. C2×#14583589C2semidirect
5. C2×#14583588C2semidirect
6. C2×#14583584C2semidirect
7. C2×#14583578C2semidirect
8. C2×#14583530C2semidirect
9. C2×#14583514C2semidirect
10. C2×#14583507C2semidirect
11. C2×#14583470C2semidirect
12. C2×#14583453C2semidirect
13. C2×#14583431C2semidirect
15. C22×#13063305C2semidirect
16. C2×#14583376C2semidirect
17. C2×#117×D43C2semidirect
18. C2×C43×#520C2semidirect
21. #14583617C22semidirect
22. #14583604C22semidirect
23. #14583589C22semidirect
24. #14583588C22semidirect
25. #14583584C22semidirect
26. #14583578C22semidirect
27. #14583530C22semidirect
28. #14583514C22semidirect
29. #14583507C22semidirect
30. #14583470C22semidirect
31. #14583453C22semidirect
32. C2×#13063324C22semidirect
33. C2×#13063324C22semidirect
34. C2×#13063323C22semidirect
35. #14583431C22semidirect
38. C2×#13063318C22semidirect
39. C2×#13063318C22semidirect
40. C2×#13063317C22semidirect
41. C2×#13063316C22semidirect
42. C2×#13063316C22semidirect
43. C2×#13063315C22semidirect
44. C2×#13063315C22semidirect
45. C2×#13063312C22semidirect
56. C2×#13063305C22semidirect
58. C2×#13063304C22semidirect
59. C2×#13063304C22semidirect
60. C2×#13063304C22semidirect
67. #14583376C22semidirect
68. C2×C4×Dic86C22semidirect
69. C2×C4×Dic86C22semidirect
70. C2×C4×Dic86C22semidirect
71. C2×#13063290C22semidirect
72. C2×#13063290C22semidirect
78. C2×#13063284C22semidirect
85. #117×D43C22semidirect
93. C43×#520C22semidirect
94. C2×C4×Q8×C43C22semidirect
96. C2×C4×D4×C43C22semidirect
98. C2×#117×C43C22semidirect
100. C22×C4⋊C4×C43C22semidirect
119. #13063324C23semidirect
120. #13063324C23semidirect
121. #13063323C23semidirect
124. #13063318C23semidirect
125. #13063318C23semidirect
126. #13063317C23semidirect
127. #13063316C23semidirect
128. #13063316C23semidirect
129. #13063315C23semidirect
130. #13063315C23semidirect
131. #13063312C23semidirect
142. #13063304C23semidirect
143. #13063304C23semidirect
144. #13063304C23semidirect
151. C4×Dic86C23semidirect
152. C4×Dic86C23semidirect
153. C4×Dic86C23semidirect
154. #13063290C23semidirect
155. #13063290C23semidirect
161. #13063284C23semidirect
218. C4×Q8×C43C23semidirect
220. C4×D4×C43C23semidirect
222. #117×C43C23semidirect
229. C2×C4⋊C4×C43C23semidirect
459. C2×#520D43semidirect
464. C2×C43#3495semidirect
519. #520C2×D43semidirect
526. C2×C4×Q8C2×D43semidirect
531. C2×C4×D4C2×D43semidirect
543. C2×#117C2×D43semidirect
548. C22×C4⋊C4C2×D43semidirect
552. C43C2×#3495semidirect
617. C4×Q8C22×D43semidirect
622. C4×D4C22×D43semidirect
633. #117C22×D43semidirect
660. C2×C4⋊C4C22×D43semidirect
899. C2#19148348direct (N × H)

Maximal subgroups

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

subgroupindex
#191483482
C2×#145836172
C2×#145836042
C2×#145835892
C2×#145835882
C2×#145835842
C2×#145835782
C2×#145835302
C2×#145835142
C2×#145835072
C2×#145834702
C2×#145834532
C2×#145834312
C2×#145834062
C22×#130633052
C2×#145833762
C2×#117×D432
C2×C43×#5202
C2×#349543