Finite Group Databasebeta

← C2×#19148350 #26005030

Subgroups — C2×#19148350 #26005030

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#19148350C2132yesmaximal, direct product factor
2C2×#14583623C212yesmaximal, complemented
3C2×#14583610C212yesmaximal, complemented
4C2×#14583591C214yesmaximal, complemented
5C2×#14583587C212yesmaximal, complemented
6C2×#14583587C212yesmaximal, complemented
7C2×#14583576C214yesmaximal, complemented
8C2×#14583523C212yesmaximal, complemented
9C2×#14583512C212yesmaximal, complemented
10C2×#14583475C211yesmaximal, characteristic, complemented
11C2×#14583454C212yesmaximal, complemented
12C2×#14583434C212yesmaximal, complemented
13C2×#14583411C211yesmaximal, characteristic
14C22×#13063305C211yesmaximal, characteristic, complemented
15C2×#14583380C211yesmaximal, characteristic, complemented
16C2×#14583376C211yesmaximal, characteristic, complemented
17C2×#117×D43C211yesmaximal, characteristic, complemented
18C2×C43×#544C211yesmaximal, characteristic, complemented
19C22×#10621898C2211yescharacteristic
20C23×Dic86C2211yescharacteristic
21C23×C4×D43C2211yescharacteristic
22#14583623C22132yescomplemented
23#14583610C22132yescomplemented
24#14583591C22164yescomplemented
25#14583587C22132yescomplemented
26#14583587C22132yescomplemented
27#14583576C22164yescomplemented
28#14583523C22132yescomplemented
29#14583512C22132yescomplemented
30#14583475C22116yescomplemented
31#14583454C22132yescomplemented
32C2×#13063325C2212yescomplemented
33#14583434C22132yescomplemented
34C2×#13063320C2214yes—
35C2×#13063320C2214yes—
36C2×#13063320C2214yescomplemented
37C2×#13063320C2214yescomplemented
38C2×#13063316C2214yescomplemented
39C2×#13063316C2214yescomplemented
40C2×#13063316C2214yescomplemented
41C2×#13063314C2214yes—
42C2×#13063313C2212yescomplemented
43#14583411C22116yes—
44C2×#13063310C2214yes—
45C2×#13063310C2214yes—
46C2×#13063309C2214yes—
47C2×#13063309C2212yes—
48C2×#13063305C2212yes—
49C2×#13063305C2212yes—
50C2×#13063305C2212yes—
51C2×#13063305C2212yes—
52C2×#13063305C2211yescharacteristic
53C2×#13063305C2211yescharacteristic
54C2×#13063305C22116yescomplemented
55C2×#13063305C2212yescomplemented
56C2×#13063305C2212yescomplemented
57C2×#13063301C2214yes—
58C2×#13063301C2214yescomplemented
59C2×#13063300C2211yescharacteristic
60C2×#13063300C2211yescharacteristic
61C2×#13063295C2212yes—
62#14583380C22116yescomplemented
63#14583376C22116yescomplemented
64C2×Q8×Dic43C2214yescomplemented
65C2×C4×Dic86C2212yescomplemented
66C2×C4×Dic86C2212yescomplemented
67C2×#13063290C2212yescomplemented
68C2×#13063290C2212yescomplemented
69C2×#13063290C2212yescomplemented
70C2×C4×D172C2212yes—
71C2×C4×D172C2212yes—
72C2×#13063287C2214yes—
73C2×#13063287C2212yescomplemented
74C2×C4×C22⋊D43C2214yes—
75C2×#13063284C2211yescharacteristic
76C2×#13063283C2214yes—
77C2×#13063283C2211yescharacteristic
78C2×#13063283C2211yescharacteristic
79C2×#13063283C2212yescomplemented
80C2×#13063283C2214yescomplemented
81C2×#13063282C2212yes—
82C2×#13063281C2214yes—
83C2×#13063281C2212yes—
84#117×D43C22116yescomplemented
85C22×C4⋊Dic43C2212yes—
86C2×C4⋊C4×D43C2211yescharacteristic
87C2×C4⋊C4×D43C2211yescharacteristic
88C2×C4⋊C4×D43C2212yescomplemented
89C22×(C2×D43)⋊C4C2212yes—
90C2×C22⋊C4×D43C2212yes—
91C2×C42×D43C2212yes—
92C43×#544C22116yescomplemented
93C2×C4⋊Q8×C43C2212yescomplemented
94C2×C4⋊Q8×C43C2212yescomplemented
95C2×#125×C43C2212yescomplemented
96C2×#125×C43C2212yescomplemented
97C2×C22⋊Q8×C43C2214yes—
98C2×#117×C43C2211yescharacteristic
99C2×#117×C43C2211yescharacteristic
100C22×C4⋊C4×C43C2211yescharacteristic
101C24×D43C2311yescharacteristic
102C2×#10621898—28no—
103C2×#10621898C2318yes—
104C22×Dic86—28no—
105C22×Dic86C2312yes—
106C22×Dic86C2311yescharacteristic
107C22×Dic86C2312yes—
108C22×Dic86C2318yes—
109C22×D172C2312yes—
110C22×D172C2311yescharacteristic
111C22×D172C2312yes—
112C22×C22⋊D43C2312yes—
113C23×Dic43C2312yes—
114C23×Dic43C2311yescharacteristic
115C22×C4×D43—28no—
116C22×C4×D43C2311yescharacteristic
117C22×C4×D43C2312yes—
118C22×C4×D43C2311yescharacteristic
119C22×C4×D43C2312yes—
120C22×C4×D43C2318yes—
121C22×C4×D43C2311yescharacteristic
122C22×C4×D43C2311yescharacteristic
123C22×C4×D43C2312yes—
124C22×C4×D43C2314yes—
125#13063325C23116yescomplemented
126#13063320C23132yes—
127#13063320C23132yes—
128#13063320C23132yescomplemented
129#13063320C23132yescomplemented
130#13063316C23132yescomplemented
131#13063316C23132yescomplemented
132#13063316C23132yescomplemented
133#13063314C23132yes—
134#13063313C23116yescomplemented
135#13063310C23132yes—
136#13063310C23132yes—
137#13063309C23132yes—
138#13063309C23116yes—
139#13063305C23116yes—
140#13063305C23116yes—
141#13063305C23116yes—
142#13063305C23116yes—
143#13063305C2318yes—
144#13063305C2318yes—
145#13063305C23116yescomplemented
146#13063305C23116yescomplemented
147#13063301C23132yes—
148#13063301C23132yescomplemented
149#13063300C2318yes—
150#13063300C2318yes—
151#13063295C23116yes—
152Q8×Dic43C23132yescomplemented
153C4×Dic86C23116yescomplemented
154C4×Dic86C23116yescomplemented
155#13063290C23116yescomplemented
156#13063290C23116yescomplemented
157#13063290C23116yescomplemented
158C4×D172C23116yes—
159C4×D172C23116yes—
160#13063287C23132yes—
161#13063287C23116yescomplemented
162C4×C22⋊D43C23132yes—
163#13063284C2318yes—
164#13063283C23132yes—
165#13063283C2318yes—
166#13063283C2318yes—
167#13063283C23132yescomplemented
168#13063283C23116yescomplemented
169#13063282C23116yes—
170#13063281C23132yes—
171#13063281C23116yes—
172C2×C4⋊Dic43C23116yes—
173C2×C4⋊Dic43C2311yescharacteristic
174C2×C4⋊Dic43C2311yescharacteristic
175C2×C4⋊Dic43C2314yes—
176C2×C4⋊Dic43C2314yes—
177C2×C4⋊Dic43C2314yes—
178C2×C4⋊Dic43C2312yes—
179C2×C4⋊Dic43C2312yes—
180C2×C4⋊Dic43C2314yes—
181C2×Dic43⋊C4C2312yes—
182C2×Dic43⋊C4C2312yes—
183C2×Dic43⋊C4C2314yes—
184C2×Dic43⋊C4C2314yes—
185C2×Dic43⋊C4C2314yes—
186C4⋊C4×D43C2318yes—
187C4⋊C4×D43C2318yes—
188C4⋊C4×D43C23116yescomplemented
189C2×C22⋊Dic43C2312yes—
190C2×(C2×D43)⋊C4C23116yes—
191C2×(C2×D43)⋊C4C2312yes—
192C2×(C2×D43)⋊C4C2312yes—
193C2×(C2×D43)⋊C4C2314yes—
194C2×(C2×D43)⋊C4C2314yes—
195C2×(C2×D43)⋊C4C2312yes—
196C2×(C2×D43)⋊C4C2312yes—
197C2×(C2×D43)⋊C4C2314yes—
198C2×(C2×D43)⋊C4C2314yes—
199C2×(C2×D43)⋊C4C2314yes—
200C2×(C2×D43)⋊C4C2312yes—
201C2×(C2×D43)⋊C4C2312yes—
202C22⋊C4×D43C23116yes—
203C2×C4×Dic43C2312yes—
204C2×C4×Dic43C2312yes—
205C2×C4×Dic43C2312yes—
206C2×C4×Dic43C2314yes—
207C2×C4×Dic43C2314yes—
208C2×C4×Dic43C2314yes—
209C42×D43C23116yes—
210C22×Q8×C43C2314yes—
211C23×C4×C43C2312yes—
212C23×C4×C43C2311yescharacteristic
213C4⋊Q8×C43C23116yescomplemented
214C4⋊Q8×C43C23116yescomplemented
215#125×C43C23116yescomplemented
216#125×C43C23116yescomplemented
217C22⋊Q8×C43C23132yes—
218#117×C43C2318yes—
219#117×C43C2318yes—
220C2×C4⋊C4×C43C2312yes—
221C2×C4⋊C4×C43C2312yes—
222C2×C4⋊C4×C43C2318yes—
223C2×C4⋊C4×C43C2311yescharacteristic
224C2×C4⋊C4×C43C2311yescharacteristic
225C2×C4⋊C4×C43C2311yescharacteristic
226C2×C4⋊C4×C43C2311yescharacteristic
227C2×C4⋊C4×C43C2314yes—
228C2×C4⋊C4×C43C2314yes—
229C2×C4⋊C4×C43C2314yes—
230C2×C22⋊C4×C43C2312yes—
231C2×C22⋊C4×C43C2312yes—
232C2×C42×C43C2312yes—
233C2×C42×C43C2312yes—
234C24×C43C2411yescharacteristic
235C23×D43—24no—
236C23×D43—24no—
237C23×D43—42no—
238C23×D43C2411yescharacteristic
239C23×D43C2412yes—
240C23×D43C2414yes—
241C23×D43C2411yescharacteristic
242C2×Q8×C43—48no—
243C2×Q8×C43C24116yes—
244C22×C4×C43—44no—
245C22×C4×C43#4118yes—
246C22×C4×C43C2412yes—
247C22×C4×C43C2412yes—
248C22×C4×C43C2412yes—
249C22×C4×C43C2412yes—
250C22×C4×C43C2414yes—
251C22×C4×C43C2418yes—
252C22×C4×C43C2411yescharacteristic
253C22×C4×C43C2411yescharacteristic
254C22×C4×C43C2414yes—
255C2×C22⋊D43—28no—
256C2×C22⋊D43C2418yes—
257C22×Dic43—24no—
258C22×Dic43—28no—
259C22×Dic43C2412yes—
260C22×Dic43C2411yescharacteristic
261C22×Dic43C2412yes—
262C22×Dic43C2414yes—
263C22×Dic43C2412yes—
264C22×Dic43C2411yescharacteristic
265C22×Dic43C2418yes—
266C22×Dic43C2414yes—
267#10621898—232no—
268C2×D172—24no—
269C2×D172—28no—
270C2×D172—44no—
271C2×D172C2418yes—
272C2×D172C2414yes—
273C2×D172C2418yes—
274C2×C4×D43—24no—
275C2×C4×D43—24no—
276C2×C4×D43—24no—
277C2×C4×D43—24no—
278C2×C4×D43—232no—
279C2×C4×D43—28no—
280C2×C4×D43—28no—
281C2×C4×D43—44no—
282C2×C4×D43—48no—
283C2×C4×D43C2414yes—
284C2×C4×D43C2418yes—
285C2×C4×D43C2414yes—
286C2×C4×D43C2418yes—
287C2×C4×D43C2414yes—
288C2×C4×D43C2414yes—
289C2×C4×D43C2418yes—
290C2×C4×D43C24116yes—
291C2×Dic86—28no—
292C2×Dic86—28no—
293C2×Dic86—232no—
294C2×Dic86—24no—
295C2×Dic86C2418yes—
296C2×Dic86C2414yes—
297C2×Dic86C2418yes—
298C4⋊C4×C43C2418yes—
299C4⋊C4×C43C2418yes—
300C4⋊C4×C43C2414yes—
301C4⋊C4×C43C2414yes—
302C4⋊C4×C43C2414yes—
303C4⋊C4×C43C2414yes—
304C4⋊C4×C43C24116yes—
305C4⋊C4×C43C24116yes—
306C4⋊C4×C43C24116yes—
307C22⋊C4×C43C2418yes—
308C22⋊C4×C43C2418yes—
309C42×C43C2418yes—
310C42×C43C2418yes—
311C22⋊Dic43C2418yes—
312(C2×D43)⋊C4C2418yes—
313(C2×D43)⋊C4C2418yes—
314(C2×D43)⋊C4C24116yes—
315(C2×D43)⋊C4C24116yes—
316(C2×D43)⋊C4C2418yes—
317(C2×D43)⋊C4C2418yes—
318(C2×D43)⋊C4C24116yes—
319(C2×D43)⋊C4C24116yes—
320(C2×D43)⋊C4C24116yes—
321(C2×D43)⋊C4C2418yes—
322(C2×D43)⋊C4C2418yes—
323C4⋊Dic43C2414yes—
324C4⋊Dic43C2414yes—
325C4⋊Dic43C24116yes—
326C4⋊Dic43C24116yes—
327C4⋊Dic43C24116yes—
328C4⋊Dic43C2418yes—
329C4⋊Dic43C2418yes—
330C4⋊Dic43C24116yes—
331Dic43⋊C4C2418yes—
332Dic43⋊C4C2418yes—
333Dic43⋊C4C24116yes—
334Dic43⋊C4C24116yes—
335Dic43⋊C4C24116yes—
336C4×Dic43C2418yes—
337C4×Dic43C2418yes—
338C4×Dic43C2418yes—
339C4×Dic43C24116yes—
340C4×Dic43C24116yes—
341C4×Dic43C24116yes—
342C23×C43—22no—
343C23×C43—22no—
344C23×C43C2×#4114yes—
345C23×C43C2512yes—
346C23×C43C2511yescharacteristic
347C22×D43—22no—
348C22×D43—22no—
349C22×D43—28no—
350C22×D43—22no—
351C22×D43—24no—
352C22×D43—24no—
353C22×D43—22no—
354C22×D43—24no—
355C22×D43—22no—
356C22×D43—28no—
357C22×D43—44no—
358C22×D43—416no—
359C22×D432−1+414yes—
360C22×D43C2512yes—
361C22×D43C2514yes—
362C22×D43C2512yes—
363Q8×C43—416no—
364C2×C4×C43—24no—
365C2×C4×C43—24no—
366C2×C4×C43—28no—
367C2×C4×C43—24no—
368C2×C4×C43—24no—
369C2×C4×C43—48no—
370C2×C4×C43C2×#4114yes—
371C2×C4×C43C2×#4114yes—
372C2×C4×C43C2×#41116yes—
373C2×C4×C43C2514yes—
374C2×C4×C43C2514yes—
375C2×C4×C43C2514yes—
376C2×C4×C43C2514yes—
377C2×C4×C43C2518yes—
378C2×C4×C43C2512yes—
379C2×C4×C43C2512yes—
380C22⋊D43—216no—
381C2×Dic43—216no—
382C2×Dic43—28no—
383C2×Dic43—24no—
384C2×Dic43—28no—
385C2×Dic43—22no—
386C2×Dic43—22no—
387C2×Dic43—24no—
388C2×Dic43—24no—
389C2×Dic43C2514yes—
390C2×Dic43C2514yes—
391C2×Dic43C2512yes—
392C2×Dic43C2514yes—
393C2×Dic43C2518yes—
394C2×Dic43C2512yes—
395D172—216no—
396D172—28no—
397D172—48no—
398C4×D43—216no—
399C4×D43—28no—
400C4×D43—28no—
401C4×D43—28no—
402C4×D43—28no—
403C4×D43—216no—
404C4×D43—416no—
405C4×D43—48no—
406Dic86—216no—
407Dic86—216no—
408Dic86—28no—
409C2×#3495—431nomaximal, Sylow
410C22×C43—22no—
411C22×C43—22no—
412C22×C43—28no—
413C22×C43C22×#4114yes—
414C22×C43C22×#4112yes—
415C22×C43C2×2−1+412yes—
416C22×C43#58512yes—
417C22×C43C2611yescharacteristic
418C2×D43—22no—
419C2×D43—22no—
420C2×D43—28no—
421C2×D43—22no—
422C2×D43—24no—
423C2×D43—22no—
424C2×D43—24no—
425C2×D43—22no—
426C2×D43—24no—
427C2×D43—416no—
428C2×D43—48no—
429C2×D43—44no—
430C2×D43C2×2−1+414yes—
431C4×C43—24no—
432C4×C43—24no—
433C4×C43—28no—
434C4×C43—24no—
435C4×C43—24no—
436C4×C43C22×#4114yes—
437C4×C43C22×#4114yes—
438Dic43—28no—
439Dic43—24no—
440Dic43—22no—
441Dic43—22no—
442Dic43—24no—
443Dic43—24no—
444#3495—4332no—
445C2×#556—432no—
446C2×#554—432no—
447C2×#552—432no—
448C2×#552—432no—
449C2×#552—434no—
450C2×#551—434no—
451C2×#544D4311yescharacteristic, complemented
452C2×#542—432no—
453C2×#541—432no—
454C2×#536—431no—
455C2×#533—432no—
456C2×#529—432no—
457C2×#525—431no—
458C22×C22⋊Q8—431no—
459C2×#520—431no—
460C2×#519—431no—
461C22×#117—431no—
462C2×C43—24no—
463C2×C43#349514yescomplemented
464C2×C43C23×#4111yescharacteristic
465C2×C43C22×2−1+411yescharacteristic
466C2×C43C2×#58511yescharacteristic
467D43—24no—
468D43—44no—
469D43—42no—
470C22×#41—431no—
471C23×Q8—431no—
472C24×C4—431no—
473#556—4332no—
474#554—4332no—
475#552—4332no—
476#552—4332no—
477#552—4364no—
478#551—4364no—
479#544C2×D43116yescomplemented
480#542—4332no—
481#541—4332no—
482#536—4316no—
483#533—4332no—
484C2×C4⋊Q8—432no—
485C2×C4⋊Q8C2×D4312yescomplemented
486C2×C4⋊Q8C2×D4312yescomplemented
487#529—4332no—
488C2×#126—434no—
489C2×#126—434no—
490C2×#126—434no—
491C2×#126—434no—
492C2×#125—434no—
493C2×#125—434no—
494C2×#125—434no—
495C2×#125C2×D4312yescomplemented
496C2×#125C2×D4312yescomplemented
497C2×#124—434no—
498C2×#124—432no—
499#525—4316no—
500C2×#123—434no—
501C2×#123—434no—
502C2×#123—432no—
503C2×#123—434no—
504C2×C22⋊Q8—434no—
505C2×C22⋊Q8—434no—
506C2×C22⋊Q8—432no—
507C2×C22⋊Q8—432no—
508C2×C22⋊Q8—432no—
509C2×C22⋊Q8—432no—
510C2×C22⋊Q8—431no—
511C2×C22⋊Q8—431no—
512C2×C22⋊Q8—4316no—
513C2×C22⋊Q8—432no—
514C2×C22⋊Q8—432no—
515C2×C22⋊Q8C2×D4314yes—
516C2×#121—431no—
517C2×#121—431no—
518C2×#120—432no—
519#520—4316no—
520#519—4316no—
521C2×C4×Q8—434no—
522C2×C4×Q8—432no—
523C2×C4×Q8—432no—
524C2×C4×Q8—432no—
525C2×C4×Q8—432no—
526C2×C4×Q8—432no—
527C2×C4×D4—434no—
528C2×C4×D4—434no—
529C2×C4×D4—432no—
530C2×C4×D4—432no—
531C2×C4×D4—432no—
532C2×#117—431no—
533C2×#117—4316no—
534C2×#117—431no—
535C2×#117—431no—
536C2×#117—434no—
537C2×#117—432no—
538C2×#117—434no—
539C2×#117—432no—
540C2×#117—434no—
541C2×#117—432no—
542C2×#117C2×D4311yescharacteristic
543C2×#117C2×D4311yescharacteristic
544C22×C4⋊C4—432no—
545C22×C4⋊C4—431no—
546C22×C4⋊C4—431no—
547C22×C4⋊C4—432no—
548C22×C4⋊C4C2×D4311yescharacteristic
549C22×C22⋊C4—432no—
550C22×C22⋊C4—432no—
551C22×C42—432no—
552C43C2×#349511yescharacteristic, complemented, Sylow
553C25—431no—
554C2×#41—438no—
555C2×#41—868no—
556C22×Q8—432no—
557C22×Q8—432no—
558C22×Q8—431no—
559C22×Q8—438no—
560C22×Q8—868no—
561C22×Q8C22×D4314yes—
562C22×D4—432no—
563C22×D4—432no—
564C22×D4—431no—
565C22×D4—432no—
566C23×C4—432no—
567C23×C4—431no—
568C23×C4—432no—
569C23×C4—431no—
570C23×C4—432no—
571C23×C4—431no—
572C23×C4—431no—
573C23×C4—438no—
574C23×C4—431no—
575C23×C4—432no—
576C23×C4—434no—
577C23×C4—868no—
578C23×C4C22×D4312yes—
579C23×C4C22×D4311yescharacteristic
580C4⋊Q8—4316no—
581C4⋊Q8C22×D43116yescomplemented
582C4⋊Q8C22×D43116yescomplemented
583#126—4332no—
584#126—4332no—
585#126—4332no—
586#126—4332no—
587#125—4332no—
588#125—4332no—
589#125—4332no—
590#125C22×D43116yescomplemented
591#125C22×D43116yescomplemented
592#124—4332no—
593#124—4316no—
594#123—4332no—
595#123—4332no—
596#123—4316no—
597#123—4332no—
598C22⋊Q8—4332no—
599C22⋊Q8—4332no—
600C22⋊Q8—4316no—
601C22⋊Q8—4316no—
602C22⋊Q8—4316no—
603C22⋊Q8—4316no—
604C22⋊Q8—438no—
605C22⋊Q8—438no—
606C22⋊Q8—4316no—
607C22⋊Q8—4316no—
608C22⋊Q8C22×D43132yes—
609#121—438no—
610#121—438no—
611#120—4316no—
612C4×Q8—4332no—
613C4×Q8—4316no—
614C4×Q8—4316no—
615C4×Q8—4316no—
616C4×Q8—4316no—
617C4×Q8—4316no—
618C4×D4—4332no—
619C4×D4—4316no—
620C4×D4—4332no—
621C4×D4—4316no—
622C4×D4—4316no—
623#117—438no—
624#117—438no—
625#117—438no—
626#117—4316no—
627#117—4332no—
628#117—4332no—
629#117—4316no—
630#117—4332no—
631#117—4316no—
632#117C22×D4318yes—
633#117C22×D4318yes—
634C2×C4⋊C4—431no—
635C2×C4⋊C4—431no—
636C2×C4⋊C4—432no—
637C2×C4⋊C4—432no—
638C2×C4⋊C4—434no—
639C2×C4⋊C4—434no—
640C2×C4⋊C4—434no—
641C2×C4⋊C4—4316no—
642C2×C4⋊C4—434no—
643C2×C4⋊C4—434no—
644C2×C4⋊C4—434no—
645C2×C4⋊C4—432no—
646C2×C4⋊C4—432no—
647C2×C4⋊C4—434no—
648C2×C4⋊C4—438no—
649C2×C4⋊C4—438no—
650C2×C4⋊C4—4316no—
651C2×C4⋊C4C22×D4312yes—
652C2×C4⋊C4C22×D4311yescharacteristic
653C2×C4⋊C4C22×D4311yescharacteristic
654C2×C4⋊C4C22×D4312yes—
655C2×C4⋊C4C22×D4318yes—
656C2×C4⋊C4C22×D4314yes—
657C2×C4⋊C4C22×D4314yes—
658C2×C4⋊C4C22×D4311yescharacteristic
659C2×C4⋊C4C22×D4311yescharacteristic
660C2×C4⋊C4C22×D4314yes—
661C2×C22⋊C4—432no—
662C2×C22⋊C4—432no—
663C2×C22⋊C4—432no—
664C2×C22⋊C4—434no—
665C2×C22⋊C4—434no—
666C2×C22⋊C4—4316no—
667C2×C22⋊C4—432no—
668C2×C22⋊C4—432no—
669C2×C22⋊C4—434no—
670C2×C22⋊C4—434no—
671C2×C22⋊C4—432no—
672C2×C22⋊C4—432no—
673C2×C22⋊C4—434no—
674C2×C22⋊C4—4316no—
675C2×C22⋊C4C22×D4312yes—
676C2×C22⋊C4C22×D4312yes—
677C2×C42—432no—
678C2×C42—432no—
679C2×C42—434no—
680C2×C42—434no—
681C2×C42—434no—
682C2×C42—432no—
683C2×C42—4316no—
684C2×C42C22×D4312yes—
685C2×C42C22×D4312yes—
686C24—431no—
687C24—431no—
688C24—432no—
689C24—434no—
690C24—864no—
691C24—864no—
692C24—1722no—
693C24C23×D4311yescharacteristic
694#41—8632no—
695C2×Q8—48no—
696C2×Q8—438no—
697C2×Q8—438no—
698C2×Q8—434no—
699C2×Q8—868no—
700C2×Q8—868no—
701C2×Q8—8632no—
702C2×Q8—864no—
703C2×Q8C23×D43116yes—
704C2×D4—438no—
705C2×D4—438no—
706C2×D4—434no—
707C2×D4—438no—
708C2×D4—868no—
709C2×D4—868no—
710C2×D4—864no—
711C2×D4—1724no—
712C22×C4—44no—
713C22×C4—438no—
714C22×C4—434no—
715C22×C4—432no—
716C22×C4—431no—
717C22×C4—432no—
718C22×C4—434no—
719C22×C4—432no—
720C22×C4—431no—
721C22×C4—434no—
722C22×C4—438no—
723C22×C4—434no—
724C22×C4—438no—
725C22×C4—434no—
726C22×C4—434no—
727C22×C4—438no—
728C22×C4—4316no—
729C22×C4—868no—
730C22×C4—864no—
731C22×C4—868no—
732C22×C4—864no—
733C22×C4—864no—
734C22×C4—864no—
735C22×C4—864no—
736C22×C4—8632no—
737C22×C4—868no—
738C22×C4—1728no—
739C22×C4—1724no—
740C22×C4#1062190218yes—
741C22×C4C23×D4312yes—
742C22×C4C23×D4312yes—
743C22×C4C23×D4312yes—
744C22×C4C23×D4312yes—
745C22×C4C23×D4314yes—
746C22×C4C23×D4318yes—
747C22×C4C23×D4314yes—
748C22×C4C23×D4311yescharacteristic
749C22×C4C23×D4311yescharacteristic
750C4⋊C4—434no—
751C4⋊C4—434no—
752C4⋊C4—438no—
753C4⋊C4—438no—
754C4⋊C4—4316no—
755C4⋊C4—4316no—
756C4⋊C4—4316no—
757C4⋊C4—4316no—
758C4⋊C4—4316no—
759C4⋊C4—4316no—
760C4⋊C4—438no—
761C4⋊C4—438no—
762C4⋊C4—4316no—
763C4⋊C4C23×D4318yes—
764C4⋊C4C23×D4314yes—
765C4⋊C4C23×D4314yes—
766C4⋊C4C23×D4318yes—
767C4⋊C4C23×D43116yes—
768C4⋊C4C23×D43116yes—
769C4⋊C4C23×D4314yes—
770C4⋊C4C23×D4314yes—
771C4⋊C4C23×D43116yes—
772C22⋊C4—438no—
773C22⋊C4—438no—
774C22⋊C4—438no—
775C22⋊C4—4316no—
776C22⋊C4—4316no—
777C22⋊C4—438no—
778C22⋊C4—438no—
779C22⋊C4—4316no—
780C22⋊C4—4316no—
781C22⋊C4—438no—
782C22⋊C4—438no—
783C22⋊C4—4316no—
784C22⋊C4C23×D4318yes—
785C22⋊C4C23×D4318yes—
786C42—438no—
787C42—438no—
788C42—438no—
789C42—4316no—
790C42—4316no—
791C42—4316no—
792C42C23×D4318yes—
793C42C23×D4318yes—
794C23—22no—
795C23—22no—
796C23—434no—
797C23—432no—
798C23—432no—
799C23—434no—
800C23—868no—
801C23—862no—
802C23—862no—
803C23—868no—
804C23—862no—
805C23—864no—
806C23—864no—
807C23—862no—
808C23—864no—
809C23—862no—
810C23—1724no—
811C23—17216no—
812C23C2×#1062190214yes—
813C23C24×D4312yes—
814C23C24×D4311yescharacteristic
815Q8—416no—
816Q8—8616no—
817Q8—8616no—
818Q8—868no—
819D4—8616no—
820D4—8616no—
821D4—868no—
822D4—1728no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—28no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—48no—
829C2×C4—434no—
830C2×C4—432no—
831C2×C4—434no—
832C2×C4—438no—
833C2×C4—434no—
834C2×C4—432no—
835C2×C4—8616no—
836C2×C4—868no—
837C2×C4—862no—
838C2×C4—862no—
839C2×C4—864no—
840C2×C4—8616no—
841C2×C4—868no—
842C2×C4—864no—
843C2×C4—864no—
844C2×C4—868no—
845C2×C4—868no—
846C2×C4—868no—
847C2×C4—868no—
848C2×C4—8616no—
849C2×C4—17216no—
850C2×C4—1728no—
851C2×C4C2×#1062190214yes—
852C2×C4C2×#1062190214yes—
853C2×C4C2×#10621902116yes—
854C2×C4C24×D4314yes—
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—434no—
865C22—868no—
866C22—862no—
867C22—862no—
868C22—862no—
869C22—864no—
870C22—864no—
871C22—862no—
872C22—864no—
873C22—862no—
874C22—17216no—
875C22—1724no—
876C22—1728no—
877C22C22×#1062190214yes—
878C22C22×#1062190212yes—
879C222−1+4×D4312yes—
880C22#1458373412yes—
881C22C25×D4311yescharacteristic
882C4—24no—
883C4—24no—
884C4—28no—
885C4—24no—
886C4—24no—
887C4—862no—
888C4—862no—
889C4—864no—
890C4—868no—
891C4—864no—
892C4—864no—
893C4C22×#1062190214yes—
894C4C22×#1062190214yes—
895C2—24no—
896C2—864no—
897C2—1722no—
898C2—1724no—
899C2#1914835014yesdirect product factor
900C2C23×#1062190211yescharacteristic
901C2C2×2−1+4×D4311yescharacteristic
902C2C2×#1458373411yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#544C2
socleC23×C43C25
prime radicalC2×#14583411C2
hypercenterC2×#544D43
hypocenterC43C2×#3495
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #19148350C2direct (N × H)
2. C2×#14583623C2semidirect
3. C2×#14583610C2semidirect
4. C2×#14583591C2semidirect
5. C2×#14583587C2semidirect
6. C2×#14583587C2semidirect
7. C2×#14583576C2semidirect
8. C2×#14583523C2semidirect
9. C2×#14583512C2semidirect
10. C2×#14583475C2semidirect
11. C2×#14583454C2semidirect
12. C2×#14583434C2semidirect
14. C22×#13063305C2semidirect
15. C2×#14583380C2semidirect
16. C2×#14583376C2semidirect
17. C2×#117×D43C2semidirect
18. C2×C43×#544C2semidirect
22. #14583623C22semidirect
23. #14583610C22semidirect
24. #14583591C22semidirect
25. #14583587C22semidirect
26. #14583587C22semidirect
27. #14583576C22semidirect
28. #14583523C22semidirect
29. #14583512C22semidirect
30. #14583475C22semidirect
31. #14583454C22semidirect
32. C2×#13063325C22semidirect
33. #14583434C22semidirect
36. C2×#13063320C22semidirect
37. C2×#13063320C22semidirect
38. C2×#13063316C22semidirect
39. C2×#13063316C22semidirect
40. C2×#13063316C22semidirect
42. C2×#13063313C22semidirect
54. C2×#13063305C22semidirect
55. C2×#13063305C22semidirect
56. C2×#13063305C22semidirect
58. C2×#13063301C22semidirect
62. #14583380C22semidirect
63. #14583376C22semidirect
64. C2×Q8×Dic43C22semidirect
65. C2×C4×Dic86C22semidirect
66. C2×C4×Dic86C22semidirect
67. C2×#13063290C22semidirect
68. C2×#13063290C22semidirect
69. C2×#13063290C22semidirect
73. C2×#13063287C22semidirect
79. C2×#13063283C22semidirect
80. C2×#13063283C22semidirect
84. #117×D43C22semidirect
88. C2×C4⋊C4×D43C22semidirect
92. C43×#544C22semidirect
93. C2×C4⋊Q8×C43C22semidirect
94. C2×C4⋊Q8×C43C22semidirect
95. C2×#125×C43C22semidirect
96. C2×#125×C43C22semidirect
125. #13063325C23semidirect
128. #13063320C23semidirect
129. #13063320C23semidirect
130. #13063316C23semidirect
131. #13063316C23semidirect
132. #13063316C23semidirect
134. #13063313C23semidirect
145. #13063305C23semidirect
146. #13063305C23semidirect
148. #13063301C23semidirect
152. Q8×Dic43C23semidirect
153. C4×Dic86C23semidirect
154. C4×Dic86C23semidirect
155. #13063290C23semidirect
156. #13063290C23semidirect
157. #13063290C23semidirect
161. #13063287C23semidirect
167. #13063283C23semidirect
168. #13063283C23semidirect
188. C4⋊C4×D43C23semidirect
213. C4⋊Q8×C43C23semidirect
214. C4⋊Q8×C43C23semidirect
215. #125×C43C23semidirect
216. #125×C43C23semidirect
451. C2×#544D43semidirect
463. C2×C43#3495semidirect
479. #544C2×D43semidirect
485. C2×C4⋊Q8C2×D43semidirect
486. C2×C4⋊Q8C2×D43semidirect
495. C2×#125C2×D43semidirect
496. C2×#125C2×D43semidirect
552. C43C2×#3495semidirect
581. C4⋊Q8C22×D43semidirect
582. C4⋊Q8C22×D43semidirect
590. #125C22×D43semidirect
591. #125C22×D43semidirect
899. C2#19148350direct (N × H)

Maximal subgroups

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

subgroupindex
#191483502
C2×#145836232
C2×#145836102
C2×#145835912
C2×#145835872
C2×#145835762
C2×#145835232
C2×#145835122
C2×#145834752
C2×#145834542
C2×#145834342
C2×#145834112
C22×#130633052
C2×#145833802
C2×#145833762
C2×#117×D432
C2×C43×#5442
C2×#349543