Finite Group Databasebeta

← C2×#19148459 #26004675

Subgroups — C2×#19148459 #26004675

Order 11008.

7130 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148459C2132yesmaximal, direct product factor
2C2×#14583631C212yesmaximal, complemented
3C2×#14583624C212yesmaximal, complemented
4C2×#14583623C212yesmaximal, complemented
5C2×#14583620C212yesmaximal, complemented
6C2×#14583618C212yesmaximal, complemented
7C2×#14583607C212yesmaximal, complemented
8C2×#14583591C212yesmaximal, complemented
9C2×#14583583C212yesmaximal, complemented
10C2×#14583493C214yesmaximal, complemented
11C2×#14583473C211yesmaximal, characteristic, complemented
12C2×#14583452C211yesmaximal, characteristic, complemented
13C2×#14583445C211yesmaximal, characteristic
14C2×#14583426C214yesmaximal, complemented
15C2×#14583382C211yesmaximal, characteristic, complemented
16C2×#14583379C211yesmaximal, characteristic, complemented
17C22×Q8×Dic43C211yesmaximal, characteristic, complemented
18C2×C43×#536C211yesmaximal, characteristic, complemented
19C22×#10621898C2211yescharacteristic
20#14583631C22132yescomplemented
21#14583624C22132yescomplemented
22#14583623C22132yescomplemented
23#14583620C22132yescomplemented
24#14583618C22132yescomplemented
25#14583607C22132yescomplemented
26#14583591C22132yescomplemented
27#14583583C22132yescomplemented
28#14583493C22164yescomplemented
29#14583473C22116yescomplemented
30#14583452C22116yescomplemented
31#14583445C22116yes—
32C2×#13063324C2211yescharacteristic
33C2×#13063324C2211yescharacteristic
34C2×#13063323C2211yescharacteristic
35C2×#13063323C2212yes—
36C2×#13063321C2211yescharacteristic
37#14583426C22164yescomplemented
38C2×#13063320C2214yes—
39C2×#13063320C2214yes—
40C2×#13063318C2214yes—
41C2×#13063318C2214yes—
42C2×#13063316C2211yescharacteristic
43C2×#13063316C2211yescharacteristic
44C2×#13063316C2214yes—
45C2×#13063315C2214yes—
46C2×#13063315C2214yes—
47C2×#13063314C2211yescharacteristic
48C2×#13063314C2212yes—
49C2×#13063312C2211yescharacteristic
50C2×#13063311C2214yes—
51C2×#13063309C2214yes—
52C2×#13063308C2214yes—
53C2×#13063307C2214yes—
54C2×#13063305C2214yes—
55C2×#13063302C2212yes—
56C2×#13063302C2214yes—
57C2×#13063302C2212yes—
58C2×#13063301C2212yes—
59C2×#13063301C2212yes—
60C2×#13063297C2212yes—
61C2×#13063297C2212yes—
62#14583382C22116yescomplemented
63#14583379C22116yescomplemented
64C2×Q8×Dic43C2212yes—
65C2×Q8×Dic43C2212yes—
66C2×Q8×Dic43C2212yes—
67C2×Q8×Dic43C2212yes—
68C2×Q8×Dic43C2212yes—
69C2×Q8×Dic43C22116yescomplemented
70C2×C4×Dic86C2212yes—
71C2×C4×Dic86C2212yes—
72C2×C4×Dic86C2212yes—
73C2×#13063290C2214yes—
74C2×C4×D172C2212yes—
75C2×D4×Dic43C2214yes—
76C2×D4×Dic43C2212yes—
77C2×C4×C22⋊D43C2212yes—
78C2×C4×C22⋊D43C2212yes—
79C2×(C22⋊D43)⋊C4C2214yes—
80C2×(C22⋊D43)⋊C4C2214yes—
81C2×#13063284C2212yes—
82C2×#13063284C2211yescharacteristic
83C2×#13063283C2212yes—
84C2×#13063283C2214yes—
85C2×#13063281C2214yes—
86C22×C4⋊Dic43C2211yescharacteristic
87C22×C4⋊Dic43C2212yes—
88C22×C4⋊Dic43C2212yes—
89C2×C4⋊C4×D43C2212yes—
90C22×C4×Dic43C2212yes—
91C22×C4×Dic43C2211yescharacteristic
92C22×#41×C43C2211yescharacteristic
93C23×Q8×C43C2211yescharacteristic
94C43×#536C22116yescomplemented
95C2×C4⋊Q8×C43C2212yes—
96C2×#124×C43C2212yes—
97C2×#123×C43C2214yes—
98C2×C22⋊Q8×C43C2212yes—
99C2×C22⋊Q8×C43C2212yes—
100C2×#117×C43C2211yescharacteristic
101C2×#10621898—28no—
102C2×#10621898C2318yes—
103C22×Dic86C2312yes—
104C22×Dic86C2311yescharacteristic
105C22×Dic86C2312yes—
106C22×D172C2311yescharacteristic
107C22×C22⋊D43C2312yes—
108C22×C22⋊D43C2312yes—
109C22×C22⋊D43C2312yes—
110C23×Dic43C2311yescharacteristic
111C23×Dic43C2312yes—
112C23×Dic43C2311yescharacteristic
113C23×Dic43C2314yes—
114C22×C4×D43C2312yes—
115C22×C4×D43C2314yes—
116#13063324C2318yes—
117#13063324C2318yes—
118#13063323C23116yes—
119#13063323C2318yes—
120#13063321C2318yes—
121#13063320C23132yes—
122#13063320C23132yes—
123#13063318C23132yes—
124#13063318C23132yes—
125#13063316C2318yes—
126#13063316C2318yes—
127#13063316C23132yes—
128#13063315C23132yes—
129#13063315C23132yes—
130#13063314C2318yes—
131#13063314C23116yes—
132#13063312C2318yes—
133#13063311C23132yes—
134#13063309C23132yes—
135#13063308C23132yes—
136#13063307C23132yes—
137#13063305C23132yes—
138#13063302C23132yes—
139#13063302C23116yes—
140#13063302C23116yes—
141#13063301C23116yes—
142#13063301C23116yes—
143#13063297C23116yes—
144#13063297C23116yes—
145Q8×Dic43C23116yes—
146Q8×Dic43C23116yes—
147Q8×Dic43C23116yes—
148Q8×Dic43C23116yes—
149Q8×Dic43C23116yes—
150C4×Dic86C23116yes—
151C4×Dic86C23116yes—
152C4×Dic86C23116yes—
153#13063290C23132yes—
154C4×D172C23116yes—
155D4×Dic43C23116yes—
156D4×Dic43C23132yes—
157C4×C22⋊D43C23116yes—
158C4×C22⋊D43C23116yes—
159(C22⋊D43)⋊C4C23132yes—
160(C22⋊D43)⋊C4C23132yes—
161#13063284C23116yes—
162#13063284C2318yes—
163#13063283C23132yes—
164#13063283C23116yes—
165#13063281C23132yes—
166C2×C4⋊Dic43C23116yes—
167C2×C4⋊Dic43C2312yes—
168C2×C4⋊Dic43C2311yescharacteristic
169C2×C4⋊Dic43C2312yes—
170C2×C4⋊Dic43C2314yes—
171C2×C4⋊Dic43C2314yes—
172C2×C4⋊Dic43C2314yes—
173C2×C4⋊Dic43C2318yes—
174C2×C4⋊Dic43C23116yes—
175C2×C4⋊Dic43C2312yes—
176C2×C4⋊Dic43C2311yescharacteristic
177C2×C4⋊Dic43C2312yes—
178C2×Dic43⋊C4C2314yes—
179C2×Dic43⋊C4C2312yes—
180C2×Dic43⋊C4C2314yes—
181C2×Dic43⋊C4C2312yes—
182C2×Dic43⋊C4C2312yes—
183C2×Dic43⋊C4C2312yes—
184C2×Dic43⋊C4C2314yes—
185C2×Dic43⋊C4C2312yes—
186C2×Dic43⋊C4C2312yes—
187C4⋊C4×D43C23116yes—
188C2×C22⋊Dic43C2312yes—
189C2×C22⋊Dic43C2312yes—
190C2×C22⋊Dic43C2314yes—
191C2×C22⋊Dic43C2312yes—
192C2×(C2×D43)⋊C4C2312yes—
193C2×(C2×D43)⋊C4C2314yes—
194C2×(C2×D43)⋊C4C2314yes—
195C2×(C2×D43)⋊C4C2314yes—
196C2×(C2×D43)⋊C4C2312yes—
197C2×C4×Dic43C2314yes—
198C2×C4×Dic43C2314yes—
199C2×C4×Dic43C2311yescharacteristic
200C2×C4×Dic43C2311yescharacteristic
201C2×C4×Dic43C2311yescharacteristic
202C2×C4×Dic43C2311yescharacteristic
203C2×C4×Dic43C23116yes—
204C2×C4×Dic43C2318yes—
205C2×C4×Dic43C2314yes—
206C2×C4×Dic43C2314yes—
207C2×C4×Dic43C2312yes—
208C2×#41×C43—28no—
209C2×#41×C43C2318yes—
210C22×Q8×C43—28no—
211C22×Q8×C43C2312yes—
212C22×Q8×C43C2312yes—
213C22×Q8×C43C2311yescharacteristic
214C22×Q8×C43C2318yes—
215C22×D4×C43C2312yes—
216C22×D4×C43C2311yescharacteristic
217C23×C4×C43C2312yes—
218C23×C4×C43C2312yes—
219C23×C4×C43C2311yescharacteristic
220C4⋊Q8×C43C23116yes—
221#124×C43C23116yes—
222#123×C43C23132yes—
223C22⋊Q8×C43C23116yes—
224C22⋊Q8×C43C23116yes—
225#117×C43C2318yes—
226C2×C4⋊C4×C43C2311yescharacteristic
227C2×C4⋊C4×C43C2311yescharacteristic
228C2×C4⋊C4×C43C2314yes—
229C2×C4⋊C4×C43C2314yes—
230C2×C22⋊C4×C43C2312yes—
231C2×C22⋊C4×C43C2314yes—
232C2×C22⋊C4×C43C2314yes—
233C2×C42×C43C2312yes—
234C24×C43C2412yes—
235C24×C43C2411yescharacteristic
236C23×D43C2412yes—
237#41×C43—232no—
238C2×Q8×C43—28no—
239C2×Q8×C43—28no—
240C2×Q8×C43—232no—
241C2×Q8×C43—24no—
242C2×Q8×C43C2418yes—
243C2×Q8×C43C2418yes—
244C2×Q8×C43C2414yes—
245C2×D4×C43—24no—
246C2×D4×C43—28no—
247C2×D4×C43C2418yes—
248C2×D4×C43C2414yes—
249C22×C4×C43—28no—
250C22×C4×C43—28no—
251C22×C4×C43#4118yes—
252C22×C4×C43C2412yes—
253C22×C4×C43C2412yes—
254C22×C4×C43C2414yes—
255C22×C4×C43C2412yes—
256C22×C4×C43C2418yes—
257C22×C4×C43C2418yes—
258C22×C4×C43C2411yescharacteristic
259C22×C4×C43C2411yescharacteristic
260C22×C4×C43C2414yes—
261C2×C22⋊D43—28no—
262C2×C22⋊D43—28no—
263C2×C22⋊D43—44no—
264C2×C22⋊D43C2418yes—
265C2×C22⋊D43C2418yes—
266C2×C22⋊D43C2418yes—
267C22×Dic43—24no—
268C22×Dic43—42no—
269C22×Dic43—44no—
270C22×Dic43—48no—
271C22×Dic43C2411yescharacteristic
272C22×Dic43C2414yes—
273C22×Dic43C2414yes—
274C22×Dic43C2412yes—
275C22×Dic43C2411yescharacteristic
276C22×Dic43C2412yes—
277C22×Dic43C2411yescharacteristic
278C22×Dic43C2412yes—
279C22×Dic43C2418yes—
280C22×Dic43C2414yes—
281C22×Dic43C24116yes—
282C22×Dic43C2411yescharacteristic
283#10621898—232no—
284C2×D172—24no—
285C2×D172C2414yes—
286C2×C4×D43—28no—
287C2×C4×D43—48no—
288C2×C4×D43C2418yes—
289C2×C4×D43C24116yes—
290C2×Dic86—24no—
291C2×Dic86—28no—
292C2×Dic86—44no—
293C2×Dic86C2418yes—
294C2×Dic86C2414yes—
295C2×Dic86C2418yes—
296C4⋊C4×C43C2414yes—
297C4⋊C4×C43C2414yes—
298C4⋊C4×C43C24116yes—
299C4⋊C4×C43C24116yes—
300C22⋊C4×C43C2418yes—
301C22⋊C4×C43C24116yes—
302C22⋊C4×C43C24116yes—
303C42×C43C2418yes—
304C22⋊Dic43C2418yes—
305C22⋊Dic43C2418yes—
306C22⋊Dic43C24116yes—
307C22⋊Dic43C2418yes—
308(C2×D43)⋊C4C2418yes—
309(C2×D43)⋊C4C24116yes—
310(C2×D43)⋊C4C24116yes—
311(C2×D43)⋊C4C24116yes—
312(C2×D43)⋊C4C2418yes—
313C4⋊Dic43C2418yes—
314C4⋊Dic43C2414yes—
315C4⋊Dic43C2418yes—
316C4⋊Dic43C24116yes—
317C4⋊Dic43C24116yes—
318C4⋊Dic43C24116yes—
319C4⋊Dic43C2418yes—
320C4⋊Dic43C2414yes—
321C4⋊Dic43C2418yes—
322Dic43⋊C4C24116yes—
323Dic43⋊C4C2418yes—
324Dic43⋊C4C24116yes—
325Dic43⋊C4C2418yes—
326Dic43⋊C4C2418yes—
327Dic43⋊C4C2418yes—
328Dic43⋊C4C24116yes—
329Dic43⋊C4C2418yes—
330Dic43⋊C4C2418yes—
331C4×Dic43C24116yes—
332C4×Dic43C24116yes—
333C4×Dic43C2414yes—
334C4×Dic43C2414yes—
335C4×Dic43C2414yes—
336C4×Dic43C2414yes—
337C4×Dic43C24116yes—
338C4×Dic43C24116yes—
339C4×Dic43C2418yes—
340C23×C43—22no—
341C23×C43—22no—
342C23×C43—24no—
343C23×C43—24no—
344C23×C43—24no—
345C23×C43C2×#4114yes—
346C23×C43C2514yes—
347C23×C43C2512yes—
348C23×C43C2511yescharacteristic
349C22×D43—24no—
350C22×D43—24no—
351C22×D43—24no—
352C22×D43C2514yes—
353Q8×C43—216no—
354Q8×C43—216no—
355Q8×C43—28no—
356D4×C43—216no—
357D4×C43—28no—
358C2×C4×C43—24no—
359C2×C4×C43—216no—
360C2×C4×C43—28no—
361C2×C4×C43—24no—
362C2×C4×C43—24no—
363C2×C4×C43—216no—
364C2×C4×C43C2×#4114yes—
365C2×C4×C43C2×#4114yes—
366C2×C4×C43C2×#41116yes—
367C2×C4×C43C2518yes—
368C2×C4×C43C2514yes—
369C2×C4×C43C2514yes—
370C2×C4×C43C2514yes—
371C2×C4×C43C2512yes—
372C2×C4×C43C2512yes—
373C22⋊D43—216no—
374C22⋊D43—216no—
375C22⋊D43—48no—
376C2×Dic43—24no—
377C2×Dic43—24no—
378C2×Dic43—22no—
379C2×Dic43—22no—
380C2×Dic43—24no—
381C2×Dic43—28no—
382C2×Dic43—22no—
383C2×Dic43—28no—
384C2×Dic43—44no—
385C2×Dic43—416no—
386C2×Dic43—48no—
387C2×Dic432−1+414yes—
388C2×Dic43C2512yes—
389C2×Dic43C2518yes—
390C2×Dic43C2514yes—
391C2×Dic43C2514yes—
392C2×Dic43C2512yes—
393C2×Dic43C2512yes—
394C2×Dic43C2514yes—
395C2×Dic43C2512yes—
396D172—28no—
397C4×D43—216no—
398C4×D43—416no—
399Dic86—28no—
400Dic86—216no—
401Dic86—48no—
402C2×#3507—431nomaximal, Sylow
403C22×C43—22no—
404C22×C43—22no—
405C22×C43—28no—
406C22×C43—24no—
407C22×C43—24no—
408C22×C43—24no—
409C22×C43—48no—
410C22×C43C22×#4114yes—
411C22×C43C22×#4112yes—
412C22×C43C2×2−1+412yes—
413C22×C43#58512yes—
414C22×C43C2611yescharacteristic
415C2×D43—24no—
416C2×D43—24no—
417C2×D43—24no—
418C2×D43—48no—
419C4×C43—24no—
420C4×C43—28no—
421C4×C43—24no—
422C4×C43—24no—
423C4×C43C22×#4114yes—
424C4×C43C22×#4114yes—
425Dic43—24no—
426Dic43—24no—
427Dic43—22no—
428Dic43—22no—
429Dic43—24no—
430Dic43—28no—
431Dic43—22no—
432Dic43C2×2−1+414yes—
433#3507—4332no—
434C2×#559—432no—
435C2×#557—432no—
436C2×#556—432no—
437C2×#556—432no—
438C2×#556—432no—
439C2×#554—432no—
440C2×#552—432no—
441C2×#552—432no—
442C2×#539—434no—
443C2×#536—431no—
444C2×#536D4311yescharacteristic, complemented
445C2×#533—431no—
446C2×#532—431no—
447C2×#529—434no—
448C2×#520—431no—
449C2×#520—431no—
450C22×C4×Q8—431no—
451C2×C43—24no—
452C2×C43—44no—
453C2×C43#350714yescomplemented
454C2×C43C23×#4111yescharacteristic
455C2×C43C22×2−1+411yescharacteristic
456C2×C43C2×#58511yescharacteristic
457D43—44no—
458C22×#41—431no—
459C22×#41C2×D4311yescharacteristic
460C23×Q8C2×D4311yescharacteristic
461#559—4332no—
462#557—4332no—
463#556—4332no—
464#556—4332no—
465#556—4332no—
466#554—4332no—
467#552—4332no—
468#552—4332no—
469#539—4364no—
470#536—4316no—
471#536C2×D43116yescomplemented
472#533—4316no—
473#532—4316no—
474C2×C4⋊Q8—431no—
475C2×C4⋊Q8—432no—
476C2×C4⋊Q8—431no—
477C2×C4⋊Q8—431no—
478C2×C4⋊Q8C2×D4312yes—
479C2×#127—431no—
480#529—4364no—
481C2×#126—434no—
482C2×#126—434no—
483C2×#126—434no—
484C2×#126—434no—
485C2×#125—434no—
486C2×#125—431no—
487C2×#125—431no—
488C2×#125—434no—
489C2×#125—434no—
490C2×#124—431no—
491C2×#124—432no—
492C2×#124—431no—
493C2×#124—434no—
494C2×#124C2×D4312yes—
495C2×#123—434no—
496C2×#123—434no—
497C2×#123—434no—
498C2×#123C2×D4314yes—
499C2×C22⋊Q8—432no—
500C2×C22⋊Q8—432no—
501C2×C22⋊Q8—434no—
502C2×C22⋊Q8—432no—
503C2×C22⋊Q8—432no—
504C2×C22⋊Q8—434no—
505C2×C22⋊Q8C2×D4312yes—
506C2×C22⋊Q8C2×D4312yes—
507C2×#121—432no—
508C2×#121—432no—
509#520—4316no—
510#520—4316no—
511C2×C4×Q8—432no—
512C2×C4×Q8—432no—
513C2×C4×Q8—432no—
514C2×C4×Q8—432no—
515C2×C4×Q8—432no—
516C2×C4×Q8—4316no—
517C2×C4×Q8—434no—
518C2×C4×Q8—432no—
519C2×C4×Q8—432no—
520C2×C4×Q8—432no—
521C2×C4×D4—434no—
522C2×C4×D4—432no—
523C2×C4×D4—432no—
524C2×C4×D4—432no—
525C2×C4×D4—434no—
526C2×C4×D4—434no—
527C2×C4×D4—432no—
528C2×#117—431no—
529C2×#117—432no—
530C2×#117—432no—
531C2×#117—434no—
532C2×#117—434no—
533C2×#117C2×D4311yescharacteristic
534C22×C4⋊C4—431no—
535C22×C4⋊C4—432no—
536C22×C4⋊C4—432no—
537C22×C4⋊C4—432no—
538C22×C42—432no—
539C22×C42—431no—
540C43C2×#350711yescharacteristic, complemented, Sylow
541C2×#41—28no—
542C2×#41—438no—
543C2×#41—868no—
544C2×#41C22×D4318yes—
545C22×Q8—28no—
546C22×Q8—432no—
547C22×Q8—431no—
548C22×Q8—432no—
549C22×Q8C22×D4312yes—
550C22×Q8C22×D4312yes—
551C22×Q8C22×D4311yescharacteristic
552C22×Q8C22×D4318yes—
553C22×D4—432no—
554C22×D4—432no—
555C22×D4—432no—
556C22×D4—431no—
557C22×D4C22×D4312yes—
558C22×D4C22×D4311yescharacteristic
559C23×C4—431no—
560C23×C4—432no—
561C23×C4—431no—
562C23×C4—434no—
563C23×C4—432no—
564C23×C4—434no—
565C23×C4C22×D4312yes—
566C23×C4C22×D4312yes—
567C23×C4C22×D4311yescharacteristic
568C4⋊Q8—438no—
569C4⋊Q8—4316no—
570C4⋊Q8—438no—
571C4⋊Q8—438no—
572C4⋊Q8C22×D43116yes—
573#127—438no—
574#126—4332no—
575#126—4332no—
576#126—4332no—
577#126—4332no—
578#125—4332no—
579#125—438no—
580#125—438no—
581#125—4332no—
582#125—4332no—
583#124—438no—
584#124—4316no—
585#124—438no—
586#124—4332no—
587#124C22×D43116yes—
588#123—4332no—
589#123—4332no—
590#123—4332no—
591#123C22×D43132yes—
592C22⋊Q8—4316no—
593C22⋊Q8—4316no—
594C22⋊Q8—4332no—
595C22⋊Q8—4316no—
596C22⋊Q8—4316no—
597C22⋊Q8—4332no—
598C22⋊Q8C22×D43116yes—
599C22⋊Q8C22×D43116yes—
600#121—4316no—
601#121—4316no—
602C4×Q8—4316no—
603C4×Q8—4316no—
604C4×Q8—4316no—
605C4×Q8—4316no—
606C4×Q8—4316no—
607C4×Q8—4332no—
608C4×Q8—4316no—
609C4×Q8—4316no—
610C4×Q8—4316no—
611C4×D4—4332no—
612C4×D4—4316no—
613C4×D4—4316no—
614C4×D4—4316no—
615C4×D4—4332no—
616C4×D4—4332no—
617C4×D4—4316no—
618#117—438no—
619#117—4316no—
620#117—4316no—
621#117—4332no—
622#117—4332no—
623#117C22×D4318yes—
624C2×C4⋊C4—432no—
625C2×C4⋊C4—431no—
626C2×C4⋊C4—432no—
627C2×C4⋊C4—434no—
628C2×C4⋊C4—434no—
629C2×C4⋊C4—438no—
630C2×C4⋊C4—434no—
631C2×C4⋊C4—434no—
632C2×C4⋊C4—4316no—
633C2×C4⋊C4—4316no—
634C2×C4⋊C4—431no—
635C2×C4⋊C4—432no—
636C2×C4⋊C4—432no—
637C2×C4⋊C4—434no—
638C2×C4⋊C4—432no—
639C2×C4⋊C4—432no—
640C2×C4⋊C4—432no—
641C2×C4⋊C4—432no—
642C2×C4⋊C4—432no—
643C2×C4⋊C4—434no—
644C2×C4⋊C4—432no—
645C2×C4⋊C4—4316no—
646C2×C4⋊C4C22×D4311yescharacteristic
647C2×C4⋊C4C22×D4311yescharacteristic
648C2×C4⋊C4C22×D4314yes—
649C2×C4⋊C4C22×D4314yes—
650C2×C22⋊C4—432no—
651C2×C22⋊C4—432no—
652C2×C22⋊C4—434no—
653C2×C22⋊C4—432no—
654C2×C22⋊C4—432no—
655C2×C22⋊C4—434no—
656C2×C22⋊C4—434no—
657C2×C22⋊C4—432no—
658C2×C22⋊C4—434no—
659C2×C22⋊C4C22×D4314yes—
660C2×C22⋊C4C22×D4312yes—
661C2×C22⋊C4C22×D4314yes—
662C2×C42—434no—
663C2×C42—434no—
664C2×C42—434no—
665C2×C42—432no—
666C2×C42—431no—
667C2×C42—431no—
668C2×C42—434no—
669C2×C42—431no—
670C2×C42—431no—
671C2×C42—4316no—
672C2×C42—438no—
673C2×C42C22×D4312yes—
674C24—432no—
675C24C23×D4312yes—
676C24C23×D4311yescharacteristic
677#41—232no—
678#41—8632no—
679C2×Q8—28no—
680C2×Q8—28no—
681C2×Q8—232no—
682C2×Q8—24no—
683C2×Q8—438no—
684C2×Q8—434no—
685C2×Q8—438no—
686C2×Q8—868no—
687C2×Q8—864no—
688C2×Q8—1724no—
689C2×Q8C23×D4318yes—
690C2×Q8C23×D4318yes—
691C2×Q8C23×D4314yes—
692C2×D4—28no—
693C2×D4—24no—
694C2×D4—438no—
695C2×D4—438no—
696C2×D4—438no—
697C2×D4—434no—
698C2×D4—868no—
699C2×D4—868no—
700C2×D4—864no—
701C2×D4—1724no—
702C2×D4C23×D4318yes—
703C2×D4C23×D4314yes—
704C22×C4—28no—
705C22×C4—28no—
706C22×C4—431no—
707C22×C4—434no—
708C22×C4—431no—
709C22×C4—434no—
710C22×C4—432no—
711C22×C4—431no—
712C22×C4—432no—
713C22×C4—431no—
714C22×C4—432no—
715C22×C4—438no—
716C22×C4—434no—
717C22×C4—4316no—
718C22×C4—438no—
719C22×C4—4316no—
720C22×C4—864no—
721C22×C4—868no—
722C22×C4—1728no—
723C22×C4—1724no—
724C22×C4—1728no—
725C22×C4—1722no—
726C22×C4#1062190018yes—
727C22×C4C23×D4318yes—
728C22×C4C23×D4318yes—
729C22×C4C23×D4312yes—
730C22×C4C23×D4314yes—
731C22×C4C23×D4312yes—
732C22×C4C23×D4312yes—
733C22×C4C23×D4314yes—
734C22×C4C23×D4311yescharacteristic
735C22×C4C23×D4311yescharacteristic
736C4⋊C4—438no—
737C4⋊C4—434no—
738C4⋊C4—438no—
739C4⋊C4—4316no—
740C4⋊C4—4316no—
741C4⋊C4—4316no—
742C4⋊C4—4316no—
743C4⋊C4—434no—
744C4⋊C4—438no—
745C4⋊C4—438no—
746C4⋊C4—4316no—
747C4⋊C4—438no—
748C4⋊C4—438no—
749C4⋊C4—438no—
750C4⋊C4—438no—
751C4⋊C4—438no—
752C4⋊C4—4316no—
753C4⋊C4—438no—
754C4⋊C4C23×D4314yes—
755C4⋊C4C23×D4314yes—
756C4⋊C4C23×D43116yes—
757C4⋊C4C23×D43116yes—
758C22⋊C4—438no—
759C22⋊C4—438no—
760C22⋊C4—4316no—
761C22⋊C4—438no—
762C22⋊C4—438no—
763C22⋊C4—4316no—
764C22⋊C4—4316no—
765C22⋊C4—438no—
766C22⋊C4—4316no—
767C22⋊C4C23×D43116yes—
768C22⋊C4C23×D4318yes—
769C22⋊C4C23×D43116yes—
770C42—4316no—
771C42—434no—
772C42—434no—
773C42—4316no—
774C42—434no—
775C42—434no—
776C42—4316no—
777C42—4316no—
778C42—438no—
779C42C23×D4318yes—
780C23—22no—
781C23—22no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—434no—
786C23—864no—
787C23—864no—
788C23—864no—
789C23C2×#1062190014yes—
790C23C24×D4314yes—
791C23C24×D4312yes—
792C23C24×D4311yescharacteristic
793Q8—216no—
794Q8—216no—
795Q8—28no—
796Q8—8616no—
797Q8—868no—
798Q8—1728no—
799D4—216no—
800D4—28no—
801D4—8616no—
802D4—8616no—
803D4—868no—
804D4—1728no—
805C2×C4—24no—
806C2×C4—216no—
807C2×C4—28no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—216no—
811C2×C4—434no—
812C2×C4—432no—
813C2×C4—432no—
814C2×C4—438no—
815C2×C4—434no—
816C2×C4—432no—
817C2×C4—434no—
818C2×C4—432no—
819C2×C4—434no—
820C2×C4—868no—
821C2×C4—864no—
822C2×C4—862no—
823C2×C4—864no—
824C2×C4—868no—
825C2×C4—864no—
826C2×C4—862no—
827C2×C4—862no—
828C2×C4—8616no—
829C2×C4—17216no—
830C2×C4—1728no—
831C2×C4—17216no—
832C2×C4—1724no—
833C2×C4C2×#1062190014yes—
834C2×C4C2×#1062190014yes—
835C2×C4C2×#10621900116yes—
836C2×C4C24×D4314yes—
837C2×C4C24×D4318yes—
838C2×C4C24×D4314yes—
839C2×C4C24×D4314yes—
840C2×C4C24×D4312yes—
841C2×C4C24×D4312yes—
842C22—22no—
843C22—22no—
844C22—28no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—48no—
849C22—864no—
850C22—864no—
851C22—864no—
852C22—1728no—
853C22C22×#1062190014yes—
854C22C22×#1062190012yes—
855C222−1+4×D4312yes—
856C22#1458373612yes—
857C22C25×D4311yescharacteristic
858C4—24no—
859C4—28no—
860C4—24no—
861C4—24no—
862C4—434no—
863C4—864no—
864C4—862no—
865C4—864no—
866C4—868no—
867C4—864no—
868C4—862no—
869C4—862no—
870C4C22×#1062190014yes—
871C4C22×#1062190014yes—
872C2—24no—
873C2—44no—
874C2—1724no—
875C2#1914845914yesdirect product factor
876C2C23×#1062190011yescharacteristic
877C2C2×2−1+4×D4311yescharacteristic
878C2C2×#1458373611yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#536C2
socleC23×C43C25
prime radicalC2×#14583445C2
hypercenterC2×#536D43
hypocenterC43C2×#3507
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. #19148459C2direct (N × H)
2. C2×#14583631C2semidirect
3. C2×#14583624C2semidirect
4. C2×#14583623C2semidirect
5. C2×#14583620C2semidirect
6. C2×#14583618C2semidirect
7. C2×#14583607C2semidirect
8. C2×#14583591C2semidirect
9. C2×#14583583C2semidirect
10. C2×#14583493C2semidirect
11. C2×#14583473C2semidirect
12. C2×#14583452C2semidirect
14. C2×#14583426C2semidirect
15. C2×#14583382C2semidirect
16. C2×#14583379C2semidirect
17. C22×Q8×Dic43C2semidirect
18. C2×C43×#536C2semidirect
20. #14583631C22semidirect
21. #14583624C22semidirect
22. #14583623C22semidirect
23. #14583620C22semidirect
24. #14583618C22semidirect
25. #14583607C22semidirect
26. #14583591C22semidirect
27. #14583583C22semidirect
28. #14583493C22semidirect
29. #14583473C22semidirect
30. #14583452C22semidirect
37. #14583426C22semidirect
62. #14583382C22semidirect
63. #14583379C22semidirect
69. C2×Q8×Dic43C22semidirect
94. C43×#536C22semidirect
444. C2×#536D43semidirect
453. C2×C43#3507semidirect
471. #536C2×D43semidirect
540. C43C2×#3507semidirect
875. C2#19148459direct (N × H)

Maximal subgroups

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

subgroupindex
#191484592
C2×#145836312
C2×#145836242
C2×#145836232
C2×#145836202
C2×#145836182
C2×#145836072
C2×#145835912
C2×#145835832
C2×#145834932
C2×#145834732
C2×#145834522
C2×#145834452
C2×#145834262
C2×#145833822
C2×#145833792
C22×Q8×Dic432
C2×C43×#5362
C2×#350743