Finite Group Databasebeta

← C2×#19149083 #26004317

Subgroups — C2×#19149083 #26004317

Order 11008.

6446 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149083C2132yesmaximal, direct product factor
2C2×#14583650C214yesmaximal, complemented
3C2×Q8×Dic86C211yesmaximal, characteristic, complemented
4C2×#14583628C211yesmaximal, characteristic, complemented
5C2×#14583627C212yesmaximal, complemented
6C2×#14583622C212yesmaximal, complemented
7C2×#14583622C211yesmaximal, characteristic, complemented
8C2×#14583620C212yesmaximal, complemented
9C2×#14583609C211yesmaximal, characteristic, complemented
10C2×#14583583C212yesmaximal, complemented
11C2×#14583526C212yesmaximal, complemented
12C2×#14583520C212yesmaximal
13C2×#14583511C212yesmaximal, complemented
14C2×#14583510C212yesmaximal, complemented
15C2×#14583508C214yesmaximal, complemented
16C2×#14583456C211yesmaximal, characteristic, complemented
17C2×#14583433C211yesmaximal, characteristic
18C2×C43×#533C211yesmaximal, characteristic, complemented
19#14583650C22164yescomplemented
20Q8×Dic86C22116yescomplemented
21#14583628C22116yescomplemented
22#14583627C22132yescomplemented
23#14583622C22132yescomplemented
24#14583622C22116yescomplemented
25#14583620C22132yescomplemented
26#14583609C22116yescomplemented
27#14583583C22132yescomplemented
28#14583526C22132yescomplemented
29#14583520C22132yes—
30#14583511C22132yescomplemented
31#14583510C22132yescomplemented
32#14583508C22164yescomplemented
33#14583456C22116yescomplemented
34C2×#13063325C2211yescharacteristic
35C2×#13063325C2211yescharacteristic
36C2×#13063325C2212yes—
37C2×#13063325C2212yes—
38C2×#13063324C2212yes—
39C2×#13063324C2214yes—
40C2×#13063323C2214yes—
41#14583433C22116yes—
42C2×#13063320C2214yes—
43C2×#13063320C2214yes—
44C2×#13063320C2214yes—
45C2×#13063320C2214yes—
46C2×#13063319C2212yes—
47C2×#13063318C2214yes—
48C2×#13063318C2214yes—
49C2×#13063317C2211yescharacteristic
50C2×#13063317C2212yes—
51C2×#13063317C2212yes—
52C2×#13063316C2212yes—
53C2×#13063316C2214yes—
54C2×#13063315C2214yes—
55C2×#13063315C2214yes—
56C2×#13063315C2214yes—
57C2×#13063315C2214yes—
58C2×#13063313C2211yescharacteristic
59C2×#13063313C2212yes—
60C2×#13063311C2214yes—
61C2×#13063308C2212yes—
62C2×#13063307C2214yes—
63C2×#13063304C2211yescharacteristic
64C2×#13063304C2212yes—
65C2×#13063304C2212yes—
66C2×#13063303C2214yes—
67C2×#13063303C2214yes—
68C2×#13063301C2212yes—
69C2×#13063301C2212yes—
70C2×#13063301C2214yes—
71C2×#13063299C2211yescharacteristic
72C2×Q8×Dic43C2212yes—
73C2×Q8×Dic43C2212yes—
74C2×C4×Dic86C2211yescharacteristic
75C2×C4×Dic86C2212yes—
76C2×C4×Dic86C2212yes—
77C2×C4×Dic86C2212yes—
78C2×C4×Dic86C2212yes—
79C2×C4×Dic86C2212yes—
80C2×#13063290C2214yes—
81C2×C4×D172C2211yescharacteristic
82C2×C4×D172C2212yes—
83C2×C4×C22⋊D43C2212yes—
84C2×#13063284C2212yes—
85C2×#13063283C2214yes—
86C2×#13063283C2212yes—
87C2×#13063282C2212yes—
88C2×C4⋊C4×D43C2212yes—
89C43×#533C22116yescomplemented
90C2×C4⋊Q8×C43C2211yescharacteristic
91C2×C4⋊Q8×C43C2211yescharacteristic
92C2×#125×C43C2212yes—
93C2×C22⋊Q8×C43C2211yescharacteristic
94C2×C22⋊Q8×C43C2211yescharacteristic
95C2×C22⋊Q8×C43C2212yes—
96C2×C4×Q8×C43C2211yescharacteristic
97C2×C4×Q8×C43C2212yes—
98C2×C4×Q8×C43C2211yescharacteristic
99C2×#117×C43C2212yes—
100C22×C42×C43C2211yescharacteristic
101C22×Dic86C2311yescharacteristic
102C22×Dic86C2312yes—
103C22×Dic86C2314yes—
104C22×Dic86C2312yes—
105C22×D172C2311yescharacteristic
106C22×C22⋊D43C2312yes—
107C22×C4×D43C2312yes—
108C22×C4×D43C2314yes—
109#13063325C2318yes—
110#13063325C2318yes—
111#13063325C23116yes—
112#13063325C23116yes—
113#13063324C23116yes—
114#13063324C23132yes—
115#13063323C23132yes—
116#13063320C23132yes—
117#13063320C23132yes—
118#13063320C23132yes—
119#13063320C23132yes—
120#13063319C23116yes—
121#13063318C23132yes—
122#13063318C23132yes—
123#13063317C23116yes—
124#13063317C2318yes—
125#13063317C23116yes—
126#13063316C23116yes—
127#13063316C23132yes—
128#13063315C23132yes—
129#13063315C23132yes—
130#13063315C23132yes—
131#13063315C23132yes—
132#13063313C2318yes—
133#13063313C23116yes—
134#13063311C23132yes—
135#13063308C23116yes—
136#13063307C23132yes—
137#13063304C23116yes—
138#13063304C2318yes—
139#13063304C23116yes—
140#13063303C23132yes—
141#13063303C23132yes—
142#13063301C23116yes—
143#13063301C23116yes—
144#13063301C23132yes—
145#13063299C2318yes—
146Q8×Dic43C23116yes—
147Q8×Dic43C23116yes—
148C4×Dic86C23116yes—
149C4×Dic86C23116yes—
150C4×Dic86C23116yes—
151C4×Dic86C23116yes—
152C4×Dic86C2318yes—
153C4×Dic86C23116yes—
154#13063290C23132yes—
155C4×D172C2318yes—
156C4×D172C23116yes—
157C4×C22⋊D43C23116yes—
158#13063284C23116yes—
159#13063283C23132yes—
160#13063283C23116yes—
161#13063282C23116yes—
162C2×C4⋊Dic43C2312yes—
163C2×C4⋊Dic43C2312yes—
164C2×C4⋊Dic43C2314yes—
165C2×C4⋊Dic43C2311yescharacteristic
166C2×C4⋊Dic43C2312yes—
167C2×C4⋊Dic43C2311yescharacteristic
168C2×C4⋊Dic43C2312yes—
169C2×C4⋊Dic43C2314yes—
170C2×C4⋊Dic43C2314yes—
171C2×Dic43⋊C4C2314yes—
172C2×Dic43⋊C4C2312yes—
173C2×Dic43⋊C4C2312yes—
174C2×Dic43⋊C4C2312yes—
175C2×Dic43⋊C4C2314yes—
176C2×Dic43⋊C4C2314yes—
177C2×Dic43⋊C4C2314yes—
178C2×Dic43⋊C4C2314yes—
179C2×Dic43⋊C4C2314yes—
180C2×Dic43⋊C4C2314yes—
181C2×Dic43⋊C4C2312yes—
182C4⋊C4×D43C23116yes—
183C2×C22⋊Dic43C2314yes—
184C2×C22⋊Dic43C2312yes—
185C2×(C2×D43)⋊C4C2312yes—
186C2×(C2×D43)⋊C4C2312yes—
187C2×(C2×D43)⋊C4C2312yes—
188C2×(C2×D43)⋊C4C2314yes—
189C2×(C2×D43)⋊C4C2314yes—
190C2×(C2×D43)⋊C4C2314yes—
191C2×(C2×D43)⋊C4C2312yes—
192C2×C4×Dic43C2312yes—
193C2×C4×Dic43C2314yes—
194C2×C4×Dic43C2314yes—
195C2×C4×Dic43C2314yes—
196C2×C4×Dic43C2314yes—
197C22×Q8×C43C2311yescharacteristic
198C22×Q8×C43C2311yescharacteristic
199C22×Q8×C43C2312yes—
200C23×C4×C43C2311yescharacteristic
201C23×C4×C43C2311yescharacteristic
202C23×C4×C43C2311yescharacteristic
203C4⋊Q8×C43C2318yes—
204C4⋊Q8×C43C2318yes—
205#125×C43C23116yes—
206C22⋊Q8×C43C2318yes—
207C22⋊Q8×C43C2318yes—
208C22⋊Q8×C43C23116yes—
209C4×Q8×C43C2318yes—
210C4×Q8×C43C23116yes—
211C4×Q8×C43C2318yes—
212#117×C43C23116yes—
213C2×C4⋊C4×C43C2312yes—
214C2×C4⋊C4×C43C2312yes—
215C2×C4⋊C4×C43C2312yes—
216C2×C4⋊C4×C43C2312yes—
217C2×C4⋊C4×C43C2312yes—
218C2×C4⋊C4×C43C2312yes—
219C2×C4⋊C4×C43C2311yescharacteristic
220C2×C4⋊C4×C43C2311yescharacteristic
221C2×C4⋊C4×C43C2312yes—
222C2×C22⋊C4×C43C2312yes—
223C2×C22⋊C4×C43C2312yes—
224C2×C42×C43C2311yescharacteristic
225C2×C42×C43C2311yescharacteristic
226C2×C42×C43C2311yescharacteristic
227C2×C42×C43C2311yescharacteristic
228C2×C42×C43C2318yes—
229C2×C42×C43C2312yes—
230C2×C42×C43C2312yes—
231C24×C43C2411yescharacteristic
232C23×D43C2412yes—
233C2×Q8×C43—24no—
234C2×Q8×C43—24no—
235C2×Q8×C43—44no—
236C2×Q8×C43C2414yes—
237C2×Q8×C43C2414yes—
238C2×Q8×C43C2418yes—
239C22×C4×C43—24no—
240C22×C4×C43—24no—
241C22×C4×C43—42no—
242C22×C4×C43C2411yescharacteristic
243C22×C4×C43C2411yescharacteristic
244C22×C4×C43C2411yescharacteristic
245C22×C4×C43C2411yescharacteristic
246C22×C4×C43C2414yes—
247C22×C4×C43C2414yes—
248C22×C4×C43C2412yes—
249C22×C4×C43C2412yes—
250C22×C4×C43C2412yes—
251C22×C4×C43C2412yes—
252C22×C4×C43C2414yes—
253C22×C4×C43C2411yescharacteristic
254C22×C4×C43C2411yescharacteristic
255C2×C22⋊D43—44no—
256C2×C22⋊D43C2418yes—
257C22×Dic43C2412yes—
258C22×Dic43C2414yes—
259C22×Dic43C2412yes—
260C22×Dic43C2412yes—
261C22×Dic43C2414yes—
262C2×D172—24no—
263C2×D172C2414yes—
264C2×C4×D43—28no—
265C2×C4×D43—48no—
266C2×C4×D43C2418yes—
267C2×C4×D43C24116yes—
268C2×Dic86—24no—
269C2×Dic86—28no—
270C2×Dic86—44no—
271C2×Dic86—48no—
272C2×Dic86C2418yes—
273C2×Dic86C2414yes—
274C2×Dic86C24116yes—
275C2×Dic86C2418yes—
276C4⋊C4×C43C2418yes—
277C4⋊C4×C43C2418yes—
278C4⋊C4×C43C2418yes—
279C4⋊C4×C43C2418yes—
280C4⋊C4×C43C2418yes—
281C4⋊C4×C43C2418yes—
282C4⋊C4×C43C2414yes—
283C4⋊C4×C43C2414yes—
284C4⋊C4×C43C2418yes—
285C22⋊C4×C43C2418yes—
286C22⋊C4×C43C2418yes—
287C42×C43C2414yes—
288C42×C43C2414yes—
289C42×C43C2414yes—
290C42×C43C2414yes—
291C42×C43C2418yes—
292C42×C43C2418yes—
293C22⋊Dic43C24116yes—
294C22⋊Dic43C2418yes—
295(C2×D43)⋊C4C2418yes—
296(C2×D43)⋊C4C2418yes—
297(C2×D43)⋊C4C2418yes—
298(C2×D43)⋊C4C24116yes—
299(C2×D43)⋊C4C24116yes—
300(C2×D43)⋊C4C24116yes—
301(C2×D43)⋊C4C2418yes—
302C4⋊Dic43C2418yes—
303C4⋊Dic43C2418yes—
304C4⋊Dic43C24116yes—
305C4⋊Dic43C2414yes—
306C4⋊Dic43C2418yes—
307C4⋊Dic43C2414yes—
308C4⋊Dic43C2418yes—
309C4⋊Dic43C24116yes—
310C4⋊Dic43C24116yes—
311Dic43⋊C4C24116yes—
312Dic43⋊C4C2418yes—
313Dic43⋊C4C2418yes—
314Dic43⋊C4C2418yes—
315Dic43⋊C4C24116yes—
316Dic43⋊C4C24116yes—
317Dic43⋊C4C24116yes—
318Dic43⋊C4C24116yes—
319Dic43⋊C4C24116yes—
320Dic43⋊C4C24116yes—
321Dic43⋊C4C2418yes—
322C4×Dic43C2418yes—
323C4×Dic43C24116yes—
324C4×Dic43C24116yes—
325C4×Dic43C24116yes—
326C4×Dic43C24116yes—
327C23×C43—22no—
328C23×C43—22no—
329C23×C43—22no—
330C23×C43C2512yes—
331C23×C43C2511yescharacteristic
332C22×D43—24no—
333C22×D43—24no—
334C22×D43—24no—
335C22×D43C2514yes—
336Q8×C43—28no—
337Q8×C43—28no—
338Q8×C43—48no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—24no—
342C2×C4×C43—24no—
343C2×C4×C43—22no—
344C2×C4×C43—24no—
345C2×C4×C43—24no—
346C2×C4×C43—22no—
347C2×C4×C43—28no—
348C2×C4×C43—28no—
349C2×C4×C43—44no—
350C2×C4×C432−1+414yes—
351C2×C4×C432−1+414yes—
352C2×C4×C43C2512yes—
353C2×C4×C43C2514yes—
354C2×C4×C43C2514yes—
355C2×C4×C43C2514yes—
356C2×C4×C43C2512yes—
357C2×C4×C43C2512yes—
358C2×C4×C43C2514yes—
359C2×C4×C43C2512yes—
360C2×C4×C43C2512yes—
361C2×C4×C43C2512yes—
362C22⋊D43—48no—
363C2×Dic43—24no—
364C2×Dic43—28no—
365C2×Dic43—24no—
366C2×Dic43—28no—
367C2×Dic43—24no—
368C2×Dic43C2514yes—
369C2×Dic43C2514yes—
370C2×Dic43C2518yes—
371C2×Dic43C2514yes—
372C2×Dic43C2518yes—
373D172—28no—
374C4×D43—216no—
375C4×D43—416no—
376Dic86—216no—
377Dic86—28no—
378Dic86—48no—
379Dic86—416no—
380C2×#3555—431nomaximal, Sylow
381C22×C43—22no—
382C22×C43—22no—
383C22×C43—22no—
384C22×C43—44no—
385C22×C43C2×2−1+412yes—
386C22×C43C2×2−1+412yes—
387C22×C43#58512yes—
388C22×C43C2611yescharacteristic
389C2×D43—24no—
390C2×D43—24no—
391C2×D43—24no—
392C2×D43—48no—
393C4×C43—22no—
394C4×C43—22no—
395C4×C43—24no—
396C4×C43—24no—
397C4×C43—22no—
398C4×C43—24no—
399C4×C43—24no—
400C4×C43—22no—
401C4×C43C2×2−1+414yes—
402C4×C43C2×2−1+414yes—
403Dic43—24no—
404Dic43—28no—
405Dic43—24no—
406Dic43—28no—
407Dic43—24no—
408#3555—4332no—
409C2×#563—434no—
410C2×Q82—431no—
411C2×#557—432no—
412C2×#557—431no—
413C2×#556—432no—
414C2×#556—432no—
415C2×#556—431no—
416C2×#554—431no—
417C2×#552—432no—
418C2×#544—432no—
419C2×#542—432no—
420C2×#541—432no—
421C2×#541—434no—
422C2×#541—432no—
423C2×#533—431no—
424C2×#533D4311yescharacteristic, complemented
425C2×#529—431no—
426C2×C43—42no—
427C2×C43#355514yescomplemented
428C2×C43C22×2−1+411yescharacteristic
429C2×C43C22×2−1+411yescharacteristic
430C2×C43C2×#58511yescharacteristic
431D43—44no—
432#563—4364no—
433Q82—4316no—
434#557—4332no—
435#557—4316no—
436#556—4332no—
437#556—4332no—
438#556—4316no—
439#554—4316no—
440#552—4332no—
441#544—4332no—
442#542—4332no—
443#541—4332no—
444#541—4364no—
445#541—4332no—
446#533—4316no—
447#533C2×D43116yescomplemented
448C2×C4⋊Q8—434no—
449C2×C4⋊Q8—434no—
450C2×C4⋊Q8—432no—
451C2×C4⋊Q8—431no—
452C2×C4⋊Q8—431no—
453C2×C4⋊Q8—432no—
454C2×C4⋊Q8—432no—
455C2×C4⋊Q8C2×D4311yescharacteristic
456C2×C4⋊Q8C2×D4311yescharacteristic
457#529—4316no—
458C2×#126—434no—
459C2×#126—434no—
460C2×#126—434no—
461C2×#126—434no—
462C2×#126—434no—
463C2×#126—434no—
464C2×#126—432no—
465C2×#125—434no—
466C2×#125—434no—
467C2×#125—434no—
468C2×#125—434no—
469C2×#125—434no—
470C2×#125—432no—
471C2×#125—431no—
472C2×#125—432no—
473C2×#125—432no—
474C2×#125C2×D4312yes—
475C2×#124—434no—
476C2×#124—431no—
477C2×#124—432no—
478C2×#123—432no—
479C2×#123—434no—
480C2×C22⋊Q8—432no—
481C2×C22⋊Q8—432no—
482C2×C22⋊Q8—434no—
483C2×C22⋊Q8—431no—
484C2×C22⋊Q8—432no—
485C2×C22⋊Q8—432no—
486C2×C22⋊Q8—434no—
487C2×C22⋊Q8—434no—
488C2×C22⋊Q8C2×D4311yescharacteristic
489C2×C22⋊Q8C2×D4311yescharacteristic
490C2×C22⋊Q8C2×D4312yes—
491C2×#121—431no—
492C2×C4×Q8—432no—
493C2×C4×Q8—432no—
494C2×C4×Q8—434no—
495C2×C4×Q8—431no—
496C2×C4×Q8—432no—
497C2×C4×Q8—432no—
498C2×C4×Q8—432no—
499C2×C4×Q8—432no—
500C2×C4×Q8—432no—
501C2×C4×Q8C2×D4311yescharacteristic
502C2×C4×Q8C2×D4312yes—
503C2×C4×Q8C2×D4311yescharacteristic
504C2×C4×D4—432no—
505C2×C4×D4—431no—
506C2×C4×D4—432no—
507C2×#117—432no—
508C2×#117—434no—
509C2×#117—432no—
510C2×#117—432no—
511C2×#117C2×D4312yes—
512C22×C4⋊C4—432no—
513C22×C42C2×D4311yescharacteristic
514C43C2×#355511yescharacteristic, complemented, Sylow
515C22×Q8—431no—
516C22×Q8—432no—
517C22×Q8—432no—
518C22×Q8—434no—
519C22×Q8C22×D4311yescharacteristic
520C22×Q8C22×D4311yescharacteristic
521C22×Q8C22×D4312yes—
522C22×D4—432no—
523C22×D4—431no—
524C23×C4—432no—
525C23×C4—434no—
526C23×C4C22×D4311yescharacteristic
527C23×C4C22×D4311yescharacteristic
528C23×C4C22×D4311yescharacteristic
529C4⋊Q8—4332no—
530C4⋊Q8—4332no—
531C4⋊Q8—4316no—
532C4⋊Q8—438no—
533C4⋊Q8—438no—
534C4⋊Q8—4316no—
535C4⋊Q8—4316no—
536C4⋊Q8C22×D4318yes—
537C4⋊Q8C22×D4318yes—
538#126—4332no—
539#126—4332no—
540#126—4332no—
541#126—4332no—
542#126—4332no—
543#126—4332no—
544#126—4316no—
545#125—4332no—
546#125—4332no—
547#125—4332no—
548#125—4332no—
549#125—4332no—
550#125—4316no—
551#125—438no—
552#125—4316no—
553#125—4316no—
554#125C22×D43116yes—
555#124—4332no—
556#124—438no—
557#124—4316no—
558#123—4316no—
559#123—4332no—
560C22⋊Q8—4316no—
561C22⋊Q8—4316no—
562C22⋊Q8—4332no—
563C22⋊Q8—438no—
564C22⋊Q8—4316no—
565C22⋊Q8—4316no—
566C22⋊Q8—4332no—
567C22⋊Q8—4332no—
568C22⋊Q8C22×D4318yes—
569C22⋊Q8C22×D4318yes—
570C22⋊Q8C22×D43116yes—
571#121—438no—
572C4×Q8—4316no—
573C4×Q8—4316no—
574C4×Q8—4332no—
575C4×Q8—438no—
576C4×Q8—4316no—
577C4×Q8—4316no—
578C4×Q8—4316no—
579C4×Q8—4316no—
580C4×Q8—4316no—
581C4×Q8C22×D4318yes—
582C4×Q8C22×D43116yes—
583C4×Q8C22×D4318yes—
584C4×D4—4316no—
585C4×D4—438no—
586C4×D4—4316no—
587#117—4316no—
588#117—4332no—
589#117—4316no—
590#117—4316no—
591#117C22×D43116yes—
592C2×C4⋊C4—432no—
593C2×C4⋊C4—434no—
594C2×C4⋊C4—432no—
595C2×C4⋊C4—432no—
596C2×C4⋊C4—434no—
597C2×C4⋊C4—432no—
598C2×C4⋊C4—431no—
599C2×C4⋊C4—432no—
600C2×C4⋊C4—432no—
601C2×C4⋊C4—431no—
602C2×C4⋊C4—434no—
603C2×C4⋊C4—434no—
604C2×C4⋊C4—434no—
605C2×C4⋊C4—434no—
606C2×C4⋊C4—434no—
607C2×C4⋊C4—432no—
608C2×C4⋊C4—434no—
609C2×C4⋊C4—432no—
610C2×C4⋊C4—434no—
611C2×C4⋊C4—434no—
612C2×C4⋊C4—4316no—
613C2×C4⋊C4C22×D4311yescharacteristic
614C2×C4⋊C4C22×D4312yes—
615C2×C4⋊C4C22×D4311yescharacteristic
616C2×C4⋊C4C22×D4312yes—
617C2×C4⋊C4C22×D4312yes—
618C2×C4⋊C4C22×D4312yes—
619C2×C4⋊C4C22×D4312yes—
620C2×C4⋊C4C22×D4312yes—
621C2×C4⋊C4C22×D4312yes—
622C2×C22⋊C4—434no—
623C2×C22⋊C4—432no—
624C2×C22⋊C4—432no—
625C2×C22⋊C4—432no—
626C2×C22⋊C4—432no—
627C2×C22⋊C4—434no—
628C2×C22⋊C4—434no—
629C2×C22⋊C4—432no—
630C2×C22⋊C4—434no—
631C2×C22⋊C4C22×D4312yes—
632C2×C22⋊C4C22×D4312yes—
633C2×C42—434no—
634C2×C42—432no—
635C2×C42—434no—
636C2×C42—434no—
637C2×C42—434no—
638C2×C42C22×D4311yescharacteristic
639C2×C42C22×D4312yes—
640C2×C42C22×D4312yes—
641C2×C42C22×D4311yescharacteristic
642C2×C42C22×D4311yescharacteristic
643C2×C42C22×D4311yescharacteristic
644C2×C42C22×D4318yes—
645C24—432no—
646C24C23×D4311yescharacteristic
647C2×Q8—24no—
648C2×Q8—24no—
649C2×Q8—44no—
650C2×Q8—434no—
651C2×Q8—438no—
652C2×Q8—438no—
653C2×Q8—4316no—
654C2×Q8—864no—
655C2×Q8—868no—
656C2×Q8—1724no—
657C2×Q8—1728no—
658C2×Q8C23×D4314yes—
659C2×Q8C23×D4314yes—
660C2×Q8C23×D4318yes—
661C2×D4—438no—
662C2×D4—434no—
663C2×D4—864no—
664C2×D4—1724no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—42no—
668C22×C4—434no—
669C22×C4—432no—
670C22×C4—432no—
671C22×C4—432no—
672C22×C4—434no—
673C22×C4—438no—
674C22×C4—4316no—
675C22×C4—868no—
676C22×C4—1728no—
677C22×C4C23×D4314yes—
678C22×C4C23×D4314yes—
679C22×C4C23×D4311yescharacteristic
680C22×C4C23×D4312yes—
681C22×C4C23×D4312yes—
682C22×C4C23×D4312yes—
683C22×C4C23×D4311yescharacteristic
684C22×C4C23×D4311yescharacteristic
685C22×C4C23×D4311yescharacteristic
686C22×C4C23×D4312yes—
687C22×C4C23×D4314yes—
688C22×C4C23×D4311yescharacteristic
689C22×C4C23×D4311yescharacteristic
690C4⋊C4—438no—
691C4⋊C4—4316no—
692C4⋊C4—438no—
693C4⋊C4—438no—
694C4⋊C4—4316no—
695C4⋊C4—438no—
696C4⋊C4—434no—
697C4⋊C4—438no—
698C4⋊C4—438no—
699C4⋊C4—434no—
700C4⋊C4—4316no—
701C4⋊C4—4316no—
702C4⋊C4—4316no—
703C4⋊C4—4316no—
704C4⋊C4—4316no—
705C4⋊C4—438no—
706C4⋊C4—4316no—
707C4⋊C4—438no—
708C4⋊C4—4316no—
709C4⋊C4—4316no—
710C4⋊C4C23×D4314yes—
711C4⋊C4C23×D4318yes—
712C4⋊C4C23×D4314yes—
713C4⋊C4C23×D4318yes—
714C4⋊C4C23×D4318yes—
715C4⋊C4C23×D4318yes—
716C4⋊C4C23×D4318yes—
717C4⋊C4C23×D4318yes—
718C4⋊C4C23×D4318yes—
719C22⋊C4—4316no—
720C22⋊C4—438no—
721C22⋊C4—438no—
722C22⋊C4—438no—
723C22⋊C4—438no—
724C22⋊C4—4316no—
725C22⋊C4—4316no—
726C22⋊C4—438no—
727C22⋊C4—4316no—
728C22⋊C4C23×D4318yes—
729C22⋊C4C23×D4318yes—
730C42—4316no—
731C42—438no—
732C42—4316no—
733C42—4316no—
734C42—4316no—
735C42C23×D4314yes—
736C42C23×D4314yes—
737C42C23×D4314yes—
738C42C23×D4314yes—
739C42C23×D4318yes—
740C42C23×D4318yes—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—434no—
745C23—864no—
746C23—864no—
747C23—864no—
748C23C24×D4312yes—
749C23C24×D4311yescharacteristic
750Q8—28no—
751Q8—28no—
752Q8—48no—
753Q8—868no—
754Q8—8616no—
755Q8—1728no—
756Q8—17216no—
757D4—868no—
758D4—1728no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—44no—
770C2×C4—438no—
771C2×C4—434no—
772C2×C4—434no—
773C2×C4—434no—
774C2×C4—438no—
775C2×C4—864no—
776C2×C4—868no—
777C2×C4—864no—
778C2×C4—868no—
779C2×C4—864no—
780C2×C4—8616no—
781C2×C4—17216no—
782C2×C4#1306337214yes—
783C2×C4#1306337314yes—
784C2×C4C24×D4312yes—
785C2×C4C24×D4314yes—
786C2×C4C24×D4314yes—
787C2×C4C24×D4314yes—
788C2×C4C24×D4312yes—
789C2×C4C24×D4312yes—
790C2×C4C24×D4312yes—
791C2×C4C24×D4314yes—
792C2×C4C24×D4312yes—
793C2×C4C24×D4312yes—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—44no—
798C22—864no—
799C22—864no—
800C22—864no—
801C22—1728no—
802C22C2×#1306337212yes—
803C22C2×#1306337312yes—
804C22#1458373512yes—
805C22C25×D4311yescharacteristic
806C4—22no—
807C4—24no—
808C4—24no—
809C4—22no—
810C4—22no—
811C4—22no—
812C4—24no—
813C4—24no—
814C4—864no—
815C4—868no—
816C4—864no—
817C4—868no—
818C4—864no—
819C4C2×#1306337214yes—
820C4C2×#1306337314yes—
821C2—42no—
822C2—1724no—
823C2#1914908314yesdirect product factor
824C2C22×#1306337211yescharacteristic
825C2C22×#1306337311yescharacteristic
826C2C2×#1458373511yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#533C2
socleC23×C43C25
prime radicalC2×#13063299C22
hypercenterC2×#533D43
hypocenterC43C2×#3555
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #19149083C2direct (N × H)
2. C2×#14583650C2semidirect
3. C2×Q8×Dic86C2semidirect
4. C2×#14583628C2semidirect
5. C2×#14583627C2semidirect
6. C2×#14583622C2semidirect
7. C2×#14583622C2semidirect
8. C2×#14583620C2semidirect
9. C2×#14583609C2semidirect
10. C2×#14583583C2semidirect
11. C2×#14583526C2semidirect
13. C2×#14583511C2semidirect
14. C2×#14583510C2semidirect
15. C2×#14583508C2semidirect
16. C2×#14583456C2semidirect
18. C2×C43×#533C2semidirect
19. #14583650C22semidirect
20. Q8×Dic86C22semidirect
21. #14583628C22semidirect
22. #14583627C22semidirect
23. #14583622C22semidirect
24. #14583622C22semidirect
25. #14583620C22semidirect
26. #14583609C22semidirect
27. #14583583C22semidirect
28. #14583526C22semidirect
30. #14583511C22semidirect
31. #14583510C22semidirect
32. #14583508C22semidirect
33. #14583456C22semidirect
89. C43×#533C22semidirect
424. C2×#533D43semidirect
427. C2×C43#3555semidirect
447. #533C2×D43semidirect
514. C43C2×#3555semidirect
823. C2#19149083direct (N × H)

Maximal subgroups

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

subgroupindex
#191490832
C2×#145836502
C2×Q8×Dic862
C2×#145836282
C2×#145836272
C2×#145836222
C2×#145836202
C2×#145836092
C2×#145835832
C2×#145835262
C2×#145835202
C2×#145835112
C2×#145835102
C2×#145835082
C2×#145834562
C2×#145834332
C2×C43×#5332
C2×#355543