Finite Group Databasebeta

← C2×#19148496 #26004964

Subgroups — C2×#19148496 #26004964

Order 11008.

7758 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148496C2132yesmaximal, direct product factor
2C2×#14583618C212yesmaximal, complemented
3C2×#14583613C212yesmaximal, complemented
4C2×#14583608C212yesmaximal, complemented
5C2×#14583599C212yesmaximal, complemented
6C2×#14583596C212yesmaximal, complemented
7C2×#14583557C212yesmaximal, complemented
8C2×#14583556C212yesmaximal, complemented
9C2×#14583548C212yesmaximal, complemented
10C2×#14583516C212yesmaximal, complemented
11C2×#14583514C212yesmaximal, complemented
12C2×#14583478C212yesmaximal, complemented
13C2×#14583456C211yesmaximal, characteristic, complemented
14C2×#14583454C211yesmaximal, characteristic, complemented
15C2×#14583447C211yesmaximal, characteristic, complemented
16C2×#14583447C211yesmaximal, characteristic, complemented
17C2×C4⋊Q8×D43C211yesmaximal, characteristic, complemented
18C2×#14583378C212yesmaximal, complemented
19C2×C4×#10621898C211yesmaximal, characteristic, complemented
20C2×C43×#532C211yesmaximal, characteristic, complemented
21C22×#10621898C2211yescharacteristic
22C22×#10621900C2212yes—
23C22×#10621900C2212yes—
24C22×Q8×D43C2212yes—
25#14583618C22132yescomplemented
26#14583613C22132yescomplemented
27#14583608C22132yescomplemented
28#14583599C22132yescomplemented
29#14583596C22132yescomplemented
30#14583557C22132yescomplemented
31#14583556C22132yescomplemented
32#14583548C22132yescomplemented
33#14583516C22132yescomplemented
34#14583514C22132yescomplemented
35#14583478C22132yescomplemented
36#14583456C22116yescomplemented
37#14583454C22116yescomplemented
38#14583447C22116yescomplemented
39#14583447C22116yescomplemented
40C2×#13063325C2211yescharacteristic
41C2×#13063325C2211yescharacteristic
42C2×#13063324C2212yes—
43C2×#13063324C2212yes—
44C2×#13063323C2212yes—
45C4⋊Q8×D43C22116yescomplemented
46C2×#13063318C2214yes—
47C2×#13063318C2214yes—
48C2×#13063317C2212yes—
49C2×#13063316C2212yes—
50C2×#13063312C2212yes—
51C2×#13063312C2214yes—
52C2×#13063312C2212yes—
53C2×#13063311C2214yes—
54C2×#13063308C2214yes—
55C2×#13063306C2214yes—
56C2×#13063305C2212yes—
57C2×#13063304C2212yes—
58C2×#13063304C2214yes—
59C2×#13063304C2212yes—
60C2×#13063302C2214yes—
61C2×#13063302C2214yes—
62C2×#13063301C2212yes—
63C2×#13063298C2214yes—
64C2×#13063297C2214yes—
65C2×#13063296C2212yes—
66C2×#13063296C2214yes—
67C2×#13063296C2212yes—
68C2×#13063296C2212yes—
69C2×#13063296C2212yes—
70#14583378C22132yescomplemented
71C4×#10621898C22116yescomplemented
72C2×Q8×Dic43C2212yes—
73C2×C4×Dic86C2212yes—
74C2×C4×Dic86C2212yes—
75C2×C4×Dic86C2211yescharacteristic
76C2×C4×Dic86C2211yescharacteristic
77C2×#13063290C2212yes—
78C2×C4×D172C2211yescharacteristic
79C2×C4×D172C2211yescharacteristic
80C2×D4×Dic43C2212yes—
81C2×D4×Dic43C2212yes—
82C2×D4×Dic43C2212yes—
83C2×D4×Dic43C2212yes—
84C2×C4×C22⋊D43C2214yes—
85C2×C4×C22⋊D43C2211yescharacteristic
86C2×C4×C22⋊D43C2211yescharacteristic
87C2×C4×C22⋊D43C2211yescharacteristic
88C2×C4×C22⋊D43C2211yescharacteristic
89C2×(C22⋊D43)⋊C4C2214yes—
90C2×#13063284C2212yes—
91C2×#13063284C2211yescharacteristic
92C2×#13063283C2212yes—
93C2×#13063282C2211yescharacteristic
94C2×#13063282C2211yescharacteristic
95C2×#13063281C2214yes—
96C22×Dic43⋊C4C2214yes—
97C2×C4⋊C4×D43C2212yes—
98C2×C4⋊C4×D43C2212yes—
99C2×C42×D43C2211yescharacteristic
100C2×C42×D43C2211yescharacteristic
101C22×#41×C43C2212yes—
102C43×#532C22116yescomplemented
103C2×C4⋊Q8×C43C2211yescharacteristic
104C2×#127×C43C2211yescharacteristic
105C2×#124×C43C2212yes—
106C2×#121×C43C2212yes—
107C2×#121×C43C2212yes—
108C2×C4×D4×C43C2212yes—
109C2×C4×D4×C43C2212yes—
110C22×C42×C43C2211yescharacteristic
111C2×#10621898—28no—
112C2×#10621898C2318yes—
113C2×#10621900—216no—
114C2×#10621900—48no—
115C2×#10621900C23116yes—
116C2×#10621900C23116yes—
117C22×Dic86C2312yes—
118C22×Dic86C2311yescharacteristic
119C22×Dic86C2312yes—
120C22×Dic86C2314yes—
121C2×Q8×D43—48no—
122C2×Q8×D43C23116yes—
123C22×D172C2311yescharacteristic
124C22×C22⋊D43C2314yes—
125C22×C22⋊D43C2311yescharacteristic
126C22×C22⋊D43C2311yescharacteristic
127C22×C22⋊D43C2314yes—
128C23×Dic43C2314yes—
129C23×Dic43C2314yes—
130C22×C4×D43C2311yescharacteristic
131C22×C4×D43C2311yescharacteristic
132C22×C4×D43C2311yescharacteristic
133C22×C4×D43C2311yescharacteristic
134C22×C4×D43C2311yescharacteristic
135C22×C4×D43C2314yes—
136C22×C4×D43C2311yescharacteristic
137#13063325C2318yes—
138#13063325C2318yes—
139#13063324C23116yes—
140#13063324C23116yes—
141#13063323C23116yes—
142#13063318C23132yes—
143#13063318C23132yes—
144#13063317C23116yes—
145#13063316C23116yes—
146#13063312C23132yes—
147#13063312C23116yes—
148#13063312C23116yes—
149#13063311C23132yes—
150#13063308C23132yes—
151#13063306C23132yes—
152#13063305C23116yes—
153#13063304C23132yes—
154#13063304C23116yes—
155#13063304C23116yes—
156#13063302C23132yes—
157#13063302C23132yes—
158#13063301C23116yes—
159#13063298C23132yes—
160#13063297C23132yes—
161#13063296C23116yes—
162#13063296C23132yes—
163#13063296C23116yes—
164#13063296C23116yes—
165#13063296C23116yes—
166Q8×Dic43C23116yes—
167C4×Dic86C23116yes—
168C4×Dic86C2318yes—
169C4×Dic86C2318yes—
170C4×Dic86C23116yes—
171#13063290C23116yes—
172C4×D172C2318yes—
173C4×D172C2318yes—
174D4×Dic43C23116yes—
175D4×Dic43C23116yes—
176D4×Dic43C23116yes—
177D4×Dic43C23116yes—
178C4×C22⋊D43C2318yes—
179C4×C22⋊D43C23132yes—
180C4×C22⋊D43C2318yes—
181C4×C22⋊D43C2318yes—
182C4×C22⋊D43C2318yes—
183(C22⋊D43)⋊C4C23132yes—
184#13063284C23116yes—
185#13063284C2318yes—
186#13063283C23116yes—
187#13063282C2318yes—
188#13063282C2318yes—
189#13063281C23132yes—
190C2×C4⋊Dic43C2312yes—
191C2×C4⋊Dic43C2312yes—
192C2×C4⋊Dic43C2312yes—
193C2×C4⋊Dic43C2311yescharacteristic
194C2×C4⋊Dic43C2311yescharacteristic
195C2×C4⋊Dic43C2312yes—
196C2×C4⋊Dic43C2314yes—
197C2×Dic43⋊C4C2314yes—
198C2×Dic43⋊C4C2314yes—
199C2×Dic43⋊C4C2311yescharacteristic
200C2×Dic43⋊C4C23132yes—
201C2×Dic43⋊C4C2314yes—
202C2×Dic43⋊C4C2314yes—
203C2×Dic43⋊C4C2311yescharacteristic
204C2×Dic43⋊C4C2311yescharacteristic
205C2×Dic43⋊C4C2311yescharacteristic
206C2×Dic43⋊C4C2314yes—
207C4⋊C4×D43C23116yes—
208C4⋊C4×D43C23116yes—
209C2×C22⋊Dic43C2314yes—
210C2×C22⋊Dic43C2311yescharacteristic
211C2×C22⋊Dic43C2311yescharacteristic
212C2×C22⋊Dic43C2314yes—
213C2×C22⋊Dic43C2314yes—
214C2×C22⋊Dic43C2314yes—
215C2×C22⋊Dic43C2314yes—
216C2×(C2×D43)⋊C4C2311yescharacteristic
217C2×(C2×D43)⋊C4C2311yescharacteristic
218C2×(C2×D43)⋊C4C2311yescharacteristic
219C2×(C2×D43)⋊C4C2311yescharacteristic
220C2×(C2×D43)⋊C4C2314yes—
221C2×C4×Dic43C2311yescharacteristic
222C2×C4×Dic43C2311yescharacteristic
223C2×C4×Dic43C2311yescharacteristic
224C2×C4×Dic43C2311yescharacteristic
225C2×C4×Dic43C2311yescharacteristic
226C2×C4×Dic43C2311yescharacteristic
227C2×C4×Dic43C2314yes—
228C2×C4×Dic43C2314yes—
229C42×D43C2318yes—
230C42×D43C2318yes—
231C2×#41×C43—48no—
232C2×#41×C43C23116yes—
233C22×Q8×C43C2312yes—
234C22×D4×C43C2312yes—
235C22×D4×C43C2312yes—
236C22×D4×C43C2312yes—
237C22×D4×C43C2314yes—
238C23×C4×C43C2311yescharacteristic
239C23×C4×C43C2311yescharacteristic
240C23×C4×C43C2311yescharacteristic
241C23×C4×C43C2314yes—
242C4⋊Q8×C43C2318yes—
243#127×C43C2318yes—
244#124×C43C23116yes—
245#121×C43C23116yes—
246#121×C43C23116yes—
247C4×D4×C43C23116yes—
248C4×D4×C43C23116yes—
249C2×C4⋊C4×C43C2312yes—
250C2×C4⋊C4×C43C2312yes—
251C2×C22⋊C4×C43C2314yes—
252C2×C22⋊C4×C43C2314yes—
253C2×C42×C43C2311yescharacteristic
254C2×C42×C43C2311yescharacteristic
255C2×C42×C43C2311yescharacteristic
256C2×C42×C43C2311yescharacteristic
257C2×C42×C43C2318yes—
258C24×C43C2414yes—
259C24×C43C2411yescharacteristic
260C23×D43C2411yescharacteristic
261C23×D43C2411yescharacteristic
262#41×C43—432no—
263C2×Q8×C43—28no—
264C2×Q8×C43C2418yes—
265C2×D4×C43—28no—
266C2×D4×C43—28no—
267C2×D4×C43—28no—
268C2×D4×C43—48no—
269C2×D4×C43C2418yes—
270C2×D4×C43C2418yes—
271C2×D4×C43C2418yes—
272C2×D4×C43C24116yes—
273C22×C4×C43—24no—
274C22×C4×C43—24no—
275C22×C4×C43—24no—
276C22×C4×C43—48no—
277C22×C4×C43C2411yescharacteristic
278C22×C4×C43C2411yescharacteristic
279C22×C4×C43C2414yes—
280C22×C4×C43C2414yes—
281C22×C4×C43C2411yescharacteristic
282C22×C4×C43C2414yes—
283C22×C4×C43C2414yes—
284C22×C4×C43C24116yes—
285C22×C4×C43C2411yescharacteristic
286C22×C4×C43C2411yescharacteristic
287C22×C4×C43C2411yescharacteristic
288C2×C22⋊D43—24no—
289C2×C22⋊D43—216no—
290C2×C22⋊D43—24no—
291C2×C22⋊D43—48no—
292C2×C22⋊D43C24116yes—
293C2×C22⋊D43C2414yes—
294C2×C22⋊D43C2414yes—
295C2×C22⋊D43C24116yes—
296C22×Dic43—216no—
297C22×Dic43—48no—
298C22×Dic43C2411yescharacteristic
299C22×Dic43C2411yescharacteristic
300C22×Dic43C2411yescharacteristic
301C22×Dic43C2414yes—
302C22×Dic43C2411yescharacteristic
303C22×Dic43C2411yescharacteristic
304C22×Dic43C2414yes—
305C22×Dic43C24116yes—
306C22×Dic43C24116yes—
307C22×Dic43C2411yescharacteristic
308Q8×D43—432no—
309#10621900—264no—
310#10621900—432no—
311#10621898—232no—
312C2×D172—24no—
313C2×D172C2414yes—
314C2×C4×D43—24no—
315C2×C4×D43—24no—
316C2×C4×D43—24no—
317C2×C4×D43—24no—
318C2×C4×D43—24no—
319C2×C4×D43—48no—
320C2×C4×D43#4118yescomplemented
321C2×C4×D43C2414yes—
322C2×C4×D43C2414yes—
323C2×C4×D43C2414yes—
324C2×C4×D43C2414yes—
325C2×C4×D43C2414yes—
326C2×C4×D43C24116yes—
327C2×C4×D43C2414yes—
328C2×Dic86—28no—
329C2×Dic86—28no—
330C2×Dic86—24no—
331C2×Dic86—48no—
332C2×Dic86C2418yes—
333C2×Dic86C2414yes—
334C2×Dic86C2418yes—
335C2×Dic86C24116yes—
336C4⋊C4×C43C2418yes—
337C4⋊C4×C43C2418yes—
338C22⋊C4×C43C24116yes—
339C22⋊C4×C43C24116yes—
340C42×C43C2414yes—
341C42×C43C2414yes—
342C42×C43C2414yes—
343C42×C43C2414yes—
344C22⋊Dic43C24116yes—
345C22⋊Dic43C2414yes—
346C22⋊Dic43C2414yes—
347C22⋊Dic43C24116yes—
348C22⋊Dic43C24116yes—
349C22⋊Dic43C24116yes—
350C22⋊Dic43C24116yes—
351(C2×D43)⋊C4C2414yes—
352(C2×D43)⋊C4C2414yes—
353(C2×D43)⋊C4C2414yes—
354(C2×D43)⋊C4C2414yes—
355(C2×D43)⋊C4C24116yes—
356C4⋊Dic43C2418yes—
357C4⋊Dic43C2418yes—
358C4⋊Dic43C2418yes—
359C4⋊Dic43C2414yes—
360C4⋊Dic43C2414yes—
361C4⋊Dic43C2418yes—
362C4⋊Dic43C24116yes—
363Dic43⋊C4C24116yes—
364Dic43⋊C4C24116yes—
365Dic43⋊C4C2414yes—
366Dic43⋊C4C24116yes—
367Dic43⋊C4C24116yes—
368Dic43⋊C4C2414yes—
369Dic43⋊C4C2414yes—
370Dic43⋊C4C2414yes—
371Dic43⋊C4C24116yes—
372C4×Dic43C2414yes—
373C4×Dic43C2414yes—
374C4×Dic43C2414yes—
375C4×Dic43C2414yes—
376C4×Dic43C2414yes—
377C4×Dic43C2414yes—
378C4×Dic43C24116yes—
379C4×Dic43C24116yes—
380C23×C43—28no—
381C23×C43—22no—
382C23×C43—28no—
383C23×C43—22no—
384C23×C43—22no—
385C23×C43—28no—
386C23×C43C2512yes—
387C23×C43C2518yes—
388C23×C43C2511yescharacteristic
389C22×D43—22no—
390C22×D43—22no—
391C22×D43—22no—
392C22×D43—22no—
393C22×D43—22no—
394C22×D43C2×#4114yes—
395C22×D43C2512yes—
396C22×D43C2512yes—
397Q8×C43—216no—
398D4×C43—216no—
399D4×C43—216no—
400D4×C43—216no—
401D4×C43—416no—
402C2×C4×C43—22no—
403C2×C4×C43—28no—
404C2×C4×C43—22no—
405C2×C4×C43—22no—
406C2×C4×C43—28no—
407C2×C4×C43—28no—
408C2×C4×C43—28no—
409C2×C4×C43—416no—
410C2×C4×C43C2×#4114yes—
411C2×C4×C43H(5,𝔽2)14yes—
412C2×C4×C432−1+414yes—
413C2×C4×C43C2512yes—
414C2×C4×C43C2518yes—
415C2×C4×C43C2512yes—
416C2×C4×C43C2512yes—
417C2×C4×C43C2512yes—
418C2×C4×C43C2512yes—
419C2×C4×C43C2512yes—
420C22⋊D43—28no—
421C22⋊D43—232no—
422C22⋊D43—28no—
423C22⋊D43—416no—
424C2×Dic43—22no—
425C2×Dic43—28no—
426C2×Dic43—28no—
427C2×Dic43—22no—
428C2×Dic43—22no—
429C2×Dic43—22no—
430C2×Dic43—22no—
431C2×Dic43—232no—
432C2×Dic43—416no—
433C2×Dic43C2×#4114yes—
434C2×Dic43C2512yes—
435C2×Dic43C2512yes—
436C2×Dic43C2512yes—
437C2×Dic43C2518yes—
438C2×Dic43C2512yes—
439C2×Dic43C2512yes—
440C2×Dic43C2518yes—
441C2×Dic43C2512yes—
442D172—28no—
443C4×D43—28no—
444C4×D43—28no—
445C4×D43—28no—
446C4×D43—28no—
447C4×D43—28no—
448C4×D43—416no—
449C4×D43C2×#41116yescomplemented
450Dic86—216no—
451Dic86—216no—
452Dic86—28no—
453Dic86—416no—
454C2×#3511—431nomaximal, Sylow
455C22×C43—28no—
456C22×C43—22no—
457C22×C43—28no—
458C22×C43—22no—
459C22×C43—22no—
460C22×C43—28no—
461C22×C43—416no—
462C22×C43—44no—
463C22×C43C22×#4112yes—
464C22×C43C2×H(5,𝔽2)12yes—
465C22×C43C2×2−1+412yes—
466C22×C43C2611yescharacteristic
467C2×D43—22no—
468C2×D43—22no—
469C2×D43—28no—
470C2×D43—22no—
471C2×D43—22no—
472C2×D43—22no—
473C2×D43—44no—
474C2×D43C22×#4114yes—
475C4×C43—22no—
476C4×C43—28no—
477C4×C43—22no—
478C4×C43—22no—
479C4×C43C22×#4114yes—
480C4×C43C2×H(5,𝔽2)14yes—
481C4×C43C2×2−1+414yes—
482Dic43—22no—
483Dic43—28no—
484Dic43—28no—
485Dic43—22no—
486Dic43—22no—
487Dic43—22no—
488Dic43—22no—
489Dic43C22×#4114yes—
490#3511—4332no—
491C2×#556—432no—
492C2×#555—432no—
493C2×#554—432no—
494C2×#553—432no—
495C2×#553—432no—
496C2×#548—432no—
497C2×#548—432no—
498C2×#547—432no—
499C2×#542—432no—
500C2×#542—432no—
501C2×#537—432no—
502C2×#533—431no—
503C2×#533—431no—
504C2×#532—431no—
505C2×#532—431no—
506C2×#532D4311yescharacteristic, complemented
507C22×C4⋊Q8—431no—
508C2×#520—432no—
509C2×C4×#41—431no—
510C2×C43—48no—
511C2×C43—42no—
512C2×C43#351114yescomplemented
513C2×C43C23×#4111yescharacteristic
514C2×C43C22×H(5,𝔽2)11yescharacteristic
515C2×C43C22×2−1+411yescharacteristic
516D43—24no—
517D43—42no—
518C22×#41—432no—
519C22×#41—432no—
520C22×#41—431no—
521C22×#41C2×D4312yes—
522C23×Q8—432no—
523#556—4332no—
524#555—4332no—
525#554—4332no—
526#553—4332no—
527#553—4332no—
528#548—4332no—
529#548—4332no—
530#547—4332no—
531#542—4332no—
532#542—4332no—
533#537—4332no—
534#533—4316no—
535#533—4316no—
536#532—4316no—
537#532—4316no—
538#532C2×D43116yescomplemented
539C2×C4⋊Q8—432no—
540C2×C4⋊Q8—4316no—
541C2×C4⋊Q8—432no—
542C2×C4⋊Q8—432no—
543C2×C4⋊Q8—431no—
544C2×C4⋊Q8—431no—
545C2×C4⋊Q8C2×D4311yescharacteristic
546C2×#127C2×D4311yescharacteristic
547C2×#126—434no—
548C2×#126—434no—
549C2×#125—432no—
550C2×#125—432no—
551C2×#124—432no—
552C2×#124—432no—
553C2×#124—434no—
554C2×#124—434no—
555C2×#124C2×D4312yes—
556C2×#123—434no—
557C2×#123—434no—
558C2×C22⋊Q8—432no—
559C2×C22⋊Q8—432no—
560C2×C22⋊Q8—432no—
561C2×C22⋊Q8—434no—
562C2×C22⋊Q8—432no—
563C2×C22⋊Q8—434no—
564C2×C22⋊Q8—434no—
565C2×#121—432no—
566C2×#121—432no—
567C2×#121—432no—
568C2×#121—432no—
569C2×#121—434no—
570C2×#121—434no—
571C2×#121—434no—
572C2×#121C2×D4312yes—
573C2×#121C2×D4312yes—
574#520—4332no—
575C4×#41—4316no—
576C2×C4×Q8—432no—
577C2×C4×Q8—432no—
578C2×C4×Q8—431no—
579C2×C4×Q8—431no—
580C2×C4×Q8—432no—
581C2×C4×Q8—432no—
582C2×C4×D4—432no—
583C2×C4×D4—432no—
584C2×C4×D4—432no—
585C2×C4×D4—432no—
586C2×C4×D4—431no—
587C2×C4×D4—431no—
588C2×C4×D4—431no—
589C2×C4×D4—431no—
590C2×C4×D4—434no—
591C2×C4×D4—434no—
592C2×C4×D4—431no—
593C2×C4×D4—431no—
594C2×C4×D4C2×D4312yes—
595C2×C4×D4C2×D4312yes—
596C2×#117—431no—
597C2×#117—432no—
598C2×#117—432no—
599C2×#117—434no—
600C2×#117—431no—
601C2×#117—431no—
602C22×C4⋊C4—434no—
603C22×C4⋊C4—432no—
604C22×C4⋊C4—432no—
605C22×C42—431no—
606C22×C42—431no—
607C22×C42C2×D4311yescharacteristic
608C43C2×#351111yescharacteristic, complemented, Sylow
609C2×#41—48no—
610C2×#41—4316no—
611C2×#41—4316no—
612C2×#41—438no—
613C2×#41—868no—
614C2×#41—8616no—
615C2×#41—1728no—
616C2×#41C22×D43116yes—
617C22×Q8—4316no—
618C22×Q8—431no—
619C22×Q8—432no—
620C22×Q8—432no—
621C22×Q8—434no—
622C22×Q8—1728no—
623C22×Q8C22×D4312yes—
624C22×D4—431no—
625C22×D4—431no—
626C22×D4—434no—
627C22×D4—434no—
628C22×D4—431no—
629C22×D4C22×D4312yes—
630C22×D4C22×D4312yes—
631C22×D4C22×D4312yes—
632C22×D4C22×D4314yes—
633C23×C4—431no—
634C23×C4—434no—
635C23×C4—434no—
636C23×C4—431no—
637C23×C4—431no—
638C23×C4—431no—
639C23×C4—431no—
640C23×C4—431no—
641C23×C4—434no—
642C23×C4C22×D4311yescharacteristic
643C23×C4C22×D4311yescharacteristic
644C23×C4C22×D4311yescharacteristic
645C23×C4C22×D4314yes—
646C4⋊Q8—4316no—
647C4⋊Q8—4316no—
648C4⋊Q8—4316no—
649C4⋊Q8—438no—
650C4⋊Q8—438no—
651C4⋊Q8C22×D4318yes—
652#127C22×D4318yes—
653#126—4332no—
654#126—4332no—
655#125—4316no—
656#125—4316no—
657#124—4316no—
658#124—4316no—
659#124—4332no—
660#124—4332no—
661#124C22×D43116yes—
662#123—4332no—
663#123—4332no—
664C22⋊Q8—4316no—
665C22⋊Q8—4316no—
666C22⋊Q8—4316no—
667C22⋊Q8—4332no—
668C22⋊Q8—4316no—
669C22⋊Q8—4332no—
670C22⋊Q8—4332no—
671#121—4316no—
672#121—4316no—
673#121—4316no—
674#121—4316no—
675#121—4332no—
676#121—4332no—
677#121—4332no—
678#121C22×D43116yes—
679#121C22×D43116yes—
680C4×Q8—4316no—
681C4×Q8—4316no—
682C4×Q8—438no—
683C4×Q8—438no—
684C4×Q8—4316no—
685C4×Q8—4316no—
686C4×D4—4316no—
687C4×D4—4316no—
688C4×D4—4316no—
689C4×D4—4316no—
690C4×D4—438no—
691C4×D4—438no—
692C4×D4—438no—
693C4×D4—438no—
694C4×D4—4332no—
695C4×D4—4332no—
696C4×D4—438no—
697C4×D4—438no—
698C4×D4C22×D43116yes—
699C4×D4C22×D43116yes—
700#117—438no—
701#117—4316no—
702#117—4316no—
703#117—4332no—
704#117—438no—
705#117—438no—
706C2×C4⋊C4—431no—
707C2×C4⋊C4—434no—
708C2×C4⋊C4—432no—
709C2×C4⋊C4—432no—
710C2×C4⋊C4—434no—
711C2×C4⋊C4—434no—
712C2×C4⋊C4—4332no—
713C2×C4⋊C4—434no—
714C2×C4⋊C4—431no—
715C2×C4⋊C4—432no—
716C2×C4⋊C4—431no—
717C2×C4⋊C4—431no—
718C2×C4⋊C4—431no—
719C2×C4⋊C4—431no—
720C2×C4⋊C4—432no—
721C2×C4⋊C4—434no—
722C2×C4⋊C4—434no—
723C2×C4⋊C4—4316no—
724C2×C4⋊C4—4316no—
725C2×C4⋊C4C22×D4312yes—
726C2×C4⋊C4C22×D4312yes—
727C2×C22⋊C4—434no—
728C2×C22⋊C4—431no—
729C2×C22⋊C4—431no—
730C2×C22⋊C4—434no—
731C2×C22⋊C4—434no—
732C2×C22⋊C4—434no—
733C2×C22⋊C4—434no—
734C2×C22⋊C4—431no—
735C2×C22⋊C4—431no—
736C2×C22⋊C4—431no—
737C2×C22⋊C4—431no—
738C2×C22⋊C4—434no—
739C2×C22⋊C4C22×D4314yes—
740C2×C22⋊C4C22×D4314yes—
741C2×C42—431no—
742C2×C42—434no—
743C2×C42—434no—
744C2×C42—431no—
745C2×C42—431no—
746C2×C42—431no—
747C2×C42—431no—
748C2×C42—431no—
749C2×C42—438no—
750C2×C42—438no—
751C2×C42C22×D4311yescharacteristic
752C2×C42C22×D4311yescharacteristic
753C2×C42C22×D4311yescharacteristic
754C2×C42C22×D4318yes—
755C2×C42C22×D4311yescharacteristic
756C24—431no—
757C24—431no—
758C24C23×D4311yescharacteristic
759C24C23×D4314yes—
760#41—432no—
761#41—8632no—
762#41—8664no—
763#41—17232no—
764C2×Q8—28no—
765C2×Q8—434no—
766C2×Q8—438no—
767C2×Q8—438no—
768C2×Q8—4316no—
769C2×Q8—864no—
770C2×Q8—868no—
771C2×Q8—868no—
772C2×Q8—1728no—
773C2×Q8—17232no—
774C2×Q8C23×D4318yes—
775C2×D4—28no—
776C2×D4—28no—
777C2×D4—28no—
778C2×D4—48no—
779C2×D4—434no—
780C2×D4—434no—
781C2×D4—4316no—
782C2×D4—4316no—
783C2×D4—434no—
784C2×D4—864no—
785C2×D4—864no—
786C2×D4—864no—
787C2×D4—8616no—
788C2×D4—1728no—
789C2×D4C23×D4318yes—
790C2×D4C23×D4318yes—
791C2×D4C23×D4318yes—
792C2×D4C23×D43116yes—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—48no—
797C22×C4—431no—
798C22×C4—438no—
799C22×C4—434no—
800C22×C4—4316no—
801C22×C4—431no—
802C22×C4—431no—
803C22×C4—431no—
804C22×C4—434no—
805C22×C4—431no—
806C22×C4—431no—
807C22×C4—434no—
808C22×C4—4316no—
809C22×C4—434no—
810C22×C4—434no—
811C22×C4—434no—
812C22×C4—434no—
813C22×C4—434no—
814C22×C4—4316no—
815C22×C4—8616no—
816C22×C4—864no—
817C22×C4—864no—
818C22×C4—864no—
819C22×C4—864no—
820C22×C4—864no—
821C22×C4—1728no—
822C22×C4—1728no—
823C22×C4C23×D4314yes—
824C22×C4C23×D4314yes—
825C22×C4C23×D4314yes—
826C22×C4C23×D4311yescharacteristic
827C22×C4C23×D4314yes—
828C22×C4C23×D4311yescharacteristic
829C22×C4C23×D4311yescharacteristic
830C22×C4C23×D43116yes—
831C22×C4C23×D4311yescharacteristic
832C22×C4C23×D4311yescharacteristic
833C22×C4C23×D4311yescharacteristic
834C4⋊C4—434no—
835C4⋊C4—4316no—
836C4⋊C4—438no—
837C4⋊C4—438no—
838C4⋊C4—4316no—
839C4⋊C4—4316no—
840C4⋊C4—4316no—
841C4⋊C4—434no—
842C4⋊C4—438no—
843C4⋊C4—434no—
844C4⋊C4—434no—
845C4⋊C4—434no—
846C4⋊C4—434no—
847C4⋊C4—438no—
848C4⋊C4—4316no—
849C4⋊C4—4316no—
850C4⋊C4C23×D4318yes—
851C4⋊C4C23×D4318yes—
852C22⋊C4—4316no—
853C22⋊C4—434no—
854C22⋊C4—434no—
855C22⋊C4—4316no—
856C22⋊C4—4316no—
857C22⋊C4—4316no—
858C22⋊C4—4316no—
859C22⋊C4—434no—
860C22⋊C4—434no—
861C22⋊C4—434no—
862C22⋊C4—434no—
863C22⋊C4—4316no—
864C22⋊C4C23×D43116yes—
865C22⋊C4C23×D43116yes—
866C42—434no—
867C42—434no—
868C42—434no—
869C42—434no—
870C42—434no—
871C42—434no—
872C42—4316no—
873C42—4316no—
874C42C23×D4314yes—
875C42C23×D4314yes—
876C42C23×D4314yes—
877C42C23×D4314yes—
878C23—22no—
879C23—28no—
880C23—22no—
881C23—28no—
882C23—22no—
883C23—28no—
884C23—434no—
885C23—432no—
886C23—432no—
887C23—862no—
888C23—862no—
889C23—862no—
890C23—862no—
891C23—862no—
892C23C24×D4312yes—
893C23C24×D4318yes—
894C23C24×D4311yescharacteristic
895Q8—216no—
896Q8—868no—
897Q8—8616no—
898Q8—8616no—
899Q8—17216no—
900D4—216no—
901D4—216no—
902D4—216no—
903D4—416no—
904D4—868no—
905D4—868no—
906D4—868no—
907D4—8632no—
908D4—17216no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—28no—
912C2×C4—22no—
913C2×C4—28no—
914C2×C4—28no—
915C2×C4—28no—
916C2×C4—416no—
917C2×C4—434no—
918C2×C4—432no—
919C2×C4—4316no—
920C2×C4—432no—
921C2×C4—432no—
922C2×C4—432no—
923C2×C4—432no—
924C2×C4—438no—
925C2×C4—432no—
926C2×C4—438no—
927C2×C4—8632no—
928C2×C4—868no—
929C2×C4—862no—
930C2×C4—862no—
931C2×C4—862no—
932C2×C4—868no—
933C2×C4—862no—
934C2×C4—862no—
935C2×C4—868no—
936C2×C4—868no—
937C2×C4—868no—
938C2×C4—868no—
939C2×C4—868no—
940C2×C4—17216no—
941C2×C4—17216no—
942C2×C4#41×D4314yes—
943C2×C4#1306337014yes—
944C2×C4#1306337214yes—
945C2×C4C24×D4312yes—
946C2×C4C24×D4318yes—
947C2×C4C24×D4312yes—
948C2×C4C24×D4312yes—
949C2×C4C24×D4312yes—
950C2×C4C24×D4312yes—
951C2×C4C24×D4312yes—
952C22—22no—
953C22—28no—
954C22—22no—
955C22—28no—
956C22—22no—
957C22—28no—
958C22—44no—
959C22—416no—
960C22—434no—
961C22—862no—
962C22—862no—
963C22—868no—
964C22—862no—
965C22—862no—
966C22—862no—
967C22—1724no—
968C22C2×#41×D4312yes—
969C22C2×#1306337012yes—
970C22C2×#1306337212yes—
971C22C25×D4311yescharacteristic
972C4—22no—
973C4—22no—
974C4—28no—
975C4—22no—
976C4—434no—
977C4—868no—
978C4—862no—
979C4—862no—
980C4—862no—
981C4—868no—
982C4—862no—
983C4—862no—
984C4C2×#41×D4314yes—
985C4C2×#1306337014yes—
986C4C2×#1306337214yes—
987C2—42no—
988C2—48no—
989C2—864no—
990C2—1722no—
991C2#1914849614yesdirect product factor
992C2C22×#41×D4311yescharacteristic
993C2C22×#1306337011yescharacteristic
994C2C22×#1306337211yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#532C2
socleC23×C43C25
hypercenterC2×#532D43
hypocenterC43C2×#3511
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #19148496C2direct (N × H)
2. C2×#14583618C2semidirect
3. C2×#14583613C2semidirect
4. C2×#14583608C2semidirect
5. C2×#14583599C2semidirect
6. C2×#14583596C2semidirect
7. C2×#14583557C2semidirect
8. C2×#14583556C2semidirect
9. C2×#14583548C2semidirect
10. C2×#14583516C2semidirect
11. C2×#14583514C2semidirect
12. C2×#14583478C2semidirect
13. C2×#14583456C2semidirect
14. C2×#14583454C2semidirect
15. C2×#14583447C2semidirect
16. C2×#14583447C2semidirect
17. C2×C4⋊Q8×D43C2semidirect
18. C2×#14583378C2semidirect
19. C2×C4×#10621898C2semidirect
20. C2×C43×#532C2semidirect
25. #14583618C22semidirect
26. #14583613C22semidirect
27. #14583608C22semidirect
28. #14583599C22semidirect
29. #14583596C22semidirect
30. #14583557C22semidirect
31. #14583556C22semidirect
32. #14583548C22semidirect
33. #14583516C22semidirect
34. #14583514C22semidirect
35. #14583478C22semidirect
36. #14583456C22semidirect
37. #14583454C22semidirect
38. #14583447C22semidirect
39. #14583447C22semidirect
45. C4⋊Q8×D43C22semidirect
70. #14583378C22semidirect
71. C4×#10621898C22semidirect
102. C43×#532C22semidirect
320. C2×C4×D43#41semidirect
449. C4×D43C2×#41semidirect
506. C2×#532D43semidirect
512. C2×C43#3511semidirect
538. #532C2×D43semidirect
608. C43C2×#3511semidirect
991. C2#19148496direct (N × H)

Maximal subgroups

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

subgroupindex
#191484962
C2×#145836182
C2×#145836132
C2×#145836082
C2×#145835992
C2×#145835962
C2×#145835572
C2×#145835562
C2×#145835482
C2×#145835162
C2×#145835142
C2×#145834782
C2×#145834562
C2×#145834542
C2×#145834472
C2×C4⋊Q8×D432
C2×#145833782
C2×C4×#106218982
C2×C43×#5322
C2×#351143