Finite Group Databasebeta

← C2×#19148988 #26004391

Subgroups — C2×#19148988 #26004391

Order 11008.

7810 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148988C2132yesmaximal, direct product factor
2C2×#14583644C214yesmaximal, complemented
3C2×#14583609C211yesmaximal, characteristic, complemented
4C2×#14583608C212yesmaximal, complemented
5C2×#14583606C211yesmaximal, characteristic, complemented
6C2×#14583569C211yesmaximal, characteristic, complemented
7C2×#14583569C212yesmaximal, complemented
8C2×#14583549C212yesmaximal, complemented
9C2×#14583548C212yesmaximal, complemented
10C2×#14583503C212yesmaximal, complemented
11C2×#14583500C212yesmaximal, complemented
12C2×#14583478C212yesmaximal, complemented
13C2×#14583477C212yesmaximal, complemented
14C2×#14583476C214yesmaximal, complemented
15C2×#14583453C211yesmaximal, characteristic, complemented
16C2×#14583447C211yesmaximal, characteristic, complemented
17C2×#14583446C211yesmaximal, characteristic, complemented
18C2×C43×#550C211yesmaximal, characteristic, complemented
19C22×#10621898C2212yes—
20C22×#10621900C2212yes—
21C22×#10621900C2214yes—
22C22×#10621900C2212yes—
23#14583644C22164yescomplemented
24#14583609C22116yescomplemented
25#14583608C22132yescomplemented
26#14583606C22116yescomplemented
27#14583569C22116yescomplemented
28#14583569C22132yescomplemented
29#14583549C22132yescomplemented
30#14583548C22132yescomplemented
31#14583503C22132yescomplemented
32#14583500C22132yescomplemented
33#14583478C22132yescomplemented
34#14583477C22132yescomplemented
35#14583476C22164yescomplemented
36#14583453C22116yescomplemented
37#14583447C22116yescomplemented
38#14583446C22116yescomplemented
39C2×#13063325C2211yescharacteristic
40C2×#13063324C2211yescharacteristic
41C2×#13063324C2211yescharacteristic
42C2×#13063323C2211yescharacteristic
43C2×#13063321C2211yescharacteristic
44C2×#13063321C2212yes—
45C2×#13063317C2212yes—
46C2×#13063316C2212yes—
47C2×#13063315C2212yes—
48C2×#13063312C2212yes—
49C2×#13063311C2212yes—
50C2×#13063308C2214yes—
51C2×#13063307C2214yes—
52C2×#13063306C2214yes—
53C2×#13063306C2214yes—
54C2×#13063305C2211yescharacteristic
55C2×#13063304C2212yes—
56C2×#13063304C2214yes—
57C2×#13063303C2214yes—
58C2×#13063303C2212yes—
59C2×#13063302C2214yes—
60C2×#13063302C2214yes—
61C2×#13063302C2214yes—
62C2×#13063301C2212yes—
63C2×#13063301C2211yescharacteristic
64C2×#13063300C2211yescharacteristic
65C2×#13063299C2214yes—
66C2×#13063298C2212yes—
67C2×#13063298C2214yes—
68C2×#13063297C2214yes—
69C2×#13063297C2214yes—
70C2×#13063297C2214yes—
71C2×#13063297C2214yes—
72C2×#13063297C2214yes—
73C2×#13063296C2212yes—
74C2×#13063296C2214yes—
75C2×#13063296C2211yescharacteristic
76C2×#13063296C2212yes—
77C2×#13063296C2212yes—
78C2×C4×Dic86C2211yescharacteristic
79C2×C4×Dic86C2212yes—
80C2×C4×D172C2211yescharacteristic
81C2×C4×D172C2212yes—
82C2×D4×Dic43C2212yes—
83C2×D4×Dic43C2212yes—
84C2×D4×Dic43C2212yes—
85C2×D4×Dic43C2212yes—
86C2×C4×C22⋊D43C2212yes—
87C2×#13063282C2212yes—
88C22×C4⋊Dic43C2212yes—
89C22×Dic43⋊C4C2214yes—
90C2×C4⋊C4×D43C2212yes—
91C2×C42×D43C2211yescharacteristic
92C22×#41×C43C2212yes—
93C43×#550C22116yescomplemented
94C2×#127×C43C2211yescharacteristic
95C2×#127×C43C2212yes—
96C2×#121×C43C2212yes—
97C2×#121×C43C2214yes—
98C2×C4×Q8×C43C2211yescharacteristic
99C2×C4×D4×C43C2211yescharacteristic
100C2×C4×D4×C43C2212yes—
101C2×#10621898—48no—
102C2×#10621898C23116yes—
103C2×#10621900—48no—
104C2×#10621900—416no—
105C2×#10621900—48no—
106C2×#10621900C23132yes—
107C2×#10621900C23116yes—
108C2×#10621900C23116yes—
109C22×Dic86C2312yes—
110C22×Dic86C2311yescharacteristic
111C22×Dic86C2312yes—
112C22×Dic86C2312yes—
113C22×D172C2311yescharacteristic
114C22×D172C2312yes—
115C22×C22⋊D43C2312yes—
116C22×C22⋊D43C2314yes—
117C22×C22⋊D43C2312yes—
118C22×C22⋊D43C2312yes—
119C22×C22⋊D43C2314yes—
120C22×C22⋊D43C2314yes—
121C23×Dic43C2314yes—
122C23×Dic43C2314yes—
123C23×Dic43C2314yes—
124C22×C4×D43C2311yescharacteristic
125C22×C4×D43C2311yescharacteristic
126C22×C4×D43C2311yescharacteristic
127C22×C4×D43C2312yes—
128C22×C4×D43C2314yes—
129#13063325C2318yes—
130#13063324C2318yes—
131#13063324C2318yes—
132#13063323C2318yes—
133#13063321C2318yes—
134#13063321C23116yes—
135#13063317C23116yes—
136#13063316C23116yes—
137#13063315C23116yes—
138#13063312C23116yes—
139#13063311C23116yes—
140#13063308C23132yes—
141#13063307C23132yes—
142#13063306C23132yes—
143#13063306C23132yes—
144#13063305C2318yes—
145#13063304C23116yes—
146#13063304C23132yes—
147#13063303C23132yes—
148#13063303C23116yes—
149#13063302C23132yes—
150#13063302C23132yes—
151#13063302C23132yes—
152#13063301C23116yes—
153#13063301C2318yes—
154#13063300C2318yes—
155#13063299C23132yes—
156#13063298C23116yes—
157#13063298C23132yes—
158#13063297C23132yes—
159#13063297C23132yes—
160#13063297C23132yes—
161#13063297C23132yes—
162#13063297C23132yes—
163#13063296C23132yes—
164#13063296C23116yes—
165#13063296C2318yes—
166#13063296C23116yes—
167#13063296C23116yes—
168C4×Dic86C2318yes—
169C4×Dic86C23116yes—
170C4×D172C2318yes—
171C4×D172C23116yes—
172D4×Dic43C23116yes—
173D4×Dic43C23116yes—
174D4×Dic43C23116yes—
175D4×Dic43C23116yes—
176C4×C22⋊D43C23116yes—
177#13063282C23116yes—
178C2×C4⋊Dic43C2312yes—
179C2×C4⋊Dic43C2311yescharacteristic
180C2×C4⋊Dic43C23116yes—
181C2×C4⋊Dic43C2314yes—
182C2×C4⋊Dic43C2312yes—
183C2×C4⋊Dic43C2311yescharacteristic
184C2×C4⋊Dic43C2312yes—
185C2×Dic43⋊C4C2314yes—
186C2×Dic43⋊C4C2312yes—
187C2×Dic43⋊C4C2312yes—
188C2×Dic43⋊C4C23132yes—
189C2×Dic43⋊C4C2314yes—
190C2×Dic43⋊C4C2314yes—
191C2×Dic43⋊C4C2312yes—
192C2×Dic43⋊C4C2312yes—
193C2×Dic43⋊C4C2312yes—
194C2×Dic43⋊C4C2312yes—
195C4⋊C4×D43C23116yes—
196C2×C22⋊Dic43C2312yes—
197C2×C22⋊Dic43C2314yes—
198C2×C22⋊Dic43C2314yes—
199C2×C22⋊Dic43C2314yes—
200C2×C22⋊Dic43C2314yes—
201C2×(C2×D43)⋊C4C2312yes—
202C2×(C2×D43)⋊C4C2312yes—
203C2×(C2×D43)⋊C4C2312yes—
204C2×(C2×D43)⋊C4C2312yes—
205C2×(C2×D43)⋊C4C2314yes—
206C2×C4×Dic43C2311yescharacteristic
207C2×C4×Dic43C2311yescharacteristic
208C2×C4×Dic43C2311yescharacteristic
209C2×C4×Dic43C2312yes—
210C42×D43C2318yes—
211C2×#41×C43—48no—
212C2×#41×C43C23116yes—
213C22×Q8×C43C2311yescharacteristic
214C22×D4×C43C2311yescharacteristic
215C22×D4×C43C2312yes—
216C22×D4×C43C2312yes—
217C22×D4×C43C2314yes—
218C22×D4×C43C2312yes—
219C22×D4×C43C2314yes—
220C23×C4×C43C2312yes—
221C23×C4×C43C2314yes—
222#127×C43C2318yes—
223#127×C43C23116yes—
224#121×C43C23132yes—
225#121×C43C23116yes—
226C4×Q8×C43C2318yes—
227C4×D4×C43C2318yes—
228C4×D4×C43C23116yes—
229C2×C4⋊C4×C43C2311yescharacteristic
230C2×C4⋊C4×C43C2311yescharacteristic
231C2×C4⋊C4×C43C2312yes—
232C2×C22⋊C4×C43C2314yes—
233C2×C22⋊C4×C43C2312yes—
234C2×C42×C43C2311yescharacteristic
235C2×C42×C43C2312yes—
236C24×C43C2414yes—
237C24×C43C2412yes—
238C23×D43C2411yescharacteristic
239C23×D43C2412yes—
240#41×C43—432no—
241C2×Q8×C43—24no—
242C2×Q8×C43C2414yes—
243C2×D4×C43—28no—
244C2×D4×C43—24no—
245C2×D4×C43—28no—
246C2×D4×C43—48no—
247C2×D4×C43—44no—
248C2×D4×C43—48no—
249C2×D4×C43C2414yes—
250C2×D4×C43C2418yes—
251C2×D4×C43C2418yes—
252C2×D4×C43C24116yes—
253C2×D4×C43C2418yes—
254C2×D4×C43C24116yes—
255C22×C4×C43—28no—
256C22×C4×C43—48no—
257C22×C4×C43C2411yescharacteristic
258C22×C4×C43C2412yes—
259C22×C4×C43C2412yes—
260C22×C4×C43C2412yes—
261C22×C4×C43C2418yes—
262C22×C4×C43C24116yes—
263C22×C4×C43C2411yescharacteristic
264C22×C4×C43C2411yescharacteristic
265C2×C22⋊D43—28no—
266C2×C22⋊D43—48no—
267C2×C22⋊D43—48no—
268C2×C22⋊D43—48no—
269C2×C22⋊D43—44no—
270C2×C22⋊D43—44no—
271C2×C22⋊D43C2418yes—
272C2×C22⋊D43C24116yes—
273C2×C22⋊D43C2418yes—
274C2×C22⋊D43C2418yes—
275C2×C22⋊D43C24116yes—
276C2×C22⋊D43C24116yes—
277C22×Dic43—216no—
278C22×Dic43—48no—
279C22×Dic43—48no—
280C22×Dic43C2411yescharacteristic
281C22×Dic43C2411yescharacteristic
282C22×Dic43C2412yes—
283C22×Dic43C2412yes—
284C22×Dic43C2412yes—
285C22×Dic43C2414yes—
286C22×Dic43C24116yes—
287C22×Dic43C24116yes—
288C22×Dic43C24116yes—
289C22×Dic43C2411yescharacteristic
290#10621900—432no—
291#10621900—464no—
292#10621900—432no—
293#10621898—432no—
294C2×D172—24no—
295C2×D172—44no—
296C2×D172C2414yes—
297C2×D172C2418yes—
298C2×C4×D43—28no—
299C2×C4×D43—24no—
300C2×C4×D43—24no—
301C2×C4×D43—24no—
302C2×C4×D43—48no—
303C2×C4×D43C2414yes—
304C2×C4×D43C2414yes—
305C2×C4×D43C2414yes—
306C2×C4×D43C2418yes—
307C2×C4×D43C24116yes—
308C2×Dic86—24no—
309C2×Dic86—28no—
310C2×Dic86—44no—
311C2×Dic86—44no—
312C2×Dic86C2418yes—
313C2×Dic86C2414yes—
314C2×Dic86C2418yes—
315C2×Dic86C2418yes—
316C4⋊C4×C43C2414yes—
317C4⋊C4×C43C2414yes—
318C4⋊C4×C43C2418yes—
319C22⋊C4×C43C24116yes—
320C22⋊C4×C43C2418yes—
321C42×C43C2414yes—
322C42×C43C2418yes—
323C22⋊Dic43C2418yes—
324C22⋊Dic43C24116yes—
325C22⋊Dic43C24116yes—
326C22⋊Dic43C24116yes—
327C22⋊Dic43C24116yes—
328(C2×D43)⋊C4C2418yes—
329(C2×D43)⋊C4C2418yes—
330(C2×D43)⋊C4C2418yes—
331(C2×D43)⋊C4C2418yes—
332(C2×D43)⋊C4C24116yes—
333C4⋊Dic43C2418yes—
334C4⋊Dic43C2414yes—
335C4⋊Dic43C24116yes—
336C4⋊Dic43C2418yes—
337C4⋊Dic43C2414yes—
338C4⋊Dic43C2418yes—
339Dic43⋊C4C24116yes—
340Dic43⋊C4C2418yes—
341Dic43⋊C4C2418yes—
342Dic43⋊C4C24116yes—
343Dic43⋊C4C24116yes—
344Dic43⋊C4C2418yes—
345Dic43⋊C4C2418yes—
346Dic43⋊C4C2418yes—
347Dic43⋊C4C2418yes—
348C4×Dic43C2414yes—
349C4×Dic43C2414yes—
350C4×Dic43C2414yes—
351C4×Dic43C2418yes—
352C23×C43—28no—
353C23×C43—24no—
354C23×C43—28no—
355C23×C43—24no—
356C23×C43—28no—
357C23×C43—24no—
358C23×C43C2518yes—
359C23×C43C2514yes—
360C23×C43C2511yescharacteristic
361C22×D43—22no—
362C22×D43—24no—
363C22×D43—22no—
364C22×D43—24no—
365C22×D43—22no—
366C22×D43—24no—
367C22×D43C2512yes—
368C22×D43C2514yes—
369Q8×C43—28no—
370D4×C43—216no—
371D4×C43—28no—
372D4×C43—216no—
373D4×C43—416no—
374D4×C43—48no—
375D4×C43—416no—
376C2×C4×C43—24no—
377C2×C4×C43—22no—
378C2×C4×C43—24no—
379C2×C4×C43—24no—
380C2×C4×C43—216no—
381C2×C4×C43—416no—
382C2×C4×C43H(5,𝔽2)14yes—
383C2×C4×C432−1+414yes—
384C2×C4×C43C2512yes—
385C2×C4×C43C2514yes—
386C2×C4×C43C2514yes—
387C2×C4×C43C2514yes—
388C2×C4×C43C2512yes—
389C2×C4×C43C2512yes—
390C22⋊D43—216no—
391C22⋊D43—48no—
392C22⋊D43—48no—
393C22⋊D43—416no—
394C22⋊D43—416no—
395C22⋊D43—416no—
396C2×Dic43—24no—
397C2×Dic43—24no—
398C2×Dic43—22no—
399C2×Dic43—24no—
400C2×Dic43—28no—
401C2×Dic43—22no—
402C2×Dic43—232no—
403C2×Dic43—416no—
404C2×Dic43—416no—
405C2×Dic43H(5,𝔽2)14yes—
406C2×Dic43C2512yes—
407C2×Dic43C2512yes—
408C2×Dic43C2514yes—
409C2×Dic43C2514yes—
410C2×Dic43C2514yes—
411C2×Dic43C2518yes—
412C2×Dic43C2512yes—
413D172—28no—
414D172—48no—
415C4×D43—28no—
416C4×D43—216no—
417C4×D43—28no—
418C4×D43—28no—
419C4×D43—416no—
420Dic86—28no—
421Dic86—216no—
422Dic86—48no—
423Dic86—48no—
424C2×#3548—431nomaximal, Sylow
425C22×C43—28no—
426C22×C43—24no—
427C22×C43—28no—
428C22×C43—24no—
429C22×C43—28no—
430C22×C43—24no—
431C22×C43—416no—
432C22×C43—48no—
433C22×C43C2×H(5,𝔽2)12yes—
434C22×C43C2×H(5,𝔽2)12yes—
435C22×C43C2×2−1+412yes—
436C22×C43C2611yescharacteristic
437C2×D43—22no—
438C2×D43—24no—
439C2×D43—22no—
440C2×D43—24no—
441C2×D43—22no—
442C2×D43—24no—
443C2×D43—44no—
444C2×D43—48no—
445C4×C43—24no—
446C4×C43—22no—
447C4×C43—24no—
448C4×C43—24no—
449C4×C43C2×H(5,𝔽2)14yes—
450C4×C43C2×2−1+414yes—
451Dic43—24no—
452Dic43—24no—
453Dic43—22no—
454Dic43—24no—
455Dic43—28no—
456Dic43—22no—
457Dic43C2×H(5,𝔽2)14yes—
458#3548—4332no—
459C2×#562—434no—
460C2×#554—431no—
461C2×#554—431no—
462C2×#554—432no—
463C2×#550—432no—
464C2×#550—431no—
465C2×#550D4311yescharacteristic, complemented
466C2×#547—432no—
467C2×#547—432no—
468C2×#540—432no—
469C2×#540—432no—
470C2×#537—432no—
471C2×#537—434no—
472C2×#537—432no—
473C2×#533—431no—
474C2×#532—431no—
475C2×#532—431no—
476C2×C43—48no—
477C2×C43—44no—
478C2×C43#354814yescomplemented
479C2×C43C22×H(5,𝔽2)11yescharacteristic
480C2×C43C22×H(5,𝔽2)11yescharacteristic
481C2×C43C22×2−1+411yescharacteristic
482D43—42no—
483D43—44no—
484C22×#41—432no—
485C22×#41—434no—
486C22×#41—432no—
487C22×#41—432no—
488C22×#41C2×D4312yes—
489#562—4364no—
490#554—4316no—
491#554—4316no—
492#554—4332no—
493#550—4332no—
494#550—4316no—
495#550C2×D43116yescomplemented
496#547—4332no—
497#547—4332no—
498#540—4332no—
499#540—4332no—
500#537—4332no—
501#537—4364no—
502#537—4332no—
503#533—4316no—
504#532—4316no—
505#532—4316no—
506C2×C4⋊Q8—431no—
507C2×C4⋊Q8—431no—
508C2×C4⋊Q8—431no—
509C2×C4⋊Q8—431no—
510C2×#127—431no—
511C2×#127—432no—
512C2×#127C2×D4311yescharacteristic
513C2×#127C2×D4312yes—
514C2×#125—432no—
515C2×#125—432no—
516C2×#125—432no—
517C2×#124—432no—
518C2×#124—432no—
519C2×#123—434no—
520C2×#123—434no—
521C2×#123—434no—
522C2×#123—434no—
523C2×C22⋊Q8—431no—
524C2×C22⋊Q8—432no—
525C2×C22⋊Q8—432no—
526C2×C22⋊Q8—434no—
527C2×C22⋊Q8—432no—
528C2×C22⋊Q8—434no—
529C2×C22⋊Q8—431no—
530C2×C22⋊Q8—434no—
531C2×C22⋊Q8—434no—
532C2×C22⋊Q8—434no—
533C2×#121—432no—
534C2×#121—431no—
535C2×#121—432no—
536C2×#121—432no—
537C2×#121—434no—
538C2×#121—434no—
539C2×#121—434no—
540C2×#121—434no—
541C2×#121—434no—
542C2×#121—434no—
543C2×#121—434no—
544C2×#121—431no—
545C2×#121—432no—
546C2×#121—434no—
547C2×#121C2×D4312yes—
548C2×#121C2×D4314yes—
549C2×C4×Q8—431no—
550C2×C4×Q8—432no—
551C2×C4×Q8C2×D4311yescharacteristic
552C2×C4×D4—432no—
553C2×C4×D4—432no—
554C2×C4×D4—432no—
555C2×C4×D4—432no—
556C2×C4×D4—432no—
557C2×C4×D4—431no—
558C2×C4×D4—432no—
559C2×C4×D4C2×D4311yescharacteristic
560C2×C4×D4C2×D4312yes—
561C2×#117—432no—
562C22×C4⋊C4—434no—
563C22×C4⋊C4—432no—
564C22×C4⋊C4—432no—
565C22×C42—431no—
566C43C2×#354811yescharacteristic, complemented, Sylow
567C2×#41—48no—
568C2×#41—4316no—
569C2×#41—4332no—
570C2×#41—4316no—
571C2×#41—4316no—
572C2×#41—1728no—
573C2×#41—1728no—
574C2×#41—1728no—
575C2×#41—17216no—
576C2×#41C22×D43116yes—
577C22×Q8—432no—
578C22×Q8—431no—
579C22×Q8—432no—
580C22×Q8—432no—
581C22×Q8C22×D4311yescharacteristic
582C22×D4—432no—
583C22×D4—434no—
584C22×D4—432no—
585C22×D4—434no—
586C22×D4—434no—
587C22×D4—432no—
588C22×D4—431no—
589C22×D4—432no—
590C22×D4C22×D4312yes—
591C22×D4C22×D4311yescharacteristic
592C22×D4C22×D4312yes—
593C22×D4C22×D4314yes—
594C22×D4C22×D4314yes—
595C22×D4C22×D4312yes—
596C23×C4—434no—
597C23×C4—434no—
598C23×C4—434no—
599C23×C4—432no—
600C23×C4—431no—
601C23×C4—431no—
602C23×C4—431no—
603C23×C4—434no—
604C23×C4C22×D4312yes—
605C23×C4C22×D4314yes—
606C4⋊Q8—438no—
607C4⋊Q8—438no—
608C4⋊Q8—438no—
609C4⋊Q8—438no—
610#127—438no—
611#127—4316no—
612#127C22×D4318yes—
613#127C22×D43116yes—
614#125—4316no—
615#125—4316no—
616#125—4316no—
617#124—4316no—
618#124—4316no—
619#123—4332no—
620#123—4332no—
621#123—4332no—
622#123—4332no—
623C22⋊Q8—438no—
624C22⋊Q8—4316no—
625C22⋊Q8—4316no—
626C22⋊Q8—4332no—
627C22⋊Q8—4316no—
628C22⋊Q8—438no—
629C22⋊Q8—4332no—
630C22⋊Q8—4332no—
631C22⋊Q8—4332no—
632C22⋊Q8—4332no—
633#121—4316no—
634#121—4316no—
635#121—438no—
636#121—4332no—
637#121—4332no—
638#121—4316no—
639#121—4332no—
640#121—4332no—
641#121—4332no—
642#121—4332no—
643#121—4332no—
644#121—438no—
645#121—4316no—
646#121—4332no—
647#121C22×D43116yes—
648#121C22×D43132yes—
649C4×Q8—4316no—
650C4×Q8—438no—
651C4×Q8C22×D4318yes—
652C4×D4—4316no—
653C4×D4—4316no—
654C4×D4—4316no—
655C4×D4—4316no—
656C4×D4—4316no—
657C4×D4—438no—
658C4×D4—4316no—
659C4×D4C22×D4318yes—
660C4×D4C22×D43116yes—
661#117—4316no—
662C2×C4⋊C4—432no—
663C2×C4⋊C4—432no—
664C2×C4⋊C4—432no—
665C2×C4⋊C4—431no—
666C2×C4⋊C4—434no—
667C2×C4⋊C4—434no—
668C2×C4⋊C4—434no—
669C2×C4⋊C4—434no—
670C2×C4⋊C4—4332no—
671C2×C4⋊C4—4316no—
672C2×C4⋊C4—432no—
673C2×C4⋊C4—432no—
674C2×C4⋊C4—432no—
675C2×C4⋊C4—431no—
676C2×C4⋊C4—432no—
677C2×C4⋊C4—432no—
678C2×C4⋊C4—432no—
679C2×C4⋊C4—4316no—
680C2×C4⋊C4C22×D4311yescharacteristic
681C2×C4⋊C4C22×D4311yescharacteristic
682C2×C4⋊C4C22×D4312yes—
683C2×C22⋊C4—434no—
684C2×C22⋊C4—434no—
685C2×C22⋊C4—434no—
686C2×C22⋊C4—434no—
687C2×C22⋊C4—432no—
688C2×C22⋊C4—432no—
689C2×C22⋊C4—432no—
690C2×C22⋊C4—434no—
691C2×C22⋊C4—432no—
692C2×C22⋊C4—432no—
693C2×C22⋊C4C22×D4314yes—
694C2×C22⋊C4C22×D4312yes—
695C2×C42—432no—
696C2×C42—431no—
697C2×C42—431no—
698C2×C42—431no—
699C2×C42—438no—
700C2×C42C22×D4312yes—
701C2×C42C22×D4311yescharacteristic
702C24—431no—
703C24—432no—
704C24C23×D4314yes—
705C24C23×D4312yes—
706#41—432no—
707#41—17232no—
708#41—17232no—
709#41—17232no—
710#41—17264no—
711C2×Q8—24no—
712C2×Q8—438no—
713C2×Q8—434no—
714C2×Q8—438no—
715C2×Q8—438no—
716C2×Q8—868no—
717C2×Q8—864no—
718C2×Q8—1724no—
719C2×Q8—1724no—
720C2×Q8C23×D4314yes—
721C2×D4—28no—
722C2×D4—28no—
723C2×D4—24no—
724C2×D4—48no—
725C2×D4—44no—
726C2×D4—48no—
727C2×D4—438no—
728C2×D4—4316no—
729C2×D4—438no—
730C2×D4—4316no—
731C2×D4—4316no—
732C2×D4—438no—
733C2×D4—434no—
734C2×D4—438no—
735C2×D4—868no—
736C2×D4—864no—
737C2×D4—1724no—
738C2×D4—1728no—
739C2×D4—1728no—
740C2×D4—1724no—
741C2×D4—1724no—
742C2×D4—1728no—
743C2×D4C23×D4318yes—
744C2×D4C23×D4314yes—
745C2×D4C23×D4318yes—
746C2×D4C23×D43116yes—
747C2×D4C23×D43116yes—
748C2×D4C23×D4318yes—
749C22×C4—28no—
750C22×C4—48no—
751C22×C4—431no—
752C22×C4—4316no—
753C22×C4—431no—
754C22×C4—431no—
755C22×C4—432no—
756C22×C4—432no—
757C22×C4—434no—
758C22×C4—432no—
759C22×C4—4316no—
760C22×C4—4316no—
761C22×C4—434no—
762C22×C4—434no—
763C22×C4—434no—
764C22×C4—438no—
765C22×C4—4316no—
766C22×C4—864no—
767C22×C4—8616no—
768C22×C4—868no—
769C22×C4—864no—
770C22×C4—864no—
771C22×C4—1728no—
772C22×C4—1728no—
773C22×C4—1728no—
774C22×C4C23×D4318yes—
775C22×C4C23×D4311yescharacteristic
776C22×C4C23×D4312yes—
777C22×C4C23×D4312yes—
778C22×C4C23×D4312yes—
779C22×C4C23×D43116yes—
780C22×C4C23×D4311yescharacteristic
781C22×C4C23×D4311yescharacteristic
782C4⋊C4—438no—
783C4⋊C4—438no—
784C4⋊C4—438no—
785C4⋊C4—434no—
786C4⋊C4—4316no—
787C4⋊C4—4316no—
788C4⋊C4—4316no—
789C4⋊C4—4316no—
790C4⋊C4—438no—
791C4⋊C4—438no—
792C4⋊C4—438no—
793C4⋊C4—434no—
794C4⋊C4—438no—
795C4⋊C4—438no—
796C4⋊C4—438no—
797C4⋊C4C23×D4314yes—
798C4⋊C4C23×D4314yes—
799C4⋊C4C23×D4318yes—
800C22⋊C4—4316no—
801C22⋊C4—4316no—
802C22⋊C4—4316no—
803C22⋊C4—4316no—
804C22⋊C4—438no—
805C22⋊C4—438no—
806C22⋊C4—438no—
807C22⋊C4—4316no—
808C22⋊C4—438no—
809C22⋊C4—438no—
810C22⋊C4C23×D43116yes—
811C22⋊C4C23×D4318yes—
812C42—434no—
813C42—434no—
814C42—434no—
815C42—438no—
816C42C23×D4314yes—
817C42C23×D4318yes—
818C23—28no—
819C23—24no—
820C23—24no—
821C23—28no—
822C23—28no—
823C23—24no—
824C23—432no—
825C23—434no—
826C23—862no—
827C23—864no—
828C23—862no—
829C23—864no—
830C23—862no—
831C23—864no—
832C23C24×D4318yes—
833C23C24×D4314yes—
834C23C24×D4311yescharacteristic
835Q8—28no—
836Q8—8616no—
837Q8—868no—
838Q8—1728no—
839Q8—1728no—
840D4—216no—
841D4—216no—
842D4—28no—
843D4—416no—
844D4—48no—
845D4—416no—
846D4—8616no—
847D4—868no—
848D4—1728no—
849D4—17216no—
850D4—17216no—
851D4—1728no—
852D4—1728no—
853D4—17216no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—216no—
859C2×C4—416no—
860C2×C4—434no—
861C2×C4—432no—
862C2×C4—432no—
863C2×C4—432no—
864C2×C4—434no—
865C2×C4—434no—
866C2×C4—438no—
867C2×C4—434no—
868C2×C4—868no—
869C2×C4—8632no—
870C2×C4—868no—
871C2×C4—864no—
872C2×C4—864no—
873C2×C4—862no—
874C2×C4—864no—
875C2×C4—862no—
876C2×C4—8616no—
877C2×C4—868no—
878C2×C4—868no—
879C2×C4—17216no—
880C2×C4—17216no—
881C2×C4—17216no—
882C2×C4#1306337014yes—
883C2×C4#1306337214yes—
884C2×C4C24×D4312yes—
885C2×C4C24×D4314yes—
886C2×C4C24×D4314yes—
887C2×C4C24×D4314yes—
888C2×C4C24×D4312yes—
889C2×C4C24×D4312yes—
890C22—28no—
891C22—24no—
892C22—24no—
893C22—28no—
894C22—28no—
895C22—24no—
896C22—416no—
897C22—48no—
898C22—862no—
899C22—864no—
900C22—862no—
901C22—864no—
902C22—862no—
903C22—864no—
904C22—1724no—
905C22—1728no—
906C22H(5,𝔽2)×D4312yes—
907C22C2×#1306337012yes—
908C22C2×#1306337212yes—
909C22C25×D4311yescharacteristic
910C4—22no—
911C4—24no—
912C4—24no—
913C4—24no—
914C4—434no—
915C4—868no—
916C4—864no—
917C4—864no—
918C4—862no—
919C4—864no—
920C4—862no—
921C4C2×#1306337014yes—
922C4C2×#1306337214yes—
923C2—48no—
924C2—44no—
925C2—1722no—
926C2—1724no—
927C2#1914898814yesdirect product factor
928C2C2×H(5,𝔽2)×D4311yescharacteristic
929C2C22×#1306337011yescharacteristic
930C2C22×#1306337211yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#550C2
socleC23×C43C25
hypercenterC2×#550D43
hypocenterC43C2×#3548
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. #19148988C2direct (N × H)
2. C2×#14583644C2semidirect
3. C2×#14583609C2semidirect
4. C2×#14583608C2semidirect
5. C2×#14583606C2semidirect
6. C2×#14583569C2semidirect
7. C2×#14583569C2semidirect
8. C2×#14583549C2semidirect
9. C2×#14583548C2semidirect
10. C2×#14583503C2semidirect
11. C2×#14583500C2semidirect
12. C2×#14583478C2semidirect
13. C2×#14583477C2semidirect
14. C2×#14583476C2semidirect
15. C2×#14583453C2semidirect
16. C2×#14583447C2semidirect
17. C2×#14583446C2semidirect
18. C2×C43×#550C2semidirect
23. #14583644C22semidirect
24. #14583609C22semidirect
25. #14583608C22semidirect
26. #14583606C22semidirect
27. #14583569C22semidirect
28. #14583569C22semidirect
29. #14583549C22semidirect
30. #14583548C22semidirect
31. #14583503C22semidirect
32. #14583500C22semidirect
33. #14583478C22semidirect
34. #14583477C22semidirect
35. #14583476C22semidirect
36. #14583453C22semidirect
37. #14583447C22semidirect
38. #14583446C22semidirect
93. C43×#550C22semidirect
465. C2×#550D43semidirect
478. C2×C43#3548semidirect
495. #550C2×D43semidirect
566. C43C2×#3548semidirect
927. C2#19148988direct (N × H)

Maximal subgroups

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

subgroupindex
#191489882
C2×#145836442
C2×#145836092
C2×#145836082
C2×#145836062
C2×#145835692
C2×#145835492
C2×#145835482
C2×#145835032
C2×#145835002
C2×#145834782
C2×#145834772
C2×#145834762
C2×#145834532
C2×#145834472
C2×#145834462
C2×C43×#5502
C2×#354843