Finite Group Databasebeta

← C2×#13082999 #15661471

Subgroups — C2×#13082999 #15661471

Order 2816.

7182 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#13082999C2132yesmaximal, direct product factor
2C2×#10623178C214yesmaximal, complemented
3C2×#10623265C211yesmaximal, characteristic, complemented
4C2×#10623063C212yesmaximal, complemented
5C2×#10623261C211yesmaximal, characteristic, complemented
6C2×#10623061C212yesmaximal, complemented
7C2×#10623112C212yesmaximal, complemented
8C2×#10623258C211yesmaximal, characteristic, complemented
9C2×#10623107C212yesmaximal, complemented
10C2×#10623257C211yesmaximal, characteristic, complemented
11C2×#10623220C212yesmaximal, complemented
12C2×#10623113C214yesmaximal, complemented
13C2×#10623229C212yesmaximal, complemented
14C2×#10623160C212yesmaximal, complemented
15C2×#10623159C212yesmaximal, complemented
16C2×#10623008C211yesmaximal, characteristic, complemented
17C2×#10623010C211yesmaximal, characteristic, complemented
18C2×C11×#533C211yesmaximal, characteristic, complemented
19C22×#4343C2212yes—
20C22×Q8×D11C2212yes—
21C22×#4339C2212yes—
22C11×#533C22116yescomplemented
23C2×C11×C4⋊Q8C2211yescharacteristic
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×#125C2212yes—
26C2×C11×C22⋊Q8C2212yes—
27C2×C11×C22⋊Q8C2212yes—
28C2×C4×Q8×C11C2212yes—
29C2×C4×Q8×C11C2212yes—
30C2×C11×#117C2212yes—
31C22×C42×C11C2211yescharacteristic
32C2×#67000C2214yes—
33C2×#66999C2212yes—
34C2×#66999C2212yes—
35C2×#66999C2214yes—
36C2×#66983C2211yescharacteristic
37C2×#66983C2211yescharacteristic
38C2×#66983C2211yescharacteristic
39C2×#66983C2212yes—
40C2×#66982C2212yes—
41C2×C4×C22⋊D11C2212yes—
42C2×#66977C2211yescharacteristic
43#10623265C22116yescomplemented
44#10623261C22116yescomplemented
45#10623258C22116yescomplemented
46#10623257C22116yescomplemented
47#10623229C22132yescomplemented
48#10623220C22132yescomplemented
49#10623178C22164yescomplemented
50#10623160C22132yescomplemented
51#10623159C22132yescomplemented
52#10623113C22164yescomplemented
53#10623112C22132yescomplemented
54#10623107C22132yescomplemented
55#10623063C22132yescomplemented
56#10623061C22132yescomplemented
57C2×#66950C2212yes—
58C2×#66950C2214yes—
59C2×#66949C2214yes—
60C2×#66949C2214yes—
61C2×#66948C2212yes—
62C2×#66948C2212yes—
63C2×#66948C2212yes—
64C2×#66948C2214yes—
65C2×#66948C2214yes—
66C2×#66947C2214yes—
67C2×#66947C2214yes—
68C2×#66947C2214yes—
69C2×#66946C2212yes—
70C2×#66946C2212yes—
71C2×#66945C2212yes—
72C2×#66945C2212yes—
73C2×C4⋊C4×D11C2212yes—
74C2×C4⋊C4×D11C2212yes—
75C2×#66943C2212yes—
76C2×#66942C2214yes—
77C2×#66941C2212yes—
78C2×#66941C2214yes—
79C2×#66938C2214yes—
80C2×#66937C2214yes—
81C2×#66937C2214yes—
82C2×#66936C2214yes—
83#10623010C22116yescomplemented
84C2×#66929C2214yes—
85C2×#66929C2212yes—
86#10623008C22116yescomplemented
87C2×#66928C2211yescharacteristic
88C2×#66928C2214yes—
89C2×#66928C2212yes—
90C2×#66927C2211yescharacteristic
91C2×C4×D44C2212yes—
92C2×C4×D44C2214yes—
93C2×C4×D44C2211yescharacteristic
94C2×C4×D44C2211yescharacteristic
95C2×C4×D44C2211yescharacteristic
96C2×#66925C2214yes—
97C2×#66925C2212yes—
98C2×#66923C2211yescharacteristic
99C2×#66922C2211yescharacteristic
100C2×C4×Dic22C2211yescharacteristic
101C22×Q8×C11C2312yes—
102C22×Q8×C11C2312yes—
103C23×C4×C11C2311yescharacteristic
104C23×C4×C11C2311yescharacteristic
105C23×C4×C11C2311yescharacteristic
106C22×C22⋊D11C2312yes—
107C22×C22⋊D11C2312yes—
108C22×C22⋊D11C2312yes—
109C2×#4343—48no—
110C2×#4343C23116yes—
111C2×Q8×D11—48no—
112C2×Q8×D11C23116yes—
113C2×#4339—48no—
114C2×#4339C23116yes—
115C22×D44C2311yescharacteristic
116C22×D44C2311yescharacteristic
117C22×D44C2311yescharacteristic
118C22×D44C2312yes—
119C22×D44C2314yes—
120C22×D44C2312yes—
121C22×D44C2314yes—
122C22×C4×D11C2312yes—
123C22×C4×D11C2312yes—
124C22×C4×D11C2312yes—
125C22×C4×D11C2314yes—
126C22×C4×D11C2314yes—
127C22×C4×D11C2314yes—
128C22×Dic22C2311yescharacteristic
129C22×Dic22C2312yes—
130C22×Dic22C2314yes—
131C11×C4⋊Q8C2318yes—
132C11×C4⋊Q8C2318yes—
133C11×#125C23116yes—
134C11×C22⋊Q8C23116yes—
135C11×C22⋊Q8C23116yes—
136C4×Q8×C11C23116yes—
137C4×Q8×C11C23116yes—
138C11×#117C23116yes—
139C2×C11×C4⋊C4C2312yes—
140C2×C11×C4⋊C4C2314yes—
141C2×C11×C4⋊C4C2314yes—
142C2×C11×C4⋊C4C2312yes—
143C2×C11×C4⋊C4C2312yes—
144C2×C11×C4⋊C4C2312yes—
145C2×C11×C22⋊C4C2314yes—
146C2×C42×C11C2311yescharacteristic
147C2×C42×C11C2311yescharacteristic
148C2×C42×C11C2311yescharacteristic
149C2×C42×C11C2314yes—
150C2×C42×C11C2311yescharacteristic
151C2×C42×C11C2318yes—
152C2×C22⋊Dic11C2312yes—
153#67000C23132yes—
154#66999C23116yes—
155#66999C23116yes—
156#66999C23132yes—
157#66983C2318yes—
158#66983C2318yes—
159#66983C23116yes—
160#66983C2318yes—
161#66982C23116yes—
162C4×C22⋊D11C23116yes—
163C2×(C2×D11)⋊C4C2312yes—
164C2×(C2×D11)⋊C4C2312yes—
165C2×(C2×D11)⋊C4C2312yes—
166C2×(C2×D11)⋊C4C2314yes—
167C2×(C2×D11)⋊C4C2312yes—
168C2×(C2×D11)⋊C4C2312yes—
169C2×(C2×D11)⋊C4C2312yes—
170C2×(C2×D11)⋊C4C2312yes—
171C2×(C2×D11)⋊C4C2312yes—
172C2×(C2×D11)⋊C4C2314yes—
173C2×(C2×D11)⋊C4C2314yes—
174C2×(C2×D11)⋊C4C2314yes—
175C2×(C2×D11)⋊C4C2314yes—
176C2×C4⋊Dic11C2311yescharacteristic
177C2×C4⋊Dic11C2311yescharacteristic
178C2×C4⋊Dic11C2312yes—
179C2×C4⋊Dic11C2311yescharacteristic
180C2×C4⋊Dic11C2311yescharacteristic
181C2×C4⋊Dic11C2314yes—
182#66977C2318yes—
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C2314yes—
188C2×Dic11⋊C4C2314yes—
189C2×Dic11⋊C4C2314yes—
190C2×C4×Dic11C2312yes—
191C2×C4×Dic11C2314yes—
192#66950C23116yes—
193#66950C23132yes—
194#66949C23132yes—
195#66949C23132yes—
196#66948C23116yes—
197#66948C23116yes—
198#66948C23116yes—
199#66948C23132yes—
200#66948C23132yes—
201#66947C23132yes—
202#66947C23132yes—
203#66947C23132yes—
204#66946C23116yes—
205#66946C23116yes—
206#66945C23116yes—
207#66945C23116yes—
208C4⋊C4×D11C23116yes—
209C4⋊C4×D11C23116yes—
210#66943C23116yes—
211#66942C23132yes—
212#66941C23116yes—
213#66941C23132yes—
214#66938C23132yes—
215#66937C23132yes—
216#66937C23132yes—
217#66936C23132yes—
218#66929C23116yes—
219#66929C23132yes—
220#66928C23116yes—
221#66928C2318yes—
222#66928C23132yes—
223#66927C2318yes—
224C4×D44C2318yes—
225C4×D44C2318yes—
226C4×D44C2318yes—
227C4×D44C23116yes—
228C4×D44C23132yes—
229#66925C23116yes—
230#66925C23132yes—
231#66923C2318yes—
232#66922C2318yes—
233C4×Dic22C2318yes—
234C2×#3547—111nomaximal, Sylow
235C24×C11C2411yescharacteristic
236C23×D11C2412yes—
237C23×D11C2412yes—
238C23×D11C2412yes—
239C2×Q8×C11—28no—
240C2×Q8×C11—44no—
241C2×Q8×C11C2418yes—
242C2×Q8×C11C2418yes—
243C22×C4×C11—24no—
244C22×C4×C11—24no—
245C22×C4×C11—42no—
246C22×C4×C11C2414yes—
247C22×C4×C11C2411yescharacteristic
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C22×C4×C11C2414yes—
252C22×C4×C11C2414yes—
253C22×C4×C11C2414yes—
254C22×C4×C11C2414yes—
255C22×C4×C11C2411yescharacteristic
256C22×C4×C11C2411yescharacteristic
257C2×C22⋊D11—44no—
258C2×C22⋊D11—44no—
259C2×C22⋊D11—44no—
260C2×C22⋊D11C2418yes—
261C2×C22⋊D11C2418yes—
262C2×C22⋊D11C2418yes—
263C22×Dic11C2412yes—
264C22×Dic11C2412yes—
265C22×Dic11C2412yes—
266C22×Dic11C2412yes—
267C22×Dic11C2412yes—
268#4343—432no—
269Q8×D11—432no—
270#4339—432no—
271C2×D44—24no—
272C2×D44—24no—
273C2×D44—24no—
274C2×D44—48no—
275C2×D44—44no—
276C2×D44—44no—
277C2×D44—48no—
278C2×D44C2414yes—
279C2×D44C2414yes—
280C2×D44C2414yes—
281C2×D44C2418yes—
282C2×D44C24116yes—
283C2×D44C2418yes—
284C2×D44C24116yes—
285C2×C4×D11—28no—
286C2×C4×D11—28no—
287C2×C4×D11—28no—
288C2×C4×D11—48no—
289C2×C4×D11—48no—
290C2×C4×D11—48no—
291C2×C4×D11C2418yes—
292C2×C4×D11C2418yes—
293C2×C4×D11C2418yes—
294C2×C4×D11C24116yes—
295C2×C4×D11C24116yes—
296C2×C4×D11C24116yes—
297C2×Dic22—24no—
298C2×Dic22—44no—
299C2×Dic22—48no—
300C2×Dic22C2414yes—
301C2×Dic22C2418yes—
302C2×Dic22C24116yes—
303C11×C4⋊C4C2418yes—
304C11×C4⋊C4C24116yes—
305C11×C4⋊C4C24116yes—
306C11×C4⋊C4C2418yes—
307C11×C4⋊C4C2418yes—
308C11×C4⋊C4C2418yes—
309C11×C22⋊C4C24116yes—
310C42×C11C2414yes—
311C42×C11C2414yes—
312C42×C11C2414yes—
313C42×C11C24116yes—
314C42×C11C2414yes—
315C22⋊Dic11C2418yes—
316(C2×D11)⋊C4C2418yes—
317(C2×D11)⋊C4C2418yes—
318(C2×D11)⋊C4C2418yes—
319(C2×D11)⋊C4C24116yes—
320(C2×D11)⋊C4C2418yes—
321(C2×D11)⋊C4C2418yes—
322(C2×D11)⋊C4C2418yes—
323(C2×D11)⋊C4C2418yes—
324(C2×D11)⋊C4C2418yes—
325(C2×D11)⋊C4C24116yes—
326(C2×D11)⋊C4C24116yes—
327(C2×D11)⋊C4C24116yes—
328(C2×D11)⋊C4C24116yes—
329C4⋊Dic11C2414yes—
330C4⋊Dic11C2414yes—
331C4⋊Dic11C2418yes—
332C4⋊Dic11C2414yes—
333C4⋊Dic11C2414yes—
334C4⋊Dic11C24116yes—
335Dic11⋊C4C2418yes—
336Dic11⋊C4C2418yes—
337Dic11⋊C4C2418yes—
338Dic11⋊C4C2418yes—
339Dic11⋊C4C24116yes—
340Dic11⋊C4C24116yes—
341Dic11⋊C4C24116yes—
342C4×Dic11C2418yes—
343C4×Dic11C24116yes—
344#3547—1132no—
345C2×#562—114no—
346C2×#555—111no—
347C2×#555—112no—
348C2×#554—111no—
349C2×#553—112no—
350C2×#552—112no—
351C2×D4×Q8—111no—
352C2×#548—112no—
353C2×#547—111no—
354C2×#544—112no—
355C2×#542—114no—
356C2×#540—112no—
357C2×#537—112no—
358C2×#536—112no—
359C2×#533D1111yescharacteristic, complemented
360C2×#532—111no—
361C2×#529—111no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11C2512yes—
366C23×C11C2511yescharacteristic
367C22×D11—24no—
368C22×D11—24no—
369C22×D11—24no—
370C22×D11—24no—
371C22×D11—24no—
372C22×D11—24no—
373C22×D11—24no—
374C22×D11—24no—
375C22×D11—24no—
376C22×D11C2514yes—
377C22×D11C2514yes—
378C22×D11C2514yes—
379Q8×C11—216no—
380Q8×C11—48no—
381C2×C4×C11—22no—
382C2×C4×C11—28no—
383C2×C4×C11—22no—
384C2×C4×C11—28no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—28no—
388C2×C4×C11—28no—
389C2×C4×C11—44no—
390C2×C4×C11H(5,𝔽2)14yes—
391C2×C4×C112−1+414yes—
392C2×C4×C11C2518yes—
393C2×C4×C11C2512yes—
394C2×C4×C11C2512yes—
395C2×C4×C11C2512yes—
396C2×C4×C11C2512yes—
397C2×C4×C11C2518yes—
398C2×C4×C11C2512yes—
399C2×C4×C11C2512yes—
400C22⋊D11—48no—
401C22⋊D11—48no—
402C22⋊D11—48no—
403C2×Dic11—24no—
404C2×Dic11—24no—
405C2×Dic11—24no—
406C2×Dic11—24no—
407C2×Dic11—24no—
408C2×Dic11C2514yes—
409C2×Dic11C2514yes—
410C2×Dic11C2514yes—
411C2×Dic11C2514yes—
412C2×Dic11C2514yes—
413D44—28no—
414D44—28no—
415D44—28no—
416D44—48no—
417D44—416no—
418D44—48no—
419D44—416no—
420C4×D11—216no—
421C4×D11—216no—
422C4×D11—216no—
423C4×D11—416no—
424C4×D11—416no—
425C4×D11—416no—
426Dic22—28no—
427Dic22—48no—
428Dic22—416no—
429C22×#41—112no—
430C22×#41—112no—
431C23×Q8—112no—
432#562—1164no—
433#555—1116no—
434#555—1132no—
435#554—1116no—
436#553—1132no—
437#552—1132no—
438D4×Q8—1116no—
439#548—1132no—
440#547—1116no—
441#544—1132no—
442#542—1164no—
443#540—1132no—
444#537—1132no—
445#536—1132no—
446#533C2×D11116yescomplemented
447#532—1116no—
448C2×C4⋊Q8—114no—
449C2×C4⋊Q8—112no—
450C2×C4⋊Q8—111no—
451C2×C4⋊Q8C2×D1111yescharacteristic
452C2×C4⋊Q8C2×D1111yescharacteristic
453C2×#127—111no—
454#529—1116no—
455C2×#126—112no—
456C2×#126—114no—
457C2×#125—114no—
458C2×#125—112no—
459C2×#125—111no—
460C2×#125C2×D1112yes—
461C2×#124—114no—
462C2×#124—114no—
463C2×#124—111no—
464C2×#124—112no—
465C2×#124—114no—
466C2×#123—112no—
467C2×#123—114no—
468C2×#123—114no—
469C2×#123—114no—
470C2×#123—114no—
471C2×C22⋊Q8—112no—
472C2×C22⋊Q8—112no—
473C2×C22⋊Q8—114no—
474C2×C22⋊Q8—111no—
475C2×C22⋊Q8—114no—
476C2×C22⋊Q8—114no—
477C2×C22⋊Q8—112no—
478C2×C22⋊Q8—114no—
479C2×C22⋊Q8C2×D1112yes—
480C2×C22⋊Q8C2×D1112yes—
481C2×#121—111no—
482C2×#121—111no—
483C2×#121—111no—
484C2×#121—112no—
485C2×#121—114no—
486C2×#121—112no—
487C2×#121—112no—
488C2×#121—114no—
489C2×#121—112no—
490C2×#121—114no—
491C2×#121—114no—
492C2×C4×Q8—111no—
493C2×C4×Q8C2×D1112yes—
494C2×C4×Q8C2×D1112yes—
495C2×C4×D4—112no—
496C2×C4×D4—112no—
497C2×C4×D4—112no—
498C2×C4×D4—111no—
499C2×C4×D4—111no—
500C2×C4×D4—112no—
501C2×C4×D4—111no—
502C2×C4×D4—114no—
503C2×#117—112no—
504C2×#117—112no—
505C2×#117—112no—
506C2×#117—114no—
507C2×#117C2×D1112yes—
508C22×C4⋊C4—112no—
509C22×C4⋊C4—112no—
510C22×C42C2×D1111yescharacteristic
511C22×C11—22no—
512C22×C11—22no—
513C22×C11—22no—
514C22×C11—44no—
515C22×C11C2×H(5,𝔽2)12yes—
516C22×C11C2×2−1+412yes—
517C22×C11#58512yes—
518C22×C11C2611yescharacteristic
519C2×D11—24no—
520C2×D11—24no—
521C2×D11—24no—
522C2×D11—24no—
523C2×D11—24no—
524C2×D11—24no—
525C2×D11—24no—
526C2×D11—24no—
527C2×D11—24no—
528C2×D11—48no—
529C2×D11—48no—
530C2×D11—48no—
531C4×C11—22no—
532C4×C11—28no—
533C4×C11—22no—
534C4×C11—22no—
535C4×C11—22no—
536C4×C11—28no—
537C4×C11C2×H(5,𝔽2)14yes—
538C4×C11C2×2−1+414yes—
539Dic11—24no—
540Dic11—24no—
541Dic11—24no—
542Dic11—24no—
543Dic11—24no—
544C2×#41—1116no—
545C2×#41—1116no—
546C2×#41—448no—
547C2×#41—448no—
548C22×Q8—1116no—
549C22×Q8—111no—
550C22×Q8—114no—
551C22×Q8—112no—
552C22×Q8—448no—
553C22×Q8C22×D1112yes—
554C22×Q8C22×D1112yes—
555C22×D4—112no—
556C22×D4—112no—
557C22×D4—112no—
558C22×D4—111no—
559C22×D4—111no—
560C22×D4—111no—
561C22×D4—114no—
562C22×D4—112no—
563C22×D4—114no—
564C22×D4—112no—
565C23×C4—112no—
566C23×C4—112no—
567C23×C4—112no—
568C23×C4—114no—
569C23×C4—114no—
570C23×C4—114no—
571C23×C4C22×D1111yescharacteristic
572C23×C4C22×D1111yescharacteristic
573C23×C4C22×D1111yescharacteristic
574C4⋊Q8—1132no—
575C4⋊Q8—1116no—
576C4⋊Q8—118no—
577C4⋊Q8C22×D1118yes—
578C4⋊Q8C22×D1118yes—
579#127—118no—
580#126—1116no—
581#126—1132no—
582#125—1132no—
583#125—1116no—
584#125—118no—
585#125C22×D11116yes—
586#124—1132no—
587#124—1132no—
588#124—118no—
589#124—1116no—
590#124—1132no—
591#123—1116no—
592#123—1132no—
593#123—1132no—
594#123—1132no—
595#123—1132no—
596C22⋊Q8—1116no—
597C22⋊Q8—1116no—
598C22⋊Q8—1132no—
599C22⋊Q8—118no—
600C22⋊Q8—1116no—
601C22⋊Q8—1132no—
602C22⋊Q8—1132no—
603C22⋊Q8—1132no—
604C22⋊Q8C22×D11116yes—
605C22⋊Q8C22×D11116yes—
606#121—118no—
607#121—118no—
608#121—118no—
609#121—1116no—
610#121—1132no—
611#121—1116no—
612#121—1116no—
613#121—1132no—
614#121—1116no—
615#121—1132no—
616#121—1132no—
617C4×Q8—118no—
618C4×Q8C22×D11116yes—
619C4×Q8C22×D11116yes—
620C4×D4—1116no—
621C4×D4—1116no—
622C4×D4—1116no—
623C4×D4—118no—
624C4×D4—118no—
625C4×D4—1116no—
626C4×D4—118no—
627C4×D4—1132no—
628#117—1116no—
629#117—1116no—
630#117—1116no—
631#117—1132no—
632#117C22×D11116yes—
633C2×C4⋊C4—111no—
634C2×C4⋊C4—111no—
635C2×C4⋊C4—114no—
636C2×C4⋊C4—114no—
637C2×C4⋊C4—111no—
638C2×C4⋊C4—111no—
639C2×C4⋊C4—112no—
640C2×C4⋊C4—114no—
641C2×C4⋊C4—112no—
642C2×C4⋊C4—112no—
643C2×C4⋊C4—112no—
644C2×C4⋊C4—114no—
645C2×C4⋊C4—112no—
646C2×C4⋊C4—1116no—
647C2×C4⋊C4—1116no—
648C2×C4⋊C4C22×D1112yes—
649C2×C4⋊C4C22×D1112yes—
650C2×C4⋊C4C22×D1112yes—
651C2×C4⋊C4C22×D1114yes—
652C2×C4⋊C4C22×D1114yes—
653C2×C4⋊C4C22×D1112yes—
654C2×C22⋊C4—112no—
655C2×C22⋊C4—112no—
656C2×C22⋊C4—112no—
657C2×C22⋊C4—112no—
658C2×C22⋊C4—114no—
659C2×C22⋊C4—114no—
660C2×C22⋊C4—114no—
661C2×C22⋊C4—112no—
662C2×C22⋊C4—112no—
663C2×C22⋊C4—114no—
664C2×C22⋊C4—112no—
665C2×C22⋊C4—114no—
666C2×C22⋊C4—112no—
667C2×C22⋊C4—112no—
668C2×C22⋊C4C22×D1114yes—
669C2×C42—114no—
670C2×C42—112no—
671C2×C42C22×D1111yescharacteristic
672C2×C42C22×D1114yes—
673C2×C42C22×D1111yescharacteristic
674C2×C42C22×D1111yescharacteristic
675C2×C42C22×D1111yescharacteristic
676C2×C42C22×D1118yes—
677C2×C11—42no—
678C2×C11#354714yescomplemented
679C2×C11C22×H(5,𝔽2)11yescharacteristic
680C2×C11C22×2−1+411yescharacteristic
681C2×C11C2×#58511yescharacteristic
682D11—44no—
683D11—44no—
684D11—44no—
685C24—112no—
686C24—112no—
687C24—112no—
688C24C23×D1111yescharacteristic
689#41—4432no—
690#41—4432no—
691C2×Q8—28no—
692C2×Q8—44no—
693C2×Q8—114no—
694C2×Q8—1116no—
695C2×Q8—118no—
696C2×Q8—224no—
697C2×Q8—448no—
698C2×Q8—444no—
699C2×Q8—4432no—
700C2×Q8C23×D1118yes—
701C2×Q8C23×D1118yes—
702C2×D4—118no—
703C2×D4—118no—
704C2×D4—118no—
705C2×D4—114no—
706C2×D4—114no—
707C2×D4—114no—
708C2×D4—1116no—
709C2×D4—118no—
710C2×D4—1116no—
711C2×D4—118no—
712C2×D4—224no—
713C2×D4—224no—
714C2×D4—224no—
715C2×D4—444no—
716C2×D4—448no—
717C2×D4—444no—
718C2×D4—448no—
719C2×D4—444no—
720C2×D4—444no—
721C2×D4—444no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—42no—
725C22×C4—112no—
726C22×C4—112no—
727C22×C4—112no—
728C22×C4—112no—
729C22×C4—112no—
730C22×C4—118no—
731C22×C4—118no—
732C22×C4—118no—
733C22×C4—1116no—
734C22×C4—1116no—
735C22×C4—1116no—
736C22×C4—228no—
737C22×C4—228no—
738C22×C4—228no—
739C22×C4—448no—
740C22×C4—448no—
741C22×C4—448no—
742C22×C4C23×D1114yes—
743C22×C4C23×D1114yes—
744C22×C4C23×D1114yes—
745C22×C4C23×D1111yescharacteristic
746C22×C4C23×D1111yescharacteristic
747C22×C4C23×D1111yescharacteristic
748C22×C4C23×D1111yescharacteristic
749C22×C4C23×D1114yes—
750C22×C4C23×D1114yes—
751C22×C4C23×D1111yescharacteristic
752C22×C4C23×D1111yescharacteristic
753C4⋊C4—114no—
754C4⋊C4—114no—
755C4⋊C4—1116no—
756C4⋊C4—1116no—
757C4⋊C4—114no—
758C4⋊C4—114no—
759C4⋊C4—118no—
760C4⋊C4—1116no—
761C4⋊C4—118no—
762C4⋊C4—118no—
763C4⋊C4—118no—
764C4⋊C4—1116no—
765C4⋊C4—118no—
766C4⋊C4C23×D1118yes—
767C4⋊C4C23×D1118yes—
768C4⋊C4C23×D1118yes—
769C4⋊C4C23×D11116yes—
770C4⋊C4C23×D11116yes—
771C4⋊C4C23×D1118yes—
772C22⋊C4—118no—
773C22⋊C4—118no—
774C22⋊C4—118no—
775C22⋊C4—118no—
776C22⋊C4—1116no—
777C22⋊C4—1116no—
778C22⋊C4—1116no—
779C22⋊C4—118no—
780C22⋊C4—118no—
781C22⋊C4—1116no—
782C22⋊C4—118no—
783C22⋊C4—1116no—
784C22⋊C4—118no—
785C22⋊C4—118no—
786C22⋊C4C23×D11116yes—
787C42—1116no—
788C42—118no—
789C42C23×D1114yes—
790C42C23×D1114yes—
791C42C23×D1114yes—
792C42C23×D1114yes—
793C42C23×D11116yes—
794C11C2×#354711yescharacteristic, complemented, Sylow
795C23—22no—
796C23—22no—
797C23—22no—
798C23—114no—
799C23—114no—
800C23—114no—
801C23—224no—
802C23—224no—
803C23—224no—
804C23—224no—
805C23—224no—
806C23—224no—
807C23—224no—
808C23—224no—
809C23—224no—
810C23C24×D1112yes—
811C23C24×D1111yescharacteristic
812Q8—216no—
813Q8—48no—
814Q8—228no—
815Q8—4416no—
816Q8—448no—
817D4—228no—
818D4—228no—
819D4—228no—
820D4—448no—
821D4—4416no—
822D4—448no—
823D4—4416no—
824D4—448no—
825D4—448no—
826D4—448no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—28no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—44no—
836C2×C4—114no—
837C2×C4—114no—
838C2×C4—114no—
839C2×C4—114no—
840C2×C4—114no—
841C2×C4—224no—
842C2×C4—224no—
843C2×C4—224no—
844C2×C4—224no—
845C2×C4—224no—
846C2×C4—2216no—
847C2×C4—2216no—
848C2×C4—2216no—
849C2×C4—4416no—
850C2×C4—4416no—
851C2×C4—4416no—
852C2×C4#6704014yes—
853C2×C4#6704214yes—
854C2×C4C24×D1118yes—
855C2×C4C24×D1112yes—
856C2×C4C24×D1112yes—
857C2×C4C24×D1112yes—
858C2×C4C24×D1112yes—
859C2×C4C24×D1118yes—
860C2×C4C24×D1112yes—
861C2×C4C24×D1112yes—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—44no—
866C22—224no—
867C22—224no—
868C22—224no—
869C22—224no—
870C22—224no—
871C22—224no—
872C22—224no—
873C22—224no—
874C22—224no—
875C22—448no—
876C22—448no—
877C22—448no—
878C22C2×#6704012yes—
879C22C2×#6704212yes—
880C22#1062345312yes—
881C22C25×D1111yescharacteristic
882C4—22no—
883C4—28no—
884C4—22no—
885C4—22no—
886C4—22no—
887C4—28no—
888C4—224no—
889C4—224no—
890C4—224no—
891C4—224no—
892C4—224no—
893C4C2×#6704014yes—
894C4C2×#6704214yes—
895C2—42no—
896C2—444no—
897C2—444no—
898C2—444no—
899C2#1308299914yesdirect product factor
900C2C22×#6704211yescharacteristic
901C2C22×#6704011yescharacteristic
902C2C2×#1062345311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#533C2
socleC23×C11C25
hypercenterC2×#533D11
hypocenterC11C2×#3547
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #13082999C2direct (N × H)
2. C2×#10623178C2semidirect
3. C2×#10623265C2semidirect
4. C2×#10623063C2semidirect
5. C2×#10623261C2semidirect
6. C2×#10623061C2semidirect
7. C2×#10623112C2semidirect
8. C2×#10623258C2semidirect
9. C2×#10623107C2semidirect
10. C2×#10623257C2semidirect
11. C2×#10623220C2semidirect
12. C2×#10623113C2semidirect
13. C2×#10623229C2semidirect
14. C2×#10623160C2semidirect
15. C2×#10623159C2semidirect
16. C2×#10623008C2semidirect
17. C2×#10623010C2semidirect
18. C2×C11×#533C2semidirect
22. C11×#533C22semidirect
43. #10623265C22semidirect
44. #10623261C22semidirect
45. #10623258C22semidirect
46. #10623257C22semidirect
47. #10623229C22semidirect
48. #10623220C22semidirect
49. #10623178C22semidirect
50. #10623160C22semidirect
51. #10623159C22semidirect
52. #10623113C22semidirect
53. #10623112C22semidirect
54. #10623107C22semidirect
55. #10623063C22semidirect
56. #10623061C22semidirect
83. #10623010C22semidirect
86. #10623008C22semidirect
359. C2×#533D11semidirect
446. #533C2×D11semidirect
678. C2×C11#3547semidirect
794. C11C2×#3547semidirect
899. C2#13082999direct (N × H)

Maximal subgroups

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

subgroupindex
#130829992
C2×#106231782
C2×#106232652
C2×#106230632
C2×#106232612
C2×#106230612
C2×#106231122
C2×#106232582
C2×#106231072
C2×#106232572
C2×#106232202
C2×#106231132
C2×#106232292
C2×#106231602
C2×#106231592
C2×#106230082
C2×#106230102
C2×C11×#5332
C2×#354711