Finite Group Databasebeta

← C2×#13082516 #15662147

Subgroups — C2×#13082516 #15662147

Order 2816.

7758 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082516C2132yesmaximal, direct product factor
2C2×#10623064C212yesmaximal, complemented
3C2×#10623094C211yesmaximal, characteristic, complemented
4C2×#10623261C211yesmaximal, characteristic, complemented
5C2×#10623074C211yesmaximal, characteristic, complemented
6C2×#10623145C212yesmaximal, complemented
7C2×#10623061C212yesmaximal, complemented
8C2×#10623208C214yesmaximal, complemented
9C2×#10623142C212yesmaximal, complemented
10C2×#10623200C214yesmaximal, complemented
11C2×#10623139C212yesmaximal, complemented
12C2×#10623048C212yesmaximal, complemented
13C2×#10623079C211yesmaximal, characteristic, complemented
14C2×#10623127C212yesmaximal, complemented
15C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
16C2×#10623054C212yesmaximal, complemented
17C2×C4×#4341C211yesmaximal, characteristic, complemented
18C2×C11×#555C211yesmaximal, characteristic, complemented
19C22×Q8×D11C2212yes—
20C22×#4341C2211yescharacteristic
21C22×#4341C2214yes—
22C22×#4339C2212yes—
23C11×#555C22116yescomplemented
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×#124C2214yes—
26C2×C11×#121C2212yes—
27C2×C11×#121C2212yes—
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C11×#117C2212yes—
31C2×C11×#117C2212yes—
32C2×#66999C2214yes—
33C2×#66997C2212yes—
34C2×#66993C2211yescharacteristic
35C2×#66992C2214yes—
36C2×#66991C2211yescharacteristic
37C2×#66991C2214yes—
38C2×#66991C2212yes—
39C2×#66988C2214yes—
40C2×D4×Dic11C2212yes—
41C2×D4×Dic11C2211yescharacteristic
42C2×#66983C2212yes—
43C2×C4×C22⋊D11C2212yes—
44C2×C4×C22⋊D11C2212yes—
45C2×#66979C2212yes—
46C22×C4⋊Dic11C2212yes—
47C2×#66977C2212yes—
48C22×C4×Dic11C2212yes—
49#10623261C22116yescomplemented
50D11×C4⋊Q8C22116yescomplemented
51#10623208C22164yescomplemented
52#10623200C22164yescomplemented
53#10623145C22132yescomplemented
54#10623142C22132yescomplemented
55#10623139C22132yescomplemented
56#10623127C22132yescomplemented
57#10623094C22116yescomplemented
58#10623079C22116yescomplemented
59#10623074C22116yescomplemented
60C4×#4341C22116yescomplemented
61#10623064C22132yescomplemented
62#10623061C22132yescomplemented
63#10623054C22132yescomplemented
64#10623048C22132yescomplemented
65C2×#66950C2212yes—
66C2×#66948C2211yescharacteristic
67C2×#66946C2212yes—
68C2×#66945C2212yes—
69C2×#66945C2211yescharacteristic
70C2×C4⋊C4×D11C2212yes—
71C2×C4⋊C4×D11C2212yes—
72C2×C4⋊C4×D11C2212yes—
73C2×#66943C2212yes—
74C2×#66943C2212yes—
75C2×#66941C2212yes—
76C2×#66941C2212yes—
77C2×#66941C2211yescharacteristic
78C2×#66940C2211yescharacteristic
79C2×#66938C2214yes—
80C2×#66938C2212yes—
81C2×#66938C2214yes—
82C2×#66937C2214yes—
83C2×#66937C2212yes—
84C2×#66936C2214yes—
85C2×(C22⋊D11)⋊C4C2214yes—
86C2×(C22⋊D11)⋊C4C2214yes—
87C2×(C22⋊D11)⋊C4C2212yes—
88C2×#66932C2214yes—
89C2×#66931C2214yes—
90C2×#66931C2214yes—
91C2×#66931C2214yes—
92C2×#66930C2212yes—
93C2×#66929C2214yes—
94C2×C4×D44C2214yes—
95C2×C4×D44C2211yescharacteristic
96C2×C42×D11C2211yescharacteristic
97C2×#66922C2211yescharacteristic
98C2×C4×Dic22C2211yescharacteristic
99C2×C4×Dic22C2214yes—
100C2×C4×Dic22C2214yes—
101C22×Q8×C11C2312yes—
102C22×D4×C11C2311yescharacteristic
103C22×D4×C11C2311yescharacteristic
104C22×D4×C11C2314yes—
105C23×C4×C11C2312yes—
106C23×C4×C11C2312yes—
107C22×C22⋊D11C2312yes—
108C22×C22⋊D11C2312yes—
109C22×C22⋊D11C2312yes—
110C22×C22⋊D11C2312yes—
111C22×C22⋊D11C2314yes—
112C23×Dic11C2312yes—
113C23×Dic11C2312yes—
114C23×Dic11C2314yes—
115C2×Q8×D11—48no—
116C2×Q8×D11C23116yes—
117C2×#4341—28no—
118C2×#4341—416no—
119C2×#4341C2318yes—
120C2×#4341C23132yes—
121C2×#4339—216no—
122C2×#4339C23116yes—
123C22×D44C2312yes—
124C22×D44C2311yescharacteristic
125C22×C4×D11C2311yescharacteristic
126C22×C4×D11C2311yescharacteristic
127C22×C4×D11C2312yes—
128C22×C4×D11C2314yes—
129C22×C4×D11C2314yes—
130C22×C4×D11C2311yescharacteristic
131C22×Dic22C2312yes—
132C22×Dic22C2314yes—
133C22×Dic22C2311yescharacteristic
134C22×Dic22C2312yes—
135C11×C4⋊Q8C2318yes—
136C11×#124C23132yes—
137C11×#121C23116yes—
138C11×#121C23116yes—
139C4×D4×C11C2318yes—
140C4×D4×C11C2318yes—
141C11×#117C23116yes—
142C11×#117C23116yes—
143C2×C11×C4⋊C4C2311yescharacteristic
144C2×C11×C4⋊C4C2311yescharacteristic
145C2×C11×C4⋊C4C2312yes—
146C2×C11×C4⋊C4C2312yes—
147C2×C11×C22⋊C4C2312yes—
148C2×C11×C22⋊C4C2314yes—
149C2×C11×C22⋊C4C2312yes—
150C2×C11×C22⋊C4C2314yes—
151C2×C42×C11C2314yes—
152C2×C42×C11C2311yescharacteristic
153C2×C22⋊Dic11C2312yes—
154C2×C22⋊Dic11C2314yes—
155C2×C22⋊Dic11C2314yes—
156C2×C22⋊Dic11C2312yes—
157#66999C23132yes—
158#66997C23116yes—
159#66993C2318yes—
160#66992C23132yes—
161#66991C2318yes—
162#66991C23116yes—
163#66991C23132yes—
164#66988C23132yes—
165D4×Dic11C2318yes—
166D4×Dic11C23116yes—
167#66983C23116yes—
168C4×C22⋊D11C23116yes—
169C4×C22⋊D11C23116yes—
170C2×(C2×D11)⋊C4C2312yes—
171C2×(C2×D11)⋊C4C2314yes—
172C2×(C2×D11)⋊C4C2312yes—
173C2×(C2×D11)⋊C4C2312yes—
174C2×(C2×D11)⋊C4C2314yes—
175#66979C23116yes—
176C2×C4⋊Dic11C2314yes—
177C2×C4⋊Dic11C2314yes—
178C2×C4⋊Dic11C2311yescharacteristic
179C2×C4⋊Dic11C2312yes—
180C2×C4⋊Dic11C2312yes—
181C2×C4⋊Dic11C2311yescharacteristic
182C2×C4⋊Dic11C23116yes—
183#66977C23116yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2314yes—
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C2314yes—
188C2×Dic11⋊C4C2314yes—
189C2×Dic11⋊C4C2312yes—
190C2×Dic11⋊C4C2314yes—
191C2×C4×Dic11C2312yes—
192C2×C4×Dic11C2314yes—
193C2×C4×Dic11C2312yes—
194C2×C4×Dic11C2312yes—
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2311yescharacteristic
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C23116yes—
199#66950C23116yes—
200#66948C2318yes—
201#66946C23116yes—
202#66945C2318yes—
203#66945C23116yes—
204C4⋊C4×D11C23116yes—
205C4⋊C4×D11C23116yes—
206C4⋊C4×D11C23116yes—
207#66943C23116yes—
208#66943C23116yes—
209#66941C23116yes—
210#66941C23116yes—
211#66941C2318yes—
212#66940C2318yes—
213#66938C23132yes—
214#66938C23116yes—
215#66938C23132yes—
216#66937C23132yes—
217#66937C23116yes—
218#66936C23132yes—
219(C22⋊D11)⋊C4C23132yes—
220(C22⋊D11)⋊C4C23132yes—
221(C22⋊D11)⋊C4C23116yes—
222#66932C23132yes—
223#66931C23132yes—
224#66931C23132yes—
225#66931C23132yes—
226#66930C23116yes—
227#66929C23132yes—
228C4×D44C2318yes—
229C4×D44C23132yes—
230C42×D11C2318yes—
231#66922C2318yes—
232C4×Dic22C2318yes—
233C4×Dic22C23132yes—
234C4×Dic22C23132yes—
235C2×#3511—111nomaximal, Sylow
236C24×C11C2412yes—
237C24×C11C2412yes—
238C23×D11C2412yes—
239C23×D11C2411yescharacteristic
240C2×Q8×C11—44no—
241C2×Q8×C11C2418yes—
242C2×D4×C11—24no—
243C2×D4×C11—24no—
244C2×D4×C11—48no—
245C2×D4×C11C2414yes—
246C2×D4×C11C2414yes—
247C2×D4×C11C24116yes—
248C22×C4×C11—28no—
249C22×C4×C11—28no—
250C22×C4×C11C2412yes—
251C22×C4×C11C2418yes—
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2412yes—
254C22×C4×C11C2414yes—
255C22×C4×C11C2418yes—
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C2×C22⋊D11—28no—
259C2×C22⋊D11—28no—
260C2×C22⋊D11—28no—
261C2×C22⋊D11—28no—
262C2×C22⋊D11—48no—
263C2×C22⋊D11C2418yes—
264C2×C22⋊D11C2418yes—
265C2×C22⋊D11C2418yes—
266C2×C22⋊D11C2418yes—
267C2×C22⋊D11C24116yes—
268C22×Dic11—28no—
269C22×Dic11—28no—
270C22×Dic11—48no—
271C22×Dic11C2418yes—
272C22×Dic11C2418yes—
273C22×Dic11C2411yescharacteristic
274C22×Dic11C2412yes—
275C22×Dic11C2412yes—
276C22×Dic11C2412yes—
277C22×Dic11C2414yes—
278C22×Dic11C24116yes—
279C22×Dic11C2411yescharacteristic
280C22×Dic11C2411yescharacteristic
281Q8×D11—432no—
282#4341—232no—
283#4341—464no—
284#4339—264no—
285C2×D44—28no—
286C2×D44—24no—
287C2×D44C2418yes—
288C2×D44C2414yes—
289C2×C4×D11—24no—
290C2×C4×D11—28no—
291C2×C4×D11—24no—
292C2×C4×D11—48no—
293C2×C4×D11—48no—
294C2×C4×D11#4118yescomplemented
295C2×C4×D11C2414yes—
296C2×C4×D11C2414yes—
297C2×C4×D11C2418yes—
298C2×C4×D11C24116yes—
299C2×C4×D11C24116yes—
300C2×C4×D11C2414yes—
301C2×Dic22—28no—
302C2×Dic22—216no—
303C2×Dic22—24no—
304C2×Dic22—44no—
305C2×Dic22C2418yes—
306C2×Dic22C24116yes—
307C2×Dic22C2414yes—
308C2×Dic22C2418yes—
309C11×C4⋊C4C2414yes—
310C11×C4⋊C4C2414yes—
311C11×C4⋊C4C2418yes—
312C11×C4⋊C4C2418yes—
313C11×C22⋊C4C2418yes—
314C11×C22⋊C4C24116yes—
315C11×C22⋊C4C2418yes—
316C11×C22⋊C4C24116yes—
317C42×C11C24116yes—
318C42×C11C2414yes—
319C22⋊Dic11C2418yes—
320C22⋊Dic11C24116yes—
321C22⋊Dic11C24116yes—
322C22⋊Dic11C2418yes—
323(C2×D11)⋊C4C2418yes—
324(C2×D11)⋊C4C24116yes—
325(C2×D11)⋊C4C2418yes—
326(C2×D11)⋊C4C2418yes—
327(C2×D11)⋊C4C24116yes—
328C4⋊Dic11C24116yes—
329C4⋊Dic11C24116yes—
330C4⋊Dic11C2414yes—
331C4⋊Dic11C2418yes—
332C4⋊Dic11C2418yes—
333C4⋊Dic11C2414yes—
334Dic11⋊C4C2418yes—
335Dic11⋊C4C24116yes—
336Dic11⋊C4C2418yes—
337Dic11⋊C4C24116yes—
338Dic11⋊C4C24116yes—
339Dic11⋊C4C2418yes—
340Dic11⋊C4C24116yes—
341C4×Dic11C2418yes—
342C4×Dic11C24116yes—
343C4×Dic11C2418yes—
344C4×Dic11C2418yes—
345C4×Dic11C2414yes—
346C4×Dic11C2414yes—
347C4×Dic11C2414yes—
348#3511—1132no—
349C2×#556—112no—
350C2×#555—111no—
351C2×#555D1111yescharacteristic, complemented
352C2×#554—111no—
353C2×#554—111no—
354C2×#553—112no—
355C2×#553—112no—
356C2×#548—114no—
357C2×#547—112no—
358C2×#542—114no—
359C2×#537—112no—
360C2×#533—112no—
361C2×#532—112no—
362C2×#532—111no—
363C22×C4⋊Q8—111no—
364C2×#520—112no—
365C2×C4×#41—111no—
366C23×C11—24no—
367C23×C11—24no—
368C23×C11—24no—
369C23×C11—24no—
370C23×C11—24no—
371C23×C11—24no—
372C23×C11C2514yes—
373C23×C11C2514yes—
374C23×C11C2511yescharacteristic
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—24no—
378C22×D11—24no—
379C22×D11—24no—
380C22×D11C2×#4114yes—
381C22×D11C2514yes—
382C22×D11C2512yes—
383Q8×C11—48no—
384D4×C11—28no—
385D4×C11—28no—
386D4×C11—416no—
387C2×C4×C11—24no—
388C2×C4×C11—28no—
389C2×C4×C11—22no—
390C2×C4×C11—24no—
391C2×C4×C11—216no—
392C2×C4×C11—216no—
393C2×C4×C11C2×#4114yes—
394C2×C4×C112−1+414yes—
395C2×C4×C11C2514yes—
396C2×C4×C11C2512yes—
397C2×C4×C11C2514yes—
398C2×C4×C11C2518yes—
399C2×C4×C11C2512yes—
400C2×C4×C11C2512yes—
401C22⋊D11—216no—
402C22⋊D11—216no—
403C22⋊D11—216no—
404C22⋊D11—216no—
405C22⋊D11—416no—
406C2×Dic11—24no—
407C2×Dic11—24no—
408C2×Dic11—28no—
409C2×Dic11—24no—
410C2×Dic11—22no—
411C2×Dic11—216no—
412C2×Dic11—216no—
413C2×Dic11—416no—
414C2×Dic11C2×#4114yes—
415C2×Dic11H(5,𝔽2)14yes—
416C2×Dic11C2512yes—
417C2×Dic11C2514yes—
418C2×Dic11C2514yes—
419C2×Dic11C2514yes—
420C2×Dic11C2518yes—
421C2×Dic11C2512yes—
422C2×Dic11C2512yes—
423D44—216no—
424D44—28no—
425C4×D11—216no—
426C4×D11—28no—
427C4×D11—28no—
428C4×D11—416no—
429C4×D11—416no—
430C4×D11C2×#41116yescomplemented
431Dic22—28no—
432Dic22—216no—
433Dic22—232no—
434Dic22—48no—
435C22×#41—111no—
436C22×#41—114no—
437C22×#41—112no—
438C23×Q8—112no—
439#556—1132no—
440#555—1116no—
441#555C2×D11116yescomplemented
442#554—1116no—
443#554—1116no—
444#553—1132no—
445#553—1132no—
446#548—1164no—
447#547—1132no—
448#542—1164no—
449#537—1132no—
450#533—1132no—
451#532—1132no—
452#532—1116no—
453C2×C4⋊Q8—112no—
454C2×C4⋊Q8—1116no—
455C2×C4⋊Q8—112no—
456C2×C4⋊Q8—112no—
457C2×C4⋊Q8—111no—
458C2×C4⋊Q8—111no—
459C2×C4⋊Q8C2×D1111yescharacteristic
460C2×#127—111no—
461C2×#126—114no—
462C2×#126—114no—
463C2×#125—112no—
464C2×#125—112no—
465C2×#124—112no—
466C2×#124—114no—
467C2×#124—114no—
468C2×#124C2×D1114yes—
469C2×#123—114no—
470C2×#123—114no—
471C2×C22⋊Q8—114no—
472C2×C22⋊Q8—112no—
473C2×C22⋊Q8—112no—
474C2×C22⋊Q8—114no—
475C2×C22⋊Q8—114no—
476C2×C22⋊Q8—114no—
477C2×#121—111no—
478C2×#121—112no—
479C2×#121—114no—
480C2×#121—114no—
481C2×#121—112no—
482C2×#121—111no—
483C2×#121—112no—
484C2×#121—114no—
485C2×#121C2×D1112yes—
486C2×#121C2×D1112yes—
487#520—1132no—
488C4×#41—1116no—
489C2×C4×Q8—111no—
490C2×C4×Q8—111no—
491C2×C4×Q8—114no—
492C2×C4×Q8—114no—
493C2×C4×D4—111no—
494C2×C4×D4—112no—
495C2×C4×D4—112no—
496C2×C4×D4—112no—
497C2×C4×D4—112no—
498C2×C4×D4—112no—
499C2×C4×D4—114no—
500C2×C4×D4—114no—
501C2×C4×D4—114no—
502C2×C4×D4—111no—
503C2×C4×D4C2×D1111yescharacteristic
504C2×C4×D4C2×D1111yescharacteristic
505C2×#117—112no—
506C2×#117—111no—
507C2×#117—112no—
508C2×#117—112no—
509C2×#117C2×D1112yes—
510C2×#117C2×D1112yes—
511C22×C4⋊C4—112no—
512C22×C4⋊C4—112no—
513C22×C4⋊C4—112no—
514C22×C4⋊C4—112no—
515C22×C42—112no—
516C22×C42—111no—
517C22×C11—24no—
518C22×C11—24no—
519C22×C11—24no—
520C22×C11—24no—
521C22×C11—24no—
522C22×C11—24no—
523C22×C11—48no—
524C22×C11—48no—
525C22×C11C22×#4112yes—
526C22×C11C2×H(5,𝔽2)12yes—
527C22×C11C2×2−1+412yes—
528C22×C11C2611yescharacteristic
529C2×D11—22no—
530C2×D11—22no—
531C2×D11—28no—
532C2×D11—24no—
533C2×D11—24no—
534C2×D11—24no—
535C2×D11—48no—
536C2×D11C22×#4114yes—
537C4×C11—24no—
538C4×C11—28no—
539C4×C11—22no—
540C4×C11—24no—
541C4×C11C22×#4114yes—
542C4×C11C2×2−1+414yes—
543Dic11—24no—
544Dic11—24no—
545Dic11—28no—
546Dic11—24no—
547Dic11—22no—
548Dic11C22×#4114yes—
549Dic11C2×H(5,𝔽2)14yes—
550C2×#41—118no—
551C2×#41—1132no—
552C2×#41—1116no—
553C2×#41—2216no—
554C2×#41—228no—
555C2×#41—4416no—
556C22×Q8—1116no—
557C22×Q8—111no—
558C22×Q8—112no—
559C22×Q8—114no—
560C22×Q8—112no—
561C22×Q8—448no—
562C22×Q8C22×D1112yes—
563C22×D4—112no—
564C22×D4—112no—
565C22×D4—112no—
566C22×D4—112no—
567C22×D4—114no—
568C22×D4—111no—
569C22×D4—112no—
570C22×D4C22×D1111yescharacteristic
571C22×D4C22×D1111yescharacteristic
572C22×D4C22×D1114yes—
573C23×C4—111no—
574C23×C4—112no—
575C23×C4—112no—
576C23×C4—114no—
577C23×C4—111no—
578C23×C4—112no—
579C23×C4—111no—
580C23×C4—114no—
581C23×C4—114no—
582C23×C4C22×D1112yes—
583C23×C4C22×D1112yes—
584C4⋊Q8—1116no—
585C4⋊Q8—1116no—
586C4⋊Q8—1116no—
587C4⋊Q8—118no—
588C4⋊Q8—118no—
589C4⋊Q8C22×D1118yes—
590#127—118no—
591#126—1132no—
592#126—1132no—
593#125—1116no—
594#125—1116no—
595#124—1116no—
596#124—1132no—
597#124—1132no—
598#124C22×D11132yes—
599#123—1132no—
600#123—1132no—
601C22⋊Q8—1132no—
602C22⋊Q8—1116no—
603C22⋊Q8—1116no—
604C22⋊Q8—1132no—
605C22⋊Q8—1132no—
606C22⋊Q8—1132no—
607#121—1132no—
608#121—118no—
609#121—1116no—
610#121—1132no—
611#121—1116no—
612#121—118no—
613#121—1116no—
614#121—1132no—
615#121C22×D11116yes—
616#121C22×D11116yes—
617C4×Q8—118no—
618C4×Q8—118no—
619C4×Q8—1132no—
620C4×Q8—1132no—
621C4×D4—118no—
622C4×D4—1116no—
623C4×D4—1116no—
624C4×D4—1116no—
625C4×D4—1116no—
626C4×D4—1116no—
627C4×D4—1132no—
628C4×D4—1132no—
629C4×D4—1132no—
630C4×D4—118no—
631C4×D4C22×D1118yes—
632C4×D4C22×D1118yes—
633#117—1116no—
634#117—118no—
635#117—1116no—
636#117—1116no—
637#117C22×D11116yes—
638#117C22×D11116yes—
639C2×C4⋊C4—111no—
640C2×C4⋊C4—112no—
641C2×C4⋊C4—112no—
642C2×C4⋊C4—114no—
643C2×C4⋊C4—114no—
644C2×C4⋊C4—114no—
645C2×C4⋊C4—1116no—
646C2×C4⋊C4—114no—
647C2×C4⋊C4—111no—
648C2×C4⋊C4—112no—
649C2×C4⋊C4—112no—
650C2×C4⋊C4—112no—
651C2×C4⋊C4—114no—
652C2×C4⋊C4—114no—
653C2×C4⋊C4—1116no—
654C2×C4⋊C4—1116no—
655C2×C4⋊C4—1116no—
656C2×C4⋊C4C22×D1112yes—
657C2×C4⋊C4C22×D1112yes—
658C2×C4⋊C4C22×D1111yescharacteristic
659C2×C4⋊C4C22×D1111yescharacteristic
660C2×C22⋊C4—112no—
661C2×C22⋊C4—114no—
662C2×C22⋊C4—114no—
663C2×C22⋊C4—112no—
664C2×C22⋊C4—112no—
665C2×C22⋊C4—114no—
666C2×C22⋊C4—114no—
667C2×C22⋊C4—112no—
668C2×C22⋊C4—112no—
669C2×C22⋊C4C22×D1112yes—
670C2×C22⋊C4C22×D1114yes—
671C2×C22⋊C4C22×D1114yes—
672C2×C22⋊C4C22×D1112yes—
673C2×C42—112no—
674C2×C42—114no—
675C2×C42—111no—
676C2×C42—112no—
677C2×C42—111no—
678C2×C42—112no—
679C2×C42—1116no—
680C2×C42—111no—
681C2×C42—118no—
682C2×C42C22×D1114yes—
683C2×C42C22×D1111yescharacteristic
684C2×C11—44no—
685C2×C11—44no—
686C2×C11#351114yescomplemented
687C2×C11C23×#4111yescharacteristic
688C2×C11C22×H(5,𝔽2)11yescharacteristic
689C2×C11C22×2−1+411yescharacteristic
690D11—24no—
691D11—44no—
692C24—111no—
693C24—112no—
694C24C23×D1112yes—
695C24C23×D1112yes—
696#41—2264no—
697#41—2232no—
698#41—4464no—
699C2×Q8—44no—
700C2×Q8—114no—
701C2×Q8—118no—
702C2×Q8—1116no—
703C2×Q8—118no—
704C2×Q8—2216no—
705C2×Q8—228no—
706C2×Q8—224no—
707C2×Q8—444no—
708C2×Q8—4432no—
709C2×Q8C23×D1118yes—
710C2×D4—24no—
711C2×D4—24no—
712C2×D4—48no—
713C2×D4—118no—
714C2×D4—118no—
715C2×D4—118no—
716C2×D4—118no—
717C2×D4—1116no—
718C2×D4—114no—
719C2×D4—118no—
720C2×D4—228no—
721C2×D4—228no—
722C2×D4—228no—
723C2×D4—228no—
724C2×D4—228no—
725C2×D4—224no—
726C2×D4—448no—
727C2×D4C23×D1114yes—
728C2×D4C23×D1114yes—
729C2×D4C23×D11116yes—
730C22×C4—28no—
731C22×C4—28no—
732C22×C4—111no—
733C22×C4—111no—
734C22×C4—118no—
735C22×C4—114no—
736C22×C4—118no—
737C22×C4—118no—
738C22×C4—111no—
739C22×C4—112no—
740C22×C4—112no—
741C22×C4—112no—
742C22×C4—114no—
743C22×C4—1116no—
744C22×C4—114no—
745C22×C4—114no—
746C22×C4—118no—
747C22×C4—1116no—
748C22×C4—1116no—
749C22×C4—224no—
750C22×C4—228no—
751C22×C4—228no—
752C22×C4—228no—
753C22×C4—224no—
754C22×C4—448no—
755C22×C4—448no—
756C22×C4—448no—
757C22×C4C23×D1118yes—
758C22×C4C23×D1118yes—
759C22×C4C23×D1112yes—
760C22×C4C23×D1111yescharacteristic
761C22×C4C23×D1112yes—
762C22×C4C23×D1114yes—
763C22×C4C23×D1111yescharacteristic
764C22×C4C23×D1111yescharacteristic
765C4⋊C4—114no—
766C4⋊C4—118no—
767C4⋊C4—118no—
768C4⋊C4—1116no—
769C4⋊C4—1116no—
770C4⋊C4—1116no—
771C4⋊C4—1116no—
772C4⋊C4—114no—
773C4⋊C4—118no—
774C4⋊C4—118no—
775C4⋊C4—118no—
776C4⋊C4—1116no—
777C4⋊C4—1116no—
778C4⋊C4C23×D1118yes—
779C4⋊C4C23×D1118yes—
780C4⋊C4C23×D1114yes—
781C4⋊C4C23×D1114yes—
782C22⋊C4—118no—
783C22⋊C4—1116no—
784C22⋊C4—1116no—
785C22⋊C4—118no—
786C22⋊C4—118no—
787C22⋊C4—1116no—
788C22⋊C4—1116no—
789C22⋊C4—118no—
790C22⋊C4—118no—
791C22⋊C4C23×D1118yes—
792C22⋊C4C23×D11116yes—
793C22⋊C4C23×D11116yes—
794C22⋊C4C23×D1118yes—
795C42—114no—
796C42—118no—
797C42—114no—
798C42—118no—
799C42—114no—
800C42—118no—
801C42—1116no—
802C42C23×D1114yes—
803C42C23×D11116yes—
804C11C2×#351111yescharacteristic, complemented, Sylow
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—114no—
812C23—112no—
813C23—114no—
814C23—222no—
815C23—222no—
816C23—224no—
817C23—224no—
818C23—224no—
819C23C24×D1114yes—
820C23C24×D1114yes—
821C23C24×D1111yescharacteristic
822Q8—48no—
823Q8—2232no—
824Q8—2216no—
825Q8—228no—
826Q8—448no—
827D4—28no—
828D4—28no—
829D4—416no—
830D4—2216no—
831D4—2216no—
832D4—2216no—
833D4—2216no—
834D4—2216no—
835D4—228no—
836D4—4416no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—22no—
840C2×C4—28no—
841C2×C4—216no—
842C2×C4—216no—
843C2×C4—114no—
844C2×C4—114no—
845C2×C4—112no—
846C2×C4—112no—
847C2×C4—1116no—
848C2×C4—112no—
849C2×C4—114no—
850C2×C4—114no—
851C2×C4—114no—
852C2×C4—118no—
853C2×C4—228no—
854C2×C4—2216no—
855C2×C4—2216no—
856C2×C4—224no—
857C2×C4—224no—
858C2×C4—222no—
859C2×C4—224no—
860C2×C4—228no—
861C2×C4—2216no—
862C2×C4—228no—
863C2×C4—4416no—
864C2×C4—4416no—
865C2×C4—4416no—
866C2×C4#41×D1114yes—
867C2×C4#6704314yes—
868C2×C4C24×D1114yes—
869C2×C4C24×D1112yes—
870C2×C4C24×D1114yes—
871C2×C4C24×D1118yes—
872C2×C4C24×D1112yes—
873C2×C4C24×D1112yes—
874C22—24no—
875C22—24no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—24no—
880C22—48no—
881C22—48no—
882C22—114no—
883C22—222no—
884C22—222no—
885C22—228no—
886C22—224no—
887C22—224no—
888C22—224no—
889C22—448no—
890C22C2×#41×D1112yes—
891C22C2×#6704312yes—
892C22D11×H(5,𝔽2)12yes—
893C22C25×D1111yescharacteristic
894C4—24no—
895C4—22no—
896C4—28no—
897C4—24no—
898C4—114no—
899C4—114no—
900C4—224no—
901C4—224no—
902C4—224no—
903C4—228no—
904C4—222no—
905C4C2×#41×D1114yes—
906C4C2×#6704314yes—
907C2—44no—
908C2—44no—
909C2—224no—
910C2—444no—
911C2#1308251614yesdirect product factor
912C2C22×#41×D1111yescharacteristic
913C2C2×D11×H(5,𝔽2)11yescharacteristic
914C2C22×#6704311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#555C2
socleC23×C11C25
hypercenterC2×#555D11
hypocenterC11C2×#3511
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. #13082516C2direct (N × H)
2. C2×#10623064C2semidirect
3. C2×#10623094C2semidirect
4. C2×#10623261C2semidirect
5. C2×#10623074C2semidirect
6. C2×#10623145C2semidirect
7. C2×#10623061C2semidirect
8. C2×#10623208C2semidirect
9. C2×#10623142C2semidirect
10. C2×#10623200C2semidirect
11. C2×#10623139C2semidirect
12. C2×#10623048C2semidirect
13. C2×#10623079C2semidirect
14. C2×#10623127C2semidirect
15. C2×D11×C4⋊Q8C2semidirect
16. C2×#10623054C2semidirect
17. C2×C4×#4341C2semidirect
18. C2×C11×#555C2semidirect
23. C11×#555C22semidirect
49. #10623261C22semidirect
50. D11×C4⋊Q8C22semidirect
51. #10623208C22semidirect
52. #10623200C22semidirect
53. #10623145C22semidirect
54. #10623142C22semidirect
55. #10623139C22semidirect
56. #10623127C22semidirect
57. #10623094C22semidirect
58. #10623079C22semidirect
59. #10623074C22semidirect
60. C4×#4341C22semidirect
61. #10623064C22semidirect
62. #10623061C22semidirect
63. #10623054C22semidirect
64. #10623048C22semidirect
294. C2×C4×D11#41semidirect
351. C2×#555D11semidirect
430. C4×D11C2×#41semidirect
441. #555C2×D11semidirect
686. C2×C11#3511semidirect
804. C11C2×#3511semidirect
911. C2#13082516direct (N × H)

Maximal subgroups

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

subgroupindex
#130825162
C2×#106230642
C2×#106230942
C2×#106232612
C2×#106230742
C2×#106231452
C2×#106230612
C2×#106232082
C2×#106231422
C2×#106232002
C2×#106231392
C2×#106230482
C2×#106230792
C2×#106231272
C2×D11×C4⋊Q82
C2×#106230542
C2×C4×#43412
C2×C11×#5552
C2×#351111