Finite Group Databasebeta

← #16771461

Subgroups — #16771461

Order 3328.

11346 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719650C212yesmaximal, complemented
2#13128622C218yesmaximal, complemented
3#13128615C214yesmaximal, complemented
4#13128608C214yesmaximal, complemented
5#13128605C212yesmaximal, complemented
6#13128602C212yesmaximal, complemented
7#13128600C211yesmaximal, characteristic, complemented
8#13128597C214yesmaximal, complemented
9#13128595C212yesmaximal, complemented
10#13128593C214yesmaximal, complemented
11#13128323C214yesmaximal, complemented
12#13128320C218yesmaximal, complemented
13D4×#6129C214yesmaximal, complemented
14#13128164C212yesmaximal, complemented
15#13128162C214yesmaximal, complemented
16C2×#11719301C214yesmaximal, complemented
17D13×#532C212yesmaximal, complemented
18C2×C4×#6129C211yesmaximal, characteristic, complemented
19C13×#3496C211yesmaximal, characteristic, complemented
20C2×C13×H(5,𝔽2)C2212yescomplemented
21#11719650—232no—
22C2×#88257C2214yescomplemented
23C2×#88257C2218yescomplemented
24C2×#41×D13C2218yescomplemented
25C2×#41×D13C2214yescomplemented
26C2×#88251C2218yescomplemented
27C2×#88251C2212yescomplemented
28C2×#88251C2218yescomplemented
29C22×#6129C2211yescharacteristic
30C22×#6129C2218yescomplemented
31C22×#6129C2218yescomplemented
32C13×#547C2214yescomplemented
33C13×#546C2218yescomplemented
34D42×C13C2214yescomplemented
35C13×#537C2212yescomplemented
36C13×#534C2214yescomplemented
37C13×#532C2212yescomplemented
38C2×C13×#121C2214yescomplemented
39C2×C4×D4×C13C2211yescharacteristic, complemented
40#11719538C2214yescomplemented
41#11719537C2214yescomplemented
42#11719534C2218yescomplemented
43#11719529C2218yescomplemented
44#11719511C2218yescomplemented
45#11719509C2218yescomplemented
46C2×#88194C2214yescomplemented
47C2×#88193C2218yescomplemented
48D4×C22⋊D13C2218yescomplemented
49D4×C22⋊D13C2218yescomplemented
50C2×D4×Dic13C2211yescharacteristic, complemented
51C2×D4×Dic13C2214yescomplemented
52C2×#88184C2214yescomplemented
53C2×C4×C22⋊D13C2212yescomplemented
54C22×C4×Dic13C2212yescomplemented
55#11719432C2214yescomplemented
56#11719430C2212yescomplemented
57D13×C4⋊Q8C2212yescomplemented
58#11719423C2214yescomplemented
59#11719421C2212yescomplemented
60D13×#127C2212yescomplemented
61#11719382C2218yescomplemented
62D13×#124C2214yescomplemented
63#11719373C2214yescomplemented
64#11719361C22116yescomplemented
65#11719360C22116yescomplemented
66#11719359C22116yescomplemented
67#11719353C22116yescomplemented
68#11719338C2218yescomplemented
69#11719337C2218yescomplemented
70#11719333C2218yescomplemented
71#11719332C2218yescomplemented
72#11719316C2218yescomplemented
73#11719315C22116yescomplemented
74#11719314C2218yescomplemented
75#11719312C2218yescomplemented
76#11719311C2218yescomplemented
77#11719310C2218yescomplemented
78D13×#121C2214yescomplemented
79D13×#121C2214yescomplemented
80#11719304C2218yescomplemented
81#11719303C2218yescomplemented
82#11719302C2218yescomplemented
83#11719302C2218yescomplemented
84#11719301C2218yescomplemented
85#11719301C2218yescomplemented
86#11719301C2218yescomplemented
87#11719301C2218yescomplemented
88#11719301C2218yescomplemented
89#11719301C2218yescomplemented
90#11719301C2214yescomplemented
91#11719301C2214yescomplemented
92#11719301C2218yescomplemented
93#11719297C22116yescomplemented
94#11719296C22116yescomplemented
95#11719295C22116yescomplemented
96#11719291C22116yescomplemented
97#11719260C2214yescomplemented
98#11719259C2218yescomplemented
99#11719258C2214yescomplemented
100#11719257C2218yescomplemented
101D4×D52C2214yescomplemented
102#11719253C2214yescomplemented
103#11719253C2214yescomplemented
104C4×D4×D13C2214yescomplemented
105C4×D4×D13C2214yescomplemented
106D4×Dic26C2214yescomplemented
107C4×#6129C2214yescomplemented
108C4×#6129C2214yescomplemented
109C4×#6129C2214yescomplemented
110C4×#6129C2214yescomplemented
111#11719215C2212yescomplemented
112#11719212C2218yescomplemented
113C2×#88147C2214yescomplemented
114C2×#88146C2211yescharacteristic, complemented
115C2×#88142C2214yescomplemented
116C2×#88141C2211yescharacteristic, complemented
117#11719198C2214yescomplemented
118C2×#88139C2218yescomplemented
119#11719195C22116yescomplemented
120C2×#88135C2212yescomplemented
121C2×#88135C2218yescomplemented
122C2×#88131C2212yescomplemented
123#11719182C2212yescomplemented
124C2×C42×D13C2211yescharacteristic, complemented
125C2×C4×Dic26C2211yescharacteristic, complemented
126C13×H(5,𝔽2)—216no—
127C2×C13×#41C2318yes—
128C2×C13×#41C2314yes—
129C22×D4×C13C2318yes—
130C22×D4×C13C2318yes—
131C22×D4×C13C2314yes—
132C22×D4×C13C2311yescharacteristic
133C23×C4×C13C2312yes—
134C22×C22⋊D13C23116yes—
135C22×C22⋊D13C2318yes—
136C22×C22⋊D13C2318yes—
137C22×C22⋊D13C2318yes—
138C22×C22⋊D13C2312yes—
139C23×Dic13C2318yes—
140C23×Dic13C2312yes—
141C23×Dic13C2312yes—
142#88257—264no—
143#88257—232no—
144#41×D13—264no—
145#41×D13—232no—
146C2×#6131C2314yes—
147C2×Q8×D13C2314yes—
148C2×Q8×D13C2318yes—
149#88251—216no—
150#88251—264no—
151#88251—264no—
152C2×#6129—264no—
153C2×#6129—264no—
154C2×#6129D4116yescomplemented
155C2×#6129C2318yes—
156C2×#6129C23116yes—
157C2×#6129C23116yes—
158C2×#6129C23116yes—
159C2×#6129C2318yes—
160C2×#6129C23116yes—
161C2×#6129C2318yes—
162C2×#6129C2314yes—
163C2×#6129C2314yes—
164C2×#6129C2314yes—
165C2×D4×D13C2318yes—
166C2×D4×D13C23116yes—
167C2×D4×D13C2318yes—
168C2×D4×D13C2314yes—
169C2×D4×D13C2314yes—
170C2×D4×D13C2314yes—
171C2×#6127C2314yes—
172C2×#6127C23116yes—
173C2×#6127C2318yes—
174C2×#6127C2318yes—
175C22×D52C2314yes—
176C22×C4×D13C2318yes—
177C22×C4×D13C2318yes—
178C22×C4×D13C2311yescharacteristic
179C22×C4×D13C2311yescharacteristic
180C22×C4×D13C2311yescharacteristic
181C22×Dic26C2318yes—
182C22×Dic26C2318yes—
183C22×Dic26C2311yescharacteristic
184C13×C4⋊Q8C2312yes—
185C13×#127C2312yes—
186C13×#124C2314yes—
187C13×#123C23116yes—
188C13×C22⋊Q8C2318yes—
189C13×#121C2314yes—
190C13×#121C2318yes—
191C13×#121C2318yes—
192C13×#121C2318yes—
193C13×#121C2314yes—
194C13×#121C2318yes—
195C13×#120C23116yes—
196C4×D4×C13C2314yes—
197C4×D4×C13C2314yes—
198C4×D4×C13C2314yes—
199C4×D4×C13C2314yes—
200C2×C13×C4⋊C4C2311yescharacteristic
201C2×C13×C4⋊C4C2314yes—
202C2×C13×C22⋊C4C2312yes—
203C2×C13×C22⋊C4C2318yes—
204C2×C42×C13C2311yescharacteristic
205#88207C23116yes—
206C2×C22⋊Dic13C2312yes—
207C2×C22⋊Dic13C2318yes—
208#88201C2314yes—
209#88200C2318yes—
210#88198C2314yes—
211#88194C2314yes—
212#88194C2318yes—
213#88194C2314yes—
214#88194C2318yes—
215#88194C2318yes—
216#88194C2314yes—
217#88193C23116yes—
218#88193C23116yes—
219#88193C2318yes—
220#88193C23116yes—
221#88193C23116yes—
222#88193C2318yes—
223#88193C23116yes—
224#88192C2314yes—
225#88192C2318yes—
226#88192C2314yes—
227#88191C23116yes—
228#88191C23116yes—
229#88190C2314yes—
230#88189C23116yes—
231D4×Dic13C2314yes—
232D4×Dic13C2314yes—
233D4×Dic13C2318yes—
234D4×Dic13C2314yes—
235D4×Dic13C2318yes—
236D4×Dic13C2318yes—
237D4×Dic13C2314yes—
238#88184C2314yes—
239#88184C2314yes—
240#88184C2318yes—
241#88184C2318yes—
242#88184C2318yes—
243#88184C2318yes—
244#88183C23116yes—
245C4×C22⋊D13C2318yes—
246C4×C22⋊D13C2318yes—
247C4×C22⋊D13C2318yes—
248C4×C22⋊D13C2318yes—
249C2×#6103C2318yes—
250C2×#6103C2312yes—
251C2×#6103C2318yes—
252C2×C4⋊Dic13C2311yescharacteristic
253C2×C4⋊Dic13C2314yes—
254#88178C2318yes—
255C2×#6101C2312yes—
256C2×#6101C2312yes—
257C2×#6101C2318yes—
258C2×C4×Dic13C2312yes—
259C2×C4×Dic13C2311yescharacteristic
260C2×C4×Dic13C2311yescharacteristic
261C2×C4×Dic13C2311yescharacteristic
262C2×C4×Dic13C2312yes—
263C2×C4×Dic13C2314yes—
264C2×C4×Dic13C2312yes—
265C2×C4×Dic13C2314yes—
266C2×C4×Dic13C2314yes—
267C2×C4×Dic13C2314yes—
268#88151C2318yes—
269#88150C23116yes—
270#88150C23116yes—
271#88149C2314yes—
272#88149C2314yes—
273#88149C2318yes—
274#88148C23116yes—
275#88147C2314yes—
276#88147C2314yes—
277#88147C2318yes—
278#88147C2318yes—
279#88147C2318yes—
280#88146C2314yes—
281#88146C2314yes—
282C4⋊C4×D13C2314yes—
283C4⋊C4×D13C2314yes—
284#88142C2314yes—
285#88142C2314yes—
286#88142C2318yes—
287#88142C2318yes—
288#88142C2318yes—
289#88141C2314yes—
290#88141C2314yes—
291#88140C23116yes—
292#88139C23116yes—
293#88139C2318yes—
294#88139C23116yes—
295#88139C23116yes—
296#88139C2318yes—
297#88138C2318yes—
298#88138C23116yes—
299#88138C2318yes—
300#88138C23116yes—
301#88137C23116yes—
302#88136C23116yes—
303#88136C23116yes—
304#88135C2318yes—
305#88135C23116yes—
306#88135C2318yes—
307#88135C2318yes—
308#88135C23116yes—
309#88135C23116yes—
310#88135C2318yes—
311C22⋊C4×D13C2318yes—
312C22⋊C4×D13C2318yes—
313#88132C23116yes—
314#88132C23116yes—
315#88131C2318yes—
316#88131C2318yes—
317#88129C2314yes—
318#88128C2312yes—
319C4×D52C2314yes—
320C4×D52C2314yes—
321C42×D13C2312yes—
322C42×D13C2312yes—
323C42×D13C2312yes—
324C42×D13C2312yes—
325#88123C2312yes—
326C4×Dic26C2314yes—
327C4×Dic26C2314yes—
328#62812—131nomaximal, Sylow
329C24×C13C2418yes—
330C24×C13C2412yes—
331C23×D13C2418yes—
332C23×D13C2418yes—
333C23×D13C2411yescharacteristic
334C13×#41—232no—
335C13×#41—216no—
336C2×Q8×C13C2414yes—
337C2×D4×C13—232no—
338C2×D4×C13—232no—
339C2×D4×C13—48no—
340C2×D4×C13C2×D418yescomplemented
341C2×D4×C13C2414yes—
342C2×D4×C13C24116yes—
343C2×D4×C13C2414yes—
344C2×D4×C13C2418yes—
345C2×D4×C13C2418yes—
346C2×D4×C13C2414yes—
347C2×D4×C13C2414yes—
348C22×C4×C13—44no—
349C22×C4×C13C2411yescharacteristic
350C22×C4×C13C2414yes—
351C22×C4×C13C2418yes—
352C22×C4×C13C2418yes—
353C22×C4×C13C2412yes—
354C22×C4×C13C2414yes—
355C22×C4×C13C2411yescharacteristic
356C22×C4×C13C2411yescharacteristic
357C2×C22⋊D13—232no—
358C2×C22⋊D13—264no—
359C2×C22⋊D13—232no—
360C2×C22⋊D13—416no—
361C2×C22⋊D13C2×D4116yescomplemented
362C2×C22⋊D13C2418yes—
363C2×C22⋊D13C24116yes—
364C2×C22⋊D13C2418yes—
365C2×C22⋊D13C24116yes—
366C2×C22⋊D13C2418yes—
367C2×C22⋊D13C2418yes—
368C2×C22⋊D13C24116yes—
369C2×C22⋊D13C2418yes—
370C2×C22⋊D13C2418yes—
371C22×Dic13—232no—
372C22×Dic13—44no—
373C22×Dic13C2×D4116yescomplemented
374C22×Dic13C24116yes—
375C22×Dic13C2418yes—
376C22×Dic13C2414yes—
377C22×Dic13C2418yes—
378C22×Dic13C2411yescharacteristic
379C22×Dic13C2414yes—
380C22×Dic13C2411yescharacteristic
381C22×Dic13C2412yes—
382C22×Dic13C2414yes—
383C22×Dic13C2414yes—
384C22×Dic13C2411yescharacteristic
385C22×Dic13C2412yes—
386#6131—216no—
387Q8×D13—216no—
388Q8×D13—232no—
389#6129—232no—
390#6129—264no—
391#6129—264no—
392#6129—232no—
393#6129—264no—
394#6129—264no—
395#6129—216no—
396#6129—232no—
397#6129C2×D4132yescomplemented
398#6129C2×D4132yescomplemented
399D4×D13—232no—
400D4×D13—232no—
401D4×D13—264no—
402D4×D13—216no—
403D4×D13—48no—
404D4×D13—48no—
405#6127—216no—
406#6127—264no—
407#6127—232no—
408#6127—232no—
409C2×D52—48no—
410C2×D52C2414yes—
411C2×D52C2414yes—
412C2×D52C2418yes—
413C2×D52C2414yes—
414C2×D52C2418yes—
415C2×C4×D13—232no—
416C2×C4×D13—232no—
417C2×C4×D13—42no—
418C2×C4×D13—42no—
419C2×C4×D13C2×D418yescomplemented
420C2×C4×D13C2412yes—
421C2×C4×D13C2412yes—
422C2×C4×D13C2418yes—
423C2×C4×D13C2418yes—
424C2×C4×D13C2418yes—
425C2×C4×D13C24116yes—
426C2×C4×D13C2412yes—
427C2×C4×D13C2412yes—
428C2×C4×D13C2412yes—
429C2×C4×D13C2412yes—
430C2×Dic26—232no—
431C2×Dic26—232no—
432C2×Dic26C2×D418yescomplemented
433C2×Dic26C2414yes—
434C2×Dic26C24116yes—
435C2×Dic26C2418yes—
436C2×Dic26C2414yes—
437C13×C4⋊C4C2414yes—
438C13×C4⋊C4C2414yes—
439C13×C4⋊C4C2418yes—
440C13×C4⋊C4C2414yes—
441C13×C22⋊C4C2418yes—
442C13×C22⋊C4C2418yes—
443C13×C22⋊C4C24116yes—
444C13×C22⋊C4C2418yes—
445C42×C13C2412yes—
446C42×C13C2412yes—
447C22⋊Dic13C2418yes—
448C22⋊Dic13C2418yes—
449C22⋊Dic13C24116yes—
450C22⋊Dic13C2418yes—
451#6103C2418yes—
452#6103C2418yes—
453#6103C2418yes—
454#6103C2418yes—
455#6103C2418yes—
456#6103C24116yes—
457#6103C24116yes—
458C4⋊Dic13C2414yes—
459C4⋊Dic13C2414yes—
460C4⋊Dic13C2414yes—
461C4⋊Dic13C2418yes—
462#6101C2418yes—
463#6101C2418yes—
464#6101C2418yes—
465#6101C24116yes—
466#6101C2418yes—
467C4×Dic13C2414yes—
468C4×Dic13C2414yes—
469C4×Dic13C2412yes—
470C4×Dic13C2412yes—
471C4×Dic13C2411yescharacteristic
472C4×Dic13C2411yescharacteristic
473C4×Dic13C2412yes—
474C4×Dic13C2412yes—
475C4×Dic13C2411yescharacteristic
476C4×Dic13C2411yescharacteristic
477C4×Dic13C2414yes—
478C4×Dic13C2414yes—
479C4×Dic13C2414yes—
480C4×Dic13C2414yes—
481C2×#585—132no—
482#3500—138no—
483#3499—134no—
484#3498—134no—
485#3497—132no—
486#3497—132no—
487#3496—132no—
488#3496—134no—
489#3496—134no—
490#3496—131no—
491#3496D1311yescharacteristic, complemented
492D4×#41—134no—
493D4×#41—138no—
494D4×#41—134no—
495#3449—132no—
496#3449—134no—
497C2×#532—132no—
498C2×#532—134no—
499C2×C4×#41—131no—
500C23×C13—216no—
501C23×C13—42no—
502C23×C13—42no—
503C23×C13—48no—
504C23×C13—48no—
505C23×C13C22×D418yes—
506C23×C13C2518yes—
507C23×C13C2514yes—
508C23×C13C2511yescharacteristic
509C22×D13—216no—
510C22×D13—216no—
511C22×D13—41no—
512C22×D13—41no—
513C22×D13—48no—
514C22×D13—48no—
515C22×D13—48no—
516C22×D13—48no—
517C22×D13C22×D414yes—
518C22×D13C2518yes—
519C22×D13C2512yes—
520Q8×C13—28no—
521D4×C13—232no—
522D4×C13—216no—
523D4×C13—28no—
524D4×C13—28no—
525D4×C13—44no—
526D4×C13—48no—
527D4×C13C22×D4116yes—
528C2×C4×C13—216no—
529C2×C4×C13—216no—
530C2×C4×C13—22no—
531C2×C4×C13—28no—
532C2×C4×C13—41no—
533C2×C4×C13—44no—
534C2×C4×C13—42no—
535C2×C4×C13C22×D414yes—
536C2×C4×C13C2511yescharacteristic
537C2×C4×C13C2514yes—
538C2×C4×C13C2512yes—
539C2×C4×C13C2518yes—
540C2×C4×C13C2512yes—
541C2×C4×C13C2511yescharacteristic
542C22⋊D13—232no—
543C22⋊D13—216no—
544C22⋊D13—216no—
545C22⋊D13—216no—
546C22⋊D13—232no—
547C22⋊D13—216no—
548C22⋊D13—48no—
549C22⋊D13—416no—
550C22⋊D13C22×D4132yes—
551C2×Dic13—216no—
552C2×Dic13—232no—
553C2×Dic13—216no—
554C2×Dic13—22no—
555C2×Dic13—28no—
556C2×Dic13—41no—
557C2×Dic13—44no—
558C2×Dic13—42no—
559C2×Dic13C22×D4116yes—
560C2×Dic13C22×D418yes—
561C2×Dic13C22×D4116yes—
562C2×Dic13C22×D414yes—
563C2×Dic13C2511yescharacteristic
564C2×Dic13C2512yes—
565C2×Dic13C2514yes—
566C2×Dic13C2518yes—
567C2×Dic13C2511yescharacteristic
568C2×Dic13C2511yescharacteristic
569C2×Dic13C2514yes—
570C2×Dic13C2511yescharacteristic
571D52—216no—
572D52—28no—
573D52—28no—
574D52—48no—
575D52—44no—
576C4×D13—216no—
577C4×D13—216no—
578C4×D13—24no—
579C4×D13—216no—
580C4×D13—232no—
581C4×D13—24no—
582C4×D13—42no—
583C4×D13—42no—
584C4×D13C22×D418yes—
585C4×D13C22×D418yes—
586Dic26—28no—
587Dic26—216no—
588Dic26—232no—
589Dic26C22×D4116yes—
590#585—2632no—
591C2×2−1+4—134no—
592C2×2−1+4—138no—
593C2×H(5,𝔽2)—138no—
594C2×H(5,𝔽2)—132no—
595C2×H(5,𝔽2)—138no—
596C2×H(5,𝔽2)C2×D1312yescomplemented
597C22×#41—134no—
598C22×#41—138no—
599C22×#41—131no—
600C22×#41—138no—
601C22×#41—138no—
602#550—134no—
603#550—138no—
604#550—134no—
605D4×Q8—134no—
606D4×Q8—138no—
607D4×Q8—134no—
608#548—138no—
609#548—138no—
610#548—138no—
611#548—138no—
612#547—138no—
613#547—1316no—
614#547—138no—
615#547—134no—
616#547—138no—
617#547C2×D1314yescomplemented
618#546—138no—
619#546—138no—
620#546—1316no—
621#546—1316no—
622#546—1316no—
623#546—138no—
624#546—1316no—
625#546C2×D1318yescomplemented
626D42—138no—
627D42—138no—
628D42—138no—
629D42—1316no—
630D42—134no—
631D42C2×D1314yescomplemented
632#537—134no—
633#537—138no—
634#537—138no—
635#537—132no—
636#537C2×D1312yescomplemented
637#536—1316no—
638#536—138no—
639#535—138no—
640#535—1316no—
641#534—138no—
642#534—138no—
643#534—134no—
644#534C2×D1314yescomplemented
645#532—134no—
646#532—132no—
647#532—132no—
648#532—134no—
649#532—134no—
650#532—134no—
651#532—138no—
652#532—138no—
653#532—138no—
654#532—138no—
655#532—138no—
656#532—138no—
657#532—138no—
658#532—134no—
659#532—134no—
660#532—132no—
661#532C2×D1312yescomplemented
662C2×C4⋊Q8—132no—
663C2×C4⋊Q8—134no—
664C2×#127—134no—
665C2×#127—132no—
666C2×#124—134no—
667C2×#124—138no—
668#525—1316no—
669#525—138no—
670#525—138no—
671#525—1316no—
672C2×#121—138no—
673C2×#121—134no—
674C2×#121—134no—
675C2×#121—134no—
676C2×#121C2×D1314yescomplemented
677C4×#41—134no—
678C4×#41—134no—
679C4×#41—134no—
680C4×#41—134no—
681C2×C4×Q8—131no—
682C2×C4×Q8—131no—
683C2×C4×D4—131no—
684C2×C4×D4—134no—
685C2×C4×D4—132no—
686C2×C4×D4—134no—
687C2×C4×D4—134no—
688C2×C4×D4—134no—
689C2×C4×D4—132no—
690C2×C4×D4—138no—
691C2×C4×D4C2×D1311yescharacteristic, complemented
692C2×#117—131no—
693C2×#117—132no—
694C22×C42—132no—
695C22×C42—131no—
696C22×C13—21no—
697C22×C13—24no—
698C22×C13—21no—
699C22×C13—24no—
700C22×C13—28no—
701C22×C13—28no—
702C22×C13—28no—
703C22×C13—48no—
704C22×C13—816no—
705C22×C13C23×D418yes—
706C22×C13C23×D412yes—
707C22×C13C2611yescharacteristic
708C2×D13—22no—
709C2×D13—22no—
710C2×D13—28no—
711C2×D13—28no—
712C2×D13—28no—
713C2×D13—44no—
714C2×D13—816no—
715C2×D13—816no—
716C2×D13C23×D414yes—
717C4×C13—28no—
718C4×C13—22no—
719C4×C13—21no—
720C4×C13—24no—
721C4×C13C23×D414yes—
722C4×C13#58512yescomplemented
723Dic13—28no—
724Dic13—22no—
725Dic13—21no—
726Dic13—24no—
727Dic13C23×D412yes—
728Dic13C23×D418yes—
729Dic13C23×D412yes—
730Dic13#58512yescomplemented
7312−1+4—2632no—
7322−1+4—2664no—
733H(5,𝔽2)—216no—
734H(5,𝔽2)—2664no—
735H(5,𝔽2)—2664no—
736H(5,𝔽2)—2616no—
737C2×#41—134no—
738C2×#41—1316no—
739C2×#41—134no—
740C2×#41—134no—
741C2×#41—1316no—
742C2×#41—134no—
743C2×#41—138no—
744C2×#41—1316no—
745C2×#41—1316no—
746C2×#41—138no—
747C2×#41—1316no—
748C2×#41—138no—
749C2×#41—138no—
750C2×#41—134no—
751C2×#41—1316no—
752C2×#41—138no—
753C2×#41—2664no—
754C2×#41—2632no—
755C2×#41—2664no—
756C2×#41—2664no—
757C2×#41C22×D1314yes—
758C2×#41C22×D1318yes—
759C22×Q8—134no—
760C22×Q8—138no—
761C22×Q8—131no—
762C22×Q8—138no—
763C22×Q8—138no—
764C22×D4—132no—
765C22×D4—138no—
766C22×D4—138no—
767C22×D4—1316no—
768C22×D4—138no—
769C22×D4—138no—
770C22×D4—134no—
771C22×D4—1316no—
772C22×D4—138no—
773C22×D4—134no—
774C22×D4—134no—
775C22×D4—134no—
776C22×D4C22×D1318yes—
777C22×D4C22×D1318yes—
778C22×D4C22×D1314yes—
779C22×D4C22×D1311yescharacteristic
780C23×C4—132no—
781C23×C4—131no—
782C23×C4—138no—
783C23×C4—132no—
784C23×C4—138no—
785C23×C4—138no—
786C23×C4—131no—
787C23×C4—131no—
788C23×C4C22×D1312yes—
789C4⋊Q8—134no—
790C4⋊Q8—134no—
791C4⋊Q8—134no—
792C4⋊Q8—138no—
793C4⋊Q8—138no—
794C4⋊Q8—138no—
795C4⋊Q8—132no—
796C4⋊Q8C22×D1312yes—
797#127—134no—
798#127—138no—
799#127—134no—
800#127—138no—
801#127—134no—
802#127—138no—
803#127—132no—
804#127C22×D1312yes—
805#124—134no—
806#124—134no—
807#124—138no—
808#124—138no—
809#124—1316no—
810#124—1316no—
811#124—1316no—
812#124—134no—
813#124C22×D1314yes—
814#123—1316no—
815#123—1316no—
816#123—1316no—
817#123—1316no—
818#123—1316no—
819#123C22×D13116yes—
820C22⋊Q8—138no—
821C22⋊Q8—138no—
822C22⋊Q8—1316no—
823C22⋊Q8—1316no—
824C22⋊Q8—138no—
825C22⋊Q8—1316no—
826C22⋊Q8—1316no—
827C22⋊Q8C22×D1318yes—
828#121—138no—
829#121—1316no—
830#121—138no—
831#121—134no—
832#121—1316no—
833#121—134no—
834#121—1316no—
835#121—138no—
836#121—1316no—
837#121—1316no—
838#121—134no—
839#121—138no—
840#121—134no—
841#121—138no—
842#121—138no—
843#121—138no—
844#121—134no—
845#121—134no—
846#121—138no—
847#121—138no—
848#121—138no—
849#121—1316no—
850#121—1316no—
851#121C22×D1314yes—
852#121C22×D1314yes—
853#121C22×D1318yes—
854#121C22×D1318yes—
855#121C22×D1318yes—
856#121C22×D1318yes—
857#120—1316no—
858#120—1316no—
859#120—1316no—
860#120—1316no—
861#120—1316no—
862#120C22×D13116yes—
863C4×Q8—134no—
864C4×Q8—134no—
865C4×Q8—134no—
866C4×Q8—134no—
867C4×D4—134no—
868C4×D4—134no—
869C4×D4—134no—
870C4×D4—138no—
871C4×D4—134no—
872C4×D4—138no—
873C4×D4—138no—
874C4×D4—138no—
875C4×D4—138no—
876C4×D4—138no—
877C4×D4—138no—
878C4×D4—134no—
879C4×D4—134no—
880C4×D4—138no—
881C4×D4—138no—
882C4×D4—138no—
883C4×D4—138no—
884C4×D4—138no—
885C4×D4—138no—
886C4×D4—138no—
887C4×D4—1316no—
888C4×D4—1316no—
889C4×D4—1316no—
890C4×D4—134no—
891C4×D4—134no—
892C4×D4C22×D1314yes—
893C4×D4C22×D1314yes—
894C4×D4C22×D1314yes—
895C4×D4C22×D1314yes—
896#117—134no—
897#117—134no—
898#117—138no—
899#117—138no—
900C2×C4⋊C4—132no—
901C2×C4⋊C4—132no—
902C2×C4⋊C4—131no—
903C2×C4⋊C4—138no—
904C2×C4⋊C4—134no—
905C2×C4⋊C4—134no—
906C2×C4⋊C4—134no—
907C2×C4⋊C4C22×D1311yescharacteristic
908C2×C4⋊C4C22×D1314yes—
909C2×C22⋊C4—132no—
910C2×C22⋊C4—138no—
911C2×C22⋊C4—132no—
912C2×C22⋊C4—138no—
913C2×C22⋊C4—138no—
914C2×C22⋊C4—138no—
915C2×C22⋊C4—138no—
916C2×C22⋊C4C22×D1312yes—
917C2×C22⋊C4C22×D1318yes—
918C2×C42—132no—
919C2×C42—131no—
920C2×C42—134no—
921C2×C42—134no—
922C2×C42—132no—
923C2×C42—132no—
924C2×C42—131no—
925C2×C42—134no—
926C2×C42—134no—
927C2×C42—131no—
928C2×C42—132no—
929C2×C42—132no—
930C2×C42—132no—
931C2×C42—132no—
932C2×C42C22×D1311yescharacteristic
933C2×C13—22no—
934C2×C13—28no—
935C2×C13—48no—
936C2×C13C24×D411yescharacteristic
937C2×C13C2×#58511yescharacteristic
938C2×C13C2×#58511yescharacteristic
939D13—24no—
940D13—48no—
941C24—131no—
942C24—138no—
943C24—138no—
944C24C23×D1318yes—
945C24C23×D1312yes—
946#41—232no—
947#41—216no—
948#41—1332no—
949#41—1332no—
950#41—2632no—
951#41—2664no—
952#41—2632no—
953#41—2632no—
954#41—2664no—
955#41—2616no—
956#41—2664no—
957#41—2664no—
958#41—2616no—
959#41—2664no—
960#41—2632no—
961#41—2632no—
962#41—2616no—
963C2×Q8—138no—
964C2×Q8—134no—
965C2×Q8—1316no—
966C2×Q8—134no—
967C2×Q8—138no—
968C2×Q8—2632no—
969C2×Q8—2632no—
970C2×Q8—2616no—
971C2×Q8—2632no—
972C2×Q8C23×D1314yes—
973C2×D4—232no—
974C2×D4—232no—
975C2×D4—48no—
976C2×D4—1316no—
977C2×D4—138no—
978C2×D4—138no—
979C2×D4—138no—
980C2×D4—1316no—
981C2×D4—138no—
982C2×D4—1316no—
983C2×D4—138no—
984C2×D4—138no—
985C2×D4—1316no—
986C2×D4—134no—
987C2×D4—138no—
988C2×D4—134no—
989C2×D4—138no—
990C2×D4—134no—
991C2×D4—2616no—
992C2×D4—2632no—
993C2×D4—2664no—
994C2×D4—2632no—
995C2×D4—2664no—
996C2×D4—2632no—
997C2×D4—2632no—
998C2×D4—528no—
999C2×D4—528no—
1000C2×D4—528no—
1001C2×D4—5216no—
1002C2×D4D4×D1318yescomplemented
1003C2×D4C23×D1314yes—
1004C2×D4C23×D13116yes—
1005C2×D4C23×D1318yes—
1006C2×D4C23×D1314yes—
1007C2×D4C23×D1318yes—
1008C2×D4C23×D1314yes—
1009C2×D4C23×D1314yes—
1010C22×C4—44no—
1011C22×C4—1316no—
1012C22×C4—131no—
1013C22×C4—132no—
1014C22×C4—134no—
1015C22×C4—134no—
1016C22×C4—138no—
1017C22×C4—132no—
1018C22×C4—132no—
1019C22×C4—131no—
1020C22×C4—134no—
1021C22×C4—138no—
1022C22×C4—138no—
1023C22×C4—1316no—
1024C22×C4—134no—
1025C22×C4—131no—
1026C22×C4—132no—
1027C22×C4—132no—
1028C22×C4—132no—
1029C22×C4—138no—
1030C22×C4—138no—
1031C22×C4—1316no—
1032C22×C4—138no—
1033C22×C4—132no—
1034C22×C4—132no—
1035C22×C4—2632no—
1036C22×C4—2632no—
1037C22×C4—2632no—
1038C22×C4—522no—
1039C22×C4—522no—
1040C22×C4—524no—
1041C22×C4C23×D1311yescharacteristic
1042C22×C4C23×D1314yes—
1043C22×C4C23×D1318yes—
1044C22×C4C23×D1318yes—
1045C22×C4C23×D1314yes—
1046C22×C4C23×D1312yes—
1047C22×C4C23×D1311yescharacteristic
1048C22×C4C23×D1311yescharacteristic
1049C4⋊C4—138no—
1050C4⋊C4—134no—
1051C4⋊C4—138no—
1052C4⋊C4—138no—
1053C4⋊C4—134no—
1054C4⋊C4—1316no—
1055C4⋊C4—138no—
1056C4⋊C4—138no—
1057C4⋊C4—134no—
1058C4⋊C4C23×D1314yes—
1059C4⋊C4C23×D1314yes—
1060C4⋊C4C23×D1314yes—
1061C4⋊C4C23×D1318yes—
1062C22⋊C4—138no—
1063C22⋊C4—138no—
1064C22⋊C4—1316no—
1065C22⋊C4—138no—
1066C22⋊C4—138no—
1067C22⋊C4—138no—
1068C22⋊C4—138no—
1069C22⋊C4—1316no—
1070C22⋊C4—138no—
1071C22⋊C4—1316no—
1072C22⋊C4—138no—
1073C22⋊C4C23×D1318yes—
1074C22⋊C4C23×D1318yes—
1075C22⋊C4C23×D1318yes—
1076C22⋊C4C23×D13116yes—
1077C42—131no—
1078C42—131no—
1079C42—131no—
1080C42—131no—
1081C42—134no—
1082C42—132no—
1083C42—134no—
1084C42—132no—
1085C42—134no—
1086C42—134no—
1087C42—132no—
1088C42—134no—
1089C42—132no—
1090C42—134no—
1091C42C23×D1312yes—
1092C42C23×D1312yes—
1093C13#6281211yescharacteristic, complemented, Sylow
1094C23—216no—
1095C23—42no—
1096C23—42no—
1097C23—48no—
1098C23—48no—
1099C23—132no—
1100C23—134no—
1101C23—138no—
1102C23—2616no—
1103C23—2616no—
1104C23—521no—
1105C23—521no—
1106C23—528no—
1107C23—528no—
1108C23—528no—
1109C23—528no—
1110C23C2×D4×D1318yes—
1111C23C24×D1318yes—
1112C23C24×D1314yes—
1113C23C24×D1311yescharacteristic
1114Q8—28no—
1115Q8—1316no—
1116Q8—2616no—
1117Q8—2632no—
1118Q8—268no—
1119D4—232no—
1120D4—216no—
1121D4—28no—
1122D4—28no—
1123D4—48no—
1124D4—44no—
1125D4—1332no—
1126D4—2616no—
1127D4—2616no—
1128D4—2632no—
1129D4—2616no—
1130D4—2616no—
1131D4—2632no—
1132D4—2616no—
1133D4—268no—
1134D4—268no—
1135D4—524no—
1136D4—528no—
1137D4—5216no—
1138D4—528no—
1139D4C2×D4×D13116yes—
1140C2×C4—216no—
1141C2×C4—216no—
1142C2×C4—22no—
1143C2×C4—28no—
1144C2×C4—44no—
1145C2×C4—42no—
1146C2×C4—41no—
1147C2×C4—134no—
1148C2×C4—1316no—
1149C2×C4—138no—
1150C2×C4—1316no—
1151C2×C4—131no—
1152C2×C4—131no—
1153C2×C4—131no—
1154C2×C4—134no—
1155C2×C4—138no—
1156C2×C4—138no—
1157C2×C4—131no—
1158C2×C4—134no—
1159C2×C4—132no—
1160C2×C4—138no—
1161C2×C4—2616no—
1162C2×C4—2632no—
1163C2×C4—264no—
1164C2×C4—2616no—
1165C2×C4—2616no—
1166C2×C4—2632no—
1167C2×C4—262no—
1168C2×C4—268no—
1169C2×C4—2616no—
1170C2×C4—2616no—
1171C2×C4—264no—
1172C2×C4—522no—
1173C2×C4—522no—
1174C2×C4—524no—
1175C2×C4—522no—
1176C2×C4—521no—
1177C2×C4C2×D4×D1314yes—
1178C2×C4C24×D1311yescharacteristic
1179C2×C4C24×D1314yes—
1180C2×C4C24×D1312yes—
1181C2×C4C24×D1318yes—
1182C2×C4C24×D1312yes—
1183C2×C4C24×D1311yescharacteristic
1184C22—21no—
1185C22—24no—
1186C22—21no—
1187C22—24no—
1188C22—28no—
1189C22—28no—
1190C22—28no—
1191C22—48no—
1192C22—816no—
1193C22—134no—
1194C22—262no—
1195C22—262no—
1196C22—268no—
1197C22—268no—
1198C22—268no—
1199C22—524no—
1200C22—10416no—
1201C22—10416no—
1202C22C22×D4×D1318yes—
1203C22C22×D4×D1312yes—
1204C22C25×D1311yescharacteristic
1205C4—28no—
1206C4—22no—
1207C4—21no—
1208C4—24no—
1209C4—132no—
1210C4—132no—
1211C4—138no—
1212C4—132no—
1213C4—268no—
1214C4—261no—
1215C4—264no—
1216C4—262no—
1217C4C22×D4×D1314yes—
1218C4#1171965012yescomplemented
1219C2—22no—
1220C2—28no—
1221C2—48no—
1222C2—264no—
1223C2—528no—
1224C2C23×D4×D1311yescharacteristic
1225C2D13×#58511yescharacteristic
1226C2C2×#1171965011yescharacteristic
subgroupG/H
center, FrattiniC22C25×D13
commutator, socle, cosocleC22×C13C26
FittingC13×#3496C2
hypercenter#3496D13
hypocenterC13#62812
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. C2×#11719650C2semidirect
2. #13128622C2semidirect
3. #13128615C2semidirect
4. #13128608C2semidirect
5. #13128605C2semidirect
6. #13128602C2semidirect
7. #13128600C2semidirect
8. #13128597C2semidirect
9. #13128595C2semidirect
10. #13128593C2semidirect
11. #13128323C2semidirect
12. #13128320C2semidirect
13. D4×#6129C2semidirect
14. #13128164C2semidirect
15. #13128162C2semidirect
16. C2×#11719301C2semidirect
17. D13×#532C2semidirect
18. C2×C4×#6129C2semidirect
19. C13×#3496C2semidirect
20. C2×C13×H(5,𝔽2)C22semidirect
22. C2×#88257C22semidirect
23. C2×#88257C22semidirect
24. C2×#41×D13C22semidirect
25. C2×#41×D13C22semidirect
26. C2×#88251C22semidirect
27. C2×#88251C22semidirect
28. C2×#88251C22semidirect
30. C22×#6129C22semidirect
31. C22×#6129C22semidirect
32. C13×#547C22semidirect
33. C13×#546C22semidirect
34. D42×C13C22semidirect
35. C13×#537C22semidirect
36. C13×#534C22semidirect
37. C13×#532C22semidirect
38. C2×C13×#121C22semidirect
39. C2×C4×D4×C13C22semidirect
40. #11719538C22semidirect
41. #11719537C22semidirect
42. #11719534C22semidirect
43. #11719529C22semidirect
44. #11719511C22semidirect
45. #11719509C22semidirect
46. C2×#88194C22semidirect
47. C2×#88193C22semidirect
48. D4×C22⋊D13C22semidirect
49. D4×C22⋊D13C22semidirect
50. C2×D4×Dic13C22semidirect
51. C2×D4×Dic13C22semidirect
52. C2×#88184C22semidirect
53. C2×C4×C22⋊D13C22semidirect
54. C22×C4×Dic13C22semidirect
55. #11719432C22semidirect
56. #11719430C22semidirect
57. D13×C4⋊Q8C22semidirect
58. #11719423C22semidirect
59. #11719421C22semidirect
60. D13×#127C22semidirect
61. #11719382C22semidirect
62. D13×#124C22semidirect
63. #11719373C22semidirect
64. #11719361C22semidirect
65. #11719360C22semidirect
66. #11719359C22semidirect
67. #11719353C22semidirect
68. #11719338C22semidirect
69. #11719337C22semidirect
70. #11719333C22semidirect
71. #11719332C22semidirect
72. #11719316C22semidirect
73. #11719315C22semidirect
74. #11719314C22semidirect
75. #11719312C22semidirect
76. #11719311C22semidirect
77. #11719310C22semidirect
78. D13×#121C22semidirect
79. D13×#121C22semidirect
80. #11719304C22semidirect
81. #11719303C22semidirect
82. #11719302C22semidirect
83. #11719302C22semidirect
84. #11719301C22semidirect
85. #11719301C22semidirect
86. #11719301C22semidirect
87. #11719301C22semidirect
88. #11719301C22semidirect
89. #11719301C22semidirect
90. #11719301C22semidirect
91. #11719301C22semidirect
92. #11719301C22semidirect
93. #11719297C22semidirect
94. #11719296C22semidirect
95. #11719295C22semidirect
96. #11719291C22semidirect
97. #11719260C22semidirect
98. #11719259C22semidirect
99. #11719258C22semidirect
100. #11719257C22semidirect
101. D4×D52C22semidirect
102. #11719253C22semidirect
103. #11719253C22semidirect
104. C4×D4×D13C22semidirect
105. C4×D4×D13C22semidirect
106. D4×Dic26C22semidirect
107. C4×#6129C22semidirect
108. C4×#6129C22semidirect
109. C4×#6129C22semidirect
110. C4×#6129C22semidirect
111. #11719215C22semidirect
112. #11719212C22semidirect
113. C2×#88147C22semidirect
114. C2×#88146C22semidirect
115. C2×#88142C22semidirect
116. C2×#88141C22semidirect
117. #11719198C22semidirect
118. C2×#88139C22semidirect
119. #11719195C22semidirect
120. C2×#88135C22semidirect
121. C2×#88135C22semidirect
122. C2×#88131C22semidirect
123. #11719182C22semidirect
124. C2×C42×D13C22semidirect
125. C2×C4×Dic26C22semidirect
154. C2×#6129D4semidirect
340. C2×D4×C13C2×D4semidirect
361. C2×C22⋊D13C2×D4semidirect
373. C22×Dic13C2×D4semidirect
397. #6129C2×D4semidirect
398. #6129C2×D4semidirect
419. C2×C4×D13C2×D4semidirect
432. C2×Dic26C2×D4semidirect
491. #3496D13semidirect
596. C2×H(5,𝔽2)C2×D13semidirect
617. #547C2×D13semidirect
625. #546C2×D13semidirect
631. D42C2×D13semidirect
636. #537C2×D13semidirect
644. #534C2×D13semidirect
661. #532C2×D13semidirect
676. C2×#121C2×D13semidirect
691. C2×C4×D4C2×D13semidirect
722. C4×C13#585semidirect
730. Dic13#585semidirect
1002. C2×D4D4×D13semidirect
1093. C13#62812semidirect
1218. C4#11719650semidirect

Maximal subgroups

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

subgroupindex
C2×#117196502
#131286222
#131286152
#131286082
#131286052
#131286022
#131286002
#131285972
#131285952
#131285932
#131283232
#131283202
D4×#61292
#131281642
#131281622
C2×#117193012
D13×#5322
C2×C4×#61292
C13×#34962
#6281213