Finite Group Databasebeta

← #16771468

Subgroups — #16771468

Order 3328.

11346 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719652C211yesmaximal, characteristic, complemented
2C2×#11719650C211yesmaximal, characteristic, complemented
3#13128629C211yesmaximal, characteristic, complemented
4#13128626C213yesmaximal, complemented
5#13128623C213yesmaximal, complemented
6#13128618C213yesmaximal, complemented
7#13128617C211yesmaximal, characteristic, complemented
8#13128611C213yesmaximal, complemented
9#13128610C211yesmaximal, characteristic, complemented
10#13128604C214yesmaximal, complemented
11#13128596C2112yesmaximal, complemented
12#13128325C214yesmaximal, complemented
13#13128320C2112yesmaximal, complemented
14#13128168C213yesmaximal, complemented
15#13128167C213yesmaximal, complemented
16C2×#11719373C213yesmaximal, complemented
17D13×#532C213yesmaximal, complemented
18C4×#41×D13C211yesmaximal, characteristic, complemented
19C13×#3500C211yesmaximal, characteristic, complemented
20C2×C13×2−1+4C2211yescharacteristic, complemented
21C2×C13×H(5,𝔽2)C2211yescharacteristic, complemented
22#11719652—216no—
23#11719650—216no—
24C2×#88257C2212yescomplemented
25C2×#88257C2211yescharacteristic, complemented
26C2×#88257C2213yescomplemented
27C2×#88256C2216yescomplemented
28C2×#88256C2211yescharacteristic, complemented
29C2×#88256C2213yescomplemented
30C2×#41×D13C2211yescharacteristic
31C2×#41×D13C2216yescomplemented
32C2×#41×D13C2212yescomplemented
33C2×#41×D13C2213yescomplemented
34C2×#41×D13C2213yescomplemented
35C2×#88254C2212yescomplemented
36C2×#88254C2213yescomplemented
37C22×#6131C2212yescomplemented
38C22×#6131C2213yescomplemented
39C2×#88251C2216yescomplemented
40C2×#88251C2213yescomplemented
41C22×#6129C2216yescomplemented
42C22×#6129C2213yescomplemented
43C13×#548C2214yescomplemented
44C13×#546C22112yescomplemented
45C13×#536C2213yescomplemented
46C13×#535C2213yescomplemented
47C13×#532C2213yescomplemented
48C2×C13×#124C2213yescomplemented
49C4×C13×#41C2211yescharacteristic, complemented
50#11719539C2214yescomplemented
51#11719537C2213yescomplemented
52#11719537C2213yescomplemented
53#11719535C2213yescomplemented
54#41×Dic13C2211yescharacteristic, complemented
55#11719530C2213yescomplemented
56#11719529C22112yescomplemented
57#11719521C2213yescomplemented
58Q8×C22⋊D13C2214yescomplemented
59C2×#88198C2213yescomplemented
60#11719510C2213yescomplemented
61C2×#88194C2213yescomplemented
62D4×C22⋊D13C22112yescomplemented
63#11719430C2213yescomplemented
64#11719429C2216yescomplemented
65D13×C4⋊Q8C2213yescomplemented
66#11719421C2213yescomplemented
67#11719420C2216yescomplemented
68D13×#127C2213yescomplemented
69#11719382C22112yescomplemented
70#11719381C22112yescomplemented
71#11719380C2216yescomplemented
72#11719379C2216yescomplemented
73D13×#124C2213yescomplemented
74D13×#124C2213yescomplemented
75#11719373C22112yescomplemented
76#11719373C22112yescomplemented
77#11719373C2216yescomplemented
78#11719373C2216yescomplemented
79#11719373C2211yescharacteristic, complemented
80#11719373C2213yescomplemented
81#11719373C2216yescomplemented
82#11719361C22112yescomplemented
83#11719360C22124yescomplemented
84#11719358C22112yescomplemented
85#11719337C22112yescomplemented
86#11719336C22112yescomplemented
87#11719334C22112yescomplemented
88#11719332C22112yescomplemented
89#11719315C22124yescomplemented
90#11719314C22112yescomplemented
91#11719313C22112yescomplemented
92#11719311C22112yescomplemented
93D13×#121C22112yescomplemented
94#11719304C22112yescomplemented
95#11719301C22112yescomplemented
96#11719295C22124yescomplemented
97#11719294C22112yescomplemented
98#11719291C22112yescomplemented
99#11719281C2214yescomplemented
100C4×#6131C2212yescomplemented
101C4×Q8×D13C2212yescomplemented
102#11719259C22112yescomplemented
103#11719257C22112yescomplemented
104#11719255C22112yescomplemented
105#11719253C22112yescomplemented
106C4×D4×D13C2216yescomplemented
107C4×D4×D13C22112yescomplemented
108C4×#6129C2216yescomplemented
109#11719231C2213yescomplemented
110#11719230C2213yescomplemented
111#11719227C2213yescomplemented
112D13×#117C2213yescomplemented
113#11719195C22124yescomplemented
114C2×#88138C22112yescomplemented
115C2×#88135C22112yescomplemented
116#11719182C2213yescomplemented
117C2×#88129C2213yescomplemented
118C4×#6127C2213yescomplemented
119C2×C42×D13C2213yescomplemented
120C13×2−1+4—28no—
121C13×H(5,𝔽2)—28no—
122C2×C13×#41C2316yes—
123C2×C13×#41C2313yes—
124C2×C13×#41C2313yes—
125C2×C13×#41C2312yes—
126C2×C13×#41C2311yescharacteristic
127C22×Q8×C13C2313yes—
128C22×Q8×C13C2312yes—
129C22×D4×C13C2316yes—
130C22×D4×C13C2313yes—
131C22×C22⋊D13C2316yes—
132C22×C22⋊D13C23112yes—
133C22×C22⋊D13C23112yes—
134C23×Dic13C2316yes—
135#88257—28no—
136#88257—216no—
137#88257—224no—
138#88256—28no—
139#88256—248no—
140#88256—224no—
141#41×D13—216no—
142#41×D13—248no—
143#41×D13—224no—
144#41×D13—224no—
145#41×D13D4116yescomplemented
146#88254—216no—
147#88254—224no—
148C2×#6131—216no—
149C2×#6131—224no—
150C2×#6131C2316yes—
151C2×#6131C2311yescharacteristic
152C2×#6131C2313yes—
153C2×#6131C2312yes—
154C2×#6131C2316yes—
155C2×#6131C2316yes—
156C2×#6131C2316yes—
157C2×#6131C2311yescharacteristic
158C2×Q8×D13C2313yes—
159C2×Q8×D13C2313yes—
160C2×Q8×D13C2312yes—
161C2×Q8×D13C2316yes—
162C2×Q8×D13C2311yescharacteristic
163#88251—248no—
164#88251—224no—
165C2×#6129—248no—
166C2×#6129—224no—
167C2×#6129C2316yes—
168C2×#6129C2316yes—
169C2×#6129C2316yes—
170C2×#6129C2316yes—
171C2×#6129C2316yes—
172C2×#6129C2316yes—
173C2×#6129C23112yes—
174C2×#6129C2313yes—
175C2×#6129C2316yes—
176C2×#6129C2311yescharacteristic
177C2×#6129C2313yes—
178C2×D4×D13C2316yes—
179C2×D4×D13C2316yes—
180C2×D4×D13C23112yes—
181C2×D4×D13C2316yes—
182C2×D4×D13C2316yes—
183C2×D4×D13C2313yes—
184C2×D4×D13C2313yes—
185C2×D4×D13C23112yes—
186C2×D4×D13C2313yes—
187C2×#6127C2313yes—
188C2×#6127C2313yes—
189C2×#6127C23112yes—
190C2×#6127C2316yes—
191C2×#6127C2316yes—
192C2×#6127C2316yes—
193C2×#6127C2316yes—
194C2×#6127C2313yes—
195C22×D52C2313yes—
196C22×D52C2316yes—
197C22×D52C2316yes—
198C22×C4×D13C2316yes—
199C22×C4×D13C2316yes—
200C22×C4×D13C2316yes—
201C22×C4×D13C2316yes—
202C22×C4×D13C2313yes—
203C22×Dic26C2313yes—
204C22×Dic26C2316yes—
205C13×C4⋊Q8C2313yes—
206C13×#127C2313yes—
207C13×#124C2313yes—
208C13×#124C2316yes—
209C13×#124C23112yes—
210C13×#124C2311yescharacteristic
211C13×#123C23112yes—
212C13×C22⋊Q8C23112yes—
213C13×#121C23112yes—
214C13×#121C23112yes—
215C13×#120C23112yes—
216C4×Q8×C13C2312yes—
217C4×D4×C13C2316yes—
218C4×D4×C13C23112yes—
219C13×#117C2313yes—
220C2×C13×C22⋊C4C23112yes—
221C2×C42×C13C2313yes—
222#88207C23112yes—
223#88201C2313yes—
224#88201C2313yes—
225#88200C23112yes—
226Q8×Dic13C2312yes—
227#88198C2311yescharacteristic
228#88198C2313yes—
229#88198C2316yes—
230#88198C23112yes—
231#88194C23112yes—
232#88194C2313yes—
233#88194C2316yes—
234#88194C23112yes—
235#88194C2311yescharacteristic
236#88193C23112yes—
237#88193C23124yes—
238#88193C23112yes—
239#88192C23112yes—
240#88192C23112yes—
241#88191C23112yes—
242#88191C23124yes—
243#88190C2313yes—
244#88190C2313yes—
245#88189C23112yes—
246D4×Dic13C2316yes—
247D4×Dic13C23112yes—
248#88184C23112yes—
249#88184C23112yes—
250#88183C23112yes—
251C4×C22⋊D13C23112yes—
252C4×C22⋊D13C23112yes—
253C4×C22⋊D13C23112yes—
254C2×#6103C23112yes—
255#88180C2313yes—
256#88178C23112yes—
257C2×#6101C23112yes—
258C2×C4×Dic13C2316yes—
259C2×C4×Dic13C2313yes—
260#88151C23112yes—
261#88150C23124yes—
262#88149C23112yes—
263#88149C23112yes—
264#88148C23124yes—
265#88147C23112yes—
266#88147C2316yes—
267#88146C2316yes—
268C4⋊C4×D13C23112yes—
269C4⋊C4×D13C2316yes—
270#88142C23112yes—
271#88141C2316yes—
272#88140C23112yes—
273#88139C23112yes—
274#88139C23112yes—
275#88138C23112yes—
276#88138C23124yes—
277#88138C23124yes—
278#88138C23124yes—
279#88138C23124yes—
280#88138C2314yes—
281#88137C23124yes—
282#88136C23124yes—
283#88136C23112yes—
284#88135C23112yes—
285#88135C23124yes—
286#88135C23124yes—
287#88135C23124yes—
288#88135C23112yes—
289#88135C2314yes—
290C22⋊C4×D13C23112yes—
291C22⋊C4×D13C2316yes—
292C22⋊C4×D13C23112yes—
293#88132C23124yes—
294#88131C2316yes—
295#88129C2316yes—
296#88129C2313yes—
297#88129C23112yes—
298#88129C2311yescharacteristic
299#88128C2313yes—
300C4×D52C2316yes—
301C4×D52C23112yes—
302#88126C2316yes—
303C42×D13C2313yes—
304C42×D13C2313yes—
305C42×D13C2311yescharacteristic
306C42×D13C2313yes—
307C42×D13C2316yes—
308C42×D13C2316yes—
309#88123C2313yes—
310C4×Dic26C2316yes—
311#62812—131nomaximal, Sylow
312C24×C13C2416yes—
313C23×D13C2416yes—
314C23×D13C2416yes—
315C23×D13C2416yes—
316C23×D13C2413yes—
317C13×#41—28no—
318C13×#41—224no—
319C13×#41—212no—
320C13×#41—212no—
321C13×#41C2×D418yescomplemented
322C2×Q8×C13—28no—
323C2×Q8×C13—212no—
324C2×Q8×C13C2413yes—
325C2×Q8×C13C2416yes—
326C2×Q8×C13C2411yescharacteristic
327C2×Q8×C13C2411yescharacteristic
328C2×D4×C13—224no—
329C2×D4×C13—212no—
330C2×D4×C13C2416yes—
331C2×D4×C13C2411yescharacteristic
332C2×D4×C13C2413yes—
333C2×D4×C13C2416yes—
334C2×D4×C13C2416yes—
335C2×D4×C13C24112yes—
336C2×D4×C13C2413yes—
337C22×C4×C13C2416yes—
338C22×C4×C13C2416yes—
339C22×C4×C13C2416yes—
340C22×C4×C13C2416yes—
341C22×C4×C13C2413yes—
342C2×C22⋊D13—224no—
343C2×C22⋊D13—248no—
344C2×C22⋊D13—424no—
345C2×C22⋊D13C24112yes—
346C2×C22⋊D13C2414yes—
347C2×C22⋊D13C2416yes—
348C2×C22⋊D13C24112yes—
349C2×C22⋊D13C2416yes—
350C2×C22⋊D13C2416yes—
351C2×C22⋊D13C2412yes—
352C2×C22⋊D13C2416yes—
353C2×C22⋊D13C2416yes—
354C2×C22⋊D13C24124yes—
355C2×C22⋊D13C2416yes—
356C22×Dic13—224no—
357C22×Dic13C24112yes—
358C22×Dic13C2416yes—
359C22×Dic13C2416yes—
360C22×Dic13C2412yes—
361C22×Dic13C2416yes—
362C22×Dic13C2413yes—
363#6131—28no—
364#6131—224no—
365#6131—224no—
366#6131—212no—
367#6131—224no—
368#6131—224no—
369#6131—24no—
370#6131C2×D418yescomplemented
371Q8×D13—28no—
372Q8×D13—212no—
373Q8×D13—212no—
374Q8×D13—224no—
375Q8×D13C2×D418yescomplemented
376#6129—224no—
377#6129—248no—
378#6129—224no—
379#6129—224no—
380#6129—224no—
381#6129—212no—
382#6129—224no—
383#6129—224no—
384#6129—24no—
385#6129—224no—
386#6129C2×D4124yescomplemented
387D4×D13—224no—
388D4×D13—224no—
389D4×D13—224no—
390D4×D13—248no—
391D4×D13—224no—
392D4×D13—212no—
393D4×D13—212no—
394D4×D13—424no—
395D4×D13C2×D4124yescomplemented
396#6127—212no—
397#6127—212no—
398#6127—248no—
399#6127—224no—
400#6127—224no—
401#6127—224no—
402#6127—224no—
403#6127C2×D4124yescomplemented
404C2×D52—224no—
405C2×D52—212no—
406C2×D52—224no—
407C2×D52C2411yescharacteristic
408C2×D52C2413yes—
409C2×D52C2416yes—
410C2×D52C24112yes—
411C2×D52C2416yes—
412C2×D52C2412yes—
413C2×D52C24112yes—
414C2×D52C2413yes—
415C2×C4×D13—224no—
416C2×C4×D13—224no—
417C2×C4×D13—224no—
418C2×C4×D13—412no—
419C2×C4×D13C2×D4124yescomplemented
420C2×C4×D13C2412yes—
421C2×C4×D13C2416yes—
422C2×C4×D13C2416yes—
423C2×C4×D13C2416yes—
424C2×C4×D13C2416yes—
425C2×C4×D13C2416yes—
426C2×C4×D13C2416yes—
427C2×C4×D13C24112yes—
428C2×C4×D13C2412yes—
429C2×C4×D13C2416yes—
430C2×C4×D13C2416yes—
431C2×C4×D13C2411yescharacteristic
432C2×C4×D13C2413yes—
433C2×C4×D13C2413yes—
434C2×C4×D13C2413yes—
435C2×Dic26—212no—
436C2×Dic26—224no—
437C2×Dic26C2411yescharacteristic
438C2×Dic26C2413yes—
439C2×Dic26C2416yes—
440C2×Dic26C2416yes—
441C2×Dic26C2416yes—
442C2×Dic26C2413yes—
443C13×C4⋊C4C2416yes—
444C13×C4⋊C4C24112yes—
445C13×C22⋊C4C2416yes—
446C13×C22⋊C4C24124yes—
447C13×C22⋊C4C2414yes—
448C13×C22⋊C4C24112yes—
449C42×C13C2416yes—
450C42×C13C2413yes—
451C42×C13C2411yescharacteristic
452C22⋊Dic13C2416yes—
453C22⋊Dic13C24112yes—
454C22⋊Dic13C24112yes—
455#6103C24112yes—
456#6103C2414yes—
457#6103C24112yes—
458#6103C24124yes—
459#6103C24112yes—
460#6103C24112yes—
461C4⋊Dic13C2416yes—
462C4⋊Dic13C24112yes—
463#6101C24112yes—
464#6101C24124yes—
465#6101C24112yes—
466#6101C2414yes—
467C4×Dic13C2416yes—
468C4×Dic13C2412yes—
469C4×Dic13C2411yescharacteristic
470C4×Dic13C2413yes—
471C4×Dic13C2416yes—
472C4×Dic13C2416yes—
473C4×Dic13C2416yes—
474C2×#585—131no—
475C2×#585—131no—
476#3500—133no—
477#3500—133no—
478#3500—131no—
479#3500D1311yescharacteristic, complemented
480#3499—131no—
481#3499—133no—
482#3498—131no—
483#3498—133no—
484#3497—134no—
485#3496—1312no—
486D4×#41—134no—
487D4×#41—1312no—
488#3449—133no—
489#3449—133no—
490C2×#532—133no—
491C2×#532—133no—
492C2×C4×#41—131no—
493C23×C13—212no—
494C23×C13—412no—
495C23×C13C2512yes—
496C23×C13C2516yes—
497C23×C13C2513yes—
498C22×D13—212no—
499C22×D13—212no—
500C22×D13—212no—
501C22×D13—46no—
502C22×D13—412no—
503C22×D13—412no—
504C22×D13—412no—
505C22×D13C22×D4112yes—
506C22×D13C2516yes—
507C22×D13C2512yes—
508C22×D13C2513yes—
509C22×D13C2511yescharacteristic
510Q8×C13—22no—
511Q8×C13—26no—
512Q8×C13—212no—
513Q8×C13C22×D414yes—
514D4×C13—212no—
515D4×C13—212no—
516D4×C13—22no—
517D4×C13—26no—
518D4×C13—212no—
519D4×C13—412no—
520D4×C13C22×D4112yes—
521C2×C4×C13—212no—
522C2×C4×C13—212no—
523C2×C4×C13—212no—
524C2×C4×C13—46no—
525C2×C4×C13C22×D4112yes—
526C2×C4×C13C2512yes—
527C2×C4×C13C2516yes—
528C2×C4×C13C2516yes—
529C2×C4×C13C2512yes—
530C2×C4×C13C2511yescharacteristic
531C2×C4×C13C2513yes—
532C22⋊D13—212no—
533C22⋊D13—212no—
534C22⋊D13—24no—
535C22⋊D13—224no—
536C22⋊D13—212no—
537C22⋊D13—212no—
538C22⋊D13—212no—
539C22⋊D13—28no—
540C22⋊D13—224no—
541C22⋊D13—424no—
542C22⋊D13C22×D4124yes—
543C2×Dic13—212no—
544C2×Dic13—224no—
545C2×Dic13—24no—
546C2×Dic13—212no—
547C2×Dic13—212no—
548C2×Dic13C22×D4112yes—
549C2×Dic13C2516yes—
550C2×Dic13C2516yes—
551C2×Dic13C2512yes—
552C2×Dic13C2511yescharacteristic
553C2×Dic13C2513yes—
554C2×Dic13C2512yes—
555D52—224no—
556D52—212no—
557D52—24no—
558D52—26no—
559D52—212no—
560D52—22no—
561D52—412no—
562D52C22×D4112yes—
563C4×D13—212no—
564C4×D13—212no—
565C4×D13—212no—
566C4×D13—212no—
567C4×D13—24no—
568C4×D13—212no—
569C4×D13—224no—
570C4×D13—24no—
571C4×D13—212no—
572C4×D13—46no—
573C4×D13—46no—
574C4×D13C22×D4112yes—
575C4×D13C22×D414yes—
576C4×D13C22×D4112yes—
577C4×D13C22×D4112yes—
578Dic26—26no—
579Dic26—212no—
580Dic26—22no—
581Dic26—212no—
582Dic26—212no—
583Dic26C22×D4112yes—
584#585—2616no—
585#585—2616no—
586C2×2−1+4—132no—
587C2×2−1+4—133no—
588C2×2−1+4—131no—
589C2×2−1+4—132no—
590C2×2−1+4—133no—
591C2×2−1+4C2×D1311yescharacteristic, complemented
592C2×H(5,𝔽2)—136no—
593C2×H(5,𝔽2)—133no—
594C2×H(5,𝔽2)—131no—
595C2×H(5,𝔽2)—136no—
596C2×H(5,𝔽2)—133no—
597C2×H(5,𝔽2)C2×D1311yescharacteristic, complemented
598C22×#41—131no—
599C22×#41—133no—
600C22×#41—133no—
601C22×#41—132no—
602C22×#41—136no—
603C22×#41—133no—
604C22×#41—132no—
605C22×#41—133no—
606C22×#41—136no—
607#550—134no—
608#550—1312no—
609D4×Q8—134no—
610D4×Q8—1312no—
611#548—1312no—
612#548—134no—
613#548—1312no—
614#548C2×D1314yescomplemented
615#547—1312no—
616#547—1324no—
617#547—1312no—
618#546—1312no—
619#546—1324no—
620#546—1312no—
621#546—1312no—
622#546—1324no—
623#546C2×D13112yescomplemented
624D42—1312no—
625D42—1312no—
626D42—1324no—
627#537—1312no—
628#537—1312no—
629#536—133no—
630#536—133no—
631#536—136no—
632#536—136no—
633#536—133no—
634#536C2×D1313yescomplemented
635#535—133no—
636#535—133no—
637#535—136no—
638#535—136no—
639#535—133no—
640#535C2×D1313yescomplemented
641#534—1312no—
642#534—1312no—
643#532—133no—
644#532—133no—
645#532—133no—
646#532—133no—
647#532—131no—
648#532—133no—
649#532—136no—
650#532—1312no—
651#532—1312no—
652#532—136no—
653#532—136no—
654#532—1312no—
655#532—1312no—
656#532—133no—
657#532C2×D1313yescomplemented
658C2×C4⋊Q8—133no—
659C2×C4⋊Q8—133no—
660C2×#127—133no—
661C2×#127—133no—
662C2×#124—133no—
663C2×#124—133no—
664C2×#124—133no—
665C2×#124C2×D1313yescomplemented
666#525—1312no—
667#525—1312no—
668#525—1312no—
669#525—1312no—
670C2×#121—1312no—
671C2×#121—1312no—
672C4×#41—131no—
673C4×#41—132no—
674C4×#41—136no—
675C4×#41—133no—
676C4×#41—133no—
677C4×#41C2×D1311yescharacteristic, complemented
678C2×C4×Q8—132no—
679C2×C4×D4—136no—
680C2×C4×D4—1312no—
681C2×C4×D4—1312no—
682C2×#117—133no—
683C22×C42—133no—
684C22×C13—26no—
685C22×C13—26no—
686C22×C13—22no—
687C22×C13—212no—
688C22×C13—24no—
689C22×C13—812no—
690C22×C13C23×D416yes—
691C22×C13C2611yescharacteristic
692C2×D13—22no—
693C2×D13—26no—
694C2×D13—26no—
695C2×D13—22no—
696C2×D13—24no—
697C2×D13—212no—
698C2×D13—412no—
699C2×D13—812no—
700C2×D13—812no—
701C2×D13—812no—
702C2×D13C23×D416yes—
703C2×D13C23×D412yes—
704C4×C13—22no—
705C4×C13—26no—
706C4×C13—22no—
707C4×C13—26no—
708C4×C13C23×D412yes—
709C4×C13C23×D416yes—
710Dic13—22no—
711Dic13—26no—
712Dic13—26no—
713Dic13C23×D416yes—
714Dic13C23×D412yes—
715Dic13#58514yescomplemented
7162−1+4—28no—
7172−1+4—2616no—
7182−1+4—2624no—
7192−1+4—2616no—
7202−1+4—2624no—
7212−1+4—268no—
722H(5,𝔽2)—28no—
723H(5,𝔽2)—2648no—
724H(5,𝔽2)—2624no—
725H(5,𝔽2)—2648no—
726H(5,𝔽2)—2624no—
727H(5,𝔽2)—268no—
728C2×#41—1316no—
729C2×#41—131no—
730C2×#41—136no—
731C2×#41—131no—
732C2×#41—133no—
733C2×#41—136no—
734C2×#41—136no—
735C2×#41—136no—
736C2×#41—132no—
737C2×#41—133no—
738C2×#41—136no—
739C2×#41—136no—
740C2×#41—136no—
741C2×#41—131no—
742C2×#41—133no—
743C2×#41—136no—
744C2×#41—136no—
745C2×#41—136no—
746C2×#41—1312no—
747C2×#41—136no—
748C2×#41—133no—
749C2×#41—133no—
750C2×#41—133no—
751C2×#41—136no—
752C2×#41—136no—
753C2×#41—136no—
754C2×#41—1312no—
755C2×#41—136no—
756C2×#41—2624no—
757C2×#41—2624no—
758C2×#41—2624no—
759C2×#41—2624no—
760C2×#41—2648no—
761C2×#41—2616no—
762C2×#41—2616no—
763C2×#41—2648no—
764C2×#41C22×D1313yes—
765C2×#41C22×D1313yes—
766C2×#41C22×D1316yes—
767C2×#41C22×D1312yes—
768C2×#41C22×D1311yescharacteristic
769C22×Q8—131no—
770C22×Q8—133no—
771C22×Q8—133no—
772C22×Q8—136no—
773C22×Q8—132no—
774C22×Q8—133no—
775C22×Q8—136no—
776C22×Q8C22×D1313yes—
777C22×Q8C22×D1312yes—
778C22×D4—133no—
779C22×D4—136no—
780C22×D4—1312no—
781C22×D4—1312no—
782C22×D4—136no—
783C22×D4—136no—
784C22×D4—133no—
785C22×D4—133no—
786C22×D4—1312no—
787C22×D4—136no—
788C22×D4—136no—
789C22×D4—1312no—
790C22×D4—136no—
791C22×D4—133no—
792C22×D4—136no—
793C22×D4C22×D1313yes—
794C22×D4C22×D1316yes—
795C23×C4—133no—
796C23×C4—136no—
797C23×C4—136no—
798C23×C4—136no—
799C23×C4—136no—
800C23×C4—136no—
801C4⋊Q8—131no—
802C4⋊Q8—133no—
803C4⋊Q8—136no—
804C4⋊Q8—1312no—
805C4⋊Q8—1312no—
806C4⋊Q8—133no—
807C4⋊Q8C22×D1313yes—
808#127—131no—
809#127—133no—
810#127—136no—
811#127—1312no—
812#127—1312no—
813#127—133no—
814#127C22×D1313yes—
815#124—133no—
816#124—133no—
817#124—133no—
818#124—133no—
819#124—1312no—
820#124—1312no—
821#124—131no—
822#124—133no—
823#124—136no—
824#124—1312no—
825#124C22×D1311yescharacteristic
826#124C22×D1313yes—
827#124C22×D1316yes—
828#124C22×D13112yes—
829#123—1312no—
830#123—1312no—
831#123—1324no—
832#123—1324no—
833#123—1312no—
834#123C22×D13112yes—
835C22⋊Q8—1312no—
836C22⋊Q8—1312no—
837C22⋊Q8—1324no—
838C22⋊Q8—1312no—
839C22⋊Q8—1324no—
840C22⋊Q8C22×D13112yes—
841#121—1312no—
842#121—1312no—
843#121—1312no—
844#121—1312no—
845#121—1324no—
846#121—1312no—
847#121—1312no—
848#121—1312no—
849#121—1312no—
850#121—134no—
851#121—1312no—
852#121—1324no—
853#121—1324no—
854#121—1324no—
855#121—1324no—
856#121C22×D13112yes—
857#121C22×D13112yes—
858#120—1312no—
859#120—1312no—
860#120—1324no—
861#120—1324no—
862#120—1312no—
863#120C22×D13112yes—
864C4×Q8—132no—
865C4×Q8—136no—
866C4×Q8—136no—
867C4×Q8C22×D1312yes—
868C4×D4—136no—
869C4×D4—1312no—
870C4×D4—1312no—
871C4×D4—1312no—
872C4×D4—1312no—
873C4×D4—136no—
874C4×D4—1312no—
875C4×D4—134no—
876C4×D4—1312no—
877C4×D4—1312no—
878C4×D4—1324no—
879C4×D4—1324no—
880C4×D4—1324no—
881C4×D4—136no—
882C4×D4—1312no—
883C4×D4C22×D1316yes—
884C4×D4C22×D13112yes—
885#117—133no—
886#117—136no—
887#117—136no—
888#117—136no—
889#117C22×D1313yes—
890C2×C4⋊C4—1312no—
891C2×C4⋊C4—136no—
892C2×C4⋊C4—1312no—
893C2×C22⋊C4—1312no—
894C2×C22⋊C4—136no—
895C2×C22⋊C4—1312no—
896C2×C22⋊C4—1312no—
897C2×C22⋊C4C22×D13112yes—
898C2×C42—136no—
899C2×C42—133no—
900C2×C42—133no—
901C2×C42—136no—
902C2×C42—136no—
903C2×C42—133no—
904C2×C42—133no—
905C2×C42—131no—
906C2×C42C22×D1313yes—
907C2×C13—26no—
908C2×C13—42no—
909C2×C13—46no—
910C2×C13C24×D411yescharacteristic
911C2×C13C2×#58512yes—
912D13—22no—
913D13—26no—
914D13—46no—
915D13—42no—
916C24—133no—
917C24—136no—
918C24—136no—
919C24—136no—
920C24C23×D1316yes—
921#41—28no—
922#41—224no—
923#41—212no—
924#41—212no—
925#41—138no—
926#41—1324no—
927#41—1324no—
928#41—2624no—
929#41—2624no—
930#41—2648no—
931#41—2624no—
932#41—2624no—
933#41—2624no—
934#41—2624no—
935#41—2612no—
936#41—264no—
937#41—2624no—
938#41—2624no—
939#41—2624no—
940#41—2612no—
941#41—264no—
942#41—2624no—
943#41—2624no—
944#41—2624no—
945#41—2648no—
946#41—2624no—
947#41—2624no—
948#41—268no—
949#41—2624no—
950#41—2612no—
951#41—2612no—
952#41D4×D1318yescomplemented
953C2×Q8—28no—
954C2×Q8—212no—
955C2×Q8—138no—
956C2×Q8—133no—
957C2×Q8—136no—
958C2×Q8—136no—
959C2×Q8—136no—
960C2×Q8—131no—
961C2×Q8—133no—
962C2×Q8—2624no—
963C2×Q8—2612no—
964C2×Q8—2612no—
965C2×Q8—2624no—
966C2×Q8—268no—
967C2×Q8—2612no—
968C2×Q8C23×D1316yes—
969C2×Q8C23×D1311yescharacteristic
970C2×Q8C23×D1313yes—
971C2×Q8C23×D1311yescharacteristic
972C2×D4—224no—
973C2×D4—212no—
974C2×D4—136no—
975C2×D4—1324no—
976C2×D4—134no—
977C2×D4—1312no—
978C2×D4—1312no—
979C2×D4—136no—
980C2×D4—136no—
981C2×D4—132no—
982C2×D4—136no—
983C2×D4—136no—
984C2×D4—136no—
985C2×D4—1324no—
986C2×D4—133no—
987C2×D4—1312no—
988C2×D4—132no—
989C2×D4—136no—
990C2×D4—136no—
991C2×D4—131no—
992C2×D4—133no—
993C2×D4—1312no—
994C2×D4—2624no—
995C2×D4—2624no—
996C2×D4—2612no—
997C2×D4—2612no—
998C2×D4—2648no—
999C2×D4—2624no—
1000C2×D4—2624no—
1001C2×D4—2624no—
1002C2×D4—2648no—
1003C2×D4—2624no—
1004C2×D4—2624no—
1005C2×D4—2612no—
1006C2×D4—5224no—
1007C2×D4—5224no—
1008C2×D4C23×D1316yes—
1009C2×D4C23×D1316yes—
1010C2×D4C23×D1316yes—
1011C2×D4C23×D1311yescharacteristic
1012C2×D4C23×D1313yes—
1013C2×D4C23×D13112yes—
1014C2×D4C23×D1313yes—
1015C22×C4—133no—
1016C22×C4—1324no—
1017C22×C4—131no—
1018C22×C4—133no—
1019C22×C4—133no—
1020C22×C4—133no—
1021C22×C4—136no—
1022C22×C4—136no—
1023C22×C4—132no—
1024C22×C4—136no—
1025C22×C4—1312no—
1026C22×C4—132no—
1027C22×C4—136no—
1028C22×C4—136no—
1029C22×C4—136no—
1030C22×C4—132no—
1031C22×C4—136no—
1032C22×C4—1312no—
1033C22×C4—136no—
1034C22×C4—136no—
1035C22×C4—136no—
1036C22×C4—136no—
1037C22×C4—2624no—
1038C22×C4—2624no—
1039C22×C4—2624no—
1040C22×C4—2624no—
1041C22×C4—5212no—
1042C22×C4C23×D1316yes—
1043C22×C4C23×D1316yes—
1044C22×C4C23×D1316yes—
1045C22×C4C23×D1316yes—
1046C22×C4C23×D1313yes—
1047C4⋊C4—134no—
1048C4⋊C4—1312no—
1049C4⋊C4—1312no—
1050C4⋊C4—136no—
1051C4⋊C4—1324no—
1052C4⋊C4—1312no—
1053C4⋊C4C23×D1316yes—
1054C4⋊C4C23×D13112yes—
1055C22⋊C4—136no—
1056C22⋊C4—1312no—
1057C22⋊C4—1312no—
1058C22⋊C4—1312no—
1059C22⋊C4—134no—
1060C22⋊C4—1312no—
1061C22⋊C4—1312no—
1062C22⋊C4—1312no—
1063C22⋊C4—1324no—
1064C22⋊C4C23×D1314yes—
1065C22⋊C4C23×D13112yes—
1066C22⋊C4C23×D1316yes—
1067C22⋊C4C23×D13124yes—
1068C42—132no—
1069C42—131no—
1070C42—136no—
1071C42—133no—
1072C42—136no—
1073C42—136no—
1074C42—136no—
1075C42C23×D1311yescharacteristic
1076C42C23×D1313yes—
1077C42C23×D1316yes—
1078C13#6281211yescharacteristic, complemented, Sylow
1079C23—212no—
1080C23—412no—
1081C23—133no—
1082C23—131no—
1083C23—1312no—
1084C23—132no—
1085C23—136no—
1086C23—2612no—
1087C23—2612no—
1088C23—2612no—
1089C23—526no—
1090C23—5212no—
1091C23—5212no—
1092C23—5212no—
1093C23C24×D1312yes—
1094C23C24×D1316yes—
1095C23C24×D1313yes—
1096Q8—212no—
1097Q8—26no—
1098Q8—22no—
1099Q8—1312no—
1100Q8—2612no—
1101Q8—2612no—
1102Q8—2612no—
1103Q8—266no—
1104Q8—262no—
1105Q8C2×D4×D1314yes—
1106D4—212no—
1107D4—212no—
1108D4—212no—
1109D4—26no—
1110D4—22no—
1111D4—412no—
1112D4—1324no—
1113D4—1312no—
1114D4—264no—
1115D4—2612no—
1116D4—2624no—
1117D4—2612no—
1118D4—2612no—
1119D4—268no—
1120D4—2624no—
1121D4—264no—
1122D4—2612no—
1123D4—2624no—
1124D4—2612no—
1125D4—2612no—
1126D4—2612no—
1127D4—266no—
1128D4—262no—
1129D4—5212no—
1130D4—5224no—
1131D4C2×D4×D13112yes—
1132C2×C4—212no—
1133C2×C4—212no—
1134C2×C4—212no—
1135C2×C4—46no—
1136C2×C4—1312no—
1137C2×C4—132no—
1138C2×C4—131no—
1139C2×C4—133no—
1140C2×C4—134no—
1141C2×C4—1312no—
1142C2×C4—1312no—
1143C2×C4—1312no—
1144C2×C4—136no—
1145C2×C4—132no—
1146C2×C4—136no—
1147C2×C4—264no—
1148C2×C4—2612no—
1149C2×C4—2624no—
1150C2×C4—264no—
1151C2×C4—2612no—
1152C2×C4—2612no—
1153C2×C4—2612no—
1154C2×C4—264no—
1155C2×C4—2612no—
1156C2×C4—2624no—
1157C2×C4—2612no—
1158C2×C4—2612no—
1159C2×C4—2612no—
1160C2×C4—2612no—
1161C2×C4—526no—
1162C2×C4—526no—
1163C2×C4C2×D4×D13112yes—
1164C2×C4C24×D1312yes—
1165C2×C4C24×D1316yes—
1166C2×C4C24×D1312yes—
1167C2×C4C24×D1316yes—
1168C2×C4C24×D1311yescharacteristic
1169C2×C4C24×D1313yes—
1170C22—26no—
1171C22—22no—
1172C22—26no—
1173C22—24no—
1174C22—212no—
1175C22—812no—
1176C22—132no—
1177C22—136no—
1178C22—262no—
1179C22—266no—
1180C22—266no—
1181C22—262no—
1182C22—264no—
1183C22—2612no—
1184C22—5212no—
1185C22—10412no—
1186C22—10412no—
1187C22—10412no—
1188C22C22×D4×D1316yes—
1189C22C25×D1311yescharacteristic
1190C4—22no—
1191C4—26no—
1192C4—22no—
1193C4—26no—
1194C4—132no—
1195C4—136no—
1196C4—134no—
1197C4—262no—
1198C4—266no—
1199C4—266no—
1200C4C22×D4×D1316yes—
1201C4C22×D4×D1312yes—
1202C2—26no—
1203C2—46no—
1204C2—42no—
1205C2—262no—
1206C2—266no—
1207C2—526no—
1208C2—522no—
1209C2C23×D4×D1311yescharacteristic
1210C2D13×#58512yes—
subgroupG/H
center, FrattiniC22C25×D13
commutator, socle, cosocleC22×C13C26
FittingC13×#3500C2
hypercenter#3500D13
hypocenterC13#62812
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #3500

Complements

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

NH ≅ G/Ntype
1. C2×#11719652C2semidirect
2. C2×#11719650C2semidirect
3. #13128629C2semidirect
4. #13128626C2semidirect
5. #13128623C2semidirect
6. #13128618C2semidirect
7. #13128617C2semidirect
8. #13128611C2semidirect
9. #13128610C2semidirect
10. #13128604C2semidirect
11. #13128596C2semidirect
12. #13128325C2semidirect
13. #13128320C2semidirect
14. #13128168C2semidirect
15. #13128167C2semidirect
16. C2×#11719373C2semidirect
17. D13×#532C2semidirect
18. C4×#41×D13C2semidirect
19. C13×#3500C2semidirect
20. C2×C13×2−1+4C22semidirect
21. C2×C13×H(5,𝔽2)C22semidirect
24. C2×#88257C22semidirect
25. C2×#88257C22semidirect
26. C2×#88257C22semidirect
27. C2×#88256C22semidirect
28. C2×#88256C22semidirect
29. C2×#88256C22semidirect
31. C2×#41×D13C22semidirect
32. C2×#41×D13C22semidirect
33. C2×#41×D13C22semidirect
34. C2×#41×D13C22semidirect
35. C2×#88254C22semidirect
36. C2×#88254C22semidirect
37. C22×#6131C22semidirect
38. C22×#6131C22semidirect
39. C2×#88251C22semidirect
40. C2×#88251C22semidirect
41. C22×#6129C22semidirect
42. C22×#6129C22semidirect
43. C13×#548C22semidirect
44. C13×#546C22semidirect
45. C13×#536C22semidirect
46. C13×#535C22semidirect
47. C13×#532C22semidirect
48. C2×C13×#124C22semidirect
49. C4×C13×#41C22semidirect
50. #11719539C22semidirect
51. #11719537C22semidirect
52. #11719537C22semidirect
53. #11719535C22semidirect
54. #41×Dic13C22semidirect
55. #11719530C22semidirect
56. #11719529C22semidirect
57. #11719521C22semidirect
58. Q8×C22⋊D13C22semidirect
59. C2×#88198C22semidirect
60. #11719510C22semidirect
61. C2×#88194C22semidirect
62. D4×C22⋊D13C22semidirect
63. #11719430C22semidirect
64. #11719429C22semidirect
65. D13×C4⋊Q8C22semidirect
66. #11719421C22semidirect
67. #11719420C22semidirect
68. D13×#127C22semidirect
69. #11719382C22semidirect
70. #11719381C22semidirect
71. #11719380C22semidirect
72. #11719379C22semidirect
73. D13×#124C22semidirect
74. D13×#124C22semidirect
75. #11719373C22semidirect
76. #11719373C22semidirect
77. #11719373C22semidirect
78. #11719373C22semidirect
79. #11719373C22semidirect
80. #11719373C22semidirect
81. #11719373C22semidirect
82. #11719361C22semidirect
83. #11719360C22semidirect
84. #11719358C22semidirect
85. #11719337C22semidirect
86. #11719336C22semidirect
87. #11719334C22semidirect
88. #11719332C22semidirect
89. #11719315C22semidirect
90. #11719314C22semidirect
91. #11719313C22semidirect
92. #11719311C22semidirect
93. D13×#121C22semidirect
94. #11719304C22semidirect
95. #11719301C22semidirect
96. #11719295C22semidirect
97. #11719294C22semidirect
98. #11719291C22semidirect
99. #11719281C22semidirect
100. C4×#6131C22semidirect
101. C4×Q8×D13C22semidirect
102. #11719259C22semidirect
103. #11719257C22semidirect
104. #11719255C22semidirect
105. #11719253C22semidirect
106. C4×D4×D13C22semidirect
107. C4×D4×D13C22semidirect
108. C4×#6129C22semidirect
109. #11719231C22semidirect
110. #11719230C22semidirect
111. #11719227C22semidirect
112. D13×#117C22semidirect
113. #11719195C22semidirect
114. C2×#88138C22semidirect
115. C2×#88135C22semidirect
116. #11719182C22semidirect
117. C2×#88129C22semidirect
118. C4×#6127C22semidirect
119. C2×C42×D13C22semidirect
145. #41×D13D4semidirect
321. C13×#41C2×D4semidirect
370. #6131C2×D4semidirect
375. Q8×D13C2×D4semidirect
386. #6129C2×D4semidirect
395. D4×D13C2×D4semidirect
403. #6127C2×D4semidirect
419. C2×C4×D13C2×D4semidirect
479. #3500D13semidirect
591. C2×2−1+4C2×D13semidirect
597. C2×H(5,𝔽2)C2×D13semidirect
614. #548C2×D13semidirect
623. #546C2×D13semidirect
634. #536C2×D13semidirect
640. #535C2×D13semidirect
657. #532C2×D13semidirect
665. C2×#124C2×D13semidirect
677. C4×#41C2×D13semidirect
715. Dic13#585semidirect
952. #41D4×D13semidirect
1078. C13#62812semidirect

Maximal subgroups

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

subgroupindex
C2×#117196522
C2×#117196502
#131286292
#131286262
#131286232
#131286182
#131286172
#131286112
#131286102
#131286042
#131285962
#131283252
#131283202
#131281682
#131281672
C2×#117193732
D13×#5322
C4×#41×D132
C13×#35002
#6281213