Finite Group Databasebeta

← #16737745

Subgroups — #16737745

Order 3328.

1768 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128747C211yesmaximal, characteristic, complemented
2#13126301C214yesmaximal, complemented
3#13125980C211yesmaximal, characteristic, complemented
4#13125977C211yesmaximal, characteristic, complemented
5#13125964C211yesmaximal, characteristic, complemented
6#13125961C211yesmaximal, characteristic, complemented
7#13125792C211yesmaximal, characteristic, complemented
8#13125788C211yesmaximal, characteristic, complemented
9#13125769C211yesmaximal, characteristic, complemented
10#13125765C211yesmaximal, characteristic, complemented
11#13125742C214yesmaximal, complemented
12#13125577C211yesmaximal, characteristic, complemented
13#13125570C211yesmaximal, characteristic, complemented
14#13125396C211yesmaximal, characteristic, complemented
15#13125391C211yesmaximal, characteristic, complemented
16#13125113C214yesmaximal, complemented
17#13125107C214yesmaximal, complemented
18#13123480C211yesmaximal, characteristic, complemented
19C13×#3511C211yesmaximal, characteristic, complemented
20C13×#556—21no—
21C13×#555—21no—
22C13×#554—21no—
23C13×#553—21no—
24C13×#553—21no—
25C13×#548—21no—
26C13×#548—21no—
27C13×#547—21no—
28C13×#542C2212yes—
29C13×#542C2212yes—
30C13×#537C2212yes—
31C13×#533C2211yescharacteristic
32C13×#533C2211yescharacteristic
33C13×#532C2211yescharacteristic
34C13×#532C2211yescharacteristic
35C13×#532C2211yescharacteristic
36C2×C13×C4⋊Q8C2211yescharacteristic
37C13×#520C2212yes—
38C4×C13×#41C2211yescharacteristic
39#11719538C2212yes—
40#11719289—21no—
41#11719284—21no—
42#11719270—21no—
43#11719270—21no—
44#11719268—21no—
45#11719257—21no—
46#11719257—21no—
47#11719256—21no—
48#11719239C2212yes—
49#11719239C2212yes—
50#11719228C2212yes—
51#11719182C2211yescharacteristic
52#11719182C2211yescharacteristic
53#11719182C2211yescharacteristic
54#11719175C2211yescharacteristic
55#11719175C2211yescharacteristic
56C2×#88123C2211yescharacteristic
57#11718900C2214yes—
58#11718899C2214yes—
59#11718895C2212yes—
60#11718755C2214yes—
61#11718754C2211yescharacteristic
62#11718754C2211yescharacteristic
63#11718753C2211yescharacteristic
64#11718749C2211yescharacteristic
65#11718749C2211yescharacteristic
66#11718746C2211yescharacteristic
67#11718745C2214yes—
68#11718742C2211yescharacteristic
69#11718742C2211yescharacteristic
70#11718740C2211yescharacteristic
71#11718740C2211yescharacteristic
72#11718740C2211yescharacteristic
73#11718740C2211yescharacteristic
74#11718737C2211yescharacteristic
75#11718734C2211yescharacteristic
76#11718731C2211yescharacteristic
77#11718731C2211yescharacteristic
78#11718718C2214yes—
79#11718715C2214yes—
80#11718713C2214yes—
81#11718709C2214yes—
82#11718708C2214yes—
83#11718704C2214yes—
84#11718702C2214yes—
85#11718700C2214yes—
86#11718698C2214yes—
87#11718695C2214yes—
88#11718691C2214yes—
89#11718689C2214yes—
90C4×#6106C2214yes—
91#11718681C2214yes—
92C4×#6105C2214yes—
93#11718677C2214yes—
94#11718675C2214yes—
95#11718669C2214yes—
96#11718661C2212yes—
97#11718661C2212yes—
98#11718660C2212yes—
99#11718632C2214yes—
100#11718629C2214yes—
101#11718586C2211yescharacteristic
102#11718586C2211yescharacteristic
103#11718586C2211yescharacteristic
104#11718586C2211yescharacteristic
105C4×#6099C2211yescharacteristic
106C2×C4×#1055C2211yescharacteristic
107C2×C13×#41—21no—
108C2×C13×#41—21no—
109C2×C13×#41C2312yes—
110C2×C13×#41C2311yescharacteristic
111C22×Q8×C13—21no—
112C2×#6127—21no—
113C2×#6127—21no—
114C2×#6127C2312yes—
115C22×Dic26—21no—
116C13×C4⋊Q8—21no—
117C13×C4⋊Q8—21no—
118C13×C4⋊Q8C2311yescharacteristic
119C13×C4⋊Q8C2311yescharacteristic
120C13×C4⋊Q8C2311yescharacteristic
121C13×C4⋊Q8C2312yes—
122C13×#127C2311yescharacteristic
123C13×#126—22no—
124C13×#126—22no—
125C13×#125—21no—
126C13×#125—21no—
127C13×#124—22no—
128C13×#124—22no—
129C13×#124—21no—
130C13×#124—21no—
131C13×#124C2312yes—
132C13×#123—22no—
133C13×#123—22no—
134C13×C22⋊Q8—22no—
135C13×C22⋊Q8—21no—
136C13×C22⋊Q8—21no—
137C13×C22⋊Q8—22no—
138C13×C22⋊Q8—22no—
139C13×C22⋊Q8C2312yes—
140C13×C22⋊Q8C2312yes—
141C13×#121—22no—
142C13×#121—22no—
143C13×#121—22no—
144C13×#121—21no—
145C13×#121—21no—
146C13×#121—21no—
147C13×#121—21no—
148C13×#121C2312yes—
149C13×#121C2312yes—
150C4×Q8×C13—21no—
151C4×Q8×C13—21no—
152C4×Q8×C13D411yescharacteristic
153C4×Q8×C13D411yescharacteristic
154C4×Q8×C13C2312yes—
155C4×Q8×C13C2312yes—
156C4×D4×C13—22no—
157C4×D4×C13—22no—
158C4×D4×C13—21no—
159C4×D4×C13—21no—
160C4×D4×C13—21no—
161C4×D4×C13—21no—
162C4×D4×C13D411yescharacteristic
163C4×D4×C13D411yescharacteristic
164C4×D4×C13D411yescharacteristic
165C4×D4×C13D411yescharacteristic
166C4×D4×C13D411yescharacteristic
167C4×D4×C13D411yescharacteristic
168C4×D4×C13C2312yes—
169C4×D4×C13C2312yes—
170C13×#117—21no—
171C13×#117—21no—
172C13×#117—22no—
173C13×#117C2311yescharacteristic
174C13×#117C2311yescharacteristic
175C13×#117C2311yescharacteristic
176C2×C13×C4⋊C4—21no—
177C2×C13×C4⋊C4—22no—
178C2×C13×C4⋊C4C2312yes—
179C2×C42×C13C2311yescharacteristic
180C2×C42×C13C2311yescharacteristic
181C2×C42×C13C2311yescharacteristic
182#88200—22no—
183C2×#6107C2314yes—
184C2×#6106C2314yes—
185#88193—22no—
186#88193—22no—
187#88192—22no—
188C2×#6105C2314yes—
189C2×#6104C2314yes—
190#88184—21no—
191#88184—21no—
192#88184—21no—
193#88184—21no—
194#88184C2312yes—
195#88184C2312yes—
196#88180—21no—
197#88180—21no—
198C2×C4⋊Dic13—21no—
199C2×C4⋊Dic13C2312yes—
200#88178—21no—
201#88178—21no—
202#88178C2312yes—
203#88178C2312yes—
204C2×#6099C2312yes—
205C22×#1055C2312yes—
206#88152—22no—
207#88152—22no—
208#88150—22no—
209#88150—22no—
210#88146—22no—
211C4⋊C4×D13—22no—
212#88139—22no—
213#88139—22no—
214#88137—22no—
215#88137—22no—
216#88135—22no—
217#88135—22no—
218#88129—21no—
219#88129—21no—
220#88129C2312yes—
221#88128C2311yescharacteristic
222C4×D52—21no—
223C4×D52—21no—
224C4×D52—21no—
225C4×D52—21no—
226C4×D52C2312yes—
227C4×D52C2312yes—
228#88124—21no—
229#88124—21no—
230#88123—21no—
231#88123—21no—
232#88123C2311yescharacteristic
233#88123C2311yescharacteristic
234#88123C2311yescharacteristic
235#88123C2312yes—
236C4×Dic26—21no—
237C4×Dic26—21no—
238C4×Dic26C2312yes—
239C4×Dic26C2312yes—
240#88075C2314yes—
241#88075C2314yes—
242#88072C2314yes—
243#88072C2314yes—
244C22⋊#1055C2312yes—
245C22⋊#1055C2312yes—
246C22⋊#1055C2312yes—
247C22⋊#1055C2312yes—
248#88050C2314yes—
249#88050C2314yes—
250#88049C2314yes—
251#88049C2314yes—
252#88048C2314yes—
253#88048C2314yes—
254#88048C2314yes—
255#88048C2314yes—
256C4⋊#1055C2312yes—
257C4⋊#1055C2312yes—
258C4⋊#1055C2312yes—
259C4⋊#1055C2312yes—
260#88043C2312yes—
261C4×#1055C2312yes—
262C4×#1055C2311yescharacteristic
263C4×#1055C2311yescharacteristic
264C4×#1055C2311yescharacteristic
265C4×#1055C2311yescharacteristic
266#61015—131nomaximal, Sylow
267C13×#41—42no—
268C13×#41—44no—
269C13×#41—82no—
270C13×#41—82no—
271C2×Q8×C13—21no—
272C2×Q8×C13—21no—
273C2×Q8×C13—22no—
274C2×Q8×C13—82no—
275C2×Q8×C13C2×D411yescharacteristic
276C2×Q8×C13C2412yes—
277C2×D4×C13—22no—
278C2×D4×C13—22no—
279C2×D4×C13—22no—
280C2×D4×C13—21no—
281C2×D4×C13—21no—
282C2×D4×C13C2×D411yescharacteristic
283C2×D4×C13C2×D411yescharacteristic
284C2×D4×C13C2×D411yescharacteristic
285C2×D4×C13C2412yes—
286C22×C4×C13—22no—
287C22×C4×C13—22no—
288C22×C4×C13—22no—
289C22×C4×C13—22no—
290C22×C4×C13C2×D411yescharacteristic
291C22×C4×C13C2×D411yescharacteristic
292C22×C4×C13C2×D411yescharacteristic
293C22×C4×C13C2×D411yescharacteristic
294C22×C4×C13C2×D411yescharacteristic
295C22×C4×C13C2×D411yescharacteristic
296C22×C4×C13C2411yescharacteristic
297C22×C4×C13C2411yescharacteristic
298C22×C4×C13C2411yescharacteristic
299C2×C22⋊D13—22no—
300C2×C22⋊D13—22no—
301C2×C22⋊D13—22no—
302C22×Dic13—22no—
303#6127—44no—
304#6127—82no—
305#6127—82no—
306C2×D52—21no—
307C2×D52—21no—
308C2×D52C2412yes—
309C2×C4×D13—22no—
310C2×C4×D13—22no—
311C2×C4×D13—22no—
312C2×Dic26—21no—
313C2×Dic26—21no—
314C2×Dic26—22no—
315C2×Dic26—82no—
316C2×Dic26C2412yes—
317C13×C4⋊C4—22no—
318C13×C4⋊C4—21no—
319C13×C4⋊C4—21no—
320C13×C4⋊C4—22no—
321C13×C4⋊C4—22no—
322C13×C4⋊C4—22no—
323C13×C4⋊C4—21no—
324C13×C4⋊C4—21no—
325C13×C4⋊C4—22no—
326C13×C4⋊C4—22no—
327C13×C4⋊C4C2×D411yescharacteristic
328C13×C4⋊C4C2×D411yescharacteristic
329C13×C4⋊C4C2×D411yescharacteristic
330C13×C4⋊C4C2×D411yescharacteristic
331C13×C4⋊C4C2×D411yescharacteristic
332C13×C4⋊C4C2×D411yescharacteristic
333C13×C4⋊C4C2412yes—
334C13×C4⋊C4C2412yes—
335C13×C22⋊C4—22no—
336C13×C22⋊C4—22no—
337C13×C22⋊C4—22no—
338C13×C22⋊C4—22no—
339C13×C22⋊C4—22no—
340C13×C22⋊C4—22no—
341C13×C22⋊C4—22no—
342C13×C22⋊C4—22no—
343C13×C22⋊C4C2×D411yescharacteristic
344C13×C22⋊C4C2×D411yescharacteristic
345C13×C22⋊C4C2×D411yescharacteristic
346C13×C22⋊C4C2×D411yescharacteristic
347C13×C22⋊C4C2×D411yescharacteristic
348C13×C22⋊C4C2×D411yescharacteristic
349C42×C13—22no—
350C42×C13—22no—
351C42×C13C2×D411yescharacteristic
352C42×C13C2×D411yescharacteristic
353C42×C13C2×D411yescharacteristic
354C42×C13C2×D411yescharacteristic
355C42×C13C2×D411yescharacteristic
356C42×C13C2×D411yescharacteristic
357C42×C13C2411yescharacteristic
358C42×C13C2411yescharacteristic
359C42×C13C2411yescharacteristic
360C42×C13C2411yescharacteristic
361C22⋊Dic13—22no—
362C22⋊Dic13—22no—
363#6107—44no—
364#6106—44no—
365#6105—44no—
366#6104—44no—
367#6103—22no—
368#6103—22no—
369#6103—22no—
370#6103—22no—
371#6103—22no—
372#6103—22no—
373C4⋊Dic13—21no—
374C4⋊Dic13—22no—
375C4⋊Dic13—21no—
376C4⋊Dic13—21no—
377C4⋊Dic13—22no—
378C4⋊Dic13—21no—
379C4⋊Dic13C2412yes—
380C4⋊Dic13C2412yes—
381#6101—22no—
382#6101—22no—
383#6101—22no—
384#6101—22no—
385C4×Dic13—22no—
386C4×Dic13—22no—
387#6099—42no—
388C2×#1055—42no—
389C2×#1055C2412yes—
390C2×#1055C2412yes—
391C2×#1055C2412yes—
392C2×#1055C2412yes—
393#3511—131no—
394#3511D1311yescharacteristic, complemented
395#3263—134no—
396#3229—131no—
397#3229—131no—
398#3227—131no—
399#3227—131no—
400#3210—131no—
401#3210—131no—
402#3207—131no—
403#3207—131no—
404#3204—134no—
405#3185—131no—
406#3184—131no—
407#3167—131no—
408#3167—131no—
409#3125—134no—
410#3125—134no—
411#2922—131no—
412C23×C13—22no—
413C23×C13C22×D411yescharacteristic
414C23×C13C22×D411yescharacteristic
415C23×C13C22×D411yescharacteristic
416C22×D13—22no—
417Q8×C13—24no—
418Q8×C13—41no—
419Q8×C13—42no—
420Q8×C13—42no—
421Q8×C13—82no—
422D4×C13—24no—
423D4×C13—41no—
424D4×C13—41no—
425D4×C13—41no—
426D4×C13—44no—
427D4×C13—42no—
428D4×C13—42no—
429D4×C13—82no—
430D4×C13—82no—
431C2×C4×C13—22no—
432C2×C4×C13—22no—
433C2×C4×C13—22no—
434C2×C4×C13—22no—
435C2×C4×C13—22no—
436C2×C4×C13—22no—
437C2×C4×C13—22no—
438C2×C4×C13—22no—
439C2×C4×C13—22no—
440C2×C4×C13—22no—
441C2×C4×C13—22no—
442C2×C4×C13—22no—
443C2×C4×C13—44no—
444C2×C4×C13—82no—
445C2×C4×C13—82no—
446C2×C4×C13—82no—
447C2×C4×C13C22×D411yescharacteristic
448C2×C4×C13C22×D411yescharacteristic
449C2×C4×C13C22×D411yescharacteristic
450C2×C4×C13C22×D411yescharacteristic
451C2×C4×C13C22×D411yescharacteristic
452C2×C4×C13C22×D411yescharacteristic
453C2×C4×C13C22×D411yescharacteristic
454C2×C4×C13C22×D411yescharacteristic
455C2×C4×C13C22×D411yescharacteristic
456C2×C4×C13C22×D411yescharacteristic
457C2×C4×C13C22×D411yescharacteristic
458C2×C4×C13C2511yescharacteristic
459C22⋊D13—44no—
460C22⋊D13—82no—
461C22⋊D13—82no—
462C2×Dic13—22no—
463C2×Dic13—22no—
464C2×Dic13—22no—
465C2×Dic13—82no—
466D52—24no—
467D52—42no—
468D52—42no—
469C4×D13—44no—
470C4×D13—82no—
471C4×D13—82no—
472Dic26—24no—
473Dic26—42no—
474Dic26—42no—
475Dic26—82no—
476#1055—22no—
477#1055—22no—
478#1055—22no—
479#1055—22no—
480#556—21no—
481#556—261no—
482#555—21no—
483#555—261no—
484#554—21no—
485#554—261no—
486#553—21no—
487#553—21no—
488#553—261no—
489#553—261no—
490#548—21no—
491#548—21no—
492#548—261no—
493#548—261no—
494#547—21no—
495#547—261no—
496#542—132no—
497#542—132no—
498#542C2×D1312yes—
499#542C2×D1312yes—
500#537—132no—
501#537C2×D1312yes—
502#533—131no—
503#533—131no—
504#533C2×D1311yescharacteristic
505#533C2×D1311yescharacteristic
506#532—131no—
507#532—131no—
508#532—131no—
509#532C2×D1311yescharacteristic
510#532C2×D1311yescharacteristic
511#532C2×D1311yescharacteristic
512C2×C4⋊Q8—131no—
513C2×C4⋊Q8C2×D1311yescharacteristic
514#520—132no—
515#520C2×D1312yes—
516C4×#41C2×D1311yescharacteristic
517#498—131no—
518#498—131no—
519#498—131no—
520#498—131no—
521#494—131no—
522#493—131no—
523#492—131no—
524#492—131no—
525#487—131no—
526#487—131no—
527#487—131no—
528#487—131no—
529#486—131no—
530#486—131no—
531#486—131no—
532#486—131no—
533#483—134no—
534#483—134no—
535#481—134no—
536#481—134no—
537#476—134no—
538#476—134no—
539#475—134no—
540#475—134no—
541#470—134no—
542#469—134no—
543#465—134no—
544#465—134no—
545#464—134no—
546#464—134no—
547#463—134no—
548#463—134no—
549#452—134no—
550#452—134no—
551#449—134no—
552#449—134no—
553#442—134no—
554#441—134no—
555C4×SD16—134no—
556C4×SD16—134no—
557#433—132no—
558#433—132no—
559#431—131no—
560#431—131no—
561#431—131no—
562#431—131no—
563#424—132no—
564#408—132no—
565C4×M16—131no—
566C2×C4×C8—131no—
567C22×C13—21no—
568C22×C13—21no—
569C22×C13—21no—
570C22×C13—21no—
571C22×C13—21no—
572C22×C13—21no—
573C22×C13—21no—
574C22×C13—21no—
575C22×C13—21no—
576C22×C13—42no—
577C22×C13—42no—
578C22×C13—42no—
579C22×C13C23×D411yescharacteristic
580C2×D13—42no—
581C2×D13—42no—
582C2×D13—42no—
583C4×C13—21no—
584C4×C13—21no—
585C4×C13—21no—
586C4×C13—21no—
587C4×C13—21no—
588C4×C13—21no—
589C4×C13—21no—
590C4×C13—21no—
591C4×C13—21no—
592C4×C13—42no—
593C4×C13—42no—
594C4×C13—42no—
595C4×C13#57712yes—
596C4×C13#57712yes—
597C4×C13#58512yes—
598Dic13—42no—
599Dic13—42no—
600Dic13—42no—
601C2×#41—21no—
602C2×#41—21no—
603C2×#41—132no—
604C2×#41—261no—
605C2×#41—261no—
606C2×#41C22×D1312yes—
607C2×#41C22×D1311yescharacteristic
608C22×Q8—21no—
609C22×Q8—261no—
610C2×Q16—134no—
611C2×SD16—134no—
612C2×SD16—134no—
613C2×D8—134no—
614C2×M16—132no—
615C22×C8—132no—
616C4⋊Q8—21no—
617C4⋊Q8—21no—
618C4⋊Q8—131no—
619C4⋊Q8—131no—
620C4⋊Q8—132no—
621C4⋊Q8—131no—
622C4⋊Q8—261no—
623C4⋊Q8—261no—
624C4⋊Q8C22×D1311yescharacteristic
625C4⋊Q8C22×D1311yescharacteristic
626C4⋊Q8C22×D1311yescharacteristic
627C4⋊Q8C22×D1312yes—
628#127—131no—
629#127C22×D1311yescharacteristic
630#126—22no—
631#126—22no—
632#126—262no—
633#126—262no—
634#125—21no—
635#125—21no—
636#125—261no—
637#125—261no—
638#124—22no—
639#124—22no—
640#124—21no—
641#124—21no—
642#124—132no—
643#124—262no—
644#124—262no—
645#124—261no—
646#124—261no—
647#124C22×D1312yes—
648#123—22no—
649#123—22no—
650#123—262no—
651#123—262no—
652C22⋊Q8—22no—
653C22⋊Q8—21no—
654C22⋊Q8—21no—
655C22⋊Q8—22no—
656C22⋊Q8—22no—
657C22⋊Q8—132no—
658C22⋊Q8—132no—
659C22⋊Q8—262no—
660C22⋊Q8—261no—
661C22⋊Q8—261no—
662C22⋊Q8—262no—
663C22⋊Q8—262no—
664C22⋊Q8C22×D1312yes—
665C22⋊Q8C22×D1312yes—
666#121—22no—
667#121—22no—
668#121—22no—
669#121—21no—
670#121—21no—
671#121—21no—
672#121—21no—
673#121—132no—
674#121—132no—
675#121—262no—
676#121—262no—
677#121—262no—
678#121—261no—
679#121—261no—
680#121—261no—
681#121—261no—
682#121C22×D1312yes—
683#121C22×D1312yes—
684C4×Q8—21no—
685C4×Q8—21no—
686C4×Q8—132no—
687C4×Q8—132no—
688C4×Q8—261no—
689C4×Q8—261no—
690C4×Q8C22⋊D1311yescharacteristic
691C4×Q8C22⋊D1311yescharacteristic
692C4×Q8C22×D1312yes—
693C4×Q8C22×D1312yes—
694C4×D4—22no—
695C4×D4—22no—
696C4×D4—21no—
697C4×D4—21no—
698C4×D4—21no—
699C4×D4—21no—
700C4×D4—132no—
701C4×D4—132no—
702C4×D4—262no—
703C4×D4—262no—
704C4×D4—261no—
705C4×D4—261no—
706C4×D4—261no—
707C4×D4—261no—
708C4×D4C22⋊D1311yescharacteristic
709C4×D4C22⋊D1311yescharacteristic
710C4×D4C22⋊D1311yescharacteristic
711C4×D4C22⋊D1311yescharacteristic
712C4×D4C22⋊D1311yescharacteristic
713C4×D4C22⋊D1311yescharacteristic
714C4×D4C22×D1312yes—
715C4×D4C22×D1312yes—
716#117—21no—
717#117—21no—
718#117—22no—
719#117—261no—
720#117—261no—
721#117—262no—
722#117C22×D1311yescharacteristic
723#117C22×D1311yescharacteristic
724#117C22×D1311yescharacteristic
725C2×C4⋊C4—21no—
726C2×C4⋊C4—22no—
727C2×C4⋊C4—132no—
728C2×C4⋊C4—261no—
729C2×C4⋊C4—262no—
730C2×C4⋊C4C22×D1312yes—
731C2×C42C22×D1311yescharacteristic
732C2×C42C22×D1311yescharacteristic
733C2×C42C22×D1311yescharacteristic
734#106—134no—
735#106—134no—
736#106—134no—
737#106—134no—
738C4⋊C8—132no—
739C4⋊C8—132no—
740C4⋊C8—132no—
741C4⋊C8—132no—
742#103—134no—
743#103—134no—
744#103—134no—
745#103—134no—
746#102—134no—
747#102—134no—
748#102—134no—
749#102—134no—
750C22⋊C8—132no—
751C22⋊C8—132no—
752C22⋊C8—132no—
753C22⋊C8—132no—
754#97—132no—
755C4×C8—131no—
756C4×C8—131no—
757C4×C8—132no—
758C4×C8—131no—
759C4×C8—131no—
760C2×C13—41no—
761C2×C13—41no—
762C2×C13—41no—
763C2×C13—82no—
764C2×C13#344911yescharacteristic
765C2×C13C2×#57711yescharacteristic
766C2×C13C2×#57711yescharacteristic
767D13—82no—
768#41—42no—
769#41—44no—
770#41—82no—
771#41—82no—
772#41—524no—
773#41—1042no—
774#41—1042no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—22no—
778C2×Q8—82no—
779C2×Q8—132no—
780C2×Q8—261no—
781C2×Q8—261no—
782C2×Q8—262no—
783C2×Q8—1042no—
784C2×Q8C2×C22⋊D1311yescharacteristic
785C2×Q8C23×D1312yes—
786C2×D4—22no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—132no—
792C2×D4—262no—
793C2×D4—262no—
794C2×D4—262no—
795C2×D4—261no—
796C2×D4—261no—
797C2×D4C2×C22⋊D1311yescharacteristic
798C2×D4C2×C22⋊D1311yescharacteristic
799C2×D4C2×C22⋊D1311yescharacteristic
800C2×D4C23×D1312yes—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—262no—
806C22×C4—262no—
807C22×C4—262no—
808C22×C4—262no—
809C22×C4C2×C22⋊D1311yescharacteristic
810C22×C4C2×C22⋊D1311yescharacteristic
811C22×C4C2×C22⋊D1311yescharacteristic
812C22×C4C2×C22⋊D1311yescharacteristic
813C22×C4C2×C22⋊D1311yescharacteristic
814C22×C4C2×C22⋊D1311yescharacteristic
815C22×C4C23×D1311yescharacteristic
816C22×C4C23×D1311yescharacteristic
817C22×C4C23×D1311yescharacteristic
818Q16—524no—
819SD16—524no—
820SD16—524no—
821D8—524no—
822M16—522no—
823C2×C8—132no—
824C2×C8—132no—
825C2×C8—132no—
826C2×C8—132no—
827C2×C8—522no—
828C4⋊C4—22no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—22no—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—22no—
837C4⋊C4—22no—
838C4⋊C4—132no—
839C4⋊C4—132no—
840C4⋊C4—262no—
841C4⋊C4—261no—
842C4⋊C4—261no—
843C4⋊C4—262no—
844C4⋊C4—262no—
845C4⋊C4—262no—
846C4⋊C4—261no—
847C4⋊C4—261no—
848C4⋊C4—262no—
849C4⋊C4—262no—
850C4⋊C4C2×C22⋊D1311yescharacteristic
851C4⋊C4C2×C22⋊D1311yescharacteristic
852C4⋊C4C2×C22⋊D1311yescharacteristic
853C4⋊C4C2×C22⋊D1311yescharacteristic
854C4⋊C4C2×C22⋊D1311yescharacteristic
855C4⋊C4C2×C22⋊D1311yescharacteristic
856C4⋊C4C23×D1312yes—
857C4⋊C4C23×D1312yes—
858C22⋊C4—22no—
859C22⋊C4—22no—
860C22⋊C4—22no—
861C22⋊C4—22no—
862C22⋊C4—22no—
863C22⋊C4—22no—
864C22⋊C4—22no—
865C22⋊C4—22no—
866C22⋊C4—262no—
867C22⋊C4—262no—
868C22⋊C4—262no—
869C22⋊C4—262no—
870C22⋊C4—262no—
871C22⋊C4—262no—
872C22⋊C4—262no—
873C22⋊C4—262no—
874C22⋊C4C2×C22⋊D1311yescharacteristic
875C22⋊C4C2×C22⋊D1311yescharacteristic
876C22⋊C4C2×C22⋊D1311yescharacteristic
877C22⋊C4C2×C22⋊D1311yescharacteristic
878C22⋊C4C2×C22⋊D1311yescharacteristic
879C22⋊C4C2×C22⋊D1311yescharacteristic
880C42—22no—
881C42—22no—
882C42—262no—
883C42—262no—
884C42C2×C22⋊D1311yescharacteristic
885C42C2×C22⋊D1311yescharacteristic
886C42C2×C22⋊D1311yescharacteristic
887C42C2×C22⋊D1311yescharacteristic
888C42C2×C22⋊D1311yescharacteristic
889C42C2×C22⋊D1311yescharacteristic
890C42C23×D1311yescharacteristic
891C42C23×D1311yescharacteristic
892C42C23×D1311yescharacteristic
893C42C23×D1311yescharacteristic
894C13#6101511yescharacteristic, complemented, Sylow
895C23—22no—
896C23—262no—
897C23C22×C22⋊D1311yescharacteristic
898C23C22×C22⋊D1311yescharacteristic
899C23C22×C22⋊D1311yescharacteristic
900Q8—24no—
901Q8—41no—
902Q8—42no—
903Q8—42no—
904Q8—82no—
905Q8—264no—
906Q8—522no—
907Q8—522no—
908Q8—1042no—
909D4—24no—
910D4—41no—
911D4—41no—
912D4—41no—
913D4—44no—
914D4—42no—
915D4—42no—
916D4—82no—
917D4—82no—
918D4—264no—
919D4—524no—
920D4—522no—
921D4—522no—
922D4—1042no—
923D4—1042no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—44no—
937C2×C4—82no—
938C2×C4—82no—
939C2×C4—82no—
940C2×C4—262no—
941C2×C4—262no—
942C2×C4—262no—
943C2×C4—524no—
944C2×C4—1042no—
945C2×C4—1042no—
946C2×C4—1042no—
947C2×C4C22×C22⋊D1311yescharacteristic
948C2×C4C22×C22⋊D1311yescharacteristic
949C2×C4C22×C22⋊D1311yescharacteristic
950C2×C4C22×C22⋊D1311yescharacteristic
951C2×C4C22×C22⋊D1311yescharacteristic
952C2×C4C22×C22⋊D1311yescharacteristic
953C2×C4C22×C22⋊D1311yescharacteristic
954C2×C4C22×C22⋊D1311yescharacteristic
955C2×C4C22×C22⋊D1311yescharacteristic
956C2×C4C22×C22⋊D1311yescharacteristic
957C2×C4C22×C22⋊D1311yescharacteristic
958C2×C4C24×D1311yescharacteristic
959C8—262no—
960C8—262no—
961C8—262no—
962C8—262no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—21no—
968C22—21no—
969C22—21no—
970C22—21no—
971C22—21no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—522no—
976C22—522no—
977C22—522no—
978C22C23×C22⋊D1311yescharacteristic
979C4—21no—
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—522no—
992C4—522no—
993C4—522no—
994C4#1171954112yes—
995C4#1171954212yes—
996C4#1171964812yes—
997C2—41no—
998C2—41no—
999C2—41no—
1000C2—82no—
1001C2—1042no—
1002C2#1312816511yescharacteristic
1003C2C2×#1171954211yescharacteristic
1004C2C2×#1171954111yescharacteristic
subgroupG/H
centerC22C23×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC13×#3511C2
socleC22×C13C23×D4
hypercenter#3511D13
hypocenterC13#61015
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #13128747C2semidirect
2. #13126301C2semidirect
3. #13125980C2semidirect
4. #13125977C2semidirect
5. #13125964C2semidirect
6. #13125961C2semidirect
7. #13125792C2semidirect
8. #13125788C2semidirect
9. #13125769C2semidirect
10. #13125765C2semidirect
11. #13125742C2semidirect
12. #13125577C2semidirect
13. #13125570C2semidirect
14. #13125396C2semidirect
15. #13125391C2semidirect
16. #13125113C2semidirect
17. #13125107C2semidirect
18. #13123480C2semidirect
19. C13×#3511C2semidirect
394. #3511D13semidirect
894. C13#61015semidirect

Maximal subgroups

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

subgroupindex
#131287472
#131263012
#131259802
#131259772
#131259642
#131259612
#131257922
#131257882
#131257692
#131257652
#131257422
#131255772
#131255702
#131253962
#131253912
#131251132
#131251072
#131234802
C13×#35112
#6101513