Finite Group Databasebeta

← #15879414

Subgroups — #15879414

Order 3328.

1148 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128394C211yesmaximal, characteristic
2D4×#6099C211yesmaximal, characteristic, complemented
3#13115817C211yesmaximal, characteristic, complemented
4#13115779C211yesmaximal, characteristic, complemented
5#13115284C211yesmaximal, characteristic, complemented
6#13115279C211yesmaximal, characteristic, complemented
7#13115136C211yesmaximal, characteristic, complemented
8#13115136C211yesmaximal, characteristic, complemented
9#13114936C211yesmaximal, characteristic, complemented
10#13114936C211yesmaximal, characteristic, complemented
11#13114857C211yesmaximal, characteristic, complemented
12#13114647C211yesmaximal, characteristic, complemented
13#13114546C211yesmaximal, characteristic, complemented
14C2×#11718115C211yesmaximal, characteristic, complemented
15C13×#2290C211yesmaximal, characteristic, complemented
16C2×C4×D4×C13C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C22×C42×C13C2211yescharacteristic
19#11719511—21no—
20#11719496C2211yescharacteristic
21#11719496C2211yescharacteristic
22C2×#88180C2211yescharacteristic
23C2×#88180C2211yescharacteristic
24C22×#6099C2211yescharacteristic
25C22×#6099C2211yescharacteristic
26#11719270C411yescharacteristic, complemented
27#11719270C411yescharacteristic, complemented
28#11719268C411yescharacteristic, complemented
29#11719262—21no—
30#11719260C411yescharacteristic, complemented
31#11719248C411yescharacteristic, complemented
32#11719247C411yescharacteristic, complemented
33#11719246C411yescharacteristic, complemented
34#11719246C411yescharacteristic, complemented
35#11719243—21no—
36#11719243—21no—
37C4×#6129—21no—
38#11719218—21no—
39#11719200—21no—
40#11719200—21no—
41C4×#6127C2211yescharacteristic
42#11719175C2211yescharacteristic
43C13×#388—21no—
44C13×#387—21no—
45C13×#386—21no—
46C13×#385—21no—
47C4×C13×C4⋊C4C2211yescharacteristic
48C4×C13×C22⋊C4C2211yescharacteristic
49C4×C13×C22⋊C4C2211yescharacteristic
50C13×#376C2211yescharacteristic
51#11718868C2211yescharacteristic
52#11718868C2211yescharacteristic
53#11718673—21no—
54#11718672—21no—
55#11718672—21no—
56D4×#1055—21no—
57C2×#88045C2211yescharacteristic
58C2×#88045C2211yescharacteristic
59C2×#88045C2211yescharacteristic
60C2×#88045C2211yescharacteristic
61#11718585C2211yescharacteristic
62C4×#6099C2211yescharacteristic
63#11718115C2211yescharacteristic
64#11718115C2211yescharacteristic
65#11718115C2211yescharacteristic
66#11718115C2211yescharacteristic
67#11718115C2211yescharacteristic
68#11718115C2211yescharacteristic
69#11718115C2211yescharacteristic
70#11718115C2211yescharacteristic
71#11718115C2211yescharacteristic
72#11718115C2211yescharacteristic
73#11718115C2211yescharacteristic
74#11718115C2211yescharacteristic
75C22×D4×C13D411yescharacteristic
76C23×C4×C13—21no—
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C2×#6129—21no—
80C2×#6127C2311yescharacteristic
81C4×D4×C13C2×C411yescharacteristic
82C4×D4×C13C2×C411yescharacteristic
83C4×D4×C13C2×C411yescharacteristic
84C4×D4×C13C2×C411yescharacteristic
85C4×D4×C13D411yescharacteristic
86C4×D4×C13D411yescharacteristic
87C4×D4×C13D411yescharacteristic
88C4×D4×C13D411yescharacteristic
89C13×#117—22no—
90C13×#117—41no—
91C2×C13×C4⋊C4—21no—
92C2×C13×C4⋊C4—21no—
93C2×C13×C4⋊C4D411yescharacteristic
94C2×C13×C22⋊C4—21no—
95C2×C13×C22⋊C4—21no—
96C2×C13×C22⋊C4—21no—
97C2×C13×C22⋊C4D411yescharacteristic
98C2×C13×C22⋊C4D411yescharacteristic
99C2×C42×C13—22no—
100C2×C42×C13—21no—
101C2×C42×C13—41no—
102C2×C42×C13C2311yescharacteristic
103C2×C42×C13C2311yescharacteristic
104C2×C42×C13C2311yescharacteristic
105C2×C42×C13C2311yescharacteristic
106C2×C42×C13C2311yescharacteristic
107#88207—21no—
108#88207—21no—
109C2×C22⋊Dic13—21no—
110C2×C22⋊Dic13—21no—
111#88193—21no—
112#88193—21no—
113#88192—21no—
114#88190—21no—
115#88189—21no—
116#88189—21no—
117D4×Dic13—21no—
118#88184C2×C411yescharacteristic
119#88184C2×C411yescharacteristic
120#88184C2×C411yescharacteristic, complemented
121#88184C2×C411yescharacteristic, complemented
122#88183—21no—
123#88183—21no—
124C4×C22⋊D13—21no—
125C4×C22⋊D13—21no—
126C4×C22⋊D13—21no—
127C4×C22⋊D13—21no—
128C4×C22⋊D13—21no—
129C4×C22⋊D13—21no—
130#88180—21no—
131#88180—21no—
132#88180—21no—
133#88180—21no—
134#88180C2×C411yescharacteristic
135#88180C2×C411yescharacteristic
136#88180C2×C411yescharacteristic, complemented
137#88180C2×C411yescharacteristic, complemented
138#88180C2311yescharacteristic
139#88180C2311yescharacteristic
140#88180C2311yescharacteristic
141C2×C4⋊Dic13C2×C411yescharacteristic
142C2×C4⋊Dic13C2×C411yescharacteristic
143C2×C4⋊Dic13C2×C411yescharacteristic, complemented
144C2×C4⋊Dic13C2×C411yescharacteristic, complemented
145#88178—21no—
146#88178—21no—
147#88178C2×C411yescharacteristic
148#88178C2×C411yescharacteristic
149#88178C2×C411yescharacteristic, complemented
150#88178C2×C411yescharacteristic, complemented
151C2×C4×Dic13—21no—
152C2×C4×Dic13—21no—
153C2×#6099—21no—
154C2×#6099—21no—
155C2×#6099—22no—
156C2×#6099—22no—
157C2×#6099—41no—
158C2×#6099—41no—
159C2×#6099C2311yescharacteristic
160C2×#6099C2311yescharacteristic
161C2×#6099C2311yescharacteristic
162C2×#6099C2311yescharacteristic
163C22×#1055—21no—
164C22×#1055—21no—
165#88152—21no—
166#88152—21no—
167#88151—21no—
168#88146—21no—
169#88144—21no—
170#88143—21no—
171#88143—21no—
172#88141—21no—
173#88140—21no—
174#88140—21no—
175#88139—21no—
176#88139—21no—
177#88137—21no—
178#88137—21no—
179#88135—21no—
180#88135—21no—
181#88133—21no—
182#88133—21no—
183#88133—21no—
184#88133—21no—
185#88132—21no—
186#88132—21no—
187#88131—21no—
188#88131—21no—
189C4×D52C2×C411yescharacteristic, complemented
190C4×D52C2×C411yescharacteristic, complemented
191#88126—21no—
192C42×D13—21no—
193#88124C2×C411yescharacteristic, complemented
194#88124C2×C411yescharacteristic, complemented
195#88123C2×C411yescharacteristic, complemented
196#88123C2×C411yescharacteristic, complemented
197C4×Dic26—21no—
198C4×Dic26—21no—
199C4×Dic26C2×C411yescharacteristic, complemented
200C4×Dic26C2×C411yescharacteristic, complemented
201C13×#95—21no—
202C13×#95—21no—
203C13×#95—21no—
204C13×#95—21no—
205C13×#95—21no—
206C22⋊#1055—21no—
207C22⋊#1055—21no—
208C22⋊#1055—21no—
209C22⋊#1055—21no—
210#88045—22no—
211#88045—22no—
212#88045—41no—
213#88045—41no—
214C4⋊#1055—21no—
215C4⋊#1055—21no—
216#88043—21no—
217C4×#1055—21no—
218#22506—131nomaximal, Sylow
219C24×C13C2×D411yescharacteristic
220C24×C13C2×D411yescharacteristic
221C2×D4×C13—42no—
222C2×D4×C13C22⋊C411yescharacteristic
223C2×D4×C13C22⋊C411yescharacteristic
224C2×D4×C13C22⋊C411yescharacteristic
225C2×D4×C13C22⋊C411yescharacteristic
226C22×C4×C13—21no—
227C22×C4×C13—21no—
228C22×C4×C13—21no—
229C22×C4×C13—21no—
230C22×C4×C13—21no—
231C22×C4×C13—21no—
232C22×C4×C13—21no—
233C22×C4×C13—21no—
234C22×C4×C13—21no—
235C22×C4×C13—21no—
236C22×C4×C13—21no—
237C22×C4×C13—21no—
238C22×C4×C13—42no—
239C22×C4×C13—42no—
240C22×C4×C13—42no—
241C22×C4×C13C22×C411yescharacteristic
242C22×C4×C13C22×C411yescharacteristic
243C22×C4×C13C22×C411yescharacteristic
244C22×C4×C13C22×C411yescharacteristic
245C22×C4×C13C2×D411yescharacteristic
246C22×C4×C13C2×D411yescharacteristic
247C22×C4×C13C2×D411yescharacteristic
248C22×C4×C13C2×D411yescharacteristic
249C22×C4×C13C2×D411yescharacteristic
250C22×C4×C13C2×D411yescharacteristic
251C22×C4×C13C2×D411yescharacteristic
252C22×C4×C13C2×D411yescharacteristic
253C22×C4×C13C2411yescharacteristic
254C2×C22⋊D13—21no—
255C2×C22⋊D13—21no—
256C2×C22⋊D13—21no—
257C2×C22⋊D13—21no—
258C2×C22⋊D13—21no—
259C22×Dic13—21no—
260C22×Dic13—21no—
261C22×Dic13—21no—
262C22×Dic13—21no—
263#6129—44no—
264#6127—21no—
265#6127—21no—
266#6127—21no—
267#6127—21no—
268C2×D52C22×C411yescharacteristic
269C2×C4×D13—21no—
270C2×C4×D13—21no—
271C2×C4×D13—21no—
272C2×Dic26—21no—
273C2×Dic26—21no—
274C2×Dic26C22×C411yescharacteristic
275C13×C4⋊C4—42no—
276C13×C4⋊C4—42no—
277C13×C4⋊C4C22⋊C411yescharacteristic
278C13×C4⋊C4C22⋊C411yescharacteristic
279C13×C4⋊C4C22⋊C411yescharacteristic
280C13×C4⋊C4C22⋊C411yescharacteristic
281C13×C22⋊C4—42no—
282C13×C22⋊C4—42no—
283C13×C22⋊C4—42no—
284C13×C22⋊C4C22⋊C411yescharacteristic
285C13×C22⋊C4C22⋊C411yescharacteristic
286C13×C22⋊C4C22⋊C411yescharacteristic
287C13×C22⋊C4C22⋊C411yescharacteristic
288C13×C22⋊C4C22⋊C411yescharacteristic
289C13×C22⋊C4C22⋊C411yescharacteristic
290C13×C22⋊C4C22⋊C411yescharacteristic
291C13×C22⋊C4C22⋊C411yescharacteristic
292C42×C13—21no—
293C42×C13—21no—
294C42×C13—21no—
295C42×C13—21no—
296C42×C13—21no—
297C42×C13—21no—
298C42×C13—21no—
299C42×C13—42no—
300C42×C13C22×C411yescharacteristic
301C42×C13C22×C411yescharacteristic
302C42×C13C2×D411yescharacteristic
303C42×C13C2×D411yescharacteristic
304C42×C13#4112yescomplemented
305C22⋊Dic13—21no—
306C22⋊Dic13—21no—
307C22⋊Dic13—21no—
308C22⋊Dic13—21no—
309C22⋊Dic13—21no—
310C22⋊Dic13—21no—
311C22⋊Dic13—21no—
312C22⋊Dic13—21no—
313C22⋊Dic13—21no—
314C22⋊Dic13—21no—
315C22⋊Dic13—21no—
316#6103—21no—
317#6103—21no—
318#6103—21no—
319#6103—21no—
320#6103—21no—
321#6103—21no—
322C4⋊Dic13—21no—
323C4⋊Dic13—21no—
324C4⋊Dic13—21no—
325C4⋊Dic13—21no—
326C4⋊Dic13—21no—
327C4⋊Dic13—21no—
328C4⋊Dic13C22×C411yescharacteristic
329C4⋊Dic13C22×C411yescharacteristic
330C4⋊Dic13C22×C411yescharacteristic
331C4⋊Dic13C22×C411yescharacteristic
332C4⋊Dic13C22×C411yescharacteristic
333C4⋊Dic13C22×C411yescharacteristic
334#6101—21no—
335#6101—21no—
336#6101—21no—
337#6101—21no—
338#6101—21no—
339#6101—21no—
340#6101—21no—
341#6101—21no—
342#6101—21no—
343#6101—21no—
344C4×Dic13—21no—
345C4×Dic13—21no—
346C4×Dic13—21no—
347C4×Dic13—21no—
348C4×Dic13—21no—
349C4×Dic13—21no—
350C4×Dic13—21no—
351C4×Dic13—21no—
352C4×Dic13—21no—
353#6099—21no—
354#6099—21no—
355#6099—21no—
356#6099—21no—
357#6099—21no—
358#6099—21no—
359#6099—21no—
360#6099—42no—
361#6099—42no—
362#6099#4112yescomplemented
363C2×#1055—21no—
364C2×#1055—21no—
365C2×#1055—21no—
366C2×#1055—21no—
367C2×#1055—42no—
368C2×#1055—42no—
369#3475—131no—
370D4×M16—131no—
371#2290D1311yescharacteristic, complemented
372#1995—131no—
373#1986—131no—
374#1897—131no—
375#1896—131no—
376#1871—131no—
377#1871—131no—
378#1826—131no—
379#1826—131no—
380#1806—131no—
381#1759—131no—
382#1733—131no—
383C2×#339—131no—
384C23×C13—21no—
385C23×C13—21no—
386C23×C13—22no—
387C23×C13—21no—
388C23×C13—21no—
389C23×C13—41no—
390C23×C13—41no—
391C23×C13—41no—
392C23×C13C2×C22⋊C411yescharacteristic
393C23×C13C2×C22⋊C411yescharacteristic
394C23×C13C2×C22⋊C411yescharacteristic
395C23×C13C2×C22⋊C411yescharacteristic
396C23×C13C22×D411yescharacteristic
397C22×D13—21no—
398D4×C13—22no—
399D4×C13—22no—
400D4×C13—41no—
401D4×C13—41no—
402C2×C4×C13—21no—
403C2×C4×C13—21no—
404C2×C4×C13—21no—
405C2×C4×C13—21no—
406C2×C4×C13—21no—
407C2×C4×C13—21no—
408C2×C4×C13—21no—
409C2×C4×C13—21no—
410C2×C4×C13—21no—
411C2×C4×C13—21no—
412C2×C4×C13—21no—
413C2×C4×C13—21no—
414C2×C4×C13—21no—
415C2×C4×C13—21no—
416C2×C4×C13—21no—
417C2×C4×C13—21no—
418C2×C4×C13—21no—
419C2×C4×C13—21no—
420C2×C4×C13—21no—
421C2×C4×C13—21no—
422C2×C4×C13—22no—
423C2×C4×C13—22no—
424C2×C4×C13—41no—
425C2×C4×C13—41no—
426C2×C4×C13—41no—
427C2×C4×C13—41no—
428C2×C4×C13—41no—
429C2×C4×C13—48no—
430C2×C4×C13—41no—
431C2×C4×C13—41no—
432C2×C4×C13—41no—
433C2×C4×C13—41no—
434C2×C4×C13—41no—
435C2×C4×C13—41no—
436C2×C4×C13—41no—
437C2×C4×C13C2×C22⋊C411yescharacteristic
438C2×C4×C13C2×C22⋊C411yescharacteristic
439C2×C4×C13C2×C22⋊C411yescharacteristic
440C2×C4×C13C2×C22⋊C411yescharacteristic
441C2×C4×C13C2×C22⋊C411yescharacteristic
442C2×C4×C13C2×C22⋊C411yescharacteristic
443C2×C4×C13C2×C22⋊C411yescharacteristic
444C2×C4×C13C2×C22⋊C411yescharacteristic
445C2×C4×C13C23×C411yescharacteristic
446C2×C4×C13C22×D411yescharacteristic
447C2×C4×C13C2×#4111yescharacteristic
448C2×C4×C13C2×#4111yescharacteristic
449C2×C4×C13H(5,𝔽2)11yescharacteristic
450C2×C4×C132−1+411yescharacteristic
451C22⋊D13—42no—
452C22⋊D13—41no—
453C22⋊D13—41no—
454C22⋊D13—42no—
455C22⋊D13—81no—
456C22⋊D13—81no—
457C2×Dic13—21no—
458C2×Dic13—21no—
459C2×Dic13—21no—
460C2×Dic13—21no—
461C2×Dic13—21no—
462C2×Dic13—21no—
463C2×Dic13—21no—
464C2×Dic13—42no—
465C2×Dic13—42no—
466C2×Dic13—81no—
467C2×Dic13—81no—
468D52—21no—
469D52—21no—
470C4×D13—42no—
471C4×D13—41no—
472C4×D13—41no—
473C4×D13—81no—
474Dic26—21no—
475Dic26—21no—
476Dic26—42no—
477Dic26—81no—
478#1055—22no—
479#1055—41no—
480#1055—41no—
481#1055—41no—
482C22×M16—131no—
483C22×M16—131no—
484#556—131no—
485#555—131no—
486#554—131no—
487#553—131no—
488#553—131no—
489#552—131no—
490#552—131no—
491#552—261no—
492#551—261no—
493#551—261no—
494#547—131no—
495#546—261no—
496#533—131no—
497#529—261no—
498#529—261no—
499#529—261no—
500#525—131no—
501#525—131no—
502C4×#41—131no—
503C4×#41—261no—
504C2×C4×D4C2×D1311yescharacteristic
505C2×#117—131no—
506C2×#117—131no—
507C2×#117C2×D1311yescharacteristic
508C22×C42C2×D1311yescharacteristic
509#436—261no—
510#435—261no—
511#435—261no—
512C8×D4—261no—
513#423—131no—
514C2×#104—131no—
515C2×#104—131no—
516C2×#104—131no—
517C2×#104—131no—
518#407—131no—
519#407—131no—
520C4×M16—131no—
521#388—21no—
522#387—21no—
523#386—21no—
524#385—21no—
525C4×C4⋊C4C2×D1311yescharacteristic
526C4×C22⋊C4C2×D1311yescharacteristic
527C4×C22⋊C4C2×D1311yescharacteristic
528#376C2×D1311yescharacteristic
529#339—131no—
530#339—131no—
531#339—131no—
532#339—131no—
533#339—131no—
534#339—131no—
535#339—131no—
536#339—131no—
537#339—131no—
538#339—131no—
539#339—131no—
540#339—131no—
541C22×C13—21no—
542C22×C13—21no—
543C22×C13—21no—
544C22×C13—21no—
545C22×C13—21no—
546C22×C13—21no—
547C22×C13—21no—
548C22×C13—21no—
549C22×C13—21no—
550C22×C13—21no—
551C22×C13—21no—
552C22×C13—21no—
553C22×C13—21no—
554C22×C13—42no—
555C22×C13—42no—
556C22×C13—81no—
557C22×C13—81no—
558C22×C13#42112yes—
559C22×C13C22×C22⋊C411yescharacteristic
560C22×C13#54611yescharacteristic
561C22×C13#54711yescharacteristic
562C2×D13—41no—
563C2×D13—41no—
564C2×D13—41no—
565C4×C13—21no—
566C4×C13—21no—
567C4×C13—21no—
568C4×C13—21no—
569C4×C13—21no—
570C4×C13—21no—
571C4×C13—21no—
572C4×C13—21no—
573C4×C13—42no—
574C4×C13—42no—
575C4×C13—81no—
576C4×C13—81no—
577C4×C13C4×#4111yescharacteristic
578C4×C13#52011yescharacteristic
579C4×C13#54611yescharacteristic
580C4×C13#54711yescharacteristic
581Dic13—41no—
582Dic13—41no—
583Dic13—41no—
584Dic13—41no—
585Dic13—41no—
586Dic13—41no—
587Dic13—41no—
588C2×#41—131no—
589C2×#41—261no—
590C22×D4C22⋊D1311yescharacteristic
591C23×C4—21no—
592C23×C4C22×D1311yescharacteristic
593C23×C4C22×D1311yescharacteristic
594C2×M16—131no—
595C2×M16—131no—
596C2×M16—131no—
597C2×M16—131no—
598C2×M16—261no—
599C2×M16—261no—
600C2×M16—262no—
601C2×M16—262no—
602C2×M16—521no—
603C2×M16—521no—
604C22×C8—261no—
605C22×C8—261no—
606C4⋊Q8—131no—
607C4⋊Q8—131no—
608#126—261no—
609#126—261no—
610#126—261no—
611#126—261no—
612#126—261no—
613#126—261no—
614#125—131no—
615#125—131no—
616#125—261no—
617#125—261no—
618#125—261no—
619#124—261no—
620#124—261no—
621#124—261no—
622#123—261no—
623#123—261no—
624#123—261no—
625#123—261no—
626#123—261no—
627#123—261no—
628#123—261no—
629#123—261no—
630C22⋊Q8—131no—
631C22⋊Q8—131no—
632C22⋊Q8—131no—
633C22⋊Q8—131no—
634C22⋊Q8—261no—
635C22⋊Q8—261no—
636C22⋊Q8—261no—
637C22⋊Q8—261no—
638C22⋊Q8—261no—
639#121—131no—
640#121—131no—
641#121—131no—
642#121—131no—
643#121—261no—
644#121—261no—
645#121—261no—
646#120—261no—
647#120—261no—
648C4×Q8—131no—
649C4×Q8—131no—
650C4×Q8—261no—
651C4×Q8—261no—
652C4×Q8—261no—
653C4×D4—131no—
654C4×D4—131no—
655C4×D4—261no—
656C4×D4—261no—
657C4×D4—261no—
658C4×D4—261no—
659C4×D4—261no—
660C4×D4—261no—
661C4×D4—261no—
662C4×D4—261no—
663C4×D4—261no—
664C4×D4C4×D1311yescharacteristic
665C4×D4C4×D1311yescharacteristic
666C4×D4C4×D1311yescharacteristic
667C4×D4C4×D1311yescharacteristic
668C4×D4D5211yescharacteristic
669C4×D4D5211yescharacteristic
670C4×D4D5211yescharacteristic
671C4×D4D5211yescharacteristic
672#117—22no—
673#117—41no—
674#117—131no—
675#117—131no—
676#117—131no—
677#117—131no—
678#117—131no—
679#117—131no—
680#117—131no—
681#117—261no—
682#117—261no—
683#117—261no—
684#117—261no—
685#117—261no—
686#117—261no—
687#117—261no—
688#117—261no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—131no—
692C2×C4⋊C4—131no—
693C2×C4⋊C4—131no—
694C2×C4⋊C4—131no—
695C2×C4⋊C4C22⋊D1311yescharacteristic
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—261no—
700C2×C22⋊C4—261no—
701C2×C22⋊C4C22⋊D1311yescharacteristic
702C2×C22⋊C4C22⋊D1311yescharacteristic
703C2×C42—22no—
704C2×C42—21no—
705C2×C42—41no—
706C2×C42—261no—
707C2×C42—261no—
708C2×C42—261no—
709C2×C42C22×D1311yescharacteristic
710C2×C42C22×D1311yescharacteristic
711C2×C42C22×D1311yescharacteristic
712C2×C42C22×D1311yescharacteristic
713C2×C42C22×D1311yescharacteristic
714C4⋊C8—261no—
715C4⋊C8—261no—
716#104—262no—
717#104—262no—
718#104—521no—
719#104—521no—
720C22⋊C8—261no—
721C22⋊C8—261no—
722C22⋊C8—261no—
723C22⋊C8—261no—
724#97—261no—
725C4×C8—261no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731C2×C13—21no—
732C2×C13—21no—
733C2×C13—22no—
734C2×C13—41no—
735C2×C13—41no—
736C2×C13—41no—
737C2×C13#233911yescharacteristic
738C2×C13C2×#42111yescharacteristic
739C2×C13#290111yescharacteristic
740D13—81no—
741C24C2×C22⋊D1311yescharacteristic
742C24C2×C22⋊D1311yescharacteristic
743#41—261no—
744#41—261no—
745#41—261no—
746#41—261no—
747#41—524no—
748C2×Q8—131no—
749C2×Q8—261no—
750C2×Q8—261no—
751C2×D4—42no—
752C2×D4—131no—
753C2×D4—261no—
754C2×D4—261no—
755C2×D4—261no—
756C2×D4—261no—
757C2×D4—261no—
758C2×D4#610311yescharacteristic
759C2×D4#610311yescharacteristic
760C2×D4#610311yescharacteristic
761C2×D4#610311yescharacteristic
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—261no—
778C22×C4—261no—
779C22×C4—261no—
780C22×C4—261no—
781C22×C4—261no—
782C22×C4—261no—
783C22×C4—261no—
784C22×C4C2×C4×D1311yescharacteristic
785C22×C4C2×C4×D1311yescharacteristic
786C22×C4C2×C4×D1311yescharacteristic
787C22×C4C2×C4×D1311yescharacteristic
788C22×C4C2×D5211yescharacteristic
789C22×C4C2×D5211yescharacteristic
790C22×C4C2×D5211yescharacteristic
791C22×C4C2×D5211yescharacteristic
792C22×C4C2×C22⋊D1311yescharacteristic
793C22×C4C2×C22⋊D1311yescharacteristic
794C22×C4C2×C22⋊D1311yescharacteristic
795C22×C4C2×C22⋊D1311yescharacteristic
796C22×C4C23×D1311yescharacteristic
797M16—132no—
798M16—261no—
799M16—261no—
800M16—261no—
801M16—261no—
802M16—261no—
803M16—261no—
804M16—261no—
805M16—522no—
806M16—522no—
807C2×C8—261no—
808C2×C8—261no—
809C2×C8—261no—
810C2×C8—261no—
811C2×C8—522no—
812C2×C8—522no—
813C4⋊C4—42no—
814C4⋊C4—42no—
815C4⋊C4—131no—
816C4⋊C4—131no—
817C4⋊C4—131no—
818C4⋊C4—131no—
819C4⋊C4—131no—
820C4⋊C4—131no—
821C4⋊C4—261no—
822C4⋊C4—261no—
823C4⋊C4—261no—
824C4⋊C4—261no—
825C4⋊C4—261no—
826C4⋊C4—261no—
827C4⋊C4—261no—
828C4⋊C4—261no—
829C4⋊C4—261no—
830C4⋊C4—261no—
831C4⋊C4—261no—
832C4⋊C4—261no—
833C4⋊C4—261no—
834C4⋊C4—261no—
835C4⋊C4—261no—
836C4⋊C4—261no—
837C4⋊C4#610311yescharacteristic
838C4⋊C4#610311yescharacteristic
839C4⋊C4#610311yescharacteristic
840C4⋊C4#610311yescharacteristic
841C22⋊C4—42no—
842C22⋊C4—42no—
843C22⋊C4—42no—
844C22⋊C4—261no—
845C22⋊C4—261no—
846C22⋊C4—261no—
847C22⋊C4—261no—
848C22⋊C4—261no—
849C22⋊C4—261no—
850C22⋊C4—261no—
851C22⋊C4—261no—
852C22⋊C4—261no—
853C22⋊C4—261no—
854C22⋊C4—261no—
855C22⋊C4—261no—
856C22⋊C4—261no—
857C22⋊C4—261no—
858C22⋊C4—261no—
859C22⋊C4—261no—
860C22⋊C4—261no—
861C22⋊C4#610311yescharacteristic
862C22⋊C4#610311yescharacteristic
863C22⋊C4#610311yescharacteristic
864C22⋊C4#610311yescharacteristic
865C22⋊C4#610311yescharacteristic
866C22⋊C4#610311yescharacteristic
867C22⋊C4#610311yescharacteristic
868C22⋊C4#610311yescharacteristic
869C42—21no—
870C42—21no—
871C42—21no—
872C42—21no—
873C42—21no—
874C42—21no—
875C42—21no—
876C42—42no—
877C42—261no—
878C42—261no—
879C42—261no—
880C42—261no—
881C42—261no—
882C42—261no—
883C42—261no—
884C42—261no—
885C42—261no—
886C42C2×C4×D1311yescharacteristic
887C42C2×C4×D1311yescharacteristic
888C42C2×D5211yescharacteristic
889C42C2×D5211yescharacteristic
890C42#612912yescomplemented
891C13#2250611yescharacteristic, complemented, Sylow
892C23—22no—
893C23—21no—
894C23—21no—
895C23—21no—
896C23—21no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—261no—
901C23C2×#610311yescharacteristic
902C23C2×#610311yescharacteristic
903C23C2×#610311yescharacteristic
904C23C2×#610311yescharacteristic
905C23C22×C22⋊D1311yescharacteristic
906Q8—261no—
907Q8—261no—
908Q8—522no—
909Q8—1041no—
910D4—22no—
911D4—22no—
912D4—41no—
913D4—41no—
914D4—261no—
915D4—261no—
916D4—522no—
917D4—522no—
918D4—521no—
919D4—521no—
920D4—1041no—
921D4—1041no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—48no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—261no—
958C2×C4—261no—
959C2×C4—261no—
960C2×C4—261no—
961C2×C4—261no—
962C2×C4—261no—
963C2×C4—261no—
964C2×C4—522no—
965C2×C4—522no—
966C2×C4—522no—
967C2×C4—521no—
968C2×C4—521no—
969C2×C4—1041no—
970C2×C4—1041no—
971C2×C4—1041no—
972C2×C4C2×#610311yescharacteristic
973C2×C4C2×#610311yescharacteristic
974C2×C4C2×#610311yescharacteristic
975C2×C4C2×#610311yescharacteristic
976C2×C4C2×#610311yescharacteristic
977C2×C4C2×#610311yescharacteristic
978C2×C4C2×#610311yescharacteristic
979C2×C4C2×#610311yescharacteristic
980C2×C4C22×C4×D1311yescharacteristic
981C2×C4C22×D5211yescharacteristic
982C2×C4C2×#612911yescharacteristic
983C2×C4#8825111yescharacteristic
984C2×C4#41×D1311yescharacteristic
985C2×C4#8825711yescharacteristic
986C8—262no—
987C8—521no—
988C8—521no—
989C8—521no—
990C22—21no—
991C22—21no—
992C22—21no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—42no—
1004C22—42no—
1005C22—81no—
1006C22—81no—
1007C22—521no—
1008C22—521no—
1009C22—521no—
1010C22#1171866612yes—
1011C22C22×#610311yescharacteristic
1012C22#1171951111yescharacteristic
1013C22#1171952911yescharacteristic
1014C4—21no—
1015C4—21no—
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—42no—
1023C4—42no—
1024C4—81no—
1025C4—81no—
1026C4—521no—
1027C4—521no—
1028C4—521no—
1029C4—521no—
1030C4—521no—
1031C4—521no—
1032C4—521no—
1033C4C4×#612911yescharacteristic
1034C4#1171925111yescharacteristic
1035C4#1171925911yescharacteristic
1036C4#1171926011yescharacteristic
1037C2—21no—
1038C2—21no—
1039C2—22no—
1040C2—41no—
1041C2—41no—
1042C2—41no—
1043C2—1041no—
1044C2#1311766111yescharacteristic
1045C2C2×#1171866611yescharacteristic
1046C2#1312338411yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2290C2
socleC22×C13C22×C22⋊C4
prime radical#13128394C2
cosocleC22×C4×C13C24
hypercenter#2290D13
hypocenterC13#22506
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ #2290

Complements

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

NH ≅ G/Ntype
2. D4×#6099C2semidirect
3. #13115817C2semidirect
4. #13115779C2semidirect
5. #13115284C2semidirect
6. #13115279C2semidirect
7. #13115136C2semidirect
8. #13115136C2semidirect
9. #13114936C2semidirect
10. #13114936C2semidirect
11. #13114857C2semidirect
12. #13114647C2semidirect
13. #13114546C2semidirect
14. C2×#11718115C2semidirect
15. C13×#2290C2semidirect
26. #11719270C4semidirect
27. #11719270C4semidirect
28. #11719268C4semidirect
30. #11719260C4semidirect
31. #11719248C4semidirect
32. #11719247C4semidirect
33. #11719246C4semidirect
34. #11719246C4semidirect
120. #88184C2×C4semidirect
121. #88184C2×C4semidirect
136. #88180C2×C4semidirect
137. #88180C2×C4semidirect
143. C2×C4⋊Dic13C2×C4semidirect
144. C2×C4⋊Dic13C2×C4semidirect
149. #88178C2×C4semidirect
150. #88178C2×C4semidirect
189. C4×D52C2×C4semidirect
190. C4×D52C2×C4semidirect
193. #88124C2×C4semidirect
194. #88124C2×C4semidirect
195. #88123C2×C4semidirect
196. #88123C2×C4semidirect
199. C4×Dic26C2×C4semidirect
200. C4×Dic26C2×C4semidirect
304. C42×C13#41semidirect
362. #6099#41semidirect
371. #2290D13semidirect
890. C42#6129semidirect
891. C13#22506semidirect

Maximal subgroups

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

subgroupindex
#131283942
D4×#60992
#131158172
#131157792
#131152842
#131152792
#131151362
#131149362
#131148572
#131146472
#131145462
C2×#117181152
C13×#22902
#2250613