Finite Group Databasebeta

← #15883656

Subgroups — #15883656

Order 3328.

1058 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124054C211yesmaximal, characteristic
2C2×#11718484C211yesmaximal, characteristic, complemented
3#13123561C211yesmaximal, characteristic, complemented
4#13123285C211yesmaximal, characteristic, complemented
5#13115726C211yesmaximal, characteristic, complemented
6#13115544C211yesmaximal, characteristic, complemented
7#13115487C211yesmaximal, characteristic, complemented
8#13115279C211yesmaximal, characteristic, complemented
9#13115161C211yesmaximal, characteristic, complemented
10#13115160C211yesmaximal, characteristic, complemented
11#13115109C211yesmaximal, characteristic, complemented
12#13115041C211yesmaximal, characteristic, complemented
13#13114681C211yesmaximal, characteristic, complemented
14#13114598C211yesmaximal, characteristic, complemented
15C22×C13×#104C211yesmaximal, characteristic, complemented
16C22×C13×#41C2211yescharacteristic
17C22×C13×M16C2211yescharacteristic
18C22×C42×C13C2211yescharacteristic
19C2×#88204C2211yescharacteristic
20C2×#88204C2211yescharacteristic
21C2×#88202C2211yescharacteristic
22C2×#88202C2211yescharacteristic
23#11719496C2211yescharacteristic
24C2×#88161C2211yescharacteristic, complemented
25C2×C13×#104—24no—
26C2×C13×#104C2211yescharacteristic
27C2×C13×#104C2211yescharacteristic
28C2×C13×#104C2211yescharacteristic
29C2×C13×#104C2211yescharacteristic
30#11718900C411yescharacteristic, complemented
31#11718900C411yescharacteristic, complemented
32#11718899C411yescharacteristic, complemented
33#11718899C411yescharacteristic, complemented
34#11718895—21no—
35#11718895—21no—
36#11718895C2211yescharacteristic
37#11718895C2211yescharacteristic
38#11718894C2211yescharacteristic
39#11718894C2211yescharacteristic
40#11718889C411yescharacteristic, complemented
41#11718888C411yescharacteristic, complemented
42#11718879C411yescharacteristic, complemented
43#11718878C411yescharacteristic, complemented
44#11718868—21no—
45#11718868C2211yescharacteristic
46C2×C22⋊#1055—21no—
47C2×C22⋊#1055C2211yescharacteristic
48C2×C22⋊#1055C2211yescharacteristic
49#11718790C2211yescharacteristic, complemented
50#11718789—21no—
51#11718788—21no—
52C2×#88062C2211yescharacteristic, complemented
53C2×#88062C2211yescharacteristic, complemented
54#11718783C2211yescharacteristic, complemented
55#11718780C2211yescharacteristic, complemented
56#11718772—21no—
57C8×C22⋊D13—21no—
58C2×#88045C2211yescharacteristic, complemented
59C2×#88045C2211yescharacteristic, complemented
60C2×#88043C2211yescharacteristic, complemented
61C2×#88043C2211yescharacteristic, complemented
62#11718484—24no—
63#11718150C2211yescharacteristic, complemented
64#11718150C2211yescharacteristic, complemented
65#11718116C2211yescharacteristic, complemented
66#11718116C2211yescharacteristic, complemented
67#11718115C2211yescharacteristic, complemented
68#11718115C2211yescharacteristic, complemented
69C2×C13×#41—21no—
70C2×C13×#41—21no—
71C2×C13×#41—22no—
72C2×C13×#41—22no—
73C2×C13×#41—41no—
74C2×C13×#41—41no—
75C2×C13×#41C2×C411yescharacteristic
76C2×C13×#41C2×C411yescharacteristic
77C2×C13×#41C2311yescharacteristic
78C2×C13×#41C2311yescharacteristic
79C22×Q8×C13C2×C411yescharacteristic
80C22×D4×C13—21no—
81C22×D4×C13C2×C411yescharacteristic
82C23×C4×C13—21no—
83C23×C4×C13—21no—
84C23×C4×C13C2311yescharacteristic
85C2×#6127C2311yescharacteristic
86C2×C13×M16—21no—
87C2×C13×M16—22no—
88C2×C13×M16—41no—
89C2×C13×M16C2311yescharacteristic
90C2×C13×M16C2311yescharacteristic
91C22×C8×C13—21no—
92C2×C42×C13—22no—
93C2×C42×C13—21no—
94C2×C42×C13—41no—
95C2×C42×C13C2311yescharacteristic
96C2×C42×C13C2311yescharacteristic
97#88207—21no—
98#88204—22no—
99#88204—22no—
100#88204—41no—
101#88204—41no—
102#88202—22no—
103#88202—22no—
104#88202—41no—
105#88202—41no—
106C2×#6107C2×C411yescharacteristic, complemented
107C2×#6107C2×C411yescharacteristic, complemented
108C2×#6106C2×C411yescharacteristic, complemented
109C2×#6106C2×C411yescharacteristic, complemented
110C2×#6105C2×C411yescharacteristic, complemented
111C2×#6105C2×C411yescharacteristic, complemented
112C2×#6104C2×C411yescharacteristic, complemented
113C2×#6104C2×C411yescharacteristic, complemented
114#88184C2×C411yescharacteristic
115#88184C2×C411yescharacteristic
116#88183—21no—
117C4×C22⋊D13—21no—
118C4×C22⋊D13—21no—
119#88180C2311yescharacteristic
120#88178C2×C411yescharacteristic
121#88178C2×C411yescharacteristic
122C2×#6099—21no—
123C2×#6099—21no—
124C2×#6099C2311yescharacteristic
125C2×#6099C2311yescharacteristic
126C22×#1055—21no—
127C22×#1055—21no—
128C22×#1055C2311yescharacteristic
129C22×#1055C2311yescharacteristic
130C22×#1055C2311yescharacteristic
131C22×#1055C2311yescharacteristic
132#88161—22no—
133#88161—41no—
134C2×#6094—21no—
135C2×C8×D13—21no—
136C13×#104—22no—
137C13×#104—22no—
138C13×#104—22no—
139C13×#104D414yescomplemented
140#88075C2×C411yescharacteristic, complemented
141#88075C2×C411yescharacteristic, complemented
142#88075C2×C411yescharacteristic, complemented
143#88075C2×C411yescharacteristic, complemented
144#88072C2×C411yescharacteristic, complemented
145#88072C2×C411yescharacteristic, complemented
146#88072C2×C411yescharacteristic, complemented
147#88072C2×C411yescharacteristic, complemented
148C22⋊#1055—21no—
149C22⋊#1055—21no—
150C22⋊#1055—21no—
151C22⋊#1055—21no—
152C22⋊#1055—21no—
153C22⋊#1055—21no—
154C22⋊#1055C2×C411yescharacteristic
155C22⋊#1055C2×C411yescharacteristic
156C22⋊#1055C2×C411yescharacteristic
157C22⋊#1055C2×C411yescharacteristic
158C22⋊#1055D411yescharacteristic
159C22⋊#1055D411yescharacteristic
160C22⋊#1055D411yescharacteristic
161C22⋊#1055D411yescharacteristic
162#88062—22no—
163#88062—41no—
164#88060—21no—
165#88060—21no—
166#88055—21no—
167#88054—21no—
168#88054—21no—
169C8×Dic13—21no—
170#88045—22no—
171#88045—41no—
172#88043—22no—
173#88043—41no—
174#22886—131nomaximal, Sylow
175C24×C13—21no—
176C24×C13#4111yescharacteristic
177C13×#41—21no—
178C13×#41—21no—
179C13×#41—22no—
180C13×#41—22no—
181C13×#41—21no—
182C13×#41—21no—
183C13×#41—21no—
184C13×#41—21no—
185C13×#41—42no—
186C13×#41—42no—
187C13×#41—41no—
188C13×#41—41no—
189C13×#41—42no—
190C13×#41—42no—
191C13×#41C2×D412yes—
192C13×#41#4112yes—
193C2×Q8×C13—21no—
194C2×Q8×C13—22no—
195C2×Q8×C13—41no—
196C2×Q8×C13C22×C411yescharacteristic
197C2×Q8×C13C22×C411yescharacteristic
198C2×D4×C13—21no—
199C2×D4×C13—22no—
200C2×D4×C13—21no—
201C2×D4×C13—21no—
202C2×D4×C13—21no—
203C2×D4×C13—21no—
204C2×D4×C13—41no—
205C2×D4×C13—42no—
206C2×D4×C13—42no—
207C2×D4×C13C22×C411yescharacteristic
208C2×D4×C13C22×C411yescharacteristic
209C22×C4×C13—21no—
210C22×C4×C13—21no—
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13—21no—
214C22×C4×C13—21no—
215C22×C4×C13—21no—
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—21no—
219C22×C4×C13—21no—
220C22×C4×C13—42no—
221C22×C4×C13—42no—
222C22×C4×C13—42no—
223C22×C4×C13—42no—
224C22×C4×C13—42no—
225C22×C4×C13C22×C411yescharacteristic
226C22×C4×C13C22×C411yescharacteristic
227C22×C4×C13C2×D411yescharacteristic
228C22×C4×C13C2×D411yescharacteristic
229C22×C4×C13#4111yescharacteristic
230C22×C4×C13C2411yescharacteristic
231C2×C22⋊D13—21no—
232C2×C22⋊D13—21no—
233C2×C22⋊D13—21no—
234#6127—21no—
235#6127—21no—
236#6127—21no—
237#6127—21no—
238C2×D52C22×C411yescharacteristic
239C2×C4×D13—21no—
240C2×Dic26C22×C411yescharacteristic
241C13×M16—21no—
242C13×M16—21no—
243C13×M16—21no—
244C13×M16—42no—
245C13×M16C2×D412yes—
246C2×C8×C13—21no—
247C2×C8×C13—21no—
248C2×C8×C13—42no—
249C42×C13—21no—
250C42×C13—21no—
251C42×C13—21no—
252C42×C13—42no—
253C42×C13C2×D412yes—
254C22⋊Dic13—21no—
255C22⋊Dic13—21no—
256C22⋊Dic13—21no—
257#6107—22no—
258#6107—41no—
259#6106—22no—
260#6106—41no—
261#6105—22no—
262#6105—41no—
263#6104—22no—
264#6104—41no—
265#6103—21no—
266#6103—21no—
267C4⋊Dic13C22×C411yescharacteristic
268C4⋊Dic13C22×C411yescharacteristic
269#6101—21no—
270#6101—21no—
271C4×Dic13—21no—
272#6099—21no—
273#6099—21no—
274#6099—21no—
275#6099—21no—
276#6099—42no—
277#6099—42no—
278C2×#1055—21no—
279C2×#1055—21no—
280C2×#1055—21no—
281C2×#1055—21no—
282C2×#1055—21no—
283C2×#1055—21no—
284C2×#1055—21no—
285C2×#1055—21no—
286C2×#1055—21no—
287C2×#1055—21no—
288C2×#1055—42no—
289C2×#1055—42no—
290C2×#1055C22×C411yescharacteristic
291C2×#1055C22×C411yescharacteristic
292C2×#1055C22×C411yescharacteristic
293C2×#1055C22×C411yescharacteristic
294C2×#1055C2×D411yescharacteristic
295C2×#1055C2×D411yescharacteristic
296C2×#1055C2×D411yescharacteristic
297C2×#1055C2×D411yescharacteristic
298#6094—42no—
299C8×D13—42no—
300#3002—131no—
301C2×#444—131no—
302#2933—131no—
303C22×#104D1311yescharacteristic, complemented
304#2880—131no—
305#1975—131no—
306#1938—131no—
307#1929—131no—
308#1896—131no—
309#1876—131no—
310#1876—131no—
311#1866—131no—
312#1855—131no—
313#1765—131no—
314#1749—131no—
315C23×C13—21no—
316C23×C13—21no—
317C23×C13—21no—
318C23×C13—22no—
319C23×C13—21no—
320C23×C13—41no—
321C23×C13—42no—
322C23×C13—42no—
323C23×C13—81no—
324C23×C13C4×D411yescharacteristic
325C23×C13C4×D411yescharacteristic
326C23×C13C2×#4111yescharacteristic
327C22×D13—21no—
328Q8×C13—21no—
329Q8×C13—21no—
330Q8×C13—21no—
331Q8×C13—42no—
332Q8×C13C4×D412yes—
333D4×C13—22no—
334D4×C13—22no—
335D4×C13—21no—
336D4×C13—21no—
337D4×C13—21no—
338D4×C13—42no—
339D4×C13—42no—
340D4×C13—42no—
341D4×C13—41no—
342D4×C13—41no—
343D4×C13C4×D412yes—
344C2×C4×C13—21no—
345C2×C4×C13—21no—
346C2×C4×C13—21no—
347C2×C4×C13—21no—
348C2×C4×C13—21no—
349C2×C4×C13—21no—
350C2×C4×C13—21no—
351C2×C4×C13—22no—
352C2×C4×C13—21no—
353C2×C4×C13—21no—
354C2×C4×C13—22no—
355C2×C4×C13—21no—
356C2×C4×C13—21no—
357C2×C4×C13—22no—
358C2×C4×C13—21no—
359C2×C4×C13—22no—
360C2×C4×C13—42no—
361C2×C4×C13—42no—
362C2×C4×C13—42no—
363C2×C4×C13—41no—
364C2×C4×C13—41no—
365C2×C4×C13—41no—
366C2×C4×C13—48no—
367C2×C4×C13—41no—
368C2×C4×C13—41no—
369C2×C4×C13—41no—
370C2×C4×C13C4×D411yescharacteristic
371C2×C4×C13C4×D411yescharacteristic
372C2×C4×C13C23×C411yescharacteristic
373C2×C4×C13C22×D411yescharacteristic
374C2×C4×C13C22×D411yescharacteristic
375C2×C4×C13C2×#4111yescharacteristic
376C2×C4×C13H(5,𝔽2)11yescharacteristic
377C2×C4×C13H(5,𝔽2)11yescharacteristic
378C22⋊D13—41no—
379C22⋊D13—41no—
380C22⋊D13—42no—
381C22⋊D13—81no—
382C2×Dic13—21no—
383C2×Dic13—21no—
384C2×Dic13—21no—
385D52—21no—
386D52—21no—
387C4×D13—41no—
388C4×D13—41no—
389Dic26—21no—
390Dic26—21no—
391C8×C13—22no—
392C8×C13—41no—
393#1055—21no—
394#1055—21no—
395#1055—21no—
396#1055—21no—
397#1055—21no—
398#1055—21no—
399#1055—21no—
400#1055—21no—
401#1055—41no—
402#1055—41no—
403C22×#41C2×D1311yescharacteristic
404C2×#135—131no—
405C2×#135—131no—
406C2×#131—131no—
407C2×#131—131no—
408C2×#131—131no—
409C22×M16C2×D1311yescharacteristic
410#525—131no—
411C22×C42C2×D1311yescharacteristic
412#452—131no—
413#452—131no—
414#451—131no—
415#450—131no—
416#449—131no—
417#449—131no—
418#448—131no—
419#447—131no—
420#444—264no—
421#436—261no—
422#435—261no—
423#435—261no—
424C8×D4—261no—
425C2×#108—131no—
426C2×#108—131no—
427#424—131no—
428C2×#104—24no—
429C2×#104—131no—
430C2×#104—131no—
431C2×#104C2×D1311yescharacteristic
432C2×#104C2×D1311yescharacteristic
433C2×#104C2×D1311yescharacteristic
434C2×#104C2×D1311yescharacteristic
435#416—131no—
436#416—131no—
437#408—131no—
438#408—131no—
439#408—131no—
440#408—261no—
441#408—261no—
442#407—131no—
443#407—261no—
444C2×C22⋊C8—131no—
445C2×C22⋊C8—131no—
446C2×C22⋊C8—261no—
447#405—131no—
448C2×#97—131no—
449C2×#97—131no—
450#341—131no—
451#341—131no—
452#339—131no—
453#339—131no—
454#336—131no—
455#336—131no—
456C22×C13—21no—
457C22×C13—21no—
458C22×C13—21no—
459C22×C13—21no—
460C22×C13—21no—
461C22×C13—22no—
462C22×C13—21no—
463C22×C13—21no—
464C22×C13—42no—
465C22×C13—42no—
466C22×C13—41no—
467C22×C13—41no—
468C22×C13—41no—
469C22×C13—41no—
470C22×C13—41no—
471C22×C13—84no—
472C22×C13#44412yescomplemented
473C22×C13C2×C4×D411yescharacteristic
474C22×C13#54611yescharacteristic
475C22×C13#55111yescharacteristic
476C2×D13—41no—
477C2×D13—41no—
478C2×D13—41no—
479C4×C13—21no—
480C4×C13—21no—
481C4×C13—22no—
482C4×C13—42no—
483C4×C13—42no—
484C4×C13—41no—
485C4×C13C2×C4×D411yescharacteristic
486C4×C13#51811yescharacteristic
487C4×C13D4211yescharacteristic
488C4×C13#54611yescharacteristic
489Dic13—41no—
490Dic13—41no—
491Dic13—41no—
492C2×#41—21no—
493C2×#41—21no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—131no—
499C2×#41C4×D1311yescharacteristic
500C2×#41C4×D1311yescharacteristic
501C2×#41C22×D1311yescharacteristic
502C2×#41C22×D1311yescharacteristic
503C22×Q8C4×D1311yescharacteristic
504C22×D4—21no—
505C22×D4C4×D1311yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4C22×D1311yescharacteristic
509#135—262no—
510#135—262no—
511#135—521no—
512#135—521no—
513C2×Q16—131no—
514C2×Q16—131no—
515C2×SD16—131no—
516C2×SD16—131no—
517C2×SD16—131no—
518C2×SD16—131no—
519C2×D8—131no—
520C2×D8—131no—
521#131—262no—
522#131—262no—
523#131—262no—
524#131—521no—
525#131—521no—
526#131—521no—
527C2×M16—21no—
528C2×M16—22no—
529C2×M16—41no—
530C2×M16—131no—
531C2×M16—131no—
532C2×M16—261no—
533C2×M16—261no—
534C2×M16—261no—
535C2×M16C22×D1311yescharacteristic
536C2×M16C22×D1311yescharacteristic
537C22×C8—21no—
538C22×C8—131no—
539C22×C8—131no—
540C22×C8—131no—
541C22×C8—131no—
542C22×C8—261no—
543C22×C8—261no—
544C22×C8—261no—
545#123—261no—
546C22⋊Q8—131no—
547C22⋊Q8—131no—
548#121—131no—
549#121—131no—
550#120—261no—
551C4×D4—261no—
552C4×D4—261no—
553#117—131no—
554C2×C42—22no—
555C2×C42—21no—
556C2×C42—41no—
557C2×C42C22×D1311yescharacteristic
558C2×C42C22×D1311yescharacteristic
559#108—262no—
560#108—521no—
561C4⋊C8—261no—
562C4⋊C8—261no—
563#104—22no—
564#104—22no—
565#104—22no—
566#104—262no—
567#104—521no—
568#104C22⋊D1314yescomplemented
569#103—131no—
570#103—131no—
571#103—131no—
572#103—131no—
573#102—131no—
574#102—131no—
575#102—131no—
576#102—131no—
577C22⋊C8—131no—
578C22⋊C8—131no—
579C22⋊C8—131no—
580C22⋊C8—131no—
581C22⋊C8—131no—
582C22⋊C8—131no—
583C22⋊C8—131no—
584C22⋊C8—131no—
585C22⋊C8—261no—
586C22⋊C8—261no—
587C22⋊C8—261no—
588C22⋊C8—261no—
589C22⋊C8—261no—
590C22⋊C8—261no—
591C22⋊C8—261no—
592C22⋊C8—261no—
593#97—261no—
594#97—262no—
595#97—521no—
596C4×C8—261no—
597C2×C13—21no—
598C2×C13—22no—
599C2×C13—21no—
600C2×C13—41no—
601C2×C13—42no—
602C2×C13—81no—
603C2×C13#235811yescharacteristic
604C2×C13C2×#44411yescharacteristic
605C2×C13#295611yescharacteristic
606D13—81no—
607C24—21no—
608C24#612911yescharacteristic
609#41—21no—
610#41—21no—
611#41—22no—
612#41—22no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—42no—
618#41—42no—
619#41—41no—
620#41—41no—
621#41—42no—
622#41—42no—
623#41—261no—
624#41—261no—
625#41—261no—
626#41—261no—
627#41#612712yes—
628#41C2×C22⋊D1312yes—
629C2×Q8—21no—
630C2×Q8—22no—
631C2×Q8—41no—
632C2×Q8—131no—
633C2×Q8C2×C4×D1311yescharacteristic
634C2×Q8C2×C4×D1311yescharacteristic
635C2×D4—21no—
636C2×D4—22no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—41no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—131no—
645C2×D4—261no—
646C2×D4—261no—
647C2×D4—261no—
648C2×D4C2×C4×D1311yescharacteristic
649C2×D4C2×C4×D1311yescharacteristic
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—261no—
667C22×C4C2×C4×D1311yescharacteristic
668C22×C4C2×C4×D1311yescharacteristic
669C22×C4D4×D1311yescharacteristic
670C22×C4D4×D1311yescharacteristic
671C22×C4#612911yescharacteristic
672C22×C4C23×D1311yescharacteristic
673Q16—262no—
674Q16—521no—
675SD16—262no—
676SD16—262no—
677SD16—521no—
678SD16—521no—
679D8—262no—
680D8—521no—
681M16—21no—
682M16—21no—
683M16—21no—
684M16—42no—
685M16—261no—
686M16—261no—
687M16—261no—
688M16—261no—
689M16—522no—
690M16—522no—
691M16—522no—
692M16C2×C22⋊D1312yes—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—42no—
696C2×C8—131no—
697C2×C8—131no—
698C2×C8—131no—
699C2×C8—131no—
700C2×C8—131no—
701C2×C8—131no—
702C2×C8—131no—
703C2×C8—131no—
704C2×C8—261no—
705C2×C8—261no—
706C2×C8—261no—
707C2×C8—261no—
708C2×C8—261no—
709C2×C8—261no—
710C2×C8—261no—
711C2×C8—261no—
712C2×C8—261no—
713C2×C8—261no—
714C2×C8—522no—
715C2×C8—522no—
716C2×C8—522no—
717C4⋊C4—131no—
718C4⋊C4—131no—
719C4⋊C4—261no—
720C4⋊C4—261no—
721C22⋊C4—261no—
722C22⋊C4—261no—
723C22⋊C4—261no—
724C22⋊C4—261no—
725C22⋊C4—261no—
726C42—21no—
727C42—21no—
728C42—21no—
729C42—42no—
730C42—261no—
731C42C2×C22⋊D1312yes—
732C13#2288611yescharacteristic, complemented, Sylow
733C23—21no—
734C23—21no—
735C23—22no—
736C23—21no—
737C23—21no—
738C23—41no—
739C23—42no—
740C23—42no—
741C23—81no—
742C23—261no—
743C23#8813511yescharacteristic
744C23#8813511yescharacteristic
745C23C2×#612911yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—42no—
750Q8—261no—
751Q8—261no—
752Q8C4×C22⋊D1312yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—41no—
762D4—41no—
763D4—261no—
764D4—261no—
765D4—521no—
766D4—522no—
767D4—521no—
768D4—1041no—
769D4C4×C22⋊D1312yes—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—22no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—48no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—261no—
797C2×C4—261no—
798C2×C4—261no—
799C2×C4—521no—
800C2×C4—521no—
801C2×C4#8813511yescharacteristic
802C2×C4#8813511yescharacteristic
803C2×C4C22×C4×D1311yescharacteristic
804C2×C4C2×#612711yescharacteristic
805C2×C4C2×D4×D1311yescharacteristic
806C2×C4#8825111yescharacteristic
807C2×C4#8825111yescharacteristic
808C2×C4C22×C22⋊D1311yescharacteristic
809C8—22no—
810C8—41no—
811C8—261no—
812C8—261no—
813C8—261no—
814C8—261no—
815C8—261no—
816C8—261no—
817C8—261no—
818C8—261no—
819C8—521no—
820C8—521no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—21no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—84no—
837C22—521no—
838C22—521no—
839C22—521no—
840C22#1171848412yescomplemented
841C22C2×#8813511yescharacteristic
842C22#1171920011yescharacteristic
843C22#1171951111yescharacteristic
844C4—21no—
845C4—21no—
846C4—22no—
847C4—42no—
848C4—42no—
849C4—41no—
850C4—521no—
851C4—521no—
852C4—521no—
853C4#1171919111yescharacteristic
854C4#1171919511yescharacteristic
855C4C2×C4×C22⋊D1311yescharacteristic
856C4D4×C22⋊D1311yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—1041no—
864C2#1311781511yescharacteristic
865C2C2×#1171848411yescharacteristic
866C2#1312374211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC22×C13×#104C2
socleC22×C13C2×C4×D4
prime radical#13124054C2
cosocleC22×C4×C13C24
hypercenterC22×#104D13
hypocenterC13#22886
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C2×#11718484C2semidirect
3. #13123561C2semidirect
4. #13123285C2semidirect
5. #13115726C2semidirect
6. #13115544C2semidirect
7. #13115487C2semidirect
8. #13115279C2semidirect
9. #13115161C2semidirect
10. #13115160C2semidirect
11. #13115109C2semidirect
12. #13115041C2semidirect
13. #13114681C2semidirect
14. #13114598C2semidirect
15. C22×C13×#104C2semidirect
24. C2×#88161C22semidirect
30. #11718900C4semidirect
31. #11718900C4semidirect
32. #11718899C4semidirect
33. #11718899C4semidirect
40. #11718889C4semidirect
41. #11718888C4semidirect
42. #11718879C4semidirect
43. #11718878C4semidirect
49. #11718790C22semidirect
52. C2×#88062C22semidirect
53. C2×#88062C22semidirect
54. #11718783C22semidirect
55. #11718780C22semidirect
58. C2×#88045C22semidirect
59. C2×#88045C22semidirect
60. C2×#88043C22semidirect
61. C2×#88043C22semidirect
63. #11718150C22semidirect
64. #11718150C22semidirect
65. #11718116C22semidirect
66. #11718116C22semidirect
67. #11718115C22semidirect
68. #11718115C22semidirect
106. C2×#6107C2×C4semidirect
107. C2×#6107C2×C4semidirect
108. C2×#6106C2×C4semidirect
109. C2×#6106C2×C4semidirect
110. C2×#6105C2×C4semidirect
111. C2×#6105C2×C4semidirect
112. C2×#6104C2×C4semidirect
113. C2×#6104C2×C4semidirect
139. C13×#104D4semidirect
140. #88075C2×C4semidirect
141. #88075C2×C4semidirect
142. #88075C2×C4semidirect
143. #88075C2×C4semidirect
144. #88072C2×C4semidirect
145. #88072C2×C4semidirect
146. #88072C2×C4semidirect
147. #88072C2×C4semidirect
303. C22×#104D13semidirect
472. C22×C13#444semidirect
568. #104C22⋊D13semidirect
732. C13#22886semidirect
840. C22#11718484semidirect

Maximal subgroups

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

subgroupindex
#131240542
C2×#117184842
#131235612
#131232852
#131157262
#131155442
#131154872
#131152792
#131151612
#131151602
#131151092
#131150412
#131146812
#131145982
C22×C13×#1042
#2288613