Finite Group Databasebeta

← #15883661

Subgroups — #15883661

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#13124058C211yesmaximal, characteristic
2C2×#11718378C211yesmaximal, characteristic, complemented
3#13123557C211yesmaximal, characteristic, complemented
4C22×#88045C211yesmaximal, characteristic, complemented
5#13123282C211yesmaximal, characteristic, complemented
6#13115729C211yesmaximal, characteristic, complemented
7#13115547C211yesmaximal, characteristic, complemented
8#13115485C211yesmaximal, characteristic, complemented
9#13115279C211yesmaximal, characteristic, complemented
10#13115162C211yesmaximal, characteristic, complemented
11#13115162C211yesmaximal, characteristic, complemented
12#13115114C211yesmaximal, characteristic, complemented
13#13115043C211yesmaximal, characteristic, complemented
14#13114680C211yesmaximal, characteristic, complemented
15C13×#1749C211yesmaximal, characteristic, complemented
16C22×#6127C2211yescharacteristic
17C22×C42×C13C2211yescharacteristic
18#11719496C2211yescharacteristic
19C22×#6099C2211yescharacteristic
20C2×#88158C2211yescharacteristic
21C2×#88158C2211yescharacteristic
22C2×#88155C2211yescharacteristic
23C2×#88155C2211yescharacteristic
24C2×#88155C2211yescharacteristic, complemented
25C2×C13×C22⋊C8C2211yescharacteristic
26C2×C13×C22⋊C8C2211yescharacteristic
27C2×C13×#97C2211yescharacteristic, complemented
28C2×C13×#97C2211yescharacteristic, complemented
29#11718868C2211yescharacteristic
30#11718774C2211yescharacteristic
31#11718774C2211yescharacteristic
32#11718771C2211yescharacteristic
33#11718771C2211yescharacteristic
34#11718771C2211yescharacteristic, complemented
35C2×#88059C2211yescharacteristic, complemented
36C2×#88059C2211yescharacteristic, complemented
37#11718763C2211yescharacteristic, complemented
38#11718762C2211yescharacteristic, complemented
39C2×#88045—24no—
40C2×#88045C2211yescharacteristic
41C2×#88045C2211yescharacteristic
42C2×#88045C2211yescharacteristic
43C2×#88045C2211yescharacteristic
44C2×#88045C2211yescharacteristic, complemented
45C2×#88045C2211yescharacteristic, complemented
46#11718400C411yescharacteristic, complemented
47#11718399C411yescharacteristic, complemented
48#11718395C411yescharacteristic, complemented
49#11718395C411yescharacteristic, complemented
50#11718394C411yescharacteristic, complemented
51#11718394C411yescharacteristic, complemented
52#11718393C411yescharacteristic, complemented
53#11718392C411yescharacteristic, complemented
54#11718391—21no—
55#11718390—21no—
56#11718389—21no—
57#11718388—21no—
58#11718388—21no—
59#11718387—21no—
60#11718386—21no—
61D13×C22⋊C8—21no—
62#11718378—24no—
63C13×#336C2211yescharacteristic, complemented
64C13×#336C2211yescharacteristic, complemented
65#11718144C2211yescharacteristic, complemented
66#11718144C2211yescharacteristic, complemented
67#11718115C2211yescharacteristic, complemented
68#11718115C2211yescharacteristic, complemented
69C23×C4×C13—21no—
70C23×C4×C13C2311yescharacteristic
71C22×C22⋊D13—21no—
72C2×#6127—21no—
73C2×#6127—21no—
74C2×#6127—22no—
75C2×#6127—22no—
76C2×#6127—41no—
77C2×#6127—41no—
78C2×#6127C2×C411yescharacteristic
79C2×#6127C2×C411yescharacteristic
80C2×#6127C2311yescharacteristic
81C2×#6127C2311yescharacteristic
82C2×#6127C2311yescharacteristic
83C22×D52C2×C411yescharacteristic
84C22×C4×D13—21no—
85C22×Dic26C2×C411yescharacteristic
86C22×C8×C13C2311yescharacteristic
87C22×C8×C13C2311yescharacteristic
88C22×C8×C13C2311yescharacteristic
89C22×C8×C13C2311yescharacteristic
90C2×C42×C13—22no—
91C2×C42×C13—21no—
92C2×C42×C13—41no—
93C2×C42×C13C2311yescharacteristic
94C2×C42×C13C2311yescharacteristic
95#88207—21no—
96#88184C2×C411yescharacteristic
97#88184C2×C411yescharacteristic
98#88183—21no—
99C4×C22⋊D13—21no—
100C4×C22⋊D13—21no—
101#88180C2311yescharacteristic
102#88178C2×C411yescharacteristic
103#88178C2×C411yescharacteristic
104C2×#6099—21no—
105C2×#6099—22no—
106C2×#6099—41no—
107C2×#6099C2311yescharacteristic
108C2×#6099C2311yescharacteristic
109C2×#6099C2311yescharacteristic
110C2×#6099C2311yescharacteristic
111C22×#1055—21no—
112C2×Dic52C2×C411yescharacteristic, complemented
113C2×Dic52C2×C411yescharacteristic, complemented
114#88158—22no—
115#88158—22no—
116#88158—41no—
117#88158—41no—
118C2×D104C2×C411yescharacteristic, complemented
119C2×D104C2×C411yescharacteristic, complemented
120C2×#6095C2×C411yescharacteristic, complemented
121C2×#6095C2×C411yescharacteristic, complemented
122C2×#6095C2×C411yescharacteristic, complemented
123C2×#6095C2×C411yescharacteristic, complemented
124#88155—22no—
125#88155—22no—
126#88155—22no—
127#88155—41no—
128#88155—41no—
129#88155—41no—
130C2×#6094—21no—
131C2×#6094—21no—
132C2×#6094—21no—
133C2×C8×D13—21no—
134C2×C8×D13—21no—
135C2×C8×D13—21no—
136C13×C22⋊C8C2×C411yescharacteristic
137C13×C22⋊C8C2×C411yescharacteristic
138C13×C22⋊C8C2×C411yescharacteristic
139C13×C22⋊C8C2×C411yescharacteristic
140C13×C22⋊C8D411yescharacteristic
141C13×C22⋊C8D411yescharacteristic
142C13×C22⋊C8D411yescharacteristic
143C13×C22⋊C8D411yescharacteristic
144C13×#97—22no—
145C13×#97—41no—
146C22⋊#1055—21no—
147C22⋊#1055—21no—
148#88061C2×C411yescharacteristic, complemented
149#88061C2×C411yescharacteristic, complemented
150#88061C2×C411yescharacteristic, complemented
151#88061C2×C411yescharacteristic, complemented
152#88060—21no—
153#88060—21no—
154#88060—21no—
155#88060—21no—
156#88060—21no—
157#88060—21no—
158#88059—22no—
159#88059—41no—
160#88056C2×C411yescharacteristic, complemented
161#88056C2×C411yescharacteristic, complemented
162#88056C2×C411yescharacteristic, complemented
163#88056C2×C411yescharacteristic, complemented
164#88055—21no—
165#88054—21no—
166#88054—21no—
167C8×Dic13—21no—
168#88045—22no—
169#88045—22no—
170#88045—22no—
171#88045—22no—
172#88045—41no—
173#88045D414yescomplemented
174#22886—131nomaximal, Sylow
175C24×C13#4111yescharacteristic
176C23×D13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—42no—
184C22×C4×C13—42no—
185C22×C4×C13—42no—
186C22×C4×C13C22×C411yescharacteristic
187C22×C4×C13C22×C411yescharacteristic
188C22×C4×C13C2×D411yescharacteristic
189C22×C4×C13C2×D411yescharacteristic
190C22×C4×C13#4111yescharacteristic
191C22×C4×C13C2411yescharacteristic
192C2×C22⋊D13—21no—
193C2×C22⋊D13—21no—
194C2×C22⋊D13—21no—
195C2×C22⋊D13—21no—
196C2×C22⋊D13—21no—
197C2×C22⋊D13—21no—
198C2×C22⋊D13—21no—
199C2×C22⋊D13—42no—
200C2×C22⋊D13—42no—
201C22×Dic13—21no—
202#6127—21no—
203#6127—21no—
204#6127—21no—
205#6127—21no—
206#6127—21no—
207#6127—21no—
208#6127—21no—
209#6127—21no—
210#6127—21no—
211#6127—21no—
212#6127—22no—
213#6127—22no—
214#6127—41no—
215#6127—41no—
216#6127—42no—
217#6127—42no—
218#6127—42no—
219#6127—42no—
220#6127C2×D412yes—
221#6127#4112yes—
222C2×D52—22no—
223C2×D52—21no—
224C2×D52—41no—
225C2×D52C22×C411yescharacteristic
226C2×D52C22×C411yescharacteristic
227C2×D52C22×C411yescharacteristic
228C2×C4×D13—21no—
229C2×C4×D13—21no—
230C2×C4×D13—21no—
231C2×C4×D13—21no—
232C2×C4×D13—21no—
233C2×C4×D13—42no—
234C2×C4×D13—42no—
235C2×Dic26—22no—
236C2×Dic26—21no—
237C2×Dic26—41no—
238C2×Dic26C22×C411yescharacteristic
239C2×Dic26C22×C411yescharacteristic
240C2×Dic26C22×C411yescharacteristic
241C2×C8×C13—21no—
242C2×C8×C13—21no—
243C2×C8×C13—21no—
244C2×C8×C13—21no—
245C2×C8×C13—21no—
246C2×C8×C13—21no—
247C2×C8×C13—21no—
248C2×C8×C13—21no—
249C2×C8×C13C22×C411yescharacteristic
250C2×C8×C13C22×C411yescharacteristic
251C2×C8×C13C22×C411yescharacteristic
252C2×C8×C13C22×C411yescharacteristic
253C2×C8×C13C2×D411yescharacteristic
254C2×C8×C13C2×D411yescharacteristic
255C2×C8×C13C2×D411yescharacteristic
256C2×C8×C13C2×D411yescharacteristic
257C42×C13—21no—
258C42×C13—21no—
259C42×C13—21no—
260C42×C13—42no—
261C42×C13C2×D412yes—
262C22⋊Dic13—21no—
263C22⋊Dic13—21no—
264C22⋊Dic13—21no—
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—21no—
277#6099—21no—
278#6099—21no—
279#6099—42no—
280#6099C2×D412yes—
281C2×#1055—21no—
282C2×#1055—21no—
283C2×#1055—21no—
284C2×#1055—21no—
285C2×#1055—42no—
286Dic52—22no—
287Dic52—41no—
288D104—22no—
289D104—41no—
290#6095—22no—
291#6095—22no—
292#6095—41no—
293#6095—41no—
294#6094—42no—
295#6094—42no—
296#6094—42no—
297C8×D13—42no—
298C8×D13—42no—
299C8×D13—42no—
300#3002—131no—
301C2×#444—131no—
302#2933—131no—
303C22×#104—131no—
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#1749D1311yescharacteristic, complemented
315C23×C13—21no—
316C23×C13—21no—
317C23×C13—22no—
318C23×C13—41no—
319C23×C13C4×D411yescharacteristic
320C23×C13C4×D411yescharacteristic
321C23×C13C2×#4111yescharacteristic
322C22×D13—21no—
323C22×D13—21no—
324C22×D13—21no—
325C22×D13—42no—
326C22×D13—42no—
327C22×D13—81no—
328C2×C4×C13—21no—
329C2×C4×C13—21no—
330C2×C4×C13—21no—
331C2×C4×C13—21no—
332C2×C4×C13—21no—
333C2×C4×C13—21no—
334C2×C4×C13—21no—
335C2×C4×C13—21no—
336C2×C4×C13—21no—
337C2×C4×C13—21no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—41no—
341C2×C4×C13—41no—
342C2×C4×C13—41no—
343C2×C4×C13—48no—
344C2×C4×C13—41no—
345C2×C4×C13C4×D411yescharacteristic
346C2×C4×C13C4×D411yescharacteristic
347C2×C4×C13C23×C411yescharacteristic
348C2×C4×C13C22×D411yescharacteristic
349C2×C4×C13C22×D411yescharacteristic
350C2×C4×C13C2×#4111yescharacteristic
351C2×C4×C13H(5,𝔽2)11yescharacteristic
352C2×C4×C13H(5,𝔽2)11yescharacteristic
353C22⋊D13—22no—
354C22⋊D13—22no—
355C22⋊D13—42no—
356C22⋊D13—42no—
357C22⋊D13—41no—
358C22⋊D13—41no—
359C22⋊D13—41no—
360C22⋊D13—41no—
361C22⋊D13—42no—
362C22⋊D13—81no—
363C2×Dic13—21no—
364C2×Dic13—21no—
365C2×Dic13—21no—
366C2×Dic13—21no—
367C2×Dic13—21no—
368C2×Dic13—42no—
369D52—21no—
370D52—21no—
371D52—21no—
372D52—21no—
373D52—21no—
374D52—42no—
375D52C4×D412yes—
376C4×D13—22no—
377C4×D13—22no—
378C4×D13—42no—
379C4×D13—42no—
380C4×D13—41no—
381C4×D13—41no—
382C4×D13—41no—
383C4×D13—41no—
384Dic26—21no—
385Dic26—21no—
386Dic26—21no—
387Dic26—21no—
388Dic26—21no—
389Dic26—42no—
390Dic26C4×D412yes—
391C8×C13—21no—
392C8×C13—21no—
393C8×C13—21no—
394C8×C13—21no—
395C8×C13—21no—
396C8×C13—21no—
397C8×C13—21no—
398C8×C13—21no—
399#1055—22no—
400#1055—41no—
401#1055—41no—
402#1055—41no—
403C22×#41—131no—
404C2×#135—131no—
405C2×#135—131no—
406C2×#131—131no—
407C2×#131—131no—
408C2×#131—131no—
409C22×M16—131no—
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—131no—
429C2×#104—131no—
430C2×#104—131no—
431C2×#104—131no—
432C2×#104—131no—
433C2×#104—131no—
434C2×#104—264no—
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—261no—
445C2×C22⋊C8C2×D1311yescharacteristic
446C2×C22⋊C8C2×D1311yescharacteristic
447#405—131no—
448C2×#97C2×D1311yescharacteristic, complemented
449C2×#97C2×D1311yescharacteristic, complemented
450#341—131no—
451#341—131no—
452#339—131no—
453#339—131no—
454#336C2×D1311yescharacteristic, complemented
455#336C2×D1311yescharacteristic, complemented
456C22×C13—21no—
457C22×C13—21no—
458C22×C13—21no—
459C22×C13—21no—
460C22×C13—21no—
461C22×C13—21no—
462C22×C13—21no—
463C22×C13—42no—
464C22×C13—42no—
465C22×C13#44412yescomplemented
466C22×C13C2×C4×D411yescharacteristic
467C22×C13#54611yescharacteristic
468C22×C13#55111yescharacteristic
469C2×D13—22no—
470C2×D13—41no—
471C2×D13—41no—
472C2×D13—41no—
473C2×D13—41no—
474C2×D13—41no—
475C2×D13—41no—
476C2×D13—41no—
477C2×D13—41no—
478C2×D13—84no—
479C4×C13—21no—
480C4×C13—21no—
481C4×C13—42no—
482C4×C13—42no—
483C4×C13C2×C4×D411yescharacteristic
484C4×C13#51811yescharacteristic
485C4×C13D4211yescharacteristic
486C4×C13#54611yescharacteristic
487Dic13—22no—
488Dic13—41no—
489Dic13—41no—
490Dic13—41no—
491Dic13—41no—
492C2×#41—131no—
493C2×#41—131no—
494C2×#41—131no—
495C2×#41—131no—
496C2×#41—131no—
497C2×#41—262no—
498C2×#41—262no—
499C2×#41—261no—
500C2×#41—261no—
501C2×#41—521no—
502C2×#41—521no—
503C22×Q8—131no—
504C22×D4—131no—
505C22×D4—261no—
506C23×C4—21no—
507C23×C4—261no—
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—131no—
528C2×M16—131no—
529C2×M16—131no—
530C2×M16—131no—
531C2×M16—261no—
532C2×M16—261no—
533C2×M16—261no—
534C2×M16—261no—
535C2×M16—262no—
536C2×M16—521no—
537C22×C8—261no—
538C22×C8—261no—
539C22×C8—261no—
540C22×C8—261no—
541C22×C8C22×D1311yescharacteristic
542C22×C8C22×D1311yescharacteristic
543C22×C8C22×D1311yescharacteristic
544C22×C8C22×D1311yescharacteristic
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—134no—
564#104—262no—
565#104—262no—
566#104—262no—
567#104—262no—
568#104—521no—
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—261no—
578C22⋊C8—261no—
579C22⋊C8—261no—
580C22⋊C8—261no—
581C22⋊C8—261no—
582C22⋊C8—261no—
583C22⋊C8—261no—
584C22⋊C8—261no—
585C22⋊C8C4×D1311yescharacteristic
586C22⋊C8C4×D1311yescharacteristic
587C22⋊C8C4×D1311yescharacteristic
588C22⋊C8C4×D1311yescharacteristic
589C22⋊C8D5211yescharacteristic
590C22⋊C8D5211yescharacteristic
591C22⋊C8D5211yescharacteristic
592C22⋊C8D5211yescharacteristic
593#97—22no—
594#97—41no—
595#97—261no—
596C4×C8—261no—
597C2×C13—21no—
598C2×C13—22no—
599C2×C13—21no—
600C2×C13—41no—
601C2×C13#235811yescharacteristic
602C2×C13C2×#44411yescharacteristic
603C2×C13#295611yescharacteristic
604D13—42no—
605D13—81no—
606D13—81no—
607C24—261no—
608C24#612711yescharacteristic
609#41—132no—
610#41—132no—
611#41—262no—
612#41—262no—
613#41—261no—
614#41—261no—
615#41—261no—
616#41—261no—
617#41—261no—
618#41—261no—
619#41—261no—
620#41—261no—
621#41—261no—
622#41—261no—
623#41—522no—
624#41—522no—
625#41—521no—
626#41—521no—
627#41—522no—
628#41—522no—
629C2×Q8—131no—
630C2×Q8—131no—
631C2×Q8—131no—
632C2×Q8—262no—
633C2×Q8—261no—
634C2×Q8—521no—
635C2×D4—131no—
636C2×D4—131no—
637C2×D4—131no—
638C2×D4—262no—
639C2×D4—261no—
640C2×D4—261no—
641C2×D4—261no—
642C2×D4—261no—
643C2×D4—261no—
644C2×D4—261no—
645C2×D4—261no—
646C2×D4—261no—
647C2×D4—521no—
648C2×D4—522no—
649C2×D4—522no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—261no—
660C22×C4—261no—
661C22×C4—261no—
662C22×C4—261no—
663C22×C4—261no—
664C22×C4—261no—
665C22×C4—522no—
666C22×C4—522no—
667C22×C4C2×C4×D1311yescharacteristic
668C22×C4C2×C4×D1311yescharacteristic
669C22×C4C2×D5211yescharacteristic
670C22×C4C2×D5211yescharacteristic
671C22×C4#612711yescharacteristic
672C22×C4C23×D1311yescharacteristic
673Q16—262no—
674Q16—521no—
675SD16—262no—
676SD16—262no—
677SD16—521no—
678SD16—521no—
679D8—262no—
680D8—521no—
681M16—132no—
682M16—261no—
683M16—261no—
684M16—261no—
685M16—261no—
686M16—261no—
687M16—261no—
688M16—261no—
689M16—522no—
690M16—522no—
691M16—522no—
692M16—522no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—261no—
702C2×C8—261no—
703C2×C8—261no—
704C2×C8—261no—
705C2×C8—522no—
706C2×C8—522no—
707C2×C8—522no—
708C2×C8—522no—
709C2×C8C2×C4×D1311yescharacteristic
710C2×C8C2×C4×D1311yescharacteristic
711C2×C8C2×C4×D1311yescharacteristic
712C2×C8C2×C4×D1311yescharacteristic
713C2×C8C2×D5211yescharacteristic
714C2×C8C2×D5211yescharacteristic
715C2×C8C2×D5211yescharacteristic
716C2×C8C2×D5211yescharacteristic
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—
731C42D4×D1312yes—
732C13#2288611yescharacteristic, complemented, Sylow
733C23—21no—
734C23—21no—
735C23—22no—
736C23—41no—
737C23—261no—
738C23—261no—
739C23—261no—
740C23—522no—
741C23—522no—
742C23—1041no—
743C23C4×D5211yescharacteristic
744C23C4×D5211yescharacteristic
745C23C2×#612711yescharacteristic
746Q8—132no—
747Q8—261no—
748Q8—261no—
749Q8—261no—
750Q8—261no—
751Q8—261no—
752Q8—522no—
753D4—132no—
754D4—262no—
755D4—262no—
756D4—261no—
757D4—261no—
758D4—261no—
759D4—261no—
760D4—261no—
761D4—522no—
762D4—522no—
763D4—522no—
764D4—521no—
765D4—521no—
766D4—521no—
767D4—521no—
768D4—522no—
769D4—1041no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—48no—
786C2×C4—41no—
787C2×C4—261no—
788C2×C4—262no—
789C2×C4—262no—
790C2×C4—261no—
791C2×C4—261no—
792C2×C4—261no—
793C2×C4—261no—
794C2×C4—522no—
795C2×C4—522no—
796C2×C4—522no—
797C2×C4—521no—
798C2×C4—521no—
799C2×C4—521no—
800C2×C4—521no—
801C2×C4C4×D5211yescharacteristic
802C2×C4C4×D5211yescharacteristic
803C2×C4C22×C4×D1311yescharacteristic
804C2×C4C22×D5211yescharacteristic
805C2×C4C2×D4×D1311yescharacteristic
806C2×C4#8825111yescharacteristic
807C2×C4#41×D1311yescharacteristic
808C2×C4#8825611yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—21no—
814C8—21no—
815C8—21no—
816C8—21no—
817C8—262no—
818C8—521no—
819C8—521no—
820C8—521no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—42no—
829C22—42no—
830C22—262no—
831C22—521no—
832C22—521no—
833C22—521no—
834C22—521no—
835C22—521no—
836C22—521no—
837C22—521no—
838C22—521no—
839C22—1044no—
840C22#1171837812yescomplemented
841C22C2×C4×D5211yescharacteristic
842C22#1171919511yescharacteristic
843C22#1171923211yescharacteristic
844C4—21no—
845C4—21no—
846C4—42no—
847C4—42no—
848C4—262no—
849C4—521no—
850C4—521no—
851C4—521no—
852C4—521no—
853C4C4×D4×D1311yescharacteristic
854C4#1171925011yescharacteristic
855C4D4×D5211yescharacteristic
856C4#1171925911yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—522no—
862C2—1041no—
863C2—1041no—
864C2#1311781811yescharacteristic
865C2C2×#1171837811yescharacteristic
866C2#1312374711yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1749C2
socleC22×C13C2×C4×D4
prime radical#13124058C2
cosocleC22×C4×C13C24
hypercenter#1749D13
hypocenterC13#22886
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #1749

Complements

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

NH ≅ G/Ntype
2. C2×#11718378C2semidirect
3. #13123557C2semidirect
4. C22×#88045C2semidirect
5. #13123282C2semidirect
6. #13115729C2semidirect
7. #13115547C2semidirect
8. #13115485C2semidirect
9. #13115279C2semidirect
10. #13115162C2semidirect
11. #13115162C2semidirect
12. #13115114C2semidirect
13. #13115043C2semidirect
14. #13114680C2semidirect
15. C13×#1749C2semidirect
24. C2×#88155C22semidirect
27. C2×C13×#97C22semidirect
28. C2×C13×#97C22semidirect
34. #11718771C22semidirect
35. C2×#88059C22semidirect
36. C2×#88059C22semidirect
37. #11718763C22semidirect
38. #11718762C22semidirect
44. C2×#88045C22semidirect
45. C2×#88045C22semidirect
46. #11718400C4semidirect
47. #11718399C4semidirect
48. #11718395C4semidirect
49. #11718395C4semidirect
50. #11718394C4semidirect
51. #11718394C4semidirect
52. #11718393C4semidirect
53. #11718392C4semidirect
63. C13×#336C22semidirect
64. C13×#336C22semidirect
65. #11718144C22semidirect
66. #11718144C22semidirect
67. #11718115C22semidirect
68. #11718115C22semidirect
112. C2×Dic52C2×C4semidirect
113. C2×Dic52C2×C4semidirect
118. C2×D104C2×C4semidirect
119. C2×D104C2×C4semidirect
120. C2×#6095C2×C4semidirect
121. C2×#6095C2×C4semidirect
122. C2×#6095C2×C4semidirect
123. C2×#6095C2×C4semidirect
148. #88061C2×C4semidirect
149. #88061C2×C4semidirect
150. #88061C2×C4semidirect
151. #88061C2×C4semidirect
160. #88056C2×C4semidirect
161. #88056C2×C4semidirect
162. #88056C2×C4semidirect
163. #88056C2×C4semidirect
173. #88045D4semidirect
314. #1749D13semidirect
448. C2×#97C2×D13semidirect
449. C2×#97C2×D13semidirect
454. #336C2×D13semidirect
455. #336C2×D13semidirect
465. C22×C13#444semidirect
732. C13#22886semidirect
840. C22#11718378semidirect

Maximal subgroups

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

subgroupindex
#131240582
C2×#117183782
#131235572
C22×#880452
#131232822
#131157292
#131155472
#131154852
#131152792
#131151622
#131151142
#131150432
#131146802
C13×#17492
#2288613