Finite Group Databasebeta

← #15829190

Subgroups — #15829190

Order 3328.

1060 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719261C211yesmaximal, characteristic
2#13123871C211yesmaximal, characteristic, complemented
3#13113206C211yesmaximal, characteristic, complemented
4#13113203C211yesmaximal, characteristic, complemented
5#13113201C211yesmaximal, characteristic, complemented
6#13113199C211yesmaximal, characteristic, complemented
7#13113185C211yesmaximal, characteristic, complemented
8#13113182C211yesmaximal, characteristic, complemented
9#13113172C211yesmaximal, characteristic, complemented
10#13113168C211yesmaximal, characteristic, complemented
11#13113162C211yesmaximal, characteristic, complemented
12#13113152C211yesmaximal, characteristic, complemented
13#13113148C211yesmaximal, characteristic, complemented
14C2×#11718060C211yesmaximal, characteristic, complemented
15C13×#2974C211yesmaximal, characteristic, complemented
16C2×C4×D4×C13C2211yescharacteristic
17C2×#88191C411yescharacteristic
18C2×#88189C411yescharacteristic
19C2×#88183C2211yescharacteristic
20C2×C4×C22⋊D13C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C2×#88178C2211yescharacteristic
23#11719261—21no—
24#11719261—21no—
25#11719261—21no—
26#11719261—21no—
27#11719261—21no—
28#11719261—21no—
29#11719261—21no—
30#11719261—21no—
31C2×#88152C411yescharacteristic
32C2×#88150C411yescharacteristic
33C2×#88139C411yescharacteristic
34C2×#88137C411yescharacteristic
35C2×C22⋊C4×D13C411yescharacteristic
36C2×#88131C411yescharacteristic
37C2×#88130C2211yescharacteristic
38C2×#88126C2211yescharacteristic
39C13×#436—21no—
40C13×#435—21no—
41C13×#435—21no—
42C8×D4×C13—21no—
43C13×#432C2211yescharacteristic, complemented
44C13×#431C2211yescharacteristic, complemented
45C13×#407C2211yescharacteristic
46C13×#407C2211yescharacteristic, complemented
47C2×C13×C22⋊C8C2211yescharacteristic
48C2×C13×C22⋊C8C2211yescharacteristic, complemented
49#11718868C2211yescharacteristic
50#11718868C2211yescharacteristic, complemented
51C2×C22⋊#1055C2211yescharacteristic
52C2×C22⋊#1055C2211yescharacteristic, complemented
53#11718673—21no—
54#11718672—21no—
55#11718672—21no—
56D4×#1055—21no—
57#11718587C2211yescharacteristic, complemented
58#11718586C2211yescharacteristic, complemented
59#11718061C2211yescharacteristic, complemented
60#11718061C2211yescharacteristic, complemented
61#11718061C2211yescharacteristic, complemented
62#11718061C2211yescharacteristic, complemented
63#11718061C2211yescharacteristic, complemented
64#11718061C2211yescharacteristic, complemented
65#11718061C2211yescharacteristic, complemented
66#11718061C2211yescharacteristic, complemented
67#11718060C2211yescharacteristic
68#11718060C2211yescharacteristic
69#11718060C2211yescharacteristic
70#11718060C2211yescharacteristic
71#11718060C2211yescharacteristic
72#11718060C2211yescharacteristic
73#11718060C2211yescharacteristic
74#11718060C2211yescharacteristic
75C24×D13C2×C411yescharacteristic
76C22×D4×C13C2×C411yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C22×C22⋊D13C2×C411yescharacteristic
80C22×C22⋊D13C2×C411yescharacteristic
81C23×Dic13C2×C411yescharacteristic
82C22×C4×D13C2×C411yescharacteristic
83C22×C4×D13C2×C411yescharacteristic
84C22×Dic26C2×C411yescharacteristic
85C2×C13×M16—21no—
86C2×C13×M16—21no—
87C22×C8×C13—21no—
88C22×C8×C13—21no—
89C4×D4×C13D411yescharacteristic
90C4×D4×C13D411yescharacteristic
91C4×D4×C13D411yescharacteristic
92C4×D4×C13D411yescharacteristic
93C4×D4×C13D411yescharacteristic
94C4×D4×C13D411yescharacteristic
95C4×D4×C13D411yescharacteristic
96C4×D4×C13D411yescharacteristic
97C2×C13×C4⋊C4C2×C411yescharacteristic
98C2×C13×C22⋊C4C2×C411yescharacteristic
99C2×C13×C22⋊C4C2×C411yescharacteristic
100C2×C42×C13C2311yescharacteristic
101C2×C22⋊Dic13C2×C411yescharacteristic
102C2×C22⋊Dic13C2×C411yescharacteristic
103C2×C22⋊Dic13C2×C411yescharacteristic
104C2×C22⋊Dic13C2×C411yescharacteristic
105#88191—21no—
106#88191—21no—
107#88191—21no—
108#88191—21no—
109#88189—21no—
110#88189—21no—
111#88189—21no—
112#88189—21no—
113#88183—21no—
114#88183—21no—
115#88183—21no—
116#88183—21no—
117C4×C22⋊D13—21no—
118C4×C22⋊D13—21no—
119C4×C22⋊D13—21no—
120C4×C22⋊D13—21no—
121C2×#6103—21no—
122C2×#6103—21no—
123C2×#6103—21no—
124C2×#6103—21no—
125C2×#6103C2×C411yescharacteristic
126C2×#6103C2×C411yescharacteristic
127C2×#6103C2×C411yescharacteristic
128C2×#6103C2×C411yescharacteristic
129C2×#6103C2×C411yescharacteristic
130C2×#6103C2×C411yescharacteristic
131C2×#6103C2311yescharacteristic
132C2×#6103C2311yescharacteristic
133C2×C4⋊Dic13C2×C411yescharacteristic
134#88178—21no—
135#88178—21no—
136#88178—21no—
137#88178—21no—
138C2×#6101C2×C411yescharacteristic
139C2×#6101C2×C411yescharacteristic
140C2×#6101C2×C411yescharacteristic
141C2×#6101C2×C411yescharacteristic
142C2×#6101C2311yescharacteristic
143C2×#6101C2311yescharacteristic
144C2×C4×Dic13C2×C411yescharacteristic
145C2×C4×Dic13C2×C411yescharacteristic
146C2×#6099—21no—
147C2×#6099—21no—
148C22×#1055—21no—
149C22×#1055—21no—
150#88152—21no—
151#88152—21no—
152#88152—21no—
153#88152—21no—
154#88150—21no—
155#88150—21no—
156#88150—21no—
157#88150—21no—
158#88139—21no—
159#88139—21no—
160#88139—21no—
161#88139—21no—
162#88137—21no—
163#88137—21no—
164#88137—21no—
165#88137—21no—
166C22⋊C4×D13—21no—
167C22⋊C4×D13—21no—
168C22⋊C4×D13—21no—
169C22⋊C4×D13—21no—
170#88131—21no—
171#88131—21no—
172#88131—21no—
173#88131—21no—
174#88130—21no—
175#88130—21no—
176#88130—21no—
177#88130—21no—
178#88126—21no—
179#88126—21no—
180#88126—21no—
181#88126—21no—
182C13×C4⋊C8—21no—
183C13×C4⋊C8—21no—
184C13×C22⋊C8—21no—
185C13×C22⋊C8—21no—
186C13×C22⋊C8—21no—
187C13×C22⋊C8—21no—
188C13×C22⋊C8C2311yescharacteristic
189C13×C22⋊C8C2311yescharacteristic
190C13×C22⋊C8C2311yescharacteristic
191C13×C22⋊C8C2311yescharacteristic
192C13×#97—21no—
193C4×C8×C13—21no—
194C22⋊#1055—21no—
195C22⋊#1055—21no—
196C22⋊#1055—21no—
197C22⋊#1055—21no—
198C22⋊#1055C2311yescharacteristic
199C22⋊#1055C2311yescharacteristic
200C22⋊#1055C2311yescharacteristic
201C22⋊#1055C2311yescharacteristic
202C4⋊#1055—21no—
203C4⋊#1055—21no—
204#88043—21no—
205C4×#1055—21no—
206#17422—131nomaximal, Sylow
207C24×C13C22×C411yescharacteristic
208C24×C13C22×C411yescharacteristic
209C23×D13—21no—
210C23×D13—21no—
211C23×D13—22no—
212C23×D13—41no—
213C23×D13—42no—
214C23×D13—81no—
215C23×D13C22×C411yescharacteristic
216C23×D13C22×C411yescharacteristic
217C2×D4×C13—42no—
218C2×D4×C13C22⋊C411yescharacteristic
219C2×D4×C13C22⋊C411yescharacteristic
220C2×D4×C13C22⋊C411yescharacteristic
221C2×D4×C13C22⋊C411yescharacteristic
222C22×C4×C13—81no—
223C22×C4×C13—81no—
224C22×C4×C13C22×C411yescharacteristic
225C22×C4×C13C22×C411yescharacteristic
226C22×C4×C13C22×C411yescharacteristic
227C22×C4×C13C22×C411yescharacteristic
228C22×C4×C13C2×D411yescharacteristic
229C22×C4×C13C2×D411yescharacteristic
230C22×C4×C13C2×D411yescharacteristic
231C22×C4×C13C2×D411yescharacteristic
232C22×C4×C13C2×D411yescharacteristic
233C22×C4×C13C2×D411yescharacteristic
234C22×C4×C13C2×D411yescharacteristic
235C22×C4×C13C2×D411yescharacteristic
236C22×C4×C13C2411yescharacteristic
237C2×C22⋊D13—21no—
238C2×C22⋊D13—21no—
239C2×C22⋊D13—22no—
240C2×C22⋊D13—21no—
241C2×C22⋊D13—21no—
242C2×C22⋊D13—41no—
243C2×C22⋊D13—81no—
244C22×Dic13—21no—
245C22×Dic13—21no—
246C22×Dic13—42no—
247C22×Dic13C22×C411yescharacteristic
248C22×Dic13C22×C411yescharacteristic
249C22×Dic13C22×C411yescharacteristic
250C22×Dic13C22×C411yescharacteristic
251C22×Dic13C22×C411yescharacteristic
252C22×Dic13C22×C411yescharacteristic
253C2×C4×D13—22no—
254C2×C4×D13—21no—
255C2×C4×D13—21no—
256C2×C4×D13—21no—
257C2×C4×D13—21no—
258C2×C4×D13—41no—
259C2×C4×D13—81no—
260C2×Dic26—21no—
261C2×Dic26—21no—
262C2×Dic26—81no—
263C13×M16—81no—
264C13×M16—81no—
265C2×C8×C13—21no—
266C2×C8×C13—21no—
267C2×C8×C13—21no—
268C2×C8×C13—21no—
269C2×C8×C13—81no—
270C2×C8×C13—81no—
271C13×C4⋊C4C22⋊C411yescharacteristic
272C13×C4⋊C4C22⋊C411yescharacteristic
273C13×C4⋊C4C22⋊C411yescharacteristic
274C13×C4⋊C4C22⋊C411yescharacteristic
275C13×C22⋊C4C22⋊C411yescharacteristic
276C13×C22⋊C4C22⋊C411yescharacteristic
277C13×C22⋊C4C22⋊C411yescharacteristic
278C13×C22⋊C4C22⋊C411yescharacteristic
279C13×C22⋊C4C22⋊C411yescharacteristic
280C13×C22⋊C4C22⋊C411yescharacteristic
281C13×C22⋊C4C22⋊C411yescharacteristic
282C13×C22⋊C4C22⋊C411yescharacteristic
283C42×C13C2×D411yescharacteristic
284C42×C13C2×D411yescharacteristic
285C42×C13C2×D411yescharacteristic
286C42×C13C2×D411yescharacteristic
287C22⋊Dic13—21no—
288C22⋊Dic13—21no—
289C22⋊Dic13—21no—
290C22⋊Dic13—21no—
291C22⋊Dic13—21no—
292C22⋊Dic13—21no—
293C22⋊Dic13—21no—
294C22⋊Dic13—21no—
295#6103—21no—
296#6103—21no—
297#6103—21no—
298#6103—21no—
299#6103—21no—
300#6103—21no—
301#6103—21no—
302#6103—21no—
303#6103—21no—
304#6103—21no—
305#6103—21no—
306#6103—21no—
307#6103—21no—
308#6103—21no—
309#6103—21no—
310#6103—21no—
311C4⋊Dic13—21no—
312C4⋊Dic13—21no—
313#6101—21no—
314#6101—21no—
315#6101—21no—
316#6101—21no—
317#6101—21no—
318#6101—21no—
319#6101—21no—
320#6101—21no—
321#6101—21no—
322#6101—21no—
323#6101—21no—
324#6101—21no—
325C4×Dic13—21no—
326C4×Dic13—21no—
327C4×Dic13—21no—
328C4×Dic13—21no—
329#6099—81no—
330#6099—81no—
331C2×#1055—21no—
332C2×#1055—21no—
333C2×#1055—21no—
334C2×#1055—21no—
335C2×#1055—81no—
336C2×#1055—81no—
337C2×#551—131no—
338#2974—131no—
339#2974D1311yescharacteristic, complemented
340#1473—131no—
341#1473—131no—
342#1472—131no—
343#1472—131no—
344#1468—131no—
345#1468—131no—
346#1465—131no—
347#1464—131no—
348#1462—131no—
349#1459—131no—
350#1458—131no—
351C2×#323—131no—
352C23×C13—21no—
353C23×C13—21no—
354C23×C13—22no—
355C23×C13—21no—
356C23×C13—21no—
357C23×C13—41no—
358C23×C13—41no—
359C23×C13—41no—
360C23×C13C2×C22⋊C411yescharacteristic
361C23×C13C2×C22⋊C411yescharacteristic
362C23×C13C2×C22⋊C411yescharacteristic
363C23×C13C2×C22⋊C411yescharacteristic
364C23×C13C23×C411yescharacteristic
365C22×D13—21no—
366C22×D13—21no—
367C22×D13—21no—
368C22×D13—21no—
369C22×D13—21no—
370C22×D13—42no—
371C22×D13—42no—
372C22×D13—41no—
373C22×D13—41no—
374C22×D13—42no—
375C22×D13—42no—
376C22×D13—41no—
377C22×D13—41no—
378C22×D13—81no—
379C22×D13—81no—
380C22×D13—84no—
381C22×D13—84no—
382C22×D13#13112yes—
383D4×C13—22no—
384D4×C13—22no—
385D4×C13—41no—
386D4×C13—41no—
387C2×C4×C13—21no—
388C2×C4×C13—21no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—41no—
395C2×C4×C13—41no—
396C2×C4×C13—41no—
397C2×C4×C13—41no—
398C2×C4×C13—41no—
399C2×C4×C13—41no—
400C2×C4×C13—41no—
401C2×C4×C13C2×C22⋊C411yescharacteristic
402C2×C4×C13C2×C22⋊C411yescharacteristic
403C2×C4×C13C2×C22⋊C411yescharacteristic
404C2×C4×C13C2×C22⋊C411yescharacteristic
405C2×C4×C13C2×C22⋊C411yescharacteristic
406C2×C4×C13C2×C22⋊C411yescharacteristic
407C2×C4×C13C2×C22⋊C411yescharacteristic
408C2×C4×C13C2×C22⋊C411yescharacteristic
409C2×C4×C13C22×D411yescharacteristic
410C2×C4×C13C22×D411yescharacteristic
411C22⋊D13—42no—
412C22⋊D13—42no—
413C22⋊D13—81no—
414C22⋊D13—81no—
415C2×Dic13—21no—
416C2×Dic13—21no—
417C2×Dic13—21no—
418C2×Dic13—21no—
419C2×Dic13—21no—
420C2×Dic13—21no—
421C2×Dic13—21no—
422C2×Dic13—21no—
423C2×Dic13—21no—
424C2×Dic13—21no—
425C2×Dic13—42no—
426C2×Dic13—42no—
427C2×Dic13—41no—
428C2×Dic13—41no—
429C2×Dic13—41no—
430C2×Dic13—41no—
431C4×D13—42no—
432C4×D13—42no—
433C4×D13—81no—
434C4×D13—81no—
435Dic26—81no—
436Dic26—81no—
437C8×C13—41no—
438C8×C13—41no—
439C8×C13—41no—
440C8×C13—41no—
441#1055—41no—
442#1055—41no—
443#1055—41no—
444#1055—41no—
445#551—261no—
446#551—261no—
447#551—261no—
448#551—261no—
449#551—261no—
450#551—261no—
451#551—261no—
452#551—261no—
453C2×#126—131no—
454C2×#126—131no—
455C2×#124—131no—
456C2×#123—131no—
457C2×#123—131no—
458C2×#123—131no—
459C2×C22⋊Q8—131no—
460C2×C22⋊Q8—131no—
461C2×#120—131no—
462C2×C4×D4—131no—
463C2×C4×D4C2×D1311yescharacteristic
464C2×#117—131no—
465C2×#117—131no—
466C22×C22⋊C4—131no—
467C22×C22⋊C4—131no—
468#436—21no—
469#436—261no—
470#435—21no—
471#435—21no—
472#435—261no—
473#435—261no—
474C8×D4—21no—
475C8×D4—261no—
476#432—131no—
477#432C2×D1311yescharacteristic, complemented
478#431—131no—
479#431C2×D1311yescharacteristic, complemented
480#407—131no—
481#407—131no—
482#407C2×D1311yescharacteristic
483#407C2×D1311yescharacteristic, complemented
484C2×C22⋊C8—131no—
485C2×C22⋊C8—131no—
486C2×C22⋊C8C2×D1311yescharacteristic
487C2×C22⋊C8C2×D1311yescharacteristic, complemented
488#324—131no—
489#324—131no—
490#324—131no—
491#324—131no—
492#324—131no—
493#324—131no—
494#324—131no—
495#324—131no—
496#323—131no—
497#323—131no—
498#323—131no—
499#323—131no—
500#323—131no—
501#323—131no—
502#323—131no—
503#323—131no—
504C22×C13—21no—
505C22×C13—21no—
506C22×C13—21no—
507C22×C13—21no—
508C22×C13—21no—
509C22×C13—21no—
510C22×C13—21no—
511C22×C13—21no—
512C22×C13—21no—
513C22×C13—21no—
514C22×C13—21no—
515C22×C13—21no—
516C22×C13—21no—
517C22×C13—42no—
518C22×C13—42no—
519C22×C13—81no—
520C22×C13—81no—
521C22×C13#41312yes—
522C22×C13C22×C22⋊C411yescharacteristic
523C22×C13C2×#13111yescharacteristic
524C22×C13#56811yescharacteristic
525C2×D13—22no—
526C2×D13—42no—
527C2×D13—41no—
528C2×D13—41no—
529C2×D13—42no—
530C2×D13—41no—
531C2×D13—41no—
532C2×D13—41no—
533C2×D13—84no—
534C2×D13—84no—
535C2×D13—81no—
536C2×D13—81no—
537C4×C13—21no—
538C4×C13—21no—
539C4×C13—21no—
540C4×C13—21no—
541C4×C13—21no—
542C4×C13—21no—
543C4×C13—21no—
544C4×C13—21no—
545C4×C13—21no—
546C4×C13—21no—
547Dic13—41no—
548Dic13—41no—
549Dic13—41no—
550Dic13—41no—
551Dic13—41no—
552Dic13—41no—
553C25—131no—
554C22×Q8—131no—
555C22×D4—131no—
556C22×D4—131no—
557C22×D4C4×D1311yescharacteristic
558C23×C4—131no—
559C23×C4—131no—
560C23×C4—131no—
561C23×C4C22×D1311yescharacteristic
562C23×C4C22×D1311yescharacteristic
563C2×M16—21no—
564C2×M16—21no—
565C2×M16—261no—
566C2×M16—261no—
567C22×C8—21no—
568C22×C8—21no—
569C22×C8—261no—
570C22×C8—261no—
571#126—261no—
572#126—261no—
573#126—261no—
574#126—261no—
575#126—261no—
576#126—261no—
577#126—261no—
578#126—261no—
579#124—261no—
580#124—261no—
581#124—261no—
582#124—261no—
583#123—261no—
584#123—261no—
585#123—261no—
586#123—261no—
587#123—261no—
588#123—261no—
589#123—261no—
590#123—261no—
591#123—261no—
592#123—261no—
593#123—261no—
594#123—261no—
595C22⋊Q8—261no—
596C22⋊Q8—261no—
597C22⋊Q8—261no—
598C22⋊Q8—261no—
599C22⋊Q8—261no—
600C22⋊Q8—261no—
601C22⋊Q8—261no—
602C22⋊Q8—261no—
603#120—261no—
604#120—261no—
605#120—261no—
606#120—261no—
607C4×D4—261no—
608C4×D4—261no—
609C4×D4—261no—
610C4×D4—261no—
611C4×D4D5211yescharacteristic
612C4×D4D5211yescharacteristic
613C4×D4D5211yescharacteristic
614C4×D4D5211yescharacteristic
615C4×D4C22⋊D1311yescharacteristic
616C4×D4C22⋊D1311yescharacteristic
617C4×D4C22⋊D1311yescharacteristic
618C4×D4C22⋊D1311yescharacteristic
619#117—261no—
620#117—261no—
621#117—261no—
622#117—261no—
623#117—261no—
624#117—261no—
625#117—261no—
626#117—261no—
627C2×C4⋊C4—131no—
628C2×C4⋊C4—131no—
629C2×C4⋊C4—131no—
630C2×C4⋊C4—131no—
631C2×C4⋊C4—131no—
632C2×C4⋊C4—131no—
633C2×C4⋊C4—131no—
634C2×C4⋊C4C4×D1311yescharacteristic
635C2×C22⋊C4—131no—
636C2×C22⋊C4—131no—
637C2×C22⋊C4—131no—
638C2×C22⋊C4—131no—
639C2×C22⋊C4—131no—
640C2×C22⋊C4—131no—
641C2×C22⋊C4—131no—
642C2×C22⋊C4—131no—
643C2×C22⋊C4—131no—
644C2×C22⋊C4—131no—
645C2×C22⋊C4—131no—
646C2×C22⋊C4—131no—
647C2×C22⋊C4—261no—
648C2×C22⋊C4—261no—
649C2×C22⋊C4—261no—
650C2×C22⋊C4—261no—
651C2×C22⋊C4—261no—
652C2×C22⋊C4—261no—
653C2×C22⋊C4—261no—
654C2×C22⋊C4—261no—
655C2×C22⋊C4C4×D1311yescharacteristic
656C2×C22⋊C4C4×D1311yescharacteristic
657C2×C42—131no—
658C2×C42—131no—
659C2×C42C22×D1311yescharacteristic
660C4⋊C8—21no—
661C4⋊C8—21no—
662C4⋊C8—261no—
663C4⋊C8—261no—
664C22⋊C8—21no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8—21no—
668C22⋊C8—131no—
669C22⋊C8—131no—
670C22⋊C8—131no—
671C22⋊C8—131no—
672C22⋊C8—261no—
673C22⋊C8—261no—
674C22⋊C8—261no—
675C22⋊C8—261no—
676C22⋊C8C22×D1311yescharacteristic
677C22⋊C8C22×D1311yescharacteristic
678C22⋊C8C22×D1311yescharacteristic
679C22⋊C8C22×D1311yescharacteristic
680#97—21no—
681#97—261no—
682C4×C8—21no—
683C4×C8—261no—
684C2×C13—21no—
685C2×C13—21no—
686C2×C13—22no—
687C2×C13—41no—
688C2×C13—41no—
689C2×C13—41no—
690C2×C13#288011yescharacteristic
691C2×C13#288311yescharacteristic
692C2×C13C2×#41311yescharacteristic
693D13—42no—
694D13—81no—
695C24—131no—
696C24—131no—
697C24—262no—
698C24—261no—
699C24—261no—
700C24—521no—
701C24—522no—
702C24—1041no—
703C24C2×C4×D1311yescharacteristic
704C24C2×C4×D1311yescharacteristic
705C2×Q8—261no—
706C2×Q8—261no—
707C2×Q8—1041no—
708C2×D4—42no—
709C2×D4—262no—
710C2×D4—261no—
711C2×D4—261no—
712C2×D4—261no—
713C2×D4—261no—
714C2×D4—521no—
715C2×D4—1041no—
716C2×D4#610311yescharacteristic
717C2×D4#610311yescharacteristic
718C2×D4#610311yescharacteristic
719C2×D4#610311yescharacteristic
720C22×C4—81no—
721C22×C4—81no—
722C22×C4—131no—
723C22×C4—131no—
724C22×C4—131no—
725C22×C4—131no—
726C22×C4—131no—
727C22×C4—131no—
728C22×C4—262no—
729C22×C4—261no—
730C22×C4—261no—
731C22×C4—261no—
732C22×C4—261no—
733C22×C4—261no—
734C22×C4—261no—
735C22×C4—521no—
736C22×C4—522no—
737C22×C4—1041no—
738C22×C4C2×C4×D1311yescharacteristic
739C22×C4C2×C4×D1311yescharacteristic
740C22×C4C2×C4×D1311yescharacteristic
741C22×C4C2×C4×D1311yescharacteristic
742C22×C4C2×D5211yescharacteristic
743C22×C4C2×D5211yescharacteristic
744C22×C4C2×D5211yescharacteristic
745C22×C4C2×D5211yescharacteristic
746C22×C4C2×C22⋊D1311yescharacteristic
747C22×C4C2×C22⋊D1311yescharacteristic
748C22×C4C2×C22⋊D1311yescharacteristic
749C22×C4C2×C22⋊D1311yescharacteristic
750C22×C4C23×D1311yescharacteristic
751M16—81no—
752M16—81no—
753M16—1041no—
754M16—1041no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—81no—
760C2×C8—81no—
761C2×C8—261no—
762C2×C8—261no—
763C2×C8—261no—
764C2×C8—261no—
765C2×C8—1041no—
766C2×C8—1041no—
767C4⋊C4—261no—
768C4⋊C4—261no—
769C4⋊C4—261no—
770C4⋊C4—261no—
771C4⋊C4—261no—
772C4⋊C4—261no—
773C4⋊C4—261no—
774C4⋊C4—261no—
775C4⋊C4—261no—
776C4⋊C4—261no—
777C4⋊C4—261no—
778C4⋊C4—261no—
779C4⋊C4—261no—
780C4⋊C4—261no—
781C4⋊C4#610311yescharacteristic
782C4⋊C4#610311yescharacteristic
783C4⋊C4#610311yescharacteristic
784C4⋊C4#610311yescharacteristic
785C22⋊C4—261no—
786C22⋊C4—261no—
787C22⋊C4—261no—
788C22⋊C4—261no—
789C22⋊C4—261no—
790C22⋊C4—261no—
791C22⋊C4—261no—
792C22⋊C4—261no—
793C22⋊C4—261no—
794C22⋊C4—261no—
795C22⋊C4—261no—
796C22⋊C4—261no—
797C22⋊C4—261no—
798C22⋊C4—261no—
799C22⋊C4—261no—
800C22⋊C4—261no—
801C22⋊C4—261no—
802C22⋊C4—261no—
803C22⋊C4—261no—
804C22⋊C4—261no—
805C22⋊C4—261no—
806C22⋊C4—261no—
807C22⋊C4—261no—
808C22⋊C4—261no—
809C22⋊C4#610311yescharacteristic
810C22⋊C4#610311yescharacteristic
811C22⋊C4#610311yescharacteristic
812C22⋊C4#610311yescharacteristic
813C22⋊C4#610311yescharacteristic
814C22⋊C4#610311yescharacteristic
815C22⋊C4#610311yescharacteristic
816C22⋊C4#610311yescharacteristic
817C42—261no—
818C42—261no—
819C42—261no—
820C42—261no—
821C42C2×D5211yescharacteristic
822C42C2×D5211yescharacteristic
823C42C2×C22⋊D1311yescharacteristic
824C42C2×C22⋊D1311yescharacteristic
825C13#1742211yescharacteristic, complemented, Sylow
826C23—21no—
827C23—21no—
828C23—22no—
829C23—21no—
830C23—21no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—132no—
835C23—261no—
836C23—261no—
837C23—261no—
838C23—261no—
839C23—261no—
840C23—522no—
841C23—522no—
842C23—521no—
843C23—521no—
844C23—522no—
845C23—521no—
846C23—521no—
847C23—522no—
848C23—1041no—
849C23—1041no—
850C23—1044no—
851C23—1044no—
852C23C2×#610311yescharacteristic
853C23C2×#610311yescharacteristic
854C23C2×#610311yescharacteristic
855C23C2×#610311yescharacteristic
856C23C22×C4×D1311yescharacteristic
857Q8—1041no—
858Q8—1041no—
859D4—22no—
860D4—22no—
861D4—41no—
862D4—41no—
863D4—522no—
864D4—522no—
865D4—1041no—
866D4—1041no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—261no—
882C2×C4—261no—
883C2×C4—261no—
884C2×C4—261no—
885C2×C4—261no—
886C2×C4—261no—
887C2×C4—261no—
888C2×C4—261no—
889C2×C4—261no—
890C2×C4—261no—
891C2×C4—522no—
892C2×C4—522no—
893C2×C4—522no—
894C2×C4—522no—
895C2×C4—521no—
896C2×C4—521no—
897C2×C4—521no—
898C2×C4—521no—
899C2×C4—1041no—
900C2×C4—1041no—
901C2×C4C2×#610311yescharacteristic
902C2×C4C2×#610311yescharacteristic
903C2×C4C2×#610311yescharacteristic
904C2×C4C2×#610311yescharacteristic
905C2×C4C2×#610311yescharacteristic
906C2×C4C2×#610311yescharacteristic
907C2×C4C2×#610311yescharacteristic
908C2×C4C2×#610311yescharacteristic
909C2×C4C22×D5211yescharacteristic
910C2×C4C22×C22⋊D1311yescharacteristic
911C8—41no—
912C8—41no—
913C8—41no—
914C8—41no—
915C8—521no—
916C8—521no—
917C8—521no—
918C8—521no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—21no—
926C22—21no—
927C22—21no—
928C22—21no—
929C22—21no—
930C22—21no—
931C22—21no—
932C22—42no—
933C22—42no—
934C22—81no—
935C22—81no—
936C22—262no—
937C22—522no—
938C22—522no—
939C22—521no—
940C22—521no—
941C22—521no—
942C22—521no—
943C22—521no—
944C22—1044no—
945C22—1041no—
946C22—1041no—
947C22—1044no—
948C22#1171879312yes—
949C22D13×#13111yescharacteristic
950C22#1171945511yescharacteristic
951C22C22×#610311yescharacteristic
952C4—21no—
953C4—21no—
954C4—21no—
955C4—21no—
956C4—21no—
957C4—21no—
958C4—21no—
959C4—21no—
960C4—21no—
961C4—21no—
962C4—521no—
963C4—521no—
964C4—521no—
965C4—521no—
966C4—521no—
967C4—521no—
968C2—21no—
969C2—21no—
970C2—22no—
971C2—41no—
972C2—41no—
973C2—41no—
974C2—522no—
975C2—1041no—
976C2#1312328311yescharacteristic
977C2#1312329611yescharacteristic
978C2C2×#1171879311yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC23×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2974C2
socleC22×C13C22×C22⋊C4
prime radicalC2×#88191C4
cosocleC22×C4×C13C24
hypercenter#2974D13
hypocenterC13#17422
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #13123871C2semidirect
3. #13113206C2semidirect
4. #13113203C2semidirect
5. #13113201C2semidirect
6. #13113199C2semidirect
7. #13113185C2semidirect
8. #13113182C2semidirect
9. #13113172C2semidirect
10. #13113168C2semidirect
11. #13113162C2semidirect
12. #13113152C2semidirect
13. #13113148C2semidirect
14. C2×#11718060C2semidirect
15. C13×#2974C2semidirect
43. C13×#432C22semidirect
44. C13×#431C22semidirect
46. C13×#407C22semidirect
48. C2×C13×C22⋊C8C22semidirect
50. #11718868C22semidirect
52. C2×C22⋊#1055C22semidirect
57. #11718587C22semidirect
58. #11718586C22semidirect
59. #11718061C22semidirect
60. #11718061C22semidirect
61. #11718061C22semidirect
62. #11718061C22semidirect
63. #11718061C22semidirect
64. #11718061C22semidirect
65. #11718061C22semidirect
66. #11718061C22semidirect
339. #2974D13semidirect
477. #432C2×D13semidirect
479. #431C2×D13semidirect
483. #407C2×D13semidirect
487. C2×C22⋊C8C2×D13semidirect
825. C13#17422semidirect

Maximal subgroups

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

subgroupindex
C2×#117192612
#131238712
#131132062
#131132032
#131132012
#131131992
#131131852
#131131822
#131131722
#131131682
#131131622
#131131522
#131131482
C2×#117180602
C13×#29742
#1742213