Finite Group Databasebeta

← #15878992

Subgroups — #15878992

Order 3328.

1424 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#6129C211yesmaximal, characteristic
2C2×#11718672C211yesmaximal, characteristic, complemented
3#13115776C211yesmaximal, characteristic, complemented
4#13115775C211yesmaximal, characteristic, complemented
5#13115133C211yesmaximal, characteristic, complemented
6#13115131C211yesmaximal, characteristic, complemented
7#13115128C211yesmaximal, characteristic, complemented
8#13115126C211yesmaximal, characteristic, complemented
9#13114902C211yesmaximal, characteristic, complemented
10#13114902C211yesmaximal, characteristic, complemented
11#13114813C211yesmaximal, characteristic, complemented
12#13114599C211yesmaximal, characteristic, complemented
13#13114529C211yesmaximal, characteristic, complemented
14C2×#11718142C211yesmaximal, characteristic, complemented
15C2×C13×#435C211yesmaximal, characteristic, complemented
16C22×#6129C411yescharacteristic
17C22×C13×M16C2211yescharacteristic
18C23×C8×C13C2211yescharacteristic
19C2×C4×D4×C13C2211yescharacteristic
20C2×D4×Dic13C411yescharacteristic
21C2×C4×C22⋊D13C2211yescharacteristic
22C2×C4×C22⋊D13C2211yescharacteristic
23C22×C4×Dic13C2211yescharacteristic
24C22×C4×Dic13C2211yescharacteristic
25C22×#6099C2211yescharacteristic
26C23×#1055C2211yescharacteristic
27C4×#6129—24no—
28C4×#6129—24no—
29C2×#88146C411yescharacteristic
30C2×#88141C411yescharacteristic
31C2×#88135C411yescharacteristic
32C2×#88135C411yescharacteristic
33C2×#88131C411yescharacteristic
34C2×#88131C411yescharacteristic
35C2×C42×D13C2211yescharacteristic
36C2×C4×Dic26C2211yescharacteristic
37C13×#435—24no—
38C2×C13×C4⋊C8C2211yescharacteristic
39C2×C13×C22⋊C8C2211yescharacteristic
40C2×C13×C22⋊C8C2211yescharacteristic
41C2×C13×#97C2211yescharacteristic
42C2×C22⋊#1055C2211yescharacteristic
43C2×C22⋊#1055C2211yescharacteristic
44C2×#88060C2211yescharacteristic
45C2×#88060C2211yescharacteristic
46C2×#88060C2211yescharacteristic
47C2×#88060C2211yescharacteristic
48#11718672—24no—
49C2×C4⋊#1055C2211yescharacteristic
50C2×#88043C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718142C2211yescharacteristic
60#11718142C2211yescharacteristic
61#11718142C2211yescharacteristic
62#11718142C2211yescharacteristic
63C22×D4×C13C2×C411yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C22×C22⋊D13C2×C411yescharacteristic
67C22×C22⋊D13C2×C411yescharacteristic
68C23×Dic13C2×C411yescharacteristic
69C23×Dic13C2×C411yescharacteristic
70C23×Dic13C2×C411yescharacteristic
71C23×Dic13C2×C411yescharacteristic
72C2×#6129—24no—
73C2×#6129—24no—
74C2×#6129—24no—
75C22×C4×D13C2×C411yescharacteristic
76C22×C4×D13C2×C411yescharacteristic
77C22×C4×D13C2311yescharacteristic
78C22×Dic26C2×C411yescharacteristic
79C2×C13×M16—22no—
80C2×C13×M16—22no—
81C2×C13×M16—41no—
82C22×C8×C13—22no—
83C22×C8×C13—22no—
84C22×C8×C13—41no—
85C22×C8×C13C2311yescharacteristic
86C22×C8×C13C2311yescharacteristic
87C22×C8×C13C2311yescharacteristic
88C22×C8×C13C2311yescharacteristic
89C4×D4×C13D414yes—
90C4×D4×C13D414yes—
91C2×C13×C4⋊C4C2×C411yescharacteristic
92C2×C13×C22⋊C4C2×C411yescharacteristic
93C2×C13×C22⋊C4C2×C411yescharacteristic
94C2×C42×C13C2311yescharacteristic
95C2×C22⋊Dic13C2×C411yescharacteristic
96C2×C22⋊Dic13C2×C411yescharacteristic
97D4×Dic13—24no—
98C4×C22⋊D13—22no—
99C4×C22⋊D13—22no—
100C4×C22⋊D13—22no—
101C4×C22⋊D13—22no—
102C2×#6103C2×C411yescharacteristic
103C2×#6103C2×C411yescharacteristic
104C2×C4⋊Dic13C2×C411yescharacteristic
105C2×#6101C2×C411yescharacteristic
106C2×#6101C2×C411yescharacteristic
107C2×#6101C2×C411yescharacteristic
108C2×#6101C2×C411yescharacteristic
109C2×C4×Dic13—22no—
110C2×C4×Dic13—22no—
111C2×C4×Dic13—22no—
112C2×C4×Dic13—22no—
113C2×C4×Dic13C2×C411yescharacteristic
114C2×C4×Dic13C2×C411yescharacteristic
115C2×C4×Dic13C2×C411yescharacteristic
116C2×C4×Dic13C2×C411yescharacteristic
117C2×C4×Dic13C2×C411yescharacteristic
118C2×C4×Dic13C2×C411yescharacteristic
119C2×C4×Dic13C2311yescharacteristic
120C2×C4×Dic13C2311yescharacteristic
121C2×C4×Dic13C2311yescharacteristic
122C2×#6099—22no—
123C2×#6099—22no—
124C2×#6099—41no—
125C22×#1055—22no—
126C22×#1055—22no—
127C22×#1055—41no—
128C22×#1055C2311yescharacteristic
129C22×#1055C2311yescharacteristic
130C22×#1055C2311yescharacteristic
131C22×#1055C2311yescharacteristic
132#88146—24no—
133#88141—24no—
134#88135—24no—
135#88135—24no—
136#88131—24no—
137#88131—24no—
138C42×D13—22no—
139C42×D13—22no—
140C4×Dic26—22no—
141C4×Dic26—22no—
142C13×C4⋊C8—22no—
143C13×C22⋊C8—22no—
144C13×C22⋊C8—22no—
145C13×#97—22no—
146C22⋊#1055—22no—
147C22⋊#1055—22no—
148#88060—22no—
149#88060—22no—
150#88060—41no—
151#88060—41no—
152C4⋊#1055—22no—
153#88043—22no—
154#22471—131nomaximal, Sylow
155C24×C13C22×C411yescharacteristic
156C24×C13C22×C411yescharacteristic
157C23×D13C22×C411yescharacteristic
158C2×D4×C13—22no—
159C2×D4×C13—22no—
160C2×D4×C13C22⋊C414yes—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13C22×C411yescharacteristic
170C22×C4×C13C22×C411yescharacteristic
171C22×C4×C13C22×C411yescharacteristic
172C22×C4×C13C22×C411yescharacteristic
173C22×C4×C13C2×D412yes—
174C22×C4×C13C2×D412yes—
175C22×C4×C13C2×D412yes—
176C22×C4×C13C2×D412yes—
177C22×C4×C13C2411yescharacteristic
178C2×C22⋊D13—22no—
179C2×C22⋊D13—22no—
180C2×C22⋊D13—22no—
181C2×C22⋊D13—22no—
182C2×C22⋊D13—22no—
183C2×C22⋊D13M1614yescomplemented
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—41no—
194C22×Dic13—41no—
195C22×Dic13M1614yescomplemented
196C22×Dic13C22×C411yescharacteristic
197C22×Dic13C22×C411yescharacteristic
198C22×Dic13C22×C411yescharacteristic
199C22×Dic13C22×C411yescharacteristic
200C22×Dic13C22×C411yescharacteristic
201C22×Dic13C22×C411yescharacteristic
202C22×Dic13C22×C411yescharacteristic
203#6129—232no—
204C2×C4×D13—22no—
205C2×C4×D13—22no—
206C2×C4×D13—22no—
207C2×C4×D13—22no—
208C2×C4×D13—21no—
209C2×C4×D13—21no—
210C2×C4×D13—21no—
211C2×C4×D13—21no—
212C2×C4×D13—21no—
213C2×C4×D13—21no—
214C2×C4×D13—22no—
215C2×C4×D13—41no—
216C2×Dic26—22no—
217C2×Dic26—22no—
218C2×Dic26—22no—
219C13×M16—44no—
220C2×C8×C13—21no—
221C2×C8×C13—21no—
222C2×C8×C13—21no—
223C2×C8×C13—21no—
224C2×C8×C13—21no—
225C2×C8×C13—21no—
226C2×C8×C13—21no—
227C2×C8×C13—21no—
228C2×C8×C13—21no—
229C2×C8×C13—21no—
230C2×C8×C13—21no—
231C2×C8×C13—44no—
232C2×C8×C13#4112yescomplemented
233C13×C4⋊C4C22⋊C414yes—
234C13×C22⋊C4C22⋊C414yes—
235C13×C22⋊C4C22⋊C414yes—
236C42×C13C2×D412yes—
237C42×C13C2×D412yes—
238C22⋊Dic13—22no—
239C22⋊Dic13—22no—
240#6103—22no—
241#6103—22no—
242C4⋊Dic13—22no—
243#6101—22no—
244#6101—22no—
245#6101—22no—
246#6101—22no—
247C4×Dic13—22no—
248C4×Dic13—22no—
249C4×Dic13—22no—
250C4×Dic13—22no—
251C4×Dic13—22no—
252C4×Dic13—22no—
253C4×Dic13—21no—
254C4×Dic13—21no—
255C4×Dic13—21no—
256C4×Dic13—21no—
257C4×Dic13—21no—
258C4×Dic13—21no—
259#6099—44no—
260C2×#1055—21no—
261C2×#1055—21no—
262C2×#1055—21no—
263C2×#1055—21no—
264C2×#1055—21no—
265C2×#1055—21no—
266C2×#1055—21no—
267C2×#1055—21no—
268C2×#1055—21no—
269C2×#1055—21no—
270C2×#1055—21no—
271C2×#1055—44no—
272C2×#1055#4112yescomplemented
273C2×C4×#41—131no—
274C2×#435—131no—
275C2×#435D1311yescharacteristic, complemented
276#1985—131no—
277#1985—131no—
278#1870—131no—
279#1870—131no—
280#1869—131no—
281#1869—131no—
282#1817—131no—
283#1817—131no—
284#1797—131no—
285#1749—131no—
286#1728—131no—
287C2×#336—131no—
288C23×C13—21no—
289C23×C13—21no—
290C23×C13—21no—
291C23×C13—21no—
292C23×C13—21no—
293C23×C13—21no—
294C23×C13—21no—
295C23×C13—21no—
296C23×C13—21no—
297C23×C13—21no—
298C23×C13C2×C22⋊C412yes—
299C23×C13C2×C22⋊C412yes—
300C23×C13C2×M1612yes—
301C23×C13C2×M1612yes—
302C23×C13C23×C411yescharacteristic
303C22×D13—21no—
304C22×D13—21no—
305C22×D13—21no—
306C22×D13—21no—
307C22×D13—21no—
308C22×D13—21no—
309C22×D13C2×M1612yes—
310D4×C13—28no—
311C2×C4×C13—21no—
312C2×C4×C13—21no—
313C2×C4×C13—21no—
314C2×C4×C13—21no—
315C2×C4×C13—21no—
316C2×C4×C13—21no—
317C2×C4×C13—21no—
318C2×C4×C13—21no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13C2×C22⋊C412yes—
328C2×C4×C13C2×C22⋊C412yes—
329C2×C4×C13C2×C22⋊C412yes—
330C2×C4×C13C2×C22⋊C412yes—
331C2×C4×C13C22×D411yescharacteristic
332C2×C4×C13C22×D411yescharacteristic
333C2×C4×C13C2×#4111yescharacteristic
334C2×C4×C13C2×#4111yescharacteristic
335C2×C4×C13H(5,𝔽2)11yescharacteristic
336C2×C4×C132−1+411yescharacteristic
337C22⋊D13—28no—
338C22⋊D13—28no—
339C2×Dic13—28no—
340C2×Dic13—21no—
341C2×Dic13—21no—
342C2×Dic13—21no—
343C2×Dic13—21no—
344C2×Dic13—21no—
345C2×Dic13—21no—
346C2×Dic13—21no—
347C2×Dic13—21no—
348C2×Dic13—28no—
349C2×Dic13—21no—
350C2×Dic13—21no—
351C2×Dic13—21no—
352C2×Dic13—21no—
353C2×Dic13—21no—
354C2×Dic13—21no—
355C2×Dic13—21no—
356C2×Dic13—21no—
357C2×Dic13—21no—
358C2×Dic13—44no—
359C2×Dic13—44no—
360C2×Dic13C2×M1612yes—
361C2×Dic13C2×M1612yes—
362C2×Dic13C2×M1612yes—
363C2×Dic13#13112yes—
364C4×D13—28no—
365C4×D13—44no—
366C4×D13—41no—
367C4×D13—41no—
368C4×D13—41no—
369C4×D13—41no—
370Dic26—28no—
371C8×C13—22no—
372C8×C13—41no—
373C8×C13—41no—
374C8×C13—41no—
375#1055—22no—
376#1055—41no—
377#1055—41no—
378#1055—41no—
379C22×#41—131no—
380C22×M16—131no—
381C22×M16C2×D1311yescharacteristic
382C23×C8—131no—
383C23×C8C2×D1311yescharacteristic
384C4×#41—264no—
385C4×#41—264no—
386C2×C4×Q8—131no—
387C2×C4×Q8—131no—
388C2×C4×D4—131no—
389C2×C4×D4—131no—
390C2×C4×D4—131no—
391C2×C4×D4—131no—
392C2×C4×D4—131no—
393C2×C4×D4C2×D1311yescharacteristic
394C2×#117—131no—
395C2×#117—131no—
396C2×#117—131no—
397C22×C42—131no—
398C22×C42—131no—
399C22×C42—131no—
400#435—24no—
401#435—264no—
402C2×C4⋊C8—131no—
403C2×C4⋊C8C2×D1311yescharacteristic
404C2×C22⋊C8—131no—
405C2×C22⋊C8—131no—
406C2×C22⋊C8—131no—
407C2×C22⋊C8—131no—
408C2×C22⋊C8—131no—
409C2×C22⋊C8—131no—
410C2×C22⋊C8C2×D1311yescharacteristic
411C2×C22⋊C8C2×D1311yescharacteristic
412C2×#97—131no—
413C2×#97C2×D1311yescharacteristic
414#336—131no—
415#336—131no—
416#336—131no—
417#336—131no—
418#336—131no—
419#336—131no—
420#336—131no—
421#336—131no—
422#336—131no—
423#336—131no—
424#336—131no—
425#336—131no—
426C22×C13—22no—
427C22×C13—22no—
428C22×C13—22no—
429C22×C13—22no—
430C22×C13—22no—
431C22×C13—22no—
432C22×C13—22no—
433C22×C13—22no—
434C22×C13—22no—
435C22×C13—41no—
436C22×C13—41no—
437C22×C13—41no—
438C22×C13—41no—
439C22×C13#40714yes—
440C22×C13C22×C22⋊C411yescharacteristic
441C22×C13C4×#4111yescharacteristic
442C22×C13#52011yescharacteristic
443C22×C13C22×M1611yescharacteristic
444C22×C13C22×M1611yescharacteristic
445C22×C13C2×#13111yescharacteristic
446C22×C13#56811yescharacteristic
447C2×D13—22no—
448C2×D13—22no—
449C2×D13—22no—
450C2×D13—41no—
451C2×D13—41no—
452C2×D13—41no—
453C2×D13—41no—
454C4×C13—22no—
455C4×C13—22no—
456C4×C13—22no—
457C4×C13—22no—
458C4×C13#54611yescharacteristic
459C4×C13#54611yescharacteristic
460C4×C13#54711yescharacteristic
461C4×C13#54711yescharacteristic
462Dic13—22no—
463Dic13—22no—
464Dic13—22no—
465Dic13—22no—
466Dic13—41no—
467Dic13—41no—
468Dic13—41no—
469C2×#41—264no—
470C2×#41—264no—
471C2×#41—264no—
472C22×Q8—131no—
473C22×D4—131no—
474C22×D4—131no—
475C22×D4C4×D1311yescharacteristic
476C23×C4—131no—
477C23×C4—131no—
478C23×C4—131no—
479C23×C4—131no—
480C23×C4—131no—
481C23×C4—131no—
482C23×C4—131no—
483C23×C4C22×D1311yescharacteristic
484C23×C4C22×D1311yescharacteristic
485C2×M16—22no—
486C2×M16—22no—
487C2×M16—41no—
488C2×M16—262no—
489C2×M16—262no—
490C2×M16—521no—
491C22×C8—22no—
492C22×C8—22no—
493C22×C8—41no—
494C22×C8—131no—
495C22×C8—131no—
496C22×C8—131no—
497C22×C8—131no—
498C22×C8—262no—
499C22×C8—262no—
500C22×C8—521no—
501C22×C8C22×D1311yescharacteristic
502C22×C8C22×D1311yescharacteristic
503C22×C8C22×D1311yescharacteristic
504C22×C8C22×D1311yescharacteristic
505C4×Q8—264no—
506C4×Q8—262no—
507C4×Q8—262no—
508C4×D4—264no—
509C4×D4—262no—
510C4×D4—262no—
511C4×D4—262no—
512C4×D4—262no—
513C4×D4—264no—
514C4×D4—264no—
515C4×D4D5214yes—
516C4×D4C22⋊D1314yes—
517#117—264no—
518#117—264no—
519#117—264no—
520C2×C4⋊C4—131no—
521C2×C4⋊C4—131no—
522C2×C4⋊C4—131no—
523C2×C4⋊C4—131no—
524C2×C4⋊C4—131no—
525C2×C4⋊C4C4×D1311yescharacteristic
526C2×C22⋊C4—131no—
527C2×C22⋊C4—131no—
528C2×C22⋊C4—131no—
529C2×C22⋊C4—131no—
530C2×C22⋊C4C4×D1311yescharacteristic
531C2×C22⋊C4C4×D1311yescharacteristic
532C2×C42—131no—
533C2×C42—131no—
534C2×C42—131no—
535C2×C42—131no—
536C2×C42—131no—
537C2×C42—131no—
538C2×C42—131no—
539C2×C42—131no—
540C2×C42—131no—
541C2×C42—262no—
542C2×C42—262no—
543C2×C42—262no—
544C2×C42—262no—
545C2×C42—262no—
546C2×C42—262no—
547C2×C42C22×D1311yescharacteristic
548C4⋊C8—22no—
549C4⋊C8—262no—
550C22⋊C8—22no—
551C22⋊C8—22no—
552C22⋊C8—262no—
553C22⋊C8—262no—
554C22⋊C8—262no—
555C22⋊C8—262no—
556C22⋊C8—521no—
557C22⋊C8—521no—
558#97—22no—
559#97—262no—
560C2×C13—24no—
561C2×C13—42no—
562C2×C13#233911yescharacteristic
563C2×C13C2×#40711yescharacteristic
564C2×C13#288011yescharacteristic
565C2×C13#296511yescharacteristic
566C2×C13#297011yescharacteristic
567C2×C13#298911yescharacteristic
568C2×C13#299011yescharacteristic
569D13—42no—
570C24—131no—
571C24C2×C4×D1311yescharacteristic
572C24C2×C4×D1311yescharacteristic
573#41—2632no—
574C2×Q8—262no—
575C2×Q8—262no—
576C2×Q8—262no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—134no—
580C2×D4—262no—
581C2×D4—262no—
582C2×D4—262no—
583C2×D4—262no—
584C2×D4—262no—
585C2×D4#610314yes—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—134no—
595C22×C4—131no—
596C22×C4—131no—
597C22×C4—131no—
598C22×C4—131no—
599C22×C4—131no—
600C22×C4—131no—
601C22×C4—131no—
602C22×C4—262no—
603C22×C4—262no—
604C22×C4—262no—
605C22×C4—262no—
606C22×C4—262no—
607C22×C4—262no—
608C22×C4—262no—
609C22×C4—262no—
610C22×C4—262no—
611C22×C4—262no—
612C22×C4—262no—
613C22×C4—262no—
614C22×C4—262no—
615C22×C4—262no—
616C22×C4—261no—
617C22×C4—261no—
618C22×C4—261no—
619C22×C4—261no—
620C22×C4—261no—
621C22×C4—261no—
622C22×C4—521no—
623C22×C4—521no—
624C22×C4—521no—
625C22×C4C2×C4×D1311yescharacteristic
626C22×C4C2×C4×D1311yescharacteristic
627C22×C4C2×C4×D1311yescharacteristic
628C22×C4C2×C4×D1311yescharacteristic
629C22×C4C2×D5212yes—
630C22×C4C2×D5212yes—
631C22×C4C2×C22⋊D1312yes—
632C22×C4C2×C22⋊D1312yes—
633C22×C4C23×D1311yescharacteristic
634M16—44no—
635M16—524no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—44no—
648C2×C8—132no—
649C2×C8—261no—
650C2×C8—261no—
651C2×C8—261no—
652C2×C8—261no—
653C2×C8—261no—
654C2×C8—261no—
655C2×C8—261no—
656C2×C8—261no—
657C2×C8—261no—
658C2×C8—261no—
659C2×C8—261no—
660C2×C8—524no—
661C2×C8#612912yescomplemented
662C4⋊C4—262no—
663C4⋊C4—262no—
664C4⋊C4—262no—
665C4⋊C4—262no—
666C4⋊C4—262no—
667C4⋊C4#610314yes—
668C22⋊C4—262no—
669C22⋊C4—262no—
670C22⋊C4—262no—
671C22⋊C4—262no—
672C22⋊C4#610314yes—
673C22⋊C4#610314yes—
674C42—262no—
675C42—262no—
676C42—262no—
677C42—262no—
678C42—262no—
679C42—262no—
680C42—261no—
681C42—261no—
682C42—261no—
683C42—261no—
684C42—261no—
685C42—261no—
686C42C2×D5212yes—
687C42C2×C22⋊D1312yes—
688C13#2247111yescharacteristic, complemented, Sylow
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—132no—
700C23—261no—
701C23—261no—
702C23—261no—
703C23—261no—
704C23—261no—
705C23—261no—
706C23M16×D1312yes—
707C23M16×D1312yes—
708C23C2×#610312yes—
709C23C2×#610312yes—
710C23C22×C4×D1311yescharacteristic
711Q8—268no—
712D4—28no—
713D4—268no—
714D4—268no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—132no—
732C2×C4—132no—
733C2×C4—132no—
734C2×C4—132no—
735C2×C4—268no—
736C2×C4—268no—
737C2×C4—261no—
738C2×C4—261no—
739C2×C4—261no—
740C2×C4—261no—
741C2×C4—261no—
742C2×C4—261no—
743C2×C4—261no—
744C2×C4—261no—
745C2×C4—268no—
746C2×C4—261no—
747C2×C4—261no—
748C2×C4—261no—
749C2×C4—261no—
750C2×C4—261no—
751C2×C4—261no—
752C2×C4—261no—
753C2×C4—261no—
754C2×C4—261no—
755C2×C4—524no—
756C2×C4—524no—
757C2×C4—524no—
758C2×C4—521no—
759C2×C4—521no—
760C2×C4—521no—
761C2×C4—521no—
762C2×C4C2×#610312yes—
763C2×C4C2×#610312yes—
764C2×C4C2×#610312yes—
765C2×C4C2×#610312yes—
766C2×C4C22×D5211yescharacteristic
767C2×C4C2×#612911yescharacteristic
768C2×C4#8825111yescharacteristic
769C2×C4#41×D1311yescharacteristic
770C2×C4#8825711yescharacteristic
771C2×C4C22×C22⋊D1311yescharacteristic
772C8—22no—
773C8—41no—
774C8—41no—
775C8—41no—
776C8—262no—
777C8—521no—
778C8—521no—
779C8—521no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—262no—
794C22—262no—
795C22—262no—
796C22—521no—
797C22—521no—
798C22—521no—
799C22—521no—
800C22#1171878714yes—
801C22C4×#612911yescharacteristic
802C22#1171925111yescharacteristic
803C22C2×M16×D1311yescharacteristic
804C22C2×M16×D1311yescharacteristic
805C22D13×#13111yescharacteristic
806C22#1171945511yescharacteristic
807C22C22×#610311yescharacteristic
808C4—22no—
809C4—22no—
810C4—22no—
811C4—22no—
812C4—262no—
813C4—262no—
814C4—262no—
815C4—262no—
816C4—521no—
817C4—521no—
818C4—521no—
819C4#1171925911yescharacteristic
820C4#1171926011yescharacteristic
821C4#1171951111yescharacteristic
822C4#1171952911yescharacteristic
823C2—24no—
824C2—42no—
825C2—522no—
826C2#1311766111yescharacteristic
827C2C2×#1171878711yescharacteristic
828C2#1312328311yescharacteristic
829C2#1312379611yescharacteristic
830C2#1312384611yescharacteristic
831C2#1312394811yescharacteristic
832C2#1312395611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC2×C13×#435C2
prime radicalC22×#6129C4
cosocleC22×C4×C13C24
hypercenterC2×#435D13
hypocenterC13#22471
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×#11718672C2semidirect
3. #13115776C2semidirect
4. #13115775C2semidirect
5. #13115133C2semidirect
6. #13115131C2semidirect
7. #13115128C2semidirect
8. #13115126C2semidirect
9. #13114902C2semidirect
10. #13114902C2semidirect
11. #13114813C2semidirect
12. #13114599C2semidirect
13. #13114529C2semidirect
14. C2×#11718142C2semidirect
15. C2×C13×#435C2semidirect
183. C2×C22⋊D13M16semidirect
195. C22×Dic13M16semidirect
232. C2×C8×C13#41semidirect
272. C2×#1055#41semidirect
275. C2×#435D13semidirect
661. C2×C8#6129semidirect
688. C13#22471semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#61292
C2×#117186722
#131157762
#131157752
#131151332
#131151312
#131151282
#131151262
#131149022
#131148132
#131145992
#131145292
C2×#117181422
C2×C13×#4352
#2247113