Finite Group Databasebeta

← #15785338

Subgroups — #15785338

Order 3328.

1650 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88141C211yesmaximal, characteristic
2C2×#11718316C211yesmaximal, characteristic
3C2×#11718639C211yesmaximal, characteristic
4#13113106C211yesmaximal, characteristic
5#13113106C211yesmaximal, characteristic
6#13113089C211yesmaximal, characteristic
7#13113067C211yesmaximal, characteristic
8#13113067C211yesmaximal, characteristic
9#13113065C211yesmaximal, characteristic
10#13113062C211yesmaximal, characteristic
11#13113061C211yesmaximal, characteristic
12#13113061C211yesmaximal, characteristic
13#13113060C211yesmaximal, characteristic
14#95×Dic13C211yesmaximal, characteristic
15C13×#1441C211yesmaximal, characteristic
16C23×Dic26C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C22×#6101C2211yescharacteristic
21C22×#6101C2211yescharacteristic
22C22×C4×Dic13C2211yescharacteristic
23C22×C4×Dic13C2211yescharacteristic
24C22×C4×Dic13C2211yescharacteristic
25C22×C4×Dic13C2211yescharacteristic
26C22×C4×Dic13C2211yescharacteristic
27C2×#88141—24no—
28C2×#88141—24no—
29C2×#88141C418yescomplemented
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×#88071C2211yescharacteristic
36C2×#88071C2211yescharacteristic
37C2×#88071C2211yescharacteristic
38C2×#88071C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54#11718639—24no—
55#11718316—24no—
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C22×Dic26—22no—
72C22×Dic26—22no—
73C22×Dic26—22no—
74C22×Dic26—22no—
75C22×Dic26—22no—
76C22×Dic26—22no—
77C22×Dic26C2×C414yes—
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—41no—
83C2×C13×C4⋊C4C2×C414yes—
84C2×C4⋊Dic13—22no—
85C2×C4⋊Dic13—22no—
86C2×C4⋊Dic13—41no—
87C2×#6101—22no—
88C2×#6101—22no—
89C2×#6101C2×C414yes—
90C2×#6101C2×C414yes—
91C2×#6101D414yes—
92C2×#6101D414yes—
93C2×C4×Dic13—22no—
94C2×C4×Dic13—22no—
95C2×C4×Dic13—22no—
96C2×C4×Dic13—22no—
97C2×C4×Dic13—22no—
98C2×C4×Dic13—22no—
99C2×C4×Dic13—22no—
100C2×C4×Dic13—22no—
101C2×C4×Dic13—22no—
102C2×C4×Dic13—22no—
103C2×C4×Dic13—41no—
104C2×C4×Dic13—41no—
105C2×C4×Dic13C2×C414yes—
106C2×C4×Dic13C2×C414yes—
107C2×C4×Dic13C2×C414yes—
108#88141—232no—
109C13×#95—22no—
110C13×#95—22no—
111C13×#95—22no—
112C13×#95—22no—
113C13×#95—41no—
114#88071—22no—
115#88071—22no—
116#88071—22no—
117#88071—22no—
118#88071—22no—
119#88071—22no—
120#88071—22no—
121#88071—22no—
122#88071—22no—
123#88071—22no—
124#88071—22no—
125#88071—22no—
126#88071—22no—
127#88071—22no—
128#88071—22no—
129#88071—22no—
130#88071—22no—
131#88071—41no—
132#88071Q814yescomplemented
133#13927—131nomaximal, Sylow
134C24×C13C2411yescharacteristic
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
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×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13C22×C412yes—
176C22×C4×C13C22×C412yes—
177C22×C4×C13C22×C412yes—
178C22×C4×C13C2×D412yes—
179C22×C4×C13C2×D412yes—
180C22×C4×C13C2×Q812yes—
181C22×C4×C13#4112yes—
182C22×C4×C13#4112yes—
183C22×C4×C13#4112yes—
184C22×Dic13—21no—
185C22×Dic13—21no—
186C22×Dic13—21no—
187C22×Dic13—21no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—21no—
191C22×Dic13—21no—
192C22×Dic13—21no—
193C22×Dic13—21no—
194C22×Dic13—21no—
195C22×Dic13—21no—
196C22×Dic13—21no—
197C22×Dic13—21no—
198C22×Dic13—21no—
199C22×Dic13—21no—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—21no—
203C22×Dic13—21no—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13—21no—
218C22×Dic13—21no—
219C22×Dic13—21no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225C22×Dic13—21no—
226C22×Dic13C22×C412yes—
227C22×Dic13C22×C412yes—
228C22×Dic13C22×C412yes—
229C22×Dic13C22×C412yes—
230C22×Dic13C2×D412yes—
231C22×Dic13C2×D412yes—
232C22×Dic13C2×D412yes—
233C22×Dic13C2×D412yes—
234C22×Dic13C2×Q812yes—
235C22×Dic13C2×Q812yes—
236C22×Dic13#4112yes—
237C22×Dic13#4112yes—
238C22×Dic13#4112yes—
239C22×Dic13#4112yes—
240C2×Dic26—28no—
241C2×Dic26—28no—
242C2×Dic26—28no—
243C2×Dic26—28no—
244C2×Dic26—28no—
245C2×Dic26—28no—
246C2×Dic26—28no—
247C13×C4⋊C4—28no—
248C13×C4⋊C4—44no—
249C4⋊Dic13—44no—
250#6101—28no—
251#6101C22⋊C4116yes—
252C4×Dic13—28no—
253C4×Dic13—28no—
254C4×Dic13—28no—
255C4×Dic13—44no—
256C4×Dic13—44no—
257C22×C4×Q8—131no—
258C2×#387—131no—
259C2×#387—131no—
260#1446—131no—
261#1446—131no—
262#1441—131no—
263#1441D1311yescharacteristic
264#1436—131no—
265#1436—131no—
266C4⋊#95—131no—
267#1434—131no—
268#1434—131no—
269#1434—131no—
270#1434—131no—
271C4×#95—131no—
272C23×C13C23×C411yescharacteristic
273C23×C13C22×D411yescharacteristic
274C23×C13C22×D411yescharacteristic
275C23×C13C22×Q811yescharacteristic
276C23×C13C2×#4111yescharacteristic
277C23×C13C2×#4111yescharacteristic
278C23×C13C2×#4111yescharacteristic
279C23×C13C2×#4111yescharacteristic
280C23×C13C2×#4111yescharacteristic
281C23×C13C2×#4111yescharacteristic
282C23×C13C2×#4111yescharacteristic
283C23×C13H(5,𝔽2)11yescharacteristic
284C23×C132−1+411yescharacteristic
285C23×C132−1+411yescharacteristic
286C23×C132−1+411yescharacteristic
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—41no—
309C2×C4×C13—41no—
310C2×C4×C13—41no—
311C2×C4×C13—41no—
312C2×C4×C13—41no—
313C2×C4×C13—41no—
314C2×C4×C13—41no—
315C2×C4×C13—41no—
316C2×C4×C13—41no—
317C2×C4×C13—41no—
318C2×C4×C13—41no—
319C2×C4×C13—41no—
320C2×C4×C13—41no—
321C2×C4×C13—41no—
322C2×C4×C13—41no—
323C2×C4×C13—41no—
324C2×C4×C13—41no—
325C2×C4×C13—41no—
326C2×C4×C13—41no—
327C2×C4×C13—41no—
328C2×C4×C13—41no—
329C2×C4×C13—41no—
330C2×C4×C13—41no—
331C2×C4×C13—41no—
332C2×C4×C13—41no—
333C2×C4×C13—41no—
334C2×C4×C13C2×C22⋊C414yes—
335C2×C4×C13#11714yes—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—22no—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—22no—
348C2×Dic13—22no—
349C2×Dic13—22no—
350C2×Dic13—22no—
351C2×Dic13—22no—
352C2×Dic13—22no—
353C2×Dic13—22no—
354C2×Dic13—22no—
355C2×Dic13—22no—
356C2×Dic13—22no—
357C2×Dic13—22no—
358C2×Dic13—22no—
359C2×Dic13—22no—
360C2×Dic13—22no—
361C2×Dic13—22no—
362C2×Dic13—22no—
363C2×Dic13—22no—
364C2×Dic13—22no—
365C2×Dic13—22no—
366C2×Dic13—41no—
367C2×Dic13—41no—
368C2×Dic13—41no—
369C2×Dic13—41no—
370C2×Dic13—41no—
371C2×Dic13—41no—
372C2×Dic13—41no—
373C2×Dic13—41no—
374C2×Dic13—41no—
375C2×Dic13—41no—
376C2×Dic13—41no—
377C2×Dic13—41no—
378C2×Dic13—41no—
379C2×Dic13—41no—
380C2×Dic13—41no—
381C2×Dic13—41no—
382C2×Dic13—41no—
383C2×Dic13—41no—
384C2×Dic13—41no—
385C2×Dic13—41no—
386C2×Dic13—41no—
387C2×Dic13—41no—
388C2×Dic13C2×C22⋊C414yes—
389C2×Dic13C2×C22⋊C414yes—
390C2×Dic13#11714yes—
391C2×Dic13C4×Q814yes—
392Dic26—232no—
393C23×Q8—131no—
394C2×C4×Q8—138no—
395C2×C4×Q8—264no—
396C2×C4×Q8—264no—
397C22×C4⋊C4—131no—
398C22×C4⋊C4—131no—
399C22×C4⋊C4—131no—
400C22×C4⋊C4C2×D1311yescharacteristic
401C22×C4⋊C4C2×D1311yescharacteristic
402C22×C42—131no—
403C22×C42—131no—
404C22×C42—131no—
405C22×C42—131no—
406C22×C42—131no—
407#387—264no—
408#387—264no—
409C2×#95—131no—
410C2×#95—131no—
411C2×#95—131no—
412C2×#95—131no—
413C2×#95—131no—
414C2×#95—131no—
415C2×#95—131no—
416C2×#95—131no—
417C2×#95—131no—
418C2×#95—131no—
419C2×#95—131no—
420C2×#95—131no—
421C2×#95—131no—
422C2×#95—131no—
423C2×#95—131no—
424C2×#95—131no—
425C2×#95—131no—
426C2×#95—131no—
427C2×#95—131no—
428C2×#95C2×D1311yescharacteristic
429C2×#95C2×D1311yescharacteristic
430C2×#95C2×D1311yescharacteristic
431C2×#95C2×D1311yescharacteristic
432C2×#95C2×D1311yescharacteristic
433C22×C13C22×C22⋊C411yescharacteristic
434C22×C13C2×#11711yescharacteristic
435C22×C13C2×#11711yescharacteristic
436C22×C13C2×C4×Q811yescharacteristic
437C22×C13C4×#4111yescharacteristic
438C22×C13#51911yescharacteristic
439C22×C13#52011yescharacteristic
440C22×C13#52511yescharacteristic
441C22×C13#52511yescharacteristic
442C22×C13#52511yescharacteristic
443C22×C13#52511yescharacteristic
444C22×C13#52911yescharacteristic
445C22×C13#52911yescharacteristic
446C22×C13#53311yescharacteristic
447C22×C13#53311yescharacteristic
448C22×C13#54111yescharacteristic
449C22×C13#54111yescharacteristic
450C22×C13#54211yescharacteristic
451C22×C13#54211yescharacteristic
452C22×C13#54611yescharacteristic
453C22×C13#54611yescharacteristic
454C22×C13#54711yescharacteristic
455C22×C13#54711yescharacteristic
456C22×C13#54811yescharacteristic
457C22×C13#54811yescharacteristic
458C22×C13D4×Q811yescharacteristic
459C22×C13D4×Q811yescharacteristic
460C22×C13#55211yescharacteristic
461C22×C13#55211yescharacteristic
462C22×C13#55411yescharacteristic
463C22×C13#55611yescharacteristic
464C22×C13#55611yescharacteristic
465C22×C13#55611yescharacteristic
466C22×C13#55711yescharacteristic
467C22×C13#55911yescharacteristic
468C4×C13—24no—
469C4×C13—24no—
470C4×C13—42no—
471C4×C13—42no—
472C4×C13—42no—
473C4×C13—81no—
474C4×C13—81no—
475Dic13—24no—
476Dic13—24no—
477Dic13—24no—
478Dic13—24no—
479Dic13—42no—
480Dic13—42no—
481Dic13—81no—
482Dic13—81no—
483C22×Q8—134no—
484C22×Q8—262no—
485C22×Q8—262no—
486C22×Q8—262no—
487C22×Q8—262no—
488C22×Q8—262no—
489C22×Q8—262no—
490C23×C4—131no—
491C23×C4—131no—
492C23×C4—131no—
493C23×C4—131no—
494C23×C4—131no—
495C23×C4—131no—
496C23×C4—131no—
497C23×C4—131no—
498C23×C4C22×D1311yescharacteristic
499C23×C4C22×D1311yescharacteristic
500C23×C4C22×D1311yescharacteristic
501C23×C4C22×D1311yescharacteristic
502C23×C4C22×D1311yescharacteristic
503C23×C4C22×D1311yescharacteristic
504C23×C4C22×D1311yescharacteristic
505C4×Q8—2632no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—41no—
511C2×C4⋊C4—134no—
512C2×C4⋊C4—134no—
513C2×C4⋊C4—134no—
514C2×C4⋊C4—134no—
515C2×C4⋊C4—262no—
516C2×C4⋊C4—262no—
517C2×C4⋊C4—262no—
518C2×C4⋊C4—262no—
519C2×C4⋊C4—521no—
520C2×C4⋊C4C4×D1314yes—
521C2×C42—134no—
522C2×C42—134no—
523C2×C42—134no—
524C2×C42—262no—
525C2×C42—262no—
526C2×C42—262no—
527C2×C42—262no—
528C2×C42—262no—
529C2×C42—262no—
530C2×C42—262no—
531C2×C42—262no—
532C2×C42—262no—
533C2×C42—262no—
534C2×C42—521no—
535C2×C42—521no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—41no—
541#95—134no—
542#95—262no—
543#95—262no—
544#95—262no—
545#95—262no—
546#95—262no—
547#95—262no—
548#95—262no—
549#95—262no—
550#95—262no—
551#95—262no—
552#95—262no—
553#95—262no—
554#95—262no—
555#95—262no—
556#95—262no—
557#95—262no—
558#95—262no—
559#95—521no—
560C2×C13#228011yescharacteristic
561C2×C13#229511yescharacteristic
562C2×C13#232011yescharacteristic
563C2×C13#233911yescharacteristic
564C2×C13Q8×C22⋊C411yescharacteristic
565C2×C13#235511yescharacteristic
566C2×C13#235611yescharacteristic
567C2×C13#245811yescharacteristic
568C2×C13#245811yescharacteristic
569C2×C13#246211yescharacteristic
570C2×C13#246211yescharacteristic
571C2×C13#246511yescharacteristic
572C2×C13#246511yescharacteristic
573C2×C13#246911yescharacteristic
574C2×C13#246911yescharacteristic
575C24C23×D1311yescharacteristic
576C2×Q8—268no—
577C2×Q8—268no—
578C2×Q8—268no—
579C2×Q8—268no—
580C2×Q8—268no—
581C2×Q8—268no—
582C2×Q8—268no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
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—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—132no—
624C22×C4—132no—
625C22×C4—132no—
626C22×C4—132no—
627C22×C4—132no—
628C22×C4—132no—
629C22×C4—132no—
630C22×C4—132no—
631C22×C4—132no—
632C22×C4—132no—
633C22×C4—132no—
634C22×C4—132no—
635C22×C4—132no—
636C22×C4—132no—
637C22×C4—261no—
638C22×C4—261no—
639C22×C4—261no—
640C22×C4—261no—
641C22×C4—261no—
642C22×C4—261no—
643C22×C4—261no—
644C22×C4—261no—
645C22×C4—261no—
646C22×C4—261no—
647C22×C4—261no—
648C22×C4—261no—
649C22×C4—261no—
650C22×C4—261no—
651C22×C4—261no—
652C22×C4—261no—
653C22×C4—261no—
654C22×C4—261no—
655C22×C4—261no—
656C22×C4—261no—
657C22×C4—261no—
658C22×C4—261no—
659C22×C4—261no—
660C22×C4—261no—
661C22×C4—261no—
662C22×C4—261no—
663C22×C4—261no—
664C22×C4—261no—
665C22×C4—261no—
666C22×C4—261no—
667C22×C4—261no—
668C22×C4—261no—
669C22×C4—261no—
670C22×C4—261no—
671C22×C4—261no—
672C22×C4—261no—
673C22×C4—261no—
674C22×C4—261no—
675C22×C4—261no—
676C22×C4—261no—
677C22×C4—261no—
678C22×C4—261no—
679C22×C4C2×C4×D1312yes—
680C22×C4C2×C4×D1312yes—
681C22×C4C2×C4×D1312yes—
682C22×C4D4×D1312yes—
683C22×C4D4×D1312yes—
684C22×C4#612912yes—
685C22×C4#612912yes—
686C22×C4Q8×D1312yes—
687C22×C4#613112yes—
688C4⋊C4—28no—
689C4⋊C4—44no—
690C4⋊C4—1316no—
691C4⋊C4—268no—
692C4⋊C4—524no—
693C42—268no—
694C42—268no—
695C42—268no—
696C42—524no—
697C42—524no—
698C13#1392711yescharacteristic, complemented, Sylow
699C23C22×C4×D1311yescharacteristic
700C23C2×D4×D1311yescharacteristic
701C23C2×D4×D1311yescharacteristic
702C23C2×#612911yescharacteristic
703C23C2×#612911yescharacteristic
704C23#8825111yescharacteristic
705C23C2×Q8×D1311yescharacteristic
706C23C2×#613111yescharacteristic
707C23#8825411yescharacteristic
708C23#41×D1311yescharacteristic
709C23#41×D1311yescharacteristic
710C23#41×D1311yescharacteristic
711C23#41×D1311yescharacteristic
712C23#8825711yescharacteristic
713C23#8825711yescharacteristic
714Q8—2632no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
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—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—134no—
763C2×C4—134no—
764C2×C4—134no—
765C2×C4—134no—
766C2×C4—262no—
767C2×C4—262no—
768C2×C4—262no—
769C2×C4—262no—
770C2×C4—262no—
771C2×C4—262no—
772C2×C4—262no—
773C2×C4—262no—
774C2×C4—262no—
775C2×C4—262no—
776C2×C4—262no—
777C2×C4—262no—
778C2×C4—262no—
779C2×C4—262no—
780C2×C4—262no—
781C2×C4—262no—
782C2×C4—262no—
783C2×C4—262no—
784C2×C4—262no—
785C2×C4—262no—
786C2×C4—262no—
787C2×C4—262no—
788C2×C4—262no—
789C2×C4—262no—
790C2×C4—262no—
791C2×C4—262no—
792C2×C4—262no—
793C2×C4—262no—
794C2×C4—262no—
795C2×C4—262no—
796C2×C4—521no—
797C2×C4—521no—
798C2×C4—521no—
799C2×C4—521no—
800C2×C4—521no—
801C2×C4—521no—
802C2×C4—521no—
803C2×C4—521no—
804C2×C4—521no—
805C2×C4—521no—
806C2×C4—521no—
807C2×C4—521no—
808C2×C4—521no—
809C2×C4—521no—
810C2×C4—521no—
811C2×C4—521no—
812C2×C4—521no—
813C2×C4—521no—
814C2×C4—521no—
815C2×C4—521no—
816C2×C4—521no—
817C2×C4—521no—
818C2×C4C22⋊C4×D1314yes—
819C2×C4#8814614yes—
820C22C2×C22⋊C4×D1311yescharacteristic
821C22C2×#8814611yescharacteristic
822C22D13×#11711yescharacteristic
823C22C4×#612911yescharacteristic
824C22#1171925111yescharacteristic
825C22C4×Q8×D1311yescharacteristic
826C22#1171927711yescharacteristic
827C22#1171929611yescharacteristic
828C22#1171930511yescharacteristic
829C22#1171930811yescharacteristic
830C22#1171931111yescharacteristic
831C22#1171931111yescharacteristic
832C22#1171931511yescharacteristic
833C22#1171931611yescharacteristic
834C22#1171932711yescharacteristic
835C22#1171933011yescharacteristic
836C22#1171933211yescharacteristic
837C22#1171933211yescharacteristic
838C22#1171933711yescharacteristic
839C22#1171933811yescharacteristic
840C22#1171934111yescharacteristic
841C22#1171934611yescharacteristic
842C22#1171935511yescharacteristic
843C22#1171936011yescharacteristic
844C22#1171936911yescharacteristic
845C22#1171938211yescharacteristic
846C22#1171939011yescharacteristic
847C22#1171939611yescharacteristic
848C22#1171939811yescharacteristic
849C22#1171940211yescharacteristic
850C22#1171940711yescharacteristic
851C22#1171940711yescharacteristic
852C22#1171943211yescharacteristic
853C22#1171943311yescharacteristic
854C22#1171943811yescharacteristic
855C4—24no—
856C4—24no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—81no—
861C4—81no—
862C4—264no—
863C4—264no—
864C4—264no—
865C4—264no—
866C4—522no—
867C4—522no—
868C4—1041no—
869C4—1041no—
870C2#1311721811yescharacteristic
871C2#1311730711yescharacteristic
872C2#1311748311yescharacteristic
873C2#1311766211yescharacteristic
874C2#1311767011yescharacteristic
875C2#1311779011yescharacteristic
876C2#1311779811yescharacteristic
877C2#1311875911yescharacteristic
878C2#1311876111yescharacteristic
879C2#1311881911yescharacteristic
880C2#1311882111yescharacteristic
881C2#1311885811yescharacteristic
882C2#1311886011yescharacteristic
883C2#1311891811yescharacteristic
884C2#1311892011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1441C2
socle, prime radical, cosocleC24×C13C24
hypercenter#1441D13
hypocenterC13#13927
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
29. C2×#88141C4semidirect
132. #88071Q8semidirect
698. C13#13927semidirect

Maximal subgroups

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

subgroupindex
C22×#881412
C2×#117183162
C2×#117186392
#131131062
#131130892
#131130672
#131130652
#131130622
#131130612
#131130602
#95×Dic132
C13×#14412
#1392713