Finite Group Databasebeta

← #16022916

Subgroups — #16022916

Order 3328.

2220 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719390C211yesmaximal, characteristic
2#13117935C212yesmaximal
3#13117933C212yesmaximal
4#13117928C211yesmaximal, characteristic
5#13117895C211yesmaximal, characteristic
6#13117891C212yesmaximal
7#13117794C211yesmaximal, characteristic
8#13117790C212yesmaximal
9#13117756C211yesmaximal, characteristic
10#13117755C211yesmaximal, characteristic
11#13117750C211yesmaximal, characteristic
12#13117407C211yesmaximal, characteristic
13#13117407C212yesmaximal
14#125×Dic13C211yesmaximal, characteristic
15#13117395C211yesmaximal, characteristic
16#13117393C212yesmaximal
17#13117393C212yesmaximal
18C4×#88141C211yesmaximal, characteristic
19C4×#88141C211yesmaximal, characteristic
20C4×#88141C211yesmaximal, characteristic
21C4×#88141C211yesmaximal, characteristic
22C4×#88141C212yesmaximal
23C13×#2370C211yesmaximal, characteristic
24C2×C13×#125C2211yescharacteristic
25#11719390C4116yescomplemented
26C2×#88144C2211yescharacteristic
27C2×#88143C2212yes—
28C2×#88143C2212yes—
29C2×#88142C2212yes—
30C2×#88142C2211yescharacteristic
31C2×#88141C2211yescharacteristic
32C2×#88141C2211yescharacteristic
33C2×#88141C2211yescharacteristic
34C2×#88141C2212yes—
35C2×#88141C2211yescharacteristic
36C2×#88141C2211yescharacteristic
37C2×#88141C2212yes—
38C2×#88141C2211yescharacteristic
39C2×C4×Dic26C2211yescharacteristic
40C2×C4×Dic26C2211yescharacteristic
41C2×C4×Dic26C2212yes—
42C2×C4×Dic26C2211yescharacteristic
43C2×C4×Dic26C2211yescharacteristic
44C13×#389C2211yescharacteristic
45C13×#389C2211yescharacteristic
46C13×#389C2212yes—
47C13×#387C2212yes—
48C13×#387C2212yes—
49C4×C13×C4⋊C4C2211yescharacteristic
50C4×C13×C4⋊C4C2211yescharacteristic
51C4×C13×C4⋊C4C2211yescharacteristic
52C4×C13×C4⋊C4C2211yescharacteristic
53C4×C13×C4⋊C4C2212yes—
54#11718646C2211yescharacteristic
55#11718646C2211yescharacteristic
56#11718642C2212yes—
57#11718642C2212yes—
58#11718639C2212yes—
59#11718638C2211yescharacteristic
60#11718637C2212yes—
61#11718637C2211yescharacteristic
62C4⋊C4×Dic13C2212yes—
63C4⋊C4×Dic13C2211yescharacteristic
64C4⋊C4×Dic13C2211yescharacteristic
65C4⋊C4×Dic13C2211yescharacteristic
66C4⋊C4×Dic13C2211yescharacteristic
67C4⋊C4×Dic13C2212yes—
68C4⋊C4×Dic13C2211yescharacteristic
69C4⋊C4×Dic13C2211yescharacteristic
70C4⋊C4×Dic13C2211yescharacteristic
71C4⋊C4×Dic13C2211yescharacteristic
72C4⋊C4×Dic13C2212yes—
73C4⋊C4×Dic13C2212yes—
74#11718633C2212yes—
75#11718633C2212yes—
76#11718633C2212yes—
77#11718633C2212yes—
78#11718633C2212yes—
79#11718597C2211yescharacteristic
80#11718594C2212yes—
81#11718594C2212yes—
82C4×#6101C2211yescharacteristic
83C4×#6101C2211yescharacteristic
84C4×#6101C2212yes—
85C4×#6101C2212yes—
86C4×#6101C2212yes—
87C4×#6101C2212yes—
88C4×#6101C2212yes—
89C42×Dic13C2212yes—
90C42×Dic13C2212yes—
91C42×Dic13C2211yescharacteristic
92C42×Dic13C2211yescharacteristic
93C42×Dic13C2212yes—
94C42×Dic13C2211yescharacteristic
95#11718589C2211yescharacteristic
96#11718589C2211yescharacteristic
97#11718589C2212yes—
98#11718316C2212yes—
99#11718316C2212yes—
100#11718315C2212yes—
101#11718315C2212yes—
102#11718314C2212yes—
103#11718311C2212yes—
104#11718311C2212yes—
105#11718310C2211yescharacteristic
106#11718310C2212yes—
107#11718310C2212yes—
108#11718310C2211yescharacteristic
109#11718310C2212yes—
110#11718310C2212yes—
111#11718310C2212yes—
112#11718310C2212yes—
113#11718310C2211yescharacteristic
114#11718310C2212yes—
115#11718310C2212yes—
116#11718310C2212yes—
117#11718310C2211yescharacteristic
118#11718310C2212yes—
119#11718308C2212yes—
120#11718308C2212yes—
121#11718307C2212yes—
122#11718307C2212yes—
123#11718307C2212yes—
124C22×Dic26C2312yes—
125C22×Dic26C2311yescharacteristic
126C22×Dic26C2311yescharacteristic
127C13×#125C2×C418yes—
128C2×C13×C4⋊C4C2311yescharacteristic
129C2×C13×C4⋊C4C2311yescharacteristic
130C2×C13×C4⋊C4C2312yes—
131C2×C13×C4⋊C4C2311yescharacteristic
132C2×C13×C4⋊C4C2312yes—
133C2×C13×C4⋊C4C2312yes—
134C2×C13×C4⋊C4C2311yescharacteristic
135C2×C13×C4⋊C4C2311yescharacteristic
136C2×C13×C4⋊C4C2312yes—
137C2×C13×C4⋊C4C2311yescharacteristic
138C2×C42×C13C2312yes—
139C2×C42×C13C2311yescharacteristic
140C2×C42×C13C2311yescharacteristic
141C2×C42×C13C2312yes—
142C2×C42×C13C2312yes—
143C2×C42×C13C2311yescharacteristic
144C2×C4⋊Dic13C2312yes—
145C2×C4⋊Dic13C2311yescharacteristic
146C2×C4⋊Dic13C2311yescharacteristic
147C2×C4⋊Dic13C2312yes—
148C2×C4⋊Dic13C2311yescharacteristic
149C2×C4⋊Dic13C2311yescharacteristic
150C2×C4⋊Dic13C2312yes—
151C2×#6101C2312yes—
152C2×#6101C2312yes—
153C2×#6101C2312yes—
154C2×#6101C2312yes—
155C2×#6101C2311yescharacteristic
156C2×#6101C2311yescharacteristic
157C2×#6101C2312yes—
158C2×#6101C2312yes—
159C2×#6101C2311yescharacteristic
160C2×#6101C2312yes—
161C2×#6101C2311yescharacteristic
162C2×#6101C2312yes—
163C2×#6101C2311yescharacteristic
164C2×#6101C2312yes—
165C2×#6101C2312yes—
166C2×#6101C2312yes—
167C2×#6101C2312yes—
168C2×#6101C2312yes—
169C2×#6101C2311yescharacteristic
170C2×C4×Dic13C2312yes—
171C2×C4×Dic13C2312yes—
172C2×C4×Dic13C2312yes—
173C2×C4×Dic13C2312yes—
174C2×C4×Dic13C2311yescharacteristic
175C2×C4×Dic13C2312yes—
176C2×C4×Dic13C2311yescharacteristic
177C2×C4×Dic13C2312yes—
178C2×C4×Dic13C2311yescharacteristic
179C2×C4×Dic13C2312yes—
180C2×C4×Dic13C2311yescharacteristic
181C2×C4×Dic13C2311yescharacteristic
182C2×C4×Dic13C2311yescharacteristic
183C2×C4×Dic13C2311yescharacteristic
184C2×C4×Dic13C2311yescharacteristic
185C2×C4×Dic13C2311yescharacteristic
186C2×C4×Dic13C2312yes—
187C2×C4×Dic13C2311yescharacteristic
188C2×C4×Dic13C2311yescharacteristic
189C2×C4×Dic13C2312yes—
190C2×C4×Dic13C2311yescharacteristic
191C2×C4×Dic13C2311yescharacteristic
192C2×C4×Dic13C2312yes—
193C2×C4×Dic13C2311yescharacteristic
194C2×C4×Dic13C2312yes—
195C2×C4×Dic13C2312yes—
196C2×C4×Dic13C2312yes—
197C2×C4×Dic13C2311yescharacteristic
198C2×C4×Dic13C2311yescharacteristic
199#88144C2×C418yes—
200#88143C2×C4116yes—
201#88143C2×C4116yes—
202#88142C2×C418yes—
203#88142C2×C4116yes—
204#88141—24no—
205#88141—24no—
206#88141—24no—
207#88141—28no—
208#88141C2×C418yes—
209#88141C2×C4116yes—
210#88141C2×C418yes—
211#88141Q818yescomplemented
212C4×Dic26—24no—
213C4×Dic26—24no—
214C4×Dic26—28no—
215C4×Dic26C2×C418yes—
216C4×Dic26C2×C418yes—
217C13×#95C2311yescharacteristic
218C13×#95C2311yescharacteristic
219C13×#95C2312yes—
220C13×#95C2312yes—
221C13×#95C2312yes—
222C13×#95C2312yes—
223C13×#95C2312yes—
224#88071C2312yes—
225#88071C2312yes—
226#88071C2312yes—
227#88071C2312yes—
228#88071C2312yes—
229#88071C2312yes—
230#88071C2312yes—
231#88071C2312yes—
232#88071C2312yes—
233#88071C2311yescharacteristic
234#88071C2311yescharacteristic
235#88071C2312yes—
236#88071C2312yes—
237#88071C2312yes—
238#88071C2312yes—
239#88071C2312yes—
240#88071C2311yescharacteristic
241#88071C2311yescharacteristic
242C4×#557—131nomaximal, Sylow
243C22×C4×C13C2411yescharacteristic
244C22×C4×C13C2412yes—
245C22×C4×C13C2411yescharacteristic
246C22×C4×C13C2411yescharacteristic
247C22×C4×C13C2412yes—
248C22×C4×C13C2411yescharacteristic
249C22×C4×C13C2412yes—
250C22×C4×C13C2412yes—
251C22×C4×C13C2411yescharacteristic
252C22×C4×C13C2411yescharacteristic
253C22×C4×C13C2411yescharacteristic
254C22×Dic13C2412yes—
255C22×Dic13C2411yescharacteristic
256C22×Dic13C2412yes—
257C22×Dic13C2411yescharacteristic
258C22×Dic13C2411yescharacteristic
259C22×Dic13C2411yescharacteristic
260C22×Dic13C2412yes—
261C22×Dic13C2411yescharacteristic
262C22×Dic13C2411yescharacteristic
263C22×Dic13C2412yes—
264C22×Dic13C2411yescharacteristic
265C22×Dic13C2411yescharacteristic
266C2×Dic26—24no—
267C2×Dic26—22no—
268C2×Dic26—24no—
269C2×Dic26—22no—
270C2×Dic26C22×C414yes—
271C2×Dic26C22×C418yes—
272C2×Dic26C22×C414yes—
273C2×Dic26C2×Q814yes—
274C2×Dic26#4114yes—
275C13×C4⋊C4—22no—
276C13×C4⋊C4—22no—
277C13×C4⋊C4—24no—
278C13×C4⋊C4—22no—
279C13×C4⋊C4—42no—
280C13×C4⋊C4C22×C414yes—
281C13×C4⋊C4C22×C418yes—
282C13×C4⋊C4C22×C414yes—
283C13×C4⋊C4C22×C418yes—
284C13×C4⋊C4C2×Q814yes—
285C42×C13—24no—
286C42×C13—22no—
287C42×C13—22no—
288C42×C13—42no—
289C42×C13—42no—
290C42×C13C22×C414yes—
291C4⋊Dic13—22no—
292C4⋊Dic13—22no—
293C4⋊Dic13—24no—
294C4⋊Dic13—42no—
295C4⋊Dic13C22×C414yes—
296C4⋊Dic13C22×C414yes—
297C4⋊Dic13C22×C418yes—
298#6101—24no—
299#6101—24no—
300#6101—22no—
301#6101—24no—
302#6101—24no—
303#6101—22no—
304#6101—24no—
305#6101—24no—
306#6101—22no—
307#6101—42no—
308#6101C22×C414yes—
309#6101C22×C418yes—
310#6101C22×C414yes—
311#6101C22×C418yes—
312#6101C22×C418yes—
313#6101C22×C418yes—
314#6101C22×C418yes—
315#6101C2×Q818yes—
316#6101#4114yes—
317C4×Dic13—22no—
318C4×Dic13—22no—
319C4×Dic13—24no—
320C4×Dic13—24no—
321C4×Dic13—24no—
322C4×Dic13—24no—
323C4×Dic13—22no—
324C4×Dic13—24no—
325C4×Dic13—22no—
326C4×Dic13—22no—
327C4×Dic13—24no—
328C4×Dic13—22no—
329C4×Dic13—24no—
330C4×Dic13—22no—
331C4×Dic13—22no—
332C4×Dic13—22no—
333C4×Dic13—24no—
334C4×Dic13—41no—
335C4×Dic13—41no—
336C4×Dic13—42no—
337C4×Dic13—41no—
338C4×Dic13C22×C414yes—
339C4×Dic13C22×C418yes—
340C4×Dic13C22×C414yes—
341C4×Dic13C22×C418yes—
342C4×Dic13C22×C418yes—
343C4×Dic13C2×Q814yes—
344C4×Dic13C2×Q818yes—
345C4×Dic13#4114yes—
346C2×#557—131no—
347#2370—132no—
348#2370—131no—
349#2370—132no—
350#2370D1311yescharacteristic
351#2365—132no—
352#2365—131no—
353#2355—132no—
354#2355—131no—
355#2351—131no—
356#2351—131no—
357Q8×C4⋊C4—131no—
358C4×C4⋊Q8—132no—
359C4×C4⋊Q8—131no—
360C4×#125—131no—
361C4×#125—132no—
362C4×#125—132no—
363C4×#125—131no—
364C42×Q8—131no—
365C42×Q8—131no—
366C42×Q8—132no—
367C42×Q8—131no—
368C42×Q8—131no—
369C23×C13C2511yescharacteristic
370C2×C4×C13—22no—
371C2×C4×C13—21no—
372C2×C4×C13—21no—
373C2×C4×C13—21no—
374C2×C4×C13—22no—
375C2×C4×C13—21no—
376C2×C4×C13—22no—
377C2×C4×C13—21no—
378C2×C4×C13—22no—
379C2×C4×C13—21no—
380C2×C4×C13—21no—
381C2×C4×C13—22no—
382C2×C4×C13—21no—
383C2×C4×C13—22no—
384C2×C4×C13—22no—
385C2×C4×C13—22no—
386C2×C4×C13—21no—
387C2×C4×C13—21no—
388C2×C4×C13—21no—
389C2×C4×C13—21no—
390C2×C4×C13—21no—
391C2×C4×C13—21no—
392C2×C4×C13—22no—
393C2×C4×C13C23×C412yes—
394C2×C4×C13C23×C414yes—
395C2×C4×C13C23×C414yes—
396C2×C4×C13C23×C412yes—
397C2×C4×C13C23×C412yes—
398C2×C4×C13C22×Q814yes—
399C2×C4×C13C22×Q812yes—
400C2×C4×C13C2×#4112yes—
401C2×C4×C13C2×#4112yes—
402C2×C4×C13C2×#4112yes—
403C2×Dic13—21no—
404C2×Dic13—21no—
405C2×Dic13—21no—
406C2×Dic13—22no—
407C2×Dic13—21no—
408C2×Dic13—22no—
409C2×Dic13—21no—
410C2×Dic13—21no—
411C2×Dic13—21no—
412C2×Dic13—21no—
413C2×Dic13—21no—
414C2×Dic13—21no—
415C2×Dic13—21no—
416C2×Dic13—21no—
417C2×Dic13—22no—
418C2×Dic13—22no—
419C2×Dic13—22no—
420C2×Dic13—22no—
421C2×Dic13—22no—
422C2×Dic13—22no—
423C2×Dic13—21no—
424C2×Dic13C23×C412yes—
425C2×Dic13C23×C412yes—
426C2×Dic13C23×C414yes—
427C2×Dic13C23×C412yes—
428C2×Dic13C23×C414yes—
429C2×Dic13C23×C412yes—
430C2×Dic13C22×Q812yes—
431C2×Dic13C22×Q814yes—
432C2×Dic13C22×Q812yes—
433C2×Dic13C2×#4112yes—
434C2×Dic13C2×#4114yes—
435C2×Dic13C2×#4112yes—
436C2×Dic13C2×#4112yes—
437C2×Dic13C2×#4112yes—
438C2×Dic132−1+412yes—
439Dic26—216no—
440Dic26—28no—
441Dic26C4×Q8116yescomplemented
442#557—1316no—
443C2×C4⋊Q8—132no—
444C2×C4⋊Q8—131no—
445C2×#125—132no—
446C2×#125—132no—
447C2×#125—131no—
448C2×#125C2×D1311yescharacteristic
449C2×C4×Q8—131no—
450C2×C4×Q8—131no—
451C2×C4×Q8—132no—
452C2×C4×Q8—131no—
453C2×C4×Q8—131no—
454C2×C4×Q8—132no—
455C2×C4×Q8—131no—
456C2×C4×Q8—131no—
457C2×C4×Q8—131no—
458C2×C4×Q8—131no—
459C2×C4×Q8—131no—
460C2×C4×Q8—131no—
461C2×C4×Q8—132no—
462#391—132no—
463#391—132no—
464#391—132no—
465#389—132no—
466#389—131no—
467#389—132no—
468#389—131no—
469#389—132no—
470#389—132no—
471#389—132no—
472#389—131no—
473#389—131no—
474#389—132no—
475#389—132no—
476#389—132no—
477#389C2×D1311yescharacteristic
478#389C2×D1311yescharacteristic
479#389C2×D1312yes—
480#387—132no—
481#387—132no—
482#387—132no—
483#387—132no—
484#387—132no—
485#387—132no—
486#387—132no—
487#387—132no—
488#387—132no—
489#387—132no—
490#387C2×D1312yes—
491#387C2×D1312yes—
492#384—132no—
493#384—131no—
494#382—131no—
495#382—131no—
496#382—132no—
497#382—132no—
498C4×C4⋊C4—132no—
499C4×C4⋊C4—132no—
500C4×C4⋊C4—131no—
501C4×C4⋊C4—132no—
502C4×C4⋊C4—131no—
503C4×C4⋊C4—131no—
504C4×C4⋊C4—131no—
505C4×C4⋊C4—132no—
506C4×C4⋊C4—131no—
507C4×C4⋊C4—131no—
508C4×C4⋊C4—131no—
509C4×C4⋊C4—131no—
510C4×C4⋊C4—131no—
511C4×C4⋊C4—131no—
512C4×C4⋊C4—132no—
513C4×C4⋊C4—132no—
514C4×C4⋊C4—132no—
515C4×C4⋊C4—132no—
516C4×C4⋊C4—132no—
517C4×C4⋊C4—132no—
518C4×C4⋊C4—132no—
519C4×C4⋊C4—132no—
520C4×C4⋊C4—131no—
521C4×C4⋊C4—132no—
522C4×C4⋊C4—132no—
523C4×C4⋊C4—132no—
524C4×C4⋊C4—132no—
525C4×C4⋊C4—131no—
526C4×C4⋊C4—132no—
527C4×C4⋊C4—132no—
528C4×C4⋊C4—132no—
529C4×C4⋊C4—131no—
530C4×C4⋊C4—131no—
531C4×C4⋊C4C2×D1311yescharacteristic
532C4×C4⋊C4C2×D1311yescharacteristic
533C4×C4⋊C4C2×D1311yescharacteristic
534C4×C4⋊C4C2×D1312yes—
535C4×C4⋊C4C2×D1311yescharacteristic
536C43—132no—
537C43—131no—
538C43—132no—
539C43—131no—
540C43—132no—
541C43—131no—
542C22×C13C24×C411yescharacteristic
543C22×C13C23×Q811yescharacteristic
544C22×C13C22×#4111yescharacteristic
545C22×C13C22×#4111yescharacteristic
546C22×C13C22×#4111yescharacteristic
547C22×C13C2×2−1+411yescharacteristic
548C22×C13#58511yescharacteristic
549C4×C13—22no—
550C4×C13—24no—
551C4×C13—22no—
552C4×C13—24no—
553C4×C13—24no—
554C4×C13—22no—
555C4×C13—22no—
556C4×C13—42no—
557C4×C13—41no—
558C4×C13—41no—
559C4×C13C2×C4×Q814yes—
560Dic13—24no—
561Dic13—22no—
562Dic13—22no—
563Dic13—22no—
564Dic13—22no—
565Dic13—22no—
566Dic13—41no—
567Dic13—42no—
568Dic13—42no—
569Dic13C2×C4×Q818yes—
570Dic13C4×#4114yes—
571Dic13#55714yescomplemented
572C22×Q8—131no—
573C22×Q8—132no—
574C22×Q8—131no—
575C4⋊Q8—1316no—
576C4⋊Q8—138no—
577#125—1316no—
578#125—1316no—
579#125—138no—
580#125C4×D1318yes—
581C4×Q8—138no—
582C4×Q8—1316no—
583C4×Q8—138no—
584C4×Q8—138no—
585C4×Q8—138no—
586C4×Q8—138no—
587C4×Q8—268no—
588C4×Q8—264no—
589C4×Q8—264no—
590C4×Q8—264no—
591C4×Q8—268no—
592C4×Q8—264no—
593C4×Q8—264no—
594C2×C4⋊C4—131no—
595C2×C4⋊C4—131no—
596C2×C4⋊C4—132no—
597C2×C4⋊C4—131no—
598C2×C4⋊C4—132no—
599C2×C4⋊C4—131no—
600C2×C4⋊C4—132no—
601C2×C4⋊C4—132no—
602C2×C4⋊C4—131no—
603C2×C4⋊C4—132no—
604C2×C4⋊C4—132no—
605C2×C4⋊C4—132no—
606C2×C4⋊C4—132no—
607C2×C4⋊C4—132no—
608C2×C4⋊C4—132no—
609C2×C4⋊C4—131no—
610C2×C4⋊C4—132no—
611C2×C4⋊C4—131no—
612C2×C4⋊C4—132no—
613C2×C4⋊C4—131no—
614C2×C4⋊C4—132no—
615C2×C4⋊C4—131no—
616C2×C4⋊C4—131no—
617C2×C4⋊C4—132no—
618C2×C4⋊C4—132no—
619C2×C4⋊C4—132no—
620C2×C4⋊C4C22×D1311yescharacteristic
621C2×C4⋊C4C22×D1311yescharacteristic
622C2×C4⋊C4C22×D1312yes—
623C2×C4⋊C4C22×D1311yescharacteristic
624C2×C4⋊C4C22×D1312yes—
625C2×C4⋊C4C22×D1312yes—
626C2×C4⋊C4C22×D1311yescharacteristic
627C2×C4⋊C4C22×D1311yescharacteristic
628C2×C4⋊C4C22×D1312yes—
629C2×C4⋊C4C22×D1311yescharacteristic
630C2×C42—131no—
631C2×C42—132no—
632C2×C42—132no—
633C2×C42—131no—
634C2×C42—132no—
635C2×C42—131no—
636C2×C42—132no—
637C2×C42—131no—
638C2×C42—131no—
639C2×C42—132no—
640C2×C42—131no—
641C2×C42—132no—
642C2×C42—131no—
643C2×C42—132no—
644C2×C42—131no—
645C2×C42—132no—
646C2×C42—132no—
647C2×C42—132no—
648C2×C42—131no—
649C2×C42—131no—
650C2×C42—132no—
651C2×C42—131no—
652C2×C42—131no—
653C2×C42—131no—
654C2×C42—132no—
655C2×C42—131no—
656C2×C42—131no—
657C2×C42—132no—
658C2×C42—131no—
659C2×C42C22×D1312yes—
660C2×C42C22×D1311yescharacteristic
661C2×C42C22×D1311yescharacteristic
662C2×C42C22×D1312yes—
663C2×C42C22×D1312yes—
664C2×C42C22×D1311yescharacteristic
665#95—131no—
666#95—132no—
667#95—131no—
668#95—132no—
669#95—132no—
670#95—132no—
671#95—131no—
672#95—132no—
673#95—131no—
674#95—132no—
675#95—132no—
676#95—132no—
677#95—132no—
678#95—132no—
679#95—132no—
680#95—132no—
681#95—132no—
682#95—132no—
683#95C22×D1311yescharacteristic
684#95C22×D1311yescharacteristic
685#95C22×D1312yes—
686#95C22×D1312yes—
687#95C22×D1312yes—
688#95C22×D1312yes—
689#95C22×D1312yes—
690C2×C13C22×C4×Q811yescharacteristic
691C2×C13C2×C4×#4111yescharacteristic
692C2×C13C4×2−1+411yescharacteristic
693C2×C13C2×#55711yescharacteristic
694C2×C13Q8×#4111yescharacteristic
695C2×C13#348011yescharacteristic
696C2×C13#348211yescharacteristic
697C2×Q8—134no—
698C2×Q8—138no—
699C2×Q8—134no—
700C2×Q8—134no—
701C2×Q8—134no—
702C2×Q8—264no—
703C2×Q8—264no—
704C2×Q8—262no—
705C2×Q8—262no—
706C22×C4—131no—
707C22×C4—132no—
708C22×C4—131no—
709C22×C4—131no—
710C22×C4—131no—
711C22×C4—131no—
712C22×C4—131no—
713C22×C4—131no—
714C22×C4—132no—
715C22×C4—132no—
716C22×C4—131no—
717C22×C4—132no—
718C22×C4C23×D1311yescharacteristic
719C22×C4C23×D1311yescharacteristic
720C22×C4C23×D1312yes—
721C22×C4C23×D1311yescharacteristic
722C22×C4C23×D1312yes—
723C22×C4C23×D1312yes—
724C22×C4C23×D1311yescharacteristic
725C22×C4C23×D1312yes—
726C22×C4C23×D1311yescharacteristic
727C22×C4C23×D1311yescharacteristic
728C22×C4C23×D1311yescharacteristic
729C4⋊C4—22no—
730C4⋊C4—24no—
731C4⋊C4—22no—
732C4⋊C4—22no—
733C4⋊C4—42no—
734C4⋊C4—134no—
735C4⋊C4—138no—
736C4⋊C4—138no—
737C4⋊C4—134no—
738C4⋊C4—134no—
739C4⋊C4—138no—
740C4⋊C4—138no—
741C4⋊C4—134no—
742C4⋊C4—138no—
743C4⋊C4—138no—
744C4⋊C4—138no—
745C4⋊C4—134no—
746C4⋊C4—264no—
747C4⋊C4—264no—
748C4⋊C4—262no—
749C4⋊C4—264no—
750C4⋊C4—264no—
751C4⋊C4—262no—
752C4⋊C4—264no—
753C4⋊C4—264no—
754C4⋊C4—262no—
755C4⋊C4—264no—
756C4⋊C4—262no—
757C4⋊C4—262no—
758C4⋊C4—522no—
759C4⋊C4—522no—
760C4⋊C4C2×C4×D1318yes—
761C4⋊C4C2×C4×D1314yes—
762C4⋊C4C2×C4×D1314yes—
763C4⋊C4C2×C4×D1318yes—
764C4⋊C4Q8×D1314yes—
765C42—24no—
766C42—22no—
767C42—22no—
768C42—42no—
769C42—42no—
770C42—138no—
771C42—138no—
772C42—134no—
773C42—138no—
774C42—134no—
775C42—138no—
776C42—134no—
777C42—134no—
778C42—264no—
779C42—264no—
780C42—264no—
781C42—264no—
782C42—262no—
783C42—264no—
784C42—262no—
785C42—262no—
786C42—264no—
787C42—262no—
788C42—264no—
789C42—262no—
790C42—262no—
791C42—264no—
792C42—262no—
793C42—262no—
794C42—262no—
795C42—521no—
796C42—521no—
797C42—522no—
798C42—521no—
799C42C2×C4×D1314yes—
800C13C4×#55711yescharacteristic, complemented, Sylow
801C23C24×D1311yescharacteristic
802Q8—1316no—
803Q8—2616no—
804Q8—268no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—22no—
823C2×C4—21no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—134no—
829C2×C4—132no—
830C2×C4—132no—
831C2×C4—134no—
832C2×C4—132no—
833C2×C4—132no—
834C2×C4—132no—
835C2×C4—134no—
836C2×C4—132no—
837C2×C4—132no—
838C2×C4—132no—
839C2×C4—132no—
840C2×C4—134no—
841C2×C4—132no—
842C2×C4—132no—
843C2×C4—261no—
844C2×C4—261no—
845C2×C4—262no—
846C2×C4—261no—
847C2×C4—261no—
848C2×C4—262no—
849C2×C4—261no—
850C2×C4—261no—
851C2×C4—261no—
852C2×C4—261no—
853C2×C4—261no—
854C2×C4—261no—
855C2×C4—262no—
856C2×C4—262no—
857C2×C4—262no—
858C2×C4—261no—
859C2×C4—261no—
860C2×C4—262no—
861C2×C4—262no—
862C2×C4—261no—
863C2×C4—262no—
864C2×C4C22×C4×D1312yes—
865C2×C4C22×C4×D1314yes—
866C2×C4C22×C4×D1314yes—
867C2×C4C22×C4×D1312yes—
868C2×C4C22×C4×D1312yes—
869C2×C4C2×Q8×D1314yes—
870C2×C4C2×Q8×D1312yes—
871C2×C4#41×D1312yes—
872C2×C4#41×D1312yes—
873C2×C4#41×D1312yes—
874C22C23×C4×D1311yescharacteristic
875C22C22×Q8×D1311yescharacteristic
876C22C2×#41×D1311yescharacteristic
877C22C2×#41×D1311yescharacteristic
878C22C2×#41×D1311yescharacteristic
879C22#1171965011yescharacteristic
880C22D13×2−1+411yescharacteristic
881C4—22no—
882C4—24no—
883C4—22no—
884C4—22no—
885C4—24no—
886C4—24no—
887C4—22no—
888C4—41no—
889C4—41no—
890C4—42no—
891C4—138no—
892C4—134no—
893C4—134no—
894C4—262no—
895C4—262no—
896C4—264no—
897C4—262no—
898C4—262no—
899C4—262no—
900C4—522no—
901C4—521no—
902C4—522no—
903C4C4×Q8×D1314yes—
904C2C2×C4×Q8×D1311yescharacteristic
905C2C4×#41×D1311yescharacteristic
906C2#1312804711yescharacteristic
907C2D13×#55711yescharacteristic
908C2#1312841511yescharacteristic
909C2#1312843011yescharacteristic
910C2#1312845011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2370C2
socle, prime radical, cosocleC23×C13C25
hypercenter#2370D13
hypocenterC13C4×#557
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2370

Complements

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

NH ≅ G/Ntype
25. #11719390C4semidirect
211. #88141Q8semidirect
441. Dic26C4×Q8semidirect
571. Dic13#557semidirect
800. C13C4×#557semidirect

Maximal subgroups

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

subgroupindex
C2×#117193902
#131179352
#131179332
#131179282
#131178952
#131178912
#131177942
#131177902
#131177562
#131177552
#131177502
#131174072
#125×Dic132
#131173952
#131173932
C4×#881412
C13×#23702
C4×#55713