Finite Group Databasebeta

← #16023718

Subgroups — #16023718

Order 3328.

2106 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88143C211yesmaximal, characteristic
2#13117939C212yesmaximal, complemented
3#13117938C212yesmaximal, complemented
4#13117935C212yesmaximal, complemented
5#13117929C212yesmaximal, complemented
6#13117714C211yesmaximal, characteristic
7#13117708C211yesmaximal, characteristic
8#13117706C211yesmaximal, characteristic
9#13117706C211yesmaximal, characteristic
10#13117705C211yesmaximal, characteristic
11#13117700C211yesmaximal, characteristic
12#13117700C211yesmaximal, characteristic
13#13117641C212yesmaximal, complemented
14#13117634C212yesmaximal, complemented
15#13117438C211yesmaximal, characteristic
16#13117437C211yesmaximal, characteristic
17#13117393C212yesmaximal, complemented
18C4×#88143C212yesmaximal, complemented
19#13117227C211yesmaximal, characteristic
20#13117192C211yesmaximal, characteristic
21#13117191C211yesmaximal, characteristic
22#117×Dic13C211yesmaximal, characteristic
23C13×#2344C211yesmaximal, characteristic
24C2×C13×#117C2211yescharacteristic
25C2×C13×#117C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C2×#88180C2211yescharacteristic
28C2×#88180C2211yescharacteristic
29C22×C4⋊Dic13C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×#6101C2211yescharacteristic
33C22×#6101C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C2×#88143C4116yescomplemented
36C2×#88143C2211yescharacteristic
37C2×#88143C2211yescharacteristic
38C2×#88143C2211yescharacteristic
39C2×#88143C2211yescharacteristic
40C2×#88143C2211yescharacteristic
41C2×#88143C2211yescharacteristic
42C2×#88143C2211yescharacteristic
43C2×#88143C2211yescharacteristic
44C2×#88131C2211yescharacteristic
45C2×#88131C2211yescharacteristic
46C13×#389C2212yes—
47C13×#387C2212yes—
48C13×#387C2212yes—
49C13×#381C2211yescharacteristic
50C13×#381C2211yescharacteristic
51C13×#380C2211yescharacteristic
52C4×C13×C4⋊C4C2212yes—
53C4×C13×C22⋊C4C2211yescharacteristic
54#11718873C2211yescharacteristic
55#11718872C2211yescharacteristic
56#11718872C2211yescharacteristic
57C4×C22⋊Dic13C2211yescharacteristic
58#11718646C2212yes—
59#11718642C2212yes—
60#11718642C2212yes—
61#11718639C2212yes—
62#11718639C2212yes—
63#11718639C2212yes—
64#11718639C2212yes—
65#11718639C2212yes—
66C4⋊C4×Dic13C2212yes—
67C4⋊C4×Dic13C2212yes—
68C4⋊C4×Dic13C2212yes—
69C4⋊C4×Dic13C2212yes—
70C4⋊C4×Dic13C2212yes—
71#11718633C2212yes—
72#11718633C2212yes—
73#11718633C2212yes—
74#11718604C2211yescharacteristic
75#11718604C2211yescharacteristic
76#11718603C2211yescharacteristic
77#11718603C2211yescharacteristic
78#11718603C2211yescharacteristic
79#11718603C2211yescharacteristic
80C22⋊C4×Dic13C2211yescharacteristic
81C22⋊C4×Dic13C2211yescharacteristic
82C22⋊C4×Dic13C2211yescharacteristic
83C22⋊C4×Dic13C2211yescharacteristic
84C22⋊C4×Dic13C2211yescharacteristic
85C22⋊C4×Dic13C2211yescharacteristic
86C22⋊C4×Dic13C2211yescharacteristic
87C22⋊C4×Dic13C2211yescharacteristic
88C4×C4⋊Dic13C2212yes—
89C4×C4⋊Dic13C2212yes—
90#11718594C2212yes—
91#11718594C2212yes—
92#11718594C2212yes—
93#11718593C2212yes—
94C4×#6101C2212yes—
95C4×#6101C2212yes—
96C4×#6101C2212yes—
97C4×#6101C2212yes—
98C4×#6101C2212yes—
99C42×Dic13C2212yes—
100#11718316C2212yes—
101#11718316C2212yes—
102#11718316C2212yes—
103#11718316C2212yes—
104#11718316C2212yes—
105#11718315C2212yes—
106#11718315C2212yes—
107#11718314C2212yes—
108#11718314C2212yes—
109#11718313C2212yes—
110#11718313C2212yes—
111#11718313C2212yes—
112#11718312C2212yes—
113#11718311C2212yes—
114#11718310C2212yes—
115#11718310C2212yes—
116#11718310C2212yes—
117#11718310C2212yes—
118#11718310C2212yes—
119#11718310C2212yes—
120#11718309C2212yes—
121#11718308C2212yes—
122#11718308C2212yes—
123#11718308C2212yes—
124C23×C4×C13C2311yescharacteristic
125C23×C4×C13C2311yescharacteristic
126C23×C4×C13C2311yescharacteristic
127C23×Dic13C2311yescharacteristic
128C23×Dic13C2311yescharacteristic
129C23×Dic13C2311yescharacteristic
130C23×Dic13C2311yescharacteristic
131C13×#117—24no—
132C13×#117—24no—
133C2×C13×C4⋊C4C2×C418yes—
134C2×C13×C4⋊C4C2312yes—
135C2×C13×C4⋊C4C2312yes—
136C2×C13×C4⋊C4C2312yes—
137C2×C13×C4⋊C4C2311yescharacteristic
138C2×C13×C4⋊C4C2311yescharacteristic
139C2×C13×C4⋊C4C2311yescharacteristic
140C2×C13×C4⋊C4C2311yescharacteristic
141C2×C13×C22⋊C4C2311yescharacteristic
142C2×C13×C22⋊C4C2311yescharacteristic
143C2×C13×C22⋊C4C2311yescharacteristic
144C2×C13×C22⋊C4C2311yescharacteristic
145C2×C42×C13C2312yes—
146C2×C42×C13C2312yes—
147C2×C42×C13C2312yes—
148C2×C22⋊Dic13C2311yescharacteristic
149C2×C22⋊Dic13C2311yescharacteristic
150C2×C22⋊Dic13C2311yescharacteristic
151C2×C22⋊Dic13C2311yescharacteristic
152#88180—24no—
153#88180—24no—
154C2×C4⋊Dic13C2×C418yes—
155C2×C4⋊Dic13C2312yes—
156C2×C4⋊Dic13C2312yes—
157C2×C4⋊Dic13C2312yes—
158C2×C4⋊Dic13C2311yescharacteristic
159C2×C4⋊Dic13C2311yescharacteristic
160C2×C4⋊Dic13C2311yescharacteristic
161C2×C4⋊Dic13C2311yescharacteristic
162C2×#6101C2×C418yes—
163C2×#6101C2×C418yes—
164C2×#6101C2×C418yes—
165C2×#6101C2×C418yes—
166C2×#6101C2312yes—
167C2×#6101C2312yes—
168C2×#6101C2312yes—
169C2×#6101C2312yes—
170C2×#6101C2312yes—
171C2×#6101C2312yes—
172C2×#6101C2311yescharacteristic
173C2×#6101C2311yescharacteristic
174C2×#6101C2311yescharacteristic
175C2×#6101C2311yescharacteristic
176C2×#6101C2311yescharacteristic
177C2×#6101C2311yescharacteristic
178C2×#6101C2311yescharacteristic
179C2×#6101C2311yescharacteristic
180C2×#6101C2311yescharacteristic
181C2×#6101C2311yescharacteristic
182C2×#6101C2311yescharacteristic
183C2×#6101C2311yescharacteristic
184C2×#6101C2311yescharacteristic
185C2×#6101C2311yescharacteristic
186C2×#6101C2311yescharacteristic
187C2×#6101C2311yescharacteristic
188C2×C4×Dic13C2×C418yes—
189C2×C4×Dic13C2312yes—
190C2×C4×Dic13C2312yes—
191C2×C4×Dic13C2312yes—
192C2×C4×Dic13C2312yes—
193C2×C4×Dic13C2312yes—
194C2×C4×Dic13C2312yes—
195C2×C4×Dic13C2312yes—
196C2×C4×Dic13C2312yes—
197C2×C4×Dic13C2312yes—
198C2×C4×Dic13C2312yes—
199C2×C4×Dic13C2312yes—
200C2×C4×Dic13C2312yes—
201C2×C4×Dic13C2312yes—
202C2×C4×Dic13C2311yescharacteristic
203C2×C4×Dic13C2311yescharacteristic
204C2×C4×Dic13C2311yescharacteristic
205C2×C4×Dic13C2311yescharacteristic
206#88143C2×C418yes—
207#88143C2×C418yes—
208#88143C2×C418yes—
209#88143C2×C418yes—
210#88143C2×C418yes—
211#88143C2×C418yes—
212#88143C2×C418yes—
213#88143C2×C418yes—
214#88131—24no—
215#88131—24no—
216C13×#95C2312yes—
217C13×#95C2312yes—
218C13×#95C2312yes—
219C13×#95C2312yes—
220C13×#95C2312yes—
221C13×#95C2312yes—
222#88071C2312yes—
223#88071C2312yes—
224#88071C2312yes—
225#88071C2312yes—
226#88071C2312yes—
227#88071C2312yes—
228#88071C2312yes—
229#88071C2312yes—
230#88071C2312yes—
231#88071C2312yes—
232#88071C2312yes—
233#88071C2312yes—
234#88071C2312yes—
235#88071C2312yes—
236#88071C2312yes—
237#88071C2312yes—
238#88071C2312yes—
239#88071C2312yes—
240#88071C2312yes—
241#88071C2312yes—
242#88071C2312yes—
243#88071C2312yes—
244#34239—131nomaximal, Sylow
245C24×C13C2411yescharacteristic
246C22×C4×C13—22no—
247C22×C4×C13—22no—
248C22×C4×C13—22no—
249C22×C4×C13—22no—
250C22×C4×C13—42no—
251C22×C4×C13C22×C414yes—
252C22×C4×C13C22×C414yes—
253C22×C4×C13C22×C414yes—
254C22×C4×C13C2412yes—
255C22×C4×C13C2412yes—
256C22×C4×C13C2412yes—
257C22×C4×C13C2411yescharacteristic
258C22×C4×C13C2411yescharacteristic
259C22×C4×C13C2411yescharacteristic
260C22×C4×C13C2411yescharacteristic
261C22×C4×C13C2411yescharacteristic
262C22×C4×C13C2411yescharacteristic
263C22×C4×C13C2412yes—
264C22×Dic13—22no—
265C22×Dic13—22no—
266C22×Dic13—24no—
267C22×Dic13—42no—
268C22×Dic13—42no—
269C22×Dic13C22×C414yes—
270C22×Dic13C22×C414yes—
271C22×Dic13C22×C414yes—
272C22×Dic13C22×C414yes—
273C22×Dic13C2412yes—
274C22×Dic13C2412yes—
275C22×Dic13C2412yes—
276C22×Dic13C2411yescharacteristic
277C22×Dic13C2411yescharacteristic
278C22×Dic13C2411yescharacteristic
279C22×Dic13C2411yescharacteristic
280C22×Dic13C2411yescharacteristic
281C22×Dic13C2411yescharacteristic
282C22×Dic13C2411yescharacteristic
283C22×Dic13C2412yes—
284C22×Dic13C2411yescharacteristic
285C13×C4⋊C4—24no—
286C13×C4⋊C4—24no—
287C13×C4⋊C4—42no—
288C13×C4⋊C4C22×C414yes—
289C13×C4⋊C4C22×C414yes—
290C13×C4⋊C4C22×C414yes—
291C13×C4⋊C4C22×C414yes—
292C13×C22⋊C4—22no—
293C13×C22⋊C4—22no—
294C13×C22⋊C4—22no—
295C13×C22⋊C4#4114yes—
296C42×C13—24no—
297C42×C13—24no—
298C42×C13—42no—
299C22⋊Dic13—22no—
300C22⋊Dic13—22no—
301C22⋊Dic13—22no—
302C22⋊Dic13#4114yes—
303C4⋊Dic13—24no—
304C4⋊Dic13—24no—
305C4⋊Dic13—42no—
306C4⋊Dic13C22×C414yes—
307C4⋊Dic13C22×C414yes—
308C4⋊Dic13C22×C414yes—
309C4⋊Dic13C22×C414yes—
310#6101—24no—
311#6101—24no—
312#6101—24no—
313#6101—24no—
314#6101—42no—
315#6101—42no—
316#6101C22×C414yes—
317#6101C22×C414yes—
318#6101C22×C414yes—
319#6101C22×C414yes—
320#6101C22×C414yes—
321#6101C22×C414yes—
322#6101C22×C414yes—
323#6101C22×C414yes—
324#6101C22×C414yes—
325#6101C22×C414yes—
326#6101C22×C414yes—
327#6101C22×C414yes—
328#6101C22×C414yes—
329#6101C22×C414yes—
330#6101C22×C414yes—
331#6101C22×C414yes—
332C4×Dic13—24no—
333C4×Dic13—24no—
334C4×Dic13—24no—
335C4×Dic13—24no—
336C4×Dic13—24no—
337C4×Dic13—24no—
338C4×Dic13—42no—
339C4×Dic13—42no—
340C4×Dic13—42no—
341C4×Dic13—42no—
342C4×Dic13—42no—
343C4×Dic13—42no—
344C4×Dic13—42no—
345C4×Dic13C22×C414yes—
346C4×Dic13C22×C414yes—
347C4×Dic13C22×C414yes—
348C4×Dic13C22×C414yes—
349C22×#125—131no—
350#2371—132no—
351#2371—132no—
352#2370—132no—
353#2370—132no—
354#2345—131no—
355#2345—131no—
356#2344—131no—
357#2344—131no—
358#2344—131no—
359#2344—131no—
360#2344—131no—
361#2344D1311yescharacteristic
362#2336—132no—
363#2336—132no—
364#2313—131no—
365#2313—131no—
366C4×#125—132no—
367C4×#125—132no—
368#2283—131no—
369#2274—131no—
370#2274—131no—
371C4×#117—131no—
372C23×C13—22no—
373C23×C13—22no—
374C23×C13C23×C412yes—
375C23×C13C2×#4112yes—
376C23×C13C2×#4112yes—
377C23×C13C2511yescharacteristic
378C2×C4×C13—28no—
379C2×C4×C13—28no—
380C2×C4×C13—21no—
381C2×C4×C13—21no—
382C2×C4×C13—21no—
383C2×C4×C13—21no—
384C2×C4×C13—21no—
385C2×C4×C13—21no—
386C2×C4×C13—21no—
387C2×C4×C13—21no—
388C2×C4×C13—22no—
389C2×C4×C13—22no—
390C2×C4×C13—22no—
391C2×C4×C13—22no—
392C2×C4×C13—22no—
393C2×C4×C13—22no—
394C2×C4×C13—22no—
395C2×C4×C13—22no—
396C2×C4×C13—22no—
397C2×C4×C13—22no—
398C2×C4×C13—22no—
399C2×C4×C13—22no—
400C2×C4×C13—22no—
401C2×C4×C13—44no—
402C2×C4×C13C23×C412yes—
403C2×C4×C13C23×C412yes—
404C2×C4×C13C23×C412yes—
405C2×C4×C13C23×C412yes—
406C2×C4×C13C23×C412yes—
407C2×C4×C13C23×C412yes—
408C2×C4×C13C2×#4114yes—
409C2×Dic13—28no—
410C2×Dic13—21no—
411C2×Dic13—21no—
412C2×Dic13—21no—
413C2×Dic13—21no—
414C2×Dic13—22no—
415C2×Dic13—22no—
416C2×Dic13—22no—
417C2×Dic13—22no—
418C2×Dic13—22no—
419C2×Dic13—22no—
420C2×Dic13—22no—
421C2×Dic13—28no—
422C2×Dic13—22no—
423C2×Dic13—22no—
424C2×Dic13—22no—
425C2×Dic13—22no—
426C2×Dic13—22no—
427C2×Dic13—22no—
428C2×Dic13—22no—
429C2×Dic13—22no—
430C2×Dic13—22no—
431C2×Dic13—44no—
432C2×Dic13—44no—
433C2×Dic13C23×C412yes—
434C2×Dic13C23×C412yes—
435C2×Dic13C23×C412yes—
436C2×Dic13C23×C412yes—
437C2×Dic13C23×C412yes—
438C2×Dic13C23×C412yes—
439C2×Dic13C23×C412yes—
440C2×Dic13C23×C412yes—
441C2×Dic13C2×#4114yes—
442C2×Dic132−1+414yes—
443C2×#125—1316no—
444C2×#125—131no—
445C2×#125—131no—
446C2×#125—131no—
447C2×#125—131no—
448C2×#125—131no—
449C2×#125—131no—
450C2×#125—131no—
451C2×#125—131no—
452C2×#117—131no—
453C2×#117—131no—
454C2×#117—131no—
455C2×#117—131no—
456C2×#117C2×D1311yescharacteristic
457C2×#117C2×D1311yescharacteristic
458C22×C4⋊C4—131no—
459C22×C4⋊C4—131no—
460C22×C4⋊C4—131no—
461C22×C4⋊C4—131no—
462C22×C4⋊C4—131no—
463C22×C4⋊C4C2×D1311yescharacteristic
464C22×C42—131no—
465#389—132no—
466#389—132no—
467#389—132no—
468#389—132no—
469#389—132no—
470#389—132no—
471#389—132no—
472#389C2×D1312yes—
473#387—132no—
474#387—132no—
475#387—132no—
476#387—132no—
477#387—132no—
478#387—132no—
479#387—132no—
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#387—132no—
491#387—132no—
492#387—132no—
493#387—132no—
494#387—132no—
495#387C2×D1312yes—
496#387C2×D1312yes—
497#383—132no—
498#382—132no—
499#381—131no—
500#381—131no—
501#381—131no—
502#381—131no—
503#381C2×D1311yescharacteristic
504#381C2×D1311yescharacteristic
505#380—131no—
506#380—131no—
507#380—131no—
508#380—131no—
509#380—131no—
510#380C2×D1311yescharacteristic
511C4×C4⋊C4—132no—
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—132no—
521C4×C4⋊C4—132no—
522C4×C4⋊C4—132no—
523C4×C4⋊C4—132no—
524C4×C4⋊C4—132no—
525C4×C4⋊C4—132no—
526C4×C4⋊C4—132no—
527C4×C4⋊C4—132no—
528C4×C4⋊C4—132no—
529C4×C4⋊C4C2×D1312yes—
530C4×C22⋊C4—131no—
531C4×C22⋊C4—131no—
532C4×C22⋊C4—131no—
533C4×C22⋊C4—131no—
534C4×C22⋊C4—131no—
535C4×C22⋊C4—131no—
536C4×C22⋊C4—131no—
537C4×C22⋊C4—131no—
538C4×C22⋊C4—131no—
539C4×C22⋊C4C2×D1311yescharacteristic
540#376—132no—
541#376—132no—
542C43—132no—
543C22×C13—22no—
544C22×C13—22no—
545C22×C13—24no—
546C22×C13—24no—
547C22×C13C4×#4114yes—
548C22×C13C24×C411yescharacteristic
549C22×C13C22×#4111yescharacteristic
550C22×C13C22×#4111yescharacteristic
551C22×C13C2×2−1+412yes—
552C22×C13#58512yes—
553C4×C13—22no—
554C4×C13—22no—
555C4×C13—22no—
556C4×C13—22no—
557C4×C13—22no—
558C4×C13—22no—
559C4×C13—24no—
560C4×C13—42no—
561C4×C13—42no—
562C4×C13—42no—
563Dic13—22no—
564Dic13—22no—
565Dic13—22no—
566Dic13—22no—
567Dic13—22no—
568Dic13—22no—
569Dic13—22no—
570Dic13—24no—
571Dic13—42no—
572Dic13—42no—
573Dic13—42no—
574Dic13#51914yes—
575C23×C4—131no—
576C23×C4—131no—
577C23×C4—131no—
578C23×C4—131no—
579C23×C4C22×D1311yescharacteristic
580C23×C4C22×D1311yescharacteristic
581C23×C4C22×D1311yescharacteristic
582#125—138no—
583#125—138no—
584#125—138no—
585#125—138no—
586#125—138no—
587#125—138no—
588#125—138no—
589#125—138no—
590#117—24no—
591#117—24no—
592#117—264no—
593#117—264no—
594#117—264no—
595#117—264no—
596C2×C4⋊C4—138no—
597C2×C4⋊C4—138no—
598C2×C4⋊C4—138no—
599C2×C4⋊C4—138no—
600C2×C4⋊C4—138no—
601C2×C4⋊C4—131no—
602C2×C4⋊C4—131no—
603C2×C4⋊C4—131no—
604C2×C4⋊C4—131no—
605C2×C4⋊C4—131no—
606C2×C4⋊C4—131no—
607C2×C4⋊C4—131no—
608C2×C4⋊C4—131no—
609C2×C4⋊C4—131no—
610C2×C4⋊C4—131no—
611C2×C4⋊C4—131no—
612C2×C4⋊C4—131no—
613C2×C4⋊C4—131no—
614C2×C4⋊C4—131no—
615C2×C4⋊C4—131no—
616C2×C4⋊C4—131no—
617C2×C4⋊C4—131no—
618C2×C4⋊C4—131no—
619C2×C4⋊C4—131no—
620C2×C4⋊C4—131no—
621C2×C4⋊C4—132no—
622C2×C4⋊C4—132no—
623C2×C4⋊C4—132no—
624C2×C4⋊C4—132no—
625C2×C4⋊C4—132no—
626C2×C4⋊C4—132no—
627C2×C4⋊C4—132no—
628C2×C4⋊C4—132no—
629C2×C4⋊C4—132no—
630C2×C4⋊C4C4×D1318yes—
631C2×C4⋊C4C22×D1312yes—
632C2×C4⋊C4C22×D1312yes—
633C2×C4⋊C4C22×D1312yes—
634C2×C4⋊C4C22×D1311yescharacteristic
635C2×C4⋊C4C22×D1311yescharacteristic
636C2×C4⋊C4C22×D1311yescharacteristic
637C2×C4⋊C4C22×D1311yescharacteristic
638C2×C22⋊C4—131no—
639C2×C22⋊C4—131no—
640C2×C22⋊C4—131no—
641C2×C22⋊C4—131no—
642C2×C22⋊C4C22×D1311yescharacteristic
643C2×C22⋊C4C22×D1311yescharacteristic
644C2×C22⋊C4C22×D1311yescharacteristic
645C2×C22⋊C4C22×D1311yescharacteristic
646C2×C42—138no—
647C2×C42—131no—
648C2×C42—131no—
649C2×C42—131no—
650C2×C42—131no—
651C2×C42—132no—
652C2×C42—132no—
653C2×C42—132no—
654C2×C42—132no—
655C2×C42—132no—
656C2×C42—132no—
657C2×C42—132no—
658C2×C42—132no—
659C2×C42—132no—
660C2×C42—132no—
661C2×C42—132no—
662C2×C42—132no—
663C2×C42—132no—
664C2×C42C22×D1312yes—
665C2×C42C22×D1312yes—
666C2×C42C22×D1312yes—
667#95—132no—
668#95—132no—
669#95—132no—
670#95—132no—
671#95—132no—
672#95—132no—
673#95—132no—
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#95—132no—
684#95—132no—
685#95—132no—
686#95—132no—
687#95—132no—
688#95—132no—
689#95C22×D1312yes—
690#95C22×D1312yes—
691#95C22×D1312yes—
692#95C22×D1312yes—
693#95C22×D1312yes—
694#95C22×D1312yes—
695C2×C13—24no—
696C2×C13C2×C4×#4111yescharacteristic
697C2×C13C2×#51911yescharacteristic
698C2×C13#342811yescharacteristic
699C2×C13#351512yes—
700C2×C13#351512yes—
701C24C23×D1311yescharacteristic
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—42no—
707C22×C4—131no—
708C22×C4—134no—
709C22×C4—134no—
710C22×C4—131no—
711C22×C4—132no—
712C22×C4—131no—
713C22×C4—131no—
714C22×C4—131no—
715C22×C4—131no—
716C22×C4—131no—
717C22×C4—131no—
718C22×C4—134no—
719C22×C4—134no—
720C22×C4—132no—
721C22×C4—132no—
722C22×C4—132no—
723C22×C4—264no—
724C22×C4—262no—
725C22×C4—262no—
726C22×C4—522no—
727C22×C4—522no—
728C22×C4C2×C4×D1314yes—
729C22×C4C2×C4×D1314yes—
730C22×C4C2×C4×D1314yes—
731C22×C4C23×D1312yes—
732C22×C4C23×D1312yes—
733C22×C4C23×D1312yes—
734C22×C4C23×D1311yescharacteristic
735C22×C4C23×D1311yescharacteristic
736C22×C4C23×D1311yescharacteristic
737C22×C4C23×D1311yescharacteristic
738C22×C4C23×D1311yescharacteristic
739C22×C4C23×D1311yescharacteristic
740C22×C4C23×D1312yes—
741C4⋊C4—24no—
742C4⋊C4—24no—
743C4⋊C4—42no—
744C4⋊C4—134no—
745C4⋊C4—134no—
746C4⋊C4—134no—
747C4⋊C4—134no—
748C4⋊C4—134no—
749C4⋊C4—134no—
750C4⋊C4—134no—
751C4⋊C4—134no—
752C4⋊C4—134no—
753C4⋊C4—134no—
754C4⋊C4—134no—
755C4⋊C4—134no—
756C4⋊C4—134no—
757C4⋊C4—134no—
758C4⋊C4—134no—
759C4⋊C4—134no—
760C4⋊C4—134no—
761C4⋊C4—134no—
762C4⋊C4—134no—
763C4⋊C4—134no—
764C4⋊C4—264no—
765C4⋊C4—264no—
766C4⋊C4—264no—
767C4⋊C4—264no—
768C4⋊C4—264no—
769C4⋊C4—264no—
770C4⋊C4—522no—
771C4⋊C4—522no—
772C4⋊C4—522no—
773C4⋊C4C2×C4×D1314yes—
774C4⋊C4C2×C4×D1314yes—
775C4⋊C4C2×C4×D1314yes—
776C4⋊C4C2×C4×D1314yes—
777C22⋊C4—22no—
778C22⋊C4—22no—
779C22⋊C4—22no—
780C22⋊C4—134no—
781C22⋊C4—262no—
782C22⋊C4—262no—
783C22⋊C4—262no—
784C22⋊C4#612914yes—
785C42—24no—
786C42—24no—
787C42—42no—
788C42—134no—
789C42—134no—
790C42—134no—
791C42—134no—
792C42—264no—
793C42—264no—
794C42—264no—
795C42—264no—
796C42—264no—
797C42—264no—
798C42—522no—
799C42—522no—
800C42—522no—
801C42—522no—
802C42—522no—
803C42—522no—
804C42—522no—
805C13#3423911yescharacteristic, complemented, Sylow
806C23—22no—
807C23—22no—
808C23C22×C4×D1312yes—
809C23C2×#612912yes—
810C23#41×D1312yes—
811C23C24×D1311yescharacteristic
812C2×C4—28no—
813C2×C4—28no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—44no—
836C2×C4—132no—
837C2×C4—134no—
838C2×C4—132no—
839C2×C4—132no—
840C2×C4—132no—
841C2×C4—132no—
842C2×C4—132no—
843C2×C4—132no—
844C2×C4—132no—
845C2×C4—134no—
846C2×C4—268no—
847C2×C4—268no—
848C2×C4—261no—
849C2×C4—261no—
850C2×C4—261no—
851C2×C4—261no—
852C2×C4—262no—
853C2×C4—262no—
854C2×C4—262no—
855C2×C4—262no—
856C2×C4—262no—
857C2×C4—262no—
858C2×C4—262no—
859C2×C4—262no—
860C2×C4—262no—
861C2×C4—262no—
862C2×C4—262no—
863C2×C4—262no—
864C2×C4—262no—
865C2×C4—262no—
866C2×C4—262no—
867C2×C4—262no—
868C2×C4—524no—
869C2×C4—524no—
870C2×C4C22×C4×D1312yes—
871C2×C4C22×C4×D1312yes—
872C2×C4C22×C4×D1312yes—
873C2×C4C22×C4×D1312yes—
874C2×C4C22×C4×D1312yes—
875C2×C4C22×C4×D1312yes—
876C2×C4C2×#612914yes—
877C22—22no—
878C22—24no—
879C22—24no—
880C22—22no—
881C22C4×#612914yes—
882C22C23×C4×D1311yescharacteristic
883C22C22×#612911yescharacteristic
884C22C2×#41×D1311yescharacteristic
885C22#1171964812yes—
886C22D13×2−1+412yes—
887C4—22no—
888C4—22no—
889C4—22no—
890C4—22no—
891C4—24no—
892C4—22no—
893C4—22no—
894C4—42no—
895C4—42no—
896C4—42no—
897C4—134no—
898C4—262no—
899C4—262no—
900C4—262no—
901C4—264no—
902C4—262no—
903C4—262no—
904C4—262no—
905C4—262no—
906C4—522no—
907C4—522no—
908C4—522no—
909C2—24no—
910C2C2×C4×#612911yescharacteristic
911C2D13×#51911yescharacteristic
912C2#1312803711yescharacteristic
913C2#1312880112yes—
914C2#1312880312yes—
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2344C2
socle, cosocleC23×C13C25
prime radicalC24×C13C24
hypercenter#2344D13
hypocenterC13#34239
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2344

Complements

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

NH ≅ G/Ntype
2. #13117939C2semidirect
3. #13117938C2semidirect
4. #13117935C2semidirect
5. #13117929C2semidirect
13. #13117641C2semidirect
14. #13117634C2semidirect
17. #13117393C2semidirect
18. C4×#88143C2semidirect
35. C2×#88143C4semidirect
805. C13#34239semidirect

Maximal subgroups

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

subgroupindex
C22×#881432
#131179392
#131179382
#131179352
#131179292
#131177142
#131177082
#131177062
#131177052
#131177002
#131176412
#131176342
#131174382
#131174372
#131173932
C4×#881432
#131172272
#131171922
#131171912
#117×Dic132
C13×#23442
#3423913