Finite Group Databasebeta

← #16028186

Subgroups — #16028186

Order 3328.

1940 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719272C211yesmaximal, characteristic
2#13118021C212yesmaximal
3#13118018C212yesmaximal
4#13117935C212yesmaximal
5#13117892C211yesmaximal, characteristic
6#13117890C211yesmaximal, characteristic
7#13117890C211yesmaximal, characteristic
8#13117794C212yesmaximal
9#13117788C211yesmaximal, characteristic
10#13117755C211yesmaximal, characteristic
11#13117750C211yesmaximal, characteristic
12#13117640C212yesmaximal
13#13117634C212yesmaximal
14#13117574C212yesmaximal
15#13117553C211yesmaximal, characteristic
16#13117552C211yesmaximal, characteristic
17#13117487C211yesmaximal, characteristic
18#13117484C212yesmaximal
19#13117483C211yesmaximal, characteristic
20C4×#88198C211yesmaximal, characteristic
21#13117312C211yesmaximal, characteristic
22#13117307C211yesmaximal, characteristic
23C13×#2351C211yesmaximal, characteristic
24C2×C4×Q8×C13C2211yescharacteristic
25C2×C4×Q8×C13C2211yescharacteristic
26C2×C4×Q8×C13C2211yescharacteristic
27C2×#88198C2211yescharacteristic
28C2×#88198C2211yescharacteristic
29#11719272C4116yescomplemented
30C2×#88143C2212yes—
31C2×#88143C2212yes—
32C2×#88141C2211yescharacteristic
33C2×#88141C2211yescharacteristic
34C2×#88141C2211yescharacteristic
35C2×#88141C2211yescharacteristic
36C2×#88124C2212yes—
37C2×#88123C2211yescharacteristic
38C2×C4×Dic26C2211yescharacteristic
39C2×C4×Dic26C2211yescharacteristic
40C2×C4×Dic26C2212yes—
41C2×C4×Dic26C2211yescharacteristic
42C13×#389C2211yescharacteristic
43C13×#389C2211yescharacteristic
44C13×#389C2212yes—
45C13×#389C2212yes—
46C13×#382C2212yes—
47C13×#382C2211yescharacteristic
48C4×C13×C4⋊C4C2212yes—
49C4×C13×C4⋊C4C2211yescharacteristic
50#11718891C2211yescharacteristic
51#11718891C2211yescharacteristic
52#11718646C2211yescharacteristic
53#11718646C2211yescharacteristic
54#11718642C2212yes—
55#11718642C2212yes—
56#11718639C2212yes—
57#11718639C2212yes—
58#11718639C2212yes—
59#11718639C2211yescharacteristic
60#11718639C2212yes—
61#11718639C2212yes—
62#11718639C2212yes—
63#11718639C2211yescharacteristic
64#11718638C2212yes—
65#11718638C2211yescharacteristic
66#11718637C2211yescharacteristic
67#11718637C2212yes—
68C4⋊C4×Dic13C2211yescharacteristic
69C4⋊C4×Dic13C2212yes—
70C4⋊C4×Dic13C2211yescharacteristic
71C4⋊C4×Dic13C2212yes—
72C4⋊C4×Dic13C2212yes—
73#11718635C2211yescharacteristic
74#11718635C2211yescharacteristic
75#11718634C2212yes—
76#11718633C2212yes—
77#11718633C2212yes—
78#11718633C2212yes—
79#11718633C2212yes—
80#11718633C2212yes—
81#11718633C2212yes—
82#11718633C2211yescharacteristic
83#11718633C2211yescharacteristic
84#11718598C2212yes—
85#11718597C2212yes—
86C4×C4⋊Dic13C2211yescharacteristic
87#11718594C2212yes—
88#11718594C2212yes—
89#11718594C2212yes—
90#11718594C2212yes—
91#11718593C2211yescharacteristic
92#11718593C2211yescharacteristic
93C4×#6101C2211yescharacteristic
94C4×#6101C2211yescharacteristic
95C4×#6101C2212yes—
96C4×#6101C2212yes—
97C4×#6101C2212yes—
98C4×#6101C2212yes—
99C42×Dic13C2211yescharacteristic
100#11718590C2211yescharacteristic
101#11718590C2211yescharacteristic
102#11718316C2212yes—
103#11718316C2212yes—
104#11718315C2212yes—
105#11718315C2212yes—
106#11718315C2212yes—
107#11718315C2212yes—
108#11718315C2212yes—
109#11718315C2212yes—
110#11718314C2211yescharacteristic
111#11718314C2212yes—
112#11718314C2211yescharacteristic
113#11718313C2212yes—
114#11718312C2212yes—
115#11718311C2212yes—
116#11718310C2212yes—
117#11718310C2212yes—
118#11718309C2212yes—
119#11718308C2212yes—
120#11718308C2212yes—
121#11718307C2211yescharacteristic
122#11718307C2212yes—
123#11718307C2211yescharacteristic
124C22×Q8×C13C2311yescharacteristic
125C22×Dic26C2311yescharacteristic
126C22×Dic26C2311yescharacteristic
127C22×Dic26C2311yescharacteristic
128C4×Q8×C13—42no—
129C4×Q8×C13—42no—
130C4×Q8×C13C2×C418yes—
131C2×C13×C4⋊C4C2312yes—
132C2×C13×C4⋊C4C2311yescharacteristic
133C2×C13×C4⋊C4C2311yescharacteristic
134C2×C13×C4⋊C4C2311yescharacteristic
135C2×C13×C4⋊C4C2311yescharacteristic
136C2×C13×C4⋊C4C2312yes—
137C2×C13×C4⋊C4C2312yes—
138C2×C13×C4⋊C4C2312yes—
139C2×C13×C4⋊C4C2311yescharacteristic
140C2×C13×C4⋊C4C2312yes—
141C2×C42×C13C2311yescharacteristic
142C2×C42×C13C2311yescharacteristic
143C2×C42×C13C2312yes—
144C2×C42×C13C2312yes—
145C2×C42×C13C2311yescharacteristic
146C2×C42×C13C2312yes—
147#88198C2×C418yes—
148#88198C2×C418yes—
149C2×C4⋊Dic13C2311yescharacteristic
150C2×C4⋊Dic13C2311yescharacteristic
151C2×C4⋊Dic13C2312yes—
152C2×C4⋊Dic13C2312yes—
153C2×C4⋊Dic13C2312yes—
154C2×C4⋊Dic13C2311yescharacteristic
155C2×C4⋊Dic13C2312yes—
156C2×#6101C2311yescharacteristic
157C2×#6101C2312yes—
158C2×#6101C2311yescharacteristic
159C2×#6101C2311yescharacteristic
160C2×#6101C2312yes—
161C2×#6101C2312yes—
162C2×#6101C2312yes—
163C2×#6101C2312yes—
164C2×#6101C2311yescharacteristic
165C2×#6101C2312yes—
166C2×#6101C2311yescharacteristic
167C2×#6101C2311yescharacteristic
168C2×#6101C2312yes—
169C2×#6101C2312yes—
170C2×#6101C2312yes—
171C2×#6101C2312yes—
172C2×#6101C2312yes—
173C2×#6101C2312yes—
174C2×C4×Dic13C2311yescharacteristic
175C2×C4×Dic13C2311yescharacteristic
176C2×C4×Dic13C2312yes—
177C2×C4×Dic13C2311yescharacteristic
178C2×C4×Dic13C2311yescharacteristic
179C2×C4×Dic13C2311yescharacteristic
180C2×C4×Dic13C2312yes—
181C2×C4×Dic13C2312yes—
182C2×C4×Dic13C2312yes—
183C2×C4×Dic13C2312yes—
184C2×C4×Dic13C2312yes—
185C2×C4×Dic13C2312yes—
186C2×C4×Dic13C2311yescharacteristic
187C2×C4×Dic13C2312yes—
188C2×C4×Dic13C2312yes—
189C2×C4×Dic13C2311yescharacteristic
190C2×C4×Dic13C2311yescharacteristic
191#88143C2×C4116yes—
192#88143C2×C4116yes—
193#88141—42no—
194#88141—42no—
195#88141C2×C418yes—
196#88141C2×C418yes—
197#88124C2×C4116yes—
198#88123C2×C418yes—
199C4×Dic26—42no—
200C4×Dic26—42no—
201C4×Dic26C2×C4116yes—
202C4×Dic26C2×C418yes—
203C13×#95C2311yescharacteristic
204C13×#95C2312yes—
205C13×#95C2311yescharacteristic
206C13×#95C2312yes—
207C13×#95C2312yes—
208C13×#95C2312yes—
209#88071C2311yescharacteristic
210#88071C2312yes—
211#88071C2311yescharacteristic
212#88071C2312yes—
213#88071C2311yescharacteristic
214#88071C2311yescharacteristic
215#88071C2312yes—
216#88071C2311yescharacteristic
217#88071C2311yescharacteristic
218#88071C2311yescharacteristic
219#88071C2312yes—
220#88071C2312yes—
221#88071C2312yes—
222#88071C2312yes—
223#88071C2312yes—
224#88071C2312yes—
225#88071C2312yes—
226#88071C2312yes—
227#88071C2311yescharacteristic
228#88071C2311yescharacteristic
229#88071C2311yescharacteristic
230#88071C2312yes—
231#88071C2312yes—
232#88071C2311yescharacteristic
233#88071C2311yescharacteristic
234#88071C2312yes—
235#88071C2312yes—
236#88071C2312yes—
237#88071C2312yes—
238#88071C2312yes—
239#88071C2312yes—
240#34488—131nomaximal, Sylow
241C2×Q8×C13—22no—
242C2×Q8×C13—22no—
243C2×Q8×C13C22×C414yes—
244C22×C4×C13C2411yescharacteristic
245C22×C4×C13C2412yes—
246C22×C4×C13C2411yescharacteristic
247C22×C4×C13C2412yes—
248C22×C4×C13C2411yescharacteristic
249C22×C4×C13C2411yescharacteristic
250C22×C4×C13C2412yes—
251C22×C4×C13C2411yescharacteristic
252C22×C4×C13C2412yes—
253C22×C4×C13C2411yescharacteristic
254C22×C4×C13C2411yescharacteristic
255C22×Dic13C2411yescharacteristic
256C22×Dic13C2411yescharacteristic
257C22×Dic13C2412yes—
258C22×Dic13C2411yescharacteristic
259C22×Dic13C2411yescharacteristic
260C22×Dic13C2412yes—
261C22×Dic13C2411yescharacteristic
262C22×Dic13C2411yescharacteristic
263C22×Dic13C2411yescharacteristic
264C22×Dic13C2412yes—
265C22×Dic13C2412yes—
266C22×Dic13C2411yescharacteristic
267C2×Dic26—22no—
268C2×Dic26—22no—
269C2×Dic26—22no—
270C2×Dic26—22no—
271C2×Dic26—22no—
272C2×Dic26—22no—
273C2×Dic26C22×C414yes—
274C2×Dic26C22×C414yes—
275C2×Dic26C22×C414yes—
276C13×C4⋊C4—22no—
277C13×C4⋊C4—22no—
278C13×C4⋊C4—24no—
279C13×C4⋊C4—22no—
280C13×C4⋊C4—41no—
281C13×C4⋊C4—42no—
282C13×C4⋊C4—42no—
283C13×C4⋊C4—42no—
284C13×C4⋊C4C22×C414yes—
285C13×C4⋊C4C22×C418yes—
286C42×C13—22no—
287C42×C13—22no—
288C42×C13—42no—
289C42×C13—42no—
290C42×C13C22×C414yes—
291C42×C13C22×C418yes—
292C4⋊Dic13—22no—
293C4⋊Dic13—22no—
294C4⋊Dic13—42no—
295C4⋊Dic13—42no—
296C4⋊Dic13C22×C418yes—
297C4⋊Dic13C22×C414yes—
298C4⋊Dic13C22×C418yes—
299#6101—22no—
300#6101—22no—
301#6101—24no—
302#6101—22no—
303#6101—42no—
304#6101—42no—
305#6101—42no—
306#6101—42no—
307#6101—41no—
308#6101—42no—
309#6101C22×C414yes—
310#6101C22×C414yes—
311#6101C22×C418yes—
312#6101C22×C418yes—
313#6101C22×C418yes—
314#6101C22×C418yes—
315#6101C22×C418yes—
316#6101C22×C418yes—
317C4×Dic13—22no—
318C4×Dic13—22no—
319C4×Dic13—22no—
320C4×Dic13—22no—
321C4×Dic13—24no—
322C4×Dic13—22no—
323C4×Dic13—42no—
324C4×Dic13—42no—
325C4×Dic13—42no—
326C4×Dic13—42no—
327C4×Dic13—42no—
328C4×Dic13—41no—
329C4×Dic13—42no—
330C4×Dic13C22×C418yes—
331C4×Dic13C22×C418yes—
332C4×Dic13C22×C414yes—
333C4×Dic13C22×C414yes—
334C2×#557—131no—
335#2382—132no—
336#2382—132no—
337#2370—132no—
338#2365—131no—
339#2365—131no—
340#2365—131no—
341#2355—131no—
342#2355—132no—
343#2351—131no—
344#2351D1311yescharacteristic
345Q8×C4⋊C4—131no—
346#2336—132no—
347#2336—132no—
348#2330—132no—
349#2327—131no—
350#2327—131no—
351#2320—131no—
352#2320—132no—
353#2320—131no—
354C4×C4⋊Q8—131no—
355#2295—131no—
356#2295—131no—
357C23×C13C2511yescharacteristic
358Q8×C13—28no—
359C2×C4×C13—21no—
360C2×C4×C13—22no—
361C2×C4×C13—21no—
362C2×C4×C13—21no—
363C2×C4×C13—22no—
364C2×C4×C13—21no—
365C2×C4×C13—21no—
366C2×C4×C13—22no—
367C2×C4×C13—21no—
368C2×C4×C13—22no—
369C2×C4×C13—21no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—21no—
373C2×C4×C13—21no—
374C2×C4×C13—22no—
375C2×C4×C13—21no—
376C2×C4×C13—21no—
377C2×C4×C13—21no—
378C2×C4×C13—22no—
379C2×C4×C13—21no—
380C2×C4×C13—22no—
381C2×C4×C13—22no—
382C2×C4×C13—21no—
383C2×C4×C13—21no—
384C2×C4×C13C23×C414yes—
385C2×C4×C13C23×C414yes—
386C2×C4×C13C23×C412yes—
387C2×C4×C13C23×C412yes—
388C2×C4×C13C23×C412yes—
389C2×C4×C13H(5,𝔽2)12yes—
390C2×C4×C132−1+412yes—
391C2×C4×C132−1+412yes—
392C2×Dic13—22no—
393C2×Dic13—22no—
394C2×Dic13—21no—
395C2×Dic13—21no—
396C2×Dic13—21no—
397C2×Dic13—21no—
398C2×Dic13—22no—
399C2×Dic13—22no—
400C2×Dic13—21no—
401C2×Dic13—21no—
402C2×Dic13—21no—
403C2×Dic13—21no—
404C2×Dic13—22no—
405C2×Dic13—21no—
406C2×Dic13—21no—
407C2×Dic13—22no—
408C2×Dic13—21no—
409C2×Dic13—21no—
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—21no—
419C2×Dic13—21no—
420C2×Dic13C23×C412yes—
421C2×Dic13C23×C412yes—
422C2×Dic13C23×C412yes—
423C2×Dic13C23×C414yes—
424C2×Dic13C23×C414yes—
425C2×Dic13C23×C412yes—
426C2×Dic132−1+412yes—
427C2×Dic132−1+412yes—
428Dic26—28no—
429Dic26—28no—
430Dic26—28no—
431#557—1316no—
432C2×C4⋊Q8—131no—
433C2×C4⋊Q8—131no—
434C2×C4⋊Q8—131no—
435C2×#125—132no—
436C2×#125—132no—
437C2×#125—132no—
438C2×C4×Q8—131no—
439C2×C4×Q8—131no—
440C2×C4×Q8—131no—
441C2×C4×Q8—131no—
442C2×C4×Q8—132no—
443C2×C4×Q8—131no—
444C2×C4×Q8—131no—
445C2×C4×Q8—131no—
446C2×C4×Q8C2×D1311yescharacteristic
447C2×C4×Q8C2×D1311yescharacteristic
448C2×C4×Q8C2×D1311yescharacteristic
449#391—131no—
450#391—131no—
451#391—131no—
452#391—131no—
453#391—131no—
454#391—131no—
455#391—131no—
456#391—132no—
457#391—131no—
458#389—132no—
459#389—132no—
460#389—131no—
461#389—131no—
462#389—132no—
463#389—131no—
464#389—132no—
465#389—132no—
466#389—132no—
467#389—132no—
468#389—131no—
469#389—132no—
470#389—132no—
471#389C2×D1311yescharacteristic
472#389C2×D1312yes—
473#389C2×D1312yes—
474#389C2×D1311yescharacteristic
475#387—132no—
476#387—132no—
477#387—132no—
478#387—132no—
479#387—132no—
480#387—132no—
481#387—132no—
482#387—131no—
483#387—132no—
484#387—131no—
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#387—131no—
496#387—132no—
497#387—132no—
498#387—132no—
499#387—131no—
500#387—132no—
501#384—131no—
502#384—132no—
503#383—132no—
504#383—132no—
505#382—132no—
506#382—131no—
507#382—132no—
508#382—132no—
509#382C2×D1312yes—
510#382C2×D1311yescharacteristic
511C4×C4⋊C4—131no—
512C4×C4⋊C4—132no—
513C4×C4⋊C4—132no—
514C4×C4⋊C4—131no—
515C4×C4⋊C4—132no—
516C4×C4⋊C4—132no—
517C4×C4⋊C4—132no—
518C4×C4⋊C4—131no—
519C4×C4⋊C4—132no—
520C4×C4⋊C4—132no—
521C4×C4⋊C4—131no—
522C4×C4⋊C4—131no—
523C4×C4⋊C4—132no—
524C4×C4⋊C4—132no—
525C4×C4⋊C4C2×D1312yes—
526C4×C4⋊C4C2×D1311yescharacteristic
527#376—131no—
528#376—131no—
529#376—132no—
530C43—131no—
531C22×C13C24×C411yescharacteristic
532C22×C13C2×H(5,𝔽2)11yescharacteristic
533C22×C13C2×2−1+411yescharacteristic
534C22×C13C2×2−1+411yescharacteristic
535C22×C13C2×2−1+411yescharacteristic
536C22×C13C2×2−1+411yescharacteristic
537C22×C13#58511yescharacteristic
538C4×C13—22no—
539C4×C13—24no—
540C4×C13—22no—
541C4×C13—24no—
542C4×C13—22no—
543C4×C13—41no—
544C4×C13—42no—
545C4×C13—42no—
546C4×C13—41no—
547C4×C13—41no—
548C4×C13#52014yes—
549Dic13—22no—
550Dic13—24no—
551Dic13—24no—
552Dic13—22no—
553Dic13—22no—
554Dic13—41no—
555Dic13—41no—
556Dic13—42no—
557Dic13—41no—
558Dic13—42no—
559Dic13—41no—
560Dic13#51914yes—
561C22×Q8—131no—
562C22×Q8—131no—
563C22×Q8—131no—
564C22×Q8C22×D1311yescharacteristic
565C4⋊Q8—138no—
566C4⋊Q8—138no—
567C4⋊Q8—138no—
568#125—1316no—
569#125—1316no—
570#125—1316no—
571C4×Q8—42no—
572C4×Q8—42no—
573C4×Q8—138no—
574C4×Q8—138no—
575C4×Q8—1316no—
576C4×Q8—138no—
577C4×Q8—522no—
578C4×Q8—522no—
579C4×Q8—522no—
580C4×Q8—522no—
581C4×Q8C4×D1318yes—
582C2×C4⋊C4—131no—
583C2×C4⋊C4—131no—
584C2×C4⋊C4—132no—
585C2×C4⋊C4—132no—
586C2×C4⋊C4—131no—
587C2×C4⋊C4—132no—
588C2×C4⋊C4—132no—
589C2×C4⋊C4—132no—
590C2×C4⋊C4—132no—
591C2×C4⋊C4—132no—
592C2×C4⋊C4—132no—
593C2×C4⋊C4—131no—
594C2×C4⋊C4—131no—
595C2×C4⋊C4—132no—
596C2×C4⋊C4—131no—
597C2×C4⋊C4—131no—
598C2×C4⋊C4—131no—
599C2×C4⋊C4—132no—
600C2×C4⋊C4—132no—
601C2×C4⋊C4—132no—
602C2×C4⋊C4—132no—
603C2×C4⋊C4—132no—
604C2×C4⋊C4—131no—
605C2×C4⋊C4—132no—
606C2×C4⋊C4—132no—
607C2×C4⋊C4C22×D1311yescharacteristic
608C2×C4⋊C4C22×D1311yescharacteristic
609C2×C4⋊C4C22×D1312yes—
610C2×C4⋊C4C22×D1311yescharacteristic
611C2×C4⋊C4C22×D1312yes—
612C2×C4⋊C4C22×D1312yes—
613C2×C4⋊C4C22×D1312yes—
614C2×C4⋊C4C22×D1311yescharacteristic
615C2×C4⋊C4C22×D1311yescharacteristic
616C2×C4⋊C4C22×D1312yes—
617C2×C42—132no—
618C2×C42—132no—
619C2×C42—131no—
620C2×C42—131no—
621C2×C42—131no—
622C2×C42—131no—
623C2×C42—131no—
624C2×C42—131no—
625C2×C42—131no—
626C2×C42—132no—
627C2×C42—132no—
628C2×C42—132no—
629C2×C42—132no—
630C2×C42—132no—
631C2×C42—131no—
632C2×C42—132no—
633C2×C42—132no—
634C2×C42C22×D1311yescharacteristic
635C2×C42C22×D1311yescharacteristic
636C2×C42C22×D1312yes—
637C2×C42C22×D1312yes—
638C2×C42C22×D1312yes—
639C2×C42C22×D1311yescharacteristic
640#95—131no—
641#95—131no—
642#95—132no—
643#95—131no—
644#95—131no—
645#95—131no—
646#95—131no—
647#95—131no—
648#95—131no—
649#95—132no—
650#95—132no—
651#95—131no—
652#95—132no—
653#95—131no—
654#95—132no—
655#95—132no—
656#95—132no—
657#95—132no—
658#95—132no—
659#95—132no—
660#95—132no—
661#95—132no—
662#95—132no—
663#95—132no—
664#95—132no—
665#95—132no—
666#95—132no—
667#95—132no—
668#95—132no—
669#95—131no—
670#95—131no—
671#95C22×D1312yes—
672#95C22×D1312yes—
673#95C22×D1312yes—
674#95C22×D1311yescharacteristic
675#95C22×D1312yes—
676#95C22×D1311yescharacteristic
677C2×C13C2×#51911yescharacteristic
678C2×C13C2×#52011yescharacteristic
679C2×C13C4×2−1+411yescharacteristic
680C2×C13#355211yescharacteristic
681C2×C13#355411yescharacteristic
682C2×C13#355511yescharacteristic
683C2×C13#355611yescharacteristic
684C2×Q8—22no—
685C2×Q8—22no—
686C2×Q8—134no—
687C2×Q8—134no—
688C2×Q8—134no—
689C2×Q8—262no—
690C2×Q8—262no—
691C2×Q8—262no—
692C2×Q8—262no—
693C2×Q8—262no—
694C2×Q8—262no—
695C2×Q8C2×C4×D1314yes—
696C22×C4—131no—
697C22×C4—131no—
698C22×C4—131no—
699C22×C4—131no—
700C22×C4—132no—
701C22×C4—132no—
702C22×C4—131no—
703C22×C4—131no—
704C22×C4—132no—
705C22×C4—131no—
706C22×C4—131no—
707C22×C4—132no—
708C22×C4C23×D1311yescharacteristic
709C22×C4C23×D1312yes—
710C22×C4C23×D1311yescharacteristic
711C22×C4C23×D1311yescharacteristic
712C22×C4C23×D1312yes—
713C22×C4C23×D1311yescharacteristic
714C22×C4C23×D1312yes—
715C22×C4C23×D1311yescharacteristic
716C22×C4C23×D1312yes—
717C22×C4C23×D1311yescharacteristic
718C22×C4C23×D1311yescharacteristic
719C4⋊C4—22no—
720C4⋊C4—22no—
721C4⋊C4—24no—
722C4⋊C4—22no—
723C4⋊C4—42no—
724C4⋊C4—42no—
725C4⋊C4—41no—
726C4⋊C4—42no—
727C4⋊C4—134no—
728C4⋊C4—134no—
729C4⋊C4—138no—
730C4⋊C4—138no—
731C4⋊C4—134no—
732C4⋊C4—138no—
733C4⋊C4—138no—
734C4⋊C4—138no—
735C4⋊C4—138no—
736C4⋊C4—138no—
737C4⋊C4—138no—
738C4⋊C4—262no—
739C4⋊C4—262no—
740C4⋊C4—264no—
741C4⋊C4—262no—
742C4⋊C4—262no—
743C4⋊C4—262no—
744C4⋊C4—522no—
745C4⋊C4—522no—
746C4⋊C4—522no—
747C4⋊C4—522no—
748C4⋊C4—521no—
749C4⋊C4—522no—
750C4⋊C4—522no—
751C4⋊C4—522no—
752C4⋊C4C2×C4×D1314yes—
753C4⋊C4C2×C4×D1318yes—
754C42—22no—
755C42—22no—
756C42—42no—
757C42—42no—
758C42—138no—
759C42—138no—
760C42—134no—
761C42—134no—
762C42—262no—
763C42—264no—
764C42—262no—
765C42—262no—
766C42—262no—
767C42—262no—
768C42—522no—
769C42—522no—
770C42—522no—
771C42—522no—
772C42—522no—
773C42—522no—
774C42—521no—
775C42C2×C4×D1318yes—
776C42C2×C4×D1314yes—
777C13#3448811yescharacteristic, complemented, Sylow
778C23C24×D1311yescharacteristic
779Q8—28no—
780Q8—268no—
781Q8—268no—
782Q8—268no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—21no—
789C2×C4—22no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—21no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—22no—
808C2×C4—132no—
809C2×C4—132no—
810C2×C4—132no—
811C2×C4—132no—
812C2×C4—132no—
813C2×C4—132no—
814C2×C4—134no—
815C2×C4—134no—
816C2×C4—262no—
817C2×C4—262no—
818C2×C4—262no—
819C2×C4—262no—
820C2×C4—261no—
821C2×C4—261no—
822C2×C4—261no—
823C2×C4—261no—
824C2×C4—261no—
825C2×C4—261no—
826C2×C4—261no—
827C2×C4—261no—
828C2×C4—262no—
829C2×C4—261no—
830C2×C4—261no—
831C2×C4—262no—
832C2×C4—261no—
833C2×C4—261no—
834C2×C4—262no—
835C2×C4—262no—
836C2×C4—261no—
837C2×C4—261no—
838C2×C4—261no—
839C2×C4—262no—
840C2×C4—261no—
841C2×C4—261no—
842C2×C4—261no—
843C2×C4—262no—
844C2×C4C22×C4×D1314yes—
845C2×C4C22×C4×D1312yes—
846C2×C4C22×C4×D1312yes—
847C2×C4C22×C4×D1314yes—
848C2×C4C22×C4×D1312yes—
849C2×C4#8825112yes—
850C2×C4#8825412yes—
851C2×C4#8825712yes—
852C22C23×C4×D1311yescharacteristic
853C22C2×#8825111yescharacteristic
854C22C2×#8825411yescharacteristic
855C22C2×#8825711yescharacteristic
856C22#1171964811yescharacteristic
857C22D13×2−1+411yescharacteristic
858C22D13×2−1+411yescharacteristic
859C4—22no—
860C4—22no—
861C4—24no—
862C4—22no—
863C4—24no—
864C4—41no—
865C4—42no—
866C4—41no—
867C4—41no—
868C4—42no—
869C4—134no—
870C4—262no—
871C4—264no—
872C4—264no—
873C4—262no—
874C4—262no—
875C4—521no—
876C4—521no—
877C4—522no—
878C4—521no—
879C4—522no—
880C4—521no—
881C4#1171920914yes—
882C2D13×#51911yescharacteristic
883C2C2×#1171920911yescharacteristic
884C2C4×#8825711yescharacteristic
885C2#1312926711yescharacteristic
886C2#1312929411yescharacteristic
887C2#1312931611yescharacteristic
888C2#1312932811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2351C2
socle, prime radical, cosocleC23×C13C25
hypercenter#2351D13
hypocenterC13#34488
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2351

Complements

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

NH ≅ G/Ntype
29. #11719272C4semidirect
777. C13#34488semidirect

Maximal subgroups

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

subgroupindex
C2×#117192722
#131180212
#131180182
#131179352
#131178922
#131178902
#131177942
#131177882
#131177552
#131177502
#131176402
#131176342
#131175742
#131175532
#131175522
#131174872
#131174842
#131174832
C4×#881982
#131173122
#131173072
C13×#23512
#3448813