Finite Group Databasebeta

← #25261867

Subgroups — #25261867

Order 11008.

1940 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583625C211yesmaximal, characteristic
2#19137780C212yesmaximal
3#19137778C212yesmaximal
4#19137696C211yesmaximal, characteristic
5#19137691C211yesmaximal, characteristic
6#19137650C212yesmaximal
7#19137648C211yesmaximal, characteristic
8#19137552C211yesmaximal, characteristic
9#19137551C211yesmaximal, characteristic
10#19137551C211yesmaximal, characteristic
11#19137512C212yesmaximal
12C4⋊C4×Dic86C211yesmaximal, characteristic
13#19137398C212yesmaximal
14#19137396C212yesmaximal
15#19137336C211yesmaximal, characteristic
16#19137335C211yesmaximal, characteristic
17#19137310C212yesmaximal
18#19137245C212yesmaximal
19#19137240C211yesmaximal, characteristic
20#19137166C211yesmaximal, characteristic
21#19137070C211yesmaximal, characteristic
22#19137067C211yesmaximal, characteristic
23C43×#2320C211yesmaximal, characteristic
24#14583625C4116yescomplemented
25C2×#13063324C2212yes—
26C2×#13063324C2211yescharacteristic
27C2×#13063317C2211yescharacteristic
28C2×#13063317C2212yes—
29C2×#13063316C2211yescharacteristic
30C2×#13063316C2212yes—
31C2×Q8×Dic43C2211yescharacteristic
32C2×Q8×Dic43C2211yescharacteristic
33C2×C4×Dic86C2212yes—
34C2×C4×Dic86C2211yescharacteristic
35C2×C4×Dic86C2212yes—
36C2×#13063290C2212yes—
37C2×#13063290C2212yes—
38#14582806C2211yescharacteristic
39#14582806C2211yescharacteristic
40#14582803C2211yescharacteristic
41#14582803C2212yes—
42#14582803C2211yescharacteristic
43#14582803C2212yes—
44#14582797C2211yescharacteristic
45#14582797C2211yescharacteristic
46#14582797C2212yes—
47#14582796C2211yescharacteristic
48#14582796C2211yescharacteristic
49#14582796C2212yes—
50#14582796C2212yes—
51#14582796C2212yes—
52#14582796C2212yes—
53#14582796C2212yes—
54#14582795C2211yescharacteristic
55#14582795C2212yes—
56#14582795C2211yescharacteristic
57#14582795C2212yes—
58#14582794C2212yes—
59#14582794C2212yes—
60#14582786C2212yes—
61#14582786C2211yescharacteristic
62#14582786C2211yescharacteristic
63#14582786C2212yes—
64#14582786C2212yes—
65#14582785C2212yes—
66#14582785C2212yes—
67#14582784C2212yes—
68#14582784C2212yes—
69#14582784C2212yes—
70#14582784C2212yes—
71#14582784C2212yes—
72#14582784C2212yes—
73#14582783C2212yes—
74#14582782C2212yes—
75#14582782C2212yes—
76#14582782C2211yescharacteristic
77#14582782C2211yescharacteristic
78#14582782C2212yes—
79#14582782C2212yes—
80#14582781C2212yes—
81#14582781C2212yes—
82#14582780C2212yes—
83#14582780C2212yes—
84#14582769C2211yescharacteristic
85#14582768C2211yescharacteristic
86#14582768C2211yescharacteristic
87#14582766C2212yes—
88#14582765C2212yes—
89#14582763C2212yes—
90#14582763C2212yes—
91#14582763C2212yes—
92C4⋊C4×Dic43C2211yescharacteristic
93C4⋊C4×Dic43C2211yescharacteristic
94C4⋊C4×Dic43C2211yescharacteristic
95C4⋊C4×Dic43C2211yescharacteristic
96C4⋊C4×Dic43C2211yescharacteristic
97C4⋊C4×Dic43C2211yescharacteristic
98C4×Dic43⋊C4C2211yescharacteristic
99C4×Dic43⋊C4C2211yescharacteristic
100C4×Dic43⋊C4C2212yes—
101C4×C4⋊Dic43C2211yescharacteristic
102C4×C4⋊Dic43C2211yescharacteristic
103C4×C4⋊Dic43C2211yescharacteristic
104C4×C4⋊Dic43C2212yes—
105#14582750C2212yes—
106#14582750C2212yes—
107#14582750C2212yes—
108#14582750C2212yes—
109#14582750C2212yes—
110#14582745C2211yescharacteristic
111#14582744C2212yes—
112C42×Dic43C2211yescharacteristic
113C2×C4×Q8×C43C2211yescharacteristic
114C43×#391C2211yescharacteristic
115C43×#391C2211yescharacteristic
116C43×#389C2211yescharacteristic
117C43×#389C2211yescharacteristic
118C43×#387C2212yes—
119C43×#387C2212yes—
120C43×#383C2212yes—
121C43×#382C2212yes—
122C4×C4⋊C4×C43C2211yescharacteristic
123C43×#376C2211yescharacteristic
124C22×Dic86C2312yes—
125C22×Dic86C2311yescharacteristic
126#13063324C2×C4116yes—
127#13063324C2×C418yes—
128#13063317C2×C418yes—
129#13063317C2×C4116yes—
130#13063316C2×C418yes—
131#13063316C2×C4116yes—
132Q8×Dic43C2×C418yes—
133Q8×Dic43C2×C418yes—
134C4×Dic86—44no—
135C4×Dic86C2×C418yes—
136C4×Dic86C2×C4116yes—
137#13063290—44no—
138#13063290—44no—
139C2×C4⋊Dic43C2311yescharacteristic
140C2×C4⋊Dic43C2311yescharacteristic
141C2×C4⋊Dic43C2311yescharacteristic
142C2×C4⋊Dic43C2312yes—
143C2×C4⋊Dic43C2311yescharacteristic
144C2×C4⋊Dic43C2312yes—
145C2×C4⋊Dic43C2312yes—
146C2×C4⋊Dic43C2312yes—
147C2×C4⋊Dic43C2312yes—
148C2×C4⋊Dic43C2311yescharacteristic
149C2×C4⋊Dic43C2311yescharacteristic
150C2×C4⋊Dic43C2311yescharacteristic
151C2×Dic43⋊C4C2312yes—
152C2×Dic43⋊C4C2311yescharacteristic
153C2×Dic43⋊C4C2311yescharacteristic
154C2×Dic43⋊C4C2311yescharacteristic
155C2×Dic43⋊C4C2312yes—
156C2×Dic43⋊C4C2311yescharacteristic
157C2×Dic43⋊C4C2312yes—
158C2×Dic43⋊C4C2312yes—
159C2×Dic43⋊C4C2312yes—
160C2×Dic43⋊C4C2312yes—
161C2×Dic43⋊C4C2312yes—
162C2×Dic43⋊C4C2312yes—
163C2×Dic43⋊C4C2311yescharacteristic
164C2×Dic43⋊C4C2312yes—
165C2×Dic43⋊C4C2312yes—
166C2×Dic43⋊C4C2312yes—
167C2×Dic43⋊C4C2312yes—
168C2×Dic43⋊C4C2311yescharacteristic
169C2×C4×Dic43C2311yescharacteristic
170C2×C4×Dic43C2311yescharacteristic
171C2×C4×Dic43C2311yescharacteristic
172C2×C4×Dic43C2311yescharacteristic
173C2×C4×Dic43C2311yescharacteristic
174C2×C4×Dic43C2312yes—
175C2×C4×Dic43C2311yescharacteristic
176C2×C4×Dic43C2312yes—
177C2×C4×Dic43C2312yes—
178C2×C4×Dic43C2312yes—
179C2×C4×Dic43C2312yes—
180C2×C4×Dic43C2312yes—
181C2×C4×Dic43C2312yes—
182C2×C4×Dic43C2312yes—
183C2×C4×Dic43C2311yescharacteristic
184C2×C4×Dic43C2312yes—
185C2×C4×Dic43C2311yescharacteristic
186C2×C4×Dic43C2312yes—
187C43⋊#95C2312yes—
188C43⋊#95C2311yescharacteristic
189C43⋊#95C2311yescharacteristic
190C43⋊#95C2311yescharacteristic
191C43⋊#95C2311yescharacteristic
192C43⋊#95C2312yes—
193C43⋊#95C2312yes—
194C43⋊#95C2312yes—
195C43⋊#95C2312yes—
196C43⋊#95C2312yes—
197C43⋊#95C2312yes—
198C43⋊#95C2312yes—
199C43⋊#95C2312yes—
200C43⋊#95C2312yes—
201C43⋊#95C2312yes—
202C43⋊#95C2312yes—
203C43⋊#95C2312yes—
204C43⋊#95C2311yescharacteristic
205C43⋊#95C2311yescharacteristic
206C43⋊#95C2311yescharacteristic
207C43⋊#95C2312yes—
208C43⋊#95C2312yes—
209C43⋊#95C2311yescharacteristic
210C43⋊#95C2311yescharacteristic
211C43⋊#95C2311yescharacteristic
212C43⋊#95C2312yes—
213C22×Q8×C43C2311yescharacteristic
214C4×Q8×C43C2×C418yes—
215C2×C4⋊C4×C43C2311yescharacteristic
216C2×C4⋊C4×C43C2311yescharacteristic
217C2×C4⋊C4×C43C2312yes—
218C2×C4⋊C4×C43C2312yes—
219C2×C4⋊C4×C43C2312yes—
220C2×C4⋊C4×C43C2311yescharacteristic
221C2×C42×C43C2311yescharacteristic
222C2×C42×C43C2311yescharacteristic
223C2×C42×C43C2312yes—
224C2×C42×C43C2311yescharacteristic
225C2×C42×C43C2312yes—
226#95×C43C2312yes—
227#95×C43C2312yes—
228#95×C43C2312yes—
229#95×C43C2312yes—
230#95×C43C2312yes—
231#95×C43C2312yes—
232#95×C43C2311yescharacteristic
233#95×C43C2311yescharacteristic
234#95×C43C2311yescharacteristic
235#95×C43C2312yes—
236#95×C43C2311yescharacteristic
237C2×Q8×C43—22no—
238C2×Q8×C43—22no—
239C2×Q8×C43C22×C414yes—
240C22×C4×C43C2411yescharacteristic
241C22×C4×C43C2411yescharacteristic
242C22×C4×C43C2412yes—
243C22×C4×C43C2411yescharacteristic
244C22×C4×C43C2411yescharacteristic
245C22×C4×C43C2412yes—
246C22×C4×C43C2411yescharacteristic
247C22×C4×C43C2412yes—
248C22×C4×C43C2411yescharacteristic
249C22×C4×C43C2412yes—
250C22×C4×C43C2411yescharacteristic
251C22×Dic43C2411yescharacteristic
252C22×Dic43C2411yescharacteristic
253C22×Dic43C2411yescharacteristic
254C22×Dic43C2412yes—
255C22×Dic43C2412yes—
256C22×Dic43C2411yescharacteristic
257C22×Dic43C2412yes—
258C22×Dic43C2411yescharacteristic
259C22×Dic43C2411yescharacteristic
260C22×Dic43C2412yes—
261C22×Dic43C2411yescharacteristic
262C22×Dic43C2411yescharacteristic
263C2×Dic86—24no—
264C2×Dic86—22no—
265C2×Dic86—24no—
266C2×Dic86—22no—
267C2×Dic86C22×C418yes—
268C2×Dic86C22×C414yes—
269C4⋊C4×C43—22no—
270C4⋊C4×C43—22no—
271C4⋊C4×C43—42no—
272C4⋊C4×C43—42no—
273C4⋊C4×C43C22×C418yes—
274C4⋊C4×C43C22×C414yes—
275C42×C43—22no—
276C42×C43—22no—
277C42×C43—42no—
278C42×C43C22×C418yes—
279C42×C43C22×C414yes—
280C4⋊Dic43—22no—
281C4⋊Dic43—22no—
282C4⋊Dic43—22no—
283C4⋊Dic43—41no—
284C4⋊Dic43—42no—
285C4⋊Dic43—42no—
286C4⋊Dic43C22×C418yes—
287C4⋊Dic43C22×C414yes—
288C4⋊Dic43C22×C418yes—
289C4⋊Dic43C22×C414yes—
290C4⋊Dic43C22×C418yes—
291C4⋊Dic43C22×C414yes—
292Dic43⋊C4—22no—
293Dic43⋊C4—24no—
294Dic43⋊C4—24no—
295Dic43⋊C4—22no—
296Dic43⋊C4—22no—
297Dic43⋊C4—42no—
298Dic43⋊C4—42no—
299Dic43⋊C4—41no—
300Dic43⋊C4—42no—
301Dic43⋊C4—42no—
302Dic43⋊C4—42no—
303Dic43⋊C4—42no—
304Dic43⋊C4C22×C414yes—
305Dic43⋊C4C22×C414yes—
306Dic43⋊C4C22×C418yes—
307Dic43⋊C4C22×C418yes—
308Dic43⋊C4C22×C418yes—
309Dic43⋊C4C22×C418yes—
310C4×Dic43—22no—
311C4×Dic43—22no—
312C4×Dic43—22no—
313C4×Dic43—24no—
314C4×Dic43—22no—
315C4×Dic43—22no—
316C4×Dic43—42no—
317C4×Dic43—42no—
318C4×Dic43—41no—
319C4×Dic43—42no—
320C4×Dic43—42no—
321C4×Dic43—42no—
322C4×Dic43—42no—
323C4×Dic43—42no—
324C4×Dic43C22×C418yes—
325C4×Dic43C22×C414yes—
326C4×Dic43C22×C418yes—
327C4×Dic43C22×C414yes—
328C23×C43C2511yescharacteristic
329Q8×C43—28no—
330C2×C4×C43—22no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—21no—
338C2×C4×C43—22no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—22no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—22no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—21no—
350C2×C4×C43—21no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—21no—
354C2×C4×C43—21no—
355C2×C4×C43—22no—
356C2×C4×C43C23×C414yes—
357C2×C4×C43C23×C412yes—
358C2×C4×C43C23×C412yes—
359C2×C4×C43C23×C414yes—
360C2×C4×C43C23×C412yes—
361C2×C4×C432−1+412yes—
362C2×C4×C432−1+412yes—
363C2×Dic43—21no—
364C2×Dic43—22no—
365C2×Dic43—21no—
366C2×Dic43—21no—
367C2×Dic43—21no—
368C2×Dic43—22no—
369C2×Dic43—21no—
370C2×Dic43—22no—
371C2×Dic43—21no—
372C2×Dic43—22no—
373C2×Dic43—21no—
374C2×Dic43—21no—
375C2×Dic43—22no—
376C2×Dic43—21no—
377C2×Dic43—22no—
378C2×Dic43—21no—
379C2×Dic43—21no—
380C2×Dic43—21no—
381C2×Dic43—21no—
382C2×Dic43—21no—
383C2×Dic43—21no—
384C2×Dic43—22no—
385C2×Dic43—22no—
386C2×Dic43—21no—
387C2×Dic43—22no—
388C2×Dic43—21no—
389C2×Dic43—22no—
390C2×Dic43C23×C412yes—
391C2×Dic43C23×C412yes—
392C2×Dic43C23×C414yes—
393C2×Dic43C23×C414yes—
394C2×Dic43C23×C412yes—
395C2×Dic43C23×C412yes—
396C2×Dic43H(5,𝔽2)12yes—
397C2×Dic432−1+412yes—
398C2×Dic432−1+412yes—
399Dic86—216no—
400Dic86—28no—
401#34488—431nomaximal, Sylow
402C22×C43C24×C411yescharacteristic
403C22×C43C2×H(5,𝔽2)11yescharacteristic
404C22×C43C2×2−1+411yescharacteristic
405C22×C43C2×2−1+411yescharacteristic
406C22×C43C2×2−1+411yescharacteristic
407C22×C43C2×2−1+411yescharacteristic
408C22×C43#58511yescharacteristic
409C4×C43—24no—
410C4×C43—24no—
411C4×C43—22no—
412C4×C43—22no—
413C4×C43—42no—
414C4×C43—41no—
415C4×C43—41no—
416C4×C43—42no—
417C4×C43—41no—
418C4×C43—41no—
419C4×C43#51914yes—
420Dic43—24no—
421Dic43—22no—
422Dic43—22no—
423Dic43—24no—
424Dic43—22no—
425Dic43—22no—
426Dic43—41no—
427Dic43—42no—
428Dic43—42no—
429Dic43—41no—
430Dic43—41no—
431Dic43#52014yes—
432C2×#557—431no—
433#2382—432no—
434#2382—432no—
435#2370—431no—
436#2370—431no—
437#2365—431no—
438#2365—432no—
439#2355—431no—
440#2355—431no—
441#2355—431no—
442#2351—432no—
443Q8×C4⋊C4—431no—
444#2336—432no—
445#2336—432no—
446#2330—431no—
447#2330—431no—
448#2327—432no—
449#2320—431no—
450#2320—432no—
451#2320D4311yescharacteristic
452C4×C4⋊Q8—431no—
453#2295—431no—
454#2295—431no—
455C2×C43C2×#51911yescharacteristic
456C2×C43C2×#52011yescharacteristic
457C2×C43C4×2−1+411yescharacteristic
458C2×C43#355211yescharacteristic
459C2×C43#355411yescharacteristic
460C2×C43#355511yescharacteristic
461C2×C43#355611yescharacteristic
462#557—4316no—
463C2×C4⋊Q8—431no—
464C2×C4⋊Q8—432no—
465C2×#125—431no—
466C2×#125—432no—
467C2×#125—431no—
468C2×#125—432no—
469C2×C4×Q8—431no—
470C2×C4×Q8—431no—
471C2×C4×Q8—432no—
472C2×C4×Q8—432no—
473C2×C4×Q8—432no—
474C2×C4×Q8—431no—
475C2×C4×Q8—432no—
476C2×C4×Q8C2×D4311yescharacteristic
477#391—431no—
478#391—431no—
479#391—432no—
480#391—432no—
481#391—431no—
482#391—431no—
483#391C2×D4311yescharacteristic
484#391C2×D4311yescharacteristic
485#389—432no—
486#389—432no—
487#389—431no—
488#389—432no—
489#389—432no—
490#389—431no—
491#389—431no—
492#389—431no—
493#389—432no—
494#389—431no—
495#389—432no—
496#389—432no—
497#389—432no—
498#389—432no—
499#389—432no—
500#389—431no—
501#389C2×D4311yescharacteristic
502#389C2×D4311yescharacteristic
503#387—432no—
504#387—432no—
505#387—432no—
506#387—432no—
507#387—432no—
508#387—432no—
509#387—432no—
510#387—432no—
511#387—432no—
512#387—432no—
513#387—432no—
514#387—432no—
515#387—432no—
516#387—432no—
517#387—431no—
518#387—431no—
519#387—432no—
520#387—432no—
521#387—432no—
522#387—431no—
523#387—432no—
524#387—432no—
525#387—432no—
526#387—431no—
527#387C2×D4312yes—
528#387C2×D4312yes—
529#384—431no—
530#384—431no—
531#384—431no—
532#383—432no—
533#383C2×D4312yes—
534#382—432no—
535#382—432no—
536#382—432no—
537#382—432no—
538#382C2×D4312yes—
539C4×C4⋊C4—431no—
540C4×C4⋊C4—431no—
541C4×C4⋊C4—431no—
542C4×C4⋊C4—431no—
543C4×C4⋊C4—431no—
544C4×C4⋊C4—431no—
545C4×C4⋊C4—431no—
546C4×C4⋊C4—431no—
547C4×C4⋊C4—432no—
548C4×C4⋊C4—432no—
549C4×C4⋊C4—431no—
550C4×C4⋊C4—431no—
551C4×C4⋊C4—431no—
552C4×C4⋊C4—432no—
553C4×C4⋊C4—432no—
554C4×C4⋊C4—432no—
555C4×C4⋊C4—432no—
556C4×C4⋊C4—432no—
557C4×C4⋊C4C2×D4311yescharacteristic
558#376—431no—
559#376—432no—
560#376C2×D4311yescharacteristic
561C43—431no—
562C43#3448811yescharacteristic, complemented, Sylow
563C22×Q8—432no—
564C22×Q8—431no—
565C22×Q8C22×D4311yescharacteristic
566C4⋊Q8—438no—
567C4⋊Q8—4316no—
568#125—438no—
569#125—4316no—
570#125—438no—
571#125—4316no—
572C4×Q8—438no—
573C4×Q8—438no—
574C4×Q8—4316no—
575C4×Q8—438no—
576C4×Q8—1724no—
577C4×Q8—1724no—
578C4×Q8—1724no—
579C4×Q8C4×D4318yes—
580C2×C4⋊C4—431no—
581C2×C4⋊C4—432no—
582C2×C4⋊C4—431no—
583C2×C4⋊C4—431no—
584C2×C4⋊C4—432no—
585C2×C4⋊C4—432no—
586C2×C4⋊C4—431no—
587C2×C4⋊C4—431no—
588C2×C4⋊C4—432no—
589C2×C4⋊C4—432no—
590C2×C4⋊C4—432no—
591C2×C4⋊C4—432no—
592C2×C4⋊C4—431no—
593C2×C4⋊C4—432no—
594C2×C4⋊C4—432no—
595C2×C4⋊C4—431no—
596C2×C4⋊C4—431no—
597C2×C4⋊C4—431no—
598C2×C4⋊C4—431no—
599C2×C4⋊C4—431no—
600C2×C4⋊C4—432no—
601C2×C4⋊C4—432no—
602C2×C4⋊C4—432no—
603C2×C4⋊C4—432no—
604C2×C4⋊C4—431no—
605C2×C4⋊C4—432no—
606C2×C4⋊C4—432no—
607C2×C4⋊C4—432no—
608C2×C4⋊C4—431no—
609C2×C4⋊C4—432no—
610C2×C4⋊C4C22×D4311yescharacteristic
611C2×C4⋊C4C22×D4311yescharacteristic
612C2×C4⋊C4C22×D4312yes—
613C2×C4⋊C4C22×D4312yes—
614C2×C4⋊C4C22×D4311yescharacteristic
615C2×C4⋊C4C22×D4312yes—
616C2×C42—431no—
617C2×C42—432no—
618C2×C42—431no—
619C2×C42—432no—
620C2×C42—431no—
621C2×C42—432no—
622C2×C42—431no—
623C2×C42—431no—
624C2×C42—431no—
625C2×C42—431no—
626C2×C42—432no—
627C2×C42—432no—
628C2×C42—432no—
629C2×C42—432no—
630C2×C42—432no—
631C2×C42—431no—
632C2×C42—432no—
633C2×C42—432no—
634C2×C42C22×D4311yescharacteristic
635C2×C42C22×D4311yescharacteristic
636C2×C42C22×D4312yes—
637C2×C42C22×D4311yescharacteristic
638C2×C42C22×D4312yes—
639#95—432no—
640#95—431no—
641#95—431no—
642#95—432no—
643#95—432no—
644#95—431no—
645#95—431no—
646#95—431no—
647#95—431no—
648#95—432no—
649#95—432no—
650#95—432no—
651#95—432no—
652#95—432no—
653#95—432no—
654#95—432no—
655#95—432no—
656#95—432no—
657#95—432no—
658#95—432no—
659#95—432no—
660#95—431no—
661#95—431no—
662#95—431no—
663#95—431no—
664#95—432no—
665#95C22×D4312yes—
666#95C22×D4311yescharacteristic
667#95C22×D4311yescharacteristic
668#95C22×D4311yescharacteristic
669#95C22×D4311yescharacteristic
670#95C22×D4312yes—
671#95C22×D4312yes—
672#95C22×D4312yes—
673#95C22×D4312yes—
674#95C22×D4312yes—
675#95C22×D4312yes—
676C2×Q8—22no—
677C2×Q8—22no—
678C2×Q8—438no—
679C2×Q8—434no—
680C2×Q8—862no—
681C2×Q8—864no—
682C2×Q8—864no—
683C2×Q8—862no—
684C2×Q8C2×C4×D4314yes—
685C22×C4—431no—
686C22×C4—431no—
687C22×C4—431no—
688C22×C4—431no—
689C22×C4—432no—
690C22×C4—431no—
691C22×C4—432no—
692C22×C4—431no—
693C22×C4—431no—
694C22×C4—431no—
695C22×C4—432no—
696C22×C4—432no—
697C22×C4C23×D4311yescharacteristic
698C22×C4C23×D4311yescharacteristic
699C22×C4C23×D4312yes—
700C22×C4C23×D4311yescharacteristic
701C22×C4C23×D4312yes—
702C22×C4C23×D4311yescharacteristic
703C22×C4C23×D4312yes—
704C22×C4C23×D4312yes—
705C22×C4C23×D4311yescharacteristic
706C22×C4C23×D4311yescharacteristic
707C22×C4C23×D4311yescharacteristic
708C4⋊C4—22no—
709C4⋊C4—22no—
710C4⋊C4—42no—
711C4⋊C4—42no—
712C4⋊C4—434no—
713C4⋊C4—438no—
714C4⋊C4—434no—
715C4⋊C4—438no—
716C4⋊C4—434no—
717C4⋊C4—438no—
718C4⋊C4—434no—
719C4⋊C4—438no—
720C4⋊C4—434no—
721C4⋊C4—438no—
722C4⋊C4—438no—
723C4⋊C4—438no—
724C4⋊C4—864no—
725C4⋊C4—862no—
726C4⋊C4—862no—
727C4⋊C4—864no—
728C4⋊C4—862no—
729C4⋊C4—862no—
730C4⋊C4—862no—
731C4⋊C4—862no—
732C4⋊C4—1722no—
733C4⋊C4—1722no—
734C4⋊C4—1722no—
735C4⋊C4—1722no—
736C4⋊C4—1721no—
737C4⋊C4—1722no—
738C4⋊C4—1722no—
739C4⋊C4—1722no—
740C4⋊C4—1721no—
741C4⋊C4—1722no—
742C4⋊C4C2×C4×D4318yes—
743C4⋊C4C2×C4×D4314yes—
744C42—22no—
745C42—22no—
746C42—42no—
747C42—438no—
748C42—434no—
749C42—438no—
750C42—434no—
751C42—864no—
752C42—862no—
753C42—862no—
754C42—862no—
755C42—862no—
756C42—862no—
757C42—1722no—
758C42—1722no—
759C42—1722no—
760C42—1722no—
761C42—1722no—
762C42—1722no—
763C42—1722no—
764C42—1721no—
765C42C2×C4×D4318yes—
766C42C2×C4×D4314yes—
767C23C24×D4311yescharacteristic
768Q8—28no—
769Q8—868no—
770Q8—8616no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—21no—
795C2×C4—22no—
796C2×C4—21no—
797C2×C4—432no—
798C2×C4—432no—
799C2×C4—432no—
800C2×C4—432no—
801C2×C4—432no—
802C2×C4—434no—
803C2×C4—434no—
804C2×C4—432no—
805C2×C4—432no—
806C2×C4—861no—
807C2×C4—861no—
808C2×C4—862no—
809C2×C4—861no—
810C2×C4—861no—
811C2×C4—862no—
812C2×C4—861no—
813C2×C4—862no—
814C2×C4—861no—
815C2×C4—862no—
816C2×C4—861no—
817C2×C4—861no—
818C2×C4—862no—
819C2×C4—862no—
820C2×C4—861no—
821C2×C4—861no—
822C2×C4—861no—
823C2×C4—861no—
824C2×C4—861no—
825C2×C4—861no—
826C2×C4—861no—
827C2×C4—862no—
828C2×C4—862no—
829C2×C4—861no—
830C2×C4—862no—
831C2×C4—861no—
832C2×C4—862no—
833C2×C4C22×C4×D4314yes—
834C2×C4C22×C4×D4312yes—
835C2×C4C22×C4×D4314yes—
836C2×C4C22×C4×D4312yes—
837C2×C4C22×C4×D4312yes—
838C2×C4#1306337212yes—
839C2×C4#1306337212yes—
840C22C23×C4×D4311yescharacteristic
841C22H(5,𝔽2)×D4311yescharacteristic
842C222−1+4×D4311yescharacteristic
843C222−1+4×D4311yescharacteristic
844C22C2×#1306337211yescharacteristic
845C22C2×#1306337211yescharacteristic
846C22#1458373611yescharacteristic
847C4—24no—
848C4—22no—
849C4—24no—
850C4—22no—
851C4—42no—
852C4—41no—
853C4—41no—
854C4—41no—
855C4—42no—
856C4—41no—
857C4—434no—
858C4—864no—
859C4—862no—
860C4—862no—
861C4—862no—
862C4—864no—
863C4—862no—
864C4—1722no—
865C4—1722no—
866C4—1721no—
867C4—1721no—
868C4—1721no—
869C4#1458337614yes—
870C2C2×#1458337611yescharacteristic
871C2#520×D4311yescharacteristic
872C2#1914780411yescharacteristic
873C2#1914903111yescharacteristic
874C2#1914906411yescharacteristic
875C2#1914907211yescharacteristic
876C2#1914908811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2320C2
socle, prime radical, cosocleC23×C43C25
hypercenter#2320D43
hypocenterC43#34488
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2320

Complements

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

NH ≅ G/Ntype
24. #14583625C4semidirect
562. C43#34488semidirect

Maximal subgroups

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

subgroupindex
C2×#145836252
#191377802
#191377782
#191376962
#191376912
#191376502
#191376482
#191375522
#191375512
#191375122
C4⋊C4×Dic862
#191373982
#191373962
#191373362
#191373352
#191373102
#191372452
#191372402
#191371662
#191370702
#191370672
C43×#23202
#3448843