Finite Group Databasebeta

← #25261907

Subgroups — #25261907

Order 11008.

1840 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583625C211yesmaximal, characteristic
2#19137780C212yesmaximal
3#19137773C212yesmaximal
4#19137699C212yesmaximal
5#19137691C211yesmaximal, characteristic
6#19137690C211yesmaximal, characteristic
7#19137681C211yesmaximal, characteristic
8#19137562C212yesmaximal
9#19137559C211yesmaximal, characteristic
10#19137559C211yesmaximal, characteristic
11#19137552C211yesmaximal, characteristic
12#19137550C211yesmaximal, characteristic
13#19137396C212yesmaximal
14#19137395C212yesmaximal
15#19137342C211yesmaximal, characteristic
16#19137340C212yesmaximal
17#19137336C211yesmaximal, characteristic
18#19137245C212yesmaximal
19#19137240C211yesmaximal, characteristic
20#19137154C211yesmaximal, characteristic
21#19137070C211yesmaximal, characteristic
22#19137067C211yesmaximal, characteristic
23C43×#2320C211yesmaximal, characteristic
24#14583625C4116yescomplemented
25C2×#13063324C2212yes—
26C2×#13063324C2211yescharacteristic
27C2×#13063317C2211yescharacteristic
28C2×#13063317C2212yes—
29C2×#13063316C2212yes—
30C2×#13063316C2211yescharacteristic
31C2×Q8×Dic43C2211yescharacteristic
32C2×Q8×Dic43C2211yescharacteristic
33C2×C4×Dic86C2211yescharacteristic
34C2×C4×Dic86C2212yes—
35#14582806C2211yescharacteristic
36#14582806C2211yescharacteristic
37#14582805C2212yes—
38#14582804C2212yes—
39#14582804C2212yes—
40#14582803C2211yescharacteristic
41#14582803C2211yescharacteristic
42#14582803C2212yes—
43#14582803C2212yes—
44#14582797C2211yescharacteristic
45#14582797C2211yescharacteristic
46#14582796C2211yescharacteristic
47#14582796C2211yescharacteristic
48#14582796C2212yes—
49#14582796C2212yes—
50#14582796C2212yes—
51#14582795C2211yescharacteristic
52#14582795C2211yescharacteristic
53#14582794C2212yes—
54#14582794C2212yes—
55#14582786C2212yes—
56#14582786C2212yes—
57#14582786C2211yescharacteristic
58#14582786C2212yes—
59#14582786C2212yes—
60#14582786C2211yescharacteristic
61#14582786C2212yes—
62#14582785C2212yes—
63#14582785C2212yes—
64#14582784C2212yes—
65#14582784C2212yes—
66#14582784C2212yes—
67#14582784C2212yes—
68#14582784C2212yes—
69#14582784C2212yes—
70#14582783C2212yes—
71#14582782C2212yes—
72#14582782C2212yes—
73#14582782C2211yescharacteristic
74#14582782C2211yescharacteristic
75#14582782C2212yes—
76#14582782C2212yes—
77#14582781C2212yes—
78#14582781C2212yes—
79#14582780C2212yes—
80#14582780C2212yes—
81#14582769C2211yescharacteristic
82#14582766C2212yes—
83#14582766C2212yes—
84#14582766C2212yes—
85#14582765C2212yes—
86#14582764C2211yescharacteristic
87#14582764C2211yescharacteristic
88#14582763C2212yes—
89C4⋊C4×Dic43C2211yescharacteristic
90C4⋊C4×Dic43C2211yescharacteristic
91C4⋊C4×Dic43C2211yescharacteristic
92C4⋊C4×Dic43C2211yescharacteristic
93C4⋊C4×Dic43C2211yescharacteristic
94C4⋊C4×Dic43C2211yescharacteristic
95C4⋊C4×Dic43C2212yes—
96C4⋊C4×Dic43C2212yes—
97C4×Dic43⋊C4C2211yescharacteristic
98C4×Dic43⋊C4C2211yescharacteristic
99C4×Dic43⋊C4C2212yes—
100C4×C4⋊Dic43C2212yes—
101C4×C4⋊Dic43C2212yes—
102C4×C4⋊Dic43C2211yescharacteristic
103C4×C4⋊Dic43C2211yescharacteristic
104C4×C4⋊Dic43C2211yescharacteristic
105#14582750C2212yes—
106#14582750C2212yes—
107#14582750C2212yes—
108#14582745C2211yescharacteristic
109#14582744C2212yes—
110#14582744C2212yes—
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×C4116yes—
131#13063316C2×C418yes—
132Q8×Dic43C2×C418yes—
133Q8×Dic43C2×C418yes—
134C4×Dic86C2×C418yes—
135C4×Dic86C2×C4116yes—
136C2×C4⋊Dic43C2311yescharacteristic
137C2×C4⋊Dic43C2311yescharacteristic
138C2×C4⋊Dic43C2311yescharacteristic
139C2×C4⋊Dic43C2312yes—
140C2×C4⋊Dic43C2312yes—
141C2×C4⋊Dic43C2311yescharacteristic
142C2×C4⋊Dic43C2312yes—
143C2×C4⋊Dic43C2312yes—
144C2×C4⋊Dic43C2312yes—
145C2×C4⋊Dic43C2311yescharacteristic
146C2×C4⋊Dic43C2311yescharacteristic
147C2×C4⋊Dic43C2311yescharacteristic
148C2×Dic43⋊C4C2311yescharacteristic
149C2×Dic43⋊C4C2311yescharacteristic
150C2×Dic43⋊C4C2312yes—
151C2×Dic43⋊C4C2311yescharacteristic
152C2×Dic43⋊C4C2312yes—
153C2×Dic43⋊C4C2312yes—
154C2×Dic43⋊C4C2311yescharacteristic
155C2×Dic43⋊C4C2312yes—
156C2×Dic43⋊C4C2311yescharacteristic
157C2×Dic43⋊C4C2311yescharacteristic
158C2×Dic43⋊C4C2312yes—
159C2×Dic43⋊C4C2312yes—
160C2×Dic43⋊C4C2312yes—
161C2×Dic43⋊C4C2312yes—
162C2×C4×Dic43C2311yescharacteristic
163C2×C4×Dic43C2312yes—
164C2×C4×Dic43C2311yescharacteristic
165C2×C4×Dic43C2311yescharacteristic
166C2×C4×Dic43C2311yescharacteristic
167C2×C4×Dic43C2311yescharacteristic
168C2×C4×Dic43C2312yes—
169C2×C4×Dic43C2312yes—
170C2×C4×Dic43C2312yes—
171C2×C4×Dic43C2312yes—
172C2×C4×Dic43C2312yes—
173C2×C4×Dic43C2312yes—
174C2×C4×Dic43C2311yescharacteristic
175C2×C4×Dic43C2312yes—
176C2×C4×Dic43C2311yescharacteristic
177C2×C4×Dic43C2312yes—
178C2×C4×Dic43C2312yes—
179C2×C4×Dic43C2311yescharacteristic
180C43⋊#95C2311yescharacteristic
181C43⋊#95C2311yescharacteristic
182C43⋊#95C2312yes—
183C43⋊#95C2312yes—
184C43⋊#95C2312yes—
185C43⋊#95C2312yes—
186C43⋊#95C2312yes—
187C43⋊#95C2312yes—
188C43⋊#95C2312yes—
189C43⋊#95C2312yes—
190C43⋊#95C2312yes—
191C43⋊#95C2312yes—
192C43⋊#95C2312yes—
193C43⋊#95C2312yes—
194C43⋊#95C2312yes—
195C43⋊#95C2312yes—
196C43⋊#95C2312yes—
197C43⋊#95C2311yescharacteristic
198C43⋊#95C2311yescharacteristic
199C43⋊#95C2312yes—
200C43⋊#95C2312yes—
201C43⋊#95C2312yes—
202C43⋊#95C2311yescharacteristic
203C43⋊#95C2311yescharacteristic
204C43⋊#95C2311yescharacteristic
205C43⋊#95C2311yescharacteristic
206C43⋊#95C2312yes—
207C43⋊#95C2312yes—
208C43⋊#95C2311yescharacteristic
209C43⋊#95C2311yescharacteristic
210C22×Q8×C43C2311yescharacteristic
211C4×Q8×C43C2×C418yes—
212C2×C4⋊C4×C43C2311yescharacteristic
213C2×C4⋊C4×C43C2311yescharacteristic
214C2×C4⋊C4×C43C2312yes—
215C2×C4⋊C4×C43C2312yes—
216C2×C4⋊C4×C43C2312yes—
217C2×C4⋊C4×C43C2311yescharacteristic
218C2×C42×C43C2311yescharacteristic
219C2×C42×C43C2311yescharacteristic
220C2×C42×C43C2312yes—
221C2×C42×C43C2311yescharacteristic
222C2×C42×C43C2312yes—
223#95×C43C2312yes—
224#95×C43C2312yes—
225#95×C43C2312yes—
226#95×C43C2312yes—
227#95×C43C2312yes—
228#95×C43C2312yes—
229#95×C43C2311yescharacteristic
230#95×C43C2312yes—
231#95×C43C2311yescharacteristic
232#95×C43C2311yescharacteristic
233#95×C43C2311yescharacteristic
234C2×Q8×C43—22no—
235C2×Q8×C43—22no—
236C2×Q8×C43C22×C414yes—
237C22×C4×C43C2411yescharacteristic
238C22×C4×C43C2411yescharacteristic
239C22×C4×C43C2411yescharacteristic
240C22×C4×C43C2412yes—
241C22×C4×C43C2411yescharacteristic
242C22×C4×C43C2412yes—
243C22×C4×C43C2411yescharacteristic
244C22×C4×C43C2412yes—
245C22×C4×C43C2411yescharacteristic
246C22×C4×C43C2412yes—
247C22×C4×C43C2411yescharacteristic
248C22×Dic43C2411yescharacteristic
249C22×Dic43C2411yescharacteristic
250C22×Dic43C2411yescharacteristic
251C22×Dic43C2412yes—
252C22×Dic43C2412yes—
253C22×Dic43C2411yescharacteristic
254C22×Dic43C2411yescharacteristic
255C22×Dic43C2412yes—
256C22×Dic43C2411yescharacteristic
257C22×Dic43C2411yescharacteristic
258C22×Dic43C2412yes—
259C22×Dic43C2411yescharacteristic
260C2×Dic86—42no—
261C2×Dic86—41no—
262C2×Dic86—41no—
263C2×Dic86—42no—
264C2×Dic86C22×C418yes—
265C2×Dic86C22×C414yes—
266C4⋊C4×C43—22no—
267C4⋊C4×C43—22no—
268C4⋊C4×C43—42no—
269C4⋊C4×C43—42no—
270C4⋊C4×C43C22×C418yes—
271C4⋊C4×C43C22×C414yes—
272C42×C43—22no—
273C42×C43—22no—
274C42×C43—42no—
275C42×C43C22×C418yes—
276C42×C43C22×C414yes—
277C4⋊Dic43—22no—
278C4⋊Dic43—22no—
279C4⋊Dic43—22no—
280C4⋊Dic43—42no—
281C4⋊Dic43—42no—
282C4⋊Dic43—41no—
283C4⋊Dic43C22×C418yes—
284C4⋊Dic43C22×C414yes—
285C4⋊Dic43C22×C418yes—
286C4⋊Dic43C22×C414yes—
287C4⋊Dic43C22×C418yes—
288C4⋊Dic43C22×C414yes—
289Dic43⋊C4—22no—
290Dic43⋊C4—41no—
291Dic43⋊C4—42no—
292Dic43⋊C4—42no—
293Dic43⋊C4—41no—
294Dic43⋊C4—41no—
295Dic43⋊C4—42no—
296Dic43⋊C4—42no—
297Dic43⋊C4C22×C414yes—
298Dic43⋊C4C22×C414yes—
299Dic43⋊C4C22×C418yes—
300Dic43⋊C4C22×C418yes—
301Dic43⋊C4C22×C418yes—
302Dic43⋊C4C22×C418yes—
303C4×Dic43—22no—
304C4×Dic43—22no—
305C4×Dic43—22no—
306C4×Dic43—24no—
307C4×Dic43—41no—
308C4×Dic43—42no—
309C4×Dic43—42no—
310C4×Dic43—41no—
311C4×Dic43—42no—
312C4×Dic43—42no—
313C4×Dic43—42no—
314C4×Dic43—42no—
315C4×Dic43—41no—
316C4×Dic43—42no—
317C4×Dic43C22×C418yes—
318C4×Dic43C22×C414yes—
319C4×Dic43C22×C418yes—
320C4×Dic43C22×C414yes—
321C23×C43C2511yescharacteristic
322Q8×C43—28no—
323C2×C4×C43—21no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—22no—
331C2×C4×C43—21no—
332C2×C4×C43—22no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—22no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—22no—
346C2×C4×C43—21no—
347C2×C4×C43—22no—
348C2×C4×C43—21no—
349C2×C4×C43C23×C414yes—
350C2×C4×C43C23×C412yes—
351C2×C4×C43C23×C412yes—
352C2×C4×C43C23×C414yes—
353C2×C4×C43C23×C412yes—
354C2×C4×C432−1+412yes—
355C2×C4×C432−1+412yes—
356C2×Dic43—21no—
357C2×Dic43—22no—
358C2×Dic43—21no—
359C2×Dic43—21no—
360C2×Dic43—21no—
361C2×Dic43—21no—
362C2×Dic43—21no—
363C2×Dic43—22no—
364C2×Dic43—22no—
365C2×Dic43—21no—
366C2×Dic43—21no—
367C2×Dic43—22no—
368C2×Dic43—21no—
369C2×Dic43—21no—
370C2×Dic43—21no—
371C2×Dic43—21no—
372C2×Dic43—21no—
373C2×Dic43—21no—
374C2×Dic43—22no—
375C2×Dic43—22no—
376C2×Dic43—21no—
377C2×Dic43—21no—
378C2×Dic43—22no—
379C2×Dic43—22no—
380C2×Dic43—21no—
381C2×Dic43—22no—
382C2×Dic43—22no—
383C2×Dic43—21no—
384C2×Dic43—21no—
385C2×Dic43C23×C412yes—
386C2×Dic43C23×C412yes—
387C2×Dic43C23×C414yes—
388C2×Dic43C23×C412yes—
389C2×Dic43C23×C414yes—
390C2×Dic43C23×C412yes—
391C2×Dic432−1+412yes—
392Dic86—48no—
393Dic86—44no—
394#34490—431nomaximal, Sylow
395C22×C43C24×C411yescharacteristic
396C22×C43C2×2−1+411yescharacteristic
397C22×C43C2×2−1+411yescharacteristic
398C22×C43C2×2−1+411yescharacteristic
399C22×C43#58511yescharacteristic
400C22×C43#58511yescharacteristic
401C22×C43#58511yescharacteristic
402C4×C43—24no—
403C4×C43—24no—
404C4×C43—22no—
405C4×C43—22no—
406C4×C43—41no—
407C4×C43—42no—
408C4×C43—41no—
409C4×C43—41no—
410C4×C43—41no—
411C4×C43—42no—
412C4×C43#51914yes—
413Dic43—22no—
414Dic43—24no—
415Dic43—22no—
416Dic43—22no—
417Dic43—24no—
418Dic43—22no—
419Dic43—22no—
420Dic43—42no—
421Dic43—42no—
422Dic43—41no—
423Dic43—41no—
424Dic43—41no—
425C2×#557—431no—
426#2382—432no—
427#2381—432no—
428#2371—432no—
429#2370—431no—
430#2370—431no—
431#2369—431no—
432#2356—431no—
433#2356—431no—
434#2356—432no—
435#2355—431no—
436#2355—431no—
437#2336—432no—
438#2336—432no—
439#2331—431no—
440#2331—432no—
441#2330—431no—
442#2320—431no—
443#2320—432no—
444#2320D4311yescharacteristic
445C4×#125—431no—
446#2295—431no—
447#2295—431no—
448C2×C43C2×#51911yescharacteristic
449C2×C43#342811yescharacteristic
450C2×C43C4×2−1+411yescharacteristic
451C2×C43#355511yescharacteristic
452C2×C43#355711yescharacteristic
453C2×C43#356311yescharacteristic
454C2×C43#356511yescharacteristic
455#557—4316no—
456C2×C4⋊Q8—431no—
457C2×C4⋊Q8—432no—
458C2×#125—431no—
459C2×#125—432no—
460C2×#125—431no—
461C2×#125—432no—
462C2×C4×Q8—431no—
463C2×C4×Q8—431no—
464C2×C4×Q8—432no—
465C2×C4×Q8—431no—
466C2×C4×Q8C2×D4311yescharacteristic
467#391—431no—
468#391—431no—
469#391—432no—
470#391—432no—
471#391—432no—
472#391—432no—
473#391—432no—
474#391—431no—
475#391—431no—
476#391C2×D4311yescharacteristic
477#391C2×D4311yescharacteristic
478#389—432no—
479#389—432no—
480#389—431no—
481#389—431no—
482#389—431no—
483#389—431no—
484#389—432no—
485#389—432no—
486#389—432no—
487#389—431no—
488#389—431no—
489#389C2×D4311yescharacteristic
490#389C2×D4311yescharacteristic
491#387—432no—
492#387—432no—
493#387—432no—
494#387—432no—
495#387—432no—
496#387—432no—
497#387—432no—
498#387—432no—
499#387—432no—
500#387—432no—
501#387—432no—
502#387—431no—
503#387—432no—
504#387—432no—
505#387—432no—
506#387—432no—
507#387—432no—
508#387—431no—
509#387—432no—
510#387—432no—
511#387—432no—
512#387—431no—
513#387—432no—
514#387—432no—
515#387—431no—
516#387—432no—
517#387C2×D4312yes—
518#387C2×D4312yes—
519#384—431no—
520#383—432no—
521#383—432no—
522#383—432no—
523#383C2×D4312yes—
524#382—431no—
525#382—431no—
526#382—432no—
527#382—432no—
528#382C2×D4312yes—
529C4×C4⋊C4—431no—
530C4×C4⋊C4—431no—
531C4×C4⋊C4—432no—
532C4×C4⋊C4—431no—
533C4×C4⋊C4—431no—
534C4×C4⋊C4—431no—
535C4×C4⋊C4—432no—
536C4×C4⋊C4—431no—
537C4×C4⋊C4—431no—
538C4×C4⋊C4—431no—
539C4×C4⋊C4—432no—
540C4×C4⋊C4—432no—
541C4×C4⋊C4—432no—
542C4×C4⋊C4—431no—
543C4×C4⋊C4—431no—
544C4×C4⋊C4—431no—
545C4×C4⋊C4—432no—
546C4×C4⋊C4—432no—
547C4×C4⋊C4—432no—
548C4×C4⋊C4C2×D4311yescharacteristic
549#376—431no—
550#376—432no—
551#376—432no—
552#376—432no—
553#376C2×D4311yescharacteristic
554C43—431no—
555C43#3449011yescharacteristic, complemented, Sylow
556C22×Q8—432no—
557C22×Q8—431no—
558C22×Q8C22×D4311yescharacteristic
559C4⋊Q8—438no—
560C4⋊Q8—4316no—
561#125—438no—
562#125—4316no—
563#125—438no—
564#125—4316no—
565C4×Q8—438no—
566C4×Q8—438no—
567C4×Q8—4316no—
568C4×Q8—438no—
569C4×Q8C4×D4318yes—
570C2×C4⋊C4—431no—
571C2×C4⋊C4—432no—
572C2×C4⋊C4—431no—
573C2×C4⋊C4—432no—
574C2×C4⋊C4—431no—
575C2×C4⋊C4—431no—
576C2×C4⋊C4—432no—
577C2×C4⋊C4—431no—
578C2×C4⋊C4—432no—
579C2×C4⋊C4—432no—
580C2×C4⋊C4—432no—
581C2×C4⋊C4—432no—
582C2×C4⋊C4—431no—
583C2×C4⋊C4—431no—
584C2×C4⋊C4—431no—
585C2×C4⋊C4—431no—
586C2×C4⋊C4—432no—
587C2×C4⋊C4—432no—
588C2×C4⋊C4—431no—
589C2×C4⋊C4—431no—
590C2×C4⋊C4—431no—
591C2×C4⋊C4—432no—
592C2×C4⋊C4—432no—
593C2×C4⋊C4—431no—
594C2×C4⋊C4—432no—
595C2×C4⋊C4—432no—
596C2×C4⋊C4C22×D4311yescharacteristic
597C2×C4⋊C4C22×D4311yescharacteristic
598C2×C4⋊C4C22×D4312yes—
599C2×C4⋊C4C22×D4312yes—
600C2×C4⋊C4C22×D4311yescharacteristic
601C2×C4⋊C4C22×D4312yes—
602C2×C42—431no—
603C2×C42—432no—
604C2×C42—431no—
605C2×C42—432no—
606C2×C42—431no—
607C2×C42—431no—
608C2×C42—432no—
609C2×C42—431no—
610C2×C42—431no—
611C2×C42—431no—
612C2×C42—431no—
613C2×C42—432no—
614C2×C42—432no—
615C2×C42—432no—
616C2×C42—432no—
617C2×C42—432no—
618C2×C42—432no—
619C2×C42—432no—
620C2×C42C22×D4311yescharacteristic
621C2×C42C22×D4311yescharacteristic
622C2×C42C22×D4312yes—
623C2×C42C22×D4311yescharacteristic
624C2×C42C22×D4312yes—
625#95—431no—
626#95—432no—
627#95—431no—
628#95—432no—
629#95—432no—
630#95—432no—
631#95—431no—
632#95—432no—
633#95—431no—
634#95—431no—
635#95—431no—
636#95—432no—
637#95—431no—
638#95—431no—
639#95—432no—
640#95—432no—
641#95—432no—
642#95—432no—
643#95—432no—
644#95—432no—
645#95—432no—
646#95—431no—
647#95—432no—
648#95—432no—
649#95—432no—
650#95—432no—
651#95—432no—
652#95—432no—
653#95—431no—
654#95—432no—
655#95C22×D4312yes—
656#95C22×D4312yes—
657#95C22×D4312yes—
658#95C22×D4311yescharacteristic
659#95C22×D4311yescharacteristic
660#95C22×D4311yescharacteristic
661#95C22×D4311yescharacteristic
662#95C22×D4312yes—
663#95C22×D4312yes—
664#95C22×D4312yes—
665#95C22×D4312yes—
666C2×Q8—22no—
667C2×Q8—22no—
668C2×Q8—438no—
669C2×Q8—434no—
670C2×Q8—1721no—
671C2×Q8—1722no—
672C2×Q8—1722no—
673C2×Q8—1721no—
674C2×Q8C2×C4×D4314yes—
675C22×C4—431no—
676C22×C4—431no—
677C22×C4—431no—
678C22×C4—432no—
679C22×C4—431no—
680C22×C4—432no—
681C22×C4—431no—
682C22×C4—431no—
683C22×C4—431no—
684C22×C4—431no—
685C22×C4—432no—
686C22×C4—432no—
687C22×C4C23×D4311yescharacteristic
688C22×C4C23×D4312yes—
689C22×C4C23×D4311yescharacteristic
690C22×C4C23×D4311yescharacteristic
691C22×C4C23×D4312yes—
692C22×C4C23×D4311yescharacteristic
693C22×C4C23×D4312yes—
694C22×C4C23×D4312yes—
695C22×C4C23×D4311yescharacteristic
696C22×C4C23×D4311yescharacteristic
697C22×C4C23×D4311yescharacteristic
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—42no—
701C4⋊C4—42no—
702C4⋊C4—434no—
703C4⋊C4—438no—
704C4⋊C4—434no—
705C4⋊C4—438no—
706C4⋊C4—434no—
707C4⋊C4—438no—
708C4⋊C4—434no—
709C4⋊C4—438no—
710C4⋊C4—434no—
711C4⋊C4—438no—
712C4⋊C4—438no—
713C4⋊C4—438no—
714C4⋊C4—862no—
715C4⋊C4—862no—
716C4⋊C4—862no—
717C4⋊C4—862no—
718C4⋊C4—1722no—
719C4⋊C4—1721no—
720C4⋊C4—1721no—
721C4⋊C4—1722no—
722C4⋊C4—1721no—
723C4⋊C4—1722no—
724C4⋊C4—1722no—
725C4⋊C4—1722no—
726C4⋊C4—1721no—
727C4⋊C4—1722no—
728C4⋊C4C2×C4×D4318yes—
729C4⋊C4C2×C4×D4314yes—
730C42—22no—
731C42—22no—
732C42—42no—
733C42—438no—
734C42—434no—
735C42—438no—
736C42—434no—
737C42—862no—
738C42—864no—
739C42—862no—
740C42—862no—
741C42—1722no—
742C42—1722no—
743C42—1722no—
744C42—1721no—
745C42—1722no—
746C42—1722no—
747C42—1722no—
748C42—1722no—
749C42—1721no—
750C42—1721no—
751C42C2×C4×D4318yes—
752C42C2×C4×D4314yes—
753C23C24×D4311yescharacteristic
754Q8—28no—
755Q8—1724no—
756Q8—1728no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—432no—
784C2×C4—432no—
785C2×C4—434no—
786C2×C4—432no—
787C2×C4—434no—
788C2×C4—432no—
789C2×C4—432no—
790C2×C4—861no—
791C2×C4—862no—
792C2×C4—861no—
793C2×C4—861no—
794C2×C4—862no—
795C2×C4—861no—
796C2×C4—861no—
797C2×C4—861no—
798C2×C4—861no—
799C2×C4—861no—
800C2×C4—862no—
801C2×C4—862no—
802C2×C4—861no—
803C2×C4—861no—
804C2×C4—861no—
805C2×C4—861no—
806C2×C4—861no—
807C2×C4—861no—
808C2×C4—862no—
809C2×C4—862no—
810C2×C4—861no—
811C2×C4—861no—
812C2×C4—862no—
813C2×C4—862no—
814C2×C4—861no—
815C2×C4—862no—
816C2×C4—862no—
817C2×C4—861no—
818C2×C4—861no—
819C2×C4C22×C4×D4314yes—
820C2×C4C22×C4×D4312yes—
821C2×C4C22×C4×D4314yes—
822C2×C4C22×C4×D4312yes—
823C2×C4C22×C4×D4312yes—
824C2×C4#1306337212yes—
825C2×C4#1306337212yes—
826C22C23×C4×D4311yescharacteristic
827C222−1+4×D4311yescharacteristic
828C22C2×#1306337211yescharacteristic
829C22C2×#1306337211yescharacteristic
830C22#1458373411yescharacteristic
831C22#1458373611yescharacteristic
832C22#1458373611yescharacteristic
833C4—24no—
834C4—22no—
835C4—24no—
836C4—22no—
837C4—41no—
838C4—42no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—42no—
843C4—862no—
844C4—864no—
845C4—862no—
846C4—862no—
847C4—864no—
848C4—862no—
849C4—862no—
850C4—1722no—
851C4—1722no—
852C4—1721no—
853C4—1721no—
854C4—1721no—
855C4#1458337614yes—
856C2C2×#1458337611yescharacteristic
857C2#1914779511yescharacteristic
858C2#1914780411yescharacteristic
859C2#1914908111yescharacteristic
860C2#1914910311yescharacteristic
861C2#1914920011yescharacteristic
862C2#1914924611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2320C2
socle, prime radical, cosocleC23×C43C25
hypercenter#2320D43
hypocenterC43#34490
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2320

Complements

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

NH ≅ G/Ntype
24. #14583625C4semidirect
555. C43#34490semidirect

Maximal subgroups

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

subgroupindex
C2×#145836252
#191377802
#191377732
#191376992
#191376912
#191376902
#191376812
#191375622
#191375592
#191375522
#191375502
#191373962
#191373952
#191373422
#191373402
#191373362
#191372452
#191372402
#191371542
#191370702
#191370672
C43×#23202
#3449043