Finite Group Databasebeta

← #25134590

Subgroups — #25134590

Order 11008.

1404 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic86C211yesmaximal, characteristic
2C2×#14583155C211yesmaximal, characteristic, complemented
3C2×#14583054C211yesmaximal, characteristic, complemented
4C2×#14583054C211yesmaximal, characteristic, complemented
5C2×#14582907C211yesmaximal, characteristic, complemented
6#19135841C211yesmaximal, characteristic, complemented
7#19135791C211yesmaximal, characteristic, complemented
8#19135694C211yesmaximal, characteristic, complemented
9#19135603C211yesmaximal, characteristic, complemented
10#19134939C211yesmaximal, characteristic, complemented
11#19134907C211yesmaximal, characteristic, complemented
12#19134893C211yesmaximal, characteristic
13#19134862C211yesmaximal, characteristic, complemented
14#19134529C211yesmaximal, characteristic, complemented
15C43×#2415C211yesmaximal, characteristic
16C23×Dic86C2211yescharacteristic
17C23×Dic86C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621885C2211yescharacteristic
21C22×#10621877C2211yescharacteristic
22D4×Dic86—24no—
23D4×Dic86—24no—
24C2×#13063325C2211yescharacteristic
25C2×#13063324—21no—
26C2×#13063304C2211yescharacteristic
27C2×#13063304C2211yescharacteristic
28C2×#13063302—21no—
29C2×#13063302—21no—
30C2×C4×Dic86C2211yescharacteristic
31C2×D4×Dic43—21no—
32#14583155—24no—
33#14583054—24no—
34#14583054—24no—
35C2×#13063256C2211yescharacteristic
36#14582907—24no—
37C2×#13063249C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×#13063248C2211yescharacteristic
43C2×#13063248C2211yescharacteristic
44C2×#13063248C2211yescharacteristic
45C2×#13063248C2211yescharacteristic
46C2×#13063248C2211yescharacteristic
47C2×C22⋊(C43⋊C8)C2211yescharacteristic
48C2×C22⋊(C43⋊C8)C2211yescharacteristic
49C2×C22⋊(C43⋊C8)C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53#14582654C2211yescharacteristic
54C2×C22⋊Q8×C43C2211yescharacteristic
55C2×C22⋊Q8×C43C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic
57C2×#117×C43C2211yescharacteristic
58C43×#397—21no—
59C43×#394—21no—
60C43×#391C2211yescharacteristic
61C43×#389—21no—
62C43×#389C2211yescharacteristic
63C43×#388—21no—
64C43×#380C2211yescharacteristic
65C22×Dic86—22no—
66C22×Dic86—22no—
67C22×Dic86—22no—
68C22×Dic86—21no—
69C22×Dic86—21no—
70C22×Dic86—22no—
71C22×Dic86—22no—
72C22×Dic86—22no—
73C22×Dic86—22no—
74C22×Dic86—41no—
75C22×Dic86—41no—
76C22×Dic86—41no—
77C22×Dic86—41no—
78C22×Dic86D414yes—
79C22×Dic86C2311yescharacteristic
80C22×Dic86C2311yescharacteristic
81C22×Dic86C2311yescharacteristic
82C23×Dic43—21no—
83C23×Dic43—21no—
84C2×#10621885—22no—
85C2×#10621885—22no—
86C2×#10621885—22no—
87C2×#10621885—22no—
88C2×#10621885—22no—
89C2×#10621885—22no—
90C2×#10621885—41no—
91C2×#10621885—41no—
92C2×#10621885—41no—
93C2×#10621877—22no—
94C2×#10621877—22no—
95C2×#10621877—41no—
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2311yescharacteristic
98C22×C43⋊C8C2311yescharacteristic
99C22×C43⋊C8C2311yescharacteristic
100#13063325—22no—
101#13063325—22no—
102#13063324—28no—
103#13063304—22no—
104#13063304—22no—
105#13063304—22no—
106#13063304D414yes—
107#13063302—28no—
108#13063302—28no—
109C4×Dic86—22no—
110C4×Dic86—22no—
111D4×Dic43—28no—
112C2×C4⋊Dic43—21no—
113C2×C4⋊Dic43—21no—
114C2×C4⋊Dic43C2311yescharacteristic
115C2×Dic43⋊C4—21no—
116C2×Dic43⋊C4—21no—
117C2×Dic43⋊C4—21no—
118C2×C22⋊Dic43—21no—
119C2×C22⋊Dic43—21no—
120C2×C4×Dic43—21no—
121#13063256—22no—
122#13063249—22no—
123#13063248—22no—
124#13063248—22no—
125#13063248—22no—
126#13063248—22no—
127#13063248—22no—
128#13063248—22no—
129#13063248—22no—
130#13063248—41no—
131#13063248D414yescomplemented
132C22⋊(C43⋊C8)—22no—
133C22⋊(C43⋊C8)—22no—
134C22⋊(C43⋊C8)—41no—
135C22×Q8×C43C2311yescharacteristic
136C22×D4×C43D411yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C22⋊Q8×C43—22no—
140C22⋊Q8×C43—22no—
141C22⋊Q8×C43—22no—
142C22⋊Q8×C43—41no—
143C4×D4×C43—22no—
144C4×D4×C43—22no—
145#117×C43—22no—
146#117×C43—41no—
147C2×C4⋊C4×C43—21no—
148C2×C4⋊C4×C43—21no—
149C2×C4⋊C4×C43—21no—
150C2×C4⋊C4×C43D411yescharacteristic
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C4⋊C4×C43C2311yescharacteristic
154C2×C22⋊C4×C43—21no—
155C2×C22⋊C4×C43—21no—
156C2×C22⋊C4×C43—21no—
157C2×C22⋊C4×C43—21no—
158C2×C22⋊C4×C43D411yescharacteristic
159C2×C22⋊C4×C43D411yescharacteristic
160C2×C42×C43—21no—
161C2×C42×C43C2311yescharacteristic
162#95×C43—21no—
163#95×C43—21no—
164#95×C43—21no—
165#95×C43—21no—
166C24×C43C2×D411yescharacteristic
167C24×C43C2×D411yescharacteristic
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×D4×C43—22no—
175C2×D4×C43—22no—
176C2×D4×C43—22no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43C2×D412yes—
192C22×C4×C43C2×D412yes—
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2411yescharacteristic
198C22×Dic43—24no—
199C22×Dic43—24no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—42no—
205C22×Dic43—42no—
206C22×Dic43—42no—
207C22×Dic43—42no—
208C2×Dic86—21no—
209C2×Dic86—21no—
210C2×Dic86—21no—
211C2×Dic86—21no—
212C2×Dic86—21no—
213C2×Dic86—21no—
214C2×Dic86—21no—
215C2×Dic86—21no—
216C2×Dic86—21no—
217C2×Dic86—21no—
218C2×Dic86—21no—
219C2×Dic86—28no—
220C2×Dic86—24no—
221C2×Dic86—24no—
222C2×Dic86—21no—
223C2×Dic86—21no—
224C2×Dic86—44no—
225C2×Dic86—44no—
226C2×Dic86—44no—
227C2×Dic86—44no—
228C2×Dic86—44no—
229C2×Dic86—44no—
230C2×Dic86—42no—
231C2×Dic86—42no—
232C2×Dic86—42no—
233C2×Dic86—42no—
234C2×Dic86—44no—
235C2×Dic86C2×D412yes—
236C2×Dic86C2×D412yes—
237C2×Dic86C2×D412yes—
238C2×Dic86C2×D412yes—
239C2×Dic86#4112yes—
240C4⋊C4×C43—22no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—42no—
247C4⋊C4×C43—42no—
248C4⋊C4×C43—42no—
249C4⋊C4×C43C2×D412yes—
250C22⋊C4×C43—22no—
251C22⋊C4×C43—22no—
252C22⋊C4×C43—42no—
253C22⋊C4×C43—42no—
254C22⋊C4×C43—42no—
255C22⋊C4×C43—42no—
256C42×C43—21no—
257C42×C43—21no—
258C42×C43—42no—
259C22⋊Dic43—24no—
260C22⋊Dic43—24no—
261#10621885—44no—
262#10621885—44no—
263#10621885—44no—
264C4⋊Dic43—24no—
265C4⋊Dic43—24no—
266C4⋊Dic43—21no—
267C4⋊Dic43C2×D412yes—
268Dic43⋊C4—24no—
269Dic43⋊C4—24no—
270Dic43⋊C4—24no—
271C4×Dic43—24no—
272#10621877—44no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8C2×D412yes—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43—21no—
294C23×C43—21no—
295C23×C43—21no—
296C23×C43—21no—
297C23×C43#12012yes—
298C23×C43#13712yes—
299C23×C43C22×D411yescharacteristic
300Q8×C43—41no—
301Q8×C43—41no—
302Q8×C43—41no—
303Q8×C43—41no—
304D4×C43—28no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—22no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43#12012yes—
336C2×C4×C43#13712yes—
337C2×C4×C43C22×D411yescharacteristic
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C22×D411yescharacteristic
340C2×C4×C43C2×#4111yescharacteristic
341C2×C4×C43H(5,𝔽2)11yescharacteristic
342C2×C4×C43H(5,𝔽2)11yescharacteristic
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—48no—
350C2×Dic43—48no—
351C2×Dic43—41no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357Dic86—22no—
358Dic86—22no—
359Dic86—22no—
360Dic86—22no—
361Dic86—22no—
362Dic86—22no—
363Dic86—22no—
364Dic86—48no—
365Dic86—48no—
366Dic86—41no—
367Dic86—41no—
368Dic86—41no—
369Dic86—41no—
370Dic86#12114yes—
371C43⋊C8—22no—
372C43⋊C8—41no—
373C43⋊C8—41no—
374C43⋊C8—41no—
375#24453—431nomaximal, Sylow
376C22×C43—22no—
377C22×C43—22no—
378C22×C43—22no—
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—41no—
383C22×C43—41no—
384C22×C43—41no—
385C22×C43—41no—
386C22×C43—41no—
387C22×C43—41no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43C2×#12011yescharacteristic
391C22×C43D4211yescharacteristic
392C22×C43#54611yescharacteristic
393C22×C43C2×#13711yescharacteristic
394C22×C43C2×#13711yescharacteristic
395C22×C43#57811yescharacteristic
396C22×C43#57811yescharacteristic
397C4×C43—22no—
398C4×C43—22no—
399C4×C43—41no—
400C4×C43—41no—
401C4×C43—42no—
402C4×C43—81no—
403C4×C43—81no—
404C4×C43—81no—
405C4×C43C2×#12111yescharacteristic
406C4×C43#53411yescharacteristic
407C4×C43D4211yescharacteristic
408C4×C43#54611yescharacteristic
409Dic43—24no—
410Dic43—42no—
411Dic43—42no—
412Dic43—42no—
413C2×D4×Q8—431no—
414C2×#470—431no—
415C2×#451—431no—
416C2×#451—431no—
417C2×#419—431no—
418#2415D4311yescharacteristic
419#2043—431no—
420#2035—431no—
421#2016—431no—
422#2001—431no—
423#1878—431no—
424#1873—431no—
425#1870—431no—
426#1865—431no—
427#1787—431no—
428C2×C43—42no—
429C2×C43—42no—
430C2×C43#241011yescharacteristic
431C2×C43#300411yescharacteristic
432C2×C43#301111yescharacteristic
433C2×C43#327011yescharacteristic
434C2×C43#327611yescharacteristic
435C2×C43#331211yescharacteristic
436C2×C43#332811yescharacteristic
437C23×Q8—431no—
438C23×Q8—431no—
439C22×Q16—431no—
440C22×Q16—431no—
441C22×Q16—431no—
442C22×M16—431no—
443D4×Q8—864no—
444D4×Q8—864no—
445C2×C4⋊Q8—431no—
446C2×C4⋊Q8—861no—
447C2×C22⋊Q8—431no—
448C2×C22⋊Q8—431no—
449C2×C22⋊Q8—861no—
450C2×C22⋊Q8—861no—
451C2×C22⋊Q8C2×D4311yescharacteristic
452C2×C22⋊Q8C2×D4311yescharacteristic
453C2×C4×Q8—431no—
454C2×C4×D4—861no—
455C2×C4×D4C2×D4311yescharacteristic
456C2×#117C2×D4311yescharacteristic
457#470—864no—
458#451—864no—
459#451—864no—
460C2×#106—431no—
461#419—864no—
462C2×#103—431no—
463C2×#103—431no—
464C2×#103—431no—
465C2×#103—431no—
466C2×#103—431no—
467C2×#103—431no—
468C2×#103—431no—
469C2×#103—431no—
470C2×#103—431no—
471C2×#103—431no—
472C2×C22⋊C8—431no—
473C2×C22⋊C8—431no—
474C2×C22⋊C8—431no—
475#397—21no—
476#394—21no—
477#391C2×D4311yescharacteristic
478#389—21no—
479#389C2×D4311yescharacteristic
480#388—21no—
481#380C2×D4311yescharacteristic
482#340—431no—
483#340—431no—
484#336—431no—
485#336—431no—
486C43#2445311yescharacteristic, complemented, Sylow
487C22×Q8—434no—
488C22×Q8—431no—
489C22×Q8—431no—
490C22×Q8—431no—
491C22×Q8—862no—
492C22×Q8—862no—
493C22×Q8—862no—
494C22×Q8—862no—
495C22×Q8—862no—
496C22×Q8—862no—
497C22×Q8—862no—
498C22×Q8—861no—
499C22×Q8—861no—
500C22×Q8—1721no—
501C22×Q8—1721no—
502C22×Q8—1721no—
503C22×Q8—1721no—
504C22×Q8C22×D4311yescharacteristic
505C22×D4C22⋊D4311yescharacteristic
506C23×C4—861no—
507C23×C4—861no—
508C23×C4C22×D4311yescharacteristic
509C23×C4C22×D4311yescharacteristic
510C2×Q16—862no—
511C2×Q16—862no—
512C2×Q16—862no—
513C2×Q16—862no—
514C2×Q16—862no—
515C2×Q16—862no—
516C2×Q16—1721no—
517C2×Q16—1721no—
518C2×Q16—1721no—
519C2×M16—862no—
520C2×M16—862no—
521C2×M16—1721no—
522C22×C8—431no—
523C22×C8—431no—
524C22×C8—431no—
525C22×C8—431no—
526C4⋊Q8—862no—
527C4⋊Q8—862no—
528C4⋊Q8—868no—
529C22⋊Q8—22no—
530C22⋊Q8—22no—
531C22⋊Q8—22no—
532C22⋊Q8—41no—
533C22⋊Q8—434no—
534C22⋊Q8—868no—
535C22⋊Q8—868no—
536C22⋊Q8—862no—
537C22⋊Q8—862no—
538C22⋊Q8—862no—
539C4×Q8—862no—
540C4×Q8—862no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—868no—
544#117—22no—
545#117—41no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—431no—
550C2×C4⋊C4—861no—
551C2×C4⋊C4—861no—
552C2×C4⋊C4—861no—
553C2×C4⋊C4—861no—
554C2×C4⋊C4—861no—
555C2×C4⋊C4C22⋊D4311yescharacteristic
556C2×C4⋊C4C22×D4311yescharacteristic
557C2×C4⋊C4C22×D4311yescharacteristic
558C2×C4⋊C4C22×D4311yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4C22⋊D4311yescharacteristic
566C2×C22⋊C4C22⋊D4311yescharacteristic
567C2×C42—21no—
568C2×C42—861no—
569C2×C42C22×D4311yescharacteristic
570#106—862no—
571#103—434no—
572#103—862no—
573#103—862no—
574#103—862no—
575#103—862no—
576#103—862no—
577#103—862no—
578#103—862no—
579#103—862no—
580#103—1721no—
581C22⋊C8—862no—
582C22⋊C8—862no—
583C22⋊C8—1721no—
584#95—21no—
585#95—21no—
586#95—21no—
587#95—21no—
588C24C2×C22⋊D4311yescharacteristic
589C24C2×C22⋊D4311yescharacteristic
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—432no—
597C2×Q8—432no—
598C2×Q8—432no—
599C2×Q8—432no—
600C2×Q8—432no—
601C2×Q8—864no—
602C2×Q8—868no—
603C2×Q8—864no—
604C2×Q8—861no—
605C2×Q8—861no—
606C2×Q8—861no—
607C2×Q8—861no—
608C2×Q8—861no—
609C2×Q8—861no—
610C2×Q8—861no—
611C2×Q8—861no—
612C2×Q8—861no—
613C2×Q8—861no—
614C2×Q8—861no—
615C2×Q8—861no—
616C2×Q8—861no—
617C2×Q8—1722no—
618C2×Q8—1722no—
619C2×Q8—1722no—
620C2×Q8—1722no—
621C2×Q8—1724no—
622C2×Q8—1724no—
623C2×Q8—1724no—
624C2×Q8—1724no—
625C2×Q8—1724no—
626C2×Q8—1724no—
627C2×Q8—1724no—
628C2×D4—22no—
629C2×D4—22no—
630C2×D4—22no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—861no—
646C22×C4—864no—
647C22×C4—864no—
648C22×C4—861no—
649C22×C4—861no—
650C22×C4—861no—
651C22×C4—1722no—
652C22×C4—1722no—
653C22×C4—1722no—
654C22×C4—1722no—
655C22×C4D4×D4312yes—
656C22×C4D4×D4312yes—
657C22×C4C2×C22⋊D4311yescharacteristic
658C22×C4C2×C22⋊D4311yescharacteristic
659C22×C4C2×C22⋊D4311yescharacteristic
660C22×C4C2×C22⋊D4311yescharacteristic
661C22×C4C23×D4311yescharacteristic
662Q16—1724no—
663Q16—1724no—
664Q16—1724no—
665M16—1724no—
666C2×C8—432no—
667C2×C8—861no—
668C2×C8—861no—
669C2×C8—861no—
670C2×C8—861no—
671C2×C8—861no—
672C2×C8—861no—
673C2×C8—861no—
674C2×C8—861no—
675C2×C8—861no—
676C2×C8—861no—
677C2×C8—861no—
678C4⋊C4—22no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—42no—
685C4⋊C4—42no—
686C4⋊C4—42no—
687C4⋊C4—432no—
688C4⋊C4—864no—
689C4⋊C4—864no—
690C4⋊C4—864no—
691C4⋊C4—864no—
692C4⋊C4—864no—
693C4⋊C4—861no—
694C4⋊C4D4×D4312yes—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—864no—
702C22⋊C4—864no—
703C42—21no—
704C42—21no—
705C42—42no—
706C42—864no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23#1306329312yes—
720C23#1306335512yes—
721C23C22×C22⋊D4311yescharacteristic
722Q8—41no—
723Q8—41no—
724Q8—41no—
725Q8—41no—
726Q8—434no—
727Q8—862no—
728Q8—862no—
729Q8—862no—
730Q8—862no—
731Q8—862no—
732Q8—862no—
733Q8—862no—
734Q8—1728no—
735Q8—1728no—
736Q8—1721no—
737Q8—1721no—
738Q8—1721no—
739Q8—1721no—
740D4—28no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—862no—
775C2×C4—862no—
776C2×C4—862no—
777C2×C4—1728no—
778C2×C4—1728no—
779C2×C4—1721no—
780C2×C4—1721no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4—1721no—
784C2×C4—1721no—
785C2×C4#1306329312yes—
786C2×C4#1306335512yes—
787C2×C4C2×D4×D4311yescharacteristic
788C2×C4C2×D4×D4311yescharacteristic
789C2×C4C2×D4×D4311yescharacteristic
790C2×C4#41×D4311yescharacteristic
791C2×C4#1306337011yescharacteristic
792C2×C4#1306337111yescharacteristic
793C8—862no—
794C8—1721no—
795C8—1721no—
796C8—1721no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22C2×#1306329311yescharacteristic
812C22D4×C22⋊D4311yescharacteristic
813C22#1458353711yescharacteristic
814C22C2×#1306335511yescharacteristic
815C22C2×#1306335511yescharacteristic
816C22#1458371411yescharacteristic
817C22#1458371411yescharacteristic
818C4—22no—
819C4—22no—
820C4—41no—
821C4—41no—
822C4—42no—
823C4—81no—
824C4—81no—
825C4—81no—
826C4—864no—
827C4—1722no—
828C4—1722no—
829C4—1722no—
830C4#121×D4311yescharacteristic
831C4#1458345711yescharacteristic
832C4#1458353311yescharacteristic
833C4#1458353811yescharacteristic
834C2—42no—
835C2—42no—
836C2#1913796611yescharacteristic
837C2#1914382811yescharacteristic
838C2#1914388811yescharacteristic
839C2#1914616111yescharacteristic
840C2#1914623711yescharacteristic
841C2#1914664011yescharacteristic
842C2#1914687211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2415C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
hypercenter#2415D43
hypocenterC43#24453
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2415

Complements

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

NH ≅ G/Ntype
2. C2×#14583155C2semidirect
3. C2×#14583054C2semidirect
4. C2×#14583054C2semidirect
5. C2×#14582907C2semidirect
6. #19135841C2semidirect
7. #19135791C2semidirect
8. #19135694C2semidirect
9. #19135603C2semidirect
10. #19134939C2semidirect
11. #19134907C2semidirect
13. #19134862C2semidirect
14. #19134529C2semidirect
131. #13063248D4semidirect
486. C43#24453semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic862
C2×#145831552
C2×#145830542
C2×#145829072
#191358412
#191357912
#191356942
#191356032
#191349392
#191349072
#191348932
#191348622
#191345292
C43×#24152
#2445343