Finite Group Databasebeta

← #25062790

Subgroups — #25062790

Order 11008.

1046 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583572C211yesmaximal, characteristic
2#19143255C211yesmaximal, characteristic, complemented
3#19143249C211yesmaximal, characteristic, complemented
4#19132963C211yesmaximal, characteristic, complemented
5#19132963C211yesmaximal, characteristic, complemented
6#19132945C211yesmaximal, characteristic, complemented
7#19132945C211yesmaximal, characteristic, complemented
8#19132943C211yesmaximal, characteristic, complemented
9#19132934C211yesmaximal, characteristic, complemented
10#19132928C211yesmaximal, characteristic, complemented
11#19132921C211yesmaximal, characteristic, complemented
12#19132914C211yesmaximal, characteristic, complemented
13#19132908C211yesmaximal, characteristic, complemented
14C2×#14582622C211yesmaximal, characteristic, complemented
15C43×#1468C211yesmaximal, characteristic, complemented
16#14583572—21no—
17#14583572—21no—
18#14583572—21no—
19#14583572—21no—
20#14583572—21no—
21#14583572—21no—
22#14583572—21no—
23#14583572—21no—
24C2×#13063320C411yescharacteristic
25C2×#13063320C2211yescharacteristic
26C2×#13063311C2211yescharacteristic
27C2×#13063309C411yescharacteristic
28C2×#13063307C411yescharacteristic
29C2×#13063305C411yescharacteristic
30C2×#13063302C411yescharacteristic
31C2×#13063293C411yescharacteristic
32C2×D4×Dic43C411yescharacteristic
33C2×(C22⋊D43)⋊C4C2211yescharacteristic
34C2×#13063284C2211yescharacteristic
35C2×#13063283C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C2×C22⋊C4×D43C411yescharacteristic
38#14582957—21no—
39#14582957—21no—
40#14582957—21no—
41#14582957—21no—
42#14582953C2211yescharacteristic, complemented
43#14582953C2211yescharacteristic, complemented
44#14582953C2211yescharacteristic, complemented
45#14582953C2211yescharacteristic, complemented
46#14582949C2211yescharacteristic, complemented
47#14582949C2211yescharacteristic, complemented
48#14582949C2211yescharacteristic, complemented
49#14582949C2211yescharacteristic, complemented
50#14582927—21no—
51#14582925—21no—
52#14582863C2211yescharacteristic
53C2×C22⋊(C43⋊C8)C2211yescharacteristic
54#14582857—21no—
55#14582854—21no—
56#14582625C2211yescharacteristic, complemented
57#14582625C2211yescharacteristic, complemented
58#14582623C2211yescharacteristic, complemented
59#14582623C2211yescharacteristic, complemented
60#14582622C2211yescharacteristic
61#14582622C2211yescharacteristic
62#14582622C2211yescharacteristic
63#14582622C2211yescharacteristic
64#14582622C2211yescharacteristic
65#14582622C2211yescharacteristic
66#14582622C2211yescharacteristic
67#14582622C2211yescharacteristic
68C2×#123×C43C2211yescharacteristic
69C43×#407C2211yescharacteristic
70C2×C22⋊C8×C43C2211yescharacteristic
71C43×#324C2211yescharacteristic, complemented
72C43×#324C2211yescharacteristic, complemented
73C43×#323C2211yescharacteristic, complemented
74C43×#323C2211yescharacteristic, complemented
75C24×D43C2×C411yescharacteristic
76C22×Dic86C2×C411yescharacteristic
77C22×C22⋊D43C2×C411yescharacteristic
78C22×C22⋊D43C2×C411yescharacteristic
79C23×Dic43C2×C411yescharacteristic
80C23×Dic43C2×C411yescharacteristic
81C22×C4×D43C2×C411yescharacteristic
82C22×C4×D43C2×C411yescharacteristic
83C2×#10621877—21no—
84C22×C43⋊C8—21no—
85#13063320—21no—
86#13063320—21no—
87#13063320—21no—
88#13063320—21no—
89#13063320—21no—
90#13063320—21no—
91#13063320—21no—
92#13063320—21no—
93#13063311—21no—
94#13063311—21no—
95#13063311—21no—
96#13063311—21no—
97#13063309—21no—
98#13063309—21no—
99#13063309—21no—
100#13063309—21no—
101#13063307—21no—
102#13063307—21no—
103#13063307—21no—
104#13063307—21no—
105#13063305—21no—
106#13063305—21no—
107#13063305—21no—
108#13063305—21no—
109#13063302—21no—
110#13063302—21no—
111#13063302—21no—
112#13063302—21no—
113#13063293—21no—
114#13063293—21no—
115#13063293—21no—
116#13063293—21no—
117D4×Dic43—21no—
118D4×Dic43—21no—
119D4×Dic43—21no—
120D4×Dic43—21no—
121(C22⋊D43)⋊C4—21no—
122(C22⋊D43)⋊C4—21no—
123(C22⋊D43)⋊C4—21no—
124(C22⋊D43)⋊C4—21no—
125#13063284D411yescharacteristic
126#13063284D411yescharacteristic
127#13063284D411yescharacteristic
128#13063284D411yescharacteristic
129#13063284D411yescharacteristic
130#13063284D411yescharacteristic
131#13063284D411yescharacteristic
132#13063284D411yescharacteristic
133#13063283—21no—
134#13063283—21no—
135#13063283—21no—
136#13063283—21no—
137C2×C4⋊Dic43C2×C411yescharacteristic
138C2×C4⋊Dic43C2×C411yescharacteristic
139C2×C4⋊Dic43C2×C411yescharacteristic
140C2×C4⋊Dic43C2×C411yescharacteristic
141C2×Dic43⋊C4C2×C411yescharacteristic
142C2×Dic43⋊C4C2×C411yescharacteristic
143C2×C22⋊Dic43C2×C411yescharacteristic
144C2×C22⋊Dic43C2×C411yescharacteristic
145C2×C22⋊Dic43C2×C411yescharacteristic
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4C2×C411yescharacteristic
151C2×(C2×D43)⋊C4C2×C411yescharacteristic
152C2×(C2×D43)⋊C4C2×C411yescharacteristic
153C2×(C2×D43)⋊C4C2×C411yescharacteristic
154C2×(C2×D43)⋊C4C2×C411yescharacteristic
155C2×(C2×D43)⋊C4C2×C411yescharacteristic
156C2×(C2×D43)⋊C4C2311yescharacteristic
157C2×(C2×D43)⋊C4C2311yescharacteristic
158C22⋊C4×D43—21no—
159C22⋊C4×D43—21no—
160C22⋊C4×D43—21no—
161C22⋊C4×D43—21no—
162C2×C4×Dic43C2×C411yescharacteristic
163C2×C4×Dic43C2311yescharacteristic
164C2×C4×Dic43C2311yescharacteristic
165Dic43⋊C8—21no—
166Dic43⋊C8—21no—
167Dic43⋊C8—21no—
168Dic43⋊C8—21no—
169Dic43⋊C8—21no—
170Dic43⋊C8—21no—
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173C22⋊(C43⋊C8)—21no—
174C22⋊(C43⋊C8)—21no—
175C22⋊(C43⋊C8)C2311yescharacteristic
176C22⋊(C43⋊C8)C2311yescharacteristic
177C22⋊(C43⋊C8)C2311yescharacteristic
178C22⋊(C43⋊C8)C2311yescharacteristic
179#13063235—21no—
180#13063235—21no—
181#13063235—21no—
182#13063235—21no—
183C8×Dic43—21no—
184C8×Dic43—21no—
185C8×Dic43—21no—
186C8×Dic43—21no—
187C22×D4×C43C2×C411yescharacteristic
188C23×C4×C43C2311yescharacteristic
189C2×M16×C43—21no—
190C22×C8×C43—21no—
191#123×C43—21no—
192#123×C43—21no—
193#123×C43—21no—
194#123×C43—21no—
195C2×C4⋊C4×C43C2×C411yescharacteristic
196C2×C4⋊C4×C43C2311yescharacteristic
197C2×C22⋊C4×C43C2×C411yescharacteristic
198C2×C22⋊C4×C43C2×C411yescharacteristic
199C2×C22⋊C4×C43C2311yescharacteristic
200C22⋊C8×C43—21no—
201C22⋊C8×C43—21no—
202C22⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43C2311yescharacteristic
204C22⋊C8×C43C2311yescharacteristic
205C22⋊C8×C43C2311yescharacteristic
206C24×C43C22×C411yescharacteristic
207C24×C43C22×C411yescharacteristic
208C23×D43—21no—
209C23×D43—21no—
210C23×D43—22no—
211C23×D43—41no—
212C23×D43—42no—
213C23×D43—81no—
214C23×D43C22×C411yescharacteristic
215C23×D43C22×C411yescharacteristic
216C2×D4×C43—21no—
217C2×D4×C43—21no—
218C2×D4×C43—42no—
219C22×C4×C43—42no—
220C22×C4×C43C22×C411yescharacteristic
221C22×C4×C43C22×C411yescharacteristic
222C22×C4×C43C22×C411yescharacteristic
223C22×C4×C43C22×C411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2411yescharacteristic
229C2×C22⋊D43—21no—
230C2×C22⋊D43—21no—
231C2×C22⋊D43—21no—
232C2×C22⋊D43—21no—
233C2×C22⋊D43—22no—
234C2×C22⋊D43—41no—
235C2×C22⋊D43—81no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43—81no—
241C22×Dic43—81no—
242C22×Dic43C22×C411yescharacteristic
243C22×Dic43C22×C411yescharacteristic
244C22×Dic43C22×C411yescharacteristic
245C22×Dic43C22×C411yescharacteristic
246C22×Dic43C22×C411yescharacteristic
247C22×Dic43C22×C411yescharacteristic
248C2×C4×D43—21no—
249C2×C4×D43—21no—
250C2×C4×D43—21no—
251C2×C4×D43—21no—
252C2×C4×D43—22no—
253C2×C4×D43—41no—
254C2×C4×D43—81no—
255C2×Dic86—21no—
256C2×Dic86—21no—
257C2×Dic86—81no—
258M16×C43—42no—
259C2×C8×C43—21no—
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C2×C8×C43—21no—
263C2×C8×C43—42no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—21no—
268C22⋊C4×C43—21no—
269C22⋊C4×C43—21no—
270C22⋊C4×C43—21no—
271C22⋊C4×C43—21no—
272C22⋊C4×C43—21no—
273C22⋊C4×C43—21no—
274C22⋊Dic43—21no—
275C22⋊Dic43—21no—
276C22⋊Dic43C22⋊C411yescharacteristic
277C22⋊Dic43C22⋊C411yescharacteristic
278C22⋊Dic43C22⋊C411yescharacteristic
279C22⋊Dic43C22⋊C411yescharacteristic
280C22⋊Dic43C22⋊C411yescharacteristic
281C22⋊Dic43C22⋊C411yescharacteristic
282C22⋊Dic43C22⋊C411yescharacteristic
283C22⋊Dic43C22⋊C411yescharacteristic
284(C2×D43)⋊C4—21no—
285(C2×D43)⋊C4—21no—
286(C2×D43)⋊C4—21no—
287(C2×D43)⋊C4—21no—
288(C2×D43)⋊C4—21no—
289(C2×D43)⋊C4—21no—
290(C2×D43)⋊C4—21no—
291(C2×D43)⋊C4—21no—
292(C2×D43)⋊C4—21no—
293(C2×D43)⋊C4—21no—
294(C2×D43)⋊C4—21no—
295(C2×D43)⋊C4—21no—
296(C2×D43)⋊C4—21no—
297(C2×D43)⋊C4—21no—
298(C2×D43)⋊C4—21no—
299(C2×D43)⋊C4—21no—
300C4⋊Dic43—21no—
301C4⋊Dic43—21no—
302C4⋊Dic43—21no—
303C4⋊Dic43—21no—
304C4⋊Dic43C22⋊C411yescharacteristic
305C4⋊Dic43C22⋊C411yescharacteristic
306C4⋊Dic43C22⋊C411yescharacteristic
307C4⋊Dic43C22⋊C411yescharacteristic
308C4⋊Dic43C22⋊C411yescharacteristic
309C4⋊Dic43C22⋊C411yescharacteristic
310C4⋊Dic43C22⋊C411yescharacteristic
311C4⋊Dic43C22⋊C411yescharacteristic
312Dic43⋊C4—21no—
313Dic43⋊C4—21no—
314Dic43⋊C4—21no—
315Dic43⋊C4—21no—
316C4×Dic43—21no—
317C4×Dic43—21no—
318C4×Dic43C2×D411yescharacteristic
319C4×Dic43C2×D411yescharacteristic
320C4×Dic43C2×D411yescharacteristic
321C4×Dic43C2×D411yescharacteristic
322C4×Dic43C2×D411yescharacteristic
323C4×Dic43C2×D411yescharacteristic
324C4×Dic43C2×D411yescharacteristic
325C4×Dic43C2×D411yescharacteristic
326#10621877—42no—
327C2×C43⋊C8—21no—
328C2×C43⋊C8—21no—
329C2×C43⋊C8—21no—
330C2×C43⋊C8—21no—
331C2×C43⋊C8—42no—
332C23×C43—21no—
333C23×C43—21no—
334C23×C43—22no—
335C23×C43—21no—
336C23×C43—21no—
337C23×C43—21no—
338C23×C43—41no—
339C23×C43—41no—
340C23×C43—41no—
341C23×C43C2×C22⋊C411yescharacteristic
342C23×C43C2×C22⋊C411yescharacteristic
343C23×C43C23×C411yescharacteristic
344C22×D43—21no—
345C22×D43—21no—
346C22×D43—21no—
347C22×D43—21no—
348C22×D43—21no—
349C22×D43—42no—
350C22×D43—42no—
351C22×D43—41no—
352C22×D43—41no—
353C22×D43—42no—
354C22×D43—42no—
355C22×D43—41no—
356C22×D43—41no—
357C22×D43—81no—
358C22×D43—81no—
359C22×D43—84no—
360C22×D43—84no—
361C22×D43#13112yes—
362D4×C43—42no—
363D4×C43—42no—
364C2×C4×C43—22no—
365C2×C4×C43—22no—
366C2×C4×C43—21no—
367C2×C4×C43—21no—
368C2×C4×C43—21no—
369C2×C4×C43—21no—
370C2×C4×C43—21no—
371C2×C4×C43—41no—
372C2×C4×C43—41no—
373C2×C4×C43—41no—
374C2×C4×C43—41no—
375C2×C4×C43—41no—
376C2×C4×C43—41no—
377C2×C4×C43C2×C22⋊C411yescharacteristic
378C2×C4×C43C2×C22⋊C411yescharacteristic
379C2×C4×C43C22×D411yescharacteristic
380C2×C4×C43C22×D411yescharacteristic
381C22⋊D43—42no—
382C22⋊D43—42no—
383C22⋊D43—81no—
384C22⋊D43—81no—
385C2×Dic43—21no—
386C2×Dic43—21no—
387C2×Dic43—21no—
388C2×Dic43—21no—
389C2×Dic43—21no—
390C2×Dic43—21no—
391C2×Dic43—41no—
392C2×Dic43—41no—
393C2×Dic43—41no—
394C2×Dic43—41no—
395C2×Dic43—81no—
396C2×Dic43—81no—
397C2×Dic43—81no—
398C2×Dic43—81no—
399C2×Dic43C2×C22⋊C411yescharacteristic
400C2×Dic43C2×C22⋊C411yescharacteristic
401C2×Dic43C2×C22⋊C411yescharacteristic
402C2×Dic43C2×C22⋊C411yescharacteristic
403C2×Dic43C2×C22⋊C411yescharacteristic
404C2×Dic43C2×C22⋊C411yescharacteristic
405C2×Dic43C2×C22⋊C411yescharacteristic
406C2×Dic43C2×C22⋊C411yescharacteristic
407C4×D43—42no—
408C4×D43—42no—
409C4×D43—81no—
410C4×D43—81no—
411Dic86—81no—
412Dic86—81no—
413C8×C43—41no—
414C8×C43—41no—
415C8×C43—41no—
416C8×C43—41no—
417C43⋊C8—41no—
418C43⋊C8—41no—
419C43⋊C8—41no—
420C43⋊C8—41no—
421#17412—431nomaximal, Sylow
422C22×C43—21no—
423C22×C43—21no—
424C22×C43—21no—
425C22×C43—21no—
426C22×C43—21no—
427C22×C43—21no—
428C22×C43—21no—
429C22×C43—42no—
430C22×C43—42no—
431C22×C43—41no—
432C22×C43—41no—
433C22×C43—41no—
434C22×C43—81no—
435C22×C43—81no—
436C22×C43#41012yes—
437C22×C43C22×C22⋊C411yescharacteristic
438C22×C43C2×#13111yescharacteristic
439C22×C43#56811yescharacteristic
440C2×D43—22no—
441C2×D43—42no—
442C2×D43—41no—
443C2×D43—41no—
444C2×D43—42no—
445C2×D43—41no—
446C2×D43—41no—
447C2×D43—41no—
448C2×D43—84no—
449C2×D43—84no—
450C2×D43—81no—
451C2×D43—81no—
452C4×C43—21no—
453C4×C43—21no—
454C4×C43—21no—
455C4×C43—21no—
456C4×C43—41no—
457C4×C43—41no—
458C4×C43—41no—
459Dic43—21no—
460Dic43—21no—
461Dic43—21no—
462Dic43—21no—
463Dic43—21no—
464Dic43—21no—
465Dic43—21no—
466Dic43—21no—
467Dic43—41no—
468Dic43—41no—
469C2×#551—431no—
470#2924—431no—
471#2924—431no—
472#1473—431no—
473#1473—431no—
474#1469—431no—
475#1469—431no—
476#1468—431no—
477#1468D4311yescharacteristic, complemented
478#1466—431no—
479#1464—431no—
480#1462—431no—
481#1460—431no—
482#1458—431no—
483C2×#323—431no—
484C2×C43—21no—
485C2×C43—21no—
486C2×C43—22no—
487C2×C43—41no—
488C2×C43—81no—
489C2×C43#288011yescharacteristic
490C2×C43C2×#41011yescharacteristic
491C2×C43#288811yescharacteristic
492D43—42no—
493D43—81no—
494#551—861no—
495#551—861no—
496#551—861no—
497#551—861no—
498#551—861no—
499#551—861no—
500#551—861no—
501#551—861no—
502C2×#126—431no—
503C2×#126—431no—
504C2×#124—431no—
505C2×#123—431no—
506C2×#123—431no—
507C2×#123C2×D4311yescharacteristic
508C2×C22⋊Q8—431no—
509C2×C22⋊Q8—431no—
510C2×#120—431no—
511C2×C4×D4—431no—
512C2×C4×D4—431no—
513C2×#117—431no—
514C2×#117—431no—
515C22×C22⋊C4—431no—
516C22×C22⋊C4—431no—
517#433—861no—
518#433—861no—
519#433—861no—
520#433—861no—
521#432—431no—
522#432—431no—
523#432—431no—
524#432—431no—
525#431—431no—
526#431—431no—
527#431—431no—
528#431—431no—
529#424—861no—
530#424—861no—
531#407—431no—
532#407C2×D4311yescharacteristic
533C2×C22⋊C8—431no—
534C2×C22⋊C8C2×D4311yescharacteristic
535#405—861no—
536#405—861no—
537#324—431no—
538#324—431no—
539#324C2×D4311yescharacteristic, complemented
540#324C2×D4311yescharacteristic, complemented
541#323—431no—
542#323—431no—
543#323—431no—
544#323—431no—
545#323—431no—
546#323—431no—
547#323—431no—
548#323—431no—
549#323—431no—
550#323—431no—
551#323C2×D4311yescharacteristic, complemented
552#323C2×D4311yescharacteristic, complemented
553C43#1741211yescharacteristic, complemented, Sylow
554C25—431no—
555C22×Q8—431no—
556C22×D4—431no—
557C22×D4—431no—
558C22×D4C4×D4311yescharacteristic
559C23×C4—431no—
560C23×C4—431no—
561C23×C4—431no—
562C23×C4—431no—
563C23×C4C22×D4311yescharacteristic
564C2×M16—21no—
565C2×M16—861no—
566C22×C8—21no—
567C22×C8—861no—
568#126—861no—
569#126—861no—
570#126—861no—
571#126—861no—
572#126—861no—
573#126—861no—
574#126—861no—
575#126—861no—
576#124—861no—
577#124—861no—
578#124—861no—
579#124—861no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—861no—
585#123—861no—
586#123—861no—
587#123—861no—
588#123—861no—
589#123—861no—
590#123—861no—
591#123—861no—
592C22⋊Q8—861no—
593C22⋊Q8—861no—
594C22⋊Q8—861no—
595C22⋊Q8—861no—
596C22⋊Q8—861no—
597C22⋊Q8—861no—
598C22⋊Q8—861no—
599C22⋊Q8—861no—
600#120—861no—
601#120—861no—
602#120—861no—
603#120—861no—
604C4×D4—861no—
605C4×D4—861no—
606C4×D4—861no—
607C4×D4—861no—
608C4×D4—861no—
609C4×D4—861no—
610C4×D4—861no—
611C4×D4—861no—
612#117—431no—
613#117—431no—
614#117—431no—
615#117—431no—
616#117—431no—
617#117—431no—
618#117—431no—
619#117—431no—
620#117—861no—
621#117—861no—
622#117—861no—
623#117—861no—
624C2×C4⋊C4—431no—
625C2×C4⋊C4—431no—
626C2×C4⋊C4—431no—
627C2×C4⋊C4—431no—
628C2×C4⋊C4—431no—
629C2×C4⋊C4—431no—
630C2×C4⋊C4C4×D4311yescharacteristic
631C2×C4⋊C4C22×D4311yescharacteristic
632C2×C22⋊C4—431no—
633C2×C22⋊C4—431no—
634C2×C22⋊C4—431no—
635C2×C22⋊C4—431no—
636C2×C22⋊C4—431no—
637C2×C22⋊C4—431no—
638C2×C22⋊C4—431no—
639C2×C22⋊C4—431no—
640C2×C22⋊C4—431no—
641C2×C22⋊C4—431no—
642C2×C22⋊C4—431no—
643C2×C22⋊C4—861no—
644C2×C22⋊C4—861no—
645C2×C22⋊C4—861no—
646C2×C22⋊C4—861no—
647C2×C22⋊C4—861no—
648C2×C22⋊C4—861no—
649C2×C22⋊C4—861no—
650C2×C22⋊C4—861no—
651C2×C22⋊C4C4×D4311yescharacteristic
652C2×C22⋊C4C4×D4311yescharacteristic
653C2×C22⋊C4C22×D4311yescharacteristic
654C2×C42—431no—
655C2×C42—431no—
656C2×C42—431no—
657C4⋊C8—861no—
658C4⋊C8—861no—
659C4⋊C8—861no—
660C4⋊C8—861no—
661C4⋊C8—861no—
662C4⋊C8—861no—
663C4⋊C8—861no—
664C4⋊C8—861no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8—431no—
668C22⋊C8—431no—
669C22⋊C8—431no—
670C22⋊C8—431no—
671C22⋊C8—861no—
672C22⋊C8—861no—
673C22⋊C8C22×D4311yescharacteristic
674C22⋊C8C22×D4311yescharacteristic
675C22⋊C8C22×D4311yescharacteristic
676C22⋊C8C22×D4311yescharacteristic
677#97—861no—
678#97—861no—
679#97—861no—
680#97—861no—
681C4×C8—861no—
682C4×C8—861no—
683C4×C8—861no—
684C4×C8—861no—
685C24—431no—
686C24—431no—
687C24—862no—
688C24—861no—
689C24—861no—
690C24—3441no—
691C24—1721no—
692C24—1722no—
693C24C2×C4×D4311yescharacteristic
694C24C2×C4×D4311yescharacteristic
695C2×Q8—861no—
696C2×Q8—861no—
697C2×Q8—3441no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—42no—
701C2×D4—861no—
702C2×D4—861no—
703C2×D4—861no—
704C2×D4—861no—
705C2×D4—862no—
706C2×D4—3441no—
707C2×D4—1721no—
708C22×C4—42no—
709C22×C4—431no—
710C22×C4—431no—
711C22×C4—431no—
712C22×C4—431no—
713C22×C4—431no—
714C22×C4—431no—
715C22×C4—861no—
716C22×C4—861no—
717C22×C4—861no—
718C22×C4—861no—
719C22×C4—862no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—3441no—
725C22×C4—3441no—
726C22×C4—3441no—
727C22×C4—1721no—
728C22×C4C2×C4×D4311yescharacteristic
729C22×C4C2×C4×D4311yescharacteristic
730C22×C4C2×C4×D4311yescharacteristic
731C22×C4C2×C4×D4311yescharacteristic
732C22×C4D4×D4311yescharacteristic
733C22×C4D4×D4311yescharacteristic
734C22×C4D4×D4311yescharacteristic
735C22×C4D4×D4311yescharacteristic
736C22×C4C23×D4311yescharacteristic
737M16—42no—
738M16—1722no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—42no—
744C2×C8—861no—
745C2×C8—861no—
746C2×C8—861no—
747C2×C8—861no—
748C2×C8—1722no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—431no—
754C4⋊C4—431no—
755C4⋊C4—431no—
756C4⋊C4—431no—
757C4⋊C4—431no—
758C4⋊C4—431no—
759C4⋊C4—431no—
760C4⋊C4—431no—
761C4⋊C4—861no—
762C4⋊C4—861no—
763C4⋊C4—861no—
764C4⋊C4—861no—
765C4⋊C4—861no—
766C4⋊C4—861no—
767C4⋊C4—861no—
768C4⋊C4—861no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—431no—
776C22⋊C4—431no—
777C22⋊C4—431no—
778C22⋊C4—431no—
779C22⋊C4—431no—
780C22⋊C4—431no—
781C22⋊C4—431no—
782C22⋊C4—431no—
783C22⋊C4—861no—
784C22⋊C4—861no—
785C22⋊C4—861no—
786C22⋊C4—861no—
787C22⋊C4—861no—
788C22⋊C4—861no—
789C22⋊C4—861no—
790C22⋊C4—861no—
791C22⋊C4—861no—
792C22⋊C4—861no—
793C22⋊C4—861no—
794C22⋊C4—861no—
795C22⋊C4—861no—
796C22⋊C4—861no—
797C22⋊C4—861no—
798C22⋊C4—861no—
799C22⋊C4—861no—
800C22⋊C4—861no—
801C42—431no—
802C42—431no—
803C42—431no—
804C42—431no—
805C42—431no—
806C42—431no—
807C42—431no—
808C42—431no—
809C42—861no—
810C42—861no—
811C23—22no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—432no—
821C23—861no—
822C23—861no—
823C23—861no—
824C23—861no—
825C23—861no—
826C23—3441no—
827C23—3441no—
828C23—3444no—
829C23—3444no—
830C23—1722no—
831C23—1722no—
832C23—1721no—
833C23—1721no—
834C23—1722no—
835C23—1721no—
836C23—1721no—
837C23—1722no—
838C23C22⋊C4×D4311yescharacteristic
839C23C22⋊C4×D4311yescharacteristic
840C23C22×C4×D4311yescharacteristic
841Q8—3441no—
842Q8—3441no—
843D4—42no—
844D4—42no—
845D4—3441no—
846D4—3441no—
847D4—1722no—
848D4—1722no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—431no—
863C2×C4—431no—
864C2×C4—431no—
865C2×C4—431no—
866C2×C4—431no—
867C2×C4—431no—
868C2×C4—431no—
869C2×C4—431no—
870C2×C4—861no—
871C2×C4—861no—
872C2×C4—861no—
873C2×C4—861no—
874C2×C4—861no—
875C2×C4—861no—
876C2×C4—3441no—
877C2×C4—3441no—
878C2×C4—3441no—
879C2×C4—3441no—
880C2×C4—3441no—
881C2×C4—3441no—
882C2×C4—1722no—
883C2×C4—1722no—
884C2×C4—1721no—
885C2×C4—1721no—
886C2×C4—1721no—
887C2×C4—1721no—
888C2×C4C22⋊C4×D4311yescharacteristic
889C2×C4C22⋊C4×D4311yescharacteristic
890C2×C4C2×D4×D4311yescharacteristic
891C2×C4C2×D4×D4311yescharacteristic
892C8—41no—
893C8—41no—
894C8—41no—
895C8—41no—
896C8—1721no—
897C8—1721no—
898C8—1721no—
899C8—1721no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—42no—
908C22—42no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—81no—
913C22—81no—
914C22—862no—
915C22—3441no—
916C22—3441no—
917C22—3444no—
918C22—3444no—
919C22—1722no—
920C22—1722no—
921C22—1721no—
922C22—1721no—
923C22—1721no—
924C22—1721no—
925C22—1721no—
926C22#1458287112yes—
927C22C2×C22⋊C4×D4311yescharacteristic
928C22#131×D4311yescharacteristic
929C22#1458366411yescharacteristic
930C4—21no—
931C4—21no—
932C4—21no—
933C4—21no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—861no—
938C4—861no—
939C4—861no—
940C4—861no—
941C4—861no—
942C4—861no—
943C4—861no—
944C4—861no—
945C4—1721no—
946C4—1721no—
947C2—21no—
948C2—21no—
949C2—22no—
950C2—41no—
951C2—81no—
952C2—3441no—
953C2—1722no—
954C2#1914304311yescharacteristic
955C2C2×#1458287111yescharacteristic
956C2#1914307211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1468C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063293C4
cosocleC22×C4×C43C24
hypercenter#1468D43
hypocenterC43#17412
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1468

Complements

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

NH ≅ G/Ntype
2. #19143255C2semidirect
3. #19143249C2semidirect
4. #19132963C2semidirect
5. #19132963C2semidirect
6. #19132945C2semidirect
7. #19132945C2semidirect
8. #19132943C2semidirect
9. #19132934C2semidirect
10. #19132928C2semidirect
11. #19132921C2semidirect
12. #19132914C2semidirect
13. #19132908C2semidirect
14. C2×#14582622C2semidirect
15. C43×#1468C2semidirect
42. #14582953C22semidirect
43. #14582953C22semidirect
44. #14582953C22semidirect
45. #14582953C22semidirect
46. #14582949C22semidirect
47. #14582949C22semidirect
48. #14582949C22semidirect
49. #14582949C22semidirect
56. #14582625C22semidirect
57. #14582625C22semidirect
58. #14582623C22semidirect
59. #14582623C22semidirect
71. C43×#324C22semidirect
72. C43×#324C22semidirect
73. C43×#323C22semidirect
74. C43×#323C22semidirect
477. #1468D43semidirect
539. #324C2×D43semidirect
540. #324C2×D43semidirect
551. #323C2×D43semidirect
552. #323C2×D43semidirect
553. C43#17412semidirect

Maximal subgroups

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

subgroupindex
C2×#145835722
#191432552
#191432492
#191329632
#191329452
#191329432
#191329342
#191329282
#191329212
#191329142
#191329082
C2×#145826222
C43×#14682
#1741243