Finite Group Databasebeta

← #25062791

Subgroups — #25062791

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×#14583574C211yesmaximal, characteristic
2#19143254C211yesmaximal, characteristic, complemented
3#19143248C211yesmaximal, characteristic, complemented
4#19132964C211yesmaximal, characteristic, complemented
5#19132945C211yesmaximal, characteristic, complemented
6#19132945C211yesmaximal, characteristic, complemented
7#19132942C211yesmaximal, characteristic, complemented
8#19132942C211yesmaximal, characteristic, complemented
9#19132935C211yesmaximal, characteristic, complemented
10#19132928C211yesmaximal, characteristic, complemented
11#19132920C211yesmaximal, characteristic, complemented
12#19132915C211yesmaximal, characteristic, complemented
13#19132908C211yesmaximal, characteristic, complemented
14#323×D43C211yesmaximal, characteristic, complemented
15C43×#1473C211yesmaximal, characteristic, complemented
16#14583574—21no—
17#14583574—21no—
18#14583574—21no—
19#14583574—21no—
20#14583574—21no—
21#14583574—21no—
22#14583574—21no—
23#14583574—21no—
24C2×#13063318C411yescharacteristic
25C2×#13063311C2211yescharacteristic
26C2×#13063310C411yescharacteristic
27C2×#13063310C2211yescharacteristic
28C2×#13063307C411yescharacteristic
29C2×#13063305C411yescharacteristic
30C2×#13063303C411yescharacteristic
31C2×#13063295C411yescharacteristic
32C2×C4×D172C2211yescharacteristic
33C2×#13063287C411yescharacteristic
34C2×#13063283C2211yescharacteristic
35C2×#13063282C2211yescharacteristic
36C2×C22⋊C4×D43C411yescharacteristic
37C2×C22⋊C4×D43C2211yescharacteristic
38#14582961—21no—
39#14582959—21no—
40#14582959—21no—
41#14582958—21no—
42#14582956C2211yescharacteristic, complemented
43#14582953C2211yescharacteristic, complemented
44#14582953C2211yescharacteristic, complemented
45#14582952C2211yescharacteristic, complemented
46#14582949C2211yescharacteristic, complemented
47#14582949C2211yescharacteristic, complemented
48#14582924—21no—
49#14582924—21no—
50#14582861C2211yescharacteristic
51#14582861C2211yescharacteristic
52C22⋊C8×D43C2211yescharacteristic
53C22⋊C8×D43C2211yescharacteristic
54#14582856—21no—
55#14582853—21no—
56#14582625C2211yescharacteristic, complemented
57#14582625C2211yescharacteristic, complemented
58#14582623C2211yescharacteristic
59#14582623C2211yescharacteristic
60#14582622C2211yescharacteristic
61#14582622C2211yescharacteristic
62#14582622C2211yescharacteristic
63#14582622C2211yescharacteristic
64#14582622C2211yescharacteristic, complemented
65#14582622C2211yescharacteristic, complemented
66#14582622C2211yescharacteristic, complemented
67#14582622C2211yescharacteristic, complemented
68C2×#126×C43C2211yescharacteristic
69C43×#432C2211yescharacteristic, complemented
70C43×#431C2211yescharacteristic, complemented
71C43×#324C2211yescharacteristic, complemented
72C43×#324C2211yescharacteristic, complemented
73C43×#323C2211yescharacteristic
74C43×#323C2211yescharacteristic
75C24×D43C2×C411yescharacteristic
76C22×Dic86C2×C411yescharacteristic
77C22×D172C2×C411yescharacteristic
78C22×D172C2×C411yescharacteristic
79C22×C22⋊D43C2×C411yescharacteristic
80C22×C4×D43C2×C411yescharacteristic
81C22×C4×D43C2×C411yescharacteristic
82C22×C4×D43C2×C411yescharacteristic
83C22×C4×D43C2×C411yescharacteristic
84C22×C4×D43C2311yescharacteristic
85C2×#10621872—21no—
86C2×#10621872—21no—
87C2×C8×D43—21no—
88C2×C8×D43—21no—
89#13063318—21no—
90#13063318—21no—
91#13063318—21no—
92#13063318—21no—
93#13063311—21no—
94#13063311—21no—
95#13063311—21no—
96#13063311—21no—
97#13063310—21no—
98#13063310—21no—
99#13063310—21no—
100#13063310—21no—
101#13063310—21no—
102#13063310—21no—
103#13063310—21no—
104#13063310—21no—
105#13063307—21no—
106#13063307—21no—
107#13063307—21no—
108#13063307—21no—
109#13063305—21no—
110#13063305—21no—
111#13063305—21no—
112#13063305—21no—
113#13063303—21no—
114#13063303—21no—
115#13063303—21no—
116#13063303—21no—
117#13063295—21no—
118#13063295—21no—
119#13063295—21no—
120#13063295—21no—
121C4×D172—21no—
122C4×D172—21no—
123C4×D172—21no—
124C4×D172—21no—
125#13063287—21no—
126#13063287—21no—
127#13063287—21no—
128#13063287—21no—
129#13063283—21no—
130#13063283—21no—
131#13063283—21no—
132#13063283—21no—
133#13063282D411yescharacteristic
134#13063282D411yescharacteristic
135#13063282D411yescharacteristic
136#13063282D411yescharacteristic
137#13063282D411yescharacteristic
138#13063282D411yescharacteristic
139#13063282D411yescharacteristic
140#13063282D411yescharacteristic
141C2×C4⋊Dic43C2×C411yescharacteristic
142C2×C4⋊Dic43C2×C411yescharacteristic
143C2×Dic43⋊C4C2×C411yescharacteristic
144C2×Dic43⋊C4C2×C411yescharacteristic
145C2×Dic43⋊C4C2×C411yescharacteristic
146C2×C22⋊Dic43C2×C411yescharacteristic
147C2×C22⋊Dic43C2×C411yescharacteristic
148C2×(C2×D43)⋊C4C2×C411yescharacteristic
149C2×(C2×D43)⋊C4C2×C411yescharacteristic
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)⋊C4C2311yescharacteristic
156C2×(C2×D43)⋊C4C2311yescharacteristic
157C22⋊C4×D43—21no—
158C22⋊C4×D43—21no—
159C22⋊C4×D43—21no—
160C22⋊C4×D43—21no—
161C22⋊C4×D43—21no—
162C22⋊C4×D43—21no—
163C22⋊C4×D43—21no—
164C22⋊C4×D43—21no—
165C2×C4×Dic43C2×C411yescharacteristic
166C2×C4×Dic43C2311yescharacteristic
167C4⋊(C43⋊C8)—21no—
168C4⋊(C43⋊C8)—21no—
169Dic43⋊C8—21no—
170Dic43⋊C8—21no—
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173C22⋊(C43⋊C8)C2311yescharacteristic
174C22⋊(C43⋊C8)C2311yescharacteristic
175C22⋊(C43⋊C8)C2311yescharacteristic
176C22⋊(C43⋊C8)C2311yescharacteristic
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181#13063236—21no—
182#13063235—21no—
183#13063235—21no—
184C4×C43⋊C8—21no—
185C8×Dic43—21no—
186C8×Dic43—21no—
187#126×C43—21no—
188#126×C43—21no—
189#126×C43—21no—
190#126×C43—21no—
191C2×C4⋊C4×C43C2×C411yescharacteristic
192C2×C4⋊C4×C43C2×C411yescharacteristic
193C2×C4⋊C4×C43C2311yescharacteristic
194C2×C22⋊C4×C43C2×C411yescharacteristic
195C2×C22⋊C4×C43C2×C411yescharacteristic
196C2×C22⋊C4×C43C2311yescharacteristic
197C2×C42×C43C2311yescharacteristic
198C4⋊C8×C43—21no—
199C4⋊C8×C43—21no—
200C22⋊C8×C43C2311yescharacteristic
201C22⋊C8×C43C2311yescharacteristic
202C22⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43C2311yescharacteristic
204#97×C43—21no—
205C4×C8×C43—21no—
206C24×C43C22×C411yescharacteristic
207C23×D43—21no—
208C23×D43—21no—
209C23×D43—22no—
210C23×D43—41no—
211C23×D43—42no—
212C23×D43—81no—
213C23×D43C22×C411yescharacteristic
214C23×D43C22×C411yescharacteristic
215C23×D43C22×C411yescharacteristic
216C22×C4×C43C22×C411yescharacteristic
217C22×C4×C43C22×C411yescharacteristic
218C22×C4×C43C22×C411yescharacteristic
219C22×C4×C43C22×C411yescharacteristic
220C22×C4×C43C22×C411yescharacteristic
221C22×C4×C43C2411yescharacteristic
222C2×C22⋊D43—21no—
223C2×C22⋊D43—21no—
224C2×C22⋊D43—81no—
225C22×Dic43C22×C411yescharacteristic
226C22×Dic43C22×C411yescharacteristic
227C22×Dic43C22×C411yescharacteristic
228C22×Dic43C22×C411yescharacteristic
229C22×Dic43C22×C411yescharacteristic
230C2×D172—21no—
231C2×D172—21no—
232C2×D172—21no—
233C2×D172—21no—
234C2×D172—22no—
235C2×D172—41no—
236C2×D172—42no—
237C2×C4×D43—21no—
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43—21no—
241C2×C4×D43—21no—
242C2×C4×D43—21no—
243C2×C4×D43—21no—
244C2×C4×D43—21no—
245C2×C4×D43—22no—
246C2×C4×D43—42no—
247C2×C4×D43—41no—
248C2×C4×D43—81no—
249C2×C4×D43—81no—
250C2×C4×D43—81no—
251C2×C4×D43C2×D411yescharacteristic
252C2×C4×D43C2×D411yescharacteristic
253C2×C4×D43C2×D411yescharacteristic
254C2×C4×D43C2×D411yescharacteristic
255C2×Dic86—21no—
256C2×Dic86—21no—
257C2×Dic86—81no—
258C2×C8×C43—21no—
259C2×C8×C43—21no—
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43—21no—
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—
274C42×C43C2×D411yescharacteristic
275C42×C43C2×D411yescharacteristic
276C42×C43C2×D411yescharacteristic
277C42×C43C2×D411yescharacteristic
278C22⋊Dic43—21no—
279C22⋊Dic43—21no—
280C22⋊Dic43—21no—
281C22⋊Dic43—21no—
282(C2×D43)⋊C4—21no—
283(C2×D43)⋊C4—21no—
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)⋊C4C22⋊C411yescharacteristic
297(C2×D43)⋊C4C22⋊C411yescharacteristic
298(C2×D43)⋊C4C22⋊C411yescharacteristic
299(C2×D43)⋊C4C22⋊C411yescharacteristic
300(C2×D43)⋊C4C22⋊C411yescharacteristic
301(C2×D43)⋊C4C22⋊C411yescharacteristic
302(C2×D43)⋊C4C22⋊C411yescharacteristic
303(C2×D43)⋊C4C22⋊C411yescharacteristic
304C4⋊Dic43—21no—
305C4⋊Dic43—21no—
306C4⋊Dic43—21no—
307C4⋊Dic43—21no—
308Dic43⋊C4—21no—
309Dic43⋊C4—21no—
310Dic43⋊C4C22⋊C411yescharacteristic
311Dic43⋊C4C22⋊C411yescharacteristic
312Dic43⋊C4C22⋊C411yescharacteristic
313Dic43⋊C4C22⋊C411yescharacteristic
314Dic43⋊C4C22⋊C411yescharacteristic
315Dic43⋊C4C22⋊C411yescharacteristic
316Dic43⋊C4C22⋊C411yescharacteristic
317Dic43⋊C4C22⋊C411yescharacteristic
318C4×Dic43—21no—
319C4×Dic43—21no—
320C4×Dic43C2×D411yescharacteristic
321C4×Dic43C2×D411yescharacteristic
322C4×Dic43C2×D411yescharacteristic
323C4×Dic43C2×D411yescharacteristic
324C2×C43⋊C8—21no—
325C2×C43⋊C8—21no—
326C2×C43⋊C8—21no—
327C2×C43⋊C8—21no—
328#10621872—42no—
329#10621872—42no—
330C8×D43—42no—
331C8×D43—42no—
332C23×C43—21no—
333C23×C43—21no—
334C23×C43—21no—
335C23×C43—41no—
336C23×C43—41no—
337C23×C43C23×C411yescharacteristic
338C22×D43—21no—
339C22×D43—21no—
340C22×D43—21no—
341C22×D43—21no—
342C22×D43—22no—
343C22×D43—21no—
344C22×D43—21no—
345C22×D43—21no—
346C22×D43—41no—
347C22×D43—42no—
348C22×D43—42no—
349C22×D43—42no—
350C22×D43—41no—
351C22×D43—41no—
352C22×D43—42no—
353C22×D43—41no—
354C22×D43—41no—
355C22×D43—81no—
356C22×D43—81no—
357C22×D43—84no—
358C22×D43—84no—
359C22×D43C2×C22⋊C411yescharacteristic
360C22×D43C2×C22⋊C411yescharacteristic
361C22×D43#13112yes—
362C2×C4×C43—21no—
363C2×C4×C43—21no—
364C2×C4×C43—21no—
365C2×C4×C43—21no—
366C2×C4×C43—21no—
367C2×C4×C43—21no—
368C2×C4×C43—21no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—41no—
372C2×C4×C43—41no—
373C2×C4×C43C2×C22⋊C411yescharacteristic
374C2×C4×C43C2×C22⋊C411yescharacteristic
375C2×C4×C43C2×C22⋊C411yescharacteristic
376C2×C4×C43C2×C22⋊C411yescharacteristic
377C2×C4×C43C22×D411yescharacteristic
378C2×C4×C43C22×D411yescharacteristic
379C22⋊D43—81no—
380C22⋊D43—81no—
381C2×Dic43—21no—
382C2×Dic43—21no—
383C2×Dic43—21no—
384C2×Dic43—21no—
385C2×Dic43—41no—
386C2×Dic43—41no—
387C2×Dic43—41no—
388C2×Dic43—41no—
389C2×Dic43C2×C22⋊C411yescharacteristic
390C2×Dic43C2×C22⋊C411yescharacteristic
391C2×Dic43C2×C22⋊C411yescharacteristic
392C2×Dic43C2×C22⋊C411yescharacteristic
393C2×Dic43C2×C22⋊C411yescharacteristic
394C2×Dic43C2×C22⋊C411yescharacteristic
395D172—42no—
396D172—42no—
397D172—42no—
398D172—42no—
399C4×D43—22no—
400C4×D43—22no—
401C4×D43—41no—
402C4×D43—41no—
403C4×D43—42no—
404C4×D43—42no—
405C4×D43—81no—
406C4×D43—81no—
407C4×D43—81no—
408C4×D43—81no—
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—41no—
425C22×C43—41no—
426C22×C43—41no—
427C22×C43—81no—
428C22×C43—81no—
429C22×C43C22×C22⋊C411yescharacteristic
430C22×C43C2×#13111yescharacteristic
431C22×C43#56811yescharacteristic
432C2×D43—21no—
433C2×D43—21no—
434C2×D43—21no—
435C2×D43—22no—
436C2×D43—21no—
437C2×D43—21no—
438C2×D43—42no—
439C2×D43—42no—
440C2×D43—42no—
441C2×D43—41no—
442C2×D43—41no—
443C2×D43—42no—
444C2×D43—41no—
445C2×D43—41no—
446C2×D43—41no—
447C2×D43—84no—
448C2×D43—84no—
449C2×D43—81no—
450C2×D43—81no—
451C2×D43#41012yes—
452C4×C43—21no—
453C4×C43—21no—
454C4×C43—21no—
455C4×C43—21no—
456C4×C43—21no—
457C4×C43—21no—
458C4×C43—41no—
459C4×C43—41no—
460C4×C43—41no—
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#1473D4311yescharacteristic, complemented
474#1469—431no—
475#1469—431no—
476#1468—431no—
477#1468—431no—
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—81no—
487C2×C43#288011yescharacteristic
488C2×C43C2×#41011yescharacteristic
489C2×C43#288811yescharacteristic
490D43—22no—
491D43—41no—
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×#126C2×D4311yescharacteristic
504C2×#124—431no—
505C2×#123—431no—
506C2×#123—431no—
507C2×#123—431no—
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#432C2×D4311yescharacteristic, complemented
525#431—431no—
526#431—431no—
527#431—431no—
528#431C2×D4311yescharacteristic, complemented
529#424—861no—
530#424—861no—
531#407—431no—
532#407—431no—
533C2×C22⋊C8—431no—
534C2×C22⋊C8—431no—
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
552#323C2×D4311yescharacteristic
553C43#1741211yescharacteristic, complemented, Sylow
554C25—431no—
555C22×Q8—431no—
556C22×D4—431no—
557C22×D4—431no—
558C22×D4—431no—
559C23×C4—431no—
560C23×C4—431no—
561C23×C4—431no—
562C23×C4—431no—
563C23×C4—431no—
564C2×M16—861no—
565C2×M16—861no—
566C22×C8—861no—
567C22×C8—861no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
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—861no—
581#123—861no—
582#123—861no—
583#123—861no—
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⋊C4C4×D4311yescharacteristic
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×C42C22×D4311yescharacteristic
657C4⋊C8—21no—
658C4⋊C8—21no—
659C4⋊C8—861no—
660C4⋊C8—861no—
661C4⋊C8—861no—
662C4⋊C8—861no—
663C4⋊C8—861no—
664C4⋊C8—861no—
665C22⋊C8—431no—
666C22⋊C8—431no—
667C22⋊C8—431no—
668C22⋊C8—431no—
669C22⋊C8—861no—
670C22⋊C8—861no—
671C22⋊C8—861no—
672C22⋊C8—861no—
673C22⋊C8C22×D4311yescharacteristic
674C22⋊C8C22×D4311yescharacteristic
675C22⋊C8C22×D4311yescharacteristic
676C22⋊C8C22×D4311yescharacteristic
677#97—21no—
678#97—861no—
679#97—861no—
680#97—861no—
681C4×C8—21no—
682C4×C8—861no—
683C4×C8—861no—
684C4×C8—861no—
685C24—431no—
686C24—431no—
687C24—431no—
688C24—862no—
689C24—861no—
690C24—861no—
691C24—3441no—
692C24—1721no—
693C24—1722no—
694C24C2×C4×D4311yescharacteristic
695C2×Q8—861no—
696C2×Q8—861no—
697C2×Q8—3441no—
698C2×D4—861no—
699C2×D4—861no—
700C2×D4—862no—
701C2×D4—861no—
702C2×D4—861no—
703C2×D4—861no—
704C2×D4—861no—
705C2×D4—3441no—
706C2×D4—1721no—
707C2×D4—1722no—
708C22×C4—431no—
709C22×C4—431no—
710C22×C4—431no—
711C22×C4—431no—
712C22×C4—431no—
713C22×C4—431no—
714C22×C4—431no—
715C22×C4—431no—
716C22×C4—431no—
717C22×C4—861no—
718C22×C4—861no—
719C22×C4—861no—
720C22×C4—861no—
721C22×C4—862no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—861no—
726C22×C4—3441no—
727C22×C4—3441no—
728C22×C4—3441no—
729C22×C4—1721no—
730C22×C4—1722no—
731C22×C4C2×C4×D4311yescharacteristic
732C22×C4C2×C4×D4311yescharacteristic
733C22×C4C2×C4×D4311yescharacteristic
734C22×C4C2×C4×D4311yescharacteristic
735C22×C4C2×C4×D4311yescharacteristic
736C22×C4C23×D4311yescharacteristic
737M16—1722no—
738M16—1722no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—861no—
744C2×C8—861no—
745C2×C8—861no—
746C2×C8—861no—
747C2×C8—1722no—
748C2×C8—1722no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—431no—
756C4⋊C4—431no—
757C4⋊C4—431no—
758C4⋊C4—431no—
759C4⋊C4—431no—
760C4⋊C4—431no—
761C4⋊C4—431no—
762C4⋊C4—431no—
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—861no—
806C42—861no—
807C42D4×D4311yescharacteristic
808C42D4×D4311yescharacteristic
809C42D4×D4311yescharacteristic
810C42D4×D4311yescharacteristic
811C23—21no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—431no—
817C23—431no—
818C23—432no—
819C23—862no—
820C23—861no—
821C23—861no—
822C23—861no—
823C23—861no—
824C23—861no—
825C23—861no—
826C23—861no—
827C23—3441no—
828C23—3441no—
829C23—3444no—
830C23—3444no—
831C23—1721no—
832C23—1721no—
833C23—1721no—
834C23—1721no—
835C23—1721no—
836C23—1722no—
837C23—1722no—
838C23—1722no—
839C23—1722no—
840C23C22×C4×D4311yescharacteristic
841Q8—3441no—
842Q8—3441no—
843D4—3441no—
844D4—3441no—
845D4—1722no—
846D4—1722no—
847D4—1722no—
848D4—1722no—
849C2×C4—21no—
850C2×C4—21no—
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—431no—
861C2×C4—431no—
862C2×C4—431no—
863C2×C4—431no—
864C2×C4—431no—
865C2×C4—431no—
866C2×C4—862no—
867C2×C4—862no—
868C2×C4—861no—
869C2×C4—861no—
870C2×C4—861no—
871C2×C4—861no—
872C2×C4—3441no—
873C2×C4—3441no—
874C2×C4—3441no—
875C2×C4—3441no—
876C2×C4—3441no—
877C2×C4—3441no—
878C2×C4—1721no—
879C2×C4—1721no—
880C2×C4—1722no—
881C2×C4—1722no—
882C2×C4—1721no—
883C2×C4—1721no—
884C2×C4—1721no—
885C2×C4—1721no—
886C2×C4C22⋊C4×D4311yescharacteristic
887C2×C4C22⋊C4×D4311yescharacteristic
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—41no—
903C22—41no—
904C22—41no—
905C22—81no—
906C22—81no—
907C22—432no—
908C22—861no—
909C22—861no—
910C22—862no—
911C22—861no—
912C22—861no—
913C22—861no—
914C22—3441no—
915C22—3441no—
916C22—3444no—
917C22—3444no—
918C22—1722no—
919C22—1722no—
920C22—1722no—
921C22—1722no—
922C22—1721no—
923C22—1721no—
924C22—1721no—
925C22—1721no—
926C22—1721no—
927C22C2×C22⋊C4×D4311yescharacteristic
928C22#131×D4311yescharacteristic
929C22#1458366411yescharacteristic
930C4—21no—
931C4—21no—
932C4—21no—
933C4—21no—
934C4—21no—
935C4—21no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—861no—
940C4—861no—
941C4—861no—
942C4—861no—
943C4—861no—
944C4—861no—
945C4—1721no—
946C4—1721no—
947C2—21no—
948C2—21no—
949C2—81no—
950C2—862no—
951C2—3441no—
952C2—1721no—
953C2—1722no—
954C2#1914304311yescharacteristic
955C2#410×D4311yescharacteristic
956C2#1914307211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1473C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063295C4
cosocleC22×C4×C43C24
hypercenter#1473D43
hypocenterC43#17412
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1473

Complements

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

NH ≅ G/Ntype
2. #19143254C2semidirect
3. #19143248C2semidirect
4. #19132964C2semidirect
5. #19132945C2semidirect
6. #19132945C2semidirect
7. #19132942C2semidirect
8. #19132942C2semidirect
9. #19132935C2semidirect
10. #19132928C2semidirect
11. #19132920C2semidirect
12. #19132915C2semidirect
13. #19132908C2semidirect
14. #323×D43C2semidirect
15. C43×#1473C2semidirect
42. #14582956C22semidirect
43. #14582953C22semidirect
44. #14582953C22semidirect
45. #14582952C22semidirect
46. #14582949C22semidirect
47. #14582949C22semidirect
56. #14582625C22semidirect
57. #14582625C22semidirect
64. #14582622C22semidirect
65. #14582622C22semidirect
66. #14582622C22semidirect
67. #14582622C22semidirect
69. C43×#432C22semidirect
70. C43×#431C22semidirect
71. C43×#324C22semidirect
72. C43×#324C22semidirect
473. #1473D43semidirect
524. #432C2×D43semidirect
528. #431C2×D43semidirect
539. #324C2×D43semidirect
540. #324C2×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×#145835742
#191432542
#191432482
#191329642
#191329452
#191329422
#191329352
#191329282
#191329202
#191329152
#191329082
#323×D432
C43×#14732
#1741243