Finite Group Databasebeta

← #25062839

Subgroups — #25062839

Order 11008.

1002 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583611C211yesmaximal, characteristic
2#19143254C211yesmaximal, characteristic, complemented
3#19143248C211yesmaximal, characteristic, complemented
4#19132953C211yesmaximal, characteristic, complemented
5#19132953C211yesmaximal, characteristic, complemented
6#19132947C211yesmaximal, characteristic, complemented
7#19132945C211yesmaximal, characteristic, complemented
8#19132945C211yesmaximal, characteristic, complemented
9#19132930C211yesmaximal, characteristic, complemented
10#19132927C211yesmaximal, characteristic, complemented
11#19132926C211yesmaximal, characteristic, complemented
12#19132910C211yesmaximal, characteristic, complemented
13#19132907C211yesmaximal, characteristic, complemented
14#19132906C211yesmaximal, characteristic, complemented
15C43×#1469C211yesmaximal, characteristic, complemented
16#14583611—21no—
17#14583611—21no—
18#14583611—21no—
19#14583611—21no—
20#14583611—21no—
21#14583611—21no—
22#14583611—21no—
23#14583611—21no—
24C2×#13063323C411yescharacteristic
25C2×#13063314C411yescharacteristic
26C2×#13063311C411yescharacteristic
27C2×#13063311C2211yescharacteristic
28C2×#13063298C411yescharacteristic
29C2×#13063298C2211yescharacteristic
30C2×#13063297C411yescharacteristic
31C2×#13063297C411yescharacteristic
32C2×(C22⋊D43)⋊C4C411yescharacteristic
33C2×(C22⋊D43)⋊C4C2211yescharacteristic
34C2×#13063282C2211yescharacteristic
35C2×#13063282C2211yescharacteristic
36C2×#13063281C411yescharacteristic
37C2×#13063281C2211yescharacteristic
38#14582961—21no—
39#14582959—21no—
40#14582959—21no—
41#14582958—21no—
42#14582956C2211yescharacteristic
43#14582953C2211yescharacteristic
44#14582953C2211yescharacteristic
45#14582952C2211yescharacteristic
46#14582949C2211yescharacteristic
47#14582949C2211yescharacteristic
48#14582924—21no—
49#14582924—21no—
50#14582861C2211yescharacteristic
51#14582861C2211yescharacteristic
52C22⋊C8×D43C2211yescharacteristic
53C22⋊C8×D43C2211yescharacteristic
54#14582856—21no—
55#14582853—21no—
56#14582624C2211yescharacteristic
57#14582624C2211yescharacteristic
58#14582624C2211yescharacteristic
59#14582624C2211yescharacteristic
60#14582623C2211yescharacteristic
61#14582623C2211yescharacteristic
62#14582623C2211yescharacteristic
63#14582623C2211yescharacteristic
64#14582622C2211yescharacteristic
65#14582622C2211yescharacteristic
66#14582622C2211yescharacteristic
67#14582622C2211yescharacteristic
68C2×#124×C43C2211yescharacteristic
69C43×#432C2211yescharacteristic
70C43×#431C2211yescharacteristic
71C43×#323C2211yescharacteristic
72C43×#323C2211yescharacteristic
73C43×#323C2211yescharacteristic
74C43×#323C2211yescharacteristic
75C22×Dic86C2×C411yescharacteristic
76C22×D172C2×C411yescharacteristic
77C22×C22⋊D43C2×C411yescharacteristic
78C22×C22⋊D43C2×C411yescharacteristic
79C22×C22⋊D43C2×C411yescharacteristic
80C22×C22⋊D43C2×C411yescharacteristic
81C23×Dic43C2×C411yescharacteristic
82C23×Dic43C2×C411yescharacteristic
83C22×C4×D43C2×C411yescharacteristic
84C22×C4×D43C2311yescharacteristic
85C2×#10621872—21no—
86C2×#10621872—21no—
87C2×C8×D43—21no—
88C2×C8×D43—21no—
89#13063323—21no—
90#13063323—21no—
91#13063323—21no—
92#13063323—21no—
93#13063314—21no—
94#13063314—21no—
95#13063314—21no—
96#13063314—21no—
97#13063311—21no—
98#13063311—21no—
99#13063311—21no—
100#13063311—21no—
101#13063311—21no—
102#13063311—21no—
103#13063311—21no—
104#13063311—21no—
105#13063298—21no—
106#13063298—21no—
107#13063298—21no—
108#13063298—21no—
109#13063298—21no—
110#13063298—21no—
111#13063298—21no—
112#13063298—21no—
113#13063297—21no—
114#13063297—21no—
115#13063297—21no—
116#13063297—21no—
117#13063297—21no—
118#13063297—21no—
119#13063297—21no—
120#13063297—21no—
121(C22⋊D43)⋊C4—21no—
122(C22⋊D43)⋊C4—21no—
123(C22⋊D43)⋊C4—21no—
124(C22⋊D43)⋊C4—21no—
125(C22⋊D43)⋊C4—21no—
126(C22⋊D43)⋊C4—21no—
127(C22⋊D43)⋊C4—21no—
128(C22⋊D43)⋊C4—21no—
129#13063282—21no—
130#13063282—21no—
131#13063282—21no—
132#13063282—21no—
133#13063282D411yescharacteristic
134#13063282D411yescharacteristic
135#13063282D411yescharacteristic
136#13063282D411yescharacteristic
137#13063282D411yescharacteristic
138#13063282D411yescharacteristic
139#13063282D411yescharacteristic
140#13063282D411yescharacteristic
141#13063281—21no—
142#13063281—21no—
143#13063281—21no—
144#13063281—21no—
145#13063281—21no—
146#13063281—21no—
147#13063281—21no—
148#13063281—21no—
149C2×Dic43⋊C4C2×C411yescharacteristic
150C2×Dic43⋊C4C2×C411yescharacteristic
151C2×Dic43⋊C4C2×C411yescharacteristic
152C2×Dic43⋊C4C2×C411yescharacteristic
153C2×Dic43⋊C4C2×C411yescharacteristic
154C2×Dic43⋊C4C2311yescharacteristic
155C2×C22⋊Dic43C2×C411yescharacteristic
156C2×C22⋊Dic43C2×C411yescharacteristic
157C2×(C2×D43)⋊C4C2×C411yescharacteristic
158C2×(C2×D43)⋊C4C2×C411yescharacteristic
159C2×(C2×D43)⋊C4C2×C411yescharacteristic
160C2×(C2×D43)⋊C4C2×C411yescharacteristic
161C2×(C2×D43)⋊C4C2×C411yescharacteristic
162C2×(C2×D43)⋊C4C2311yescharacteristic
163C2×C4×Dic43C2×C411yescharacteristic
164C2×C4×Dic43C2×C411yescharacteristic
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—
187C22×Q8×C43C2×C411yescharacteristic
188C22×D4×C43C2×C411yescharacteristic
189#124×C43—21no—
190#124×C43—21no—
191#124×C43—21no—
192#124×C43—21no—
193C2×C22⋊C4×C43C2×C411yescharacteristic
194C2×C22⋊C4×C43C2×C411yescharacteristic
195C2×C22⋊C4×C43C2311yescharacteristic
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
207C24×C43C22×C411yescharacteristic
208C23×D43C22×C411yescharacteristic
209C23×D43C22×C411yescharacteristic
210C2×Q8×C43—21no—
211C2×Q8×C43—21no—
212C2×Q8×C43—81no—
213C2×D4×C43—21no—
214C2×D4×C43—21no—
215C2×D4×C43—81no—
216C22×C4×C43C22×C411yescharacteristic
217C22×C4×C43C22×C411yescharacteristic
218C22×C4×C43C22×C411yescharacteristic
219C22×C4×C43C22×C411yescharacteristic
220C22×C4×C43C2411yescharacteristic
221C2×C22⋊D43—21no—
222C2×C22⋊D43—21no—
223C2×C22⋊D43—21no—
224C2×C22⋊D43—21no—
225C2×C22⋊D43—22no—
226C2×C22⋊D43—21no—
227C2×C22⋊D43—21no—
228C2×C22⋊D43—21no—
229C2×C22⋊D43—21no—
230C2×C22⋊D43—41no—
231C2×C22⋊D43—42no—
232C2×C22⋊D43—81no—
233C2×C22⋊D43—81no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—22no—
239C22×Dic43—41no—
240C22×Dic43—42no—
241C22×Dic43C22×C411yescharacteristic
242C22×Dic43C22×C411yescharacteristic
243C22×Dic43C22×C411yescharacteristic
244C22×Dic43C22×C411yescharacteristic
245C22×Dic43C22×C411yescharacteristic
246C22×Dic43C22×C411yescharacteristic
247C2×D172—21no—
248C2×D172—21no—
249C2×D172—81no—
250C2×C4×D43—21no—
251C2×C4×D43—21no—
252C2×C4×D43—22no—
253C2×C4×D43—41no—
254C2×C4×D43—42no—
255C2×C4×D43C2×D411yescharacteristic
256C2×C4×D43C2×D411yescharacteristic
257C2×C4×D43C2×D411yescharacteristic
258C2×C4×D43C2×D411yescharacteristic
259C2×Dic86—21no—
260C2×Dic86—21no—
261C2×Dic86—81no—
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C22⋊C4×C43—21no—
267C22⋊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)⋊C4C22⋊C411yescharacteristic
291(C2×D43)⋊C4C22⋊C411yescharacteristic
292(C2×D43)⋊C4C22⋊C411yescharacteristic
293(C2×D43)⋊C4C22⋊C411yescharacteristic
294(C2×D43)⋊C4C22⋊C411yescharacteristic
295(C2×D43)⋊C4C22⋊C411yescharacteristic
296(C2×D43)⋊C4C22⋊C411yescharacteristic
297(C2×D43)⋊C4C22⋊C411yescharacteristic
298Dic43⋊C4—21no—
299Dic43⋊C4—21no—
300Dic43⋊C4—21no—
301Dic43⋊C4—21no—
302Dic43⋊C4—21no—
303Dic43⋊C4—21no—
304Dic43⋊C4—21no—
305Dic43⋊C4—21no—
306Dic43⋊C4C22⋊C411yescharacteristic
307Dic43⋊C4C22⋊C411yescharacteristic
308Dic43⋊C4C22⋊C411yescharacteristic
309Dic43⋊C4C22⋊C411yescharacteristic
310Dic43⋊C4C22⋊C411yescharacteristic
311Dic43⋊C4C22⋊C411yescharacteristic
312Dic43⋊C4C22⋊C411yescharacteristic
313Dic43⋊C4C22⋊C411yescharacteristic
314C4×Dic43—21no—
315C4×Dic43—21no—
316C4×Dic43—21no—
317C4×Dic43—21no—
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—21no—
336C23×C43—21no—
337C23×C43—21no—
338C23×C43—41no—
339C23×C43—41no—
340C23×C43—41no—
341C23×C43—41no—
342C23×C43C23×C411yescharacteristic
343C22×D43—21no—
344C22×D43—21no—
345C22×D43—21no—
346C22×D43—21no—
347C22×D43—21no—
348C22×D43—41no—
349C22×D43—41no—
350C22×D43—41no—
351C22×D43—41no—
352C22×D43C2×C22⋊C411yescharacteristic
353C22×D43C2×C22⋊C411yescharacteristic
354Q8×C43—81no—
355Q8×C43—81no—
356D4×C43—81no—
357D4×C43—81no—
358C2×C4×C43—21no—
359C2×C4×C43—21no—
360C2×C4×C43—21no—
361C2×C4×C43—21no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43C2×C22⋊C411yescharacteristic
367C2×C4×C43C2×C22⋊C411yescharacteristic
368C2×C4×C43C2×C22⋊C411yescharacteristic
369C2×C4×C43C2×C22⋊C411yescharacteristic
370C2×C4×C43C22×D411yescharacteristic
371C2×C4×C43C22×D411yescharacteristic
372C22⋊D43—42no—
373C22⋊D43—42no—
374C22⋊D43—42no—
375C22⋊D43—42no—
376C22⋊D43—81no—
377C22⋊D43—81no—
378C22⋊D43—81no—
379C22⋊D43—81no—
380C2×Dic43—21no—
381C2×Dic43—21no—
382C2×Dic43—21no—
383C2×Dic43—21no—
384C2×Dic43—22no—
385C2×Dic43—21no—
386C2×Dic43—21no—
387C2×Dic43—41no—
388C2×Dic43—42no—
389C2×Dic43—42no—
390C2×Dic43—42no—
391C2×Dic43—42no—
392C2×Dic43—41no—
393C2×Dic43—41no—
394C2×Dic43C2×C22⋊C411yescharacteristic
395C2×Dic43C2×C22⋊C411yescharacteristic
396C2×Dic43C2×C22⋊C411yescharacteristic
397C2×Dic43C2×C22⋊C411yescharacteristic
398C2×Dic43C2×C22⋊C411yescharacteristic
399C2×Dic43C2×C22⋊C411yescharacteristic
400C2×Dic43#13112yes—
401D172—81no—
402D172—81no—
403C4×D43—22no—
404C4×D43—22no—
405C4×D43—41no—
406C4×D43—41no—
407C4×D43—42no—
408C4×D43—42no—
409Dic86—81no—
410Dic86—81no—
411C8×C43—41no—
412C8×C43—41no—
413C8×C43—41no—
414C8×C43—41no—
415C43⋊C8—41no—
416C43⋊C8—41no—
417C43⋊C8—41no—
418C43⋊C8—41no—
419#17418—431nomaximal, Sylow
420C22×C43—21no—
421C22×C43—21no—
422C22×C43—41no—
423C22×C43—41no—
424C22×C43—41no—
425C22×C43—41no—
426C22×C43—41no—
427C22×C43—41no—
428C22×C43—81no—
429C22×C43—81no—
430C22×C43—81no—
431C22×C43—81no—
432C22×C43C22×C22⋊C411yescharacteristic
433C22×C43C2×#13111yescharacteristic
434C22×C43#56811yescharacteristic
435C2×D43—21no—
436C2×D43—21no—
437C2×D43—21no—
438C2×D43—21no—
439C2×D43—21no—
440C2×D43—21no—
441C2×D43—41no—
442C2×D43—41no—
443C2×D43—41no—
444C2×D43—81no—
445C2×D43—81no—
446C2×D43—81no—
447C2×D43—81no—
448C4×C43—21no—
449C4×C43—21no—
450C4×C43—21no—
451C4×C43—21no—
452C4×C43—21no—
453C4×C43—21no—
454C4×C43—41no—
455C4×C43—41no—
456Dic43—22no—
457Dic43—21no—
458Dic43—21no—
459Dic43—21no—
460Dic43—21no—
461Dic43—21no—
462Dic43—41no—
463Dic43—41no—
464Dic43#41012yes—
465C2×#555—431no—
466#2924—431no—
467#2924—431no—
468#1471—431no—
469#1471—431no—
470#1469—431no—
471#1469—431no—
472#1469—431no—
473#1469D4311yescharacteristic, complemented
474#1465—431no—
475#1464—431no—
476#1464—431no—
477#1459—431no—
478#1458—431no—
479#1458—431no—
480C2×C43—21no—
481C2×C43—21no—
482C2×C43—81no—
483C2×C43—81no—
484C2×C43#288011yescharacteristic
485C2×C43C2×#41011yescharacteristic
486C2×C43#288811yescharacteristic
487D43—41no—
488D43—41no—
489D43—81no—
490#555—861no—
491#555—861no—
492#555—861no—
493#555—861no—
494#555—861no—
495#555—861no—
496#555—861no—
497#555—861no—
498C2×C4⋊Q8—431no—
499C2×#124—431no—
500C2×#124—431no—
501C2×#124—431no—
502C2×#124C2×D4311yescharacteristic
503C2×#121—431no—
504C2×#121—431no—
505C2×#121—431no—
506C2×#121—431no—
507C2×C4×D4—431no—
508C2×C4×D4—431no—
509C2×#117—431no—
510C2×#117—431no—
511C2×#117—431no—
512C2×#117—431no—
513#433—861no—
514#433—861no—
515#433—861no—
516#433—861no—
517#432—431no—
518#432—431no—
519#432—431no—
520#432C2×D4311yescharacteristic
521#431—431no—
522#431—431no—
523#431—431no—
524#431C2×D4311yescharacteristic
525#424—861no—
526#424—861no—
527#407—431no—
528#407—431no—
529C2×C22⋊C8—431no—
530C2×C22⋊C8—431no—
531#405—861no—
532#405—861no—
533#324—431no—
534#324—431no—
535#324—431no—
536#324—431no—
537#323—431no—
538#323—431no—
539#323—431no—
540#323—431no—
541#323—431no—
542#323—431no—
543#323—431no—
544#323—431no—
545#323C2×D4311yescharacteristic
546#323C2×D4311yescharacteristic
547#323C2×D4311yescharacteristic
548#323C2×D4311yescharacteristic
549C43#1741811yescharacteristic, complemented, Sylow
550C22×Q8—431no—
551C22×Q8C4×D4311yescharacteristic
552C22×D4—431no—
553C22×D4—431no—
554C22×D4—431no—
555C22×D4—431no—
556C22×D4—431no—
557C22×D4C4×D4311yescharacteristic
558C23×C4—431no—
559C23×C4—431no—
560C23×C4—431no—
561C23×C4—431no—
562C2×M16—861no—
563C2×M16—861no—
564C22×C8—861no—
565C22×C8—861no—
566C4⋊Q8—861no—
567C4⋊Q8—861no—
568C4⋊Q8—861no—
569C4⋊Q8—861no—
570#124—21no—
571#124—21no—
572#124—21no—
573#124—21no—
574#124—861no—
575#124—861no—
576#124—861no—
577#124—861no—
578#124—861no—
579#124—861no—
580#124—861no—
581#124—861no—
582#124—861no—
583#124—861no—
584#124—861no—
585#124—861no—
586#121—861no—
587#121—861no—
588#121—861no—
589#121—861no—
590#121—861no—
591#121—861no—
592#121—861no—
593#121—861no—
594#121—861no—
595#121—861no—
596#121—861no—
597#121—861no—
598#121—861no—
599#121—861no—
600#121—861no—
601#121—861no—
602C4×D4—861no—
603C4×D4—861no—
604C4×D4—861no—
605C4×D4—861no—
606C4×D4—861no—
607C4×D4—861no—
608C4×D4—861no—
609C4×D4—861no—
610#117—431no—
611#117—431no—
612#117—431no—
613#117—431no—
614#117—431no—
615#117—431no—
616#117—431no—
617#117—431no—
618#117—861no—
619#117—861no—
620#117—861no—
621#117—861no—
622#117—861no—
623#117—861no—
624#117—861no—
625#117—861no—
626#117—861no—
627#117—861no—
628#117—861no—
629#117—861no—
630C2×C4⋊C4—431no—
631C2×C4⋊C4—431no—
632C2×C4⋊C4—431no—
633C2×C4⋊C4—431no—
634C2×C4⋊C4—431no—
635C2×C4⋊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—431no—
644C2×C22⋊C4C4×D4311yescharacteristic
645C2×C22⋊C4C4×D4311yescharacteristic
646C2×C22⋊C4C22×D4311yescharacteristic
647C2×C22⋊C4C22×D4311yescharacteristic
648C2×C42—431no—
649C2×C42—431no—
650C2×C42—431no—
651C2×C42—431no—
652C2×C42C22×D4311yescharacteristic
653C4⋊C8—21no—
654C4⋊C8—21no—
655C4⋊C8—861no—
656C4⋊C8—861no—
657C4⋊C8—861no—
658C4⋊C8—861no—
659C4⋊C8—861no—
660C4⋊C8—861no—
661C22⋊C8—431no—
662C22⋊C8—431no—
663C22⋊C8—431no—
664C22⋊C8—431no—
665C22⋊C8—861no—
666C22⋊C8—861no—
667C22⋊C8—861no—
668C22⋊C8—861no—
669C22⋊C8C22×D4311yescharacteristic
670C22⋊C8C22×D4311yescharacteristic
671C22⋊C8C22×D4311yescharacteristic
672C22⋊C8C22×D4311yescharacteristic
673#97—21no—
674#97—861no—
675#97—861no—
676#97—861no—
677C4×C8—21no—
678C4×C8—861no—
679C4×C8—861no—
680C4×C8—861no—
681C24—431no—
682C24—431no—
683C24C2×C4×D4311yescharacteristic
684C24C2×C4×D4311yescharacteristic
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—81no—
688C2×Q8—861no—
689C2×Q8—861no—
690C2×Q8—3441no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—81no—
694C2×D4—861no—
695C2×D4—861no—
696C2×D4—861no—
697C2×D4—861no—
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—3441no—
707C2×D4—3441no—
708C2×D4—1721no—
709C2×D4—1722no—
710C22×C4—431no—
711C22×C4—431no—
712C22×C4—431no—
713C22×C4—431no—
714C22×C4—431no—
715C22×C4—431no—
716C22×C4—431no—
717C22×C4—431no—
718C22×C4—431no—
719C22×C4—431no—
720C22×C4—862no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—862no—
726C22×C4—861no—
727C22×C4—861no—
728C22×C4—1721no—
729C22×C4—1722no—
730C22×C4—1721no—
731C22×C4—1722no—
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—431no—
750C4⋊C4—431no—
751C4⋊C4—431no—
752C4⋊C4—431no—
753C4⋊C4—431no—
754C4⋊C4—431no—
755C4⋊C4—431no—
756C4⋊C4—431no—
757C4⋊C4—861no—
758C4⋊C4—861no—
759C4⋊C4—861no—
760C4⋊C4—861no—
761C4⋊C4—861no—
762C4⋊C4—861no—
763C4⋊C4—861no—
764C4⋊C4—861no—
765C22⋊C4—21no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—21no—
773C22⋊C4—431no—
774C22⋊C4—431no—
775C22⋊C4—431no—
776C22⋊C4—431no—
777C22⋊C4—431no—
778C22⋊C4—431no—
779C22⋊C4—431no—
780C22⋊C4—431no—
781C22⋊C4—861no—
782C22⋊C4—861no—
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—
793C42—431no—
794C42—431no—
795C42—431no—
796C42—431no—
797C42—861no—
798C42—861no—
799C42—861no—
800C42—861no—
801C42—861no—
802C42—861no—
803C42D4×D4311yescharacteristic
804C42D4×D4311yescharacteristic
805C42D4×D4311yescharacteristic
806C42D4×D4311yescharacteristic
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—431no—
818C23—431no—
819C23—861no—
820C23—861no—
821C23—861no—
822C23—861no—
823C23—861no—
824C23—1721no—
825C23—1721no—
826C23—1721no—
827C23—1721no—
828C23C22×C4×D4311yescharacteristic
829Q8—81no—
830Q8—81no—
831Q8—3441no—
832Q8—3441no—
833D4—81no—
834D4—81no—
835D4—3441no—
836D4—3441no—
837D4—3441no—
838D4—3441no—
839D4—3441no—
840D4—3441no—
841D4—1722no—
842D4—1722no—
843D4—1722no—
844D4—1722no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—431no—
854C2×C4—431no—
855C2×C4—431no—
856C2×C4—431no—
857C2×C4—431no—
858C2×C4—431no—
859C2×C4—432no—
860C2×C4—862no—
861C2×C4—862no—
862C2×C4—862no—
863C2×C4—861no—
864C2×C4—861no—
865C2×C4—861no—
866C2×C4—861no—
867C2×C4—861no—
868C2×C4—861no—
869C2×C4—1721no—
870C2×C4—1721no—
871C2×C4—1722no—
872C2×C4—1722no—
873C2×C4—1722no—
874C2×C4—1721no—
875C2×C4—1722no—
876C2×C4—1722no—
877C2×C4—1722no—
878C2×C4—1721no—
879C2×C4—1721no—
880C2×C4C22⋊C4×D4311yescharacteristic
881C2×C4C22⋊C4×D4311yescharacteristic
882C2×C4C22⋊C4×D4311yescharacteristic
883C2×C4C22⋊C4×D4311yescharacteristic
884C2×C4C2×D4×D4311yescharacteristic
885C2×C4C2×D4×D4311yescharacteristic
886C8—41no—
887C8—41no—
888C8—41no—
889C8—41no—
890C8—1721no—
891C8—1721no—
892C8—1721no—
893C8—1721no—
894C22—21no—
895C22—21no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—861no—
907C22—861no—
908C22—861no—
909C22—861no—
910C22—861no—
911C22—861no—
912C22—3441no—
913C22—3441no—
914C22—3441no—
915C22—3441no—
916C22—1721no—
917C22—1721no—
918C22—1721no—
919C22C2×C22⋊C4×D4311yescharacteristic
920C22#131×D4311yescharacteristic
921C22#1458366411yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—41no—
929C4—41no—
930C4—432no—
931C4—862no—
932C4—861no—
933C4—861no—
934C4—861no—
935C4—861no—
936C4—861no—
937C4—1721no—
938C4—1721no—
939C2—21no—
940C2—21no—
941C2—81no—
942C2—81no—
943C2—3441no—
944C2—1721no—
945C2—1721no—
946C2#1914304311yescharacteristic
947C2#410×D4311yescharacteristic
948C2#1914307111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1469C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583611C2
cosocleC22×C4×C43C24
hypercenter#1469D43
hypocenterC43#17418
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1469

Complements

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

NH ≅ G/Ntype
2. #19143254C2semidirect
3. #19143248C2semidirect
4. #19132953C2semidirect
5. #19132953C2semidirect
6. #19132947C2semidirect
7. #19132945C2semidirect
8. #19132945C2semidirect
9. #19132930C2semidirect
10. #19132927C2semidirect
11. #19132926C2semidirect
12. #19132910C2semidirect
13. #19132907C2semidirect
14. #19132906C2semidirect
15. C43×#1469C2semidirect
473. #1469D43semidirect
549. C43#17418semidirect

Maximal subgroups

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

subgroupindex
C2×#145836112
#191432542
#191432482
#191329532
#191329472
#191329452
#191329302
#191329272
#191329262
#191329102
#191329072
#191329062
C43×#14692
#1741843