Finite Group Databasebeta

← #25062852

Subgroups — #25062852

Order 11008.

938 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583616C211yesmaximal, characteristic
2#19143254C211yesmaximal, characteristic, complemented
3#19143248C211yesmaximal, characteristic, complemented
4#19132964C211yesmaximal, characteristic, complemented
5#19132961C211yesmaximal, characteristic, complemented
6#19132961C211yesmaximal, characteristic, complemented
7#19132957C211yesmaximal, characteristic, complemented
8#19132957C211yesmaximal, characteristic, complemented
9#19132938C211yesmaximal, characteristic, complemented
10#19132937C211yesmaximal, characteristic, complemented
11#19132930C211yesmaximal, characteristic
12#19132918C211yesmaximal, characteristic, complemented
13#19132917C211yesmaximal, characteristic, complemented
14#19132910C211yesmaximal, characteristic
15C43×#1473C211yesmaximal, characteristic, complemented
16#14583616—21no—
17#14583616—21no—
18#14583616—21no—
19#14583616—21no—
20#14583616—21no—
21#14583616—21no—
22#14583616—21no—
23#14583616—21no—
24C2×#13063324C411yescharacteristic
25C2×#13063320C411yescharacteristic
26C2×#13063320C411yescharacteristic
27C2×#13063318C2211yescharacteristic
28C2×#13063311C411yescharacteristic
29C2×#13063311C411yescharacteristic
30C2×#13063303C2211yescharacteristic
31C2×#13063302C411yescharacteristic
32C2×C4×Dic86C2211yescharacteristic
33C2×#13063290C411yescharacteristic
34C2×#13063290C2211yescharacteristic
35C2×(C22⋊D43)⋊C4C2211yescharacteristic
36C2×#13063282C2211yescharacteristic
37C2×#13063281C411yescharacteristic
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#14582625C2211yescharacteristic
57#14582625C2211yescharacteristic
58#14582624C2211yescharacteristic
59#14582624C2211yescharacteristic
60#14582624C2211yescharacteristic
61#14582624C2211yescharacteristic
62#14582624C2211yescharacteristic
63#14582624C2211yescharacteristic
64#14582624C2211yescharacteristic
65#14582624C2211yescharacteristic
66#14582623C2211yescharacteristic
67#14582623C2211yescharacteristic
68C2×#126×C43C2211yescharacteristic
69C43×#432C2211yescharacteristic
70C43×#431C2211yescharacteristic
71C43×#324C2211yescharacteristic
72C43×#324C2211yescharacteristic
73C43×#323C2211yescharacteristic
74C43×#323C2211yescharacteristic
75C22×Dic86C2×C411yescharacteristic
76C22×Dic86C2×C411yescharacteristic
77C22×Dic86C2×C411yescharacteristic
78C22×C22⋊D43C2×C411yescharacteristic
79C23×Dic43C2×C411yescharacteristic
80C22×C4×D43C2311yescharacteristic
81C2×#10621872—21no—
82C2×#10621872—21no—
83C2×C8×D43—21no—
84C2×C8×D43—21no—
85#13063324—21no—
86#13063324—21no—
87#13063324—21no—
88#13063324—21no—
89#13063320—21no—
90#13063320—21no—
91#13063320—21no—
92#13063320—21no—
93#13063320—21no—
94#13063320—21no—
95#13063320—21no—
96#13063320—21no—
97#13063318—21no—
98#13063318—21no—
99#13063318—21no—
100#13063318—21no—
101#13063311—21no—
102#13063311—21no—
103#13063311—21no—
104#13063311—21no—
105#13063311—21no—
106#13063311—21no—
107#13063311—21no—
108#13063311—21no—
109#13063303—21no—
110#13063303—21no—
111#13063303—21no—
112#13063303—21no—
113#13063302—21no—
114#13063302—21no—
115#13063302—21no—
116#13063302—21no—
117C4×Dic86—21no—
118C4×Dic86—21no—
119C4×Dic86—21no—
120C4×Dic86—21no—
121#13063290—21no—
122#13063290—21no—
123#13063290—21no—
124#13063290—21no—
125#13063290—21no—
126#13063290—21no—
127#13063290—21no—
128#13063290—21no—
129(C22⋊D43)⋊C4—21no—
130(C22⋊D43)⋊C4—21no—
131(C22⋊D43)⋊C4—21no—
132(C22⋊D43)⋊C4—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—
145C2×C4⋊Dic43C2×C411yescharacteristic
146C2×C4⋊Dic43C2×C411yescharacteristic
147C2×Dic43⋊C4C2×C411yescharacteristic
148C2×Dic43⋊C4C2×C411yescharacteristic
149C2×Dic43⋊C4C2×C411yescharacteristic
150C2×Dic43⋊C4C2×C411yescharacteristic
151C2×Dic43⋊C4C2×C411yescharacteristic
152C2×Dic43⋊C4C2311yescharacteristic
153C2×Dic43⋊C4C2311yescharacteristic
154C2×C22⋊Dic43C2×C411yescharacteristic
155C2×C22⋊Dic43C2×C411yescharacteristic
156C2×(C2×D43)⋊C4C2×C411yescharacteristic
157C2×(C2×D43)⋊C4C2×C411yescharacteristic
158C2×(C2×D43)⋊C4C2×C411yescharacteristic
159C2×(C2×D43)⋊C4C2×C411yescharacteristic
160C2×(C2×D43)⋊C4C2×C411yescharacteristic
161C2×C4×Dic43C2×C411yescharacteristic
162C2×C4×Dic43C2×C411yescharacteristic
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—
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×D43C22×C411yescharacteristic
208C22×C4×C43C22×C411yescharacteristic
209C22×C4×C43C22×C411yescharacteristic
210C22×C4×C43C22×C411yescharacteristic
211C22×C4×C43C22×C411yescharacteristic
212C22×C4×C43C22×C411yescharacteristic
213C22×C4×C43C2411yescharacteristic
214C2×C22⋊D43—22no—
215C2×C22⋊D43—21no—
216C2×C22⋊D43—21no—
217C2×C22⋊D43—41no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—42no—
221C22×Dic43C22×C411yescharacteristic
222C22×Dic43C22×C411yescharacteristic
223C22×Dic43C22×C411yescharacteristic
224C22×Dic43C22×C411yescharacteristic
225C22×Dic43C22×C411yescharacteristic
226C22×Dic43C22×C411yescharacteristic
227C22×Dic43C22×C411yescharacteristic
228C2×C4×D43—42no—
229C2×C4×D43C2×D411yescharacteristic
230C2×C4×D43C2×D411yescharacteristic
231C2×C4×D43C2×D411yescharacteristic
232C2×C4×D43C2×D411yescharacteristic
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86—22no—
240C2×Dic86—22no—
241C2×Dic86—41no—
242C2×Dic86—41no—
243C2×Dic86—42no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C22⋊C4×C43—21no—
255C22⋊C4×C43—21no—
256C22⋊C4×C43—21no—
257C22⋊C4×C43—21no—
258C22⋊C4×C43—21no—
259C22⋊C4×C43—21no—
260C42×C43C2×D411yescharacteristic
261C42×C43C2×D411yescharacteristic
262C42×C43C2×D411yescharacteristic
263C42×C43C2×D411yescharacteristic
264C22⋊Dic43—21no—
265C22⋊Dic43—21no—
266C22⋊Dic43—21no—
267C22⋊Dic43—21no—
268(C2×D43)⋊C4—21no—
269(C2×D43)⋊C4—21no—
270(C2×D43)⋊C4—21no—
271(C2×D43)⋊C4—21no—
272(C2×D43)⋊C4—21no—
273(C2×D43)⋊C4—21no—
274(C2×D43)⋊C4C22⋊C411yescharacteristic
275(C2×D43)⋊C4C22⋊C411yescharacteristic
276(C2×D43)⋊C4C22⋊C411yescharacteristic
277(C2×D43)⋊C4C22⋊C411yescharacteristic
278(C2×D43)⋊C4C22⋊C411yescharacteristic
279(C2×D43)⋊C4C22⋊C411yescharacteristic
280(C2×D43)⋊C4C22⋊C411yescharacteristic
281(C2×D43)⋊C4C22⋊C411yescharacteristic
282C4⋊Dic43—21no—
283C4⋊Dic43—21no—
284C4⋊Dic43—21no—
285C4⋊Dic43—21no—
286Dic43⋊C4—21no—
287Dic43⋊C4—21no—
288Dic43⋊C4—21no—
289Dic43⋊C4—21no—
290Dic43⋊C4—21no—
291Dic43⋊C4—21no—
292Dic43⋊C4—21no—
293Dic43⋊C4—21no—
294Dic43⋊C4—21no—
295Dic43⋊C4—21no—
296Dic43⋊C4C22⋊C411yescharacteristic
297Dic43⋊C4C22⋊C411yescharacteristic
298Dic43⋊C4C22⋊C411yescharacteristic
299Dic43⋊C4C22⋊C411yescharacteristic
300Dic43⋊C4C22⋊C411yescharacteristic
301Dic43⋊C4C22⋊C411yescharacteristic
302Dic43⋊C4C22⋊C411yescharacteristic
303Dic43⋊C4C22⋊C411yescharacteristic
304C4×Dic43—21no—
305C4×Dic43—21no—
306C4×Dic43—21no—
307C4×Dic43—21no—
308C4×Dic43—21no—
309C4×Dic43—21no—
310C4×Dic43—21no—
311C4×Dic43—21no—
312C4×Dic43—21no—
313C4×Dic43—21no—
314C4×Dic43C2×D411yescharacteristic
315C4×Dic43C2×D411yescharacteristic
316C4×Dic43C2×D411yescharacteristic
317C4×Dic43C2×D411yescharacteristic
318C2×C43⋊C8—21no—
319C2×C43⋊C8—21no—
320C2×C43⋊C8—21no—
321C2×C43⋊C8—21no—
322#10621872—42no—
323#10621872—42no—
324C8×D43—42no—
325C8×D43—42no—
326C23×C43—21no—
327C23×C43—21no—
328C23×C43—21no—
329C23×C43—41no—
330C23×C43—41no—
331C23×C43C23×C411yescharacteristic
332C22×D43—21no—
333C22×D43—21no—
334C22×D43—41no—
335C22×D43—41no—
336C22×D43C2×C22⋊C411yescharacteristic
337C22×D43C2×C22⋊C411yescharacteristic
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43C2×C22⋊C411yescharacteristic
350C2×C4×C43C2×C22⋊C411yescharacteristic
351C2×C4×C43C2×C22⋊C411yescharacteristic
352C2×C4×C43C2×C22⋊C411yescharacteristic
353C2×C4×C43C22×D411yescharacteristic
354C2×C4×C43C22×D411yescharacteristic
355C22⋊D43—42no—
356C22⋊D43—42no—
357C2×Dic43—21no—
358C2×Dic43—21no—
359C2×Dic43—21no—
360C2×Dic43—21no—
361C2×Dic43—22no—
362C2×Dic43—21no—
363C2×Dic43—21no—
364C2×Dic43—21no—
365C2×Dic43—21no—
366C2×Dic43—21no—
367C2×Dic43—41no—
368C2×Dic43—42no—
369C2×Dic43—42no—
370C2×Dic43—41no—
371C2×Dic43—41no—
372C2×Dic43C2×C22⋊C411yescharacteristic
373C2×Dic43C2×C22⋊C411yescharacteristic
374C2×Dic43C2×C22⋊C411yescharacteristic
375C2×Dic43C2×C22⋊C411yescharacteristic
376C2×Dic43C2×C22⋊C411yescharacteristic
377C2×Dic43C2×C22⋊C411yescharacteristic
378C2×Dic43#13112yes—
379C4×D43—22no—
380C4×D43—22no—
381C4×D43—41no—
382C4×D43—41no—
383Dic86—42no—
384Dic86—42no—
385Dic86—42no—
386Dic86—42no—
387Dic86—42no—
388Dic86—42no—
389C8×C43—41no—
390C8×C43—41no—
391C8×C43—41no—
392C8×C43—41no—
393C43⋊C8—41no—
394C43⋊C8—41no—
395C43⋊C8—41no—
396C43⋊C8—41no—
397#17420—431nomaximal, Sylow
398C22×C43—21no—
399C22×C43—21no—
400C22×C43—41no—
401C22×C43—41no—
402C22×C43—41no—
403C22×C43—81no—
404C22×C43—81no—
405C22×C43C22×C22⋊C411yescharacteristic
406C22×C43C2×#13111yescharacteristic
407C22×C43#56811yescharacteristic
408C2×D43—21no—
409C2×D43—21no—
410C2×D43—21no—
411C2×D43—21no—
412C2×D43—21no—
413C2×D43—21no—
414C2×D43—81no—
415C2×D43—81no—
416C4×C43—21no—
417C4×C43—21no—
418C4×C43—21no—
419C4×C43—21no—
420C4×C43—21no—
421C4×C43—21no—
422C4×C43—41no—
423C4×C43—41no—
424C4×C43—41no—
425Dic43—22no—
426Dic43—21no—
427Dic43—21no—
428Dic43—21no—
429Dic43—21no—
430Dic43—21no—
431Dic43—41no—
432Dic43—41no—
433Dic43—41no—
434Dic43#41012yes—
435C2×#556—431no—
436#2924—431no—
437#2924—431no—
438#1473—431no—
439#1473—431no—
440#1473—431no—
441#1473D4311yescharacteristic, complemented
442#1472—431no—
443#1472—431no—
444#1467—431no—
445#1467—431no—
446#1465—431no—
447#1461—431no—
448#1461—431no—
449#1459—431no—
450C2×C43—21no—
451C2×C43—21no—
452C2×C43—81no—
453C2×C43#288011yescharacteristic
454C2×C43C2×#41011yescharacteristic
455C2×C43#288911yescharacteristic
456D43—41no—
457D43—41no—
458#556—861no—
459#556—861no—
460#556—861no—
461#556—861no—
462#556—861no—
463#556—861no—
464#556—861no—
465#556—861no—
466C2×C4⋊Q8—431no—
467C2×#126—431no—
468C2×#126—431no—
469C2×#126—431no—
470C2×#126C2×D4311yescharacteristic
471C2×#124—431no—
472C2×#124—431no—
473C2×C22⋊Q8—431no—
474C2×C22⋊Q8—431no—
475C2×C4×Q8—431no—
476C2×C4×Q8—431no—
477C2×C4×Q8—431no—
478C2×C4×D4—431no—
479C2×#117—431no—
480C2×#117—431no—
481#433—861no—
482#433—861no—
483#433—861no—
484#433—861no—
485#432—431no—
486#432—431no—
487#432—431no—
488#432C2×D4311yescharacteristic
489#431—431no—
490#431—431no—
491#431—431no—
492#431C2×D4311yescharacteristic
493#424—861no—
494#424—861no—
495#407—431no—
496#407—431no—
497C2×C22⋊C8—431no—
498C2×C22⋊C8—431no—
499#405—861no—
500#405—861no—
501#324—431no—
502#324—431no—
503#324—431no—
504#324—431no—
505#324—431no—
506#324—431no—
507#324—431no—
508#324—431no—
509#324—431no—
510#324—431no—
511#324C2×D4311yescharacteristic
512#324C2×D4311yescharacteristic
513#323—431no—
514#323—431no—
515#323C2×D4311yescharacteristic
516#323C2×D4311yescharacteristic
517C43#1742011yescharacteristic, complemented, Sylow
518C22×Q8—431no—
519C22×Q8—431no—
520C22×Q8—431no—
521C22×D4—431no—
522C23×C4—431no—
523C23×C4—431no—
524C2×M16—861no—
525C2×M16—861no—
526C22×C8—861no—
527C22×C8—861no—
528C4⋊Q8—861no—
529C4⋊Q8—861no—
530C4⋊Q8—861no—
531C4⋊Q8—861no—
532#126—21no—
533#126—21no—
534#126—21no—
535#126—21no—
536#126—861no—
537#126—861no—
538#126—861no—
539#126—861no—
540#126—861no—
541#126—861no—
542#126—861no—
543#126—861no—
544#126—861no—
545#126—861no—
546#126—861no—
547#126—861no—
548#124—861no—
549#124—861no—
550#124—861no—
551#124—861no—
552#124—861no—
553#124—861no—
554#124—861no—
555#124—861no—
556C22⋊Q8—861no—
557C22⋊Q8—861no—
558C22⋊Q8—861no—
559C22⋊Q8—861no—
560C22⋊Q8—861no—
561C22⋊Q8—861no—
562C22⋊Q8—861no—
563C22⋊Q8—861no—
564C4×Q8—861no—
565C4×Q8—861no—
566C4×Q8—861no—
567C4×Q8—861no—
568C4×Q8—861no—
569C4×Q8—861no—
570C4×Q8—861no—
571C4×Q8—861no—
572C4×Q8—861no—
573C4×Q8—861no—
574C4×Q8—861no—
575C4×Q8—861no—
576C4×D4—861no—
577C4×D4—861no—
578C4×D4—861no—
579C4×D4—861no—
580#117—431no—
581#117—431no—
582#117—431no—
583#117—431no—
584#117—431no—
585#117—431no—
586#117—431no—
587#117—431no—
588#117—861no—
589#117—861no—
590#117—861no—
591#117—861no—
592C2×C4⋊C4—431no—
593C2×C4⋊C4—431no—
594C2×C4⋊C4—431no—
595C2×C4⋊C4—431no—
596C2×C4⋊C4—431no—
597C2×C4⋊C4—431no—
598C2×C4⋊C4—431no—
599C2×C4⋊C4—431no—
600C2×C4⋊C4—431no—
601C2×C4⋊C4C4×D4311yescharacteristic
602C2×C4⋊C4C4×D4311yescharacteristic
603C2×C4⋊C4C22×D4311yescharacteristic
604C2×C22⋊C4—431no—
605C2×C22⋊C4—431no—
606C2×C22⋊C4—431no—
607C2×C22⋊C4—431no—
608C2×C22⋊C4—431no—
609C2×C22⋊C4—431no—
610C2×C22⋊C4—431no—
611C2×C22⋊C4C4×D4311yescharacteristic
612C2×C22⋊C4C4×D4311yescharacteristic
613C2×C22⋊C4C22×D4311yescharacteristic
614C2×C42—431no—
615C2×C42—431no—
616C2×C42—431no—
617C2×C42—431no—
618C2×C42—431no—
619C2×C42—431no—
620C2×C42C22×D4311yescharacteristic
621C4⋊C8—21no—
622C4⋊C8—21no—
623C4⋊C8—861no—
624C4⋊C8—861no—
625C4⋊C8—861no—
626C4⋊C8—861no—
627C4⋊C8—861no—
628C4⋊C8—861no—
629C22⋊C8—431no—
630C22⋊C8—431no—
631C22⋊C8—431no—
632C22⋊C8—431no—
633C22⋊C8—861no—
634C22⋊C8—861no—
635C22⋊C8—861no—
636C22⋊C8—861no—
637C22⋊C8C22×D4311yescharacteristic
638C22⋊C8C22×D4311yescharacteristic
639C22⋊C8C22×D4311yescharacteristic
640C22⋊C8C22×D4311yescharacteristic
641#97—21no—
642#97—861no—
643#97—861no—
644#97—861no—
645C4×C8—21no—
646C4×C8—861no—
647C4×C8—861no—
648C4×C8—861no—
649C24—431no—
650C24C2×C4×D4311yescharacteristic
651C2×Q8—861no—
652C2×Q8—861no—
653C2×Q8—861no—
654C2×Q8—861no—
655C2×Q8—862no—
656C2×Q8—862no—
657C2×Q8—861no—
658C2×Q8—861no—
659C2×Q8—1721no—
660C2×Q8—1721no—
661C2×Q8—1722no—
662C2×D4—862no—
663C2×D4—861no—
664C2×D4—861no—
665C2×D4—1721no—
666C22×C4—431no—
667C22×C4—431no—
668C22×C4—431no—
669C22×C4—431no—
670C22×C4—431no—
671C22×C4—431no—
672C22×C4—431no—
673C22×C4—431no—
674C22×C4—431no—
675C22×C4—431no—
676C22×C4—431no—
677C22×C4—861no—
678C22×C4—861no—
679C22×C4—1722no—
680C22×C4—1722no—
681C22×C4C2×C4×D4311yescharacteristic
682C22×C4C2×C4×D4311yescharacteristic
683C22×C4C2×C4×D4311yescharacteristic
684C22×C4C2×C4×D4311yescharacteristic
685C22×C4C2×C4×D4311yescharacteristic
686C22×C4C23×D4311yescharacteristic
687M16—1722no—
688M16—1722no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—861no—
694C2×C8—861no—
695C2×C8—861no—
696C2×C8—861no—
697C2×C8—1722no—
698C2×C8—1722no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—431no—
706C4⋊C4—431no—
707C4⋊C4—431no—
708C4⋊C4—431no—
709C4⋊C4—431no—
710C4⋊C4—431no—
711C4⋊C4—431no—
712C4⋊C4—431no—
713C4⋊C4—861no—
714C4⋊C4—861no—
715C4⋊C4—861no—
716C4⋊C4—861no—
717C4⋊C4—861no—
718C4⋊C4—861no—
719C4⋊C4—861no—
720C4⋊C4—861no—
721C4⋊C4—861no—
722C4⋊C4—861no—
723C4⋊C4—861no—
724C4⋊C4—861no—
725C4⋊C4—861no—
726C4⋊C4—861no—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—431no—
734C22⋊C4—431no—
735C22⋊C4—431no—
736C22⋊C4—431no—
737C22⋊C4—431no—
738C22⋊C4—431no—
739C22⋊C4—431no—
740C22⋊C4—431no—
741C22⋊C4—861no—
742C22⋊C4—861no—
743C22⋊C4—861no—
744C22⋊C4—861no—
745C22⋊C4—861no—
746C22⋊C4—861no—
747C22⋊C4—861no—
748C22⋊C4—861no—
749C22⋊C4—861no—
750C22⋊C4—861no—
751C42—431no—
752C42—431no—
753C42—431no—
754C42—431no—
755C42—861no—
756C42—861no—
757C42—861no—
758C42—861no—
759C42—861no—
760C42—861no—
761C42—861no—
762C42—861no—
763C42—861no—
764C42—861no—
765C42D4×D4311yescharacteristic
766C42D4×D4311yescharacteristic
767C42D4×D4311yescharacteristic
768C42D4×D4311yescharacteristic
769C23—21no—
770C23—21no—
771C23—21no—
772C23—41no—
773C23—41no—
774C23—431no—
775C23—431no—
776C23—861no—
777C23—861no—
778C23—1721no—
779C23—1721no—
780C23C22×C4×D4311yescharacteristic
781Q8—1722no—
782Q8—1722no—
783Q8—1722no—
784Q8—1722no—
785Q8—1722no—
786Q8—1722no—
787D4—1722no—
788D4—1722no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—431no—
801C2×C4—431no—
802C2×C4—431no—
803C2×C4—431no—
804C2×C4—431no—
805C2×C4—431no—
806C2×C4—432no—
807C2×C4—862no—
808C2×C4—862no—
809C2×C4—862no—
810C2×C4—861no—
811C2×C4—861no—
812C2×C4—861no—
813C2×C4—861no—
814C2×C4—861no—
815C2×C4—861no—
816C2×C4—861no—
817C2×C4—861no—
818C2×C4—861no—
819C2×C4—1721no—
820C2×C4—1721no—
821C2×C4—1722no—
822C2×C4—1721no—
823C2×C4—1722no—
824C2×C4—1721no—
825C2×C4—1721no—
826C2×C4C22⋊C4×D4311yescharacteristic
827C2×C4C22⋊C4×D4311yescharacteristic
828C2×C4C22⋊C4×D4311yescharacteristic
829C2×C4C22⋊C4×D4311yescharacteristic
830C2×C4C2×D4×D4311yescharacteristic
831C2×C4C2×D4×D4311yescharacteristic
832C8—41no—
833C8—41no—
834C8—41no—
835C8—41no—
836C8—1721no—
837C8—1721no—
838C8—1721no—
839C8—1721no—
840C22—21no—
841C22—21no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—81no—
846C22—81no—
847C22—861no—
848C22—861no—
849C22—861no—
850C22—861no—
851C22—861no—
852C22—861no—
853C22—3441no—
854C22—3441no—
855C22C2×C22⋊C4×D4311yescharacteristic
856C22#131×D4311yescharacteristic
857C22#1458366411yescharacteristic
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—432no—
868C4—862no—
869C4—861no—
870C4—861no—
871C4—861no—
872C4—861no—
873C4—861no—
874C4—1721no—
875C4—1721no—
876C4—1721no—
877C2—21no—
878C2—21no—
879C2—81no—
880C2—1721no—
881C2—1721no—
882C2#1914304311yescharacteristic
883C2#410×D4311yescharacteristic
884C2#1914307611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1473C2
socleC22×C43C22×C22⋊C4
prime radicalC22×C22⋊D43C2×C4
cosocleC22×C4×C43C24
hypercenter#1473D43
hypocenterC43#17420
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. #19132961C2semidirect
6. #19132961C2semidirect
7. #19132957C2semidirect
8. #19132957C2semidirect
9. #19132938C2semidirect
10. #19132937C2semidirect
12. #19132918C2semidirect
13. #19132917C2semidirect
15. C43×#1473C2semidirect
441. #1473D43semidirect
517. C43#17420semidirect

Maximal subgroups

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

subgroupindex
C2×#145836162
#191432542
#191432482
#191329642
#191329612
#191329572
#191329382
#191329372
#191329302
#191329182
#191329172
#191329102
C43×#14732
#1742043