Finite Group Databasebeta

← #25062927

Subgroups — #25062927

Order 11008.

1016 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583633C211yesmaximal, characteristic
2#19143631C211yesmaximal, characteristic, complemented
3#19143626C211yesmaximal, characteristic, complemented
4#19132945C211yesmaximal, characteristic, complemented
5#19132945C211yesmaximal, characteristic, complemented
6#19132943C211yesmaximal, characteristic, complemented
7#19132942C211yesmaximal, characteristic, complemented
8#19132942C211yesmaximal, characteristic, complemented
9#19132937C211yesmaximal, characteristic, complemented
10#19132931C211yesmaximal, characteristic, complemented
11#19132930C211yesmaximal, characteristic, complemented
12#19132917C211yesmaximal, characteristic, complemented
13#19132911C211yesmaximal, characteristic, complemented
14#19132910C211yesmaximal, characteristic, complemented
15C43×#1468C211yesmaximal, characteristic, complemented
16#14583633—21no—
17#14583633—21no—
18#14583633—21no—
19#14583633—21no—
20#14583633—21no—
21#14583633—21no—
22#14583633—21no—
23#14583633—21no—
24C2×#13063321C411yescharacteristic
25C2×#13063311C411yescharacteristic
26C2×#13063311C411yescharacteristic
27C2×#13063311C411yescharacteristic
28C2×#13063311C2211yescharacteristic
29C2×#13063310C411yescharacteristic
30C2×#13063310C2211yescharacteristic
31C2×#13063306C411yescharacteristic
32C2×#13063290C411yescharacteristic
33C2×#13063290C2211yescharacteristic
34C2×C4×C22⋊D43C2211yescharacteristic
35C2×C4×C22⋊D43C2211yescharacteristic
36C2×(C22⋊D43)⋊C4C411yescharacteristic
37C2×(C22⋊D43)⋊C4C2211yescharacteristic
38#14582975—21no—
39#14582974—21no—
40#14582973—21no—
41#14582970—21no—
42#14582968—21no—
43#14582967—21no—
44C8×C22⋊D43—21no—
45(C22⋊D43)⋊C8—21no—
46#14582953C2211yescharacteristic
47#14582953C2211yescharacteristic
48#14582949C2211yescharacteristic
49#14582949C2211yescharacteristic
50#14582863C2211yescharacteristic
51#14582861C2211yescharacteristic
52#14582861C2211yescharacteristic
53C2×C22⋊(C43⋊C8)C2211yescharacteristic
54C22⋊C8×D43C2211yescharacteristic
55C22⋊C8×D43C2211yescharacteristic
56#14582625C2211yescharacteristic
57#14582625C2211yescharacteristic
58#14582624C2211yescharacteristic
59#14582624C2211yescharacteristic
60#14582624C2211yescharacteristic
61#14582624C2211yescharacteristic
62#14582623C2211yescharacteristic
63#14582623C2211yescharacteristic
64#14582622C2211yescharacteristic
65#14582622C2211yescharacteristic
66#14582622C2211yescharacteristic
67#14582622C2211yescharacteristic
68C2×#123×C43C2211yescharacteristic
69C43×#407C2211yescharacteristic
70C2×C22⋊C8×C43C2211yescharacteristic
71C43×#324C2211yescharacteristic
72C43×#324C2211yescharacteristic
73C43×#323C2211yescharacteristic
74C43×#323C2211yescharacteristic
75C22×Dic86C2×C411yescharacteristic
76C22×Dic86C2×C411yescharacteristic
77C22×D172C2×C411yescharacteristic
78C22×C22⋊D43C2×C411yescharacteristic
79C22×C22⋊D43C2×C411yescharacteristic
80C22×C22⋊D43C2×C411yescharacteristic
81C22×C22⋊D43C2×C411yescharacteristic
82C23×Dic43C2×C411yescharacteristic
83C22×C4×D43C2×C411yescharacteristic
84C22×C4×D43C2311yescharacteristic
85C2×#10621877—21no—
86C2×#10621872—21no—
87C2×#10621872—21no—
88C22×C43⋊C8—21no—
89C2×C8×D43—21no—
90C2×C8×D43—21no—
91#13063321—21no—
92#13063321—21no—
93#13063321—21no—
94#13063321—21no—
95#13063311—21no—
96#13063311—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#13063311—21no—
106#13063311—21no—
107#13063311—21no—
108#13063311—21no—
109#13063311—21no—
110#13063311—21no—
111#13063310—21no—
112#13063310—21no—
113#13063310—21no—
114#13063310—21no—
115#13063310—21no—
116#13063310—21no—
117#13063310—21no—
118#13063310—21no—
119#13063306—21no—
120#13063306—21no—
121#13063306—21no—
122#13063306—21no—
123#13063290—21no—
124#13063290—21no—
125#13063290—21no—
126#13063290—21no—
127#13063290—21no—
128#13063290—21no—
129#13063290—21no—
130#13063290—21no—
131C4×C22⋊D43—21no—
132C4×C22⋊D43—21no—
133C4×C22⋊D43—21no—
134C4×C22⋊D43—21no—
135C4×C22⋊D43D411yescharacteristic
136C4×C22⋊D43D411yescharacteristic
137C4×C22⋊D43D411yescharacteristic
138C4×C22⋊D43D411yescharacteristic
139C4×C22⋊D43D411yescharacteristic
140C4×C22⋊D43D411yescharacteristic
141C4×C22⋊D43D411yescharacteristic
142C4×C22⋊D43D411yescharacteristic
143(C22⋊D43)⋊C4—21no—
144(C22⋊D43)⋊C4—21no—
145(C22⋊D43)⋊C4—21no—
146(C22⋊D43)⋊C4—21no—
147(C22⋊D43)⋊C4—21no—
148(C22⋊D43)⋊C4—21no—
149(C22⋊D43)⋊C4—21no—
150(C22⋊D43)⋊C4—21no—
151C2×Dic43⋊C4C2×C411yescharacteristic
152C2×Dic43⋊C4C2×C411yescharacteristic
153C2×Dic43⋊C4C2×C411yescharacteristic
154C2×Dic43⋊C4C2311yescharacteristic
155C2×C22⋊Dic43C2×C411yescharacteristic
156C2×C22⋊Dic43C2×C411yescharacteristic
157C2×C22⋊Dic43C2×C411yescharacteristic
158C2×(C2×D43)⋊C4C2×C411yescharacteristic
159C2×(C2×D43)⋊C4C2×C411yescharacteristic
160C2×(C2×D43)⋊C4C2×C411yescharacteristic
161C2×(C2×D43)⋊C4C2×C411yescharacteristic
162C2×(C2×D43)⋊C4C2×C411yescharacteristic
163C2×(C2×D43)⋊C4C2311yescharacteristic
164C2×C4×Dic43C2×C411yescharacteristic
165C2×C4×Dic43C2×C411yescharacteristic
166C2×C4×Dic43C2×C411yescharacteristic
167C2×C4×Dic43C2×C411yescharacteristic
168C2×C4×Dic43C2311yescharacteristic
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(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181(C2×D43)⋊C8—21no—
182(C2×D43)⋊C8—21no—
183#13063235—21no—
184#13063235—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×D43C22×C411yescharacteristic
209C23×D43C22×C411yescharacteristic
210C2×D4×C43—21no—
211C2×D4×C43—21no—
212C2×D4×C43—81no—
213C22×C4×C43—81no—
214C22×C4×C43C22×C411yescharacteristic
215C22×C4×C43C22×C411yescharacteristic
216C22×C4×C43C22×C411yescharacteristic
217C22×C4×C43C22×C411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2411yescharacteristic
223C2×C22⋊D43—21no—
224C2×C22⋊D43—21no—
225C2×C22⋊D43—22no—
226C2×C22⋊D43—22no—
227C2×C22⋊D43—21no—
228C2×C22⋊D43—21no—
229C2×C22⋊D43—21no—
230C2×C22⋊D43—21no—
231C2×C22⋊D43—41no—
232C2×C22⋊D43—41no—
233C2×C22⋊D43—42no—
234C2×C22⋊D43—42no—
235C2×C22⋊D43C22⋊C411yescharacteristic
236C2×C22⋊D43C22⋊C411yescharacteristic
237C2×C22⋊D43C22⋊C411yescharacteristic
238C2×C22⋊D43C22⋊C411yescharacteristic
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—81no—
242C22×Dic43C22×C411yescharacteristic
243C22×Dic43C22×C411yescharacteristic
244C22×Dic43C22×C411yescharacteristic
245C22×Dic43C22×C411yescharacteristic
246C22×Dic43C22×C411yescharacteristic
247C22×Dic43C22×C411yescharacteristic
248C2×D172—21no—
249C2×D172—21no—
250C2×D172—81no—
251C2×C4×D43—21no—
252C2×C4×D43—21no—
253C2×C4×D43—81no—
254C2×C4×D43—81no—
255C2×C4×D43C2×D411yescharacteristic
256C2×C4×D43C2×D411yescharacteristic
257C2×C4×D43C2×D411yescharacteristic
258C2×C4×D43C2×D411yescharacteristic
259C2×Dic86—21no—
260C2×Dic86—21no—
261C2×Dic86—21no—
262C2×Dic86—21no—
263C2×Dic86—22no—
264C2×Dic86—41no—
265C2×Dic86—42no—
266M16×C43—81no—
267C2×C8×C43—21no—
268C2×C8×C43—21no—
269C2×C8×C43—21no—
270C2×C8×C43—21no—
271C2×C8×C43—81no—
272C4⋊C4×C43—21no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43—21no—
275C4⋊C4×C43—21no—
276C22⋊C4×C43—21no—
277C22⋊C4×C43—21no—
278C22⋊C4×C43—21no—
279C22⋊C4×C43—21no—
280C22⋊C4×C43—21no—
281C22⋊C4×C43—21no—
282C22⋊Dic43—21no—
283C22⋊Dic43—21no—
284C22⋊Dic43—21no—
285C22⋊Dic43—21no—
286C22⋊Dic43C22⋊C411yescharacteristic
287C22⋊Dic43C22⋊C411yescharacteristic
288C22⋊Dic43C22⋊C411yescharacteristic
289C22⋊Dic43C22⋊C411yescharacteristic
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—
300(C2×D43)⋊C4C22⋊C411yescharacteristic
301(C2×D43)⋊C4C22⋊C411yescharacteristic
302(C2×D43)⋊C4C22⋊C411yescharacteristic
303(C2×D43)⋊C4C22⋊C411yescharacteristic
304Dic43⋊C4—21no—
305Dic43⋊C4—21no—
306Dic43⋊C4—21no—
307Dic43⋊C4—21no—
308Dic43⋊C4—21no—
309Dic43⋊C4—21no—
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×Dic43—21no—
321C4×Dic43—21no—
322C4×Dic43C2×D411yescharacteristic
323C4×Dic43C2×D411yescharacteristic
324C4×Dic43C2×D411yescharacteristic
325C4×Dic43C2×D411yescharacteristic
326#10621877—81no—
327C2×C43⋊C8—21no—
328C2×C43⋊C8—21no—
329C2×C43⋊C8—21no—
330C2×C43⋊C8—21no—
331C2×C43⋊C8—81no—
332#10621872—81no—
333#10621872—81no—
334C8×D43—81no—
335C8×D43—81no—
336C23×C43—21no—
337C23×C43—21no—
338C23×C43—21no—
339C23×C43—21no—
340C23×C43—21no—
341C23×C43—41no—
342C23×C43—41no—
343C23×C43—41no—
344C23×C43—41no—
345C23×C43C2×C22⋊C411yescharacteristic
346C23×C43C2×C22⋊C411yescharacteristic
347C23×C43C23×C411yescharacteristic
348C22×D43—21no—
349C22×D43—21no—
350C22×D43—21no—
351C22×D43—21no—
352C22×D43—21no—
353C22×D43—41no—
354C22×D43—41no—
355C22×D43—41no—
356C22×D43—41no—
357C22×D43C2×C22⋊C411yescharacteristic
358C22×D43C2×C22⋊C411yescharacteristic
359D4×C43—81no—
360D4×C43—81no—
361C2×C4×C43—21no—
362C2×C4×C43—21no—
363C2×C4×C43—21no—
364C2×C4×C43—21no—
365C2×C4×C43—21no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—41no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—41no—
372C2×C4×C43—41no—
373C2×C4×C43—41no—
374C2×C4×C43C2×C22⋊C411yescharacteristic
375C2×C4×C43C2×C22⋊C411yescharacteristic
376C2×C4×C43C22×D411yescharacteristic
377C2×C4×C43C22×D411yescharacteristic
378C22⋊D43—22no—
379C22⋊D43—22no—
380C22⋊D43—41no—
381C22⋊D43—41no—
382C22⋊D43—42no—
383C22⋊D43—42no—
384C22⋊D43—42no—
385C22⋊D43—42no—
386C22⋊D43—42no—
387C22⋊D43—42no—
388C2×Dic43—21no—
389C2×Dic43—21no—
390C2×Dic43—21no—
391C2×Dic43—21no—
392C2×Dic43—22no—
393C2×Dic43—21no—
394C2×Dic43—21no—
395C2×Dic43—41no—
396C2×Dic43—41no—
397C2×Dic43—41no—
398C2×Dic43—81no—
399C2×Dic43—81no—
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×Dic43#13112yes—
407D172—81no—
408D172—81no—
409C4×D43—41no—
410C4×D43—41no—
411C4×D43—41no—
412C4×D43—41no—
413C4×D43—81no—
414C4×D43—81no—
415Dic86—42no—
416Dic86—42no—
417Dic86—42no—
418Dic86—42no—
419C8×C43—41no—
420C8×C43—41no—
421C8×C43—41no—
422C8×C43—41no—
423C43⋊C8—41no—
424C43⋊C8—41no—
425C43⋊C8—41no—
426C43⋊C8—41no—
427#17429—431nomaximal, Sylow
428C22×C43—21no—
429C22×C43—21no—
430C22×C43—21no—
431C22×C43—21no—
432C22×C43—21no—
433C22×C43—21no—
434C22×C43—21no—
435C22×C43—21no—
436C22×C43—41no—
437C22×C43—41no—
438C22×C43—41no—
439C22×C43—81no—
440C22×C43—81no—
441C22×C43—81no—
442C22×C43—81no—
443C22×C43C22×C22⋊C411yescharacteristic
444C22×C43C2×#13111yescharacteristic
445C22×C43#56811yescharacteristic
446C2×D43—21no—
447C2×D43—21no—
448C2×D43—21no—
449C2×D43—21no—
450C2×D43—21no—
451C2×D43—21no—
452C2×D43—41no—
453C2×D43—41no—
454C2×D43—41no—
455C2×D43—81no—
456C2×D43—81no—
457C2×D43—81no—
458C2×D43—81no—
459C4×C43—21no—
460C4×C43—21no—
461C4×C43—21no—
462C4×C43—21no—
463C4×C43—41no—
464C4×C43—41no—
465C4×C43—41no—
466Dic43—21no—
467Dic43—21no—
468Dic43—22no—
469Dic43—21no—
470Dic43—21no—
471Dic43—21no—
472Dic43—41no—
473Dic43—41no—
474Dic43#41312yes—
475C2×#559—431no—
476#2974—431no—
477#2974—431no—
478#1469—431no—
479#1469—431no—
480#1468—431no—
481#1468—431no—
482#1468—431no—
483#1468D4311yescharacteristic, complemented
484#1467—431no—
485#1465—431no—
486#1465—431no—
487#1461—431no—
488#1459—431no—
489#1459—431no—
490C2×C43—21no—
491C2×C43—21no—
492C2×C43—41no—
493C2×C43—41no—
494C2×C43—81no—
495C2×C43#288011yescharacteristic
496C2×C43#288311yescharacteristic
497C2×C43C2×#41311yescharacteristic
498D43—41no—
499D43—41no—
500D43—81no—
501#559—861no—
502#559—861no—
503#559—861no—
504#559—861no—
505#559—861no—
506#559—861no—
507#559—861no—
508#559—861no—
509C2×#127—431no—
510C2×#124—431no—
511C2×#124—431no—
512C2×#124—431no—
513C2×#124—431no—
514C2×#123—431no—
515C2×#123—431no—
516C2×#123—431no—
517C2×#123C2×D4311yescharacteristic
518C2×C4×Q8—431no—
519C2×C4×Q8—431no—
520C2×C4×D4—431no—
521C2×C4×D4—431no—
522C2×C4×D4—431no—
523C2×C4×D4—431no—
524#436—861no—
525#436—861no—
526#435—861no—
527#435—861no—
528#435—861no—
529#435—861no—
530C8×D4—861no—
531C8×D4—861no—
532#432—431no—
533#432—431no—
534#431—431no—
535#431—431no—
536#407—431no—
537#407—431no—
538#407—431no—
539#407C2×D4311yescharacteristic
540C2×C22⋊C8—431no—
541C2×C22⋊C8—431no—
542C2×C22⋊C8—431no—
543C2×C22⋊C8C2×D4311yescharacteristic
544#324—431no—
545#324—431no—
546#324—431no—
547#324—431no—
548#324—431no—
549#324—431no—
550#324C2×D4311yescharacteristic
551#324C2×D4311yescharacteristic
552#323—431no—
553#323—431no—
554#323—431no—
555#323—431no—
556#323—431no—
557#323—431no—
558#323C2×D4311yescharacteristic
559#323C2×D4311yescharacteristic
560C43#1742911yescharacteristic, complemented, Sylow
561C22×Q8—431no—
562C22×Q8—431no—
563C22×D4—431no—
564C22×D4—431no—
565C22×D4—431no—
566C22×D4—431no—
567C22×D4—431no—
568C22×D4C4×D4311yescharacteristic
569C23×C4—431no—
570C23×C4—431no—
571C23×C4—431no—
572C23×C4C22×D4311yescharacteristic
573C2×M16—21no—
574C2×M16—861no—
575C2×M16—861no—
576C2×M16—861no—
577C22×C8—21no—
578C22×C8—861no—
579C22×C8—861no—
580C22×C8—861no—
581#127—861no—
582#127—861no—
583#127—861no—
584#127—861no—
585#124—861no—
586#124—861no—
587#124—861no—
588#124—861no—
589#124—861no—
590#124—861no—
591#124—861no—
592#124—861no—
593#124—861no—
594#124—861no—
595#124—861no—
596#124—861no—
597#124—861no—
598#124—861no—
599#124—861no—
600#124—861no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—861no—
606#123—861no—
607#123—861no—
608#123—861no—
609#123—861no—
610#123—861no—
611#123—861no—
612#123—861no—
613#123—861no—
614#123—861no—
615#123—861no—
616#123—861no—
617C4×Q8—861no—
618C4×Q8—861no—
619C4×Q8—861no—
620C4×Q8—861no—
621C4×Q8—861no—
622C4×Q8—861no—
623C4×Q8—861no—
624C4×Q8—861no—
625C4×D4—431no—
626C4×D4—431no—
627C4×D4—431no—
628C4×D4—431no—
629C4×D4—431no—
630C4×D4—431no—
631C4×D4—431no—
632C4×D4—431no—
633C4×D4—861no—
634C4×D4—861no—
635C4×D4—861no—
636C4×D4—861no—
637C4×D4—861no—
638C4×D4—861no—
639C4×D4—861no—
640C4×D4—861no—
641C4×D4—861no—
642C4×D4—861no—
643C4×D4—861no—
644C4×D4—861no—
645C2×C4⋊C4—431no—
646C2×C4⋊C4—431no—
647C2×C4⋊C4—431no—
648C2×C4⋊C4—431no—
649C2×C4⋊C4C4×D4311yescharacteristic
650C2×C4⋊C4C22×D4311yescharacteristic
651C2×C22⋊C4—431no—
652C2×C22⋊C4—431no—
653C2×C22⋊C4—431no—
654C2×C22⋊C4—431no—
655C2×C22⋊C4—431no—
656C2×C22⋊C4—431no—
657C2×C22⋊C4—431no—
658C2×C22⋊C4—431no—
659C2×C22⋊C4—431no—
660C2×C22⋊C4C4×D4311yescharacteristic
661C2×C22⋊C4C4×D4311yescharacteristic
662C2×C22⋊C4C22×D4311yescharacteristic
663C2×C42—431no—
664C2×C42—431no—
665C2×C42—431no—
666C2×C42—431no—
667C2×C42—431no—
668C4⋊C8—861no—
669C4⋊C8—861no—
670C4⋊C8—861no—
671C4⋊C8—861no—
672C22⋊C8—21no—
673C22⋊C8—21no—
674C22⋊C8—431no—
675C22⋊C8—431no—
676C22⋊C8—431no—
677C22⋊C8—431no—
678C22⋊C8—861no—
679C22⋊C8—861no—
680C22⋊C8—861no—
681C22⋊C8—861no—
682C22⋊C8—861no—
683C22⋊C8—861no—
684C22⋊C8C22×D4311yescharacteristic
685C22⋊C8C22×D4311yescharacteristic
686C22⋊C8C22×D4311yescharacteristic
687C22⋊C8C22×D4311yescharacteristic
688#97—861no—
689#97—861no—
690C4×C8—861no—
691C4×C8—861no—
692C24—431no—
693C24—431no—
694C24C2×C4×D4311yescharacteristic
695C24C2×C4×D4311yescharacteristic
696C2×Q8—861no—
697C2×Q8—861no—
698C2×Q8—861no—
699C2×Q8—861no—
700C2×Q8—862no—
701C2×Q8—1721no—
702C2×Q8—1722no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—81no—
706C2×D4—431no—
707C2×D4—431no—
708C2×D4—431no—
709C2×D4—431no—
710C2×D4—861no—
711C2×D4—861no—
712C2×D4—861no—
713C2×D4—861no—
714C2×D4—862no—
715C2×D4—862no—
716C2×D4—861no—
717C2×D4—861no—
718C2×D4—861no—
719C2×D4—861no—
720C2×D4—3441no—
721C2×D4—1722no—
722C2×D4—1721no—
723C2×D4—1721no—
724C2×D4—1722no—
725C22×C4—81no—
726C22×C4—431no—
727C22×C4—431no—
728C22×C4—431no—
729C22×C4—431no—
730C22×C4—431no—
731C22×C4—431no—
732C22×C4—431no—
733C22×C4—431no—
734C22×C4—431no—
735C22×C4—431no—
736C22×C4—861no—
737C22×C4—861no—
738C22×C4—861no—
739C22×C4—861no—
740C22×C4—3441no—
741C22×C4—3441no—
742C22×C4—3441no—
743C22×C4C2×C4×D4311yescharacteristic
744C22×C4C2×C4×D4311yescharacteristic
745C22×C4C2×C4×D4311yescharacteristic
746C22×C4C2×C4×D4311yescharacteristic
747C22×C4D4×D4311yescharacteristic
748C22×C4D4×D4311yescharacteristic
749C22×C4D4×D4311yescharacteristic
750C22×C4D4×D4311yescharacteristic
751C22×C4C23×D4311yescharacteristic
752M16—81no—
753M16—3441no—
754M16—3441no—
755M16—3441no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C2×C8—861no—
762C2×C8—861no—
763C2×C8—861no—
764C2×C8—861no—
765C2×C8—3441no—
766C2×C8—3441no—
767C2×C8—3441no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—431no—
773C4⋊C4—431no—
774C4⋊C4—431no—
775C4⋊C4—431no—
776C4⋊C4—861no—
777C4⋊C4—861no—
778C4⋊C4—861no—
779C4⋊C4—861no—
780C4⋊C4—861no—
781C4⋊C4—861no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—431no—
789C22⋊C4—431no—
790C22⋊C4—431no—
791C22⋊C4—431no—
792C22⋊C4—431no—
793C22⋊C4—431no—
794C22⋊C4—431no—
795C22⋊C4—431no—
796C22⋊C4—861no—
797C22⋊C4—861no—
798C22⋊C4—861no—
799C22⋊C4—861no—
800C22⋊C4—861no—
801C22⋊C4—861no—
802C22⋊C4—861no—
803C22⋊C4—861no—
804C22⋊C4—861no—
805C22⋊C4—861no—
806C22⋊C4—861no—
807C22⋊C4—861no—
808C22⋊C4—861no—
809C22⋊C4—861no—
810C42—431no—
811C42—431no—
812C42—431no—
813C42—431no—
814C42—861no—
815C42—861no—
816C42—861no—
817C42—861no—
818C42—861no—
819C42—861no—
820C42—861no—
821C42—861no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—431no—
832C23—431no—
833C23—861no—
834C23—861no—
835C23—861no—
836C23—861no—
837C23—861no—
838C23—1721no—
839C23—1721no—
840C23—1721no—
841C23—1721no—
842C23C22⋊C4×D4311yescharacteristic
843C23C22⋊C4×D4311yescharacteristic
844C23C22×C4×D4311yescharacteristic
845Q8—1722no—
846Q8—1722no—
847Q8—1722no—
848Q8—1722no—
849D4—81no—
850D4—81no—
851D4—862no—
852D4—862no—
853D4—3441no—
854D4—3441no—
855D4—1722no—
856D4—1721no—
857D4—1721no—
858D4—1722no—
859D4—1722no—
860D4—1722no—
861D4—1722no—
862D4—1722no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—431no—
877C2×C4—431no—
878C2×C4—431no—
879C2×C4—431no—
880C2×C4—431no—
881C2×C4—431no—
882C2×C4—432no—
883C2×C4—862no—
884C2×C4—861no—
885C2×C4—861no—
886C2×C4—861no—
887C2×C4—861no—
888C2×C4—861no—
889C2×C4—861no—
890C2×C4—3441no—
891C2×C4—3441no—
892C2×C4—3441no—
893C2×C4—3441no—
894C2×C4—1721no—
895C2×C4—1721no—
896C2×C4—1721no—
897C2×C4—1721no—
898C2×C4—1721no—
899C2×C4—1721no—
900C2×C4—1721no—
901C2×C4C22⋊C4×D4311yescharacteristic
902C2×C4C22⋊C4×D4311yescharacteristic
903C2×C4C2×D4×D4311yescharacteristic
904C2×C4C2×D4×D4311yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C8—1721no—
910C8—1721no—
911C8—1721no—
912C8—1721no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—861no—
929C22—861no—
930C22—861no—
931C22—861no—
932C22—861no—
933C22—861no—
934C22—3441no—
935C22—3441no—
936C22—3441no—
937C22—3441no—
938C22—1721no—
939C22—1721no—
940C22—1721no—
941C22C2×C22⋊C4×D4311yescharacteristic
942C22#131×D4311yescharacteristic
943C22#1458366411yescharacteristic
944C4—21no—
945C4—21no—
946C4—21no—
947C4—21no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—432no—
952C4—862no—
953C4—861no—
954C4—861no—
955C4—861no—
956C4—861no—
957C4—861no—
958C4—1721no—
959C4—1721no—
960C2—21no—
961C2—21no—
962C2—41no—
963C2—41no—
964C2—81no—
965C2—3441no—
966C2—1721no—
967C2—1721no—
968C2#1914304311yescharacteristic
969C2#1914305311yescharacteristic
970C2#413×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1468C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063321C4
cosocleC22×C4×C43C24
hypercenter#1468D43
hypocenterC43#17429
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. #19143631C2semidirect
3. #19143626C2semidirect
4. #19132945C2semidirect
5. #19132945C2semidirect
6. #19132943C2semidirect
7. #19132942C2semidirect
8. #19132942C2semidirect
9. #19132937C2semidirect
10. #19132931C2semidirect
11. #19132930C2semidirect
12. #19132917C2semidirect
13. #19132911C2semidirect
14. #19132910C2semidirect
15. C43×#1468C2semidirect
483. #1468D43semidirect
560. C43#17429semidirect

Maximal subgroups

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

subgroupindex
C2×#145836332
#191436312
#191436262
#191329452
#191329432
#191329422
#191329372
#191329312
#191329302
#191329172
#191329112
#191329102
C43×#14682
#1742943