Finite Group Databasebeta

← #25062900

Subgroups — #25062900

Order 11008.

996 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583603C211yesmaximal, characteristic
2#19143631C211yesmaximal, characteristic
3#19143626C211yesmaximal, characteristic
4#19132959C211yesmaximal, characteristic, complemented
5#19132957C211yesmaximal, characteristic, complemented
6#19132957C211yesmaximal, characteristic, complemented
7#19132949C211yesmaximal, characteristic, complemented
8#19132949C211yesmaximal, characteristic, complemented
9#19132937C211yesmaximal, characteristic, complemented
10#19132924C211yesmaximal, characteristic, complemented
11#19132923C211yesmaximal, characteristic, complemented
12#19132917C211yesmaximal, characteristic, complemented
13C2×#14582624C211yesmaximal, characteristic, complemented
14#324×D43C211yesmaximal, characteristic, complemented
15C43×#1472C211yesmaximal, characteristic, complemented
16#14583603—21no—
17#14583603—21no—
18#14583603—21no—
19#14583603—21no—
20#14583603—21no—
21#14583603—21no—
22#14583603—21no—
23#14583603—21no—
24C2×#13063323C411yescharacteristic
25C2×#13063315C411yescharacteristic
26C2×#13063315C2211yescharacteristic
27C2×#13063303C411yescharacteristic
28C2×#13063303C2211yescharacteristic
29C2×#13063302C411yescharacteristic
30C2×#13063302C411yescharacteristic
31C2×#13063301C411yescharacteristic
32C2×#13063290C2211yescharacteristic
33C2×C4×C22⋊D43C2211yescharacteristic
34C2×(C22⋊D43)⋊C4C411yescharacteristic
35C2×(C22⋊D43)⋊C4C411yescharacteristic
36C22×Dic43⋊C4C2211yescharacteristic
37C2×C4⋊C4×D43C2211yescharacteristic
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#14582625C2211yescharacteristic
59#14582625C2211yescharacteristic
60#14582624C2211yescharacteristic
61#14582624C2211yescharacteristic
62#14582624C2211yescharacteristic
63#14582624C2211yescharacteristic
64#14582624C2211yescharacteristic
65#14582624C2211yescharacteristic
66#14582624C2211yescharacteristic
67#14582624C2211yescharacteristic
68C2×C22⋊Q8×C43C2211yescharacteristic
69C43×#407C2211yescharacteristic
70C2×C22⋊C8×C43C2211yescharacteristic
71C43×#324C2211yescharacteristic
72C43×#324C2211yescharacteristic
73C43×#324C2211yescharacteristic
74C43×#324C2211yescharacteristic
75C22×Dic86C2×C411yescharacteristic
76C22×Dic86C2×C411yescharacteristic
77C22×C22⋊D43C2×C411yescharacteristic
78C23×Dic43C2×C411yescharacteristic
79C23×Dic43C2×C411yescharacteristic
80C22×C4×D43C2×C411yescharacteristic
81C22×C4×D43C2×C411yescharacteristic
82C22×C4×D43C2311yescharacteristic
83C2×#10621877—21no—
84C2×#10621872—21no—
85C2×#10621872—21no—
86C22×C43⋊C8—21no—
87C2×C8×D43—21no—
88C2×C8×D43—21no—
89#13063323—21no—
90#13063323—21no—
91#13063323—21no—
92#13063323—21no—
93#13063315—21no—
94#13063315—21no—
95#13063315—21no—
96#13063315—21no—
97#13063315—21no—
98#13063315—21no—
99#13063315—21no—
100#13063315—21no—
101#13063303—21no—
102#13063303—21no—
103#13063303—21no—
104#13063303—21no—
105#13063303—21no—
106#13063303—21no—
107#13063303—21no—
108#13063303—21no—
109#13063302—21no—
110#13063302—21no—
111#13063302—21no—
112#13063302—21no—
113#13063302—21no—
114#13063302—21no—
115#13063302—21no—
116#13063302—21no—
117#13063301—21no—
118#13063301—21no—
119#13063301—21no—
120#13063301—21no—
121#13063290—21no—
122#13063290—21no—
123#13063290—21no—
124#13063290—21no—
125C4×C22⋊D43D411yescharacteristic
126C4×C22⋊D43D411yescharacteristic
127C4×C22⋊D43D411yescharacteristic
128C4×C22⋊D43D411yescharacteristic
129C4×C22⋊D43D411yescharacteristic
130C4×C22⋊D43D411yescharacteristic
131C4×C22⋊D43D411yescharacteristic
132C4×C22⋊D43D411yescharacteristic
133(C22⋊D43)⋊C4—21no—
134(C22⋊D43)⋊C4—21no—
135(C22⋊D43)⋊C4—21no—
136(C22⋊D43)⋊C4—21no—
137(C22⋊D43)⋊C4—21no—
138(C22⋊D43)⋊C4—21no—
139(C22⋊D43)⋊C4—21no—
140(C22⋊D43)⋊C4—21no—
141C2×C4⋊Dic43C2×C411yescharacteristic
142C2×C4⋊Dic43C2×C411yescharacteristic
143C2×Dic43⋊C4—21no—
144C2×Dic43⋊C4—21no—
145C2×Dic43⋊C4—21no—
146C2×Dic43⋊C4—21no—
147C2×Dic43⋊C4C2×C411yescharacteristic
148C2×Dic43⋊C4C2×C411yescharacteristic
149C2×Dic43⋊C4C2×C411yescharacteristic
150C2×Dic43⋊C4C2×C411yescharacteristic
151C2×Dic43⋊C4C2×C411yescharacteristic
152C2×Dic43⋊C4C2×C411yescharacteristic
153C2×Dic43⋊C4C2×C411yescharacteristic
154C2×Dic43⋊C4C2×C411yescharacteristic
155C2×Dic43⋊C4C2×C411yescharacteristic
156C2×Dic43⋊C4C2311yescharacteristic
157C2×Dic43⋊C4C2311yescharacteristic
158C4⋊C4×D43—21no—
159C4⋊C4×D43—21no—
160C4⋊C4×D43—21no—
161C4⋊C4×D43—21no—
162C2×C22⋊Dic43C2×C411yescharacteristic
163C2×(C2×D43)⋊C4C2×C411yescharacteristic
164C2×(C2×D43)⋊C4C2×C411yescharacteristic
165C2×(C2×D43)⋊C4C2×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×Q8×C43C2×C411yescharacteristic
188C23×C4×C43C2311yescharacteristic
189C2×M16×C43—21no—
190C22×C8×C43—21no—
191C22⋊Q8×C43—21no—
192C22⋊Q8×C43—21no—
193C22⋊Q8×C43—21no—
194C22⋊Q8×C43—21no—
195C2×C4⋊C4×C43C2×C411yescharacteristic
196C2×C4⋊C4×C43C2311yescharacteristic
197C2×C4⋊C4×C43C2311yescharacteristic
198C2×C22⋊C4×C43C2×C411yescharacteristic
199C2×C22⋊C4×C43C2×C411yescharacteristic
200C22⋊C8×C43—21no—
201C22⋊C8×C43—21no—
202C22⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43C2311yescharacteristic
204C22⋊C8×C43C2311yescharacteristic
205C22⋊C8×C43C2311yescharacteristic
206C24×C43C22×C411yescharacteristic
207C23×D43C22×C411yescharacteristic
208C2×Q8×C43—21no—
209C2×Q8×C43—21no—
210C2×Q8×C43—81no—
211C22×C4×C43—81no—
212C22×C4×C43C22×C411yescharacteristic
213C22×C4×C43C22×C411yescharacteristic
214C22×C4×C43C22×C411yescharacteristic
215C22×C4×C43C22×C411yescharacteristic
216C22×C4×C43C22×C411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2411yescharacteristic
222C2×C22⋊D43—24no—
223C2×C22⋊D43C22⋊C411yescharacteristic
224C2×C22⋊D43C22⋊C411yescharacteristic
225C2×C22⋊D43C22⋊C411yescharacteristic
226C2×C22⋊D43C22⋊C411yescharacteristic
227C22×Dic43—22no—
228C22×Dic43—21no—
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43—21no—
232C22×Dic43—41no—
233C22×Dic43—81no—
234C22×Dic43C22×C411yescharacteristic
235C22×Dic43C22×C411yescharacteristic
236C22×Dic43C22×C411yescharacteristic
237C22×Dic43C22×C411yescharacteristic
238C22×Dic43C22×C411yescharacteristic
239C22×Dic43C22×C411yescharacteristic
240C22×Dic43C22×C411yescharacteristic
241C2×C4×D43—22no—
242C2×C4×D43—21no—
243C2×C4×D43—21no—
244C2×C4×D43—21no—
245C2×C4×D43—21no—
246C2×C4×D43—41no—
247C2×C4×D43—81no—
248C2×C4×D43—81no—
249C2×C4×D43C2×D411yescharacteristic
250C2×C4×D43C2×D411yescharacteristic
251C2×C4×D43C2×D411yescharacteristic
252C2×C4×D43C2×D411yescharacteristic
253C2×Dic86—21no—
254C2×Dic86—21no—
255C2×Dic86—22no—
256C2×Dic86—21no—
257C2×Dic86—21no—
258C2×Dic86—41no—
259C2×Dic86—81no—
260M16×C43—81no—
261C2×C8×C43—21no—
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—81no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43—21no—
271C4⋊C4×C43—21no—
272C22⋊C4×C43—21no—
273C22⋊C4×C43—21no—
274C22⋊C4×C43—21no—
275C22⋊C4×C43—21no—
276C22⋊Dic43C22⋊C411yescharacteristic
277C22⋊Dic43C22⋊C411yescharacteristic
278C22⋊Dic43C22⋊C411yescharacteristic
279C22⋊Dic43C22⋊C411yescharacteristic
280(C2×D43)⋊C4—21no—
281(C2×D43)⋊C4—21no—
282(C2×D43)⋊C4—21no—
283(C2×D43)⋊C4—21no—
284(C2×D43)⋊C4C22⋊C411yescharacteristic
285(C2×D43)⋊C4C22⋊C411yescharacteristic
286(C2×D43)⋊C4C22⋊C411yescharacteristic
287(C2×D43)⋊C4C22⋊C411yescharacteristic
288C4⋊Dic43—21no—
289C4⋊Dic43—21no—
290C4⋊Dic43—21no—
291C4⋊Dic43—21no—
292Dic43⋊C4—21no—
293Dic43⋊C4—21no—
294Dic43⋊C4—21no—
295Dic43⋊C4—21no—
296Dic43⋊C4—21no—
297Dic43⋊C4—21no—
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⋊C4—21no—
307Dic43⋊C4—21no—
308Dic43⋊C4—21no—
309Dic43⋊C4—21no—
310Dic43⋊C4—21no—
311Dic43⋊C4—21no—
312Dic43⋊C4C22⋊C411yescharacteristic
313Dic43⋊C4C22⋊C411yescharacteristic
314Dic43⋊C4C22⋊C411yescharacteristic
315Dic43⋊C4C22⋊C411yescharacteristic
316C4×Dic43—21no—
317C4×Dic43—21no—
318C4×Dic43—21no—
319C4×Dic43—21no—
320C4×Dic43C2×D411yescharacteristic
321C4×Dic43C2×D411yescharacteristic
322C4×Dic43C2×D411yescharacteristic
323C4×Dic43C2×D411yescharacteristic
324#10621877—81no—
325C2×C43⋊C8—21no—
326C2×C43⋊C8—21no—
327C2×C43⋊C8—21no—
328C2×C43⋊C8—21no—
329C2×C43⋊C8—81no—
330#10621872—81no—
331#10621872—81no—
332C8×D43—81no—
333C8×D43—81no—
334C23×C43—21no—
335C23×C43—21no—
336C23×C43—22no—
337C23×C43—41no—
338C23×C43C2×C22⋊C411yescharacteristic
339C23×C43C2×C22⋊C411yescharacteristic
340C23×C43C23×C411yescharacteristic
341C22×D43—21no—
342C22×D43—21no—
343C22×D43—22no—
344C22×D43—41no—
345C22×D43C2×C22⋊C411yescharacteristic
346C22×D43C2×C22⋊C411yescharacteristic
347Q8×C43—81no—
348Q8×C43—81no—
349C2×C4×C43—21no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—21no—
353C2×C4×C43—21no—
354C2×C4×C43—21no—
355C2×C4×C43—21no—
356C2×C4×C43—21no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43C2×C22⋊C411yescharacteristic
366C2×C4×C43C2×C22⋊C411yescharacteristic
367C2×C4×C43C22×D411yescharacteristic
368C2×C4×C43C22×D411yescharacteristic
369C22⋊D43—22no—
370C22⋊D43—22no—
371C22⋊D43—22no—
372C22⋊D43#10114yes—
373C2×Dic43—21no—
374C2×Dic43—21no—
375C2×Dic43—21no—
376C2×Dic43—21no—
377C2×Dic43—22no—
378C2×Dic43—21no—
379C2×Dic43—21no—
380C2×Dic43—21no—
381C2×Dic43—21no—
382C2×Dic43—21no—
383C2×Dic43—41no—
384C2×Dic43—42no—
385C2×Dic43—42no—
386C2×Dic43—41no—
387C2×Dic43—41no—
388C2×Dic43—81no—
389C2×Dic43—81no—
390C2×Dic43C2×C22⋊C411yescharacteristic
391C2×Dic43C2×C22⋊C411yescharacteristic
392C2×Dic43C2×C22⋊C411yescharacteristic
393C2×Dic43C2×C22⋊C411yescharacteristic
394C2×Dic43C2×C22⋊C411yescharacteristic
395C2×Dic43C2×C22⋊C411yescharacteristic
396C2×Dic43#13112yes—
397C4×D43—41no—
398C4×D43—41no—
399C4×D43—41no—
400C4×D43—41no—
401C4×D43—42no—
402C4×D43—42no—
403C4×D43—81no—
404C4×D43—81no—
405Dic86—42no—
406Dic86—42no—
407Dic86—81no—
408Dic86—81no—
409C8×C43—41no—
410C8×C43—41no—
411C8×C43—41no—
412C8×C43—41no—
413C43⋊C8—41no—
414C43⋊C8—41no—
415C43⋊C8—41no—
416C43⋊C8—41no—
417#17426—431nomaximal, Sylow
418C22×C43—21no—
419C22×C43—21no—
420C22×C43—21no—
421C22×C43—21no—
422C22×C43—21no—
423C22×C43—21no—
424C22×C43—21no—
425C22×C43—42no—
426C22×C43—42no—
427C22×C43C2×#10112yes—
428C22×C43C22×C22⋊C411yescharacteristic
429C22×C43C2×#13111yescharacteristic
430C22×C43#56811yescharacteristic
431C2×D43—21no—
432C2×D43—21no—
433C2×D43—21no—
434C2×D43—21no—
435C2×D43—21no—
436C2×D43—42no—
437C2×D43—42no—
438C2×D43C2×#10112yes—
439C4×C43—21no—
440C4×C43—21no—
441C4×C43—21no—
442C4×C43—21no—
443C4×C43—41no—
444C4×C43—41no—
445C4×C43—41no—
446C4×C43—41no—
447Dic43—22no—
448Dic43—21no—
449Dic43—21no—
450Dic43—21no—
451Dic43—21no—
452Dic43—21no—
453Dic43—41no—
454Dic43—41no—
455Dic43—41no—
456Dic43C2×#10112yes—
457C2×#554—431no—
458#2974—431no—
459#2974—431no—
460#1472—431no—
461#1472—431no—
462#1472—431no—
463#1472D4311yescharacteristic, complemented
464#1470—431no—
465#1470—431no—
466#1467—431no—
467#1463—431no—
468#1463—431no—
469#1461—431no—
470C2×#324—431no—
471C2×#324—431no—
472C2×C43—21no—
473C2×C43—21no—
474C2×C43—22no—
475C2×C43—41no—
476C2×C43#288011yescharacteristic
477C2×C43#288311yescharacteristic
478C2×C43C22×#10111yescharacteristic
479D43—22no—
480D43—41no—
481#554—861no—
482#554—861no—
483#554—861no—
484#554—861no—
485#554—861no—
486#554—861no—
487#554—861no—
488#554—861no—
489C2×C4⋊Q8—431no—
490C2×#125—431no—
491C2×#125—431no—
492C2×C22⋊Q8—431no—
493C2×C22⋊Q8—431no—
494C2×C22⋊Q8—431no—
495C2×C22⋊Q8—431no—
496C2×C22⋊Q8—431no—
497C2×C22⋊Q8C2×D4311yescharacteristic
498C2×C4×Q8—431no—
499C2×C4×D4—431no—
500C2×C4×D4—431no—
501C2×C4×D4—431no—
502C22×C4⋊C4—431no—
503C22×C4⋊C4—431no—
504#436—861no—
505#436—861no—
506#435—861no—
507#435—861no—
508#435—861no—
509#435—861no—
510C8×D4—861no—
511C8×D4—861no—
512#432—431no—
513#432—431no—
514#431—431no—
515#431—431no—
516#407—431no—
517#407—431no—
518#407—431no—
519#407C2×D4311yescharacteristic
520C2×C22⋊C8—431no—
521C2×C22⋊C8—431no—
522C2×C22⋊C8—431no—
523C2×C22⋊C8C2×D4311yescharacteristic
524#324—431no—
525#324—431no—
526#324—431no—
527#324—431no—
528#324—431no—
529#324—431no—
530#324—431no—
531#324—431no—
532#324—431no—
533#324—431no—
534#324—431no—
535#324—431no—
536#324C2×D4311yescharacteristic
537#324C2×D4311yescharacteristic
538#324C2×D4311yescharacteristic
539#324C2×D4311yescharacteristic
540C43#1742611yescharacteristic, complemented, Sylow
541C22×Q8—431no—
542C22×Q8—431no—
543C22×Q8C4×D4311yescharacteristic
544C22×D4—431no—
545C23×C4—431no—
546C23×C4—431no—
547C23×C4—431no—
548C23×C4—431no—
549C23×C4—431no—
550C23×C4C22×D4311yescharacteristic
551C2×M16—21no—
552C2×M16—861no—
553C2×M16—861no—
554C2×M16—861no—
555C22×C8—21no—
556C22×C8—861no—
557C22×C8—861no—
558C22×C8—861no—
559C4⋊Q8—861no—
560C4⋊Q8—861no—
561C4⋊Q8—861no—
562C4⋊Q8—861no—
563#125—861no—
564#125—861no—
565#125—861no—
566#125—861no—
567#125—861no—
568#125—861no—
569#125—861no—
570#125—861no—
571C22⋊Q8—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—861no—
576C22⋊Q8—861no—
577C22⋊Q8—861no—
578C22⋊Q8—861no—
579C22⋊Q8—861no—
580C22⋊Q8—861no—
581C22⋊Q8—861no—
582C22⋊Q8—861no—
583C22⋊Q8—861no—
584C22⋊Q8—861no—
585C22⋊Q8—861no—
586C22⋊Q8—861no—
587C22⋊Q8—861no—
588C22⋊Q8—861no—
589C22⋊Q8—861no—
590C22⋊Q8—861no—
591C22⋊Q8—861no—
592C22⋊Q8—861no—
593C22⋊Q8—861no—
594C22⋊Q8—861no—
595C4×Q8—861no—
596C4×Q8—861no—
597C4×Q8—861no—
598C4×Q8—861no—
599C4×D4—431no—
600C4×D4—431no—
601C4×D4—431no—
602C4×D4—431no—
603C4×D4—431no—
604C4×D4—431no—
605C4×D4—431no—
606C4×D4—431no—
607C4×D4—861no—
608C4×D4—861no—
609C4×D4—861no—
610C4×D4—861no—
611C4×D4—861no—
612C4×D4—861no—
613C4×D4—861no—
614C4×D4—861no—
615C2×C4⋊C4—431no—
616C2×C4⋊C4—431no—
617C2×C4⋊C4—431no—
618C2×C4⋊C4—431no—
619C2×C4⋊C4—431no—
620C2×C4⋊C4—431no—
621C2×C4⋊C4—431no—
622C2×C4⋊C4—431no—
623C2×C4⋊C4—431no—
624C2×C4⋊C4—431no—
625C2×C4⋊C4—431no—
626C2×C4⋊C4—431no—
627C2×C4⋊C4—431no—
628C2×C4⋊C4—861no—
629C2×C4⋊C4—861no—
630C2×C4⋊C4—861no—
631C2×C4⋊C4—861no—
632C2×C4⋊C4—861no—
633C2×C4⋊C4—861no—
634C2×C4⋊C4—861no—
635C2×C4⋊C4—861no—
636C2×C4⋊C4C4×D4311yescharacteristic
637C2×C4⋊C4C22×D4311yescharacteristic
638C2×C4⋊C4C22×D4311yescharacteristic
639C2×C22⋊C4—431no—
640C2×C22⋊C4—431no—
641C2×C22⋊C4—431no—
642C2×C22⋊C4—431no—
643C2×C22⋊C4C4×D4311yescharacteristic
644C2×C22⋊C4C4×D4311yescharacteristic
645C2×C42—431no—
646C2×C42—431no—
647C2×C42—431no—
648C4⋊C8—861no—
649C4⋊C8—861no—
650C4⋊C8—861no—
651C4⋊C8—861no—
652C22⋊C8—21no—
653C22⋊C8—21no—
654C22⋊C8—431no—
655C22⋊C8—431no—
656C22⋊C8—431no—
657C22⋊C8—431no—
658C22⋊C8—861no—
659C22⋊C8—861no—
660C22⋊C8—861no—
661C22⋊C8—861no—
662C22⋊C8—861no—
663C22⋊C8—861no—
664C22⋊C8C22×D4311yescharacteristic
665C22⋊C8C22×D4311yescharacteristic
666C22⋊C8C22×D4311yescharacteristic
667C22⋊C8C22×D4311yescharacteristic
668#97—861no—
669#97—861no—
670C4×C8—861no—
671C4×C8—861no—
672C24—431no—
673C24C2×C4×D4311yescharacteristic
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—81no—
677C2×Q8—861no—
678C2×Q8—861no—
679C2×Q8—861no—
680C2×Q8—861no—
681C2×Q8—862no—
682C2×Q8—3441no—
683C2×Q8—1721no—
684C2×D4—431no—
685C2×D4—431no—
686C2×D4—431no—
687C2×D4—431no—
688C2×D4—864no—
689C22×C4—81no—
690C22×C4—431no—
691C22×C4—431no—
692C22×C4—431no—
693C22×C4—431no—
694C22×C4—431no—
695C22×C4—431no—
696C22×C4—431no—
697C22×C4—431no—
698C22×C4—431no—
699C22×C4—431no—
700C22×C4—431no—
701C22×C4—862no—
702C22×C4—861no—
703C22×C4—861no—
704C22×C4—861no—
705C22×C4—861no—
706C22×C4—862no—
707C22×C4—861no—
708C22×C4—861no—
709C22×C4—861no—
710C22×C4—861no—
711C22×C4—3441no—
712C22×C4—3441no—
713C22×C4—3441no—
714C22×C4—1721no—
715C22×C4—1721no—
716C22×C4C2×C4×D4311yescharacteristic
717C22×C4C2×C4×D4311yescharacteristic
718C22×C4C2×C4×D4311yescharacteristic
719C22×C4C2×C4×D4311yescharacteristic
720C22×C4C2×C4×D4311yescharacteristic
721C22×C4D4×D4311yescharacteristic
722C22×C4D4×D4311yescharacteristic
723C22×C4D4×D4311yescharacteristic
724C22×C4D4×D4311yescharacteristic
725C22×C4C23×D4311yescharacteristic
726M16—81no—
727M16—3441no—
728M16—3441no—
729M16—3441no—
730C2×C8—21no—
731C2×C8—21no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—81no—
735C2×C8—861no—
736C2×C8—861no—
737C2×C8—861no—
738C2×C8—861no—
739C2×C8—3441no—
740C2×C8—3441no—
741C2×C8—3441no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—431no—
749C4⋊C4—431no—
750C4⋊C4—431no—
751C4⋊C4—431no—
752C4⋊C4—861no—
753C4⋊C4—861no—
754C4⋊C4—861no—
755C4⋊C4—861no—
756C4⋊C4—861no—
757C4⋊C4—861no—
758C4⋊C4—861no—
759C4⋊C4—861no—
760C4⋊C4—861no—
761C4⋊C4—861no—
762C4⋊C4—861no—
763C4⋊C4—861no—
764C4⋊C4—861no—
765C4⋊C4—861no—
766C4⋊C4—861no—
767C4⋊C4—861no—
768C4⋊C4—861no—
769C4⋊C4—861no—
770C4⋊C4—861no—
771C4⋊C4—861no—
772C4⋊C4—861no—
773C4⋊C4—861no—
774C4⋊C4—861no—
775C4⋊C4—861no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—431no—
781C22⋊C4—431no—
782C22⋊C4—431no—
783C22⋊C4—431no—
784C22⋊C4—431no—
785C22⋊C4—431no—
786C22⋊C4—431no—
787C22⋊C4—431no—
788C22⋊C4—861no—
789C22⋊C4—861no—
790C22⋊C4—861no—
791C22⋊C4—861no—
792C42—431no—
793C42—431no—
794C42—431no—
795C42—431no—
796C42—861no—
797C42—861no—
798C42—861no—
799C42—861no—
800C23—22no—
801C23—21no—
802C23—21no—
803C23—41no—
804C23—431no—
805C23—431no—
806C23—862no—
807C23—861no—
808C23—861no—
809C23—1721no—
810C23C22⋊C4×D4311yescharacteristic
811C23C22⋊C4×D4311yescharacteristic
812C23C22×C4×D4311yescharacteristic
813Q8—81no—
814Q8—81no—
815Q8—3441no—
816Q8—3441no—
817Q8—1722no—
818Q8—1722no—
819D4—434no—
820D4—862no—
821D4—862no—
822D4—862no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—431no—
840C2×C4—431no—
841C2×C4—431no—
842C2×C4—431no—
843C2×C4—431no—
844C2×C4—431no—
845C2×C4—432no—
846C2×C4—862no—
847C2×C4—861no—
848C2×C4—861no—
849C2×C4—861no—
850C2×C4—861no—
851C2×C4—861no—
852C2×C4—861no—
853C2×C4—861no—
854C2×C4—861no—
855C2×C4—861no—
856C2×C4—3441no—
857C2×C4—3441no—
858C2×C4—3441no—
859C2×C4—3441no—
860C2×C4—1721no—
861C2×C4—1721no—
862C2×C4—1721no—
863C2×C4—1721no—
864C2×C4—1722no—
865C2×C4—1722no—
866C2×C4—1721no—
867C2×C4—1722no—
868C2×C4—1722no—
869C2×C4—1721no—
870C2×C4—1721no—
871C2×C4C22⋊C4×D4311yescharacteristic
872C2×C4C22⋊C4×D4311yescharacteristic
873C2×C4C2×D4×D4311yescharacteristic
874C2×C4C2×D4×D4311yescharacteristic
875C8—41no—
876C8—41no—
877C8—41no—
878C8—41no—
879C8—1721no—
880C8—1721no—
881C8—1721no—
882C8—1721no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—21no—
887C22—21no—
888C22—21no—
889C22—21no—
890C22—42no—
891C22—42no—
892C22—432no—
893C22—861no—
894C22—861no—
895C22—861no—
896C22—861no—
897C22—861no—
898C22—1722no—
899C22—1722no—
900C22#101×D4312yes—
901C22C2×C22⋊C4×D4311yescharacteristic
902C22#131×D4311yescharacteristic
903C22#1458366411yescharacteristic
904C4—21no—
905C4—21no—
906C4—21no—
907C4—21no—
908C4—41no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—432no—
913C4—862no—
914C4—861no—
915C4—861no—
916C4—861no—
917C4—861no—
918C4—861no—
919C4—1721no—
920C4—1721no—
921C4—1721no—
922C2—21no—
923C2—21no—
924C2—22no—
925C2—41no—
926C2—862no—
927C2—1721no—
928C2#1914304311yescharacteristic
929C2#1914305311yescharacteristic
930C2C2×#101×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1472C2
socleC22×C43C22×C22⋊C4
prime radicalC22×C22⋊D43C2×C4
cosocleC22×C4×C43C24
hypercenter#1472D43
hypocenterC43#17426
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

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

NH ≅ G/Ntype
4. #19132959C2semidirect
5. #19132957C2semidirect
6. #19132957C2semidirect
7. #19132949C2semidirect
8. #19132949C2semidirect
9. #19132937C2semidirect
10. #19132924C2semidirect
11. #19132923C2semidirect
12. #19132917C2semidirect
13. C2×#14582624C2semidirect
14. #324×D43C2semidirect
15. C43×#1472C2semidirect
463. #1472D43semidirect
540. C43#17426semidirect

Maximal subgroups

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

subgroupindex
C2×#145836032
#191436312
#191436262
#191329592
#191329572
#191329492
#191329372
#191329242
#191329232
#191329172
C2×#145826242
#324×D432
C43×#14722
#1742643