Finite Group Databasebeta

← #25107698

Subgroups — #25107698

Order 11008.

1156 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582974C211yesmaximal, characteristic, complemented
2C2×#14582862C211yesmaximal, characteristic, complemented
3C4×#13063295C211yesmaximal, characteristic
4#19135392C211yesmaximal, characteristic, complemented
5#19135388C211yesmaximal, characteristic, complemented
6#19135206C211yesmaximal, characteristic, complemented
7#19135200C211yesmaximal, characteristic, complemented
8#19135200C211yesmaximal, characteristic, complemented
9#19135199C211yesmaximal, characteristic, complemented
10#19134892C211yesmaximal, characteristic, complemented
11#19134891C211yesmaximal, characteristic, complemented
12#19134891C211yesmaximal, characteristic, complemented
13#19134504C211yesmaximal, characteristic, complemented
14#19134379C211yesmaximal, characteristic, complemented
15C43×#1851C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C22×#10621872C2211yescharacteristic, complemented
19C2×#13063295C411yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22C2×C4×C22⋊D43C2211yescharacteristic
23#14582974—24no—
24C2×Dic43⋊C8C2211yescharacteristic, complemented
25#14582862—24no—
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33C2×(C2×D43)⋊C8C2211yescharacteristic
34C2×(C2×D43)⋊C8C2211yescharacteristic
35C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
36C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
37C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
38C2×#13063236C2211yescharacteristic, complemented
39C2×C4×C43⋊C8C2211yescharacteristic, complemented
40C2×C8×Dic43C2211yescharacteristic, complemented
41#14582777C411yescharacteristic
42#14582777C411yescharacteristic
43#14582776C411yescharacteristic
44#14582774C411yescharacteristic
45#14582773C411yescharacteristic
46#14582773C411yescharacteristic
47#14582754C411yescharacteristic
48C4×(C2×D43)⋊C4C2211yescharacteristic
49C4×(C2×D43)⋊C4C2211yescharacteristic
50#14582654C2211yescharacteristic, complemented
51#14582654C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53#14582653C2211yescharacteristic, complemented
54C22×M16×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic, complemented
56C2×C4⋊C8×C43C2211yescharacteristic, complemented
57C2×C22⋊C8×C43C2211yescharacteristic
58C4×C22⋊C4×C43C2211yescharacteristic
59C43×#336C2211yescharacteristic, complemented
60C43×#336C2211yescharacteristic, complemented
61C24×D43C2×C411yescharacteristic
62C22×D172C2×C411yescharacteristic
63C22×D172C2×C411yescharacteristic
64C22×C22⋊D43C2×C411yescharacteristic
65C23×Dic43C2×C411yescharacteristic
66C22×C4×D43—22no—
67C22×C4×D43—22no—
68C22×C4×D43—41no—
69C22×C4×D43—41no—
70C22×C4×D43—41no—
71C22×C4×D43—41no—
72C22×C4×D43C2×C411yescharacteristic
73C22×C4×D43C2×C411yescharacteristic
74C22×C4×D43C2311yescharacteristic
75C22×C4×D43C2311yescharacteristic
76C22×C4×D43C2311yescharacteristic
77C2×#10621877—41no—
78C2×#10621877—41no—
79C2×#10621877D414yescomplemented
80C2×#10621872—22no—
81C2×#10621872—41no—
82C2×#10621872—41no—
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87#13063295—24no—
88C4×D172—41no—
89C4×D172—41no—
90C4×D172—41no—
91C4×D172—41no—
92C4×C22⋊D43—22no—
93C4×C22⋊D43—22no—
94C2×C4⋊Dic43C2×C411yescharacteristic
95C2×C4⋊Dic43C2×C411yescharacteristic
96C2×Dic43⋊C4C2×C411yescharacteristic
97C2×C22⋊Dic43C2×C411yescharacteristic
98C2×(C2×D43)⋊C4C2×C411yescharacteristic
99C2×(C2×D43)⋊C4C2×C411yescharacteristic
100C2×(C2×D43)⋊C4C2×C411yescharacteristic
101C2×(C2×D43)⋊C4C2×C411yescharacteristic
102C2×(C2×D43)⋊C4C2×C411yescharacteristic
103C2×(C2×D43)⋊C4C2×C411yescharacteristic
104C2×(C2×D43)⋊C4C2×C411yescharacteristic
105C2×(C2×D43)⋊C4C2×C411yescharacteristic
106C2×(C2×D43)⋊C4C2×C411yescharacteristic
107C2×C4×Dic43C2311yescharacteristic
108Dic43⋊C8—22no—
109C22⋊(C43⋊C8)—22no—
110(C2×D43)⋊C8—22no—
111(C2×D43)⋊C8—22no—
112(C2×D43)⋊C8—22no—
113(C2×D43)⋊C8—22no—
114(C2×D43)⋊C8—22no—
115(C2×D43)⋊C8—41no—
116(C2×D43)⋊C8—41no—
117(C2×D43)⋊C8—41no—
118(C2×D43)⋊C8—41no—
119(C2×D43)⋊C8—41no—
120(C2×D43)⋊C8—41no—
121#13063236—41no—
122C4×C43⋊C8—41no—
123C8×Dic43—22no—
124C43⋊#95C2×C411yescharacteristic
125C43⋊#95C2×C411yescharacteristic
126C43⋊#95C2×C411yescharacteristic
127C43⋊#95C2×C411yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C2×M16×C43—22no—
130C2×M16×C43—41no—
131C2×M16×C43—41no—
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C22×C8×C43C2311yescharacteristic
136C2×C22⋊C4×C43C2×C411yescharacteristic
137C2×C22⋊C4×C43C2×C411yescharacteristic
138C2×C42×C43C2311yescharacteristic
139C2×C42×C43C2311yescharacteristic
140C4⋊C8×C43—41no—
141C4⋊C8×C43—41no—
142C22⋊C8×C43—22no—
143#95×C43C2×C411yescharacteristic
144#95×C43C2×C411yescharacteristic
145C24×C43C22×C411yescharacteristic
146C23×D43—22no—
147C23×D43—22no—
148C23×D43—22no—
149C23×D43—41no—
150C23×D43—41no—
151C23×D43—41no—
152C23×D43—41no—
153C23×D43C22×C411yescharacteristic
154C23×D43C22×C411yescharacteristic
155C23×D43C22×C411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43C22×C411yescharacteristic
161C22×C4×C43C22×C411yescharacteristic
162C22×C4×C43C22×C411yescharacteristic
163C22×C4×C43C22×C411yescharacteristic
164C22×C4×C43C22×C411yescharacteristic
165C22×C4×C43C2×D412yes—
166C22×C4×C43#4112yes—
167C22×C4×C43C2411yescharacteristic
168C2×C22⋊D43—22no—
169C2×C22⋊D43—22no—
170C2×C22⋊D43—41no—
171C22×Dic43—22no—
172C22×Dic43—41no—
173C22×Dic43—41no—
174C22×Dic43C22×C411yescharacteristic
175C22×Dic43C22×C411yescharacteristic
176C22×Dic43C22×C411yescharacteristic
177C22×Dic43C22×C411yescharacteristic
178C22×Dic43C22×C411yescharacteristic
179C2×D172—22no—
180C2×D172—22no—
181C2×D172—22no—
182C2×D172—41no—
183C2×D172—41no—
184C2×D172—41no—
185C2×C4×D43—22no—
186C2×C4×D43—22no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×C4×D43—21no—
193C2×C4×D43—21no—
194C2×C4×D43—21no—
195C2×C4×D43—21no—
196C2×C4×D43—21no—
197C2×C4×D43—21no—
198C2×C4×D43—21no—
199C2×C4×D43—21no—
200C2×C4×D43—21no—
201C2×C4×D43—21no—
202C2×C4×D43—21no—
203C2×C4×D43—21no—
204C2×C4×D43—21no—
205C2×C4×D43—41no—
206C2×C4×D43—41no—
207C2×C4×D43—41no—
208C2×C4×D43—41no—
209C2×C4×D43—44no—
210C2×C4×D43—44no—
211C2×C4×D43—44no—
212C2×C4×D43—44no—
213M16×C43—44no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—21no—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C22⋊C4×C43—22no—
227C22⋊C4×C43—41no—
228C42×C43—21no—
229C42×C43—21no—
230C42×C43—21no—
231C42×C43—21no—
232C22⋊Dic43—22no—
233(C2×D43)⋊C4—22no—
234(C2×D43)⋊C4—22no—
235(C2×D43)⋊C4—22no—
236(C2×D43)⋊C4—41no—
237(C2×D43)⋊C4—41no—
238(C2×D43)⋊C4—41no—
239(C2×D43)⋊C4—41no—
240(C2×D43)⋊C4—41no—
241(C2×D43)⋊C4M1614yescomplemented
242C4⋊Dic43—41no—
243C4⋊Dic43—41no—
244Dic43⋊C4—22no—
245C4×Dic43—21no—
246C4×Dic43—21no—
247#10621877—44no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8C2×D412yes—
259C2×C43⋊C8C2×D412yes—
260#10621872—44no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43C4×D412yes—
268C23×C43C23×C411yescharacteristic
269C22×D43—21no—
270C22×D43—21no—
271C22×D43—21no—
272C22×D43—21no—
273C22×D43—21no—
274C22×D43—21no—
275C22×D43—21no—
276C22×D43—21no—
277C22×D43—21no—
278C22×D43—21no—
279C22×D43—21no—
280C22×D43—21no—
281C22×D43—21no—
282C22×D43—21no—
283C22×D43—21no—
284C22×D43—21no—
285C22×D43—21no—
286C22×D43—21no—
287C22×D43—21no—
288C22×D43—44no—
289C22×D43—44no—
290C22×D43—44no—
291C22×D43—44no—
292C22×D43—44no—
293C22×D43—44no—
294C22×D43—44no—
295C22×D43C2×M1612yes—
296C22×D43#13112yes—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43C4×D412yes—
315C2×C4×C43C2×M1612yes—
316C2×C4×C43C22×D411yescharacteristic
317C2×C4×C43C2×#4111yescharacteristic
318C2×C4×C43H(5,𝔽2)11yescharacteristic
319C2×C4×C43H(5,𝔽2)11yescharacteristic
320C2×C4×C43H(5,𝔽2)11yescharacteristic
321C2×C4×C43H(5,𝔽2)11yescharacteristic
322C22⋊D43—44no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—21no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43—21no—
329C2×Dic43—21no—
330C2×Dic43—21no—
331C2×Dic43—21no—
332C2×Dic43—21no—
333C2×Dic43—21no—
334C2×Dic43—21no—
335C2×Dic43—21no—
336C2×Dic43—21no—
337C2×Dic43—44no—
338C2×Dic43C2×M1612yes—
339D172—44no—
340D172—44no—
341C4×D43—44no—
342C4×D43—44no—
343C4×D43—41no—
344C4×D43—41no—
345C4×D43—41no—
346C4×D43—41no—
347C4×D43—41no—
348C4×D43—41no—
349C4×D43—41no—
350C4×D43—41no—
351C4×D43—41no—
352C4×D43—41no—
353C4×D43—41no—
354C4×D43—41no—
355C8×C43—41no—
356C8×C43—41no—
357C8×C43—41no—
358C8×C43—41no—
359C43⋊C8—22no—
360C43⋊C8—22no—
361C43⋊C8—41no—
362C43⋊C8—41no—
363#22038—431nomaximal, Sylow
364C22×C43—22no—
365C22×C43—22no—
366C22×C43—22no—
367C22×C43—41no—
368C22×C43—41no—
369C22×C43—41no—
370C22×C43—41no—
371C22×C43C2×C4×D411yescharacteristic
372C22×C43#51811yescharacteristic
373C22×C43#51811yescharacteristic
374C22×C43C22×M1611yescharacteristic
375C22×C43C2×#13111yescharacteristic
376C22×C43#56811yescharacteristic
377C22×C43#56811yescharacteristic
378C2×D43—22no—
379C2×D43—22no—
380C2×D43—22no—
381C2×D43—22no—
382C2×D43—22no—
383C2×D43—22no—
384C2×D43—416no—
385C2×D43—41no—
386C2×D43—41no—
387C2×D43—41no—
388C2×D43—41no—
389C2×D43—41no—
390C2×D43—41no—
391C2×D43—41no—
392C2×D43—41no—
393C2×D43—41no—
394C2×D43—41no—
395C2×D43—41no—
396C2×D43—41no—
397C2×D43—41no—
398C2×D43—41no—
399C2×D43—41no—
400C4×C43—22no—
401C4×C43—22no—
402C4×C43—41no—
403C4×C43—41no—
404C4×C43—41no—
405C4×C43#53411yescharacteristic
406C4×C43#53511yescharacteristic
407C4×C43#53811yescharacteristic
408C4×C43#53811yescharacteristic
409Dic43—22no—
410Dic43—41no—
411Dic43—41no—
412Dic43—41no—
413Dic43—41no—
414C2×#436—431no—
415C2×#407—431no—
416C4×#120—431no—
417#1955—431no—
418#1954—431no—
419#1924—431no—
420#1923—431no—
421#1923—431no—
422#1923—431no—
423#1870—431no—
424#1870—431no—
425#1870—431no—
426#1851D4311yescharacteristic, complemented
427#1779—431no—
428#1753—431no—
429C2×C43—42no—
430C2×C43#232111yescharacteristic
431C2×C43#293311yescharacteristic
432C2×C43D4×M1611yescharacteristic
433C2×C43#297411yescharacteristic
434C2×C43#297511yescharacteristic
435C2×C43#297611yescharacteristic
436C2×C43#297811yescharacteristic
437D43—42no—
438D43—42no—
439D43—81no—
440C24×C4—431no—
441C22×M16—431no—
442C22×M16—431no—
443C22×M16C2×D4311yescharacteristic
444C2×#120—431no—
445C2×C4×D4—431no—
446C2×C4×D4—431no—
447C2×C4×D4—431no—
448#436—864no—
449C2×C4⋊C8—431no—
450C2×C4⋊C8C2×D4311yescharacteristic, complemented
451C2×C4⋊C8C2×D4311yescharacteristic, complemented
452#407—864no—
453C2×C22⋊C8—431no—
454C2×C22⋊C8—431no—
455C2×C22⋊C8—431no—
456C2×C22⋊C8—431no—
457C2×C22⋊C8—431no—
458C2×C22⋊C8—431no—
459C2×C22⋊C8—431no—
460C2×C22⋊C8—431no—
461C2×C22⋊C8—431no—
462C2×C22⋊C8—431no—
463C2×C22⋊C8—431no—
464C2×C22⋊C8—431no—
465C2×C22⋊C8C2×D4311yescharacteristic
466C2×#97—431no—
467C2×C4×C8—431no—
468C2×C4×C8—431no—
469#386—431no—
470#386—431no—
471#386—431no—
472#385—431no—
473#385—431no—
474#385—431no—
475#379—431no—
476C4×C22⋊C4—431no—
477C4×C22⋊C4—431no—
478C4×C22⋊C4C2×D4311yescharacteristic
479#336—431no—
480#336—431no—
481#336—431no—
482#336—431no—
483#336C2×D4311yescharacteristic, complemented
484#336C2×D4311yescharacteristic, complemented
485C43#2203811yescharacteristic, complemented, Sylow
486C25—431no—
487C22×D4—431no—
488C22×D4—431no—
489C22×D4—431no—
490C23×C4—431no—
491C23×C4—431no—
492C23×C4—431no—
493C23×C4—431no—
494C23×C4—431no—
495C23×C4—431no—
496C23×C4—862no—
497C23×C4—862no—
498C23×C4—1721no—
499C23×C4—1721no—
500C23×C4—1721no—
501C23×C4—1721no—
502C23×C4C22×D4311yescharacteristic
503C2×M16—22no—
504C2×M16—41no—
505C2×M16—41no—
506C2×M16—434no—
507C2×M16—862no—
508C2×M16—1721no—
509C2×M16—1721no—
510C2×M16—1721no—
511C2×M16—1721no—
512C22×C8—431no—
513C22×C8—431no—
514C22×C8—431no—
515C22×C8—431no—
516C22×C8C22×D4311yescharacteristic
517C22×C8C22×D4311yescharacteristic
518C22×C8C22×D4311yescharacteristic
519C22×C8C22×D4311yescharacteristic
520#120—864no—
521C4×D4—862no—
522C4×D4—862no—
523C4×D4—1721no—
524C4×D4—1721no—
525C4×D4—1721no—
526C4×D4—1721no—
527C2×C4⋊C4—431no—
528C2×C4⋊C4—431no—
529C2×C4⋊C4—431no—
530C2×C22⋊C4—431no—
531C2×C22⋊C4—431no—
532C2×C22⋊C4—431no—
533C2×C22⋊C4—431no—
534C2×C22⋊C4—431no—
535C2×C22⋊C4—431no—
536C2×C22⋊C4—431no—
537C2×C22⋊C4—431no—
538C2×C22⋊C4—431no—
539C2×C22⋊C4—431no—
540C2×C22⋊C4C4×D4311yescharacteristic
541C2×C22⋊C4C4×D4311yescharacteristic
542C2×C42—431no—
543C2×C42C22×D4311yescharacteristic
544C2×C42C22×D4311yescharacteristic
545C4⋊C8—41no—
546C4⋊C8—41no—
547C4⋊C8—862no—
548C22⋊C8—22no—
549C22⋊C8—862no—
550C22⋊C8—862no—
551C22⋊C8—862no—
552C22⋊C8—862no—
553C22⋊C8—862no—
554C22⋊C8—862no—
555C22⋊C8—1721no—
556C22⋊C8—1721no—
557C22⋊C8—1721no—
558C22⋊C8—1721no—
559C22⋊C8—1721no—
560C22⋊C8—1721no—
561#97—1721no—
562C4×C8—862no—
563C4×C8—1721no—
564#95—431no—
565#95—431no—
566#95—431no—
567#95—431no—
568#95C4×D4311yescharacteristic
569#95C4×D4311yescharacteristic
570C24—431no—
571C24—431no—
572C24—431no—
573C24—862no—
574C24—862no—
575C24—862no—
576C24—1721no—
577C24—1721no—
578C24—1721no—
579C24—1721no—
580C24C2×C4×D4311yescharacteristic
581C2×D4—862no—
582C2×D4—862no—
583C2×D4—862no—
584C2×D4—862no—
585C2×D4—862no—
586C2×D4—1721no—
587C2×D4—1721no—
588C2×D4—1721no—
589C2×D4—1721no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—431no—
595C22×C4—431no—
596C22×C4—431no—
597C22×C4—431no—
598C22×C4—431no—
599C22×C4—862no—
600C22×C4—862no—
601C22×C4—862no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4—861no—
605C22×C4—861no—
606C22×C4—861no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—861no—
614C22×C4—861no—
615C22×C4—861no—
616C22×C4—861no—
617C22×C4—861no—
618C22×C4—861no—
619C22×C4—861no—
620C22×C4—1721no—
621C22×C4—1721no—
622C22×C4—1721no—
623C22×C4—1721no—
624C22×C4—1724no—
625C22×C4—1724no—
626C22×C4—1724no—
627C22×C4—1724no—
628C22×C4—1721no—
629C22×C4—1721no—
630C22×C4C2×C4×D4311yescharacteristic
631C22×C4C2×C4×D4311yescharacteristic
632C22×C4C2×C4×D4311yescharacteristic
633C22×C4C2×C4×D4311yescharacteristic
634C22×C4C2×C4×D4311yescharacteristic
635C22×C4D4×D4312yes—
636C22×C4#1062190212yes—
637C22×C4C23×D4311yescharacteristic
638M16—44no—
639M16—1724no—
640M16—1724no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—432no—
654C2×C8—432no—
655C2×C8—861no—
656C2×C8—861no—
657C2×C8—861no—
658C2×C8—861no—
659C2×C8—861no—
660C2×C8—861no—
661C2×C8—861no—
662C2×C8—861no—
663C2×C8—861no—
664C2×C8—861no—
665C4⋊C4—862no—
666C4⋊C4—1721no—
667C4⋊C4—1721no—
668C22⋊C4—22no—
669C22⋊C4—41no—
670C22⋊C4—434no—
671C22⋊C4—862no—
672C22⋊C4—862no—
673C22⋊C4—862no—
674C22⋊C4—862no—
675C22⋊C4—1721no—
676C22⋊C4—1721no—
677C22⋊C4—1721no—
678C22⋊C4—1721no—
679C22⋊C4—1721no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—861no—
685C42—861no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—432no—
693C23—432no—
694C23—861no—
695C23—861no—
696C23—861no—
697C23—861no—
698C23—861no—
699C23—861no—
700C23—861no—
701C23—861no—
702C23—861no—
703C23—861no—
704C23—861no—
705C23—861no—
706C23—861no—
707C23—861no—
708C23—861no—
709C23—861no—
710C23—861no—
711C23—861no—
712C23—861no—
713C23—1724no—
714C23—1724no—
715C23—1724no—
716C23—1724no—
717C23—1724no—
718C23—1724no—
719C23—1724no—
720C23#1306328712yes—
721C23C22×C4×D4311yescharacteristic
722D4—1724no—
723D4—1724no—
724D4—1724no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—432no—
743C2×C4—861no—
744C2×C4—861no—
745C2×C4—861no—
746C2×C4—861no—
747C2×C4—861no—
748C2×C4—861no—
749C2×C4—861no—
750C2×C4—861no—
751C2×C4—861no—
752C2×C4—861no—
753C2×C4—861no—
754C2×C4—861no—
755C2×C4—861no—
756C2×C4—861no—
757C2×C4—1724no—
758C2×C4—1724no—
759C2×C4—1724no—
760C2×C4—1721no—
761C2×C4—1721no—
762C2×C4—1721no—
763C2×C4—1721no—
764C2×C4—1721no—
765C2×C4—1721no—
766C2×C4—1721no—
767C2×C4—1721no—
768C2×C4—1721no—
769C2×C4—1721no—
770C2×C4—1721no—
771C2×C4—1721no—
772C2×C4#1306328712yes—
773C2×C4M16×D4312yes—
774C2×C4C2×D4×D4311yescharacteristic
775C2×C4C2×#1062190211yescharacteristic
776C2×C4#1306337011yescharacteristic
777C2×C4#1306337011yescharacteristic
778C2×C4#1306337111yescharacteristic
779C2×C4#1306337111yescharacteristic
780C8—41no—
781C8—41no—
782C8—41no—
783C8—41no—
784C8—862no—
785C8—862no—
786C8—1721no—
787C8—1721no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—862no—
796C22—862no—
797C22—862no—
798C22—862no—
799C22—862no—
800C22—862no—
801C22—17216no—
802C22—1721no—
803C22—1721no—
804C22—1721no—
805C22—1721no—
806C22—1721no—
807C22—1721no—
808C22—1721no—
809C22—1721no—
810C22—1721no—
811C22—1721no—
812C22—1721no—
813C22—1721no—
814C22—1721no—
815C22—1721no—
816C22—1721no—
817C22C2×#1306328711yescharacteristic
818C22#1458337111yescharacteristic
819C22#1458337111yescharacteristic
820C22C2×M16×D4311yescharacteristic
821C22#131×D4311yescharacteristic
822C22#1458366411yescharacteristic
823C22#1458366511yescharacteristic
824C4—22no—
825C4—22no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—862no—
830C4—1721no—
831C4—1721no—
832C4—1721no—
833C4—1721no—
834C4#1458346011yescharacteristic
835C4#1458346411yescharacteristic
836C4#1458348911yescharacteristic
837C4#1458348911yescharacteristic
838C2—42no—
839C2—3441no—
840C2—1722no—
841C2—1722no—
842C2#1913725211yescharacteristic
843C2#1914331911yescharacteristic
844C2#1914333011yescharacteristic
845C2#1914362511yescharacteristic
846C2#1914363311yescharacteristic
847C2#1914364211yescharacteristic
848C2#1914365211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1851C2
prime radicalC2×#13063295C4
cosocleC22×C4×C43C24
hypercenter#1851D43
hypocenterC43#22038
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
1. C2×#14582974C2semidirect
2. C2×#14582862C2semidirect
4. #19135392C2semidirect
5. #19135388C2semidirect
6. #19135206C2semidirect
7. #19135200C2semidirect
8. #19135200C2semidirect
9. #19135199C2semidirect
10. #19134892C2semidirect
11. #19134891C2semidirect
12. #19134891C2semidirect
13. #19134504C2semidirect
14. #19134379C2semidirect
15. C43×#1851C2semidirect
18. C22×#10621872C22semidirect
24. C2×Dic43⋊C8C22semidirect
35. C2×(C2×D43)⋊C8C22semidirect
36. C2×(C2×D43)⋊C8C22semidirect
37. C2×(C2×D43)⋊C8C22semidirect
38. C2×#13063236C22semidirect
39. C2×C4×C43⋊C8C22semidirect
40. C2×C8×Dic43C22semidirect
50. #14582654C22semidirect
51. #14582654C22semidirect
52. #14582653C22semidirect
53. #14582653C22semidirect
55. C2×C4⋊C8×C43C22semidirect
56. C2×C4⋊C8×C43C22semidirect
59. C43×#336C22semidirect
60. C43×#336C22semidirect
79. C2×#10621877D4semidirect
241. (C2×D43)⋊C4M16semidirect
426. #1851D43semidirect
450. C2×C4⋊C8C2×D43semidirect
451. C2×C4⋊C8C2×D43semidirect
483. #336C2×D43semidirect
484. #336C2×D43semidirect
485. C43#22038semidirect

Maximal subgroups

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

subgroupindex
C2×#145829742
C2×#145828622
C4×#130632952
#191353922
#191353882
#191352062
#191352002
#191351992
#191348922
#191348912
#191345042
#191343792
C43×#18512
#2203843