Finite Group Databasebeta

← #25110350

Subgroups — #25110350

Order 11008.

1030 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582972C211yesmaximal, characteristic, complemented
2C4×#13063321C211yesmaximal, characteristic
3#19135394C211yesmaximal, characteristic, complemented
4#19135392C211yesmaximal, characteristic, complemented
5#19134892C211yesmaximal, characteristic, complemented
6#19134892C211yesmaximal, characteristic, complemented
7#19134889C211yesmaximal, characteristic, complemented
8#19134889C211yesmaximal, characteristic, complemented
9#19134887C211yesmaximal, characteristic, complemented
10#19134887C211yesmaximal, characteristic, complemented
11#19134884C211yesmaximal, characteristic, complemented
12#19134884C211yesmaximal, characteristic, complemented
13#19134711C211yesmaximal, characteristic, complemented
14#19134343C211yesmaximal, characteristic, complemented
15C2×C43×#435C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×#13063321C411yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C4×C22⋊D43C2211yescharacteristic
21C2×C4×C22⋊D43C2211yescharacteristic
22C2×C4×C22⋊D43C2211yescharacteristic
23C2×C4×C22⋊D43C2211yescharacteristic
24#14582972—24no—
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33C2×(C2×D43)⋊C8C2211yescharacteristic
34C2×(C2×D43)⋊C8C2211yescharacteristic
35C2×(C2×D43)⋊C8C2211yescharacteristic
36C2×#13063236C2211yescharacteristic
37#14582802C411yescharacteristic
38#14582800C411yescharacteristic
39#14582799C411yescharacteristic
40#14582799C411yescharacteristic
41#14582799C411yescharacteristic
42#14582799C411yescharacteristic
43#14582768C411yescharacteristic
44C42×Dic43C2211yescharacteristic
45#14582653C2211yescharacteristic
46#14582653C2211yescharacteristic
47#14582653C2211yescharacteristic
48#14582653C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×M16×C43C2211yescharacteristic
54C23×C8×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C43×#435—24no—
57C2×C4⋊C8×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×#97×C43C2211yescharacteristic
61C22×D172C2×C411yescharacteristic
62C22×C22⋊D43C2×C411yescharacteristic
63C22×C22⋊D43C2×C411yescharacteristic
64C22×C22⋊D43C2×C411yescharacteristic
65C22×C22⋊D43C2×C411yescharacteristic
66C22×C4×D43C2311yescharacteristic
67C22×C4×D43C2311yescharacteristic
68C2×#10621872—22no—
69C2×#10621872—41no—
70C2×#10621872—41no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C2×C8×D43—22no—
76C2×C8×D43—41no—
77C2×C8×D43—41no—
78#13063321—24no—
79C4×D172—22no—
80C4×D172—22no—
81C4×C22⋊D43—41no—
82C4×C22⋊D43—41no—
83C4×C22⋊D43—41no—
84C4×C22⋊D43—41no—
85C4×C22⋊D43—41no—
86C4×C22⋊D43—41no—
87C4×C22⋊D43—41no—
88C4×C22⋊D43—41no—
89C2×C4⋊Dic43C2×C411yescharacteristic
90C2×Dic43⋊C4C2×C411yescharacteristic
91C2×Dic43⋊C4C2×C411yescharacteristic
92C2×Dic43⋊C4C2×C411yescharacteristic
93C2×Dic43⋊C4C2×C411yescharacteristic
94C2×C22⋊Dic43C2×C411yescharacteristic
95C2×C22⋊Dic43C2×C411yescharacteristic
96C2×C22⋊Dic43C2×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×C4×Dic43C2×C411yescharacteristic
105C2×C4×Dic43C2×C411yescharacteristic
106C2×C4×Dic43C2×C411yescharacteristic
107C2×C4×Dic43C2×C411yescharacteristic
108C2×C4×Dic43C2311yescharacteristic
109C2×C4×Dic43C2311yescharacteristic
110C4⋊(C43⋊C8)—22no—
111C22⋊(C43⋊C8)—41no—
112C22⋊(C43⋊C8)—41no—
113C22⋊(C43⋊C8)—41no—
114C22⋊(C43⋊C8)—41no—
115(C2×D43)⋊C8—22no—
116(C2×D43)⋊C8—22no—
117(C2×D43)⋊C8—41no—
118(C2×D43)⋊C8—41no—
119(C2×D43)⋊C8—41no—
120(C2×D43)⋊C8—41no—
121#13063236—22no—
122C22×D4×C43C2×C411yescharacteristic
123C23×C4×C43C2311yescharacteristic
124C23×C4×C43C2311yescharacteristic
125C2×M16×C43—22no—
126C2×M16×C43—41no—
127C2×M16×C43—41no—
128C22×C8×C43—22no—
129C22×C8×C43—41no—
130C22×C8×C43—41no—
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C4×D4×C43—22no—
136C4×D4×C43—22no—
137C2×C4⋊C4×C43C2×C411yescharacteristic
138C2×C22⋊C4×C43C2×C411yescharacteristic
139C2×C22⋊C4×C43C2×C411yescharacteristic
140C2×C42×C43C2311yescharacteristic
141C4⋊C8×C43—22no—
142C22⋊C8×C43—22no—
143C22⋊C8×C43—22no—
144#97×C43D414yescomplemented
145C24×C43C22×C411yescharacteristic
146C24×C43C22×C411yescharacteristic
147C23×D43C22×C411yescharacteristic
148C23×D43C22×C411yescharacteristic
149C2×D4×C43—22no—
150C2×D4×C43—22no—
151C2×D4×C43—41no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43C22×C411yescharacteristic
165C22×C4×C43C22×C411yescharacteristic
166C22×C4×C43C22×C411yescharacteristic
167C22×C4×C43C22×C411yescharacteristic
168C22×C4×C43C2411yescharacteristic
169C2×C22⋊D43—22no—
170C2×C22⋊D43—22no—
171C2×C22⋊D43—22no—
172C2×C22⋊D43—22no—
173C2×C22⋊D43—22no—
174C2×C22⋊D43—41no—
175C2×C22⋊D43—41no—
176C2×C22⋊D43—41no—
177C2×C22⋊D43—41no—
178C2×C22⋊D43—41no—
179C2×C22⋊D43—41no—
180C2×C22⋊D43M1614yescomplemented
181C22×Dic43C22×C411yescharacteristic
182C22×Dic43C22×C411yescharacteristic
183C22×Dic43C22×C411yescharacteristic
184C22×Dic43C22×C411yescharacteristic
185C22×Dic43C22×C411yescharacteristic
186C22×Dic43C22×C411yescharacteristic
187C2×D172—22no—
188C2×D172—22no—
189C2×D172—41no—
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—
202M16×C43—44no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—44no—
214C2×C8×C43C2×D412yes—
215C2×C8×C43C2×D412yes—
216C4⋊C4×C43—22no—
217C22⋊C4×C43—22no—
218C22⋊C4×C43—22no—
219C42×C43C2×D412yes—
220C42×C43#4112yes—
221C22⋊Dic43—41no—
222C22⋊Dic43—41no—
223C22⋊Dic43—41no—
224C22⋊Dic43—41no—
225(C2×D43)⋊C4—22no—
226(C2×D43)⋊C4—22no—
227(C2×D43)⋊C4—41no—
228(C2×D43)⋊C4—41no—
229(C2×D43)⋊C4—41no—
230(C2×D43)⋊C4—41no—
231C4⋊Dic43—22no—
232Dic43⋊C4—41no—
233Dic43⋊C4—41no—
234Dic43⋊C4—41no—
235Dic43⋊C4—41no—
236C4×Dic43—21no—
237C4×Dic43—21no—
238C4×Dic43—21no—
239C4×Dic43—21no—
240C4×Dic43—22no—
241C4×Dic43—22no—
242C4×Dic43—41no—
243C4×Dic43—41no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
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—
256#10621872—44no—
257C8×D43—44no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43C2×M1612yes—
272C23×C43C23×C411yescharacteristic
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×D43C2×M1612yes—
287D4×C43—44no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43C4×D412yes—
307C2×C4×C43C4×D412yes—
308C2×C4×C43C22×D411yescharacteristic
309C2×C4×C43C2×#4111yescharacteristic
310C2×C4×C43H(5,𝔽2)11yescharacteristic
311C2×C4×C43H(5,𝔽2)11yescharacteristic
312C2×C4×C43H(5,𝔽2)11yescharacteristic
313C2×C4×C43H(5,𝔽2)11yescharacteristic
314C22⋊D43—44no—
315C22⋊D43—44no—
316C22⋊D43—44no—
317C22⋊D43—44no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
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×Dic43C2×M1612yes—
335C2×Dic43#13112yes—
336D172—44no—
337C4×D43—41no—
338C4×D43—41no—
339C4×D43—41no—
340C4×D43—41no—
341C4×D43—41no—
342C4×D43—41no—
343C4×D43—41no—
344C4×D43—41no—
345C8×C43—22no—
346C8×C43—22no—
347C8×C43—41no—
348C8×C43—41no—
349C43⋊C8—41no—
350C43⋊C8—41no—
351C43⋊C8—41no—
352C43⋊C8—41no—
353#22266—431nomaximal, Sylow
354C22×C43—22no—
355C22×C43—22no—
356C22×C43—22no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—41no—
367C22×C43—41no—
368C22×C43C2×C4×D411yescharacteristic
369C22×C43#51811yescharacteristic
370C22×C43#51811yescharacteristic
371C22×C43C22×M1611yescharacteristic
372C22×C43C2×#13111yescharacteristic
373C22×C43#56811yescharacteristic
374C22×C43#56811yescharacteristic
375C2×D43—22no—
376C2×D43—22no—
377C2×D43—22no—
378C2×D43—41no—
379C2×D43—41no—
380C2×D43—41no—
381C2×D43—41no—
382C2×D43—41no—
383C2×D43—41no—
384C2×D43—41no—
385C2×D43—41no—
386C2×D43—41no—
387C2×D43—41no—
388C2×D43—41no—
389C4×C43—22no—
390C4×C43—22no—
391C4×C43—41no—
392C4×C43—41no—
393C4×C43#53511yescharacteristic
394C4×C43#53511yescharacteristic
395C4×C43#54011yescharacteristic
396C4×C43#54011yescharacteristic
397Dic43—22no—
398Dic43—22no—
399Dic43—41no—
400Dic43—41no—
401Dic43—41no—
402Dic43—41no—
403C2×#435—431no—
404C2×#435D4311yescharacteristic, complemented
405C4×#127—431no—
406#1955—431no—
407#1955—431no—
408#1870—431no—
409#1870—431no—
410#1870—431no—
411#1870—431no—
412#1869—431no—
413#1869—431no—
414#1869—431no—
415#1869—431no—
416#1831—431no—
417#1745—431no—
418C2×C43—42no—
419C2×C43—81no—
420C2×C43#232811yescharacteristic
421C2×C43D4×M1611yescharacteristic
422C2×C43#293511yescharacteristic
423C2×C43#297311yescharacteristic
424C2×C43#297411yescharacteristic
425C2×C43#298011yescharacteristic
426C2×C43#298111yescharacteristic
427D43—42no—
428D43—81no—
429C22×M16—431no—
430C22×M16C2×D4311yescharacteristic
431C23×C8—431no—
432C23×C8C2×D4311yescharacteristic
433C2×#127—431no—
434C2×C4×D4—431no—
435C2×C4×D4—431no—
436C2×C4×D4—431no—
437C2×C4×D4—431no—
438C2×C4×D4—431no—
439C2×C4×D4C2×D4311yescharacteristic
440#435—24no—
441#435—864no—
442C2×C4⋊C8—431no—
443C2×C4⋊C8C2×D4311yescharacteristic
444C2×C22⋊C8—431no—
445C2×C22⋊C8—431no—
446C2×C22⋊C8—431no—
447C2×C22⋊C8—431no—
448C2×C22⋊C8—431no—
449C2×C22⋊C8—431no—
450C2×C22⋊C8—431no—
451C2×C22⋊C8—431no—
452C2×C22⋊C8—431no—
453C2×C22⋊C8—431no—
454C2×C22⋊C8C2×D4311yescharacteristic
455C2×C22⋊C8C2×D4311yescharacteristic
456C2×#97—431no—
457C2×#97C2×D4311yescharacteristic
458#390—431no—
459#390—431no—
460#390—431no—
461#390—431no—
462#390—431no—
463#390—431no—
464#384—431no—
465C43—431no—
466#336—431no—
467#336—431no—
468#336—431no—
469#336—431no—
470#336—431no—
471#336—431no—
472#336—431no—
473#336—431no—
474C43#2226611yescharacteristic, complemented, Sylow
475C22×D4—431no—
476C22×D4—431no—
477C22×D4—431no—
478C22×D4—431no—
479C22×D4—431no—
480C22×D4C4×D4311yescharacteristic
481C23×C4—431no—
482C23×C4—431no—
483C23×C4C22×D4311yescharacteristic
484C23×C4C22×D4311yescharacteristic
485C2×M16—22no—
486C2×M16—41no—
487C2×M16—41no—
488C2×M16—862no—
489C2×M16—1721no—
490C2×M16—1721no—
491C22×C8—22no—
492C22×C8—41no—
493C22×C8—41no—
494C22×C8—431no—
495C22×C8—431no—
496C22×C8—431no—
497C22×C8—431no—
498C22×C8—862no—
499C22×C8—1721no—
500C22×C8—1721no—
501C22×C8C22×D4311yescharacteristic
502C22×C8C22×D4311yescharacteristic
503C22×C8C22×D4311yescharacteristic
504C22×C8C22×D4311yescharacteristic
505#127—864no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—862no—
509C4×D4—862no—
510C4×D4—1721no—
511C4×D4—1721no—
512C4×D4—1721no—
513C4×D4—1721no—
514C4×D4—1721no—
515C4×D4—1721no—
516C4×D4—1721no—
517C4×D4—1721no—
518C2×C4⋊C4—431no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—431no—
523C2×C4⋊C4C4×D4311yescharacteristic
524C2×C22⋊C4—431no—
525C2×C22⋊C4—431no—
526C2×C22⋊C4—431no—
527C2×C22⋊C4—431no—
528C2×C22⋊C4—431no—
529C2×C22⋊C4—431no—
530C2×C22⋊C4—431no—
531C2×C22⋊C4—431no—
532C2×C22⋊C4—431no—
533C2×C22⋊C4—431no—
534C2×C22⋊C4C4×D4311yescharacteristic
535C2×C22⋊C4C4×D4311yescharacteristic
536C2×C42—431no—
537C2×C42—431no—
538C2×C42—431no—
539C2×C42—431no—
540C2×C42—431no—
541C2×C42—431no—
542C2×C42C22×D4311yescharacteristic
543C4⋊C8—22no—
544C4⋊C8—862no—
545C22⋊C8—22no—
546C22⋊C8—22no—
547C22⋊C8—862no—
548C22⋊C8—862no—
549C22⋊C8—1721no—
550C22⋊C8—1721no—
551C22⋊C8—1721no—
552C22⋊C8—1721no—
553C22⋊C8—1721no—
554C22⋊C8—1721no—
555C22⋊C8—1721no—
556C22⋊C8—1721no—
557#97—862no—
558#97C22⋊D4314yescomplemented
559C24—431no—
560C24—431no—
561C24C2×C4×D4311yescharacteristic
562C24C2×C4×D4311yescharacteristic
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—41no—
566C2×D4—434no—
567C2×D4—862no—
568C2×D4—862no—
569C2×D4—862no—
570C2×D4—862no—
571C2×D4—862no—
572C2×D4—862no—
573C2×D4—862no—
574C2×D4—1721no—
575C2×D4—1721no—
576C2×D4—1721no—
577C2×D4—1721no—
578C2×D4—1721no—
579C2×D4—1721no—
580C2×D4—1721no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—431no—
594C22×C4—431no—
595C22×C4—431no—
596C22×C4—431no—
597C22×C4—431no—
598C22×C4—431no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—861no—
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×C4C2×C4×D4311yescharacteristic
612C22×C4C2×C4×D4311yescharacteristic
613C22×C4C2×C4×D4311yescharacteristic
614C22×C4C2×C4×D4311yescharacteristic
615C22×C4C23×D4311yescharacteristic
616M16—44no—
617M16—1724no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—44no—
629C2×C8—861no—
630C2×C8—861no—
631C2×C8—861no—
632C2×C8—861no—
633C2×C8—861no—
634C2×C8—861no—
635C2×C8—861no—
636C2×C8—861no—
637C2×C8—861no—
638C2×C8—861no—
639C2×C8—861no—
640C2×C8—861no—
641C2×C8—1724no—
642C2×C8C2×C22⋊D4312yes—
643C2×C8C2×C22⋊D4312yes—
644C4⋊C4—22no—
645C4⋊C4—862no—
646C4⋊C4—1721no—
647C4⋊C4—1721no—
648C4⋊C4—1721no—
649C4⋊C4—1721no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—862no—
653C22⋊C4—862no—
654C22⋊C4—1721no—
655C22⋊C4—1721no—
656C22⋊C4—1721no—
657C22⋊C4—1721no—
658C22⋊C4—1721no—
659C22⋊C4—1721no—
660C22⋊C4—1721no—
661C22⋊C4—1721no—
662C42—862no—
663C42—862no—
664C42—861no—
665C42—861no—
666C42—861no—
667C42—861no—
668C42—1721no—
669C42—1721no—
670C42#1062189812yes—
671C42C2×C22⋊D4312yes—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—432no—
686C23—861no—
687C23—861no—
688C23—861no—
689C23—861no—
690C23—861no—
691C23—861no—
692C23—861no—
693C23—861no—
694C23—861no—
695C23—861no—
696C23—861no—
697C23—861no—
698C23—861no—
699C23M16×D4312yes—
700C23C22×C4×D4311yescharacteristic
701D4—44no—
702D4—1724no—
703D4—1724no—
704D4—1724no—
705D4—1724no—
706D4—1724no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—432no—
726C2×C4—432no—
727C2×C4—861no—
728C2×C4—861no—
729C2×C4—861no—
730C2×C4—861no—
731C2×C4—861no—
732C2×C4—861no—
733C2×C4—861no—
734C2×C4—861no—
735C2×C4—861no—
736C2×C4—861no—
737C2×C4—861no—
738C2×C4—861no—
739C2×C4—861no—
740C2×C4—861no—
741C2×C4—861no—
742C2×C4—861no—
743C2×C4—1721no—
744C2×C4—1721no—
745C2×C4—1721no—
746C2×C4—1721no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4C4×C22⋊D4312yes—
752C2×C4C4×C22⋊D4312yes—
753C2×C4C22×C22⋊D4311yescharacteristic
754C2×C4C2×#1062189811yescharacteristic
755C2×C4#1306337011yescharacteristic
756C2×C4#1306337011yescharacteristic
757C2×C4#1306337111yescharacteristic
758C2×C4#1306337111yescharacteristic
759C8—22no—
760C8—22no—
761C8—41no—
762C8—41no—
763C8—1721no—
764C8—1721no—
765C8—1721no—
766C8—1721no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—862no—
782C22—862no—
783C22—862no—
784C22—1721no—
785C22—1721no—
786C22—1721no—
787C22—1721no—
788C22—1721no—
789C22—1721no—
790C22—1721no—
791C22—1721no—
792C22—1721no—
793C22—1721no—
794C22—1721no—
795C22C2×C4×C22⋊D4311yescharacteristic
796C22#1458337111yescharacteristic
797C22#1458337111yescharacteristic
798C22C2×M16×D4311yescharacteristic
799C22#131×D4311yescharacteristic
800C22#1458366411yescharacteristic
801C22#1458366511yescharacteristic
802C4—22no—
803C4—22no—
804C4—41no—
805C4—41no—
806C4—862no—
807C4—862no—
808C4—1721no—
809C4—1721no—
810C4—1721no—
811C4—1721no—
812C4#1458346311yescharacteristic
813C4#1458346611yescharacteristic
814C4#1458350011yescharacteristic
815C4#1458350011yescharacteristic
816C2—42no—
817C2—81no—
818C2—3441no—
819C2—1722no—
820C2#1913731711yescharacteristic
821C2M16×C22⋊D4311yescharacteristic
822C2#1914333711yescharacteristic
823C2#1914362011yescharacteristic
824C2#1914362511yescharacteristic
825C2#1914366311yescharacteristic
826C2#1914366711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC2×C43×#435C2
prime radicalC2×#13063321C4
cosocleC22×C4×C43C24
hypercenterC2×#435D43
hypocenterC43#22266
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#14582972C2semidirect
3. #19135394C2semidirect
4. #19135392C2semidirect
5. #19134892C2semidirect
6. #19134892C2semidirect
7. #19134889C2semidirect
8. #19134889C2semidirect
9. #19134887C2semidirect
10. #19134887C2semidirect
11. #19134884C2semidirect
12. #19134884C2semidirect
13. #19134711C2semidirect
14. #19134343C2semidirect
15. C2×C43×#435C2semidirect
144. #97×C43D4semidirect
180. C2×C22⋊D43M16semidirect
404. C2×#435D43semidirect
474. C43#22266semidirect
558. #97C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145829722
C4×#130633212
#191353942
#191353922
#191348922
#191348892
#191348872
#191348842
#191347112
#191343432
C2×C43×#4352
#2226643