Finite Group Databasebeta

← #25107707

Subgroups — #25107707

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×#14582978C211yesmaximal, characteristic, complemented
2C2×#14582861C211yesmaximal, characteristic, complemented
3C4×#13063295C211yesmaximal, characteristic
4#19135392C211yesmaximal, characteristic, complemented
5#19135387C211yesmaximal, characteristic, complemented
6#19135210C211yesmaximal, characteristic, complemented
7#19135202C211yesmaximal, characteristic, complemented
8#19135201C211yesmaximal, characteristic, complemented
9#19134891C211yesmaximal, characteristic, complemented
10#19134891C211yesmaximal, characteristic, complemented
11#19134889C211yesmaximal, characteristic, complemented
12#19134776C211yesmaximal, characteristic, complemented
13#19134504C211yesmaximal, characteristic, complemented
14#19134377C211yesmaximal, characteristic, complemented
15C43×#1923C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×#10621872C2211yescharacteristic, complemented
20C2×#13063295C411yescharacteristic
21C2×C4×D172C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23C2×C4×C22⋊D43C2211yescharacteristic
24#14582978—24no—
25C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
26C2×Dic43⋊C8C2211yescharacteristic, complemented
27#14582861—24no—
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×(C2×D43)⋊C8C2211yescharacteristic, complemented
37C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
38C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
39C2×#13063236C2211yescharacteristic, 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
54C2×C4⋊C8×C43C2211yescharacteristic, complemented
55C2×C22⋊C8×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C2×C4×C8×C43C2211yescharacteristic, complemented
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×#10621872—22no—
78C2×#10621872—22no—
79C2×#10621872—41no—
80C2×#10621872—41no—
81C2×#10621872—41no—
82C2×#10621872—41no—
83C2×#10621872—41no—
84C2×#10621872—41no—
85C2×#10621872D414yescomplemented
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88C22×C43⋊C8C2311yescharacteristic
89C22×C43⋊C8C2311yescharacteristic
90#13063295—24no—
91C4×D172—22no—
92C4×D172—22no—
93C4×D172—41no—
94C4×D172—41no—
95C4×C22⋊D43—41no—
96C4×C22⋊D43—41no—
97C2×C4⋊Dic43C2×C411yescharacteristic
98C2×C4⋊Dic43C2×C411yescharacteristic
99C2×Dic43⋊C4C2×C411yescharacteristic
100C2×C22⋊Dic43C2×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×(C2×D43)⋊C4C2×C411yescharacteristic
108C2×(C2×D43)⋊C4C2×C411yescharacteristic
109C2×(C2×D43)⋊C4C2×C411yescharacteristic
110C2×C4×Dic43C2311yescharacteristic
111C4⋊(C43⋊C8)—22no—
112Dic43⋊C8—41no—
113C22⋊(C43⋊C8)—22no—
114C22⋊(C43⋊C8)—41no—
115(C2×D43)⋊C8—22no—
116(C2×D43)⋊C8—22no—
117(C2×D43)⋊C8—22no—
118(C2×D43)⋊C8—22no—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—41no—
121(C2×D43)⋊C8—41no—
122(C2×D43)⋊C8—41no—
123(C2×D43)⋊C8—41no—
124#13063236—41no—
125C8×Dic43—41no—
126C43⋊#95C2×C411yescharacteristic
127C43⋊#95C2×C411yescharacteristic
128C43⋊#95C2×C411yescharacteristic
129C43⋊#95C2×C411yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C2×C22⋊C4×C43C2×C411yescharacteristic
136C2×C22⋊C4×C43C2×C411yescharacteristic
137C2×C42×C43C2311yescharacteristic
138C2×C42×C43C2311yescharacteristic
139C4⋊C8×C43—41no—
140C22⋊C8×C43—22no—
141C22⋊C8×C43—41no—
142C4×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×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43C22×C411yescharacteristic
163C22×C4×C43C22×C411yescharacteristic
164C22×C4×C43C22×C411yescharacteristic
165C22×C4×C43C22×C411yescharacteristic
166C22×C4×C43C22×C411yescharacteristic
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—21no—
186C2×C4×D43—21no—
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—22no—
202C2×C4×D43—22no—
203C2×C4×D43—41no—
204C2×C4×D43—41no—
205C2×C4×D43—41no—
206C2×C4×D43—41no—
207C2×C4×D43—44no—
208C2×C4×D43—44no—
209C2×C4×D43—44no—
210C2×C4×D43—44no—
211C2×C4×D43C2×D412yes—
212C2×C4×D43#4112yes—
213C2×C8×C43—21no—
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×C43C2×D412yes—
225C22⋊C4×C43—22no—
226C22⋊C4×C43—22no—
227C42×C43—21no—
228C42×C43—21no—
229C42×C43—21no—
230C42×C43—21no—
231C22⋊Dic43—41no—
232(C2×D43)⋊C4—22no—
233(C2×D43)⋊C4—22no—
234(C2×D43)⋊C4—22no—
235(C2×D43)⋊C4—41no—
236(C2×D43)⋊C4—41no—
237(C2×D43)⋊C4—41no—
238(C2×D43)⋊C4—41no—
239(C2×D43)⋊C4—41no—
240(C2×D43)⋊C4M1614yescomplemented
241C4⋊Dic43—22no—
242C4⋊Dic43—41no—
243Dic43⋊C4—41no—
244C4×Dic43—21no—
245C4×Dic43—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—
256C2×C43⋊C8—21no—
257C2×C43⋊C8C2×D412yes—
258#10621872—44no—
259#10621872—44no—
260#10621872—44no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43#13112yes—
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×D43C4×D412yes—
296C22×D43C2×M1612yes—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
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—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
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—44no—
337C2×Dic43C4×D412yes—
338C2×Dic43C2×M1612yes—
339D172—44no—
340D172—44no—
341C4×D43—22no—
342C4×D43—22no—
343C4×D43—22no—
344C4×D43—22no—
345C4×D43—44no—
346C4×D43—44no—
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—22no—
356C8×C43—41no—
357C8×C43—41no—
358C8×C43—41no—
359C43⋊C8—22no—
360C43⋊C8—41no—
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—41no—
402C4×C43—41no—
403C4×C43—41no—
404C4×C43—41no—
405C4×C43#53411yescharacteristic
406C4×C43#53511yescharacteristic
407C4×C43#53811yescharacteristic
408C4×C43#53811yescharacteristic
409Dic43—22no—
410Dic43—22no—
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#1923D4311yescharacteristic, complemented
423#1870—431no—
424#1870—431no—
425#1870—431no—
426#1851—431no—
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×M16—431no—
444C2×#120—431no—
445C2×C4×D4—431no—
446C2×C4×D4—431no—
447C2×C4×D4—431no—
448#436—864no—
449C2×C4⋊C8—431no—
450C2×C4⋊C8—431no—
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⋊C8C2×D4311yescharacteristic
465C2×C22⋊C8C2×D4311yescharacteristic
466C2×#97—431no—
467C2×C4×C8—431no—
468C2×C4×C8C2×D4311yescharacteristic, complemented
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—434no—
504C2×M16—862no—
505C2×M16—862no—
506C2×M16—1721no—
507C2×M16—1721no—
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—862no—
547C4⋊C8—1721no—
548C22⋊C8—22no—
549C22⋊C8—41no—
550C22⋊C8—862no—
551C22⋊C8—862no—
552C22⋊C8—862no—
553C22⋊C8—862no—
554C22⋊C8—862no—
555C22⋊C8—862no—
556C22⋊C8—1721no—
557C22⋊C8—1721no—
558C22⋊C8—1721no—
559C22⋊C8—1721no—
560C22⋊C8—1721no—
561#97—1721no—
562C4×C8—22no—
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—21no—
595C22×C4—21no—
596C22×C4—431no—
597C22×C4—431no—
598C22×C4—432no—
599C22×C4—432no—
600C22×C4—431no—
601C22×C4—431no—
602C22×C4—431no—
603C22×C4—862no—
604C22×C4—862no—
605C22×C4—862no—
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—861no—
621C22×C4—861no—
622C22×C4—1721no—
623C22×C4—1721no—
624C22×C4—1721no—
625C22×C4—1721no—
626C22×C4—1724no—
627C22×C4—1724no—
628C22×C4—1724no—
629C22×C4—1724no—
630C22×C4—1721no—
631C22×C4—1721no—
632C22×C4C2×C4×D4311yescharacteristic
633C22×C4C2×C4×D4311yescharacteristic
634C22×C4C2×C4×D4311yescharacteristic
635C22×C4C2×C4×D4311yescharacteristic
636C22×C4C2×C4×D4311yescharacteristic
637C22×C4C23×D4311yescharacteristic
638M16—1724no—
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—432no—
653C2×C8—861no—
654C2×C8—861no—
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×C8D4×D4312yes—
665C4⋊C4—862no—
666C4⋊C4—1721no—
667C4⋊C4—1721no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—434no—
671C22⋊C4—862no—
672C22⋊C4—862no—
673C22⋊C4—862no—
674C22⋊C4—1721no—
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#1306333112yes—
721C23C22×C4×D4311yescharacteristic
722D4—1724no—
723D4—1724no—
724D4—1724no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—432no—
744C2×C4—432no—
745C2×C4—861no—
746C2×C4—861no—
747C2×C4—861no—
748C2×C4—861no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—861no—
754C2×C4—861no—
755C2×C4—861no—
756C2×C4—861no—
757C2×C4—861no—
758C2×C4—861no—
759C2×C4—861no—
760C2×C4—861no—
761C2×C4—861no—
762C2×C4—1724no—
763C2×C4—1724no—
764C2×C4—1724no—
765C2×C4—1721no—
766C2×C4—1721no—
767C2×C4—1721no—
768C2×C4—1721no—
769C2×C4—1721no—
770C2×C4—1721no—
771C2×C4—1721no—
772C2×C4—1721no—
773C2×C4M16×D4312yes—
774C2×C4C2×D4×D4311yescharacteristic
775C2×C4#41×D4311yescharacteristic
776C2×C4#1306337011yescharacteristic
777C2×C4#1306337111yescharacteristic
778C2×C4#1306337111yescharacteristic
779C2×C4#1306337111yescharacteristic
780C8—22no—
781C8—41no—
782C8—41no—
783C8—41no—
784C8—862no—
785C8—1721no—
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—
817C22C4×D4×D4311yescharacteristic
818C22#1458337111yescharacteristic
819C22#1458337311yescharacteristic
820C22C2×M16×D4311yescharacteristic
821C22C2×#1306333111yescharacteristic
822C22#1458366411yescharacteristic
823C22#1458366411yescharacteristic
824C4—22no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—862no—
830C4—862no—
831C4—1721no—
832C4—1721no—
833C4—1721no—
834C4#1458346011yescharacteristic
835C4#1458346511yescharacteristic
836C4#1458348311yescharacteristic
837C4#1458348811yescharacteristic
838C2—42no—
839C2—3441no—
840C2—1722no—
841C2—1722no—
842C2#1913725711yescharacteristic
843C2#1914331511yescharacteristic
844C2#1914332811yescharacteristic
845C2#1914362911yescharacteristic
846C2#1914363311yescharacteristic
847C2#1914363711yescharacteristic
848C2#1914365611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1923C2
prime radicalC2×#13063295C4
cosocleC22×C4×C43C24
hypercenter#1923D43
hypocenterC43#22038
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. C2×#14582978C2semidirect
2. C2×#14582861C2semidirect
4. #19135392C2semidirect
5. #19135387C2semidirect
6. #19135210C2semidirect
7. #19135202C2semidirect
8. #19135201C2semidirect
9. #19134891C2semidirect
10. #19134891C2semidirect
11. #19134889C2semidirect
12. #19134776C2semidirect
13. #19134504C2semidirect
14. #19134377C2semidirect
15. C43×#1923C2semidirect
19. C22×#10621872C22semidirect
25. C2×C4⋊(C43⋊C8)C22semidirect
26. C2×Dic43⋊C8C22semidirect
36. C2×(C2×D43)⋊C8C22semidirect
37. C2×(C2×D43)⋊C8C22semidirect
38. C2×(C2×D43)⋊C8C22semidirect
39. C2×#13063236C22semidirect
40. C2×C8×Dic43C22semidirect
50. #14582654C22semidirect
51. #14582654C22semidirect
52. #14582653C22semidirect
53. #14582653C22semidirect
54. C2×C4⋊C8×C43C22semidirect
57. C2×C4×C8×C43C22semidirect
59. C43×#336C22semidirect
60. C43×#336C22semidirect
85. C2×#10621872D4semidirect
240. (C2×D43)⋊C4M16semidirect
422. #1923D43semidirect
451. C2×C4⋊C8C2×D43semidirect
468. 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×#145829782
C2×#145828612
C4×#130632952
#191353922
#191353872
#191352102
#191352022
#191352012
#191348912
#191348892
#191347762
#191345042
#191343772
C43×#19232
#2203843