Finite Group Databasebeta

← #25107709

Subgroups — #25107709

Order 11008.

1028 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582867C211yesmaximal, characteristic, complemented
2#19137810C211yesmaximal, characteristic
3#19135391C211yesmaximal, characteristic, complemented
4#19135387C211yesmaximal, characteristic, complemented
5#19135207C211yesmaximal, characteristic, complemented
6#19135201C211yesmaximal, characteristic, complemented
7#19135201C211yesmaximal, characteristic, complemented
8#19135200C211yesmaximal, characteristic, complemented
9#19134892C211yesmaximal, characteristic, complemented
10#19134892C211yesmaximal, characteristic, complemented
11#19134888C211yesmaximal, characteristic, complemented
12#19134772C211yesmaximal, characteristic, complemented
13#19134506C211yesmaximal, characteristic, complemented
14#19134376C211yesmaximal, characteristic, complemented
15C2×C43×#436C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C23×C43⋊C8C2211yescharacteristic
18C2×C4×C22⋊D43C2211yescharacteristic
19C2×C4×C22⋊D43C2211yescharacteristic
20C2×Dic43⋊C8C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22#14582867—24no—
23C2×C22⋊(C43⋊C8)C2211yescharacteristic
24C2×C22⋊(C43⋊C8)C2211yescharacteristic
25C2×C22⋊(C43⋊C8)C2211yescharacteristic
26C2×(C2×D43)⋊C8C2211yescharacteristic
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×#13063235C2211yescharacteristic
35C2×C8×Dic43C2211yescharacteristic
36#14582819C411yescharacteristic
37#14582816C411yescharacteristic
38#14582814C411yescharacteristic
39#14582814C411yescharacteristic
40#14582811C411yescharacteristic
41#14582808C411yescharacteristic
42#14582807C411yescharacteristic
43#14582807C411yescharacteristic
44C4×(C2×D43)⋊C4C2211yescharacteristic
45C4×(C2×D43)⋊C4C2211yescharacteristic
46C4×C22⋊Dic43C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×M16×C43C2211yescharacteristic
54C22×M16×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C43×#436—24no—
57C2×C4⋊C8×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×C4×C8×C43C2211yescharacteristic
61C2×#10621898—22no—
62C2×#10621898—22no—
63C2×#10621898—41no—
64C2×#10621898—41no—
65C2×#10621898—41no—
66C2×#10621898—41no—
67C22×Dic86C2×C411yescharacteristic
68C22×D172C2×C411yescharacteristic
69C22×C22⋊D43C2×C411yescharacteristic
70C22×C22⋊D43C2×C411yescharacteristic
71C22×C22⋊D43C2×C411yescharacteristic
72C22×C22⋊D43C2×C411yescharacteristic
73C22×C4×D43C2311yescharacteristic
74C22×C4×D43C2311yescharacteristic
75C22×C43⋊C8—22no—
76C22×C43⋊C8—41no—
77C22×C43⋊C8—41no—
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C4×C22⋊D43—41no—
83C4×C22⋊D43—41no—
84C4×C22⋊D43—41no—
85C4×C22⋊D43—41no—
86C2×Dic43⋊C4C2×C411yescharacteristic
87C2×Dic43⋊C4C2×C411yescharacteristic
88C2×C22⋊Dic43C2×C411yescharacteristic
89C2×C22⋊Dic43C2×C411yescharacteristic
90C2×C22⋊Dic43C2×C411yescharacteristic
91C2×C22⋊Dic43C2×C411yescharacteristic
92C2×(C2×D43)⋊C4C2×C411yescharacteristic
93C2×(C2×D43)⋊C4C2×C411yescharacteristic
94C2×(C2×D43)⋊C4C2×C411yescharacteristic
95C2×(C2×D43)⋊C4C2×C411yescharacteristic
96C2×(C2×D43)⋊C4C2×C411yescharacteristic
97C2×(C2×D43)⋊C4C2×C411yescharacteristic
98C2×C4×Dic43C2311yescharacteristic
99C2×C4×Dic43C2311yescharacteristic
100Dic43⋊C8—41no—
101Dic43⋊C8—41no—
102C22⋊(C43⋊C8)—22no—
103C22⋊(C43⋊C8)—41no—
104C22⋊(C43⋊C8)—41no—
105(C2×D43)⋊C8—22no—
106(C2×D43)⋊C8—22no—
107(C2×D43)⋊C8—22no—
108(C2×D43)⋊C8—22no—
109(C2×D43)⋊C8—41no—
110(C2×D43)⋊C8—41no—
111(C2×D43)⋊C8—41no—
112(C2×D43)⋊C8—41no—
113#13063235—41no—
114C8×Dic43—41no—
115C43⋊#95C2×C411yescharacteristic
116C43⋊#95C2×C411yescharacteristic
117C43⋊#95C2×C411yescharacteristic
118C43⋊#95C2×C411yescharacteristic
119C43⋊#95C2×C411yescharacteristic
120C43⋊#95C2×C411yescharacteristic
121C22×D4×C43C2×C411yescharacteristic
122C23×C4×C43C2311yescharacteristic
123C23×C4×C43C2311yescharacteristic
124C2×M16×C43—22no—
125C2×M16×C43—41no—
126C2×M16×C43—41no—
127C2×M16×C43—41no—
128C2×M16×C43—41no—
129C2×M16×C43D414yescomplemented
130C22×C8×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134C4×D4×C43—22no—
135C4×D4×C43—22no—
136C2×C4⋊C4×C43C2×C411yescharacteristic
137C2×C22⋊C4×C43C2×C411yescharacteristic
138C2×C22⋊C4×C43C2×C411yescharacteristic
139C2×C42×C43C2311yescharacteristic
140C4⋊C8×C43—22no—
141C22⋊C8×C43—22no—
142C22⋊C8×C43—22no—
143C4×C8×C43—22no—
144C24×C43C22×C411yescharacteristic
145C24×C43C22×C411yescharacteristic
146C23×D43C22×C411yescharacteristic
147C23×D43C22×C411yescharacteristic
148C2×D4×C43—22no—
149C2×D4×C43—22no—
150C2×D4×C43—41no—
151C22×C4×C43—21no—
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×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—22no—
171C2×C22⋊D43—41no—
172C2×C22⋊D43—41no—
173C2×C22⋊D43—41no—
174C2×C22⋊D43—41no—
175C2×C22⋊D43—41no—
176C2×C22⋊D43—41no—
177C2×C22⋊D43—41no—
178C2×C22⋊D43—41no—
179C2×C22⋊D43—41no—
180C22×Dic43C22×C411yescharacteristic
181C22×Dic43C22×C411yescharacteristic
182C22×Dic43C22×C411yescharacteristic
183C22×Dic43C22×C411yescharacteristic
184C22×Dic43C22×C411yescharacteristic
185C22×Dic43C22×C411yescharacteristic
186#10621898—44no—
187#10621898—44no—
188#10621898—44no—
189#10621898—44no—
190C2×D172—22no—
191C2×D172—41no—
192C2×D172—41no—
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×Dic86—22no—
206C2×Dic86—41no—
207C2×Dic86—41no—
208M16×C43—44no—
209M16×C43—44no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
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×C43C2×D412yes—
221C2×C8×C43C2×D412yes—
222C4⋊C4×C43—22no—
223C22⋊C4×C43—22no—
224C22⋊C4×C43—22no—
225C42×C43—21no—
226C42×C43—21no—
227C22⋊Dic43—22no—
228C22⋊Dic43—41no—
229C22⋊Dic43—41no—
230C22⋊Dic43—41no—
231(C2×D43)⋊C4—22no—
232(C2×D43)⋊C4—22no—
233(C2×D43)⋊C4—22no—
234(C2×D43)⋊C4—41no—
235(C2×D43)⋊C4—41no—
236(C2×D43)⋊C4—41no—
237Dic43⋊C4—41no—
238Dic43⋊C4—41no—
239C4×Dic43—21no—
240C4×Dic43—21no—
241C4×Dic43—21no—
242C4×Dic43—21no—
243C2×C43⋊C8—21no—
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—44no—
256C23×C43—21no—
257C23×C43—21no—
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×C43C4×D412yes—
270C23×C43C23×C411yescharacteristic
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—
285D4×C43—44no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43C4×D412yes—
305C2×C4×C43#13112yes—
306C2×C4×C43C22×D411yescharacteristic
307C2×C4×C43C2×#4111yescharacteristic
308C2×C4×C43H(5,𝔽2)11yescharacteristic
309C2×C4×C43H(5,𝔽2)11yescharacteristic
310C2×C4×C43H(5,𝔽2)11yescharacteristic
311C2×C4×C43H(5,𝔽2)11yescharacteristic
312C22⋊D43—44no—
313C22⋊D43—44no—
314C22⋊D43—44no—
315C22⋊D43—44no—
316C2×Dic43—21no—
317C2×Dic43—21no—
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#13112yes—
334D172—44no—
335C4×D43—41no—
336C4×D43—41no—
337C4×D43—41no—
338C4×D43—41no—
339C4×D43—41no—
340C4×D43—41no—
341C4×D43—41no—
342C4×D43—41no—
343Dic86—44no—
344C8×C43—22no—
345C8×C43—22no—
346C8×C43—41no—
347C8×C43—41no—
348C43⋊C8—41no—
349C43⋊C8—41no—
350C43⋊C8—41no—
351C43⋊C8—41no—
352#22039—431nomaximal, Sylow
353C22×C43—22no—
354C22×C43—22no—
355C22×C43—22no—
356C22×C43—41no—
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×C43C2×C4×D411yescharacteristic
368C22×C43#51811yescharacteristic
369C22×C43#51811yescharacteristic
370C22×C43C2×#13111yescharacteristic
371C22×C43C2×#13111yescharacteristic
372C22×C43#56811yescharacteristic
373C22×C43#56811yescharacteristic
374C2×D43—41no—
375C2×D43—41no—
376C2×D43—41no—
377C2×D43—41no—
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—
388C4×C43—22no—
389C4×C43—22no—
390C4×C43—41no—
391C4×C43—41no—
392C4×C43#53411yescharacteristic
393C4×C43#53511yescharacteristic
394C4×C43#53811yescharacteristic
395C4×C43#53811yescharacteristic
396Dic43—22no—
397Dic43—41no—
398Dic43—41no—
399Dic43—41no—
400Dic43—41no—
401Dic43—41no—
402C2×#436D4311yescharacteristic, complemented
403C2×#408—431no—
404#2388—431no—
405#1955—431no—
406#1954—431no—
407#1924—431no—
408#1923—431no—
409#1923—431no—
410#1923—431no—
411#1870—431no—
412#1870—431no—
413#1869—431no—
414#1850—431no—
415#1780—431no—
416#1753—431no—
417C2×C43—42no—
418C2×C43—81no—
419C2×C43#232111yescharacteristic
420C2×C43#293311yescharacteristic
421C2×C43#293511yescharacteristic
422C2×C43#297611yescharacteristic
423C2×C43#297811yescharacteristic
424C2×C43#297911yescharacteristic
425C2×C43#298111yescharacteristic
426D43—81no—
427D43—81no—
428C22×#41—431no—
429C22×M16C2×D4311yescharacteristic
430C22×M16C2×D4311yescharacteristic
431C23×C8—431no—
432C2×C4×D4—431no—
433C2×C4×D4—431no—
434C2×C4×D4C2×D4311yescharacteristic
435#436—24no—
436C2×C4⋊C8—431no—
437C2×C4⋊C8—431no—
438C2×C4⋊C8C2×D4311yescharacteristic
439#408—864no—
440C2×C22⋊C8—431no—
441C2×C22⋊C8—431no—
442C2×C22⋊C8—431no—
443C2×C22⋊C8—431no—
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⋊C8C2×D4311yescharacteristic
452C2×C22⋊C8C2×D4311yescharacteristic
453C2×#97—431no—
454C2×C4×C8—431no—
455C2×C4×C8C2×D4311yescharacteristic
456#395—431no—
457#394—431no—
458#394—431no—
459#394—431no—
460#393—431no—
461#392—431no—
462#392—431no—
463#392—431no—
464C4×C22⋊C4—431no—
465C4×C22⋊C4—431no—
466C4×C22⋊C4—431no—
467#336—431no—
468#336—431no—
469#336—431no—
470#336—431no—
471#336—431no—
472#336—431no—
473C43#2203911yescharacteristic, complemented, Sylow
474C2×#41—862no—
475C2×#41—862no—
476C2×#41—1721no—
477C2×#41—1721no—
478C2×#41—1721no—
479C2×#41—1721no—
480C22×Q8—431no—
481C22×D4—431no—
482C22×D4—431no—
483C22×D4—431no—
484C22×D4—431no—
485C22×D4—431no—
486C22×D4C4×D4311yescharacteristic
487C23×C4—431no—
488C23×C4—431no—
489C23×C4C22×D4311yescharacteristic
490C23×C4C22×D4311yescharacteristic
491C2×M16—22no—
492C2×M16—41no—
493C2×M16—41no—
494C2×M16—41no—
495C2×M16—41no—
496C2×M16C22⋊D4314yescomplemented
497C22×C8—431no—
498C22×C8—431no—
499C22×C8—431no—
500C22×C8—431no—
501C22×C8—862no—
502C22×C8—1721no—
503C22×C8—1721no—
504C22×C8C22×D4311yescharacteristic
505C22×C8C22×D4311yescharacteristic
506C22×C8C22×D4311yescharacteristic
507C22×C8C22×D4311yescharacteristic
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—1721no—
511C4×D4—1721no—
512C4×D4—1721no—
513C4×D4—1721no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4C4×D4311yescharacteristic
517C2×C22⋊C4—431no—
518C2×C22⋊C4—431no—
519C2×C22⋊C4—431no—
520C2×C22⋊C4—431no—
521C2×C22⋊C4—431no—
522C2×C22⋊C4—431no—
523C2×C22⋊C4—431no—
524C2×C22⋊C4—431no—
525C2×C22⋊C4—431no—
526C2×C22⋊C4—431no—
527C2×C22⋊C4C4×D4311yescharacteristic
528C2×C22⋊C4C4×D4311yescharacteristic
529C2×C42—431no—
530C2×C42—431no—
531C2×C42C22×D4311yescharacteristic
532C4⋊C8—22no—
533C4⋊C8—1721no—
534C4⋊C8—1721no—
535C22⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—862no—
538C22⋊C8—862no—
539C22⋊C8—862no—
540C22⋊C8—862no—
541C22⋊C8—862no—
542C22⋊C8—1721no—
543C22⋊C8—1721no—
544C22⋊C8—1721no—
545C22⋊C8—1721no—
546C22⋊C8—1721no—
547C22⋊C8—1721no—
548#97—1721no—
549C4×C8—22no—
550C4×C8—1721no—
551#95—431no—
552#95—431no—
553#95—431no—
554#95—431no—
555#95—431no—
556#95—431no—
557C24—431no—
558C24—431no—
559C24C2×C4×D4311yescharacteristic
560C24C2×C4×D4311yescharacteristic
561#41—1724no—
562#41—1724no—
563#41—1724no—
564#41—1724no—
565C2×Q8—862no—
566C2×Q8—1721no—
567C2×Q8—1721no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—41no—
571C2×D4—862no—
572C2×D4—862no—
573C2×D4—862no—
574C2×D4—862no—
575C2×D4—1721no—
576C2×D4—1721no—
577C2×D4—1721no—
578C2×D4—1721no—
579C2×D4—1721no—
580C2×D4—1721no—
581C2×D4—1721no—
582C2×D4—1721no—
583C2×D4—1721no—
584C2×D4—1721no—
585C2×D4—1721no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
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—431no—
599C22×C4—431no—
600C22×C4—431no—
601C22×C4—431no—
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×C4C2×C4×D4311yescharacteristic
615C22×C4C2×C4×D4311yescharacteristic
616C22×C4C2×C4×D4311yescharacteristic
617C22×C4C2×C4×D4311yescharacteristic
618C22×C4#1062189812yes—
619C22×C4C2×C22⋊D4312yes—
620C22×C4C23×D4311yescharacteristic
621M16—44no—
622M16—44no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
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—861no—
642C2×C8—861no—
643C2×C8—861no—
644C2×C8—861no—
645C2×C8—1724no—
646C2×C8C2×C22⋊D4312yes—
647C2×C8C2×C22⋊D4312yes—
648C4⋊C4—22no—
649C4⋊C4—1721no—
650C4⋊C4—1721no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—862no—
654C22⋊C4—862no—
655C22⋊C4—862no—
656C22⋊C4—862no—
657C22⋊C4—1721no—
658C22⋊C4—1721no—
659C22⋊C4—1721no—
660C22⋊C4—1721no—
661C22⋊C4—1721no—
662C22⋊C4—1721no—
663C42—21no—
664C42—21no—
665C42—861no—
666C42—861no—
667C42—861no—
668C42—861no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—861no—
683C23—861no—
684C23—861no—
685C23—861no—
686C23—861no—
687C23—861no—
688C23—861no—
689C23—861no—
690C23—861no—
691C23—861no—
692C23—861no—
693C23—861no—
694C23—861no—
695C23—861no—
696C23C4×C22⋊D4312yes—
697C23C22×C4×D4311yescharacteristic
698Q8—1724no—
699D4—44no—
700D4—1724no—
701D4—1724no—
702D4—1724no—
703D4—1724no—
704D4—1724no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—432no—
724C2×C4—861no—
725C2×C4—861no—
726C2×C4—861no—
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—1721no—
742C2×C4—1721no—
743C2×C4—1721no—
744C2×C4—1721no—
745C2×C4—1721no—
746C2×C4—1721no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4C4×C22⋊D4312yes—
750C2×C4#1306333312yes—
751C2×C4C22×C22⋊D4311yescharacteristic
752C2×C4C2×#1062189811yescharacteristic
753C2×C4#1306337011yescharacteristic
754C2×C4#1306337011yescharacteristic
755C2×C4#1306337111yescharacteristic
756C2×C4#1306337111yescharacteristic
757C8—22no—
758C8—22no—
759C8—41no—
760C8—41no—
761C8—1721no—
762C8—1721no—
763C8—1721no—
764C8—1721no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—1721no—
780C22—1721no—
781C22—1721no—
782C22—1721no—
783C22—1721no—
784C22—1721no—
785C22—1721no—
786C22—1721no—
787C22—1721no—
788C22—1721no—
789C22—1721no—
790C22—1721no—
791C22—1721no—
792C22—1721no—
793C22C2×C4×C22⋊D4311yescharacteristic
794C22#1458337111yescharacteristic
795C22#1458337111yescharacteristic
796C22#131×D4311yescharacteristic
797C22C2×#1306333311yescharacteristic
798C22#1458366411yescharacteristic
799C22#1458366511yescharacteristic
800C4—22no—
801C4—22no—
802C4—41no—
803C4—41no—
804C4—862no—
805C4—1721no—
806C4—1721no—
807C4—1721no—
808C4—1721no—
809C4—1721no—
810C4#1458345811yescharacteristic
811C4#1458346311yescharacteristic
812C4#1458348211yescharacteristic
813C4#1458348211yescharacteristic
814C2—42no—
815C2—81no—
816C2—3441no—
817C2—3441no—
818C2#1913724911yescharacteristic
819C2#1914332011yescharacteristic
820C2#1914333711yescharacteristic
821C2#1914363911yescharacteristic
822C2#1914365211yescharacteristic
823C2#1914366011yescharacteristic
824C2#1914367211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC2×C43×#436C2
prime radical#19137810C2
cosocleC22×C4×C43C24
hypercenterC2×#436D43
hypocenterC43#22039
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C2×#14582867C2semidirect
3. #19135391C2semidirect
4. #19135387C2semidirect
5. #19135207C2semidirect
6. #19135201C2semidirect
7. #19135201C2semidirect
8. #19135200C2semidirect
9. #19134892C2semidirect
10. #19134892C2semidirect
11. #19134888C2semidirect
12. #19134772C2semidirect
13. #19134506C2semidirect
14. #19134376C2semidirect
15. C2×C43×#436C2semidirect
129. C2×M16×C43D4semidirect
402. C2×#436D43semidirect
473. C43#22039semidirect
496. C2×M16C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828672
#191378102
#191353912
#191353872
#191352072
#191352012
#191352002
#191348922
#191348882
#191347722
#191345062
#191343762
C2×C43×#4362
#2203943