Finite Group Databasebeta

← #25111886

Subgroups — #25111886

Order 11008.

1582 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583408C211yesmaximal, characteristic
2C2×#14582976C211yesmaximal, characteristic, complemented
3C2×#14582972C211yesmaximal, characteristic, complemented
4C2×#14582864C211yesmaximal, characteristic, complemented
5C2×#14582861C211yesmaximal, characteristic, complemented
6#19135390C211yesmaximal, characteristic, complemented
7#19134889C211yesmaximal, characteristic, complemented
8#19134889C211yesmaximal, characteristic, complemented
9#19134889C211yesmaximal, characteristic, complemented
10#19134884C211yesmaximal, characteristic, complemented
11#19134576C211yesmaximal, characteristic, complemented
12#19134506C211yesmaximal, characteristic, complemented
13#19134504C211yesmaximal, characteristic, complemented
14#19134364C211yesmaximal, characteristic, complemented
15C43×#1955C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C22×#10621872C2211yescharacteristic, complemented
21C22×C8×D43C2211yescharacteristic, complemented
22#14583408—24no—
23#14583408—24no—
24C2×#13063310C411yescharacteristic
25C2×#13063307C411yescharacteristic
26C2×#13063303C411yescharacteristic
27C2×#13063302C411yescharacteristic
28C2×#13063298C411yescharacteristic
29C2×#13063297C411yescharacteristic
30C2×#13063295C411yescharacteristic
31C2×#13063293C411yescharacteristic
32C2×C4×D172C2211yescharacteristic
33C2×C4×C22⋊D43C2211yescharacteristic
34C2×C4×C22⋊D43C2211yescharacteristic
35C2×#13063282C2211yescharacteristic
36#14582976—24no—
37#14582972—24no—
38C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
39#14582864—24no—
40#14582861—24no—
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
44C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
45C2×(C2×D43)⋊C8C2211yescharacteristic
46C2×(C2×D43)⋊C8C2211yescharacteristic
47C2×(C2×D43)⋊C8C2211yescharacteristic
48C2×(C2×D43)⋊C8C2211yescharacteristic
49C2×(C2×D43)⋊C8C2211yescharacteristic
50C2×(C2×D43)⋊C8C2211yescharacteristic
51C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
52C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
53C2×C4×C43⋊C8C2211yescharacteristic, complemented
54#14582653C2211yescharacteristic, complemented
55#14582653C2211yescharacteristic, complemented
56#14582653C2211yescharacteristic, complemented
57#14582653C2211yescharacteristic, complemented
58C2×C4×D4×C43C2211yescharacteristic
59C2×C4⋊C8×C43C2211yescharacteristic, complemented
60C2×C22⋊C8×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic, complemented
63C2×C22⋊C8×C43C2211yescharacteristic, complemented
64C2×#97×C43C2211yescharacteristic, complemented
65C24×D43C2×C411yescharacteristic
66C2×#10621898—22no—
67C2×#10621898—22no—
68C2×#10621898—22no—
69C2×#10621898—22no—
70C2×#10621898—41no—
71C2×#10621898—41no—
72C22×Dic86C2×C411yescharacteristic
73C22×D172C2×C411yescharacteristic
74C22×D172C2×C411yescharacteristic
75C22×C22⋊D43C2×C411yescharacteristic
76C22×C22⋊D43C2×C411yescharacteristic
77C22×C22⋊D43C2×C411yescharacteristic
78C22×C22⋊D43C2×C411yescharacteristic
79C23×Dic43C2×C411yescharacteristic
80C22×C4×D43—22no—
81C22×C4×D43—22no—
82C22×C4×D43—22no—
83C22×C4×D43—22no—
84C22×C4×D43—41no—
85C22×C4×D43—41no—
86C22×C4×D43C2×C411yescharacteristic
87C22×C4×D43C2×C411yescharacteristic
88C22×C4×D43C2311yescharacteristic
89C22×C4×D43C2311yescharacteristic
90C22×C4×D43C2311yescharacteristic
91C2×#10621872—22no—
92C2×#10621872—22no—
93C2×#10621872—22no—
94C2×#10621872—22no—
95C2×#10621872—22no—
96C2×#10621872—22no—
97C2×#10621872—41no—
98C2×#10621872—41no—
99C2×#10621872—41no—
100C22×C43⋊C8C2311yescharacteristic
101C22×C43⋊C8C2311yescharacteristic
102C22×C43⋊C8C2311yescharacteristic
103C22×C43⋊C8C2311yescharacteristic
104C2×C8×D43—22no—
105C2×C8×D43—22no—
106C2×C8×D43—41no—
107#13063310—24no—
108#13063307—24no—
109#13063303—24no—
110#13063302—24no—
111#13063298—24no—
112#13063297—24no—
113#13063295—24no—
114#13063293—24no—
115C4×D172D414yes—
116C4×D172D414yes—
117C4×C22⋊D43—22no—
118C4×C22⋊D43—22no—
119C4×C22⋊D43—22no—
120C4×C22⋊D43—22no—
121#13063282—22no—
122#13063282—22no—
123C2×C4⋊Dic43C2×C411yescharacteristic
124C2×Dic43⋊C4C2×C411yescharacteristic
125C2×Dic43⋊C4C2×C411yescharacteristic
126C2×Dic43⋊C4C2×C411yescharacteristic
127C2×Dic43⋊C4C2×C411yescharacteristic
128C2×C22⋊Dic43C2×C411yescharacteristic
129C2×C22⋊Dic43C2×C411yescharacteristic
130C2×(C2×D43)⋊C4C2×C411yescharacteristic
131C2×(C2×D43)⋊C4C2×C411yescharacteristic
132C2×(C2×D43)⋊C4C2×C411yescharacteristic
133C2×(C2×D43)⋊C4C2×C411yescharacteristic
134C2×(C2×D43)⋊C4C2×C411yescharacteristic
135C2×(C2×D43)⋊C4C2×C411yescharacteristic
136C2×C4×Dic43C2311yescharacteristic
137C4⋊(C43⋊C8)—22no—
138C22⋊(C43⋊C8)—22no—
139C22⋊(C43⋊C8)—22no—
140C22⋊(C43⋊C8)—41no—
141C22⋊(C43⋊C8)—41no—
142(C2×D43)⋊C8—22no—
143(C2×D43)⋊C8—22no—
144(C2×D43)⋊C8—22no—
145(C2×D43)⋊C8—22no—
146(C2×D43)⋊C8—22no—
147(C2×D43)⋊C8—22no—
148(C2×D43)⋊C8—22no—
149(C2×D43)⋊C8D414yescomplemented
150C4×C43⋊C8—22no—
151C22×D4×C43C2×C411yescharacteristic
152C23×C4×C43C2311yescharacteristic
153C23×C4×C43C2311yescharacteristic
154C22×C8×C43C2311yescharacteristic
155C22×C8×C43C2311yescharacteristic
156C22×C8×C43C2311yescharacteristic
157C22×C8×C43C2311yescharacteristic
158C4×D4×C43—22no—
159C4×D4×C43—22no—
160C2×C4⋊C4×C43C2×C411yescharacteristic
161C2×C22⋊C4×C43C2×C411yescharacteristic
162C2×C22⋊C4×C43C2×C411yescharacteristic
163C2×C42×C43C2311yescharacteristic
164C4⋊C8×C43—22no—
165C22⋊C8×C43—22no—
166C22⋊C8×C43—22no—
167C22⋊C8×C43—41no—
168C22⋊C8×C43—41no—
169#97×C43—22no—
170C24×C43C22×C411yescharacteristic
171C24×C43C22×C411yescharacteristic
172C23×D43—22no—
173C23×D43—22no—
174C23×D43—22no—
175C23×D43—41no—
176C23×D43—41no—
177C23×D43—41no—
178C23×D43—41no—
179C23×D43C22×C411yescharacteristic
180C23×D43C22×C411yescharacteristic
181C23×D43C22×C411yescharacteristic
182C2×D4×C43—22no—
183C2×D4×C43—22no—
184C2×D4×C43—41no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43C22×C411yescharacteristic
198C22×C4×C43C22×C411yescharacteristic
199C22×C4×C43C22×C411yescharacteristic
200C22×C4×C43C22×C411yescharacteristic
201C22×C4×C43C2411yescharacteristic
202C2×C22⋊D43—22no—
203C2×C22⋊D43—22no—
204C2×C22⋊D43—22no—
205C2×C22⋊D43—22no—
206C2×C22⋊D43—22no—
207C2×C22⋊D43—22no—
208C2×C22⋊D43—22no—
209C2×C22⋊D43—41no—
210C2×C22⋊D43—41no—
211C2×C22⋊D43—41no—
212C2×C22⋊D43—41no—
213C2×C22⋊D43—41no—
214C22×Dic43—22no—
215C22×Dic43—22no—
216C22×Dic43—41no—
217C22×Dic43C22×C411yescharacteristic
218C22×Dic43C22×C411yescharacteristic
219C22×Dic43C22×C411yescharacteristic
220C22×Dic43C22×C411yescharacteristic
221C22×Dic43C22×C411yescharacteristic
222#10621898—44no—
223#10621898—44no—
224#10621898—44no—
225#10621898—44no—
226C2×D172—22no—
227C2×D172—22no—
228C2×D172—41no—
229C2×D172—41no—
230C2×D172—41no—
231C2×D172C22⋊C414yes—
232C2×C4×D43—21no—
233C2×C4×D43—21no—
234C2×C4×D43—21no—
235C2×C4×D43—21no—
236C2×C4×D43—21no—
237C2×C4×D43—21no—
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43—21no—
241C2×C4×D43—21no—
242C2×C4×D43—21no—
243C2×C4×D43—21no—
244C2×C4×D43—22no—
245C2×C4×D43—22no—
246C2×C4×D43—22no—
247C2×C4×D43—22no—
248C2×C4×D43—41no—
249C2×C4×D43—41no—
250C2×C4×D43—44no—
251C2×C4×D43—44no—
252C2×C4×D43—44no—
253C2×C4×D43—44no—
254C2×C4×D43C2×D412yes—
255C2×C4×D43C2×D412yes—
256C2×C4×D43C2×D412yes—
257C2×C4×D43C2×D412yes—
258C2×C4×D43C2×D412yes—
259C2×C4×D43#4112yes—
260C2×Dic86—22no—
261C2×Dic86—22no—
262C2×Dic86—41no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C2×C8×C43—21no—
267C2×C8×C43—21no—
268C2×C8×C43—21no—
269C2×C8×C43—21no—
270C2×C8×C43—21no—
271C2×C8×C43—21no—
272C2×C8×C43—21no—
273C2×C8×C43—21no—
274C2×C8×C43C2×D412yes—
275C4⋊C4×C43—22no—
276C22⋊C4×C43—22no—
277C22⋊C4×C43—22no—
278C42×C43C2×D412yes—
279C42×C43C2×D412yes—
280C22⋊Dic43—22no—
281C22⋊Dic43—22no—
282(C2×D43)⋊C4—22no—
283(C2×D43)⋊C4—22no—
284(C2×D43)⋊C4—22no—
285(C2×D43)⋊C4—22no—
286(C2×D43)⋊C4C22⋊C414yes—
287(C2×D43)⋊C4C22⋊C414yes—
288C4⋊Dic43C22⋊C414yes—
289Dic43⋊C4—22no—
290Dic43⋊C4—22no—
291Dic43⋊C4—22no—
292Dic43⋊C4—22no—
293C4×Dic43—21no—
294C4×Dic43—21no—
295C2×C43⋊C8—21no—
296C2×C43⋊C8—21no—
297C2×C43⋊C8—21no—
298C2×C43⋊C8—21no—
299C2×C43⋊C8—21no—
300C2×C43⋊C8—21no—
301C2×C43⋊C8—21no—
302C2×C43⋊C8—21no—
303C2×C43⋊C8—21no—
304C2×C43⋊C8—21no—
305C2×C43⋊C8—21no—
306C2×C43⋊C8C2×D412yes—
307#10621872—44no—
308#10621872—44no—
309#10621872—44no—
310C8×D43—44no—
311C23×C43—21no—
312C23×C43—21no—
313C23×C43—21no—
314C23×C43—21no—
315C23×C43—21no—
316C23×C43—21no—
317C23×C43—21no—
318C23×C43—21no—
319C23×C43—21no—
320C23×C43—21no—
321C23×C43—21no—
322C23×C43—21no—
323C23×C43—21no—
324C23×C43#13112yes—
325C23×C43C23×C411yescharacteristic
326C22×D43—21no—
327C22×D43—21no—
328C22×D43—21no—
329C22×D43—21no—
330C22×D43—21no—
331C22×D43—21no—
332C22×D43—21no—
333C22×D43—21no—
334C22×D43—21no—
335C22×D43—21no—
336C22×D43—21no—
337C22×D43—21no—
338C22×D43—21no—
339C22×D43—21no—
340C22×D43—21no—
341C22×D43—21no—
342C22×D43—21no—
343C22×D43—21no—
344C22×D43—44no—
345C22×D43—44no—
346C22×D43—44no—
347C22×D43—44no—
348C22×D43—44no—
349C22×D43—44no—
350C22×D43—44no—
351C22×D43C2×C22⋊C412yes—
352C22×D43C2×C22⋊C412yes—
353C22×D43C4×D412yes—
354D4×C43—44no—
355C2×C4×C43—21no—
356C2×C4×C43—21no—
357C2×C4×C43—21no—
358C2×C4×C43—21no—
359C2×C4×C43—21no—
360C2×C4×C43—21no—
361C2×C4×C43—21no—
362C2×C4×C43—21no—
363C2×C4×C43—21no—
364C2×C4×C43—21no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—41no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—41no—
372C2×C4×C43—41no—
373C2×C4×C43C2×C22⋊C412yes—
374C2×C4×C43C2×C22⋊C412yes—
375C2×C4×C43C22×D411yescharacteristic
376C2×C4×C43C22×D411yescharacteristic
377C2×C4×C43C22×D411yescharacteristic
378C2×C4×C43C2×#4111yescharacteristic
379C2×C4×C43H(5,𝔽2)11yescharacteristic
380C2×C4×C43H(5,𝔽2)11yescharacteristic
381C22⋊D43—44no—
382C22⋊D43—44no—
383C22⋊D43—44no—
384C22⋊D43—44no—
385C2×Dic43—21no—
386C2×Dic43—21no—
387C2×Dic43—21no—
388C2×Dic43—21no—
389C2×Dic43—21no—
390C2×Dic43—21no—
391C2×Dic43—21no—
392C2×Dic43—21no—
393C2×Dic43—21no—
394C2×Dic43—21no—
395C2×Dic43—21no—
396C2×Dic43—21no—
397C2×Dic43—44no—
398C2×Dic43C2×C22⋊C412yes—
399C2×Dic43C2×C22⋊C412yes—
400C2×Dic43C4×D412yes—
401D172—44no—
402D172—44no—
403C4×D43—22no—
404C4×D43—22no—
405C4×D43—22no—
406C4×D43—22no—
407C4×D43—22no—
408C4×D43—22no—
409C4×D43—22no—
410C4×D43—22no—
411C4×D43—22no—
412C4×D43—22no—
413C4×D43—22no—
414C4×D43—22no—
415C4×D43—44no—
416C4×D43—44no—
417Dic86—44no—
418C8×C43—22no—
419C8×C43—41no—
420C8×C43—41no—
421C8×C43—41no—
422C43⋊C8—22no—
423C43⋊C8—41no—
424C43⋊C8—41no—
425C43⋊C8—41no—
426#22400—431nomaximal, Sylow
427C22×C43—22no—
428C22×C43—22no—
429C22×C43—22no—
430C22×C43—41no—
431C22×C43—41no—
432C22×C43—41no—
433C22×C43—41no—
434C22×C43—41no—
435C22×C43—41no—
436C22×C43—41no—
437C22×C43—41no—
438C22×C43—41no—
439C22×C43—41no—
440C22×C43—41no—
441C22×C43C22×C22⋊C411yescharacteristic
442C22×C43C2×C4×D411yescharacteristic
443C22×C43#51811yescharacteristic
444C22×C43C2×#13111yescharacteristic
445C22×C43#56811yescharacteristic
446C22×C43#56811yescharacteristic
447C22×C43#56811yescharacteristic
448C2×D43—22no—
449C2×D43—22no—
450C2×D43—22no—
451C2×D43—22no—
452C2×D43—22no—
453C2×D43—22no—
454C2×D43—22no—
455C2×D43—22no—
456C2×D43—22no—
457C2×D43—416no—
458C2×D43—41no—
459C2×D43—41no—
460C2×D43—41no—
461C2×D43—41no—
462C2×D43—41no—
463C2×D43—41no—
464C2×D43—41no—
465C2×D43—41no—
466C2×D43—41no—
467C2×D43—41no—
468C2×D43—41no—
469C2×D43—41no—
470C4×C43—22no—
471C4×C43—22no—
472C4×C43—41no—
473C4×C43—41no—
474C4×C43D4211yescharacteristic
475C4×C43D4211yescharacteristic
476C4×C43#54611yescharacteristic
477C4×C43#54611yescharacteristic
478Dic43—22no—
479Dic43—22no—
480Dic43—22no—
481Dic43—41no—
482Dic43—41no—
483C2×#525—431no—
484C2×#436—431no—
485C2×#435—431no—
486C2×#408—431no—
487C2×#407—431no—
488#1955D4311yescharacteristic, complemented
489#1954—431no—
490#1870—431no—
491#1870—431no—
492#1870—431no—
493#1869—431no—
494#1798—431no—
495#1780—431no—
496#1779—431no—
497#1750—431no—
498C2×C43—42no—
499C2×C43—81no—
500C2×C43D4×C22⋊C411yescharacteristic
501C2×C43#287911yescharacteristic
502C2×C43#288011yescharacteristic
503C2×C43#293011yescharacteristic
504C2×C43#293311yescharacteristic
505C2×C43#297611yescharacteristic
506C2×C43#297811yescharacteristic
507D43—42no—
508D43—42no—
509D43—42no—
510C22×#41—431no—
511C24×C4—431no—
512C22×M16—431no—
513C22×M16—431no—
514C22×M16—431no—
515C23×C8—431no—
516#525—864no—
517#525—864no—
518C2×#123—431no—
519C2×#123—431no—
520C2×C22⋊Q8—431no—
521C2×C22⋊Q8—431no—
522C2×#121—431no—
523C2×#121—431no—
524C2×#120—431no—
525C2×#120—431no—
526C2×C4×D4—431no—
527C2×C4×D4—431no—
528C2×C4×D4—431no—
529C2×C4×D4C2×D4311yescharacteristic
530C2×#117—431no—
531#436—864no—
532#435—864no—
533C2×C4⋊C8—431no—
534C2×C4⋊C8C2×D4311yescharacteristic, complemented
535#408—864no—
536#407—864no—
537C2×C22⋊C8—431no—
538C2×C22⋊C8—431no—
539C2×C22⋊C8—431no—
540C2×C22⋊C8—431no—
541C2×C22⋊C8—431no—
542C2×C22⋊C8—431no—
543C2×C22⋊C8—431no—
544C2×C22⋊C8—431no—
545C2×C22⋊C8—431no—
546C2×C22⋊C8—431no—
547C2×C22⋊C8—431no—
548C2×C22⋊C8—431no—
549C2×C22⋊C8C2×D4311yescharacteristic
550C2×C22⋊C8C2×D4311yescharacteristic
551C2×C22⋊C8C2×D4311yescharacteristic, complemented
552C2×C22⋊C8C2×D4311yescharacteristic, complemented
553C2×#97C2×D4311yescharacteristic, complemented
554C2×C4×C8—431no—
555#336—431no—
556#336—431no—
557#336—431no—
558#336—431no—
559C43#2240011yescharacteristic, complemented, Sylow
560C25—431no—
561C2×#41—862no—
562C2×#41—862no—
563C2×#41—862no—
564C2×#41—862no—
565C2×#41—1721no—
566C2×#41—1721no—
567C22×Q8—431no—
568C22×D4—431no—
569C22×D4—431no—
570C22×D4—431no—
571C22×D4—431no—
572C22×D4—431no—
573C22×D4—431no—
574C22×D4C4×D4311yescharacteristic
575C23×C4—431no—
576C23×C4—431no—
577C23×C4—431no—
578C23×C4—431no—
579C23×C4—431no—
580C23×C4—431no—
581C23×C4—862no—
582C23×C4—862no—
583C23×C4—862no—
584C23×C4—862no—
585C23×C4—1721no—
586C23×C4—1721no—
587C23×C4C22×D4311yescharacteristic
588C23×C4C22×D4311yescharacteristic
589C2×M16—862no—
590C2×M16—862no—
591C2×M16—862no—
592C2×M16—862no—
593C2×M16—862no—
594C2×M16—862no—
595C2×M16—1721no—
596C2×M16—1721no—
597C2×M16—1721no—
598C22×C8—431no—
599C22×C8—431no—
600C22×C8—431no—
601C22×C8—431no—
602C22×C8—862no—
603C22×C8—862no—
604C22×C8—1721no—
605C22×C8C22×D4311yescharacteristic
606C22×C8C22×D4311yescharacteristic
607C22×C8C22×D4311yescharacteristic
608C22×C8C22×D4311yescharacteristic
609#123—864no—
610#123—864no—
611C22⋊Q8—864no—
612C22⋊Q8—864no—
613#121—864no—
614#121—864no—
615#120—864no—
616#120—864no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—434no—
620C4×D4—434no—
621C4×D4—862no—
622C4×D4—862no—
623C4×D4—862no—
624C4×D4—862no—
625#117—862no—
626#117—862no—
627C2×C4⋊C4—431no—
628C2×C4⋊C4—431no—
629C2×C4⋊C4—431no—
630C2×C4⋊C4—431no—
631C2×C4⋊C4—431no—
632C2×C4⋊C4C4×D4311yescharacteristic
633C2×C22⋊C4—431no—
634C2×C22⋊C4—431no—
635C2×C22⋊C4—431no—
636C2×C22⋊C4—431no—
637C2×C22⋊C4—431no—
638C2×C22⋊C4—431no—
639C2×C22⋊C4—431no—
640C2×C22⋊C4—431no—
641C2×C22⋊C4C4×D4311yescharacteristic
642C2×C22⋊C4C4×D4311yescharacteristic
643C2×C42—431no—
644C2×C42C22×D4311yescharacteristic
645C4⋊C8—22no—
646C4⋊C8—862no—
647C22⋊C8—22no—
648C22⋊C8—22no—
649C22⋊C8—41no—
650C22⋊C8—41no—
651C22⋊C8—434no—
652C22⋊C8—862no—
653C22⋊C8—862no—
654C22⋊C8—862no—
655C22⋊C8—862no—
656C22⋊C8—862no—
657C22⋊C8—862no—
658C22⋊C8—862no—
659C22⋊C8—862no—
660C22⋊C8—862no—
661C22⋊C8—1721no—
662C22⋊C8—1721no—
663#97—22no—
664C4×C8—862no—
665C24—431no—
666C24—431no—
667C24—431no—
668C24—862no—
669C24—862no—
670C24—862no—
671C24—1721no—
672C24—1721no—
673C24—1721no—
674C24—1721no—
675C24C2×C4×D4311yescharacteristic
676C24C2×C4×D4311yescharacteristic
677#41—1724no—
678#41—1724no—
679#41—1724no—
680#41—1724no—
681C2×Q8—862no—
682C2×Q8—862no—
683C2×Q8—1721no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—41no—
687C2×D4—434no—
688C2×D4—862no—
689C2×D4—862no—
690C2×D4—862no—
691C2×D4—862no—
692C2×D4—862no—
693C2×D4—862no—
694C2×D4—862no—
695C2×D4—862no—
696C2×D4—862no—
697C2×D4—1721no—
698C2×D4—1721no—
699C2×D4—1721no—
700C2×D4—1721no—
701C2×D4—1721no—
702C2×D4—1721no—
703C2×D4—1721no—
704C2×D4—1721no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—431no—
718C22×C4—431no—
719C22×C4—431no—
720C22×C4—432no—
721C22×C4—432no—
722C22×C4—432no—
723C22×C4—432no—
724C22×C4—432no—
725C22×C4—432no—
726C22×C4—431no—
727C22×C4—431no—
728C22×C4—862no—
729C22×C4—862no—
730C22×C4—862no—
731C22×C4—862no—
732C22×C4—862no—
733C22×C4—862no—
734C22×C4—861no—
735C22×C4—861no—
736C22×C4—861no—
737C22×C4—861no—
738C22×C4—861no—
739C22×C4—861no—
740C22×C4—861no—
741C22×C4—861no—
742C22×C4—861no—
743C22×C4—861no—
744C22×C4—861no—
745C22×C4—861no—
746C22×C4—1721no—
747C22×C4—1721no—
748C22×C4—1724no—
749C22×C4—1724no—
750C22×C4—1724no—
751C22×C4—1724no—
752C22×C4—1721no—
753C22×C4C2×C4×D4311yescharacteristic
754C22×C4C2×C4×D4311yescharacteristic
755C22×C4C2×C4×D4311yescharacteristic
756C22×C4C2×C4×D4311yescharacteristic
757C22×C4C23×D4311yescharacteristic
758M16—1724no—
759M16—1724no—
760M16—1724no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—432no—
773C2×C8—861no—
774C2×C8—861no—
775C2×C8—861no—
776C2×C8—861no—
777C2×C8—861no—
778C2×C8—861no—
779C2×C8—861no—
780C2×C8—861no—
781C2×C8—861no—
782C2×C8—861no—
783C2×C8—861no—
784C2×C8—1724no—
785C2×C8D4×D4312yes—
786C4⋊C4—22no—
787C4⋊C4—434no—
788C4⋊C4—862no—
789C4⋊C4—862no—
790C4⋊C4—862no—
791C4⋊C4—862no—
792C22⋊C4—22no—
793C22⋊C4—22no—
794C22⋊C4—434no—
795C22⋊C4—434no—
796C22⋊C4—862no—
797C22⋊C4—862no—
798C22⋊C4—862no—
799C22⋊C4—862no—
800C22⋊C4—862no—
801C22⋊C4—862no—
802C42—861no—
803C42—861no—
804C42D4×D4312yes—
805C42D4×D4312yes—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—432no—
820C23—432no—
821C23—432no—
822C23—861no—
823C23—861no—
824C23—861no—
825C23—861no—
826C23—861no—
827C23—861no—
828C23—861no—
829C23—861no—
830C23—861no—
831C23—861no—
832C23—861no—
833C23—861no—
834C23—861no—
835C23—861no—
836C23—861no—
837C23—861no—
838C23—861no—
839C23—861no—
840C23—1724no—
841C23—1724no—
842C23—1724no—
843C23—1724no—
844C23—1724no—
845C23—1724no—
846C23—1724no—
847C23#1306333312yes—
848C23C22×C4×D4311yescharacteristic
849Q8—1724no—
850D4—44no—
851D4—1724no—
852D4—1724no—
853D4—1724no—
854D4—1724no—
855D4—1724no—
856D4—1724no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—432no—
876C2×C4—432no—
877C2×C4—432no—
878C2×C4—861no—
879C2×C4—861no—
880C2×C4—861no—
881C2×C4—861no—
882C2×C4—861no—
883C2×C4—861no—
884C2×C4—862no—
885C2×C4—862no—
886C2×C4—862no—
887C2×C4—862no—
888C2×C4—862no—
889C2×C4—862no—
890C2×C4—862no—
891C2×C4—862no—
892C2×C4—862no—
893C2×C4—862no—
894C2×C4—862no—
895C2×C4—862no—
896C2×C4—861no—
897C2×C4—861no—
898C2×C4—861no—
899C2×C4—861no—
900C2×C4—861no—
901C2×C4—861no—
902C2×C4—1724no—
903C2×C4—1724no—
904C2×C4—1724no—
905C2×C4C22⋊C4×D4312yes—
906C2×C4C22⋊C4×D4312yes—
907C2×C4C2×D4×D4311yescharacteristic
908C2×C4C2×D4×D4311yescharacteristic
909C2×C4C2×D4×D4311yescharacteristic
910C2×C4#41×D4311yescharacteristic
911C2×C4#1306337011yescharacteristic
912C2×C4#1306337111yescharacteristic
913C8—22no—
914C8—41no—
915C8—41no—
916C8—41no—
917C8—862no—
918C8—1721no—
919C8—1721no—
920C8—1721no—
921C22—22no—
922C22—22no—
923C22—22no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—862no—
936C22—862no—
937C22—862no—
938C22—862no—
939C22—862no—
940C22—862no—
941C22—862no—
942C22—862no—
943C22—862no—
944C22—17216no—
945C22—1721no—
946C22—1721no—
947C22—1721no—
948C22—1721no—
949C22—1721no—
950C22—1721no—
951C22—1721no—
952C22—1721no—
953C22—1721no—
954C22—1721no—
955C22—1721no—
956C22—1721no—
957C22C2×C22⋊C4×D4311yescharacteristic
958C22C4×D4×D4311yescharacteristic
959C22#1458337111yescharacteristic
960C22C2×#1306333311yescharacteristic
961C22#1458366411yescharacteristic
962C22#1458366411yescharacteristic
963C22#1458366511yescharacteristic
964C4—22no—
965C4—22no—
966C4—41no—
967C4—41no—
968C4—862no—
969C4—862no—
970C4—862no—
971C4—1721no—
972C4—1721no—
973C4#1458353311yescharacteristic
974C4#1458353411yescharacteristic
975C4#1458354211yescharacteristic
976C4#1458354611yescharacteristic
977C2—42no—
978C2—81no—
979C2—1722no—
980C2—1722no—
981C2—1722no—
982C2#1913741611yescharacteristic
983C2#1914303711yescharacteristic
984C2#1914304511yescharacteristic
985C2#1914329311yescharacteristic
986C2#1914332111yescharacteristic
987C2#1914364411yescharacteristic
988C2#1914365411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1955C2
prime radicalC2×#14583408C2
cosocleC22×C4×C43C24
hypercenter#1955D43
hypocenterC43#22400
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1955

Complements

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

NH ≅ G/Ntype
2. C2×#14582976C2semidirect
3. C2×#14582972C2semidirect
4. C2×#14582864C2semidirect
5. C2×#14582861C2semidirect
6. #19135390C2semidirect
7. #19134889C2semidirect
8. #19134889C2semidirect
9. #19134889C2semidirect
10. #19134884C2semidirect
11. #19134576C2semidirect
12. #19134506C2semidirect
13. #19134504C2semidirect
14. #19134364C2semidirect
15. C43×#1955C2semidirect
20. C22×#10621872C22semidirect
21. C22×C8×D43C22semidirect
38. C2×C4⋊(C43⋊C8)C22semidirect
43. C2×C22⋊(C43⋊C8)C22semidirect
44. C2×C22⋊(C43⋊C8)C22semidirect
51. C2×(C2×D43)⋊C8C22semidirect
52. C2×(C2×D43)⋊C8C22semidirect
53. C2×C4×C43⋊C8C22semidirect
54. #14582653C22semidirect
55. #14582653C22semidirect
56. #14582653C22semidirect
57. #14582653C22semidirect
59. C2×C4⋊C8×C43C22semidirect
62. C2×C22⋊C8×C43C22semidirect
63. C2×C22⋊C8×C43C22semidirect
64. C2×#97×C43C22semidirect
149. (C2×D43)⋊C8D4semidirect
488. #1955D43semidirect
534. C2×C4⋊C8C2×D43semidirect
551. C2×C22⋊C8C2×D43semidirect
552. C2×C22⋊C8C2×D43semidirect
553. C2×#97C2×D43semidirect
559. C43#22400semidirect

Maximal subgroups

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

subgroupindex
C2×#145834082
C2×#145829762
C2×#145829722
C2×#145828642
C2×#145828612
#191353902
#191348892
#191348842
#191345762
#191345062
#191345042
#191343642
C43×#19552
#2240043