Finite Group Databasebeta

← #25111884

Subgroups — #25111884

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×#14583411C211yesmaximal, characteristic
2C2×#14582978C211yesmaximal, characteristic, complemented
3C2×#14582972C211yesmaximal, characteristic, complemented
4C2×#14582864C211yesmaximal, characteristic, complemented
5C2×#14582861C211yesmaximal, characteristic, complemented
6#19135393C211yesmaximal, characteristic, complemented
7#19135389C211yesmaximal, characteristic, complemented
8#19134891C211yesmaximal, characteristic, complemented
9#19134891C211yesmaximal, characteristic, complemented
10#19134891C211yesmaximal, characteristic, complemented
11#19134886C211yesmaximal, characteristic, complemented
12#19134579C211yesmaximal, characteristic, complemented
13#19134506C211yesmaximal, characteristic, complemented
14#19134504C211yesmaximal, characteristic, complemented
15C43×#1750C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C22×#10621872C2211yescharacteristic, complemented
21C22×C8×D43C2211yescharacteristic, complemented
22#14583411—24no—
23#14583411—24no—
24C2×#13063309C411yescharacteristic
25C2×#13063309C411yescharacteristic
26C2×#13063305C411yescharacteristic
27C2×#13063305C411yescharacteristic
28C2×#13063300C411yescharacteristic
29C2×#13063300C411yescharacteristic
30C2×#13063295C411yescharacteristic
31C2×#13063295C411yescharacteristic
32C2×C4×D172C2211yescharacteristic
33C2×C4×D172C2211yescharacteristic
34C2×C4×D172C2211yescharacteristic
35C2×C4×D172C2211yescharacteristic
36#14582978—24no—
37#14582972—24no—
38C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
39C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
40#14582864—24no—
41#14582861—24no—
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic
46C2×(C2×D43)⋊C8C2211yescharacteristic
47C2×(C2×D43)⋊C8C2211yescharacteristic
48C2×(C2×D43)⋊C8C2211yescharacteristic
49C2×(C2×D43)⋊C8C2211yescharacteristic
50C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
51C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
52C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
53C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
54C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
55C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
56#14582654C2211yescharacteristic, complemented
57#14582654C2211yescharacteristic, complemented
58C2×#117×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C2×#97×C43C2211yescharacteristic, complemented
62C2×C4×C8×C43C2211yescharacteristic, complemented
63C43×#336C2211yescharacteristic, complemented
64C43×#336C2211yescharacteristic, 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×D172C2×C411yescharacteristic
76C22×D172C2×C411yescharacteristic
77C22×D172C2×C411yescharacteristic
78C22×C22⋊D43C2×C411yescharacteristic
79C22×C22⋊D43C2×C411yescharacteristic
80C23×Dic43C2×C411yescharacteristic
81C22×C4×D43—22no—
82C22×C4×D43—22no—
83C22×C4×D43—22no—
84C22×C4×D43—22no—
85C22×C4×D43—41no—
86C22×C4×D43—41no—
87C22×C4×D43C2×C411yescharacteristic
88C22×C4×D43C2×C411yescharacteristic
89C22×C4×D43C2311yescharacteristic
90C22×C4×D43C2311yescharacteristic
91C22×C4×D43C2311yescharacteristic
92C22×C4×D43C2311yescharacteristic
93C2×#10621872—22no—
94C2×#10621872—22no—
95C2×#10621872—22no—
96C2×#10621872—22no—
97C2×#10621872—22no—
98C2×#10621872—22no—
99C2×#10621872—41no—
100C2×#10621872—41no—
101C2×#10621872—41no—
102C22×C43⋊C8C2311yescharacteristic
103C22×C43⋊C8C2311yescharacteristic
104C22×C43⋊C8C2311yescharacteristic
105C22×C43⋊C8C2311yescharacteristic
106C2×C8×D43—22no—
107C2×C8×D43—22no—
108C2×C8×D43—41no—
109#13063309—24no—
110#13063309—24no—
111#13063305—24no—
112#13063305—24no—
113#13063300—24no—
114#13063300—24no—
115#13063295—24no—
116#13063295—24no—
117C4×D172—22no—
118C4×D172—22no—
119C4×D172—22no—
120C4×D172—22no—
121C4×D172—22no—
122C4×D172—22no—
123C4×D172D414yes—
124C4×D172D414yes—
125C2×C4⋊Dic43C2×C411yescharacteristic
126C2×C4⋊Dic43C2×C411yescharacteristic
127C2×C4⋊Dic43C2×C411yescharacteristic
128C2×C4⋊Dic43C2×C411yescharacteristic
129C2×(C2×D43)⋊C4C2×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×(C2×D43)⋊C4C2×C411yescharacteristic
137C4⋊(C43⋊C8)—22no—
138C4⋊(C43⋊C8)—22no—
139C22⋊(C43⋊C8)—22no—
140C22⋊(C43⋊C8)—22no—
141(C2×D43)⋊C8—22no—
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)⋊C8—41no—
150(C2×D43)⋊C8—41no—
151(C2×D43)⋊C8—41no—
152(C2×D43)⋊C8—41no—
153C23×C4×C43C2311yescharacteristic
154C22×C8×C43C2311yescharacteristic
155C22×C8×C43C2311yescharacteristic
156C22×C8×C43C2311yescharacteristic
157C22×C8×C43C2311yescharacteristic
158#117×C43—22no—
159#117×C43—22no—
160C2×C4⋊C4×C43C2×C411yescharacteristic
161C2×C4⋊C4×C43C2×C411yescharacteristic
162C2×C22⋊C4×C43C2×C411yescharacteristic
163C2×C22⋊C4×C43C2×C411yescharacteristic
164C2×C42×C43C2311yescharacteristic
165C2×C42×C43C2311yescharacteristic
166C22⋊C8×C43—22no—
167C22⋊C8×C43D414yescomplemented
168#97×C43—22no—
169C4×C8×C43—22no—
170C24×C43C22×C411yescharacteristic
171C23×D43—22no—
172C23×D43—22no—
173C23×D43—22no—
174C23×D43—41no—
175C23×D43—41no—
176C23×D43—41no—
177C23×D43—41no—
178C23×D43C22×C411yescharacteristic
179C23×D43C22×C411yescharacteristic
180C23×D43C22×C411yescharacteristic
181C23×D43C22×C411yescharacteristic
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43C22×C411yescharacteristic
187C22×C4×C43C22×C411yescharacteristic
188C22×C4×C43C22×C411yescharacteristic
189C22×C4×C43C22×C411yescharacteristic
190C22×C4×C43C22×C411yescharacteristic
191C22×C4×C43C2×D412yes—
192C22×C4×C43#4112yes—
193C22×C4×C43C2411yescharacteristic
194C2×C22⋊D43—22no—
195C2×C22⋊D43—22no—
196C2×C22⋊D43—22no—
197C2×C22⋊D43—22no—
198C2×C22⋊D43—41no—
199C2×C22⋊D43—41no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43—41no—
203C22×Dic43C22×C411yescharacteristic
204C22×Dic43C22×C411yescharacteristic
205C22×Dic43C22×C411yescharacteristic
206C22×Dic43C22×C411yescharacteristic
207#10621898—44no—
208#10621898—44no—
209#10621898—44no—
210#10621898—44no—
211C2×D172—22no—
212C2×D172—22no—
213C2×D172—22no—
214C2×D172—22no—
215C2×D172—22no—
216C2×D172—22no—
217C2×D172—22no—
218C2×D172—41no—
219C2×D172—41no—
220C2×D172—41no—
221C2×D172—41no—
222C2×D172—41no—
223C2×D172—41no—
224C2×D172—41no—
225C2×D172C22⋊C414yes—
226C2×C4×D43—21no—
227C2×C4×D43—21no—
228C2×C4×D43—21no—
229C2×C4×D43—21no—
230C2×C4×D43—21no—
231C2×C4×D43—21no—
232C2×C4×D43—21no—
233C2×C4×D43—21no—
234C2×C4×D43—22no—
235C2×C4×D43—22no—
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—21no—
245C2×C4×D43—21no—
246C2×C4×D43—21no—
247C2×C4×D43—21no—
248C2×C4×D43—22no—
249C2×C4×D43—22no—
250C2×C4×D43—41no—
251C2×C4×D43—41no—
252C2×C4×D43—44no—
253C2×C4×D43—44no—
254C2×C4×D43—44no—
255C2×C4×D43—44no—
256C2×C4×D43C2×D412yes—
257C2×C4×D43C2×D412yes—
258C2×C4×D43C2×D412yes—
259C2×C4×D43C2×D412yes—
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×C43C2×D412yes—
274C2×C8×C43C2×D412yes—
275C4⋊C4×C43—22no—
276C4⋊C4×C43—22no—
277C22⋊C4×C43—22no—
278C22⋊C4×C43—22no—
279C42×C43—21no—
280C42×C43—21no—
281C42×C43C2×D412yes—
282C42×C43C2×D412yes—
283(C2×D43)⋊C4—22no—
284(C2×D43)⋊C4—22no—
285(C2×D43)⋊C4—22no—
286(C2×D43)⋊C4—22no—
287(C2×D43)⋊C4—22no—
288(C2×D43)⋊C4—22no—
289(C2×D43)⋊C4C22⋊C414yes—
290(C2×D43)⋊C4C22⋊C414yes—
291C4⋊Dic43—22no—
292C4⋊Dic43—22no—
293C4⋊Dic43—22no—
294C4⋊Dic43C22⋊C414yes—
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⋊C8—21no—
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×C43C4×D412yes—
318C23×C43C23×C411yescharacteristic
319C22×D43—21no—
320C22×D43—21no—
321C22×D43—21no—
322C22×D43—21no—
323C22×D43—21no—
324C22×D43—21no—
325C22×D43—21no—
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×D43#13112yes—
354C2×C4×C43—21no—
355C2×C4×C43—21no—
356C2×C4×C43—21no—
357C2×C4×C43—21no—
358C2×C4×C43—21no—
359C2×C4×C43—21no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—21no—
365C2×C4×C43—21no—
366C2×C4×C43—21no—
367C2×C4×C43—21no—
368C2×C4×C43—21no—
369C2×C4×C43—21no—
370C2×C4×C43C2×C22⋊C412yes—
371C2×C4×C43C2×C22⋊C412yes—
372C2×C4×C43C4×D412yes—
373C2×C4×C43C22×D411yescharacteristic
374C2×C4×C43C22×D411yescharacteristic
375C2×C4×C43C22×D411yescharacteristic
376C2×C4×C43C2×#4111yescharacteristic
377C2×C4×C43H(5,𝔽2)11yescharacteristic
378C2×C4×C43H(5,𝔽2)11yescharacteristic
379C22⋊D43—44no—
380C22⋊D43—44no—
381C2×Dic43—21no—
382C2×Dic43—21no—
383C2×Dic43—21no—
384C2×Dic43—21no—
385C2×Dic43—21no—
386C2×Dic43—21no—
387C2×Dic43—21no—
388C2×Dic43—21no—
389C2×Dic43—21no—
390C2×Dic43—21no—
391C2×Dic43—44no—
392C2×Dic43C2×C22⋊C412yes—
393C2×Dic43C2×C22⋊C412yes—
394D172—44no—
395D172—44no—
396D172—44no—
397D172—44no—
398D172—44no—
399C4×D43—22no—
400C4×D43—22no—
401C4×D43—22no—
402C4×D43—22no—
403C4×D43—22no—
404C4×D43—22no—
405C4×D43—22no—
406C4×D43—22no—
407C4×D43—44no—
408C4×D43—44no—
409C4×D43—41no—
410C4×D43—41no—
411C4×D43—41no—
412C4×D43—41no—
413C4×D43—41no—
414C4×D43—41no—
415C4×D43—41no—
416C4×D43—41no—
417Dic86—44no—
418C8×C43—22no—
419C8×C43—22no—
420C8×C43—41no—
421C8×C43—41no—
422C43⋊C8—41no—
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×C43C22×C22⋊C411yescharacteristic
435C22×C43C2×C4×D411yescharacteristic
436C22×C43#51811yescharacteristic
437C22×C43C2×#13111yescharacteristic
438C22×C43#56811yescharacteristic
439C22×C43#56811yescharacteristic
440C22×C43#56811yescharacteristic
441C2×D43—22no—
442C2×D43—22no—
443C2×D43—22no—
444C2×D43—22no—
445C2×D43—22no—
446C2×D43—22no—
447C2×D43—22no—
448C2×D43—22no—
449C2×D43—22no—
450C2×D43—416no—
451C2×D43—41no—
452C2×D43—41no—
453C2×D43—41no—
454C2×D43—41no—
455C2×D43—41no—
456C2×D43—41no—
457C2×D43—41no—
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—22no—
473C4×C43—41no—
474C4×C43—41no—
475C4×C43D4211yescharacteristic
476C4×C43D4211yescharacteristic
477C4×C43#54611yescharacteristic
478C4×C43#54611yescharacteristic
479Dic43—22no—
480Dic43—22no—
481Dic43—41no—
482Dic43—41no—
483C2×#525—431no—
484C2×#436—431no—
485C2×#435—431no—
486C2×#408—431no—
487C2×#407—431no—
488#1955—431no—
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#1750D4311yescharacteristic, complemented
498C2×C43—42no—
499C2×C43D4×C22⋊C411yescharacteristic
500C2×C43#287911yescharacteristic
501C2×C43#288011yescharacteristic
502C2×C43#293011yescharacteristic
503C2×C43#293311yescharacteristic
504C2×C43#297611yescharacteristic
505C2×C43#297811yescharacteristic
506D43—42no—
507D43—42no—
508D43—42no—
509D43—81no—
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×D4—431no—
530C2×#117C2×D4311yescharacteristic
531#436—864no—
532#435—864no—
533C2×C4⋊C8—431no—
534C2×C4⋊C8—431no—
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⋊C8—431no—
550C2×C22⋊C8—431no—
551C2×C22⋊C8C2×D4311yescharacteristic
552C2×C22⋊C8C2×D4311yescharacteristic
553C2×#97C2×D4311yescharacteristic, complemented
554C2×C4×C8C2×D4311yescharacteristic, complemented
555#336—431no—
556#336—431no—
557#336C2×D4311yescharacteristic, complemented
558#336C2×D4311yescharacteristic, complemented
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×D4—431no—
575C23×C4—431no—
576C23×C4—431no—
577C23×C4—431no—
578C23×C4—431no—
579C23×C4—431no—
580C23×C4—431no—
581C23×C4—431no—
582C23×C4—862no—
583C23×C4—862no—
584C23×C4—862no—
585C23×C4—862no—
586C23×C4—1721no—
587C23×C4—1721no—
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—434no—
618C4×D4—434no—
619C4×D4—862no—
620C4×D4—862no—
621C4×D4—862no—
622C4×D4—862no—
623C4×D4—862no—
624C4×D4—862no—
625#117—22no—
626#117—22no—
627C2×C4⋊C4—431no—
628C2×C4⋊C4—431no—
629C2×C4⋊C4—431no—
630C2×C4⋊C4—431no—
631C2×C4⋊C4C4×D4311yescharacteristic
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×C42C22×D4311yescharacteristic
644C2×C42C22×D4311yescharacteristic
645C4⋊C8—862no—
646C4⋊C8—862no—
647C22⋊C8—22no—
648C22⋊C8—862no—
649C22⋊C8—862no—
650C22⋊C8—862no—
651C22⋊C8—862no—
652C22⋊C8—862no—
653C22⋊C8—862no—
654C22⋊C8—862no—
655C22⋊C8—862no—
656C22⋊C8—862no—
657C22⋊C8—862no—
658C22⋊C8—1721no—
659C22⋊C8—1721no—
660C22⋊C8—1721no—
661C22⋊C8—1721no—
662C22⋊C8D17214yescomplemented
663#97—22no—
664C4×C8—22no—
665C24—431no—
666C24—431no—
667C24—431no—
668C24—431no—
669C24—862no—
670C24—862no—
671C24—862no—
672C24—1721no—
673C24—1721no—
674C24—1721no—
675C24—1721no—
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—434no—
685C2×D4—862no—
686C2×D4—862no—
687C2×D4—862no—
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—1721no—
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—431no—
710C22×C4—431no—
711C22×C4—432no—
712C22×C4—432no—
713C22×C4—432no—
714C22×C4—432no—
715C22×C4—431no—
716C22×C4—431no—
717C22×C4—862no—
718C22×C4—862no—
719C22×C4—862no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—861no—
726C22×C4—861no—
727C22×C4—861no—
728C22×C4—862no—
729C22×C4—862no—
730C22×C4—862no—
731C22×C4—861no—
732C22×C4—861no—
733C22×C4—861no—
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—1721no—
744C22×C4—1721no—
745C22×C4—1724no—
746C22×C4—1724no—
747C22×C4—1724no—
748C22×C4—1724no—
749C22×C4—1721no—
750C22×C4C2×C4×D4311yescharacteristic
751C22×C4C2×C4×D4311yescharacteristic
752C22×C4C2×C4×D4311yescharacteristic
753C22×C4C2×C4×D4311yescharacteristic
754C22×C4C2×C4×D4311yescharacteristic
755C22×C4C2×D17212yes—
756C22×C4#1062189812yes—
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—861no—
772C2×C8—861no—
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—1724no—
784C2×C8C2×D17212yes—
785C2×C8C2×D17212yes—
786C4⋊C4—22no—
787C4⋊C4—22no—
788C4⋊C4—434no—
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—21no—
803C42—21no—
804C42D4×D4312yes—
805C42D4×D4312yes—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—432no—
813C23—432no—
814C23—432no—
815C23—861no—
816C23—861no—
817C23—861no—
818C23—861no—
819C23—861no—
820C23—861no—
821C23—861no—
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—
847C23C4×D17212yes—
848C23C22×C4×D4311yescharacteristic
849Q8—1724no—
850D4—1724no—
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—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—432no—
874C2×C4—432no—
875C2×C4—861no—
876C2×C4—861no—
877C2×C4—861no—
878C2×C4—861no—
879C2×C4—862no—
880C2×C4—862no—
881C2×C4—862no—
882C2×C4—862no—
883C2×C4—862no—
884C2×C4—862no—
885C2×C4—862no—
886C2×C4—862no—
887C2×C4—861no—
888C2×C4—861no—
889C2×C4—861no—
890C2×C4—861no—
891C2×C4—861no—
892C2×C4—861no—
893C2×C4—1724no—
894C2×C4—1724no—
895C2×C4—1724no—
896C2×C4—1721no—
897C2×C4—1721no—
898C2×C4—1721no—
899C2×C4—1721no—
900C2×C4—1721no—
901C2×C4—1721no—
902C2×C4—1721no—
903C2×C4—1721no—
904C2×C4C22⋊C4×D4312yes—
905C2×C4C22⋊C4×D4312yes—
906C2×C4C4×D17212yes—
907C2×C4C2×D4×D4311yescharacteristic
908C2×C4C2×D4×D4311yescharacteristic
909C2×C4C22×D17211yescharacteristic
910C2×C4C2×#1062189811yescharacteristic
911C2×C4#1306337111yescharacteristic
912C2×C4#1306337111yescharacteristic
913C8—22no—
914C8—22no—
915C8—41no—
916C8—41no—
917C8—1721no—
918C8—1721no—
919C8—1721no—
920C8—1721no—
921C22—22no—
922C22—22no—
923C22—22no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—862no—
929C22—862no—
930C22—862no—
931C22—862no—
932C22—862no—
933C22—862no—
934C22—862no—
935C22—862no—
936C22—862no—
937C22—17216no—
938C22—1721no—
939C22—1721no—
940C22—1721no—
941C22—1721no—
942C22—1721no—
943C22—1721no—
944C22—1721no—
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
958C22C2×C4×D17211yescharacteristic
959C22#1458337311yescharacteristic
960C22#131×D4311yescharacteristic
961C22#1458366411yescharacteristic
962C22#1458366411yescharacteristic
963C22#1458366411yescharacteristic
964C4—22no—
965C4—22no—
966C4—22no—
967C4—41no—
968C4—41no—
969C4—862no—
970C4—862no—
971C4—1721no—
972C4—1721no—
973C4D4×D17211yescharacteristic
974C4D4×D17211yescharacteristic
975C4#1458354511yescharacteristic
976C4#1458354511yescharacteristic
977C2—42no—
978C2—3441no—
979C2—1722no—
980C2—1722no—
981C2—1722no—
982C2C22⋊C4×D17211yescharacteristic
983C2#1914303711yescharacteristic
984C2#1914304311yescharacteristic
985C2#1914330011yescharacteristic
986C2#1914332311yescharacteristic
987C2#1914364111yescharacteristic
988C2#1914365611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1750C2
prime radicalC2×#14583411C2
cosocleC22×C4×C43C24
hypercenter#1750D43
hypocenterC43#22400
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1750

Complements

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

NH ≅ G/Ntype
2. C2×#14582978C2semidirect
3. C2×#14582972C2semidirect
4. C2×#14582864C2semidirect
5. C2×#14582861C2semidirect
6. #19135393C2semidirect
7. #19135389C2semidirect
8. #19134891C2semidirect
9. #19134891C2semidirect
10. #19134891C2semidirect
11. #19134886C2semidirect
12. #19134579C2semidirect
13. #19134506C2semidirect
14. #19134504C2semidirect
15. C43×#1750C2semidirect
20. C22×#10621872C22semidirect
21. C22×C8×D43C22semidirect
38. C2×C4⋊(C43⋊C8)C22semidirect
39. C2×C4⋊(C43⋊C8)C22semidirect
50. C2×(C2×D43)⋊C8C22semidirect
51. C2×(C2×D43)⋊C8C22semidirect
52. C2×(C2×D43)⋊C8C22semidirect
53. C2×(C2×D43)⋊C8C22semidirect
54. C2×(C2×D43)⋊C8C22semidirect
55. C2×(C2×D43)⋊C8C22semidirect
56. #14582654C22semidirect
57. #14582654C22semidirect
61. C2×#97×C43C22semidirect
62. C2×C4×C8×C43C22semidirect
63. C43×#336C22semidirect
64. C43×#336C22semidirect
167. C22⋊C8×C43D4semidirect
497. #1750D43semidirect
553. C2×#97C2×D43semidirect
554. C2×C4×C8C2×D43semidirect
557. #336C2×D43semidirect
558. #336C2×D43semidirect
559. C43#22400semidirect
662. C22⋊C8D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145834112
C2×#145829782
C2×#145829722
C2×#145828642
C2×#145828612
#191353932
#191353892
#191348912
#191348862
#191345792
#191345062
#191345042
C43×#17502
#2240043