Finite Group Databasebeta

← #25020050

Subgroups — #25020050

Order 11008.

3166 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063296C211yesmaximal, characteristic
2C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic, complemented
3C2×#14582779C211yesmaximal, characteristic, complemented
4C2×#14582775C211yesmaximal, characteristic, complemented
5C2×#14582775C211yesmaximal, characteristic, complemented
6C2×#14582775C211yesmaximal, characteristic, complemented
7C2×#95×D43C211yesmaximal, characteristic, complemented
8#19132847C211yesmaximal, characteristic, complemented
9#19132842C211yesmaximal, characteristic, complemented
10#19132838C211yesmaximal, characteristic, complemented
11#19132832C211yesmaximal, characteristic, complemented
12#19132829C211yesmaximal, characteristic, complemented
13#19132817C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C43×#1438C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C23×C22⋊D43C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C23×C4×D43C2211yescharacteristic
22C2×#13063296—24no—
23C2×#13063296—24no—
24C2×#13063296C418yescomplemented
25C2×(C22⋊D43)⋊C4—24no—
26C2×(C22⋊D43)⋊C4—24no—
27C2×(C22⋊D43)⋊C4—24no—
28C22×C4⋊Dic43C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×C22⋊Dic43C2211yescharacteristic
31C22×C22⋊Dic43C2211yescharacteristic
32C22×C22⋊Dic43C2211yescharacteristic
33C22×C22⋊Dic43C2211yescharacteristic
34C22×C22⋊Dic43C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×C4×Dic43C2211yescharacteristic
38#14582779—24no—
39#14582775—24no—
40#14582775—24no—
41#14582775—24no—
42C2×C43⋊#95C2211yescharacteristic
43C2×C43⋊#95C2211yescharacteristic
44C2×C43⋊#95C2211yescharacteristic
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54#95×D43—24no—
55C23×D4×C43C2211yescharacteristic
56C22×C22⋊C4×C43C2211yescharacteristic
57C22×C22⋊C4×C43C2211yescharacteristic
58C22×C22⋊C4×C43C2211yescharacteristic
59C22×C22⋊C4×C43C2211yescharacteristic
60C2×#95×C43C2211yescharacteristic
61C2×#95×C43C2211yescharacteristic
62C24×D43C2311yescharacteristic
63C22×C22⋊D43—22no—
64C22×C22⋊D43—22no—
65C22×C22⋊D43—22no—
66C22×C22⋊D43—22no—
67C22×C22⋊D43—22no—
68C22×C22⋊D43—22no—
69C22×C22⋊D43—22no—
70C22×C22⋊D43—22no—
71C22×C22⋊D43—22no—
72C22×C22⋊D43—22no—
73C22×C22⋊D43C2×C414yes—
74C22×C22⋊D43C2×C414yescomplemented
75C22×C22⋊D43D414yes—
76C22×C22⋊D43D414yes—
77C23×Dic43—22no—
78C23×Dic43—22no—
79C23×Dic43—22no—
80C23×Dic43—22no—
81C23×Dic43—22no—
82C23×Dic43—41no—
83C23×Dic43—41no—
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2311yescharacteristic
86C23×Dic43C2311yescharacteristic
87C23×Dic43C2311yescharacteristic
88C23×Dic43C2311yescharacteristic
89C23×Dic43C2311yescharacteristic
90C23×Dic43C2311yescharacteristic
91C22×C4×D43—22no—
92C22×C4×D43—22no—
93C22×C4×D43—22no—
94C22×C4×D43—22no—
95C22×C4×D43—22no—
96C22×C4×D43—22no—
97C22×C4×D43—22no—
98C22×C4×D43—22no—
99C22×C4×D43—22no—
100C22×C4×D43—22no—
101C22×C4×D43—22no—
102C22×C4×D43—22no—
103C22×C4×D43—22no—
104C22×C4×D43—41no—
105C22×C4×D43—41no—
106C22×C4×D43—41no—
107C22×C4×D43—41no—
108C22×C4×D43—41no—
109C22×C4×D43—41no—
110C22×C4×D43C2×C414yescomplemented
111C22×C4×D43D414yescomplemented
112#13063296—232no—
113(C22⋊D43)⋊C4—232no—
114C2×C4⋊Dic43—22no—
115C2×C4⋊Dic43—22no—
116C2×C4⋊Dic43C2×C414yescomplemented
117C2×Dic43⋊C4—22no—
118C2×Dic43⋊C4—22no—
119C2×Dic43⋊C4—22no—
120C2×C22⋊Dic43—22no—
121C2×C22⋊Dic43—22no—
122C2×C22⋊Dic43—22no—
123C2×C22⋊Dic43—22no—
124C2×C22⋊Dic43—22no—
125C2×C22⋊Dic43—22no—
126C2×C22⋊Dic43—22no—
127C2×C22⋊Dic43—22no—
128C2×C22⋊Dic43—22no—
129C2×C22⋊Dic43—22no—
130C2×C22⋊Dic43—22no—
131C2×C22⋊Dic43—41no—
132C2×C22⋊Dic43—41no—
133C2×C22⋊Dic43C2×C414yescomplemented
134C2×C22⋊Dic43C2×C414yescomplemented
135C2×(C2×D43)⋊C4—22no—
136C2×(C2×D43)⋊C4—22no—
137C2×(C2×D43)⋊C4—22no—
138C2×(C2×D43)⋊C4—22no—
139C2×(C2×D43)⋊C4—22no—
140C2×(C2×D43)⋊C4D414yescomplemented
141C2×C4×Dic43—22no—
142C2×C4×Dic43—22no—
143C2×C4×Dic43—22no—
144C43⋊#95—22no—
145C43⋊#95—22no—
146C43⋊#95—22no—
147C43⋊#95—22no—
148C43⋊#95—22no—
149C43⋊#95—22no—
150C43⋊#95—22no—
151C43⋊#95—22no—
152C43⋊#95—22no—
153C43⋊#95—41no—
154C43⋊#95—41no—
155C43⋊#95D414yescomplemented
156C25×C43C2311yescharacteristic
157C25×C43C2311yescharacteristic
158C22×D4×C43—22no—
159C22×D4×C43—22no—
160C22×D4×C43—22no—
161C22×D4×C43—22no—
162C22×D4×C43—41no—
163C22×D4×C43—41no—
164C22×D4×C43C2×C414yescomplemented
165C23×C4×C43C2311yescharacteristic
166C23×C4×C43C2311yescharacteristic
167C23×C4×C43C2311yescharacteristic
168C23×C4×C43C2311yescharacteristic
169C23×C4×C43C2311yescharacteristic
170C2×C22⋊C4×C43—22no—
171C2×C22⋊C4×C43—22no—
172C2×C22⋊C4×C43—22no—
173C2×C22⋊C4×C43—22no—
174C2×C22⋊C4×C43—22no—
175C2×C22⋊C4×C43—22no—
176C2×C22⋊C4×C43—22no—
177C2×C22⋊C4×C43—22no—
178C2×C22⋊C4×C43—41no—
179C2×C22⋊C4×C43—41no—
180C2×C22⋊C4×C43—41no—
181C2×C22⋊C4×C43—41no—
182#95×C43—22no—
183#95×C43—22no—
184C24×C43—21no—
185C24×C43—21no—
186C24×C43—21no—
187C24×C43—21no—
188C24×C43—21no—
189C24×C43—21no—
190C24×C43—21no—
191C24×C43—21no—
192C24×C43—21no—
193C24×C43—21no—
194C24×C43—21no—
195C24×C43—21no—
196C24×C43—21no—
197C24×C43—21no—
198C24×C43—21no—
199C24×C43—21no—
200C24×C43—21no—
201C24×C43—21no—
202C24×C43—21no—
203C24×C43—21no—
204C24×C43—21no—
205C24×C43—21no—
206C24×C43—21no—
207C24×C43—21no—
208C24×C43—21no—
209C24×C43—21no—
210C24×C43C22×C412yes—
211C24×C43C22×C412yes—
212C24×C43C2×D412yes—
213C24×C43C2×D412yes—
214C24×C43C2411yescharacteristic
215C23×D43—21no—
216C23×D43—21no—
217C23×D43—21no—
218C23×D43—21no—
219C23×D43—21no—
220C23×D43—21no—
221C23×D43—21no—
222C23×D43—21no—
223C23×D43C22×C412yes—
224C23×D43C2×D412yes—
225C23×D43C2×D412yes—
226C23×D43C2×D412yes—
227C23×D43C2×D412yes—
228C23×D43#4112yes—
229C23×D43#4112yes—
230C2×D4×C43—28no—
231C2×D4×C43—28no—
232C2×D4×C43—44no—
233C2×D4×C43—44no—
234C2×D4×C43—44no—
235C2×D4×C43—44no—
236C2×D4×C43—44no—
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43—21no—
240C22×C4×C43—21no—
241C22×C4×C43—21no—
242C22×C4×C43—21no—
243C22×C4×C43—21no—
244C22×C4×C43—21no—
245C22×C4×C43—21no—
246C22×C4×C43—21no—
247C22×C4×C43—21no—
248C22×C4×C43—21no—
249C22×C4×C43—21no—
250C22×C4×C43—21no—
251C22×C4×C43—21no—
252C22×C4×C43—21no—
253C22×C4×C43—21no—
254C22×C4×C43—21no—
255C22×C4×C43—21no—
256C22×C4×C43—21no—
257C22×C4×C43—21no—
258C22×C4×C43—21no—
259C22×C4×C43—21no—
260C22×C4×C43—21no—
261C22×C4×C43—21no—
262C22×C4×C43—21no—
263C22×C4×C43—21no—
264C22×C4×C43—21no—
265C22×C4×C43—21no—
266C22×C4×C43C22×C412yes—
267C22×C4×C43C2×D412yes—
268C22×C4×C43C2×D412yes—
269C22×C4×C43C2×D412yes—
270C22×C4×C43#4112yes—
271C22×C4×C43#4112yes—
272C2×C22⋊D43—28no—
273C2×C22⋊D43—28no—
274C2×C22⋊D43—28no—
275C2×C22⋊D43—28no—
276C2×C22⋊D43—28no—
277C2×C22⋊D43—28no—
278C2×C22⋊D43—28no—
279C2×C22⋊D43—28no—
280C2×C22⋊D43—28no—
281C2×C22⋊D43—44no—
282C2×C22⋊D43—44no—
283C2×C22⋊D43—44no—
284C2×C22⋊D43—44no—
285C2×C22⋊D43C22⋊C4116yescomplemented
286C22×Dic43—28no—
287C22×Dic43—21no—
288C22×Dic43—21no—
289C22×Dic43—21no—
290C22×Dic43—21no—
291C22×Dic43—21no—
292C22×Dic43—21no—
293C22×Dic43—21no—
294C22×Dic43—21no—
295C22×Dic43—21no—
296C22×Dic43—21no—
297C22×Dic43—21no—
298C22×Dic43—21no—
299C22×Dic43—21no—
300C22×Dic43—21no—
301C22×Dic43—21no—
302C22×Dic43—21no—
303C22×Dic43—21no—
304C22×Dic43—21no—
305C22×Dic43—21no—
306C22×Dic43—21no—
307C22×Dic43—21no—
308C22×Dic43—21no—
309C22×Dic43—21no—
310C22×Dic43—21no—
311C22×Dic43—21no—
312C22×Dic43—21no—
313C22×Dic43—21no—
314C22×Dic43—21no—
315C22×Dic43—21no—
316C22×Dic43—21no—
317C22×Dic43—21no—
318C22×Dic43—21no—
319C22×Dic43—21no—
320C22×Dic43—21no—
321C22×Dic43—21no—
322C22×Dic43—21no—
323C22×Dic43—21no—
324C22×Dic43—21no—
325C22×Dic43—21no—
326C22×Dic43—44no—
327C22×Dic43—44no—
328C22×Dic43—44no—
329C22×Dic43—44no—
330C22×Dic43—44no—
331C22×Dic43—44no—
332C22×Dic43C22×C412yes—
333C22×Dic43C22×C412yes—
334C22×Dic43C22×C412yes—
335C22×Dic43C2×D412yes—
336C22×Dic43C2×D412yes—
337C22×Dic43C2×D412yes—
338C22×Dic43C2×D412yes—
339C22×Dic43C2×D412yes—
340C22×Dic43C2×D412yes—
341C22×Dic43#4112yes—
342C2×C4×D43—28no—
343C2×C4×D43—28no—
344C2×C4×D43—28no—
345C2×C4×D43—28no—
346C2×C4×D43—28no—
347C2×C4×D43—44no—
348C2×C4×D43—44no—
349C2×C4×D43—44no—
350C2×C4×D43—44no—
351C2×C4×D43—44no—
352C2×C4×D43—44no—
353C2×C4×D43—44no—
354C2×C4×D43—44no—
355C2×C4×D43—44no—
356C2×C4×D43—44no—
357C2×C4×D43—44no—
358C2×C4×D43—44no—
359C2×C4×D43—44no—
360C2×C4×D43—44no—
361C2×C4×D43—44no—
362C2×C4×D43—44no—
363C22⋊C4×C43—28no—
364C22⋊C4×C43—44no—
365C22⋊C4×C43—44no—
366C22⋊C4×C43—44no—
367C22⋊Dic43—28no—
368C22⋊Dic43—28no—
369C22⋊Dic43—44no—
370C22⋊Dic43—44no—
371C22⋊Dic43—44no—
372(C2×D43)⋊C4—28no—
373(C2×D43)⋊C4—44no—
374C4⋊Dic43—28no—
375Dic43⋊C4—28no—
376C4×Dic43—28no—
377C23×C43—22no—
378C23×C43—22no—
379C23×C43—22no—
380C23×C43—22no—
381C23×C43—22no—
382C23×C43—22no—
383C23×C43—22no—
384C23×C43—22no—
385C23×C43—22no—
386C23×C43—22no—
387C23×C43—22no—
388C23×C43—22no—
389C23×C43—22no—
390C23×C43—22no—
391C23×C43—22no—
392C23×C43—22no—
393C23×C43—22no—
394C23×C43—22no—
395C23×C43—22no—
396C23×C43—22no—
397C23×C43—22no—
398C23×C43—22no—
399C23×C43—22no—
400C23×C43—22no—
401C23×C43—22no—
402C23×C43—41no—
403C23×C43—41no—
404C23×C43—41no—
405C23×C43—41no—
406C23×C43—41no—
407C23×C43—41no—
408C23×C43—41no—
409C23×C43—41no—
410C23×C43—41no—
411C23×C43—41no—
412C23×C43—41no—
413C23×C43—41no—
414C23×C43—41no—
415C23×C43—41no—
416C23×C43—41no—
417C23×C43—41no—
418C23×C43—41no—
419C23×C43—41no—
420C23×C43—41no—
421C23×C43—41no—
422C23×C43—41no—
423C23×C43—41no—
424C23×C43—41no—
425C23×C43—41no—
426C23×C43—41no—
427C23×C43—41no—
428C23×C43—41no—
429C23×C43—41no—
430C23×C43—41no—
431C23×C43—41no—
432C23×C43—41no—
433C23×C43—41no—
434C23×C43—41no—
435C23×C43—41no—
436C23×C43—41no—
437C23×C43—41no—
438C23×C43—41no—
439C23×C43—41no—
440C23×C43—41no—
441C23×C43—41no—
442C23×C43—41no—
443C23×C43—41no—
444C23×C43—41no—
445C23×C43—41no—
446C23×C43C2×C22⋊C414yes—
447C23×C43C23×C411yescharacteristic
448C23×C43C22×D411yescharacteristic
449C23×C43C22×D411yescharacteristic
450C23×C43C22×D411yescharacteristic
451C23×C43C22×D411yescharacteristic
452C23×C43C22×D411yescharacteristic
453C23×C43C2×#4111yescharacteristic
454C23×C43C2×#4111yescharacteristic
455C23×C43C2×#4111yescharacteristic
456C23×C43C2×#4111yescharacteristic
457C23×C43C2×#4111yescharacteristic
458C23×C43H(5,𝔽2)11yescharacteristic
459C23×C43H(5,𝔽2)11yescharacteristic
460C23×C43H(5,𝔽2)11yescharacteristic
461C23×C432−1+411yescharacteristic
462C22×D43—22no—
463C22×D43—22no—
464C22×D43—22no—
465C22×D43—22no—
466C22×D43—22no—
467C22×D43—22no—
468C22×D43—22no—
469C22×D43—22no—
470C22×D43—22no—
471C22×D43—22no—
472C22×D43—22no—
473C22×D43—22no—
474C22×D43—22no—
475C22×D43—22no—
476C22×D43—22no—
477C22×D43—22no—
478C22×D43—22no—
479C22×D43—22no—
480C22×D43—22no—
481C22×D43—22no—
482C22×D43—22no—
483C22×D43—22no—
484C22×D43—22no—
485C22×D43—22no—
486C22×D43—22no—
487C22×D43—22no—
488C22×D43—22no—
489C22×D43—22no—
490C22×D43C2×C22⋊C414yes—
491C22×D43C4×D414yes—
492C22×D43C4×D414yes—
493C22×D43#12014yes—
494C22×D43#12114yes—
495C22×D43#12114yes—
496C22×D43#12314yes—
497D4×C43—416no—
498C2×C4×C43—22no—
499C2×C4×C43—22no—
500C2×C4×C43—22no—
501C2×C4×C43—22no—
502C2×C4×C43—22no—
503C2×C4×C43—22no—
504C2×C4×C43—22no—
505C2×C4×C43—22no—
506C2×C4×C43—22no—
507C2×C4×C43—22no—
508C2×C4×C43—22no—
509C2×C4×C43—22no—
510C2×C4×C43—22no—
511C2×C4×C43—22no—
512C2×C4×C43—22no—
513C2×C4×C43—41no—
514C2×C4×C43—41no—
515C2×C4×C43—41no—
516C2×C4×C43—41no—
517C2×C4×C43—41no—
518C2×C4×C43—41no—
519C2×C4×C43—41no—
520C2×C4×C43—41no—
521C2×C4×C43—41no—
522C2×C4×C43—41no—
523C2×C4×C43—41no—
524C2×C4×C43—41no—
525C2×C4×C43—41no—
526C2×C4×C43—41no—
527C2×C4×C43—41no—
528C2×C4×C43—41no—
529C2×C4×C43—41no—
530C2×C4×C43—41no—
531C2×C4×C43—41no—
532C2×C4×C43C4×D414yescomplemented
533C22⋊D43—232no—
534C22⋊D43—416no—
535C2×Dic43—22no—
536C2×Dic43—22no—
537C2×Dic43—22no—
538C2×Dic43—22no—
539C2×Dic43—22no—
540C2×Dic43—22no—
541C2×Dic43—22no—
542C2×Dic43—22no—
543C2×Dic43—22no—
544C2×Dic43—22no—
545C2×Dic43—22no—
546C2×Dic43—22no—
547C2×Dic43—22no—
548C2×Dic43—22no—
549C2×Dic43—22no—
550C2×Dic43—22no—
551C2×Dic43—22no—
552C2×Dic43—22no—
553C2×Dic43—22no—
554C2×Dic43—22no—
555C2×Dic43—22no—
556C2×Dic43—22no—
557C2×Dic43—22no—
558C2×Dic43—22no—
559C2×Dic43—416no—
560C2×Dic43—41no—
561C2×Dic43—41no—
562C2×Dic43—41no—
563C2×Dic43—41no—
564C2×Dic43—41no—
565C2×Dic43—41no—
566C2×Dic43—41no—
567C2×Dic43—41no—
568C2×Dic43—41no—
569C2×Dic43—41no—
570C2×Dic43—41no—
571C2×Dic43—41no—
572C2×Dic43—41no—
573C2×Dic43—41no—
574C2×Dic43—41no—
575C2×Dic43—41no—
576C2×Dic43—41no—
577C2×Dic43—41no—
578C2×Dic43—41no—
579C2×Dic43—41no—
580C2×Dic43—41no—
581C2×Dic43—41no—
582C2×Dic43—41no—
583C2×Dic43C2×C22⋊C414yes—
584C2×Dic43#12114yescomplemented
585C4×D43—416no—
586C4×D43—416no—
587C4×D43—416no—
588#14023—431nomaximal, Sylow
589C22×C43—24no—
590C22×C43—24no—
591C22×C43—24no—
592C22×C43—42no—
593C22×C43—42no—
594C22×C43—42no—
595C22×C43—42no—
596C22×C43—42no—
597C22×C43—42no—
598C22×C43—42no—
599C22×C43—42no—
600C22×C43—42no—
601C22×C43—42no—
602C22×C43—42no—
603C22×C43—42no—
604C22×C43—42no—
605C22×C43—42no—
606C22×C43—42no—
607C22×C43—42no—
608C22×C43—42no—
609C22×C43—42no—
610C22×C43—42no—
611C22×C43—81no—
612C22×C43—81no—
613C22×C43—81no—
614C22×C43—81no—
615C22×C43—81no—
616C22×C43—81no—
617C22×C43—81no—
618C22×C43—81no—
619C22×C43C22×C22⋊C411yescharacteristic
620C22×C43C2×C4×D411yescharacteristic
621C22×C43C2×C4×D411yescharacteristic
622C22×C43C2×C4×D411yescharacteristic
623C22×C43C4×#4111yescharacteristic
624C22×C43#51811yescharacteristic
625C22×C43#52011yescharacteristic
626C22×C43C2×#12011yescharacteristic
627C22×C43C2×#12111yescharacteristic
628C22×C43C2×#12111yescharacteristic
629C22×C43C2×#12111yescharacteristic
630C22×C43C2×#12311yescharacteristic
631C22×C43#52511yescharacteristic
632C22×C43#52911yescharacteristic
633C22×C43#53211yescharacteristic
634C22×C43#53411yescharacteristic
635C22×C43#53711yescharacteristic
636C22×C43#53811yescharacteristic
637C22×C43#53911yescharacteristic
638C22×C43D4211yescharacteristic
639C22×C43D4211yescharacteristic
640C22×C43D4211yescharacteristic
641C22×C43#54611yescharacteristic
642C22×C43#54611yescharacteristic
643C22×C43#54611yescharacteristic
644C22×C43#54611yescharacteristic
645C22×C43#54611yescharacteristic
646C22×C43#54611yescharacteristic
647C22×C43#54711yescharacteristic
648C22×C43#54711yescharacteristic
649C22×C43#54711yescharacteristic
650C22×C43#54811yescharacteristic
651C22×C43#55311yescharacteristic
652C22×C43#55311yescharacteristic
653C22×C43#55311yescharacteristic
654C2×D43—24no—
655C2×D43—24no—
656C2×D43—24no—
657C2×D43—24no—
658C2×D43—24no—
659C2×D43—24no—
660C2×D43—24no—
661C2×D43—24no—
662C2×D43—24no—
663C2×D43—24no—
664C2×D43—24no—
665C2×D43—24no—
666C2×D43—24no—
667C2×D43—24no—
668C2×D43#38618yescomplemented
669C4×C43—24no—
670C4×C43—42no—
671C4×C43—42no—
672C4×C43—42no—
673C4×C43—81no—
674Dic43—24no—
675Dic43—24no—
676Dic43—42no—
677Dic43—42no—
678Dic43—42no—
679Dic43—42no—
680Dic43—81no—
681C22×#121—431no—
682C22×C4×D4—431no—
683C2×#386—431no—
684C2×#386—431no—
685C2×#386—431no—
686C2×#386—431no—
687C22×#95—431no—
688#1441—431no—
689#1440—431no—
690#1439—431no—
691#1438D4311yescharacteristic, complemented
692#1437—431no—
693#1436—431no—
694C22⋊#95—431no—
695C22⋊#95—431no—
696C2×C43—44no—
697C2×C43—82no—
698C2×C43C2×#38611yescharacteristic
699C2×C43C4×#12111yescharacteristic
700C2×C43#232511yescharacteristic
701C2×C43D4×C22⋊C411yescharacteristic
702C2×C43#233911yescharacteristic
703C2×C43#236111yescharacteristic
704C2×C43#236411yescharacteristic
705C2×C43#241011yescharacteristic
706C2×C43#241611yescharacteristic
707C2×C43#242411yescharacteristic
708C2×C43#242511yescharacteristic
709C2×C43#243011yescharacteristic
710C2×C43#244311yescharacteristic
711C2×C43#244411yescharacteristic
712C2×C43#254311yescharacteristic
713D43—28no—
714C23×D4—431no—
715C23×D4—431no—
716C23×D4C2×D4311yescharacteristic
717C24×C4—431no—
718C24×C4—431no—
719C24×C4—431no—
720C24×C4—431no—
721C2×#121—438no—
722C2×#121—864no—
723C2×#121—864no—
724C2×C4×D4—864no—
725C2×C4×D4—864no—
726C2×C4×D4—864no—
727C22×C4⋊C4—431no—
728C22×C4⋊C4—431no—
729C22×C22⋊C4—431no—
730C22×C22⋊C4—431no—
731C22×C22⋊C4—431no—
732C22×C22⋊C4—431no—
733C22×C22⋊C4—431no—
734C22×C22⋊C4—431no—
735C22×C22⋊C4—431no—
736C22×C22⋊C4C2×D4311yescharacteristic
737C22×C22⋊C4C2×D4311yescharacteristic
738C22×C22⋊C4C2×D4311yescharacteristic
739C22×C22⋊C4C2×D4311yescharacteristic
740C22×C42—431no—
741#386—864no—
742#386—864no—
743#386—864no—
744#386—864no—
745C2×#95—431no—
746C2×#95—431no—
747C2×#95—431no—
748C2×#95—431no—
749C2×#95—431no—
750C2×#95—431no—
751C2×#95—431no—
752C2×#95—431no—
753C2×#95—431no—
754C2×#95—431no—
755C2×#95—431no—
756C2×#95—431no—
757C2×#95—864no—
758C2×#95C2×D4311yescharacteristic
759C2×#95C2×D4311yescharacteristic
760C43#1402311yescharacteristic, complemented, Sylow
761C25—431no—
762C25C22×D4311yescharacteristic
763C25C22×D4311yescharacteristic
764C22×D4—22no—
765C22×D4—22no—
766C22×D4—22no—
767C22×D4—22no—
768C22×D4—41no—
769C22×D4—41no—
770C22×D4—434no—
771C22×D4—434no—
772C22×D4—434no—
773C22×D4—434no—
774C22×D4—862no—
775C22×D4—862no—
776C22×D4—862no—
777C22×D4—862no—
778C22×D4—862no—
779C22×D4—862no—
780C22×D4—862no—
781C22×D4—862no—
782C22×D4—862no—
783C22×D4—862no—
784C22×D4C4×D4314yescomplemented
785C23×C4—431no—
786C23×C4—431no—
787C23×C4—431no—
788C23×C4—431no—
789C23×C4—431no—
790C23×C4—431no—
791C23×C4—434no—
792C23×C4—434no—
793C23×C4—431no—
794C23×C4—862no—
795C23×C4—862no—
796C23×C4—862no—
797C23×C4—862no—
798C23×C4—862no—
799C23×C4—862no—
800C23×C4—862no—
801C23×C4—862no—
802C23×C4—862no—
803C23×C4—862no—
804C23×C4—862no—
805C23×C4—862no—
806C23×C4—862no—
807C23×C4—862no—
808C23×C4—862no—
809C23×C4—862no—
810C23×C4—862no—
811C23×C4—862no—
812C23×C4—1721no—
813C23×C4—1721no—
814C23×C4—1721no—
815C23×C4—1721no—
816C23×C4—1721no—
817C23×C4—1721no—
818C23×C4—1721no—
819C23×C4—1721no—
820C23×C4C22×D4311yescharacteristic
821C23×C4C22×D4311yescharacteristic
822C23×C4C22×D4311yescharacteristic
823C23×C4C22×D4311yescharacteristic
824C23×C4C22×D4311yescharacteristic
825#121—8632no—
826C4×D4—8632no—
827C2×C4⋊C4—434no—
828C2×C4⋊C4—862no—
829C2×C4⋊C4—862no—
830C2×C4⋊C4—862no—
831C2×C4⋊C4—862no—
832C2×C4⋊C4—862no—
833C2×C22⋊C4—22no—
834C2×C22⋊C4—22no—
835C2×C22⋊C4—22no—
836C2×C22⋊C4—22no—
837C2×C22⋊C4—22no—
838C2×C22⋊C4—22no—
839C2×C22⋊C4—22no—
840C2×C22⋊C4—22no—
841C2×C22⋊C4—41no—
842C2×C22⋊C4—41no—
843C2×C22⋊C4—41no—
844C2×C22⋊C4—41no—
845C2×C22⋊C4—434no—
846C2×C22⋊C4—434no—
847C2×C22⋊C4—434no—
848C2×C22⋊C4—862no—
849C2×C22⋊C4—862no—
850C2×C22⋊C4—862no—
851C2×C22⋊C4—862no—
852C2×C22⋊C4—862no—
853C2×C22⋊C4—862no—
854C2×C22⋊C4—862no—
855C2×C22⋊C4—862no—
856C2×C22⋊C4—862no—
857C2×C22⋊C4—862no—
858C2×C22⋊C4—862no—
859C2×C22⋊C4—862no—
860C2×C22⋊C4—862no—
861C2×C22⋊C4—862no—
862C2×C22⋊C4—862no—
863C2×C22⋊C4—862no—
864C2×C22⋊C4—1721no—
865C2×C22⋊C4—1721no—
866C2×C42—862no—
867C2×C42—862no—
868C2×C42—862no—
869#95—22no—
870#95—22no—
871#95—434no—
872#95—862no—
873#95—862no—
874#95—862no—
875#95—862no—
876#95—862no—
877#95—862no—
878#95—862no—
879#95—862no—
880#95—862no—
881#95—1721no—
882#95—1721no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—21no—
896C24—21no—
897C24—21no—
898C24—21no—
899C24—21no—
900C24—21no—
901C24—21no—
902C24—21no—
903C24—21no—
904C24—21no—
905C24—21no—
906C24—21no—
907C24—21no—
908C24—21no—
909C24—432no—
910C24—432no—
911C24—432no—
912C24—432no—
913C24—432no—
914C24—432no—
915C24—432no—
916C24—861no—
917C24—861no—
918C24—861no—
919C24—861no—
920C24—861no—
921C24—861no—
922C24—861no—
923C24—861no—
924C24C2×C4×D4312yes—
925C24C2×C4×D4312yes—
926C24D4×D4312yes—
927C24D4×D4312yes—
928C24C23×D4311yescharacteristic
929C2×D4—28no—
930C2×D4—28no—
931C2×D4—44no—
932C2×D4—44no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—44no—
936C2×D4—4316no—
937C2×D4—868no—
938C2×D4—868no—
939C2×D4—868no—
940C2×D4—868no—
941C2×D4—868no—
942C2×D4—868no—
943C2×D4—868no—
944C2×D4—868no—
945C2×D4—868no—
946C2×D4—1724no—
947C2×D4—1724no—
948C2×D4—1724no—
949C2×D4—1724no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—432no—
980C22×C4—432no—
981C22×C4—432no—
982C22×C4—432no—
983C22×C4—432no—
984C22×C4—432no—
985C22×C4—432no—
986C22×C4—432no—
987C22×C4—432no—
988C22×C4—432no—
989C22×C4—868no—
990C22×C4—868no—
991C22×C4—868no—
992C22×C4—868no—
993C22×C4—861no—
994C22×C4—861no—
995C22×C4—861no—
996C22×C4—861no—
997C22×C4—861no—
998C22×C4—861no—
999C22×C4—861no—
1000C22×C4—861no—
1001C22×C4—868no—
1002C22×C4—861no—
1003C22×C4—861no—
1004C22×C4—861no—
1005C22×C4—861no—
1006C22×C4—861no—
1007C22×C4—861no—
1008C22×C4—861no—
1009C22×C4—861no—
1010C22×C4—861no—
1011C22×C4—861no—
1012C22×C4—861no—
1013C22×C4—861no—
1014C22×C4—861no—
1015C22×C4—861no—
1016C22×C4—861no—
1017C22×C4—861no—
1018C22×C4—861no—
1019C22×C4—861no—
1020C22×C4—861no—
1021C22×C4—861no—
1022C22×C4—861no—
1023C22×C4—861no—
1024C22×C4—861no—
1025C22×C4—861no—
1026C22×C4—868no—
1027C22×C4—861no—
1028C22×C4—861no—
1029C22×C4—861no—
1030C22×C4—861no—
1031C22×C4—861no—
1032C22×C4—861no—
1033C22×C4—861no—
1034C22×C4—1724no—
1035C22×C4—1724no—
1036C22×C4—1724no—
1037C22×C4—1724no—
1038C22×C4—1724no—
1039C22×C4—1724no—
1040C22×C4—1724no—
1041C22×C4—1724no—
1042C22×C4—1724no—
1043C22×C4—1724no—
1044C22×C4—1724no—
1045C22×C4—1724no—
1046C22×C4—1724no—
1047C22×C4—1724no—
1048C22×C4—1724no—
1049C22×C4—1724no—
1050C22×C4—1724no—
1051C22×C4—1724no—
1052C22×C4—1724no—
1053C22×C4—1724no—
1054C22×C4—1724no—
1055C22×C4—1724no—
1056C22×C4C2×C4×D4312yes—
1057C22×C4D4×D4312yes—
1058C22×C4D4×D4312yes—
1059C22×C4D4×D4312yes—
1060C22×C4#1062190012yes—
1061C22×C4#1062190012yes—
1062C4⋊C4—868no—
1063C4⋊C4—868no—
1064C22⋊C4—28no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—868no—
1069C22⋊C4—868no—
1070C22⋊C4—868no—
1071C22⋊C4—1724no—
1072C22⋊C4—1724no—
1073C22⋊C4—1724no—
1074C22⋊C4—1724no—
1075C42—868no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—434no—
1146C23—434no—
1147C23—434no—
1148C23—434no—
1149C23—434no—
1150C23—434no—
1151C23—434no—
1152C23—862no—
1153C23—862no—
1154C23—862no—
1155C23—862no—
1156C23—862no—
1157C23—862no—
1158C23—862no—
1159C23—862no—
1160C23—862no—
1161C23—862no—
1162C23—862no—
1163C23—862no—
1164C23—862no—
1165C23—862no—
1166C23—862no—
1167C23—862no—
1168C23—862no—
1169C23—862no—
1170C23—862no—
1171C23—862no—
1172C23—862no—
1173C23—862no—
1174C23—862no—
1175C23—862no—
1176C23—862no—
1177C23—862no—
1178C23—862no—
1179C23—862no—
1180C23C22⋊C4×D4314yes—
1181C23C22×C4×D4311yescharacteristic
1182C23C2×D4×D4311yescharacteristic
1183C23C2×D4×D4311yescharacteristic
1184C23C2×D4×D4311yescharacteristic
1185C23C2×D4×D4311yescharacteristic
1186C23C2×D4×D4311yescharacteristic
1187C23#41×D4311yescharacteristic
1188C23#41×D4311yescharacteristic
1189C23#41×D4311yescharacteristic
1190C23C2×#1062190011yescharacteristic
1191C23C2×#1062190011yescharacteristic
1192C23#1306337011yescharacteristic
1193C23#1306337011yescharacteristic
1194C23#1306337011yescharacteristic
1195C23#1306337211yescharacteristic
1196D4—416no—
1197D4—8632no—
1198D4—17216no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—434no—
1234C2×C4—434no—
1235C2×C4—862no—
1236C2×C4—862no—
1237C2×C4—862no—
1238C2×C4—862no—
1239C2×C4—862no—
1240C2×C4—862no—
1241C2×C4—862no—
1242C2×C4—862no—
1243C2×C4—862no—
1244C2×C4—862no—
1245C2×C4—862no—
1246C2×C4—862no—
1247C2×C4—862no—
1248C2×C4—862no—
1249C2×C4—862no—
1250C2×C4—862no—
1251C2×C4—862no—
1252C2×C4—862no—
1253C2×C4—862no—
1254C2×C4—862no—
1255C2×C4—862no—
1256C2×C4—862no—
1257C2×C4—862no—
1258C2×C4—862no—
1259C2×C4—17216no—
1260C2×C4—17216no—
1261C2×C4—17216no—
1262C2×C4—17216no—
1263C2×C4—1721no—
1264C2×C4—1721no—
1265C2×C4—1721no—
1266C2×C4—1721no—
1267C2×C4—1721no—
1268C2×C4—1721no—
1269C2×C4—1721no—
1270C2×C4—1721no—
1271C2×C4—1721no—
1272C2×C4—1721no—
1273C2×C4—1721no—
1274C2×C4—1721no—
1275C2×C4—1721no—
1276C2×C4—1721no—
1277C2×C4—1721no—
1278C2×C4—1721no—
1279C2×C4—1721no—
1280C2×C4—1721no—
1281C2×C4—1721no—
1282C2×C4—1721no—
1283C2×C4—1721no—
1284C2×C4—1721no—
1285C2×C4—1721no—
1286C2×C4(C22⋊D43)⋊C414yescomplemented
1287C22—24no—
1288C22—24no—
1289C22—24no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22—42no—
1303C22—42no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—438no—
1318C22—864no—
1319C22—864no—
1320C22—864no—
1321C22—864no—
1322C22—864no—
1323C22—864no—
1324C22—864no—
1325C22—864no—
1326C22—864no—
1327C22—864no—
1328C22—864no—
1329C22—864no—
1330C22—864no—
1331C22—864no—
1332C22C2×C22⋊C4×D4311yescharacteristic
1333C22C4×D4×D4311yescharacteristic
1334C22C4×D4×D4311yescharacteristic
1335C22C2×(C22⋊D43)⋊C411yescharacteristic
1336C22C4×#1062190011yescharacteristic
1337C22#1458337211yescharacteristic
1338C22#1458337811yescharacteristic
1339C22#120×D4311yescharacteristic
1340C22#121×D4311yescharacteristic
1341C22#121×D4311yescharacteristic
1342C22#121×D4311yescharacteristic
1343C22#123×D4311yescharacteristic
1344C22#1458340911yescharacteristic
1345C22#1458342811yescharacteristic
1346C22#1458344711yescharacteristic
1347C22#1458345911yescharacteristic
1348C22#1458347811yescharacteristic
1349C22#1458348111yescharacteristic
1350C22#1458349211yescharacteristic
1351C22#1458353111yescharacteristic
1352C22#1458353111yescharacteristic
1353C22#1458353411yescharacteristic
1354C22#1458353611yescharacteristic
1355C22#1458353611yescharacteristic
1356C22#1458353611yescharacteristic
1357C22#1458353611yescharacteristic
1358C22#1458353811yescharacteristic
1359C22#1458354611yescharacteristic
1360C22#1458354711yescharacteristic
1361C22#1458354911yescharacteristic
1362C22#1458354911yescharacteristic
1363C22#1458355711yescharacteristic
1364C22#1458359411yescharacteristic
1365C22#1458359611yescharacteristic
1366C22#1458359611yescharacteristic
1367C4—24no—
1368C4—42no—
1369C4—42no—
1370C4—42no—
1371C4—81no—
1372C4—864no—
1373C4—864no—
1374C4—3441no—
1375C4—1722no—
1376C4—1722no—
1377C4—1722no—
1378C4—1722no—
1379C2—44no—
1380C2—82no—
1381C2—868no—
1382C2#386×D4311yescharacteristic
1383C2#1913711111yescharacteristic
1384C2#1913729711yescharacteristic
1385C2#1913741111yescharacteristic
1386C2#1913742111yescharacteristic
1387C2#1913761611yescharacteristic
1388C2#1913764411yescharacteristic
1389C2#1913796211yescharacteristic
1390C2#1913802811yescharacteristic
1391C2#1913813411yescharacteristic
1392C2#1913814711yescharacteristic
1393C2#1913819811yescharacteristic
1394C2#1913832311yescharacteristic
1395C2#1913833811yescharacteristic
1396C2#1913955011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1438C2
socle, cosocleC24×C43C24
prime radicalC22×#13063296C2
hypercenter#1438D43
hypocenterC43#14023
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C22×(C22⋊D43)⋊C4C2semidirect
3. C2×#14582779C2semidirect
4. C2×#14582775C2semidirect
5. C2×#14582775C2semidirect
6. C2×#14582775C2semidirect
7. C2×#95×D43C2semidirect
8. #19132847C2semidirect
9. #19132842C2semidirect
10. #19132838C2semidirect
11. #19132832C2semidirect
12. #19132829C2semidirect
13. #19132817C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×#1438C2semidirect
24. C2×#13063296C4semidirect
74. C22×C22⋊D43C2×C4semidirect
110. C22×C4×D43C2×C4semidirect
111. C22×C4×D43D4semidirect
116. C2×C4⋊Dic43C2×C4semidirect
133. C2×C22⋊Dic43C2×C4semidirect
134. C2×C22⋊Dic43C2×C4semidirect
140. C2×(C2×D43)⋊C4D4semidirect
155. C43⋊#95D4semidirect
164. C22×D4×C43C2×C4semidirect
285. C2×C22⋊D43C22⋊C4semidirect
532. C2×C4×C43C4×D4semidirect
584. C2×Dic43#121semidirect
668. C2×D43#386semidirect
691. #1438D43semidirect
760. C43#14023semidirect
784. C22×D4C4×D43semidirect
1286. C2×C4(C22⋊D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130632962
C22×(C22⋊D43)⋊C42
C2×#145827792
C2×#145827752
C2×#95×D432
#191328472
#191328422
#191328382
#191328322
#191328292
#191328172
(C2×D43)⋊#952
C43×#14382
#1402343