Finite Group Databasebeta

← #25019401

Subgroups — #25019401

Order 11008.

3058 conjugacy classes of subgroups.

The subgroup lattice has 1388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063298C211yesmaximal, characteristic
2C22×C4×C22⋊D43C211yesmaximal, characteristic, complemented
3C2×#14582799C211yesmaximal, characteristic, complemented
4C2×#14582778C211yesmaximal, characteristic, complemented
5C2×#14582777C211yesmaximal, characteristic, complemented
6C2×#14582758C211yesmaximal, characteristic, complemented
7C2×#14582746C211yesmaximal, characteristic, complemented
8#19132844C211yesmaximal, characteristic, complemented
9#19132843C211yesmaximal, characteristic, complemented
10#19132835C211yesmaximal, characteristic, complemented
11#19132834C211yesmaximal, characteristic, complemented
12Dic43⋊#95C211yesmaximal, characteristic, complemented
13Dic43⋊#95C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C43×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C22⋊D43C2211yescharacteristic
18C23×C22⋊D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C2×#13063298—24no—
22C2×#13063298—24no—
23C2×#13063298C418yescomplemented
24C2×C4×C22⋊D43—24no—
25C2×C4×C22⋊D43—24no—
26C2×C4×C22⋊D43—24no—
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×C22⋊Dic43C2211yescharacteristic
31C22×C22⋊Dic43C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×(C2×D43)⋊C4C2211yescharacteristic
39C22×(C2×D43)⋊C4C2211yescharacteristic
40C22×C4×Dic43C2211yescharacteristic
41C22×C4×Dic43C2211yescharacteristic
42#14582799—24no—
43#14582778—24no—
44#14582777—24no—
45#14582758—24no—
46#14582746—24no—
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C24×C4×C43C2211yescharacteristic
56C22×C22⋊C4×C43C2211yescharacteristic
57C22×C22⋊C4×C43C2211yescharacteristic
58C2×#95×C43C2211yescharacteristic
59C2×#95×C43C2211yescharacteristic
60C2×#95×C43C2211yescharacteristic
61C2×#95×C43C2211yescharacteristic
62C24×D43C2311yescharacteristic
63C24×D43C2311yescharacteristic
64C22×D172—22no—
65C22×D172—22no—
66C22×D172—22no—
67C22×D172—22no—
68C22×D172—41no—
69C22×D172—41no—
70C22×D172C2×C414yescomplemented
71C22×C22⋊D43—22no—
72C22×C22⋊D43—22no—
73C22×C22⋊D43—22no—
74C22×C22⋊D43—22no—
75C22×C22⋊D43—22no—
76C22×C22⋊D43—22no—
77C22×C22⋊D43—22no—
78C22×C22⋊D43—22no—
79C22×C22⋊D43—41no—
80C22×C22⋊D43—41no—
81C22×C22⋊D43C2×C414yes—
82C22×C22⋊D43C2×C414yescomplemented
83C22×C22⋊D43D414yes—
84C22×C22⋊D43D414yes—
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—41no—
103C22×C4×D43—41no—
104C22×C4×D43C2×C414yescomplemented
105#13063298—232no—
106C4×C22⋊D43—232no—
107C2×Dic43⋊C4—22no—
108C2×Dic43⋊C4—22no—
109C2×Dic43⋊C4—22no—
110C2×Dic43⋊C4—22no—
111C2×Dic43⋊C4—22no—
112C2×Dic43⋊C4—22no—
113C2×Dic43⋊C4—22no—
114C2×Dic43⋊C4C2×C414yescomplemented
115C2×Dic43⋊C4D414yescomplemented
116C2×C22⋊Dic43—22no—
117C2×C22⋊Dic43—22no—
118C2×C22⋊Dic43—22no—
119C2×C22⋊Dic43—22no—
120C2×C22⋊Dic43—22no—
121C2×C22⋊Dic43—41no—
122C2×(C2×D43)⋊C4—22no—
123C2×(C2×D43)⋊C4—22no—
124C2×(C2×D43)⋊C4—22no—
125C2×(C2×D43)⋊C4—22no—
126C2×(C2×D43)⋊C4—22no—
127C2×(C2×D43)⋊C4—22no—
128C2×(C2×D43)⋊C4—22no—
129C2×(C2×D43)⋊C4—22no—
130C2×(C2×D43)⋊C4—22no—
131C2×(C2×D43)⋊C4—22no—
132C2×(C2×D43)⋊C4—22no—
133C2×(C2×D43)⋊C4—22no—
134C2×(C2×D43)⋊C4—22no—
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)⋊C4—41no—
141C2×(C2×D43)⋊C4—41no—
142C2×(C2×D43)⋊C4—41no—
143C2×(C2×D43)⋊C4—41no—
144C2×(C2×D43)⋊C4C2×C414yescomplemented
145C2×(C2×D43)⋊C4D414yescomplemented
146C2×C4×Dic43—22no—
147C2×C4×Dic43—22no—
148C2×C4×Dic43—22no—
149C2×C4×Dic43—22no—
150C2×C4×Dic43—22no—
151C2×C4×Dic43D414yescomplemented
152C43⋊#95—22no—
153C43⋊#95—22no—
154C43⋊#95—22no—
155C43⋊#95—22no—
156C43⋊#95—22no—
157C43⋊#95—41no—
158C43⋊#95—41no—
159C43⋊#95—41no—
160C25×C43C2311yescharacteristic
161C23×C4×C43—22no—
162C23×C4×C43—22no—
163C23×C4×C43—22no—
164C23×C4×C43—22no—
165C23×C4×C43—22no—
166C23×C4×C43—41no—
167C23×C4×C43—41no—
168C23×C4×C43C2311yescharacteristic
169C23×C4×C43C2311yescharacteristic
170C23×C4×C43C2311yescharacteristic
171C23×C4×C43C2311yescharacteristic
172C23×C4×C43C2311yescharacteristic
173C23×C4×C43C2311yescharacteristic
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×C43C2×C414yescomplemented
180#95×C43—22no—
181#95×C43—22no—
182#95×C43—22no—
183#95×C43—41no—
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×C43C22×C412yes—
197C24×C43C2×D412yes—
198C24×C43C2×D412yes—
199C24×C43C2411yescharacteristic
200C23×D43—21no—
201C23×D43—21no—
202C23×D43—21no—
203C23×D43—21no—
204C23×D43—21no—
205C23×D43—21no—
206C23×D43—21no—
207C23×D43—21no—
208C23×D43—21no—
209C23×D43—21no—
210C23×D43—21no—
211C23×D43—21no—
212C23×D43—21no—
213C23×D43—21no—
214C23×D43—21no—
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×D43—21no—
224C23×D43C22×C412yes—
225C23×D43C22×C412yes—
226C23×D43C2×D412yes—
227C23×D43C2×D412yes—
228C23×D43C2×D412yes—
229C23×D43#4112yes—
230C22×C4×C43—28no—
231C22×C4×C43—21no—
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—21no—
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×C43—44no—
267C22×C4×C43—44no—
268C22×C4×C43—44no—
269C22×C4×C43—44no—
270C22×C4×C43—44no—
271C22×C4×C43—44no—
272C22×C4×C43C22×C412yes—
273C22×C4×C43C22×C412yes—
274C22×C4×C43C2×D412yes—
275C22×C4×C43C2×D412yes—
276C22×C4×C43C2×D412yes—
277C22×C4×C43#4112yes—
278C22×C4×C43#4112yes—
279C2×C22⋊D43—28no—
280C2×C22⋊D43—28no—
281C2×C22⋊D43—28no—
282C2×C22⋊D43—28no—
283C2×C22⋊D43—28no—
284C2×C22⋊D43—28no—
285C2×C22⋊D43—28no—
286C2×C22⋊D43—28no—
287C2×C22⋊D43—44no—
288C2×C22⋊D43—44no—
289C2×C22⋊D43—44no—
290C2×C22⋊D43—44no—
291C2×C22⋊D43—44no—
292C2×C22⋊D43C22⋊C4116yescomplemented
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×Dic43C22×C412yes—
325C22×Dic43C22×C412yes—
326C22×Dic43C2×D412yes—
327C22×Dic43C2×D412yes—
328C22×Dic43C2×D412yes—
329C22×Dic43C2×D412yes—
330C22×Dic43C2×D412yes—
331C22×Dic43C2×D412yes—
332C22×Dic43C2×D412yes—
333C22×Dic43#4112yes—
334C22×Dic43#4112yes—
335C2×D172—28no—
336C2×D172—28no—
337C2×D172—44no—
338C2×D172—44no—
339C2×D172—44no—
340C2×D172—44no—
341C2×D172—44no—
342C2×C4×D43—28no—
343C2×C4×D43—28no—
344C2×C4×D43—28no—
345C2×C4×D43—28no—
346C2×C4×D43—44no—
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—
356C22⋊C4×C43—28no—
357C22⋊C4×C43—44no—
358C22⋊Dic43—28no—
359C22⋊Dic43—44no—
360(C2×D43)⋊C4—28no—
361(C2×D43)⋊C4—28no—
362(C2×D43)⋊C4—28no—
363(C2×D43)⋊C4—28no—
364(C2×D43)⋊C4—44no—
365(C2×D43)⋊C4—44no—
366(C2×D43)⋊C4—44no—
367(C2×D43)⋊C4—44no—
368Dic43⋊C4—28no—
369Dic43⋊C4—28no—
370Dic43⋊C4—44no—
371C4×Dic43—28no—
372C4×Dic43—44no—
373C23×C43—22no—
374C23×C43—22no—
375C23×C43—22no—
376C23×C43—22no—
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—41no—
392C23×C43—41no—
393C23×C43—41no—
394C23×C43—41no—
395C23×C43—41no—
396C23×C43—41no—
397C23×C43—41no—
398C23×C43—41no—
399C23×C43—41no—
400C23×C43—41no—
401C23×C43—41no—
402C23×C43—41no—
403C23×C43—41no—
404C23×C43—41no—
405C23×C43—41no—
406C23×C43—41no—
407C23×C43C2×C22⋊C414yes—
408C23×C43C23×C411yescharacteristic
409C23×C43C22×D411yescharacteristic
410C23×C43C22×D411yescharacteristic
411C23×C43C22×D411yescharacteristic
412C23×C43C22×D411yescharacteristic
413C23×C43C22×D411yescharacteristic
414C23×C43C2×#4111yescharacteristic
415C23×C43C2×#4111yescharacteristic
416C23×C43C2×#4111yescharacteristic
417C23×C43C2×#4111yescharacteristic
418C23×C43C2×#4111yescharacteristic
419C23×C43H(5,𝔽2)11yescharacteristic
420C23×C43H(5,𝔽2)11yescharacteristic
421C23×C43H(5,𝔽2)11yescharacteristic
422C23×C432−1+411yescharacteristic
423C22×D43—22no—
424C22×D43—22no—
425C22×D43—22no—
426C22×D43—22no—
427C22×D43—22no—
428C22×D43—22no—
429C22×D43—22no—
430C22×D43—22no—
431C22×D43—22no—
432C22×D43—22no—
433C22×D43—22no—
434C22×D43—22no—
435C22×D43—22no—
436C22×D43—22no—
437C22×D43—22no—
438C22×D43—22no—
439C22×D43—22no—
440C22×D43—22no—
441C22×D43—22no—
442C22×D43—22no—
443C22×D43—22no—
444C22×D43—22no—
445C22×D43—22no—
446C22×D43—22no—
447C22×D43—22no—
448C22×D43—22no—
449C22×D43—22no—
450C22×D43—22no—
451C22×D43—22no—
452C22×D43—22no—
453C22×D43—22no—
454C22×D43—22no—
455C22×D43—22no—
456C22×D43—22no—
457C22×D43—22no—
458C22×D43—22no—
459C22×D43—41no—
460C22×D43—41no—
461C22×D43—41no—
462C22×D43—41no—
463C22×D43—41no—
464C22×D43—41no—
465C22×D43—41no—
466C22×D43—41no—
467C22×D43—41no—
468C22×D43—41no—
469C22×D43—41no—
470C22×D43—41no—
471C22×D43—41no—
472C22×D43—41no—
473C22×D43—41no—
474C22×D43—41no—
475C22×D43—41no—
476C22×D43—41no—
477C22×D43—41no—
478C22×D43—41no—
479C22×D43—41no—
480C22×D43—41no—
481C22×D43—41no—
482C22×D43—41no—
483C22×D43—41no—
484C22×D43—41no—
485C22×D43—41no—
486C22×D43—41no—
487C22×D43—41no—
488C22×D43—41no—
489C22×D43—41no—
490C22×D43—41no—
491C22×D43C2×C22⋊C414yes—
492C22×D43C4×D414yescomplemented
493C2×C4×C43—22no—
494C2×C4×C43—22no—
495C2×C4×C43—22no—
496C2×C4×C43—22no—
497C2×C4×C43—22no—
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—416no—
512C2×C4×C43—41no—
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×C43—41no—
533C2×C4×C43—41no—
534C2×C4×C43—41no—
535C2×C4×C43#12114yescomplemented
536C22⋊D43—232no—
537C22⋊D43—416no—
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—41no—
551C2×Dic43—41no—
552C2×Dic43—41no—
553C2×Dic43—41no—
554C2×Dic43—41no—
555C2×Dic43—41no—
556C2×Dic43—41no—
557C2×Dic43—41no—
558C2×Dic43—41no—
559C2×Dic43—41no—
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×Dic43C2×C22⋊C414yes—
574C2×Dic43C4×D414yes—
575C2×Dic43C4×D414yes—
576C2×Dic43#12014yes—
577C2×Dic43#12114yes—
578C2×Dic43#12114yes—
579C2×Dic43#12314yes—
580D172—416no—
581C4×D43—416no—
582C4×D43—416no—
583#13970—431nomaximal, Sylow
584C22×C43—24no—
585C22×C43—24no—
586C22×C43—24no—
587C22×C43—42no—
588C22×C43—42no—
589C22×C43—42no—
590C22×C43—42no—
591C22×C43—42no—
592C22×C43—42no—
593C22×C43—42no—
594C22×C43—42no—
595C22×C43—42no—
596C22×C43—42no—
597C22×C43—42no—
598C22×C43—42no—
599C22×C43C22×C22⋊C411yescharacteristic
600C22×C43C2×C4×D411yescharacteristic
601C22×C43C2×C4×D411yescharacteristic
602C22×C43C2×C4×D411yescharacteristic
603C22×C43C4×#4111yescharacteristic
604C22×C43#51811yescharacteristic
605C22×C43#52011yescharacteristic
606C22×C43C2×#12011yescharacteristic
607C22×C43C2×#12111yescharacteristic
608C22×C43C2×#12111yescharacteristic
609C22×C43C2×#12111yescharacteristic
610C22×C43C2×#12311yescharacteristic
611C22×C43#52511yescharacteristic
612C22×C43#52911yescharacteristic
613C22×C43#53211yescharacteristic
614C22×C43#53511yescharacteristic
615C22×C43#53711yescharacteristic
616C22×C43#54011yescharacteristic
617C22×C43#54211yescharacteristic
618C22×C43D4211yescharacteristic
619C22×C43D4211yescharacteristic
620C22×C43D4211yescharacteristic
621C22×C43#54611yescharacteristic
622C22×C43#54611yescharacteristic
623C22×C43#54611yescharacteristic
624C22×C43#54611yescharacteristic
625C22×C43#54611yescharacteristic
626C22×C43#54711yescharacteristic
627C22×C43#54711yescharacteristic
628C22×C43#54711yescharacteristic
629C22×C43#54811yescharacteristic
630C22×C43#55011yescharacteristic
631C22×C43#55311yescharacteristic
632C22×C43#55311yescharacteristic
633C22×C43#55511yescharacteristic
634C2×D43—24no—
635C2×D43—24no—
636C2×D43—24no—
637C2×D43—24no—
638C2×D43—24no—
639C2×D43—24no—
640C2×D43—42no—
641C2×D43—42no—
642C2×D43—42no—
643C2×D43—42no—
644C2×D43—42no—
645C2×D43—42no—
646C2×D43—42no—
647C2×D43—42no—
648C2×D43—42no—
649C2×D43—42no—
650C2×D43—42no—
651C2×D43—42no—
652C2×D43—42no—
653C2×D43—42no—
654C2×D43—42no—
655C2×D43—42no—
656C2×D43—42no—
657C2×D43—42no—
658C2×D43—42no—
659C2×D43—42no—
660C2×D43—42no—
661C2×D43—42no—
662C2×D43—42no—
663C2×D43—42no—
664C4×C43—24no—
665C4×C43—42no—
666C4×C43—42no—
667C4×C43—42no—
668C4×C43—42no—
669C4×C43—81no—
670Dic43—42no—
671Dic43—42no—
672Dic43—42no—
673Dic43—42no—
674Dic43—81no—
675Dic43#38618yescomplemented
676C22×#121—431no—
677C22×C4×D4—431no—
678C2×#390—431no—
679C2×#386—431no—
680C2×#386—431no—
681C2×#380—431no—
682C2×C4×C22⋊C4—431no—
683#1440—431no—
684#1440—431no—
685#1438—431no—
686#1438—431no—
687C4⋊#95—431no—
688C4⋊#95—431no—
689C22⋊#95—431no—
690C22⋊#95D4311yescharacteristic, complemented
691C2×C43—44no—
692C2×C43C2×#38611yescharacteristic
693C2×C43C4×#12111yescharacteristic
694C2×C43#232411yescharacteristic
695C2×C43D4×C22⋊C411yescharacteristic
696C2×C43#233911yescharacteristic
697C2×C43#236111yescharacteristic
698C2×C43#236311yescharacteristic
699C2×C43#240711yescharacteristic
700C2×C43#240811yescharacteristic
701C2×C43#242011yescharacteristic
702C2×C43#242211yescharacteristic
703C2×C43#242711yescharacteristic
704C2×C43#242811yescharacteristic
705C2×C43#253511yescharacteristic
706C2×C43#253711yescharacteristic
707D43—44no—
708D43—44no—
709C23×D4—431no—
710C23×D4—431no—
711C23×D4—431no—
712C24×C4—431no—
713C24×C4—431no—
714C24×C4C2×D4311yescharacteristic
715C2×#121—438no—
716C2×#121—864no—
717C2×#121—864no—
718C2×C4×D4—864no—
719C2×C4×D4—864no—
720C2×C4×D4—864no—
721C22×C4⋊C4—431no—
722C22×C4⋊C4—431no—
723C22×C4⋊C4—431no—
724C22×C22⋊C4—431no—
725C22×C22⋊C4—431no—
726C22×C22⋊C4—431no—
727C22×C22⋊C4—431no—
728C22×C22⋊C4—431no—
729C22×C22⋊C4—431no—
730C22×C22⋊C4—431no—
731C22×C22⋊C4—431no—
732C22×C22⋊C4—431no—
733C22×C22⋊C4—431no—
734C22×C22⋊C4C2×D4311yescharacteristic
735C22×C22⋊C4C2×D4311yescharacteristic
736C22×C42—431no—
737C22×C42—431no—
738#390—864no—
739#386—864no—
740#386—864no—
741#380—864no—
742C4×C22⋊C4—864no—
743C2×#95—431no—
744C2×#95—431no—
745C2×#95—431no—
746C2×#95—431no—
747C2×#95—431no—
748C2×#95—431no—
749C2×#95—431no—
750C2×#95—431no—
751C2×#95C2×D4311yescharacteristic
752C2×#95C2×D4311yescharacteristic
753C2×#95C2×D4311yescharacteristic
754C2×#95C2×D4311yescharacteristic
755C43#1397011yescharacteristic, complemented, Sylow
756C25—431no—
757C25—431no—
758C25C22×D4311yescharacteristic
759C22×D4—434no—
760C22×D4—434no—
761C22×D4—434no—
762C22×D4—434no—
763C22×D4—434no—
764C22×D4—862no—
765C22×D4—862no—
766C22×D4—862no—
767C22×D4—862no—
768C22×D4—862no—
769C22×D4—862no—
770C22×D4—862no—
771C22×D4—862no—
772C22×D4—862no—
773C22×D4—862no—
774C22×D4—862no—
775C22×D4—862no—
776C22×D4—1721no—
777C22×D4—1721no—
778C22×D4—1721no—
779C22×D4—1721no—
780C23×C4—22no—
781C23×C4—22no—
782C23×C4—22no—
783C23×C4—22no—
784C23×C4—22no—
785C23×C4—41no—
786C23×C4—41no—
787C23×C4—431no—
788C23×C4—431no—
789C23×C4—431no—
790C23×C4—431no—
791C23×C4—431no—
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—1721no—
806C23×C4—1721no—
807C23×C4C22×D4311yescharacteristic
808C23×C4C22×D4311yescharacteristic
809C23×C4C22×D4311yescharacteristic
810C23×C4C22×D4311yescharacteristic
811C23×C4C22×D4311yescharacteristic
812C23×C4C22×D4311yescharacteristic
813#121—8632no—
814C4×D4—8632no—
815C2×C4⋊C4—434no—
816C2×C4⋊C4—434no—
817C2×C4⋊C4—862no—
818C2×C4⋊C4—862no—
819C2×C4⋊C4—862no—
820C2×C4⋊C4—862no—
821C2×C4⋊C4—862no—
822C2×C4⋊C4—862no—
823C2×C4⋊C4—862no—
824C2×C22⋊C4—22no—
825C2×C22⋊C4—22no—
826C2×C22⋊C4—22no—
827C2×C22⋊C4—22no—
828C2×C22⋊C4—41no—
829C2×C22⋊C4—434no—
830C2×C22⋊C4—434no—
831C2×C22⋊C4—862no—
832C2×C22⋊C4—862no—
833C2×C22⋊C4—862no—
834C2×C22⋊C4—862no—
835C2×C22⋊C4—862no—
836C2×C22⋊C4—862no—
837C2×C22⋊C4—862no—
838C2×C22⋊C4—862no—
839C2×C22⋊C4—862no—
840C2×C22⋊C4—862no—
841C2×C22⋊C4—862no—
842C2×C22⋊C4—862no—
843C2×C22⋊C4—862no—
844C2×C22⋊C4—862no—
845C2×C22⋊C4—862no—
846C2×C22⋊C4—862no—
847C2×C22⋊C4—862no—
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—1721no—
855C2×C22⋊C4—1721no—
856C2×C22⋊C4—1721no—
857C2×C22⋊C4—1721no—
858C2×C22⋊C4—1721no—
859C2×C22⋊C4C4×D4314yescomplemented
860C2×C42—434no—
861C2×C42—862no—
862C2×C42—862no—
863C2×C42—862no—
864C2×C42—862no—
865C2×C42—862no—
866#95—22no—
867#95—22no—
868#95—22no—
869#95—41no—
870#95—862no—
871#95—862no—
872#95—862no—
873#95—862no—
874#95—862no—
875#95—1721no—
876#95—1721no—
877#95—1721no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—432no—
891C24—432no—
892C24—432no—
893C24—432no—
894C24—432no—
895C24—432no—
896C24—861no—
897C24—861no—
898C24—861no—
899C24—861no—
900C24—861no—
901C24—861no—
902C24—861no—
903C24—861no—
904C24—861no—
905C24—861no—
906C24—861no—
907C24—861no—
908C24—861no—
909C24—861no—
910C24—861no—
911C24—861no—
912C24—861no—
913C24—861no—
914C24—861no—
915C24—861no—
916C24—861no—
917C24—861no—
918C24—861no—
919C24—861no—
920C24C2×C4×D4312yes—
921C24D4×D4312yes—
922C24D4×D4312yes—
923C24C23×D4311yescharacteristic
924C2×D4—4316no—
925C2×D4—868no—
926C2×D4—868no—
927C2×D4—868no—
928C2×D4—868no—
929C2×D4—868no—
930C2×D4—868no—
931C2×D4—868no—
932C2×D4—868no—
933C2×D4—868no—
934C2×D4—868no—
935C2×D4—1724no—
936C2×D4—1724no—
937C2×D4—1724no—
938C2×D4—1724no—
939C2×D4—1724no—
940C2×D4—1724no—
941C2×D4—1724no—
942C2×D4—1724no—
943C2×D4—1724no—
944C2×D4—1724no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—28no—
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—21no—
980C22×C4—21no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—432no—
988C22×C4—432no—
989C22×C4—432no—
990C22×C4—432no—
991C22×C4—432no—
992C22×C4—432no—
993C22×C4—432no—
994C22×C4—432no—
995C22×C4—432no—
996C22×C4—432no—
997C22×C4—432no—
998C22×C4—868no—
999C22×C4—868no—
1000C22×C4—868no—
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—861no—
1027C22×C4—861no—
1028C22×C4—861no—
1029C22×C4—861no—
1030C22×C4—861no—
1031C22×C4—861no—
1032C22×C4—861no—
1033C22×C4—1724no—
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×C4C2×C4×D4312yes—
1044C22×C4C2×C4×D4312yes—
1045C22×C4#1062189812yes—
1046C22×C4#1062189812yes—
1047C22×C4D4×D4312yes—
1048C22×C4D4×D4312yes—
1049C22×C4D4×D4312yes—
1050C4⋊C4—868no—
1051C4⋊C4—868no—
1052C4⋊C4—1724no—
1053C22⋊C4—28no—
1054C22⋊C4—44no—
1055C22⋊C4—868no—
1056C22⋊C4—868no—
1057C22⋊C4—868no—
1058C22⋊C4—868no—
1059C22⋊C4—868no—
1060C22⋊C4—1724no—
1061C22⋊C4—1724no—
1062C22⋊C4—1724no—
1063C22⋊C4—1724no—
1064C22⋊C4—1724no—
1065C42—868no—
1066C42—1724no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—434no—
1102C23—434no—
1103C23—862no—
1104C23—862no—
1105C23—862no—
1106C23—862no—
1107C23—862no—
1108C23—862no—
1109C23—862no—
1110C23—862no—
1111C23—862no—
1112C23—862no—
1113C23—862no—
1114C23—862no—
1115C23—862no—
1116C23—862no—
1117C23—862no—
1118C23—862no—
1119C23—862no—
1120C23—862no—
1121C23—862no—
1122C23—862no—
1123C23—862no—
1124C23—862no—
1125C23—862no—
1126C23—862no—
1127C23—862no—
1128C23—862no—
1129C23—862no—
1130C23—862no—
1131C23—862no—
1132C23—862no—
1133C23—862no—
1134C23—862no—
1135C23—862no—
1136C23—862no—
1137C23—862no—
1138C23—862no—
1139C23—1721no—
1140C23—1721no—
1141C23—1721no—
1142C23—1721no—
1143C23—1721no—
1144C23—1721no—
1145C23—1721no—
1146C23—1721no—
1147C23—1721no—
1148C23—1721no—
1149C23—1721no—
1150C23—1721no—
1151C23—1721no—
1152C23—1721no—
1153C23—1721no—
1154C23—1721no—
1155C23—1721no—
1156C23—1721no—
1157C23—1721no—
1158C23—1721no—
1159C23—1721no—
1160C23—1721no—
1161C23—1721no—
1162C23—1721no—
1163C23—1721no—
1164C23—1721no—
1165C23—1721no—
1166C23—1721no—
1167C23—1721no—
1168C23—1721no—
1169C23—1721no—
1170C23—1721no—
1171C23C22⋊C4×D4314yes—
1172C23C22×C4×D4311yescharacteristic
1173C23C2×D4×D4311yescharacteristic
1174C23C2×D4×D4311yescharacteristic
1175C23C2×D4×D4311yescharacteristic
1176C23C2×D4×D4311yescharacteristic
1177C23C2×D4×D4311yescharacteristic
1178C23#41×D4311yescharacteristic
1179C23#41×D4311yescharacteristic
1180C23#41×D4311yescharacteristic
1181C23C2×#1062189811yescharacteristic
1182C23C2×#1062189811yescharacteristic
1183C23#1306337011yescharacteristic
1184C23#1306337011yescharacteristic
1185C23#1306337111yescharacteristic
1186C23#1306337311yescharacteristic
1187D4—8632no—
1188D4—17216no—
1189D4—17216no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
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—416no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
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—434no—
1233C2×C4—434no—
1234C2×C4—434no—
1235C2×C4—434no—
1236C2×C4—434no—
1237C2×C4—434no—
1238C2×C4—434no—
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—17216no—
1252C2×C4—17216no—
1253C2×C4—1721no—
1254C2×C4—1721no—
1255C2×C4—1721no—
1256C2×C4—1721no—
1257C2×C4—1721no—
1258C2×C4—1721no—
1259C2×C4—1721no—
1260C2×C4—1721no—
1261C2×C4—1721no—
1262C2×C4—1721no—
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#1306329814yescomplemented
1277C22—24no—
1278C22—24no—
1279C22—24no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—864no—
1293C22—864no—
1294C22—864no—
1295C22—864no—
1296C22—864no—
1297C22—864no—
1298C22—1722no—
1299C22—1722no—
1300C22—1722no—
1301C22—1722no—
1302C22—1722no—
1303C22—1722no—
1304C22—1722no—
1305C22—1722no—
1306C22—1722no—
1307C22—1722no—
1308C22—1722no—
1309C22—1722no—
1310C22—1722no—
1311C22—1722no—
1312C22—1722no—
1313C22—1722no—
1314C22—1722no—
1315C22—1722no—
1316C22—1722no—
1317C22—1722no—
1318C22—1722no—
1319C22—1722no—
1320C22—1722no—
1321C22—1722no—
1322C22C2×C22⋊C4×D4311yescharacteristic
1323C22C4×D4×D4311yescharacteristic
1324C22C4×D4×D4311yescharacteristic
1325C22C4×D4×D4311yescharacteristic
1326C22C4×#1062189811yescharacteristic
1327C22#1458337111yescharacteristic
1328C22#1458338011yescharacteristic
1329C22#120×D4311yescharacteristic
1330C22#121×D4311yescharacteristic
1331C22#121×D4311yescharacteristic
1332C22C2×#1306329811yescharacteristic
1333C22#123×D4311yescharacteristic
1334C22#1458340811yescharacteristic
1335C22#1458342711yescharacteristic
1336C22#1458344611yescharacteristic
1337C22#1458346411yescharacteristic
1338C22#1458347911yescharacteristic
1339C22#1458350111yescharacteristic
1340C22#1458351911yescharacteristic
1341C22#1458353111yescharacteristic
1342C22#1458353111yescharacteristic
1343C22#1458353311yescharacteristic
1344C22#1458353811yescharacteristic
1345C22#1458353911yescharacteristic
1346C22#1458353911yescharacteristic
1347C22#1458353911yescharacteristic
1348C22#1458354111yescharacteristic
1349C22#1458355011yescharacteristic
1350C22#1458355011yescharacteristic
1351C22#1458355111yescharacteristic
1352C22#1458355911yescharacteristic
1353C22#1458357011yescharacteristic
1354C22#1458359411yescharacteristic
1355C22#1458359811yescharacteristic
1356C22#1458361211yescharacteristic
1357C4—24no—
1358C4—42no—
1359C4—42no—
1360C4—42no—
1361C4—42no—
1362C4—81no—
1363C4—438no—
1364C4—3441no—
1365C4—1722no—
1366C4—1722no—
1367C4—1722no—
1368C4—1722no—
1369C2—44no—
1370C2—1724no—
1371C2—1724no—
1372C2#386×D4311yescharacteristic
1373C2C4×#1306329811yescharacteristic
1374C2#1913728711yescharacteristic
1375C2#1913741311yescharacteristic
1376C2#1913742211yescharacteristic
1377C2#1913761411yescharacteristic
1378C2#1913763411yescharacteristic
1379C2#1913793911yescharacteristic
1380C2#1913795011yescharacteristic
1381C2#1913808611yescharacteristic
1382C2#1913810811yescharacteristic
1383C2#1913817111yescharacteristic
1384C2#1913818211yescharacteristic
1385C2#1913949511yescharacteristic
1386C2#1913951011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C22⋊#95C2
socle, cosocleC24×C43C24
prime radicalC22×#13063298C2
hypercenterC22⋊#95D43
hypocenterC43#13970
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D43C2semidirect
3. C2×#14582799C2semidirect
4. C2×#14582778C2semidirect
5. C2×#14582777C2semidirect
6. C2×#14582758C2semidirect
7. C2×#14582746C2semidirect
8. #19132844C2semidirect
9. #19132843C2semidirect
10. #19132835C2semidirect
11. #19132834C2semidirect
12. Dic43⋊#95C2semidirect
13. Dic43⋊#95C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×C22⋊#95C2semidirect
23. C2×#13063298C4semidirect
70. C22×D172C2×C4semidirect
82. C22×C22⋊D43C2×C4semidirect
104. C22×C4×D43C2×C4semidirect
114. C2×Dic43⋊C4C2×C4semidirect
115. C2×Dic43⋊C4D4semidirect
144. C2×(C2×D43)⋊C4C2×C4semidirect
145. C2×(C2×D43)⋊C4D4semidirect
151. C2×C4×Dic43D4semidirect
179. C2×C22⋊C4×C43C2×C4semidirect
292. C2×C22⋊D43C22⋊C4semidirect
492. C22×D43C4×D4semidirect
535. C2×C4×C43#121semidirect
675. Dic43#386semidirect
690. C22⋊#95D43semidirect
755. C43#13970semidirect
859. C2×C22⋊C4C4×D43semidirect
1276. C2×C4#13063298semidirect

Maximal subgroups

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

subgroupindex
C22×#130632982
C22×C4×C22⋊D432
C2×#145827992
C2×#145827782
C2×#145827772
C2×#145827582
C2×#145827462
#191328442
#191328432
#191328352
#191328342
Dic43⋊#952
(C2×D43)⋊#952
C43×C22⋊#952
#1397043