Finite Group Databasebeta

← #25023927

Subgroups — #25023927

Order 11008.

2594 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063296C211yesmaximal, characteristic
2C2×#14582799C211yesmaximal, characteristic, complemented
3C2×#14582793C211yesmaximal, characteristic, complemented
4C2×#14582778C211yesmaximal, characteristic, complemented
5C2×#14582772C211yesmaximal, characteristic, complemented
6C2×#14582758C211yesmaximal, characteristic, complemented
7#19132847C211yesmaximal, characteristic, complemented
8#19132838C211yesmaximal, characteristic, complemented
9#19132838C211yesmaximal, characteristic, complemented
10#19132836C211yesmaximal, characteristic, complemented
11#19132834C211yesmaximal, characteristic, complemented
12#19132834C211yesmaximal, characteristic, complemented
13#19132829C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C2×C43×#386C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C23×C22⋊D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C2×#13063296—24no—
20C2×#13063296—24no—
21C2×#13063296C418yescomplemented
22C22×C4⋊Dic43C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C22×C22⋊Dic43C2211yescharacteristic
29C22×C22⋊Dic43C2211yescharacteristic
30C22×C22⋊Dic43C2211yescharacteristic
31C22×C22⋊Dic43C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×C4×Dic43C2211yescharacteristic
37#14582799—24no—
38#14582793—24no—
39#14582778—24no—
40#14582772—24no—
41#14582758—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
52C23×D4×C43C2211yescharacteristic
53C24×C4×C43C2211yescharacteristic
54C22×C22⋊C4×C43C2211yescharacteristic
55C22×C22⋊C4×C43C2211yescharacteristic
56C22×C22⋊C4×C43C2211yescharacteristic
57C43×#386—24no—
58C2×#95×C43C2211yescharacteristic
59C2×#95×C43C2211yescharacteristic
60C24×D43C2311yescharacteristic
61C22×C22⋊D43—22no—
62C22×C22⋊D43—22no—
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—41no—
70C22×C22⋊D43—41no—
71C22×C22⋊D43—41no—
72C22×C22⋊D43—41no—
73C22×C22⋊D43C2×C414yes—
74C22×C22⋊D43C2×C414yescomplemented
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C22×C4×D43—22no—
83C22×C4×D43—22no—
84C22×C4×D43—22no—
85C22×C4×D43—22no—
86C22×C4×D43—41no—
87C22×C4×D43—41no—
88C22×C4×D43C2×C414yescomplemented
89#13063296—232no—
90C2×C4⋊Dic43—22no—
91C2×C4⋊Dic43—22no—
92C2×C4⋊Dic43C2×C414yescomplemented
93C2×Dic43⋊C4—22no—
94C2×Dic43⋊C4—22no—
95C2×Dic43⋊C4—22no—
96C2×Dic43⋊C4—22no—
97C2×Dic43⋊C4—22no—
98C2×Dic43⋊C4—22no—
99C2×Dic43⋊C4—41no—
100C2×Dic43⋊C4—41no—
101C2×Dic43⋊C4—41no—
102C2×C22⋊Dic43—22no—
103C2×C22⋊Dic43—22no—
104C2×C22⋊Dic43—22no—
105C2×C22⋊Dic43—22no—
106C2×C22⋊Dic43—22no—
107C2×C22⋊Dic43—22no—
108C2×C22⋊Dic43—41no—
109C2×C22⋊Dic43—41no—
110C2×C22⋊Dic43—41no—
111C2×C22⋊Dic43—41no—
112C2×C22⋊Dic43—41no—
113C2×C22⋊Dic43—41no—
114C2×C22⋊Dic43—41no—
115C2×C22⋊Dic43—41no—
116C2×C22⋊Dic43C2×C414yes—
117C2×C22⋊Dic43C2×C414yescomplemented
118C2×C22⋊Dic43D414yes—
119C2×C22⋊Dic43D414yes—
120C2×(C2×D43)⋊C4—22no—
121C2×(C2×D43)⋊C4—22no—
122C2×(C2×D43)⋊C4—22no—
123C2×(C2×D43)⋊C4—22no—
124C2×(C2×D43)⋊C4—22no—
125C2×(C2×D43)⋊C4—41no—
126C2×(C2×D43)⋊C4—41no—
127C2×(C2×D43)⋊C4—41no—
128C2×(C2×D43)⋊C4—41no—
129C2×(C2×D43)⋊C4—41no—
130C2×(C2×D43)⋊C4—41no—
131C2×(C2×D43)⋊C4D414yescomplemented
132C2×C4×Dic43—22no—
133C2×C4×Dic43—22no—
134C2×C4×Dic43—41no—
135C43⋊#95—22no—
136C43⋊#95—22no—
137C43⋊#95—22no—
138C43⋊#95—22no—
139C43⋊#95—22no—
140C43⋊#95—22no—
141C43⋊#95—22no—
142C43⋊#95—22no—
143C43⋊#95—41no—
144C43⋊#95—41no—
145C25×C43C2311yescharacteristic
146C25×C43C2311yescharacteristic
147C22×D4×C43—22no—
148C22×D4×C43—22no—
149C22×D4×C43—22no—
150C22×D4×C43—22no—
151C22×D4×C43—41no—
152C22×D4×C43—41no—
153C22×D4×C43C2×C414yes—
154C23×C4×C43—22no—
155C23×C4×C43—22no—
156C23×C4×C43—22no—
157C23×C4×C43—41no—
158C23×C4×C43—41no—
159C23×C4×C43—41no—
160C23×C4×C43—41no—
161C23×C4×C43C2311yescharacteristic
162C23×C4×C43C2311yescharacteristic
163C23×C4×C43C2311yescharacteristic
164C23×C4×C43C2311yescharacteristic
165C23×C4×C43C2311yescharacteristic
166C2×C22⋊C4×C43—22no—
167C2×C22⋊C4×C43—22no—
168C2×C22⋊C4×C43—22no—
169C2×C22⋊C4×C43—22no—
170C2×C22⋊C4×C43—22no—
171C2×C22⋊C4×C43—41no—
172C2×C22⋊C4×C43—41no—
173C2×C22⋊C4×C43—41no—
174C2×C22⋊C4×C43—41no—
175#95×C43—22no—
176#95×C43D414yescomplemented
177C24×C43—21no—
178C24×C43—21no—
179C24×C43—21no—
180C24×C43—21no—
181C24×C43—21no—
182C24×C43—21no—
183C24×C43—21no—
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×C43C22×C412yes—
204C24×C43C22×C412yes—
205C24×C43C2×D412yes—
206C24×C43C2×D412yes—
207C24×C43C2411yescharacteristic
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×D43C22×C412yes—
221C23×D43C2×D412yes—
222C23×D43#4112yes—
223C2×D4×C43—28no—
224C2×D4×C43—28no—
225C2×D4×C43—44no—
226C2×D4×C43—44no—
227C2×D4×C43—44no—
228C2×D4×C43—44no—
229C2×D4×C43—44no—
230C22×C4×C43—21no—
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—44no—
260C22×C4×C43—44no—
261C22×C4×C43—44no—
262C22×C4×C43—44no—
263C22×C4×C43—44no—
264C22×C4×C43—44no—
265C22×C4×C43—44no—
266C22×C4×C43C22×C412yes—
267C22×C4×C43C2×D412yes—
268C22×C4×C43C2×D412yes—
269C22×C4×C43C2×D412yes—
270C22×C4×C43C2×D412yes—
271C22×C4×C43#4112yes—
272C2×C22⋊D43—28no—
273C2×C22⋊D43—28no—
274C2×C22⋊D43—28no—
275C2×C22⋊D43—28no—
276C2×C22⋊D43—44no—
277C2×C22⋊D43—44no—
278C2×C22⋊D43—44no—
279C2×C22⋊D43—44no—
280C2×C22⋊D43—44no—
281C2×C22⋊D43—44no—
282C2×C22⋊D43—44no—
283C2×C22⋊D43—44no—
284C2×C22⋊D43—44no—
285C2×C22⋊D43—44no—
286C22×Dic43—21no—
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—21no—
327C22×Dic43C22×C412yes—
328C22×Dic43C22×C412yes—
329C22×Dic43C22×C412yes—
330C22×Dic43C2×D412yes—
331C22×Dic43C2×D412yes—
332C22×Dic43C2×D412yes—
333C22×Dic43C2×D412yes—
334C22×Dic43C2×D412yes—
335C2×C4×D43—28no—
336C2×C4×D43—28no—
337C2×C4×D43—44no—
338C2×C4×D43—44no—
339C2×C4×D43—44no—
340C2×C4×D43—44no—
341C2×C4×D43—44no—
342C22⋊C4×C43—44no—
343C22⋊C4×C43—44no—
344C22⋊C4×C43—44no—
345C22⋊Dic43—28no—
346C22⋊Dic43—44no—
347C22⋊Dic43—44no—
348C22⋊Dic43—44no—
349C22⋊Dic43—44no—
350C22⋊Dic43C22⋊C4116yescomplemented
351(C2×D43)⋊C4—44no—
352(C2×D43)⋊C4—44no—
353(C2×D43)⋊C4—44no—
354(C2×D43)⋊C4—44no—
355C4⋊Dic43—28no—
356Dic43⋊C4—44no—
357Dic43⋊C4—44no—
358Dic43⋊C4—44no—
359C4×Dic43—44no—
360C23×C43—22no—
361C23×C43—22no—
362C23×C43—22no—
363C23×C43—22no—
364C23×C43—22no—
365C23×C43—22no—
366C23×C43—22no—
367C23×C43—22no—
368C23×C43—22no—
369C23×C43—22no—
370C23×C43—22no—
371C23×C43—22no—
372C23×C43—22no—
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—41no—
386C23×C43—41no—
387C23×C43—41no—
388C23×C43—41no—
389C23×C43—41no—
390C23×C43—41no—
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×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×C43C2×C22⋊C414yes—
430C23×C43C23×C411yescharacteristic
431C23×C43C22×D411yescharacteristic
432C23×C43C22×D411yescharacteristic
433C23×C43C22×D411yescharacteristic
434C23×C43C22×D411yescharacteristic
435C23×C43C2×#4111yescharacteristic
436C23×C43C2×#4111yescharacteristic
437C23×C43H(5,𝔽2)11yescharacteristic
438C23×C43H(5,𝔽2)11yescharacteristic
439C23×C43H(5,𝔽2)11yescharacteristic
440C23×C43H(5,𝔽2)11yescharacteristic
441C23×C43H(5,𝔽2)11yescharacteristic
442C23×C43H(5,𝔽2)11yescharacteristic
443C23×C432−1+411yescharacteristic
444C23×C432−1+411yescharacteristic
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—22no—
460C22×D43—22no—
461C22×D43—22no—
462C22×D43—22no—
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×D43C4×D414yes—
480D4×C43—416no—
481C2×C4×C43—22no—
482C2×C4×C43—22no—
483C2×C4×C43—22no—
484C2×C4×C43—22no—
485C2×C4×C43—22no—
486C2×C4×C43—22no—
487C2×C4×C43—22no—
488C2×C4×C43—22no—
489C2×C4×C43—22no—
490C2×C4×C43—22no—
491C2×C4×C43—22no—
492C2×C4×C43—22no—
493C2×C4×C43—22no—
494C2×C4×C43—22no—
495C2×C4×C43—22no—
496C2×C4×C43—416no—
497C2×C4×C43—41no—
498C2×C4×C43—41no—
499C2×C4×C43—41no—
500C2×C4×C43—41no—
501C2×C4×C43—41no—
502C2×C4×C43—41no—
503C2×C4×C43—41no—
504C2×C4×C43—41no—
505C2×C4×C43—41no—
506C2×C4×C43—41no—
507C2×C4×C43—41no—
508C2×C4×C43—41no—
509C2×C4×C43—41no—
510C2×C4×C43—41no—
511C2×C4×C43—41no—
512C2×C4×C43—41no—
513C2×C4×C43—41no—
514C2×C4×C43—41no—
515C2×C4×C43—41no—
516C2×C4×C43C4×D414yes—
517C22⋊D43—416no—
518C22⋊D43—416no—
519C2×Dic43—22no—
520C2×Dic43—22no—
521C2×Dic43—22no—
522C2×Dic43—22no—
523C2×Dic43—22no—
524C2×Dic43—22no—
525C2×Dic43—22no—
526C2×Dic43—22no—
527C2×Dic43—22no—
528C2×Dic43—22no—
529C2×Dic43—22no—
530C2×Dic43—22no—
531C2×Dic43—22no—
532C2×Dic43—22no—
533C2×Dic43—22no—
534C2×Dic43—22no—
535C2×Dic43—22no—
536C2×Dic43—22no—
537C2×Dic43—41no—
538C2×Dic43—41no—
539C2×Dic43—41no—
540C2×Dic43—41no—
541C2×Dic43—41no—
542C2×Dic43—41no—
543C2×Dic43—41no—
544C2×Dic43—41no—
545C2×Dic43—41no—
546C2×Dic43—41no—
547C2×Dic43—41no—
548C2×Dic43—41no—
549C2×Dic43—41no—
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×Dic43C2×C22⋊C414yes—
567C2×Dic43C2×C22⋊C414yes—
568C4×D43—416no—
569#14361—431nomaximal, Sylow
570C22×C43—24no—
571C22×C43—24no—
572C22×C43—24no—
573C22×C43—42no—
574C22×C43—42no—
575C22×C43—42no—
576C22×C43—42no—
577C22×C43—42no—
578C22×C43—42no—
579C22×C43—42no—
580C22×C43—42no—
581C22×C43—42no—
582C22×C43—42no—
583C22×C43—42no—
584C22×C43—42no—
585C22×C43—42no—
586C22×C43—42no—
587C22×C43—42no—
588C22×C43—42no—
589C22×C43—42no—
590C22×C43—42no—
591C22×C43—42no—
592C22×C43—81no—
593C22×C43—81no—
594C22×C43—81no—
595C22×C43—81no—
596C22×C43—81no—
597C22×C43—81no—
598C22×C43—81no—
599C22×C43—81no—
600C22×C43C22×C22⋊C411yescharacteristic
601C22×C43C2×C4×D411yescharacteristic
602C22×C43C2×C4×D411yescharacteristic
603C22×C43#51811yescharacteristic
604C22×C43#51811yescharacteristic
605C22×C43#52011yescharacteristic
606C22×C43#52011yescharacteristic
607C22×C43#53411yescharacteristic
608C22×C43#53511yescharacteristic
609C22×C43#53511yescharacteristic
610C22×C43#53611yescharacteristic
611C22×C43#53711yescharacteristic
612C22×C43#53711yescharacteristic
613C22×C43#53711yescharacteristic
614C22×C43#53711yescharacteristic
615C22×C43#53811yescharacteristic
616C22×C43#53911yescharacteristic
617C22×C43#54011yescharacteristic
618C22×C43#54211yescharacteristic
619C22×C43D4211yescharacteristic
620C22×C43D4211yescharacteristic
621C22×C43D4211yescharacteristic
622C22×C43D4211yescharacteristic
623C22×C43D4211yescharacteristic
624C22×C43#54611yescharacteristic
625C22×C43#54611yescharacteristic
626C22×C43#54611yescharacteristic
627C22×C43#54611yescharacteristic
628C22×C43#54711yescharacteristic
629C22×C43#54811yescharacteristic
630C22×C43#55311yescharacteristic
631C22×C43#56011yescharacteristic
632C22×C43#56011yescharacteristic
633C22×C43#56211yescharacteristic
634C22×C43#56211yescharacteristic
635C2×D43—24no—
636C2×D43—24no—
637C2×D43—24no—
638C2×D43—42no—
639C2×D43—42no—
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—
650C4×C43—24no—
651C4×C43—42no—
652C4×C43—42no—
653C4×C43—42no—
654C4×C43—81no—
655Dic43—24no—
656Dic43—24no—
657Dic43—42no—
658Dic43—42no—
659Dic43—81no—
660Dic43—81no—
661Dic43—81no—
662C22×#121—431no—
663C2×#390—431no—
664C2×#388—431no—
665C2×#386—431no—
666C2×#386D4311yescharacteristic, complemented
667C2×#385—431no—
668C2×#380—431no—
669#1441—431no—
670#1439—431no—
671#1439—431no—
672#1438—431no—
673#1438—431no—
674#1438—431no—
675#1436—431no—
676C22⋊#95—431no—
677C2×C43—44no—
678C2×C43—82no—
679C2×C43#231111yescharacteristic
680C2×C43#232411yescharacteristic
681C2×C43#232511yescharacteristic
682C2×C43D4×C22⋊C411yescharacteristic
683C2×C43D4×C22⋊C411yescharacteristic
684C2×C43#236111yescharacteristic
685C2×C43#237711yescharacteristic
686C2×C43#266911yescharacteristic
687C2×C43#267111yescharacteristic
688C2×C43#267211yescharacteristic
689C2×C43#267511yescharacteristic
690C2×C43#267611yescharacteristic
691C2×C43#268111yescharacteristic
692C2×C43#269111yescharacteristic
693C2×C43#270311yescharacteristic
694D43—44no—
695C23×D4—431no—
696C23×D4—431no—
697C23×D4C2×D4311yescharacteristic
698C24×C4—431no—
699C24×C4C2×D4311yescharacteristic
700C2×#121—438no—
701C2×#121—864no—
702C2×#121—864no—
703C22×C4⋊C4—431no—
704C22×C4⋊C4—431no—
705C22×C4⋊C4—431no—
706C22×C4⋊C4—431no—
707C22×C22⋊C4—431no—
708C22×C22⋊C4—431no—
709C22×C22⋊C4—431no—
710C22×C22⋊C4—431no—
711C22×C22⋊C4—431no—
712C22×C22⋊C4—431no—
713C22×C22⋊C4—431no—
714C22×C22⋊C4—431no—
715C22×C22⋊C4—431no—
716C22×C22⋊C4—431no—
717C22×C22⋊C4C2×D4311yescharacteristic
718C22×C22⋊C4C2×D4311yescharacteristic
719C22×C22⋊C4C2×D4311yescharacteristic
720C22×C42—431no—
721#390—864no—
722#388—864no—
723#386—24no—
724#386—864no—
725#385—864no—
726#380—864no—
727C2×#95—431no—
728C2×#95—431no—
729C2×#95—431no—
730C2×#95—431no—
731C2×#95—431no—
732C2×#95—431no—
733C2×#95—431no—
734C2×#95—431no—
735C2×#95—431no—
736C2×#95—431no—
737C2×#95C2×D4311yescharacteristic
738C2×#95C2×D4311yescharacteristic
739C43#1436111yescharacteristic, complemented, Sylow
740C25—431no—
741C25C22×D4311yescharacteristic
742C25C22×D4311yescharacteristic
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4—434no—
750C22×D4—434no—
751C22×D4—862no—
752C22×D4—862no—
753C22×D4—862no—
754C22×D4—862no—
755C22×D4—862no—
756C22×D4—862no—
757C22×D4—862no—
758C22×D4—862no—
759C22×D4—1721no—
760C22×D4—1721no—
761C22×D4—1721no—
762C22×D4—1721no—
763C22×D4C4×D4314yes—
764C23×C4—22no—
765C23×C4—22no—
766C23×C4—22no—
767C23×C4—41no—
768C23×C4—41no—
769C23×C4—41no—
770C23×C4—41no—
771C23×C4—431no—
772C23×C4—431no—
773C23×C4—431no—
774C23×C4—431no—
775C23×C4—434no—
776C23×C4—431no—
777C23×C4—431no—
778C23×C4—431no—
779C23×C4—862no—
780C23×C4—862no—
781C23×C4—862no—
782C23×C4—862no—
783C23×C4—1721no—
784C23×C4—1721no—
785C23×C4C22×D4311yescharacteristic
786C23×C4C22×D4311yescharacteristic
787C23×C4C22×D4311yescharacteristic
788C23×C4C22×D4311yescharacteristic
789C23×C4C22×D4311yescharacteristic
790#121—8632no—
791C2×C4⋊C4—434no—
792C2×C4⋊C4—862no—
793C2×C4⋊C4—862no—
794C2×C4⋊C4—862no—
795C2×C4⋊C4—862no—
796C2×C4⋊C4—862no—
797C2×C4⋊C4—862no—
798C2×C4⋊C4—862no—
799C2×C4⋊C4—862no—
800C2×C4⋊C4—1721no—
801C2×C4⋊C4—1721no—
802C2×C4⋊C4—1721no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—434no—
813C2×C22⋊C4—434no—
814C2×C22⋊C4—434no—
815C2×C22⋊C4—434no—
816C2×C22⋊C4—434no—
817C2×C22⋊C4—862no—
818C2×C22⋊C4—862no—
819C2×C22⋊C4—862no—
820C2×C22⋊C4—862no—
821C2×C22⋊C4—862no—
822C2×C22⋊C4—862no—
823C2×C22⋊C4—862no—
824C2×C22⋊C4—862no—
825C2×C22⋊C4—862no—
826C2×C22⋊C4—862no—
827C2×C22⋊C4—862no—
828C2×C22⋊C4—1721no—
829C2×C22⋊C4—1721no—
830C2×C22⋊C4—1721no—
831C2×C22⋊C4—1721no—
832C2×C22⋊C4—1721no—
833C2×C22⋊C4—1721no—
834C2×C22⋊C4—1721no—
835C2×C22⋊C4—1721no—
836C2×C22⋊C4—1721no—
837C2×C22⋊C4—1721no—
838C2×C22⋊C4—1721no—
839C2×C22⋊C4—1721no—
840C2×C22⋊C4—1721no—
841C2×C22⋊C4—1721no—
842C2×C42—862no—
843C2×C42—862no—
844C2×C42—1721no—
845#95—22no—
846#95—862no—
847#95—862no—
848#95—862no—
849#95—862no—
850#95—862no—
851#95—862no—
852#95—862no—
853#95—862no—
854#95—1721no—
855#95—1721no—
856#95C22⋊D4314yescomplemented
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—432no—
884C24—432no—
885C24—432no—
886C24—861no—
887C24—861no—
888C24—861no—
889C24—861no—
890C24—861no—
891C24—861no—
892C24—861no—
893C24—861no—
894C24—861no—
895C24—861no—
896C24—861no—
897C24—861no—
898C24C2×C4×D4312yes—
899C24C2×C4×D4312yes—
900C24D4×D4312yes—
901C24D4×D4312yes—
902C24C23×D4311yescharacteristic
903C2×D4—28no—
904C2×D4—28no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—868no—
911C2×D4—868no—
912C2×D4—868no—
913C2×D4—868no—
914C2×D4—1724no—
915C2×D4—1724no—
916C2×D4—1724no—
917C2×D4—1724no—
918C2×D4—1724no—
919C2×D4—1724no—
920C2×D4—1724no—
921C2×D4—1724no—
922C2×D4—1724no—
923C2×D4—1724no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—44no—
954C22×C4—44no—
955C22×C4—44no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—432no—
961C22×C4—432no—
962C22×C4—432no—
963C22×C4—432no—
964C22×C4—432no—
965C22×C4—432no—
966C22×C4—432no—
967C22×C4—432no—
968C22×C4—868no—
969C22×C4—861no—
970C22×C4—861no—
971C22×C4—861no—
972C22×C4—861no—
973C22×C4—861no—
974C22×C4—861no—
975C22×C4—861no—
976C22×C4—861no—
977C22×C4—861no—
978C22×C4—861no—
979C22×C4—861no—
980C22×C4—861no—
981C22×C4—861no—
982C22×C4—861no—
983C22×C4—861no—
984C22×C4—861no—
985C22×C4—861no—
986C22×C4—861no—
987C22×C4—861no—
988C22×C4—861no—
989C22×C4—868no—
990C22×C4—861no—
991C22×C4—861no—
992C22×C4—861no—
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—861no—
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—1724no—
1012C22×C4—1724no—
1013C22×C4—1724no—
1014C22×C4—1724no—
1015C22×C4—1724no—
1016C22×C4C2×C4×D4312yes—
1017C22×C4#1062189812yes—
1018C22×C4D4×D4312yes—
1019C22×C4C2×C22⋊D4312yes—
1020C22×C4C2×C22⋊D4312yes—
1021C22×C4C2×C22⋊D4312yes—
1022C4⋊C4—868no—
1023C4⋊C4—1724no—
1024C4⋊C4—1724no—
1025C4⋊C4—1724no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—4316no—
1030C22⋊C4—868no—
1031C22⋊C4—1724no—
1032C22⋊C4—1724no—
1033C22⋊C4—1724no—
1034C22⋊C4—1724no—
1035C22⋊C4—1724no—
1036C22⋊C4—1724no—
1037C22⋊C4—1724no—
1038C22⋊C4—1724no—
1039C42—1724no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
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—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—434no—
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—1721no—
1129C23—1721no—
1130C23—1721no—
1131C23—1721no—
1132C23—1721no—
1133C23—1721no—
1134C23—1721no—
1135C23—1721no—
1136C23—1721no—
1137C23—1721no—
1138C23—1721no—
1139C23—1721no—
1140C23—1721no—
1141C23—1721no—
1142C23—1721no—
1143C23—1721no—
1144C23C22⋊C4×D4314yes—
1145C23C22×C4×D4311yescharacteristic
1146C23C2×D4×D4311yescharacteristic
1147C23C2×D4×D4311yescharacteristic
1148C23C2×D4×D4311yescharacteristic
1149C23C22×C22⋊D4311yescharacteristic
1150C23#41×D4311yescharacteristic
1151C23C2×#1062189811yescharacteristic
1152C23#1306337011yescharacteristic
1153C23#1306337011yescharacteristic
1154C23#1306337011yescharacteristic
1155C23#1306337011yescharacteristic
1156C23#1306337011yescharacteristic
1157C23#1306337111yescharacteristic
1158C23#1306337211yescharacteristic
1159C23#1306337211yescharacteristic
1160D4—416no—
1161D4—17216no—
1162D4—17216no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—416no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—434no—
1199C2×C4—434no—
1200C2×C4—862no—
1201C2×C4—862no—
1202C2×C4—862no—
1203C2×C4—862no—
1204C2×C4—862no—
1205C2×C4—862no—
1206C2×C4—862no—
1207C2×C4—862no—
1208C2×C4—862no—
1209C2×C4—862no—
1210C2×C4—862no—
1211C2×C4—862no—
1212C2×C4—862no—
1213C2×C4—862no—
1214C2×C4—862no—
1215C2×C4—862no—
1216C2×C4—862no—
1217C2×C4—862no—
1218C2×C4—17216no—
1219C2×C4—1721no—
1220C2×C4—1721no—
1221C2×C4—1721no—
1222C2×C4—1721no—
1223C2×C4—1721no—
1224C2×C4—1721no—
1225C2×C4—1721no—
1226C2×C4—1721no—
1227C2×C4—1721no—
1228C2×C4—1721no—
1229C2×C4—1721no—
1230C2×C4—1721no—
1231C2×C4—1721no—
1232C2×C4—1721no—
1233C2×C4—1721no—
1234C2×C4—1721no—
1235C2×C4—1721no—
1236C2×C4—1721no—
1237C2×C4—1721no—
1238C2×C4—1721no—
1239C2×C4—1721no—
1240C2×C4—1721no—
1241C2×C4—1721no—
1242C2×C4—1721no—
1243C2×C4—1721no—
1244C2×C4—1721no—
1245C2×C4—1721no—
1246C2×C4—1721no—
1247C2×C4—1721no—
1248C2×C4C4×C22⋊D4314yes—
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—864no—
1280C22—864no—
1281C22—864no—
1282C22—1722no—
1283C22—1722no—
1284C22—1722no—
1285C22—1722no—
1286C22—1722no—
1287C22—1722no—
1288C22—1722no—
1289C22—1722no—
1290C22—1722no—
1291C22—1722no—
1292C22—1722no—
1293C22—1722no—
1294C22C2×C22⋊C4×D4311yescharacteristic
1295C22C4×D4×D4311yescharacteristic
1296C22C2×C4×C22⋊D4311yescharacteristic
1297C22#1458337111yescharacteristic
1298C22#1458337211yescharacteristic
1299C22#1458337811yescharacteristic
1300C22#1458337811yescharacteristic
1301C22#1458345911yescharacteristic
1302C22#1458346411yescharacteristic
1303C22#1458346611yescharacteristic
1304C22#1458347111yescharacteristic
1305C22#1458347611yescharacteristic
1306C22#1458347611yescharacteristic
1307C22#1458347711yescharacteristic
1308C22#1458347811yescharacteristic
1309C22#1458348111yescharacteristic
1310C22#1458349211yescharacteristic
1311C22#1458350011yescharacteristic
1312C22#1458351411yescharacteristic
1313C22#1458353111yescharacteristic
1314C22D4×C22⋊D4311yescharacteristic
1315C22D4×C22⋊D4311yescharacteristic
1316C22D4×C22⋊D4311yescharacteristic
1317C22#1458353311yescharacteristic
1318C22#1458353811yescharacteristic
1319C22#1458353911yescharacteristic
1320C22#1458353911yescharacteristic
1321C22#1458354111yescharacteristic
1322C22#1458355411yescharacteristic
1323C22#1458355611yescharacteristic
1324C22#1458359911yescharacteristic
1325C22#1458363711yescharacteristic
1326C22#1458363811yescharacteristic
1327C22#1458364411yescharacteristic
1328C22#1458364611yescharacteristic
1329C4—24no—
1330C4—42no—
1331C4—42no—
1332C4—42no—
1333C4—81no—
1334C4—864no—
1335C4—864no—
1336C4—3441no—
1337C4—3441no—
1338C4—3441no—
1339C4—1722no—
1340C4—1722no—
1341C2—44no—
1342C2—82no—
1343C2—1724no—
1344C2#1913718211yescharacteristic
1345C2#1913728211yescharacteristic
1346C2#1913729711yescharacteristic
1347C2#1913741311yescharacteristic
1348C2C22⋊C4×C22⋊D4311yescharacteristic
1349C2#1913760711yescharacteristic
1350C2#1913774711yescharacteristic
1351C2#1914080911yescharacteristic
1352C2#1914083211yescharacteristic
1353C2#1914085011yescharacteristic
1354C2#1914088511yescharacteristic
1355C2#1914089011yescharacteristic
1356C2#1914094711yescharacteristic
1357C2#1914107111yescharacteristic
1358C2#1914124111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#386C2
socle, cosocleC24×C43C24
prime radicalC22×#13063296C2
hypercenterC2×#386D43
hypocenterC43#14361
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×#14582799C2semidirect
3. C2×#14582793C2semidirect
4. C2×#14582778C2semidirect
5. C2×#14582772C2semidirect
6. C2×#14582758C2semidirect
7. #19132847C2semidirect
8. #19132838C2semidirect
9. #19132838C2semidirect
10. #19132836C2semidirect
11. #19132834C2semidirect
12. #19132834C2semidirect
13. #19132829C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C2×C43×#386C2semidirect
21. C2×#13063296C4semidirect
74. C22×C22⋊D43C2×C4semidirect
88. C22×C4×D43C2×C4semidirect
92. C2×C4⋊Dic43C2×C4semidirect
117. C2×C22⋊Dic43C2×C4semidirect
131. C2×(C2×D43)⋊C4D4semidirect
176. #95×C43D4semidirect
350. C22⋊Dic43C22⋊C4semidirect
666. C2×#386D43semidirect
739. C43#14361semidirect
856. #95C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130632962
C2×#145827992
C2×#145827932
C2×#145827782
C2×#145827722
C2×#145827582
#191328472
#191328382
#191328362
#191328342
#191328292
(C2×D43)⋊#952
C2×C43×#3862
#1436143