Finite Group Databasebeta

← #25018784

Subgroups — #25018784

Order 11008.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2C2×#14582778C211yesmaximal, characteristic
3C2×#14582776C211yesmaximal, characteristic
4C2×#14582774C211yesmaximal, characteristic, complemented
5C2×#14582756C211yesmaximal, characteristic, complemented
6C22×C43⋊#95C211yesmaximal, characteristic, complemented
7#19132849C211yesmaximal, characteristic, complemented
8#19132845C211yesmaximal, characteristic, complemented
9#19132841C211yesmaximal, characteristic, complemented
10#19132837C211yesmaximal, characteristic, complemented
11#19132824C211yesmaximal, characteristic, complemented
12#19132819C211yesmaximal, characteristic, complemented
13#19132817C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C2×C43×#385C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C24×Dic43C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C2×(C22⋊D43)⋊C4—24no—
21C2×(C22⋊D43)⋊C4—24no—
22C2×(C22⋊D43)⋊C4C418yescomplemented
23C22×C4⋊Dic43C2211yescharacteristic
24C22×C4⋊Dic43C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33#14582778—24no—
34#14582776—24no—
35#14582774—24no—
36#14582756—24no—
37C2×C43⋊#95—24no—
38C2×C43⋊#95C2211yescharacteristic
39C2×C43⋊#95C2211yescharacteristic
40C2×C43⋊#95C2211yescharacteristic
41C2×C43⋊#95C2211yescharacteristic
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
52C24×C4×C43C2211yescharacteristic
53C22×C4⋊C4×C43C2211yescharacteristic
54C22×C4⋊C4×C43C2211yescharacteristic
55C22×C22⋊C4×C43C2211yescharacteristic
56C22×C22⋊C4×C43C2211yescharacteristic
57C43×#385—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⋊D43C2×C414yes—
66C22×C22⋊D43D414yes—
67C22×C22⋊D43Q814yes—
68C23×Dic43—22no—
69C23×Dic43—22no—
70C23×Dic43—22no—
71C23×Dic43—22no—
72C23×Dic43—22no—
73C23×Dic43—22no—
74C23×Dic43—22no—
75C23×Dic43—22no—
76C23×Dic43—22no—
77C23×Dic43—41no—
78C23×Dic43—41no—
79C23×Dic43—41no—
80C23×Dic43—41no—
81C23×Dic43C2×C414yes—
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2311yescharacteristic
86C23×Dic43C2311yescharacteristic
87C23×Dic43C2311yescharacteristic
88C23×Dic43C2311yescharacteristic
89C22×C4×D43—22no—
90C22×C4×D43—22no—
91C22×C4×D43—22no—
92C22×C4×D43—22no—
93C22×C4×D43—41no—
94C22×C4×D43—41no—
95C22×C4×D43C2×C414yescomplemented
96(C22⋊D43)⋊C4—232no—
97C2×C4⋊Dic43—22no—
98C2×C4⋊Dic43—22no—
99C2×C4⋊Dic43—22no—
100C2×C4⋊Dic43—22no—
101C2×C4⋊Dic43—41no—
102C2×C4⋊Dic43—41no—
103C2×Dic43⋊C4—22no—
104C2×Dic43⋊C4—22no—
105C2×Dic43⋊C4C2×C414yescomplemented
106C2×C22⋊Dic43—22no—
107C2×C22⋊Dic43—22no—
108C2×C22⋊Dic43—22no—
109C2×(C2×D43)⋊C4—22no—
110C2×(C2×D43)⋊C4—22no—
111C2×(C2×D43)⋊C4—22no—
112C2×(C2×D43)⋊C4—22no—
113C2×(C2×D43)⋊C4—22no—
114C2×(C2×D43)⋊C4—22no—
115C2×(C2×D43)⋊C4—22no—
116C2×(C2×D43)⋊C4—22no—
117C2×(C2×D43)⋊C4—22no—
118C2×(C2×D43)⋊C4—22no—
119C2×(C2×D43)⋊C4—41no—
120C2×(C2×D43)⋊C4—41no—
121C2×(C2×D43)⋊C4—41no—
122C2×(C2×D43)⋊C4—41no—
123C2×(C2×D43)⋊C4C2×C414yescomplemented
124C2×C4×Dic43—22no—
125C2×C4×Dic43—22no—
126C2×C4×Dic43C2×C414yescomplemented
127C43⋊#95—22no—
128C43⋊#95—22no—
129C43⋊#95—22no—
130C43⋊#95—22no—
131C43⋊#95—22no—
132C43⋊#95—22no—
133C43⋊#95—22no—
134C43⋊#95—22no—
135C43⋊#95—22no—
136C43⋊#95—22no—
137C43⋊#95—22no—
138C43⋊#95—41no—
139C43⋊#95—41no—
140C43⋊#95D414yescomplemented
141C25×C43C2311yescharacteristic
142C23×C4×C43—22no—
143C23×C4×C43—22no—
144C23×C4×C43—22no—
145C23×C4×C43—22no—
146C23×C4×C43—22no—
147C23×C4×C43—41no—
148C23×C4×C43—41no—
149C23×C4×C43C2311yescharacteristic
150C23×C4×C43C2311yescharacteristic
151C23×C4×C43C2311yescharacteristic
152C23×C4×C43C2311yescharacteristic
153C23×C4×C43C2311yescharacteristic
154C23×C4×C43C2311yescharacteristic
155C2×C4⋊C4×C43—22no—
156C2×C4⋊C4×C43—22no—
157C2×C4⋊C4×C43—22no—
158C2×C4⋊C4×C43—22no—
159C2×C4⋊C4×C43—41no—
160C2×C4⋊C4×C43—41no—
161C2×C22⋊C4×C43—22no—
162C2×C22⋊C4×C43—22no—
163C2×C22⋊C4×C43—22no—
164C2×C22⋊C4×C43C2×C414yes—
165C2×C22⋊C4×C43D414yes—
166C2×C22⋊C4×C43D414yes—
167#95×C43—22no—
168#95×C43—22no—
169C24×C43—21no—
170C24×C43—21no—
171C24×C43—21no—
172C24×C43—21no—
173C24×C43—21no—
174C24×C43—21no—
175C24×C43—21no—
176C24×C43—21no—
177C24×C43C22×C412yes—
178C24×C43C2×D412yes—
179C24×C43C2×D412yes—
180C24×C43C2×D412yes—
181C24×C43C2×Q812yes—
182C24×C43#4112yes—
183C24×C43#4112yes—
184C24×C43C2411yescharacteristic
185C23×D43—21no—
186C23×D43—21no—
187C23×D43—21no—
188C23×D43—21no—
189C23×D43—21no—
190C23×D43—21no—
191C23×D43—21no—
192C23×D43—21no—
193C23×D43—21no—
194C23×D43—21no—
195C23×D43—21no—
196C23×D43—21no—
197C23×D43C22×C412yes—
198C23×D43C2×D412yes—
199C23×D43C2×Q812yes—
200C22×C4×C43—28no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—21no—
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43—44no—
236C22×C4×C43—44no—
237C22×C4×C43—44no—
238C22×C4×C43—44no—
239C22×C4×C43—44no—
240C22×C4×C43—44no—
241C22×C4×C43C22×C412yes—
242C22×C4×C43C22×C412yes—
243C22×C4×C43C2×D412yes—
244C22×C4×C43C2×D412yes—
245C22×C4×C43C2×D412yes—
246C22×C4×C43C2×D412yes—
247C22×C4×C43C2×D412yes—
248C22×C4×C43#4112yes—
249C2×C22⋊D43—28no—
250C2×C22⋊D43—28no—
251C2×C22⋊D43—28no—
252C2×C22⋊D43—28no—
253C2×C22⋊D43—28no—
254C2×C22⋊D43—28no—
255C2×C22⋊D43C4⋊C4116yescomplemented
256C22×Dic43—28no—
257C22×Dic43—28no—
258C22×Dic43—28no—
259C22×Dic43—21no—
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43—21no—
263C22×Dic43—21no—
264C22×Dic43—21no—
265C22×Dic43—21no—
266C22×Dic43—21no—
267C22×Dic43—21no—
268C22×Dic43—21no—
269C22×Dic43—21no—
270C22×Dic43—21no—
271C22×Dic43—21no—
272C22×Dic43—21no—
273C22×Dic43—21no—
274C22×Dic43—21no—
275C22×Dic43—21no—
276C22×Dic43—21no—
277C22×Dic43—21no—
278C22×Dic43—21no—
279C22×Dic43—21no—
280C22×Dic43—21no—
281C22×Dic43—21no—
282C22×Dic43—21no—
283C22×Dic43—21no—
284C22×Dic43—21no—
285C22×Dic43—21no—
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—44no—
300C22×Dic43—44no—
301C22×Dic43—44no—
302C22×Dic43—44no—
303C22×Dic43—44no—
304C22×Dic43—44no—
305C22×Dic43—44no—
306C22×Dic43—44no—
307C22×Dic43—44no—
308C22×Dic43—44no—
309C22×Dic43—44no—
310C22×Dic43C22×C412yes—
311C22×Dic43C22×C412yes—
312C22×Dic43C22×C412yes—
313C22×Dic43C2×D412yes—
314C22×Dic43C2×D412yes—
315C22×Dic43C2×D412yes—
316C22×Dic43C2×Q812yes—
317C22×Dic43#4112yes—
318C22×Dic43#4112yes—
319C2×C4×D43—28no—
320C2×C4×D43—28no—
321C2×C4×D43—44no—
322C2×C4×D43—44no—
323C2×C4×D43—44no—
324C2×C4×D43—44no—
325C2×C4×D43—44no—
326C4⋊C4×C43—44no—
327C4⋊C4×C43—44no—
328C22⋊C4×C43—44no—
329C22⋊C4×C43C22⋊C4116yescomplemented
330C22⋊Dic43—44no—
331(C2×D43)⋊C4—28no—
332(C2×D43)⋊C4—44no—
333(C2×D43)⋊C4—44no—
334(C2×D43)⋊C4—44no—
335(C2×D43)⋊C4—44no—
336C4⋊Dic43—44no—
337C4⋊Dic43—44no—
338Dic43⋊C4—28no—
339C4×Dic43—28no—
340C23×C43—22no—
341C23×C43—22no—
342C23×C43—22no—
343C23×C43—22no—
344C23×C43—22no—
345C23×C43—22no—
346C23×C43—22no—
347C23×C43—22no—
348C23×C43—22no—
349C23×C43—22no—
350C23×C43—22no—
351C23×C43—22no—
352C23×C43—22no—
353C23×C43—22no—
354C23×C43—22no—
355C23×C43—22no—
356C23×C43—22no—
357C23×C43—22no—
358C23×C43—22no—
359C23×C43—22no—
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×C43C2×C22⋊C414yes—
369C23×C43C2×C4⋊C414yes—
370C23×C43#11714yes—
371C23×C43#12114yes—
372C23×C43#12114yes—
373C23×C43C22⋊Q814yes—
374C23×C43C22⋊Q814yes—
375C23×C43C23×C411yescharacteristic
376C23×C43C22×D411yescharacteristic
377C23×C43C22×D411yescharacteristic
378C23×C43C22×D411yescharacteristic
379C23×C43C22×D411yescharacteristic
380C23×C43C22×Q811yescharacteristic
381C23×C43C2×#4111yescharacteristic
382C23×C43C2×#4111yescharacteristic
383C23×C43C2×#4111yescharacteristic
384C23×C43C2×#4111yescharacteristic
385C23×C43C2×#4111yescharacteristic
386C23×C43H(5,𝔽2)11yescharacteristic
387C23×C43H(5,𝔽2)11yescharacteristic
388C23×C43H(5,𝔽2)11yescharacteristic
389C23×C432−1+411yescharacteristic
390C22×D43—22no—
391C22×D43—22no—
392C22×D43—22no—
393C22×D43—22no—
394C22×D43—22no—
395C22×D43—22no—
396C22×D43—22no—
397C22×D43—22no—
398C22×D43—22no—
399C22×D43—22no—
400C22×D43—22no—
401C22×D43—22no—
402C22×D43—22no—
403C22×D43—22no—
404C22×D43—22no—
405C22×D43—22no—
406C22×D43—22no—
407C22×D43—22no—
408C22×D43—41no—
409C22×D43—41no—
410C22×D43—41no—
411C22×D43—41no—
412C22×D43—41no—
413C22×D43—41no—
414C22×D43—41no—
415C22×D43—41no—
416C22×D43—41no—
417C22×D43—41no—
418C22×D43—41no—
419C22×D43—41no—
420C22×D43—41no—
421C22×D43—41no—
422C22×D43—41no—
423C22×D43—41no—
424C22×D43C2×C4⋊C414yes—
425C2×C4×C43—22no—
426C2×C4×C43—22no—
427C2×C4×C43—22no—
428C2×C4×C43—22no—
429C2×C4×C43—22no—
430C2×C4×C43—22no—
431C2×C4×C43—22no—
432C2×C4×C43—22no—
433C2×C4×C43—22no—
434C2×C4×C43—22no—
435C2×C4×C43—22no—
436C2×C4×C43—22no—
437C2×C4×C43—22no—
438C2×C4×C43—22no—
439C2×C4×C43—22no—
440C2×C4×C43—22no—
441C2×C4×C43—22no—
442C2×C4×C43—22no—
443C2×C4×C43—416no—
444C2×C4×C43—41no—
445C2×C4×C43—41no—
446C2×C4×C43—41no—
447C2×C4×C43—41no—
448C2×C4×C43—41no—
449C2×C4×C43—41no—
450C2×C4×C43—41no—
451C2×C4×C43—41no—
452C2×C4×C43—41no—
453C2×C4×C43—41no—
454C2×C4×C43—41no—
455C2×C4×C43—41no—
456C2×C4×C43—41no—
457C2×C4×C43—41no—
458C2×C4×C43—41no—
459C2×C4×C43—41no—
460C2×C4×C43—41no—
461C2×C4×C43—41no—
462C2×C4×C43—41no—
463C2×C4×C43—41no—
464C2×C4×C43—41no—
465C2×C4×C43—41no—
466C2×C4×C43C2×C22⋊C414yes—
467C2×C4×C43C2×C22⋊C414yes—
468C22⋊D43—232no—
469C2×Dic43—22no—
470C2×Dic43—22no—
471C2×Dic43—22no—
472C2×Dic43—22no—
473C2×Dic43—22no—
474C2×Dic43—22no—
475C2×Dic43—22no—
476C2×Dic43—22no—
477C2×Dic43—22no—
478C2×Dic43—22no—
479C2×Dic43—22no—
480C2×Dic43—22no—
481C2×Dic43—22no—
482C2×Dic43—22no—
483C2×Dic43—22no—
484C2×Dic43—22no—
485C2×Dic43—22no—
486C2×Dic43—22no—
487C2×Dic43—22no—
488C2×Dic43—22no—
489C2×Dic43—22no—
490C2×Dic43—416no—
491C2×Dic43—416no—
492C2×Dic43—41no—
493C2×Dic43—41no—
494C2×Dic43—41no—
495C2×Dic43—41no—
496C2×Dic43—41no—
497C2×Dic43—41no—
498C2×Dic43—41no—
499C2×Dic43—41no—
500C2×Dic43—41no—
501C2×Dic43—41no—
502C2×Dic43—41no—
503C2×Dic43—41no—
504C2×Dic43—41no—
505C2×Dic43—41no—
506C2×Dic43—41no—
507C2×Dic43—41no—
508C2×Dic43—41no—
509C2×Dic43—41no—
510C2×Dic43—41no—
511C2×Dic43—41no—
512C2×Dic43—41no—
513C2×Dic43—41no—
514C2×Dic43—41no—
515C2×Dic43—41no—
516C2×Dic43—41no—
517C2×Dic43—41no—
518C2×Dic43C2×C4⋊C414yes—
519C2×Dic43C4×D414yes—
520C4×D43—416no—
521#13899—431nomaximal, Sylow
522C22×C43—24no—
523C22×C43—24no—
524C22×C43—24no—
525C22×C43—24no—
526C22×C43—24no—
527C22×C43—24no—
528C22×C43—24no—
529C22×C43—24no—
530C22×C43—24no—
531C22×C43—24no—
532C22×C43—24no—
533C22×C43—24no—
534C22×C43—24no—
535C22×C43—24no—
536C22×C43#38018yescomplemented
537C22×C43C22×C22⋊C411yescharacteristic
538C22×C43C22×C4⋊C411yescharacteristic
539C22×C43C2×#11711yescharacteristic
540C22×C43C2×C4×D411yescharacteristic
541C22×C43C4×#4111yescharacteristic
542C22×C43#51811yescharacteristic
543C22×C43#52011yescharacteristic
544C22×C43C2×#12111yescharacteristic
545C22×C43C2×#12111yescharacteristic
546C22×C43C2×C22⋊Q811yescharacteristic
547C22×C43C2×C22⋊Q811yescharacteristic
548C22×C43#52511yescharacteristic
549C22×C43#52511yescharacteristic
550C22×C43#52911yescharacteristic
551C22×C43#52911yescharacteristic
552C22×C43#53811yescharacteristic
553C22×C43#53811yescharacteristic
554C22×C43#53911yescharacteristic
555C22×C43#53911yescharacteristic
556C22×C43D4211yescharacteristic
557C22×C43D4211yescharacteristic
558C22×C43D4211yescharacteristic
559C22×C43#54611yescharacteristic
560C22×C43#54611yescharacteristic
561C22×C43#54611yescharacteristic
562C22×C43#54611yescharacteristic
563C22×C43#54611yescharacteristic
564C22×C43#54611yescharacteristic
565C22×C43#54711yescharacteristic
566C22×C43#54711yescharacteristic
567C22×C43#54711yescharacteristic
568C22×C43D4×Q811yescharacteristic
569C22×C43#55411yescharacteristic
570C22×C43#55411yescharacteristic
571C22×C43#55411yescharacteristic
572C2×D43—24no—
573C2×D43—24no—
574C2×D43—24no—
575C2×D43—42no—
576C2×D43—42no—
577C2×D43—42no—
578C2×D43—42no—
579C2×D43—42no—
580C2×D43—42no—
581C2×D43—42no—
582C2×D43—42no—
583C2×D43—42no—
584C2×D43—42no—
585C2×D43—42no—
586C2×D43—42no—
587C4×C43—24no—
588C4×C43—24no—
589C4×C43—42no—
590C4×C43—42no—
591C4×C43—81no—
592C4×C43—81no—
593Dic43—24no—
594Dic43—24no—
595Dic43—42no—
596Dic43—42no—
597Dic43—42no—
598Dic43—81no—
599Dic43—81no—
600C22×C4×D4—431no—
601C2×#386—431no—
602C2×#386—431no—
603C2×#385—431no—
604C2×#385D4311yescharacteristic, complemented
605C2×#380—431no—
606C22×#95—431no—
607#1441—431no—
608#1441—431no—
609#1439—431no—
610#1439—431no—
611C4⋊#95—431no—
612#1434—431no—
613C22⋊#95—431no—
614C22⋊#95—431no—
615C2×C43—28no—
616C2×C43C2×#38011yescharacteristic
617C2×C43#229011yescharacteristic
618C2×C43#231811yescharacteristic
619C2×C43D4×C22⋊C411yescharacteristic
620C2×C43#233911yescharacteristic
621C2×C43D4×C4⋊C411yescharacteristic
622C2×C43#234911yescharacteristic
623C2×C43#242411yescharacteristic
624C2×C43#242411yescharacteristic
625C2×C43#242511yescharacteristic
626C2×C43#242511yescharacteristic
627C2×C43#244911yescharacteristic
628C2×C43#244911yescharacteristic
629C2×C43#245011yescharacteristic
630C2×C43#245011yescharacteristic
631D43—44no—
632C23×D4—431no—
633C24×C4—431no—
634C24×C4—431no—
635C24×C4—431no—
636C24×C4C2×D4311yescharacteristic
637C2×C4×D4—438no—
638C2×C4×D4—864no—
639C2×C4×D4—864no—
640C22×C4⋊C4—431no—
641C22×C4⋊C4—431no—
642C22×C4⋊C4—431no—
643C22×C4⋊C4C2×D4311yescharacteristic
644C22×C4⋊C4C2×D4311yescharacteristic
645C22×C22⋊C4—431no—
646C22×C22⋊C4—431no—
647C22×C22⋊C4—431no—
648C22×C22⋊C4—431no—
649C22×C22⋊C4—431no—
650C22×C22⋊C4—431no—
651C22×C22⋊C4C2×D4311yescharacteristic
652C22×C22⋊C4C2×D4311yescharacteristic
653C22×C42—431no—
654#386—864no—
655#386—864no—
656#385—24no—
657#385—864no—
658#380—864no—
659C2×#95—431no—
660C2×#95—431no—
661C2×#95—431no—
662C2×#95—431no—
663C2×#95—431no—
664C2×#95—431no—
665C2×#95—431no—
666C2×#95—431no—
667C2×#95—431no—
668C2×#95—431no—
669C2×#95—431no—
670C2×#95—431no—
671C2×#95—431no—
672C2×#95—431no—
673C2×#95—864no—
674C2×#95C2×D4311yescharacteristic
675C2×#95C2×D4311yescharacteristic
676C43#1389911yescharacteristic, complemented, Sylow
677C25—431no—
678C25C22×D4311yescharacteristic
679C22×D4—434no—
680C22×D4—434no—
681C22×D4—434no—
682C22×D4—862no—
683C22×D4—862no—
684C22×D4—862no—
685C22×D4—862no—
686C23×C4—22no—
687C23×C4—22no—
688C23×C4—22no—
689C23×C4—22no—
690C23×C4—22no—
691C23×C4—41no—
692C23×C4—41no—
693C23×C4—431no—
694C23×C4—431no—
695C23×C4—431no—
696C23×C4—431no—
697C23×C4—431no—
698C23×C4—434no—
699C23×C4—434no—
700C23×C4—431no—
701C23×C4—431no—
702C23×C4—862no—
703C23×C4—862no—
704C23×C4—862no—
705C23×C4—862no—
706C23×C4—862no—
707C23×C4—862no—
708C23×C4—862no—
709C23×C4—862no—
710C23×C4—862no—
711C23×C4—862no—
712C23×C4—862no—
713C23×C4—862no—
714C23×C4—862no—
715C23×C4—1721no—
716C23×C4—1721no—
717C23×C4—1721no—
718C23×C4—1721no—
719C23×C4—1721no—
720C23×C4—1721no—
721C23×C4C22×D4311yescharacteristic
722C23×C4C22×D4311yescharacteristic
723C23×C4C22×D4311yescharacteristic
724C23×C4C22×D4311yescharacteristic
725C23×C4C22×D4311yescharacteristic
726C23×C4C22×D4311yescharacteristic
727C4×D4—8632no—
728C2×C4⋊C4—22no—
729C2×C4⋊C4—22no—
730C2×C4⋊C4—22no—
731C2×C4⋊C4—22no—
732C2×C4⋊C4—41no—
733C2×C4⋊C4—41no—
734C2×C4⋊C4—434no—
735C2×C4⋊C4—862no—
736C2×C4⋊C4—862no—
737C2×C4⋊C4—862no—
738C2×C4⋊C4—862no—
739C2×C4⋊C4—862no—
740C2×C4⋊C4—862no—
741C2×C4⋊C4—1721no—
742C2×C4⋊C4—1721no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—434no—
747C2×C22⋊C4—862no—
748C2×C22⋊C4—862no—
749C2×C22⋊C4—862no—
750C2×C22⋊C4—862no—
751C2×C22⋊C4—862no—
752C2×C22⋊C4—862no—
753C2×C22⋊C4—862no—
754C2×C22⋊C4—862no—
755C2×C22⋊C4—862no—
756C2×C22⋊C4—862no—
757C2×C22⋊C4—862no—
758C2×C22⋊C4—862no—
759C2×C22⋊C4—862no—
760C2×C22⋊C4—1721no—
761C2×C22⋊C4—1721no—
762C2×C22⋊C4—1721no—
763C2×C22⋊C4—1721no—
764C2×C22⋊C4C4×D4314yes—
765C2×C22⋊C4D17214yes—
766C2×C22⋊C4C22⋊D4314yes—
767C2×C42—434no—
768C2×C42—862no—
769C2×C42—862no—
770#95—22no—
771#95—22no—
772#95—434no—
773#95—862no—
774#95—862no—
775#95—862no—
776#95—862no—
777#95—862no—
778#95—862no—
779#95—862no—
780#95—862no—
781#95—862no—
782#95—862no—
783#95—862no—
784#95—1721no—
785#95—1721no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—432no—
795C24—432no—
796C24—432no—
797C24—861no—
798C24—861no—
799C24—861no—
800C24—861no—
801C24—861no—
802C24—861no—
803C24—861no—
804C24—861no—
805C24—861no—
806C24—861no—
807C24—861no—
808C24—861no—
809C24C2×C4×D4312yes—
810C24C2×D17212yes—
811C24D4×D4312yes—
812C24#1062190012yes—
813C24Q8×D4312yes—
814C24#1062190212yes—
815C24C2×C22⋊D4312yes—
816C24C23×D4311yescharacteristic
817C2×D4—4316no—
818C2×D4—868no—
819C2×D4—868no—
820C2×D4—868no—
821C2×D4—868no—
822C2×D4—868no—
823C2×D4—868no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—28no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—432no—
866C22×C4—432no—
867C22×C4—432no—
868C22×C4—432no—
869C22×C4—432no—
870C22×C4—432no—
871C22×C4—432no—
872C22×C4—432no—
873C22×C4—432no—
874C22×C4—868no—
875C22×C4—868no—
876C22×C4—861no—
877C22×C4—861no—
878C22×C4—861no—
879C22×C4—861no—
880C22×C4—861no—
881C22×C4—861no—
882C22×C4—861no—
883C22×C4—861no—
884C22×C4—868no—
885C22×C4—868no—
886C22×C4—861no—
887C22×C4—861no—
888C22×C4—861no—
889C22×C4—861no—
890C22×C4—861no—
891C22×C4—861no—
892C22×C4—861no—
893C22×C4—861no—
894C22×C4—861no—
895C22×C4—861no—
896C22×C4—861no—
897C22×C4—861no—
898C22×C4—861no—
899C22×C4—861no—
900C22×C4—861no—
901C22×C4—861no—
902C22×C4—861no—
903C22×C4—861no—
904C22×C4—868no—
905C22×C4—861no—
906C22×C4—861no—
907C22×C4—861no—
908C22×C4—861no—
909C22×C4—861no—
910C22×C4—861no—
911C22×C4—861no—
912C22×C4—861no—
913C22×C4—861no—
914C22×C4—861no—
915C22×C4—861no—
916C22×C4—861no—
917C22×C4—861no—
918C22×C4—861no—
919C22×C4—1724no—
920C22×C4—1724no—
921C22×C4—1724no—
922C22×C4—1724no—
923C22×C4—1724no—
924C22×C4—1724no—
925C22×C4—1724no—
926C22×C4—1724no—
927C22×C4—1724no—
928C22×C4—1724no—
929C22×C4—1724no—
930C22×C4—1724no—
931C22×C4—1724no—
932C22×C4—1724no—
933C22×C4—1724no—
934C22×C4—1724no—
935C22×C4C2×C4×D4312yes—
936C22×C4C2×C4×D4312yes—
937C22×C4C2×D17212yes—
938C22×C4C2×D17212yes—
939C22×C4D4×D4312yes—
940C22×C4#1062190012yes—
941C22×C4C2×C22⋊D4312yes—
942C22×C4C2×C22⋊D4312yes—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4—868no—
946C4⋊C4—1724no—
947C4⋊C4—1724no—
948C22⋊C4—44no—
949C22⋊C4—868no—
950C22⋊C4—1724no—
951C22⋊C4—1724no—
952C22⋊C4—1724no—
953C22⋊C4—1724no—
954C22⋊C4—1724no—
955C22⋊C4(C2×D43)⋊C4116yescomplemented
956C42—868no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—434no—
986C23—862no—
987C23—862no—
988C23—862no—
989C23—862no—
990C23—862no—
991C23—862no—
992C23—862no—
993C23—862no—
994C23—862no—
995C23—862no—
996C23—862no—
997C23—862no—
998C23—862no—
999C23—862no—
1000C23—862no—
1001C23—862no—
1002C23—862no—
1003C23—862no—
1004C23—1721no—
1005C23—1721no—
1006C23—1721no—
1007C23—1721no—
1008C23—1721no—
1009C23—1721no—
1010C23—1721no—
1011C23—1721no—
1012C23—1721no—
1013C23—1721no—
1014C23—1721no—
1015C23—1721no—
1016C23—1721no—
1017C23—1721no—
1018C23—1721no—
1019C23—1721no—
1020C23C2×(C2×D43)⋊C414yes—
1021C23C4⋊C4×D4314yes—
1022C23#1306328314yes—
1023C23#1306329614yes—
1024C23#1306330014yes—
1025C23#1306330114yes—
1026C23#1306330514yes—
1027C23C22×C4×D4311yescharacteristic
1028C23C2×D4×D4311yescharacteristic
1029C23C2×D4×D4311yescharacteristic
1030C23C22×C22⋊D4311yescharacteristic
1031C23C22×D17211yescharacteristic
1032C23C2×Q8×D4311yescharacteristic
1033C23#41×D4311yescharacteristic
1034C23#41×D4311yescharacteristic
1035C23C2×#1062190011yescharacteristic
1036C23C2×#1062190011yescharacteristic
1037C23C2×#1062190211yescharacteristic
1038C23#1306337011yescharacteristic
1039C23#1306337011yescharacteristic
1040C23#1306337111yescharacteristic
1041C23#1306337211yescharacteristic
1042D4—8632no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—416no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—434no—
1085C2×C4—434no—
1086C2×C4—862no—
1087C2×C4—862no—
1088C2×C4—862no—
1089C2×C4—862no—
1090C2×C4—862no—
1091C2×C4—862no—
1092C2×C4—862no—
1093C2×C4—862no—
1094C2×C4—862no—
1095C2×C4—862no—
1096C2×C4—862no—
1097C2×C4—862no—
1098C2×C4—862no—
1099C2×C4—862no—
1100C2×C4—862no—
1101C2×C4—862no—
1102C2×C4—862no—
1103C2×C4—862no—
1104C2×C4—862no—
1105C2×C4—862no—
1106C2×C4—862no—
1107C2×C4—17216no—
1108C2×C4—17216no—
1109C2×C4—1721no—
1110C2×C4—1721no—
1111C2×C4—1721no—
1112C2×C4—1721no—
1113C2×C4—1721no—
1114C2×C4—1721no—
1115C2×C4—1721no—
1116C2×C4—1721no—
1117C2×C4—1721no—
1118C2×C4—1721no—
1119C2×C4—1721no—
1120C2×C4—1721no—
1121C2×C4—1721no—
1122C2×C4—1721no—
1123C2×C4—17216no—
1124C2×C4—1721no—
1125C2×C4—1721no—
1126C2×C4—1721no—
1127C2×C4—1721no—
1128C2×C4—1721no—
1129C2×C4—1721no—
1130C2×C4—1721no—
1131C2×C4—1721no—
1132C2×C4—1721no—
1133C2×C4—1721no—
1134C2×C4—1721no—
1135C2×C4—1721no—
1136C2×C4C2×(C2×D43)⋊C414yes—
1137C2×C4C2×(C2×D43)⋊C414yes—
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—24no—
1151C22—24no—
1152C22—864no—
1153C22—864no—
1154C22—864no—
1155C22—1722no—
1156C22—1722no—
1157C22—1722no—
1158C22—1722no—
1159C22—1722no—
1160C22—1722no—
1161C22—1722no—
1162C22—1722no—
1163C22—1722no—
1164C22—1722no—
1165C22—1722no—
1166C22—1722no—
1167C22#1458275618yescomplemented
1168C22C22×(C2×D43)⋊C411yescharacteristic
1169C22C2×C4⋊C4×D4311yescharacteristic
1170C22C2×#1306328311yescharacteristic
1171C22C4×D4×D4311yescharacteristic
1172C22C4×#1062190011yescharacteristic
1173C22#1458337111yescharacteristic
1174C22#1458337811yescharacteristic
1175C22C2×#1306329611yescharacteristic
1176C22C2×#1306330011yescharacteristic
1177C22C2×#1306330111yescharacteristic
1178C22C2×#1306330511yescharacteristic
1179C22#1458340511yescharacteristic
1180C22#1458341211yescharacteristic
1181C22#1458342611yescharacteristic
1182C22#1458343511yescharacteristic
1183C22#1458348411yescharacteristic
1184C22#1458348911yescharacteristic
1185C22#1458349311yescharacteristic
1186C22#1458349811yescharacteristic
1187C22#1458353111yescharacteristic
1188C22D4×C22⋊D4311yescharacteristic
1189C22D4×D17211yescharacteristic
1190C22#1458353611yescharacteristic
1191C22#1458353711yescharacteristic
1192C22#1458354111yescharacteristic
1193C22#1458354311yescharacteristic
1194C22#1458354411yescharacteristic
1195C22#1458354411yescharacteristic
1196C22#1458354711yescharacteristic
1197C22#1458354811yescharacteristic
1198C22#1458355311yescharacteristic
1199C22#1458356211yescharacteristic
1200C22#1458360311yescharacteristic
1201C22#1458360311yescharacteristic
1202C22#1458360711yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—42no—
1206C4—42no—
1207C4—81no—
1208C4—81no—
1209C4—864no—
1210C4—864no—
1211C4—3441no—
1212C4—3441no—
1213C4—1722no—
1214C4—1722no—
1215C4—1722no—
1216C2—28no—
1217C2—1724no—
1218C2C2×#1458275611yescharacteristic
1219C2#1913703111yescharacteristic
1220C2#1913722311yescharacteristic
1221C2D4×(C2×D43)⋊C411yescharacteristic
1222C2#1913742011yescharacteristic
1223C2#1913749311yescharacteristic
1224C2#1913750111yescharacteristic
1225C2#1913812711yescharacteristic
1226C2#1913812911yescharacteristic
1227C2#1913814211yescharacteristic
1228C2#1913814411yescharacteristic
1229C2#1913840011yescharacteristic
1230C2#1913840211yescharacteristic
1231C2#1913841511yescharacteristic
1232C2#1913841711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#385C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×#385D43
hypocenterC43#13899
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C2×#14582774C2semidirect
5. C2×#14582756C2semidirect
6. C22×C43⋊#95C2semidirect
7. #19132849C2semidirect
8. #19132845C2semidirect
9. #19132841C2semidirect
10. #19132837C2semidirect
11. #19132824C2semidirect
12. #19132819C2semidirect
13. #19132817C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C2×C43×#385C2semidirect
22. C2×(C22⋊D43)⋊C4C4semidirect
95. C22×C4×D43C2×C4semidirect
105. C2×Dic43⋊C4C2×C4semidirect
123. C2×(C2×D43)⋊C4C2×C4semidirect
126. C2×C4×Dic43C2×C4semidirect
140. C43⋊#95D4semidirect
255. C2×C22⋊D43C4⋊C4semidirect
329. C22⋊C4×C43C22⋊C4semidirect
536. C22×C43#380semidirect
604. C2×#385D43semidirect
676. C43#13899semidirect
955. C22⋊C4(C2×D43)⋊C4semidirect
1167. C22#14582756semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D43)⋊C42
C2×#145827782
C2×#145827762
C2×#145827742
C2×#145827562
C22×C43⋊#952
#191328492
#191328452
#191328412
#191328372
#191328242
#191328192
#191328172
(C2×D43)⋊#952
C2×C43×#3852
#1389943