Finite Group Databasebeta

← #25019399

Subgroups — #25019399

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×#13063297C211yesmaximal, characteristic
2C22×C4×C22⋊D43C211yesmaximal, characteristic, complemented
3C2×#14582799C211yesmaximal, characteristic, complemented
4C2×#14582775C211yesmaximal, characteristic, complemented
5C2×#14582757C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
7#19132843C211yesmaximal, characteristic, complemented
8#19132842C211yesmaximal, characteristic, complemented
9#19132836C211yesmaximal, characteristic, complemented
10#19132834C211yesmaximal, characteristic, complemented
11Dic43⋊#95C211yesmaximal, characteristic, complemented
12Dic43⋊#95C211yesmaximal, characteristic, complemented
13#19132818C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C2×C43×#386C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C23×C22⋊D43C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C2×#13063297—24no—
21C2×#13063297—24no—
22C2×#13063297C418yescomplemented
23C2×C4×C22⋊D43—24no—
24C2×C4×C22⋊D43—24no—
25C2×C4×C22⋊D43—24no—
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×C22⋊Dic43C2211yescharacteristic
30C22×C22⋊Dic43C2211yescharacteristic
31C22×C22⋊Dic43C2211yescharacteristic
32C22×C22⋊Dic43C2211yescharacteristic
33C22×C22⋊Dic43C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×C4×Dic43C2211yescharacteristic
39C22×C4×Dic43C2211yescharacteristic
40#14582799—24no—
41#14582775—24no—
42#14582757—24no—
43C22⋊C4×Dic43—24no—
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
54C23×D4×C43C2211yescharacteristic
55C24×C4×C43C2211yescharacteristic
56C22×C22⋊C4×C43C2211yescharacteristic
57C22×C22⋊C4×C43C2211yescharacteristic
58C22×C22⋊C4×C43C2211yescharacteristic
59C43×#386—24no—
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—41no—
72C22×C22⋊D43—41no—
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—22no—
83C23×Dic43C2×C414yescomplemented
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—41no—
97C22×C4×D43—41no—
98#13063297—232no—
99C4×C22⋊D43—232no—
100C2×Dic43⋊C4—22no—
101C2×Dic43⋊C4—22no—
102C2×Dic43⋊C4—22no—
103C2×Dic43⋊C4—22no—
104C2×Dic43⋊C4—22no—
105C2×Dic43⋊C4—22no—
106C2×Dic43⋊C4—22no—
107C2×Dic43⋊C4C2×C414yescomplemented
108C2×Dic43⋊C4D414yescomplemented
109C2×C22⋊Dic43—22no—
110C2×C22⋊Dic43—22no—
111C2×C22⋊Dic43—22no—
112C2×C22⋊Dic43—22no—
113C2×C22⋊Dic43—22no—
114C2×C22⋊Dic43—22no—
115C2×C22⋊Dic43—22no—
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×C22⋊Dic43—41no—
123C2×C22⋊Dic43C2×C414yescomplemented
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—41no—
134C2×(C2×D43)⋊C4—41no—
135C2×(C2×D43)⋊C4C2×C414yescomplemented
136C2×C4×Dic43—22no—
137C2×C4×Dic43—22no—
138C2×C4×Dic43—22no—
139C2×C4×Dic43—22no—
140C2×C4×Dic43—22no—
141C2×C4×Dic43D414yescomplemented
142C43⋊#95—22no—
143C43⋊#95—22no—
144C43⋊#95—22no—
145C43⋊#95—22no—
146C43⋊#95—22no—
147C43⋊#95—22no—
148C43⋊#95—41no—
149C43⋊#95—41no—
150C43⋊#95—41no—
151C43⋊#95—41no—
152C25×C43C2311yescharacteristic
153C25×C43C2311yescharacteristic
154C22×D4×C43—22no—
155C22×D4×C43—22no—
156C22×D4×C43—22no—
157C22×D4×C43—22no—
158C22×D4×C43—41no—
159C22×D4×C43—41no—
160C22×D4×C43C2×C414yescomplemented
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
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—22no—
179C2×C22⋊C4×C43—41no—
180C2×C22⋊C4×C43—41no—
181C2×C22⋊C4×C43D414yescomplemented
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×C43C22×C412yes—
209C24×C43C22×C412yes—
210C24×C43C2×D412yes—
211C24×C43C2×D412yes—
212C24×C43C2×D412yes—
213C24×C43#4112yes—
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×D43—21no—
224C23×D43—21no—
225C23×D43—21no—
226C23×D43—21no—
227C23×D43C22×C412yes—
228C23×D43C2×D412yes—
229C23×D43C2×D412yes—
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—28no—
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—21no—
267C22×C4×C43—44no—
268C22×C4×C43—44no—
269C22×C4×C43—44no—
270C22×C4×C43—44no—
271C22×C4×C43—44no—
272C22×C4×C43—44no—
273C22×C4×C43C22×C412yes—
274C22×C4×C43C2×D412yes—
275C22×C4×C43C2×D412yes—
276C22×C4×C43C2×D412yes—
277C22×C4×C43C2×D412yes—
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—28no—
294C22×Dic43—28no—
295C22×Dic43—28no—
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×Dic43—21no—
328C22×Dic43—21no—
329C22×Dic43—21no—
330C22×Dic43—21no—
331C22×Dic43—21no—
332C22×Dic43—21no—
333C22×Dic43—44no—
334C22×Dic43—44no—
335C22×Dic43—44no—
336C22×Dic43—44no—
337C22×Dic43C22×C412yes—
338C22×Dic43C22×C412yes—
339C22×Dic43C22×C412yes—
340C22×Dic43C2×D412yes—
341C22×Dic43C2×D412yes—
342C22×Dic43C2×D412yes—
343C22×Dic43C2×D412yes—
344C22×Dic43C2×D412yes—
345C22×Dic43C2×D412yes—
346C22×Dic43#4112yes—
347C22×Dic43#4112yes—
348C22×Dic43#4112yes—
349C2×C4×D43—28no—
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⋊C4×C43—44no—
359C22⋊Dic43—28no—
360C22⋊Dic43—28no—
361C22⋊Dic43—28no—
362C22⋊Dic43—44no—
363C22⋊Dic43—44no—
364(C2×D43)⋊C4—28no—
365(C2×D43)⋊C4—28no—
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—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—22no—
403C23×C43—22no—
404C23×C43—22no—
405C23×C43—22no—
406C23×C43—22no—
407C23×C43—22no—
408C23×C43—22no—
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×C43C2×C22⋊C414yes—
442C23×C43C4×D414yescomplemented
443C23×C43C23×C411yescharacteristic
444C23×C43C22×D411yescharacteristic
445C23×C43C22×D411yescharacteristic
446C23×C43C22×D411yescharacteristic
447C23×C43C22×D411yescharacteristic
448C23×C43C22×D411yescharacteristic
449C23×C43C2×#4111yescharacteristic
450C23×C43C2×#4111yescharacteristic
451C23×C43C2×#4111yescharacteristic
452C23×C43C2×#4111yescharacteristic
453C23×C43C2×#4111yescharacteristic
454C23×C43H(5,𝔽2)11yescharacteristic
455C23×C43H(5,𝔽2)11yescharacteristic
456C23×C43H(5,𝔽2)11yescharacteristic
457C23×C432−1+411yescharacteristic
458C22×D43—22no—
459C22×D43—22no—
460C22×D43—22no—
461C22×D43—22no—
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—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×D43—41no—
492C22×D43C2×C22⋊C414yes—
493D4×C43—416no—
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—416no—
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×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#12114yescomplemented
530C22⋊D43—232no—
531C22⋊D43—416no—
532C2×Dic43—22no—
533C2×Dic43—22no—
534C2×Dic43—22no—
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—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×Dic43—41no—
567C2×Dic43—416no—
568C2×Dic43—41no—
569C2×Dic43—41no—
570C2×Dic43—41no—
571C2×Dic43—41no—
572C2×Dic43—41no—
573C2×Dic43—41no—
574C2×Dic43—41no—
575C2×Dic43C2×C22⋊C414yes—
576C2×Dic43C4×D414yes—
577C2×Dic43C4×D414yes—
578C2×Dic43#12014yes—
579C2×Dic43#12114yes—
580C2×Dic43#12114yes—
581C2×Dic43#12314yes—
582C4×D43—416no—
583#13970—431nomaximal, Sylow
584C22×C43—24no—
585C22×C43—24no—
586C22×C43—24no—
587C22×C43—24no—
588C22×C43—24no—
589C22×C43—24no—
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×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—42no—
612C22×C43—42no—
613C22×C43—42no—
614C22×C43C22×C22⋊C411yescharacteristic
615C22×C43C2×C4×D411yescharacteristic
616C22×C43C2×C4×D411yescharacteristic
617C22×C43C2×C4×D411yescharacteristic
618C22×C43C4×#4111yescharacteristic
619C22×C43#51811yescharacteristic
620C22×C43#52011yescharacteristic
621C22×C43C2×#12011yescharacteristic
622C22×C43C2×#12111yescharacteristic
623C22×C43C2×#12111yescharacteristic
624C22×C43C2×#12111yescharacteristic
625C22×C43C2×#12311yescharacteristic
626C22×C43#52511yescharacteristic
627C22×C43#52911yescharacteristic
628C22×C43#53211yescharacteristic
629C22×C43#53511yescharacteristic
630C22×C43#53711yescharacteristic
631C22×C43#54011yescharacteristic
632C22×C43#54211yescharacteristic
633C22×C43D4211yescharacteristic
634C22×C43D4211yescharacteristic
635C22×C43D4211yescharacteristic
636C22×C43#54611yescharacteristic
637C22×C43#54611yescharacteristic
638C22×C43#54611yescharacteristic
639C22×C43#54611yescharacteristic
640C22×C43#54611yescharacteristic
641C22×C43#54711yescharacteristic
642C22×C43#54711yescharacteristic
643C22×C43#54711yescharacteristic
644C22×C43#54811yescharacteristic
645C22×C43#55011yescharacteristic
646C22×C43#55311yescharacteristic
647C22×C43#55311yescharacteristic
648C22×C43#55511yescharacteristic
649C2×D43—24no—
650C2×D43—24no—
651C2×D43—24no—
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—81no—
669Dic43—42no—
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×#386D4311yescharacteristic, complemented
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⋊#95—431no—
691C2×C43—44no—
692C2×C43—44no—
693C2×C43C2×#38611yescharacteristic
694C2×C43C4×#12111yescharacteristic
695C2×C43#232411yescharacteristic
696C2×C43D4×C22⋊C411yescharacteristic
697C2×C43#233911yescharacteristic
698C2×C43#236111yescharacteristic
699C2×C43#236311yescharacteristic
700C2×C43#240711yescharacteristic
701C2×C43#240811yescharacteristic
702C2×C43#242011yescharacteristic
703C2×C43#242211yescharacteristic
704C2×C43#242711yescharacteristic
705C2×C43#242811yescharacteristic
706C2×C43#253511yescharacteristic
707C2×C43#253711yescharacteristic
708D43—44no—
709C23×D4—431no—
710C23×D4—431no—
711C23×D4C2×D4311yescharacteristic
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⋊C4C2×D4311yescharacteristic
734C22×C22⋊C4C2×D4311yescharacteristic
735C22×C22⋊C4C2×D4311yescharacteristic
736C22×C42—431no—
737C22×C42—431no—
738#390—864no—
739#386—24no—
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×#95—431no—
752C2×#95—431no—
753C2×#95C2×D4311yescharacteristic
754C2×#95C2×D4311yescharacteristic
755C43#1397011yescharacteristic, complemented, Sylow
756C25—431no—
757C25C22×D4311yescharacteristic
758C25C22×D4311yescharacteristic
759C22×D4—22no—
760C22×D4—22no—
761C22×D4—22no—
762C22×D4—22no—
763C22×D4—41no—
764C22×D4—41no—
765C22×D4—434no—
766C22×D4—434no—
767C22×D4—434no—
768C22×D4—434no—
769C22×D4—862no—
770C22×D4—862no—
771C22×D4—862no—
772C22×D4—862no—
773C22×D4—862no—
774C22×D4—862no—
775C22×D4—862no—
776C22×D4—862no—
777C22×D4—1721no—
778C22×D4—1721no—
779C22×D4C4×D4314yescomplemented
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—434no—
789C23×C4—431no—
790C23×C4—431no—
791C23×C4—431no—
792C23×C4—431no—
793C23×C4—431no—
794C23×C4—431no—
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—1721no—
807C23×C4—1721no—
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—22no—
829C2×C22⋊C4—22no—
830C2×C22⋊C4—41no—
831C2×C22⋊C4—41no—
832C2×C22⋊C4—434no—
833C2×C22⋊C4—434no—
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—862no—
855C2×C22⋊C4—1721no—
856C2×C22⋊C4—1721no—
857C2×C22⋊C4—1721no—
858C2×C22⋊C4—1721no—
859C2×C22⋊C4C22⋊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—862no—
869#95—862no—
870#95—862no—
871#95—862no—
872#95—862no—
873#95—862no—
874#95—1721no—
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—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—21no—
896C24—21no—
897C24—21no—
898C24—21no—
899C24—21no—
900C24—21no—
901C24—21no—
902C24—432no—
903C24—432no—
904C24—432no—
905C24—861no—
906C24—861no—
907C24—861no—
908C24—861no—
909C24—861no—
910C24—861no—
911C24—861no—
912C24—861no—
913C24—861no—
914C24—861no—
915C24—861no—
916C24—861no—
917C24C2×C4×D4312yes—
918C24C2×C4×D4312yes—
919C24#1062189812yes—
920C24D4×D4312yes—
921C24D4×D4312yes—
922C24C2×C22⋊D4312yes—
923C24C23×D4311yescharacteristic
924C2×D4—28no—
925C2×D4—28no—
926C2×D4—44no—
927C2×D4—44no—
928C2×D4—44no—
929C2×D4—44no—
930C2×D4—44no—
931C2×D4—4316no—
932C2×D4—868no—
933C2×D4—868no—
934C2×D4—868no—
935C2×D4—868no—
936C2×D4—868no—
937C2×D4—868no—
938C2×D4—868no—
939C2×D4—868no—
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—44no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4—44no—
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—432no—
990C22×C4—432no—
991C22×C4—432no—
992C22×C4—432no—
993C22×C4—868no—
994C22×C4—868no—
995C22×C4—868no—
996C22×C4—868no—
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—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—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×C4C2×C4×D4312yes—
1045C22×C4D4×D4312yes—
1046C22×C4D4×D4312yes—
1047C22×C4#1062190012yes—
1048C22×C4C2×C22⋊D4312yes—
1049C22×C4C2×C22⋊D4312yes—
1050C4⋊C4—868no—
1051C4⋊C4—868no—
1052C4⋊C4—1724no—
1053C22⋊C4—28no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—868no—
1057C22⋊C4—868no—
1058C22⋊C4—868no—
1059C22⋊C4—868no—
1060C22⋊C4—868no—
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—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—22no—
1102C23—22no—
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—434no—
1136C23—862no—
1137C23—862no—
1138C23—862no—
1139C23—862no—
1140C23—862no—
1141C23—862no—
1142C23—862no—
1143C23—862no—
1144C23—862no—
1145C23—862no—
1146C23—862no—
1147C23—862no—
1148C23—862no—
1149C23—862no—
1150C23—862no—
1151C23—862no—
1152C23—862no—
1153C23—862no—
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—
1170C23C22⋊C4×D4314yes—
1171C23C4×C22⋊D4314yescomplemented
1172C23C22×C4×D4311yescharacteristic
1173C23C2×D4×D4311yescharacteristic
1174C23C2×D4×D4311yescharacteristic
1175C23C2×D4×D4311yescharacteristic
1176C23C2×D4×D4311yescharacteristic
1177C23C22×C22⋊D4311yescharacteristic
1178C23#41×D4311yescharacteristic
1179C23#41×D4311yescharacteristic
1180C23#41×D4311yescharacteristic
1181C23C2×#1062190011yescharacteristic
1182C23C2×#1062189811yescharacteristic
1183C23#1306337011yescharacteristic
1184C23#1306337011yescharacteristic
1185C23#1306337011yescharacteristic
1186C23#1306337211yescharacteristic
1187D4—416no—
1188D4—8632no—
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—416no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
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—434no—
1226C2×C4—434no—
1227C2×C4—434no—
1228C2×C4—434no—
1229C2×C4—434no—
1230C2×C4—434no—
1231C2×C4—434no—
1232C2×C4—862no—
1233C2×C4—862no—
1234C2×C4—862no—
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—17216no—
1248C2×C4—17216no—
1249C2×C4—1721no—
1250C2×C4—1721no—
1251C2×C4—1721no—
1252C2×C4—1721no—
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#1306329714yescomplemented
1277C22—24no—
1278C22—24no—
1279C22—24no—
1280C22—24no—
1281C22—24no—
1282C22—24no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
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—864no—
1308C22—864no—
1309C22—864no—
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
1325C22C2×C4×C22⋊D4311yescharacteristic
1326C22C4×#1062190011yescharacteristic
1327C22#1458337211yescharacteristic
1328C22#1458337811yescharacteristic
1329C22#120×D4311yescharacteristic
1330C22#121×D4311yescharacteristic
1331C22#121×D4311yescharacteristic
1332C22C2×#1306329711yescharacteristic
1333C22#123×D4311yescharacteristic
1334C22#1458340811yescharacteristic
1335C22#1458342911yescharacteristic
1336C22#1458344511yescharacteristic
1337C22#1458346411yescharacteristic
1338C22#1458347811yescharacteristic
1339C22#1458349911yescharacteristic
1340C22#1458351711yescharacteristic
1341C22D4×C22⋊D4311yescharacteristic
1342C22D4×C22⋊D4311yescharacteristic
1343C22D4×C22⋊D4311yescharacteristic
1344C22#1458353611yescharacteristic
1345C22#1458353611yescharacteristic
1346C22#1458353811yescharacteristic
1347C22#1458353911yescharacteristic
1348C22#1458353911yescharacteristic
1349C22#1458354711yescharacteristic
1350C22#1458354811yescharacteristic
1351C22#1458354911yescharacteristic
1352C22#1458355811yescharacteristic
1353C22#1458356711yescharacteristic
1354C22#1458359411yescharacteristic
1355C22#1458359811yescharacteristic
1356C22#1458361311yescharacteristic
1357C4—24no—
1358C4—42no—
1359C4—42no—
1360C4—42no—
1361C4—81no—
1362C4—438no—
1363C4—3441no—
1364C4—1722no—
1365C4—1722no—
1366C4—1722no—
1367C4—1722no—
1368C4—1722no—
1369C2—44no—
1370C2—44no—
1371C2—1724no—
1372C2#386×D4311yescharacteristic
1373C2C4×#1306329711yescharacteristic
1374C2#1913728511yescharacteristic
1375C2C22⋊C4×C22⋊D4311yescharacteristic
1376C2#1913742111yescharacteristic
1377C2#1913761211yescharacteristic
1378C2#1913763611yescharacteristic
1379C2#1913793711yescharacteristic
1380C2#1913794811yescharacteristic
1381C2#1913808411yescharacteristic
1382C2#1913810611yescharacteristic
1383C2#1913816911yescharacteristic
1384C2#1913818011yescharacteristic
1385C2#1913949511yescharacteristic
1386C2#1913950911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#386C2
socle, cosocleC24×C43C24
prime radicalC22×#13063297C2
hypercenterC2×#386D43
hypocenterC43#13970
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D43C2semidirect
3. C2×#14582799C2semidirect
4. C2×#14582775C2semidirect
5. C2×#14582757C2semidirect
6. C2×C22⋊C4×Dic43C2semidirect
7. #19132843C2semidirect
8. #19132842C2semidirect
9. #19132836C2semidirect
10. #19132834C2semidirect
11. Dic43⋊#95C2semidirect
12. Dic43⋊#95C2semidirect
13. #19132818C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C2×C43×#386C2semidirect
22. C2×#13063297C4semidirect
74. C22×C22⋊D43C2×C4semidirect
83. C23×Dic43C2×C4semidirect
107. C2×Dic43⋊C4C2×C4semidirect
108. C2×Dic43⋊C4D4semidirect
123. C2×C22⋊Dic43C2×C4semidirect
135. C2×(C2×D43)⋊C4C2×C4semidirect
141. C2×C4×Dic43D4semidirect
160. C22×D4×C43C2×C4semidirect
181. C2×C22⋊C4×C43D4semidirect
292. C2×C22⋊D43C22⋊C4semidirect
442. C23×C43C4×D4semidirect
529. C2×C4×C43#121semidirect
675. Dic43#386semidirect
680. C2×#386D43semidirect
755. C43#13970semidirect
779. C22×D4C4×D43semidirect
859. C2×C22⋊C4C22⋊D43semidirect
1171. C23C4×C22⋊D43semidirect
1276. C2×C4#13063297semidirect

Maximal subgroups

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

subgroupindex
C22×#130632972
C22×C4×C22⋊D432
C2×#145827992
C2×#145827752
C2×#145827572
C2×C22⋊C4×Dic432
#191328432
#191328422
#191328362
#191328342
Dic43⋊#952
#191328182
(C2×D43)⋊#952
C2×C43×#3862
#1397043