Finite Group Databasebeta

← #25020048

Subgroups — #25020048

Order 11008.

3166 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063298C211yesmaximal, characteristic
2C22×C4×C22⋊D43C211yesmaximal, characteristic, complemented
3C2×#14582778C211yesmaximal, characteristic, complemented
4C2×#14582777C211yesmaximal, characteristic, complemented
5C2×#14582777C211yesmaximal, characteristic, complemented
6C2×#14582775C211yesmaximal, characteristic, complemented
7C2×#95×D43C211yesmaximal, characteristic, complemented
8#19132846C211yesmaximal, characteristic, complemented
9#19132844C211yesmaximal, characteristic, complemented
10#19132839C211yesmaximal, characteristic, complemented
11#19132834C211yesmaximal, characteristic, complemented
12#19132831C211yesmaximal, characteristic, complemented
13#19132826C211yesmaximal, 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
21C23×C4×D43C2211yescharacteristic
22C2×#13063298—24no—
23C2×#13063298—24no—
24C2×#13063298C418yescomplemented
25C2×C4×C22⋊D43—24no—
26C2×C4×C22⋊D43—24no—
27C2×C4×C22⋊D43—24no—
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×C4×Dic43C2211yescharacteristic
40#14582778—24no—
41#14582777—24no—
42#14582777—24no—
43#14582775—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
54#95×D43—24no—
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—22no—
69C22×D172—22no—
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—22no—
103C22×C4×D43—22no—
104C22×C4×D43—41no—
105C22×C4×D43—41no—
106C22×C4×D43—41no—
107C22×C4×D43—41no—
108C22×C4×D43—41no—
109C22×C4×D43—41no—
110C22×C4×D43C2×C414yescomplemented
111C22×C4×D43D414yescomplemented
112#13063298—232no—
113C4×C22⋊D43—232no—
114C2×Dic43⋊C4—22no—
115C2×Dic43⋊C4—22no—
116C2×Dic43⋊C4—22no—
117C2×Dic43⋊C4—22no—
118C2×Dic43⋊C4—22no—
119C2×Dic43⋊C4C2×C414yescomplemented
120C2×C22⋊Dic43—22no—
121C2×C22⋊Dic43—22no—
122C2×C22⋊Dic43—22no—
123C2×C22⋊Dic43—22no—
124C2×C22⋊Dic43—22no—
125C2×C22⋊Dic43—41no—
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—22no—
141C2×(C2×D43)⋊C4—41no—
142C2×(C2×D43)⋊C4—41no—
143C2×(C2×D43)⋊C4—41no—
144C2×(C2×D43)⋊C4—41no—
145C2×(C2×D43)⋊C4C2×C414yescomplemented
146C2×(C2×D43)⋊C4D414yescomplemented
147C2×C4×Dic43—22no—
148C2×C4×Dic43—22no—
149C2×C4×Dic43—22no—
150C43⋊#95—22no—
151C43⋊#95—22no—
152C43⋊#95—22no—
153C43⋊#95—22no—
154C43⋊#95—22no—
155C43⋊#95—22no—
156C43⋊#95—22no—
157C43⋊#95—22no—
158C43⋊#95—41no—
159C43⋊#95D414yescomplemented
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×D43C22×C412yes—
223C23×D43C22×C412yes—
224C23×D43C2×D412yes—
225C23×D43C2×D412yes—
226C23×D43C2×D412yes—
227C23×D43C2×D412yes—
228C23×D43#4112yes—
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×Dic43—21no—
325C22×Dic43—21no—
326C22×Dic43C22×C412yes—
327C22×Dic43C22×C412yes—
328C22×Dic43C2×D412yes—
329C22×Dic43C2×D412yes—
330C22×Dic43C2×D412yes—
331C22×Dic43C2×D412yes—
332C22×Dic43C2×D412yes—
333C22×Dic43C2×D412yes—
334C22×Dic43#4112yes—
335C2×D172—28no—
336C2×D172—28no—
337C2×D172—28no—
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—28no—
347C2×C4×D43—44no—
348C2×C4×D43—44no—
349C2×C4×D43—44no—
350C2×C4×D43—44no—
351C2×C4×D43—44no—
352C2×C4×D43—44no—
353C2×C4×D43—44no—
354C2×C4×D43—44no—
355C2×C4×D43—44no—
356C2×C4×D43—44no—
357C2×C4×D43—44no—
358C2×C4×D43—44no—
359C2×C4×D43—44no—
360C2×C4×D43—44no—
361C2×C4×D43—44no—
362C2×C4×D43—44no—
363C22⋊C4×C43—28no—
364C22⋊C4×C43—44no—
365C22⋊Dic43—28no—
366C22⋊Dic43—44no—
367(C2×D43)⋊C4—28no—
368(C2×D43)⋊C4—28no—
369(C2×D43)⋊C4—44no—
370(C2×D43)⋊C4—44no—
371(C2×D43)⋊C4—44no—
372(C2×D43)⋊C4—44no—
373(C2×D43)⋊C4—44no—
374Dic43⋊C4—28no—
375Dic43⋊C4—28no—
376C4×Dic43—28no—
377C23×C43—22no—
378C23×C43—22no—
379C23×C43—22no—
380C23×C43—22no—
381C23×C43—22no—
382C23×C43—22no—
383C23×C43—22no—
384C23×C43—22no—
385C23×C43—22no—
386C23×C43—22no—
387C23×C43—22no—
388C23×C43—22no—
389C23×C43—22no—
390C23×C43—22no—
391C23×C43—22no—
392C23×C43—22no—
393C23×C43—22no—
394C23×C43—22no—
395C23×C43—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×C43C2×C22⋊C414yes—
412C23×C43C23×C411yescharacteristic
413C23×C43C22×D411yescharacteristic
414C23×C43C22×D411yescharacteristic
415C23×C43C22×D411yescharacteristic
416C23×C43C22×D411yescharacteristic
417C23×C43C22×D411yescharacteristic
418C23×C43C2×#4111yescharacteristic
419C23×C43C2×#4111yescharacteristic
420C23×C43C2×#4111yescharacteristic
421C23×C43C2×#4111yescharacteristic
422C23×C43C2×#4111yescharacteristic
423C23×C43H(5,𝔽2)11yescharacteristic
424C23×C43H(5,𝔽2)11yescharacteristic
425C23×C43H(5,𝔽2)11yescharacteristic
426C23×C432−1+411yescharacteristic
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—22no—
460C22×D43—22no—
461C22×D43—22no—
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×D43C2×C22⋊C414yes—
491C22×D43C4×D414yes—
492C22×D43C4×D414yes—
493C22×D43#12014yes—
494C22×D43#12114yes—
495C22×D43#12114yes—
496C22×D43#12314yes—
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—22no—
512C2×C4×C43—22no—
513C2×C4×C43—22no—
514C2×C4×C43—22no—
515C2×C4×C43—416no—
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—41no—
536C2×C4×C43—41no—
537C2×C4×C43—41no—
538C2×C4×C43—41no—
539C2×C4×C43#12114yescomplemented
540C22⋊D43—232no—
541C22⋊D43—416no—
542C2×Dic43—22no—
543C2×Dic43—22no—
544C2×Dic43—22no—
545C2×Dic43—22no—
546C2×Dic43—22no—
547C2×Dic43—22no—
548C2×Dic43—22no—
549C2×Dic43—22no—
550C2×Dic43—22no—
551C2×Dic43—22no—
552C2×Dic43—22no—
553C2×Dic43—22no—
554C2×Dic43—22no—
555C2×Dic43—22no—
556C2×Dic43—22no—
557C2×Dic43—22no—
558C2×Dic43—22no—
559C2×Dic43—22no—
560C2×Dic43—22no—
561C2×Dic43—22no—
562C2×Dic43—22no—
563C2×Dic43—41no—
564C2×Dic43—41no—
565C2×Dic43—41no—
566C2×Dic43—41no—
567C2×Dic43—41no—
568C2×Dic43—41no—
569C2×Dic43—41no—
570C2×Dic43—41no—
571C2×Dic43—41no—
572C2×Dic43—41no—
573C2×Dic43—41no—
574C2×Dic43—41no—
575C2×Dic43—41no—
576C2×Dic43—41no—
577C2×Dic43—41no—
578C2×Dic43—41no—
579C2×Dic43—41no—
580C2×Dic43—41no—
581C2×Dic43—41no—
582C2×Dic43C2×C22⋊C414yes—
583C2×Dic43C4×D414yescomplemented
584D172—416no—
585C4×D43—416no—
586C4×D43—416no—
587C4×D43—416no—
588#14023—431nomaximal, Sylow
589C22×C43—24no—
590C22×C43—24no—
591C22×C43—24no—
592C22×C43—42no—
593C22×C43—42no—
594C22×C43—42no—
595C22×C43—42no—
596C22×C43—42no—
597C22×C43—42no—
598C22×C43—42no—
599C22×C43—42no—
600C22×C43—42no—
601C22×C43—42no—
602C22×C43—42no—
603C22×C43—42no—
604C22×C43C22×C22⋊C411yescharacteristic
605C22×C43C2×C4×D411yescharacteristic
606C22×C43C2×C4×D411yescharacteristic
607C22×C43C2×C4×D411yescharacteristic
608C22×C43C4×#4111yescharacteristic
609C22×C43#51811yescharacteristic
610C22×C43#52011yescharacteristic
611C22×C43C2×#12011yescharacteristic
612C22×C43C2×#12111yescharacteristic
613C22×C43C2×#12111yescharacteristic
614C22×C43C2×#12111yescharacteristic
615C22×C43C2×#12311yescharacteristic
616C22×C43#52511yescharacteristic
617C22×C43#52911yescharacteristic
618C22×C43#53211yescharacteristic
619C22×C43#53411yescharacteristic
620C22×C43#53711yescharacteristic
621C22×C43#53811yescharacteristic
622C22×C43#53911yescharacteristic
623C22×C43D4211yescharacteristic
624C22×C43D4211yescharacteristic
625C22×C43D4211yescharacteristic
626C22×C43#54611yescharacteristic
627C22×C43#54611yescharacteristic
628C22×C43#54611yescharacteristic
629C22×C43#54611yescharacteristic
630C22×C43#54611yescharacteristic
631C22×C43#54611yescharacteristic
632C22×C43#54711yescharacteristic
633C22×C43#54711yescharacteristic
634C22×C43#54711yescharacteristic
635C22×C43#54811yescharacteristic
636C22×C43#55311yescharacteristic
637C22×C43#55311yescharacteristic
638C22×C43#55311yescharacteristic
639C2×D43—24no—
640C2×D43—24no—
641C2×D43—24no—
642C2×D43—24no—
643C2×D43—24no—
644C2×D43—24no—
645C2×D43—24no—
646C2×D43—24no—
647C2×D43—24no—
648C2×D43—24no—
649C2×D43—24no—
650C2×D43—24no—
651C2×D43—24no—
652C2×D43—24no—
653C2×D43—42no—
654C2×D43—42no—
655C2×D43—42no—
656C2×D43—42no—
657C2×D43—42no—
658C2×D43—42no—
659C2×D43—42no—
660C2×D43—81no—
661C2×D43—81no—
662C2×D43—81no—
663C2×D43—81no—
664C2×D43—81no—
665C2×D43—81no—
666C2×D43—81no—
667C2×D43—81no—
668C2×D43#38618yescomplemented
669C4×C43—24no—
670C4×C43—42no—
671C4×C43—42no—
672C4×C43—42no—
673C4×C43—42no—
674C4×C43—81no—
675Dic43—24no—
676Dic43—24no—
677Dic43—42no—
678Dic43—42no—
679Dic43—42no—
680Dic43—81no—
681C22×#121—431no—
682C22×C4×D4—431no—
683C2×#386—431no—
684C2×#386—431no—
685C2×#386—431no—
686C2×#386—431no—
687C22×#95—431no—
688#1441—431no—
689#1440—431no—
690#1439—431no—
691#1438—431no—
692#1437—431no—
693#1436—431no—
694C22⋊#95—431no—
695C22⋊#95D4311yescharacteristic, complemented
696C2×C43—44no—
697C2×C43C2×#38611yescharacteristic
698C2×C43C4×#12111yescharacteristic
699C2×C43#232511yescharacteristic
700C2×C43D4×C22⋊C411yescharacteristic
701C2×C43#233911yescharacteristic
702C2×C43#236111yescharacteristic
703C2×C43#236411yescharacteristic
704C2×C43#241011yescharacteristic
705C2×C43#241611yescharacteristic
706C2×C43#242411yescharacteristic
707C2×C43#242511yescharacteristic
708C2×C43#243011yescharacteristic
709C2×C43#244311yescharacteristic
710C2×C43#244411yescharacteristic
711C2×C43#254311yescharacteristic
712D43—28no—
713D43—82no—
714C23×D4—431no—
715C23×D4—431no—
716C23×D4—431no—
717C24×C4—431no—
718C24×C4—431no—
719C24×C4—431no—
720C24×C4C2×D4311yescharacteristic
721C2×#121—438no—
722C2×#121—864no—
723C2×#121—864no—
724C2×C4×D4—864no—
725C2×C4×D4—864no—
726C2×C4×D4—864no—
727C22×C4⋊C4—431no—
728C22×C4⋊C4—431no—
729C22×C22⋊C4—431no—
730C22×C22⋊C4—431no—
731C22×C22⋊C4—431no—
732C22×C22⋊C4—431no—
733C22×C22⋊C4—431no—
734C22×C22⋊C4—431no—
735C22×C22⋊C4—431no—
736C22×C22⋊C4—431no—
737C22×C22⋊C4—431no—
738C22×C22⋊C4C2×D4311yescharacteristic
739C22×C22⋊C4C2×D4311yescharacteristic
740C22×C42—431no—
741#386—864no—
742#386—864no—
743#386—864no—
744#386—864no—
745C2×#95—431no—
746C2×#95—431no—
747C2×#95—431no—
748C2×#95—431no—
749C2×#95—431no—
750C2×#95—431no—
751C2×#95—431no—
752C2×#95—431no—
753C2×#95—431no—
754C2×#95—431no—
755C2×#95—864no—
756C2×#95C2×D4311yescharacteristic
757C2×#95C2×D4311yescharacteristic
758C2×#95C2×D4311yescharacteristic
759C2×#95C2×D4311yescharacteristic
760C43#1402311yescharacteristic, complemented, Sylow
761C25—431no—
762C25—431no—
763C25C22×D4311yescharacteristic
764C22×D4—434no—
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—862no—
778C22×D4—862no—
779C22×D4—862no—
780C22×D4—862no—
781C22×D4—862no—
782C22×D4—862no—
783C22×D4—1721no—
784C22×D4—1721no—
785C23×C4—22no—
786C23×C4—22no—
787C23×C4—22no—
788C23×C4—22no—
789C23×C4—22no—
790C23×C4—41no—
791C23×C4—41no—
792C23×C4—431no—
793C23×C4—431no—
794C23×C4—431no—
795C23×C4—431no—
796C23×C4—431no—
797C23×C4—434no—
798C23×C4—434no—
799C23×C4—431no—
800C23×C4—862no—
801C23×C4—862no—
802C23×C4—862no—
803C23×C4—862no—
804C23×C4—862no—
805C23×C4—862no—
806C23×C4—862no—
807C23×C4—862no—
808C23×C4—862no—
809C23×C4—862no—
810C23×C4—862no—
811C23×C4—862no—
812C23×C4—862no—
813C23×C4—1721no—
814C23×C4—1721no—
815C23×C4—1721no—
816C23×C4—1721no—
817C23×C4—1721no—
818C23×C4—1721no—
819C23×C4C22×D4311yescharacteristic
820C23×C4C22×D4311yescharacteristic
821C23×C4C22×D4311yescharacteristic
822C23×C4C22×D4311yescharacteristic
823C23×C4C22×D4311yescharacteristic
824C23×C4C22×D4311yescharacteristic
825#121—8632no—
826C4×D4—8632no—
827C2×C4⋊C4—434no—
828C2×C4⋊C4—862no—
829C2×C4⋊C4—862no—
830C2×C4⋊C4—862no—
831C2×C4⋊C4—862no—
832C2×C4⋊C4—862no—
833C2×C22⋊C4—22no—
834C2×C22⋊C4—22no—
835C2×C22⋊C4—22no—
836C2×C22⋊C4—22no—
837C2×C22⋊C4—41no—
838C2×C22⋊C4—434no—
839C2×C22⋊C4—434no—
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—862no—
856C2×C22⋊C4—862no—
857C2×C22⋊C4—862no—
858C2×C22⋊C4—862no—
859C2×C22⋊C4—862no—
860C2×C22⋊C4—1721no—
861C2×C22⋊C4—1721no—
862C2×C22⋊C4—1721no—
863C2×C22⋊C4—1721no—
864C2×C22⋊C4—1721no—
865C2×C22⋊C4C4×D4314yescomplemented
866C2×C42—862no—
867C2×C42—862no—
868C2×C42—862no—
869#95—22no—
870#95—22no—
871#95—22no—
872#95—41no—
873#95—434no—
874#95—862no—
875#95—862no—
876#95—862no—
877#95—862no—
878#95—862no—
879#95—862no—
880#95—862no—
881#95—862no—
882#95—1721no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—432no—
896C24—432no—
897C24—432no—
898C24—432no—
899C24—432no—
900C24—432no—
901C24—432no—
902C24—432no—
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—
920C24—861no—
921C24—861no—
922C24—861no—
923C24—861no—
924C24—861no—
925C24C2×C4×D4312yes—
926C24D4×D4312yes—
927C24D4×D4312yes—
928C24C23×D4311yescharacteristic
929C2×D4—4316no—
930C2×D4—868no—
931C2×D4—868no—
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—868no—
941C2×D4—1724no—
942C2×D4—1724no—
943C2×D4—1724no—
944C2×D4—1724no—
945C2×D4—1724no—
946C2×D4—1724no—
947C2×D4—1724no—
948C2×D4—1724no—
949C2×D4—1724no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—28no—
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—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—432no—
993C22×C4—432no—
994C22×C4—432no—
995C22×C4—432no—
996C22×C4—432no—
997C22×C4—432no—
998C22×C4—432no—
999C22×C4—432no—
1000C22×C4—432no—
1001C22×C4—868no—
1002C22×C4—868no—
1003C22×C4—868no—
1004C22×C4—868no—
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—868no—
1032C22×C4—861no—
1033C22×C4—861no—
1034C22×C4—861no—
1035C22×C4—861no—
1036C22×C4—861no—
1037C22×C4—861no—
1038C22×C4—861no—
1039C22×C4—1724no—
1040C22×C4—1724no—
1041C22×C4—1724no—
1042C22×C4—1724no—
1043C22×C4—1724no—
1044C22×C4—1724no—
1045C22×C4—1724no—
1046C22×C4—1724no—
1047C22×C4—1724no—
1048C22×C4—1724no—
1049C22×C4—1724no—
1050C22×C4—1724no—
1051C22×C4—1724no—
1052C22×C4—1724no—
1053C22×C4—1724no—
1054C22×C4—1724no—
1055C22×C4C2×C4×D4312yes—
1056C22×C4C2×C4×D4312yes—
1057C22×C4#1062189812yes—
1058C22×C4#1062189812yes—
1059C22×C4D4×D4312yes—
1060C22×C4D4×D4312yes—
1061C22×C4D4×D4312yes—
1062C4⋊C4—868no—
1063C4⋊C4—868no—
1064C22⋊C4—28no—
1065C22⋊C4—44no—
1066C22⋊C4—868no—
1067C22⋊C4—868no—
1068C22⋊C4—868no—
1069C22⋊C4—1724no—
1070C22⋊C4—1724no—
1071C22⋊C4—1724no—
1072C22⋊C4—1724no—
1073C22⋊C4—1724no—
1074C22⋊C4—1724no—
1075C42—868no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—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—41no—
1110C23—434no—
1111C23—434no—
1112C23—434no—
1113C23—434no—
1114C23—434no—
1115C23—434no—
1116C23—434no—
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—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—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—
1171C23—1721no—
1172C23—1721no—
1173C23—1721no—
1174C23—1721no—
1175C23—1721no—
1176C23—1721no—
1177C23—1721no—
1178C23—1721no—
1179C23—1721no—
1180C23C22⋊C4×D4314yes—
1181C23C22×C4×D4311yescharacteristic
1182C23C2×D4×D4311yescharacteristic
1183C23C2×D4×D4311yescharacteristic
1184C23C2×D4×D4311yescharacteristic
1185C23C2×D4×D4311yescharacteristic
1186C23C2×D4×D4311yescharacteristic
1187C23#41×D4311yescharacteristic
1188C23#41×D4311yescharacteristic
1189C23#41×D4311yescharacteristic
1190C23C2×#1062189811yescharacteristic
1191C23C2×#1062189811yescharacteristic
1192C23#1306337011yescharacteristic
1193C23#1306337011yescharacteristic
1194C23#1306337111yescharacteristic
1195C23#1306337311yescharacteristic
1196D4—8632no—
1197D4—17216no—
1198D4—17216no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—416no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—434no—
1242C2×C4—434no—
1243C2×C4—862no—
1244C2×C4—862no—
1245C2×C4—862no—
1246C2×C4—862no—
1247C2×C4—862no—
1248C2×C4—862no—
1249C2×C4—862no—
1250C2×C4—862no—
1251C2×C4—862no—
1252C2×C4—862no—
1253C2×C4—862no—
1254C2×C4—862no—
1255C2×C4—862no—
1256C2×C4—862no—
1257C2×C4—862no—
1258C2×C4—862no—
1259C2×C4—862no—
1260C2×C4—862no—
1261C2×C4—862no—
1262C2×C4—862no—
1263C2×C4—862no—
1264C2×C4—17216no—
1265C2×C4—17216no—
1266C2×C4—17216no—
1267C2×C4—1721no—
1268C2×C4—1721no—
1269C2×C4—1721no—
1270C2×C4—1721no—
1271C2×C4—1721no—
1272C2×C4—1721no—
1273C2×C4—1721no—
1274C2×C4—1721no—
1275C2×C4—1721no—
1276C2×C4—1721no—
1277C2×C4—1721no—
1278C2×C4—1721no—
1279C2×C4—1721no—
1280C2×C4—1721no—
1281C2×C4—1721no—
1282C2×C4—1721no—
1283C2×C4—1721no—
1284C2×C4—1721no—
1285C2×C4—1721no—
1286C2×C4#1306329814yescomplemented
1287C22—24no—
1288C22—24no—
1289C22—24no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22—438no—
1303C22—864no—
1304C22—864no—
1305C22—864no—
1306C22—864no—
1307C22—864no—
1308C22—864no—
1309C22—864no—
1310C22—864no—
1311C22—864no—
1312C22—864no—
1313C22—864no—
1314C22—864no—
1315C22—864no—
1316C22—864no—
1317C22—3441no—
1318C22—3441no—
1319C22—3441no—
1320C22—3441no—
1321C22—3441no—
1322C22—3441no—
1323C22—3441no—
1324C22—3441no—
1325C22—1722no—
1326C22—1722no—
1327C22—1722no—
1328C22—1722no—
1329C22—1722no—
1330C22—1722no—
1331C22—1722no—
1332C22C2×C22⋊C4×D4311yescharacteristic
1333C22C4×D4×D4311yescharacteristic
1334C22C4×D4×D4311yescharacteristic
1335C22C4×D4×D4311yescharacteristic
1336C22C4×#1062189811yescharacteristic
1337C22#1458337111yescharacteristic
1338C22#1458338011yescharacteristic
1339C22#120×D4311yescharacteristic
1340C22#121×D4311yescharacteristic
1341C22#121×D4311yescharacteristic
1342C22C2×#1306329811yescharacteristic
1343C22#123×D4311yescharacteristic
1344C22#1458340811yescharacteristic
1345C22#1458342711yescharacteristic
1346C22#1458344611yescharacteristic
1347C22#1458345911yescharacteristic
1348C22#1458347911yescharacteristic
1349C22#1458348511yescharacteristic
1350C22#1458349511yescharacteristic
1351C22#1458353111yescharacteristic
1352C22#1458353111yescharacteristic
1353C22#1458353311yescharacteristic
1354C22#1458353811yescharacteristic
1355C22#1458353911yescharacteristic
1356C22#1458353911yescharacteristic
1357C22#1458353911yescharacteristic
1358C22#1458354111yescharacteristic
1359C22#1458354511yescharacteristic
1360C22#1458355011yescharacteristic
1361C22#1458355011yescharacteristic
1362C22#1458355111yescharacteristic
1363C22#1458355911yescharacteristic
1364C22#1458359311yescharacteristic
1365C22#1458359411yescharacteristic
1366C22#1458359911yescharacteristic
1367C4—24no—
1368C4—42no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—81no—
1373C4—864no—
1374C4—864no—
1375C4—3441no—
1376C4—1722no—
1377C4—1722no—
1378C4—1722no—
1379C2—44no—
1380C2—868no—
1381C2—3442no—
1382C2#386×D4311yescharacteristic
1383C2C4×#1306329811yescharacteristic
1384C2#1913729211yescharacteristic
1385C2#1913741311yescharacteristic
1386C2#1913742211yescharacteristic
1387C2#1913761411yescharacteristic
1388C2#1913764611yescharacteristic
1389C2#1913797111yescharacteristic
1390C2#1913803711yescharacteristic
1391C2#1913813011yescharacteristic
1392C2#1913814311yescharacteristic
1393C2#1913820411yescharacteristic
1394C2#1913832911yescharacteristic
1395C2#1913834411yescharacteristic
1396C2#1913955411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C22⋊#95C2
socle, cosocleC24×C43C24
prime radicalC22×#13063298C2
hypercenterC22⋊#95D43
hypocenterC43#14023
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×#14582778C2semidirect
4. C2×#14582777C2semidirect
5. C2×#14582777C2semidirect
6. C2×#14582775C2semidirect
7. C2×#95×D43C2semidirect
8. #19132846C2semidirect
9. #19132844C2semidirect
10. #19132839C2semidirect
11. #19132834C2semidirect
12. #19132831C2semidirect
13. #19132826C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×C22⋊#95C2semidirect
24. C2×#13063298C4semidirect
70. C22×D172C2×C4semidirect
82. C22×C22⋊D43C2×C4semidirect
110. C22×C4×D43C2×C4semidirect
111. C22×C4×D43D4semidirect
119. C2×Dic43⋊C4C2×C4semidirect
145. C2×(C2×D43)⋊C4C2×C4semidirect
146. C2×(C2×D43)⋊C4D4semidirect
159. C43⋊#95D4semidirect
179. C2×C22⋊C4×C43C2×C4semidirect
292. C2×C22⋊D43C22⋊C4semidirect
539. C2×C4×C43#121semidirect
583. C2×Dic43C4×D4semidirect
668. C2×D43#386semidirect
695. C22⋊#95D43semidirect
760. C43#14023semidirect
865. C2×C22⋊C4C4×D43semidirect
1286. 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×#145827782
C2×#145827772
C2×#145827752
C2×#95×D432
#191328462
#191328442
#191328392
#191328342
#191328312
#191328262
(C2×D43)⋊#952
C43×C22⋊#952
#1402343