Finite Group Databasebeta

← #25019558

Subgroups — #25019558

Order 11008.

2070 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582777C211yesmaximal, characteristic
2C2×#14582777C211yesmaximal, characteristic
3C2×#14582761C211yesmaximal, characteristic, complemented
4C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
5C2×#14582746C211yesmaximal, characteristic, complemented
6#19132855C211yesmaximal, characteristic, complemented
7#19132841C211yesmaximal, characteristic, complemented
8#19132841C211yesmaximal, characteristic, complemented
9#19132835C211yesmaximal, characteristic
10#19132833C211yesmaximal, characteristic, complemented
11#19132831C211yesmaximal, characteristic, complemented
12#19132829C211yesmaximal, characteristic, complemented
13#19132819C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C43×#1434C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C22×(C2×D43)⋊C4C2211yescharacteristic
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C22×(C2×D43)⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊C4C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×(C2×D43)⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×C4×Dic43C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32#14582777—24no—
33#14582777C418yescomplemented
34#14582761—24no—
35C4×(C2×D43)⋊C4—24no—
36#14582746—24no—
37C2×C43⋊#95C2211yescharacteristic
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
49C22×C42×C43C2211yescharacteristic
50C2×#95×C43C2211yescharacteristic
51C2×#95×C43C2211yescharacteristic
52C2×#95×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C24×D43C2311yescharacteristic
57C24×D43C2311yescharacteristic
58C22×D172—22no—
59C22×D172—22no—
60C22×D172—22no—
61C22×D172—22no—
62C22×D172—41no—
63C22×D172—41no—
64C22×D172C2×C414yes—
65C23×Dic43C2311yescharacteristic
66C23×Dic43C2311yescharacteristic
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C22×C4×D43—22no—
72C22×C4×D43—22no—
73C22×C4×D43—22no—
74C22×C4×D43—22no—
75C22×C4×D43—22no—
76C22×C4×D43—22no—
77C22×C4×D43—22no—
78C22×C4×D43—22no—
79C22×C4×D43—22no—
80C22×C4×D43—41no—
81C22×C4×D43—41no—
82C22×C4×D43—41no—
83C22×C4×D43—41no—
84C22×C4×D43C2×C414yescomplemented
85C2×C4⋊Dic43—22no—
86C2×C4⋊Dic43—41no—
87C2×C4⋊Dic43—41no—
88C2×(C2×D43)⋊C4—22no—
89C2×(C2×D43)⋊C4—22no—
90C2×(C2×D43)⋊C4—22no—
91C2×(C2×D43)⋊C4—22no—
92C2×(C2×D43)⋊C4—22no—
93C2×(C2×D43)⋊C4—22no—
94C2×(C2×D43)⋊C4—22no—
95C2×(C2×D43)⋊C4—22no—
96C2×(C2×D43)⋊C4—22no—
97C2×(C2×D43)⋊C4—22no—
98C2×(C2×D43)⋊C4—22no—
99C2×(C2×D43)⋊C4—22no—
100C2×(C2×D43)⋊C4—22no—
101C2×(C2×D43)⋊C4—22no—
102C2×(C2×D43)⋊C4—22no—
103C2×(C2×D43)⋊C4—22no—
104C2×(C2×D43)⋊C4—22no—
105C2×(C2×D43)⋊C4—22no—
106C2×(C2×D43)⋊C4—41no—
107C2×(C2×D43)⋊C4—41no—
108C2×(C2×D43)⋊C4—41no—
109C2×(C2×D43)⋊C4—41no—
110C2×(C2×D43)⋊C4—41no—
111C2×(C2×D43)⋊C4—41no—
112C2×(C2×D43)⋊C4—41no—
113C2×(C2×D43)⋊C4—41no—
114C2×(C2×D43)⋊C4C2×C414yes—
115C2×(C2×D43)⋊C4C2×C414yes—
116C2×(C2×D43)⋊C4C2×C414yescomplemented
117C2×(C2×D43)⋊C4D414yes—
118C2×C4×Dic43—22no—
119C2×C4×Dic43—22no—
120C2×C4×Dic43—22no—
121C2×C4×Dic43—22no—
122C2×C4×Dic43—41no—
123C2×C4×Dic43—41no—
124C43⋊#95—22no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C43⋊#95—22no—
130C43⋊#95—22no—
131C43⋊#95—22no—
132C43⋊#95—22no—
133C43⋊#95—41no—
134C43⋊#95—41no—
135C43⋊#95C2×C414yescomplemented
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C2×C42×C43—22no—
144C2×C42×C43—22no—
145C2×C42×C43—41no—
146#95×C43—22no—
147#95×C43—41no—
148#95×C43—41no—
149#95×C43—41no—
150#95×C43C2×C414yescomplemented
151#95×C43D414yescomplemented
152C24×C43C2411yescharacteristic
153C23×D43—21no—
154C23×D43—21no—
155C23×D43—21no—
156C23×D43—21no—
157C23×D43—21no—
158C23×D43—21no—
159C23×D43—21no—
160C23×D43—21no—
161C23×D43—21no—
162C23×D43—21no—
163C23×D43—21no—
164C23×D43—21no—
165C23×D43—21no—
166C23×D43—21no—
167C23×D43—21no—
168C23×D43—21no—
169C23×D43—21no—
170C23×D43—21no—
171C23×D43—21no—
172C23×D43—21no—
173C23×D43—21no—
174C23×D43—21no—
175C23×D43—21no—
176C23×D43—21no—
177C23×D43C22×C412yes—
178C23×D43C22×C412yes—
179C23×D43C2×D412yes—
180C23×D43#4112yes—
181C23×D43#4112yes—
182C23×D43#4112yes—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
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×C43C22×C412yes—
224C22×C4×C43C22×C412yes—
225C22×C4×C43C22×C412yes—
226C22×C4×C43C2×D412yes—
227C22×C4×C43C2×D412yes—
228C22×C4×C43C2×D412yes—
229C22×C4×C43C2×D412yes—
230C22×C4×C43#4112yes—
231C22×C4×C43#4112yes—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—21no—
244C22×Dic43—21no—
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—21no—
251C22×Dic43—21no—
252C22×Dic43—21no—
253C22×Dic43—21no—
254C22×Dic43—21no—
255C22×Dic43—21no—
256C22×Dic43—21no—
257C22×Dic43—21no—
258C22×Dic43—21no—
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×Dic43C22×C412yes—
269C22×Dic43C22×C412yes—
270C22×Dic43C2×D412yes—
271C22×Dic43#4112yes—
272C22×Dic43#4112yes—
273C22×Dic43#4112yes—
274C2×D172—28no—
275C2×D172—28no—
276C2×D172—44no—
277C2×D172—44no—
278C2×D172—44no—
279C2×D172—44no—
280C2×D172—44no—
281C2×C4×D43—28no—
282C2×C4×D43—28no—
283C2×C4×D43—28no—
284C2×C4×D43—44no—
285C2×C4×D43—44no—
286C2×C4×D43—44no—
287C2×C4×D43—44no—
288C2×C4×D43—44no—
289C2×C4×D43—44no—
290C2×C4×D43—44no—
291C2×C4×D43—44no—
292C2×C4×D43—44no—
293C2×C4×D43—44no—
294C2×C4×D43—44no—
295C42×C43—44no—
296(C2×D43)⋊C4—28no—
297(C2×D43)⋊C4—28no—
298(C2×D43)⋊C4—28no—
299(C2×D43)⋊C4—28no—
300(C2×D43)⋊C4—44no—
301(C2×D43)⋊C4—44no—
302(C2×D43)⋊C4—44no—
303(C2×D43)⋊C4—44no—
304(C2×D43)⋊C4—44no—
305(C2×D43)⋊C4—44no—
306C4⋊Dic43—44no—
307C4×Dic43—44no—
308C4×Dic43—44no—
309C23×C43C23×C411yescharacteristic
310C23×C43C22×D411yescharacteristic
311C23×C43C22×D411yescharacteristic
312C23×C43C2×#4111yescharacteristic
313C23×C43C2×#4111yescharacteristic
314C23×C43C2×#4111yescharacteristic
315C23×C43C2×#4111yescharacteristic
316C23×C43C2×#4111yescharacteristic
317C23×C43C2×#4111yescharacteristic
318C23×C43C2×#4111yescharacteristic
319C23×C43C2×#4111yescharacteristic
320C23×C43H(5,𝔽2)11yescharacteristic
321C23×C43H(5,𝔽2)11yescharacteristic
322C23×C43H(5,𝔽2)11yescharacteristic
323C23×C43H(5,𝔽2)11yescharacteristic
324C22×D43—22no—
325C22×D43—22no—
326C22×D43—22no—
327C22×D43—22no—
328C22×D43—22no—
329C22×D43—22no—
330C22×D43—22no—
331C22×D43—22no—
332C22×D43—22no—
333C22×D43—22no—
334C22×D43—22no—
335C22×D43—22no—
336C22×D43—22no—
337C22×D43—22no—
338C22×D43—22no—
339C22×D43—22no—
340C22×D43—22no—
341C22×D43—22no—
342C22×D43—22no—
343C22×D43—22no—
344C22×D43—22no—
345C22×D43—22no—
346C22×D43—22no—
347C22×D43—22no—
348C22×D43—22no—
349C22×D43—22no—
350C22×D43—22no—
351C22×D43—22no—
352C22×D43—22no—
353C22×D43—22no—
354C22×D43—22no—
355C22×D43—22no—
356C22×D43—22no—
357C22×D43—22no—
358C22×D43—22no—
359C22×D43—22no—
360C22×D43—41no—
361C22×D43—41no—
362C22×D43—41no—
363C22×D43—41no—
364C22×D43—41no—
365C22×D43—41no—
366C22×D43—41no—
367C22×D43—41no—
368C22×D43—41no—
369C22×D43—41no—
370C22×D43—41no—
371C22×D43—41no—
372C22×D43—41no—
373C22×D43—41no—
374C22×D43—41no—
375C22×D43—41no—
376C22×D43—41no—
377C22×D43—41no—
378C22×D43—41no—
379C22×D43—41no—
380C22×D43—41no—
381C22×D43—41no—
382C22×D43—41no—
383C22×D43—41no—
384C22×D43—41no—
385C22×D43—41no—
386C22×D43—41no—
387C22×D43—41no—
388C22×D43—41no—
389C22×D43—41no—
390C22×D43—41no—
391C22×D43—41no—
392C22×D43#11714yes—
393C22×D43C4×D414yes—
394C2×C4×C43—22no—
395C2×C4×C43—22no—
396C2×C4×C43—22no—
397C2×C4×C43—22no—
398C2×C4×C43—22no—
399C2×C4×C43—22no—
400C2×C4×C43—22no—
401C2×C4×C43—22no—
402C2×C4×C43—22no—
403C2×C4×C43—22no—
404C2×C4×C43—22no—
405C2×C4×C43—22no—
406C2×C4×C43—22no—
407C2×C4×C43—22no—
408C2×C4×C43—22no—
409C2×C4×C43—22no—
410C2×C4×C43—22no—
411C2×C4×C43—22no—
412C2×C4×C43—22no—
413C2×C4×C43—22no—
414C2×C4×C43—22no—
415C2×C4×C43—22no—
416C2×C4×C43—22no—
417C2×C4×C43—22no—
418C2×C4×C43—41no—
419C2×C4×C43—41no—
420C2×C4×C43—41no—
421C2×C4×C43—41no—
422C2×C4×C43—41no—
423C2×C4×C43—41no—
424C2×C4×C43—41no—
425C2×C4×C43—41no—
426C2×C4×C43—41no—
427C2×C4×C43—41no—
428C2×C4×C43—41no—
429C2×C4×C43—41no—
430C2×C4×C43—41no—
431C2×C4×C43—41no—
432C2×C4×C43—41no—
433C2×C4×C43—41no—
434C2×C4×C43—41no—
435C2×C4×C43—41no—
436C2×C4×C43—41no—
437C2×C4×C43—41no—
438C2×C4×C43—41no—
439C2×C4×C43—41no—
440C2×C4×C43—41no—
441C2×C4×C43—41no—
442C2×C4×C43C4×D414yes—
443C2×Dic43—22no—
444C2×Dic43—22no—
445C2×Dic43—22no—
446C2×Dic43—22no—
447C2×Dic43—22no—
448C2×Dic43—22no—
449C2×Dic43—22no—
450C2×Dic43—22no—
451C2×Dic43—22no—
452C2×Dic43—22no—
453C2×Dic43—22no—
454C2×Dic43—22no—
455C2×Dic43—22no—
456C2×Dic43—22no—
457C2×Dic43—22no—
458C2×Dic43—41no—
459C2×Dic43—41no—
460C2×Dic43—41no—
461C2×Dic43—41no—
462C2×Dic43—41no—
463C2×Dic43—41no—
464C2×Dic43—41no—
465C2×Dic43—41no—
466C2×Dic43—41no—
467C2×Dic43—41no—
468C2×Dic43—41no—
469C2×Dic43—41no—
470C2×Dic43—41no—
471C2×Dic43—41no—
472C2×Dic43—41no—
473C2×Dic43—41no—
474C2×Dic43—41no—
475C2×Dic43—41no—
476C2×Dic43—41no—
477C2×Dic43—41no—
478C2×Dic43—41no—
479C2×Dic43—41no—
480C2×Dic43—41no—
481C2×Dic43—41no—
482C2×Dic43—41no—
483C2×Dic43—41no—
484C2×Dic43#12314yes—
485D172—416no—
486C4×D43—416no—
487C4×D43—416no—
488#13984—431nomaximal, Sylow
489C22×C43C2×#11711yescharacteristic
490C22×C43C2×C4×D411yescharacteristic
491C22×C43C2×C4×D411yescharacteristic
492C22×C43C4×#4111yescharacteristic
493C22×C43C4×#4111yescharacteristic
494C22×C43#51811yescharacteristic
495C22×C43#51811yescharacteristic
496C22×C43C2×#12311yescharacteristic
497C22×C43#52511yescharacteristic
498C22×C43#52511yescharacteristic
499C22×C43#52511yescharacteristic
500C22×C43#52911yescharacteristic
501C22×C43#52911yescharacteristic
502C22×C43#52911yescharacteristic
503C22×C43#52911yescharacteristic
504C22×C43#53811yescharacteristic
505C22×C43#53811yescharacteristic
506C22×C43#54011yescharacteristic
507C22×C43#54011yescharacteristic
508C22×C43D4211yescharacteristic
509C22×C43#54611yescharacteristic
510C22×C43#54611yescharacteristic
511C22×C43#54611yescharacteristic
512C22×C43#54611yescharacteristic
513C22×C43#54611yescharacteristic
514C22×C43#55011yescharacteristic
515C22×C43#55111yescharacteristic
516C22×C43#55111yescharacteristic
517C22×C43#55111yescharacteristic
518C22×C43#55111yescharacteristic
519C22×C43#55111yescharacteristic
520C22×C43#55311yescharacteristic
521C22×C43#55311yescharacteristic
522C22×C43#55311yescharacteristic
523C22×C43#55511yescharacteristic
524C2×D43—24no—
525C2×D43—24no—
526C2×D43—24no—
527C2×D43—24no—
528C2×D43—24no—
529C2×D43—24no—
530C2×D43—42no—
531C2×D43—42no—
532C2×D43—42no—
533C2×D43—42no—
534C2×D43—42no—
535C2×D43—42no—
536C2×D43—42no—
537C2×D43—42no—
538C2×D43—42no—
539C2×D43—42no—
540C2×D43—42no—
541C2×D43—42no—
542C2×D43—42no—
543C2×D43—42no—
544C2×D43—42no—
545C2×D43—42no—
546C2×D43—42no—
547C2×D43—42no—
548C2×D43—42no—
549C2×D43—42no—
550C2×D43—42no—
551C2×D43—42no—
552C2×D43—42no—
553C2×D43—42no—
554C4×C43—24no—
555C4×C43—42no—
556C4×C43—42no—
557C4×C43—42no—
558C4×C43—42no—
559C4×C43—42no—
560C4×C43—42no—
561Dic43—24no—
562Dic43—42no—
563Dic43—42no—
564Dic43—42no—
565Dic43—81no—
566Dic43—81no—
567C2×#386—431no—
568C2×#386—431no—
569C2×#381—431no—
570C2×C4×C22⋊C4—431no—
571C2×C4×C22⋊C4—431no—
572#1443—431no—
573#1439—431no—
574#1439—431no—
575#1438—431no—
576#1437—431no—
577#1437—431no—
578#1436—431no—
579#1434—431no—
580#1434D4311yescharacteristic, complemented
581C22⋊#95—431no—
582C2×C43#229011yescharacteristic
583C2×C43C4×#12311yescharacteristic
584C2×C43#233311yescharacteristic
585C2×C43#234211yescharacteristic
586C2×C43#235311yescharacteristic
587C2×C43#235811yescharacteristic
588C2×C43#236311yescharacteristic
589C2×C43#241811yescharacteristic
590C2×C43#242011yescharacteristic
591C2×C43#245611yescharacteristic
592C2×C43#245711yescharacteristic
593C2×C43#245711yescharacteristic
594C2×C43#247111yescharacteristic
595C2×C43#257211yescharacteristic
596C2×C43#257611yescharacteristic
597D43—44no—
598D43—44no—
599C23×D4—431no—
600C24×C4—431no—
601C24×C4—431no—
602C22×C4⋊C4—431no—
603C22×C22⋊C4—431no—
604C22×C22⋊C4—431no—
605C22×C22⋊C4—431no—
606C22×C22⋊C4—431no—
607C22×C22⋊C4—431no—
608C22×C22⋊C4—431no—
609C22×C22⋊C4—431no—
610C22×C22⋊C4—431no—
611C22×C22⋊C4—431no—
612C22×C22⋊C4—431no—
613C22×C42—431no—
614C22×C42—431no—
615C22×C42C2×D4311yescharacteristic
616#386—438no—
617#386—864no—
618#381—864no—
619C4×C22⋊C4—864no—
620C4×C22⋊C4—864no—
621C2×#95—431no—
622C2×#95—431no—
623C2×#95—431no—
624C2×#95—431no—
625C2×#95—431no—
626C2×#95—431no—
627C2×#95—431no—
628C2×#95—431no—
629C2×#95—431no—
630C2×#95—431no—
631C2×#95—431no—
632C2×#95—431no—
633C2×#95C2×D4311yescharacteristic
634C2×#95C2×D4311yescharacteristic
635C2×#95C2×D4311yescharacteristic
636C2×#95C2×D4311yescharacteristic
637C2×#95C2×D4311yescharacteristic
638C2×#95C2×D4311yescharacteristic
639C43#1398411yescharacteristic, complemented, Sylow
640C25—431no—
641C25—431no—
642C22×D4—434no—
643C22×D4—862no—
644C22×D4—862no—
645C22×D4—862no—
646C22×D4—862no—
647C22×D4—1721no—
648C22×D4—1721no—
649C23×C4—431no—
650C23×C4—431no—
651C23×C4—431no—
652C23×C4—431no—
653C23×C4—434no—
654C23×C4—431no—
655C23×C4—431no—
656C23×C4—862no—
657C23×C4—862no—
658C23×C4—862no—
659C23×C4—862no—
660C23×C4—862no—
661C23×C4—862no—
662C23×C4—862no—
663C23×C4—862no—
664C23×C4—862no—
665C23×C4—1721no—
666C23×C4—1721no—
667C23×C4—1721no—
668C23×C4—1721no—
669C23×C4C22×D4311yescharacteristic
670C23×C4C22×D4311yescharacteristic
671C23×C4C22×D4311yescharacteristic
672C23×C4C22×D4311yescharacteristic
673C23×C4C22×D4311yescharacteristic
674C23×C4C22×D4311yescharacteristic
675C23×C4C22×D4311yescharacteristic
676C2×C4⋊C4—862no—
677C2×C4⋊C4—1721no—
678C2×C4⋊C4—1721no—
679C2×C22⋊C4—434no—
680C2×C22⋊C4—434no—
681C2×C22⋊C4—434no—
682C2×C22⋊C4—434no—
683C2×C22⋊C4—862no—
684C2×C22⋊C4—862no—
685C2×C22⋊C4—862no—
686C2×C22⋊C4—862no—
687C2×C22⋊C4—862no—
688C2×C22⋊C4—862no—
689C2×C22⋊C4—862no—
690C2×C22⋊C4—862no—
691C2×C22⋊C4—862no—
692C2×C22⋊C4—862no—
693C2×C22⋊C4—862no—
694C2×C22⋊C4—862no—
695C2×C22⋊C4—862no—
696C2×C22⋊C4—862no—
697C2×C22⋊C4—862no—
698C2×C22⋊C4—862no—
699C2×C22⋊C4—862no—
700C2×C22⋊C4—862no—
701C2×C22⋊C4—1721no—
702C2×C22⋊C4—1721no—
703C2×C22⋊C4—1721no—
704C2×C22⋊C4—1721no—
705C2×C22⋊C4—1721no—
706C2×C22⋊C4—1721no—
707C2×C22⋊C4—1721no—
708C2×C22⋊C4—1721no—
709C2×C42—22no—
710C2×C42—22no—
711C2×C42—41no—
712C2×C42—862no—
713C2×C42—862no—
714C2×C42—862no—
715C2×C42—862no—
716C2×C42—1721no—
717C2×C42—1721no—
718#95—22no—
719#95—41no—
720#95—41no—
721#95—41no—
722#95—434no—
723#95—862no—
724#95—862no—
725#95—862no—
726#95—862no—
727#95—862no—
728#95—862no—
729#95—862no—
730#95—862no—
731#95—862no—
732#95—1721no—
733#95—1721no—
734#95C4×D4314yescomplemented
735#95D17214yescomplemented
736C24—432no—
737C24—432no—
738C24—432no—
739C24—432no—
740C24—432no—
741C24—432no—
742C24—861no—
743C24—861no—
744C24—861no—
745C24—861no—
746C24—861no—
747C24—861no—
748C24—861no—
749C24—861no—
750C24—861no—
751C24—861no—
752C24—861no—
753C24—861no—
754C24—861no—
755C24—861no—
756C24—861no—
757C24—861no—
758C24—861no—
759C24—861no—
760C24—861no—
761C24—861no—
762C24—861no—
763C24—861no—
764C24—861no—
765C24—861no—
766C24C23×D4311yescharacteristic
767C2×D4—868no—
768C2×D4—868no—
769C2×D4—1724no—
770C2×D4—1724no—
771C2×D4—1724no—
772C2×D4—1724no—
773C2×D4—1724no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—432no—
815C22×C4—432no—
816C22×C4—432no—
817C22×C4—432no—
818C22×C4—432no—
819C22×C4—432no—
820C22×C4—868no—
821C22×C4—868no—
822C22×C4—861no—
823C22×C4—861no—
824C22×C4—861no—
825C22×C4—861no—
826C22×C4—861no—
827C22×C4—861no—
828C22×C4—861no—
829C22×C4—861no—
830C22×C4—861no—
831C22×C4—861no—
832C22×C4—861no—
833C22×C4—861no—
834C22×C4—861no—
835C22×C4—861no—
836C22×C4—861no—
837C22×C4—861no—
838C22×C4—861no—
839C22×C4—861no—
840C22×C4—861no—
841C22×C4—861no—
842C22×C4—861no—
843C22×C4—861no—
844C22×C4—868no—
845C22×C4—861no—
846C22×C4—861no—
847C22×C4—861no—
848C22×C4—861no—
849C22×C4—861no—
850C22×C4—861no—
851C22×C4—861no—
852C22×C4—861no—
853C22×C4—861no—
854C22×C4—861no—
855C22×C4—861no—
856C22×C4—861no—
857C22×C4—861no—
858C22×C4—861no—
859C22×C4—1724no—
860C22×C4—1724no—
861C22×C4—1724no—
862C22×C4—1724no—
863C22×C4—1724no—
864C22×C4—1724no—
865C22×C4—1724no—
866C22×C4—1724no—
867C22×C4—1724no—
868C22×C4—1724no—
869C22×C4—1724no—
870C22×C4C2×C4×D4312yes—
871C22×C4C2×C4×D4312yes—
872C22×C4C2×C4×D4312yes—
873C22×C4C2×D17212yes—
874C22×C4C2×D17212yes—
875C22×C4C2×D17212yes—
876C22×C4#1062189812yes—
877C22×C4D4×D4312yes—
878C22×C4#1062190212yes—
879C4⋊C4—1724no—
880C22⋊C4—868no—
881C22⋊C4—868no—
882C22⋊C4—868no—
883C22⋊C4—868no—
884C22⋊C4—1724no—
885C22⋊C4—1724no—
886C22⋊C4—1724no—
887C22⋊C4—1724no—
888C22⋊C4—1724no—
889C22⋊C4—1724no—
890C42—44no—
891C42—1724no—
892C42—1724no—
893C23—434no—
894C23—434no—
895C23—862no—
896C23—862no—
897C23—862no—
898C23—862no—
899C23—862no—
900C23—862no—
901C23—862no—
902C23—862no—
903C23—862no—
904C23—862no—
905C23—862no—
906C23—862no—
907C23—862no—
908C23—862no—
909C23—862no—
910C23—862no—
911C23—862no—
912C23—862no—
913C23—862no—
914C23—862no—
915C23—862no—
916C23—862no—
917C23—862no—
918C23—862no—
919C23—862no—
920C23—862no—
921C23—862no—
922C23—862no—
923C23—862no—
924C23—862no—
925C23—862no—
926C23—862no—
927C23—862no—
928C23—862no—
929C23—862no—
930C23—862no—
931C23—1721no—
932C23—1721no—
933C23—1721no—
934C23—1721no—
935C23—1721no—
936C23—1721no—
937C23—1721no—
938C23—1721no—
939C23—1721no—
940C23—1721no—
941C23—1721no—
942C23—1721no—
943C23—1721no—
944C23—1721no—
945C23—1721no—
946C23—1721no—
947C23—1721no—
948C23—1721no—
949C23—1721no—
950C23—1721no—
951C23—1721no—
952C23—1721no—
953C23—1721no—
954C23—1721no—
955C23—1721no—
956C23—1721no—
957C23—1721no—
958C23—1721no—
959C23—1721no—
960C23—1721no—
961C23—1721no—
962C23—1721no—
963C23C22×C4×D4311yescharacteristic
964C23C2×D4×D4311yescharacteristic
965C23C22×D17211yescharacteristic
966C23#41×D4311yescharacteristic
967C23#41×D4311yescharacteristic
968C23#41×D4311yescharacteristic
969C23#41×D4311yescharacteristic
970C23#41×D4311yescharacteristic
971C23#41×D4311yescharacteristic
972C23C2×#1062189811yescharacteristic
973C23C2×#1062190211yescharacteristic
974C23#1306337011yescharacteristic
975C23#1306337011yescharacteristic
976C23#1306337111yescharacteristic
977C23#1306337111yescharacteristic
978D4—17216no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—434no—
1028C2×C4—862no—
1029C2×C4—862no—
1030C2×C4—862no—
1031C2×C4—862no—
1032C2×C4—862no—
1033C2×C4—862no—
1034C2×C4—862no—
1035C2×C4—862no—
1036C2×C4—862no—
1037C2×C4—862no—
1038C2×C4—862no—
1039C2×C4—862no—
1040C2×C4—862no—
1041C2×C4—862no—
1042C2×C4—862no—
1043C2×C4—17216no—
1044C2×C4—17216no—
1045C2×C4—1721no—
1046C2×C4—1721no—
1047C2×C4—1721no—
1048C2×C4—1721no—
1049C2×C4—1721no—
1050C2×C4—1721no—
1051C2×C4—1721no—
1052C2×C4—1721no—
1053C2×C4—1721no—
1054C2×C4—1721no—
1055C2×C4—1721no—
1056C2×C4—1721no—
1057C2×C4—1721no—
1058C2×C4—1721no—
1059C2×C4—1721no—
1060C2×C4—1721no—
1061C2×C4—1721no—
1062C2×C4—1721no—
1063C2×C4—1721no—
1064C2×C4—1721no—
1065C2×C4—1721no—
1066C2×C4—1721no—
1067C2×C4—1721no—
1068C2×C4—1721no—
1069C2×C4—1721no—
1070C2×C4—1721no—
1071C2×C4C4×D17214yes—
1072C22—864no—
1073C22—864no—
1074C22—864no—
1075C22—864no—
1076C22—864no—
1077C22—864no—
1078C22—1722no—
1079C22—1722no—
1080C22—1722no—
1081C22—1722no—
1082C22—1722no—
1083C22—1722no—
1084C22—1722no—
1085C22—1722no—
1086C22—1722no—
1087C22—1722no—
1088C22—1722no—
1089C22—1722no—
1090C22—1722no—
1091C22—1722no—
1092C22—1722no—
1093C22—1722no—
1094C22—1722no—
1095C22—1722no—
1096C22—1722no—
1097C22—1722no—
1098C22—1722no—
1099C22—1722no—
1100C22—1722no—
1101C22—1722no—
1102C22#117×D4311yescharacteristic
1103C22C4×D4×D4311yescharacteristic
1104C22C2×C4×D17211yescharacteristic
1105C22#1458336711yescharacteristic
1106C22C4×#1062190211yescharacteristic
1107C22#1458337111yescharacteristic
1108C22#1458337111yescharacteristic
1109C22#123×D4311yescharacteristic
1110C22#1458341111yescharacteristic
1111C22#1458341111yescharacteristic
1112C22#1458341211yescharacteristic
1113C22#1458342711yescharacteristic
1114C22#1458342711yescharacteristic
1115C22#1458343211yescharacteristic
1116C22#1458343411yescharacteristic
1117C22#1458348311yescharacteristic
1118C22#1458348811yescharacteristic
1119C22#1458349911yescharacteristic
1120C22#1458350111yescharacteristic
1121C22D4×D17211yescharacteristic
1122C22#1458353911yescharacteristic
1123C22#1458354111yescharacteristic
1124C22#1458354411yescharacteristic
1125C22#1458354411yescharacteristic
1126C22#1458354611yescharacteristic
1127C22#1458357111yescharacteristic
1128C22#1458357311yescharacteristic
1129C22#1458357411yescharacteristic
1130C22#1458357411yescharacteristic
1131C22#1458357611yescharacteristic
1132C22#1458357911yescharacteristic
1133C22#1458359411yescharacteristic
1134C22#1458359711yescharacteristic
1135C22#1458360211yescharacteristic
1136C22#1458361211yescharacteristic
1137C4—24no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—42no—
1144C4—864no—
1145C4—3441no—
1146C4—3441no—
1147C4—1722no—
1148C4—1722no—
1149C4—1722no—
1150C2—1724no—
1151C2—1724no—
1152C2#1913703911yescharacteristic
1153C2#1913711611yescharacteristic
1154C2#1913735811yescharacteristic
1155C2#1913743911yescharacteristic
1156C2#1913753411yescharacteristic
1157C2#1913757711yescharacteristic
1158C2#1913763511yescharacteristic
1159C2#1913806211yescharacteristic
1160C2#1913808611yescharacteristic
1161C2#1913848511yescharacteristic
1162C2#1913850011yescharacteristic
1163C2#1913850911yescharacteristic
1164C2#1913870411yescharacteristic
1165C2#1913984311yescharacteristic
1166C2#1913989711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1434C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1434D43
hypocenterC43#13984
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C2×#14582761C2semidirect
4. C2×C4×(C2×D43)⋊C4C2semidirect
5. C2×#14582746C2semidirect
6. #19132855C2semidirect
7. #19132841C2semidirect
8. #19132841C2semidirect
10. #19132833C2semidirect
11. #19132831C2semidirect
12. #19132829C2semidirect
13. #19132819C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×#1434C2semidirect
33. #14582777C4semidirect
84. C22×C4×D43C2×C4semidirect
116. C2×(C2×D43)⋊C4C2×C4semidirect
135. C43⋊#95C2×C4semidirect
150. #95×C43C2×C4semidirect
151. #95×C43D4semidirect
580. #1434D43semidirect
639. C43#13984semidirect
734. #95C4×D43semidirect
735. #95D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145827772
C2×#145827612
C2×C4×(C2×D43)⋊C42
C2×#145827462
#191328552
#191328412
#191328352
#191328332
#191328312
#191328292
#191328192
(C2×D43)⋊#952
C43×#14342
#1398443