Finite Group Databasebeta

← #25021033

Subgroups — #25021033

Order 11008.

2158 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063308C211yesmaximal, characteristic
2C2×#14582799C211yesmaximal, characteristic
3C2×#14582783C211yesmaximal, characteristic, complemented
4C2×C4×Dic43⋊C4C211yesmaximal, characteristic, complemented
5#19132846C211yesmaximal, characteristic, complemented
6#19132839C211yesmaximal, characteristic, complemented
7#19132838C211yesmaximal, characteristic, complemented
8#19132834C211yesmaximal, characteristic
9#19132833C211yesmaximal, characteristic, complemented
10#19132833C211yesmaximal, characteristic, complemented
11#19132832C211yesmaximal, characteristic, complemented
12#19132831C211yesmaximal, characteristic, complemented
13#19132826C211yesmaximal, characteristic, complemented
14#19132818C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C2×#13063308—24no—
18C2×#13063308—24no—
19C2×#13063308C418yescomplemented
20C22×Dic43⋊C4C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×C22⋊Dic43C2211yescharacteristic
25C22×C22⋊Dic43C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35#14582799—24no—
36#14582783—24no—
37C4×Dic43⋊C4—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
50C24×C4×C43C2211yescharacteristic
51C22×C22⋊C4×C43C2211yescharacteristic
52C22×C22⋊C4×C43C2211yescharacteristic
53C22×C42×C43C2211yescharacteristic
54C22×C42×C43C2211yescharacteristic
55C4×C22⋊C4×C43—24no—
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C24×D43C2311yescharacteristic
59C22×C22⋊D43—22no—
60C22×C22⋊D43—22no—
61C22×C22⋊D43—22no—
62C22×C22⋊D43—22no—
63C22×C22⋊D43—41no—
64C22×C22⋊D43—41no—
65C22×C22⋊D43C2×C414yes—
66C23×Dic43C2311yescharacteristic
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73#13063308—232no—
74C2×Dic43⋊C4—22no—
75C2×Dic43⋊C4—22no—
76C2×Dic43⋊C4—22no—
77C2×Dic43⋊C4—22no—
78C2×Dic43⋊C4—22no—
79C2×Dic43⋊C4—22no—
80C2×Dic43⋊C4—22no—
81C2×Dic43⋊C4—41no—
82C2×Dic43⋊C4C2×C414yes—
83C2×Dic43⋊C4C2×C414yes—
84C2×Dic43⋊C4D414yes—
85C2×Dic43⋊C4D414yes—
86C2×C22⋊Dic43—22no—
87C2×C22⋊Dic43—22no—
88C2×C22⋊Dic43—22no—
89C2×C22⋊Dic43—22no—
90C2×C22⋊Dic43—22no—
91C2×C22⋊Dic43—22no—
92C2×C22⋊Dic43—41no—
93C2×C22⋊Dic43—41no—
94C2×C22⋊Dic43C2×C414yes—
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—22no—
107C2×(C2×D43)⋊C4—41no—
108C2×(C2×D43)⋊C4—41no—
109C2×(C2×D43)⋊C4—41no—
110C2×(C2×D43)⋊C4—41no—
111C2×(C2×D43)⋊C4C2×C414yes—
112C2×(C2×D43)⋊C4C2×C414yes—
113C2×C4×Dic43—22no—
114C2×C4×Dic43—22no—
115C2×C4×Dic43—22no—
116C2×C4×Dic43—22no—
117C2×C4×Dic43—22no—
118C2×C4×Dic43—41no—
119C43⋊#95—22no—
120C43⋊#95—22no—
121C43⋊#95—22no—
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C43⋊#95—41no—
128C43⋊#95—41no—
129C43⋊#95—41no—
130C43⋊#95—41no—
131C25×C43C2311yescharacteristic
132C23×C4×C43—22no—
133C23×C4×C43—22no—
134C23×C4×C43—22no—
135C23×C4×C43—22no—
136C23×C4×C43—41no—
137C23×C4×C43—41no—
138C23×C4×C43C2×C414yes—
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C2×C22⋊C4×C43—22no—
146C2×C22⋊C4×C43—22no—
147C2×C22⋊C4×C43—22no—
148C2×C22⋊C4×C43—22no—
149C2×C22⋊C4×C43—22no—
150C2×C22⋊C4×C43D414yes—
151C2×C42×C43—22no—
152C2×C42×C43—22no—
153C2×C42×C43—22no—
154C2×C42×C43—22no—
155C2×C42×C43—41no—
156C2×C42×C43—41no—
157#95×C43—22no—
158#95×C43—22no—
159C24×C43—21no—
160C24×C43—21no—
161C24×C43—21no—
162C24×C43—21no—
163C24×C43—21no—
164C24×C43—21no—
165C24×C43—21no—
166C24×C43—21no—
167C24×C43—21no—
168C24×C43—21no—
169C24×C43—21no—
170C24×C43—21no—
171C24×C43C22×C412yes—
172C24×C43C2×D412yes—
173C24×C43#4112yes—
174C24×C43C2411yescharacteristic
175C23×D43—21no—
176C23×D43—21no—
177C23×D43—21no—
178C23×D43—21no—
179C23×D43—21no—
180C23×D43—21no—
181C23×D43—21no—
182C23×D43—21no—
183C23×D43—21no—
184C23×D43—21no—
185C23×D43—21no—
186C23×D43—21no—
187C23×D43—21no—
188C23×D43—21no—
189C23×D43C22×C412yes—
190C22×C4×C43—28no—
191C22×C4×C43—28no—
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×C43—21no—
224C22×C4×C43—44no—
225C22×C4×C43—44no—
226C22×C4×C43—44no—
227C22×C4×C43—44no—
228C22×C4×C43—44no—
229C22×C4×C43C22×C412yes—
230C22×C4×C43C22×C412yes—
231C22×C4×C43C2×D412yes—
232C22×C4×C43C2×D412yes—
233C22×C4×C43C2×D412yes—
234C22×C4×C43C2×D412yes—
235C22×C4×C43#4112yes—
236C22×C4×C43#4112yes—
237C22×C4×C43#4112yes—
238C22×C4×C43#4112yes—
239C2×C22⋊D43—28no—
240C2×C22⋊D43—28no—
241C2×C22⋊D43—44no—
242C2×C22⋊D43—44no—
243C2×C22⋊D43—44no—
244C2×C22⋊D43—44no—
245C2×C22⋊D43—44no—
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×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×Dic43C22×C412yes—
287C22×Dic43C22×C412yes—
288C22×Dic43C22×C412yes—
289C22×Dic43C2×D412yes—
290C22×Dic43C2×D412yes—
291C22×Dic43C2×D412yes—
292C22×Dic43C2×D412yes—
293C22×Dic43#4112yes—
294C22×Dic43#4112yes—
295C22⋊C4×C43—28no—
296C22⋊C4×C43—28no—
297C42×C43—44no—
298C42×C43—44no—
299C22⋊Dic43—28no—
300C22⋊Dic43—44no—
301C22⋊Dic43—44no—
302(C2×D43)⋊C4—28no—
303(C2×D43)⋊C4—28no—
304(C2×D43)⋊C4—44no—
305(C2×D43)⋊C4—44no—
306(C2×D43)⋊C4—44no—
307(C2×D43)⋊C4—44no—
308Dic43⋊C4—28no—
309Dic43⋊C4—28no—
310Dic43⋊C4—44no—
311Dic43⋊C4C22⋊C4116yescomplemented
312C4×Dic43—28no—
313C4×Dic43—44no—
314C23×C43—22no—
315C23×C43—22no—
316C23×C43—22no—
317C23×C43—22no—
318C23×C43—22no—
319C23×C43—22no—
320C23×C43—22no—
321C23×C43—22no—
322C23×C43—22no—
323C23×C43—22no—
324C23×C43—22no—
325C23×C43—22no—
326C23×C43—22no—
327C23×C43—22no—
328C23×C43—22no—
329C23×C43—22no—
330C23×C43—22no—
331C23×C43—22no—
332C23×C43—41no—
333C23×C43—41no—
334C23×C43—41no—
335C23×C43—41no—
336C23×C43—41no—
337C23×C43—41no—
338C23×C43—41no—
339C23×C43—41no—
340C23×C43—41no—
341C23×C43—41no—
342C23×C43—41no—
343C23×C43—41no—
344C23×C43—41no—
345C23×C43—41no—
346C23×C43—41no—
347C23×C43—41no—
348C23×C43C4×D414yes—
349C23×C43C23×C411yescharacteristic
350C23×C43C22×D411yescharacteristic
351C23×C43C22×D411yescharacteristic
352C23×C43C22×D411yescharacteristic
353C23×C43C2×#4111yescharacteristic
354C23×C43C2×#4111yescharacteristic
355C23×C43C2×#4111yescharacteristic
356C23×C43C2×#4111yescharacteristic
357C23×C43C2×#4111yescharacteristic
358C23×C43C2×#4111yescharacteristic
359C23×C43C2×#4111yescharacteristic
360C23×C43H(5,𝔽2)11yescharacteristic
361C23×C43H(5,𝔽2)11yescharacteristic
362C23×C43H(5,𝔽2)11yescharacteristic
363C23×C432−1+411yescharacteristic
364C22×D43—22no—
365C22×D43—22no—
366C22×D43—22no—
367C22×D43—22no—
368C22×D43—22no—
369C22×D43—22no—
370C22×D43—22no—
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—41no—
393C22×D43—41no—
394C22×D43—41no—
395C22×D43—41no—
396C22×D43—41no—
397C22×D43—41no—
398C22×D43—41no—
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—22no—
419C2×C4×C43—22no—
420C2×C4×C43—22no—
421C2×C4×C43—22no—
422C2×C4×C43—22no—
423C2×C4×C43—416no—
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×C43C2×C22⋊C414yes—
441C2×C4×C43#12314yescomplemented
442C22⋊D43—416no—
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—22no—
459C2×Dic43—22no—
460C2×Dic43—22no—
461C2×Dic43—22no—
462C2×Dic43—22no—
463C2×Dic43—22no—
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—41no—
485C2×Dic43—41no—
486C2×Dic43—41no—
487C2×Dic43—41no—
488C2×Dic43—41no—
489C2×Dic43—41no—
490C2×Dic43C2×C22⋊C414yes—
491C2×Dic43C2×C22⋊C414yes—
492#14095—431nomaximal, Sylow
493C22×C43—24no—
494C22×C43—24no—
495C22×C43—24no—
496C22×C43—42no—
497C22×C43—42no—
498C22×C43—42no—
499C22×C43—42no—
500C22×C43—42no—
501C22×C43—42no—
502C22×C43—42no—
503C22×C43—42no—
504C22×C43—42no—
505C22×C43—42no—
506C22×C43—42no—
507C22×C43—42no—
508C22×C43C22×C22⋊C411yescharacteristic
509C22×C43C2×C4×D411yescharacteristic
510C22×C43C4×#4111yescharacteristic
511C22×C43C4×#4111yescharacteristic
512C22×C43C4×#4111yescharacteristic
513C22×C43#51811yescharacteristic
514C22×C43#52011yescharacteristic
515C22×C43C2×#12311yescharacteristic
516C22×C43#52511yescharacteristic
517C22×C43#52511yescharacteristic
518C22×C43#52511yescharacteristic
519C22×C43#52911yescharacteristic
520C22×C43#52911yescharacteristic
521C22×C43#53211yescharacteristic
522C22×C43#53211yescharacteristic
523C22×C43#53811yescharacteristic
524C22×C43#53911yescharacteristic
525C22×C43#54011yescharacteristic
526C22×C43#54211yescharacteristic
527C22×C43D4211yescharacteristic
528C22×C43D4211yescharacteristic
529C22×C43#54611yescharacteristic
530C22×C43#54611yescharacteristic
531C22×C43#54611yescharacteristic
532C22×C43#54711yescharacteristic
533C22×C43#54811yescharacteristic
534C22×C43#54811yescharacteristic
535C22×C43#55011yescharacteristic
536C22×C43#55011yescharacteristic
537C22×C43#55111yescharacteristic
538C22×C43#55111yescharacteristic
539C22×C43#55211yescharacteristic
540C22×C43#55311yescharacteristic
541C22×C43#55311yescharacteristic
542C22×C43#55911yescharacteristic
543C2×D43—42no—
544C2×D43—42no—
545C2×D43—42no—
546C2×D43—42no—
547C2×D43—42no—
548C2×D43—42no—
549C2×D43—42no—
550C2×D43—81no—
551C2×D43—81no—
552C2×D43—81no—
553C2×D43—81no—
554C2×D43—81no—
555C2×D43—81no—
556C2×D43—81no—
557C2×D43—81no—
558C4×C43—24no—
559C4×C43—24no—
560C4×C43—42no—
561C4×C43—42no—
562C4×C43—42no—
563C4×C43—42no—
564Dic43—24no—
565Dic43—24no—
566Dic43—42no—
567Dic43—42no—
568Dic43—42no—
569Dic43—81no—
570Dic43—81no—
571C22×#123—431no—
572C2×#390—431no—
573C2×#387—431no—
574C2×C4×C4⋊C4—431no—
575C2×C4×C22⋊C4D4311yescharacteristic, complemented
576#1441—431no—
577#1439—431no—
578#1439—431no—
579#1438—431no—
580#1437—431no—
581#1437—431no—
582#1437—431no—
583#1437—431no—
584#1436—431no—
585C22⋊#95—431no—
586C2×C43—44no—
587C2×C43#229711yescharacteristic
588C2×C43C4×#12311yescharacteristic
589C2×C43#233511yescharacteristic
590C2×C43D4×C22⋊C411yescharacteristic
591C2×C43#234111yescharacteristic
592C2×C43#235911yescharacteristic
593C2×C43#237411yescharacteristic
594C2×C43#244311yescharacteristic
595C2×C43#244511yescharacteristic
596C2×C43#245611yescharacteristic
597C2×C43#245811yescharacteristic
598C2×C43#246111yescharacteristic
599C2×C43#247111yescharacteristic
600C2×C43#255411yescharacteristic
601C2×C43#255811yescharacteristic
602D43—82no—
603C23×D4—431no—
604C24×C4C2×D4311yescharacteristic
605C2×#123—438no—
606C2×#123—864no—
607C2×#123—864no—
608C22×C4⋊C4—431no—
609C22×C4⋊C4—431no—
610C22×C4⋊C4—431no—
611C22×C4⋊C4—431no—
612C22×C22⋊C4—431no—
613C22×C22⋊C4—431no—
614C22×C22⋊C4—431no—
615C22×C22⋊C4—431no—
616C22×C22⋊C4—431no—
617C22×C22⋊C4—431no—
618C22×C22⋊C4—431no—
619C22×C22⋊C4—431no—
620C22×C22⋊C4—431no—
621C22×C22⋊C4C2×D4311yescharacteristic
622C22×C22⋊C4C2×D4311yescharacteristic
623C22×C42—431no—
624C22×C42—431no—
625C22×C42C2×D4311yescharacteristic
626C22×C42C2×D4311yescharacteristic
627#390—864no—
628#387—864no—
629C4×C4⋊C4—864no—
630C4×C22⋊C4—24no—
631C2×#95—431no—
632C2×#95—431no—
633C2×#95—431no—
634C2×#95—431no—
635C2×#95—431no—
636C2×#95—431no—
637C2×#95—431no—
638C2×#95—431no—
639C2×#95—431no—
640C2×#95—431no—
641C2×#95—431no—
642C2×#95—431no—
643C2×#95C2×D4311yescharacteristic
644C2×#95C2×D4311yescharacteristic
645C43#1409511yescharacteristic, complemented, Sylow
646C25—431no—
647C25C22×D4311yescharacteristic
648C22×D4—434no—
649C22×D4—862no—
650C22×D4—862no—
651C22×D4—862no—
652C22×D4—862no—
653C22×D4—1721no—
654C22×D4—1721no—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—41no—
660C23×C4—41no—
661C23×C4—431no—
662C23×C4—431no—
663C23×C4—431no—
664C23×C4—431no—
665C23×C4—431no—
666C23×C4—431no—
667C23×C4—431no—
668C23×C4C4×D4314yes—
669C23×C4C22×D4311yescharacteristic
670C23×C4C22×D4311yescharacteristic
671C23×C4C22×D4311yescharacteristic
672C23×C4C22×D4311yescharacteristic
673C23×C4C22×D4311yescharacteristic
674C23×C4C22×D4311yescharacteristic
675#123—8632no—
676C2×C4⋊C4—434no—
677C2×C4⋊C4—434no—
678C2×C4⋊C4—434no—
679C2×C4⋊C4—434no—
680C2×C4⋊C4—862no—
681C2×C4⋊C4—862no—
682C2×C4⋊C4—862no—
683C2×C4⋊C4—862no—
684C2×C4⋊C4—862no—
685C2×C4⋊C4—862no—
686C2×C4⋊C4—862no—
687C2×C4⋊C4—1721no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—434no—
694C2×C22⋊C4—434no—
695C2×C22⋊C4—434no—
696C2×C22⋊C4—862no—
697C2×C22⋊C4—862no—
698C2×C22⋊C4—862no—
699C2×C22⋊C4—862no—
700C2×C22⋊C4—862no—
701C2×C22⋊C4—862no—
702C2×C22⋊C4—862no—
703C2×C22⋊C4—862no—
704C2×C22⋊C4—862no—
705C2×C22⋊C4—862no—
706C2×C22⋊C4—862no—
707C2×C22⋊C4—862no—
708C2×C22⋊C4—862no—
709C2×C22⋊C4—862no—
710C2×C22⋊C4—862no—
711C2×C22⋊C4—862no—
712C2×C22⋊C4—862no—
713C2×C22⋊C4—862no—
714C2×C22⋊C4—1721no—
715C2×C22⋊C4—1721no—
716C2×C22⋊C4—1721no—
717C2×C22⋊C4—1721no—
718C2×C22⋊C4—1721no—
719C2×C22⋊C4—1721no—
720C2×C22⋊C4C22⋊D4314yes—
721C2×C42—22no—
722C2×C42—22no—
723C2×C42—22no—
724C2×C42—22no—
725C2×C42—41no—
726C2×C42—41no—
727C2×C42—862no—
728C2×C42—862no—
729C2×C42—862no—
730C2×C42—862no—
731C2×C42—862no—
732C2×C42—1721no—
733#95—22no—
734#95—22no—
735#95—862no—
736#95—862no—
737#95—862no—
738#95—862no—
739#95—862no—
740#95—862no—
741#95—862no—
742#95—862no—
743#95—1721no—
744#95—1721no—
745#95—1721no—
746#95—1721no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—432no—
760C24—861no—
761C24—861no—
762C24—861no—
763C24—861no—
764C24—861no—
765C24—861no—
766C24—861no—
767C24—861no—
768C24—861no—
769C24—861no—
770C24—861no—
771C24—861no—
772C24—861no—
773C24—861no—
774C24C2×C4×D4312yes—
775C24#1062189812yes—
776C24C2×C22⋊D4312yes—
777C24C23×D4311yescharacteristic
778C2×D4—868no—
779C2×D4—868no—
780C2×D4—1724no—
781C2×D4—1724no—
782C2×D4—1724no—
783C2×D4—1724no—
784C2×D4—1724no—
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—28no—
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—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—28no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—432no—
825C22×C4—432no—
826C22×C4—432no—
827C22×C4—432no—
828C22×C4—432no—
829C22×C4—432no—
830C22×C4—432no—
831C22×C4—432no—
832C22×C4—432no—
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—861no—
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—861no—
860C22×C4—861no—
861C22×C4—861no—
862C22×C4—861no—
863C22×C4—861no—
864C22×C4—861no—
865C22×C4—861no—
866C22×C4—861no—
867C22×C4—861no—
868C22×C4—861no—
869C22×C4—861no—
870C22×C4—861no—
871C22×C4—861no—
872C22×C4—861no—
873C22×C4C2×C4×D4312yes—
874C22×C4C2×C4×D4312yes—
875C22×C4#1062189812yes—
876C22×C4#1062189812yes—
877C22×C4#1062189812yes—
878C22×C4#1062189812yes—
879C22×C4D4×D4312yes—
880C22×C4D4×D4312yes—
881C22×C4C2×C22⋊D4312yes—
882C22×C4C2×C22⋊D4312yes—
883C4⋊C4—4316no—
884C4⋊C4—868no—
885C4⋊C4—868no—
886C4⋊C4—1724no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—868no—
890C22⋊C4—868no—
891C22⋊C4—868no—
892C22⋊C4—1724no—
893C22⋊C4—1724no—
894C22⋊C4—1724no—
895C22⋊C4—1724no—
896C22⋊C4—1724no—
897C22⋊C4—1724no—
898C42—44no—
899C42—44no—
900C42—868no—
901C42—1724no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—862no—
937C23—862no—
938C23—862no—
939C23—862no—
940C23—862no—
941C23—862no—
942C23—862no—
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—
963C23—1721no—
964C23—1721no—
965C23—1721no—
966C23—1721no—
967C23—1721no—
968C23—1721no—
969C23—1721no—
970C23—1721no—
971C23C4×C22⋊D4314yes—
972C23C22×C4×D4311yescharacteristic
973C23C2×D4×D4311yescharacteristic
974C23C2×D4×D4311yescharacteristic
975C23C22×C22⋊D4311yescharacteristic
976C23#41×D4311yescharacteristic
977C23#41×D4311yescharacteristic
978C23C2×#1062189811yescharacteristic
979C23C2×#1062189811yescharacteristic
980C23C2×#1062189811yescharacteristic
981C23C2×#1062189811yescharacteristic
982C23C2×#1062189811yescharacteristic
983C23#1306337011yescharacteristic
984C23#1306337011yescharacteristic
985C23#1306337111yescharacteristic
986C23#1306337211yescharacteristic
987D4—17216no—
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—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—416no—
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—41no—
1028C2×C4—41no—
1029C2×C4—434no—
1030C2×C4—434no—
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—862no—
1044C2×C4—862no—
1045C2×C4—862no—
1046C2×C4—862no—
1047C2×C4—862no—
1048C2×C4—862no—
1049C2×C4—862no—
1050C2×C4—862no—
1051C2×C4—862no—
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×C4—1721no—
1072C2×C4—1721no—
1073C2×C4—1721no—
1074C2×C4—1721no—
1075C2×C4—1721no—
1076C2×C4—1721no—
1077C2×C4—1721no—
1078C2×C4C22⋊C4×D4314yes—
1079C2×C4#1306330814yescomplemented
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—3441no—
1096C22—3441no—
1097C22—3441no—
1098C22—3441no—
1099C22—3441no—
1100C22—3441no—
1101C22—3441no—
1102C22—3441no—
1103C22—1722no—
1104C22—1722no—
1105C22—1722no—
1106C22—1722no—
1107C22—1722no—
1108C22—1722no—
1109C22—1722no—
1110C22C2×C22⋊C4×D4311yescharacteristic
1111C22C2×C4×C22⋊D4311yescharacteristic
1112C22#1458336711yescharacteristic
1113C22C4×#1062189811yescharacteristic
1114C22C4×#1062189811yescharacteristic
1115C22#1458337211yescharacteristic
1116C22#1458337911yescharacteristic
1117C22C2×#1306330811yescharacteristic
1118C22#1458340811yescharacteristic
1119C22#1458340811yescharacteristic
1120C22#1458341011yescharacteristic
1121C22#1458343311yescharacteristic
1122C22#1458343311yescharacteristic
1123C22#1458344611yescharacteristic
1124C22#1458344611yescharacteristic
1125C22#1458348211yescharacteristic
1126C22#1458349111yescharacteristic
1127C22#1458350011yescharacteristic
1128C22#1458351411yescharacteristic
1129C22D4×C22⋊D4311yescharacteristic
1130C22D4×C22⋊D4311yescharacteristic
1131C22#1458353711yescharacteristic
1132C22#1458353911yescharacteristic
1133C22#1458353911yescharacteristic
1134C22#1458354811yescharacteristic
1135C22#1458355811yescharacteristic
1136C22#1458355811yescharacteristic
1137C22#1458357011yescharacteristic
1138C22#1458357011yescharacteristic
1139C22#1458357311yescharacteristic
1140C22#1458357811yescharacteristic
1141C22#1458358211yescharacteristic
1142C22#1458359811yescharacteristic
1143C22#1458359911yescharacteristic
1144C22#1458363211yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—864no—
1152C4—864no—
1153C4—3441no—
1154C4—3441no—
1155C4—1722no—
1156C4—1722no—
1157C4—1722no—
1158C2—44no—
1159C2—3442no—
1160C2#1913708111yescharacteristic
1161C2C4×#1306330811yescharacteristic
1162C2#1913738511yescharacteristic
1163C2C22⋊C4×C22⋊D4311yescharacteristic
1164C2#1913743511yescharacteristic
1165C2#1913758711yescharacteristic
1166C2#1913772611yescharacteristic
1167C2#1913832411yescharacteristic
1168C2#1913835411yescharacteristic
1169C2#1913848711yescharacteristic
1170C2#1913851711yescharacteristic
1171C2#1913855611yescharacteristic
1172C2#1913870611yescharacteristic
1173C2#1913965511yescharacteristic
1174C2#1913970911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C4×C22⋊C4×C43C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×C4×C22⋊C4D43
hypocenterC43#14095
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#14582783C2semidirect
4. C2×C4×Dic43⋊C4C2semidirect
5. #19132846C2semidirect
6. #19132839C2semidirect
7. #19132838C2semidirect
9. #19132833C2semidirect
10. #19132833C2semidirect
11. #19132832C2semidirect
12. #19132831C2semidirect
13. #19132826C2semidirect
14. #19132818C2semidirect
15. C2×C4×C22⋊C4×C43C2semidirect
19. C2×#13063308C4semidirect
311. Dic43⋊C4C22⋊C4semidirect
441. C2×C4×C43#123semidirect
575. C2×C4×C22⋊C4D43semidirect
645. C43#14095semidirect
1079. C2×C4#13063308semidirect

Maximal subgroups

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

subgroupindex
C22×#130633082
C2×#145827992
C2×#145827832
C2×C4×Dic43⋊C42
#191328462
#191328392
#191328382
#191328342
#191328332
#191328322
#191328312
#191328262
#191328182
C2×C4×C22⋊C4×C432
#1409543