Finite Group Databasebeta

← #25018108

Subgroups — #25018108

Order 11008.

2298 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582774C211yesmaximal, characteristic
2C2×C4⋊C4×Dic43C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×Dic43C211yesmaximal, characteristic
4C2×C22⋊C4×Dic43C211yesmaximal, characteristic
5C2×C4×C22⋊Dic43C211yesmaximal, characteristic
6C22×C43⋊#95C211yesmaximal, characteristic
7#19132829C211yesmaximal, characteristic, complemented
8#19132829C211yesmaximal, characteristic, complemented
9#19132827C211yesmaximal, characteristic, complemented
10#19132827C211yesmaximal, characteristic, complemented
11#19132824C211yesmaximal, characteristic, complemented
12#19132820C211yesmaximal, characteristic, complemented
13#19132817C211yesmaximal, characteristic
14#95×Dic43C211yesmaximal, characteristic, complemented
15C2×C43×#385C211yesmaximal, characteristic
16C24×Dic43C2211yescharacteristic
17C24×Dic43C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C22×C22⋊Dic43C2211yescharacteristic
21C22×C22⋊Dic43C2211yescharacteristic
22C22×C4×Dic43C2211yescharacteristic
23C22×C4×Dic43C2211yescharacteristic
24C22×C4×Dic43C2211yescharacteristic
25C22×C4×Dic43C2211yescharacteristic
26C22×C4×Dic43C2211yescharacteristic
27C22×C4×Dic43C2211yescharacteristic
28#14582774C418yescomplemented
29C4⋊C4×Dic43—24no—
30C22⋊C4×Dic43—24no—
31C22⋊C4×Dic43C418yescomplemented
32C4×C22⋊Dic43—24no—
33C2×C43⋊#95—24no—
34C2×C43⋊#95C2211yescharacteristic
35C2×C43⋊#95C2211yescharacteristic
36C2×C43⋊#95C2211yescharacteristic
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
49C2×C43⋊#95C2211yescharacteristic
50C24×C4×C43C2211yescharacteristic
51C22×C4⋊C4×C43C2211yescharacteristic
52C22×C4⋊C4×C43C2211yescharacteristic
53C22×C22⋊C4×C43C2211yescharacteristic
54C22×C22⋊C4×C43C2211yescharacteristic
55C43×#385C418yescomplemented
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C23×Dic43—22no—
59C23×Dic43—22no—
60C23×Dic43—22no—
61C23×Dic43—22no—
62C23×Dic43—22no—
63C23×Dic43—22no—
64C23×Dic43—22no—
65C23×Dic43—22no—
66C23×Dic43—41no—
67C23×Dic43—41no—
68C23×Dic43—41no—
69C23×Dic43—41no—
70C23×Dic43C2×C414yes—
71C23×Dic43C2×C414yes—
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C2×C4⋊Dic43—22no—
81C2×C4⋊Dic43—22no—
82C2×C4⋊Dic43—41no—
83C2×C4⋊Dic43—41no—
84C2×C4⋊Dic43C2×C414yescomplemented
85C2×C4⋊Dic43C2×C414yescomplemented
86C2×C22⋊Dic43—22no—
87C2×C22⋊Dic43—22no—
88C2×C22⋊Dic43C2×C414yes—
89C2×C22⋊Dic43C2×C414yes—
90C2×C22⋊Dic43D414yes—
91C2×C22⋊Dic43Q814yes—
92C2×C4×Dic43—22no—
93C2×C4×Dic43—22no—
94C2×C4×Dic43—22no—
95C2×C4×Dic43—22no—
96C2×C4×Dic43—22no—
97C2×C4×Dic43—22no—
98C2×C4×Dic43—22no—
99C2×C4×Dic43—22no—
100C2×C4×Dic43—22no—
101C2×C4×Dic43—22no—
102C2×C4×Dic43—41no—
103C2×C4×Dic43—41no—
104C2×C4×Dic43—41no—
105C2×C4×Dic43—41no—
106C2×C4×Dic43—41no—
107C2×C4×Dic43—41no—
108C2×C4×Dic43C2×C414yescomplemented
109C2×C4×Dic43C2×C414yescomplemented
110C43⋊#95—22no—
111C43⋊#95—22no—
112C43⋊#95—22no—
113C43⋊#95—22no—
114C43⋊#95—22no—
115C43⋊#95—22no—
116C43⋊#95—22no—
117C43⋊#95—22no—
118C43⋊#95—22no—
119C43⋊#95—41no—
120C43⋊#95—41no—
121C43⋊#95C2×C414yescomplemented
122C43⋊#95C2×C414yescomplemented
123C43⋊#95C2×C414yescomplemented
124C43⋊#95C2×C414yescomplemented
125C43⋊#95D414yes—
126C25×C43C2311yescharacteristic
127C23×C4×C43—22no—
128C23×C4×C43—22no—
129C23×C4×C43—22no—
130C23×C4×C43—22no—
131C23×C4×C43—41no—
132C23×C4×C43—41no—
133C23×C4×C43C2×C414yes—
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43—22no—
141C2×C4⋊C4×C43—22no—
142C2×C4⋊C4×C43—41no—
143C2×C4⋊C4×C43—41no—
144C2×C4⋊C4×C43C2×C414yescomplemented
145C2×C4⋊C4×C43C2×C414yescomplemented
146C2×C22⋊C4×C43—22no—
147C2×C22⋊C4×C43—22no—
148C2×C22⋊C4×C43C2×C414yes—
149C2×C22⋊C4×C43C2×C414yes—
150C2×C22⋊C4×C43C2×C414yes—
151C2×C22⋊C4×C43C2×C414yes—
152#95×C43C2×C414yescomplemented
153#95×C43C2×C414yescomplemented
154C24×C43—21no—
155C24×C43—21no—
156C24×C43—21no—
157C24×C43—21no—
158C24×C43—21no—
159C24×C43—21no—
160C24×C43—21no—
161C24×C43—21no—
162C24×C43C22×C412yes—
163C24×C43C22×C412yes—
164C24×C43C22×C412yes—
165C24×C43C2×D412yes—
166C24×C43C2×Q812yes—
167C24×C43#4112yes—
168C24×C43#4112yes—
169C24×C43C2411yescharacteristic
170C22×C4×C43—28no—
171C22×C4×C43—28no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
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—44no—
203C22×C4×C43—44no—
204C22×C4×C43—44no—
205C22×C4×C43—44no—
206C22×C4×C43—44no—
207C22×C4×C43C22×C412yes—
208C22×C4×C43C22×C412yes—
209C22×C4×C43C22×C412yes—
210C22×C4×C43C22×C412yes—
211C22×C4×C43C22×C412yes—
212C22×C4×C43C22×C412yes—
213C22×C4×C43C22×C412yes—
214C22×C4×C43C22×C412yes—
215C22×C4×C43C22×C412yes—
216C22×C4×C43C22×C412yes—
217C22×C4×C43C2×D412yes—
218C22×C4×C43#4112yes—
219C22×Dic43—28no—
220C22×Dic43—28no—
221C22×Dic43—28no—
222C22×Dic43—28no—
223C22×Dic43—21no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43—21no—
228C22×Dic43—21no—
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43—21no—
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—44no—
264C22×Dic43—44no—
265C22×Dic43—44no—
266C22×Dic43—44no—
267C22×Dic43—44no—
268C22×Dic43—44no—
269C22×Dic43—44no—
270C22×Dic43—44no—
271C22×Dic43—44no—
272C22×Dic43—44no—
273C22×Dic43C22×C412yes—
274C22×Dic43C22×C412yes—
275C22×Dic43C22×C412yes—
276C22×Dic43C22×C412yes—
277C22×Dic43C22×C412yes—
278C22×Dic43C22×C412yes—
279C22×Dic43C22×C412yes—
280C22×Dic43C22×C412yes—
281C22×Dic43C2×D412yes—
282C22×Dic43C2×D412yes—
283C22×Dic43C2×D412yes—
284C22×Dic43C2×D412yes—
285C22×Dic43C2×Q812yes—
286C22×Dic43C2×Q812yes—
287C22×Dic43#4112yes—
288C22×Dic43#4112yes—
289C4⋊C4×C43—28no—
290C4⋊C4×C43—44no—
291C22⋊C4×C43—28no—
292C22⋊C4×C43C42116yescomplemented
293C22⋊Dic43—28no—
294C22⋊Dic43C4⋊C4116yescomplemented
295C4⋊Dic43—28no—
296C4⋊Dic43—44no—
297C4×Dic43—28no—
298C4×Dic43—44no—
299C4×Dic43—44no—
300C4×Dic43—44no—
301C4×Dic43—44no—
302C4×Dic43—44no—
303C23×C43—22no—
304C23×C43—22no—
305C23×C43—22no—
306C23×C43—22no—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—22no—
311C23×C43—22no—
312C23×C43—22no—
313C23×C43—22no—
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×C43C2×C4214yes—
332C23×C43C2×C4⋊C414yes—
333C23×C43#11714yes—
334C23×C43C4×D414yes—
335C23×C43C4×D414yes—
336C23×C43C4×Q814yes—
337C23×C43C4×Q814yes—
338C23×C43C23×C411yescharacteristic
339C23×C43C23×C411yescharacteristic
340C23×C43C23×C411yescharacteristic
341C23×C43C22×D411yescharacteristic
342C23×C43C22×D411yescharacteristic
343C23×C43C22×Q811yescharacteristic
344C23×C43C2×#4111yescharacteristic
345C23×C43C2×#4111yescharacteristic
346C23×C43C2×#4111yescharacteristic
347C23×C43C2×#4111yescharacteristic
348C23×C43C2×#4111yescharacteristic
349C23×C43H(5,𝔽2)11yescharacteristic
350C23×C43H(5,𝔽2)11yescharacteristic
351C23×C43H(5,𝔽2)11yescharacteristic
352C23×C432−1+411yescharacteristic
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—22no—
365C2×C4×C43—22no—
366C2×C4×C43—22no—
367C2×C4×C43—22no—
368C2×C4×C43—22no—
369C2×C4×C43—22no—
370C2×C4×C43—22no—
371C2×C4×C43—22no—
372C2×C4×C43—22no—
373C2×C4×C43—22no—
374C2×C4×C43—22no—
375C2×C4×C43—22no—
376C2×C4×C43—22no—
377C2×C4×C43—22no—
378C2×C4×C43—22no—
379C2×C4×C43—22no—
380C2×C4×C43—416no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—41no—
385C2×C4×C43—41no—
386C2×C4×C43—41no—
387C2×C4×C43—41no—
388C2×C4×C43—41no—
389C2×C4×C43—41no—
390C2×C4×C43—41no—
391C2×C4×C43—41no—
392C2×C4×C43—41no—
393C2×C4×C43C2×C4214yes—
394C2×C4×C43C2×C4214yes—
395C2×C4×C43C4×D414yes—
396C2×Dic43—22no—
397C2×Dic43—22no—
398C2×Dic43—22no—
399C2×Dic43—22no—
400C2×Dic43—22no—
401C2×Dic43—22no—
402C2×Dic43—22no—
403C2×Dic43—22no—
404C2×Dic43—22no—
405C2×Dic43—22no—
406C2×Dic43—22no—
407C2×Dic43—22no—
408C2×Dic43—22no—
409C2×Dic43—22no—
410C2×Dic43—22no—
411C2×Dic43—22no—
412C2×Dic43—22no—
413C2×Dic43—22no—
414C2×Dic43—22no—
415C2×Dic43—22no—
416C2×Dic43—22no—
417C2×Dic43—22no—
418C2×Dic43—22no—
419C2×Dic43—22no—
420C2×Dic43—22no—
421C2×Dic43—22no—
422C2×Dic43—22no—
423C2×Dic43—22no—
424C2×Dic43—22no—
425C2×Dic43—22no—
426C2×Dic43—22no—
427C2×Dic43—22no—
428C2×Dic43—22no—
429C2×Dic43—22no—
430C2×Dic43—22no—
431C2×Dic43—22no—
432C2×Dic43—416no—
433C2×Dic43—416no—
434C2×Dic43—41no—
435C2×Dic43—41no—
436C2×Dic43—41no—
437C2×Dic43—41no—
438C2×Dic43—41no—
439C2×Dic43—41no—
440C2×Dic43—41no—
441C2×Dic43—41no—
442C2×Dic43—41no—
443C2×Dic43—41no—
444C2×Dic43—41no—
445C2×Dic43—41no—
446C2×Dic43—41no—
447C2×Dic43—41no—
448C2×Dic43—41no—
449C2×Dic43—41no—
450C2×Dic43C2×C4⋊C414yes—
451C2×Dic43C2×C4⋊C414yes—
452C2×Dic43C4×D414yes—
453C2×Dic43C4×D414yes—
454#13814—431nomaximal, Sylow
455C22×C43—24no—
456C22×C43—24no—
457C22×C43—24no—
458C22×C43—24no—
459C22×C43—24no—
460C22×C43—24no—
461C22×C43—24no—
462C22×C43—24no—
463C22×C43—24no—
464C22×C43—24no—
465C22×C43—24no—
466C22×C43—24no—
467C22×C43—24no—
468C22×C43—24no—
469C22×C43C4×C4⋊C418yescomplemented
470C22×C43C22×C4211yescharacteristic
471C22×C43C22×C4⋊C411yescharacteristic
472C22×C43C2×#11711yescharacteristic
473C22×C43C2×C4×D411yescharacteristic
474C22×C43C2×C4×D411yescharacteristic
475C22×C43C2×C4×D411yescharacteristic
476C22×C43C2×C4×D411yescharacteristic
477C22×C43C2×C4×D411yescharacteristic
478C22×C43C2×C4×Q811yescharacteristic
479C22×C43C2×C4×Q811yescharacteristic
480C22×C43C4×#4111yescharacteristic
481C22×C43C4×#4111yescharacteristic
482C22×C43C4×#4111yescharacteristic
483C22×C43#51811yescharacteristic
484C22×C43#51811yescharacteristic
485C22×C43#51811yescharacteristic
486C22×C43#52011yescharacteristic
487C22×C43#52011yescharacteristic
488C22×C43#52011yescharacteristic
489C22×C43D4211yescharacteristic
490C22×C43#54611yescharacteristic
491C22×C43#54611yescharacteristic
492C22×C43#54611yescharacteristic
493C22×C43#54611yescharacteristic
494C22×C43#54711yescharacteristic
495C22×C43D4×Q811yescharacteristic
496C22×C43#55111yescharacteristic
497C22×C43#55111yescharacteristic
498C22×C43#55111yescharacteristic
499C22×C43#55111yescharacteristic
500C22×C43#55211yescharacteristic
501C22×C43#55211yescharacteristic
502C22×C43#55411yescharacteristic
503C22×C43#55411yescharacteristic
504C22×C43#55411yescharacteristic
505C4×C43—24no—
506C4×C43—24no—
507C4×C43—24no—
508C4×C43—42no—
509C4×C43—42no—
510C4×C43—42no—
511Dic43—24no—
512Dic43—24no—
513Dic43—24no—
514Dic43—24no—
515Dic43—42no—
516Dic43—42no—
517Dic43—42no—
518Dic43—42no—
519C2×#385—431no—
520C2×#385D4311yescharacteristic
521C2×C4×C4⋊C4—431no—
522C2×C4×C22⋊C4—431no—
523C2×C4×C22⋊C4—431no—
524C2×C4×C22⋊C4—431no—
525C22×#95—431no—
526#1436—431no—
527#1436—431no—
528#1436—431no—
529#1436—431no—
530C4⋊#95—431no—
531#1434—431no—
532C22⋊#95—431no—
533C4×#95—431no—
534C2×C43—28no—
535C2×C43C2×C4×C4⋊C411yescharacteristic
536C2×C43C42×D411yescharacteristic
537C2×C43#227511yescharacteristic
538C2×C43#234211yescharacteristic
539C2×C43#234311yescharacteristic
540C2×C43D4×C4⋊C411yescharacteristic
541C2×C43#234911yescharacteristic
542C2×C43#235811yescharacteristic
543C2×C43#235811yescharacteristic
544C2×C43#235911yescharacteristic
545C2×C43#235911yescharacteristic
546C2×C43#236011yescharacteristic
547C2×C43#236011yescharacteristic
548C2×C43#236811yescharacteristic
549C2×C43#236811yescharacteristic
550C24×C4—431no—
551C24×C4—431no—
552C24×C4C2×D4311yescharacteristic
553C22×C4⋊C4—431no—
554C22×C4⋊C4—431no—
555C22×C4⋊C4C2×D4311yescharacteristic
556C22×C4⋊C4C2×D4311yescharacteristic
557C22×C22⋊C4—431no—
558C22×C22⋊C4—431no—
559C22×C22⋊C4C2×D4311yescharacteristic
560C22×C22⋊C4C2×D4311yescharacteristic
561C22×C42—431no—
562C22×C42—431no—
563C22×C42—431no—
564C22×C42—431no—
565C22×C42—431no—
566C22×C42—431no—
567#385—438no—
568#385Dic4318yescomplemented
569C4×C4⋊C4—864no—
570C4×C22⋊C4—438no—
571C4×C22⋊C4—864no—
572C4×C22⋊C4—864no—
573C2×#95—431no—
574C2×#95—431no—
575C2×#95—431no—
576C2×#95—431no—
577C2×#95—431no—
578C2×#95—431no—
579C2×#95—431no—
580C2×#95—431no—
581C2×#95—431no—
582C2×#95—431no—
583C2×#95—431no—
584C2×#95—431no—
585C2×#95—431no—
586C2×#95—431no—
587C2×#95—431no—
588C2×#95—431no—
589C2×#95—864no—
590C2×#95C2×D4311yescharacteristic
591C2×#95C2×D4311yescharacteristic
592C43#1381411yescharacteristic, complemented, Sylow
593C25C22×D4311yescharacteristic
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—41no—
599C23×C4—41no—
600C23×C4—431no—
601C23×C4—431no—
602C23×C4—431no—
603C23×C4—431no—
604C23×C4—431no—
605C23×C4—431no—
606C23×C4—431no—
607C23×C4—431no—
608C23×C4—434no—
609C23×C4—434no—
610C23×C4—862no—
611C23×C4—862no—
612C23×C4—862no—
613C23×C4—862no—
614C23×C4—862no—
615C23×C4—862no—
616C23×C4—862no—
617C23×C4—862no—
618C23×C4—1721no—
619C23×C4—1721no—
620C23×C4—1721no—
621C23×C4—1721no—
622C23×C4C2×Dic4314yes—
623C23×C4C22×D4311yescharacteristic
624C23×C4C22×D4311yescharacteristic
625C23×C4C22×D4311yescharacteristic
626C23×C4C22×D4311yescharacteristic
627C23×C4C22×D4311yescharacteristic
628C23×C4C22×D4311yescharacteristic
629C2×C4⋊C4—22no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—434no—
634C2×C4⋊C4—434no—
635C2×C4⋊C4—862no—
636C2×C4⋊C4—862no—
637C2×C4⋊C4—1721no—
638C2×C4⋊C4—1721no—
639C2×C4⋊C4C2×Dic4314yescomplemented
640C2×C4⋊C4C2×Dic4314yescomplemented
641C2×C22⋊C4—22no—
642C2×C22⋊C4—22no—
643C2×C22⋊C4—434no—
644C2×C22⋊C4—434no—
645C2×C22⋊C4—434no—
646C2×C22⋊C4—434no—
647C2×C22⋊C4—862no—
648C2×C22⋊C4—862no—
649C2×C22⋊C4C4×D4314yes—
650C2×C22⋊C4C4×D4314yes—
651C2×C22⋊C4C2×Dic4314yes—
652C2×C22⋊C4C2×Dic4314yes—
653C2×C42—434no—
654C2×C42—434no—
655C2×C42—862no—
656C2×C42—862no—
657C2×C42—862no—
658C2×C42—862no—
659C2×C42—862no—
660C2×C42—862no—
661C2×C42—862no—
662C2×C42—862no—
663C2×C42—862no—
664C2×C42—862no—
665C2×C42—1721no—
666C2×C42—1721no—
667C2×C42—1721no—
668C2×C42—1721no—
669C2×C42—1721no—
670C2×C42—1721no—
671#95—434no—
672#95—434no—
673#95—434no—
674#95—434no—
675#95—434no—
676#95—862no—
677#95—862no—
678#95—862no—
679#95—862no—
680#95—862no—
681#95—862no—
682#95—862no—
683#95—862no—
684#95—862no—
685#95—1721no—
686#95—1721no—
687#95C2×Dic4314yescomplemented
688#95C2×Dic4314yescomplemented
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24C2×C4×D4312yes—
698C24C2×C4×D4312yes—
699C24D4×D4312yes—
700C24#1062190012yes—
701C24Q8×D4312yes—
702C24#1062190212yes—
703C24C22×Dic4312yes—
704C24C23×D4311yescharacteristic
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—28no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—28no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—432no—
743C22×C4—432no—
744C22×C4—432no—
745C22×C4—432no—
746C22×C4—432no—
747C22×C4—432no—
748C22×C4—432no—
749C22×C4—432no—
750C22×C4—432no—
751C22×C4—432no—
752C22×C4—432no—
753C22×C4—432no—
754C22×C4—432no—
755C22×C4—432no—
756C22×C4—432no—
757C22×C4—432no—
758C22×C4—868no—
759C22×C4—868no—
760C22×C4—861no—
761C22×C4—861no—
762C22×C4—861no—
763C22×C4—861no—
764C22×C4—861no—
765C22×C4—861no—
766C22×C4—861no—
767C22×C4—861no—
768C22×C4—861no—
769C22×C4—861no—
770C22×C4—861no—
771C22×C4—861no—
772C22×C4—861no—
773C22×C4—861no—
774C22×C4—861no—
775C22×C4—861no—
776C22×C4—868no—
777C22×C4—868no—
778C22×C4—861no—
779C22×C4—861no—
780C22×C4—861no—
781C22×C4—861no—
782C22×C4—861no—
783C22×C4—861no—
784C22×C4—861no—
785C22×C4—861no—
786C22×C4—861no—
787C22×C4—861no—
788C22×C4—861no—
789C22×C4—861no—
790C22×C4—861no—
791C22×C4—861no—
792C22×C4—861no—
793C22×C4—861no—
794C22×C4—861no—
795C22×C4—861no—
796C22×C4—861no—
797C22×C4—861no—
798C22×C4—861no—
799C22×C4—861no—
800C22×C4—861no—
801C22×C4—861no—
802C22×C4—1724no—
803C22×C4—1724no—
804C22×C4—1724no—
805C22×C4—1724no—
806C22×C4—1724no—
807C22×C4—1724no—
808C22×C4—1724no—
809C22×C4—1724no—
810C22×C4—1724no—
811C22×C4—1724no—
812C22×C4C2×C4×D4312yes—
813C22×C4C2×C4×D4312yes—
814C22×C4C2×C4×D4312yes—
815C22×C4C2×C4×D4312yes—
816C22×C4D4×D4312yes—
817C22×C4#1062190012yes—
818C22×C4C22×Dic4312yes—
819C22×C4C22×Dic4312yes—
820C22×C4C22×Dic4312yes—
821C22×C4C22×Dic4312yes—
822C22×C4C22×Dic4312yes—
823C22×C4C22×Dic4312yes—
824C4⋊C4—28no—
825C4⋊C4—44no—
826C4⋊C4—868no—
827C4⋊C4—1724no—
828C22⋊C4—28no—
829C22⋊C4—4316no—
830C22⋊C4—868no—
831C22⋊C4C4×Dic43116yescomplemented
832C42—868no—
833C42—1724no—
834C42—1724no—
835C42—1724no—
836C42—1724no—
837C42—1724no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23C2×C4×Dic4314yes—
867C23C4⋊C4×D4314yes—
868C23#1306328314yes—
869C23#1306328714yes—
870C23D4×Dic4314yes—
871C23#1306329014yes—
872C23Q8×Dic4314yes—
873C23C22×C4×D4311yescharacteristic
874C23C22×C4×D4311yescharacteristic
875C23C23×Dic4311yescharacteristic
876C23C2×D4×D4311yescharacteristic
877C23C2×D4×D4311yescharacteristic
878C23C2×Q8×D4311yescharacteristic
879C23#41×D4311yescharacteristic
880C23#41×D4311yescharacteristic
881C23C2×#1062190011yescharacteristic
882C23C2×#1062190011yescharacteristic
883C23C2×#1062190211yescharacteristic
884C23#1306337011yescharacteristic
885C23#1306337011yescharacteristic
886C23#1306337111yescharacteristic
887C23#1306337211yescharacteristic
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—416no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—434no—
929C2×C4—434no—
930C2×C4—434no—
931C2×C4—434no—
932C2×C4—862no—
933C2×C4—862no—
934C2×C4—862no—
935C2×C4—862no—
936C2×C4—862no—
937C2×C4—862no—
938C2×C4—862no—
939C2×C4—862no—
940C2×C4—862no—
941C2×C4—862no—
942C2×C4—862no—
943C2×C4—862no—
944C2×C4—862no—
945C2×C4—862no—
946C2×C4—862no—
947C2×C4—862no—
948C2×C4—862no—
949C2×C4—862no—
950C2×C4—862no—
951C2×C4—862no—
952C2×C4—862no—
953C2×C4—862no—
954C2×C4—862no—
955C2×C4—862no—
956C2×C4—862no—
957C2×C4—862no—
958C2×C4—862no—
959C2×C4—862no—
960C2×C4—862no—
961C2×C4—862no—
962C2×C4—862no—
963C2×C4—862no—
964C2×C4—862no—
965C2×C4—862no—
966C2×C4—862no—
967C2×C4—862no—
968C2×C4—17216no—
969C2×C4—17216no—
970C2×C4—1721no—
971C2×C4—1721no—
972C2×C4—1721no—
973C2×C4—1721no—
974C2×C4—1721no—
975C2×C4—1721no—
976C2×C4—1721no—
977C2×C4—1721no—
978C2×C4—1721no—
979C2×C4—1721no—
980C2×C4—1721no—
981C2×C4—1721no—
982C2×C4—1721no—
983C2×C4—1721no—
984C2×C4—1721no—
985C2×C4—1721no—
986C2×C4C2×C4×Dic4314yes—
987C2×C4C2×C4×Dic4314yes—
988C2×C4D4×Dic4314yes—
989C22—24no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—24no—
996C22—24no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22C4⋊C4×Dic4318yescomplemented
1004C22C22×C4×Dic4311yescharacteristic
1005C22C2×C4⋊C4×D4311yescharacteristic
1006C22C2×#1306328311yescharacteristic
1007C22C4×D4×D4311yescharacteristic
1008C22C4×D4×D4311yescharacteristic
1009C22C2×#1306328711yescharacteristic
1010C22C2×D4×Dic4311yescharacteristic
1011C22C2×D4×Dic4311yescharacteristic
1012C22C2×#1306329011yescharacteristic
1013C22C2×Q8×Dic4311yescharacteristic
1014C22C4×#1062190011yescharacteristic
1015C22C4×#1062190011yescharacteristic
1016C22#41×Dic4311yescharacteristic
1017C22#1458337111yescharacteristic
1018C22#1458337111yescharacteristic
1019C22#1458337411yescharacteristic
1020C22#1458337811yescharacteristic
1021C22#1458337811yescharacteristic
1022C22#1458338211yescharacteristic
1023C22#1458353111yescharacteristic
1024C22#1458353611yescharacteristic
1025C22#1458353611yescharacteristic
1026C22#1458354011yescharacteristic
1027C22#1458354111yescharacteristic
1028C22#1458354711yescharacteristic
1029C22#1458356211yescharacteristic
1030C22#1458357211yescharacteristic
1031C22#1458357611yescharacteristic
1032C22#1458357611yescharacteristic
1033C22#1458358011yescharacteristic
1034C22#1458358611yescharacteristic
1035C22#1458359111yescharacteristic
1036C22#1458360311yescharacteristic
1037C22#1458360311yescharacteristic
1038C22#1458360711yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—24no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—864no—
1046C4—864no—
1047C4—864no—
1048C4—864no—
1049C4—1722no—
1050C4—1722no—
1051C4—1722no—
1052C4—1722no—
1053C2—28no—
1054C2C2×C4⋊C4×Dic4311yescharacteristic
1055C2C4×D4×Dic4311yescharacteristic
1056C2#1913695611yescharacteristic
1057C2#1913744211yescharacteristic
1058C2#1913745311yescharacteristic
1059C2#1913749311yescharacteristic
1060C2#1913750111yescharacteristic
1061C2#1913757111yescharacteristic
1062C2#1913757911yescharacteristic
1063C2#1913758511yescharacteristic
1064C2#1913759111yescharacteristic
1065C2#1913759511yescharacteristic
1066C2#1913760411yescharacteristic
1067C2#1913767611yescharacteristic
1068C2#1913768011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC22×C43C22×C42
FittingC2×C43×#385C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC2×#385D43
hypocenterC43#13814
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic43C2semidirect
7. #19132829C2semidirect
8. #19132829C2semidirect
9. #19132827C2semidirect
10. #19132827C2semidirect
11. #19132824C2semidirect
12. #19132820C2semidirect
14. #95×Dic43C2semidirect
28. #14582774C4semidirect
31. C22⋊C4×Dic43C4semidirect
55. C43×#385C4semidirect
84. C2×C4⋊Dic43C2×C4semidirect
85. C2×C4⋊Dic43C2×C4semidirect
108. C2×C4×Dic43C2×C4semidirect
109. C2×C4×Dic43C2×C4semidirect
121. C43⋊#95C2×C4semidirect
122. C43⋊#95C2×C4semidirect
123. C43⋊#95C2×C4semidirect
124. C43⋊#95C2×C4semidirect
144. C2×C4⋊C4×C43C2×C4semidirect
145. C2×C4⋊C4×C43C2×C4semidirect
152. #95×C43C2×C4semidirect
153. #95×C43C2×C4semidirect
292. C22⋊C4×C43C42semidirect
294. C22⋊Dic43C4⋊C4semidirect
469. C22×C43C4×C4⋊C4semidirect
568. #385Dic43semidirect
592. C43#13814semidirect
639. C2×C4⋊C4C2×Dic43semidirect
640. C2×C4⋊C4C2×Dic43semidirect
687. #95C2×Dic43semidirect
688. #95C2×Dic43semidirect
831. C22⋊C4C4×Dic43semidirect
1003. C22C4⋊C4×Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145827742
C2×C4⋊C4×Dic432
C2×C22⋊C4×Dic432
C2×C4×C22⋊Dic432
C22×C43⋊#952
#191328292
#191328272
#191328242
#191328202
#191328172
#95×Dic432
C2×C43×#3852
#1381443