Finite Group Databasebeta

← #25019474

Subgroups — #25019474

Order 11008.

2558 conjugacy classes of subgroups.

The subgroup lattice has 1230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2C2×#14582799C211yesmaximal, characteristic
3C2×#14582799C211yesmaximal, characteristic
4C2×#14582796C211yesmaximal, characteristic, complemented
5C2×#14582774C211yesmaximal, characteristic, complemented
6C2×#14582773C211yesmaximal, characteristic, complemented
7C2×#14582771C211yesmaximal, characteristic, complemented
8C2×#14582770C211yesmaximal, characteristic, complemented
9C2×#14582768C211yesmaximal, characteristic, complemented
10#19132841C211yesmaximal, characteristic, complemented
11#19132839C211yesmaximal, characteristic, complemented
12#19132838C211yesmaximal, characteristic, complemented
13Dic43⋊#95C211yesmaximal, characteristic, complemented
14#95×Dic43C211yesmaximal, characteristic, complemented
15C43×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C24×Dic43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C2×(C22⋊D43)⋊C4—24no—
20C2×(C22⋊D43)⋊C4—24no—
21C2×(C22⋊D43)⋊C4—24no—
22C22×C4⋊Dic43C2211yescharacteristic
23C22×C4⋊Dic43C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
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×C4×Dic43C2211yescharacteristic
38C22×C4×Dic43C2211yescharacteristic
39C22×C4×Dic43C2211yescharacteristic
40#14582799—24no—
41#14582799C418yescomplemented
42#14582796—24no—
43#14582774—24no—
44#14582773—24no—
45#14582771—24no—
46#14582770—24no—
47#14582768—24no—
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C22×C4⋊C4×C43C2211yescharacteristic
56C22×C22⋊C4×C43C2211yescharacteristic
57C22×C22⋊C4×C43C2211yescharacteristic
58C22×C22⋊C4×C43C2211yescharacteristic
59C2×#95×C43C2211yescharacteristic
60C2×#95×C43C2211yescharacteristic
61C2×#95×C43C2211yescharacteristic
62C24×D43C2311yescharacteristic
63C22×C22⋊D43—22no—
64C22×C22⋊D43—22no—
65C22×C22⋊D43—22no—
66C22×C22⋊D43—22no—
67C22×C22⋊D43C2×C414yes—
68C22×C22⋊D43D414yes—
69C22×C22⋊D43Q814yes—
70C23×Dic43—22no—
71C23×Dic43—22no—
72C23×Dic43—22no—
73C23×Dic43—22no—
74C23×Dic43—22no—
75C23×Dic43—41no—
76C23×Dic43—41no—
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C22×C4×D43—22no—
85C22×C4×D43—22no—
86C22×C4×D43—22no—
87C22×C4×D43—22no—
88C22×C4×D43—22no—
89C22×C4×D43—41no—
90C22×C4×D43—41no—
91(C22⋊D43)⋊C4—232no—
92C2×C4⋊Dic43—22no—
93C2×C4⋊Dic43—22no—
94C2×C4⋊Dic43—22no—
95C2×C4⋊Dic43—22no—
96C2×C4⋊Dic43—22no—
97C2×C4⋊Dic43—41no—
98C2×Dic43⋊C4—22no—
99C2×Dic43⋊C4—22no—
100C2×Dic43⋊C4—22no—
101C2×Dic43⋊C4—22no—
102C2×Dic43⋊C4—22no—
103C2×Dic43⋊C4—22no—
104C2×Dic43⋊C4—22no—
105C2×Dic43⋊C4—22no—
106C2×Dic43⋊C4—22no—
107C2×Dic43⋊C4—22no—
108C2×Dic43⋊C4—22no—
109C2×Dic43⋊C4—22no—
110C2×Dic43⋊C4—22no—
111C2×Dic43⋊C4—22no—
112C2×Dic43⋊C4—41no—
113C2×Dic43⋊C4—41no—
114C2×Dic43⋊C4C2×C414yescomplemented
115C2×Dic43⋊C4D414yes—
116C2×C22⋊Dic43—22no—
117C2×C22⋊Dic43—22no—
118C2×C22⋊Dic43—22no—
119C2×C22⋊Dic43—22no—
120C2×C22⋊Dic43—41no—
121C2×C22⋊Dic43C2×C414yescomplemented
122C2×(C2×D43)⋊C4—22no—
123C2×(C2×D43)⋊C4—22no—
124C2×(C2×D43)⋊C4—22no—
125C2×(C2×D43)⋊C4—22no—
126C2×(C2×D43)⋊C4—22no—
127C2×(C2×D43)⋊C4—22no—
128C2×(C2×D43)⋊C4—22no—
129C2×(C2×D43)⋊C4—22no—
130C2×(C2×D43)⋊C4—22no—
131C2×(C2×D43)⋊C4—22no—
132C2×(C2×D43)⋊C4—22no—
133C2×(C2×D43)⋊C4—41no—
134C2×(C2×D43)⋊C4—41no—
135C2×(C2×D43)⋊C4C2×C414yescomplemented
136C2×(C2×D43)⋊C4C2×C414yescomplemented
137C2×C4×Dic43—22no—
138C2×C4×Dic43—22no—
139C2×C4×Dic43—22no—
140C2×C4×Dic43—22no—
141C2×C4×Dic43—22no—
142C2×C4×Dic43—22no—
143C2×C4×Dic43—22no—
144C2×C4×Dic43C2×C414yescomplemented
145C2×C4×Dic43D414yes—
146C43⋊#95—22no—
147C43⋊#95—22no—
148C43⋊#95—22no—
149C43⋊#95—22no—
150C43⋊#95—22no—
151C43⋊#95D414yescomplemented
152C43⋊#95D414yescomplemented
153C25×C43C2311yescharacteristic
154C23×C4×C43C2311yescharacteristic
155C23×C4×C43C2311yescharacteristic
156C23×C4×C43C2311yescharacteristic
157C23×C4×C43C2311yescharacteristic
158C23×C4×C43C2311yescharacteristic
159C23×C4×C43C2311yescharacteristic
160C2×C4⋊C4×C43—22no—
161C2×C4⋊C4×C43—22no—
162C2×C4⋊C4×C43—41no—
163C2×C22⋊C4×C43—22no—
164C2×C22⋊C4×C43—22no—
165C2×C22⋊C4×C43—22no—
166C2×C22⋊C4×C43—22no—
167C2×C22⋊C4×C43—22no—
168C2×C22⋊C4×C43—22no—
169C2×C22⋊C4×C43—22no—
170C2×C22⋊C4×C43—41no—
171C2×C22⋊C4×C43C2×C414yescomplemented
172#95×C43—22no—
173#95×C43—22no—
174#95×C43—22no—
175C24×C43—21no—
176C24×C43—21no—
177C24×C43—21no—
178C24×C43—21no—
179C24×C43—21no—
180C24×C43—21no—
181C24×C43—21no—
182C24×C43—21no—
183C24×C43—21no—
184C24×C43—21no—
185C24×C43—21no—
186C24×C43—21no—
187C24×C43C22×C412yes—
188C24×C43C2×D412yes—
189C24×C43C2×Q812yes—
190C24×C43C2411yescharacteristic
191C23×D43—21no—
192C23×D43—21no—
193C23×D43—21no—
194C23×D43—21no—
195C23×D43—21no—
196C23×D43—21no—
197C23×D43—21no—
198C23×D43—21no—
199C23×D43—21no—
200C23×D43—21no—
201C23×D43—21no—
202C23×D43—21no—
203C23×D43C22×C412yes—
204C23×D43C2×D412yes—
205C23×D43C2×Q812yes—
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—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
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×C43C22×C412yes—
242C22×C4×C43C22×C412yes—
243C22×C4×C43C2×D412yes—
244C22×C4×C43C2×D412yes—
245C22×C4×C43C2×D412yes—
246C22×C4×C43C2×D412yes—
247C22×C4×C43#4112yes—
248C2×C22⋊D43—28no—
249C2×C22⋊D43—28no—
250C2×C22⋊D43—28no—
251C2×C22⋊D43—28no—
252C2×C22⋊D43—28no—
253C2×C22⋊D43—28no—
254C2×C22⋊D43C4⋊C4116yescomplemented
255C22×Dic43—28no—
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×Dic43—21no—
287C22×Dic43—21no—
288C22×Dic43—21no—
289C22×Dic43—44no—
290C22×Dic43—44no—
291C22×Dic43—44no—
292C22×Dic43—44no—
293C22×Dic43—44no—
294C22×Dic43—44no—
295C22×Dic43C22×C412yes—
296C22×Dic43C22×C412yes—
297C22×Dic43C22×C412yes—
298C22×Dic43C2×D412yes—
299C22×Dic43C2×D412yes—
300C22×Dic43C2×D412yes—
301C22×Dic43C2×D412yes—
302C22×Dic43C2×D412yes—
303C22×Dic43C2×D412yes—
304C22×Dic43C2×D412yes—
305C22×Dic43C2×D412yes—
306C22×Dic43C2×D412yes—
307C22×Dic43C2×Q812yes—
308C22×Dic43#4112yes—
309C22×Dic43#4112yes—
310C22×Dic43#4112yes—
311C2×C4×D43—28no—
312C2×C4×D43—44no—
313C2×C4×D43—44no—
314C2×C4×D43—44no—
315C2×C4×D43—44no—
316C2×C4×D43—44no—
317C2×C4×D43—44no—
318C4⋊C4×C43—44no—
319C22⋊C4×C43—28no—
320C22⋊C4×C43—28no—
321C22⋊C4×C43—44no—
322C22⋊Dic43—28no—
323C22⋊Dic43—44no—
324(C2×D43)⋊C4—28no—
325(C2×D43)⋊C4—28no—
326(C2×D43)⋊C4—28no—
327(C2×D43)⋊C4—44no—
328(C2×D43)⋊C4—44no—
329C4⋊Dic43—44no—
330C4⋊Dic43—44no—
331Dic43⋊C4—28no—
332Dic43⋊C4—28no—
333Dic43⋊C4—44no—
334Dic43⋊C4—44no—
335Dic43⋊C4—44no—
336Dic43⋊C4—44no—
337C4×Dic43—28no—
338C4×Dic43—28no—
339C4×Dic43—44no—
340C23×C43—22no—
341C23×C43—22no—
342C23×C43—22no—
343C23×C43—22no—
344C23×C43—22no—
345C23×C43—22no—
346C23×C43—22no—
347C23×C43—22no—
348C23×C43—22no—
349C23×C43—22no—
350C23×C43—22no—
351C23×C43—22no—
352C23×C43—22no—
353C23×C43—22no—
354C23×C43—22no—
355C23×C43—22no—
356C23×C43—22no—
357C23×C43—22no—
358C23×C43—41no—
359C23×C43—41no—
360C23×C43—41no—
361C23×C43—41no—
362C23×C43—41no—
363C23×C43—41no—
364C23×C43—41no—
365C23×C43—41no—
366C23×C43—41no—
367C23×C43—41no—
368C23×C43—41no—
369C23×C43—41no—
370C23×C43—41no—
371C23×C43—41no—
372C23×C43—41no—
373C23×C43—41no—
374C23×C43C2×C4⋊C414yes—
375C23×C43C23×C411yescharacteristic
376C23×C43C22×D411yescharacteristic
377C23×C43C22×D411yescharacteristic
378C23×C43C22×D411yescharacteristic
379C23×C43C22×D411yescharacteristic
380C23×C43C22×D411yescharacteristic
381C23×C43C22×Q811yescharacteristic
382C23×C43C2×#4111yescharacteristic
383C23×C43C2×#4111yescharacteristic
384C23×C43C2×#4111yescharacteristic
385C23×C43C2×#4111yescharacteristic
386C23×C43H(5,𝔽2)11yescharacteristic
387C23×C43H(5,𝔽2)11yescharacteristic
388C23×C432−1+411yescharacteristic
389C23×C432−1+411yescharacteristic
390C22×D43—22no—
391C22×D43—22no—
392C22×D43—22no—
393C22×D43—22no—
394C22×D43—22no—
395C22×D43—22no—
396C22×D43—22no—
397C22×D43—22no—
398C22×D43—22no—
399C22×D43—22no—
400C22×D43—22no—
401C22×D43—22no—
402C22×D43—22no—
403C22×D43—22no—
404C22×D43—22no—
405C22×D43—22no—
406C22×D43—22no—
407C22×D43—22no—
408C22×D43—41no—
409C22×D43—41no—
410C22×D43—41no—
411C22×D43—41no—
412C22×D43—41no—
413C22×D43—41no—
414C22×D43—41no—
415C22×D43—41no—
416C22×D43—41no—
417C22×D43—41no—
418C22×D43—41no—
419C22×D43—41no—
420C22×D43—41no—
421C22×D43—41no—
422C22×D43—41no—
423C22×D43—41no—
424C22×D43C2×C4⋊C414yes—
425C2×C4×C43—22no—
426C2×C4×C43—22no—
427C2×C4×C43—22no—
428C2×C4×C43—22no—
429C2×C4×C43—22no—
430C2×C4×C43—22no—
431C2×C4×C43—22no—
432C2×C4×C43—22no—
433C2×C4×C43—22no—
434C2×C4×C43—22no—
435C2×C4×C43—22no—
436C2×C4×C43—22no—
437C2×C4×C43—22no—
438C2×C4×C43—22no—
439C2×C4×C43—22no—
440C2×C4×C43—22no—
441C2×C4×C43—22no—
442C2×C4×C43—22no—
443C2×C4×C43—41no—
444C2×C4×C43—41no—
445C2×C4×C43—41no—
446C2×C4×C43—41no—
447C2×C4×C43—41no—
448C2×C4×C43—41no—
449C2×C4×C43—41no—
450C2×C4×C43—41no—
451C2×C4×C43—41no—
452C2×C4×C43—41no—
453C2×C4×C43—41no—
454C2×C4×C43—41no—
455C2×C4×C43—41no—
456C2×C4×C43—41no—
457C2×C4×C43—41no—
458C2×C4×C43—41no—
459C2×C4×C43—41no—
460C2×C4×C43—41no—
461C2×C4×C43—41no—
462C2×C4×C43—41no—
463C2×C4×C43—41no—
464C2×C4×C43—41no—
465C2×C4×C43—41no—
466C2×C4×C43C4×D414yescomplemented
467C22⋊D43—232no—
468C2×Dic43—22no—
469C2×Dic43—22no—
470C2×Dic43—22no—
471C2×Dic43—22no—
472C2×Dic43—22no—
473C2×Dic43—22no—
474C2×Dic43—22no—
475C2×Dic43—22no—
476C2×Dic43—22no—
477C2×Dic43—22no—
478C2×Dic43—22no—
479C2×Dic43—22no—
480C2×Dic43—22no—
481C2×Dic43—22no—
482C2×Dic43—22no—
483C2×Dic43—22no—
484C2×Dic43—22no—
485C2×Dic43—22no—
486C2×Dic43—22no—
487C2×Dic43—22no—
488C2×Dic43—22no—
489C2×Dic43—416no—
490C2×Dic43—41no—
491C2×Dic43—41no—
492C2×Dic43—41no—
493C2×Dic43—41no—
494C2×Dic43—41no—
495C2×Dic43—41no—
496C2×Dic43—41no—
497C2×Dic43—41no—
498C2×Dic43—41no—
499C2×Dic43—41no—
500C2×Dic43—41no—
501C2×Dic43—41no—
502C2×Dic43—41no—
503C2×Dic43—41no—
504C2×Dic43—41no—
505C2×Dic43—41no—
506C2×Dic43—41no—
507C2×Dic43—41no—
508C2×Dic43—41no—
509C2×Dic43C2×C4⋊C414yes—
510C2×Dic43C4×D414yes—
511C2×Dic43C4×D414yes—
512C2×Dic43C4×D414yescomplemented
513C2×Dic43#12014yes—
514C2×Dic43C22⋊Q814yes—
515C2×Dic43C22⋊Q814yes—
516C2×Dic43#12314yes—
517C2×Dic43#12714yes—
518C4×D43—416no—
519#13977—431nomaximal, Sylow
520C22×C43—24no—
521C22×C43—24no—
522C22×C43—24no—
523C22×C43—42no—
524C22×C43—42no—
525C22×C43—42no—
526C22×C43—42no—
527C22×C43—42no—
528C22×C43—42no—
529C22×C43—42no—
530C22×C43—42no—
531C22×C43—42no—
532C22×C43—42no—
533C22×C43—42no—
534C22×C43—42no—
535C22×C43C22×C4⋊C411yescharacteristic
536C22×C43C2×C4×D411yescharacteristic
537C22×C43C2×C4×D411yescharacteristic
538C22×C43C2×C4×D411yescharacteristic
539C22×C43C2×C4×D411yescharacteristic
540C22×C43#52011yescharacteristic
541C22×C43#52011yescharacteristic
542C22×C43C2×#12011yescharacteristic
543C22×C43C2×C22⋊Q811yescharacteristic
544C22×C43C2×C22⋊Q811yescharacteristic
545C22×C43C2×#12311yescharacteristic
546C22×C43C2×#12711yescharacteristic
547C22×C43#53211yescharacteristic
548C22×C43#53211yescharacteristic
549C22×C43#53211yescharacteristic
550C22×C43#53511yescharacteristic
551C22×C43#53611yescharacteristic
552C22×C43#54211yescharacteristic
553C22×C43#54211yescharacteristic
554C22×C43D4211yescharacteristic
555C22×C43D4211yescharacteristic
556C22×C43D4211yescharacteristic
557C22×C43D4211yescharacteristic
558C22×C43#54711yescharacteristic
559C22×C43#54711yescharacteristic
560C22×C43#54711yescharacteristic
561C22×C43#54711yescharacteristic
562C22×C43#54811yescharacteristic
563C22×C43#54811yescharacteristic
564C22×C43D4×Q811yescharacteristic
565C22×C43D4×Q811yescharacteristic
566C22×C43#55311yescharacteristic
567C22×C43#55311yescharacteristic
568C22×C43#55411yescharacteristic
569C22×C43#55411yescharacteristic
570C2×D43—24no—
571C2×D43—24no—
572C2×D43—24no—
573C2×D43—42no—
574C2×D43—42no—
575C2×D43—42no—
576C2×D43—42no—
577C2×D43—42no—
578C2×D43—42no—
579C2×D43—42no—
580C2×D43—42no—
581C2×D43—42no—
582C2×D43—42no—
583C2×D43—42no—
584C2×D43—42no—
585C4×C43—24no—
586C4×C43—42no—
587C4×C43—42no—
588C4×C43—42no—
589C4×C43—42no—
590C4×C43—81no—
591Dic43—24no—
592Dic43—24no—
593Dic43—42no—
594Dic43—42no—
595Dic43—42no—
596Dic43—81no—
597Dic43#38518yescomplemented
598C22×C4×D4—431no—
599C2×#390—431no—
600C2×#390—431no—
601C2×#389—431no—
602C2×#385—431no—
603C2×#385—431no—
604C2×#385—431no—
605C2×#385—431no—
606C2×#384—431no—
607#1439—431no—
608#1439—431no—
609#1439—431no—
610#1439D4311yescharacteristic, complemented
611C4⋊#95—431no—
612C4×#95—431no—
613C2×C43—44no—
614C2×C43C2×#38511yescharacteristic
615C2×C43C4×#12711yescharacteristic
616C2×C43#232611yescharacteristic
617C2×C43D4×C4⋊C411yescharacteristic
618C2×C43D4×C4⋊C411yescharacteristic
619C2×C43#236111yescharacteristic
620C2×C43#236111yescharacteristic
621C2×C43#242211yescharacteristic
622C2×C43#242211yescharacteristic
623C2×C43#243211yescharacteristic
624C2×C43#243311yescharacteristic
625C2×C43#245211yescharacteristic
626C2×C43#245211yescharacteristic
627C2×C43#254211yescharacteristic
628C2×C43#256611yescharacteristic
629D43—44no—
630C23×D4—431no—
631C24×C4—431no—
632C24×C4—431no—
633C2×C4×D4—864no—
634C2×C4×D4—864no—
635C2×C4×D4—864no—
636C22×C4⋊C4—431no—
637C22×C4⋊C4—431no—
638C22×C4⋊C4—431no—
639C22×C4⋊C4—431no—
640C22×C4⋊C4—431no—
641C22×C4⋊C4—431no—
642C22×C4⋊C4—431no—
643C22×C4⋊C4—431no—
644C22×C4⋊C4C2×D4311yescharacteristic
645C22×C22⋊C4—431no—
646C22×C22⋊C4—431no—
647C22×C22⋊C4—431no—
648C22×C22⋊C4—431no—
649C22×C22⋊C4—431no—
650C22×C22⋊C4—431no—
651C22×C22⋊C4—431no—
652C22×C22⋊C4C2×D4311yescharacteristic
653C22×C22⋊C4C2×D4311yescharacteristic
654C22×C22⋊C4C2×D4311yescharacteristic
655C22×C42—431no—
656C22×C42—431no—
657C22×C42—431no—
658#390—438no—
659#390—864no—
660#389—864no—
661#385—864no—
662#385—864no—
663#385—864no—
664#385—864no—
665#384—864no—
666C2×#95—431no—
667C2×#95—431no—
668C2×#95—431no—
669C2×#95—431no—
670C2×#95—431no—
671C2×#95—431no—
672C2×#95—431no—
673C2×#95C2×D4311yescharacteristic
674C2×#95C2×D4311yescharacteristic
675C2×#95C2×D4311yescharacteristic
676C43#1397711yescharacteristic, complemented, Sylow
677C25—431no—
678C25C22×D4311yescharacteristic
679C22×D4—434no—
680C22×D4—434no—
681C22×D4—434no—
682C22×D4—862no—
683C22×D4—862no—
684C22×D4—862no—
685C22×D4—862no—
686C23×C4—431no—
687C23×C4—431no—
688C23×C4—431no—
689C23×C4—431no—
690C23×C4—431no—
691C23×C4—431no—
692C23×C4—431no—
693C23×C4—862no—
694C23×C4—862no—
695C23×C4—862no—
696C23×C4—862no—
697C23×C4—862no—
698C23×C4—862no—
699C23×C4—862no—
700C23×C4—862no—
701C23×C4—862no—
702C23×C4—862no—
703C23×C4—1721no—
704C23×C4—1721no—
705C23×C4—1721no—
706C23×C4—1721no—
707C23×C4C22×D4311yescharacteristic
708C23×C4C22×D4311yescharacteristic
709C23×C4C22×D4311yescharacteristic
710C23×C4C22×D4311yescharacteristic
711C23×C4C22×D4311yescharacteristic
712C23×C4C22×D4311yescharacteristic
713C4×D4—8632no—
714C2×C4⋊C4—22no—
715C2×C4⋊C4—22no—
716C2×C4⋊C4—41no—
717C2×C4⋊C4—434no—
718C2×C4⋊C4—434no—
719C2×C4⋊C4—862no—
720C2×C4⋊C4—862no—
721C2×C4⋊C4—862no—
722C2×C4⋊C4—862no—
723C2×C4⋊C4—862no—
724C2×C4⋊C4—862no—
725C2×C4⋊C4—862no—
726C2×C4⋊C4—862no—
727C2×C4⋊C4—862no—
728C2×C4⋊C4—862no—
729C2×C4⋊C4—862no—
730C2×C4⋊C4—862no—
731C2×C4⋊C4—862no—
732C2×C4⋊C4—862no—
733C2×C4⋊C4—862no—
734C2×C4⋊C4—862no—
735C2×C4⋊C4—862no—
736C2×C4⋊C4—862no—
737C2×C4⋊C4—862no—
738C2×C4⋊C4—1721no—
739C2×C4⋊C4—1721no—
740C2×C4⋊C4—1721no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—41no—
749C2×C22⋊C4—434no—
750C2×C22⋊C4—434no—
751C2×C22⋊C4—434no—
752C2×C22⋊C4—862no—
753C2×C22⋊C4—862no—
754C2×C22⋊C4—862no—
755C2×C22⋊C4—862no—
756C2×C22⋊C4—862no—
757C2×C22⋊C4—862no—
758C2×C22⋊C4—862no—
759C2×C22⋊C4—862no—
760C2×C22⋊C4—862no—
761C2×C22⋊C4—862no—
762C2×C22⋊C4—862no—
763C2×C22⋊C4—862no—
764C2×C22⋊C4—862no—
765C2×C22⋊C4—862no—
766C2×C22⋊C4—862no—
767C2×C22⋊C4—1721no—
768C2×C22⋊C4—1721no—
769C2×C22⋊C4—1721no—
770C2×C22⋊C4C4×D4314yescomplemented
771C2×C42—434no—
772C2×C42—434no—
773C2×C42—862no—
774C2×C42—862no—
775C2×C42—862no—
776C2×C42—862no—
777C2×C42—862no—
778C2×C42—862no—
779C2×C42—862no—
780#95—22no—
781#95—22no—
782#95—22no—
783#95—434no—
784#95—434no—
785#95—862no—
786#95—862no—
787#95—862no—
788#95—862no—
789#95—862no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—21no—
800C24—21no—
801C24—21no—
802C24—432no—
803C24—432no—
804C24—432no—
805C24—861no—
806C24—861no—
807C24—861no—
808C24—861no—
809C24—861no—
810C24—861no—
811C24—861no—
812C24—861no—
813C24—861no—
814C24—861no—
815C24—861no—
816C24—861no—
817C24C2×C4×D4312yes—
818C24D4×D4312yes—
819C24Q8×D4312yes—
820C24C23×D4311yescharacteristic
821C2×D4—4316no—
822C2×D4—868no—
823C2×D4—868no—
824C2×D4—868no—
825C2×D4—868no—
826C2×D4—868no—
827C2×D4—868no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—432no—
864C22×C4—432no—
865C22×C4—432no—
866C22×C4—432no—
867C22×C4—432no—
868C22×C4—432no—
869C22×C4—432no—
870C22×C4—432no—
871C22×C4—432no—
872C22×C4—432no—
873C22×C4—432no—
874C22×C4—432no—
875C22×C4—432no—
876C22×C4—432no—
877C22×C4—432no—
878C22×C4—432no—
879C22×C4—868no—
880C22×C4—861no—
881C22×C4—861no—
882C22×C4—861no—
883C22×C4—861no—
884C22×C4—861no—
885C22×C4—861no—
886C22×C4—861no—
887C22×C4—861no—
888C22×C4—868no—
889C22×C4—861no—
890C22×C4—861no—
891C22×C4—861no—
892C22×C4—861no—
893C22×C4—861no—
894C22×C4—861no—
895C22×C4—861no—
896C22×C4—861no—
897C22×C4—861no—
898C22×C4—861no—
899C22×C4—861no—
900C22×C4—861no—
901C22×C4—861no—
902C22×C4—861no—
903C22×C4—861no—
904C22×C4—861no—
905C22×C4—861no—
906C22×C4—861no—
907C22×C4—861no—
908C22×C4—861no—
909C22×C4—861no—
910C22×C4—861no—
911C22×C4—861no—
912C22×C4—861no—
913C22×C4—861no—
914C22×C4—1724no—
915C22×C4—1724no—
916C22×C4—1724no—
917C22×C4—1724no—
918C22×C4—1724no—
919C22×C4—1724no—
920C22×C4—1724no—
921C22×C4—1724no—
922C22×C4—1724no—
923C22×C4—1724no—
924C22×C4—1724no—
925C22×C4—1724no—
926C22×C4C2×C4×D4312yes—
927C22×C4C2×C4×D4312yes—
928C22×C4D4×D4312yes—
929C22×C4D4×D4312yes—
930C22×C4D4×D4312yes—
931C22×C4D4×D4312yes—
932C22×C4#1062190012yes—
933C4⋊C4—44no—
934C4⋊C4—868no—
935C4⋊C4—868no—
936C4⋊C4—1724no—
937C4⋊C4—1724no—
938C4⋊C4—1724no—
939C4⋊C4—1724no—
940C4⋊C4—1724no—
941C4⋊C4—1724no—
942C22⋊C4—28no—
943C22⋊C4—28no—
944C22⋊C4—44no—
945C22⋊C4—868no—
946C22⋊C4—868no—
947C22⋊C4—868no—
948C22⋊C4—868no—
949C22⋊C4—1724no—
950C22⋊C4—1724no—
951C22⋊C4—1724no—
952C42—868no—
953C42—868no—
954C42—1724no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—434no—
990C23—862no—
991C23—862no—
992C23—862no—
993C23—862no—
994C23—862no—
995C23—862no—
996C23—862no—
997C23—862no—
998C23—862no—
999C23—862no—
1000C23—862no—
1001C23—862no—
1002C23—862no—
1003C23—862no—
1004C23—862no—
1005C23—862no—
1006C23—862no—
1007C23—862no—
1008C23—1721no—
1009C23—1721no—
1010C23—1721no—
1011C23—1721no—
1012C23—1721no—
1013C23—1721no—
1014C23—1721no—
1015C23—1721no—
1016C23—1721no—
1017C23—1721no—
1018C23—1721no—
1019C23—1721no—
1020C23—1721no—
1021C23—1721no—
1022C23—1721no—
1023C23—1721no—
1024C23C4⋊C4×D4314yes—
1025C23C22×C4×D4311yescharacteristic
1026C23C2×D4×D4311yescharacteristic
1027C23C2×D4×D4311yescharacteristic
1028C23C2×D4×D4311yescharacteristic
1029C23C2×D4×D4311yescharacteristic
1030C23C2×D4×D4311yescharacteristic
1031C23C2×Q8×D4311yescharacteristic
1032C23#41×D4311yescharacteristic
1033C23#41×D4311yescharacteristic
1034C23#41×D4311yescharacteristic
1035C23C2×#1062190011yescharacteristic
1036C23#1306337011yescharacteristic
1037C23#1306337111yescharacteristic
1038C23#1306337211yescharacteristic
1039C23#1306337211yescharacteristic
1040D4—8632no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—434no—
1083C2×C4—434no—
1084C2×C4—434no—
1085C2×C4—434no—
1086C2×C4—434no—
1087C2×C4—434no—
1088C2×C4—434no—
1089C2×C4—434no—
1090C2×C4—434no—
1091C2×C4—862no—
1092C2×C4—862no—
1093C2×C4—862no—
1094C2×C4—862no—
1095C2×C4—862no—
1096C2×C4—862no—
1097C2×C4—862no—
1098C2×C4—862no—
1099C2×C4—862no—
1100C2×C4—862no—
1101C2×C4—862no—
1102C2×C4—862no—
1103C2×C4—862no—
1104C2×C4—862no—
1105C2×C4—862no—
1106C2×C4—862no—
1107C2×C4—862no—
1108C2×C4—862no—
1109C2×C4—862no—
1110C2×C4—862no—
1111C2×C4—862no—
1112C2×C4—17216no—
1113C2×C4—17216no—
1114C2×C4—1721no—
1115C2×C4—1721no—
1116C2×C4—1721no—
1117C2×C4—1721no—
1118C2×C4—1721no—
1119C2×C4—1721no—
1120C2×C4—1721no—
1121C2×C4—1721no—
1122C2×C4—1721no—
1123C2×C4—1721no—
1124C2×C4—1721no—
1125C2×C4—1721no—
1126C2×C4—1721no—
1127C2×C4—1721no—
1128C2×C4—1721no—
1129C2×C4—1721no—
1130C2×C4—1721no—
1131C2×C4—1721no—
1132C2×C4—1721no—
1133C2×C4(C22⋊D43)⋊C414yescomplemented
1134C22—24no—
1135C22—24no—
1136C22—24no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—42no—
1148C22—42no—
1149C22—864no—
1150C22—864no—
1151C22—864no—
1152C22—1722no—
1153C22—1722no—
1154C22—1722no—
1155C22—1722no—
1156C22—1722no—
1157C22—1722no—
1158C22—1722no—
1159C22—1722no—
1160C22—1722no—
1161C22—1722no—
1162C22—1722no—
1163C22—1722no—
1164C22C2×C4⋊C4×D4311yescharacteristic
1165C22C4×D4×D4311yescharacteristic
1166C22C4×D4×D4311yescharacteristic
1167C22C4×D4×D4311yescharacteristic
1168C22C2×(C22⋊D43)⋊C411yescharacteristic
1169C22#1458337811yescharacteristic
1170C22#1458337911yescharacteristic
1171C22#120×D4311yescharacteristic
1172C22C22⋊Q8×D4311yescharacteristic
1173C22C22⋊Q8×D4311yescharacteristic
1174C22#123×D4311yescharacteristic
1175C22#127×D4311yescharacteristic
1176C22#1458344411yescharacteristic
1177C22#1458344411yescharacteristic
1178C22#1458344811yescharacteristic
1179C22#1458346511yescharacteristic
1180C22#1458347111yescharacteristic
1181C22#1458351311yescharacteristic
1182C22#1458351511yescharacteristic
1183C22#1458353111yescharacteristic
1184C22#1458353111yescharacteristic
1185C22#1458353311yescharacteristic
1186C22#1458353311yescharacteristic
1187C22#1458354711yescharacteristic
1188C22#1458354711yescharacteristic
1189C22#1458354711yescharacteristic
1190C22#1458354911yescharacteristic
1191C22#1458355511yescharacteristic
1192C22#1458355711yescharacteristic
1193C22#1458356211yescharacteristic
1194C22#1458356211yescharacteristic
1195C22#1458359211yescharacteristic
1196C22#1458360011yescharacteristic
1197C22#1458360311yescharacteristic
1198C22#1458360711yescharacteristic
1199C4—24no—
1200C4—42no—
1201C4—42no—
1202C4—42no—
1203C4—42no—
1204C4—81no—
1205C4—438no—
1206C4—864no—
1207C4—864no—
1208C4—3441no—
1209C4—1722no—
1210C4—1722no—
1211C4—1722no—
1212C2—44no—
1213C2—1724no—
1214C2#385×D4311yescharacteristic
1215C2#1913715911yescharacteristic
1216C2#1913730411yescharacteristic
1217C2#1913749111yescharacteristic
1218C2#1913749311yescharacteristic
1219C2#1913760611yescharacteristic
1220C2#1913760811yescharacteristic
1221C2#1913810211yescharacteristic
1222C2#1913810411yescharacteristic
1223C2#1913821811yescharacteristic
1224C2#1913822711yescharacteristic
1225C2#1913843811yescharacteristic
1226C2#1913844011yescharacteristic
1227C2#1913954311yescharacteristic
1228C2#1913979011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1439C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenter#1439D43
hypocenterC43#13977
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
4. C2×#14582796C2semidirect
5. C2×#14582774C2semidirect
6. C2×#14582773C2semidirect
7. C2×#14582771C2semidirect
8. C2×#14582770C2semidirect
9. C2×#14582768C2semidirect
10. #19132841C2semidirect
11. #19132839C2semidirect
12. #19132838C2semidirect
13. Dic43⋊#95C2semidirect
14. #95×Dic43C2semidirect
15. C43×#1439C2semidirect
41. #14582799C4semidirect
114. C2×Dic43⋊C4C2×C4semidirect
121. C2×C22⋊Dic43C2×C4semidirect
135. C2×(C2×D43)⋊C4C2×C4semidirect
136. C2×(C2×D43)⋊C4C2×C4semidirect
144. C2×C4×Dic43C2×C4semidirect
151. C43⋊#95D4semidirect
152. C43⋊#95D4semidirect
171. C2×C22⋊C4×C43C2×C4semidirect
254. C2×C22⋊D43C4⋊C4semidirect
466. C2×C4×C43C4×D4semidirect
512. C2×Dic43C4×D4semidirect
597. Dic43#385semidirect
610. #1439D43semidirect
676. C43#13977semidirect
770. C2×C22⋊C4C4×D43semidirect
1133. C2×C4(C22⋊D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D43)⋊C42
C2×#145827992
C2×#145827962
C2×#145827742
C2×#145827732
C2×#145827712
C2×#145827702
C2×#145827682
#191328412
#191328392
#191328382
Dic43⋊#952
#95×Dic432
C43×#14392
#1397743