Finite Group Databasebeta

← #25018639

Subgroups — #25018639

Order 11008.

2330 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2C2×#14582792C211yesmaximal, characteristic, complemented
3C2×#14582760C211yesmaximal, characteristic, complemented
4C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
5#19132841C211yesmaximal, characteristic, complemented
6#19132837C211yesmaximal, characteristic, complemented
7#19132834C211yesmaximal, characteristic
8#19132834C211yesmaximal, characteristic
9#19132830C211yesmaximal, characteristic, complemented
10#19132828C211yesmaximal, characteristic, complemented
11#19132824C211yesmaximal, characteristic, complemented
12#19132819C211yesmaximal, characteristic, complemented
13#19132817C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C2×C43×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C24×Dic43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C2×(C22⋊D43)⋊C4—24no—
20C2×(C22⋊D43)⋊C4—24no—
21C2×(C22⋊D43)⋊C4C418yescomplemented
22C22×C4⋊Dic43C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×C22⋊Dic43C2211yescharacteristic
25C22×C22⋊Dic43C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33#14582792—24no—
34#14582760—24no—
35C4×(C2×D43)⋊C4—24no—
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
50C22×C4⋊C4×C43C2211yescharacteristic
51C22×C22⋊C4×C43C2211yescharacteristic
52C22×C22⋊C4×C43C2211yescharacteristic
53C22×C22⋊C4×C43C2211yescharacteristic
54C22×C42×C43C2211yescharacteristic
55C43×#388—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—22no—
64C22×C22⋊D43—22no—
65C22×C22⋊D43C2×C414yes—
66C23×Dic43—22no—
67C23×Dic43—22no—
68C23×Dic43—22no—
69C23×Dic43—22no—
70C23×Dic43—41no—
71C23×Dic43—41no—
72C23×Dic43C2×C414yes—
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C22×C4×D43—22no—
81C22×C4×D43—22no—
82C22×C4×D43—22no—
83C22×C4×D43—22no—
84C22×C4×D43—41no—
85C22×C4×D43—41no—
86C22×C4×D43C2×C414yes—
87(C22⋊D43)⋊C4—232no—
88C2×C4⋊Dic43—22no—
89C2×C4⋊Dic43—22no—
90C2×C4⋊Dic43—41no—
91C2×Dic43⋊C4—22no—
92C2×Dic43⋊C4—22no—
93C2×Dic43⋊C4C2×C414yes—
94C2×C22⋊Dic43—22no—
95C2×C22⋊Dic43—22no—
96C2×C22⋊Dic43—22no—
97C2×C22⋊Dic43—22no—
98C2×C22⋊Dic43—41no—
99C2×C22⋊Dic43—41no—
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—22no—
108C2×(C2×D43)⋊C4—22no—
109C2×(C2×D43)⋊C4—22no—
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×C4×Dic43—22no—
116C2×C4×Dic43—22no—
117C2×C4×Dic43—22no—
118C2×C4×Dic43—22no—
119C2×C4×Dic43—41no—
120C2×C4×Dic43C2×C414yes—
121C43⋊#95—22no—
122C43⋊#95—22no—
123C43⋊#95—22no—
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—41no—
133C43⋊#95—41no—
134C43⋊#95D414yescomplemented
135C25×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43—22no—
143C2×C4⋊C4×C43—22no—
144C2×C4⋊C4×C43—41no—
145C2×C22⋊C4×C43—22no—
146C2×C22⋊C4×C43—22no—
147C2×C22⋊C4×C43—22no—
148C2×C22⋊C4×C43—22no—
149C2×C22⋊C4×C43—41no—
150C2×C22⋊C4×C43—41no—
151C2×C22⋊C4×C43C2×C414yes—
152C2×C22⋊C4×C43D414yes—
153C2×C22⋊C4×C43D414yes—
154C2×C42×C43—22no—
155C2×C42×C43—22no—
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×C43C2×D412yes—
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×D43C22×C412yes—
188C23×D43#4112yes—
189C23×D43#4112yes—
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×C43—21no—
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×C43C2×D412yes—
231C22×C4×C43#4112yes—
232C2×C22⋊D43—28no—
233C2×C22⋊D43—28no—
234C2×C22⋊D43—28no—
235C2×C22⋊D43—28no—
236C2×C22⋊D43—28no—
237C2×C22⋊D43—28no—
238C2×C22⋊D43—28no—
239C22×Dic43—28no—
240C22×Dic43—28no—
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×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—44no—
282C22×Dic43—44no—
283C22×Dic43—44no—
284C22×Dic43—44no—
285C22×Dic43—44no—
286C22×Dic43C22×C412yes—
287C22×Dic43C22×C412yes—
288C22×Dic43C22×C412yes—
289C22×Dic43C2×D412yes—
290C22×Dic43C2×D412yes—
291C22×Dic43#4112yes—
292C22×Dic43#4112yes—
293C22×Dic43#4112yes—
294C22×Dic43#4112yes—
295C2×C4×D43—28no—
296C2×C4×D43—28no—
297C2×C4×D43—44no—
298C2×C4×D43—44no—
299C2×C4×D43—44no—
300C2×C4×D43—44no—
301C2×C4×D43—44no—
302C4⋊C4×C43—44no—
303C22⋊C4×C43—44no—
304C22⋊C4×C43—44no—
305C22⋊C4×C43C22⋊C4116yescomplemented
306C42×C43—44no—
307C22⋊Dic43—44no—
308C22⋊Dic43—44no—
309(C2×D43)⋊C4—28no—
310(C2×D43)⋊C4—28no—
311(C2×D43)⋊C4—28no—
312(C2×D43)⋊C4—44no—
313(C2×D43)⋊C4—44no—
314C4⋊Dic43—44no—
315Dic43⋊C4—28no—
316C4×Dic43—28no—
317C4×Dic43—44no—
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—22no—
333C23×C43—22no—
334C23×C43—22no—
335C23×C43—22no—
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×C43—41no—
349C23×C43—41no—
350C23×C43—41no—
351C23×C43—41no—
352C23×C43C2×C22⋊C414yes—
353C23×C43C23×C411yescharacteristic
354C23×C43C22×D411yescharacteristic
355C23×C43C22×D411yescharacteristic
356C23×C43C22×D411yescharacteristic
357C23×C43C2×#4111yescharacteristic
358C23×C43C2×#4111yescharacteristic
359C23×C43C2×#4111yescharacteristic
360C23×C43C2×#4111yescharacteristic
361C23×C43C2×#4111yescharacteristic
362C23×C43C2×#4111yescharacteristic
363C23×C43C2×#4111yescharacteristic
364C23×C43H(5,𝔽2)11yescharacteristic
365C23×C43H(5,𝔽2)11yescharacteristic
366C23×C43H(5,𝔽2)11yescharacteristic
367C23×C432−1+411yescharacteristic
368C22×D43—22no—
369C22×D43—22no—
370C22×D43—22no—
371C22×D43—22no—
372C22×D43—22no—
373C22×D43—22no—
374C22×D43—22no—
375C22×D43—22no—
376C22×D43—22no—
377C22×D43—22no—
378C22×D43—22no—
379C22×D43—22no—
380C22×D43—22no—
381C22×D43—22no—
382C22×D43—22no—
383C22×D43—22no—
384C22×D43—22no—
385C22×D43—22no—
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—
399C22×D43—41no—
400C22×D43—41no—
401C22×D43—41no—
402C22×D43#11714yes—
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—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×C43—41no—
443C2×C4×C43C2×C22⋊C414yes—
444C2×C4×C43C2×C22⋊C414yes—
445C22⋊D43—232no—
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—22no—
465C2×Dic43—22no—
466C2×Dic43—22no—
467C2×Dic43—416no—
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×Dic43—41no—
491C2×Dic43—41no—
492C2×Dic43—41no—
493C2×Dic43—41no—
494C2×Dic43#11714yes—
495C2×Dic43C4×D414yes—
496C4×D43—416no—
497#13886—431nomaximal, Sylow
498C22×C43—24no—
499C22×C43—24no—
500C22×C43—24no—
501C22×C43—42no—
502C22×C43—42no—
503C22×C43—42no—
504C22×C43—42no—
505C22×C43—42no—
506C22×C43—42no—
507C22×C43—42no—
508C22×C43—42no—
509C22×C43—42no—
510C22×C43—42no—
511C22×C43—42no—
512C22×C43—42no—
513C22×C43C22×C22⋊C411yescharacteristic
514C22×C43C2×#11711yescharacteristic
515C22×C43C2×#11711yescharacteristic
516C22×C43C2×C4×D411yescharacteristic
517C22×C43C4×#4111yescharacteristic
518C22×C43#51811yescharacteristic
519C22×C43#52011yescharacteristic
520C22×C43#52511yescharacteristic
521C22×C43#52511yescharacteristic
522C22×C43#52511yescharacteristic
523C22×C43#52511yescharacteristic
524C22×C43#52511yescharacteristic
525C22×C43#52511yescharacteristic
526C22×C43#52911yescharacteristic
527C22×C43#52911yescharacteristic
528C22×C43#53811yescharacteristic
529C22×C43#53811yescharacteristic
530C22×C43#53911yescharacteristic
531C22×C43#53911yescharacteristic
532C22×C43D4211yescharacteristic
533C22×C43D4211yescharacteristic
534C22×C43#54611yescharacteristic
535C22×C43#54611yescharacteristic
536C22×C43#54611yescharacteristic
537C22×C43#54611yescharacteristic
538C22×C43#54711yescharacteristic
539C22×C43#54711yescharacteristic
540C22×C43#54711yescharacteristic
541C22×C43#55011yescharacteristic
542C22×C43#55311yescharacteristic
543C22×C43#55311yescharacteristic
544C22×C43#55511yescharacteristic
545C22×C43#55611yescharacteristic
546C22×C43#55911yescharacteristic
547C22×C43#55911yescharacteristic
548C2×D43—24no—
549C2×D43—24no—
550C2×D43—24no—
551C2×D43—42no—
552C2×D43—42no—
553C2×D43—42no—
554C2×D43—42no—
555C2×D43—42no—
556C2×D43—42no—
557C2×D43—42no—
558C2×D43—42no—
559C2×D43—42no—
560C2×D43—42no—
561C2×D43—42no—
562C2×D43—42no—
563C4×C43—24no—
564C4×C43—24no—
565C4×C43—42no—
566C4×C43—42no—
567C4×C43—81no—
568C4×C43—81no—
569Dic43—24no—
570Dic43—24no—
571Dic43—42no—
572Dic43—42no—
573Dic43—42no—
574Dic43—81no—
575Dic43—81no—
576C22×C4×D4—431no—
577C2×#388—431no—
578C2×#388D4311yescharacteristic, complemented
579C2×#381—431no—
580C2×C4×C22⋊C4—431no—
581#1439—431no—
582#1439—431no—
583#1438—431no—
584#1438—431no—
585#1436—431no—
586#1436—431no—
587C4⋊#95—431no—
588#1434—431no—
589C22⋊#95—431no—
590C22⋊#95—431no—
591C2×C43—44no—
592C2×C43#228011yescharacteristic
593C2×C43#229011yescharacteristic
594C2×C43#231811yescharacteristic
595C2×C43D4×C22⋊C411yescharacteristic
596C2×C43#233911yescharacteristic
597C2×C43#235411yescharacteristic
598C2×C43#235711yescharacteristic
599C2×C43#245511yescharacteristic
600C2×C43#245511yescharacteristic
601C2×C43#245611yescharacteristic
602C2×C43#245611yescharacteristic
603C2×C43#245911yescharacteristic
604C2×C43#245911yescharacteristic
605C2×C43#246611yescharacteristic
606C2×C43#246611yescharacteristic
607D43—44no—
608C23×D4—431no—
609C24×C4—431no—
610C24×C4—431no—
611C2×C4×D4—438no—
612C2×C4×D4—864no—
613C2×C4×D4—864no—
614C22×C4⋊C4—431no—
615C22×C4⋊C4—431no—
616C22×C4⋊C4C2×D4311yescharacteristic
617C22×C22⋊C4—431no—
618C22×C22⋊C4—431no—
619C22×C22⋊C4—431no—
620C22×C22⋊C4—431no—
621C22×C22⋊C4—431no—
622C22×C22⋊C4—431no—
623C22×C22⋊C4—431no—
624C22×C22⋊C4C2×D4311yescharacteristic
625C22×C22⋊C4C2×D4311yescharacteristic
626C22×C22⋊C4C2×D4311yescharacteristic
627C22×C42—431no—
628C22×C42—431no—
629C22×C42C2×D4311yescharacteristic
630#388—24no—
631#388—864no—
632#381—864no—
633C4×C22⋊C4—864no—
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×#95—431no—
644C2×#95—431no—
645C2×#95—431no—
646C2×#95—431no—
647C2×#95—431no—
648C2×#95C2×D4311yescharacteristic
649C2×#95C2×D4311yescharacteristic
650C43#1388611yescharacteristic, complemented, Sylow
651C25—431no—
652C25C22×D4311yescharacteristic
653C22×D4—434no—
654C22×D4—862no—
655C22×D4—862no—
656C22×D4—862no—
657C22×D4—862no—
658C22×D4—862no—
659C22×D4—862no—
660C23×C4—431no—
661C23×C4—431no—
662C23×C4—431no—
663C23×C4—431no—
664C23×C4—431no—
665C23×C4—434no—
666C23×C4—434no—
667C23×C4—431no—
668C23×C4—431no—
669C23×C4—862no—
670C23×C4—862no—
671C23×C4—862no—
672C23×C4—862no—
673C23×C4—862no—
674C23×C4—862no—
675C23×C4—862no—
676C23×C4—862no—
677C23×C4—1721no—
678C23×C4—1721no—
679C23×C4—1721no—
680C23×C4—1721no—
681C23×C4C22×D4311yescharacteristic
682C23×C4C22×D4311yescharacteristic
683C23×C4C22×D4311yescharacteristic
684C23×C4C22×D4311yescharacteristic
685C23×C4C22×D4311yescharacteristic
686C23×C4C22×D4311yescharacteristic
687C4×D4—8632no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—41no—
691C2×C4⋊C4—434no—
692C2×C4⋊C4—862no—
693C2×C4⋊C4—862no—
694C2×C4⋊C4—862no—
695C2×C4⋊C4—862no—
696C2×C4⋊C4—1721no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—434no—
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—862no—
715C2×C22⋊C4—862no—
716C2×C22⋊C4—862no—
717C2×C22⋊C4—862no—
718C2×C22⋊C4—1721no—
719C2×C22⋊C4—1721no—
720C2×C22⋊C4—1721no—
721C2×C22⋊C4—1721no—
722C2×C22⋊C4—1721no—
723C2×C22⋊C4—1721no—
724C2×C22⋊C4C4×D4314yes—
725C2×C22⋊C4D17214yes—
726C2×C22⋊C4C22⋊D4314yes—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—41no—
730C2×C42—434no—
731C2×C42—862no—
732C2×C42—862no—
733C2×C42—862no—
734C2×C42—862no—
735C2×C42—1721no—
736#95—22no—
737#95—22no—
738#95—434no—
739#95—862no—
740#95—862no—
741#95—862no—
742#95—862no—
743#95—862no—
744#95—862no—
745#95—862no—
746#95—862no—
747#95—862no—
748#95—862no—
749#95—862no—
750#95—1721no—
751#95—1721no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—432no—
765C24—432no—
766C24—432no—
767C24—861no—
768C24—861no—
769C24—861no—
770C24—861no—
771C24—861no—
772C24—861no—
773C24—861no—
774C24—861no—
775C24—861no—
776C24—861no—
777C24—861no—
778C24—861no—
779C24C2×C4×D4312yes—
780C24C2×D17212yes—
781C24C2×C22⋊D4312yes—
782C24C23×D4311yescharacteristic
783C2×D4—868no—
784C2×D4—868no—
785C2×D4—868no—
786C2×D4—868no—
787C2×D4—868no—
788C2×D4—868no—
789C2×D4—868no—
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—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
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—868no—
834C22×C4—868no—
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—868no—
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—868no—
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×C4—861no—
874C22×C4—861no—
875C22×C4—861no—
876C22×C4—861no—
877C22×C4—1724no—
878C22×C4—1724no—
879C22×C4—1724no—
880C22×C4—1724no—
881C22×C4—1724no—
882C22×C4—1724no—
883C22×C4—1724no—
884C22×C4—1724no—
885C22×C4—1724no—
886C22×C4—1724no—
887C22×C4C2×C4×D4312yes—
888C22×C4C2×C4×D4312yes—
889C22×C4C2×D17212yes—
890C22×C4C2×D17212yes—
891C22×C4D4×D4312yes—
892C22×C4#1062190012yes—
893C22×C4C2×C22⋊D4312yes—
894C22×C4C2×C22⋊D4312yes—
895C4⋊C4—44no—
896C4⋊C4—868no—
897C4⋊C4—1724no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—868no—
901C22⋊C4—868no—
902C22⋊C4—868no—
903C22⋊C4—1724no—
904C22⋊C4—1724no—
905C22⋊C4—1724no—
906C22⋊C4—1724no—
907C22⋊C4(C2×D43)⋊C4116yescomplemented
908C42—44no—
909C42—868no—
910C42—1724no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—434no—
946C23—862no—
947C23—862no—
948C23—862no—
949C23—862no—
950C23—862no—
951C23—862no—
952C23—862no—
953C23—862no—
954C23—862no—
955C23—862no—
956C23—862no—
957C23—862no—
958C23—862no—
959C23—862no—
960C23—862no—
961C23—862no—
962C23—862no—
963C23—862no—
964C23—1721no—
965C23—1721no—
966C23—1721no—
967C23—1721no—
968C23—1721no—
969C23—1721no—
970C23—1721no—
971C23—1721no—
972C23—1721no—
973C23—1721no—
974C23—1721no—
975C23—1721no—
976C23—1721no—
977C23—1721no—
978C23—1721no—
979C23—1721no—
980C23C2×(C2×D43)⋊C414yes—
981C23C22×C4×D4311yescharacteristic
982C23C2×D4×D4311yescharacteristic
983C23C22×C22⋊D4311yescharacteristic
984C23C22×D17211yescharacteristic
985C23#41×D4311yescharacteristic
986C23#41×D4311yescharacteristic
987C23#41×D4311yescharacteristic
988C23#41×D4311yescharacteristic
989C23#41×D4311yescharacteristic
990C23#41×D4311yescharacteristic
991C23C2×#1062190011yescharacteristic
992C23#1306337011yescharacteristic
993C23#1306337011yescharacteristic
994C23#1306337111yescharacteristic
995C23#1306337211yescharacteristic
996D4—8632no—
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—22no—
1013C2×C4—22no—
1014C2×C4—22no—
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—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—434no—
1038C2×C4—434no—
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—862no—
1053C2×C4—862no—
1054C2×C4—862no—
1055C2×C4—862no—
1056C2×C4—862no—
1057C2×C4—862no—
1058C2×C4—862no—
1059C2×C4—862no—
1060C2×C4—17216no—
1061C2×C4—17216no—
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×C4—1721no—
1079C2×C4—1721no—
1080C2×C4—1721no—
1081C2×C4—1721no—
1082C2×C4—1721no—
1083C2×C4—1721no—
1084C2×C4—1721no—
1085C2×C4—1721no—
1086C2×C4—1721no—
1087C2×C4—1721no—
1088C2×C4C2×(C2×D43)⋊C414yes—
1089C2×C4C2×(C2×D43)⋊C414yes—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—864no—
1106C22—864no—
1107C22—864no—
1108C22—1722no—
1109C22—1722no—
1110C22—1722no—
1111C22—1722no—
1112C22—1722no—
1113C22—1722no—
1114C22—1722no—
1115C22—1722no—
1116C22—1722no—
1117C22—1722no—
1118C22—1722no—
1119C22—1722no—
1120C22C22×(C2×D43)⋊C411yescharacteristic
1121C22#117×D4311yescharacteristic
1122C22#117×D4311yescharacteristic
1123C22C4×D4×D4311yescharacteristic
1124C22C4×#1062190011yescharacteristic
1125C22#1458337111yescharacteristic
1126C22#1458337811yescharacteristic
1127C22#1458340611yescharacteristic
1128C22#1458340611yescharacteristic
1129C22#1458340711yescharacteristic
1130C22#1458340911yescharacteristic
1131C22#1458341111yescharacteristic
1132C22#1458341111yescharacteristic
1133C22#1458342811yescharacteristic
1134C22#1458343211yescharacteristic
1135C22#1458348111yescharacteristic
1136C22#1458348311yescharacteristic
1137C22#1458349011yescharacteristic
1138C22#1458349211yescharacteristic
1139C22D4×C22⋊D4311yescharacteristic
1140C22D4×D17211yescharacteristic
1141C22#1458353711yescharacteristic
1142C22#1458354311yescharacteristic
1143C22#1458354411yescharacteristic
1144C22#1458354411yescharacteristic
1145C22#1458354711yescharacteristic
1146C22#1458354811yescharacteristic
1147C22#1458355311yescharacteristic
1148C22#1458356711yescharacteristic
1149C22#1458359211yescharacteristic
1150C22#1458360011yescharacteristic
1151C22#1458361111yescharacteristic
1152C22#1458361611yescharacteristic
1153C22#1458363111yescharacteristic
1154C22#1458363311yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—42no—
1158C4—42no—
1159C4—81no—
1160C4—81no—
1161C4—864no—
1162C4—864no—
1163C4—3441no—
1164C4—3441no—
1165C4—1722no—
1166C4—1722no—
1167C4—1722no—
1168C2—44no—
1169C2—1724no—
1170C2#1913697411yescharacteristic
1171C2#1913703711yescharacteristic
1172C2#1913722511yescharacteristic
1173C2D4×(C2×D43)⋊C411yescharacteristic
1174C2#1913742011yescharacteristic
1175C2#1913754111yescharacteristic
1176C2#1913756511yescharacteristic
1177C2#1913847411yescharacteristic
1178C2#1913847511yescharacteristic
1179C2#1913848411yescharacteristic
1180C2#1913849211yescharacteristic
1181C2#1913852811yescharacteristic
1182C2#1913853011yescharacteristic
1183C2#1913862711yescharacteristic
1184C2#1913862911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#388C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×#388D43
hypocenterC43#13886
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#14582792C2semidirect
3. C2×#14582760C2semidirect
4. C2×C4×(C2×D43)⋊C4C2semidirect
5. #19132841C2semidirect
6. #19132837C2semidirect
9. #19132830C2semidirect
10. #19132828C2semidirect
11. #19132824C2semidirect
12. #19132819C2semidirect
13. #19132817C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C2×C43×#388C2semidirect
21. C2×(C22⋊D43)⋊C4C4semidirect
134. C43⋊#95D4semidirect
305. C22⋊C4×C43C22⋊C4semidirect
578. C2×#388D43semidirect
650. C43#13886semidirect
907. C22⋊C4(C2×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×#145827922
C2×#145827602
C2×C4×(C2×D43)⋊C42
#191328412
#191328372
#191328342
#191328302
#191328282
#191328242
#191328192
#191328172
(C2×D43)⋊#952
C2×C43×#3882
#1388643