Finite Group Databasebeta

← C2×#19137443 #25255810

Subgroups — C2×#19137443 #25255810

Order 11008.

4990 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063283C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D43C211yesmaximal, characteristic
3C22×C22⋊C4×D43C211yesmaximal, characteristic
4#19137443C2116yesmaximal, direct product factor
5C2×#14582793C211yesmaximal, characteristic, complemented
6C2×#14582792C211yesmaximal, characteristic, complemented
7C2×#14582787C211yesmaximal, characteristic, complemented
8C2×#14582773C211yesmaximal, characteristic, complemented
9C2×#14582770C211yesmaximal, characteristic, complemented
10C2×#14582761C211yesmaximal, characteristic, complemented
11C2×#14582758C211yesmaximal, characteristic, complemented
12C2×#14582754C211yesmaximal, characteristic
13C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
14C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
15C2×#14582746C211yesmaximal, characteristic, complemented
16C2×C43×#388C211yesmaximal, characteristic, complemented
17C25×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C23×C4×D43C2211yescharacteristic
22C2×#13063283—28no—
23C2×#13063283C2218yescomplemented
24C22×C4⋊Dic43C2211yescharacteristic, complemented
25C22×Dic43⋊C4C2211yescharacteristic, complemented
26C22×Dic43⋊C4C2211yescharacteristic, complemented
27C22×C22⋊Dic43C2211yescharacteristic
28C22×C22⋊Dic43C2211yescharacteristic
29C22×C22⋊Dic43C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C2×C22⋊C4×D43—28no—
39C2×C22⋊C4×D43C4116yescomplemented
40C2×C22⋊C4×D43C2218yes—
41C2×C22⋊C4×D43C2218yes—
42C22×C4×Dic43C2211yescharacteristic, complemented
43C22×C4×Dic43C2211yescharacteristic, complemented
44C22×C4×Dic43C2211yescharacteristic, complemented
45#14582793C2218yescomplemented
46#14582792C2218yescomplemented
47#14582787C2218yescomplemented
48#14582773C2218yescomplemented
49#14582770C2218yescomplemented
50#14582761C2218yescomplemented
51#14582758C2218yescomplemented
52#14582754C2218yes—
53C4×(C2×D43)⋊C4C2218yescomplemented
54C4×(C2×D43)⋊C4C2218yescomplemented
55#14582746C2218yescomplemented
56C2×C43⋊#95C2211yescharacteristic, complemented
57C2×C43⋊#95C2211yescharacteristic, complemented
58C2×C43⋊#95C2211yescharacteristic, complemented
59C2×C43⋊#95C2211yescharacteristic, complemented
60C2×C43⋊#95C2211yescharacteristic, complemented
61C2×C43⋊#95C2211yescharacteristic, complemented
62C22×C4⋊C4×C43C2211yescharacteristic, complemented
63C22×C22⋊C4×C43C2211yescharacteristic
64C22×C22⋊C4×C43C2211yescharacteristic
65C22×C22⋊C4×C43C2211yescharacteristic
66C22×C42×C43C2211yescharacteristic, complemented
67C43×#388C2218yescomplemented
68C2×#95×C43C2211yescharacteristic, complemented
69C2×#95×C43C2211yescharacteristic, complemented
70C24×D43—24no—
71C24×D43—24no—
72C24×D43—24no—
73C24×D43—24no—
74C24×D43—42no—
75C24×D43—42no—
76C24×D43C2×C418yes—
77C24×D43C2314yes—
78C24×D43C2311yescharacteristic
79C24×D43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2311yescharacteristic
86C22×C4×D43—24no—
87C22×C4×D43—24no—
88C22×C4×D43—24no—
89C22×C4×D43—24no—
90C22×C4×D43—24no—
91C22×C4×D43—24no—
92C22×C4×D43—42no—
93C22×C4×D43—42no—
94C22×C4×D43—42no—
95C22×C4×D43—42no—
96C22×C4×D43C2×C418yescomplemented
97C22×C4×D43C2×C418yescomplemented
98C22×C4×D43C2314yes—
99C22×C4×D43C2314yes—
100C22×C4×D43C2314yes—
101C22×C4×D43C2314yes—
102#13063283—232no—
103C2×C4⋊Dic43—24no—
104C2×C4⋊Dic43C2314yescomplemented
105C2×Dic43⋊C4—42no—
106C2×Dic43⋊C4—42no—
107C2×Dic43⋊C4C2314yescomplemented
108C2×Dic43⋊C4C2314yescomplemented
109C2×C22⋊Dic43—24no—
110C2×C22⋊Dic43—42no—
111C2×C22⋊Dic43C2×C418yescomplemented
112C2×C22⋊Dic43C2314yes—
113C2×C22⋊Dic43C2314yes—
114C2×C22⋊Dic43C2314yes—
115C2×(C2×D43)⋊C4—24no—
116C2×(C2×D43)⋊C4—24no—
117C2×(C2×D43)⋊C4—24no—
118C2×(C2×D43)⋊C4—24no—
119C2×(C2×D43)⋊C4—24no—
120C2×(C2×D43)⋊C4C2×C418yes—
121C2×(C2×D43)⋊C4C2×C418yes—
122C2×(C2×D43)⋊C4D418yes—
123C2×(C2×D43)⋊C4C2314yes—
124C2×(C2×D43)⋊C4C2314yes—
125C2×(C2×D43)⋊C4C2314yes—
126C2×(C2×D43)⋊C4C2314yes—
127C2×(C2×D43)⋊C4C2314yes—
128C2×(C2×D43)⋊C4C2314yes—
129C2×(C2×D43)⋊C4C2314yes—
130C2×(C2×D43)⋊C4C2314yes—
131C22⋊C4×D43—232no—
132C22⋊C4×D43C2×C4164yescomplemented
133C2×C4×Dic43—24no—
134C2×C4×Dic43—24no—
135C2×C4×Dic43—42no—
136C2×C4×Dic43C2314yescomplemented
137C2×C4×Dic43C2314yescomplemented
138C2×C4×Dic43C2314yescomplemented
139C43⋊#95C2314yescomplemented
140C43⋊#95C2314yescomplemented
141C43⋊#95C2314yescomplemented
142C43⋊#95C2314yescomplemented
143C43⋊#95C2314yescomplemented
144C43⋊#95C2314yescomplemented
145C25×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C23×C4×C43C2311yescharacteristic
151C23×C4×C43C2311yescharacteristic
152C2×C4⋊C4×C43—24no—
153C2×C4⋊C4×C43C2314yescomplemented
154C2×C22⋊C4×C43—24no—
155C2×C22⋊C4×C43—42no—
156C2×C22⋊C4×C43C2×C418yescomplemented
157C2×C22⋊C4×C43C2314yes—
158C2×C22⋊C4×C43C2314yes—
159C2×C22⋊C4×C43C2314yes—
160C2×C42×C43—42no—
161C2×C42×C43C2314yescomplemented
162#95×C43C2314yescomplemented
163#95×C43C2314yescomplemented
164C24×C43—22no—
165C24×C43—22no—
166C24×C43—22no—
167C24×C43—22no—
168C24×C43—22no—
169C24×C43—22no—
170C24×C43C22×C414yes—
171C24×C43C2412yes—
172C24×C43C2411yescharacteristic
173C23×D43—22no—
174C23×D43—22no—
175C23×D43—22no—
176C23×D43—22no—
177C23×D43—22no—
178C23×D43—22no—
179C23×D43—22no—
180C23×D43—22no—
181C23×D43—232no—
182C23×D43—232no—
183C23×D43—28no—
184C23×D43—28no—
185C23×D43—28no—
186C23×D43—28no—
187C23×D43—416no—
188C23×D43—44no—
189C23×D43—44no—
190C23×D43—416no—
191C23×D43—416no—
192C23×D43—416no—
193C23×D43—416no—
194C23×D43C22×C4116yes—
195C23×D43C22×C414yes—
196C23×D43C22×C414yes—
197C23×D43C2×D414yes—
198C23×D43#4114yes—
199C23×D43#4114yes—
200C23×D43#4114yes—
201C23×D43C2412yes—
202C23×D43C2412yes—
203C22×C4×C43—22no—
204C22×C4×C43—22no—
205C22×C4×C43—22no—
206C22×C4×C43—22no—
207C22×C4×C43—22no—
208C22×C4×C43—22no—
209C22×C4×C43—22no—
210C22×C4×C43—22no—
211C22×C4×C43—22no—
212C22×C4×C43—22no—
213C22×C4×C43—22no—
214C22×C4×C43—22no—
215C22×C4×C43—22no—
216C22×C4×C43—22no—
217C22×C4×C43—22no—
218C22×C4×C43C22×C414yes—
219C22×C4×C43C22×C414yes—
220C22×C4×C43C2×D414yes—
221C22×C4×C43C2412yes—
222C22×C4×C43C2412yes—
223C22×C4×C43C2412yes—
224C22×C4×C43C2412yes—
225C22×C4×C43C2412yes—
226C22×C4×C43C2412yes—
227C22×Dic43—22no—
228C22×Dic43—22no—
229C22×Dic43—22no—
230C22×Dic43—22no—
231C22×Dic43—22no—
232C22×Dic43—22no—
233C22×Dic43—22no—
234C22×Dic43—22no—
235C22×Dic43—22no—
236C22×Dic43—22no—
237C22×Dic43—22no—
238C22×Dic43—22no—
239C22×Dic43—22no—
240C22×Dic43—22no—
241C22×Dic43—22no—
242C22×Dic43C22×C414yes—
243C22×Dic43C22×C414yes—
244C22×Dic43C2×D414yes—
245C22×Dic43C2412yes—
246C22×Dic43C2412yes—
247C22×Dic43C2412yes—
248C22×Dic43C2412yes—
249C22×Dic43C2412yes—
250C22×Dic43C2412yes—
251C2×C4×D43—28no—
252C2×C4×D43—28no—
253C2×C4×D43—232no—
254C2×C4×D43—28no—
255C2×C4×D43—28no—
256C2×C4×D43—28no—
257C2×C4×D43—28no—
258C2×C4×D43—416no—
259C2×C4×D43—44no—
260C2×C4×D43—44no—
261C2×C4×D43—44no—
262C2×C4×D43—44no—
263C2×C4×D43—416no—
264C2×C4×D43—416no—
265C2×C4×D43C22×C4116yescomplemented
266C2×C4×D43C22×C4116yescomplemented
267C4⋊C4×C43—28no—
268C22⋊C4×C43—28no—
269C22⋊C4×C43—44no—
270C22⋊C4×C43C22×C4116yescomplemented
271C42×C43—44no—
272C22⋊Dic43—28no—
273C22⋊Dic43—44no—
274C22⋊Dic43C22×C4116yescomplemented
275(C2×D43)⋊C4—28no—
276(C2×D43)⋊C4—28no—
277(C2×D43)⋊C4—28no—
278(C2×D43)⋊C4—28no—
279(C2×D43)⋊C4—28no—
280(C2×D43)⋊C4C22×C4116yes—
281(C2×D43)⋊C4C22×C4116yes—
282(C2×D43)⋊C4C2×D4116yes—
283C4⋊Dic43—28no—
284Dic43⋊C4—44no—
285Dic43⋊C4—44no—
286C4×Dic43—28no—
287C4×Dic43—28no—
288C4×Dic43—44no—
289C23×C43—28no—
290C23×C43—28no—
291C23×C43—28no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—44no—
299C23×C43—44no—
300C23×C43—44no—
301C23×C43—44no—
302C23×C43C23×C414yes—
303C23×C43C23×C412yes—
304C23×C43C22×D412yes—
305C23×C43C2×#4112yes—
306C23×C43C2×#4112yes—
307C23×C43C2×#4112yes—
308C23×C43H(5,𝔽2)12yes—
309C23×C43H(5,𝔽2)12yes—
310C23×C43C2511yescharacteristic
311C22×D43—28no—
312C22×D43—28no—
313C22×D43—28no—
314C22×D43—28no—
315C22×D43—28no—
316C22×D43—28no—
317C22×D43—28no—
318C22×D43—28no—
319C22×D43—28no—
320C22×D43—28no—
321C22×D43—28no—
322C22×D43—28no—
323C22×D43—22no—
324C22×D43—22no—
325C22×D43—22no—
326C22×D43—22no—
327C22×D43—22no—
328C22×D43—22no—
329C22×D43—22no—
330C22×D43—22no—
331C22×D43—232no—
332C22×D43—232no—
333C22×D43—416no—
334C22×D43—4128no—
335C22×D43—416no—
336C22×D43—416no—
337C22×D43—416no—
338C22×D43—416no—
339C22×D43#117116yescomplemented
340C22×D43C4×D4116yes—
341C22×D43C23×C414yes—
342C22×D43C23×C414yes—
343C22×D43C22×D414yes—
344C22×D43C2×#4114yes—
345C22×D43C2×#4114yes—
346C22×D43C2×#4114yes—
347C2×C4×C43—28no—
348C2×C4×C43—28no—
349C2×C4×C43—28no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
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—44no—
366C2×C4×C43—44no—
367C2×C4×C43—44no—
368C2×C4×C43C23×C414yes—
369C2×C4×C43C23×C414yes—
370C2×C4×C43C22×D414yes—
371C2×Dic43—28no—
372C2×Dic43—28no—
373C2×Dic43—28no—
374C2×Dic43—22no—
375C2×Dic43—22no—
376C2×Dic43—22no—
377C2×Dic43—22no—
378C2×Dic43—22no—
379C2×Dic43—22no—
380C2×Dic43—22no—
381C2×Dic43—22no—
382C2×Dic43—22no—
383C2×Dic43—22no—
384C2×Dic43—22no—
385C2×Dic43—22no—
386C2×Dic43—22no—
387C2×Dic43—22no—
388C2×Dic43—22no—
389C2×Dic43—44no—
390C2×Dic43—44no—
391C2×Dic43—44no—
392C2×Dic43C23×C414yes—
393C2×Dic43C23×C414yes—
394C2×Dic43C22×D414yes—
395C4×D43—232no—
396C4×D43—416no—
397C4×D43—416no—
398C4×D43—416no—
399C2×#2342—431nomaximal, Sylow
400C22×C43—24no—
401C22×C43—24no—
402C22×C43—24no—
403C22×C43—416no—
404C22×C43—42no—
405C22×C43—42no—
406C22×C43—42no—
407C22×C43—42no—
408C22×C43C2×#11714yes—
409C22×C43C2×C4×D414yes—
410C22×C43#51814yes—
411C22×C43#54614yes—
412C22×C43#54614yes—
413C22×C43#55114yes—
414C22×C43#55114yes—
415C22×C43C24×C411yescharacteristic
416C22×C43C23×D411yescharacteristic
417C22×C43C22×#4111yescharacteristic
418C22×C43C22×#4111yescharacteristic
419C22×C43C22×#4111yescharacteristic
420C22×C43C2×H(5,𝔽2)11yescharacteristic
421C22×C43C2×H(5,𝔽2)11yescharacteristic
422C2×D43—232no—
423C2×D43—232no—
424C2×D43—24no—
425C2×D43—24no—
426C2×D43—24no—
427C2×D43—24no—
428C2×D43—24no—
429C2×D43—24no—
430C2×D43—24no—
431C2×D43—24no—
432C2×D43—24no—
433C2×D43—24no—
434C2×D43—24no—
435C2×D43—24no—
436C2×D43—464no—
437C2×D43C2×#11718yescomplemented
438C2×D43C2×C4×D418yes—
439C4×C43—24no—
440C4×C43—24no—
441C4×C43—24no—
442C4×C43—42no—
443C4×C43—42no—
444C4×C43—42no—
445Dic43—24no—
446Dic43—24no—
447Dic43—24no—
448Dic43—42no—
449Dic43—42no—
450Dic43—42no—
451C22×#117—431no—
452C23×C22⋊C4—431no—
453C23×C22⋊C4—431no—
454#2342—4316no—
455C2×#388—431no—
456C2×#388—431no—
457C2×#388—431no—
458C2×#388D4311yescharacteristic, complemented
459C2×#385—431no—
460C2×#385—431no—
461C2×#381—431no—
462C2×#380—431no—
463C2×#379—431no—
464C2×C4×C22⋊C4—431no—
465C2×C4×C22⋊C4—431no—
466C2×C4×C22⋊C4—431no—
467C2×C43—44no—
468C2×C43#234218yescomplemented
469C2×C43C22×#11711yescharacteristic
470C2×C43C22×C4×D411yescharacteristic
471C2×C43C2×#51811yescharacteristic
472C2×C43C2×#54611yescharacteristic
473C2×C43C2×#54611yescharacteristic
474C2×C43C2×#55111yescharacteristic
475C2×C43C2×#55111yescharacteristic
476D43—28no—
477D43—28no—
478C26—431no—
479C24×C4—431no—
480C24×C4—431no—
481C24×C4—431no—
482C24×C4—431no—
483C2×#117—438no—
484C2×#117—868no—
485C22×C4⋊C4—431no—
486C22×C4⋊C4—431no—
487C22×C4⋊C4—431no—
488C22×C4⋊C4C2×D4311yescharacteristic, complemented
489C22×C22⋊C4—431no—
490C22×C22⋊C4—431no—
491C22×C22⋊C4—431no—
492C22×C22⋊C4—431no—
493C22×C22⋊C4—438no—
494C22×C22⋊C4—4316no—
495C22×C22⋊C4—431no—
496C22×C22⋊C4—431no—
497C22×C22⋊C4—431no—
498C22×C22⋊C4—431no—
499C22×C22⋊C4—431no—
500C22×C22⋊C4—431no—
501C22×C22⋊C4—431no—
502C22×C22⋊C4—438no—
503C22×C22⋊C4—868no—
504C22×C22⋊C4C2×D4311yescharacteristic
505C22×C22⋊C4C2×D4311yescharacteristic
506C22×C22⋊C4C2×D4311yescharacteristic
507C22×C42—431no—
508C22×C42—431no—
509C22×C42—431no—
510C22×C42C2×D4311yescharacteristic, complemented
511#388—438no—
512#388—438no—
513#388—438no—
514#388C2×D4318yescomplemented
515#385—438no—
516#385—438no—
517#381—438no—
518#380—438no—
519#379—438no—
520C4×C22⋊C4—438no—
521C4×C22⋊C4—438no—
522C4×C22⋊C4—438no—
523C2×#95—431no—
524C2×#95—431no—
525C2×#95—431no—
526C2×#95—431no—
527C2×#95—431no—
528C2×#95—431no—
529C2×#95C2×D4311yescharacteristic, complemented
530C2×#95C2×D4311yescharacteristic, complemented
531C43C2×#234211yescharacteristic, complemented, Sylow
532C25—431no—
533C25—431no—
534C25—438no—
535C25—434no—
536C25—864no—
537C25—864no—
538C25—864no—
539C25—864no—
540C25—1722no—
541C25—1722no—
542C25C22×D4311yescharacteristic
543C23×C4—431no—
544C23×C4—431no—
545C23×C4—431no—
546C23×C4—438no—
547C23×C4—434no—
548C23×C4—438no—
549C23×C4—434no—
550C23×C4—431no—
551C23×C4—431no—
552C23×C4—431no—
553C23×C4—434no—
554C23×C4—434no—
555C23×C4—864no—
556C23×C4—864no—
557C23×C4—864no—
558C23×C4—864no—
559C23×C4—864no—
560C23×C4—864no—
561C23×C4—1722no—
562C23×C4—1722no—
563C23×C4—1722no—
564C23×C4—1722no—
565C23×C4C22×D4311yescharacteristic
566C23×C4C22×D4311yescharacteristic
567C23×C4C22×D4311yescharacteristic
568C23×C4C22×D4311yescharacteristic
569C23×C4C22×D4311yescharacteristic
570C23×C4C22×D4311yescharacteristic
571#117—8632no—
572C2×C4⋊C4—24no—
573C2×C4⋊C4—434no—
574C2×C4⋊C4—434no—
575C2×C4⋊C4—434no—
576C2×C4⋊C4—864no—
577C2×C4⋊C4—1722no—
578C2×C4⋊C4—1722no—
579C2×C4⋊C4C22×D4314yescomplemented
580C2×C22⋊C4—24no—
581C2×C22⋊C4—42no—
582C2×C22⋊C4—438no—
583C2×C22⋊C4—434no—
584C2×C22⋊C4—438no—
585C2×C22⋊C4—438no—
586C2×C22⋊C4—438no—
587C2×C22⋊C4—434no—
588C2×C22⋊C4—434no—
589C2×C22⋊C4—434no—
590C2×C22⋊C4—4364no—
591C2×C22⋊C4—434no—
592C2×C22⋊C4—434no—
593C2×C22⋊C4—434no—
594C2×C22⋊C4—434no—
595C2×C22⋊C4—434no—
596C2×C22⋊C4—434no—
597C2×C22⋊C4—434no—
598C2×C22⋊C4—8632no—
599C2×C22⋊C4—864no—
600C2×C22⋊C4—864no—
601C2×C22⋊C4—864no—
602C2×C22⋊C4—864no—
603C2×C22⋊C4—864no—
604C2×C22⋊C4—864no—
605C2×C22⋊C4—1722no—
606C2×C22⋊C4C4×D4318yescomplemented
607C2×C22⋊C4C22×D4314yes—
608C2×C22⋊C4C22×D4314yes—
609C2×C22⋊C4C22×D4314yes—
610C2×C42—42no—
611C2×C42—434no—
612C2×C42—434no—
613C2×C42—434no—
614C2×C42—864no—
615C2×C42—864no—
616C2×C42—1722no—
617C2×C42C22×D4314yescomplemented
618#95—434no—
619#95—434no—
620#95—434no—
621#95—434no—
622#95—434no—
623#95—434no—
624#95C22×D4314yescomplemented
625#95C22×D4314yescomplemented
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—434no—
633C24—434no—
634C24—434no—
635C24—434no—
636C24—434no—
637C24—434no—
638C24—432no—
639C24—432no—
640C24—4316no—
641C24—868no—
642C24—8632no—
643C24—8632no—
644C24—868no—
645C24—868no—
646C24—868no—
647C24—862no—
648C24—862no—
649C24—862no—
650C24—862no—
651C24—862no—
652C24—862no—
653C24—862no—
654C24—862no—
655C24—17216no—
656C24—1724no—
657C24—1724no—
658C24—17216no—
659C24—17216no—
660C24—17216no—
661C24—17216no—
662C24C2×C4×D4314yes—
663C24C23×D4312yes—
664C24C23×D4311yescharacteristic
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—434no—
681C22×C4—434no—
682C22×C4—434no—
683C22×C4—432no—
684C22×C4—432no—
685C22×C4—432no—
686C22×C4—4316no—
687C22×C4—4316no—
688C22×C4—432no—
689C22×C4—432no—
690C22×C4—432no—
691C22×C4—868no—
692C22×C4—868no—
693C22×C4—8632no—
694C22×C4—868no—
695C22×C4—868no—
696C22×C4—868no—
697C22×C4—862no—
698C22×C4—862no—
699C22×C4—862no—
700C22×C4—862no—
701C22×C4—862no—
702C22×C4—862no—
703C22×C4—862no—
704C22×C4—862no—
705C22×C4—862no—
706C22×C4—862no—
707C22×C4—862no—
708C22×C4—862no—
709C22×C4—862no—
710C22×C4—862no—
711C22×C4—862no—
712C22×C4—868no—
713C22×C4—17216no—
714C22×C4—1724no—
715C22×C4—1724no—
716C22×C4—1724no—
717C22×C4—1724no—
718C22×C4—17216no—
719C22×C4—17216no—
720C22×C4C2×C4×D4314yes—
721C22×C4C2×C4×D4314yes—
722C22×C4D4×D4314yes—
723C22×C4C23×D4312yes—
724C22×C4C23×D4312yes—
725C22×C4C23×D4312yes—
726C22×C4C23×D4312yes—
727C22×C4C23×D4312yes—
728C22×C4C23×D4312yes—
729C4⋊C4—28no—
730C4⋊C4—868no—
731C4⋊C4—1724no—
732C4⋊C4—1724no—
733C22⋊C4—28no—
734C22⋊C4—44no—
735C22⋊C4—4316no—
736C22⋊C4—4316no—
737C22⋊C4—4316no—
738C22⋊C4—4316no—
739C22⋊C4—868no—
740C22⋊C4—868no—
741C22⋊C4—868no—
742C22⋊C4—868no—
743C22⋊C4—868no—
744C22⋊C4—868no—
745C22⋊C4—1724no—
746C22⋊C4C2×C4×D43116yescomplemented
747C42—44no—
748C42—868no—
749C42—868no—
750C42—1724no—
751C23—28no—
752C23—28no—
753C23—28no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—4316no—
765C23—4316no—
766C23—434no—
767C23—434no—
768C23—434no—
769C23—434no—
770C23—434no—
771C23—434no—
772C23—8632no—
773C23—8632no—
774C23—868no—
775C23—868no—
776C23—868no—
777C23—868no—
778C23—868no—
779C23—868no—
780C23—868no—
781C23—868no—
782C23—862no—
783C23—862no—
784C23—862no—
785C23—862no—
786C23—862no—
787C23—862no—
788C23—862no—
789C23—862no—
790C23—868no—
791C23—868no—
792C23—868no—
793C23—868no—
794C23—17216no—
795C23—17216no—
796C23—17216no—
797C23—17216no—
798C23—17216no—
799C23—172128no—
800C23C22×C4×D4314yes—
801C23C22×C4×D4312yes—
802C23C2×D4×D4312yes—
803C23#41×D4312yes—
804C23#41×D4312yes—
805C23#41×D4312yes—
806C23#1306337012yes—
807C23#1306337112yes—
808C23C24×D4311yescharacteristic
809C2×C4—28no—
810C2×C4—28no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—28no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—434no—
831C2×C4—434no—
832C2×C4—434no—
833C2×C4—8632no—
834C2×C4—868no—
835C2×C4—868no—
836C2×C4—862no—
837C2×C4—862no—
838C2×C4—862no—
839C2×C4—862no—
840C2×C4—862no—
841C2×C4—862no—
842C2×C4—868no—
843C2×C4—862no—
844C2×C4—862no—
845C2×C4—862no—
846C2×C4—862no—
847C2×C4—862no—
848C2×C4—862no—
849C2×C4—862no—
850C2×C4—862no—
851C2×C4—862no—
852C2×C4—17216no—
853C2×C4—17216no—
854C2×C4—17216no—
855C2×C4—1724no—
856C2×C4—1724no—
857C2×C4—1724no—
858C2×C4C22×C4×D4314yes—
859C2×C4C22×C4×D4314yes—
860C2×C4C2×D4×D4314yes—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—416no—
869C22—438no—
870C22—438no—
871C22—864no—
872C22—864no—
873C22—864no—
874C22—864no—
875C22—864no—
876C22—864no—
877C22—864no—
878C22—864no—
879C22—864no—
880C22—864no—
881C22—8632no—
882C22—8632no—
883C22—864no—
884C22—864no—
885C22—17264no—
886C22#117×D4314yes—
887C22C4×D4×D4314yes—
888C22#1458337114yes—
889C22#1458353814yes—
890C22#1458354214yes—
891C22#1458357414yes—
892C22#1458357714yes—
893C22C23×C4×D4311yescharacteristic
894C22C22×D4×D4311yescharacteristic
895C22C2×#41×D4311yescharacteristic
896C22C2×#41×D4311yescharacteristic
897C22C2×#41×D4311yescharacteristic
898C22C2×#1306337011yescharacteristic
899C22C2×#1306337111yescharacteristic
900C4—24no—
901C4—24no—
902C4—24no—
903C4—42no—
904C4—42no—
905C4—42no—
906C4—864no—
907C4—864no—
908C4—864no—
909C4—1722no—
910C4—1722no—
911C4—1722no—
912C2—44no—
913C2—868no—
914C2—868no—
915C2#1913744318yesdirect product factor
916C2C2×#117×D4311yescharacteristic
917C2C2×C4×D4×D4311yescharacteristic
918C2C2×#1458337111yescharacteristic
919C2C2×#1458353811yescharacteristic
920C2C2×#1458354211yescharacteristic
921C2C2×#1458357411yescharacteristic
922C2C2×#1458357711yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#388C2
socleC24×C43C24
prime radicalC25×D43C22
cosocleC23×C43C25
hypercenterC2×#388D43
hypocenterC43C2×#2342
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#13063283C2semidirect
4. #19137443C2direct (N × H)
5. C2×#14582793C2semidirect
6. C2×#14582792C2semidirect
7. C2×#14582787C2semidirect
8. C2×#14582773C2semidirect
9. C2×#14582770C2semidirect
10. C2×#14582761C2semidirect
11. C2×#14582758C2semidirect
13. C2×C4×(C2×D43)⋊C4C2semidirect
14. C2×C4×(C2×D43)⋊C4C2semidirect
15. C2×#14582746C2semidirect
16. C2×C43×#388C2semidirect
23. C2×#13063283C22semidirect
24. C22×C4⋊Dic43C22semidirect
25. C22×Dic43⋊C4C22semidirect
26. C22×Dic43⋊C4C22semidirect
39. C2×C22⋊C4×D43C4semidirect
42. C22×C4×Dic43C22semidirect
43. C22×C4×Dic43C22semidirect
44. C22×C4×Dic43C22semidirect
45. #14582793C22semidirect
46. #14582792C22semidirect
47. #14582787C22semidirect
48. #14582773C22semidirect
49. #14582770C22semidirect
50. #14582761C22semidirect
51. #14582758C22semidirect
53. C4×(C2×D43)⋊C4C22semidirect
54. C4×(C2×D43)⋊C4C22semidirect
55. #14582746C22semidirect
56. C2×C43⋊#95C22semidirect
57. C2×C43⋊#95C22semidirect
58. C2×C43⋊#95C22semidirect
59. C2×C43⋊#95C22semidirect
60. C2×C43⋊#95C22semidirect
61. C2×C43⋊#95C22semidirect
62. C22×C4⋊C4×C43C22semidirect
66. C22×C42×C43C22semidirect
67. C43×#388C22semidirect
68. C2×#95×C43C22semidirect
69. C2×#95×C43C22semidirect
96. C22×C4×D43C2×C4semidirect
97. C22×C4×D43C2×C4semidirect
104. C2×C4⋊Dic43C23semidirect
107. C2×Dic43⋊C4C23semidirect
108. C2×Dic43⋊C4C23semidirect
111. C2×C22⋊Dic43C2×C4semidirect
132. C22⋊C4×D43C2×C4semidirect
136. C2×C4×Dic43C23semidirect
137. C2×C4×Dic43C23semidirect
138. C2×C4×Dic43C23semidirect
139. C43⋊#95C23semidirect
140. C43⋊#95C23semidirect
141. C43⋊#95C23semidirect
142. C43⋊#95C23semidirect
143. C43⋊#95C23semidirect
144. C43⋊#95C23semidirect
153. C2×C4⋊C4×C43C23semidirect
156. C2×C22⋊C4×C43C2×C4semidirect
161. C2×C42×C43C23semidirect
162. #95×C43C23semidirect
163. #95×C43C23semidirect
265. C2×C4×D43C22×C4semidirect
266. C2×C4×D43C22×C4semidirect
270. C22⋊C4×C43C22×C4semidirect
274. C22⋊Dic43C22×C4semidirect
339. C22×D43#117semidirect
437. C2×D43C2×#117semidirect
458. C2×#388D43semidirect
468. C2×C43#2342semidirect
488. C22×C4⋊C4C2×D43semidirect
510. C22×C42C2×D43semidirect
514. #388C2×D43semidirect
529. C2×#95C2×D43semidirect
530. C2×#95C2×D43semidirect
531. C43C2×#2342semidirect
579. C2×C4⋊C4C22×D43semidirect
606. C2×C22⋊C4C4×D43semidirect
617. C2×C42C22×D43semidirect
624. #95C22×D43semidirect
625. #95C22×D43semidirect
746. C22⋊C4C2×C4×D43semidirect
915. C2#19137443direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130632832
C22×C22⋊C4×D432
#191374432
C2×#145827932
C2×#145827922
C2×#145827872
C2×#145827732
C2×#145827702
C2×#145827612
C2×#145827582
C2×#145827542
C2×C4×(C2×D43)⋊C42
C2×#145827462
C2×C43×#3882
C2×#234243