Finite Group Databasebeta

← C2×#19137413 #25255767

Subgroups — C2×#19137413 #25255767

Order 11008.

8774 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D4×D43C211yesmaximal, characteristic
2C22×C4×C22⋊D43C211yesmaximal, characteristic, complemented
3C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic, complemented
4C23×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
5C22×C22⋊C4×D43C211yesmaximal, characteristic, complemented
6#19137413C2116yesmaximal, direct product factor
7C2×#14582799C211yesmaximal, characteristic, complemented
8C2×#14582799C211yesmaximal, characteristic, complemented
9C2×#14582779C211yesmaximal, characteristic, complemented
10C2×#14582777C211yesmaximal, characteristic, complemented
11C2×#14582777C211yesmaximal, characteristic, complemented
12C2×#14582758C211yesmaximal, characteristic, complemented
13C2×#14582754C211yesmaximal, characteristic, complemented
14C2×#14582754C211yesmaximal, characteristic, complemented
15C2×#14582746C211yesmaximal, characteristic, complemented
16C2×C43×#386C211yesmaximal, characteristic, complemented
17C25×D43C2211yescharacteristic
18C25×D43C2211yescharacteristic
19C23×D172C2211yescharacteristic
20C23×C22⋊D43C2211yescharacteristic
21C23×C22⋊D43C2211yescharacteristic
22C22×D4×D43—28no—
23C22×D4×D43—28no—
24C22×D4×D43C4116yescomplemented
25C22×D4×D43C2218yes—
26C24×Dic43C2211yescharacteristic, complemented
27C23×C4×D43C2211yescharacteristic
28C23×C4×D43C2211yescharacteristic, complemented
29C23×C4×D43C2211yescharacteristic, complemented
30C2×C4×C22⋊D43—28no—
31C2×C4×C22⋊D43C2218yescomplemented
32C2×(C22⋊D43)⋊C4—28no—
33C2×(C22⋊D43)⋊C4C2218yescomplemented
34C22×Dic43⋊C4C2211yescharacteristic, complemented
35C22×Dic43⋊C4C2211yescharacteristic, complemented
36C22×C22⋊Dic43C2211yescharacteristic, complemented
37C22×C22⋊Dic43C2211yescharacteristic, complemented
38C22×C22⋊Dic43C2211yescharacteristic, complemented
39C22×(C2×D43)⋊C4—28no—
40C22×(C2×D43)⋊C4C2211yescharacteristic
41C22×(C2×D43)⋊C4C2211yescharacteristic
42C22×(C2×D43)⋊C4C2211yescharacteristic
43C22×(C2×D43)⋊C4C2211yescharacteristic
44C22×(C2×D43)⋊C4C2211yescharacteristic, complemented
45C22×(C2×D43)⋊C4C2211yescharacteristic, complemented
46C22×(C2×D43)⋊C4C2211yescharacteristic, complemented
47C22×(C2×D43)⋊C4C2211yescharacteristic, complemented
48C22×(C2×D43)⋊C4C2211yescharacteristic, complemented
49C22×(C2×D43)⋊C4C2211yescharacteristic, complemented
50C22×(C2×D43)⋊C4C2218yescomplemented
51C2×C22⋊C4×D43—28no—
52C2×C22⋊C4×D43C2218yescomplemented
53C22×C4×Dic43C2211yescharacteristic, complemented
54C22×C4×Dic43C2211yescharacteristic, complemented
55#14582799C2218yescomplemented
56#14582799C2218yescomplemented
57#14582779C2218yescomplemented
58#14582777C2218yescomplemented
59#14582777C2218yescomplemented
60#14582758C2218yescomplemented
61#14582754C2218yescomplemented
62#14582754C2218yescomplemented
63#14582746C2218yescomplemented
64C2×C43⋊#95C2211yescharacteristic, complemented
65C2×C43⋊#95C2211yescharacteristic, complemented
66C23×D4×C43C2211yescharacteristic
67C24×C4×C43C2211yescharacteristic, complemented
68C22×C22⋊C4×C43C2211yescharacteristic, complemented
69C22×C22⋊C4×C43C2211yescharacteristic, complemented
70C22×C22⋊C4×C43C2211yescharacteristic, complemented
71C43×#386C2218yescomplemented
72C2×#95×C43C2211yescharacteristic, complemented
73C2×#95×C43C2211yescharacteristic, complemented
74C24×D43—24no—
75C24×D43—24no—
76C24×D43—24no—
77C24×D43—24no—
78C24×D43—24no—
79C24×D43—24no—
80C24×D43—24no—
81C24×D43—24no—
82C24×D43—42no—
83C24×D43—42no—
84C24×D43—42no—
85C24×D43—42no—
86C24×D43C2×C418yescomplemented
87C24×D43C2×C418yescomplemented
88C24×D43C2311yescharacteristic
89C24×D43C2314yes—
90C24×D43C2314yes—
91C24×D43C2311yescharacteristic
92C24×D43C2311yescharacteristic
93C22×D172—24no—
94C22×D172—24no—
95C22×D172C2×C418yescomplemented
96C22×D172C2314yes—
97C22×C22⋊D43—24no—
98C22×C22⋊D43—24no—
99C22×C22⋊D43C2×C418yes—
100C22×C22⋊D43C2×C418yescomplemented
101C22×C22⋊D43D418yes—
102C22×C22⋊D43D418yes—
103C22×C22⋊D43C2314yes—
104C22×C22⋊D43C2314yes—
105C2×D4×D43—2128no—
106C2×D4×D43—232no—
107C2×D4×D43—232no—
108C2×D4×D43C2×C4164yescomplemented
109C23×Dic43—24no—
110C23×Dic43—24no—
111C23×Dic43—42no—
112C23×Dic43C2311yescharacteristic
113C23×Dic43C2311yescharacteristic
114C23×Dic43C2311yescharacteristic
115C23×Dic43C2311yescharacteristic
116C23×Dic43C2311yescharacteristic
117C23×Dic43C2314yescomplemented
118C22×C4×D43—24no—
119C22×C4×D43—24no—
120C22×C4×D43—24no—
121C22×C4×D43—24no—
122C22×C4×D43—24no—
123C22×C4×D43—24no—
124C22×C4×D43—42no—
125C22×C4×D43—42no—
126C22×C4×D43C2×C418yescomplemented
127C22×C4×D43C2314yes—
128C22×C4×D43C2314yescomplemented
129C22×C4×D43C2314yescomplemented
130C4×C22⋊D43—232no—
131(C22⋊D43)⋊C4—232no—
132C2×Dic43⋊C4—24no—
133C2×Dic43⋊C4—24no—
134C2×Dic43⋊C4C2314yescomplemented
135C2×Dic43⋊C4C2314yescomplemented
136C2×C22⋊Dic43—24no—
137C2×C22⋊Dic43—24no—
138C2×C22⋊Dic43—42no—
139C2×C22⋊Dic43C2314yescomplemented
140C2×C22⋊Dic43C2314yescomplemented
141C2×C22⋊Dic43C2314yescomplemented
142C2×(C2×D43)⋊C4—24no—
143C2×(C2×D43)⋊C4—24no—
144C2×(C2×D43)⋊C4—24no—
145C2×(C2×D43)⋊C4—24no—
146C2×(C2×D43)⋊C4—24no—
147C2×(C2×D43)⋊C4—24no—
148C2×(C2×D43)⋊C4—24no—
149C2×(C2×D43)⋊C4—232no—
150C2×(C2×D43)⋊C4—42no—
151C2×(C2×D43)⋊C4—42no—
152C2×(C2×D43)⋊C4D418yescomplemented
153C2×(C2×D43)⋊C4C2314yes—
154C2×(C2×D43)⋊C4C2314yes—
155C2×(C2×D43)⋊C4C2314yes—
156C2×(C2×D43)⋊C4C2314yes—
157C2×(C2×D43)⋊C4C2314yescomplemented
158C2×(C2×D43)⋊C4C2314yescomplemented
159C2×(C2×D43)⋊C4C2314yescomplemented
160C2×(C2×D43)⋊C4C2314yescomplemented
161C2×(C2×D43)⋊C4C2314yescomplemented
162C2×(C2×D43)⋊C4C2314yescomplemented
163C22⋊C4×D43—232no—
164C2×C4×Dic43—24no—
165C2×C4×Dic43—24no—
166C2×C4×Dic43C2314yescomplemented
167C2×C4×Dic43C2314yescomplemented
168C43⋊#95C2314yescomplemented
169C43⋊#95C2314yescomplemented
170C25×C43C2311yescharacteristic
171C25×C43C2311yescharacteristic
172C22×D4×C43—24no—
173C22×D4×C43—24no—
174C22×D4×C43C2×C418yescomplemented
175C22×D4×C43C2314yes—
176C23×C4×C43—24no—
177C23×C4×C43—24no—
178C23×C4×C43—42no—
179C23×C4×C43C2311yescharacteristic
180C23×C4×C43C2311yescharacteristic
181C23×C4×C43C2311yescharacteristic
182C23×C4×C43C2311yescharacteristic
183C23×C4×C43C2311yescharacteristic
184C23×C4×C43C2314yescomplemented
185C2×C22⋊C4×C43—24no—
186C2×C22⋊C4×C43—24no—
187C2×C22⋊C4×C43—42no—
188C2×C22⋊C4×C43C2314yescomplemented
189C2×C22⋊C4×C43C2314yescomplemented
190C2×C22⋊C4×C43C2314yescomplemented
191#95×C43C2314yescomplemented
192#95×C43C2314yescomplemented
193C24×C43—22no—
194C24×C43—22no—
195C24×C43—22no—
196C24×C43—22no—
197C24×C43—22no—
198C24×C43—22no—
199C24×C43—22no—
200C24×C43—22no—
201C24×C43—22no—
202C24×C43—22no—
203C24×C43C22×C414yes—
204C24×C43C22×C414yes—
205C24×C43C2×D414yes—
206C24×C43C2×D414yes—
207C24×C43C2412yes—
208C24×C43C2412yes—
209C24×C43C2411yescharacteristic
210C23×D43—22no—
211C23×D43—22no—
212C23×D43—22no—
213C23×D43—22no—
214C23×D43—22no—
215C23×D43—22no—
216C23×D43—22no—
217C23×D43—22no—
218C23×D43—232no—
219C23×D43—22no—
220C23×D43—28no—
221C23×D43—28no—
222C23×D43—22no—
223C23×D43—22no—
224C23×D43—22no—
225C23×D43—22no—
226C23×D43—22no—
227C23×D43—232no—
228C23×D43—232no—
229C23×D43—232no—
230C23×D43—28no—
231C23×D43—28no—
232C23×D43—28no—
233C23×D43—28no—
234C23×D43—28no—
235C23×D43—28no—
236C23×D43—416no—
237C23×D43—416no—
238C23×D43—44no—
239C23×D43—44no—
240C23×D43—44no—
241C23×D43—44no—
242C23×D43—416no—
243C23×D43—416no—
244C23×D43—416no—
245C23×D43—416no—
246C23×D43—416no—
247C23×D43—416no—
248C23×D43—416no—
249C23×D43—416no—
250C23×D43C22×C414yes—
251C23×D43C22×C414yes—
252C23×D43C22×C414yes—
253C23×D43C22×C4116yescomplemented
254C23×D43C22×C4116yescomplemented
255C23×D43C2×D414yes—
256C23×D43C2×D414yes—
257C23×D43C2×D414yes—
258C23×D43#4114yes—
259C23×D43C2412yes—
260C23×D43C2412yes—
261C23×D43C2412yes—
262C2×D4×C43—232no—
263C2×D4×C43—28no—
264C2×D4×C43—28no—
265C2×D4×C43C22×C4116yescomplemented
266C22×C4×C43—28no—
267C22×C4×C43—22no—
268C22×C4×C43—22no—
269C22×C4×C43—22no—
270C22×C4×C43—22no—
271C22×C4×C43—22no—
272C22×C4×C43—22no—
273C22×C4×C43—22no—
274C22×C4×C43—22no—
275C22×C4×C43—28no—
276C22×C4×C43—22no—
277C22×C4×C43—22no—
278C22×C4×C43—22no—
279C22×C4×C43—22no—
280C22×C4×C43—22no—
281C22×C4×C43—44no—
282C22×C4×C43—416no—
283C22×C4×C43C22×C414yes—
284C22×C4×C43C2×D414yescomplemented
285C22×C4×C43C2412yes—
286C22×C4×C43C2412yes—
287C22×C4×C43C2412yes—
288C22×C4×C43C2412yes—
289C22×C4×C43C2412yes—
290C2×C22⋊D43—232no—
291C2×C22⋊D43—28no—
292C2×C22⋊D43—28no—
293C2×C22⋊D43C22⋊C4164yescomplemented
294C2×C22⋊D43C22×C4116yes—
295C2×C22⋊D43C22×C4116yescomplemented
296C2×C22⋊D43C2×D4116yes—
297C2×C22⋊D43C2×D4116yes—
298C22×Dic43—28no—
299C22×Dic43—22no—
300C22×Dic43—22no—
301C22×Dic43—22no—
302C22×Dic43—22no—
303C22×Dic43—22no—
304C22×Dic43—22no—
305C22×Dic43—28no—
306C22×Dic43—22no—
307C22×Dic43—22no—
308C22×Dic43—22no—
309C22×Dic43—22no—
310C22×Dic43—22no—
311C22×Dic43—44no—
312C22×Dic43—416no—
313C22×Dic43C22×C414yes—
314C22×Dic43C2×D414yes—
315C22×Dic43C2×D414yes—
316C22×Dic43C2×D414yescomplemented
317C22×Dic43C2412yes—
318C22×Dic43C2412yes—
319C22×Dic43C2412yes—
320C22×Dic43C2412yes—
321C22×Dic43C2412yes—
322D4×D43—2256no—
323C2×D172—232no—
324C2×D172—28no—
325C2×D172—28no—
326C2×D172C22×C4116yescomplemented
327C2×C4×D43—232no—
328C2×C4×D43—28no—
329C2×C4×D43—28no—
330C2×C4×D43—28no—
331C2×C4×D43—28no—
332C2×C4×D43—28no—
333C2×C4×D43—28no—
334C2×C4×D43—44no—
335C2×C4×D43—44no—
336C2×C4×D43—416no—
337C2×C4×D43—416no—
338C2×C4×D43C22×C4116yescomplemented
339C22⋊C4×C43—28no—
340C22⋊C4×C43—28no—
341C22⋊C4×C43—44no—
342C22⋊Dic43—28no—
343C22⋊Dic43—28no—
344C22⋊Dic43—44no—
345(C2×D43)⋊C4—28no—
346(C2×D43)⋊C4—28no—
347(C2×D43)⋊C4—28no—
348(C2×D43)⋊C4—28no—
349(C2×D43)⋊C4—28no—
350(C2×D43)⋊C4—28no—
351(C2×D43)⋊C4—28no—
352(C2×D43)⋊C4—44no—
353(C2×D43)⋊C4—44no—
354(C2×D43)⋊C4C2×D4116yescomplemented
355Dic43⋊C4—28no—
356Dic43⋊C4—28no—
357C4×Dic43—28no—
358C4×Dic43—28no—
359C23×C43—28no—
360C23×C43—28no—
361C23×C43—28no—
362C23×C43—28no—
363C23×C43—28no—
364C23×C43—28no—
365C23×C43—22no—
366C23×C43—22no—
367C23×C43—22no—
368C23×C43—22no—
369C23×C43—28no—
370C23×C43—28no—
371C23×C43—28no—
372C23×C43—22no—
373C23×C43—22no—
374C23×C43—22no—
375C23×C43—22no—
376C23×C43—22no—
377C23×C43—22no—
378C23×C43—44no—
379C23×C43—44no—
380C23×C43—44no—
381C23×C43—44no—
382C23×C43C2×C22⋊C4116yescomplemented
383C23×C43C23×C414yes—
384C23×C43C23×C414yes—
385C23×C43C23×C412yes—
386C23×C43C22×D414yes—
387C23×C43C22×D414yes—
388C23×C43C22×D412yes—
389C23×C43C22×D412yes—
390C23×C43C22×D412yes—
391C23×C43C2×#4112yes—
392C23×C43H(5,𝔽2)12yes—
393C23×C43H(5,𝔽2)12yes—
394C23×C43C2511yescharacteristic
395C22×D43—28no—
396C22×D43—28no—
397C22×D43—28no—
398C22×D43—28no—
399C22×D43—28no—
400C22×D43—28no—
401C22×D43—28no—
402C22×D43—28no—
403C22×D43—28no—
404C22×D43—28no—
405C22×D43—28no—
406C22×D43—28no—
407C22×D43—22no—
408C22×D43—22no—
409C22×D43—22no—
410C22×D43—22no—
411C22×D43—22no—
412C22×D43—22no—
413C22×D43—22no—
414C22×D43—22no—
415C22×D43—28no—
416C22×D43—232no—
417C22×D43—28no—
418C22×D43—28no—
419C22×D43—22no—
420C22×D43—22no—
421C22×D43—22no—
422C22×D43—22no—
423C22×D43—22no—
424C22×D43—22no—
425C22×D43—232no—
426C22×D43—232no—
427C22×D43—232no—
428C22×D43—416no—
429C22×D43—416no—
430C22×D43—4128no—
431C22×D43—416no—
432C22×D43—416no—
433C22×D43—416no—
434C22×D43—416no—
435C22×D43—4128no—
436C22×D43—416no—
437C22×D43—416no—
438C22×D43—416no—
439C22×D43—416no—
440C22×D43—44no—
441C22×D43—44no—
442C22×D43—44no—
443C22×D43—44no—
444C22×D43C2×C22⋊C4116yescomplemented
445C22×D43C4×D4116yescomplemented
446C22×D43C23×C414yes—
447C22×D43C23×C414yes—
448C22×D43C23×C414yes—
449C22×D43C22×D414yes—
450C22×D43C22×D414yes—
451C22×D43C22×D414yes—
452C22×D43C2×#4114yes—
453D4×C43—232no—
454C2×C4×C43—28no—
455C2×C4×C43—28no—
456C2×C4×C43—22no—
457C2×C4×C43—22no—
458C2×C4×C43—22no—
459C2×C4×C43—22no—
460C2×C4×C43—22no—
461C2×C4×C43—22no—
462C2×C4×C43—22no—
463C2×C4×C43—22no—
464C2×C4×C43—22no—
465C2×C4×C43—22no—
466C2×C4×C43—22no—
467C2×C4×C43—22no—
468C2×C4×C43—22no—
469C2×C4×C43—416no—
470C2×C4×C43—44no—
471C2×C4×C43—44no—
472C2×C4×C43—44no—
473C2×C4×C43C23×C414yes—
474C2×C4×C43C22×D414yescomplemented
475C22⋊D43—232no—
476C22⋊D43C2×C22⋊C4164yescomplemented
477C2×Dic43—28no—
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—44no—
491C2×Dic43—44no—
492C2×Dic43—44no—
493C2×Dic43C2×C22⋊C4116yescomplemented
494C2×Dic43C23×C414yes—
495C2×Dic43C22×D414yes—
496C2×Dic43C22×D414yes—
497C2×Dic43C22×D414yescomplemented
498D172—232no—
499C4×D43—232no—
500C4×D43—416no—
501C4×D43—416no—
502C2×D4×C22⋊C4—431nomaximal, Sylow
503C22×C43—232no—
504C22×C43—24no—
505C22×C43—24no—
506C22×C43—24no—
507C22×C43—24no—
508C22×C43—24no—
509C22×C43—24no—
510C22×C43—24no—
511C22×C43—24no—
512C22×C43—24no—
513C22×C43—416no—
514C22×C43—42no—
515C22×C43—42no—
516C22×C43—42no—
517C22×C43—42no—
518C22×C43C22×C22⋊C414yes—
519C22×C43C22×C22⋊C418yescomplemented
520C22×C43C2×C4×D414yes—
521C22×C43#51814yes—
522C22×C43D4214yes—
523C22×C43D4214yes—
524C22×C43#54614yes—
525C22×C43#54614yes—
526C22×C43C24×C411yescharacteristic
527C22×C43C23×D411yescharacteristic
528C22×C43C23×D411yescharacteristic
529C22×C43C23×D411yescharacteristic
530C22×C43C22×#4111yescharacteristic
531C22×C43C2×H(5,𝔽2)11yescharacteristic
532C22×C43C2×H(5,𝔽2)11yescharacteristic
533C2×D43—232no—
534C2×D43—232no—
535C2×D43—24no—
536C2×D43—24no—
537C2×D43—24no—
538C2×D43—24no—
539C2×D43—24no—
540C2×D43—24no—
541C2×D43—24no—
542C2×D43—24no—
543C2×D43—24no—
544C2×D43—24no—
545C2×D43—24no—
546C2×D43—24no—
547C2×D43—24no—
548C2×D43—24no—
549C2×D43—24no—
550C2×D43—464no—
551C2×D43—464no—
552C2×D43—416no—
553C2×D43—42no—
554C2×D43—42no—
555C2×D43—42no—
556C2×D43—42no—
557C2×D43C22×C22⋊C418yescomplemented
558C2×D43C2×C4×D418yescomplemented
559C4×C43—24no—
560C4×C43—24no—
561C4×C43—42no—
562C4×C43—42no—
563C4×C43—42no—
564Dic43—24no—
565Dic43—42no—
566Dic43—42no—
567Dic43—42no—
568Dic43C22×C22⋊C418yescomplemented
569C24×D4—431no—
570C22×C4×D4—431no—
571C22×C4×D4—431no—
572C23×C22⋊C4—431no—
573C23×C22⋊C4—431no—
574D4×C22⋊C4—4316no—
575C2×#390—431no—
576C2×#390—431no—
577C2×#386—431no—
578C2×#386—431no—
579C2×#386—431no—
580C2×#386D4311yescharacteristic, complemented
581C2×#380—431no—
582C2×#379—431no—
583C2×#379—431no—
584C2×C4×C22⋊C4—431no—
585C2×C43—28no—
586C2×C43—44no—
587C2×C43D4×C22⋊C418yescomplemented
588C2×C43C23×C22⋊C411yescharacteristic
589C2×C43C22×C4×D411yescharacteristic
590C2×C43C2×#51811yescharacteristic
591C2×C43C2×D4211yescharacteristic
592C2×C43C2×D4211yescharacteristic
593C2×C43C2×#54611yescharacteristic
594C2×C43C2×#54611yescharacteristic
595D43—28no—
596D43—28no—
597D43—44no—
598C26—431no—
599C26—431no—
600C23×D4—431no—
601C23×D4—431no—
602C23×D4—438no—
603C23×D4—4316no—
604C23×D4—431no—
605C23×D4—868no—
606C23×D4—868no—
607C23×D4C2×D4311yescharacteristic
608C24×C4—431no—
609C24×C4—431no—
610C24×C4—431no—
611C24×C4—431no—
612C24×C4C2×D4311yescharacteristic, complemented
613C2×C4×D4—438no—
614C2×C4×D4—438no—
615C2×C4×D4—868no—
616C2×C4×D4—868no—
617C22×C4⋊C4—431no—
618C22×C4⋊C4—431no—
619C22×C22⋊C4—431no—
620C22×C22⋊C4—431no—
621C22×C22⋊C4—431no—
622C22×C22⋊C4—431no—
623C22×C22⋊C4—431no—
624C22×C22⋊C4—431no—
625C22×C22⋊C4—431no—
626C22×C22⋊C4—431no—
627C22×C22⋊C4—431no—
628C22×C22⋊C4—431no—
629C22×C22⋊C4—438no—
630C22×C22⋊C4—431no—
631C22×C22⋊C4—431no—
632C22×C22⋊C4—431no—
633C22×C22⋊C4—438no—
634C22×C22⋊C4—868no—
635C22×C22⋊C4—868no—
636C22×C22⋊C4C2×D4311yescharacteristic, complemented
637C22×C22⋊C4C2×D4311yescharacteristic, complemented
638C22×C22⋊C4C2×D4311yescharacteristic, complemented
639C22×C42—431no—
640C22×C42—431no—
641#390—438no—
642#390—438no—
643#386—438no—
644#386—438no—
645#386—438no—
646#386C2×D4318yescomplemented
647#380—438no—
648#379—438no—
649#379—438no—
650C4×C22⋊C4—438no—
651C2×#95—431no—
652C2×#95—431no—
653C2×#95C2×D4311yescharacteristic, complemented
654C2×#95C2×D4311yescharacteristic, complemented
655C43C2×D4×C22⋊C411yescharacteristic, complemented, Sylow
656C25—431no—
657C25—431no—
658C25—431no—
659C25—438no—
660C25—438no—
661C25—434no—
662C25—434no—
663C25—864no—
664C25—864no—
665C25—864no—
666C25—864no—
667C25—864no—
668C25—864no—
669C25—864no—
670C25—864no—
671C25—1722no—
672C25—1722no—
673C25—1722no—
674C25—1722no—
675C25C22×D4311yescharacteristic
676C25C22×D4311yescharacteristic
677C22×D4—24no—
678C22×D4—24no—
679C22×D4—438no—
680C22×D4—438no—
681C22×D4—438no—
682C22×D4—434no—
683C22×D4—438no—
684C22×D4—434no—
685C22×D4—4364no—
686C22×D4—438no—
687C22×D4—434no—
688C22×D4—864no—
689C22×D4—864no—
690C22×D4—864no—
691C22×D4—864no—
692C22×D4—86128no—
693C22×D4—8632no—
694C22×D4—8632no—
695C22×D4C4×D4318yescomplemented
696C22×D4C22×D4314yes—
697C23×C4—24no—
698C23×C4—24no—
699C23×C4—42no—
700C23×C4—431no—
701C23×C4—431no—
702C23×C4—438no—
703C23×C4—434no—
704C23×C4—431no—
705C23×C4—431no—
706C23×C4—431no—
707C23×C4—434no—
708C23×C4—434no—
709C23×C4—434no—
710C23×C4—864no—
711C23×C4—864no—
712C23×C4—864no—
713C23×C4—864no—
714C23×C4—864no—
715C23×C4—864no—
716C23×C4—864no—
717C23×C4—864no—
718C23×C4—1722no—
719C23×C4—1722no—
720C23×C4—1722no—
721C23×C4C22×D4311yescharacteristic
722C23×C4C22×D4311yescharacteristic
723C23×C4C22×D4311yescharacteristic
724C23×C4C22×D4311yescharacteristic
725C23×C4C22×D4311yescharacteristic
726C23×C4C22×D4314yescomplemented
727C4×D4—8632no—
728C4×D4—8632no—
729C2×C4⋊C4—434no—
730C2×C4⋊C4—434no—
731C2×C4⋊C4—864no—
732C2×C4⋊C4—864no—
733C2×C22⋊C4—24no—
734C2×C22⋊C4—24no—
735C2×C22⋊C4—42no—
736C2×C22⋊C4—438no—
737C2×C22⋊C4—434no—
738C2×C22⋊C4—434no—
739C2×C22⋊C4—434no—
740C2×C22⋊C4—434no—
741C2×C22⋊C4—434no—
742C2×C22⋊C4—434no—
743C2×C22⋊C4—434no—
744C2×C22⋊C4—434no—
745C2×C22⋊C4—434no—
746C2×C22⋊C4—434no—
747C2×C22⋊C4—434no—
748C2×C22⋊C4—434no—
749C2×C22⋊C4—434no—
750C2×C22⋊C4—8632no—
751C2×C22⋊C4—8632no—
752C2×C22⋊C4—864no—
753C2×C22⋊C4—864no—
754C2×C22⋊C4—864no—
755C2×C22⋊C4—864no—
756C2×C22⋊C4—864no—
757C2×C22⋊C4—864no—
758C2×C22⋊C4—864no—
759C2×C22⋊C4—864no—
760C2×C22⋊C4—864no—
761C2×C22⋊C4—1722no—
762C2×C22⋊C4—1722no—
763C2×C22⋊C4—1722no—
764C2×C22⋊C4C22×D4314yescomplemented
765C2×C22⋊C4C22×D4314yescomplemented
766C2×C22⋊C4C22×D4314yescomplemented
767C2×C42—434no—
768C2×C42—434no—
769C2×C42—864no—
770C2×C42—864no—
771#95—434no—
772#95—434no—
773#95C22×D4314yescomplemented
774#95C22×D4314yescomplemented
775C24—22no—
776C24—22no—
777C24—22no—
778C24—22no—
779C24—22no—
780C24—22no—
781C24—22no—
782C24—22no—
783C24—22no—
784C24—22no—
785C24—434no—
786C24—434no—
787C24—434no—
788C24—434no—
789C24—434no—
790C24—434no—
791C24—432no—
792C24—432no—
793C24—434no—
794C24—432no—
795C24—4316no—
796C24—4316no—
797C24—868no—
798C24—868no—
799C24—8632no—
800C24—868no—
801C24—868no—
802C24—8632no—
803C24—868no—
804C24—8632no—
805C24—868no—
806C24—862no—
807C24—862no—
808C24—862no—
809C24—862no—
810C24—862no—
811C24—862no—
812C24—862no—
813C24—862no—
814C24—8632no—
815C24—862no—
816C24—868no—
817C24—868no—
818C24—862no—
819C24—862no—
820C24—862no—
821C24—862no—
822C24—862no—
823C24—17216no—
824C24—1724no—
825C24—1724no—
826C24—17216no—
827C24—1724no—
828C24—1724no—
829C24—17216no—
830C24—17216no—
831C24—17216no—
832C24—17216no—
833C24—17216no—
834C24—17216no—
835C24—17216no—
836C24—17216no—
837C24C2×C4×D4314yes—
838C24C2×C4×D4314yes—
839C24D4×D4314yes—
840C24D4×D4314yes—
841C24C23×D4312yes—
842C24C23×D4312yes—
843C24C23×D4311yescharacteristic
844C2×D4—232no—
845C2×D4—28no—
846C2×D4—28no—
847C2×D4—4364no—
848C2×D4—4316no—
849C2×D4—4316no—
850C2×D4—4316no—
851C2×D4—4316no—
852C2×D4—4316no—
853C2×D4—8632no—
854C2×D4—868no—
855C2×D4—868no—
856C2×D4—8632no—
857C2×D4—868no—
858C2×D4—868no—
859C2×D4—86256no—
860C2×D4C2×C4×D43116yescomplemented
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—28no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—28no—
876C22×C4—44no—
877C22×C4—416no—
878C22×C4—434no—
879C22×C4—434no—
880C22×C4—434no—
881C22×C4—432no—
882C22×C4—434no—
883C22×C4—432no—
884C22×C4—4316no—
885C22×C4—432no—
886C22×C4—432no—
887C22×C4—432no—
888C22×C4—8632no—
889C22×C4—868no—
890C22×C4—868no—
891C22×C4—868no—
892C22×C4—868no—
893C22×C4—868no—
894C22×C4—868no—
895C22×C4—862no—
896C22×C4—862no—
897C22×C4—862no—
898C22×C4—862no—
899C22×C4—862no—
900C22×C4—862no—
901C22×C4—862no—
902C22×C4—868no—
903C22×C4—862no—
904C22×C4—862no—
905C22×C4—862no—
906C22×C4—862no—
907C22×C4—868no—
908C22×C4—1724no—
909C22×C4—1724no—
910C22×C4—17216no—
911C22×C4—17216no—
912C22×C4—1724no—
913C22×C4—17216no—
914C22×C4C2×C4×D4314yes—
915C22×C4D4×D4314yescomplemented
916C22×C4C23×D4312yes—
917C22×C4C23×D4312yes—
918C22×C4C23×D4312yes—
919C22×C4C23×D4312yes—
920C22×C4C23×D4312yes—
921C4⋊C4—868no—
922C4⋊C4—868no—
923C22⋊C4—28no—
924C22⋊C4—28no—
925C22⋊C4—44no—
926C22⋊C4—4316no—
927C22⋊C4—868no—
928C22⋊C4—868no—
929C22⋊C4—868no—
930C22⋊C4—868no—
931C22⋊C4—868no—
932C22⋊C4—868no—
933C22⋊C4—868no—
934C22⋊C4—868no—
935C22⋊C4—868no—
936C22⋊C4—1724no—
937C22⋊C4—1724no—
938C22⋊C4—1724no—
939C42—868no—
940C42—868no—
941C23—28no—
942C23—28no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—28no—
948C23—28no—
949C23—28no—
950C23—28no—
951C23—28no—
952C23—28no—
953C23—28no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—44no—
961C23—44no—
962C23—44no—
963C23—44no—
964C23—4316no—
965C23—4316no—
966C23—434no—
967C23—434no—
968C23—434no—
969C23—434no—
970C23—434no—
971C23—434no—
972C23—434no—
973C23—8632no—
974C23—8632no—
975C23—8632no—
976C23—868no—
977C23—868no—
978C23—868no—
979C23—868no—
980C23—862no—
981C23—862no—
982C23—862no—
983C23—862no—
984C23—862no—
985C23—862no—
986C23—862no—
987C23—862no—
988C23—868no—
989C23—868no—
990C23—868no—
991C23—868no—
992C23—868no—
993C23—868no—
994C23—868no—
995C23—868no—
996C23—868no—
997C23—8632no—
998C23—868no—
999C23—868no—
1000C23—862no—
1001C23—862no—
1002C23—862no—
1003C23—862no—
1004C23—862no—
1005C23—862no—
1006C23—17216no—
1007C23—17216no—
1008C23—17216no—
1009C23—17216no—
1010C23—17216no—
1011C23—172128no—
1012C23—17216no—
1013C23—17216no—
1014C23—17216no—
1015C23—17216no—
1016C23—172128no—
1017C23—17216no—
1018C23—1724no—
1019C23—1724no—
1020C23—1724no—
1021C23—1724no—
1022C23C22⋊C4×D43116yescomplemented
1023C23C22×C4×D4314yes—
1024C23C22×C4×D4314yes—
1025C23C22×C4×D4312yes—
1026C23C2×D4×D4314yes—
1027C23C2×D4×D4314yes—
1028C23C2×D4×D4312yes—
1029C23C2×D4×D4312yes—
1030C23C2×D4×D4312yes—
1031C23#41×D4312yes—
1032C23#1306337012yes—
1033C23#1306337112yes—
1034C23C24×D4311yescharacteristic
1035D4—232no—
1036D4—4364no—
1037D4—8632no—
1038D4—8632no—
1039C2×C4—28no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—28no—
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—416no—
1055C2×C4—44no—
1056C2×C4—44no—
1057C2×C4—44no—
1058C2×C4—4316no—
1059C2×C4—434no—
1060C2×C4—434no—
1061C2×C4—434no—
1062C2×C4—434no—
1063C2×C4—8632no—
1064C2×C4—862no—
1065C2×C4—862no—
1066C2×C4—868no—
1067C2×C4—862no—
1068C2×C4—862no—
1069C2×C4—862no—
1070C2×C4—862no—
1071C2×C4—862no—
1072C2×C4—862no—
1073C2×C4—862no—
1074C2×C4—862no—
1075C2×C4—862no—
1076C2×C4—17216no—
1077C2×C4—17216no—
1078C2×C4—17216no—
1079C2×C4—1724no—
1080C2×C4—1724no—
1081C2×C4—1724no—
1082C2×C4C22×C4×D4314yes—
1083C2×C4C2×D4×D4314yescomplemented
1084C22—24no—
1085C22—24no—
1086C22—24no—
1087C22—24no—
1088C22—232no—
1089C22—24no—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—416no—
1098C22—42no—
1099C22—438no—
1100C22—438no—
1101C22—864no—
1102C22—864no—
1103C22—864no—
1104C22—864no—
1105C22—864no—
1106C22—864no—
1107C22—864no—
1108C22—864no—
1109C22—8632no—
1110C22—8632no—
1111C22—864no—
1112C22—864no—
1113C22—864no—
1114C22—864no—
1115C22—864no—
1116C22—864no—
1117C22—864no—
1118C22—17264no—
1119C22—17264no—
1120C22—1722no—
1121C22—1722no—
1122C22—1722no—
1123C22—17216no—
1124C22—1722no—
1125C22C2×C22⋊C4×D4314yes—
1126C22C2×C22⋊C4×D4318yescomplemented
1127C22C4×D4×D4314yes—
1128C22#1458337114yes—
1129C22#1458353114yes—
1130C22#1458353314yes—
1131C22#1458353814yes—
1132C22#1458354114yes—
1133C22C23×C4×D4311yescharacteristic
1134C22C22×D4×D4311yescharacteristic
1135C22C22×D4×D4311yescharacteristic
1136C22C22×D4×D4311yescharacteristic
1137C22C2×#41×D4311yescharacteristic
1138C22C2×#1306337011yescharacteristic
1139C22C2×#1306337111yescharacteristic
1140C4—24no—
1141C4—24no—
1142C4—42no—
1143C4—42no—
1144C4—42no—
1145C4—438no—
1146C4—864no—
1147C4—1722no—
1148C4—1722no—
1149C4—1722no—
1150C2—28no—
1151C2—44no—
1152C2—868no—
1153C2—868no—
1154C2—1724no—
1155C2#1913741318yesdirect product factor
1156C2C22×C22⋊C4×D4311yescharacteristic
1157C2C2×C4×D4×D4311yescharacteristic
1158C2C2×#1458337111yescharacteristic
1159C2C2×#1458353111yescharacteristic
1160C2C2×#1458353311yescharacteristic
1161C2C2×#1458353811yescharacteristic
1162C2C2×#1458354111yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#386C2
socleC24×C43C24
prime radicalC23×D4×D43C2
cosocleC23×C43C25
hypercenterC2×#386D43
hypocenterC43C2×D4×C22⋊C4
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D43C2semidirect
3. C22×(C22⋊D43)⋊C4C2semidirect
4. C23×(C2×D43)⋊C4C2semidirect
5. C22×C22⋊C4×D43C2semidirect
6. #19137413C2direct (N × H)
7. C2×#14582799C2semidirect
8. C2×#14582799C2semidirect
9. C2×#14582779C2semidirect
10. C2×#14582777C2semidirect
11. C2×#14582777C2semidirect
12. C2×#14582758C2semidirect
13. C2×#14582754C2semidirect
14. C2×#14582754C2semidirect
15. C2×#14582746C2semidirect
16. C2×C43×#386C2semidirect
24. C22×D4×D43C4semidirect
26. C24×Dic43C22semidirect
28. C23×C4×D43C22semidirect
29. C23×C4×D43C22semidirect
31. C2×C4×C22⋊D43C22semidirect
33. C2×(C22⋊D43)⋊C4C22semidirect
34. C22×Dic43⋊C4C22semidirect
35. C22×Dic43⋊C4C22semidirect
36. C22×C22⋊Dic43C22semidirect
37. C22×C22⋊Dic43C22semidirect
38. C22×C22⋊Dic43C22semidirect
44. C22×(C2×D43)⋊C4C22semidirect
45. C22×(C2×D43)⋊C4C22semidirect
46. C22×(C2×D43)⋊C4C22semidirect
47. C22×(C2×D43)⋊C4C22semidirect
48. C22×(C2×D43)⋊C4C22semidirect
49. C22×(C2×D43)⋊C4C22semidirect
50. C22×(C2×D43)⋊C4C22semidirect
52. C2×C22⋊C4×D43C22semidirect
53. C22×C4×Dic43C22semidirect
54. C22×C4×Dic43C22semidirect
55. #14582799C22semidirect
56. #14582799C22semidirect
57. #14582779C22semidirect
58. #14582777C22semidirect
59. #14582777C22semidirect
60. #14582758C22semidirect
61. #14582754C22semidirect
62. #14582754C22semidirect
63. #14582746C22semidirect
64. C2×C43⋊#95C22semidirect
65. C2×C43⋊#95C22semidirect
67. C24×C4×C43C22semidirect
68. C22×C22⋊C4×C43C22semidirect
69. C22×C22⋊C4×C43C22semidirect
70. C22×C22⋊C4×C43C22semidirect
71. C43×#386C22semidirect
72. C2×#95×C43C22semidirect
73. C2×#95×C43C22semidirect
86. C24×D43C2×C4semidirect
87. C24×D43C2×C4semidirect
95. C22×D172C2×C4semidirect
100. C22×C22⋊D43C2×C4semidirect
108. C2×D4×D43C2×C4semidirect
117. C23×Dic43C23semidirect
126. C22×C4×D43C2×C4semidirect
128. C22×C4×D43C23semidirect
129. C22×C4×D43C23semidirect
134. C2×Dic43⋊C4C23semidirect
135. C2×Dic43⋊C4C23semidirect
139. C2×C22⋊Dic43C23semidirect
140. C2×C22⋊Dic43C23semidirect
141. C2×C22⋊Dic43C23semidirect
152. C2×(C2×D43)⋊C4D4semidirect
157. C2×(C2×D43)⋊C4C23semidirect
158. C2×(C2×D43)⋊C4C23semidirect
159. C2×(C2×D43)⋊C4C23semidirect
160. C2×(C2×D43)⋊C4C23semidirect
161. C2×(C2×D43)⋊C4C23semidirect
162. C2×(C2×D43)⋊C4C23semidirect
166. C2×C4×Dic43C23semidirect
167. C2×C4×Dic43C23semidirect
168. C43⋊#95C23semidirect
169. C43⋊#95C23semidirect
174. C22×D4×C43C2×C4semidirect
184. C23×C4×C43C23semidirect
188. C2×C22⋊C4×C43C23semidirect
189. C2×C22⋊C4×C43C23semidirect
190. C2×C22⋊C4×C43C23semidirect
191. #95×C43C23semidirect
192. #95×C43C23semidirect
253. C23×D43C22×C4semidirect
254. C23×D43C22×C4semidirect
265. C2×D4×C43C22×C4semidirect
284. C22×C4×C43C2×D4semidirect
293. C2×C22⋊D43C22⋊C4semidirect
295. C2×C22⋊D43C22×C4semidirect
316. C22×Dic43C2×D4semidirect
326. C2×D172C22×C4semidirect
338. C2×C4×D43C22×C4semidirect
354. (C2×D43)⋊C4C2×D4semidirect
382. C23×C43C2×C22⋊C4semidirect
444. C22×D43C2×C22⋊C4semidirect
445. C22×D43C4×D4semidirect
474. C2×C4×C43C22×D4semidirect
476. C22⋊D43C2×C22⋊C4semidirect
493. C2×Dic43C2×C22⋊C4semidirect
497. C2×Dic43C22×D4semidirect
519. C22×C43C22×C22⋊C4semidirect
557. C2×D43C22×C22⋊C4semidirect
558. C2×D43C2×C4×D4semidirect
568. Dic43C22×C22⋊C4semidirect
580. C2×#386D43semidirect
587. C2×C43D4×C22⋊C4semidirect
612. C24×C4C2×D43semidirect
636. C22×C22⋊C4C2×D43semidirect
637. C22×C22⋊C4C2×D43semidirect
638. C22×C22⋊C4C2×D43semidirect
646. #386C2×D43semidirect
653. C2×#95C2×D43semidirect
654. C2×#95C2×D43semidirect
655. C43C2×D4×C22⋊C4semidirect
695. C22×D4C4×D43semidirect
726. C23×C4C22×D43semidirect
764. C2×C22⋊C4C22×D43semidirect
765. C2×C22⋊C4C22×D43semidirect
766. C2×C22⋊C4C22×D43semidirect
773. #95C22×D43semidirect
774. #95C22×D43semidirect
860. C2×D4C2×C4×D43semidirect
915. C22×C4D4×D43semidirect
1022. C23C22⋊C4×D43semidirect
1083. C2×C4C2×D4×D43semidirect
1126. C22C2×C22⋊C4×D43semidirect
1155. C2#19137413direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D4×D432
C22×C4×C22⋊D432
C22×(C22⋊D43)⋊C42
C23×(C2×D43)⋊C42
C22×C22⋊C4×D432
#191374132
C2×#145827992
C2×#145827792
C2×#145827772
C2×#145827582
C2×#145827542
C2×#145827462
C2×C43×#3862
C2×D4×C22⋊C443