Finite Group Databasebeta

← C2×#19143641 #25961345

Subgroups — C2×#19143641 #25961345

Order 11008.

2306 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583411C211yesmaximal, characteristic
2#19143641C2116yesmaximal, direct product factor
3C2×#14582978C211yesmaximal, characteristic, complemented
4C2×#14582976C211yesmaximal, characteristic, complemented
5C2×#14582972C211yesmaximal, characteristic, complemented
6C2×#14582972C211yesmaximal, characteristic, complemented
7C2×#14582969C211yesmaximal, characteristic, complemented
8C2×#14582969C211yesmaximal, characteristic, complemented
9C2×C8×D172C211yesmaximal, characteristic, complemented
10C2×#14582964C211yesmaximal, characteristic, complemented
11C2×#14582960C211yesmaximal, characteristic, complemented
12C2×#14582864C211yesmaximal, characteristic, complemented
13C2×#14582864C211yesmaximal, characteristic, complemented
14C2×#14582861C211yesmaximal, characteristic, complemented
15C2×C22⋊C8×D43C211yesmaximal, characteristic, complemented
16C2×C43×#433C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C22×#10621872C2211yescharacteristic
21C22×#10621872C2211yescharacteristic, complemented
22C22×#10621872C2211yescharacteristic, complemented
23C22×C8×D43C2211yescharacteristic
24C22×C8×D43C2211yescharacteristic
25C22×C8×D43C2211yescharacteristic, complemented
26C22×C8×D43C2211yescharacteristic, complemented
27#14583411C418yes—
28#14583411C2218yes—
29C2×#13063309C411yescharacteristic
30C2×#13063309C411yescharacteristic
31C2×#13063305C411yescharacteristic
32C2×#13063305C411yescharacteristic
33C2×#13063300C411yescharacteristic
34C2×#13063300C411yescharacteristic
35C2×#13063295C411yescharacteristic
36C2×#13063295C411yescharacteristic
37C2×C4×D172C2211yescharacteristic
38C2×C4×D172C2211yescharacteristic
39C2×C4×D172C2211yescharacteristic
40C2×C4×D172C2211yescharacteristic
41#14582978C2218yescomplemented
42#14582976C2218yescomplemented
43#14582972C2218yescomplemented
44#14582972C2218yescomplemented
45#14582969C2218yescomplemented
46#14582969C2218yescomplemented
47C8×D172C2218yescomplemented
48#14582964C2218yescomplemented
49#14582960C2218yescomplemented
50C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
51C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
52#14582864C2218yescomplemented
53#14582864C2218yescomplemented
54#14582861C2218yescomplemented
55C2×C22⋊(C43⋊C8)C2211yescharacteristic
56C2×C22⋊(C43⋊C8)C2211yescharacteristic
57C2×(C2×D43)⋊C8C2211yescharacteristic
58C2×(C2×D43)⋊C8C2211yescharacteristic
59C2×(C2×D43)⋊C8C2211yescharacteristic
60C2×(C2×D43)⋊C8C2211yescharacteristic
61C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
62C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
63C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
64C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
65C22⋊C8×D43C2218yescomplemented
66C2×#13063236C2211yescharacteristic, complemented
67C2×C4×C43⋊C8C2211yescharacteristic, complemented
68C2×#117×C43C2211yescharacteristic
69C43×#433C2218yescomplemented
70C2×C4⋊C8×C43C2211yescharacteristic, complemented
71C2×C4⋊C8×C43C2211yescharacteristic, complemented
72C2×C22⋊C8×C43C2211yescharacteristic
73C2×C22⋊C8×C43C2211yescharacteristic
74C2×#97×C43C2211yescharacteristic, complemented
75C2×C4×C8×C43C2211yescharacteristic, complemented
76C24×D43C2×C411yescharacteristic
77C2×#10621898—42no—
78C2×#10621898—42no—
79C2×#10621898C2×C414yes—
80C2×#10621898C2314yes—
81C22×Dic86C2×C411yescharacteristic
82C22×D172C2×C411yescharacteristic
83C22×D172C2×C411yescharacteristic
84C22×D172C2×C411yescharacteristic
85C22×D172C2×C411yescharacteristic
86C22×D172C2×C411yescharacteristic
87C22×C22⋊D43C2×C411yescharacteristic
88C22×C22⋊D43C2×C411yescharacteristic
89C23×Dic43C2×C411yescharacteristic
90C22×C4×D43—42no—
91C22×C4×D43—42no—
92C22×C4×D43C2×C411yescharacteristic
93C22×C4×D43C2×C411yescharacteristic
94C22×C4×D43C2×C414yes—
95C22×C4×D43C2311yescharacteristic
96C22×C4×D43C2311yescharacteristic
97C22×C4×D43C2311yescharacteristic
98C22×C4×D43C2311yescharacteristic
99C22×C4×D43C2314yes—
100C2×#10621872—42no—
101C2×#10621872—42no—
102C2×#10621872—42no—
103C2×#10621872—42no—
104C2×#10621872C2314yes—
105C2×#10621872C2314yes—
106C2×#10621872C2314yescomplemented
107C2×#10621872C2314yescomplemented
108C22×C43⋊C8C2311yescharacteristic
109C22×C43⋊C8C2311yescharacteristic
110C22×C43⋊C8C2311yescharacteristic
111C22×C43⋊C8C2311yescharacteristic
112C2×C8×D43—42no—
113C2×C8×D43—42no—
114C2×C8×D43—42no—
115C2×C8×D43—42no—
116C2×C8×D43C2314yes—
117C2×C8×D43C2314yes—
118C2×C8×D43C2314yescomplemented
119C2×C8×D43C2314yescomplemented
120#13063309C2×C418yes—
121#13063309C2×C418yes—
122#13063305C2×C418yes—
123#13063305C2×C418yes—
124#13063300C2×C418yes—
125#13063300C2×C418yes—
126#13063295C2×C418yes—
127#13063295C2×C418yes—
128C4×D172C2×C414yes—
129C4×D172C2×C414yes—
130C4×D172C2×C414yes—
131C4×D172C2×C414yes—
132C4×D172C2314yes—
133C4×D172C2314yes—
134C4×D172C2314yes—
135C4×D172C2314yes—
136C2×C4⋊Dic43C2×C411yescharacteristic
137C2×C4⋊Dic43C2×C411yescharacteristic
138C2×C4⋊Dic43C2×C411yescharacteristic
139C2×C4⋊Dic43C2×C411yescharacteristic
140C2×(C2×D43)⋊C4C2×C411yescharacteristic
141C2×(C2×D43)⋊C4C2×C411yescharacteristic
142C2×(C2×D43)⋊C4C2×C411yescharacteristic
143C2×(C2×D43)⋊C4C2×C411yescharacteristic
144C2×(C2×D43)⋊C4C2×C411yescharacteristic
145C2×(C2×D43)⋊C4C2×C411yescharacteristic
146C2×(C2×D43)⋊C4C2×C411yescharacteristic
147C2×(C2×D43)⋊C4C2×C411yescharacteristic
148C4⋊(C43⋊C8)C2314yescomplemented
149C4⋊(C43⋊C8)C2314yescomplemented
150C22⋊(C43⋊C8)C2314yes—
151C22⋊(C43⋊C8)C2314yes—
152(C2×D43)⋊C8C2314yes—
153(C2×D43)⋊C8C2314yes—
154(C2×D43)⋊C8C2314yes—
155(C2×D43)⋊C8C2314yes—
156(C2×D43)⋊C8C2314yescomplemented
157(C2×D43)⋊C8C2314yescomplemented
158(C2×D43)⋊C8C2314yescomplemented
159(C2×D43)⋊C8C2314yescomplemented
160#13063236C2314yescomplemented
161C4×C43⋊C8C2314yescomplemented
162C23×C4×C43C2311yescharacteristic
163C22×C8×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165C22×C8×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167#117×C43C2×C414yes—
168#117×C43C2314yes—
169C2×C4⋊C4×C43C2×C411yescharacteristic
170C2×C4⋊C4×C43C2×C411yescharacteristic
171C2×C22⋊C4×C43C2×C411yescharacteristic
172C2×C22⋊C4×C43C2×C411yescharacteristic
173C2×C42×C43C2311yescharacteristic
174C2×C42×C43C2311yescharacteristic
175C4⋊C8×C43C2314yescomplemented
176C4⋊C8×C43C2314yescomplemented
177C22⋊C8×C43C2314yes—
178C22⋊C8×C43C2314yes—
179#97×C43C2314yescomplemented
180C4×C8×C43C2314yescomplemented
181C24×C43C22×C411yescharacteristic
182C23×D43—24no—
183C23×D43—42no—
184C23×D43—42no—
185C23×D43C22×C411yescharacteristic
186C23×D43C22×C411yescharacteristic
187C23×D43C22×C411yescharacteristic
188C23×D43C22×C411yescharacteristic
189C23×D43C22×C414yes—
190C22×C4×C43—22no—
191C22×C4×C43—22no—
192C22×C4×C43C22×C411yescharacteristic
193C22×C4×C43C22×C411yescharacteristic
194C22×C4×C43C22×C411yescharacteristic
195C22×C4×C43C22×C411yescharacteristic
196C22×C4×C43C22×C411yescharacteristic
197C22×C4×C43C22×C412yes—
198C22×C4×C43C2412yes—
199C22×C4×C43C2411yescharacteristic
200C2×C22⋊D43—42no—
201C2×C22⋊D43—42no—
202C2×C22⋊D43C22×C414yes—
203C2×C22⋊D43C22×C414yes—
204C22×Dic43—42no—
205C22×Dic43C22×C411yescharacteristic
206C22×Dic43C22×C411yescharacteristic
207C22×Dic43C22×C411yescharacteristic
208C22×Dic43C22×C411yescharacteristic
209C22×Dic43C22×C414yes—
210#10621898—48no—
211#10621898—44no—
212#10621898—44no—
213C2×D172—24no—
214C2×D172—24no—
215C2×D172—42no—
216C2×D172—42no—
217C2×D172—42no—
218C2×D172C22×C414yes—
219C2×D172C22×C414yes—
220C2×D172C22×C414yes—
221C2×D172C22×C414yes—
222C2×D172C22×C414yes—
223C2×C4×D43—22no—
224C2×C4×D43—22no—
225C2×C4×D43—22no—
226C2×C4×D43—22no—
227C2×C4×D43—22no—
228C2×C4×D43—22no—
229C2×C4×D43—22no—
230C2×C4×D43—22no—
231C2×C4×D43—42no—
232C2×C4×D43—42no—
233C2×C4×D43—48no—
234C2×C4×D43—44no—
235C2×C4×D43—44no—
236C2×C4×D43C22×C412yes—
237C2×C4×D43C22×C412yes—
238C2×C4×D43C22×C412yes—
239C2×C4×D43C22×C412yes—
240C2×C4×D43C22×C414yes—
241C2×C4×D43C22×C414yes—
242C2×C4×D43C2412yes—
243C2×C4×D43C2412yes—
244C2×C4×D43C2412yes—
245C2×C4×D43C2412yes—
246C2×Dic86—42no—
247C2×Dic86C22×C414yes—
248C2×C8×C43—22no—
249C2×C8×C43—22no—
250C2×C8×C43—22no—
251C2×C8×C43—22no—
252C2×C8×C43C2412yes—
253C2×C8×C43C2412yes—
254C2×C8×C43C2412yes—
255C2×C8×C43C2412yes—
256C4⋊C4×C43C22×C414yes—
257C4⋊C4×C43C22×C414yes—
258C22⋊C4×C43C22×C414yes—
259C22⋊C4×C43C22×C414yes—
260C42×C43C22×C412yes—
261C42×C43C22×C412yes—
262C42×C43C2412yes—
263C42×C43C2412yes—
264(C2×D43)⋊C4C22×C414yes—
265(C2×D43)⋊C4C22×C414yes—
266(C2×D43)⋊C4C22×C414yes—
267(C2×D43)⋊C4C22×C414yes—
268(C2×D43)⋊C4C22×C414yes—
269(C2×D43)⋊C4C22×C414yes—
270(C2×D43)⋊C4C22×C414yes—
271(C2×D43)⋊C4C22×C414yes—
272C4⋊Dic43C22×C414yes—
273C4⋊Dic43C22×C414yes—
274C4⋊Dic43C22×C414yes—
275C4⋊Dic43C22×C414yes—
276C2×C43⋊C8—22no—
277C2×C43⋊C8—22no—
278C2×C43⋊C8—22no—
279C2×C43⋊C8—22no—
280C2×C43⋊C8C2412yes—
281C2×C43⋊C8C2412yes—
282C2×C43⋊C8C2412yes—
283C2×C43⋊C8C2412yes—
284#10621872—44no—
285#10621872—44no—
286#10621872—44no—
287#10621872—44no—
288C8×D43—44no—
289C8×D43—44no—
290C8×D43—44no—
291C8×D43—44no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43C23×C412yes—
296C23×C43C23×C411yescharacteristic
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—28no—
309C22×D43—44no—
310C22×D43—44no—
311C22×D43—416no—
312C22×D43#13114yes—
313C22×D43C23×C412yes—
314C22×D43C23×C412yes—
315C22×D43C23×C412yes—
316C22×D43C23×C412yes—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—24no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43C23×C412yes—
326C2×C4×C43C23×C412yes—
327C2×C4×C43C23×C412yes—
328C2×C4×C43C23×C412yes—
329C2×C4×C43C23×C412yes—
330C2×C4×C43C23×C411yescharacteristic
331C2×C4×C43H(5,𝔽2)12yes—
332C2×C4×C43H(5,𝔽2)12yes—
333C2×C4×C43C2511yescharacteristic
334C22⋊D43—44no—
335C22⋊D43—44no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—44no—
341C2×Dic43C23×C412yes—
342C2×Dic43C23×C412yes—
343C2×Dic43C23×C412yes—
344C2×Dic43C23×C412yes—
345D172—28no—
346D172—28no—
347D172—44no—
348D172—44no—
349D172—44no—
350C4×D43—24no—
351C4×D43—24no—
352C4×D43—24no—
353C4×D43—24no—
354C4×D43—22no—
355C4×D43—22no—
356C4×D43—22no—
357C4×D43—22no—
358C4×D43—22no—
359C4×D43—22no—
360C4×D43—22no—
361C4×D43—22no—
362C4×D43—44no—
363C4×D43—44no—
364Dic86—44no—
365C8×C43—22no—
366C8×C43—22no—
367C8×C43—22no—
368C8×C43—22no—
369C43⋊C8—22no—
370C43⋊C8—22no—
371C43⋊C8—22no—
372C43⋊C8—22no—
373C2×#2976—431nomaximal, Sylow
374C22×C43—22no—
375C22×C43—22no—
376C22×C43—22no—
377C22×C43—44no—
378C22×C43#51812yes—
379C22×C43C2×#13112yes—
380C22×C43#56812yes—
381C22×C43C24×C411yescharacteristic
382C2×D43—22no—
383C2×D43—28no—
384C2×D43—22no—
385C2×D43—22no—
386C2×D43—22no—
387C2×D43—22no—
388C2×D43—22no—
389C2×D43—22no—
390C2×D43—22no—
391C2×D43—22no—
392C2×D43—22no—
393C2×D43—22no—
394C2×D43—416no—
395C2×D43—44no—
396C2×D43—44no—
397C2×D43—44no—
398C2×D43C2×#13114yes—
399C4×C43—22no—
400C4×C43—22no—
401C4×C43—22no—
402C4×C43—22no—
403C4×C43—22no—
404C4×C43#51812yes—
405C4×C43C2×H(5,𝔽2)11yescharacteristic
406C4×C43C2×H(5,𝔽2)11yescharacteristic
407Dic43—22no—
408Dic43—22no—
409Dic43—22no—
410Dic43—22no—
411C2×#525—431no—
412#2976—4316no—
413C2×#436—431no—
414C2×#436—431no—
415C2×#435—431no—
416C2×#435—431no—
417C2×#435—431no—
418C2×#435—431no—
419C2×C8×D4—431no—
420C2×C8×D4—431no—
421C2×#433—431no—
422C2×#433D4311yescharacteristic, complemented
423C2×#408—431no—
424C2×#408—431no—
425C2×#407—431no—
426C22×C22⋊C8—431no—
427C2×C43—42no—
428C2×C43#297614yescomplemented
429C2×C43C2×#51811yescharacteristic
430C2×C43C22×#13111yescharacteristic
431C2×C43C2×#56811yescharacteristic
432D43—24no—
433D43—42no—
434D43—42no—
435D43—42no—
436C22×#41—431no—
437C24×C4—431no—
438C22×M16—431no—
439C22×M16—431no—
440C22×M16—431no—
441C22×M16—431no—
442C23×C8—431no—
443C23×C8—431no—
444C23×C8—431no—
445C23×C8—431no—
446#525—438no—
447#525—438no—
448C2×#123—431no—
449C2×#123—431no—
450C2×C22⋊Q8—431no—
451C2×C22⋊Q8—431no—
452C2×#121—431no—
453C2×#121—431no—
454C2×#120—431no—
455C2×#120—431no—
456C2×C4×D4—431no—
457C2×C4×D4—431no—
458C2×C4×D4—431no—
459C2×C4×D4—431no—
460C2×#117C2×D4311yescharacteristic
461#436—438no—
462#436—438no—
463#435—438no—
464#435—438no—
465#435—438no—
466#435—438no—
467C8×D4—438no—
468C8×D4—438no—
469#433—438no—
470#433C2×D4318yescomplemented
471C2×C4⋊C8—431no—
472C2×C4⋊C8—431no—
473C2×C4⋊C8C2×D4311yescharacteristic, complemented
474C2×C4⋊C8C2×D4311yescharacteristic, complemented
475#408—438no—
476#408—438no—
477#407—438no—
478C2×C22⋊C8—431no—
479C2×C22⋊C8—431no—
480C2×C22⋊C8—431no—
481C2×C22⋊C8—431no—
482C2×C22⋊C8—431no—
483C2×C22⋊C8—431no—
484C2×C22⋊C8—431no—
485C2×C22⋊C8—431no—
486C2×C22⋊C8—431no—
487C2×C22⋊C8—431no—
488C2×C22⋊C8—438no—
489C2×C22⋊C8C2×D4311yescharacteristic
490C2×C22⋊C8C2×D4311yescharacteristic
491C2×#97—431no—
492C2×#97C2×D4311yescharacteristic, complemented
493C2×C4×C8—431no—
494C2×C4×C8C2×D4311yescharacteristic, complemented
495C43C2×#297611yescharacteristic, complemented, Sylow
496C25—431no—
497C2×#41—434no—
498C2×#41—434no—
499C2×#41—1722no—
500C2×#41—1722no—
501C22×Q8—431no—
502C22×D4—431no—
503C22×D4—431no—
504C22×D4—431no—
505C22×D4—431no—
506C22×D4—431no—
507C22×D4—431no—
508C22×D4—431no—
509C23×C4—431no—
510C23×C4—431no—
511C23×C4—431no—
512C23×C4—431no—
513C23×C4—431no—
514C23×C4—431no—
515C23×C4—431no—
516C23×C4—434no—
517C23×C4—434no—
518C23×C4—1722no—
519C23×C4—1722no—
520C23×C4C22×D4311yescharacteristic
521C2×M16—434no—
522C2×M16—434no—
523C2×M16—434no—
524C2×M16—434no—
525C2×M16—1722no—
526C2×M16—1722no—
527C2×M16—1722no—
528C2×M16—1722no—
529C22×C8—431no—
530C22×C8—431no—
531C22×C8—431no—
532C22×C8—431no—
533C22×C8—434no—
534C22×C8—434no—
535C22×C8—434no—
536C22×C8—434no—
537C22×C8—1722no—
538C22×C8—1722no—
539C22×C8—1722no—
540C22×C8—1722no—
541C22×C8C22×D4311yescharacteristic
542C22×C8C22×D4311yescharacteristic
543C22×C8C22×D4311yescharacteristic
544C22×C8C22×D4311yescharacteristic
545#123—438no—
546#123—438no—
547C22⋊Q8—438no—
548C22⋊Q8—438no—
549#121—438no—
550#121—438no—
551#120—438no—
552#120—438no—
553C4×D4—434no—
554C4×D4—434no—
555C4×D4—434no—
556C4×D4—434no—
557C4×D4—434no—
558C4×D4—434no—
559C4×D4—434no—
560C4×D4—434no—
561#117C4×D4314yes—
562#117C22×D4314yes—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—431no—
565C2×C4⋊C4—431no—
566C2×C4⋊C4—431no—
567C2×C4⋊C4C4×D4311yescharacteristic
568C2×C4⋊C4C4×D4311yescharacteristic
569C2×C22⋊C4—431no—
570C2×C22⋊C4—431no—
571C2×C22⋊C4—431no—
572C2×C22⋊C4—431no—
573C2×C22⋊C4—431no—
574C2×C22⋊C4—431no—
575C2×C22⋊C4—431no—
576C2×C22⋊C4—431no—
577C2×C22⋊C4C4×D4311yescharacteristic
578C2×C22⋊C4C4×D4311yescharacteristic
579C2×C42C22×D4311yescharacteristic
580C2×C42C22×D4311yescharacteristic
581C4⋊C8—434no—
582C4⋊C8—434no—
583C4⋊C8C22×D4314yescomplemented
584C4⋊C8C22×D4314yescomplemented
585C22⋊C8—434no—
586C22⋊C8—434no—
587C22⋊C8—434no—
588C22⋊C8—434no—
589C22⋊C8—434no—
590C22⋊C8—434no—
591C22⋊C8—434no—
592C22⋊C8—434no—
593C22⋊C8—434no—
594C22⋊C8—434no—
595C22⋊C8C22×D4314yes—
596C22⋊C8C22×D4314yes—
597#97—434no—
598#97C22×D4314yescomplemented
599C4×C8—434no—
600C4×C8C22×D4314yescomplemented
601C24—431no—
602C24—431no—
603C24—431no—
604C24—431no—
605C24—434no—
606C24—864no—
607C24—1722no—
608C24—1722no—
609C24C2×C4×D4311yescharacteristic
610#41—1728no—
611#41—1724no—
612#41—1724no—
613C2×Q8—434no—
614C2×Q8—1722no—
615C2×D4—434no—
616C2×D4—434no—
617C2×D4—434no—
618C2×D4—434no—
619C2×D4—434no—
620C2×D4—434no—
621C2×D4—434no—
622C2×D4—864no—
623C2×D4—864no—
624C2×D4—1722no—
625C2×D4—1722no—
626C2×D4—1722no—
627C2×D4—1722no—
628C2×D4—1722no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—431no—
632C22×C4—431no—
633C22×C4—431no—
634C22×C4—431no—
635C22×C4—434no—
636C22×C4—432no—
637C22×C4—432no—
638C22×C4—432no—
639C22×C4—432no—
640C22×C4—432no—
641C22×C4—432no—
642C22×C4—432no—
643C22×C4—432no—
644C22×C4—434no—
645C22×C4—434no—
646C22×C4—862no—
647C22×C4—862no—
648C22×C4—862no—
649C22×C4—862no—
650C22×C4—862no—
651C22×C4—862no—
652C22×C4—862no—
653C22×C4—862no—
654C22×C4—1728no—
655C22×C4—1724no—
656C22×C4—1724no—
657C22×C4—1722no—
658C22×C4—1722no—
659C22×C4—1722no—
660C22×C4C2×C4×D4311yescharacteristic
661C22×C4C2×C4×D4311yescharacteristic
662C22×C4C2×C4×D4311yescharacteristic
663C22×C4C2×C4×D4311yescharacteristic
664C22×C4C2×C4×D4311yescharacteristic
665C22×C4C2×C4×D4312yes—
666C22×C4C23×D4312yes—
667C22×C4C23×D4311yescharacteristic
668M16—1724no—
669M16—1724no—
670M16—1724no—
671M16—1724no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—22no—
676C2×C8—432no—
677C2×C8—432no—
678C2×C8—432no—
679C2×C8—432no—
680C2×C8—862no—
681C2×C8—862no—
682C2×C8—862no—
683C2×C8—862no—
684C2×C8—1724no—
685C2×C8—1724no—
686C2×C8—1724no—
687C2×C8—1724no—
688C2×C8C23×D4312yes—
689C2×C8C23×D4312yes—
690C2×C8C23×D4312yes—
691C2×C8C23×D4312yes—
692C4⋊C4—434no—
693C4⋊C4—434no—
694C4⋊C4—434no—
695C4⋊C4—434no—
696C4⋊C4C2×C4×D4314yes—
697C4⋊C4C2×C4×D4314yes—
698C22⋊C4—434no—
699C22⋊C4—434no—
700C22⋊C4—434no—
701C22⋊C4—434no—
702C22⋊C4—434no—
703C22⋊C4—434no—
704C22⋊C4—434no—
705C22⋊C4—434no—
706C22⋊C4C2×C4×D4314yes—
707C22⋊C4C2×C4×D4314yes—
708C42C2×C4×D4312yes—
709C42C2×C4×D4312yes—
710C42C23×D4312yes—
711C42C23×D4312yes—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—434no—
716C23—432no—
717C23—432no—
718C23—432no—
719C23—432no—
720C23—868no—
721C23—862no—
722C23—862no—
723C23—862no—
724C23—862no—
725C23—862no—
726C23—862no—
727C23—862no—
728C23—862no—
729C23—862no—
730C23—862no—
731C23—862no—
732C23—1724no—
733C23—1724no—
734C23—17216no—
735C23C22×C4×D4312yes—
736C23C22×C4×D4311yescharacteristic
737Q8—1724no—
738D4—868no—
739D4—868no—
740D4—1724no—
741D4—1724no—
742D4—1724no—
743D4—1724no—
744D4—1724no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—432no—
754C2×C4—432no—
755C2×C4—432no—
756C2×C4—432no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—864no—
762C2×C4—864no—
763C2×C4—864no—
764C2×C4—864no—
765C2×C4—862no—
766C2×C4—862no—
767C2×C4—862no—
768C2×C4—862no—
769C2×C4—862no—
770C2×C4—862no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—1724no—
774C2×C4—1724no—
775C2×C4—1724no—
776C2×C4C22×C4×D4312yes—
777C2×C4C22×C4×D4312yes—
778C2×C4C22×C4×D4312yes—
779C2×C4C22×C4×D4312yes—
780C2×C4C22×C4×D4312yes—
781C2×C4C22×C4×D4311yescharacteristic
782C2×C4#1306337112yes—
783C2×C4#1306337112yes—
784C2×C4C24×D4311yescharacteristic
785C8—22no—
786C8—22no—
787C8—22no—
788C8—22no—
789C8—862no—
790C8—862no—
791C8—862no—
792C8—862no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—434no—
798C22—862no—
799C22—868no—
800C22—862no—
801C22—862no—
802C22—862no—
803C22—862no—
804C22—862no—
805C22—862no—
806C22—862no—
807C22—862no—
808C22—862no—
809C22—862no—
810C22—17216no—
811C22—1724no—
812C22—1724no—
813C22—1724no—
814C22#1458337312yes—
815C22#131×D4312yes—
816C22#1458366412yes—
817C22C23×C4×D4311yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—22no—
823C4—862no—
824C4—862no—
825C4—862no—
826C4—862no—
827C4#1458337312yes—
828C4C2×#1306337111yescharacteristic
829C4C2×#1306337111yescharacteristic
830C2—42no—
831C2—864no—
832C2—1722no—
833C2—1722no—
834C2—1722no—
835C2#1914364114yesdirect product factor
836C2C2×#1458337311yescharacteristic
837C2C2×#131×D4311yescharacteristic
838C2C2×#1458366411yescharacteristic
subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C43×#433C2
socleC23×C43C23×C4
prime radicalC2×#14583411C2
cosocleC2×C4×C43C25
hypercenterC2×#433D43
hypocenterC43C2×#2976
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #19143641C2direct (N × H)
3. C2×#14582978C2semidirect
4. C2×#14582976C2semidirect
5. C2×#14582972C2semidirect
6. C2×#14582972C2semidirect
7. C2×#14582969C2semidirect
8. C2×#14582969C2semidirect
9. C2×C8×D172C2semidirect
10. C2×#14582964C2semidirect
11. C2×#14582960C2semidirect
12. C2×#14582864C2semidirect
13. C2×#14582864C2semidirect
14. C2×#14582861C2semidirect
15. C2×C22⋊C8×D43C2semidirect
16. C2×C43×#433C2semidirect
21. C22×#10621872C22semidirect
22. C22×#10621872C22semidirect
25. C22×C8×D43C22semidirect
26. C22×C8×D43C22semidirect
41. #14582978C22semidirect
42. #14582976C22semidirect
43. #14582972C22semidirect
44. #14582972C22semidirect
45. #14582969C22semidirect
46. #14582969C22semidirect
47. C8×D172C22semidirect
48. #14582964C22semidirect
49. #14582960C22semidirect
50. C2×C4⋊(C43⋊C8)C22semidirect
51. C2×C4⋊(C43⋊C8)C22semidirect
52. #14582864C22semidirect
53. #14582864C22semidirect
54. #14582861C22semidirect
61. C2×(C2×D43)⋊C8C22semidirect
62. C2×(C2×D43)⋊C8C22semidirect
63. C2×(C2×D43)⋊C8C22semidirect
64. C2×(C2×D43)⋊C8C22semidirect
65. C22⋊C8×D43C22semidirect
66. C2×#13063236C22semidirect
67. C2×C4×C43⋊C8C22semidirect
69. C43×#433C22semidirect
70. C2×C4⋊C8×C43C22semidirect
71. C2×C4⋊C8×C43C22semidirect
74. C2×#97×C43C22semidirect
75. C2×C4×C8×C43C22semidirect
106. C2×#10621872C23semidirect
107. C2×#10621872C23semidirect
118. C2×C8×D43C23semidirect
119. C2×C8×D43C23semidirect
148. C4⋊(C43⋊C8)C23semidirect
149. C4⋊(C43⋊C8)C23semidirect
156. (C2×D43)⋊C8C23semidirect
157. (C2×D43)⋊C8C23semidirect
158. (C2×D43)⋊C8C23semidirect
159. (C2×D43)⋊C8C23semidirect
160. #13063236C23semidirect
161. C4×C43⋊C8C23semidirect
175. C4⋊C8×C43C23semidirect
176. C4⋊C8×C43C23semidirect
179. #97×C43C23semidirect
180. C4×C8×C43C23semidirect
422. C2×#433D43semidirect
428. C2×C43#2976semidirect
470. #433C2×D43semidirect
473. C2×C4⋊C8C2×D43semidirect
474. C2×C4⋊C8C2×D43semidirect
492. C2×#97C2×D43semidirect
494. C2×C4×C8C2×D43semidirect
495. C43C2×#2976semidirect
583. C4⋊C8C22×D43semidirect
584. C4⋊C8C22×D43semidirect
598. #97C22×D43semidirect
600. C4×C8C22×D43semidirect
835. C2#19143641direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834112
#191436412
C2×#145829782
C2×#145829762
C2×#145829722
C2×#145829692
C2×C8×D1722
C2×#145829642
C2×#145829602
C2×#145828642
C2×#145828612
C2×C22⋊C8×D432
C2×C43×#4332
C2×#297643