Finite Group Databasebeta

← C2×#19143668 #25961377

Subgroups — C2×#19143668 #25961377

Order 11008.

2230 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583445C211yesmaximal, characteristic
2#19143668C2116yesmaximal, direct product factor
3C2×#14582975C211yesmaximal, characteristic, complemented
4C2×#14582974C211yesmaximal, characteristic, complemented
5C2×#14582973C211yesmaximal, characteristic, complemented
6C2×#14582970C211yesmaximal, characteristic, complemented
7C2×#14582968C211yesmaximal, characteristic, complemented
8C2×#14582967C211yesmaximal, characteristic, complemented
9C2×C8×C22⋊D43C211yesmaximal, characteristic, complemented
10C2×(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
11C2×#14582953C211yesmaximal, characteristic, complemented
12C2×#14582949C211yesmaximal, characteristic, complemented
13C2×#14582866C211yesmaximal, characteristic, complemented
14C2×#14582864C211yesmaximal, characteristic, complemented
15C2×#14582864C211yesmaximal, characteristic, complemented
16C2×C43×#408C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C22×#10621872C2211yescharacteristic
21C23×C43⋊C8C2211yescharacteristic
22C22×C8×D43C2211yescharacteristic
23C22×C8×D43C2211yescharacteristic
24#14583445C418yes—
25#14583445C2218yes—
26C2×#13063323C411yescharacteristic
27C2×#13063321C411yescharacteristic
28C2×#13063314C411yescharacteristic
29C2×#13063312C411yescharacteristic
30C2×#13063297C411yescharacteristic
31C2×#13063297C411yescharacteristic
32C2×#13063297C411yescharacteristic
33C2×#13063297C411yescharacteristic
34C2×C4×C22⋊D43C2211yescharacteristic
35C2×C4×C22⋊D43C2211yescharacteristic
36C2×C4×C22⋊D43C2211yescharacteristic
37C2×C4×C22⋊D43C2211yescharacteristic
38C22×C4×Dic43C2211yescharacteristic
39#14582975C2218yescomplemented
40#14582974C2218yescomplemented
41#14582973C2218yescomplemented
42#14582970C2218yescomplemented
43#14582968C2218yescomplemented
44#14582967C2218yescomplemented
45C8×C22⋊D43C2218yescomplemented
46(C22⋊D43)⋊C8C2218yescomplemented
47#14582953C2218yescomplemented
48#14582949C2218yescomplemented
49C2×Dic43⋊C8C2211yescharacteristic
50C2×Dic43⋊C8C2211yescharacteristic
51C2×Dic43⋊C8C2211yescharacteristic
52C2×Dic43⋊C8C2211yescharacteristic
53#14582866C2218yescomplemented
54#14582864C2218yescomplemented
55#14582864C2218yescomplemented
56C2×C22⋊(C43⋊C8)C2211yescharacteristic
57C2×C22⋊(C43⋊C8)C2211yescharacteristic
58C2×C22⋊(C43⋊C8)C2211yescharacteristic
59C2×C22⋊(C43⋊C8)C2211yescharacteristic
60C2×(C2×D43)⋊C8C2211yescharacteristic
61C2×(C2×D43)⋊C8C2211yescharacteristic
62C2×(C2×D43)⋊C8C2211yescharacteristic
63C2×(C2×D43)⋊C8C2211yescharacteristic
64C2×#13063235C2211yescharacteristic
65C2×#13063235C2211yescharacteristic
66C2×C8×Dic43C2211yescharacteristic
67C2×C8×Dic43C2211yescharacteristic
68C22×#41×C43C2211yescharacteristic
69C22×M16×C43C2211yescharacteristic
70C23×C8×C43C2211yescharacteristic
71C43×#408C2218yescomplemented
72C2×C22⋊C8×C43C2211yescharacteristic
73C2×C22⋊C8×C43C2211yescharacteristic
74C2×C22⋊C8×C43C2211yescharacteristic
75C2×C22⋊C8×C43C2211yescharacteristic
76C2×#10621898—42no—
77C2×#10621898—42no—
78C2×#10621898C2×C414yes—
79C2×#10621898C2314yes—
80C22×Dic86C2×C411yescharacteristic
81C22×D172C2×C411yescharacteristic
82C22×C22⋊D43C2×C411yescharacteristic
83C22×C22⋊D43C2×C411yescharacteristic
84C22×C22⋊D43C2×C411yescharacteristic
85C22×C22⋊D43C2×C411yescharacteristic
86C22×C22⋊D43C2×C411yescharacteristic
87C22×C22⋊D43C2×C411yescharacteristic
88C23×Dic43C2×C411yescharacteristic
89C23×Dic43C2×C411yescharacteristic
90C22×C4×D43C2311yescharacteristic
91C22×C4×D43C2311yescharacteristic
92C2×#10621877—42no—
93C2×#10621877C2314yes—
94C2×#10621872—42no—
95C2×#10621872—42no—
96C2×#10621872C2314yes—
97C2×#10621872C2314yes—
98C22×C43⋊C8—42no—
99C22×C43⋊C8C2311yescharacteristic
100C22×C43⋊C8C2311yescharacteristic
101C22×C43⋊C8C2311yescharacteristic
102C22×C43⋊C8C2311yescharacteristic
103C22×C43⋊C8C2314yes—
104C2×C8×D43—42no—
105C2×C8×D43—42no—
106C2×C8×D43C2314yes—
107C2×C8×D43C2314yes—
108#13063323C2×C418yes—
109#13063321C2×C418yes—
110#13063314C2×C418yes—
111#13063312C2×C418yes—
112#13063297C2×C418yes—
113#13063297C2×C418yes—
114#13063297C2×C418yes—
115#13063297C2×C418yes—
116C4×C22⋊D43C2×C414yes—
117C4×C22⋊D43C2×C414yes—
118C4×C22⋊D43C2×C414yes—
119C4×C22⋊D43C2×C414yes—
120C4×C22⋊D43C2314yes—
121C4×C22⋊D43C2314yes—
122C4×C22⋊D43C2314yes—
123C4×C22⋊D43C2314yes—
124C2×Dic43⋊C4C2×C411yescharacteristic
125C2×Dic43⋊C4C2×C411yescharacteristic
126C2×Dic43⋊C4C2×C411yescharacteristic
127C2×Dic43⋊C4C2×C411yescharacteristic
128C2×C22⋊Dic43C2×C411yescharacteristic
129C2×C22⋊Dic43C2×C411yescharacteristic
130C2×C22⋊Dic43C2×C411yescharacteristic
131C2×C22⋊Dic43C2×C411yescharacteristic
132C2×(C2×D43)⋊C4C2×C411yescharacteristic
133C2×(C2×D43)⋊C4C2×C411yescharacteristic
134C2×(C2×D43)⋊C4C2×C411yescharacteristic
135C2×(C2×D43)⋊C4C2×C411yescharacteristic
136C2×C4×Dic43C2×C411yescharacteristic
137C2×C4×Dic43C2×C411yescharacteristic
138C2×C4×Dic43C2×C414yes—
139C2×C4×Dic43C2311yescharacteristic
140C2×C4×Dic43C2311yescharacteristic
141C2×C4×Dic43C2314yes—
142Dic43⋊C8C2314yes—
143Dic43⋊C8C2314yes—
144Dic43⋊C8C2314yes—
145Dic43⋊C8C2314yes—
146C22⋊(C43⋊C8)C2314yes—
147C22⋊(C43⋊C8)C2314yes—
148C22⋊(C43⋊C8)C2314yes—
149C22⋊(C43⋊C8)C2314yes—
150(C2×D43)⋊C8C2314yes—
151(C2×D43)⋊C8C2314yes—
152(C2×D43)⋊C8C2314yes—
153(C2×D43)⋊C8C2314yes—
154#13063235C2314yes—
155#13063235C2314yes—
156C8×Dic43C2314yes—
157C8×Dic43C2314yes—
158C2×#41×C43—42no—
159C2×#41×C43—42no—
160C2×#41×C43C2×C414yes—
161C2×#41×C43C2314yes—
162C22×Q8×C43C2×C411yescharacteristic
163C22×D4×C43C2×C411yescharacteristic
164C22×D4×C43C2×C411yescharacteristic
165C22×D4×C43C2×C411yescharacteristic
166C23×C4×C43C2311yescharacteristic
167C23×C4×C43C2311yescharacteristic
168C23×C4×C43C2311yescharacteristic
169C2×M16×C43—42no—
170C2×M16×C43C2314yes—
171C22×C8×C43—42no—
172C22×C8×C43C2311yescharacteristic
173C22×C8×C43C2311yescharacteristic
174C22×C8×C43C2311yescharacteristic
175C22×C8×C43C2311yescharacteristic
176C22×C8×C43C2314yes—
177C22⋊C8×C43C2314yes—
178C22⋊C8×C43C2314yes—
179C22⋊C8×C43C2314yes—
180C22⋊C8×C43C2314yes—
181C24×C43C22×C411yescharacteristic
182C24×C43C22×C411yescharacteristic
183C24×C43C22×C411yescharacteristic
184C23×D43C22×C411yescharacteristic
185C23×D43C22×C411yescharacteristic
186#41×C43—48no—
187#41×C43—44no—
188#41×C43—44no—
189C2×Q8×C43—42no—
190C2×Q8×C43C22×C414yes—
191C2×D4×C43—42no—
192C2×D4×C43—42no—
193C2×D4×C43—42no—
194C2×D4×C43C22×C414yes—
195C2×D4×C43C22×C414yes—
196C2×D4×C43C22×C414yes—
197C22×C4×C43—22no—
198C22×C4×C43—22no—
199C22×C4×C43—22no—
200C22×C4×C43—22no—
201C22×C4×C43—22no—
202C22×C4×C43—22no—
203C22×C4×C43C22×C411yescharacteristic
204C22×C4×C43C22×C411yescharacteristic
205C22×C4×C43C22×C411yescharacteristic
206C22×C4×C43C22×C412yes—
207C22×C4×C43C22×C412yes—
208C22×C4×C43C22×C412yes—
209C22×C4×C43C2412yes—
210C22×C4×C43C2412yes—
211C22×C4×C43C2412yes—
212C22×C4×C43C2411yescharacteristic
213C2×C22⋊D43—24no—
214C2×C22⋊D43—24no—
215C2×C22⋊D43—42no—
216C2×C22⋊D43—42no—
217C2×C22⋊D43—42no—
218C2×C22⋊D43—42no—
219C2×C22⋊D43C22×C414yes—
220C2×C22⋊D43C22×C414yes—
221C2×C22⋊D43C22×C414yes—
222C2×C22⋊D43C22×C414yes—
223C2×C22⋊D43C22×C414yes—
224C2×C22⋊D43C22×C414yes—
225C22×Dic43—24no—
226C22×Dic43—42no—
227C22×Dic43C22×C411yescharacteristic
228C22×Dic43C22×C411yescharacteristic
229C22×Dic43C22×C411yescharacteristic
230C22×Dic43C22×C414yes—
231C22×Dic43C22×C411yescharacteristic
232C22×Dic43C22×C411yescharacteristic
233C22×Dic43C22×C414yes—
234C22×Dic43C22×C411yescharacteristic
235#10621898—48no—
236#10621898—44no—
237#10621898—44no—
238C2×D172—42no—
239C2×D172C22×C414yes—
240C2×C4×D43—22no—
241C2×C4×D43—22no—
242C2×C4×D43—22no—
243C2×C4×D43—22no—
244C2×C4×D43C22×C412yes—
245C2×C4×D43C22×C412yes—
246C2×C4×D43C2412yes—
247C2×C4×D43C2412yes—
248C2×Dic86—42no—
249C2×Dic86C22×C414yes—
250M16×C43—44no—
251C2×C8×C43—22no—
252C2×C8×C43—22no—
253C2×C8×C43—22no—
254C2×C8×C43—22no—
255C2×C8×C43—44no—
256C2×C8×C43C2412yes—
257C2×C8×C43C2412yes—
258C2×C8×C43C2412yes—
259C2×C8×C43C2412yes—
260C22⋊Dic43C22×C414yes—
261C22⋊Dic43C22×C414yes—
262C22⋊Dic43C22×C414yes—
263C22⋊Dic43C22×C414yes—
264(C2×D43)⋊C4C22×C414yes—
265(C2×D43)⋊C4C22×C414yes—
266(C2×D43)⋊C4C22×C414yes—
267(C2×D43)⋊C4C22×C414yes—
268Dic43⋊C4C22×C414yes—
269Dic43⋊C4C22×C414yes—
270Dic43⋊C4C22×C414yes—
271Dic43⋊C4C22×C414yes—
272C4×Dic43C22×C412yes—
273C4×Dic43C22×C412yes—
274C4×Dic43C22×C414yes—
275C4×Dic43C22×C414yes—
276C4×Dic43C2412yes—
277C4×Dic43C2412yes—
278#10621877—44no—
279C2×C43⋊C8—22no—
280C2×C43⋊C8—22no—
281C2×C43⋊C8—22no—
282C2×C43⋊C8—22no—
283C2×C43⋊C8—44no—
284C2×C43⋊C8C2412yes—
285C2×C43⋊C8C2412yes—
286C2×C43⋊C8C2412yes—
287C2×C43⋊C8C2412yes—
288#10621872—44no—
289#10621872—44no—
290C8×D43—44no—
291C8×D43—44no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—22no—
299C23×C43—22no—
300C23×C43—22no—
301C23×C43C23×C412yes—
302C23×C43C23×C412yes—
303C23×C43C23×C412yes—
304C23×C43C23×C411yescharacteristic
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—22no—
309C22×D43—22no—
310C22×D43—22no—
311C22×D43C23×C412yes—
312C22×D43C23×C412yes—
313Q8×C43—44no—
314D4×C43—44no—
315D4×C43—44no—
316D4×C43—44no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—24no—
321C2×C4×C43—24no—
322C2×C4×C43—24no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43C23×C412yes—
330C2×C4×C43C23×C412yes—
331C2×C4×C43C23×C412yes—
332C2×C4×C43C23×C411yescharacteristic
333C2×C4×C43H(5,𝔽2)12yes—
334C2×C4×C43H(5,𝔽2)12yes—
335C2×C4×C43C2511yescharacteristic
336C22⋊D43—28no—
337C22⋊D43—28no—
338C22⋊D43—44no—
339C22⋊D43—44no—
340C22⋊D43—44no—
341C22⋊D43—44no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—28no—
348C2×Dic43—44no—
349C2×Dic43#13114yes—
350C2×Dic43C23×C412yes—
351C2×Dic43C23×C412yes—
352C2×Dic43C23×C412yes—
353C2×Dic43C23×C412yes—
354C2×Dic43C23×C412yes—
355C2×Dic43C23×C412yes—
356D172—44no—
357C4×D43—24no—
358C4×D43—24no—
359C4×D43—22no—
360C4×D43—22no—
361C4×D43—22no—
362C4×D43—22no—
363Dic86—44no—
364C8×C43—22no—
365C8×C43—22no—
366C8×C43—22no—
367C8×C43—22no—
368C43⋊C8—22no—
369C43⋊C8—22no—
370C43⋊C8—22no—
371C43⋊C8—22no—
372C2×#2981—431nomaximal, Sylow
373C22×C43—22no—
374C22×C43—22no—
375C22×C43—22no—
376C22×C43—22no—
377C22×C43—22no—
378C22×C43—22no—
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—44no—
383C22×C43—44no—
384C22×C43—44no—
385C22×C43#51812yes—
386C22×C43C2×#13112yes—
387C22×C43#56812yes—
388C22×C43C24×C411yescharacteristic
389C2×D43—22no—
390C2×D43—22no—
391C2×D43—22no—
392C2×D43—22no—
393C2×D43—22no—
394C2×D43—22no—
395C2×D43—44no—
396C2×D43—44no—
397C4×C43—22no—
398C4×C43—22no—
399C4×C43—22no—
400C4×C43#51812yes—
401C4×C43C2×H(5,𝔽2)11yescharacteristic
402C4×C43C2×H(5,𝔽2)11yescharacteristic
403Dic43—22no—
404Dic43—22no—
405Dic43—22no—
406Dic43—22no—
407Dic43—22no—
408Dic43C2×#13114yes—
409C2×#532—431no—
410#2981—4316no—
411C2×#436—431no—
412C2×#436—431no—
413C2×#435—431no—
414C2×#435—431no—
415C2×#435—431no—
416C2×#435—431no—
417C2×C8×D4—431no—
418C2×C8×D4—431no—
419C2×#432—431no—
420C2×#431—431no—
421C2×#408—431no—
422C2×#408—431no—
423C2×#408—431no—
424C2×#408D4311yescharacteristic, complemented
425C2×C43—42no—
426C2×C43—42no—
427C2×C43—42no—
428C2×C43#298114yescomplemented
429C2×C43C2×#51811yescharacteristic
430C2×C43C22×#13111yescharacteristic
431C2×C43C2×#56811yescharacteristic
432D43—42no—
433D43—42no—
434C22×#41—431no—
435C22×#41C2×D4311yescharacteristic
436C22×M16—431no—
437C22×M16—431no—
438C22×M16—431no—
439C22×M16C2×D4311yescharacteristic
440C23×C8—431no—
441C23×C8—431no—
442C23×C8—431no—
443C23×C8C2×D4311yescharacteristic
444#532—438no—
445#532—438no—
446C2×C4⋊Q8—431no—
447C2×#127—431no—
448C2×#124—431no—
449C2×#124—431no—
450C2×#121—431no—
451C2×#121—431no—
452C2×#121—431no—
453C2×#121—431no—
454C2×C4×D4—431no—
455C2×C4×D4—431no—
456C2×C4×D4—431no—
457C2×C4×D4—431no—
458C22×C42—431no—
459#436—438no—
460#436—438no—
461#435—438no—
462#435—438no—
463#435—438no—
464#435—438no—
465C8×D4—438no—
466C8×D4—438no—
467#432—438no—
468#431—438no—
469C2×C4⋊C8—431no—
470C2×C4⋊C8—431no—
471C2×C4⋊C8—431no—
472C2×C4⋊C8—431no—
473#408—438no—
474#408—438no—
475#408—438no—
476#408C2×D4318yescomplemented
477C2×C22⋊C8—431no—
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⋊C8C2×D4311yescharacteristic
486C2×C22⋊C8C2×D4311yescharacteristic
487C2×C22⋊C8C2×D4311yescharacteristic
488C2×C22⋊C8C2×D4311yescharacteristic
489C2×#97—431no—
490C2×#97—431no—
491C2×C4×C8—431no—
492C2×C4×C8—431no—
493C43C2×#298111yescharacteristic, complemented, Sylow
494C2×#41—42no—
495C2×#41—42no—
496C2×#41—434no—
497C2×#41—434no—
498C2×#41—1722no—
499C2×#41—1722no—
500C2×#41C4×D4314yes—
501C2×#41C22×D4314yes—
502C22×Q8—431no—
503C22×Q8C4×D4311yescharacteristic
504C22×D4—431no—
505C22×D4—431no—
506C22×D4—431no—
507C22×D4—431no—
508C22×D4—431no—
509C22×D4—431no—
510C22×D4—431no—
511C22×D4C4×D4311yescharacteristic
512C22×D4C4×D4311yescharacteristic
513C22×D4C4×D4311yescharacteristic
514C23×C4—431no—
515C23×C4—431no—
516C23×C4—431no—
517C23×C4—431no—
518C23×C4C22×D4311yescharacteristic
519C23×C4C22×D4311yescharacteristic
520C23×C4C22×D4311yescharacteristic
521C2×M16—42no—
522C2×M16—434no—
523C2×M16—434no—
524C2×M16—434no—
525C2×M16—1722no—
526C2×M16—1722no—
527C2×M16—1722no—
528C2×M16C22×D4314yes—
529C22×C8—42no—
530C22×C8—431no—
531C22×C8—431no—
532C22×C8—431no—
533C22×C8—431no—
534C22×C8—434no—
535C22×C8—434no—
536C22×C8—434no—
537C22×C8—1722no—
538C22×C8—1722no—
539C22×C8—1722no—
540C22×C8C22×D4311yescharacteristic
541C22×C8C22×D4311yescharacteristic
542C22×C8C22×D4311yescharacteristic
543C22×C8C22×D4311yescharacteristic
544C22×C8C22×D4314yes—
545C4⋊Q8—438no—
546#127—438no—
547#124—438no—
548#124—438no—
549#121—438no—
550#121—438no—
551#121—438no—
552#121—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—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—431no—
565C2×C22⋊C4—431no—
566C2×C22⋊C4—431no—
567C2×C22⋊C4—431no—
568C2×C22⋊C4—431no—
569C2×C22⋊C4—431no—
570C2×C22⋊C4—431no—
571C2×C22⋊C4—431no—
572C2×C22⋊C4—431no—
573C2×C42—431no—
574C2×C42—431no—
575C2×C42—434no—
576C2×C42—434no—
577C2×C42—431no—
578C2×C42—431no—
579C4⋊C8—434no—
580C4⋊C8—434no—
581C4⋊C8—434no—
582C4⋊C8—434no—
583C22⋊C8—434no—
584C22⋊C8—434no—
585C22⋊C8—434no—
586C22⋊C8—434no—
587C22⋊C8—434no—
588C22⋊C8—434no—
589C22⋊C8—434no—
590C22⋊C8—434no—
591C22⋊C8C22×D4314yes—
592C22⋊C8C22×D4314yes—
593C22⋊C8C22×D4314yes—
594C22⋊C8C22×D4314yes—
595#97—434no—
596#97—434no—
597C4×C8—434no—
598C4×C8—434no—
599C24—431no—
600C24—431no—
601C24C2×C4×D4311yescharacteristic
602C24C2×C4×D4311yescharacteristic
603C24C2×C4×D4311yescharacteristic
604#41—44no—
605#41—44no—
606#41—48no—
607#41—1728no—
608#41—1724no—
609#41—1724no—
610C2×Q8—42no—
611C2×Q8—434no—
612C2×Q8—1722no—
613C2×Q8C2×C4×D4314yes—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—434no—
618C2×D4—434no—
619C2×D4—434no—
620C2×D4—434no—
621C2×D4—434no—
622C2×D4—434no—
623C2×D4—434no—
624C2×D4—864no—
625C2×D4—864no—
626C2×D4—1722no—
627C2×D4—1722no—
628C2×D4—1722no—
629C2×D4—1722no—
630C2×D4—1722no—
631C2×D4C2×C4×D4314yes—
632C2×D4C2×C4×D4314yes—
633C2×D4C2×C4×D4314yes—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—431no—
641C22×C4—431no—
642C22×C4—431no—
643C22×C4—431no—
644C22×C4—434no—
645C22×C4—431no—
646C22×C4—431no—
647C22×C4—434no—
648C22×C4—432no—
649C22×C4—432no—
650C22×C4—432no—
651C22×C4—432no—
652C22×C4—864no—
653C22×C4—862no—
654C22×C4—862no—
655C22×C4—862no—
656C22×C4—862no—
657C22×C4—1722no—
658C22×C4C2×C4×D4311yescharacteristic
659C22×C4C2×C4×D4312yes—
660C22×C4C2×C4×D4311yescharacteristic
661C22×C4C2×C4×D4311yescharacteristic
662C22×C4C2×C4×D4312yes—
663C22×C4C2×C4×D4312yes—
664C22×C4C23×D4312yes—
665C22×C4C23×D4312yes—
666C22×C4C23×D4312yes—
667C22×C4C23×D4311yescharacteristic
668M16—44no—
669M16—1724no—
670M16—1724no—
671M16—1724no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—22no—
676C2×C8—44no—
677C2×C8—432no—
678C2×C8—432no—
679C2×C8—432no—
680C2×C8—432no—
681C2×C8—862no—
682C2×C8—862no—
683C2×C8—862no—
684C2×C8—862no—
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—
696C22⋊C4—434no—
697C22⋊C4—434no—
698C22⋊C4—434no—
699C22⋊C4—434no—
700C22⋊C4—434no—
701C22⋊C4—434no—
702C22⋊C4—434no—
703C22⋊C4—434no—
704C42—432no—
705C42—432no—
706C42—434no—
707C42—434no—
708C42—432no—
709C42—432no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—432no—
720C23—432no—
721C23—862no—
722C23—862no—
723C23—862no—
724C23—862no—
725C23—862no—
726C23—862no—
727C23C22×C4×D4312yes—
728C23C22×C4×D4312yes—
729C23C22×C4×D4312yes—
730C23C22×C4×D4311yescharacteristic
731Q8—44no—
732Q8—1724no—
733D4—44no—
734D4—44no—
735D4—44no—
736D4—868no—
737D4—868no—
738D4—1724no—
739D4—1724no—
740D4—1724no—
741D4—1724no—
742D4—1724no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—434no—
756C2×C4—432no—
757C2×C4—432no—
758C2×C4—432no—
759C2×C4—432no—
760C2×C4—432no—
761C2×C4—432no—
762C2×C4—868no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—862no—
766C2×C4—862no—
767C2×C4—862no—
768C2×C4—864no—
769C2×C4—864no—
770C2×C4—862no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—1724no—
775C2×C4C22×C4×D4312yes—
776C2×C4C22×C4×D4312yes—
777C2×C4C22×C4×D4312yes—
778C2×C4C22×C4×D4311yescharacteristic
779C2×C4#1306337012yes—
780C2×C4#1306337012yes—
781C2×C4C24×D4311yescharacteristic
782C8—22no—
783C8—22no—
784C8—22no—
785C8—22no—
786C8—862no—
787C8—862no—
788C8—862no—
789C8—862no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—862no—
803C22—862no—
804C22—862no—
805C22—862no—
806C22—862no—
807C22—862no—
808C22—1724no—
809C22—1724no—
810C22#1458337212yes—
811C22#131×D4312yes—
812C22#1458366412yes—
813C22C23×C4×D4311yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—434no—
818C4—862no—
819C4—862no—
820C4—862no—
821C4—862no—
822C4—862no—
823C4#1458337212yes—
824C4C2×#1306337011yescharacteristic
825C4C2×#1306337011yescharacteristic
826C2—42no—
827C2—42no—
828C2—42no—
829C2—1722no—
830C2—1722no—
831C2#1914366814yesdirect product factor
832C2C2×#1458337211yescharacteristic
833C2C2×#131×D4311yescharacteristic
834C2C2×#1458366411yescharacteristic
subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C43×#408C2
socleC23×C43C23×C4
prime radicalC2×#14583445C2
cosocleC2×C4×C43C25
hypercenterC2×#408D43
hypocenterC43C2×#2981
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
2. #19143668C2direct (N × H)
3. C2×#14582975C2semidirect
4. C2×#14582974C2semidirect
5. C2×#14582973C2semidirect
6. C2×#14582970C2semidirect
7. C2×#14582968C2semidirect
8. C2×#14582967C2semidirect
9. C2×C8×C22⋊D43C2semidirect
10. C2×(C22⋊D43)⋊C8C2semidirect
11. C2×#14582953C2semidirect
12. C2×#14582949C2semidirect
13. C2×#14582866C2semidirect
14. C2×#14582864C2semidirect
15. C2×#14582864C2semidirect
16. C2×C43×#408C2semidirect
39. #14582975C22semidirect
40. #14582974C22semidirect
41. #14582973C22semidirect
42. #14582970C22semidirect
43. #14582968C22semidirect
44. #14582967C22semidirect
45. C8×C22⋊D43C22semidirect
46. (C22⋊D43)⋊C8C22semidirect
47. #14582953C22semidirect
48. #14582949C22semidirect
53. #14582866C22semidirect
54. #14582864C22semidirect
55. #14582864C22semidirect
71. C43×#408C22semidirect
424. C2×#408D43semidirect
428. C2×C43#2981semidirect
476. #408C2×D43semidirect
493. C43C2×#2981semidirect
831. C2#19143668direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834452
#191436682
C2×#145829752
C2×#145829742
C2×#145829732
C2×#145829702
C2×#145829682
C2×#145829672
C2×C8×C22⋊D432
C2×(C22⋊D43)⋊C82
C2×#145829532
C2×#145829492
C2×#145828662
C2×#145828642
C2×C43×#4082
C2×#298143