Finite Group Databasebeta

← C2×#19143648 #25961353

Subgroups — C2×#19143648 #25961353

Order 11008.

2362 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×#14583408C211yesmaximal, characteristic
2#19143648C2116yesmaximal, direct product factor
3C2×#14582973C211yesmaximal, characteristic, complemented
4C2×#14582971C211yesmaximal, characteristic, complemented
5C2×#14582970C211yesmaximal, characteristic, complemented
6C2×#14582969C211yesmaximal, characteristic, complemented
7C2×C8×D172C211yesmaximal, characteristic, complemented
8C2×C8×C22⋊D43C211yesmaximal, characteristic, complemented
9C2×(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
10C2×#14582959C211yesmaximal, characteristic, complemented
11C2×#14582958C211yesmaximal, characteristic, complemented
12C2×#14582865C211yesmaximal, characteristic, complemented
13C2×#14582864C211yesmaximal, characteristic, complemented
14C22×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
15C2×C22⋊C8×D43C211yesmaximal, characteristic, complemented
16C2×C8×D4×C43C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C22×#10621877C2211yescharacteristic, complemented
20C22×#10621872C2211yescharacteristic, complemented
21C23×C43⋊C8C2211yescharacteristic
22C22×C8×D43C2211yescharacteristic
23C22×C8×D43C2211yescharacteristic
24C22×C8×D43C2211yescharacteristic, complemented
25#14583408C418yes—
26#14583408C2218yes—
27C2×#13063310C411yescharacteristic
28C2×#13063307C411yescharacteristic
29C2×#13063303C411yescharacteristic
30C2×#13063302C411yescharacteristic
31C2×#13063298C411yescharacteristic
32C2×#13063297C411yescharacteristic
33C2×#13063295C411yescharacteristic
34C2×#13063293C411yescharacteristic
35C2×C4×D172C2211yescharacteristic
36C2×C4×C22⋊D43C2211yescharacteristic
37C2×C4×C22⋊D43C2211yescharacteristic
38C2×#13063282C2211yescharacteristic
39#14582973C2218yescomplemented
40#14582971C2218yescomplemented
41#14582970C2218yescomplemented
42#14582969C2218yescomplemented
43C8×D172C2218yescomplemented
44C8×C22⋊D43C2218yescomplemented
45(C22⋊D43)⋊C8C2218yescomplemented
46#14582959C2218yescomplemented
47#14582958C2218yescomplemented
48C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
49C2×Dic43⋊C8C2211yescharacteristic, complemented
50C2×Dic43⋊C8C2211yescharacteristic, complemented
51#14582865C2218yescomplemented
52#14582864C2218yescomplemented
53C2×C22⋊(C43⋊C8)C2211yescharacteristic
54C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
55C2×(C2×D43)⋊C8C2211yescharacteristic
56C2×(C2×D43)⋊C8C2211yescharacteristic
57C2×(C2×D43)⋊C8C2211yescharacteristic
58C2×(C2×D43)⋊C8C2211yescharacteristic
59C2×(C2×D43)⋊C8C2211yescharacteristic
60C2×(C2×D43)⋊C8C2211yescharacteristic
61C2×(C2×D43)⋊C8C2218yescomplemented
62C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
63C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
64C22⋊C8×D43C2218yescomplemented
65C2×#13063236C2211yescharacteristic, complemented
66C2×#13063235C2211yescharacteristic, complemented
67C2×C8×Dic43C2211yescharacteristic, complemented
68C23×C8×C43C2211yescharacteristic
69C23×C8×C43C2211yescharacteristic, complemented
70C2×C4×D4×C43C2211yescharacteristic
71C8×D4×C43C2218yescomplemented
72C2×C4⋊C8×C43C2211yescharacteristic, complemented
73C2×C22⋊C8×C43C2211yescharacteristic
74C2×C22⋊C8×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×C22⋊D43C2×C411yescharacteristic
85C22×C22⋊D43C2×C411yescharacteristic
86C22×C22⋊D43C2×C411yescharacteristic
87C22×C22⋊D43C2×C411yescharacteristic
88C23×Dic43C2×C411yescharacteristic
89C22×C4×D43—42no—
90C22×C4×D43—42no—
91C22×C4×D43C2×C411yescharacteristic
92C22×C4×D43C2×C411yescharacteristic
93C22×C4×D43C2×C414yes—
94C22×C4×D43C2311yescharacteristic
95C22×C4×D43C2311yescharacteristic
96C22×C4×D43C2311yescharacteristic
97C22×C4×D43C2314yes—
98C2×#10621877—42no—
99C2×#10621877C2314yescomplemented
100C2×#10621872—42no—
101C2×#10621872C2314yescomplemented
102C22×C43⋊C8—42no—
103C22×C43⋊C8C2311yescharacteristic
104C22×C43⋊C8C2311yescharacteristic
105C22×C43⋊C8C2311yescharacteristic
106C22×C43⋊C8C2311yescharacteristic
107C22×C43⋊C8C2314yes—
108C2×C8×D43—42no—
109C2×C8×D43—42no—
110C2×C8×D43—42no—
111C2×C8×D43C2314yes—
112C2×C8×D43C2314yes—
113C2×C8×D43C2314yescomplemented
114#13063310C2×C418yes—
115#13063307C2×C418yes—
116#13063303C2×C418yes—
117#13063302C2×C418yes—
118#13063298C2×C418yes—
119#13063297C2×C418yes—
120#13063295C2×C418yes—
121#13063293C2×C418yes—
122C4×D172C2×C414yes—
123C4×D172C2314yes—
124C4×C22⋊D43C2×C414yes—
125C4×C22⋊D43C2×C414yes—
126C4×C22⋊D43C2314yes—
127C4×C22⋊D43C2314yes—
128#13063282C2×C414yes—
129#13063282C2314yes—
130C2×C4⋊Dic43C2×C411yescharacteristic
131C2×Dic43⋊C4C2×C411yescharacteristic
132C2×Dic43⋊C4C2×C411yescharacteristic
133C2×Dic43⋊C4C2×C411yescharacteristic
134C2×Dic43⋊C4C2×C411yescharacteristic
135C2×C22⋊Dic43C2×C411yescharacteristic
136C2×C22⋊Dic43C2×C411yescharacteristic
137C2×(C2×D43)⋊C4C2×C411yescharacteristic
138C2×(C2×D43)⋊C4C2×C411yescharacteristic
139C2×(C2×D43)⋊C4C2×C411yescharacteristic
140C2×(C2×D43)⋊C4C2×C411yescharacteristic
141C2×(C2×D43)⋊C4C2×C411yescharacteristic
142C2×(C2×D43)⋊C4C2×C411yescharacteristic
143C2×C4×Dic43C2311yescharacteristic
144C4⋊(C43⋊C8)C2314yescomplemented
145Dic43⋊C8C2314yescomplemented
146Dic43⋊C8C2314yescomplemented
147C22⋊(C43⋊C8)C2314yes—
148C22⋊(C43⋊C8)C2314yescomplemented
149(C2×D43)⋊C8C2314yes—
150(C2×D43)⋊C8C2314yes—
151(C2×D43)⋊C8C2314yes—
152(C2×D43)⋊C8C2314yes—
153(C2×D43)⋊C8C2314yes—
154(C2×D43)⋊C8C2314yes—
155(C2×D43)⋊C8C2314yescomplemented
156(C2×D43)⋊C8C2314yescomplemented
157#13063236C2314yescomplemented
158#13063235C2314yescomplemented
159C8×Dic43C2314yescomplemented
160C22×D4×C43C2×C411yescharacteristic
161C23×C4×C43C2311yescharacteristic
162C23×C4×C43C2311yescharacteristic
163C22×C8×C43—42no—
164C22×C8×C43—42no—
165C22×C8×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169C22×C8×C43C2314yes—
170C22×C8×C43C2314yescomplemented
171C4×D4×C43C2×C414yes—
172C4×D4×C43C2314yes—
173C2×C4⋊C4×C43C2×C411yescharacteristic
174C2×C22⋊C4×C43C2×C411yescharacteristic
175C2×C22⋊C4×C43C2×C411yescharacteristic
176C2×C42×C43C2311yescharacteristic
177C4⋊C8×C43C2314yescomplemented
178C22⋊C8×C43C2314yes—
179C22⋊C8×C43C2314yescomplemented
180C4×C8×C43C2314yescomplemented
181C24×C43C22×C411yescharacteristic
182C24×C43C22×C411yescharacteristic
183C23×D43—24no—
184C23×D43—24no—
185C23×D43—42no—
186C23×D43C22×C411yescharacteristic
187C23×D43C22×C411yescharacteristic
188C23×D43C22×C414yes—
189C23×D43C22×C411yescharacteristic
190C2×D4×C43—24no—
191C2×D4×C43C22×C414yes—
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43—22no—
195C22×C4×C43—22no—
196C22×C4×C43C22×C411yescharacteristic
197C22×C4×C43C22×C411yescharacteristic
198C22×C4×C43C22×C411yescharacteristic
199C22×C4×C43C22×C411yescharacteristic
200C22×C4×C43C22×C412yes—
201C22×C4×C43C22×C412yes—
202C22×C4×C43C2412yes—
203C22×C4×C43C2412yes—
204C22×C4×C43C2411yescharacteristic
205C2×C22⋊D43—24no—
206C2×C22⋊D43—24no—
207C2×C22⋊D43—42no—
208C2×C22⋊D43—42no—
209C2×C22⋊D43C22×C414yes—
210C2×C22⋊D43C22×C414yes—
211C2×C22⋊D43C22×C414yes—
212C2×C22⋊D43C22×C414yes—
213C22×Dic43—42no—
214C22×Dic43C22×C411yescharacteristic
215C22×Dic43C22×C411yescharacteristic
216C22×Dic43C22×C411yescharacteristic
217C22×Dic43C22×C411yescharacteristic
218C22×Dic43C22×C411yescharacteristic
219C22×Dic43C22×C414yes—
220#10621898—48no—
221#10621898—44no—
222#10621898—44no—
223C2×D172—24no—
224C2×D172—42no—
225C2×D172C22×C414yes—
226C2×D172C22×C414yes—
227C2×C4×D43—22no—
228C2×C4×D43—22no—
229C2×C4×D43—22no—
230C2×C4×D43—22no—
231C2×C4×D43—22no—
232C2×C4×D43—22no—
233C2×C4×D43—42no—
234C2×C4×D43—42no—
235C2×C4×D43—48no—
236C2×C4×D43—44no—
237C2×C4×D43—44no—
238C2×C4×D43C22×C412yes—
239C2×C4×D43C22×C412yes—
240C2×C4×D43C22×C412yes—
241C2×C4×D43C22×C414yes—
242C2×C4×D43C22×C414yes—
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×C43—44no—
253C2×C8×C43—44no—
254C2×C8×C43C2412yes—
255C2×C8×C43C2412yes—
256C2×C8×C43C2412yes—
257C2×C8×C43C2412yes—
258C4⋊C4×C43C22×C414yes—
259C22⋊C4×C43C22×C414yes—
260C22⋊C4×C43C22×C414yes—
261C42×C43C22×C412yes—
262C42×C43C2412yes—
263C22⋊Dic43C22×C414yes—
264C22⋊Dic43C22×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—
271C4⋊Dic43C22×C414yes—
272Dic43⋊C4C22×C414yes—
273Dic43⋊C4C22×C414yes—
274Dic43⋊C4C22×C414yes—
275Dic43⋊C4C22×C414yes—
276C4×Dic43C22×C412yes—
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—
289C8×D43—44no—
290C8×D43—44no—
291C8×D43—44no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43#13114yes—
298C23×C43C23×C412yes—
299C23×C43C23×C412yes—
300C23×C43C23×C411yescharacteristic
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—22no—
310C22×D43—28no—
311C22×D43—44no—
312C22×D43—416no—
313C22×D43#13114yes—
314C22×D43C23×C412yes—
315C22×D43C23×C412yes—
316C22×D43C23×C412yes—
317D4×C43—28no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—24no—
323C2×C4×C43—24no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43C23×C412yes—
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—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—44no—
346C2×Dic43C23×C412yes—
347C2×Dic43C23×C412yes—
348C2×Dic43C23×C412yes—
349C2×Dic43C23×C412yes—
350C2×Dic43C23×C412yes—
351D172—28no—
352D172—44no—
353C4×D43—24no—
354C4×D43—24no—
355C4×D43—24no—
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×#2977—431nomaximal, Sylow
374C22×C43—22no—
375C22×C43—28no—
376C22×C43—22no—
377C22×C43—22no—
378C22×C43—22no—
379C22×C43—22no—
380C22×C43—44no—
381C22×C43#51812yes—
382C22×C43C2×#13112yes—
383C22×C43C2×#13114yes—
384C22×C43C2×#13112yes—
385C22×C43C24×C411yescharacteristic
386C2×D43—22no—
387C2×D43—28no—
388C2×D43—22no—
389C2×D43—22no—
390C2×D43—22no—
391C2×D43—22no—
392C2×D43—22no—
393C2×D43—22no—
394C2×D43—22no—
395C2×D43—416no—
396C2×D43—44no—
397C2×D43—44no—
398C2×D43C2×#13114yes—
399C4×C43—22no—
400C4×C43—22no—
401C4×C43—22no—
402C4×C43—22no—
403C4×C43#51812yes—
404C4×C43C2×H(5,𝔽2)11yescharacteristic
405C4×C43C2×H(5,𝔽2)11yescharacteristic
406Dic43—22no—
407Dic43—22no—
408Dic43—22no—
409Dic43—22no—
410Dic43—22no—
411C2×#525—431no—
412#2977—4316no—
413C2×#435—431no—
414C2×#435—431no—
415C2×#435—431no—
416C2×#435—431no—
417C2×C8×D4—431no—
418C2×C8×D4—431no—
419C2×C8×D4—431no—
420C2×C8×D4D4311yescharacteristic, complemented
421C2×#433—431no—
422C2×#433—431no—
423C2×#408—431no—
424C2×#408—431no—
425C22×C22⋊C8—431no—
426C22×C22⋊C8—431no—
427C2×C43—24no—
428C2×C43—42no—
429C2×C43#297714yescomplemented
430C2×C43C2×#51811yescharacteristic
431C2×C43C22×#13111yescharacteristic
432C2×C43C22×#13111yescharacteristic
433D43—24no—
434D43—42no—
435D43—42no—
436C22×#41—431no—
437C24×C4—431no—
438C22×M16—431no—
439C22×M16—431no—
440C23×C8—431no—
441C23×C8—431no—
442C23×C8—431no—
443C23×C8—431no—
444C23×C8C2×D4311yescharacteristic
445C23×C8C2×D4311yescharacteristic, complemented
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×D4C2×D4311yescharacteristic
460C2×#117—431no—
461#435—438no—
462#435—438no—
463#435—438no—
464#435—438no—
465C8×D4—438no—
466C8×D4—438no—
467C8×D4—438no—
468C8×D4C2×D4318yescomplemented
469#433—438no—
470#433—438no—
471C2×C4⋊C8—431no—
472C2×C4⋊C8—431no—
473C2×C4⋊C8—431no—
474C2×C4⋊C8C2×D4311yescharacteristic, complemented
475#408—438no—
476#408—438no—
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⋊C8—438no—
486C2×C22⋊C8—431no—
487C2×C22⋊C8—431no—
488C2×C22⋊C8—438no—
489C2×C22⋊C8C2×D4311yescharacteristic
490C2×C22⋊C8C2×D4311yescharacteristic, complemented
491C2×#97—431no—
492C2×#97—431no—
493C2×C4×C8—431no—
494C2×C4×C8C2×D4311yescharacteristic, complemented
495C43C2×#297711yescharacteristic, 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×D4C4×D4311yescharacteristic
509C23×C4—431no—
510C23×C4—431no—
511C23×C4—431no—
512C23×C4—431no—
513C23×C4—431no—
514C23×C4—431no—
515C23×C4—434no—
516C23×C4—434no—
517C23×C4—1722no—
518C23×C4—1722no—
519C23×C4C22×D4311yescharacteristic
520C23×C4C22×D4311yescharacteristic
521C2×M16—434no—
522C2×M16—434no—
523C2×M16—1722no—
524C2×M16—1722no—
525C22×C8—42no—
526C22×C8—42no—
527C22×C8—431no—
528C22×C8—431no—
529C22×C8—431no—
530C22×C8—431no—
531C22×C8—434no—
532C22×C8—434no—
533C22×C8—434no—
534C22×C8—434no—
535C22×C8—1722no—
536C22×C8—1722no—
537C22×C8—1722no—
538C22×C8—1722no—
539C22×C8C22×D4311yescharacteristic
540C22×C8C22×D4311yescharacteristic
541C22×C8C22×D4311yescharacteristic
542C22×C8C22×D4311yescharacteristic
543C22×C8C22×D4314yes—
544C22×C8C22×D4314yescomplemented
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×D4C4×D4314yes—
560C4×D4C22×D4314yes—
561#117—434no—
562#117—434no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—431no—
565C2×C4⋊C4—431no—
566C2×C4⋊C4—431no—
567C2×C4⋊C4—431no—
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×C42—431no—
580C2×C42C22×D4311yescharacteristic
581C4⋊C8—434no—
582C4⋊C8—434no—
583C4⋊C8—434no—
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×D4314yescomplemented
597#97—434no—
598#97—434no—
599C4×C8—434no—
600C4×C8C22×D4314yescomplemented
601C24—431no—
602C24—431no—
603C24—431no—
604C24—434no—
605C24—864no—
606C24—864no—
607C24—1722no—
608C24C2×C4×D4311yescharacteristic
609C24C2×C4×D4311yescharacteristic
610#41—1728no—
611#41—1724no—
612#41—1724no—
613C2×Q8—434no—
614C2×Q8—1722no—
615C2×D4—24no—
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—864no—
625C2×D4—1722no—
626C2×D4—1722no—
627C2×D4—1722no—
628C2×D4C2×C4×D4314yes—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—431no—
634C22×C4—431no—
635C22×C4—431no—
636C22×C4—431no—
637C22×C4—431no—
638C22×C4—434no—
639C22×C4—432no—
640C22×C4—432no—
641C22×C4—432no—
642C22×C4—432no—
643C22×C4—432no—
644C22×C4—432no—
645C22×C4—434no—
646C22×C4—434no—
647C22×C4—862no—
648C22×C4—862no—
649C22×C4—862no—
650C22×C4—862no—
651C22×C4—862no—
652C22×C4—862no—
653C22×C4—1728no—
654C22×C4—1724no—
655C22×C4—1724no—
656C22×C4—1722no—
657C22×C4—1722no—
658C22×C4—1722no—
659C22×C4C2×C4×D4311yescharacteristic
660C22×C4C2×C4×D4311yescharacteristic
661C22×C4C2×C4×D4311yescharacteristic
662C22×C4C2×C4×D4311yescharacteristic
663C22×C4C2×C4×D4312yes—
664C22×C4C2×C4×D4312yes—
665C22×C4C23×D4312yes—
666C22×C4C23×D4312yes—
667C22×C4C23×D4311yescharacteristic
668M16—1724no—
669M16—1724no—
670C2×C8—22no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—44no—
675C2×C8—44no—
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⋊C4—434no—
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—
708C42—432no—
709C42—432no—
710C42C2×C4×D4312yes—
711C42C23×D4312yes—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—434no—
718C23—432no—
719C23—432no—
720C23—432no—
721C23—868no—
722C23—862no—
723C23—862no—
724C23—862no—
725C23—862no—
726C23—862no—
727C23—862no—
728C23—862no—
729C23—868no—
730C23—862no—
731C23—1724no—
732C23—17216no—
733C23#1306333114yes—
734C23C22×C4×D4312yes—
735C23C22×C4×D4312yes—
736C23C22×C4×D4311yescharacteristic
737Q8—1724no—
738D4—28no—
739D4—868no—
740D4—868no—
741D4—868no—
742D4—1724no—
743D4—1724no—
744D4—1724no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—432no—
756C2×C4—432no—
757C2×C4—432no—
758C2×C4—432no—
759C2×C4—432no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—864no—
766C2×C4—864no—
767C2×C4—864no—
768C2×C4—862no—
769C2×C4—862no—
770C2×C4—862no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—1724no—
775C2×C4—1724no—
776C2×C4—1724no—
777C2×C4C22×C4×D4312yes—
778C2×C4C22×C4×D4312yes—
779C2×C4C22×C4×D4312yes—
780C2×C4C22×C4×D4312yes—
781C2×C4C22×C4×D4311yescharacteristic
782C2×C4#1306337012yes—
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—28no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—44no—
800C22—434no—
801C22—862no—
802C22—868no—
803C22—862no—
804C22—862no—
805C22—862no—
806C22—862no—
807C22—862no—
808C22—862no—
809C22—862no—
810C22—17216no—
811C22—1724no—
812C22—1724no—
813C22#1458337112yes—
814C22#131×D4312yes—
815C22C2×#1306333114yes—
816C22C2×#1306333112yes—
817C22C23×C4×D4311yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—862no—
823C4—862no—
824C4—862no—
825C4—862no—
826C4—862no—
827C4#1458337112yes—
828C4C2×#1306337011yescharacteristic
829C4C2×#1306337111yescharacteristic
830C2—24no—
831C2—42no—
832C2—864no—
833C2—1722no—
834C2—1722no—
835C2#1914364814yesdirect product factor
836C2C2×#1458337111yescharacteristic
837C2C2×#131×D4311yescharacteristic
838C2C22×#1306333111yescharacteristic
subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C8×D4×C43C2
socleC23×C43C23×C4
prime radicalC2×#14583408C2
cosocleC2×C4×C43C25
hypercenterC2×C8×D4D43
hypocenterC43C2×#2977
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
2. #19143648C2direct (N × H)
3. C2×#14582973C2semidirect
4. C2×#14582971C2semidirect
5. C2×#14582970C2semidirect
6. C2×#14582969C2semidirect
7. C2×C8×D172C2semidirect
8. C2×C8×C22⋊D43C2semidirect
9. C2×(C22⋊D43)⋊C8C2semidirect
10. C2×#14582959C2semidirect
11. C2×#14582958C2semidirect
12. C2×#14582865C2semidirect
13. C2×#14582864C2semidirect
14. C22×(C2×D43)⋊C8C2semidirect
15. C2×C22⋊C8×D43C2semidirect
16. C2×C8×D4×C43C2semidirect
19. C22×#10621877C22semidirect
20. C22×#10621872C22semidirect
24. C22×C8×D43C22semidirect
39. #14582973C22semidirect
40. #14582971C22semidirect
41. #14582970C22semidirect
42. #14582969C22semidirect
43. C8×D172C22semidirect
44. C8×C22⋊D43C22semidirect
45. (C22⋊D43)⋊C8C22semidirect
46. #14582959C22semidirect
47. #14582958C22semidirect
48. C2×C4⋊(C43⋊C8)C22semidirect
49. C2×Dic43⋊C8C22semidirect
50. C2×Dic43⋊C8C22semidirect
51. #14582865C22semidirect
52. #14582864C22semidirect
54. C2×C22⋊(C43⋊C8)C22semidirect
61. C2×(C2×D43)⋊C8C22semidirect
62. C2×(C2×D43)⋊C8C22semidirect
63. C2×(C2×D43)⋊C8C22semidirect
64. C22⋊C8×D43C22semidirect
65. C2×#13063236C22semidirect
66. C2×#13063235C22semidirect
67. C2×C8×Dic43C22semidirect
69. C23×C8×C43C22semidirect
71. C8×D4×C43C22semidirect
72. C2×C4⋊C8×C43C22semidirect
74. C2×C22⋊C8×C43C22semidirect
75. C2×C4×C8×C43C22semidirect
99. C2×#10621877C23semidirect
101. C2×#10621872C23semidirect
113. C2×C8×D43C23semidirect
144. C4⋊(C43⋊C8)C23semidirect
145. Dic43⋊C8C23semidirect
146. Dic43⋊C8C23semidirect
148. C22⋊(C43⋊C8)C23semidirect
155. (C2×D43)⋊C8C23semidirect
156. (C2×D43)⋊C8C23semidirect
157. #13063236C23semidirect
158. #13063235C23semidirect
159. C8×Dic43C23semidirect
170. C22×C8×C43C23semidirect
177. C4⋊C8×C43C23semidirect
179. C22⋊C8×C43C23semidirect
180. C4×C8×C43C23semidirect
420. C2×C8×D4D43semidirect
429. C2×C43#2977semidirect
445. C23×C8C2×D43semidirect
468. C8×D4C2×D43semidirect
474. C2×C4⋊C8C2×D43semidirect
490. C2×C22⋊C8C2×D43semidirect
494. C2×C4×C8C2×D43semidirect
495. C43C2×#2977semidirect
544. C22×C8C22×D43semidirect
584. C4⋊C8C22×D43semidirect
596. C22⋊C8C22×D43semidirect
600. C4×C8C22×D43semidirect
835. C2#19143648direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834082
#191436482
C2×#145829732
C2×#145829712
C2×#145829702
C2×#145829692
C2×C8×D1722
C2×C8×C22⋊D432
C2×(C22⋊D43)⋊C82
C2×#145829592
C2×#145829582
C2×#145828652
C2×#145828642
C22×(C2×D43)⋊C82
C2×C22⋊C8×D432
C2×C8×D4×C432
C2×#297743