Finite Group Databasebeta

← C2×#19143642 #25961346

Subgroups — C2×#19143642 #25961346

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×#14583408C211yesmaximal, characteristic
2#19143642C2116yesmaximal, direct product factor
3C2×#14582977C211yesmaximal, characteristic, complemented
4C2×#14582974C211yesmaximal, characteristic, complemented
5C2×#14582973C211yesmaximal, characteristic, complemented
6C2×#14582972C211yesmaximal, characteristic, complemented
7C2×#14582968C211yesmaximal, characteristic, complemented
8C2×#14582964C211yesmaximal, characteristic, complemented
9C2×C8×C22⋊D43C211yesmaximal, characteristic, complemented
10C2×#14582961C211yesmaximal, characteristic, complemented
11C2×#14582959C211yesmaximal, characteristic, complemented
12C2×#14582865C211yesmaximal, characteristic, complemented
13C2×#14582864C211yesmaximal, characteristic, complemented
14C2×#14582862C211yesmaximal, characteristic, complemented
15C2×C22⋊C8×D43C211yesmaximal, characteristic, complemented
16C2×C43×#435C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C22×#10621877C2211yescharacteristic
20C22×#10621877C2211yescharacteristic, complemented
21C22×#10621872C2211yescharacteristic, complemented
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#14582977C2218yescomplemented
40#14582974C2218yescomplemented
41#14582973C2218yescomplemented
42#14582972C2218yescomplemented
43#14582968C2218yescomplemented
44#14582964C2218yescomplemented
45C8×C22⋊D43C2218yescomplemented
46#14582961C2218yescomplemented
47#14582959C2218yescomplemented
48C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
49C2×Dic43⋊C8C2211yescharacteristic, complemented
50C2×Dic43⋊C8C2211yescharacteristic, complemented
51#14582865C2218yescomplemented
52#14582864C2218yescomplemented
53#14582862C2218yescomplemented
54C2×C22⋊(C43⋊C8)C2211yescharacteristic
55C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
56C2×(C2×D43)⋊C8C2211yescharacteristic
57C2×(C2×D43)⋊C8C2211yescharacteristic
58C2×(C2×D43)⋊C8C2211yescharacteristic
59C2×(C2×D43)⋊C8C2211yescharacteristic
60C2×(C2×D43)⋊C8C2211yescharacteristic
61C2×(C2×D43)⋊C8C2211yescharacteristic
62C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
63C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
64C22⋊C8×D43C2218yescomplemented
65C2×#13063235C2211yescharacteristic, complemented
66C2×C4×C43⋊C8C2211yescharacteristic, complemented
67C2×C8×Dic43C2211yescharacteristic, complemented
68C22×M16×C43C2211yescharacteristic
69C23×C8×C43C2211yescharacteristic, complemented
70C2×C4×D4×C43C2211yescharacteristic
71C43×#435C2218yescomplemented
72C2×C4⋊C8×C43C2211yescharacteristic, complemented
73C2×C22⋊C8×C43C2211yescharacteristic
74C2×C22⋊C8×C43C2211yescharacteristic, complemented
75C2×#97×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×#10621877—42no—
100C2×#10621877C2314yes—
101C2×#10621877C2314yescomplemented
102C2×#10621872—42no—
103C2×#10621872C2314yescomplemented
104C22×C43⋊C8C2311yescharacteristic
105C22×C43⋊C8C2311yescharacteristic
106C22×C43⋊C8C2311yescharacteristic
107C22×C43⋊C8C2311yescharacteristic
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#13063235C2314yescomplemented
158C4×C43⋊C8C2314yescomplemented
159C8×Dic43C2314yescomplemented
160C22×D4×C43C2×C411yescharacteristic
161C23×C4×C43C2311yescharacteristic
162C23×C4×C43C2311yescharacteristic
163C2×M16×C43—42no—
164C2×M16×C43C2314yes—
165C22×C8×C43—42no—
166C22×C8×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169C22×C8×C43C2311yescharacteristic
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
180#97×C43C2314yescomplemented
181C24×C43C22×C411yescharacteristic
182C24×C43C22×C411yescharacteristic
183C23×D43—24no—
184C23×D43—42no—
185C23×D43—42no—
186C23×D43C22×C411yescharacteristic
187C23×D43C22×C411yescharacteristic
188C23×D43C22×C411yescharacteristic
189C23×D43C22×C414yes—
190C2×D4×C43—42no—
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—42no—
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—
248M16×C43—44no—
249C2×C8×C43—22no—
250C2×C8×C43—22no—
251C2×C8×C43—22no—
252C2×C8×C43—22no—
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—
279#10621877—44no—
280C2×C43⋊C8—22no—
281C2×C43⋊C8—22no—
282C2×C43⋊C8—22no—
283C2×C43⋊C8—22no—
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—22no—
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—22no—
309C22×D43—28no—
310C22×D43—44no—
311C22×D43—44no—
312C22×D43—416no—
313C22×D43#13114yes—
314C22×D43C23×C412yes—
315C22×D43C23×C412yes—
316C22×D43C23×C412yes—
317D4×C43—44no—
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—44no—
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×#2976—431nomaximal, Sylow
374C22×C43—22no—
375C22×C43—22no—
376C22×C43—22no—
377C22×C43—22no—
378C22×C43—22no—
379C22×C43—22no—
380C22×C43—44no—
381C22×C43—44no—
382C22×C43#51812yes—
383C22×C43C2×#13112yes—
384C22×C43#56812yes—
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#2976—4316no—
413C2×#436—431no—
414C2×#436—431no—
415C2×#435—431no—
416C2×#435—431no—
417C2×#435—431no—
418C2×#435D4311yescharacteristic, complemented
419C2×C8×D4—431no—
420C2×C8×D4—431no—
421C2×#433—431no—
422C2×#433—431no—
423C2×#408—431no—
424C2×#408—431no—
425C2×#407—431no—
426C22×C22⋊C8—431no—
427C2×C43—42no—
428C2×C43—42no—
429C2×C43#297614yescomplemented
430C2×C43C2×#51811yescharacteristic
431C2×C43C22×#13111yescharacteristic
432C2×C43C2×#56811yescharacteristic
433D43—24no—
434D43—42no—
435D43—42no—
436C22×#41—431no—
437C24×C4—431no—
438C22×M16—431no—
439C22×M16—431no—
440C22×M16—431no—
441C22×M16C2×D4311yescharacteristic
442C23×C8—431no—
443C23×C8—431no—
444C23×C8—431no—
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#436—438no—
462#436—438no—
463#435—438no—
464#435—438no—
465#435—438no—
466#435C2×D4318yescomplemented
467C8×D4—438no—
468C8×D4—438no—
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—
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, complemented
491C2×#97—431no—
492C2×#97C2×D4311yescharacteristic, complemented
493C2×C4×C8—431no—
494C2×C4×C8—431no—
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×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—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×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#97C22×D4314yescomplemented
599C4×C8—434no—
600C4×C8—434no—
601C24—431no—
602C24—431no—
603C24—431no—
604C24—434no—
605C24—864no—
606C24—1722no—
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—42no—
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×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—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—
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—22no—
718C23—434no—
719C23—432no—
720C23—432no—
721C23—432no—
722C23—868no—
723C23—862no—
724C23—862no—
725C23—862no—
726C23—862no—
727C23—862no—
728C23—862no—
729C23—862no—
730C23—862no—
731C23—1724no—
732C23—1724no—
733C23—17216no—
734C23C22×C4×D4312yes—
735C23C22×C4×D4312yes—
736C23C22×C4×D4311yescharacteristic
737Q8—1724no—
738D4—44no—
739D4—868no—
740D4—868no—
741D4—1724no—
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—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—44no—
800C22—44no—
801C22—434no—
802C22—862no—
803C22—868no—
804C22—862no—
805C22—862no—
806C22—862no—
807C22—862no—
808C22—862no—
809C22—862no—
810C22—862no—
811C22—17216no—
812C22—1724no—
813C22—1724no—
814C22#1458337112yes—
815C22#131×D4312yes—
816C22#1458366512yes—
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—42no—
831C2—42no—
832C2—864no—
833C2—1722no—
834C2—1722no—
835C2#1914364214yesdirect product factor
836C2C2×#1458337111yescharacteristic
837C2C2×#131×D4311yescharacteristic
838C2C2×#1458366511yescharacteristic
subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C43×#435C2
socleC23×C43C23×C4
prime radicalC2×#14583408C2
cosocleC2×C4×C43C25
hypercenterC2×#435D43
hypocenterC43C2×#2976
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #19143642C2direct (N × H)
3. C2×#14582977C2semidirect
4. C2×#14582974C2semidirect
5. C2×#14582973C2semidirect
6. C2×#14582972C2semidirect
7. C2×#14582968C2semidirect
8. C2×#14582964C2semidirect
9. C2×C8×C22⋊D43C2semidirect
10. C2×#14582961C2semidirect
11. C2×#14582959C2semidirect
12. C2×#14582865C2semidirect
13. C2×#14582864C2semidirect
14. C2×#14582862C2semidirect
15. C2×C22⋊C8×D43C2semidirect
16. C2×C43×#435C2semidirect
20. C22×#10621877C22semidirect
21. C22×#10621872C22semidirect
24. C22×C8×D43C22semidirect
39. #14582977C22semidirect
40. #14582974C22semidirect
41. #14582973C22semidirect
42. #14582972C22semidirect
43. #14582968C22semidirect
44. #14582964C22semidirect
45. C8×C22⋊D43C22semidirect
46. #14582961C22semidirect
47. #14582959C22semidirect
48. C2×C4⋊(C43⋊C8)C22semidirect
49. C2×Dic43⋊C8C22semidirect
50. C2×Dic43⋊C8C22semidirect
51. #14582865C22semidirect
52. #14582864C22semidirect
53. #14582862C22semidirect
55. C2×C22⋊(C43⋊C8)C22semidirect
62. C2×(C2×D43)⋊C8C22semidirect
63. C2×(C2×D43)⋊C8C22semidirect
64. C22⋊C8×D43C22semidirect
65. C2×#13063235C22semidirect
66. C2×C4×C43⋊C8C22semidirect
67. C2×C8×Dic43C22semidirect
69. C23×C8×C43C22semidirect
71. C43×#435C22semidirect
72. C2×C4⋊C8×C43C22semidirect
74. C2×C22⋊C8×C43C22semidirect
75. C2×#97×C43C22semidirect
101. C2×#10621877C23semidirect
103. 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. #13063235C23semidirect
158. C4×C43⋊C8C23semidirect
159. C8×Dic43C23semidirect
170. C22×C8×C43C23semidirect
177. C4⋊C8×C43C23semidirect
179. C22⋊C8×C43C23semidirect
180. #97×C43C23semidirect
418. C2×#435D43semidirect
429. C2×C43#2976semidirect
445. C23×C8C2×D43semidirect
466. #435C2×D43semidirect
474. C2×C4⋊C8C2×D43semidirect
490. C2×C22⋊C8C2×D43semidirect
492. C2×#97C2×D43semidirect
495. C43C2×#2976semidirect
544. C22×C8C22×D43semidirect
584. C4⋊C8C22×D43semidirect
596. C22⋊C8C22×D43semidirect
598. #97C22×D43semidirect
835. C2#19143642direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834082
#191436422
C2×#145829772
C2×#145829742
C2×#145829732
C2×#145829722
C2×#145829682
C2×#145829642
C2×C8×C22⋊D432
C2×#145829612
C2×#145829592
C2×#145828652
C2×#145828642
C2×#145828622
C2×C22⋊C8×D432
C2×C43×#4352
C2×#297643