Finite Group Databasebeta

← C2×#19143752 #25961696

Subgroups — C2×#19143752 #25961696

Order 11008.

1982 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583429C211yesmaximal, characteristic
2#19143752C2116yesmaximal, direct product factor
3C2×#14583028C211yesmaximal, characteristic, complemented
4C2×C8×Dic86C211yesmaximal, characteristic, complemented
5C2×#14582974C211yesmaximal, characteristic, complemented
6C2×#14582971C211yesmaximal, characteristic, complemented
7C2×#14582970C211yesmaximal, characteristic, complemented
8C2×C8×C22⋊D43C211yesmaximal, characteristic, complemented
9C2×(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
10C2×#14582958C211yesmaximal, characteristic, complemented
11C2×#14582957C211yesmaximal, characteristic, complemented
12C2×#14582949C211yesmaximal, characteristic, complemented
13C2×#14582925C211yesmaximal, characteristic, complemented
14C2×#14582924C211yesmaximal, characteristic, complemented
15C22×Dic43⋊C8C211yesmaximal, characteristic, complemented
16C2×C8×D4×C43C211yesmaximal, characteristic, complemented
17C22×#10621877C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21#14583429C418yes—
22#14583429C2218yes—
23C2×#13063320C411yescharacteristic
24C2×#13063318C411yescharacteristic
25C2×#13063315C411yescharacteristic
26C2×#13063311C411yescharacteristic
27C2×#13063309C411yescharacteristic
28C2×#13063306C411yescharacteristic
29C2×#13063302C411yescharacteristic
30C2×#13063297C411yescharacteristic
31C2×C4×Dic86C2211yescharacteristic
32C2×C4×C22⋊D43C2211yescharacteristic
33C2×C4×C22⋊D43C2211yescharacteristic
34C2×#13063284C2211yescharacteristic
35C2×#13063282C2211yescharacteristic
36C22×C4×Dic43C2211yescharacteristic
37#14583028C2218yescomplemented
38C8×Dic86C2218yescomplemented
39#14582974C2218yescomplemented
40#14582971C2218yescomplemented
41#14582970C2218yescomplemented
42C8×C22⋊D43C2218yescomplemented
43(C22⋊D43)⋊C8C2218yescomplemented
44#14582958C2218yescomplemented
45#14582957C2218yescomplemented
46#14582949C2218yescomplemented
47#14582925C2218yescomplemented
48#14582924C2218yescomplemented
49C2×C4⋊(C43⋊C8)C2211yescharacteristic
50C2×Dic43⋊C8C2211yescharacteristic
51C2×Dic43⋊C8C2211yescharacteristic
52C2×Dic43⋊C8C2211yescharacteristic
53C2×Dic43⋊C8C2211yescharacteristic
54C2×Dic43⋊C8C2211yescharacteristic
55C2×Dic43⋊C8C2211yescharacteristic
56C2×Dic43⋊C8C2211yescharacteristic
57C2×Dic43⋊C8C2211yescharacteristic
58C2×Dic43⋊C8C2218yescomplemented
59C2×C22⋊(C43⋊C8)C2211yescharacteristic
60C2×C22⋊(C43⋊C8)C2211yescharacteristic
61C2×(C2×D43)⋊C8C2211yescharacteristic
62C2×(C2×D43)⋊C8C2211yescharacteristic
63C2×#13063236C2211yescharacteristic
64C2×#13063235C2211yescharacteristic
65C2×C8×Dic43C2211yescharacteristic
66C2×C8×Dic43C2211yescharacteristic
67C2×C8×Dic43C2211yescharacteristic
68C23×C8×C43C2211yescharacteristic
69C23×C8×C43C2211yescharacteristic
70C2×C4×D4×C43C2211yescharacteristic
71C8×D4×C43C2218yescomplemented
72C2×C4⋊C8×C43C2211yescharacteristic
73C2×C22⋊C8×C43C2211yescharacteristic
74C2×C22⋊C8×C43C2211yescharacteristic
75C2×C4×C8×C43C2211yescharacteristic
76C22×Dic86C2×C411yescharacteristic
77C22×C22⋊D43C2×C411yescharacteristic
78C22×C22⋊D43C2×C411yescharacteristic
79C23×Dic43C2×C411yescharacteristic
80C23×Dic43C2×C411yescharacteristic
81C22×C4×D43C2311yescharacteristic
82C2×#10621877—42no—
83C2×#10621877C2314yes—
84C2×#10621872—42no—
85C2×#10621872C2314yes—
86C22×C43⋊C8—42no—
87C22×C43⋊C8C2311yescharacteristic
88C22×C43⋊C8C2311yescharacteristic
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91C22×C43⋊C8C2314yes—
92C2×C8×D43—42no—
93C2×C8×D43C2314yes—
94#13063320C2×C418yes—
95#13063318C2×C418yes—
96#13063315C2×C418yes—
97#13063311C2×C418yes—
98#13063309C2×C418yes—
99#13063306C2×C418yes—
100#13063302C2×C418yes—
101#13063297C2×C418yes—
102C4×Dic86C2×C414yes—
103C4×Dic86C2314yes—
104C4×C22⋊D43C2×C414yes—
105C4×C22⋊D43C2×C414yes—
106C4×C22⋊D43C2314yes—
107C4×C22⋊D43C2314yes—
108#13063284C2×C414yes—
109#13063284C2314yes—
110#13063282C2×C414yes—
111#13063282C2314yes—
112C2×C4⋊Dic43C2×C411yescharacteristic
113C2×C4⋊Dic43C2×C411yescharacteristic
114C2×C4⋊Dic43C2×C411yescharacteristic
115C2×Dic43⋊C4C2×C411yescharacteristic
116C2×Dic43⋊C4C2×C411yescharacteristic
117C2×Dic43⋊C4C2×C411yescharacteristic
118C2×Dic43⋊C4C2×C411yescharacteristic
119C2×Dic43⋊C4C2×C411yescharacteristic
120C2×Dic43⋊C4C2×C411yescharacteristic
121C2×C22⋊Dic43C2×C411yescharacteristic
122C2×C22⋊Dic43C2×C411yescharacteristic
123C2×C22⋊Dic43C2×C411yescharacteristic
124C2×C22⋊Dic43C2×C411yescharacteristic
125C2×(C2×D43)⋊C4C2×C411yescharacteristic
126C2×(C2×D43)⋊C4C2×C411yescharacteristic
127C2×(C2×D43)⋊C4C2×C411yescharacteristic
128C2×(C2×D43)⋊C4C2×C411yescharacteristic
129C2×C4×Dic43C2×C411yescharacteristic
130C2×C4×Dic43C2×C411yescharacteristic
131C2×C4×Dic43C2×C414yes—
132C2×C4×Dic43C2311yescharacteristic
133C2×C4×Dic43C2311yescharacteristic
134C2×C4×Dic43C2314yes—
135C2×C4×Dic43C2311yescharacteristic
136C4⋊(C43⋊C8)C2314yes—
137Dic43⋊C8C2314yes—
138Dic43⋊C8C2314yes—
139Dic43⋊C8C2314yes—
140Dic43⋊C8C2314yes—
141Dic43⋊C8C2314yes—
142Dic43⋊C8C2314yes—
143Dic43⋊C8C2314yes—
144Dic43⋊C8C2314yes—
145C22⋊(C43⋊C8)C2314yes—
146C22⋊(C43⋊C8)C2314yes—
147(C2×D43)⋊C8C2314yes—
148(C2×D43)⋊C8C2314yes—
149#13063236C2314yes—
150#13063235C2314yes—
151C8×Dic43C2314yes—
152C8×Dic43C2314yes—
153C8×Dic43C2314yes—
154C22×D4×C43C2×C411yescharacteristic
155C23×C4×C43C2311yescharacteristic
156C23×C4×C43C2311yescharacteristic
157C22×C8×C43—42no—
158C22×C8×C43—42no—
159C22×C8×C43C2311yescharacteristic
160C22×C8×C43C2311yescharacteristic
161C22×C8×C43C2311yescharacteristic
162C22×C8×C43C2311yescharacteristic
163C22×C8×C43C2314yes—
164C22×C8×C43C2314yes—
165C4×D4×C43C2×C414yes—
166C4×D4×C43C2314yes—
167C2×C4⋊C4×C43C2×C411yescharacteristic
168C2×C22⋊C4×C43C2×C411yescharacteristic
169C2×C22⋊C4×C43C2×C411yescharacteristic
170C2×C42×C43C2311yescharacteristic
171C4⋊C8×C43C2314yes—
172C22⋊C8×C43C2314yes—
173C22⋊C8×C43C2314yes—
174C4×C8×C43C2314yes—
175C24×C43C22×C411yescharacteristic
176C24×C43C22×C411yescharacteristic
177C23×D43C22×C411yescharacteristic
178C2×D4×C43—24no—
179C2×D4×C43C22×C414yes—
180C22×C4×C43—22no—
181C22×C4×C43—22no—
182C22×C4×C43—22no—
183C22×C4×C43—22no—
184C22×C4×C43C22×C411yescharacteristic
185C22×C4×C43C22×C411yescharacteristic
186C22×C4×C43C22×C411yescharacteristic
187C22×C4×C43C22×C411yescharacteristic
188C22×C4×C43C22×C412yes—
189C22×C4×C43C22×C412yes—
190C22×C4×C43C2412yes—
191C22×C4×C43C2412yes—
192C22×C4×C43C2411yescharacteristic
193C2×C22⋊D43—24no—
194C2×C22⋊D43—24no—
195C2×C22⋊D43C22×C414yes—
196C2×C22⋊D43C22×C414yes—
197C22×Dic43—24no—
198C22×Dic43—24no—
199C22×Dic43C22×C411yescharacteristic
200C22×Dic43C22×C411yescharacteristic
201C22×Dic43C22×C411yescharacteristic
202C22×Dic43C22×C414yes—
203C22×Dic43C22×C414yes—
204C22×Dic43C22×C411yescharacteristic
205C22×Dic43C22×C411yescharacteristic
206C22×Dic43C22×C411yescharacteristic
207C22×Dic43C22×C411yescharacteristic
208C2×C4×D43—22no—
209C2×C4×D43—22no—
210C2×C4×D43C22×C412yes—
211C2×C4×D43C2412yes—
212C2×Dic86—24no—
213C2×Dic86C22×C414yes—
214C2×C8×C43—22no—
215C2×C8×C43—22no—
216C2×C8×C43—22no—
217C2×C8×C43—22no—
218C2×C8×C43—44no—
219C2×C8×C43—44no—
220C2×C8×C43C2412yes—
221C2×C8×C43C2412yes—
222C2×C8×C43C2412yes—
223C2×C8×C43C2412yes—
224C4⋊C4×C43C22×C414yes—
225C22⋊C4×C43C22×C414yes—
226C22⋊C4×C43C22×C414yes—
227C42×C43C22×C412yes—
228C42×C43C2412yes—
229C22⋊Dic43C22×C414yes—
230C22⋊Dic43C22×C414yes—
231C22⋊Dic43C22×C414yes—
232C22⋊Dic43C22×C414yes—
233(C2×D43)⋊C4C22×C414yes—
234(C2×D43)⋊C4C22×C414yes—
235(C2×D43)⋊C4C22×C414yes—
236(C2×D43)⋊C4C22×C414yes—
237C4⋊Dic43C22×C414yes—
238C4⋊Dic43C22×C414yes—
239C4⋊Dic43C22×C414yes—
240Dic43⋊C4C22×C414yes—
241Dic43⋊C4C22×C414yes—
242Dic43⋊C4C22×C414yes—
243Dic43⋊C4C22×C414yes—
244Dic43⋊C4C22×C414yes—
245Dic43⋊C4C22×C414yes—
246C4×Dic43C22×C412yes—
247C4×Dic43C22×C412yes—
248C4×Dic43C22×C414yes—
249C4×Dic43C22×C414yes—
250C4×Dic43C22×C412yes—
251C4×Dic43C2412yes—
252C4×Dic43C2412yes—
253C4×Dic43C2412yes—
254#10621877—44no—
255C2×C43⋊C8—22no—
256C2×C43⋊C8—22no—
257C2×C43⋊C8—22no—
258C2×C43⋊C8—22no—
259C2×C43⋊C8—44no—
260C2×C43⋊C8C2412yes—
261C2×C43⋊C8C2412yes—
262C2×C43⋊C8C2412yes—
263C2×C43⋊C8C2412yes—
264#10621872—44no—
265C8×D43—44no—
266C23×C43—22no—
267C23×C43—22no—
268C23×C43—22no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43#13114yes—
272C23×C43C23×C412yes—
273C23×C43C23×C412yes—
274C23×C43C23×C411yescharacteristic
275C22×D43—22no—
276C22×D43—22no—
277C22×D43—22no—
278C22×D43C23×C412yes—
279D4×C43—28no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—24no—
285C2×C4×C43—24no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43C23×C412yes—
291C2×C4×C43C23×C412yes—
292C2×C4×C43C23×C412yes—
293C2×C4×C43C23×C412yes—
294C2×C4×C43C23×C411yescharacteristic
295C2×C4×C43H(5,𝔽2)12yes—
296C2×C4×C432−1+412yes—
297C2×C4×C43C2511yescharacteristic
298C22⋊D43—28no—
299C22⋊D43—28no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—28no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—28no—
308C2×Dic43#13114yes—
309C2×Dic43C23×C412yes—
310C2×Dic43C23×C412yes—
311C2×Dic43C23×C412yes—
312C2×Dic43C23×C412yes—
313C2×Dic43C23×C412yes—
314C2×Dic43C23×C412yes—
315C2×Dic43C23×C412yes—
316C4×D43—24no—
317C4×D43—22no—
318C4×D43—22no—
319Dic86—28no—
320C8×C43—22no—
321C8×C43—22no—
322C8×C43—22no—
323C8×C43—22no—
324C43⋊C8—22no—
325C43⋊C8—22no—
326C43⋊C8—22no—
327C43⋊C8—22no—
328C2×#2994—431nomaximal, Sylow
329C22×C43—22no—
330C22×C43—28no—
331C22×C43—22no—
332C22×C43—22no—
333C22×C43—22no—
334C22×C43—22no—
335C22×C43—44no—
336C22×C43#52012yes—
337C22×C43C2×#13112yes—
338C22×C43C2×#13114yes—
339C22×C43C2×#13112yes—
340C22×C43C24×C411yescharacteristic
341C2×D43—22no—
342C2×D43—22no—
343C2×D43—22no—
344C2×D43—44no—
345C4×C43—22no—
346C4×C43—22no—
347C4×C43—22no—
348C4×C43—22no—
349C4×C43#52012yes—
350C4×C43C2×H(5,𝔽2)11yescharacteristic
351C4×C43C2×2−1+411yescharacteristic
352Dic43—22no—
353Dic43—22no—
354Dic43—22no—
355Dic43—22no—
356Dic43—22no—
357Dic43—22no—
358Dic43C2×#13114yes—
359C2×#529—431no—
360#2994—4316no—
361C2×#446—431no—
362C2×C8×Q8—431no—
363C2×#436—431no—
364C2×#435—431no—
365C2×#435—431no—
366C2×C8×D4—431no—
367C2×C8×D4—431no—
368C2×C8×D4D4311yescharacteristic, complemented
369C2×#433—431no—
370C2×#433—431no—
371C2×#431—431no—
372C2×#424—431no—
373C2×#424—431no—
374C22×C4⋊C8—431no—
375C2×C43—24no—
376C2×C43—42no—
377C2×C43#299414yescomplemented
378C2×C43C2×#52011yescharacteristic
379C2×C43C22×#13111yescharacteristic
380C2×C43C22×#13111yescharacteristic
381D43—42no—
382C22×M16—431no—
383C22×M16—431no—
384C23×C8—431no—
385C23×C8—431no—
386C23×C8C2×D4311yescharacteristic
387C23×C8C2×D4311yescharacteristic
388#529—438no—
389#529—438no—
390C2×#126—431no—
391C2×#126—431no—
392C2×#125—431no—
393C2×#124—431no—
394C2×#123—431no—
395C2×#123—431no—
396C2×C22⋊Q8—431no—
397C2×#121—431no—
398C2×C4×Q8—431no—
399C2×C4×D4—431no—
400C2×C4×D4—431no—
401C2×C4×D4C2×D4311yescharacteristic
402C2×#117—431no—
403C2×#117—431no—
404C22×C42—431no—
405#446—438no—
406C8×Q8—438no—
407#436—438no—
408#435—438no—
409#435—438no—
410C8×D4—438no—
411C8×D4—438no—
412C8×D4C2×D4318yescomplemented
413#433—438no—
414#433—438no—
415#431—438no—
416#424—438no—
417#424—438no—
418C2×C4⋊C8—431no—
419C2×C4⋊C8—431no—
420C2×C4⋊C8—431no—
421C2×C4⋊C8—431no—
422C2×C4⋊C8—438no—
423C2×C4⋊C8—431no—
424C2×C4⋊C8—431no—
425C2×C4⋊C8—431no—
426C2×C4⋊C8—431no—
427C2×C4⋊C8—431no—
428C2×C4⋊C8C2×D4311yescharacteristic
429C2×C22⋊C8—431no—
430C2×C22⋊C8—431no—
431C2×C22⋊C8—431no—
432C2×C22⋊C8—431no—
433C2×C22⋊C8C2×D4311yescharacteristic
434C2×C22⋊C8C2×D4311yescharacteristic
435C2×#97—431no—
436C2×#97—431no—
437C2×C4×C8—431no—
438C2×C4×C8—431no—
439C2×C4×C8—431no—
440C2×C4×C8C2×D4311yescharacteristic
441C43C2×#299411yescharacteristic, complemented, Sylow
442C22×Q8—431no—
443C22×D4—431no—
444C22×D4—431no—
445C22×D4C4×D4311yescharacteristic
446C23×C4—431no—
447C23×C4—431no—
448C23×C4—431no—
449C23×C4C22×D4311yescharacteristic
450C23×C4C22×D4311yescharacteristic
451C2×M16—434no—
452C2×M16—434no—
453C2×M16—1722no—
454C2×M16—1722no—
455C22×C8—42no—
456C22×C8—42no—
457C22×C8—431no—
458C22×C8—431no—
459C22×C8—431no—
460C22×C8—431no—
461C22×C8—434no—
462C22×C8—434no—
463C22×C8—1722no—
464C22×C8—1722no—
465C22×C8C22×D4311yescharacteristic
466C22×C8C22×D4311yescharacteristic
467C22×C8C22×D4311yescharacteristic
468C22×C8C22×D4311yescharacteristic
469C22×C8C22×D4314yes—
470C22×C8C22×D4314yes—
471#126—438no—
472#126—438no—
473#125—438no—
474#124—438no—
475#123—438no—
476#123—438no—
477C22⋊Q8—438no—
478#121—438no—
479C4×Q8—434no—
480C4×Q8—434no—
481C4×D4—434no—
482C4×D4—434no—
483C4×D4—434no—
484C4×D4—434no—
485C4×D4C4×D4314yes—
486C4×D4C22×D4314yes—
487#117—434no—
488#117—434no—
489#117—434no—
490#117—434no—
491C2×C4⋊C4—431no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4C4×D4311yescharacteristic
501C2×C22⋊C4—431no—
502C2×C22⋊C4—431no—
503C2×C22⋊C4—431no—
504C2×C22⋊C4—431no—
505C2×C22⋊C4—431no—
506C2×C22⋊C4—431no—
507C2×C22⋊C4—431no—
508C2×C22⋊C4—431no—
509C2×C22⋊C4C4×D4311yescharacteristic
510C2×C22⋊C4C4×D4311yescharacteristic
511C2×C42—431no—
512C2×C42—431no—
513C2×C42—434no—
514C2×C42—434no—
515C2×C42—431no—
516C2×C42—431no—
517C2×C42—431no—
518C2×C42C22×D4311yescharacteristic
519C4⋊C8—434no—
520C4⋊C8—434no—
521C4⋊C8—434no—
522C4⋊C8—434no—
523C4⋊C8—434no—
524C4⋊C8—434no—
525C4⋊C8—434no—
526C4⋊C8—434no—
527C4⋊C8—434no—
528C4⋊C8C22×D4314yes—
529C22⋊C8—434no—
530C22⋊C8—434no—
531C22⋊C8—434no—
532C22⋊C8—434no—
533C22⋊C8C22×D4314yes—
534C22⋊C8C22×D4314yes—
535#97—434no—
536#97—434no—
537C4×C8—434no—
538C4×C8—434no—
539C4×C8—434no—
540C4×C8C22×D4314yes—
541C24—431no—
542C24C2×C4×D4311yescharacteristic
543C24C2×C4×D4311yescharacteristic
544C2×Q8—434no—
545C2×Q8—864no—
546C2×D4—24no—
547C2×D4—434no—
548C2×D4—434no—
549C2×D4—864no—
550C2×D4—864no—
551C2×D4C2×C4×D4314yes—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—431no—
557C22×C4—431no—
558C22×C4—431no—
559C22×C4—431no—
560C22×C4—434no—
561C22×C4—434no—
562C22×C4—431no—
563C22×C4—431no—
564C22×C4—431no—
565C22×C4—432no—
566C22×C4—432no—
567C22×C4—864no—
568C22×C4—864no—
569C22×C4—862no—
570C22×C4—862no—
571C22×C4C2×C4×D4311yescharacteristic
572C22×C4C2×C4×D4312yes—
573C22×C4C2×C4×D4311yescharacteristic
574C22×C4C2×C4×D4311yescharacteristic
575C22×C4C2×C4×D4311yescharacteristic
576C22×C4C2×C4×D4312yes—
577C22×C4C23×D4312yes—
578C22×C4C23×D4312yes—
579C22×C4C23×D4311yescharacteristic
580M16—1724no—
581M16—1724no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—44no—
587C2×C8—44no—
588C2×C8—432no—
589C2×C8—432no—
590C2×C8—432no—
591C2×C8—432no—
592C2×C8—862no—
593C2×C8—862no—
594C2×C8—862no—
595C2×C8—862no—
596C2×C8—1724no—
597C2×C8—1724no—
598C2×C8C23×D4312yes—
599C2×C8C23×D4312yes—
600C2×C8C23×D4312yes—
601C2×C8C23×D4312yes—
602C4⋊C4—434no—
603C4⋊C4—434no—
604C4⋊C4—434no—
605C4⋊C4—434no—
606C4⋊C4—434no—
607C4⋊C4—434no—
608C4⋊C4—434no—
609C4⋊C4—434no—
610C4⋊C4—434no—
611C4⋊C4C2×C4×D4314yes—
612C22⋊C4—434no—
613C22⋊C4—434no—
614C22⋊C4—434no—
615C22⋊C4—434no—
616C22⋊C4—434no—
617C22⋊C4—434no—
618C22⋊C4—434no—
619C22⋊C4—434no—
620C22⋊C4C2×C4×D4314yes—
621C22⋊C4C2×C4×D4314yes—
622C42—432no—
623C42—432no—
624C42—434no—
625C42—434no—
626C42—432no—
627C42—432no—
628C42—432no—
629C42—432no—
630C42C2×C4×D4312yes—
631C42C23×D4312yes—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—432no—
638C23—862no—
639C23—862no—
640C23—862no—
641C23#1306333114yes—
642C23C22×C4×D4312yes—
643C23C22×C4×D4312yes—
644C23C22×C4×D4311yescharacteristic
645Q8—868no—
646D4—28no—
647D4—868no—
648D4—868no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—434no—
660C2×C4—432no—
661C2×C4—432no—
662C2×C4—432no—
663C2×C4—432no—
664C2×C4—432no—
665C2×C4—432no—
666C2×C4—432no—
667C2×C4—868no—
668C2×C4—862no—
669C2×C4—862no—
670C2×C4—862no—
671C2×C4—868no—
672C2×C4—862no—
673C2×C4—862no—
674C2×C4—862no—
675C2×C4—864no—
676C2×C4—862no—
677C2×C4—862no—
678C2×C4C22×C4×D4312yes—
679C2×C4C22×C4×D4312yes—
680C2×C4C22×C4×D4312yes—
681C2×C4C22×C4×D4312yes—
682C2×C4C22×C4×D4311yescharacteristic
683C2×C4#1306337012yes—
684C2×C4#1306337212yes—
685C2×C4C24×D4311yescharacteristic
686C8—22no—
687C8—22no—
688C8—22no—
689C8—22no—
690C8—862no—
691C8—862no—
692C8—862no—
693C8—862no—
694C22—22no—
695C22—28no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—44no—
701C22—862no—
702C22—862no—
703C22—862no—
704C22—1724no—
705C22#1458337812yes—
706C22#131×D4312yes—
707C22C2×#1306333114yes—
708C22C2×#1306333112yes—
709C22C23×C4×D4311yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—434no—
715C4—862no—
716C4—862no—
717C4—862no—
718C4—862no—
719C4—862no—
720C4—862no—
721C4#1458337812yes—
722C4C2×#1306337011yescharacteristic
723C4C2×#1306337211yescharacteristic
724C2—24no—
725C2—42no—
726C2—1722no—
727C2#1914375214yesdirect product factor
728C2C2×#1458337811yescharacteristic
729C2C2×#131×D4311yescharacteristic
730C2C22×#1306333111yescharacteristic
subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C8×D4×C43C2
socleC23×C43C23×C4
prime radicalC2×#13063297C4
cosocleC2×C4×C43C25
hypercenterC2×C8×D4D43
hypocenterC43C2×#2994
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. #19143752C2direct (N × H)
3. C2×#14583028C2semidirect
4. C2×C8×Dic86C2semidirect
5. C2×#14582974C2semidirect
6. C2×#14582971C2semidirect
7. C2×#14582970C2semidirect
8. C2×C8×C22⋊D43C2semidirect
9. C2×(C22⋊D43)⋊C8C2semidirect
10. C2×#14582958C2semidirect
11. C2×#14582957C2semidirect
12. C2×#14582949C2semidirect
13. C2×#14582925C2semidirect
14. C2×#14582924C2semidirect
15. C22×Dic43⋊C8C2semidirect
16. C2×C8×D4×C43C2semidirect
37. #14583028C22semidirect
38. C8×Dic86C22semidirect
39. #14582974C22semidirect
40. #14582971C22semidirect
41. #14582970C22semidirect
42. C8×C22⋊D43C22semidirect
43. (C22⋊D43)⋊C8C22semidirect
44. #14582958C22semidirect
45. #14582957C22semidirect
46. #14582949C22semidirect
47. #14582925C22semidirect
48. #14582924C22semidirect
58. C2×Dic43⋊C8C22semidirect
71. C8×D4×C43C22semidirect
368. C2×C8×D4D43semidirect
377. C2×C43#2994semidirect
412. C8×D4C2×D43semidirect
441. C43C2×#2994semidirect
727. C2#19143752direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834292
#191437522
C2×#145830282
C2×C8×Dic862
C2×#145829742
C2×#145829712
C2×#145829702
C2×C8×C22⋊D432
C2×(C22⋊D43)⋊C82
C2×#145829582
C2×#145829572
C2×#145829492
C2×#145829252
C2×#145829242
C22×Dic43⋊C82
C2×C8×D4×C432
C2×#299443