Finite Group Databasebeta

← C2×#14545283 #17978945

Subgroups — C2×#14545283 #17978945

Order 4352.

2982 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545283C2116yesmaximal, direct product factor
2C2×#11763761C211yesmaximal, characteristic
3C2×#11763760C211yesmaximal, characteristic, complemented
4C2×#11763759C211yesmaximal, characteristic, complemented
5C2×#11763759C211yesmaximal, characteristic, complemented
6C2×#11763759C211yesmaximal, characteristic, complemented
7C2×#11763759C211yesmaximal, characteristic, complemented
8C2×#11763758C211yesmaximal, characteristic, complemented
9C2×#11763758C211yesmaximal, characteristic, complemented
10C2×#11763757C211yesmaximal, characteristic
11C2×#11763756C211yesmaximal, characteristic, complemented
12C2×#11763751C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×#595C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×#595C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊#595C211yesmaximal, characteristic, complemented
16C2×#123×D17C211yesmaximal, characteristic
17C24×#595C2211yescharacteristic
18C22×C4⋊#595C2211yescharacteristic
19C22×C4⋊#595C2211yescharacteristic
20C22×C4⋊#595C2211yescharacteristic
21C22×C4⋊#595C2211yescharacteristic
22C22×C4⋊#595C2211yescharacteristic
23C22×C22⋊#595C2211yescharacteristic
24C22×C22⋊#595C2211yescharacteristic
25C22×C22⋊#595C2211yescharacteristic
26C22×C22⋊#595C2211yescharacteristic
27C22×C22⋊#595C2211yescharacteristic
28C22×C22⋊#595C2211yescharacteristic
29C22×C22⋊#595C2211yescharacteristic
30C22×C4×#595C2211yescharacteristic
31C22×C4×#595C2211yescharacteristic
32C22×C4×#595C2211yescharacteristic
33C22×C4×#595C2211yescharacteristic
34C22×C4×#595C2211yescharacteristic
35#11763761C2218yes—
36#11763760C2218yescomplemented
37#11763759C2218yescomplemented
38#11763759C2218yescomplemented
39#11763759C2218yescomplemented
40#11763759C2218yescomplemented
41#11763758C2218yescomplemented
42#11763758C2218yescomplemented
43#11763757C2218yes—
44#11763756C2218yescomplemented
45#11763751C2218yescomplemented
46C4⋊C4×#595C2218yescomplemented
47C22⋊C4×#595C2218yescomplemented
48C4×C22⋊#595C2218yescomplemented
49C2×(C2×#595)⋊C4C2211yescharacteristic
50C2×(C2×#595)⋊C4C2211yescharacteristic
51C2×(C2×#595)⋊C4C2211yescharacteristic
52C2×(C2×#595)⋊C4C2211yescharacteristic
53C2×(C2×#595)⋊C4C2211yescharacteristic
54C2×(C2×#595)⋊C4C2211yescharacteristic
55C2×(C2×#595)⋊C4C2211yescharacteristic
56C2×(C2×#595)⋊C4C2211yescharacteristic
57C2×(C2×#595)⋊C4C2211yescharacteristic
58C2×(C2×#595)⋊C4C2211yescharacteristic
59C22×D4×D17C2211yescharacteristic
60C23×C4×D17C2211yescharacteristic
61C2×#10587580C411yescharacteristic, complemented
62C2×#10587580C411yescharacteristic, complemented
63C2×#10587572C411yescharacteristic, complemented
64C2×#10587615C411yescharacteristic, complemented
65C2×#10587569C411yescharacteristic, complemented
66C2×#10587569C411yescharacteristic, complemented
67C2×#10587621C411yescharacteristic, complemented
68#123×D17C418yescomplemented
69#123×D17C2218yes—
70C2×C4⋊C4×D17C2211yescharacteristic
71C2×C4⋊C4×D17C2211yescharacteristic
72C2×C22⋊C4×D17C2211yescharacteristic
73C2×C22⋊C4×D17C2211yescharacteristic
74C2×C22⋊C4×D17C2211yescharacteristic
75C2×C17×#123C411yescharacteristic, complemented
76C24×D17C2311yescharacteristic
77C24×D17C2311yescharacteristic
78C23×#595—24no—
79C23×#595—42no—
80C23×#595—42no—
81C23×#595C2311yescharacteristic
82C23×#595C2311yescharacteristic
83C23×#595C2311yescharacteristic
84C23×#595C2311yescharacteristic
85C23×#595C2311yescharacteristic
86C23×#595C2311yescharacteristic
87C23×#595C2311yescharacteristic
88C23×#595C2311yescharacteristic
89C23×#595C2314yes—
90C22×D4×C17C2×C411yescharacteristic
91C23×C4×C17C2×C411yescharacteristic, complemented
92C22×C22⋊D17C2×C411yescharacteristic
93C22×C22⋊D17C2×C411yescharacteristic
94C23×Dic17C2×C411yescharacteristic, complemented
95C2×D4×D17—42no—
96C2×D4×D17—42no—
97C2×D4×D17C2×C414yes—
98C2×D4×D17C2314yes—
99C22×D68C2×C411yescharacteristic
100C22×C4×D17—42no—
101C22×C4×D17—42no—
102C22×C4×D17C2×C414yescomplemented
103C22×C4×D17C2×C411yescharacteristic, complemented
104C22×C4×D17C2×C411yescharacteristic, complemented
105C22×C4×D17C2311yescharacteristic
106C22×C4×D17C2311yescharacteristic
107C22×C4×D17C2311yescharacteristic
108C22×C4×D17C2311yescharacteristic
109C22×C4×D17C2311yescharacteristic
110C22×C4×D17C2314yes—
111C2×C22⋊#595—24no—
112C2×C22⋊#595—24no—
113C2×C22⋊#595—24no—
114C2×C22⋊#595—42no—
115C2×C22⋊#595—42no—
116C2×C22⋊#595—42no—
117C2×C22⋊#595—42no—
118C2×C22⋊#595C2314yes—
119C2×C22⋊#595C2314yes—
120C2×C22⋊#595C2314yes—
121C2×C22⋊#595C2314yes—
122C2×C22⋊#595C2314yes—
123C2×C22⋊#595C2314yes—
124C2×C22⋊#595C2314yes—
125C2×C4⋊#595—24no—
126C2×C4⋊#595—42no—
127C2×C4⋊#595—42no—
128C2×C4⋊#595—42no—
129C2×C4⋊#595—42no—
130C2×C4⋊#595C2314yes—
131C2×C4⋊#595C2314yes—
132C2×C4⋊#595C2314yes—
133C2×C4⋊#595C2314yes—
134C2×C4⋊#595C2314yes—
135C2×C4×#595—24no—
136C2×C4×#595—42no—
137C2×C4×#595—42no—
138C2×C4×#595—42no—
139C2×C4×#595—42no—
140C2×C4×#595C2314yes—
141C2×C4×#595C2314yes—
142C2×C4×#595C2314yes—
143C2×C4×#595C2314yes—
144C2×C4×#595C2314yes—
145C17×#123C2×C418yescomplemented
146C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
147C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
148C2×C22⋊C4×C17C2×C411yescharacteristic
149C2×C22⋊C4×C17C2×C411yescharacteristic
150C2×C22⋊C4×C17C2×C411yescharacteristic, complemented
151C2×C22⋊Dic17C2×C411yescharacteristic
152C2×C22⋊Dic17C2×C411yescharacteristic
153C2×C22⋊Dic17C2×C411yescharacteristic, complemented
154#10587621C2×C418yescomplemented
155#10587615C2×C418yescomplemented
156C2×#63227C2×C411yescharacteristic
157C2×#63227C2×C411yescharacteristic
158C2×#63227C2×C411yescharacteristic
159C2×#63227C2×C411yescharacteristic
160C2×#63227C2×C411yescharacteristic, complemented
161C2×#63227C2×C411yescharacteristic, complemented
162C2×C4⋊Dic17C2×C411yescharacteristic, complemented
163C2×C4⋊Dic17C2×C411yescharacteristic, complemented
164C2×#63225C2×C411yescharacteristic, complemented
165C2×#63225C2×C411yescharacteristic, complemented
166C2×#63225C2×C411yescharacteristic, complemented
167C2×#63225C2×C411yescharacteristic, complemented
168#10587580C2×C418yescomplemented
169#10587580C2×C418yescomplemented
170C4⋊C4×D17C2×C414yescomplemented
171C4⋊C4×D17C2×C414yescomplemented
172C4⋊C4×D17C2314yes—
173C4⋊C4×D17C2314yes—
174#10587572C2×C418yescomplemented
175#10587569C2×C418yescomplemented
176#10587569C2×C418yescomplemented
177C22⋊C4×D17C2×C414yes—
178C22⋊C4×D17C2×C414yes—
179C22⋊C4×D17C2×C414yescomplemented
180C22⋊C4×D17C2314yes—
181C22⋊C4×D17C2314yes—
182C22⋊C4×D17C2314yes—
183(C2×#595)⋊C4C2314yes—
184(C2×#595)⋊C4C2314yes—
185(C2×#595)⋊C4C2314yes—
186(C2×#595)⋊C4C2314yes—
187(C2×#595)⋊C4C2314yes—
188(C2×#595)⋊C4C2314yes—
189(C2×#595)⋊C4C2314yes—
190(C2×#595)⋊C4C2314yes—
191(C2×#595)⋊C4C2314yes—
192(C2×#595)⋊C4C2314yes—
193C24×C17C22×C411yescharacteristic
194C24×C17C22×C411yescharacteristic
195C23×D17—22no—
196C23×D17—22no—
197C23×D17—22no—
198C23×D17—22no—
199C23×D17—22no—
200C23×D17—22no—
201C23×D17—22no—
202C23×D17—22no—
203C23×D17—22no—
204C23×D17—22no—
205C23×D17—22no—
206C23×D17—22no—
207C23×D17C22×C411yescharacteristic
208C23×D17C22×C412yes—
209C23×D17C22×C411yescharacteristic
210C23×D17C22×C412yes—
211C23×D17C2412yes—
212C23×D17C2412yes—
213C23×D17C2411yescharacteristic
214C22×#595—22no—
215C22×#595—22no—
216C22×#595—22no—
217C22×#595—22no—
218C22×#595—22no—
219C22×#595—22no—
220C22×#595—22no—
221C22×#595—22no—
222C22×#595—22no—
223C22×#595—22no—
224C22×#595—22no—
225C22×#595—22no—
226C22×#595—22no—
227C22×#595—22no—
228C22×#595—22no—
229C22×#595—22no—
230C22×#595—22no—
231C22×#595—22no—
232C22×#595—22no—
233C22×#595—22no—
234C22×#595—22no—
235C22×#595—22no—
236C22×#595—28no—
237C22×#595—44no—
238C22×#595—44no—
239C22×#595—416no—
240C22×#595#4114yes—
241C22×#595#4114yes—
242C22×#595C2412yes—
243C22×#595C2412yes—
244C22×#595C2412yes—
245C22×#595C2412yes—
246C22×#595C2412yes—
247C22×#595C2412yes—
248C22×#595C2412yes—
249C22×#595C2412yes—
250C2×D4×C17—42no—
251C2×D4×C17C22×C414yes—
252C22×C4×C17—42no—
253C22×C4×C17C22×C411yescharacteristic
254C22×C4×C17C22×C411yescharacteristic
255C22×C4×C17C22×C411yescharacteristic
256C22×C4×C17C22×C411yescharacteristic
257C22×C4×C17C22×C411yescharacteristic
258C22×C4×C17C22×C414yescomplemented
259C2×C22⋊D17—42no—
260C2×C22⋊D17—42no—
261C2×C22⋊D17C22×C414yes—
262C2×C22⋊D17C22×C414yes—
263C22×Dic17—42no—
264C22×Dic17C22×C411yescharacteristic
265C22×Dic17C22×C411yescharacteristic
266C22×Dic17C22×C411yescharacteristic
267C22×Dic17C22×C411yescharacteristic
268C22×Dic17C22×C411yescharacteristic
269C22×Dic17C22×C414yescomplemented
270D4×D17—48no—
271D4×D17—44no—
272D4×D17—44no—
273C2×D68—42no—
274C2×D68C22×C414yes—
275C2×C4×D17—22no—
276C2×C4×D17—22no—
277C2×C4×D17—22no—
278C2×C4×D17—22no—
279C2×C4×D17—22no—
280C2×C4×D17—22no—
281C2×C4×D17—22no—
282C2×C4×D17—22no—
283C2×C4×D17—22no—
284C2×C4×D17—22no—
285C2×C4×D17—48no—
286C2×C4×D17—44no—
287C2×C4×D17—44no—
288C2×C4×D17—42no—
289C2×C4×D17—42no—
290C2×C4×D17C22×C412yes—
291C2×C4×D17C22×C412yes—
292C2×C4×D17C22×C412yes—
293C2×C4×D17C22×C412yes—
294C2×C4×D17C22×C412yes—
295C2×C4×D17C22×C414yescomplemented
296C2×C4×D17C22×C414yescomplemented
297C2×C4×D17C2412yes—
298C2×C4×D17C2412yes—
299C2×C4×D17C2412yes—
300C2×C4×D17C2412yes—
301C2×C4×D17C2412yes—
302C22⋊#595—28no—
303C22⋊#595—28no—
304C22⋊#595—28no—
305C22⋊#595—44no—
306C22⋊#595—44no—
307C22⋊#595—44no—
308C22⋊#595—44no—
309C4⋊#595—28no—
310C4⋊#595—44no—
311C4⋊#595—44no—
312C4⋊#595—44no—
313C4⋊#595—44no—
314C4×#595—28no—
315C4×#595—44no—
316C4×#595—44no—
317C4×#595—44no—
318C4×#595—44no—
319C4⋊C4×C17C22×C414yescomplemented
320C4⋊C4×C17C22×C414yescomplemented
321C22⋊C4×C17C22×C414yes—
322C22⋊C4×C17C22×C414yes—
323C22⋊C4×C17C22×C414yescomplemented
324C22⋊Dic17C22×C414yes—
325C22⋊Dic17C22×C414yes—
326C22⋊Dic17C22×C414yescomplemented
327#63227C22×C414yes—
328#63227C22×C414yes—
329#63227C22×C414yes—
330#63227C22×C414yes—
331#63227C22×C414yescomplemented
332#63227C22×C414yescomplemented
333C4⋊Dic17C22×C414yescomplemented
334C4⋊Dic17C22×C414yescomplemented
335#63225C22×C414yescomplemented
336#63225C22×C414yescomplemented
337#63225C22×C414yescomplemented
338#63225C22×C414yescomplemented
339C2×#2335—171nomaximal, Sylow
340C23×C17—22no—
341C23×C17—22no—
342C23×C17—22no—
343C23×C17—22no—
344C23×C17—22no—
345C23×C17—22no—
346C23×C17C23×C412yes—
347C23×C17C23×C412yes—
348C23×C17C23×C411yescharacteristic
349C22×D17—22no—
350C22×D17—22no—
351C22×D17—22no—
352C22×D17—22no—
353C22×D17—22no—
354C22×D17—22no—
355C22×D17—24no—
356C22×D17—24no—
357C22×D17—24no—
358C22×D17—24no—
359C22×D17—24no—
360C22×D17—24no—
361C22×D17—22no—
362C22×D17—22no—
363C22×D17—22no—
364C22×D17—22no—
365C22×D17—22no—
366C22×D17—22no—
367C22×D17—22no—
368C22×D17—22no—
369C22×D17—22no—
370C22×D17—22no—
371C22×D17—22no—
372C22×D17—22no—
373C22×D17—44no—
374C22×D17—44no—
375C22×D17—44no—
376C22×D17—44no—
377C22×D17—44no—
378C22×D17—44no—
379C22×D17—44no—
380C22×D17—44no—
381C22×D17C23×C412yes—
382C22×D17C23×C412yes—
383C22×D17C23×C411yescharacteristic
384C22×D17C2×#4112yes—
385C22×D17C2×#4112yes—
386C22×D17H(5,𝔽2)12yes—
387C22×D17H(5,𝔽2)12yes—
388C22×D17H(5,𝔽2)12yes—
389C22×D172−1+412yes—
390C22×D17C2511yescharacteristic
391C2×#595—28no—
392C2×#595—28no—
393C2×#595—22no—
394C2×#595—22no—
395C2×#595—22no—
396C2×#595—22no—
397C2×#595—22no—
398C2×#595—22no—
399C2×#595—22no—
400C2×#595—22no—
401C2×#595—22no—
402C2×#595—22no—
403C2×#595—22no—
404C2×#595—22no—
405C2×#595—22no—
406C2×#595—22no—
407C2×#595—22no—
408C2×#595—22no—
409C2×#595—22no—
410C2×#595—22no—
411C2×#595—22no—
412C2×#595—22no—
413C2×#595—22no—
414C2×#595—22no—
415C2×#595—416no—
416C2×#595—44no—
417C2×#595—44no—
418C2×#595—44no—
419C2×#595—44no—
420C2×#595—44no—
421C2×#595—44no—
422C2×#595C2×#4114yes—
423C2×#595C2×#4114yes—
424D4×C17—44no—
425C2×C4×C17—22no—
426C2×C4×C17—22no—
427C2×C4×C17—22no—
428C2×C4×C17—22no—
429C2×C4×C17—22no—
430C2×C4×C17—44no—
431C2×C4×C17C23×C412yes—
432C2×C4×C17C23×C412yes—
433C2×C4×C17C23×C412yes—
434C2×C4×C17C23×C412yes—
435C2×C4×C17C23×C412yes—
436C22⋊D17—44no—
437C22⋊D17—44no—
438C2×Dic17—22no—
439C2×Dic17—22no—
440C2×Dic17—22no—
441C2×Dic17—22no—
442C2×Dic17—22no—
443C2×Dic17—44no—
444C2×Dic17C23×C412yes—
445C2×Dic17C23×C412yes—
446C2×Dic17C23×C412yes—
447C2×Dic17C23×C412yes—
448C2×Dic17C23×C412yes—
449D68—44no—
450C4×D17—24no—
451C4×D17—24no—
452C4×D17—24no—
453C4×D17—24no—
454C4×D17—24no—
455C4×D17—22no—
456C4×D17—22no—
457C4×D17—22no—
458C4×D17—22no—
459C4×D17—22no—
460C4×D17—22no—
461C4×D17—22no—
462C4×D17—22no—
463C4×D17—22no—
464C4×D17—22no—
465C4×D17—44no—
466C4×D17—44no—
467C22×#123—171no—
468#2335—1716no—
469C2×#390—171no—
470C2×#389—171no—
471C2×#388—171no—
472C2×#388—171no—
473C2×#388—171no—
474C2×#388—171no—
475C2×#387—171no—
476C2×#387—171no—
477C2×#386—171no—
478C2×#385—171no—
479C2×#380—171no—
480C2×C4×C4⋊C4—171no—
481C2×C4×C22⋊C4—171no—
482C2×C4×C22⋊C4—171no—
483C22×C17—22no—
484C22×C17—22no—
485C22×C17—22no—
486C22×C17—22no—
487C22×C17—22no—
488C22×C17—22no—
489C22×C17—44no—
490C22×C17—44no—
491C22×C17C4×#4112yes—
492C22×C17#51812yes—
493C22×C17#52012yes—
494C22×C17C24×C411yescharacteristic
495C2×D17—22no—
496C2×D17—22no—
497C2×D17—22no—
498C2×D17—22no—
499C2×D17—22no—
500C2×D17—22no—
501C2×D17—44no—
502C2×D17—44no—
503C2×D17—48no—
504C2×D17—48no—
505C2×D17—42no—
506C2×D17—42no—
507C2×D17—42no—
508C2×D17—42no—
509C2×D17—42no—
510C2×D17—42no—
511C2×D17—42no—
512C2×D17—42no—
513C2×D17C4×#4112yes—
514C2×D17#51812yes—
515C2×D17#52012yes—
516C2×D17#53814yes—
517C2×D17#53914yes—
518C2×D17#54014yes—
519C2×D17#54214yes—
520C2×D17C22×#4111yescharacteristic
521C2×D17C22×#4111yescharacteristic
522C2×D17C2×H(5,𝔽2)11yescharacteristic
523C2×D17C2×H(5,𝔽2)11yescharacteristic
524C2×D17C2×H(5,𝔽2)11yescharacteristic
525C2×D17C2×2−1+411yescharacteristic
526#595—24no—
527#595—24no—
528#595—42no—
529#595—42no—
530#595—42no—
531#595—42no—
532#595—42no—
533#595—42no—
534C4×C17—22no—
535C4×C17—22no—
536C4×C17—22no—
537C4×C17—22no—
538C4×C17—22no—
539Dic17—22no—
540Dic17—22no—
541Dic17—22no—
542Dic17—22no—
543Dic17—22no—
544C23×D4—171no—
545C24×C4—171no—
546C24×C4—171no—
547C2×#123—171no—
548C2×#123—171no—
549C2×#123—178no—
550C2×#123—178no—
551C2×#123—171no—
552C2×#123—171no—
553C2×#123—171no—
554C2×#123—171no—
555C2×#123—171no—
556C2×#123#59511yescharacteristic, complemented
557C22×C4⋊C4—171no—
558C22×C4⋊C4—171no—
559C22×C4⋊C4—171no—
560C22×C4⋊C4—171no—
561C22×C4⋊C4—171no—
562C22×C4⋊C4—171no—
563C22×C4⋊C4—171no—
564C22×C22⋊C4—171no—
565C22×C22⋊C4—171no—
566C22×C22⋊C4—171no—
567C22×C22⋊C4—171no—
568C22×C22⋊C4—171no—
569C22×C22⋊C4—171no—
570C22×C22⋊C4—171no—
571C22×C22⋊C4—171no—
572C22×C22⋊C4—171no—
573C22×C22⋊C4—171no—
574C22×C42—171no—
575C22×C42—171no—
576C22×C42—171no—
577C22×C42—171no—
578C22×C42—171no—
579#390—178no—
580#389—178no—
581#388—178no—
582#388—178no—
583#388—178no—
584#388—178no—
585#387—178no—
586#387—178no—
587#386—178no—
588#385—178no—
589#380—178no—
590C4×C4⋊C4—178no—
591C4×C22⋊C4—178no—
592C4×C22⋊C4—178no—
593C2×#95—171no—
594C2×#95—171no—
595C2×#95—171no—
596C2×#95—171no—
597C2×#95—171no—
598C2×#95—171no—
599C2×#95—171no—
600C2×#95—171no—
601C2×#95—171no—
602C2×#95—171no—
603C2×C17—42no—
604C2×C17—42no—
605C2×C17#233514yescomplemented
606C2×C17C2×C4×#4111yescharacteristic
607C2×C17C2×#51811yescharacteristic
608C2×C17C2×#52011yescharacteristic
609D17—42no—
610D17—42no—
611D17#233514yescomplemented
612D17C2×#53811yescharacteristic
613D17C2×#53911yescharacteristic
614D17C2×#54011yescharacteristic
615D17C2×#54211yescharacteristic
616C25—171no—
617C25—171no—
618C22×D4—171no—
619C22×D4—171no—
620C22×D4—174no—
621C22×D4—174no—
622C22×D4—171no—
623C22×D4—682no—
624C22×D4—682no—
625C22×D4C2×#59511yescharacteristic
626C23×C4—171no—
627C23×C4—171no—
628C23×C4—171no—
629C23×C4—171no—
630C23×C4—171no—
631C23×C4—171no—
632C23×C4—171no—
633C23×C4—171no—
634C23×C4—171no—
635C23×C4—171no—
636C23×C4—174no—
637C23×C4—174no—
638C23×C4—171no—
639C23×C4—171no—
640C23×C4—171no—
641C23×C4—171no—
642C23×C4—171no—
643C23×C4—171no—
644C23×C4—174no—
645C23×C4—344no—
646C23×C4—682no—
647C23×C4—682no—
648C23×C4—682no—
649C23×C4—682no—
650C23×C4C2×#59511yescharacteristic, complemented
651#123—178no—
652#123—178no—
653#123—178no—
654#123—178no—
655#123—178no—
656#123—178no—
657#123—178no—
658#123C2×#59518yescomplemented
659C2×C4⋊C4—171no—
660C2×C4⋊C4—171no—
661C2×C4⋊C4—171no—
662C2×C4⋊C4—171no—
663C2×C4⋊C4—171no—
664C2×C4⋊C4—171no—
665C2×C4⋊C4—174no—
666C2×C4⋊C4—174no—
667C2×C4⋊C4—174no—
668C2×C4⋊C4—174no—
669C2×C4⋊C4—174no—
670C2×C4⋊C4—174no—
671C2×C4⋊C4—174no—
672C2×C4⋊C4—174no—
673C2×C4⋊C4—174no—
674C2×C4⋊C4—344no—
675C2×C4⋊C4—682no—
676C2×C4⋊C4—682no—
677C2×C4⋊C4—682no—
678C2×C4⋊C4—682no—
679C2×C4⋊C4C2×#59511yescharacteristic, complemented
680C2×C4⋊C4C2×#59511yescharacteristic, complemented
681C2×C22⋊C4—171no—
682C2×C22⋊C4—171no—
683C2×C22⋊C4—171no—
684C2×C22⋊C4—171no—
685C2×C22⋊C4—171no—
686C2×C22⋊C4—171no—
687C2×C22⋊C4—171no—
688C2×C22⋊C4—171no—
689C2×C22⋊C4—171no—
690C2×C22⋊C4—174no—
691C2×C22⋊C4—174no—
692C2×C22⋊C4—174no—
693C2×C22⋊C4—174no—
694C2×C22⋊C4—174no—
695C2×C22⋊C4—174no—
696C2×C22⋊C4—174no—
697C2×C22⋊C4—174no—
698C2×C22⋊C4—174no—
699C2×C22⋊C4—174no—
700C2×C22⋊C4—174no—
701C2×C22⋊C4—174no—
702C2×C22⋊C4—174no—
703C2×C22⋊C4—344no—
704C2×C22⋊C4—344no—
705C2×C22⋊C4—344no—
706C2×C22⋊C4—682no—
707C2×C22⋊C4—682no—
708C2×C22⋊C4—682no—
709C2×C22⋊C4—682no—
710C2×C22⋊C4C2×#59511yescharacteristic
711C2×C22⋊C4C2×#59511yescharacteristic
712C2×C22⋊C4C2×#59511yescharacteristic, complemented
713C2×C42—174no—
714C2×C42—174no—
715C2×C42—174no—
716C2×C42—174no—
717C2×C42—174no—
718C2×C42—344no—
719C2×C42—682no—
720C2×C42—682no—
721C2×C42—682no—
722C2×C42—682no—
723#95—174no—
724#95—174no—
725#95—174no—
726#95—174no—
727#95—174no—
728#95—174no—
729#95—174no—
730#95—174no—
731#95—174no—
732#95—174no—
733C17C2×#233511yescharacteristic, complemented, Sylow
734C24—171no—
735C24—172no—
736C24—172no—
737C24—172no—
738C24—172no—
739C24—171no—
740C24—171no—
741C24—342no—
742C24—342no—
743C24—342no—
744C24—342no—
745C24—342no—
746C24—342no—
747C24—342no—
748C24—342no—
749C24—342no—
750C24—342no—
751C24—342no—
752C24—342no—
753C24C22×#59511yescharacteristic
754C24C22×#59511yescharacteristic
755C2×D4—42no—
756C2×D4—174no—
757C2×D4—174no—
758C2×D4—174no—
759C2×D4—682no—
760C2×D4—684no—
761C2×D4—684no—
762C2×D4—688no—
763C2×D4—682no—
764C2×D4—682no—
765C2×D4C22×#59514yes—
766C22×C4—42no—
767C22×C4—174no—
768C22×C4—174no—
769C22×C4—172no—
770C22×C4—172no—
771C22×C4—171no—
772C22×C4—171no—
773C22×C4—171no—
774C22×C4—171no—
775C22×C4—171no—
776C22×C4—174no—
777C22×C4—172no—
778C22×C4—172no—
779C22×C4—172no—
780C22×C4—172no—
781C22×C4—172no—
782C22×C4—172no—
783C22×C4—172no—
784C22×C4—172no—
785C22×C4—172no—
786C22×C4—172no—
787C22×C4—174no—
788C22×C4—174no—
789C22×C4—172no—
790C22×C4—172no—
791C22×C4—172no—
792C22×C4—172no—
793C22×C4—172no—
794C22×C4—172no—
795C22×C4—342no—
796C22×C4—342no—
797C22×C4—342no—
798C22×C4—342no—
799C22×C4—342no—
800C22×C4—342no—
801C22×C4—342no—
802C22×C4—342no—
803C22×C4—342no—
804C22×C4—342no—
805C22×C4—348no—
806C22×C4—342no—
807C22×C4—342no—
808C22×C4—342no—
809C22×C4—342no—
810C22×C4—342no—
811C22×C4—342no—
812C22×C4—342no—
813C22×C4—342no—
814C22×C4—342no—
815C22×C4—342no—
816C22×C4—342no—
817C22×C4—342no—
818C22×C4—342no—
819C22×C4—342no—
820C22×C4—342no—
821C22×C4—342no—
822C22×C4—342no—
823C22×C4—342no—
824C22×C4—342no—
825C22×C4—342no—
826C22×C4—342no—
827C22×C4—342no—
828C22×C4—682no—
829C22×C4—682no—
830C22×C4—684no—
831C22×C4—684no—
832C22×C4—688no—
833C22×C4—682no—
834C22×C4—684no—
835C22×C4—684no—
836C22×C4—6816no—
837C22×C4C22×#59511yescharacteristic
838C22×C4C22×#59511yescharacteristic
839C22×C4C22×#59511yescharacteristic
840C22×C4C22×#59511yescharacteristic
841C22×C4C22×#59511yescharacteristic
842C22×C4C22×#59514yescomplemented
843C4⋊C4—174no—
844C4⋊C4—174no—
845C4⋊C4—174no—
846C4⋊C4—174no—
847C4⋊C4—174no—
848C4⋊C4—174no—
849C4⋊C4—348no—
850C4⋊C4—684no—
851C4⋊C4—684no—
852C4⋊C4—684no—
853C4⋊C4—684no—
854C4⋊C4C22×#59514yescomplemented
855C4⋊C4C22×#59514yescomplemented
856C22⋊C4—174no—
857C22⋊C4—174no—
858C22⋊C4—174no—
859C22⋊C4—174no—
860C22⋊C4—174no—
861C22⋊C4—174no—
862C22⋊C4—174no—
863C22⋊C4—174no—
864C22⋊C4—174no—
865C22⋊C4—348no—
866C22⋊C4—348no—
867C22⋊C4—348no—
868C22⋊C4—684no—
869C22⋊C4—684no—
870C22⋊C4—684no—
871C22⋊C4—684no—
872C22⋊C4C22×#59514yes—
873C22⋊C4C22×#59514yes—
874C22⋊C4C22×#59514yescomplemented
875C42—348no—
876C42—684no—
877C42—684no—
878C42—684no—
879C42—684no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—172no—
887C23—172no—
888C23—172no—
889C23—172no—
890C23—172no—
891C23—172no—
892C23—171no—
893C23—171no—
894C23—172no—
895C23—172no—
896C23—342no—
897C23—342no—
898C23—342no—
899C23—342no—
900C23—342no—
901C23—342no—
902C23—342no—
903C23—342no—
904C23—342no—
905C23—344no—
906C23—342no—
907C23—344no—
908C23—344no—
909C23—344no—
910C23—342no—
911C23—342no—
912C23—344no—
913C23—344no—
914C23—342no—
915C23—342no—
916C23—342no—
917C23—342no—
918C23—342no—
919C23—342no—
920C23—684no—
921C23—684no—
922C23—684no—
923C23—684no—
924C23—684no—
925C23—684no—
926C23—684no—
927C23—684no—
928C23C23×#59512yes—
929C23C23×#59512yes—
930C23C23×#59511yescharacteristic
931D4—44no—
932D4—684no—
933D4—684no—
934D4—684no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—44no—
941C2×C4—174no—
942C2×C4—174no—
943C2×C4—172no—
944C2×C4—172no—
945C2×C4—172no—
946C2×C4—172no—
947C2×C4—172no—
948C2×C4—342no—
949C2×C4—342no—
950C2×C4—342no—
951C2×C4—342no—
952C2×C4—342no—
953C2×C4—342no—
954C2×C4—342no—
955C2×C4—342no—
956C2×C4—342no—
957C2×C4—344no—
958C2×C4—344no—
959C2×C4—344no—
960C2×C4—344no—
961C2×C4—342no—
962C2×C4—344no—
963C2×C4—342no—
964C2×C4—342no—
965C2×C4—342no—
966C2×C4—348no—
967C2×C4—342no—
968C2×C4—348no—
969C2×C4—342no—
970C2×C4—342no—
971C2×C4—342no—
972C2×C4—342no—
973C2×C4—342no—
974C2×C4—342no—
975C2×C4—342no—
976C2×C4—342no—
977C2×C4—342no—
978C2×C4—342no—
979C2×C4—342no—
980C2×C4—342no—
981C2×C4—342no—
982C2×C4—342no—
983C2×C4—342no—
984C2×C4—342no—
985C2×C4—342no—
986C2×C4—342no—
987C2×C4—342no—
988C2×C4—342no—
989C2×C4—342no—
990C2×C4—342no—
991C2×C4—342no—
992C2×C4—684no—
993C2×C4—684no—
994C2×C4—684no—
995C2×C4—6816no—
996C2×C4—684no—
997C2×C4—684no—
998C2×C4—684no—
999C2×C4—684no—
1000C2×C4—684no—
1001C2×C4—684no—
1002C2×C4C23×#59512yes—
1003C2×C4C23×#59512yes—
1004C2×C4C23×#59512yes—
1005C2×C4C23×#59512yes—
1006C2×C4C23×#59512yes—
1007C22—22no—
1008C22—22no—
1009C22—22no—
1010C22—22no—
1011C22—22no—
1012C22—22no—
1013C22—44no—
1014C22—44no—
1015C22—171no—
1016C22—171no—
1017C22—172no—
1018C22—171no—
1019C22—171no—
1020C22—172no—
1021C22—171no—
1022C22—171no—
1023C22—172no—
1024C22—174no—
1025C22—174no—
1026C22—174no—
1027C22—174no—
1028C22—342no—
1029C22—342no—
1030C22—342no—
1031C22—342no—
1032C22—342no—
1033C22—342no—
1034C22—682no—
1035C22—682no—
1036C22—682no—
1037C22—682no—
1038C22—682no—
1039C22—682no—
1040C22—682no—
1041C22—682no—
1042C22—688no—
1043C22—688no—
1044C22—684no—
1045C22—684no—
1046C22#41×#59512yes—
1047C22#1176387612yes—
1048C22#1176387812yes—
1049C22C24×#59511yescharacteristic
1050C4—22no—
1051C4—22no—
1052C4—22no—
1053C4—22no—
1054C4—22no—
1055C4—344no—
1056C4—344no—
1057C4—342no—
1058C4—342no—
1059C4—342no—
1060C4—342no—
1061C4—342no—
1062C4—682no—
1063C4—682no—
1064C4—682no—
1065C4—682no—
1066C4—682no—
1067C4—682no—
1068C2—42no—
1069C2—42no—
1070C2—171no—
1071C2—171no—
1072C2—171no—
1073C2—171no—
1074C2—174no—
1075C2—682no—
1076C2—682no—
1077C2#1454528314yesdirect product factor
1078C2C2×#41×#59511yescharacteristic
1079C2C2×#1176387611yescharacteristic
1080C2C2×#1176387811yescharacteristic
subgroupG/H
centerC23C23×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC2×C17×#123C4
socleC23×C17C23×C4
prime radicalC22×D4×D17C22
cosocleC22×D17C25
hypercenterC2×#123#595
hypocenterC17C2×#2335
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #14545283C2direct (N × H)
3. C2×#11763760C2semidirect
4. C2×#11763759C2semidirect
5. C2×#11763759C2semidirect
6. C2×#11763759C2semidirect
7. C2×#11763759C2semidirect
8. C2×#11763758C2semidirect
9. C2×#11763758C2semidirect
11. C2×#11763756C2semidirect
12. C2×#11763751C2semidirect
13. C2×C4⋊C4×#595C2semidirect
14. C2×C22⋊C4×#595C2semidirect
15. C2×C4×C22⋊#595C2semidirect
36. #11763760C22semidirect
37. #11763759C22semidirect
38. #11763759C22semidirect
39. #11763759C22semidirect
40. #11763759C22semidirect
41. #11763758C22semidirect
42. #11763758C22semidirect
44. #11763756C22semidirect
45. #11763751C22semidirect
46. C4⋊C4×#595C22semidirect
47. C22⋊C4×#595C22semidirect
48. C4×C22⋊#595C22semidirect
61. C2×#10587580C4semidirect
62. C2×#10587580C4semidirect
63. C2×#10587572C4semidirect
64. C2×#10587615C4semidirect
65. C2×#10587569C4semidirect
66. C2×#10587569C4semidirect
67. C2×#10587621C4semidirect
68. #123×D17C4semidirect
75. C2×C17×#123C4semidirect
91. C23×C4×C17C2×C4semidirect
94. C23×Dic17C2×C4semidirect
102. C22×C4×D17C2×C4semidirect
103. C22×C4×D17C2×C4semidirect
104. C22×C4×D17C2×C4semidirect
145. C17×#123C2×C4semidirect
146. C2×C4⋊C4×C17C2×C4semidirect
147. C2×C4⋊C4×C17C2×C4semidirect
150. C2×C22⋊C4×C17C2×C4semidirect
153. C2×C22⋊Dic17C2×C4semidirect
154. #10587621C2×C4semidirect
155. #10587615C2×C4semidirect
160. C2×#63227C2×C4semidirect
161. C2×#63227C2×C4semidirect
162. C2×C4⋊Dic17C2×C4semidirect
163. C2×C4⋊Dic17C2×C4semidirect
164. C2×#63225C2×C4semidirect
165. C2×#63225C2×C4semidirect
166. C2×#63225C2×C4semidirect
167. C2×#63225C2×C4semidirect
168. #10587580C2×C4semidirect
169. #10587580C2×C4semidirect
170. C4⋊C4×D17C2×C4semidirect
171. C4⋊C4×D17C2×C4semidirect
174. #10587572C2×C4semidirect
175. #10587569C2×C4semidirect
176. #10587569C2×C4semidirect
179. C22⋊C4×D17C2×C4semidirect
258. C22×C4×C17C22×C4semidirect
269. C22×Dic17C22×C4semidirect
295. C2×C4×D17C22×C4semidirect
296. C2×C4×D17C22×C4semidirect
319. C4⋊C4×C17C22×C4semidirect
320. C4⋊C4×C17C22×C4semidirect
323. C22⋊C4×C17C22×C4semidirect
326. C22⋊Dic17C22×C4semidirect
331. #63227C22×C4semidirect
332. #63227C22×C4semidirect
333. C4⋊Dic17C22×C4semidirect
334. C4⋊Dic17C22×C4semidirect
335. #63225C22×C4semidirect
336. #63225C22×C4semidirect
337. #63225C22×C4semidirect
338. #63225C22×C4semidirect
556. C2×#123#595semidirect
605. C2×C17#2335semidirect
611. D17#2335semidirect
650. C23×C4C2×#595semidirect
658. #123C2×#595semidirect
679. C2×C4⋊C4C2×#595semidirect
680. C2×C4⋊C4C2×#595semidirect
712. C2×C22⋊C4C2×#595semidirect
733. C17C2×#2335semidirect
842. C22×C4C22×#595semidirect
854. C4⋊C4C22×#595semidirect
855. C4⋊C4C22×#595semidirect
874. C22⋊C4C22×#595semidirect
1077. C2#14545283direct (N × H)

Maximal subgroups

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

subgroupindex
#145452832
C2×#117637612
C2×#117637602
C2×#117637592
C2×#117637582
C2×#117637572
C2×#117637562
C2×#117637512
C2×C4⋊C4×#5952
C2×C22⋊C4×#5952
C2×C4×C22⋊#5952
C2×#123×D172
C2×#233517