Finite Group Databasebeta

← C2×#14545321 #17979015

Subgroups — C2×#14545321 #17979015

Order 4352.

2726 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545321C2116yesmaximal, direct product factor
2C2×#11763760C211yesmaximal, characteristic, complemented
3C2×#11763759C211yesmaximal, characteristic
4C2×#11763759C211yesmaximal, characteristic
5C2×#11763759C211yesmaximal, characteristic
6C2×#11763758C211yesmaximal, characteristic, complemented
7C2×#11763758C211yesmaximal, characteristic, complemented
8C2×#11763758C211yesmaximal, characteristic, complemented
9C2×#11763756C211yesmaximal, characteristic
10C2×C4⋊C4×#595C211yesmaximal, characteristic, complemented
11C2×C4⋊C4×#595C211yesmaximal, characteristic, complemented
12C2×C4×C4⋊#595C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×#595C211yesmaximal, characteristic
14C2×C22⋊C4×#595C211yesmaximal, characteristic
15C2×#11763745C211yesmaximal, characteristic, complemented
16C2×#126×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×C4×#595C2211yescharacteristic
27C22×C4×#595C2211yescharacteristic
28C22×C4×#595C2211yescharacteristic
29C22×C4×#595C2211yescharacteristic
30C22×C4×#595C2211yescharacteristic
31C22×C4×#595C2211yescharacteristic
32C22×C4×#595C2211yescharacteristic
33#11763760C2218yescomplemented
34#11763759C2218yes—
35#11763759C2218yes—
36#11763759C2218yes—
37#11763758C2218yescomplemented
38#11763758C2218yescomplemented
39#11763758C2218yescomplemented
40#11763756C2218yes—
41C4⋊C4×#595C2218yescomplemented
42C4⋊C4×#595C2218yescomplemented
43C4×C4⋊#595C2218yescomplemented
44C22⋊C4×#595C2218yes—
45C22⋊C4×#595C2218yes—
46#11763745C2218yescomplemented
47C2×(C2×#595)⋊C4C2211yescharacteristic
48C2×(C2×#595)⋊C4C2211yescharacteristic
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
59C2×#10587584C411yescharacteristic, complemented
60C2×#10587584C411yescharacteristic, complemented
61C2×#10587584C411yescharacteristic, complemented
62C2×#10587562C411yescharacteristic, complemented
63C2×#10587565C411yescharacteristic, complemented
64C2×#10587565C411yescharacteristic, complemented
65C2×#10587565C411yescharacteristic, complemented
66#126×D17C418yescomplemented
67#126×D17C2218yes—
68C2×C4⋊C4×D17C2211yescharacteristic
69C2×C4⋊C4×D17C2211yescharacteristic
70C2×C4⋊C4×D17C2211yescharacteristic
71C2×C22⋊C4×D17C2211yescharacteristic
72C2×C22⋊C4×D17C2211yescharacteristic
73C2×C22⋊C4×D17C2211yescharacteristic
74C2×C42×D17C2211yescharacteristic
75C2×C17×#126C411yescharacteristic, complemented
76C24×D17C2311yescharacteristic
77C23×#595—24no—
78C23×#595—24no—
79C23×#595—42no—
80C23×#595C2311yescharacteristic
81C23×#595C2311yescharacteristic
82C23×#595C2311yescharacteristic
83C23×#595C2311yescharacteristic
84C23×#595C2314yes—
85C23×#595C2311yescharacteristic
86C23×#595C2311yescharacteristic
87C23×#595C2311yescharacteristic
88C23×#595C2311yescharacteristic
89C22×C4×D17C2311yescharacteristic
90C22×C4×D17C2311yescharacteristic
91C22×C4×D17C2311yescharacteristic
92C22×C4×D17C2311yescharacteristic
93C22×C4×D17C2311yescharacteristic
94C22×C4×D17C2311yescharacteristic
95C2×C22⋊#595—24no—
96C2×C22⋊#595—24no—
97C2×C22⋊#595—42no—
98C2×C22⋊#595C2314yes—
99C2×C22⋊#595C2314yes—
100C2×C22⋊#595C2314yes—
101C2×C4⋊#595—24no—
102C2×C4⋊#595—24no—
103C2×C4⋊#595—24no—
104C2×C4⋊#595—24no—
105C2×C4⋊#595—42no—
106C2×C4⋊#595C2314yes—
107C2×C4⋊#595C2314yes—
108C2×C4⋊#595C2314yes—
109C2×C4⋊#595C2314yes—
110C2×C4⋊#595C2314yes—
111C2×C4×#595—24no—
112C2×C4×#595—24no—
113C2×C4×#595—24no—
114C2×C4×#595—24no—
115C2×C4×#595—42no—
116C2×C4×#595—42no—
117C2×C4×#595—42no—
118C2×C4×#595C2314yes—
119C2×C4×#595C2314yes—
120C2×C4×#595C2314yes—
121C2×C4×#595C2314yes—
122C2×C4×#595C2314yes—
123C2×C4×#595C2314yes—
124C2×C4×#595C2314yes—
125C17×#126C2×C418yescomplemented
126C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
127C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
128C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
129C2×C22⋊C4×C17C2×C411yescharacteristic
130C2×C22⋊C4×C17C2×C411yescharacteristic
131C2×C22⋊C4×C17C2×C411yescharacteristic
132C2×C42×C17C2×C411yescharacteristic, complemented
133C2×C22⋊Dic17C2×C411yescharacteristic
134C2×C22⋊Dic17C2×C411yescharacteristic
135C2×C22⋊Dic17C2×C411yescharacteristic
136C2×#63227C2×C411yescharacteristic
137C2×#63227C2×C411yescharacteristic
138C2×#63227C2×C411yescharacteristic
139C2×#63227C2×C411yescharacteristic
140C2×#63227C2×C411yescharacteristic
141C2×#63227C2×C411yescharacteristic
142C2×C4⋊Dic17C2×C411yescharacteristic, complemented
143C2×C4⋊Dic17C2×C411yescharacteristic, complemented
144C2×C4⋊Dic17C2×C411yescharacteristic, complemented
145C2×#63225C2×C411yescharacteristic, complemented
146C2×#63225C2×C411yescharacteristic, complemented
147C2×#63225C2×C411yescharacteristic, complemented
148C2×#63225C2×C411yescharacteristic, complemented
149C2×#63225C2×C411yescharacteristic, complemented
150C2×#63225C2×C411yescharacteristic, complemented
151C2×C4×Dic17C2×C411yescharacteristic, complemented
152C2×C4×Dic17C2×C411yescharacteristic, complemented
153C2×C4×Dic17C2×C411yescharacteristic, complemented
154#10587584C2×C418yescomplemented
155#10587584C2×C418yescomplemented
156#10587584C2×C418yescomplemented
157C4⋊C4×D17C2×C414yescomplemented
158C4⋊C4×D17C2×C414yescomplemented
159C4⋊C4×D17C2×C414yescomplemented
160C4⋊C4×D17C2314yes—
161C4⋊C4×D17C2314yes—
162C4⋊C4×D17C2314yes—
163C22⋊C4×D17C2×C414yes—
164C22⋊C4×D17C2×C414yes—
165C22⋊C4×D17C2×C414yes—
166C22⋊C4×D17C2314yes—
167C22⋊C4×D17C2314yes—
168C22⋊C4×D17C2314yes—
169#10587565C2×C418yescomplemented
170#10587565C2×C418yescomplemented
171#10587565C2×C418yescomplemented
172#10587562C2×C418yescomplemented
173C42×D17C2×C414yescomplemented
174C42×D17C2314yes—
175(C2×#595)⋊C4C2314yes—
176(C2×#595)⋊C4C2314yes—
177(C2×#595)⋊C4C2314yes—
178(C2×#595)⋊C4C2314yes—
179(C2×#595)⋊C4C2314yes—
180(C2×#595)⋊C4C2314yes—
181(C2×#595)⋊C4C2314yes—
182(C2×#595)⋊C4C2314yes—
183(C2×#595)⋊C4C2314yes—
184(C2×#595)⋊C4C2314yes—
185(C2×#595)⋊C4C2314yes—
186(C2×#595)⋊C4C2314yes—
187C24×C17C22×C411yescharacteristic
188C23×D17—22no—
189C23×D17—22no—
190C23×D17—22no—
191C23×D17—22no—
192C23×D17—22no—
193C23×D17—22no—
194C23×D17C22×C412yes—
195C23×D17C22×C411yescharacteristic
196C23×D17C2412yes—
197C23×D17C2411yescharacteristic
198C22×#595—22no—
199C22×#595—22no—
200C22×#595—22no—
201C22×#595—22no—
202C22×#595—22no—
203C22×#595—22no—
204C22×#595—22no—
205C22×#595—22no—
206C22×#595—22no—
207C22×#595—22no—
208C22×#595—22no—
209C22×#595—22no—
210C22×#595—22no—
211C22×#595—22no—
212C22×#595—22no—
213C22×#595—22no—
214C22×#595—22no—
215C22×#595—22no—
216C22×#595—22no—
217C22×#595—22no—
218C22×#595—28no—
219C22×#595—28no—
220C22×#595—44no—
221C22×#595—416no—
222C22×#595#4114yes—
223C22×#595#4114yes—
224C22×#595#4114yes—
225C22×#595#4114yes—
226C22×#595C2412yes—
227C22×#595C2412yes—
228C22×#595C2412yes—
229C22×#595C2412yes—
230C22×#595C2412yes—
231C22×#595C2412yes—
232C22×#595C2412yes—
233C22×#595C2412yes—
234C22×C4×C17C22×C411yescharacteristic
235C22×C4×C17C22×C411yescharacteristic
236C22×C4×C17C22×C411yescharacteristic
237C22×C4×C17C22×C411yescharacteristic
238C22×C4×C17C22×C411yescharacteristic
239C22×C4×C17C22×C411yescharacteristic
240C22×Dic17C22×C411yescharacteristic
241C22×Dic17C22×C411yescharacteristic
242C22×Dic17C22×C411yescharacteristic
243C22×Dic17C22×C411yescharacteristic
244C22×Dic17C22×C411yescharacteristic
245C22×Dic17C22×C411yescharacteristic
246C2×C4×D17—22no—
247C2×C4×D17—22no—
248C2×C4×D17—22no—
249C2×C4×D17—22no—
250C2×C4×D17—22no—
251C2×C4×D17—22no—
252C2×C4×D17—22no—
253C2×C4×D17—22no—
254C2×C4×D17—22no—
255C2×C4×D17—22no—
256C2×C4×D17—22no—
257C2×C4×D17—22no—
258C2×C4×D17C22×C412yes—
259C2×C4×D17C22×C412yes—
260C2×C4×D17C22×C412yes—
261C2×C4×D17C22×C412yes—
262C2×C4×D17C22×C412yes—
263C2×C4×D17C22×C412yes—
264C2×C4×D17C2412yes—
265C2×C4×D17C2412yes—
266C2×C4×D17C2412yes—
267C2×C4×D17C2412yes—
268C2×C4×D17C2412yes—
269C2×C4×D17C2412yes—
270C22⋊#595—28no—
271C22⋊#595—28no—
272C22⋊#595—44no—
273C4⋊#595—28no—
274C4⋊#595—28no—
275C4⋊#595—28no—
276C4⋊#595—28no—
277C4⋊#595—44no—
278C4×#595—28no—
279C4×#595—28no—
280C4×#595—28no—
281C4×#595—28no—
282C4×#595—44no—
283C4×#595—44no—
284C4×#595—44no—
285C4⋊C4×C17C22×C414yescomplemented
286C4⋊C4×C17C22×C414yescomplemented
287C4⋊C4×C17C22×C414yescomplemented
288C22⋊C4×C17C22×C414yes—
289C22⋊C4×C17C22×C414yes—
290C22⋊C4×C17C22×C414yes—
291C42×C17C22×C414yescomplemented
292C22⋊Dic17C22×C414yes—
293C22⋊Dic17C22×C414yes—
294C22⋊Dic17C22×C414yes—
295#63227C22×C414yes—
296#63227C22×C414yes—
297#63227C22×C414yes—
298#63227C22×C414yes—
299#63227C22×C414yes—
300#63227C22×C414yes—
301C4⋊Dic17C22×C414yescomplemented
302C4⋊Dic17C22×C414yescomplemented
303C4⋊Dic17C22×C414yescomplemented
304#63225C22×C414yescomplemented
305#63225C22×C414yescomplemented
306#63225C22×C414yescomplemented
307#63225C22×C414yescomplemented
308#63225C22×C414yescomplemented
309#63225C22×C414yescomplemented
310C4×Dic17C22×C414yescomplemented
311C4×Dic17C22×C414yescomplemented
312C4×Dic17C22×C414yescomplemented
313C2×#2373—171nomaximal, Sylow
314C23×C17—22no—
315C23×C17—22no—
316C23×C17—22no—
317C23×C17C23×C412yes—
318C23×C17C23×C411yescharacteristic
319C22×D17—22no—
320C22×D17—22no—
321C22×D17—22no—
322C22×D17—24no—
323C22×D17—24no—
324C22×D17—24no—
325C22×D17—22no—
326C22×D17—22no—
327C22×D17—22no—
328C22×D17—22no—
329C22×D17—22no—
330C22×D17—22no—
331C22×D17—44no—
332C22×D17—44no—
333C22×D17—44no—
334C22×D17—44no—
335C22×D17C23×C412yes—
336C22×D17C23×C411yescharacteristic
337C22×D17C2×#4112yes—
338C22×D17C2×#4112yes—
339C22×D17C2×#4112yes—
340C22×D17C2×#4112yes—
341C22×D17H(5,𝔽2)12yes—
342C22×D172−1+412yes—
343C22×D17C2511yescharacteristic
344C2×#595—28no—
345C2×#595—28no—
346C2×#595—28no—
347C2×#595—28no—
348C2×#595—22no—
349C2×#595—22no—
350C2×#595—22no—
351C2×#595—22no—
352C2×#595—22no—
353C2×#595—22no—
354C2×#595—22no—
355C2×#595—22no—
356C2×#595—22no—
357C2×#595—22no—
358C2×#595—22no—
359C2×#595—22no—
360C2×#595—22no—
361C2×#595—22no—
362C2×#595—22no—
363C2×#595—22no—
364C2×#595—22no—
365C2×#595—22no—
366C2×#595—22no—
367C2×#595—22no—
368C2×#595—416no—
369C2×#595—44no—
370C2×#595—44no—
371C2×#595—44no—
372C2×#595—44no—
373C2×#595C2×#4114yes—
374C2×#595C2×#4114yes—
375C2×#595C2×#4114yes—
376C2×#595C2×#4114yes—
377C2×C4×C17—22no—
378C2×C4×C17—22no—
379C2×C4×C17—22no—
380C2×C4×C17—22no—
381C2×C4×C17—22no—
382C2×C4×C17—22no—
383C2×C4×C17C23×C412yes—
384C2×C4×C17C23×C412yes—
385C2×C4×C17C23×C412yes—
386C2×C4×C17C23×C412yes—
387C2×C4×C17C23×C412yes—
388C2×C4×C17C23×C412yes—
389C2×Dic17—22no—
390C2×Dic17—22no—
391C2×Dic17—22no—
392C2×Dic17—22no—
393C2×Dic17—22no—
394C2×Dic17—22no—
395C2×Dic17C23×C412yes—
396C2×Dic17C23×C412yes—
397C2×Dic17C23×C412yes—
398C2×Dic17C23×C412yes—
399C2×Dic17C23×C412yes—
400C2×Dic17C23×C412yes—
401C4×D17—24no—
402C4×D17—24no—
403C4×D17—24no—
404C4×D17—24no—
405C4×D17—24no—
406C4×D17—24no—
407C4×D17—22no—
408C4×D17—22no—
409C4×D17—22no—
410C4×D17—22no—
411C4×D17—22no—
412C4×D17—22no—
413C4×D17—22no—
414C4×D17—22no—
415C4×D17—22no—
416C4×D17—22no—
417C4×D17—22no—
418C4×D17—22no—
419C22×#126—171no—
420#2373—1716no—
421C2×#389—171no—
422C2×#388—171no—
423C2×#388—171no—
424C2×#388—171no—
425C2×#387—171no—
426C2×#387—171no—
427C2×#387—171no—
428C2×#385—171no—
429C2×C4×C4⋊C4—171no—
430C2×C4×C4⋊C4—171no—
431C2×C4×C4⋊C4—171no—
432C2×C4×C22⋊C4—171no—
433C2×C4×C22⋊C4—171no—
434C2×#376—171no—
435C22×C17—22no—
436C22×C17—22no—
437C22×C17—22no—
438C22×C17—44no—
439C22×C17C4×#4112yes—
440C22×C17C4×#4112yes—
441C22×C17#52012yes—
442C22×C17C24×C411yescharacteristic
443C2×D17—22no—
444C2×D17—22no—
445C2×D17—22no—
446C2×D17—44no—
447C2×D17—48no—
448C2×D17—42no—
449C2×D17—42no—
450C2×D17—42no—
451C2×D17—42no—
452C2×D17C4×#4112yes—
453C2×D17C4×#4112yes—
454C2×D17#52012yes—
455C2×D17#55114yes—
456C2×D17#55214yes—
457C2×D17#55314yes—
458C2×D17#55614yes—
459C2×D17C22×#4111yescharacteristic
460C2×D17C22×#4111yescharacteristic
461C2×D17C22×#4111yescharacteristic
462C2×D17C22×#4111yescharacteristic
463C2×D17C2×H(5,𝔽2)11yescharacteristic
464C2×D17C2×2−1+411yescharacteristic
465#595—24no—
466#595—24no—
467#595—24no—
468#595—24no—
469#595—42no—
470#595—42no—
471#595—42no—
472#595—42no—
473C4×C17—22no—
474C4×C17—22no—
475C4×C17—22no—
476C4×C17—22no—
477C4×C17—22no—
478C4×C17—22no—
479Dic17—22no—
480Dic17—22no—
481Dic17—22no—
482Dic17—22no—
483Dic17—22no—
484Dic17—22no—
485C24×C4—171no—
486C2×#126—178no—
487C2×#126—178no—
488C2×#126—171no—
489C2×#126—171no—
490C2×#126—171no—
491C2×#126—171no—
492C2×#126—171no—
493C2×#126—171no—
494C2×#126—171no—
495C2×#126#59511yescharacteristic, complemented
496C22×C4⋊C4—171no—
497C22×C4⋊C4—171no—
498C22×C4⋊C4—171no—
499C22×C4⋊C4—171no—
500C22×C4⋊C4—171no—
501C22×C4⋊C4—171no—
502C22×C4⋊C4—171no—
503C22×C4⋊C4—171no—
504C22×C22⋊C4—171no—
505C22×C22⋊C4—171no—
506C22×C22⋊C4—171no—
507C22×C22⋊C4—171no—
508C22×C22⋊C4—171no—
509C22×C22⋊C4—171no—
510C22×C42—171no—
511C22×C42—171no—
512C22×C42—171no—
513C22×C42—171no—
514C22×C42—171no—
515C22×C42—171no—
516C22×C42—171no—
517C22×C42—171no—
518#389—178no—
519#388—178no—
520#388—178no—
521#388—178no—
522#387—178no—
523#387—178no—
524#387—178no—
525#385—178no—
526C4×C4⋊C4—178no—
527C4×C4⋊C4—178no—
528C4×C4⋊C4—178no—
529C4×C22⋊C4—178no—
530C4×C22⋊C4—178no—
531#376—178no—
532C2×#95—171no—
533C2×#95—171no—
534C2×#95—171no—
535C2×#95—171no—
536C2×#95—171no—
537C2×#95—171no—
538C2×#95—171no—
539C2×#95—171no—
540C2×#95—171no—
541C2×#95—171no—
542C2×#95—171no—
543C2×#95—171no—
544C2×C17—42no—
545C2×C17#237314yescomplemented
546C2×C17C2×C4×#4111yescharacteristic
547C2×C17C2×C4×#4111yescharacteristic
548C2×C17C2×#52011yescharacteristic
549D17—42no—
550D17#237314yescomplemented
551D17C2×#55111yescharacteristic
552D17C2×#55211yescharacteristic
553D17C2×#55311yescharacteristic
554D17C2×#55611yescharacteristic
555C25—171no—
556C23×C4—171no—
557C23×C4—171no—
558C23×C4—171no—
559C23×C4—171no—
560C23×C4—171no—
561C23×C4—171no—
562C23×C4—171no—
563C23×C4—171no—
564C23×C4—171no—
565C23×C4—171no—
566C23×C4—171no—
567C23×C4—171no—
568C23×C4—171no—
569C23×C4—171no—
570C23×C4—174no—
571C23×C4—344no—
572C23×C4—344no—
573C23×C4—682no—
574#126—178no—
575#126—178no—
576#126—178no—
577#126—178no—
578#126—178no—
579#126—178no—
580#126—178no—
581#126C2×#59518yescomplemented
582C2×C4⋊C4—171no—
583C2×C4⋊C4—171no—
584C2×C4⋊C4—171no—
585C2×C4⋊C4—171no—
586C2×C4⋊C4—171no—
587C2×C4⋊C4—171no—
588C2×C4⋊C4—171no—
589C2×C4⋊C4—171no—
590C2×C4⋊C4—171no—
591C2×C4⋊C4—174no—
592C2×C4⋊C4—174no—
593C2×C4⋊C4—174no—
594C2×C4⋊C4—174no—
595C2×C4⋊C4—174no—
596C2×C4⋊C4—174no—
597C2×C4⋊C4—174no—
598C2×C4⋊C4—174no—
599C2×C4⋊C4—174no—
600C2×C4⋊C4—174no—
601C2×C4⋊C4—174no—
602C2×C4⋊C4—344no—
603C2×C4⋊C4—344no—
604C2×C4⋊C4—344no—
605C2×C4⋊C4—344no—
606C2×C4⋊C4—682no—
607C2×C4⋊C4C2×#59511yescharacteristic, complemented
608C2×C4⋊C4C2×#59511yescharacteristic, complemented
609C2×C4⋊C4C2×#59511yescharacteristic, complemented
610C2×C22⋊C4—171no—
611C2×C22⋊C4—171no—
612C2×C22⋊C4—171no—
613C2×C22⋊C4—171no—
614C2×C22⋊C4—171no—
615C2×C22⋊C4—171no—
616C2×C22⋊C4—171no—
617C2×C22⋊C4—171no—
618C2×C22⋊C4—171no—
619C2×C22⋊C4—174no—
620C2×C22⋊C4—174no—
621C2×C22⋊C4—174no—
622C2×C22⋊C4—174no—
623C2×C22⋊C4—174no—
624C2×C22⋊C4—174no—
625C2×C22⋊C4—174no—
626C2×C22⋊C4—174no—
627C2×C22⋊C4—174no—
628C2×C22⋊C4—344no—
629C2×C22⋊C4—344no—
630C2×C22⋊C4—682no—
631C2×C22⋊C4C2×#59511yescharacteristic
632C2×C22⋊C4C2×#59511yescharacteristic
633C2×C22⋊C4C2×#59511yescharacteristic
634C2×C42—171no—
635C2×C42—171no—
636C2×C42—171no—
637C2×C42—174no—
638C2×C42—174no—
639C2×C42—174no—
640C2×C42—174no—
641C2×C42—174no—
642C2×C42—174no—
643C2×C42—174no—
644C2×C42—174no—
645C2×C42—174no—
646C2×C42—344no—
647C2×C42—344no—
648C2×C42—344no—
649C2×C42—344no—
650C2×C42—682no—
651C2×C42—682no—
652C2×C42—682no—
653C2×C42C2×#59511yescharacteristic, complemented
654#95—174no—
655#95—174no—
656#95—174no—
657#95—174no—
658#95—174no—
659#95—174no—
660#95—174no—
661#95—174no—
662#95—174no—
663#95—174no—
664#95—174no—
665#95—174no—
666C17C2×#237311yescharacteristic, complemented, Sylow
667C24—171no—
668C24—172no—
669C24—172no—
670C24—171no—
671C24—342no—
672C24—342no—
673C24—342no—
674C24—342no—
675C24—342no—
676C24—342no—
677C24C22×#59511yescharacteristic
678C22×C4—174no—
679C22×C4—174no—
680C22×C4—174no—
681C22×C4—174no—
682C22×C4—172no—
683C22×C4—172no—
684C22×C4—172no—
685C22×C4—172no—
686C22×C4—171no—
687C22×C4—171no—
688C22×C4—171no—
689C22×C4—171no—
690C22×C4—171no—
691C22×C4—171no—
692C22×C4—172no—
693C22×C4—172no—
694C22×C4—172no—
695C22×C4—172no—
696C22×C4—172no—
697C22×C4—172no—
698C22×C4—172no—
699C22×C4—172no—
700C22×C4—172no—
701C22×C4—172no—
702C22×C4—172no—
703C22×C4—172no—
704C22×C4—172no—
705C22×C4—172no—
706C22×C4—172no—
707C22×C4—172no—
708C22×C4—342no—
709C22×C4—342no—
710C22×C4—342no—
711C22×C4—342no—
712C22×C4—342no—
713C22×C4—342no—
714C22×C4—342no—
715C22×C4—342no—
716C22×C4—342no—
717C22×C4—342no—
718C22×C4—342no—
719C22×C4—342no—
720C22×C4—348no—
721C22×C4—348no—
722C22×C4—342no—
723C22×C4—342no—
724C22×C4—342no—
725C22×C4—342no—
726C22×C4—342no—
727C22×C4—342no—
728C22×C4—342no—
729C22×C4—342no—
730C22×C4—342no—
731C22×C4—342no—
732C22×C4—342no—
733C22×C4—342no—
734C22×C4—342no—
735C22×C4—342no—
736C22×C4—342no—
737C22×C4—342no—
738C22×C4—342no—
739C22×C4—342no—
740C22×C4—342no—
741C22×C4—342no—
742C22×C4—684no—
743C22×C4—6816no—
744C22×C4C22×#59511yescharacteristic
745C22×C4C22×#59511yescharacteristic
746C22×C4C22×#59511yescharacteristic
747C22×C4C22×#59511yescharacteristic
748C22×C4C22×#59511yescharacteristic
749C22×C4C22×#59511yescharacteristic
750C4⋊C4—174no—
751C4⋊C4—174no—
752C4⋊C4—174no—
753C4⋊C4—174no—
754C4⋊C4—174no—
755C4⋊C4—174no—
756C4⋊C4—174no—
757C4⋊C4—174no—
758C4⋊C4—174no—
759C4⋊C4—348no—
760C4⋊C4—348no—
761C4⋊C4—348no—
762C4⋊C4—348no—
763C4⋊C4—684no—
764C4⋊C4C22×#59514yescomplemented
765C4⋊C4C22×#59514yescomplemented
766C4⋊C4C22×#59514yescomplemented
767C22⋊C4—174no—
768C22⋊C4—174no—
769C22⋊C4—174no—
770C22⋊C4—174no—
771C22⋊C4—174no—
772C22⋊C4—174no—
773C22⋊C4—174no—
774C22⋊C4—174no—
775C22⋊C4—174no—
776C22⋊C4—348no—
777C22⋊C4—348no—
778C22⋊C4—684no—
779C22⋊C4C22×#59514yes—
780C22⋊C4C22×#59514yes—
781C22⋊C4C22×#59514yes—
782C42—174no—
783C42—174no—
784C42—174no—
785C42—348no—
786C42—348no—
787C42—348no—
788C42—348no—
789C42—684no—
790C42—684no—
791C42—684no—
792C42C22×#59514yescomplemented
793C23—22no—
794C23—22no—
795C23—22no—
796C23—172no—
797C23—172no—
798C23—172no—
799C23—172no—
800C23—172no—
801C23—172no—
802C23—171no—
803C23—171no—
804C23—172no—
805C23—342no—
806C23—342no—
807C23—342no—
808C23—342no—
809C23—342no—
810C23—344no—
811C23—344no—
812C23—342no—
813C23—344no—
814C23—342no—
815C23—342no—
816C23—342no—
817C23—684no—
818C23—684no—
819C23—684no—
820C23—684no—
821C23C23×#59512yes—
822C23C23×#59511yescharacteristic
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—174no—
830C2×C4—174no—
831C2×C4—174no—
832C2×C4—174no—
833C2×C4—172no—
834C2×C4—172no—
835C2×C4—172no—
836C2×C4—172no—
837C2×C4—172no—
838C2×C4—172no—
839C2×C4—342no—
840C2×C4—342no—
841C2×C4—342no—
842C2×C4—342no—
843C2×C4—342no—
844C2×C4—342no—
845C2×C4—342no—
846C2×C4—342no—
847C2×C4—342no—
848C2×C4—342no—
849C2×C4—344no—
850C2×C4—344no—
851C2×C4—344no—
852C2×C4—344no—
853C2×C4—342no—
854C2×C4—342no—
855C2×C4—344no—
856C2×C4—344no—
857C2×C4—342no—
858C2×C4—342no—
859C2×C4—342no—
860C2×C4—342no—
861C2×C4—342no—
862C2×C4—342no—
863C2×C4—342no—
864C2×C4—348no—
865C2×C4—348no—
866C2×C4—342no—
867C2×C4—348no—
868C2×C4—348no—
869C2×C4—342no—
870C2×C4—342no—
871C2×C4—342no—
872C2×C4—342no—
873C2×C4—342no—
874C2×C4—342no—
875C2×C4—342no—
876C2×C4—342no—
877C2×C4—342no—
878C2×C4—342no—
879C2×C4—342no—
880C2×C4—342no—
881C2×C4—342no—
882C2×C4—342no—
883C2×C4—342no—
884C2×C4—342no—
885C2×C4—342no—
886C2×C4—342no—
887C2×C4—6816no—
888C2×C4—684no—
889C2×C4—684no—
890C2×C4—684no—
891C2×C4—684no—
892C2×C4C23×#59512yes—
893C2×C4C23×#59512yes—
894C2×C4C23×#59512yes—
895C2×C4C23×#59512yes—
896C2×C4C23×#59512yes—
897C2×C4C23×#59512yes—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—44no—
902C22—171no—
903C22—171no—
904C22—171no—
905C22—171no—
906C22—172no—
907C22—172no—
908C22—171no—
909C22—171no—
910C22—172no—
911C22—174no—
912C22—174no—
913C22—174no—
914C22—174no—
915C22—342no—
916C22—342no—
917C22—342no—
918C22—682no—
919C22—682no—
920C22—682no—
921C22—682no—
922C22—688no—
923C22—684no—
924C22#41×#59512yes—
925C22#41×#59512yes—
926C22#1176387812yes—
927C22C24×#59511yescharacteristic
928C4—22no—
929C4—22no—
930C4—22no—
931C4—22no—
932C4—22no—
933C4—22no—
934C4—344no—
935C4—344no—
936C4—344no—
937C4—344no—
938C4—342no—
939C4—342no—
940C4—342no—
941C4—342no—
942C4—342no—
943C4—342no—
944C4—682no—
945C4—682no—
946C4—682no—
947C4—682no—
948C2—42no—
949C2—171no—
950C2—171no—
951C2—171no—
952C2—171no—
953C2—174no—
954C2—682no—
955C2#1454532114yesdirect product factor
956C2C2×#41×#59511yescharacteristic
957C2C2×#41×#59511yescharacteristic
958C2C2×#1176387811yescharacteristic
subgroupG/H
centerC23C23×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC2×C17×#126C4
socleC23×C17C23×C4
prime radicalC24×D17C23
cosocleC22×D17C25
hypercenterC2×#126#595
hypocenterC17C2×#2373
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #14545321C2direct (N × H)
2. C2×#11763760C2semidirect
6. C2×#11763758C2semidirect
7. C2×#11763758C2semidirect
8. C2×#11763758C2semidirect
10. C2×C4⋊C4×#595C2semidirect
11. C2×C4⋊C4×#595C2semidirect
12. C2×C4×C4⋊#595C2semidirect
15. C2×#11763745C2semidirect
33. #11763760C22semidirect
37. #11763758C22semidirect
38. #11763758C22semidirect
39. #11763758C22semidirect
41. C4⋊C4×#595C22semidirect
42. C4⋊C4×#595C22semidirect
43. C4×C4⋊#595C22semidirect
46. #11763745C22semidirect
59. C2×#10587584C4semidirect
60. C2×#10587584C4semidirect
61. C2×#10587584C4semidirect
62. C2×#10587562C4semidirect
63. C2×#10587565C4semidirect
64. C2×#10587565C4semidirect
65. C2×#10587565C4semidirect
66. #126×D17C4semidirect
75. C2×C17×#126C4semidirect
125. C17×#126C2×C4semidirect
126. C2×C4⋊C4×C17C2×C4semidirect
127. C2×C4⋊C4×C17C2×C4semidirect
128. C2×C4⋊C4×C17C2×C4semidirect
132. C2×C42×C17C2×C4semidirect
142. C2×C4⋊Dic17C2×C4semidirect
143. C2×C4⋊Dic17C2×C4semidirect
144. C2×C4⋊Dic17C2×C4semidirect
145. C2×#63225C2×C4semidirect
146. C2×#63225C2×C4semidirect
147. C2×#63225C2×C4semidirect
148. C2×#63225C2×C4semidirect
149. C2×#63225C2×C4semidirect
150. C2×#63225C2×C4semidirect
151. C2×C4×Dic17C2×C4semidirect
152. C2×C4×Dic17C2×C4semidirect
153. C2×C4×Dic17C2×C4semidirect
154. #10587584C2×C4semidirect
155. #10587584C2×C4semidirect
156. #10587584C2×C4semidirect
157. C4⋊C4×D17C2×C4semidirect
158. C4⋊C4×D17C2×C4semidirect
159. C4⋊C4×D17C2×C4semidirect
169. #10587565C2×C4semidirect
170. #10587565C2×C4semidirect
171. #10587565C2×C4semidirect
172. #10587562C2×C4semidirect
173. C42×D17C2×C4semidirect
285. C4⋊C4×C17C22×C4semidirect
286. C4⋊C4×C17C22×C4semidirect
287. C4⋊C4×C17C22×C4semidirect
291. C42×C17C22×C4semidirect
301. C4⋊Dic17C22×C4semidirect
302. C4⋊Dic17C22×C4semidirect
303. C4⋊Dic17C22×C4semidirect
304. #63225C22×C4semidirect
305. #63225C22×C4semidirect
306. #63225C22×C4semidirect
307. #63225C22×C4semidirect
308. #63225C22×C4semidirect
309. #63225C22×C4semidirect
310. C4×Dic17C22×C4semidirect
311. C4×Dic17C22×C4semidirect
312. C4×Dic17C22×C4semidirect
495. C2×#126#595semidirect
545. C2×C17#2373semidirect
550. D17#2373semidirect
581. #126C2×#595semidirect
607. C2×C4⋊C4C2×#595semidirect
608. C2×C4⋊C4C2×#595semidirect
609. C2×C4⋊C4C2×#595semidirect
653. C2×C42C2×#595semidirect
666. C17C2×#2373semidirect
764. C4⋊C4C22×#595semidirect
765. C4⋊C4C22×#595semidirect
766. C4⋊C4C22×#595semidirect
792. C42C22×#595semidirect
955. C2#14545321direct (N × H)

Maximal subgroups

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

subgroupindex
#145453212
C2×#117637602
C2×#117637592
C2×#117637582
C2×#117637562
C2×C4⋊C4×#5952
C2×C4×C4⋊#5952
C2×C22⋊C4×#5952
C2×#117637452
C2×#126×D172
C2×#237317