Finite Group Databasebeta

← C2×#14531908 #17194016

Subgroups — C2×#14531908 #17194016

Order 4352.

2726 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531908C2116yesmaximal, direct product factor
2C2×#11762708C211yesmaximal, characteristic, complemented
3C2×#11762702C211yesmaximal, characteristic
4C2×#11762702C211yesmaximal, characteristic
5C2×#11762702C211yesmaximal, characteristic
6C2×#11762695C211yesmaximal, characteristic, complemented
7C2×#11762695C211yesmaximal, characteristic, complemented
8C2×#11762695C211yesmaximal, characteristic, complemented
9C2×#11762684C211yesmaximal, characteristic
10C2×C4⋊C4×Dic17C211yesmaximal, characteristic, complemented
11C2×C4⋊C4×Dic17C211yesmaximal, characteristic, complemented
12C2×C4×C4⋊Dic17C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic17C211yesmaximal, characteristic
14C2×C22⋊C4×Dic17C211yesmaximal, characteristic
15C2×#11762655C211yesmaximal, characteristic, complemented
16C22×C17×#126C211yesmaximal, characteristic
17C24×Dic17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×C4⋊Dic17C2211yescharacteristic
21C22×C4⋊Dic17C2211yescharacteristic
22C22×C4⋊Dic17C2211yescharacteristic
23C22×C22⋊Dic17C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×C4×Dic17C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28C22×C4×Dic17C2211yescharacteristic
29C22×C4×Dic17C2211yescharacteristic
30C22×C4×Dic17C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33#11762708C2218yescomplemented
34#11762702C2218yes—
35#11762702C2218yes—
36#11762702C2218yes—
37#11762695C2218yescomplemented
38#11762695C2218yescomplemented
39#11762695C2218yescomplemented
40#11762684C2218yes—
41C4⋊C4×Dic17C2218yescomplemented
42C4⋊C4×Dic17C2218yescomplemented
43C4×C4⋊Dic17C2218yescomplemented
44C22⋊C4×Dic17C2218yes—
45C22⋊C4×Dic17C2218yes—
46#11762655C2218yescomplemented
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
53C2×#10587502C2211yescharacteristic
54C2×#10587502C2211yescharacteristic
55C2×#10587502C2211yescharacteristic
56C2×#10587502C2211yescharacteristic
57C2×#10587502C2211yescharacteristic
58C2×#10587502C2211yescharacteristic
59C2×C17×#126C4116yescomplemented
60C2×C17×#126C2218yes—
61C22×C4⋊C4×C17C2211yescharacteristic
62C22×C4⋊C4×C17C2211yescharacteristic
63C22×C4⋊C4×C17C2211yescharacteristic
64C22×C22⋊C4×C17C2211yescharacteristic
65C22×C22⋊C4×C17C2211yescharacteristic
66C22×C22⋊C4×C17C2211yescharacteristic
67C22×C42×C17C2211yescharacteristic
68C25×C17C2311yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×Dic17—24no—
76C23×Dic17—24no—
77C23×Dic17—42no—
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2314yes—
83C23×Dic17C2311yescharacteristic
84C23×Dic17C2311yescharacteristic
85C23×Dic17C2311yescharacteristic
86C23×Dic17C2311yescharacteristic
87C17×#126C2×C4164yescomplemented
88C2×C4⋊C4×C17C2×C418yescomplemented
89C2×C4⋊C4×C17C2×C418yescomplemented
90C2×C4⋊C4×C17C2×C418yescomplemented
91C2×C4⋊C4×C17C2314yes—
92C2×C4⋊C4×C17C2314yes—
93C2×C4⋊C4×C17C2314yes—
94C2×C22⋊C4×C17C2×C418yes—
95C2×C22⋊C4×C17C2×C418yes—
96C2×C22⋊C4×C17C2×C418yes—
97C2×C22⋊C4×C17C2314yes—
98C2×C22⋊C4×C17C2314yes—
99C2×C22⋊C4×C17C2314yes—
100C2×C42×C17C2×C418yescomplemented
101C2×C42×C17C2314yes—
102C2×C22⋊Dic17—24no—
103C2×C22⋊Dic17—24no—
104C2×C22⋊Dic17—42no—
105C2×C22⋊Dic17C2314yes—
106C2×C22⋊Dic17C2314yes—
107C2×C22⋊Dic17C2314yes—
108C2×C4⋊Dic17—24no—
109C2×C4⋊Dic17—24no—
110C2×C4⋊Dic17—24no—
111C2×C4⋊Dic17—24no—
112C2×C4⋊Dic17—42no—
113C2×C4⋊Dic17C2314yes—
114C2×C4⋊Dic17C2314yes—
115C2×C4⋊Dic17C2314yes—
116C2×C4⋊Dic17C2314yes—
117C2×C4⋊Dic17C2314yes—
118C2×C4×Dic17—24no—
119C2×C4×Dic17—24no—
120C2×C4×Dic17—24no—
121C2×C4×Dic17—24no—
122C2×C4×Dic17—42no—
123C2×C4×Dic17—42no—
124C2×C4×Dic17—42no—
125C2×C4×Dic17C2314yes—
126C2×C4×Dic17C2314yes—
127C2×C4×Dic17C2314yes—
128C2×C4×Dic17C2314yes—
129C2×C4×Dic17C2314yes—
130C2×C4×Dic17C2314yes—
131C2×C4×Dic17C2314yes—
132#10587502C2314yes—
133#10587502C2314yes—
134#10587502C2314yes—
135#10587502C2314yes—
136#10587502C2314yes—
137#10587502C2314yes—
138#10587502C2314yes—
139#10587502C2314yes—
140#10587502C2314yes—
141#10587502C2314yes—
142#10587502C2314yes—
143#10587502C2314yes—
144C24×C17—22no—
145C24×C17—22no—
146C24×C17—22no—
147C24×C17—22no—
148C24×C17—22no—
149C24×C17—22no—
150C24×C17C22×C414yes—
151C24×C17C2412yes—
152C24×C17C2411yescharacteristic
153C22×C4×C17—22no—
154C22×C4×C17—22no—
155C22×C4×C17—22no—
156C22×C4×C17—22no—
157C22×C4×C17—22no—
158C22×C4×C17—22no—
159C22×C4×C17—22no—
160C22×C4×C17—22no—
161C22×C4×C17—22no—
162C22×C4×C17—22no—
163C22×C4×C17—22no—
164C22×C4×C17—22no—
165C22×C4×C17C22×C414yes—
166C22×C4×C17C22×C414yes—
167C22×C4×C17C22×C414yes—
168C22×C4×C17C22×C414yes—
169C22×C4×C17C22×C414yes—
170C22×C4×C17C22×C414yes—
171C22×C4×C17C2412yes—
172C22×C4×C17C2412yes—
173C22×C4×C17C2412yes—
174C22×C4×C17C2412yes—
175C22×C4×C17C2412yes—
176C22×C4×C17C2412yes—
177C22×Dic17—22no—
178C22×Dic17—22no—
179C22×Dic17—22no—
180C22×Dic17—22no—
181C22×Dic17—22no—
182C22×Dic17—22no—
183C22×Dic17—22no—
184C22×Dic17—22no—
185C22×Dic17—22no—
186C22×Dic17—22no—
187C22×Dic17—22no—
188C22×Dic17—22no—
189C22×Dic17—22no—
190C22×Dic17—22no—
191C22×Dic17—22no—
192C22×Dic17—22no—
193C22×Dic17—22no—
194C22×Dic17—22no—
195C22×Dic17—22no—
196C22×Dic17—22no—
197C22×Dic17—28no—
198C22×Dic17—28no—
199C22×Dic17—44no—
200C22×Dic17—416no—
201C22×Dic17#4114yes—
202C22×Dic17#4114yes—
203C22×Dic17#4114yes—
204C22×Dic17#4114yes—
205C22×Dic17C2412yes—
206C22×Dic17C2412yes—
207C22×Dic17C2412yes—
208C22×Dic17C2412yes—
209C22×Dic17C2412yes—
210C22×Dic17C2412yes—
211C22×Dic17C2412yes—
212C22×Dic17C2412yes—
213C4⋊C4×C17C22×C4116yescomplemented
214C4⋊C4×C17C22×C4116yescomplemented
215C4⋊C4×C17C22×C4116yescomplemented
216C22⋊C4×C17C22×C4116yes—
217C22⋊C4×C17C22×C4116yes—
218C22⋊C4×C17C22×C4116yes—
219C42×C17C22×C4116yescomplemented
220C22⋊Dic17—28no—
221C22⋊Dic17—28no—
222C22⋊Dic17—44no—
223C4⋊Dic17—28no—
224C4⋊Dic17—28no—
225C4⋊Dic17—28no—
226C4⋊Dic17—28no—
227C4⋊Dic17—44no—
228C4×Dic17—28no—
229C4×Dic17—28no—
230C4×Dic17—28no—
231C4×Dic17—28no—
232C4×Dic17—44no—
233C4×Dic17—44no—
234C4×Dic17—44no—
235C2×#2373—171nomaximal, Sylow
236C23×C17—28no—
237C23×C17—28no—
238C23×C17—28no—
239C23×C17—22no—
240C23×C17—22no—
241C23×C17—22no—
242C23×C17—22no—
243C23×C17—22no—
244C23×C17—22no—
245C23×C17—44no—
246C23×C17—44no—
247C23×C17—44no—
248C23×C17—44no—
249C23×C17C23×C414yes—
250C23×C17C23×C412yes—
251C23×C17C2×#4112yes—
252C23×C17C2×#4112yes—
253C23×C17C2×#4112yes—
254C23×C17C2×#4112yes—
255C23×C17H(5,𝔽2)12yes—
256C23×C172−1+412yes—
257C23×C17C2511yescharacteristic
258C2×C4×C17—28no—
259C2×C4×C17—28no—
260C2×C4×C17—28no—
261C2×C4×C17—28no—
262C2×C4×C17—28no—
263C2×C4×C17—28no—
264C2×C4×C17—22no—
265C2×C4×C17—22no—
266C2×C4×C17—22no—
267C2×C4×C17—22no—
268C2×C4×C17—22no—
269C2×C4×C17—22no—
270C2×C4×C17—22no—
271C2×C4×C17—22no—
272C2×C4×C17—22no—
273C2×C4×C17—22no—
274C2×C4×C17—22no—
275C2×C4×C17—22no—
276C2×C4×C17C23×C414yes—
277C2×C4×C17C23×C414yes—
278C2×C4×C17C23×C414yes—
279C2×C4×C17C23×C414yes—
280C2×C4×C17C23×C414yes—
281C2×C4×C17C23×C414yes—
282C2×Dic17—28no—
283C2×Dic17—28no—
284C2×Dic17—28no—
285C2×Dic17—28no—
286C2×Dic17—22no—
287C2×Dic17—22no—
288C2×Dic17—22no—
289C2×Dic17—22no—
290C2×Dic17—22no—
291C2×Dic17—22no—
292C2×Dic17—22no—
293C2×Dic17—22no—
294C2×Dic17—22no—
295C2×Dic17—22no—
296C2×Dic17—22no—
297C2×Dic17—22no—
298C2×Dic17—22no—
299C2×Dic17—22no—
300C2×Dic17—22no—
301C2×Dic17—22no—
302C2×Dic17—22no—
303C2×Dic17—22no—
304C2×Dic17—22no—
305C2×Dic17—22no—
306C2×Dic17—416no—
307C2×Dic17—44no—
308C2×Dic17—44no—
309C2×Dic17—44no—
310C2×Dic17—44no—
311C2×Dic17C2×#4114yes—
312C2×Dic17C2×#4114yes—
313C2×Dic17C2×#4114yes—
314C2×Dic17C2×#4114yes—
315C22×#126D1711yescharacteristic
316#2373—1716no—
317C2×#389—171no—
318C2×#388—171no—
319C2×#388—171no—
320C2×#388—171no—
321C2×#387—171no—
322C2×#387—171no—
323C2×#387—171no—
324C2×#385—171no—
325C2×C4×C4⋊C4—171no—
326C2×C4×C4⋊C4—171no—
327C2×C4×C4⋊C4—171no—
328C2×C4×C22⋊C4—171no—
329C2×C4×C22⋊C4—171no—
330C2×#376—171no—
331C22×C17—24no—
332C22×C17—24no—
333C22×C17—24no—
334C22×C17—416no—
335C22×C17—42no—
336C22×C17—42no—
337C22×C17—42no—
338C22×C17—42no—
339C22×C17C4×#4114yes—
340C22×C17C4×#4114yes—
341C22×C17#52014yes—
342C22×C17#55114yes—
343C22×C17#55214yes—
344C22×C17#55314yes—
345C22×C17#55614yes—
346C22×C17C24×C411yescharacteristic
347C22×C17C22×#4111yescharacteristic
348C22×C17C22×#4111yescharacteristic
349C22×C17C22×#4111yescharacteristic
350C22×C17C22×#4111yescharacteristic
351C22×C17C2×H(5,𝔽2)11yescharacteristic
352C22×C17C2×2−1+411yescharacteristic
353C4×C17—24no—
354C4×C17—24no—
355C4×C17—24no—
356C4×C17—24no—
357C4×C17—24no—
358C4×C17—24no—
359Dic17—24no—
360Dic17—24no—
361Dic17—24no—
362Dic17—24no—
363Dic17—42no—
364Dic17—42no—
365Dic17—42no—
366Dic17—42no—
367C24×C4—171no—
368C2×#126Dic17116yescomplemented
369C2×#126C2×D1718yes—
370C22×C4⋊C4—171no—
371C22×C4⋊C4—171no—
372C22×C4⋊C4—171no—
373C22×C4⋊C4—171no—
374C22×C4⋊C4—171no—
375C22×C4⋊C4C2×D1711yescharacteristic
376C22×C4⋊C4C2×D1711yescharacteristic
377C22×C4⋊C4C2×D1711yescharacteristic
378C22×C22⋊C4—171no—
379C22×C22⋊C4—171no—
380C22×C22⋊C4—171no—
381C22×C22⋊C4C2×D1711yescharacteristic
382C22×C22⋊C4C2×D1711yescharacteristic
383C22×C22⋊C4C2×D1711yescharacteristic
384C22×C42—171no—
385C22×C42—171no—
386C22×C42—171no—
387C22×C42—171no—
388C22×C42—171no—
389C22×C42—171no—
390C22×C42—171no—
391C22×C42C2×D1711yescharacteristic
392#389—178no—
393#388—178no—
394#388—178no—
395#388—178no—
396#387—178no—
397#387—178no—
398#387—178no—
399#385—178no—
400C4×C4⋊C4—178no—
401C4×C4⋊C4—178no—
402C4×C4⋊C4—178no—
403C4×C22⋊C4—178no—
404C4×C22⋊C4—178no—
405#376—178no—
406C2×#95—171no—
407C2×#95—171no—
408C2×#95—171no—
409C2×#95—171no—
410C2×#95—171no—
411C2×#95—171no—
412C2×#95—171no—
413C2×#95—171no—
414C2×#95—171no—
415C2×#95—171no—
416C2×#95—171no—
417C2×#95—171no—
418C2×C17—44no—
419C2×C17#237318yescomplemented
420C2×C17C2×C4×#4111yescharacteristic
421C2×C17C2×C4×#4111yescharacteristic
422C2×C17C2×#52011yescharacteristic
423C2×C17C2×#55111yescharacteristic
424C2×C17C2×#55211yescharacteristic
425C2×C17C2×#55311yescharacteristic
426C2×C17C2×#55611yescharacteristic
427C25C22×D1711yescharacteristic
428C23×C4—171no—
429C23×C4—171no—
430C23×C4—171no—
431C23×C4—171no—
432C23×C4—171no—
433C23×C4—171no—
434C23×C4—171no—
435C23×C4—171no—
436C23×C4—174no—
437C23×C4—344no—
438C23×C4—344no—
439C23×C4—682no—
440C23×C4C22×D1711yescharacteristic
441C23×C4C22×D1711yescharacteristic
442C23×C4C22×D1711yescharacteristic
443C23×C4C22×D1711yescharacteristic
444C23×C4C22×D1711yescharacteristic
445C23×C4C22×D1711yescharacteristic
446#126C2×Dic17164yescomplemented
447C2×C4⋊C4—174no—
448C2×C4⋊C4—174no—
449C2×C4⋊C4—174no—
450C2×C4⋊C4—174no—
451C2×C4⋊C4—174no—
452C2×C4⋊C4—344no—
453C2×C4⋊C4—344no—
454C2×C4⋊C4—344no—
455C2×C4⋊C4—344no—
456C2×C4⋊C4—682no—
457C2×C4⋊C4C2×Dic1718yescomplemented
458C2×C4⋊C4C2×Dic1718yescomplemented
459C2×C4⋊C4C2×Dic1718yescomplemented
460C2×C4⋊C4C22×D1714yes—
461C2×C4⋊C4C22×D1714yes—
462C2×C4⋊C4C22×D1714yes—
463C2×C22⋊C4—174no—
464C2×C22⋊C4—174no—
465C2×C22⋊C4—174no—
466C2×C22⋊C4—344no—
467C2×C22⋊C4—344no—
468C2×C22⋊C4—682no—
469C2×C22⋊C4C2×Dic1718yes—
470C2×C22⋊C4C2×Dic1718yes—
471C2×C22⋊C4C2×Dic1718yes—
472C2×C22⋊C4C22×D1714yes—
473C2×C22⋊C4C22×D1714yes—
474C2×C22⋊C4C22×D1714yes—
475C2×C42—174no—
476C2×C42—174no—
477C2×C42—174no—
478C2×C42—174no—
479C2×C42—174no—
480C2×C42—174no—
481C2×C42—174no—
482C2×C42—344no—
483C2×C42—344no—
484C2×C42—344no—
485C2×C42—344no—
486C2×C42—682no—
487C2×C42—682no—
488C2×C42—682no—
489C2×C42C2×Dic1718yescomplemented
490C2×C42C22×D1714yes—
491#95—174no—
492#95—174no—
493#95—174no—
494#95—174no—
495#95—174no—
496#95—174no—
497#95—174no—
498#95—174no—
499#95—174no—
500#95—174no—
501#95—174no—
502#95—174no—
503C17C2×#237311yescharacteristic, complemented, Sylow
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24C22×Dic1714yes—
511C24C23×D1712yes—
512C24C23×D1711yescharacteristic
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—174no—
526C22×C4—174no—
527C22×C4—174no—
528C22×C4—174no—
529C22×C4—172no—
530C22×C4—172no—
531C22×C4—172no—
532C22×C4—172no—
533C22×C4—172no—
534C22×C4—172no—
535C22×C4—172no—
536C22×C4—172no—
537C22×C4—348no—
538C22×C4—348no—
539C22×C4—342no—
540C22×C4—342no—
541C22×C4—342no—
542C22×C4—342no—
543C22×C4—342no—
544C22×C4—342no—
545C22×C4—342no—
546C22×C4—342no—
547C22×C4—342no—
548C22×C4—342no—
549C22×C4—342no—
550C22×C4—342no—
551C22×C4—342no—
552C22×C4—342no—
553C22×C4—342no—
554C22×C4—342no—
555C22×C4—342no—
556C22×C4—342no—
557C22×C4—342no—
558C22×C4—342no—
559C22×C4—684no—
560C22×C4—6816no—
561C22×C4C22×Dic1714yes—
562C22×C4C22×Dic1714yes—
563C22×C4C22×Dic1714yes—
564C22×C4C22×Dic1714yes—
565C22×C4C22×Dic1714yes—
566C22×C4C22×Dic1714yes—
567C22×C4C23×D1712yes—
568C22×C4C23×D1712yes—
569C22×C4C23×D1712yes—
570C22×C4C23×D1712yes—
571C22×C4C23×D1712yes—
572C22×C4C23×D1712yes—
573C4⋊C4—348no—
574C4⋊C4—348no—
575C4⋊C4—348no—
576C4⋊C4—348no—
577C4⋊C4—684no—
578C4⋊C4C22×Dic17116yescomplemented
579C4⋊C4C22×Dic17116yescomplemented
580C4⋊C4C22×Dic17116yescomplemented
581C22⋊C4—348no—
582C22⋊C4—348no—
583C22⋊C4—684no—
584C22⋊C4C22×Dic17116yes—
585C22⋊C4C22×Dic17116yes—
586C22⋊C4C22×Dic17116yes—
587C42—348no—
588C42—348no—
589C42—348no—
590C42—348no—
591C42—684no—
592C42—684no—
593C42—684no—
594C42C22×Dic17116yescomplemented
595C23—28no—
596C23—28no—
597C23—28no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23#41×D1712yes—
609C23#41×D1712yes—
610C23#41×D1712yes—
611C23#41×D1712yes—
612C23#1058769612yes—
613C23#1058769712yes—
614C23C23×Dic1714yes—
615C23C23×Dic1712yes—
616C23C24×D1711yescharacteristic
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—28no—
621C2×C4—28no—
622C2×C4—28no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—174no—
636C2×C4—174no—
637C2×C4—174no—
638C2×C4—174no—
639C2×C4—348no—
640C2×C4—348no—
641C2×C4—348no—
642C2×C4—348no—
643C2×C4—342no—
644C2×C4—342no—
645C2×C4—342no—
646C2×C4—342no—
647C2×C4—342no—
648C2×C4—342no—
649C2×C4—342no—
650C2×C4—342no—
651C2×C4—342no—
652C2×C4—342no—
653C2×C4—342no—
654C2×C4—342no—
655C2×C4—342no—
656C2×C4—342no—
657C2×C4—342no—
658C2×C4—342no—
659C2×C4—342no—
660C2×C4—342no—
661C2×C4—342no—
662C2×C4—342no—
663C2×C4—6816no—
664C2×C4—684no—
665C2×C4—684no—
666C2×C4—684no—
667C2×C4—684no—
668C2×C4C23×Dic1714yes—
669C2×C4C23×Dic1714yes—
670C2×C4C23×Dic1714yes—
671C2×C4C23×Dic1714yes—
672C2×C4C23×Dic1714yes—
673C2×C4C23×Dic1714yes—
674C22—24no—
675C22—24no—
676C22—24no—
677C22—416no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22#41×Dic1714yes—
683C22#41×Dic1714yes—
684C22#1176329214yes—
685C22#1176348414yes—
686C22#1176349514yes—
687C22#1176351014yes—
688C22#1176352614yes—
689C22C24×Dic1711yescharacteristic
690C22C2×#41×D1711yescharacteristic
691C22C2×#41×D1711yescharacteristic
692C22C2×#41×D1711yescharacteristic
693C22C2×#41×D1711yescharacteristic
694C22C2×#1058769611yescharacteristic
695C22C2×#1058769711yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—24no—
700C4—24no—
701C4—24no—
702C4—344no—
703C4—344no—
704C4—344no—
705C4—344no—
706C4—682no—
707C4—682no—
708C4—682no—
709C4—682no—
710C2—44no—
711C2#1453190818yesdirect product factor
712C2C2×#41×Dic1711yescharacteristic
713C2C2×#41×Dic1711yescharacteristic
714C2C2×#1176329211yescharacteristic
715C2C2×#1176348411yescharacteristic
716C2C2×#1176349511yescharacteristic
717C2C2×#1176351011yescharacteristic
718C2C2×#1176352611yescharacteristic
subgroupG/H
centerC24C23×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC22×C17×#126C2
socleC24×C17C24
prime radicalC25×C17C23
cosocleC23×C17C25
hypercenterC22×#126D17
hypocenterC17C2×#2373
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. #14531908C2direct (N × H)
2. C2×#11762708C2semidirect
6. C2×#11762695C2semidirect
7. C2×#11762695C2semidirect
8. C2×#11762695C2semidirect
10. C2×C4⋊C4×Dic17C2semidirect
11. C2×C4⋊C4×Dic17C2semidirect
12. C2×C4×C4⋊Dic17C2semidirect
15. C2×#11762655C2semidirect
33. #11762708C22semidirect
37. #11762695C22semidirect
38. #11762695C22semidirect
39. #11762695C22semidirect
41. C4⋊C4×Dic17C22semidirect
42. C4⋊C4×Dic17C22semidirect
43. C4×C4⋊Dic17C22semidirect
46. #11762655C22semidirect
59. C2×C17×#126C4semidirect
87. C17×#126C2×C4semidirect
88. C2×C4⋊C4×C17C2×C4semidirect
89. C2×C4⋊C4×C17C2×C4semidirect
90. C2×C4⋊C4×C17C2×C4semidirect
100. C2×C42×C17C2×C4semidirect
213. C4⋊C4×C17C22×C4semidirect
214. C4⋊C4×C17C22×C4semidirect
215. C4⋊C4×C17C22×C4semidirect
219. C42×C17C22×C4semidirect
368. C2×#126Dic17semidirect
419. C2×C17#2373semidirect
446. #126C2×Dic17semidirect
457. C2×C4⋊C4C2×Dic17semidirect
458. C2×C4⋊C4C2×Dic17semidirect
459. C2×C4⋊C4C2×Dic17semidirect
489. C2×C42C2×Dic17semidirect
503. C17C2×#2373semidirect
578. C4⋊C4C22×Dic17semidirect
579. C4⋊C4C22×Dic17semidirect
580. C4⋊C4C22×Dic17semidirect
594. C42C22×Dic17semidirect
711. C2#14531908direct (N × H)

Maximal subgroups

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

subgroupindex
#145319082
C2×#117627082
C2×#117627022
C2×#117626952
C2×#117626842
C2×C4⋊C4×Dic172
C2×C4×C4⋊Dic172
C2×C22⋊C4×Dic172
C2×#117626552
C22×C17×#1262
C2×#237317