Finite Group Databasebeta

← C2×#14545318 #17979011

Subgroups — C2×#14545318 #17979011

Order 4352.

2510 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545318C2116yesmaximal, direct product factor
2C2×#11763760C212yesmaximal
3C2×#11763760C211yesmaximal, characteristic
4C2×#11763760C211yesmaximal, characteristic
5C2×#11763758C212yesmaximal
6C2×#11763758C212yesmaximal
7C2×C4⋊C4×#595C212yesmaximal
8C2×C4⋊C4×#595C211yesmaximal, characteristic
9C2×C4⋊C4×#595C211yesmaximal, characteristic
10C2×C4×C4⋊#595C211yesmaximal, characteristic
11C2×C4×C4⋊#595C211yesmaximal, characteristic
12C2×#125×D17C211yesmaximal, characteristic
13C22×C4⋊#595C2211yescharacteristic
14C22×C4⋊#595C2211yescharacteristic
15C22×C4⋊#595C2211yescharacteristic
16C22×C4⋊#595C2212yes—
17C22×C4⋊#595C2212yes—
18C22×C4⋊#595C2211yescharacteristic
19C22×C4×#595C2211yescharacteristic
20C22×C4×#595C2211yescharacteristic
21C22×C4×#595C2212yes—
22C22×C4×#595C2212yes—
23C22×C4×#595C2212yes—
24#11763760C2218yes—
25#11763760C2218yes—
26#11763760C22116yes—
27#11763758C22116yes—
28#11763758C22116yes—
29C4⋊C4×#595C2218yes—
30C4⋊C4×#595C2218yes—
31C4⋊C4×#595C22116yes—
32C4×C4⋊#595C2218yes—
33C4×C4⋊#595C2218yes—
34C2×(C2×#595)⋊C4C2211yescharacteristic
35C2×(C2×#595)⋊C4C2211yescharacteristic
36C2×(C2×#595)⋊C4C2212yes—
37C2×(C2×#595)⋊C4C2212yes—
38C2×(C2×#595)⋊C4C2212yes—
39C2×(C2×#595)⋊C4C2212yes—
40C2×(C2×#595)⋊C4C2212yes—
41C2×#10587556C411yescharacteristic, complemented
42C2×#10587576C411yescharacteristic, complemented
43C2×#10587576C411yescharacteristic, complemented
44C2×#10587575C412yescomplemented
45C2×#10587575C412yescomplemented
46#125×D17C418yescomplemented
47#125×D17C2218yes—
48C2×C4⋊C4×D17C2212yes—
49C2×C4⋊C4×D17C2211yescharacteristic
50C2×C4⋊C4×D17C2211yescharacteristic
51C2×C4⋊C4×D17C2212yes—
52C2×C42×D17C2211yescharacteristic
53C2×C17×#125C411yescharacteristic, complemented
54C23×#595C2311yescharacteristic
55C23×#595C2311yescharacteristic
56C23×#595C2312yes—
57C23×#595C2312yes—
58C23×#595C2311yescharacteristic
59C23×#595C2311yescharacteristic
60C22×C4×D17C2311yescharacteristic
61C22×C4×D17C2311yescharacteristic
62C22×C4×D17C2312yes—
63C22×C4×D17C2312yes—
64C22×C4×D17C2311yescharacteristic
65C2×C4⋊#595—24no—
66C2×C4⋊#595—24no—
67C2×C4⋊#595—28no—
68C2×C4⋊#595—24no—
69C2×C4⋊#595—44no—
70C2×C4⋊#595Q818yes—
71C2×C4⋊#595C2314yes—
72C2×C4⋊#595C2314yes—
73C2×C4⋊#595C2314yes—
74C2×C4⋊#595C2318yes—
75C2×C4⋊#595C2318yes—
76C2×C4⋊#595C2314yes—
77C2×C4×#595—28no—
78C2×C4×#595—24no—
79C2×C4×#595—24no—
80C2×C4×#595—44no—
81C2×C4×#595—44no—
82C2×C4×#595C2314yes—
83C2×C4×#595C2314yes—
84C2×C4×#595C2318yes—
85C2×C4×#595C2318yes—
86C2×C4×#595C2318yes—
87C17×#125C2×C418yescomplemented
88C2×C4⋊C4×C17C2×C412yes—
89C2×C4⋊C4×C17C2×C412yes—
90C2×C4⋊C4×C17C2×C411yescharacteristic
91C2×C4⋊C4×C17C2×C411yescharacteristic
92C2×C42×C17C2×C411yescharacteristic
93C2×C4⋊Dic17C2×C412yes—
94C2×C4⋊Dic17C2×C412yes—
95C2×C4⋊Dic17C2×C411yescharacteristic
96C2×C4⋊Dic17C2×C411yescharacteristic
97C2×#63225C2×C412yes—
98C2×#63225C2×C412yes—
99C2×#63225C2×C412yes—
100C2×#63225C2×C412yes—
101C2×#63225C2×C412yes—
102C2×#63225C2×C412yes—
103C2×C4×Dic17C2×C411yescharacteristic
104C2×C4×Dic17C2×C411yescharacteristic
105C2×C4×Dic17C2×C411yescharacteristic
106C4⋊C4×D17C2×C418yes—
107C4⋊C4×D17C2×C418yes—
108C4⋊C4×D17C2×C414yes—
109C4⋊C4×D17C2×C414yes—
110C4⋊C4×D17C2318yes—
111C4⋊C4×D17C2314yes—
112C4⋊C4×D17C2314yes—
113C4⋊C4×D17C2318yes—
114#10587576C2×C418yescomplemented
115#10587576C2×C418yescomplemented
116#10587575C2×C4116yescomplemented
117#10587575C2×C4116yescomplemented
118C42×D17C2×C414yes—
119C42×D17C2314yes—
120#10587556C2×C418yescomplemented
121(C2×#595)⋊C4C2314yes—
122(C2×#595)⋊C4C2314yes—
123(C2×#595)⋊C4C2318yes—
124(C2×#595)⋊C4C2318yes—
125(C2×#595)⋊C4C2318yes—
126(C2×#595)⋊C4C2318yes—
127(C2×#595)⋊C4C2318yes—
128C23×D17C2411yescharacteristic
129C22×#595—22no—
130C22×#595—22no—
131C22×#595—24no—
132C22×#595—22no—
133C22×#595—24no—
134C22×#595—22no—
135C22×#595—22no—
136C22×#595—22no—
137C22×#595—22no—
138C22×#595—24no—
139C22×#595—22no—
140C22×#595—24no—
141C22×#595—24no—
142C22×#595—22no—
143C22×#595—22no—
144C22×#595C2×Q818yes—
145C22×#595#4114yes—
146C22×#595#4114yes—
147C22×#595C2412yes—
148C22×#595C2414yes—
149C22×#595C2412yes—
150C22×#595C2414yes—
151C22×#595C2412yes—
152C22×#595C2412yes—
153C22×C4×C17C22×C411yescharacteristic
154C22×C4×C17C22×C411yescharacteristic
155C22×C4×C17C22×C412yes—
156C22×C4×C17C22×C412yes—
157C22×C4×C17C22×C411yescharacteristic
158C22×Dic17C22×C411yescharacteristic
159C22×Dic17C22×C411yescharacteristic
160C22×Dic17C22×C412yes—
161C22×Dic17C22×C412yes—
162C22×Dic17C22×C411yescharacteristic
163C2×C4×D17—24no—
164C2×C4×D17—22no—
165C2×C4×D17—22no—
166C2×C4×D17—24no—
167C2×C4×D17—22no—
168C2×C4×D17—24no—
169C2×C4×D17—22no—
170C2×C4×D17—24no—
171C2×C4×D17C22×C412yes—
172C2×C4×D17C22×C412yes—
173C2×C4×D17C22×C414yes—
174C2×C4×D17C22×C414yes—
175C2×C4×D17C22×C412yes—
176C2×C4×D17C2×Q814yes—
177C2×C4×D17#4114yes—
178C2×C4×D17C2412yes—
179C2×C4×D17C2414yes—
180C2×C4×D17C2414yes—
181C2×C4×D17C2412yes—
182C2×C4×D17C2412yes—
183C4⋊#595—28no—
184C4⋊#595—28no—
185C4⋊#595—216no—
186C4⋊#595—28no—
187C4⋊#595—48no—
188C4⋊#595C2×Q8116yes—
189C4×#595—216no—
190C4×#595—28no—
191C4×#595—28no—
192C4×#595—48no—
193C4×#595—48no—
194C4⋊C4×C17C22×C418yes—
195C4⋊C4×C17C22×C418yes—
196C4⋊C4×C17C22×C414yes—
197C4⋊C4×C17C22×C414yes—
198C42×C17C22×C414yes—
199C4⋊Dic17C22×C414yes—
200C4⋊Dic17C22×C414yes—
201C4⋊Dic17C22×C418yes—
202C4⋊Dic17C22×C418yes—
203#63225C22×C418yes—
204#63225C22×C418yes—
205#63225C22×C418yes—
206#63225C22×C418yes—
207#63225C22×C418yes—
208#63225C22×C418yes—
209C4×Dic17C22×C414yes—
210C4×Dic17C22×C414yes—
211C4×Dic17C22×C414yes—
212C2×#2370—171nomaximal, Sylow
213C23×C17C23×C411yescharacteristic
214C22×D17C23×C411yescharacteristic
215C22×D17C22×Q812yes—
216C22×D17C2×#4112yes—
217C22×D17C2×#4112yes—
218C22×D17C2×#4112yes—
219C22×D17H(5,𝔽2)12yes—
220C22×D172−1+412yes—
221C22×D17C2511yescharacteristic
222C2×#595—28no—
223C2×#595—28no—
224C2×#595—216no—
225C2×#595—22no—
226C2×#595—22no—
227C2×#595—24no—
228C2×#595—22no—
229C2×#595—24no—
230C2×#595—22no—
231C2×#595—22no—
232C2×#595—22no—
233C2×#595—22no—
234C2×#595—24no—
235C2×#595—22no—
236C2×#595—24no—
237C2×#595—24no—
238C2×#595—22no—
239C2×#595—22no—
240C2×#595—44no—
241C2×#595—44no—
242C2×#595—48no—
243C2×#595C22×Q818yes—
244C2×#595C2×#4114yes—
245C2×#595C2×#4114yes—
246C2×C4×C17—24no—
247C2×C4×C17—22no—
248C2×C4×C17—22no—
249C2×C4×C17—24no—
250C2×C4×C17C4×Q814yes—
251C2×C4×C17C23×C412yes—
252C2×C4×C17C23×C412yes—
253C2×C4×C17C23×C414yes—
254C2×C4×C17C23×C414yes—
255C2×C4×C17C23×C412yes—
256C2×Dic17—24no—
257C2×Dic17—22no—
258C2×Dic17—22no—
259C2×Dic17—24no—
260C2×Dic17C4×Q814yes—
261C2×Dic17C23×C412yes—
262C2×Dic17C23×C412yes—
263C2×Dic17C23×C414yes—
264C2×Dic17C23×C414yes—
265C2×Dic17C23×C412yes—
266C4×D17—28no—
267C4×D17—24no—
268C4×D17—24no—
269C4×D17—28no—
270C4×D17—24no—
271C4×D17—22no—
272C4×D17—24no—
273C4×D17—22no—
274C4×D17—22no—
275C4×D17—24no—
276C4×D17—22no—
277C4×D17—24no—
278C4×D17C4×Q818yes—
279C4×D17C22×Q814yes—
280C4×D17C2×#4114yes—
281C22×#125—171no—
282#2370—1716no—
283C2×#389—171no—
284C2×#389—171no—
285C2×#389—172no—
286C2×#387—172no—
287C2×#387—172no—
288C2×C4×C4⋊C4—171no—
289C2×C4×C4⋊C4—171no—
290C2×C4×C4⋊C4—171no—
291C2×C4×C4⋊C4—171no—
292C2×C4×C4⋊C4—172no—
293C22×C17C2×C4×Q812yes—
294C22×C17C4×#4112yes—
295C22×C17#52012yes—
296C22×C17C24×C411yescharacteristic
297C2×D17C2×C4×Q812yes—
298C2×D17C4×#4112yes—
299C2×D17#52012yes—
300C2×D17#55214yes—
301C2×D17#55314yes—
302C2×D17#55414yes—
303C2×D17#55714yes—
304C2×D17C23×Q811yescharacteristic
305C2×D17C22×#4111yescharacteristic
306C2×D17C22×#4111yescharacteristic
307C2×D17C22×#4111yescharacteristic
308C2×D17C2×H(5,𝔽2)11yescharacteristic
309C2×D17C2×2−1+411yescharacteristic
310#595—24no—
311#595—24no—
312#595—28no—
313#595—42no—
314#595—42no—
315#595—44no—
316C4×C17—24no—
317C4×C17—22no—
318C4×C17—22no—
319C4×C17—24no—
320C4×C17C2×C4×Q814yes—
321Dic17—24no—
322Dic17—22no—
323Dic17—22no—
324Dic17—24no—
325Dic17C2×C4×Q814yes—
326C2×#125—178no—
327C2×#125—178no—
328C2×#125—172no—
329C2×#125—172no—
330C2×#125—171no—
331C2×#125—171no—
332C2×#125—171no—
333C2×#125#59511yescharacteristic, complemented
334C22×C4⋊C4—171no—
335C22×C4⋊C4—172no—
336C22×C4⋊C4—171no—
337C22×C4⋊C4—171no—
338C22×C4⋊C4—172no—
339C22×C4⋊C4—171no—
340C22×C4⋊C4—171no—
341C22×C4⋊C4—171no—
342C22×C4⋊C4—172no—
343C22×C4⋊C4—172no—
344C22×C42—171no—
345C22×C42—172no—
346C22×C42—171no—
347C22×C42—171no—
348C22×C42—172no—
349C22×C42—172no—
350#389—178no—
351#389—1716no—
352#389—178no—
353#387—1716no—
354#387—1716no—
355C4×C4⋊C4—178no—
356C4×C4⋊C4—178no—
357C4×C4⋊C4—1716no—
358C4×C4⋊C4—178no—
359C4×C4⋊C4—178no—
360C2×#95—171no—
361C2×#95—172no—
362C2×#95—171no—
363C2×#95—172no—
364C2×#95—172no—
365C2×#95—172no—
366C2×#95—172no—
367C2×C17#237014yescomplemented
368C2×C17C22×C4×Q811yescharacteristic
369C2×C17C2×C4×#4111yescharacteristic
370C2×C17C2×#52011yescharacteristic
371D17#237014yescomplemented
372D17C2×#55211yescharacteristic
373D17C2×#55311yescharacteristic
374D17C2×#55411yescharacteristic
375D17C2×#55711yescharacteristic
376C23×C4—171no—
377C23×C4—171no—
378C23×C4—172no—
379C23×C4—171no—
380C23×C4—171no—
381C23×C4—172no—
382C23×C4—172no—
383C23×C4—171no—
384C23×C4—171no—
385C23×C4—172no—
386C23×C4—171no—
387#125—1716no—
388#125—1716no—
389#125—178no—
390#125—178no—
391#125—178no—
392#125C2×#59518yescomplemented
393C2×C4⋊C4—178no—
394C2×C4⋊C4—174no—
395C2×C4⋊C4—172no—
396C2×C4⋊C4—172no—
397C2×C4⋊C4—172no—
398C2×C4⋊C4—172no—
399C2×C4⋊C4—172no—
400C2×C4⋊C4—172no—
401C2×C4⋊C4—172no—
402C2×C4⋊C4—172no—
403C2×C4⋊C4—171no—
404C2×C4⋊C4—171no—
405C2×C4⋊C4—178no—
406C2×C4⋊C4—174no—
407C2×C4⋊C4—174no—
408C2×C4⋊C4—178no—
409C2×C4⋊C4—174no—
410C2×C4⋊C4—174no—
411C2×C4⋊C4—178no—
412C2×C4⋊C4—178no—
413C2×C4⋊C4—174no—
414C2×C4⋊C4—174no—
415C2×C4⋊C4—174no—
416C2×C4⋊C4—178no—
417C2×C4⋊C4—178no—
418C2×C4⋊C4—344no—
419C2×C4⋊C4—344no—
420C2×C4⋊C4—344no—
421C2×C4⋊C4—348no—
422C2×C4⋊C4—684no—
423C2×C4⋊C4C2×#59512yes—
424C2×C4⋊C4C2×#59512yes—
425C2×C4⋊C4C2×#59511yescharacteristic
426C2×C4⋊C4C2×#59511yescharacteristic
427C2×C42—171no—
428C2×C42—171no—
429C2×C42—171no—
430C2×C42—174no—
431C2×C42—174no—
432C2×C42—178no—
433C2×C42—174no—
434C2×C42—174no—
435C2×C42—178no—
436C2×C42—178no—
437C2×C42—344no—
438C2×C42—344no—
439C2×C42—348no—
440C2×C42—684no—
441C2×C42—684no—
442C2×C42C2×#59511yescharacteristic
443#95—174no—
444#95—178no—
445#95—174no—
446#95—178no—
447#95—178no—
448#95—178no—
449#95—178no—
450C17C2×#237011yescharacteristic, complemented, Sylow
451C24—171no—
452C22×C4—171no—
453C22×C4—174no—
454C22×C4—174no—
455C22×C4—172no—
456C22×C4—172no—
457C22×C4—178no—
458C22×C4—174no—
459C22×C4—174no—
460C22×C4—172no—
461C22×C4—174no—
462C22×C4—172no—
463C22×C4—171no—
464C22×C4—171no—
465C22×C4—172no—
466C22×C4—172no—
467C22×C4—172no—
468C22×C4—172no—
469C22×C4—174no—
470C22×C4—174no—
471C22×C4—172no—
472C22×C4—172no—
473C22×C4—174no—
474C22×C4—174no—
475C22×C4—172no—
476C22×C4—172no—
477C22×C4—174no—
478C22×C4—344no—
479C22×C4—342no—
480C22×C4—344no—
481C22×C4—344no—
482C22×C4—342no—
483C22×C4—342no—
484C22×C4—344no—
485C22×C4—342no—
486C22×C4—342no—
487C22×C4—342no—
488C22×C4—344no—
489C22×C4—342no—
490C22×C4—344no—
491C22×C4—342no—
492C22×C4—342no—
493C22×C4—342no—
494C22×C4—344no—
495C22×C4—344no—
496C22×C4—342no—
497C22×C4—344no—
498C22×C4—342no—
499C22×C4—342no—
500C22×C4—342no—
501C22×C4C22×#59511yescharacteristic
502C22×C4C22×#59511yescharacteristic
503C22×C4C22×#59512yes—
504C22×C4C22×#59512yes—
505C22×C4C22×#59511yescharacteristic
506C4⋊C4—1716no—
507C4⋊C4—178no—
508C4⋊C4—178no—
509C4⋊C4—178no—
510C4⋊C4—178no—
511C4⋊C4—178no—
512C4⋊C4—178no—
513C4⋊C4—178no—
514C4⋊C4—178no—
515C4⋊C4—174no—
516C4⋊C4—174no—
517C4⋊C4—348no—
518C4⋊C4—348no—
519C4⋊C4—348no—
520C4⋊C4—3416no—
521C4⋊C4—688no—
522C4⋊C4C22×#59518yes—
523C4⋊C4C22×#59518yes—
524C4⋊C4C22×#59514yes—
525C4⋊C4C22×#59514yes—
526C42—174no—
527C42—174no—
528C42—174no—
529C42—348no—
530C42—348no—
531C42—3416no—
532C42—688no—
533C42—688no—
534C42C22×#59514yes—
535C23—172no—
536C23—172no—
537C23—172no—
538C23—172no—
539C23—172no—
540C23—172no—
541C23—171no—
542C23—171no—
543C23C23×#59511yescharacteristic
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—174no—
549C2×C4—172no—
550C2×C4—174no—
551C2×C4—174no—
552C2×C4—178no—
553C2×C4—174no—
554C2×C4—178no—
555C2×C4—174no—
556C2×C4—172no—
557C2×C4—172no—
558C2×C4—174no—
559C2×C4—174no—
560C2×C4—344no—
561C2×C4—342no—
562C2×C4—344no—
563C2×C4—344no—
564C2×C4—342no—
565C2×C4—342no—
566C2×C4—344no—
567C2×C4—348no—
568C2×C4—342no—
569C2×C4—344no—
570C2×C4—344no—
571C2×C4—348no—
572C2×C4—342no—
573C2×C4—342no—
574C2×C4—344no—
575C2×C4—344no—
576C2×C4—342no—
577C2×C4—342no—
578C2×C4—3416no—
579C2×C4—348no—
580C2×C4—348no—
581C2×C4—342no—
582C2×C4—344no—
583C2×C4—342no—
584C2×C4—344no—
585C2×C4—342no—
586C2×C4—342no—
587C2×C4—344no—
588C2×C4—344no—
589C2×C4—342no—
590C2×C4—342no—
591C2×C4—344no—
592C2×C4—342no—
593C2×C4—342no—
594C2×C4—684no—
595C2×C4—688no—
596C2×C4—684no—
597C2×C4Q8×#59514yes—
598C2×C4C23×#59512yes—
599C2×C4C23×#59512yes—
600C2×C4C23×#59514yes—
601C2×C4C23×#59514yes—
602C2×C4C23×#59512yes—
603C22—171no—
604C22—171no—
605C22—172no—
606C22—171no—
607C22—171no—
608C22—172no—
609C22—171no—
610C22—171no—
611C22—172no—
612C22—174no—
613C22—174no—
614C22—174no—
615C22—174no—
616C22C2×Q8×#59512yes—
617C22#41×#59512yes—
618C22#1176387812yes—
619C22C24×#59511yescharacteristic
620C4—24no—
621C4—22no—
622C4—22no—
623C4—24no—
624C4—174no—
625C4—348no—
626C4—344no—
627C4—344no—
628C4—342no—
629C4—344no—
630C4—342no—
631C4—344no—
632C4—682no—
633C4—684no—
634C4—682no—
635C4C2×Q8×#59514yes—
636C2—171no—
637C2—171no—
638C2—171no—
639C2—174no—
640C2—171no—
641C2#1454531814yesdirect product factor
642C2C22×Q8×#59511yescharacteristic
643C2C2×#41×#59511yescharacteristic
644C2C2×#1176387811yescharacteristic
subgroupG/H
centerC23C23×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC2×C17×#125C4
socleC23×C17C23×C4
prime radicalC23×D17C24
cosocleC22×D17C25
hypercenterC2×#125#595
hypocenterC17C2×#2370
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. #14545318C2direct (N × H)
41. C2×#10587556C4semidirect
42. C2×#10587576C4semidirect
43. C2×#10587576C4semidirect
44. C2×#10587575C4semidirect
45. C2×#10587575C4semidirect
46. #125×D17C4semidirect
53. C2×C17×#125C4semidirect
87. C17×#125C2×C4semidirect
114. #10587576C2×C4semidirect
115. #10587576C2×C4semidirect
116. #10587575C2×C4semidirect
117. #10587575C2×C4semidirect
120. #10587556C2×C4semidirect
333. C2×#125#595semidirect
367. C2×C17#2370semidirect
371. D17#2370semidirect
392. #125C2×#595semidirect
450. C17C2×#2370semidirect
641. C2#14545318direct (N × H)

Maximal subgroups

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

subgroupindex
#145453182
C2×#117637602
C2×#117637582
C2×C4⋊C4×#5952
C2×C4×C4⋊#5952
C2×#125×D172
C2×#237017