Finite Group Databasebeta

← C2×#14545706 #17980273

Subgroups — C2×#14545706 #17980273

Order 4352.

2154 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545706C2116yesmaximal, direct product factor
2C2×#11763861C212yesmaximal, complemented
3C2×#11763842C212yesmaximal, complemented
4C2×#11763841C212yesmaximal, complemented
5C2×#11763839C212yesmaximal, complemented
6C2×#11763831C211yesmaximal, characteristic, complemented
7C2×#11763830C211yesmaximal, characteristic, complemented
8C2×#11763828C211yesmaximal, characteristic, complemented
9C2×#11763813C211yesmaximal, characteristic, complemented
10C2×#11763812C211yesmaximal, characteristic, complemented
11C2×#11763810C211yesmaximal, characteristic, complemented
12C2×#11763277C211yesmaximal, characteristic
13C22×#63243C2212yes—
14C22×#63247C2212yes—
15C22×#63242C2212yes—
16#11763861C22116yescomplemented
17#11763842C22116yescomplemented
18#11763841C22116yescomplemented
19#11763839C22116yescomplemented
20#11763831C2218yescomplemented
21#11763830C2218yescomplemented
22#11763828C2218yescomplemented
23#11763813C2218yescomplemented
24#11763812C2218yescomplemented
25C2×#10587544C2212yes—
26C2×#10587544C2212yes—
27#11763810C2218yescomplemented
28C2×C4⋊#3624C2211yescharacteristic
29C2×C4⋊#3624C2211yescharacteristic
30C2×C4⋊#3624C2211yescharacteristic
31C2×C4⋊#3624C2212yes—
32C2×C4⋊#3624C2211yescharacteristic
33C2×#10587543C2212yes—
34C2×#10587543C2212yes—
35C2×C22⋊#3624C2212yes—
36C2×#10587542C2212yes—
37C2×#10587542C2212yes—
38C2×C4×#3624C2212yes—
39C22×#63252C411yescharacteristic
40#11763277C418yes—
41#11763277C2218yes—
42C2×#10587573C411yescharacteristic
43C2×#10587573C2211yescharacteristic
44C2×#10587579C411yescharacteristic
45C2×#10587579C2211yescharacteristic
46C2×#10587567C411yescharacteristic
47C2×#10587567C411yescharacteristic
48C2×#10587567C2211yescharacteristic
49C2×#10587567C2211yescharacteristic
50C2×#10587558C411yescharacteristic
51C2×#10587558C411yescharacteristic
52C22×C4×Dic17C2211yescharacteristic
53C2×C42×D17C2211yescharacteristic
54C2×C42×D17C2211yescharacteristic
55C2×C17×#117C411yescharacteristic
56C23×C4×C17C2×C411yescharacteristic
57C22×C22⋊D17C2×C411yescharacteristic
58C22×C22⋊D17C2×C411yescharacteristic
59C23×Dic17C2×C411yescharacteristic
60C23×Dic17C2311yescharacteristic
61C2×#63252—28no—
62C2×#63252C2×C418yes—
63C22×D68C2×C411yescharacteristic
64C22×C4×D17C2×C411yescharacteristic
65C22×C4×D17C2×C411yescharacteristic
66C22×C4×D17C2×C411yescharacteristic
67C22×C4×D17C2×C411yescharacteristic
68C22×C4×D17C2311yescharacteristic
69C22×C4×D17C2311yescharacteristic
70C22×Dic34C2×C411yescharacteristic
71C2×#63247—44no—
72C2×#63247C2318yes—
73C22×#3624C2312yes—
74C22×#3624C2312yes—
75C22×#3624C2312yes—
76C22×#3624C2312yes—
77C2×#63243—44no—
78C2×#63243C2318yes—
79C2×#63242—44no—
80C2×#63242C2318yes—
81C17×#117C2×C418yes—
82C2×C4⋊C4×C17C2×C411yescharacteristic
83C2×C4⋊C4×C17C2×C411yescharacteristic
84C2×C22⋊C4×C17C2×C411yescharacteristic
85C2×C22⋊C4×C17C2×C411yescharacteristic
86C2×C42×C17C2×C411yescharacteristic
87C2×C42×C17C2×C411yescharacteristic
88C2×#63227C2×C411yescharacteristic
89C2×#63227C2×C411yescharacteristic
90C2×#63227C2×C411yescharacteristic
91C2×#63227C2×C411yescharacteristic
92C2×#63225C2×C411yescharacteristic
93C2×#63225C2×C411yescharacteristic
94C2×#63225C2×C411yescharacteristic
95C2×#63225C2×C411yescharacteristic
96C2×C4×Dic17C2×C411yescharacteristic
97C2×C4×Dic17C2×C411yescharacteristic
98C2×C4×Dic17C2×C411yescharacteristic
99C2×C4×Dic17C2×C411yescharacteristic
100C2×C4×Dic17C2×C414yes—
101C2×C4×Dic17C2311yescharacteristic
102C2×C4×Dic17C2311yescharacteristic
103C2×C4×Dic17C2311yescharacteristic
104C2×C4×Dic17C2311yescharacteristic
105C2×C4×Dic17C2314yes—
106#10587579C2×C418yes—
107#10587579C2×C414yes—
108#10587579C2314yes—
109#10587573C2×C418yes—
110#10587573C2×C414yes—
111#10587573C2314yes—
112#10587567C2×C418yes—
113#10587567C2×C418yes—
114#10587567C2×C414yes—
115#10587567C2×C414yes—
116#10587567C2314yes—
117#10587567C2314yes—
118#10587558C2×C418yes—
119#10587558C2×C418yes—
120C42×D17C2×C414yes—
121C42×D17C2×C414yes—
122C42×D17C2314yes—
123C42×D17C2314yes—
124C22⋊#3624C2318yes—
125#10587544C2318yes—
126#10587544C2318yes—
127#10587543C2318yes—
128#10587543C2318yes—
129#10587542C2318yes—
130#10587542C2318yes—
131C4⋊#3624C2314yes—
132C4⋊#3624C2314yes—
133C4⋊#3624C2314yes—
134C4⋊#3624C2318yes—
135C4⋊#3624C2314yes—
136C4×#3624C2318yes—
137C24×C17C22×C411yescharacteristic
138C23×D17C22×C411yescharacteristic
139C23×D17C22×C411yescharacteristic
140C22×C4×C17—24no—
141C22×C4×C17C22×C411yescharacteristic
142C22×C4×C17C22×C411yescharacteristic
143C22×C4×C17C22×C411yescharacteristic
144C22×C4×C17C22×C411yescharacteristic
145C22×C4×C17C22×C411yescharacteristic
146C22×C4×C17C22×C414yes—
147C22×C4×C17C22×C411yescharacteristic
148C2×C22⋊D17—24no—
149C2×C22⋊D17—24no—
150C2×C22⋊D17C22×C414yes—
151C2×C22⋊D17C22×C414yes—
152C22×Dic17—22no—
153C22×Dic17—22no—
154C22×Dic17—42no—
155C22×Dic17C22×C411yescharacteristic
156C22×Dic17C22×C411yescharacteristic
157C22×Dic17C22×C411yescharacteristic
158C22×Dic17C22×C412yes—
159C22×Dic17C22×C411yescharacteristic
160C22×Dic17C22×C414yes—
161C22×Dic17C22×C411yescharacteristic
162C22×Dic17C2412yes—
163C22×Dic17C2411yescharacteristic
164#63252—232no—
165C2×D68—24no—
166C2×D68C22×C414yes—
167C2×C4×D17—24no—
168C2×C4×D17—22no—
169C2×C4×D17—22no—
170C2×C4×D17—22no—
171C2×C4×D17—22no—
172C2×C4×D17—42no—
173C2×C4×D17—42no—
174C2×C4×D17M1618yescomplemented
175C2×C4×D17C22×C414yes—
176C2×C4×D17C22×C412yes—
177C2×C4×D17C22×C412yes—
178C2×C4×D17C22×C414yes—
179C2×C4×D17C22×C414yes—
180C2×C4×D17C22×C414yes—
181C2×C4×D17C2412yes—
182C2×C4×D17C2412yes—
183C2×Dic34—24no—
184C2×Dic34C22×C414yes—
185#63247—48no—
186C2×#3624—24no—
187C2×#3624—24no—
188C2×#3624—24no—
189C2×#3624—24no—
190C2×#3624C2414yes—
191C2×#3624C2414yes—
192C2×#3624C2414yes—
193C2×#3624C2414yes—
194#63243—48no—
195#63242—48no—
196C4⋊C4×C17C22×C414yes—
197C4⋊C4×C17C22×C414yes—
198C22⋊C4×C17C22×C414yes—
199C22⋊C4×C17C22×C414yes—
200C42×C17C22×C414yes—
201C42×C17C22×C414yes—
202#63227C22×C414yes—
203#63227C22×C414yes—
204#63227C22×C414yes—
205#63227C22×C414yes—
206#63225C22×C414yes—
207#63225C22×C414yes—
208#63225C22×C414yes—
209#63225C22×C414yes—
210C4×Dic17C22×C412yes—
211C4×Dic17C22×C412yes—
212C4×Dic17C22×C412yes—
213C4×Dic17C22×C414yes—
214C4×Dic17C22×C414yes—
215C4×Dic17C22×C414yes—
216C4×Dic17C22×C414yes—
217C4×Dic17C22×C412yes—
218C4×Dic17C2412yes—
219C4×Dic17C2412yes—
220C4×Dic17C2412yes—
221C4×Dic17C2412yes—
222C2×#2989—171nomaximal, Sylow
223C23×C17—22no—
224C23×C17—22no—
225C23×C17—22no—
226C23×C17C23×C412yes—
227C23×C17C23×C411yescharacteristic
228C22×D17—22no—
229C22×D17—22no—
230C22×D17—22no—
231C22×D17—22no—
232C22×D17—22no—
233C22×D17C2×M1614yes—
234C22×D17C23×C412yes—
235C22×D17C23×C412yes—
236C2×C4×C17—22no—
237C2×C4×C17—22no—
238C2×C4×C17—22no—
239C2×C4×C17—22no—
240C2×C4×C17—22no—
241C2×C4×C17—28no—
242C2×C4×C17C2×M1614yes—
243C2×C4×C17C23×C412yes—
244C2×C4×C17C23×C412yes—
245C2×C4×C17C23×C412yes—
246C2×C4×C17C23×C412yes—
247C2×C4×C17C23×C412yes—
248C2×C4×C17C23×C412yes—
249C22⋊D17—28no—
250C22⋊D17—28no—
251C2×Dic17—22no—
252C2×Dic17—22no—
253C2×Dic17—22no—
254C2×Dic17—22no—
255C2×Dic17—24no—
256C2×Dic17—22no—
257C2×Dic17—22no—
258C2×Dic17—44no—
259C2×Dic17C2×M1614yes—
260C2×Dic17C23×C412yes—
261C2×Dic17C23×C412yes—
262C2×Dic17C23×C412yes—
263C2×Dic17C23×C412yes—
264C2×Dic17C23×C411yescharacteristic
265C2×Dic17C23×C412yes—
266C2×Dic17H(5,𝔽2)12yes—
267C2×Dic172−1+412yes—
268C2×Dic17C2511yescharacteristic
269D68—28no—
270C4×D17—28no—
271C4×D17—24no—
272C4×D17—24no—
273C4×D17—22no—
274C4×D17—22no—
275C4×D17—22no—
276C4×D17—22no—
277C4×D17—44no—
278C4×D17—44no—
279C4×D17C2×M16116yescomplemented
280Dic34—28no—
281#3624—24no—
282#3624—24no—
283#3624—24no—
284#3624—24no—
285C2×C4×#41—171no—
286#2989—1716no—
287C2×#446—172no—
288C2×#436—172no—
289C2×#435—172no—
290C2×#435—172no—
291C2×#432—171no—
292C2×#432—171no—
293C2×#431—171no—
294C2×#423—171no—
295C2×#423—171no—
296C22×C4⋊C8—171no—
297C22×C17—22no—
298C22×C17—22no—
299C22×C17—22no—
300C22×C17—44no—
301C22×C17#52012yes—
302C22×C17C22×M1612yes—
303C22×C17#56812yes—
304C22×C17C24×C411yescharacteristic
305C2×D17—22no—
306C2×D17—28no—
307C2×D17—22no—
308C2×D17—22no—
309C2×D17—22no—
310C2×D17—22no—
311C2×D17—44no—
312C2×D17C22×M1614yes—
313C4×C17—22no—
314C4×C17—22no—
315C4×C17—22no—
316C4×C17—22no—
317C4×C17—22no—
318C4×C17C22×M1614yes—
319Dic17—22no—
320Dic17—22no—
321Dic17—22no—
322Dic17—22no—
323Dic17#52012yes—
324Dic17C22×M1614yes—
325Dic17C2×H(5,𝔽2)11yescharacteristic
326Dic17C2×2−1+411yescharacteristic
327C22×#41—171no—
328C22×M16—172no—
329C22×M16—172no—
330C23×C8—172no—
331C4×#41—178no—
332C4×#41—178no—
333C2×C4×Q8—171no—
334C2×C4×Q8—171no—
335C2×C4×D4—171no—
336C2×C4×D4—171no—
337C2×C4×D4—171no—
338C2×C4×D4—171no—
339C2×C4×D4—171no—
340C2×C4×D4—171no—
341C2×#117—171no—
342C2×#117—171no—
343C2×#117#59511yescharacteristic
344C22×C42—171no—
345C22×C42—171no—
346C22×C42—171no—
347#446—1716no—
348#436—1716no—
349#435—1716no—
350#435—1716no—
351#432—178no—
352#432—178no—
353#431—178no—
354#423—178no—
355#423—178no—
356C2×C4⋊C8—171no—
357C2×C4⋊C8—171no—
358C2×C4⋊C8—178no—
359C2×C4⋊C8—172no—
360C2×C4⋊C8—171no—
361C2×C4⋊C8—172no—
362C2×C4⋊C8—172no—
363C2×C4⋊C8—171no—
364C2×C22⋊C8—172no—
365C2×C22⋊C8—172no—
366C2×C22⋊C8—172no—
367C2×#97—172no—
368C2×#97—172no—
369C2×C4×C8—172no—
370C2×C17—42no—
371C2×C17#298914yescomplemented
372C2×C17C2×#52011yescharacteristic
373C2×C17C23×M1611yescharacteristic
374C2×C17C2×#56811yescharacteristic
375D17—24no—
376D17—42no—
377C2×#41—178no—
378C2×#41—348no—
379C22×Q8—171no—
380C22×D4—171no—
381C22×D4—171no—
382C22×D4—171no—
383C23×C4—171no—
384C23×C4—171no—
385C23×C4—171no—
386C23×C4—171no—
387C23×C4—171no—
388C23×C4—171no—
389C23×C4—171no—
390C23×C4—171no—
391C23×C4C2×#59511yescharacteristic
392C2×M16—178no—
393C2×M16—178no—
394C2×M16—684no—
395C2×M16—684no—
396C22×C8—172no—
397C22×C8—172no—
398C22×C8—172no—
399C22×C8—172no—
400C22×C8—178no—
401C22×C8—684no—
402C4×Q8—178no—
403C4×Q8—174no—
404C4×Q8—174no—
405C4×D4—174no—
406C4×D4—174no—
407C4×D4—178no—
408C4×D4—174no—
409C4×D4—174no—
410C4×D4—178no—
411C4×D4—178no—
412C4×D4—174no—
413C4×D4—174no—
414#117—178no—
415#117—178no—
416#117C2×#59518yes—
417C2×C4⋊C4—171no—
418C2×C4⋊C4—171no—
419C2×C4⋊C4—171no—
420C2×C4⋊C4—171no—
421C2×C4⋊C4C2×#59511yescharacteristic
422C2×C4⋊C4C2×#59511yescharacteristic
423C2×C22⋊C4—171no—
424C2×C22⋊C4—171no—
425C2×C22⋊C4—171no—
426C2×C22⋊C4—171no—
427C2×C22⋊C4C2×#59511yescharacteristic
428C2×C22⋊C4C2×#59511yescharacteristic
429C2×C42—171no—
430C2×C42—171no—
431C2×C42—171no—
432C2×C42—171no—
433C2×C42—171no—
434C2×C42—171no—
435C2×C42—171no—
436C2×C42—174no—
437C2×C42—174no—
438C2×C42—171no—
439C2×C42—174no—
440C2×C42—174no—
441C2×C42—174no—
442C2×C42—174no—
443C2×C42C2×#59511yescharacteristic
444C2×C42C2×#59511yescharacteristic
445C4⋊C8—174no—
446C4⋊C8—174no—
447C4⋊C8—174no—
448C4⋊C8—178no—
449C4⋊C8—174no—
450C4⋊C8—178no—
451C4⋊C8—178no—
452C22⋊C8—178no—
453C22⋊C8—178no—
454C22⋊C8—178no—
455#97—178no—
456#97—178no—
457C4×C8—178no—
458C17C2×#298911yescharacteristic, complemented, Sylow
459C24—171no—
460C24—171no—
461C24C22×#59511yescharacteristic
462#41—3432no—
463C2×Q8—174no—
464C2×Q8—344no—
465C2×D4—174no—
466C2×D4—174no—
467C2×D4—174no—
468C2×D4—344no—
469C2×D4—344no—
470C2×D4—344no—
471C22×C4—24no—
472C22×C4—171no—
473C22×C4—171no—
474C22×C4—178no—
475C22×C4—174no—
476C22×C4—172no—
477C22×C4—172no—
478C22×C4—171no—
479C22×C4—171no—
480C22×C4—171no—
481C22×C4—171no—
482C22×C4—174no—
483C22×C4—174no—
484C22×C4—172no—
485C22×C4—172no—
486C22×C4—172no—
487C22×C4—172no—
488C22×C4—174no—
489C22×C4—174no—
490C22×C4—342no—
491C22×C4—342no—
492C22×C4—342no—
493C22×C4—342no—
494C22×C4—342no—
495C22×C4—342no—
496C22×C4—344no—
497C22×C4—682no—
498C22×C4—682no—
499C22×C4—682no—
500C22×C4C22×#59514yes—
501C22×C4C22×#59511yescharacteristic
502C22×C4C22×#59511yescharacteristic
503C22×C4C22×#59511yescharacteristic
504C22×C4C22×#59511yescharacteristic
505C22×C4C22×#59511yescharacteristic
506C22×C4C22×#59511yescharacteristic
507M16—688no—
508M16—688no—
509C2×C8—174no—
510C2×C8—174no—
511C2×C8—174no—
512C2×C8—174no—
513C2×C8—344no—
514C2×C8—344no—
515C2×C8—344no—
516C2×C8—344no—
517C2×C8—688no—
518C4⋊C4—174no—
519C4⋊C4—174no—
520C4⋊C4—174no—
521C4⋊C4—174no—
522C4⋊C4C22×#59514yes—
523C4⋊C4C22×#59514yes—
524C22⋊C4—174no—
525C22⋊C4—174no—
526C22⋊C4—174no—
527C22⋊C4—174no—
528C22⋊C4C22×#59514yes—
529C22⋊C4C22×#59514yes—
530C42—172no—
531C42—172no—
532C42—172no—
533C42—172no—
534C42—172no—
535C42—174no—
536C42—172no—
537C42—172no—
538C42—172no—
539C42—174no—
540C42—174no—
541C42—174no—
542C42C22×#59514yes—
543C42C22×#59514yes—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—174no—
548C23—172no—
549C23—172no—
550C23—342no—
551C23—342no—
552C23—342no—
553C23—342no—
554C23—342no—
555C23C23×#59512yes—
556C23C23×#59511yescharacteristic
557Q8—348no—
558D4—348no—
559D4—348no—
560D4—348no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—28no—
567C2×C4—172no—
568C2×C4—172no—
569C2×C4—174no—
570C2×C4—171no—
571C2×C4—171no—
572C2×C4—172no—
573C2×C4—1716no—
574C2×C4—172no—
575C2×C4—172no—
576C2×C4—172no—
577C2×C4—172no—
578C2×C4—342no—
579C2×C4—342no—
580C2×C4—342no—
581C2×C4—342no—
582C2×C4—344no—
583C2×C4—344no—
584C2×C4—342no—
585C2×C4—342no—
586C2×C4—344no—
587C2×C4—342no—
588C2×C4—342no—
589C2×C4—342no—
590C2×C4—342no—
591C2×C4—348no—
592C2×C4—684no—
593C2×C4—684no—
594C2×C4—684no—
595C2×C4D17⋊M1614yes—
596C2×C4C23×#59512yes—
597C2×C4C23×#59512yes—
598C2×C4C23×#59512yes—
599C2×C4C23×#59512yes—
600C2×C4C23×#59512yes—
601C2×C4C23×#59512yes—
602C8—344no—
603C8—344no—
604C8—344no—
605C8—344no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—44no—
610C22—174no—
611C22—348no—
612C22—342no—
613C22—342no—
614C22—342no—
615C22—342no—
616C22—342no—
617C22—684no—
618C22#1176387812yes—
619C22C2×D17⋊M1612yes—
620C22#1176388812yes—
621C22C24×#59511yescharacteristic
622C4—22no—
623C4—22no—
624C4—22no—
625C4—22no—
626C4—22no—
627C4—171no—
628C4—171no—
629C4—172no—
630C4—174no—
631C4—342no—
632C4—342no—
633C4—342no—
634C4—342no—
635C4C2×D17⋊M1614yes—
636C2—42no—
637C2—344no—
638C2—682no—
639C2#1454570614yesdirect product factor
640C2C2×#1176387811yescharacteristic
641C2C22×D17⋊M1611yescharacteristic
642C2C2×#1176388811yescharacteristic
subgroupG/H
centerC23C23×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC2×C17×#117C4
socleC23×C17C23×C4
prime radicalC22×#63252C4
cosocleC2×Dic17C25
hypercenterC2×#117#595
hypocenterC17C2×#2989
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #14545706C2direct (N × H)
2. C2×#11763861C2semidirect
3. C2×#11763842C2semidirect
4. C2×#11763841C2semidirect
5. C2×#11763839C2semidirect
6. C2×#11763831C2semidirect
7. C2×#11763830C2semidirect
8. C2×#11763828C2semidirect
9. C2×#11763813C2semidirect
10. C2×#11763812C2semidirect
11. C2×#11763810C2semidirect
16. #11763861C22semidirect
17. #11763842C22semidirect
18. #11763841C22semidirect
19. #11763839C22semidirect
20. #11763831C22semidirect
21. #11763830C22semidirect
22. #11763828C22semidirect
23. #11763813C22semidirect
24. #11763812C22semidirect
27. #11763810C22semidirect
174. C2×C4×D17M16semidirect
279. C4×D17C2×M16semidirect
371. C2×C17#2989semidirect
458. C17C2×#2989semidirect
639. C2#14545706direct (N × H)

Maximal subgroups

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

subgroupindex
#145457062
C2×#117638612
C2×#117638422
C2×#117638412
C2×#117638392
C2×#117638312
C2×#117638302
C2×#117638282
C2×#117638132
C2×#117638122
C2×#117638102
C2×#117632772
C2×#298917