Finite Group Databasebeta

← C2×#14544033 #17964252

Subgroups — C2×#14544033 #17964252

Order 4352.

1718 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763780C212yesmaximal
2#14544033C218yesmaximal, direct product factor
3C2×#11763655C212yesmaximal, complemented
4C2×#11763654C212yesmaximal, complemented
5C22×C4⋊C4×D17C211yesmaximal, characteristic
6C22×#63243—22no—
7#11763780—24no—
8#11763780C2218yes—
9C2×#10587543—22no—
10C2×C22⋊#3624C2214yes—
11#11763655C2218yescomplemented
12#11763654C2218yescomplemented
13C23×C4×D17C411yescharacteristic
14C23×C4×D17C411yescharacteristic
15C23×C4×D17C2211yescharacteristic
16C22×C4⋊Dic17C2211yescharacteristic
17C22×#63225C411yescharacteristic
18C22×#63225C2211yescharacteristic
19C2×C4⋊C4×D17—22no—
20C2×C4⋊C4×D17—22no—
21C2×C4⋊C4×D17—24no—
22C2×C4⋊C4×D17C414yes—
23C2×C4⋊C4×D17C2214yes—
24C22×C4⋊C4×C17C411yescharacteristic
25C24×D17C2×C411yescharacteristic
26C23×C4×C17C2×C411yescharacteristic
27C23×C4×C17C2×C411yescharacteristic
28C23×C4×C17C2×C411yescharacteristic
29C23×Dic17C2×C411yescharacteristic
30C23×Dic17C2×C411yescharacteristic
31C23×Dic17C2311yescharacteristic
32C22×C4×D17—22no—
33C22×C4×D17—21no—
34C22×C4×D17—21no—
35C22×C4×D17—24no—
36C22×C4×D17—24no—
37C22×C4×D17—22no—
38C22×C4×D17—21no—
39C22×C4×D17—21no—
40C22×C4×D17—44no—
41C22×C4×D17—44no—
42C22×C4×D17C2×C414yes—
43C22×C4×D17C2×C414yes—
44C22×C4×D17C2×C412yes—
45C22×C4×D17D412yes—
46C22×C4×D17D412yes—
47C22×C4×D17D414yes—
48C22×C4×D17C2312yes—
49C22×#3624—24no—
50C2×#63243—28no—
51C2×#63243—48no—
52C2×C4⋊C4×C17—22no—
53C2×C4⋊C4×C17—22no—
54C2×C4⋊C4×C17C2×C414yes—
55C2×C4⋊Dic17—22no—
56C2×C4⋊Dic17—22no—
57C2×C4⋊Dic17C2×C412yes—
58C2×C4⋊Dic17C2312yes—
59C2×#63225—22no—
60C2×#63225—22no—
61C2×#63225—22no—
62C2×#63225—22no—
63C2×#63225C2×C412yes—
64C2×#63225C2×C414yes—
65C2×#63225C2312yes—
66C4⋊C4×D17—28no—
67C4⋊C4×D17—28no—
68C4⋊C4×D17—28no—
69C4⋊C4×D17—28no—
70C22⋊#3624—24no—
71C22⋊#3624C2318yes—
72#10587543—28no—
73C24×C17C22×C411yescharacteristic
74C23×D17—22no—
75C23×D17—22no—
76C23×D17—24no—
77C23×D17—24no—
78C23×D17C22⋊C412yes—
79C23×D17C22⋊C411yescharacteristic
80C23×D17C22⋊C411yescharacteristic
81C23×D17C22×C412yes—
82C22×C4×C17—21no—
83C22×C4×C17—21no—
84C22×C4×C17—22no—
85C22×C4×C17—21no—
86C22×C4×C17—21no—
87C22×C4×C17—42no—
88C22×C4×C17—42no—
89C22×C4×C17C22⋊C412yes—
90C22×C4×C17C22⋊C412yes—
91C22×C4×C17M1614yescomplemented
92C22×C4×C17C22×C412yes—
93C22×C4×C17C22×C412yes—
94C22×C4×C17C22×C412yes—
95C22×Dic17—21no—
96C22×Dic17—21no—
97C22×Dic17—22no—
98C22×Dic17—21no—
99C22×Dic17—21no—
100C22×Dic17—42no—
101C22×Dic17—42no—
102C22×Dic17M1614yescomplemented
103C22×Dic17C22×C412yes—
104C22×Dic17C22×C412yes—
105C22×Dic17C22×C411yescharacteristic
106C22×Dic17C2×D412yes—
107C22×Dic17C2×D412yes—
108C22×Dic17C2411yescharacteristic
109C2×C4×D17—216no—
110C2×C4×D17—28no—
111C2×C4×D17—28no—
112C2×C4×D17—28no—
113C2×C4×D17—24no—
114C2×C4×D17—24no—
115C2×C4×D17—28no—
116C2×C4×D17—28no—
117C2×C4×D17—24no—
118C2×C4×D17—24no—
119C2×C4×D17—44no—
120C2×C4×D17—48no—
121C2×C4×D17—44no—
122C2×C4×D17—44no—
123C2×C4×D17—44no—
124C2×C4×D17—48no—
125C2×C4×D17—44no—
126C2×C4×D17—48no—
127C2×C4×D17C22⋊C414yes—
128C2×C4×D17C22⋊C414yes—
129C2×C4×D17C2×D414yes—
130C2×C4×D17C2×D414yes—
131C2×#3624—28no—
132C2×#3624—48no—
133#63243—416no—
134C4⋊C4×C17—28no—
135C4⋊Dic17—24no—
136C4⋊Dic17—24no—
137#63225—28no—
138#63225—24no—
139#63225—24no—
140C2×#1463—171nomaximal, Sylow
141C23×C17—22no—
142C23×C17—22no—
143C23×C17C2×C22⋊C411yescharacteristic
144C23×C17C2×C22⋊C411yescharacteristic
145C23×C17C2×M1612yes—
146C23×C17C2×M1612yes—
147C23×C17C23×C411yescharacteristic
148C22×D17—216no—
149C22×D17—216no—
150C22×D17—22no—
151C22×D17—22no—
152C22×D17—24no—
153C22×D17—22no—
154C22×D17—22no—
155C22×D17—22no—
156C22×D17—22no—
157C22×D17—24no—
158C22×D17—24no—
159C22×D17—24no—
160C22×D17—24no—
161C22×D17#9914yes—
162C22×D17#10114yes—
163C22×D17C2×C22⋊C412yes—
164C22×D17C2×C22⋊C412yes—
165C2×C4×C17—22no—
166C2×C4×C17—22no—
167C2×C4×C17—24no—
168C2×C4×C17—24no—
169C2×C4×C17—24no—
170C2×C4×C17—22no—
171C2×C4×C17—42no—
172C2×C4×C17—42no—
173C2×C4×C17—42no—
174C2×C4×C17—42no—
175C2×C4×C17—42no—
176C2×C4×C17C2×C22⋊C414yes—
177C2×C4×C17C2×M1614yescomplemented
178C2×Dic17—22no—
179C2×Dic17—22no—
180C2×Dic17—24no—
181C2×Dic17—24no—
182C2×Dic17—24no—
183C2×Dic17—22no—
184C2×Dic17—41no—
185C2×Dic17—42no—
186C2×Dic17—41no—
187C2×Dic17—42no—
188C2×Dic17—42no—
189C2×Dic17—42no—
190C2×Dic17C2×C22⋊C412yes—
191C2×Dic17C2×M1614yescomplemented
192C2×Dic17C22×D412yes—
193C4×D17—216no—
194C4×D17—216no—
195C4×D17—28no—
196C4×D17—28no—
197C4×D17—44no—
198C4×D17—44no—
199C4×D17—48no—
200C4×D17—48no—
201#3624—48no—
202C23×C4⋊C4—171no—
203C2×#407—172no—
204#1463—178no—
205C2×#324—172no—
206C2×#324—172no—
207C22×C17—21no—
208C22×C17—21no—
209C22×C17—21no—
210C22×C17—21no—
211C22×C17—24no—
212C22×C17—24no—
213C22×C17#40712yes—
214C22×C17#40712yes—
215C22×C17C2×#9912yes—
216C22×C17C2×#10112yes—
217C22×C17C22×C22⋊C411yescharacteristic
218C22×C17C22×M1611yescharacteristic
219C22×C17C22×M1611yescharacteristic
220C2×D17—28no—
221C2×D17—28no—
222C2×D17—216no—
223C2×D17—22no—
224C2×D17—22no—
225C2×D17—22no—
226C2×D17—22no—
227C2×D17—28no—
228C2×D17—28no—
229C2×D17C2×#9914yes—
230C2×D17C2×#10114yes—
231C4×C17—24no—
232C4×C17—24no—
233C4×C17—42no—
234Dic17—24no—
235Dic17—22no—
236Dic17—22no—
237Dic17—42no—
238C24×C4—171no—
239C24×C4—171no—
240C24×C4—171no—
241C22×M16—342no—
242C22×C4⋊C4—171no—
243C22×C4⋊C4—171no—
244C22×C4⋊C4—171no—
245C22×C4⋊C4—174no—
246C22×C4⋊C4—174no—
247C22×C4⋊C4—342no—
248C22×C4⋊C4—342no—
249C22×C4⋊C4—344no—
250C22×C4⋊C4#59511yescharacteristic
251#407—178no—
252#407—344no—
253C2×C22⋊C8—174no—
254C2×C22⋊C8—342no—
255#324—178no—
256#324—178no—
257C2×C17—21no—
258C2×C17—21no—
259C2×C17—22no—
260C2×C17#146314yescomplemented
261C2×C17C2×#40711yescharacteristic
262C2×C17C22×#9911yescharacteristic
263C2×C17C22×#10111yescharacteristic
264D17—24no—
265D17—24no—
266C25—171no—
267C23×C4—171no—
268C23×C4—171no—
269C23×C4—172no—
270C23×C4—172no—
271C23×C4—174no—
272C23×C4—172no—
273C23×C4—172no—
274C23×C4—171no—
275C23×C4—174no—
276C23×C4—174no—
277C23×C4—344no—
278C23×C4—342no—
279C23×C4—341no—
280C23×C4—341no—
281C23×C4—342no—
282C23×C4—341no—
283C23×C4—341no—
284C23×C4—344no—
285C23×C4—684no—
286C23×C4—684no—
287C23×C4C2×#59511yescharacteristic
288C23×C4C2×#59511yescharacteristic
289C23×C4C2×#59511yescharacteristic
290C2×M16—348no—
291C2×M16—688no—
292C22×C8—344no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—172no—
296C2×C4⋊C4—172no—
297C2×C4⋊C4—172no—
298C2×C4⋊C4—174no—
299C2×C4⋊C4—172no—
300C2×C4⋊C4—348no—
301C2×C4⋊C4—348no—
302C2×C4⋊C4—348no—
303C2×C4⋊C4—348no—
304C2×C4⋊C4—342no—
305C2×C4⋊C4—342no—
306C2×C4⋊C4—342no—
307C2×C4⋊C4—342no—
308C2×C4⋊C4—342no—
309C2×C4⋊C4—342no—
310C2×C4⋊C4C2×#59514yes—
311C22⋊C8—178no—
312C22⋊C8—344no—
313C22⋊C8—348no—
314C17C2×#146311yescharacteristic, complemented, Sylow
315C24—171no—
316C24—171no—
317C24—172no—
318C24—172no—
319C24—344no—
320C24—344no—
321C24—342no—
322C24—342no—
323C24C22×#59511yescharacteristic
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4—174no—
332C22×C4—172no—
333C22×C4—172no—
334C22×C4—172no—
335C22×C4—171no—
336C22×C4—171no—
337C22×C4—174no—
338C22×C4—174no—
339C22×C4—174no—
340C22×C4—174no—
341C22×C4—172no—
342C22×C4—348no—
343C22×C4—344no—
344C22×C4—344no—
345C22×C4—348no—
346C22×C4—3416no—
347C22×C4—348no—
348C22×C4—348no—
349C22×C4—344no—
350C22×C4—344no—
351C22×C4—342no—
352C22×C4—341no—
353C22×C4—341no—
354C22×C4—348no—
355C22×C4—341no—
356C22×C4—341no—
357C22×C4—684no—
358C22×C4—688no—
359C22×C4—684no—
360C22×C4—684no—
361C22×C4—684no—
362C22×C4—688no—
363C22×C4—684no—
364C22×C4—688no—
365C22×C4—682no—
366C22×C4—682no—
367C22×C4#6324314yescomplemented
368C22×C4C22⋊#59512yes—
369C22×C4C22⋊#59512yes—
370C22×C4C22×#59512yes—
371C22×C4C22×#59512yes—
372C22×C4C22×#59512yes—
373M16—6816no—
374C2×C8—348no—
375C2×C8—688no—
376C4⋊C4—28no—
377C4⋊C4—344no—
378C4⋊C4—344no—
379C4⋊C4—344no—
380C4⋊C4—344no—
381C4⋊C4—348no—
382C23—22no—
383C23—22no—
384C23—174no—
385C23—174no—
386C23—172no—
387C23—172no—
388C23—344no—
389C23—344no—
390C23—344no—
391C23—344no—
392C23—3416no—
393C23—3416no—
394C23—344no—
395C23—342no—
396C23—342no—
397C23—342no—
398C23—342no—
399C23—342no—
400C23—342no—
401C23C2×#6324312yes—
402C23D17⋊M1612yes—
403C23C2×C22⋊#59511yescharacteristic
404C23C2×C22⋊#59511yescharacteristic
405C23C23×#59511yescharacteristic
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—172no—
418C2×C4—172no—
419C2×C4—174no—
420C2×C4—348no—
421C2×C4—348no—
422C2×C4—3416no—
423C2×C4—3416no—
424C2×C4—344no—
425C2×C4—344no—
426C2×C4—344no—
427C2×C4—342no—
428C2×C4—342no—
429C2×C4—342no—
430C2×C4—684no—
431C2×C4—684no—
432C2×C4—688no—
433C2×C4—688no—
434C2×C4—681no—
435C2×C4—682no—
436C2×C4—681no—
437C2×C4—682no—
438C2×C4—682no—
439C2×C4—682no—
440C2×C4C2×#6324314yescomplemented
441C2×C4C2×C22⋊#59514yes—
442C8—688no—
443C22—24no—
444C22—24no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—174no—
450C22—174no—
451C22—3416no—
452C22—348no—
453C22—348no—
454C22—348no—
455C22—348no—
456C22—342no—
457C22—342no—
458C22—342no—
459C22—342no—
460C22#1176378012yes—
461C22#1176378012yes—
462C22D17⋊#9912yes—
463C22D17⋊#10112yes—
464C22C22×C22⋊#59511yescharacteristic
465C22C2×D17⋊M1611yescharacteristic
466C22C22×#6324311yescharacteristic
467C4—24no—
468C4—24no—
469C4—42no—
470C4—344no—
471C4—342no—
472C4—342no—
473C4—682no—
474C2—22no—
475C2—21no—
476C2—21no—
477C2—344no—
478C2—344no—
479C2#1454403314yesdirect product factor
480C2C2×#1176378011yescharacteristic
481C2C2×D17⋊#9911yescharacteristic
482C2C2×D17⋊#10111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC23×C17C23×C4
FrattiniC23C23×#595
FittingC22×C4⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC24×D17C2×C4
cosocleC22×Dic17C24
hypercenterC22×C4⋊C4#595
hypocenterC17C2×#1463
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #14544033C2direct (N × H)
3. C2×#11763655C2semidirect
4. C2×#11763654C2semidirect
11. #11763655C22semidirect
12. #11763654C22semidirect
91. C22×C4×C17M16semidirect
102. C22×Dic17M16semidirect
177. C2×C4×C17C2×M16semidirect
191. C2×Dic17C2×M16semidirect
260. C2×C17#1463semidirect
314. C17C2×#1463semidirect
367. C22×C4#63243semidirect
440. C2×C4C2×#63243semidirect
479. C2#14544033direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117637802
#145440332
C2×#117636552
C2×#117636542
C22×C4⋊C4×D172
C2×#146317