Finite Group Databasebeta

← #17964347

Subgroups — #17964347

Order 4352.

1174 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545683C212yesmaximal, complemented
2#14544045C212yesmaximal, complemented
3#14544043C212yesmaximal, complemented
4#14544038C212yesmaximal, complemented
5#14544035C212yesmaximal, complemented
6#14544023C212yesmaximal, complemented
7#14544018C212yesmaximal, complemented
8C2×#11763290C211yesmaximal, characteristic
9#11763861—28no—
10#11763830C2214yes—
11#11763829C2214yes—
12#11763826C2214yes—
13#11763654C2214yes—
14#11763653C2214yes—
15#11763653C2214yes—
16#11763652C2214yes—
17C22×#63252C411yescharacteristic
18#11763290—28no—
19C2×#10587573C411yescharacteristic
20C2×#10587573C2211yescharacteristic
21C2×#10587579C411yescharacteristic
22C2×#10587579C2211yescharacteristic
23C2×C4×C22⋊D17C411yescharacteristic
24C2×C4×C22⋊D17C411yescharacteristic
25C2×C4×C22⋊D17C2211yescharacteristic
26C2×C4×C22⋊D17C2211yescharacteristic
27C2×#10587612C2211yescharacteristic
28C2×#10587578C2211yescharacteristic
29C2×#10587578C2211yescharacteristic
30C2×C4⋊C4×D17C411yescharacteristic
31C2×C4⋊C4×D17C411yescharacteristic
32C22×C4⋊C4×C17C411yescharacteristic
33C23×C4×C17C2×C411yescharacteristic
34C23×C4×C17C2×C411yescharacteristic
35C23×C4×C17C2×C411yescharacteristic
36C22×C22⋊D17C2×C411yescharacteristic
37C22×C22⋊D17C2×C411yescharacteristic
38C2×#63252—24no—
39C2×#63252—24no—
40C2×#63252—24no—
41C22×D68C2×C411yescharacteristic
42C22×C4×D17C2×C411yescharacteristic
43C22×C4×D17C2×C411yescharacteristic
44C22×C4×D17C2×C411yescharacteristic
45C22×C4×D17C2×C411yescharacteristic
46C22×C4×D17C2×C411yescharacteristic
47C22×C4×D17C2×C411yescharacteristic
48C22×Dic34C2×C411yescharacteristic
49C2×C4⋊C4×C17—24no—
50C2×C4⋊C4×C17C2×C411yescharacteristic
51C2×C4⋊C4×C17C2×C411yescharacteristic
52C2×C4⋊C4×C17C2×C411yescharacteristic
53C2×C4⋊C4×C17C2×C411yescharacteristic
54C2×C22⋊Dic17C2×C411yescharacteristic
55C2×C22⋊Dic17C2311yescharacteristic
56C4×C22⋊D17—24no—
57C4×C22⋊D17—24no—
58C4×C22⋊D17—24no—
59C4×C22⋊D17—24no—
60C2×#63227C2×C411yescharacteristic
61C2×#63227C2×C411yescharacteristic
62C2×#63227C2311yescharacteristic
63C2×#63227C2311yescharacteristic
64#10587612—24no—
65C2×C4⋊Dic17C2×C411yescharacteristic
66C2×C4⋊Dic17C2311yescharacteristic
67C2×#63225C2×C411yescharacteristic
68C2×#63225C2×C411yescharacteristic
69C2×#63225C2×C411yescharacteristic
70C2×#63225C2×C411yescharacteristic
71C2×C4×Dic17C2×C411yescharacteristic
72C2×C4×Dic17C2×C411yescharacteristic
73C2×C4×Dic17C2×C411yescharacteristic
74C2×C4×Dic17C2311yescharacteristic
75C2×C4×Dic17C2311yescharacteristic
76C2×C4×Dic17C2311yescharacteristic
77#10587579—24no—
78#10587579—24no—
79#10587578—24no—
80#10587578—24no—
81C4⋊C4×D17—24no—
82C4⋊C4×D17—24no—
83#10587573—24no—
84#10587573D418yes—
85C22⋊#3624C2318yes—
86#10587544—24no—
87#10587544—24no—
88#10587542—24no—
89#10587542—24no—
90C4⋊#3624—24no—
91C4×#3624—24no—
92C24×C17C22×C411yescharacteristic
93C23×D17C22×C411yescharacteristic
94C23×D17C22×C411yescharacteristic
95C22×C4×C17—22no—
96C22×C4×C17—22no—
97C22×C4×C17—22no—
98C22×C4×C17—22no—
99C22×C4×C17—22no—
100C22×C4×C17—81no—
101C22×C4×C17—81no—
102C22×C4×C17C22×C411yescharacteristic
103C22×C4×C17C22×C411yescharacteristic
104C22×C4×C17C22×C411yescharacteristic
105C22×C4×C17C22×C411yescharacteristic
106C22×C4×C17C22×C411yescharacteristic
107C22×C4×C17C22×C411yescharacteristic
108C2×C22⋊D17—22no—
109C2×C22⋊D17—22no—
110C2×C22⋊D17—22no—
111C2×C22⋊D17—22no—
112C2×C22⋊D17—22no—
113C2×C22⋊D17M1614yes—
114C22×Dic17C22×C411yescharacteristic
115C22×Dic17C22×C411yescharacteristic
116C22×Dic17C22×C411yescharacteristic
117C22×Dic17C22×C411yescharacteristic
118C22×Dic17C22×C411yescharacteristic
119C22×Dic17C2411yescharacteristic
120#63252—232no—
121C2×D68—22no—
122C2×D68—22no—
123C2×D68—22no—
124C2×C4×D17—22no—
125C2×C4×D17—22no—
126C2×C4×D17—22no—
127C2×C4×D17—22no—
128C2×C4×D17—22no—
129C2×C4×D17—22no—
130C2×C4×D17—22no—
131C2×C4×D17—22no—
132C2×C4×D17—22no—
133C2×C4×D17—81no—
134C2×C4×D17—81no—
135C2×C4×D17—81no—
136C2×C4×D17—81no—
137C2×C4×D17M1614yes—
138C2×Dic34—22no—
139C2×Dic34—22no—
140C2×Dic34C22⋊C414yes—
141C2×#3624—28no—
142C4⋊C4×C17—22no—
143C4⋊C4×C17—22no—
144C4⋊C4×C17—22no—
145C4⋊C4×C17C22⋊C414yes—
146C22⋊Dic17—22no—
147C22⋊Dic17—22no—
148#63227—22no—
149#63227—22no—
150#63227—22no—
151#63227—22no—
152C4⋊Dic17—22no—
153C4⋊Dic17—22no—
154#63225—22no—
155#63225—22no—
156#63225C22⋊C414yes—
157#63225C22⋊C414yes—
158C4×Dic17—22no—
159C4×Dic17—22no—
160C4×Dic17—22no—
161C4×Dic17C2×D414yes—
162C4×Dic17C2×D414yes—
163C4×Dic17C2×D414yes—
164#17372—171nomaximal, Sylow
165C23×C17—21no—
166C23×C17—21no—
167C23×C17—41no—
168C23×C17—41no—
169C23×C17C2×M1612yes—
170C23×C17C23×C411yescharacteristic
171C22×D17—21no—
172C22×D17—21no—
173C22×D17—21no—
174C22×D17—21no—
175C22×D17—41no—
176C22×D17—41no—
177C22×D17—41no—
178C22×D17—41no—
179C22×D17C2×M1612yes—
180C22×D17C2×M1612yes—
181C2×C4×C17—28no—
182C2×C4×C17—21no—
183C2×C4×C17—21no—
184C2×C4×C17—21no—
185C2×C4×C17—21no—
186C2×C4×C17—21no—
187C2×C4×C17—21no—
188C2×C4×C17—41no—
189C2×C4×C17—41no—
190C2×C4×C17—41no—
191C2×C4×C17—41no—
192C2×C4×C17—82no—
193C2×C4×C17—82no—
194C2×C4×C17C2×C22⋊C412yes—
195C2×C4×C17C2×C22⋊C412yes—
196C2×C4×C17C2×C22⋊C412yes—
197C2×C4×C17C2×M1612yes—
198C22⋊D17—28no—
199C22⋊D17—28no—
200C2×Dic17—21no—
201C2×Dic17—21no—
202C2×Dic17—21no—
203C2×Dic17—21no—
204C2×Dic17—41no—
205C2×Dic17—41no—
206C2×Dic17—41no—
207C2×Dic17—41no—
208C2×Dic17C2×C22⋊C412yes—
209C2×Dic17C2×C22⋊C412yes—
210C2×Dic17C2×C22⋊C412yes—
211C2×Dic17C2×M1612yes—
212C2×Dic17C2×M1612yes—
213C2×Dic17C22×D412yes—
214D68—28no—
215C4×D17—28no—
216C4×D17—28no—
217C4×D17—82no—
218C4×D17—82no—
219C4×D17—82no—
220C4×D17—82no—
221Dic34—28no—
222#3624—48no—
223C2×#520—171no—
224#2983—172no—
225#1466—172no—
226#1466—172no—
227#1464—172no—
228#1464—172no—
229#1460—172no—
230#1458—172no—
231C22×C17—21no—
232C22×C17—21no—
233C22×C17—22no—
234C22×C17—42no—
235C22×C17—42no—
236C22×C17—41no—
237C22×C17—41no—
238C22×C17C22×C22⋊C411yescharacteristic
239C22×C17C22×M1611yescharacteristic
240C22×C17C22×M1611yescharacteristic
241C2×D17—22no—
242C2×D17—22no—
243C2×D17—42no—
244C2×D17—42no—
245C2×D17—41no—
246C2×D17—41no—
247C2×D17—41no—
248C2×D17—41no—
249C2×D17—42no—
250C2×D17—42no—
251C4×C17—22no—
252C4×C17—22no—
253C4×C17—22no—
254C4×C17—22no—
255C4×C17—41no—
256C4×C17—41no—
257Dic17—22no—
258Dic17—22no—
259Dic17—22no—
260Dic17—41no—
261Dic17—41no—
262Dic17#40714yes—
263C22×#41—171no—
264#520—348no—
265C2×C4×Q8—171no—
266C2×C4×Q8—171no—
267C2×C4×D4—171no—
268C2×C4×D4—171no—
269C2×C4×D4—171no—
270C2×C4×D4—171no—
271C2×C4×D4—171no—
272C2×C4×D4—171no—
273C2×#117—171no—
274C2×#117—171no—
275C2×#117—171no—
276C22×C4⋊C4—171no—
277C22×C4⋊C4—171no—
278C22×C4⋊C4#59511yescharacteristic
279#446—348no—
280#432—174no—
281#432—174no—
282#431—174no—
283#324—174no—
284#323—174no—
285#323—174no—
286#323—174no—
287C2×C17—21no—
288C2×C17—21no—
289C2×C17—42no—
290C2×C17C2×#40711yescharacteristic
291C2×C17#288411yescharacteristic
292C2×C17#288811yescharacteristic
293D17—42no—
294D17—42no—
295C2×#41—344no—
296C2×#41—344no—
297C2×#41—344no—
298C22×Q8—171no—
299C22×D4—171no—
300C22×D4—171no—
301C22×D4—171no—
302C23×C4—171no—
303C23×C4—171no—
304C23×C4—171no—
305C23×C4—171no—
306C23×C4—171no—
307C23×C4—171no—
308C23×C4C2×#59511yescharacteristic
309C23×C4C2×#59511yescharacteristic
310C23×C4C2×#59511yescharacteristic
311C4×Q8—178no—
312C4×Q8—344no—
313C4×D4—344no—
314C4×D4—344no—
315C4×D4—344no—
316C4×D4—344no—
317C4×D4—344no—
318C4×D4—344no—
319#117—344no—
320#117—344no—
321#117—344no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—171no—
324C2×C4⋊C4—171no—
325C2×C4⋊C4—171no—
326C2×C4⋊C4—171no—
327C2×C4⋊C4—171no—
328C2×C4⋊C4—171no—
329C2×C4⋊C4—344no—
330C2×C4⋊C4—344no—
331C2×C4⋊C4C2×#59511yescharacteristic
332C2×C4⋊C4C2×#59511yescharacteristic
333C2×C4⋊C4C2×#59511yescharacteristic
334C2×C4⋊C4C2×#59511yescharacteristic
335C2×C22⋊C4—171no—
336C2×C22⋊C4—171no—
337C2×C22⋊C4—171no—
338C2×C22⋊C4—171no—
339C2×C22⋊C4—171no—
340C2×C22⋊C4—171no—
341C2×C42—171no—
342C2×C42—171no—
343C2×C42—171no—
344C2×C42—171no—
345C2×C42—171no—
346C2×C42—171no—
347C4⋊C8—344no—
348C4⋊C8—344no—
349C4⋊C8—344no—
350C22⋊C8—178no—
351#97—344no—
352#97—344no—
353C4×C8—344no—
354C17#1737211yescharacteristic, complemented, Sylow
355C24—171no—
356C24—171no—
357C24C22×#59511yescharacteristic
358#41—3432no—
359C2×Q8—174no—
360C2×Q8—342no—
361C2×Q8—342no—
362C2×D4—174no—
363C2×D4—342no—
364C2×D4—342no—
365C2×D4—342no—
366C2×D4—342no—
367C2×D4—342no—
368C2×D4—342no—
369C2×D4—342no—
370C2×D4—342no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—81no—
377C22×C4—81no—
378C22×C4—171no—
379C22×C4—171no—
380C22×C4—171no—
381C22×C4—171no—
382C22×C4—174no—
383C22×C4—171no—
384C22×C4—171no—
385C22×C4—342no—
386C22×C4—342no—
387C22×C4—342no—
388C22×C4—342no—
389C22×C4—342no—
390C22×C4—342no—
391C22×C4—342no—
392C22×C4—342no—
393C22×C4—342no—
394C22×C4—1361no—
395C22×C4—1361no—
396C22×C4—1361no—
397C22×C4—1361no—
398C22×C4C22×#59511yescharacteristic
399C22×C4C22×#59511yescharacteristic
400C22×C4C22×#59511yescharacteristic
401C22×C4C22×#59511yescharacteristic
402C22×C4C22×#59511yescharacteristic
403C22×C4C22×#59511yescharacteristic
404C2×C8—348no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—174no—
409C4⋊C4—174no—
410C4⋊C4—342no—
411C4⋊C4—342no—
412C4⋊C4—342no—
413C4⋊C4—342no—
414C4⋊C4C22⋊#59514yes—
415C22⋊C4—342no—
416C22⋊C4—342no—
417C22⋊C4—342no—
418C22⋊C4—342no—
419C22⋊C4—342no—
420C22⋊C4—342no—
421C42—174no—
422C42—174no—
423C42—174no—
424C42—342no—
425C42—342no—
426C42—342no—
427C23—21no—
428C23—21no—
429C23—41no—
430C23—41no—
431C23—172no—
432C23—172no—
433C23—341no—
434C23—341no—
435C23—341no—
436C23—341no—
437C23—681no—
438C23—681no—
439C23—681no—
440C23—681no—
441C23D17⋊M1612yes—
442C23C23×#59511yescharacteristic
443Q8—348no—
444D4—348no—
445D4—348no—
446D4—348no—
447C2×C4—28no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—82no—
459C2×C4—82no—
460C2×C4—172no—
461C2×C4—172no—
462C2×C4—172no—
463C2×C4—172no—
464C2×C4—172no—
465C2×C4—172no—
466C2×C4—348no—
467C2×C4—348no—
468C2×C4—341no—
469C2×C4—341no—
470C2×C4—341no—
471C2×C4—341no—
472C2×C4—681no—
473C2×C4—681no—
474C2×C4—681no—
475C2×C4—681no—
476C2×C4—1362no—
477C2×C4—1362no—
478C2×C4—1362no—
479C2×C4—1362no—
480C2×C4D17⋊M1612yes—
481C2×C4C2×C22⋊#59512yes—
482C2×C4C2×C22⋊#59512yes—
483C2×C4C2×C22⋊#59512yes—
484C8—688no—
485C22—21no—
486C22—21no—
487C22—22no—
488C22—42no—
489C22—42no—
490C22—41no—
491C22—41no—
492C22—342no—
493C22—342no—
494C22—682no—
495C22—682no—
496C22—682no—
497C22—682no—
498C22—681no—
499C22—681no—
500C22—681no—
501C22—681no—
502C22C22×C22⋊#59511yescharacteristic
503C22C2×D17⋊M1611yescharacteristic
504C22C2×D17⋊M1611yescharacteristic
505C4—22no—
506C4—22no—
507C4—22no—
508C4—22no—
509C4—41no—
510C4—41no—
511C4—174no—
512C4—342no—
513C4—342no—
514C4—342no—
515C4—681no—
516C4—681no—
517C2—21no—
518C2—21no—
519C2—42no—
520C2—682no—
521C2—682no—
522C2D17⋊#40711yescharacteristic
523C2#1454538511yescharacteristic
524C2#1454539411yescharacteristic
subgroupG/H
centerC22C22×C22⋊#595
commutatorC23×C17C23×C4
FrattiniC23C23×#595
FittingC22×C4⋊C4×C17C4
socleC22×C17C22×C22⋊C4
prime radicalC22×#63252C4
cosocleC22×Dic17C24
hypercenterC22×C4⋊C4#595
hypocenterC17#17372
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #14545683C2semidirect
2. #14544045C2semidirect
3. #14544043C2semidirect
4. #14544038C2semidirect
5. #14544035C2semidirect
6. #14544023C2semidirect
7. #14544018C2semidirect
354. C17#17372semidirect

Maximal subgroups

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

subgroupindex
#145456832
#145440452
#145440432
#145440382
#145440352
#145440232
#145440182
C2×#117632902
#1737217