Finite Group Databasebeta

← #16943870

Subgroups — #16943870

Order 4352.

492 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14527111C211yesmaximal, characteristic
2C2×#11762533C211yesmaximal, characteristic
3#14526732C212yesmaximal, complemented
4#14526714C212yesmaximal, complemented
5C17×#2483C211yesmaximal, characteristic
6#11762773—21no—
7C2×C22⋊#3622—21no—
8#11762533—21no—
9#11762533—21no—
10#11762533C2212yes—
11#11762533C2212yes—
12C22×C22⋊C4×C17C411yescharacteristic
13C22×C22⋊C4×C17C2211yescharacteristic
14C17×#397—21no—
15C17×#397—21no—
16C17×#385—21no—
17C17×#385C411yescharacteristic
18C17×#385C2211yescharacteristic
19C17×#381—21no—
20C17×#381C411yescharacteristic
21C17×#381C2211yescharacteristic
22C17×#379C411yescharacteristic
23C25×C17C2×C411yescharacteristic
24C23×C4×C17C2×C411yescharacteristic
25C23×C4×C17C2×C411yescharacteristic
26C23×C4×C17D411yescharacteristic
27C23×C4×C17D411yescharacteristic
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17—21no—
30C2×C22⋊C4×C17—21no—
31C2×C22⋊C4×C17—21no—
32C2×C22⋊C4×C17—21no—
33C2×C22⋊C4×C17—21no—
34C2×C22⋊C4×C17—41no—
35C2×C22⋊C4×C17—41no—
36C2×C22⋊C4×C17—41no—
37C2×C22⋊C4×C17—41no—
38C2×C22⋊C4×C17C2×C411yescharacteristic
39C2×C22⋊C4×C17C2×C411yescharacteristic
40C2×C22⋊C4×C17C2×C411yescharacteristic
41C2×C22⋊C4×C17D411yescharacteristic
42C2×C22⋊C4×C17D411yescharacteristic
43C2×C22⋊C4×C17C2311yescharacteristic
44C2×#63223—41no—
45C22×#3622—41no—
46C17×#95—21no—
47C17×#95—21no—
48C17×#95—21no—
49C17×#95—21no—
50C17×#95—21no—
51C17×#95—21no—
52C22⋊#3622—22no—
53C22⋊#3622—22no—
54C22⋊#3622—41no—
55C22⋊#3622—41no—
56C24×C17—21no—
57C24×C17—21no—
58C24×C17—22no—
59C24×C17—41no—
60C24×C17—42no—
61C24×C17—81no—
62C24×C17C22⋊C411yescharacteristic
63C24×C17C22⋊C411yescharacteristic
64C24×C17C22×C411yescharacteristic
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17—21no—
71C22×C4×C17—21no—
72C22×C4×C17—21no—
73C22×C4×C17—22no—
74C22×C4×C17—42no—
75C22×C4×C17—41no—
76C22×C4×C17—41no—
77C22×C4×C17—41no—
78C22×C4×C17—81no—
79C22×C4×C17—81no—
80C22×C4×C17C22⋊C411yescharacteristic
81C22×C4×C17C22⋊C411yescharacteristic
82C22×C4×C17C2×D411yescharacteristic
83C22×C4×C17C2×D411yescharacteristic
84C4⋊C4×C17—81no—
85C4⋊C4×C17—81no—
86C22⋊C4×C17—22no—
87C22⋊C4×C17—41no—
88C22⋊C4×C17—41no—
89C22⋊C4×C17—41no—
90C22⋊C4×C17—41no—
91C22⋊C4×C17—42no—
92C22⋊C4×C17—42no—
93C22⋊C4×C17—41no—
94C22⋊C4×C17—41no—
95C22⋊C4×C17—41no—
96C22⋊C4×C17—81no—
97#63223—82no—
98C2×#3622—42no—
99C2×#3622—42no—
100C2×#3622—82no—
101#11547—171nomaximal, Sylow
102C23×C17—22no—
103C23×C17—21no—
104C23×C17—21no—
105C23×C17—21no—
106C23×C17—21no—
107C23×C17—21no—
108C23×C17—21no—
109C23×C17—21no—
110C23×C17—41no—
111C23×C17—42no—
112C23×C17—42no—
113C23×C17—41no—
114C23×C17—41no—
115C23×C17—42no—
116C23×C17—41no—
117C23×C17—41no—
118C23×C17—42no—
119C23×C17—81no—
120C23×C17—81no—
121C23×C17—84no—
122C23×C17—84no—
123C23×C17#9911yescharacteristic
124C23×C17#9911yescharacteristic
125C23×C17C2×C22⋊C411yescharacteristic
126C23×C17#13112yes—
127C2×C4×C17—21no—
128C2×C4×C17—21no—
129C2×C4×C17—21no—
130C2×C4×C17—21no—
131C2×C4×C17—42no—
132C2×C4×C17—42no—
133C2×C4×C17—41no—
134C2×C4×C17—41no—
135C2×C4×C17—41no—
136C2×C4×C17—41no—
137C2×C4×C17—41no—
138C2×C4×C17—41no—
139C2×C4×C17—41no—
140C2×C4×C17—41no—
141C2×C4×C17—41no—
142C2×C4×C17—41no—
143C2×C4×C17—41no—
144C2×C4×C17—41no—
145C2×C4×C17—41no—
146C2×C4×C17—41no—
147C2×C4×C17—41no—
148C2×C4×C17—41no—
149C2×C4×C17—81no—
150C2×C4×C17—81no—
151C2×C4×C17—82no—
152C2×C4×C17—82no—
153#3622—82no—
154#3622—82no—
155#2483D1711yescharacteristic
156#1462—171no—
157C2×#323—171no—
158#1326—172no—
159#1317—172no—
160C22×C17—21no—
161C22×C17—21no—
162C22×C17—21no—
163C22×C17—21no—
164C22×C17—21no—
165C22×C17—21no—
166C22×C17—22no—
167C22×C17—21no—
168C22×C17—42no—
169C22×C17—42no—
170C22×C17—42no—
171C22×C17—42no—
172C22×C17—41no—
173C22×C17—41no—
174C22×C17—41no—
175C22×C17—41no—
176C22×C17—41no—
177C22×C17—84no—
178C22×C17—81no—
179C22×C17—81no—
180C22×C17—84no—
181C22×C17#35212yes—
182C22×C17#40811yescharacteristic
183C22×C17C2×#9911yescharacteristic
184C22×C17#41311yescharacteristic
185C4×C17—41no—
186C4×C17—41no—
187C4×C17—41no—
188C4×C17—41no—
189C4×C17—81no—
190C4×C17—81no—
191C4×C17—81no—
192C4×C17—81no—
193C22×C22⋊C4Dic1711yescharacteristic
194C22×C22⋊C4C2×D1711yescharacteristic
195#407—341no—
196C2×C22⋊C8—341no—
197#397—21no—
198#397—21no—
199#385—21no—
200#385Dic1711yescharacteristic
201#385C2×D1711yescharacteristic
202#381—21no—
203#381Dic1711yescharacteristic
204#381C2×D1711yescharacteristic
205#379Dic1711yescharacteristic
206#323—172no—
207#323—172no—
208#323—341no—
209#323—341no—
210C2×C17—21no—
211C2×C17—21no—
212C2×C17—22no—
213C2×C17—41no—
214C2×C17—42no—
215C2×C17—81no—
216C2×C17#146811yescharacteristic
217C2×C17C2×#35211yescharacteristic
218C2×C17#212111yescharacteristic
219C25C2×Dic1711yescharacteristic
220C23×C4C2×Dic1711yescharacteristic
221C23×C4C2×Dic1711yescharacteristic
222C23×C4C22⋊D1711yescharacteristic
223C23×C4C22⋊D1711yescharacteristic
224C2×M16—681no—
225C22×C8—681no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—41no—
233C2×C22⋊C4—41no—
234C2×C22⋊C4—41no—
235C2×C22⋊C4—41no—
236C2×C22⋊C4C2×Dic1711yescharacteristic
237C2×C22⋊C4C2×Dic1711yescharacteristic
238C2×C22⋊C4C2×Dic1711yescharacteristic
239C2×C22⋊C4C22⋊D1711yescharacteristic
240C2×C22⋊C4C22⋊D1711yescharacteristic
241C2×C22⋊C4C22×D1711yescharacteristic
242C22⋊C8—342no—
243C22⋊C8—342no—
244C22⋊C8—681no—
245C22⋊C8—681no—
246#95—21no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252C17#1154711yescharacteristic, complemented, Sylow
253C24—21no—
254C24—21no—
255C24—22no—
256C24—41no—
257C24—42no—
258C24—81no—
259C24C22⋊Dic1711yescharacteristic
260C24C22⋊Dic1711yescharacteristic
261C24C22×Dic1711yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—42no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—81no—
276C22×C4—81no—
277C22×C4C22⋊Dic1711yescharacteristic
278C22×C4C22⋊Dic1711yescharacteristic
279C22×C4C2×C22⋊D1711yescharacteristic
280C22×C4C2×C22⋊D1711yescharacteristic
281M16—1362no—
282C2×C8—682no—
283C2×C8—682no—
284C2×C8—1362no—
285C4⋊C4—81no—
286C4⋊C4—81no—
287C22⋊C4—22no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—42no—
293C22⋊C4—42no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—81no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—22no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—41no—
307C23—42no—
308C23—42no—
309C23—41no—
310C23—41no—
311C23—42no—
312C23—41no—
313C23—41no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—84no—
318C23—84no—
319C23#1058750511yescharacteristic
320C23#1058750511yescharacteristic
321C23#1058763412yes—
322C23C2×C22⋊Dic1711yescharacteristic
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—82no—
348C2×C4—82no—
349C8—1362no—
350C8—1362no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—21no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—81no—
370C22—81no—
371C22—84no—
372C22#1176259912yes—
373C22#1176277611yescharacteristic
374C22C2×#1058750511yescharacteristic
375C22#1176279311yescharacteristic
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—81no—
381C4—81no—
382C4—81no—
383C4—81no—
384C2—21no—
385C2—21no—
386C2—22no—
387C2—41no—
388C2—42no—
389C2—81no—
390C2#1452713211yescharacteristic
391C2C2×#1176259911yescharacteristic
392C2#1453043011yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC24×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#2483C2
socleC22×C17C2×#99
prime radicalC25×C17C2×C4
cosocleC2×C22⋊C4×C17C23
hypercenter#2483D17
hypocenterC17#11547
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #2483

Complements

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

NH ≅ G/Ntype
3. #14526732C2semidirect
4. #14526714C2semidirect
252. C17#11547semidirect

Maximal subgroups

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

subgroupindex
#145271112
C2×#117625332
#145267322
#145267142
C17×#24832
#1154717