Finite Group Databasebeta

← #17958279

Subgroups — #17958279

Order 4352.

392 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 88 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#14545012C211yesmaximal, characteristic, complemented
2#14545009C211yesmaximal, characteristic, complemented
3#14543723C212yesmaximal, complemented
4#14543706C212yesmaximal, complemented
5#14537476C211yesmaximal, characteristic
6C2×#10587530—21no—
7C2×#10587529—21no—
8#11763704—21no—
9#11763704—21no—
10C22⋊#63216C2212yes—
11C22⋊#63216C2212yes—
12C22×C8×D17C2211yescharacteristic
13#11763316C411yescharacteristic
14#11762878—21no—
15#11762878—21no—
16C8×C22⋊D17—21no—
17C8×C22⋊D17—21no—
18#11762837C2211yescharacteristic
19#11762776C2211yescharacteristic
20#11762772C411yescharacteristic
21#11762764C411yescharacteristic
22C2×C17×#131C411yescharacteristic
23C2×#41×C17C2×C411yescharacteristic
24C22×C4×D17C2×C411yescharacteristic
25C17×#131—42no—
26C2×M16×C17—21no—
27C2×M16×C17C2×C411yescharacteristic
28C22×C8×C17—21no—
29C22×C8×C17C2×C411yescharacteristic
30#10587632C811yescharacteristic
31#10587632C811yescharacteristic
32#10587624C811yescharacteristic
33#10587624C811yescharacteristic
34#10587623—21no—
35#10587621—21no—
36C4×C22⋊D17—21no—
37C4×C22⋊D17—21no—
38#10587612C2×C411yescharacteristic
39C2×#63223C2×C411yescharacteristic
40C22×#3622C2311yescharacteristic
41C2×C8×D17—42no—
42C2×C8×D17D411yescharacteristic
43C2×C8×D17D411yescharacteristic
44C2×C8×D17D411yescharacteristic
45C2×C8×D17D411yescharacteristic
46C2×#63216—22no—
47C2×#63216—22no—
48#10587530—42no—
49#10587529—42no—
50C22⋊#3622—21no—
51C22⋊#3622—21no—
52#10587491—21no—
53#10587491—21no—
54#10587486—21no—
55#10587485—21no—
56#10587485—21no—
57C8×Dic17—21no—
58C23×D17M1611yescharacteristic
59#41×C17—41no—
60#41×C17—41no—
61C2×Q8×C17C2×C811yescharacteristic
62C2×D4×C17—21no—
63C2×D4×C17C2×C811yescharacteristic
64C22×C4×C17—21no—
65C22×C4×C17C22×C411yescharacteristic
66C2×C22⋊D17—21no—
67C2×C22⋊D17—21no—
68C22×Dic17M1611yescharacteristic
69C2×C4×D17—41no—
70C2×C4×D17—41no—
71C2×C4×D17C22⋊C411yescharacteristic
72C2×C4×D17C22⋊C411yescharacteristic
73C2×C4×D17C2×C811yescharacteristic
74C2×C4×D17C2×C811yescharacteristic
75M16×C17—42no—
76M16×C17—41no—
77C2×C8×C17—22no—
78C2×C8×C17—21no—
79C2×C8×C17—42no—
80C2×C8×C17C22⋊C411yescharacteristic
81C2×C8×C17C22⋊C411yescharacteristic
82C22⋊Dic17—21no—
83C22⋊Dic17—21no—
84C22⋊Dic17—21no—
85#63227—21no—
86#63227—21no—
87C4⋊Dic17C2×C811yescharacteristic
88C4⋊Dic17C2×C811yescharacteristic
89#63225—21no—
90#63225—21no—
91C4×Dic17—21no—
92#63223—41no—
93C2×#3622—21no—
94C2×#3622—41no—
95C2×#3622C2×D411yescharacteristic
96C2×#3622C2×D411yescharacteristic
97C8×D17—22no—
98C8×D17—22no—
99C8×D17—41no—
100C8×D17—41no—
101#63216—42no—
102#63216—42no—
103#11470—171nomaximal, Sylow
104C23×C17—21no—
105C23×C17C2×M1611yescharacteristic
106C22×D17—22no—
107C22×D17—41no—
108C22×D17—41no—
109C22×D17C22⋊C811yescharacteristic
110C22×D17C22⋊C811yescharacteristic
111Q8×C17—41no—
112D4×C17—41no—
113D4×C17—42no—
114C2×C4×C17—21no—
115C2×C4×C17—21no—
116C2×C4×C17—21no—
117C2×C4×C17—41no—
118C2×C4×C17—41no—
119C2×C4×C17C2×C22⋊C411yescharacteristic
120C2×C4×C17C22×C811yescharacteristic
121C22⋊D17—42no—
122C22⋊D17—42no—
123C2×Dic17—21no—
124C2×Dic17—21no—
125C2×Dic17—41no—
126C2×Dic17C22⋊C811yescharacteristic
127C2×Dic17C22⋊C811yescharacteristic
128C4×D17—21no—
129C4×D17—21no—
130C4×D17—21no—
131C4×D17—21no—
132C4×D17—41no—
133C4×D17—41no—
134C8×C17—21no—
135C8×C17—41no—
136C8×C17#9912yes—
137#3622—21no—
138#3622—21no—
139#3622—41no—
140#2929—171no—
141#2112—171no—
142C2×C22⋊C16—171no—
143#1323—172no—
144#1315—172no—
145C22×C17—21no—
146C22×C17—21no—
147C22×C17—21no—
148C22×C17—41no—
149C22×C17—41no—
150C22×C17—41no—
151C22×C17C2×C22⋊C811yescharacteristic
152C2×D17—21no—
153C2×D17—21no—
154C2×D17—21no—
155C2×D17—21no—
156C2×D17—21no—
157C2×D17—44no—
158C2×D17#35012yes—
159C4×C17—21no—
160C4×C17—41no—
161C4×C17C2×#9911yescharacteristic
162C4×C17#41311yescharacteristic
163Dic17—21no—
164Dic17—21no—
165Dic17—41no—
166Dic17—41no—
167C2×#131#59511yescharacteristic
168C23×C8—171no—
169#525—171no—
170C2×M32—341no—
171C22×C16—341no—
172#435—341no—
173#435—341no—
174C8×D4—341no—
175C8×D4—341no—
176#424—171no—
177#408—171no—
178#407—171no—
179#405—171no—
180C22⋊C16—172no—
181C22⋊C16—172no—
182C22⋊C16—341no—
183C22⋊C16—341no—
184C2×C17—41no—
185C2×C17—81no—
186C2×C17#145911yescharacteristic
187C2×C17C2×#35011yescharacteristic
188C2×C17#211711yescharacteristic
189D17—22no—
190D17—41no—
191C2×#41C2×#59511yescharacteristic
192C23×C4—171no—
193#131—42no—
194C2×M16—21no—
195C2×M16—171no—
196C2×M16C2×#59511yescharacteristic
197C22×C8—21no—
198C22×C8—171no—
199C22×C8—171no—
200C22×C8—171no—
201C22×C8—171no—
202C22×C8—171no—
203C22×C8—682no—
204C22×C8C2×#59511yescharacteristic
205#123—341no—
206C22⋊Q8—171no—
207C22⋊Q8—171no—
208#121—171no—
209#121—171no—
210#120—341no—
211C4×D4—341no—
212C4×D4—341no—
213#117—171no—
214M32—682no—
215C2×C16—342no—
216C2×C16—342no—
217C2×C16—682no—
218C4⋊C8—341no—
219C4⋊C8—341no—
220C22⋊C8—341no—
221C22⋊C8—341no—
222C22⋊C8—341no—
223C22⋊C8—341no—
224#97—341no—
225C4×C8—341no—
226C17#1147011yescharacteristic, complemented, Sylow
227C24—171no—
228#41—41no—
229#41—41no—
230C2×Q8#6324211yescharacteristic
231C2×D4—21no—
232C2×D4—341no—
233C2×D4—341no—
234C2×D4#6324211yescharacteristic
235C22×C4—21no—
236C22×C4—171no—
237C22×C4—171no—
238C22×C4—171no—
239C22×C4—171no—
240C22×C4—171no—
241C22×C4—681no—
242C22×C4—681no—
243C22×C4C22×#59511yescharacteristic
244M16—42no—
245M16—41no—
246M16—681no—
247C2×C8—22no—
248C2×C8—21no—
249C2×C8—42no—
250C2×C8—171no—
251C2×C8—171no—
252C2×C8—342no—
253C2×C8—342no—
254C2×C8—341no—
255C2×C8—681no—
256C2×C8—681no—
257C2×C8—681no—
258C2×C8C22⋊#59511yescharacteristic
259C2×C8C22⋊#59511yescharacteristic
260C4⋊C4—171no—
261C4⋊C4—171no—
262C4⋊C4—341no—
263C4⋊C4—341no—
264C22⋊C4—341no—
265C22⋊C4—341no—
266C22⋊C4—341no—
267C22⋊C4—341no—
268C22⋊C4—341no—
269C42—341no—
270C16—682no—
271C16—682no—
272C23—21no—
273C23—171no—
274C23—171no—
275C23—342no—
276C23—681no—
277C23—681no—
278C23D17⋊M1611yescharacteristic
279Q8—41no—
280D4—41no—
281D4—42no—
282D4—682no—
283D4—682no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—171no—
290C2×C4—171no—
291C2×C4—341no—
292C2×C4—341no—
293C2×C4—341no—
294C2×C4—341no—
295C2×C4—341no—
296C2×C4—341no—
297C2×C4—681no—
298C2×C4—681no—
299C2×C4—681no—
300C2×C4C2×#6324211yescharacteristic
301C2×C4C2×C22⋊#59511yescharacteristic
302C8—21no—
303C8—41no—
304C8—341no—
305C8—341no—
306C8—681no—
307C8#1058755112yes—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—172no—
315C22—341no—
316C22—341no—
317C22—341no—
318C22—341no—
319C22—341no—
320C22—684no—
321C22#1176377711yescharacteristic
322C4—21no—
323C4—41no—
324C4—341no—
325C4—341no—
326C4—681no—
327C4—681no—
328C4C2×#1058755111yescharacteristic
329C4#1176379511yescharacteristic
330C2—41no—
331C2—81no—
332C2—342no—
333C2—681no—
334C2#1454401911yescharacteristic
335C2#1454502411yescharacteristic
336C2#1454502711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC2×C17×#131C4
socleC22×C17C2×C22⋊C8
prime radical#11763316C4
cosocleC22×#3622C23
hypercenterC2×#131#595
hypocenterC17#11470
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. #14545012C2semidirect
2. #14545009C2semidirect
3. #14543723C2semidirect
4. #14543706C2semidirect
226. C17#11470semidirect

Maximal subgroups

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

subgroupindex
#145450122
#145450092
#145437232
#145437062
#145374762
#1147017