Finite Group Databasebeta

← #17958267

Subgroups — #17958267

Order 4352.

418 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 92 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#14543721C212yesmaximal, complemented
4#14543704C212yesmaximal, complemented
5C2×#11762878C211yesmaximal, characteristic
6C2×#10587530—21no—
7C2×#10587529—21no—
8#11763704—21no—
9#11763704—21no—
10C22⋊#63216C2212yes—
11C22⋊#63216C2212yes—
12C22×C8×D17C2211yescharacteristic
13C2×C4×C22⋊D17C411yescharacteristic
14#11762878—21no—
15#11762878—21no—
16#11762878—21no—
17#11762878—21no—
18C2×#10587485C2211yescharacteristic
19C2×C22⋊#3622C2211yescharacteristic
20C2×#10587491C411yescharacteristic
21C2×#10587486C411yescharacteristic
22C22×M16×C17C411yescharacteristic
23C23×C4×C17C2×C411yescharacteristic
24C22×C22⋊D17C811yescharacteristic
25C22×C4×D17C2×C411yescharacteristic
26C2×M16×C17—21no—
27C2×M16×C17—21no—
28C2×M16×C17—42no—
29C22×C8×C17C2×C411yescharacteristic
30C22×C8×C17C2×C411yescharacteristic
31C2×C22⋊Dic17C811yescharacteristic
32C4×C22⋊D17—21no—
33C4×C22⋊D17—21no—
34C4×C22⋊D17—21no—
35C4×C22⋊D17—21no—
36C2×#63227C811yescharacteristic
37C2×#63225C811yescharacteristic
38C2×C4×Dic17C2×C411yescharacteristic
39C22×#3622C2×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#10587486—21no—
56#10587485—21no—
57#10587485—21no—
58C24×C17C2×C811yescharacteristic
59C23×D17C2×C811yescharacteristic
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—41no—
63C22×C4×C17—41no—
64C22×C4×C17C2×C811yescharacteristic
65C22×C4×C17C22×C411yescharacteristic
66C2×C22⋊D17—21no—
67C2×C22⋊D17—21no—
68C2×C22⋊D17—42no—
69C22×Dic17C2×C811yescharacteristic
70C22×Dic17C2×C811yescharacteristic
71C22×Dic17C2×C811yescharacteristic
72C2×C4×D17—41no—
73C2×C4×D17—41no—
74C2×C4×D17C22⋊C411yescharacteristic
75C2×C4×D17C22⋊C411yescharacteristic
76C2×C4×D17M1611yescharacteristic
77C2×C4×D17M1611yescharacteristic
78M16×C17—42no—
79M16×C17—42no—
80C2×C8×C17—22no—
81C2×C8×C17—21no—
82C2×C8×C17—41no—
83C2×C8×C17C22⋊C411yescharacteristic
84C2×C8×C17C22⋊C411yescharacteristic
85C22⋊Dic17—21no—
86C22⋊Dic17—21no—
87#63227—21no—
88#63227—21no—
89#63225—21no—
90#63225—21no—
91C4×Dic17—21no—
92C4×Dic17—21no—
93C2×#3622—21no—
94C2×#3622—41no—
95C2×#3622—41no—
96C2×#3622C2×D411yescharacteristic
97C2×#3622C2×D411yescharacteristic
98C8×D17—22no—
99C8×D17—22no—
100C8×D17—41no—
101C8×D17—41no—
102#63216—42no—
103#63216—42no—
104#11467—171nomaximal, Sylow
105C23×C17—21no—
106C23×C17—22no—
107C23×C17—41no—
108C23×C17—41no—
109C23×C17C22×C811yescharacteristic
110C22×D17—22no—
111C22×D17—22no—
112C22×D17—41no—
113C22×D17C22⋊C811yescharacteristic
114C22×D17C22⋊C811yescharacteristic
115C2×C4×C17—21no—
116C2×C4×C17—21no—
117C2×C4×C17—21no—
118C2×C4×C17—42no—
119C2×C4×C17—41no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
122C2×C4×C17C2×C22⋊C411yescharacteristic
123C2×C4×C17C2×M1611yescharacteristic
124C22⋊D17—42no—
125C22⋊D17—42no—
126C2×Dic17—21no—
127C2×Dic17—21no—
128C2×Dic17—22no—
129C2×Dic17—41no—
130C2×Dic17—41no—
131C2×Dic17C22⋊C811yescharacteristic
132C2×Dic17C22⋊C811yescharacteristic
133C4×D17—21no—
134C4×D17—21no—
135C4×D17—21no—
136C4×D17—21no—
137C4×D17—41no—
138C4×D17—41no—
139C8×C17—21no—
140C8×C17—41no—
141C8×C17#9912yes—
142#3622—21no—
143#3622—21no—
144#3622—41no—
145C2×#435—171no—
146#2112—171no—
147C2×C22⋊C16—171no—
148#1322—172no—
149#1314—172no—
150C22×C17—21no—
151C22×C17—21no—
152C22×C17—41no—
153C22×C17—41no—
154C22×C17—41no—
155C22×C17—82no—
156C22×C17C2×C22⋊C811yescharacteristic
157C22×C17#50412yes—
158C2×D17—21no—
159C2×D17—21no—
160C2×D17—21no—
161C2×D17—21no—
162C2×D17—21no—
163C2×D17—44no—
164C2×D17#34912yes—
165C4×C17—21no—
166C4×C17—41no—
167C4×C17C2×#9911yescharacteristic
168C4×C17#41311yescharacteristic
169Dic17—21no—
170Dic17—21no—
171Dic17—41no—
172Dic17—41no—
173C22×M16#59511yescharacteristic
174C23×C8—171no—
175C2×C4×D4—171no—
176C2×M32—341no—
177C22×C16—341no—
178#435—341no—
179#435—341no—
180#435—341no—
181#435—341no—
182C2×C4⋊C8—171no—
183C2×C22⋊C8—171no—
184C2×C22⋊C8—171no—
185C2×#97—171no—
186C22⋊C16—172no—
187C22⋊C16—172no—
188C22⋊C16—341no—
189C22⋊C16—341no—
190C2×C17—22no—
191C2×C17—81no—
192C2×C17#145911yescharacteristic
193C2×C17#211311yescharacteristic
194C2×C17C2×#34911yescharacteristic
195D17—22no—
196D17—41no—
197C22×D4—171no—
198C23×C4—171no—
199C23×C4C2×#59511yescharacteristic
200C2×M16—21no—
201C2×M16—21no—
202C2×M16—42no—
203C22×C8—171no—
204C22×C8—171no—
205C22×C8—171no—
206C22×C8—171no—
207C22×C8—171no—
208C22×C8—171no—
209C22×C8—682no—
210C22×C8C2×#59511yescharacteristic
211C22×C8C2×#59511yescharacteristic
212C4×D4—341no—
213C4×D4—341no—
214C4×D4—341no—
215C4×D4—341no—
216C2×C4⋊C4—171no—
217C2×C22⋊C4—171no—
218C2×C22⋊C4—171no—
219C2×C42—171no—
220M32—682no—
221C2×C16—342no—
222C2×C16—342no—
223C2×C16—682no—
224C4⋊C8—341no—
225C4⋊C8—341no—
226C22⋊C8—341no—
227C22⋊C8—341no—
228C22⋊C8—341no—
229C22⋊C8—341no—
230#97—341no—
231#97—341no—
232C17#1146711yescharacteristic, complemented, Sylow
233C24—171no—
234C24#6324211yescharacteristic
235C2×D4—341no—
236C2×D4—341no—
237C2×D4—682no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—171no—
243C22×C4—171no—
244C22×C4—171no—
245C22×C4—171no—
246C22×C4—171no—
247C22×C4—171no—
248C22×C4—171no—
249C22×C4—681no—
250C22×C4—681no—
251C22×C4#6324211yescharacteristic
252C22×C4C22×#59511yescharacteristic
253M16—42no—
254M16—42no—
255C2×C8—22no—
256C2×C8—21no—
257C2×C8—41no—
258C2×C8—171no—
259C2×C8—171no—
260C2×C8—342no—
261C2×C8—342no—
262C2×C8—341no—
263C2×C8—681no—
264C2×C8—681no—
265C2×C8—681no—
266C2×C8—681no—
267C2×C8C22⋊#59511yescharacteristic
268C2×C8C22⋊#59511yescharacteristic
269C4⋊C4—341no—
270C4⋊C4—341no—
271C22⋊C4—341no—
272C22⋊C4—341no—
273C22⋊C4—341no—
274C22⋊C4—341no—
275C42—341no—
276C42—341no—
277C16—682no—
278C16—682no—
279C23—21no—
280C23—22no—
281C23—41no—
282C23—41no—
283C23—171no—
284C23—171no—
285C23—342no—
286C23—342no—
287C23—681no—
288C23C2×#6324211yescharacteristic
289D4—682no—
290D4—682no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—171no—
299C2×C4—171no—
300C2×C4—341no—
301C2×C4—341no—
302C2×C4—341no—
303C2×C4—341no—
304C2×C4—341no—
305C2×C4—341no—
306C2×C4—342no—
307C2×C4—681no—
308C2×C4—681no—
309C2×C4—681no—
310C2×C4—681no—
311C2×C4D17⋊M1611yescharacteristic
312C2×C4C2×C22⋊#59511yescharacteristic
313C8—21no—
314C8—41no—
315C8—341no—
316C8—341no—
317C8—681no—
318C8#1058755112yes—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—82no—
325C22—172no—
326C22—341no—
327C22—341no—
328C22—341no—
329C22—341no—
330C22—341no—
331C22—684no—
332C22#1176377711yescharacteristic
333C22#1176386812yes—
334C4—21no—
335C4—41no—
336C4—341no—
337C4—341no—
338C4—681no—
339C4—681no—
340C4C2×#1058755111yescharacteristic
341C4#1176379511yescharacteristic
342C2—22no—
343C2—81no—
344C2—342no—
345C2—681no—
346C2#1454401911yescharacteristic
347C2#1454501511yescharacteristic
348C2#1454501811yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC23×C17C22×C8
FrattiniC22×C4C22×#595
FittingC22×M16×C17C4
socleC22×C17C2×C22⋊C8
prime radicalC22×C22⋊D17C8
cosocleC22×#3622C23
hypercenterC22×M16#595
hypocenterC17#11467
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
1. #14545012C2semidirect
2. #14545009C2semidirect
3. #14543721C2semidirect
4. #14543704C2semidirect
232. C17#11467semidirect

Maximal subgroups

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

subgroupindex
#145450122
#145450092
#145437212
#145437042
C2×#117628782
#1146717