Finite Group Databasebeta

← #17962117

Subgroups — #17962117

Order 4352.

394 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763730C211yesmaximal, characteristic, complemented
2C2×C22⋊#63216C211yesmaximal, characteristic
3C2×C22⋊#63216C211yesmaximal, characteristic
4C2×#11763695C211yesmaximal, characteristic, complemented
5#14543823C211yesmaximal, characteristic, complemented
6#14543823C211yesmaximal, characteristic, complemented
7#14528558C211yesmaximal, characteristic
8C22×#63216C2211yescharacteristic
9C22×#63216C2211yescharacteristic
10C22×#63216C2211yescharacteristic
11C22×#63216C2211yescharacteristic
12#11763730—22no—
13C22⋊#63216—22no—
14C22⋊#63216—22no—
15#11763695—22no—
16C23×#3622C2211yescharacteristic
17C2×C8×Dic17C2211yescharacteristic
18C2×C8×Dic17C2211yescharacteristic
19C4×C22⋊Dic17C411yescharacteristic
20#11762563C411yescharacteristic
21#11762563C411yescharacteristic
22C2×C17×C22⋊C8C411yescharacteristic
23C23×C4×C17C2×C411yescharacteristic
24C22×C8×C17C2×C411yescharacteristic
25C22×C8×C17C2×C411yescharacteristic
26C2×C22⋊Dic17C811yescharacteristic
27C2×C22⋊Dic17C811yescharacteristic
28C2×C4×Dic17C2×C411yescharacteristic
29C2×C4×Dic17C2×C411yescharacteristic
30C22×#3622—21no—
31C22×#3622—21no—
32C22×#3622—21no—
33C22×#3622—21no—
34C22×#3622—21no—
35C22×#3622—21no—
36C22×#3622C2×C411yescharacteristic
37C22×#3622C2311yescharacteristic
38C2×#63216—21no—
39C2×#63216—21no—
40C2×#63216—21no—
41C2×#63216—21no—
42C2×#63216—21no—
43C2×#63216—21no—
44C2×#63216—21no—
45C2×#63216—21no—
46C2×#63216—21no—
47C2×#63216—21no—
48C2×#63216D412yes—
49C2×#63216D412yes—
50C17×C22⋊C8—22no—
51#10587502C811yescharacteristic
52#10587502C811yescharacteristic
53C8×Dic17—21no—
54C8×Dic17—21no—
55C8×Dic17—21no—
56C8×Dic17—21no—
57C24×C17C2×C811yescharacteristic
58C22×C4×C17—21no—
59C22×C4×C17—21no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17C2×C811yescharacteristic
65C22×C4×C17C22×C411yescharacteristic
66C22×Dic17C2×C811yescharacteristic
67C22×Dic17C2×C811yescharacteristic
68C22×Dic17C2×C811yescharacteristic
69C22×Dic17C2×C811yescharacteristic
70C2×C8×C17—21no—
71C2×C8×C17—21no—
72C2×C8×C17—21no—
73C2×C8×C17—21no—
74C2×C8×C17—21no—
75C2×C8×C17M1612yes—
76C22⋊Dic17—22no—
77C22⋊Dic17C1614yescomplemented
78C4×Dic17—21no—
79C4×Dic17—21no—
80C4×Dic17—21no—
81C4×Dic17—21no—
82C2×#3622—21no—
83C2×#3622—21no—
84C2×#3622—21no—
85C2×#3622—41no—
86C2×#3622—41no—
87C2×#3622—41no—
88C2×#3622—41no—
89C2×#3622C2×D411yescharacteristic
90C2×#3622C2×D411yescharacteristic
91C2×#3622#4111yescharacteristic
92C2×#3622#4111yescharacteristic
93C2×#3622#4111yescharacteristic
94C2×#3622#4111yescharacteristic
95#63216—22no—
96#63216—22no—
97#63216—41no—
98#63216—41no—
99#13120—171nomaximal, Sylow
100C23×C17—21no—
101C23×C17—21no—
102C23×C17—21no—
103C23×C17—21no—
104C23×C17—21no—
105C23×C17—21no—
106C23×C17C2×C1612yes—
107C23×C17C22×C811yescharacteristic
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—21no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17#11711yescharacteristic
116C2×C4×C17C4×D411yescharacteristic
117C2×C4×C17C4×D411yescharacteristic
118C2×C4×C17C2×M1611yescharacteristic
119C2×C4×C17#13111yescharacteristic
120C2×C4×C17#13111yescharacteristic
121C2×Dic17—21no—
122C2×Dic17—21no—
123C2×Dic17—21no—
124C2×Dic17—21no—
125C2×Dic17—21no—
126C2×Dic17—21no—
127C2×Dic17—21no—
128C2×Dic17—21no—
129C2×Dic17—21no—
130C2×Dic17C2×C1612yes—
131C2×Dic17C2×C1612yes—
132C2×Dic17M3212yes—
133C8×C17—22no—
134C8×C17—41no—
135#3622—41no—
136#3622#12111yescharacteristic
137#3622#12311yescharacteristic
138#3622#12411yescharacteristic
139#3622#12611yescharacteristic
140C2×C4⋊C16—171no—
141C2×C22⋊C16—171no—
142C2×C22⋊C16—171no—
143C2×C4×C16—171no—
144C8×C22⋊C4—171no—
145#1374—171no—
146#1374—171no—
147C22×C17—22no—
148C22×C17—22no—
149C22×C17—22no—
150C22×C17—41no—
151C22×C17—41no—
152C22×C17—41no—
153C22×C17—41no—
154C22×C17#43111yescharacteristic
155C22×C17C8×D411yescharacteristic
156C22×C17C8×D411yescharacteristic
157C22×C17C22×C1611yescharacteristic
158C22×C17C2×M3211yescharacteristic
159C22×C17#50411yescharacteristic
160C22×C17#50411yescharacteristic
161C4×C17—41no—
162C4×C17#38811yescharacteristic
163C4×C17#43311yescharacteristic
164C4×C17#43511yescharacteristic
165C4×C17#43611yescharacteristic
166Dic17—22no—
167Dic17—22no—
168Dic17—22no—
169Dic17—41no—
170C23×C8—171no—
171C22×C16—171no—
172C22×C16—171no—
173C22×C16—171no—
174C22×C16—171no—
175C2×C22⋊C8#59511yescharacteristic
176C2×C4×C8—171no—
177C2×C4×C8—171no—
178C4×C22⋊C4—171no—
179C4⋊C16—342no—
180C22⋊C16—342no—
181C22⋊C16—342no—
182C4×C16—342no—
183#336—171no—
184#336—171no—
185C2×C17—42no—
186C2×C17#192311yescharacteristic
187C2×C17#216211yescharacteristic
188C2×C17#216411yescharacteristic
189C2×C17D4×C1611yescharacteristic
190C2×C17D4×C1611yescharacteristic
191C2×C17#216811yescharacteristic
192C2×C17#216911yescharacteristic
193C23×C4C2×#59511yescharacteristic
194C22×C8—171no—
195C22×C8—171no—
196C22×C8—341no—
197C22×C8—341no—
198C22×C8—341no—
199C22×C8—341no—
200C22×C8—341no—
201C22×C8—341no—
202C22×C8C2×#59511yescharacteristic
203C22×C8C2×#59511yescharacteristic
204C2×C22⋊C4—171no—
205C2×C22⋊C4—171no—
206C2×C42—171no—
207C2×C42—171no—
208C2×C16—172no—
209C2×C16—172no—
210C2×C16—341no—
211C2×C16—341no—
212C2×C16—341no—
213C2×C16—341no—
214C2×C16—341no—
215C2×C16—341no—
216C2×C16—341no—
217C2×C16—341no—
218C2×C16—341no—
219C2×C16—341no—
220C22⋊C8—22no—
221C4×C8—341no—
222C4×C8—341no—
223C4×C8—341no—
224C4×C8—341no—
225#95—171no—
226#95—171no—
227C17#1312011yescharacteristic, complemented, Sylow
228C24#6324211yescharacteristic
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—171no—
236C22×C4—171no—
237C22×C4—171no—
238C22×C4—171no—
239C22×C4#6324211yescharacteristic
240C22×C4C22×#59511yescharacteristic
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—21no—
246C2×C8—171no—
247C2×C8—171no—
248C2×C8—171no—
249C2×C8—171no—
250C2×C8—171no—
251C2×C8—171no—
252C2×C8—341no—
253C2×C8—341no—
254C2×C8—341no—
255C2×C8—681no—
256C2×C8—681no—
257C2×C8—681no—
258C2×C8—681no—
259C2×C8#6324712yes—
260C22⋊C4—174no—
261C22⋊C4—342no—
262C42—341no—
263C42—341no—
264C42—341no—
265C42—341no—
266C16—342no—
267C16—342no—
268C16—681no—
269C16—681no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23#1058752912yes—
277C23C2×#6324211yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—172no—
286C2×C4—172no—
287C2×C4—172no—
288C2×C4—341no—
289C2×C4—341no—
290C2×C4—341no—
291C2×C4—341no—
292C2×C4—341no—
293C2×C4—341no—
294C2×C4—341no—
295C2×C4—341no—
296C2×C4—341no—
297C2×C4#1058767711yescharacteristic
298C2×C4#1058767811yescharacteristic
299C2×C4#1058767811yescharacteristic
300C2×C4D4×#59511yescharacteristic
301C2×C4D4×#59511yescharacteristic
302C2×C4C2×#6324711yescharacteristic
303C8—22no—
304C8—41no—
305C8—171no—
306C8—171no—
307C8—171no—
308C8—171no—
309C8—681no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22#1176382611yescharacteristic
318C22#1176383611yescharacteristic
319C22#1176383611yescharacteristic
320C22C2×#1058752911yescharacteristic
321C22#1176386511yescharacteristic
322C22#1176386811yescharacteristic
323C22#1176386811yescharacteristic
324C4—41no—
325C4—342no—
326C4—342no—
327C4—342no—
328C4—681no—
329C4#1176375911yescharacteristic
330C4#1176383311yescharacteristic
331C4#1176384011yescharacteristic
332C4#1176384411yescharacteristic
333C2—42no—
334C2#1454485411yescharacteristic
335C2#1454514211yescharacteristic
336C2#1454515011yescharacteristic
337C2#1454516211yescharacteristic
338C2#1454516211yescharacteristic
339C2#1454516511yescharacteristic
340C2#1454516911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×#595
commutatorC22×C17C22×C16
FittingC2×C17×C22⋊C8C4
socleC23×C17C22×C8
prime radicalC24×C17C2×C8
cosocleC22×#3622C23
hypercenterC2×C22⋊C8#595
hypocenterC17#13120
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#11763730C2semidirect
4. C2×#11763695C2semidirect
5. #14543823C2semidirect
6. #14543823C2semidirect
77. C22⋊Dic17C16semidirect
227. C17#13120semidirect

Maximal subgroups

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

subgroupindex
C2×#117637302
C2×C22⋊#632162
C2×#117636952
#145438232
#145285582
#1312017