Finite Group Databasebeta

← #16936934

Subgroups — #16936934

Order 4352.

510 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763161C211yesmaximal, characteristic
2C2×#11763094C211yesmaximal, characteristic
3#14529721C211yesmaximal, characteristic
4C2×#11762558C211yesmaximal, characteristic
5C2×#11762554C211yesmaximal, characteristic
6#14526618C211yesmaximal, characteristic
7C2×C17×#477C211yesmaximal, characteristic
8C2×#10587555C2211yescharacteristic
9#11763161—22no—
10#11763161—22no—
11#11763094—22no—
12#11763094—22no—
13C2×#10587479—21no—
14C2×C4⋊#3622C2211yescharacteristic
15C2×C4⋊#3622C2211yescharacteristic
16C2×#10587506—21no—
17C2×#10587481—22no—
18C2×C4×#3622C2211yescharacteristic
19#11762564—22no—
20#11762558—22no—
21#11762554—22no—
22C2×C17×C4⋊Q8C2211yescharacteristic
23C2×C4×Q8×C17C2211yescharacteristic
24C17×#477—22no—
25C17×#477—22no—
26C2×C17×#107—21no—
27C2×C17×C4⋊C8C2211yescharacteristic
28C2×C17×#103—21no—
29C22×Q8×C17—21no—
30C22×Q8×C17D411yescharacteristic
31C22×Dic34—21no—
32C22×C8×C17—21no—
33C17×C4⋊Q8—21no—
34C17×C4⋊Q8—21no—
35C17×C4⋊Q8—21no—
36C17×C4⋊Q8D412yes—
37C4×Q8×C17—21no—
38C4×Q8×C17—21no—
39C4×Q8×C17—21no—
40C4×Q8×C17—21no—
41C2×C4⋊C4×C17—21no—
42C2×C4⋊C4×C17—21no—
43C2×C4⋊C4×C17—21no—
44C2×C4⋊C4×C17D411yescharacteristic
45C2×C42×C17—21no—
46C2×C42×C17C2311yescharacteristic
47C2×C4⋊Dic17—21no—
48C2×C4⋊Dic17—21no—
49C22×#3622—21no—
50C22×#3622—21no—
51C22×#3622D412yes—
52#10587555—21no—
53#10587555—21no—
54#10587555—21no—
55#10587555D412yes—
56C17×#107—24no—
57C17×C4⋊C8—21no—
58C17×C4⋊C8D412yes—
59C17×#103—24no—
60#10587506—24no—
61#10587481—28no—
62#10587479—24no—
63C4⋊#3622—21no—
64C4⋊#3622—21no—
65C4⋊#3622—21no—
66C4⋊#3622D412yes—
67C4×#3622—21no—
68C4×#3622—21no—
69C2×Q8×C17—21no—
70C2×Q8×C17—21no—
71C2×Q8×C17—21no—
72C2×Q8×C17—22no—
73C2×Q8×C17—21no—
74C2×Q8×C17—21no—
75C2×Q8×C17—41no—
76C2×Q8×C17—82no—
77C2×Q8×C17Q1612yes—
78C22×C4×C17—21no—
79C22×C4×C17—21no—
80C22×C4×C17—41no—
81C22×C4×C17C2×D411yescharacteristic
82C22×C4×C17C2×D411yescharacteristic
83C22×C4×C17#4111yescharacteristic
84C22×Dic17—41no—
85C2×Dic34—22no—
86C2×Dic34—42no—
87C2×Dic34—42no—
88C2×Dic34—41no—
89C2×C8×C17—22no—
90C2×C8×C17—41no—
91C2×C8×C17—41no—
92C4⋊C4×C17—22no—
93C4⋊C4×C17—22no—
94C4⋊C4×C17—21no—
95C4⋊C4×C17—21no—
96C4⋊C4×C17—41no—
97C4⋊C4×C17—41no—
98C4⋊C4×C17—41no—
99C4⋊C4×C17—41no—
100C42×C17—41no—
101C42×C17—41no—
102C42×C17C2×D411yescharacteristic
103C42×C17C2×D411yescharacteristic
104C42×C17C2×D411yescharacteristic
105C42×C17C2×D411yescharacteristic
106C4⋊Dic17—22no—
107C4⋊Dic17—22no—
108C4⋊Dic17—41no—
109C4⋊Dic17—41no—
110C2×#3622—22no—
111C2×#3622—22no—
112C2×#3622—22no—
113C2×#3622—22no—
114C2×#3622—41no—
115C2×#3622—41no—
116C2×#3622—41no—
117C2×#3622—42no—
118#10277—171nomaximal, Sylow
119C23×C17#12111yescharacteristic
120Q8×C17—22no—
121Q8×C17—22no—
122Q8×C17—41no—
123Q8×C17—41no—
124Q8×C17—82no—
125Q8×C17—82no—
126C2×C4×C17—22no—
127C2×C4×C17—22no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
131C2×C4×C17—42no—
132C2×C4×C17—42no—
133C2×C4×C17—82no—
134C2×C4×C17#12011yescharacteristic
135C2×C4×C17#12011yescharacteristic
136C2×C4×C17#12011yescharacteristic
137C2×C4×C17#12111yescharacteristic
138C2×C4×C17#12111yescharacteristic
139C2×C4×C17#12711yescharacteristic
140C2×C4×C17C2×Q1611yescharacteristic
141C2×C4×C17#13512yes—
142C2×C4×C17#13511yescharacteristic
143C2×C4×C17#13712yes—
144C2×C4×C17#13711yescharacteristic
145C2×C4×C17#13711yescharacteristic
146C2×Dic17—42no—
147C2×Dic17—82no—
148Dic34—44no—
149Dic34—81no—
150Dic34—81no—
151C8×C17—42no—
152#3622—42no—
153#3622—42no—
154#3622—81no—
155C2×#487—171no—
156C2×#477D1711yescharacteristic
157C2×#475—171no—
158#1984—171no—
159C2×#333—171no—
160C2×#332—171no—
161#1277—171no—
162C22×C17#39211yescharacteristic
163C22×C17#46412yes—
164C22×C17#46711yescharacteristic
165C22×C17#47011yescharacteristic
166C22×C17#47112yes—
167C4×C17—21no—
168C4×C17—21no—
169C4×C17—42no—
170C4×C17—81no—
171C4×C17—82no—
172C4×C17#45111yescharacteristic
173C4×C17#45111yescharacteristic
174C4×C17#45211yescharacteristic
175C4×C17#45212yes—
176C4×C17#45211yescharacteristic
177C4×C17#49511yescharacteristic
178C4×C17#49711yescharacteristic
179Dic17—82no—
180C2×C4⋊Q8—171no—
181C2×C4⋊Q8C2×D1711yescharacteristic
182C2×C4×Q8C2×D1711yescharacteristic
183#487—342no—
184#487—342no—
185#477—22no—
186#477—22no—
187#475—342no—
188#475—342no—
189C2×#107—21no—
190C2×#106—341no—
191C2×C4⋊C8—171no—
192C2×C4⋊C8—171no—
193C2×C4⋊C8C2×D1711yescharacteristic
194C2×#103—21no—
195C2×#103—342no—
196C2×#103—341no—
197C2×C4×C8—171no—
198#336—342no—
199#333—342no—
200#332—342no—
201C2×C17#168412yes—
202C2×C17#170412yes—
203C2×C17#200111yescharacteristic
204C2×C17#201511yescharacteristic
205C2×C17#201911yescharacteristic
206C22×Q8—21no—
207C22×Q8—341no—
208C22×Q8C22⋊D1711yescharacteristic
209C22×C8—21no—
210C22×C8—172no—
211C22×C8—341no—
212C22×C8—341no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—172no—
217C4⋊Q8—341no—
218C4⋊Q8—341no—
219C4⋊Q8—341no—
220C4⋊Q8C22⋊D1712yes—
221C4×Q8—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—341no—
229C2×C4⋊C4—341no—
230C2×C4⋊C4C22⋊D1711yescharacteristic
231C2×C42—21no—
232C2×C42C22×D1711yescharacteristic
233#107—24no—
234#106—344no—
235C4⋊C8—21no—
236C4⋊C8—172no—
237C4⋊C8—341no—
238C4⋊C8—341no—
239C4⋊C8—341no—
240C4⋊C8C22⋊D1712yes—
241#103—24no—
242#103—348no—
243#103—344no—
244C4×C8—341no—
245C4×C8—341no—
246C17#1027711yescharacteristic, complemented, Sylow
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—22no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—21no—
253C2×Q8—41no—
254C2×Q8—82no—
255C2×Q8—342no—
256C2×Q8—681no—
257C2×Q8—682no—
258C2×Q8—682no—
259C2×Q8#6323112yes—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—681no—
264C22×C4D4×D1711yescharacteristic
265C22×C4#6325411yescharacteristic
266C22×C4C2×C22⋊D1711yescharacteristic
267C2×C8—22no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—342no—
271C2×C8—342no—
272C2×C8—342no—
273C2×C8—342no—
274C2×C8—681no—
275C2×C8—681no—
276C2×C8—682no—
277C2×C8—681no—
278C4⋊C4—22no—
279C4⋊C4—21no—
280C4⋊C4—22no—
281C4⋊C4—21no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—342no—
287C4⋊C4—342no—
288C4⋊C4—681no—
289C4⋊C4—681no—
290C42—41no—
291C42—41no—
292C42D4×D1711yescharacteristic
293C42D4×D1711yescharacteristic
294C42C2×C22⋊D1711yescharacteristic
295C42C2×C22⋊D1711yescharacteristic
296C23#1058762511yescharacteristic
297Q8—22no—
298Q8—22no—
299Q8—41no—
300Q8—41no—
301Q8—82no—
302Q8—82no—
303Q8—684no—
304Q8—1361no—
305Q8—1361no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—82no—
314C2×C4—682no—
315C2×C4—1362no—
316C2×C4#1058760412yes—
317C2×C4#1058760512yes—
318C2×C4#1058762311yescharacteristic
319C2×C4#1058762311yescharacteristic
320C2×C4#1058762411yescharacteristic
321C2×C4#1058762511yescharacteristic
322C2×C4#1058762611yescharacteristic
323C2×C4#1058762811yescharacteristic
324C2×C4C2×#6323111yescharacteristic
325C2×C4#1058763611yescharacteristic
326C2×C4#1058763711yescharacteristic
327C2×C4#1058763911yescharacteristic
328C8—42no—
329C8—682no—
330C8—682no—
331C8—1361no—
332C22#1176271711yescharacteristic
333C22#1176303312yes—
334C22#1176304811yescharacteristic
335C22#1176306511yescharacteristic
336C22#1176307012yes—
337C4—21no—
338C4—21no—
339C4—42no—
340C4—81no—
341C4—82no—
342C4—1362no—
343C4#1176296411yescharacteristic
344C4#1176296511yescharacteristic
345C4#1176296911yescharacteristic
346C4#1176297012yes—
347C4#1176297111yescharacteristic
348C4#1176319411yescharacteristic
349C4#1176320211yescharacteristic
350C2#1452824412yes—
351C2#1452836812yes—
352C2#1452979211yescharacteristic
353C2#1452987511yescharacteristic
354C2#1452989811yescharacteristic
subgroupG/H
centerC23#10587625
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC2×C17×#477C2
socle, prime radicalC23×C17#121
hypercenterC2×#477D17
hypocenterC17#10277
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
246. C17#10277semidirect

Maximal subgroups

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

subgroupindex
C2×#117631612
C2×#117630942
#145297212
C2×#117625582
C2×#117625542
#145266182
C2×C17×#4772
#1027717