Finite Group Databasebeta

← #16929393

Subgroups — #16929393

Order 4352.

534 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 107 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#14532068C211yesmaximal, characteristic
2C4×#10587504C211yesmaximal, characteristic
3#14527230C212yesmaximal, complemented
4#14526676C212yesmaximal, complemented
5C17×#2973C211yesmaximal, characteristic
6C2×C4×Dic34C2211yescharacteristic
7C2×#10587504—21no—
8C4×#63223C2212yes—
9#11762747—21no—
10#11762734C411yescharacteristic
11#11762734C411yescharacteristic
12#11762723—21no—
13#11762721C411yescharacteristic
14#11762721C411yescharacteristic
15C4×C22⋊Dic17—21no—
16C4×C22⋊Dic17—21no—
17#11762655C2211yescharacteristic
18#11762578—21no—
19#11762539—24no—
20C2×C4×D4×C17C2211yescharacteristic
21C17×#435—24no—
22C17×#432C2212yes—
23C17×#407—21no—
24C2×C17×C22⋊C8—21no—
25C22×D4×C17D411yescharacteristic
26C23×C4×C17D411yescharacteristic
27C23×C4×C17D411yescharacteristic
28C22×Dic34C2×C411yescharacteristic
29C2×M16×C17—22no—
30C22×C8×C17—22no—
31C4×D4×C17—22no—
32C4×D4×C17—22no—
33C2×C4⋊C4×C17D411yescharacteristic
34C2×C22⋊C4×C17C2×C411yescharacteristic
35C2×C22⋊C4×C17C2×C411yescharacteristic
36C2×C42×C17C2311yescharacteristic
37C2×C22⋊Dic17—21no—
38C2×C22⋊Dic17—21no—
39C2×C22⋊Dic17—21no—
40C2×C22⋊Dic17—21no—
41C2×C4⋊Dic17C2×C411yescharacteristic
42C2×#63225—21no—
43C2×C4×Dic17—21no—
44C2×C4×Dic17—21no—
45C2×#63223—22no—
46C4×Dic34—22no—
47C4×Dic34—22no—
48C17×C4⋊C8D414yes—
49C17×C22⋊C8—22no—
50C17×C22⋊C8—22no—
51C17×C22⋊C8—22no—
52C17×#97—22no—
53#10587504—24no—
54#10587502—21no—
55#10587502—21no—
56#10587502—21no—
57#10587502—21no—
58#10587502—21no—
59#10587502C2×C411yescharacteristic
60#10587502C2×C411yescharacteristic
61#10587474—22no—
62C4×#3622—22no—
63C24×C17C22⋊C411yescharacteristic
64C24×C17C22⋊C411yescharacteristic
65C2×D4×C17—22no—
66C2×D4×C17—22no—
67C2×D4×C17—41no—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17—21no—
71C22×C4×C17—21no—
72C22×C4×C17—42no—
73C22×C4×C17—42no—
74C22×C4×C17C22⋊C411yescharacteristic
75C22×C4×C17C22⋊C411yescharacteristic
76C22×C4×C17C22×C411yescharacteristic
77C22×C4×C17C2×D411yescharacteristic
78C22×C4×C17C2×D411yescharacteristic
79C22×Dic17—21no—
80C22×Dic17—21no—
81C22×Dic17—21no—
82C22×Dic17—21no—
83C2×Dic34—22no—
84C2×Dic34—42no—
85M16×C17—82no—
86C2×C8×C17—24no—
87C2×C8×C17—82no—
88C4⋊C4×C17—22no—
89C22⋊C4×C17—22no—
90C22⋊C4×C17—22no—
91C42×C17C2×D412yes—
92C42×C17#4112yes—
93C22⋊Dic17—42no—
94C22⋊Dic17—42no—
95C22⋊Dic17—42no—
96C22⋊Dic17—42no—
97C4⋊Dic17—22no—
98#63225—42no—
99C4×Dic17—42no—
100C4×Dic17—41no—
101C4×Dic17—41no—
102#63223—24no—
103#63223—42no—
104C2×#3622—42no—
105#9029—171nomaximal, Sylow
106C23×C17—21no—
107C23×C17—21no—
108C23×C17—21no—
109C23×C17—21no—
110C23×C17—21no—
111C23×C17—41no—
112C23×C17—41no—
113C23×C17—41no—
114C23×C17—41no—
115C23×C17#10412yes—
116C23×C17C2×C22⋊C411yescharacteristic
117D4×C17—44no—
118C2×C4×C17—21no—
119C2×C4×C17—21no—
120C2×C4×C17—22no—
121C2×C4×C17—21no—
122C2×C4×C17—21no—
123C2×C4×C17—41no—
124C2×C4×C17—42no—
125C2×C4×C17—42no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17—81no—
129C2×C4×C17—81no—
130C2×C4×C17C4×D412yes—
131C2×C4×C17#12011yescharacteristic
132C2×C4×C17#12112yes—
133C2×C4×C17#12311yescharacteristic
134C2×Dic17—22no—
135C2×Dic17—41no—
136C2×Dic17—41no—
137C2×Dic17—41no—
138C2×Dic17—41no—
139C2×Dic17—41no—
140C2×Dic17—41no—
141C2×Dic17—41no—
142C2×Dic17—41no—
143C2×Dic17—41no—
144C2×Dic17—41no—
145C2×Dic17—41no—
146Dic34—24no—
147Dic34—42no—
148C8×C17—44no—
149#3622—44no—
150#2973D1711yescharacteristic
151#2398—171no—
152C4×#100—171no—
153#1491—172no—
154#1300—172no—
155C22×C17—21no—
156C22×C17—21no—
157C22×C17—22no—
158C22×C17—42no—
159C22×C17—42no—
160C22×C17—41no—
161C22×C17—41no—
162C22×C17—41no—
163C22×C17—41no—
164C22×C17—41no—
165C22×C17—81no—
166C22×C17—81no—
167C22×C17#38611yescharacteristic
168C22×C17C2×#10411yescharacteristic
169C22×C17#42111yescharacteristic
170C4×C17—22no—
171C4×C17—21no—
172C4×C17—22no—
173C4×C17—41no—
174C4×C17—41no—
175C4×C17#45512yes—
176Dic17—42no—
177Dic17—81no—
178Dic17—81no—
179Dic17—81no—
180C2×C4×Q8—171no—
181C2×C4×D4C2×D1711yescharacteristic
182#435—24no—
183#432C2×D1712yes—
184C2×#100—341no—
185#407—21no—
186C2×C22⋊C8—21no—
187C4×M16—172no—
188#400—341no—
189#397—171no—
190#397—171no—
191#394—341no—
192#393—171no—
193#393—171no—
194C4×C22⋊C4—341no—
195C4×C22⋊C4—341no—
196#376—171no—
197#343—341no—
198Q8⋊C8—344no—
199C2×C17—21no—
200C2×C17—21no—
201C2×C17—42no—
202C2×C17—81no—
203C2×C17#187111yescharacteristic
204C2×C17#188511yescharacteristic
205C2×C17#189111yescharacteristic
206C22×Q8—171no—
207C22×D4D6811yescharacteristic
208C23×C4C22⋊D1711yescharacteristic
209C23×C4C22⋊D1711yescharacteristic
210C2×M16—22no—
211C2×M16—342no—
212C22×C8—22no—
213C4×Q8—342no—
214C4×Q8—342no—
215C4×D4—22no—
216C4×D4—22no—
217C2×C4⋊C4—171no—
218C2×C4⋊C4—341no—
219C2×C4⋊C4D6811yescharacteristic
220C2×C22⋊C4—341no—
221C2×C22⋊C4—341no—
222C2×C22⋊C4—341no—
223C2×C22⋊C4—341no—
224C2×C22⋊C4C4×D1711yescharacteristic
225C2×C22⋊C4C4×D1711yescharacteristic
226C2×C42—341no—
227C2×C42—341no—
228C2×C42C22×D1711yescharacteristic
229C4⋊C8C22⋊D1714yes—
230#100—344no—
231C22⋊C8—22no—
232C22⋊C8—22no—
233C22⋊C8—22no—
234#97—22no—
235#97—342no—
236C4×C8—342no—
237#95—171no—
238#95—171no—
239#95—341no—
240#95—341no—
241#95—341no—
242#95—341no—
243#95—341no—
244C17#902911yescharacteristic, complemented, Sylow
245C24#6322711yescharacteristic
246C24#6322711yescharacteristic
247C2×Q8—342no—
248C2×Q8—682no—
249C2×D4—22no—
250C2×D4—22no—
251C2×D4—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—341no—
259C22×C4—341no—
260C22×C4—341no—
261C22×C4—341no—
262C22×C4#6322711yescharacteristic
263C22×C4#6322711yescharacteristic
264C22×C4C2×C4×D1711yescharacteristic
265C22×C4C2×D6811yescharacteristic
266C22×C4C2×C22⋊D1711yescharacteristic
267M16—82no—
268M16—344no—
269M16—682no—
270C2×C8—24no—
271C2×C8—82no—
272C2×C8—682no—
273C4⋊C4—22no—
274C4⋊C4—342no—
275C4⋊C4—682no—
276C22⋊C4—22no—
277C22⋊C4—22no—
278C22⋊C4—682no—
279C22⋊C4—682no—
280C22⋊C4—682no—
281C22⋊C4—682no—
282C42—682no—
283C42—681no—
284C42—681no—
285C42#6325212yes—
286C42C2×C22⋊D1712yes—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23#1058749612yes—
297C23C2×#6322711yescharacteristic
298Q8—344no—
299Q8—682no—
300D4—44no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—342no—
314C2×C4—681no—
315C2×C4—681no—
316C2×C4—681no—
317C2×C4—681no—
318C2×C4—681no—
319C2×C4—681no—
320C2×C4—681no—
321C2×C4—681no—
322C2×C4—681no—
323C2×C4—681no—
324C2×C4—681no—
325C2×C4C4×C22⋊D1712yes—
326C2×C4#1058761511yescharacteristic
327C2×C4#1058761612yes—
328C2×C4#1058763911yescharacteristic
329C8—44no—
330C8—684no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—42no—
335C22—42no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—81no—
342C22—81no—
343C22#1176268811yescharacteristic
344C22C2×#1058749611yescharacteristic
345C22#1176282511yescharacteristic
346C4—22no—
347C4—21no—
348C4—22no—
349C4—41no—
350C4—41no—
351C4—682no—
352C4—1361no—
353C4—1361no—
354C4—1361no—
355C4#1176298712yes—
356C2—21no—
357C2—21no—
358C2—42no—
359C2—81no—
360C2#1452908611yescharacteristic
361C2#1452917211yescharacteristic
362C2#1452920211yescharacteristic
subgroupG/H
centerC2×C4#10587639
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#2973C2
socleC22×C17#386
prime radicalC22×D4×C17D4
cosocleC2×C42×C17C23
hypercenter#2973D17
hypocenterC17#9029
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2973

Complements

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

NH ≅ G/Ntype
3. #14527230C2semidirect
4. #14526676C2semidirect
244. C17#9029semidirect

Maximal subgroups

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

subgroupindex
#145320682
C4×#105875042
#145272302
#145266762
C17×#29732
#902917