Finite Group Databasebeta

← #16943851

Subgroups — #16943851

Order 4352.

492 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 83 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#14533062C211yesmaximal, characteristic
2C2×#11762533C211yesmaximal, characteristic
3#14526731C212yesmaximal, complemented
4#14526713C212yesmaximal, complemented
5C17×#1462C211yesmaximal, characteristic
6C22×C22⋊Dic17C411yescharacteristic
7C2×C22⋊#3622—21no—
8#11762737—21no—
9#11762737—21no—
10#11762682—21no—
11#11762681C411yescharacteristic
12#11762681C2211yescharacteristic
13#11762672—21no—
14#11762670C411yescharacteristic
15#11762670C2211yescharacteristic
16#11762665C411yescharacteristic
17#11762533—21no—
18#11762533C2212yes—
19C22×C22⋊C4×C17C2211yescharacteristic
20C17×#407—21no—
21C17×#323—21no—
22C17×#323C2212yes—
23C25×C17C2×C411yescharacteristic
24C23×C4×C17D411yescharacteristic
25C23×C4×C17D411yescharacteristic
26C23×Dic17C2×C411yescharacteristic
27C23×Dic17C2×C411yescharacteristic
28C2×M16×C17—41no—
29C2×C22⋊C4×C17—41no—
30C2×C22⋊C4×C17—41no—
31C2×C22⋊C4×C17C2×C411yescharacteristic
32C2×C22⋊C4×C17D411yescharacteristic
33C2×C22⋊C4×C17D411yescharacteristic
34C2×C22⋊C4×C17C2311yescharacteristic
35C2×C22⋊Dic17—21no—
36C2×C22⋊Dic17—21no—
37C2×C22⋊Dic17—21no—
38C2×C22⋊Dic17—21no—
39C2×C22⋊Dic17—41no—
40C2×C22⋊Dic17—41no—
41C2×C22⋊Dic17C2×C411yescharacteristic
42C2×C22⋊Dic17C2×C411yescharacteristic
43C2×#63225—21no—
44C2×#63225—21no—
45C22×#3622—41no—
46C17×C22⋊C8—22no—
47C17×C22⋊C8—41no—
48#10587502—21no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54C22⋊#3622—22no—
55C22⋊#3622—41no—
56C24×C17—21no—
57C24×C17—21no—
58C24×C17—22no—
59C24×C17—41no—
60C24×C17—42no—
61C24×C17—81no—
62C24×C17C22⋊C411yescharacteristic
63C24×C17C22⋊C411yescharacteristic
64C24×C17C22×C411yescharacteristic
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—42no—
70C22×C4×C17—81no—
71C22×C4×C17C22⋊C411yescharacteristic
72C22×C4×C17C22⋊C411yescharacteristic
73C22×C4×C17C2×D411yescharacteristic
74C22×C4×C17C2×D411yescharacteristic
75C22×Dic17—21no—
76C22×Dic17—21no—
77C22×Dic17—21no—
78C22×Dic17—21no—
79C22×Dic17—22no—
80C22×Dic17—41no—
81C22×Dic17—41no—
82C22×Dic17—41no—
83C22×Dic17—81no—
84M16×C17—82no—
85C2×C8×C17—42no—
86C22⋊C4×C17—41no—
87C22⋊C4×C17—41no—
88C22⋊C4×C17—41no—
89C22⋊C4×C17—41no—
90C22⋊Dic17—22no—
91C22⋊Dic17—42no—
92C22⋊Dic17—42no—
93C22⋊Dic17—41no—
94C22⋊Dic17—41no—
95C22⋊Dic17—41no—
96C22⋊Dic17—81no—
97#63225—81no—
98#63225—81no—
99C2×#3622—42no—
100C2×#3622—82no—
101#11543—171nomaximal, Sylow
102C23×C17—22no—
103C23×C17—21no—
104C23×C17—21no—
105C23×C17—21no—
106C23×C17—21no—
107C23×C17—21no—
108C23×C17—21no—
109C23×C17—21no—
110C23×C17—41no—
111C23×C17—42no—
112C23×C17—42no—
113C23×C17—41no—
114C23×C17—41no—
115C23×C17—42no—
116C23×C17—41no—
117C23×C17—41no—
118C23×C17—42no—
119C23×C17—81no—
120C23×C17—81no—
121C23×C17—84no—
122C23×C17—84no—
123C23×C17#9911yescharacteristic
124C23×C17#9911yescharacteristic
125C23×C17C2×C22⋊C411yescharacteristic
126C23×C17#13112yes—
127C2×C4×C17—21no—
128C2×C4×C17—21no—
129C2×C4×C17—21no—
130C2×C4×C17—21no—
131C2×C4×C17—42no—
132C2×C4×C17—42no—
133C2×C4×C17—41no—
134C2×C4×C17—41no—
135C2×C4×C17—41no—
136C2×C4×C17—41no—
137C2×C4×C17—81no—
138C2×C4×C17—81no—
139C2×Dic17—41no—
140C2×Dic17—41no—
141C2×Dic17—41no—
142C2×Dic17—41no—
143C2×Dic17—41no—
144C2×Dic17—41no—
145C2×Dic17—41no—
146C2×Dic17—41no—
147C2×Dic17—41no—
148C2×Dic17—41no—
149C2×Dic17—41no—
150C2×Dic17—41no—
151C2×Dic17—82no—
152C2×Dic17—82no—
153C8×C17—82no—
154#3622—82no—
155#2483—171no—
156#1462D1711yescharacteristic
157C2×#323—171no—
158#1326—172no—
159#1317—172no—
160C22×C17—21no—
161C22×C17—21no—
162C22×C17—21no—
163C22×C17—21no—
164C22×C17—21no—
165C22×C17—21no—
166C22×C17—22no—
167C22×C17—21no—
168C22×C17—42no—
169C22×C17—42no—
170C22×C17—42no—
171C22×C17—42no—
172C22×C17—41no—
173C22×C17—41no—
174C22×C17—41no—
175C22×C17—41no—
176C22×C17—41no—
177C22×C17—84no—
178C22×C17—81no—
179C22×C17—81no—
180C22×C17—84no—
181C22×C17#35212yes—
182C22×C17#40811yescharacteristic
183C22×C17C2×#9911yescharacteristic
184C22×C17#41311yescharacteristic
185C4×C17—41no—
186C4×C17—41no—
187C4×C17—41no—
188C4×C17—41no—
189Dic17—81no—
190Dic17—81no—
191Dic17—81no—
192Dic17—81no—
193C22×C22⋊C4—171no—
194C22×C22⋊C4C2×D1711yescharacteristic
195#407—21no—
196C2×C22⋊C8—341no—
197#397—341no—
198#397—341no—
199#385—171no—
200#385—171no—
201#385—341no—
202#381—171no—
203#381—171no—
204#381—341no—
205#379—171no—
206#323—21no—
207#323—172no—
208#323—341no—
209#323C2×D1712yes—
210C2×C17—21no—
211C2×C17—21no—
212C2×C17—22no—
213C2×C17—41no—
214C2×C17—42no—
215C2×C17—81no—
216C2×C17#146811yescharacteristic
217C2×C17C2×#35211yescharacteristic
218C2×C17#212111yescharacteristic
219C25C4×D1711yescharacteristic
220C23×C4—171no—
221C23×C4—171no—
222C23×C4D6811yescharacteristic
223C23×C4C22⋊D1711yescharacteristic
224C2×M16—41no—
225C22×C8—681no—
226C2×C4⋊C4—341no—
227C2×C4⋊C4—341no—
228C2×C22⋊C4—41no—
229C2×C22⋊C4—41no—
230C2×C22⋊C4—171no—
231C2×C22⋊C4—171no—
232C2×C22⋊C4—341no—
233C2×C22⋊C4—341no—
234C2×C22⋊C4—341no—
235C2×C22⋊C4—341no—
236C2×C22⋊C4—681no—
237C2×C22⋊C4—681no—
238C2×C22⋊C4C4×D1711yescharacteristic
239C2×C22⋊C4D6811yescharacteristic
240C2×C22⋊C4C22⋊D1711yescharacteristic
241C2×C22⋊C4C22×D1711yescharacteristic
242C22⋊C8—22no—
243C22⋊C8—41no—
244C22⋊C8—342no—
245C22⋊C8—681no—
246#95—341no—
247#95—341no—
248#95—341no—
249#95—341no—
250#95—341no—
251#95—341no—
252C17#1154311yescharacteristic, complemented, Sylow
253C24—21no—
254C24—21no—
255C24—22no—
256C24—41no—
257C24—42no—
258C24—81no—
259C24#6322711yescharacteristic
260C24#6322711yescharacteristic
261C24C2×C4×D1711yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—42no—
267C22×C4—81no—
268C22×C4—341no—
269C22×C4—341no—
270C22×C4—341no—
271C22×C4—341no—
272C22×C4—342no—
273C22×C4—681no—
274C22×C4—681no—
275C22×C4—681no—
276C22×C4—1361no—
277C22×C4#6322711yescharacteristic
278C22×C4#6322711yescharacteristic
279C22×C4C2×D6811yescharacteristic
280C22×C4C2×C22⋊D1711yescharacteristic
281M16—82no—
282C2×C8—42no—
283C2×C8—682no—
284C2×C8—1362no—
285C4⋊C4—1361no—
286C4⋊C4—1361no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—342no—
292C22⋊C4—682no—
293C22⋊C4—682no—
294C22⋊C4—681no—
295C22⋊C4—681no—
296C22⋊C4—681no—
297C22⋊C4—1361no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—22no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—41no—
307C23—42no—
308C23—42no—
309C23—41no—
310C23—41no—
311C23—42no—
312C23—41no—
313C23—41no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—84no—
318C23—84no—
319C23#1058747711yescharacteristic
320C23#1058747711yescharacteristic
321C23#1058759312yes—
322C23C2×#6322711yescharacteristic
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—681no—
336C2×C4—681no—
337C2×C4—681no—
338C2×C4—681no—
339C2×C4—681no—
340C2×C4—681no—
341C2×C4—681no—
342C2×C4—681no—
343C2×C4—681no—
344C2×C4—681no—
345C2×C4—681no—
346C2×C4—681no—
347C2×C4—1362no—
348C2×C4—1362no—
349C8—82no—
350C8—1362no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—21no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—81no—
370C22—81no—
371C22—84no—
372C22#1176260012yes—
373C22#1176277711yescharacteristic
374C22C2×#1058747711yescharacteristic
375C22#1176279111yescharacteristic
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—1361no—
381C4—1361no—
382C4—1361no—
383C4—1361no—
384C2—21no—
385C2—21no—
386C2—22no—
387C2—41no—
388C2—42no—
389C2—81no—
390C2#1452713311yescharacteristic
391C2C2×#1176260011yescharacteristic
392C2#1453042811yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC24×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#1462C2
socleC22×C17C2×#99
prime radicalC25×C17C2×C4
cosocleC2×C22⋊C4×C17C23
hypercenter#1462D17
hypocenterC17#11543
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
3. #14526731C2semidirect
4. #14526713C2semidirect
252. C17#11543semidirect

Maximal subgroups

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

subgroupindex
#145330622
C2×#117625332
#145267312
#145267132
C17×#14622
#1154317