Finite Group Databasebeta

← #16945351

Subgroups — #16945351

Order 4352.

522 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 95 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#14533740C211yesmaximal, characteristic
2#14527105C211yesmaximal, characteristic, complemented
3#14526783C212yesmaximal, complemented
4#14526780C212yesmaximal, complemented
5C17×#1799C211yesmaximal, characteristic, complemented
6C2×#10587616C411yescharacteristic, complemented
7C2×#10587625—21no—
8#11762862—21no—
9#11762739C411yescharacteristic, complemented
10#11762734C2211yescharacteristic
11#11762726C411yescharacteristic, complemented
12#11762718C2211yescharacteristic
13#11762700—21no—
14#11762688—21no—
15#11762686—21no—
16C2×#10587502C411yescharacteristic, complemented
17#11762533—21no—
18#11762533C2212yes—
19C2×C4×D4×C17C2211yescharacteristic
20C2×C17×#99—21no—
21C17×#380—21no—
22C17×#342C2212yes—
23C22×D4×C17D411yescharacteristic
24C23×C4×C17C2×C411yescharacteristic
25C23×C4×C17D411yescharacteristic
26C22×C22⋊D17—21no—
27C22×C22⋊D17—21no—
28C23×Dic17—21no—
29C22×D68C2×C411yescharacteristic
30C4×D4×C17—41no—
31C4×D4×C17—41no—
32C2×C4⋊C4×C17—41no—
33C2×C4⋊C4×C17C2×C411yescharacteristic
34C2×C22⋊C4×C17—22no—
35C2×C22⋊C4×C17D411yescharacteristic
36C2×C22⋊C4×C17C2311yescharacteristic
37C2×C42×C17D411yescharacteristic
38C2×C22⋊Dic17—21no—
39#10587625—42no—
40#10587625—42no—
41#10587616—41no—
42#10587616—41no—
43C2×#63227—21no—
44C2×#63227—21no—
45C2×#63227—21no—
46C2×#63227—21no—
47C2×C4⋊Dic17C2×C411yescharacteristic
48C2×#63225—21no—
49C17×#99—42no—
50C17×#95—41no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502C2×C411yescharacteristic
55#10587502C2×C411yescharacteristic
56C22⋊#3622—22no—
57C4⋊#3622—41no—
58C4×#3622—41no—
59C24×C17C22⋊C411yescharacteristic
60C24×C17C2×D411yescharacteristic
61C23×D17—21no—
62C2×D4×C17—41no—
63C2×D4×C17—41no—
64C2×D4×C17D812yes—
65C2×D4×C17SD1612yes—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17—42no—
71C22×C4×C17—81no—
72C22×C4×C17—81no—
73C22×C4×C17C22⋊C411yescharacteristic
74C22×C4×C17C22⋊C411yescharacteristic
75C22×C4×C17C22⋊C411yescharacteristic
76C22×C4×C17C22×C411yescharacteristic
77C22×C4×C17C2×D411yescharacteristic
78C2×C22⋊D17—42no—
79C2×C22⋊D17—42no—
80C2×C22⋊D17—42no—
81C2×C22⋊D17—42no—
82C2×C22⋊D17—41no—
83C2×C22⋊D17—41no—
84C2×C22⋊D17—81no—
85C22×Dic17—21no—
86C22×Dic17—21no—
87C22×Dic17—21no—
88C22×Dic17—42no—
89C22×Dic17—42no—
90C22×Dic17—81no—
91C2×D68—41no—
92C2×D68—81no—
93C4⋊C4×C17—41no—
94C4⋊C4×C17—82no—
95C22⋊C4×C17—41no—
96C22⋊C4×C17—41no—
97C22⋊C4×C17—42no—
98C22⋊C4×C17—42no—
99C42×C17—21no—
100C42×C17—21no—
101C22⋊Dic17—41no—
102C22⋊Dic17—41no—
103#63227—42no—
104#63227—41no—
105#63227—41no—
106#63227—42no—
107#63227—81no—
108C4⋊Dic17—41no—
109#63225—42no—
110C2×#3622—42no—
111#11876—171nomaximal, Sylow
112C23×C17—21no—
113C23×C17—21no—
114C23×C17—21no—
115C23×C17—21no—
116C23×C17—41no—
117C23×C17—41no—
118C23×C17—41no—
119C23×C17—41no—
120C23×C17#10212yes—
121C23×C17C2×C22⋊C411yescharacteristic
122C23×C17C2×D811yescharacteristic
123C23×C17C2×SD1611yescharacteristic
124C22×D17—41no—
125C22×D17—41no—
126C22×D17—41no—
127C22×D17—41no—
128C22×D17—41no—
129C22×D17—41no—
130C22×D17—41no—
131D4×C17—42no—
132D4×C17—42no—
133C2×C4×C17—21no—
134C2×C4×C17—21no—
135C2×C4×C17—21no—
136C2×C4×C17—21no—
137C2×C4×C17—21no—
138C2×C4×C17—41no—
139C2×C4×C17—42no—
140C2×C4×C17—41no—
141C2×C4×C17—41no—
142C2×C4×C17—41no—
143C2×C4×C17—81no—
144C2×C4×C17—81no—
145C2×C4×C17—81no—
146C2×C4×C17—82no—
147C2×C4×C17—82no—
148C2×C4×C17—82no—
149C2×C4×C17#9911yescharacteristic
150C2×C4×C17#9911yescharacteristic
151C2×C4×C17#10212yes—
152C22⋊D17—82no—
153C22⋊D17—82no—
154C22⋊D17—84no—
155C2×Dic17—22no—
156C2×Dic17—41no—
157C2×Dic17—41no—
158C2×Dic17—41no—
159C2×Dic17—41no—
160C2×Dic17—41no—
161C2×Dic17—41no—
162C2×Dic17—41no—
163C2×Dic17—41no—
164C2×Dic17—84no—
165D68—82no—
166#3622—82no—
167#2543—171no—
168#1799D1711yescharacteristic, complemented
169#1460—171no—
170#1344—172no—
171#1343—172no—
172C22×C17—21no—
173C22×C17—21no—
174C22×C17—22no—
175C22×C17—21no—
176C22×C17—21no—
177C22×C17—42no—
178C22×C17—41no—
179C22×C17—41no—
180C22×C17—42no—
181C22×C17—41no—
182C22×C17—41no—
183C22×C17—41no—
184C22×C17—41no—
185C22×C17—81no—
186C22×C17C2×#9911yescharacteristic
187C22×C17C2×#10211yescharacteristic
188C22×C17#42111yescharacteristic
189C2×D17—81no—
190C2×D17—81no—
191C2×D17—81no—
192C2×D17—81no—
193C2×D17—81no—
194C2×D17—81no—
195C2×D17—81no—
196C4×C17—21no—
197C4×C17—21no—
198C4×C17—22no—
199C4×C17—41no—
200C4×C17—41no—
201C4×C17—41no—
202C4×C17—162no—
203Dic17—42no—
204Dic17—81no—
205Dic17—81no—
206C2×#121—171no—
207C2×#121—341no—
208C2×C4×D4C2×D1711yescharacteristic
209#431—341no—
210C2×#99—21no—
211#398—171no—
212#397—171no—
213#394—171no—
214#392—171no—
215#388—341no—
216#386—341no—
217#386—341no—
218#380—21no—
219C2×#95—171no—
220#342C2×D1712yes—
221#323—172no—
222#323—341no—
223C2×C17—21no—
224C2×C17—21no—
225C2×C17—41no—
226C2×C17—42no—
227C2×C17—41no—
228C2×C17#151911yescharacteristic
229C2×C17#212111yescharacteristic
230C2×C17#212611yescharacteristic
231D17—161no—
232C22×D4—171no—
233C22×D4—341no—
234C22×D4—341no—
235C22×D4C22⋊D1711yescharacteristic
236C23×C4—341no—
237C23×C4C4×D1711yescharacteristic
238C23×C4C22⋊D1711yescharacteristic
239#121—682no—
240#121—682no—
241#121—681no—
242#121—681no—
243C4×D4—41no—
244C4×D4—41no—
245C2×C4⋊C4—41no—
246C2×C4⋊C4—171no—
247C2×C4⋊C4—341no—
248C2×C4⋊C4C4×D1711yescharacteristic
249C2×C22⋊C4—22no—
250C2×C22⋊C4—341no—
251C2×C22⋊C4—341no—
252C2×C22⋊C4—341no—
253C2×C22⋊C4—341no—
254C2×C22⋊C4—341no—
255C2×C22⋊C4D6811yescharacteristic
256C2×C22⋊C4C22×D1711yescharacteristic
257C2×C42D6811yescharacteristic
258C4⋊C8—681no—
259#99—42no—
260C22⋊C8—342no—
261C4×C8—681no—
262#95—41no—
263#95—171no—
264#95—171no—
265#95—341no—
266#95—341no—
267#95—341no—
268C17#1187611yescharacteristic, complemented, Sylow
269C24—341no—
270C24#6322711yescharacteristic
271C24C2×C22⋊D1711yescharacteristic
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—681no—
275C2×D4—682no—
276C2×D4—682no—
277C2×D4—682no—
278C2×D4—682no—
279C2×D4—681no—
280C2×D4—681no—
281C2×D4—1361no—
282C2×D4—1361no—
283C2×D4#6322812yes—
284C2×D4#6323012yes—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—42no—
290C22×C4—81no—
291C22×C4—81no—
292C22×C4—341no—
293C22×C4—341no—
294C22×C4—341no—
295C22×C4—682no—
296C22×C4—682no—
297C22×C4—1361no—
298C22×C4#6322711yescharacteristic
299C22×C4#6322711yescharacteristic
300C22×C4#6322711yescharacteristic
301C22×C4C2×C4×D1711yescharacteristic
302C22×C4C2×D6811yescharacteristic
303C2×C8—682no—
304C4⋊C4—41no—
305C4⋊C4—82no—
306C4⋊C4—681no—
307C4⋊C4—682no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—42no—
311C22⋊C4—42no—
312C22⋊C4—682no—
313C22⋊C4—681no—
314C22⋊C4—681no—
315C22⋊C4—681no—
316C22⋊C4—681no—
317C22⋊C4—682no—
318C22⋊C4—1361no—
319C42—21no—
320C42—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—681no—
330C23—681no—
331C23—681no—
332C23—681no—
333C23—681no—
334C23—681no—
335C23—681no—
336C23#1058748012yes—
337C23C2×#6322711yescharacteristic
338C23C2×#6322811yescharacteristic
339C23C2×#6323011yescharacteristic
340D4—42no—
341D4—42no—
342D4—1362no—
343D4—1362no—
344D4—1362no—
345D4—1364no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—82no—
360C2×C4—82no—
361C2×C4—82no—
362C2×C4—342no—
363C2×C4—681no—
364C2×C4—681no—
365C2×C4—681no—
366C2×C4—681no—
367C2×C4—681no—
368C2×C4—681no—
369C2×C4—681no—
370C2×C4—681no—
371C2×C4—1364no—
372C2×C4#1058747711yescharacteristic
373C2×C4#1058747711yescharacteristic
374C2×C4#1058748012yes—
375C8—1362no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—22no—
380C22—21no—
381C22—42no—
382C22—41no—
383C22—41no—
384C22—42no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—81no—
390C22—1361no—
391C22—1361no—
392C22—1361no—
393C22—1361no—
394C22—1361no—
395C22—1361no—
396C22—1361no—
397C22C2×#1058747711yescharacteristic
398C22C2×#1058748011yescharacteristic
399C22#1176282711yescharacteristic
400C4—22no—
401C4—21no—
402C4—21no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—162no—
407C4—682no—
408C4—1361no—
409C4—1361no—
410C2—21no—
411C2—21no—
412C2—41no—
413C2—42no—
414C2—41no—
415C2—2721no—
416C2#1452735111yescharacteristic
417C2#1453042811yescharacteristic
418C2#1453044711yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#1799C2
socleC22×C17C2×#99
prime radical#14533740C2
cosocleC2×C22⋊C4×C17C23
hypercenter#1799D17
hypocenterC17#11876
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #14527105C2semidirect
3. #14526783C2semidirect
4. #14526780C2semidirect
5. C17×#1799C2semidirect
6. C2×#10587616C4semidirect
9. #11762739C4semidirect
11. #11762726C4semidirect
16. C2×#10587502C4semidirect
168. #1799D17semidirect
268. C17#11876semidirect

Maximal subgroups

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

subgroupindex
#145337402
#145271052
#145267832
#145267802
C17×#17992
#1187617