Finite Group Databasebeta

← #16945108

Subgroups — #16945108

Order 4352.

476 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 79 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#14534636C211yesmaximal, characteristic
2#14527122C211yesmaximal, characteristic, complemented
3#14526804C212yesmaximal, complemented
4#14526780C212yesmaximal, complemented
5C17×#1799C211yesmaximal, characteristic, complemented
6C2×#10587561C411yescharacteristic, complemented
7#11762773—21no—
8#11762735—21no—
9#11762721C411yescharacteristic, complemented
10#11762721C2211yescharacteristic
11#11762718C411yescharacteristic, complemented
12#11762718C2211yescharacteristic
13#11762717—21no—
14#11762688—21no—
15#11762688—21no—
16#11762677C411yescharacteristic, complemented
17#11762535—21no—
18#11762533C2212yes—
19C2×C4×D4×C17C2211yescharacteristic
20C2×C17×#99—21no—
21C17×#380—21no—
22C17×#342C2212yes—
23C22×D4×C17D411yescharacteristic
24C23×C4×C17D411yescharacteristic
25C23×C4×C17D411yescharacteristic
26C22×C22⋊D17—21no—
27C22×C22⋊D17—21no—
28C22×D68C2×C411yescharacteristic
29C22×Dic34C2×C411yescharacteristic
30C4×D4×C17—41no—
31C4×D4×C17—41no—
32C2×C4⋊C4×C17—41no—
33C2×C4⋊C4×C17D411yescharacteristic
34C2×C22⋊C4×C17—22no—
35C2×C22⋊C4×C17C2×C411yescharacteristic
36C2×C22⋊C4×C17C2311yescharacteristic
37C2×C42×C17C2×C411yescharacteristic
38C2×C22⋊Dic17—21no—
39C2×C22⋊Dic17—21no—
40C2×#63227—21no—
41C2×#63227—21no—
42C2×#63227—21no—
43C2×#63227—21no—
44C2×#63223—41no—
45#10587561—41no—
46#10587561—41no—
47C17×#99—42no—
48C17×#95—41no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502C2×C411yescharacteristic
54#10587502C2×C411yescharacteristic
55C22⋊#3622—22no—
56C22⋊#3622—41no—
57C24×C17C22⋊C411yescharacteristic
58C24×C17C2×D411yescharacteristic
59C23×D17—21no—
60C2×D4×C17—21no—
61C2×D4×C17—21no—
62C2×D4×C17—41no—
63C2×D4×C17—41no—
64C22×C4×C17—21no—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—42no—
69C22×C4×C17—81no—
70C22×C4×C17—81no—
71C22×C4×C17C22⋊C411yescharacteristic
72C22×C4×C17C22⋊C411yescharacteristic
73C22×C4×C17C22⋊C411yescharacteristic
74C22×C4×C17C22×C411yescharacteristic
75C22×C4×C17C2×D411yescharacteristic
76C2×C22⋊D17—42no—
77C2×C22⋊D17—41no—
78C2×C22⋊D17—41no—
79C2×C22⋊D17—81no—
80C2×C22⋊D17—81no—
81C2×C22⋊D17—81no—
82C2×C22⋊D17—81no—
83C22×Dic17—21no—
84C22×Dic17—21no—
85C22×Dic17—21no—
86C2×D68—41no—
87C2×D68—81no—
88C2×Dic34—41no—
89C2×Dic34—81no—
90C4⋊C4×C17—41no—
91C4⋊C4×C17—82no—
92C22⋊C4×C17—41no—
93C22⋊C4×C17—41no—
94C22⋊C4×C17—42no—
95C22⋊C4×C17—42no—
96C42×C17—21no—
97C42×C17—21no—
98C22⋊Dic17—81no—
99C22⋊Dic17—81no—
100#63227—42no—
101#63227—41no—
102#63227—41no—
103#63227—81no—
104#63227—81no—
105#63223—82no—
106C2×#3622—42no—
107#11825—171nomaximal, Sylow
108C23×C17—21no—
109C23×C17—21no—
110C23×C17—21no—
111C23×C17—21no—
112C23×C17—21no—
113C23×C17—41no—
114C23×C17—41no—
115C23×C17—41no—
116C23×C17—41no—
117C23×C17C2×C22⋊C411yescharacteristic
118C23×C17AGL(1,ℤ/8)11yescharacteristic
119C23×C17#13711yescharacteristic
120C22×D17—41no—
121C22×D17—41no—
122C22×D17—41no—
123C22×D17—41no—
124C22×D17—41no—
125C22×D17—41no—
126C22×D17—41no—
127D4×C17—42no—
128D4×C17—42no—
129C2×C4×C17—21no—
130C2×C4×C17—21no—
131C2×C4×C17—21no—
132C2×C4×C17—21no—
133C2×C4×C17—21no—
134C2×C4×C17—21no—
135C2×C4×C17—41no—
136C2×C4×C17—42no—
137C2×C4×C17—42no—
138C2×C4×C17—41no—
139C2×C4×C17—41no—
140C2×C4×C17—41no—
141C2×C4×C17—81no—
142C2×C4×C17—81no—
143C2×C4×C17—82no—
144C2×C4×C17—82no—
145C2×C4×C17—82no—
146C2×C4×C17#9911yescharacteristic
147C2×C4×C17#9911yescharacteristic
148C22⋊D17—82no—
149C22⋊D17—82no—
150C22⋊D17—84no—
151C2×Dic17—41no—
152C2×Dic17—41no—
153C2×Dic17—41no—
154C2×Dic17—41no—
155C2×Dic17—41no—
156C2×Dic17—41no—
157C2×Dic17—41no—
158C2×Dic17—41no—
159C2×Dic17—41no—
160D68—82no—
161Dic34—82no—
162#3622—82no—
163#2631—171no—
164#1799D1711yescharacteristic, complemented
165#1465—171no—
166#1351—172no—
167#1343—172no—
168C22×C17—21no—
169C22×C17—21no—
170C22×C17—21no—
171C22×C17—21no—
172C22×C17—41no—
173C22×C17—41no—
174C22×C17—42no—
175C22×C17—41no—
176C22×C17—41no—
177C22×C17—41no—
178C22×C17—41no—
179C22×C17—41no—
180C22×C17—81no—
181C22×C17—81no—
182C22×C17C2×#9911yescharacteristic
183C22×C17#41711yescharacteristic
184C22×C17#42111yescharacteristic
185C2×D17—81no—
186C2×D17—81no—
187C2×D17—81no—
188C2×D17—81no—
189C2×D17—81no—
190C2×D17—81no—
191C2×D17—81no—
192C4×C17—21no—
193C4×C17—21no—
194C4×C17—41no—
195C4×C17—41no—
196C4×C17—41no—
197C4×C17—41no—
198C4×C17—162no—
199Dic17—81no—
200Dic17—81no—
201Dic17—81no—
202C2×#124—171no—
203C2×C4×D4C2×D1711yescharacteristic
204C2×#99—21no—
205#407—341no—
206#397—341no—
207#393—171no—
208#393—171no—
209#392—171no—
210#392—171no—
211#392—341no—
212#386—341no—
213#386—341no—
214#383—171no—
215#380—21no—
216#342C2×D1712yes—
217#324—341no—
218#323—172no—
219C2×C17—21no—
220C2×C17—21no—
221C2×C17—41no—
222C2×C17—41no—
223C2×C17—81no—
224C2×C17#151311yescharacteristic
225C2×C17#212211yescharacteristic
226C2×C17#212711yescharacteristic
227D17—161no—
228C22×Q8—171no—
229C22×D4—171no—
230C22×D4—341no—
231C22×D4—341no—
232C22×D4C22⋊D1711yescharacteristic
233C23×C4D6811yescharacteristic
234C23×C4C22⋊D1711yescharacteristic
235C2×M16—681no—
236#124—681no—
237#124—681no—
238C4×D4—41no—
239C4×D4—41no—
240C2×C4⋊C4—41no—
241C2×C4⋊C4D6811yescharacteristic
242C2×C22⋊C4—22no—
243C2×C22⋊C4—341no—
244C2×C22⋊C4—341no—
245C2×C22⋊C4—341no—
246C2×C22⋊C4—341no—
247C2×C22⋊C4—341no—
248C2×C22⋊C4—341no—
249C2×C22⋊C4C4×D1711yescharacteristic
250C2×C22⋊C4C22×D1711yescharacteristic
251C2×C42C4×D1711yescharacteristic
252#99—42no—
253C22⋊C8—342no—
254C22⋊C8—681no—
255#95—41no—
256#95—171no—
257#95—171no—
258#95—341no—
259#95—341no—
260#95—341no—
261#95—341no—
262C17#1182511yescharacteristic, complemented, Sylow
263C24—341no—
264C24#6322711yescharacteristic
265C24C2×C22⋊D1711yescharacteristic
266C2×Q8—681no—
267C2×Q8—1361no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—681no—
273C2×D4—682no—
274C2×D4—681no—
275C2×D4—681no—
276C2×D4—1361no—
277C2×D4—1361no—
278C2×D4—1361no—
279C2×D4—1361no—
280C2×D4—1361no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—42no—
286C22×C4—81no—
287C22×C4—81no—
288C22×C4—341no—
289C22×C4—341no—
290C22×C4—341no—
291C22×C4#6322711yescharacteristic
292C22×C4#6322711yescharacteristic
293C22×C4#6322711yescharacteristic
294C22×C4C2×C4×D1711yescharacteristic
295C22×C4C2×D6811yescharacteristic
296M16—1362no—
297C2×C8—682no—
298C4⋊C4—41no—
299C4⋊C4—82no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—42no—
303C22⋊C4—42no—
304C22⋊C4—682no—
305C22⋊C4—681no—
306C22⋊C4—681no—
307C22⋊C4—1361no—
308C22⋊C4—1361no—
309C22⋊C4—1361no—
310C22⋊C4—1361no—
311C42—21no—
312C42—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—681no—
323C23—681no—
324C23—681no—
325C23—681no—
326C23—681no—
327C23—681no—
328C23—681no—
329C23C2×#6322711yescharacteristic
330C23#1058761811yescharacteristic
331C23#1058762811yescharacteristic
332Q8—1362no—
333D4—42no—
334D4—42no—
335D4—1362no—
336D4—1362no—
337D4—1362no—
338D4—1364no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—82no—
354C2×C4—82no—
355C2×C4—82no—
356C2×C4—681no—
357C2×C4—681no—
358C2×C4—681no—
359C2×C4—681no—
360C2×C4—681no—
361C2×C4—681no—
362C2×C4—681no—
363C2×C4—681no—
364C2×C4—681no—
365C2×C4#1058747711yescharacteristic
366C2×C4#1058747711yescharacteristic
367C8—1362no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—41no—
373C22—41no—
374C22—42no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—81no—
382C22—1361no—
383C22—1361no—
384C22—1361no—
385C22—1361no—
386C22—1361no—
387C22—1361no—
388C22—1361no—
389C22C2×#1058747711yescharacteristic
390C22#1176280811yescharacteristic
391C22#1176282711yescharacteristic
392C4—21no—
393C4—21no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—162no—
399C4—1361no—
400C4—1361no—
401C4—1361no—
402C2—21no—
403C2—21no—
404C2—41no—
405C2—41no—
406C2—81no—
407C2—2721no—
408C2#1452732511yescharacteristic
409C2#1453043311yescharacteristic
410C2#1453045111yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#1799C2
socleC22×C17C2×#99
prime radical#14534636C2
cosocleC2×C22⋊C4×C17C23
hypercenter#1799D17
hypocenterC17#11825
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. #14527122C2semidirect
3. #14526804C2semidirect
4. #14526780C2semidirect
5. C17×#1799C2semidirect
6. C2×#10587561C4semidirect
9. #11762721C4semidirect
11. #11762718C4semidirect
16. #11762677C4semidirect
164. #1799D17semidirect
262. C17#11825semidirect

Maximal subgroups

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

subgroupindex
#145346362
#145271222
#145268042
#145267802
C17×#17992
#1182517