Finite Group Databasebeta

← #16945103

Subgroups — #16945103

Order 4352.

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

normal subgroups only

This group has 464 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#14534668C211yesmaximal, characteristic
2#14527125C211yesmaximal, characteristic, complemented
3#14526807C212yesmaximal, complemented
4#14526780C212yesmaximal, complemented
5C17×#1799C211yesmaximal, characteristic, complemented
6C2×#10587616C411yescharacteristic, complemented
7#11762866—21no—
8#11762748C411yescharacteristic, complemented
9#11762745C2211yescharacteristic
10#11762726C411yescharacteristic, complemented
11#11762724—21no—
12#11762718C2211yescharacteristic
13#11762717—21no—
14#11762700—21no—
15#11762688—21no—
16#11762672C411yescharacteristic, 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—
28C22×D68C2×C411yescharacteristic
29C4×D4×C17—41no—
30C4×D4×C17—41no—
31C2×C4⋊C4×C17—41no—
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C22⋊C4×C17—22no—
34C2×C22⋊C4×C17D411yescharacteristic
35C2×C22⋊C4×C17C2311yescharacteristic
36C2×C42×C17D411yescharacteristic
37C2×C22⋊Dic17—21no—
38C2×C22⋊Dic17—21no—
39#10587616—41no—
40#10587616—41no—
41C2×#63227—21no—
42C2×#63227—21no—
43C2×#63227—21no—
44C2×#63227—21no—
45C2×C4⋊Dic17C2×C411yescharacteristic
46C2×#63225—21no—
47C17×#99—42no—
48C17×#95—41no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52#10587502C2×C411yescharacteristic
53#10587502C2×C411yescharacteristic
54C22⋊#3622—22no—
55C4⋊#3622—41no—
56#10587474—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—
88C4⋊C4×C17—41no—
89C4⋊C4×C17—82no—
90C22⋊C4×C17—41no—
91C22⋊C4×C17—41no—
92C22⋊C4×C17—42no—
93C22⋊C4×C17—42no—
94C42×C17—21no—
95C42×C17—21no—
96C22⋊Dic17—81no—
97C22⋊Dic17—81no—
98#63227—42no—
99#63227—41no—
100#63227—41no—
101#63227—81no—
102#63227—81no—
103C4⋊Dic17—41no—
104#63225—81no—
105C2×#3622—42no—
106#11824—171nomaximal, Sylow
107C23×C17—21no—
108C23×C17—21no—
109C23×C17—21no—
110C23×C17—21no—
111C23×C17—21no—
112C23×C17—41no—
113C23×C17—41no—
114C23×C17—41no—
115C23×C17—41no—
116C23×C17C2×C22⋊C411yescharacteristic
117C23×C17AGL(1,ℤ/8)11yescharacteristic
118C23×C17#13711yescharacteristic
119C22×D17—41no—
120C22×D17—41no—
121C22×D17—41no—
122C22×D17—41no—
123C22×D17—41no—
124C22×D17—41no—
125C22×D17—41no—
126D4×C17—42no—
127D4×C17—42no—
128C2×C4×C17—21no—
129C2×C4×C17—21no—
130C2×C4×C17—21no—
131C2×C4×C17—21no—
132C2×C4×C17—21no—
133C2×C4×C17—21no—
134C2×C4×C17—41no—
135C2×C4×C17—42no—
136C2×C4×C17—41no—
137C2×C4×C17—41no—
138C2×C4×C17—41no—
139C2×C4×C17—81no—
140C2×C4×C17—81no—
141C2×C4×C17—81no—
142C2×C4×C17—82no—
143C2×C4×C17—82no—
144C2×C4×C17—82no—
145C2×C4×C17#9911yescharacteristic
146C2×C4×C17#9911yescharacteristic
147C22⋊D17—82no—
148C22⋊D17—82no—
149C22⋊D17—84no—
150C2×Dic17—41no—
151C2×Dic17—41no—
152C2×Dic17—41no—
153C2×Dic17—41no—
154C2×Dic17—41no—
155C2×Dic17—41no—
156C2×Dic17—41no—
157C2×Dic17—41no—
158C2×Dic17—41no—
159D68—82no—
160#3622—82no—
161#2635—171no—
162#1799D1711yescharacteristic, complemented
163#1466—171no—
164#1352—172no—
165#1343—172no—
166C22×C17—21no—
167C22×C17—21no—
168C22×C17—21no—
169C22×C17—21no—
170C22×C17—41no—
171C22×C17—41no—
172C22×C17—41no—
173C22×C17—41no—
174C22×C17—41no—
175C22×C17—41no—
176C22×C17—41no—
177C22×C17—81no—
178C22×C17—81no—
179C22×C17—81no—
180C22×C17C2×#9911yescharacteristic
181C22×C17#41711yescharacteristic
182C22×C17#42111yescharacteristic
183C2×D17—81no—
184C2×D17—81no—
185C2×D17—81no—
186C2×D17—81no—
187C2×D17—81no—
188C2×D17—81no—
189C2×D17—81no—
190C4×C17—21no—
191C4×C17—21no—
192C4×C17—41no—
193C4×C17—41no—
194C4×C17—41no—
195C4×C17—41no—
196C4×C17—162no—
197Dic17—81no—
198Dic17—81no—
199Dic17—81no—
200C2×#121—171no—
201C2×C4×D4C2×D1711yescharacteristic
202#432—341no—
203C2×#99—21no—
204#400—171no—
205#399—171no—
206#394—171no—
207#394—341no—
208#392—171no—
209#392—341no—
210#388—341no—
211#386—341no—
212#381—171no—
213#380—21no—
214#342C2×D1712yes—
215#323—172no—
216#323—341no—
217C2×C17—21no—
218C2×C17—21no—
219C2×C17—41no—
220C2×C17—41no—
221C2×C17—81no—
222C2×C17#151311yescharacteristic
223C2×C17#212111yescharacteristic
224C2×C17#212811yescharacteristic
225D17—161no—
226C22×D4—171no—
227C22×D4—341no—
228C22×D4—341no—
229C22×D4C22⋊D1711yescharacteristic
230C23×C4C4×D1711yescharacteristic
231C23×C4C22⋊D1711yescharacteristic
232#121—681no—
233#121—681no—
234C4×D4—41no—
235C4×D4—41no—
236C2×C4⋊C4—41no—
237C2×C4⋊C4—171no—
238C2×C4⋊C4—341no—
239C2×C4⋊C4C4×D1711yescharacteristic
240C2×C22⋊C4—22no—
241C2×C22⋊C4—341no—
242C2×C22⋊C4—341no—
243C2×C22⋊C4—341no—
244C2×C22⋊C4—341no—
245C2×C22⋊C4—341no—
246C2×C22⋊C4—341no—
247C2×C22⋊C4D6811yescharacteristic
248C2×C22⋊C4C22×D1711yescharacteristic
249C2×C42D6811yescharacteristic
250C4⋊C8—681no—
251#99—42no—
252C22⋊C8—342no—
253#97—681no—
254#95—41no—
255#95—171no—
256#95—171no—
257#95—341no—
258#95—341no—
259#95—341no—
260C17#1182411yescharacteristic, complemented, Sylow
261C24—341no—
262C24#6322711yescharacteristic
263C24C2×C22⋊D1711yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—681no—
269C2×D4—682no—
270C2×D4—681no—
271C2×D4—681no—
272C2×D4—1361no—
273C2×D4—1361no—
274C2×D4—1361no—
275C2×D4—1361no—
276C2×D4—1361no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—42no—
282C22×C4—81no—
283C22×C4—81no—
284C22×C4—341no—
285C22×C4—341no—
286C22×C4—341no—
287C22×C4#6322711yescharacteristic
288C22×C4#6322711yescharacteristic
289C22×C4#6322711yescharacteristic
290C22×C4C2×C4×D1711yescharacteristic
291C22×C4C2×D6811yescharacteristic
292C2×C8—682no—
293C4⋊C4—41no—
294C4⋊C4—82no—
295C4⋊C4—681no—
296C4⋊C4—1361no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—42no—
300C22⋊C4—42no—
301C22⋊C4—682no—
302C22⋊C4—681no—
303C22⋊C4—681no—
304C22⋊C4—1361no—
305C22⋊C4—1361no—
306C22⋊C4—1361no—
307C22⋊C4—1361no—
308C42—21no—
309C42—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—681no—
320C23—681no—
321C23—681no—
322C23—681no—
323C23—681no—
324C23—681no—
325C23—681no—
326C23C2×#6322711yescharacteristic
327C23#1058761811yescharacteristic
328C23#1058762811yescharacteristic
329D4—42no—
330D4—42no—
331D4—1362no—
332D4—1362no—
333D4—1362no—
334D4—1364no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4—681no—
353C2×C4—681no—
354C2×C4—681no—
355C2×C4—681no—
356C2×C4—681no—
357C2×C4—681no—
358C2×C4—681no—
359C2×C4—681no—
360C2×C4—681no—
361C2×C4#1058747711yescharacteristic
362C2×C4#1058747711yescharacteristic
363C8—1362no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—1361no—
379C22—1361no—
380C22—1361no—
381C22—1361no—
382C22—1361no—
383C22—1361no—
384C22—1361no—
385C22C2×#1058747711yescharacteristic
386C22#1176280811yescharacteristic
387C22#1176282711yescharacteristic
388C4—21no—
389C4—21no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—162no—
395C4—1361no—
396C4—1361no—
397C4—1361no—
398C2—21no—
399C2—21no—
400C2—41no—
401C2—41no—
402C2—81no—
403C2—2721no—
404C2#1452732511yescharacteristic
405C2#1453042811yescharacteristic
406C2#1453045511yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#1799C2
socleC22×C17C2×#99
prime radical#14534668C2
cosocleC2×C22⋊C4×C17C23
hypercenter#1799D17
hypocenterC17#11824
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. #14527125C2semidirect
3. #14526807C2semidirect
4. #14526780C2semidirect
5. C17×#1799C2semidirect
6. C2×#10587616C4semidirect
8. #11762748C4semidirect
10. #11762726C4semidirect
16. #11762672C4semidirect
162. #1799D17semidirect
260. C17#11824semidirect

Maximal subgroups

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

subgroupindex
#145346682
#145271252
#145268072
#145267802
C17×#17992
#1182417