Finite Group Databasebeta

← #16945346

Subgroups — #16945346

Order 4352.

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

normal subgroups only

This group has 536 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#14533681C211yesmaximal, characteristic
2#14527102C211yesmaximal, characteristic, complemented
3#14526783C212yesmaximal, complemented
4#14526780C212yesmaximal, complemented
5C17×#1799C211yesmaximal, characteristic, complemented
6C2×#10587624—21no—
7C2×C4×D68C411yescharacteristic, complemented
8C2×C22⋊#3622—21no—
9#11762734C411yescharacteristic, complemented
10#11762734C2211yescharacteristic
11#11762718C411yescharacteristic, complemented
12#11762718C2211yescharacteristic
13#11762688—21no—
14#11762688—21no—
15#11762675C411yescharacteristic, complemented
16#11762666—21no—
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×C4×D17—21no—
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—
40#10587624—42no—
41#10587624—42no—
42C2×#63227—21no—
43C2×#63227—21no—
44C2×#63227—21no—
45C2×C4⋊Dic17—21no—
46C2×C4⋊Dic17C2×C411yescharacteristic
47C22×#3622—41no—
48C4×D68—41no—
49C4×D68—41no—
50C17×#99—42no—
51C17×#95—41no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55#10587502C2×C411yescharacteristic
56#10587502C2×C411yescharacteristic
57C22⋊#3622—22no—
58C22⋊#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—41no—
82C2×C22⋊D17—41no—
83C2×C22⋊D17—81no—
84C2×C22⋊D17—81no—
85C22×Dic17—21no—
86C22×Dic17—21no—
87C22×Dic17—21no—
88C2×D68—41no—
89C2×D68—42no—
90C2×C4×D17—42no—
91C2×C4×D17—42no—
92C2×C4×D17—42no—
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—42no—
102C22⋊Dic17—41no—
103C22⋊Dic17—41no—
104#63227—41no—
105#63227—41no—
106#63227—81no—
107#63227—81no—
108C4⋊Dic17—42no—
109C4⋊Dic17—41no—
110C2×#3622—42no—
111C2×#3622—82no—
112#11875—171nomaximal, Sylow
113C23×C17—21no—
114C23×C17—21no—
115C23×C17—21no—
116C23×C17—21no—
117C23×C17—41no—
118C23×C17—41no—
119C23×C17—41no—
120C23×C17—41no—
121C23×C17#10212yes—
122C23×C17C2×C22⋊C411yescharacteristic
123C23×C17C2×D811yescharacteristic
124C23×C17C2×SD1611yescharacteristic
125C22×D17—22no—
126C22×D17—41no—
127C22×D17—41no—
128C22×D17—41no—
129C22×D17—41no—
130C22×D17—41no—
131C22×D17—41no—
132D4×C17—42no—
133D4×C17—42no—
134C2×C4×C17—21no—
135C2×C4×C17—21no—
136C2×C4×C17—21no—
137C2×C4×C17—21no—
138C2×C4×C17—21no—
139C2×C4×C17—41no—
140C2×C4×C17—42no—
141C2×C4×C17—42no—
142C2×C4×C17—41no—
143C2×C4×C17—41no—
144C2×C4×C17—41no—
145C2×C4×C17—81no—
146C2×C4×C17—81no—
147C2×C4×C17—82no—
148C2×C4×C17—82no—
149C2×C4×C17—82no—
150C2×C4×C17#9911yescharacteristic
151C2×C4×C17#9911yescharacteristic
152C2×C4×C17#10212yes—
153C22⋊D17—84no—
154C22⋊D17—82no—
155C22⋊D17—82no—
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—41no—
165D68—42no—
166D68—42no—
167C4×D17—84no—
168#3622—82no—
169#2535—171no—
170#1799D1711yescharacteristic, complemented
171#1459—171no—
172#1344—172no—
173#1343—172no—
174C22×C17—21no—
175C22×C17—21no—
176C22×C17—21no—
177C22×C17—22no—
178C22×C17—21no—
179C22×C17—42no—
180C22×C17—41no—
181C22×C17—41no—
182C22×C17—41no—
183C22×C17—41no—
184C22×C17—41no—
185C22×C17—41no—
186C22×C17—81no—
187C22×C17—81no—
188C22×C17C2×#9911yescharacteristic
189C22×C17C2×#10211yescharacteristic
190C22×C17#42111yescharacteristic
191C2×D17—42no—
192C2×D17—42no—
193C2×D17—42no—
194C2×D17—81no—
195C2×D17—81no—
196C2×D17—81no—
197C2×D17—81no—
198C4×C17—21no—
199C4×C17—21no—
200C4×C17—22no—
201C4×C17—41no—
202C4×C17—41no—
203C4×C17—41no—
204C4×C17—162no—
205Dic17—81no—
206Dic17—81no—
207Dic17—81no—
208C2×#121—341no—
209C2×C4×D4—171no—
210C2×C4×D4C2×D1711yescharacteristic
211C2×#99—21no—
212C2×C22⋊C8—341no—
213#397—171no—
214#397—171no—
215#392—171no—
216#392—171no—
217#386—341no—
218#386—341no—
219#382—171no—
220#380—21no—
221#380—341no—
222#342C2×D1712yes—
223#324—341no—
224#323—172no—
225C2×C17—21no—
226C2×C17—21no—
227C2×C17—41no—
228C2×C17—42no—
229C2×C17—41no—
230C2×C17#151911yescharacteristic
231C2×C17#212011yescharacteristic
232C2×C17#212711yescharacteristic
233D17—82no—
234C22×D4—171no—
235C22×D4—341no—
236C22×D4—341no—
237C22×D4C22⋊D1711yescharacteristic
238C23×C4—341no—
239C23×C4D6811yescharacteristic
240C23×C4C22⋊D1711yescharacteristic
241C22×C8—681no—
242#121—682no—
243#121—682no—
244C4×D4—41no—
245C4×D4—41no—
246C4×D4—681no—
247C4×D4—681no—
248C2×C4⋊C4—41no—
249C2×C4⋊C4—171no—
250C2×C4⋊C4—341no—
251C2×C4⋊C4D6811yescharacteristic
252C2×C22⋊C4—22no—
253C2×C22⋊C4—341no—
254C2×C22⋊C4—341no—
255C2×C22⋊C4—341no—
256C2×C22⋊C4—341no—
257C2×C22⋊C4—341no—
258C2×C22⋊C4C4×D1711yescharacteristic
259C2×C22⋊C4C22×D1711yescharacteristic
260C2×C42C4×D1711yescharacteristic
261#99—42no—
262C22⋊C8—342no—
263C22⋊C8—681no—
264#95—41no—
265#95—171no—
266#95—171no—
267#95—341no—
268#95—341no—
269#95—341no—
270C17#1187511yescharacteristic, complemented, Sylow
271C24—341no—
272C24#6322711yescharacteristic
273C24C2×C22⋊D1711yescharacteristic
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—681no—
277C2×D4—682no—
278C2×D4—682no—
279C2×D4—682no—
280C2×D4—682no—
281C2×D4—681no—
282C2×D4—681no—
283C2×D4—1361no—
284C2×D4—1361no—
285C2×D4#6322812yes—
286C2×D4#6323012yes—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—42no—
292C22×C4—81no—
293C22×C4—81no—
294C22×C4—341no—
295C22×C4—341no—
296C22×C4—341no—
297C22×C4—682no—
298C22×C4—682no—
299C22×C4—682no—
300C22×C4#6322711yescharacteristic
301C22×C4#6322711yescharacteristic
302C22×C4#6322711yescharacteristic
303C22×C4C2×C4×D1711yescharacteristic
304C22×C4C2×D6811yescharacteristic
305C2×C8—682no—
306C2×C8—1362no—
307C4⋊C4—41no—
308C4⋊C4—82no—
309C4⋊C4—681no—
310C4⋊C4—682no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—42no—
314C22⋊C4—42no—
315C22⋊C4—682no—
316C22⋊C4—681no—
317C22⋊C4—681no—
318C22⋊C4—681no—
319C22⋊C4—681no—
320C22⋊C4—1361no—
321C22⋊C4—1361no—
322C42—21no—
323C42—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—342no—
333C23—681no—
334C23—681no—
335C23—681no—
336C23—681no—
337C23—681no—
338C23—681no—
339C23#1058748012yes—
340C23C2×#6322711yescharacteristic
341C23C2×#6322811yescharacteristic
342C23C2×#6323011yescharacteristic
343D4—42no—
344D4—42no—
345D4—682no—
346D4—682no—
347D4—1364no—
348D4—1362no—
349D4—1362no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—82no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4—681no—
367C2×C4—681no—
368C2×C4—681no—
369C2×C4—681no—
370C2×C4—681no—
371C2×C4—681no—
372C2×C4—681no—
373C2×C4—681no—
374C2×C4—681no—
375C2×C4—1364no—
376C2×C4#1058747711yescharacteristic
377C2×C4#1058747711yescharacteristic
378C2×C4#1058748012yes—
379C8—1362no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—21no—
385C22—42no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—81no—
393C22—81no—
394C22—682no—
395C22—682no—
396C22—682no—
397C22—1361no—
398C22—1361no—
399C22—1361no—
400C22—1361no—
401C22C2×#1058747711yescharacteristic
402C22C2×#1058748011yescharacteristic
403C22#1176282711yescharacteristic
404C4—22no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—162no—
411C4—1361no—
412C4—1361no—
413C4—1361no—
414C2—21no—
415C2—21no—
416C2—41no—
417C2—42no—
418C2—41no—
419C2—1362no—
420C2#1452735111yescharacteristic
421C2#1453042311yescharacteristic
422C2#1453045111yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#1799C2
socleC22×C17C2×#99
prime radical#14533681C2
cosocleC2×C22⋊C4×C17C23
hypercenter#1799D17
hypocenterC17#11875
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. #14527102C2semidirect
3. #14526783C2semidirect
4. #14526780C2semidirect
5. C17×#1799C2semidirect
7. C2×C4×D68C4semidirect
9. #11762734C4semidirect
11. #11762718C4semidirect
15. #11762675C4semidirect
170. #1799D17semidirect
270. C17#11875semidirect

Maximal subgroups

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

subgroupindex
#145336812
#145271022
#145267832
#145267802
C17×#17992
#1187517