Finite Group Databasebeta

← #16933249

Subgroups — #16933249

Order 4352.

510 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#63228C211yesmaximal, characteristic
2#14527530C211yesmaximal, characteristic, complemented
3#14527174C211yesmaximal, characteristic, complemented
4#14527105C211yesmaximal, characteristic, complemented
5#14527104C211yesmaximal, characteristic, complemented
6#14527068C211yesmaximal, characteristic, complemented
7C17×#1478C211yesmaximal, characteristic, complemented
8C22×#63228C411yescharacteristic
9C2×C4×D68C2211yescharacteristic
10C4×#63228—21no—
11C4×#63228—21no—
12C4×#63228—21no—
13C4×#63228—21no—
14#11762862C2211yescharacteristic
15#11762862C2211yescharacteristic
16C2×#10587478C411yescharacteristic
17C2×#10587503C411yescharacteristic
18C2×#10587480C411yescharacteristic
19C2×C4×#3622C2211yescharacteristic
20#11762561—21no—
21#11762559—21no—
22#11762536—22no—
23#11762533—22no—
24#11762532—22no—
25#11762531—21no—
26C8×#3622—21no—
27C2×C4×D4×C17C2211yescharacteristic
28C17×#431C2211yescharacteristic
29C17×#431C2211yescharacteristic
30C17×D4⋊C8—22no—
31C22×D4×C17C2×C411yescharacteristic
32C23×C4×C17—21no—
33C22×D68C2×C411yescharacteristic
34C22×C4×D17—21no—
35C4×D4×C17—21no—
36C4×D4×C17—21no—
37C4×D4×C17—21no—
38C4×D4×C17—21no—
39C2×C4⋊C4×C17C2×C411yescharacteristic
40C2×C22⋊C4×C17—21no—
41C2×C42×C17C2311yescharacteristic
42C2×#63228—21no—
43C2×#63228—21no—
44C2×#63228—22no—
45C2×#63228C814yescomplemented
46C2×#63227—21no—
47C2×C4⋊Dic17C2×C411yescharacteristic
48C22×#3622C2×C411yescharacteristic
49C22×#3622C2×C411yescharacteristic
50C4×D68—21no—
51C4×D68—21no—
52C4×D68—21no—
53C4×D68—21no—
54C17×C4⋊C8—21no—
55C17×C4⋊C8D412yes—
56C17×C22⋊C8—21no—
57C17×C22⋊C8—21no—
58C4×C8×C17—21no—
59C4×C8×C17—21no—
60#10587503—21no—
61#10587503—21no—
62C22⋊#3622—21no—
63C22⋊#3622D412yes—
64#10587480—21no—
65#10587480—21no—
66#10587478—21no—
67#10587478—21no—
68C4⋊#3622—21no—
69C4⋊#3622—21no—
70C4×#3622—21no—
71C4×#3622—21no—
72C4×#3622D411yescharacteristic
73C4×#3622D411yescharacteristic
74C4×#3622D411yescharacteristic
75C4×#3622D411yescharacteristic
76C24×C17—21no—
77C23×D17—21no—
78C2×D4×C17—21no—
79C2×D4×C17—21no—
80C2×D4×C17—21no—
81C2×D4×C17—21no—
82C2×D4×C17—21no—
83C2×D4×C17C2×C812yes—
84C22×C4×C17—21no—
85C22×C4×C17—41no—
86C22×C4×C17—41no—
87C22×C4×C17—82no—
88C22×C4×C17C22×C411yescharacteristic
89C22×C4×C17C2×D411yescharacteristic
90C22×C4×C17#4111yescharacteristic
91C22×Dic17—21no—
92C2×D68—21no—
93C2×D68—21no—
94C2×D68—21no—
95C2×D68—21no—
96C2×D68—21no—
97C2×D68C2×C812yes—
98C2×C4×D17—41no—
99C2×C4×D17—41no—
100C2×C4×D17—82no—
101C2×C8×C17—22no—
102C2×C8×C17—41no—
103C4⋊C4×C17—21no—
104C4⋊C4×C17—21no—
105C22⋊C4×C17—41no—
106C22⋊C4×C17—41no—
107C42×C17C2×D411yescharacteristic
108C42×C17C2×D411yescharacteristic
109C42×C17C2×D411yescharacteristic
110C42×C17#4111yescharacteristic
111#63228—24no—
112#63228—24no—
113#63227—41no—
114#63227—41no—
115C4⋊Dic17—21no—
116C4⋊Dic17—21no—
117C2×#3622—21no—
118C2×#3622—21no—
119C2×#3622—22no—
120C2×#3622—41no—
121C2×#3622C22⋊C411yescharacteristic
122C2×#3622C22⋊C411yescharacteristic
123C2×#3622C22⋊C411yescharacteristic
124C2×#3622C22⋊C411yescharacteristic
125C2×#3622C2×C812yes—
126C2×#3622M1612yes—
127#9668—171nomaximal, Sylow
128C23×C17—22no—
129C23×C17—41no—
130C23×C17—41no—
131C23×C17—81no—
132C23×C17—81no—
133C23×C17C4×D411yescharacteristic
134C22×D17—22no—
135C22×D17—41no—
136C22×D17—41no—
137C22×D17—81no—
138C22×D17—81no—
139D4×C17—22no—
140D4×C17—22no—
141D4×C17—41no—
142D4×C17—41no—
143C2×C4×C17—22no—
144C2×C4×C17—41no—
145C2×C4×C17—41no—
146C2×C4×C17—82no—
147C2×C4×C17—82no—
148C2×C4×C17—81no—
149C2×C4×C17C2×C22⋊C411yescharacteristic
150C2×C4×C17C4×D411yescharacteristic
151C2×C4×C17#12111yescharacteristic
152C2×C4×C17#12111yescharacteristic
153C2×C4×C17#12411yescharacteristic
154C2×C4×C17#12711yescharacteristic
155C2×C4×C17C22×C811yescharacteristic
156C2×C4×C17C2×M1611yescharacteristic
157C2×C4×C17#13111yescharacteristic
158C2×C4×C17#13111yescharacteristic
159C2×Dic17—41no—
160C2×Dic17—81no—
161D68—22no—
162D68—22no—
163D68—41no—
164D68—41no—
165C4×D17—82no—
166C4×D17—82no—
167C8×C17—42no—
168C8×C17—81no—
169#3622—21no—
170#3622—21no—
171#3622—42no—
172#3622—81no—
173#3622C22⋊C812yes—
174#3622C22⋊C812yes—
175C2×C4×D8—171no—
176#1564—171no—
177#1478—171no—
178#1478D1711yescharacteristic, complemented
179#1460—171no—
180#1460—171no—
181#1450—171no—
182C22×C17—21no—
183C22×C17—21no—
184C22×C17—42no—
185C22×C17—82no—
186C22×C17—82no—
187C22×C17—81no—
188C22×C17—81no—
189C22×C17#39011yescharacteristic
190C22×C17C8×D411yescharacteristic
191C22×C17#43611yescharacteristic
192C2×D17—42no—
193C2×D17—82no—
194C2×D17—81no—
195C2×D17—81no—
196C2×D17—82no—
197C4×C17—21no—
198C4×C17—21no—
199C4×C17—21no—
200C4×C17—81no—
201C4×C17C2×C22⋊C811yescharacteristic
202C4×C17#40811yescharacteristic
203C4×C17C8×D411yescharacteristic
204C4×C17#43611yescharacteristic
205C4×C17#47212yes—
206Dic17—81no—
207C22×D8—171no—
208C2×C4×D4—171no—
209C2×C4×D4C2×D1711yescharacteristic
210C4×D8—341no—
211C4×D8—341no—
212C4×D8—341no—
213C4×D8—341no—
214#431—171no—
215#431—171no—
216#431C2×D1711yescharacteristic
217#431C2×D1711yescharacteristic
218C2×#107—171no—
219C2×#102—171no—
220C2×#102—171no—
221C2×C4×C8—171no—
222#335—341no—
223#334—341no—
224D4⋊C8—22no—
225D4⋊C8—342no—
226#323—342no—
227#323—342no—
228#322—341no—
229C82—341no—
230C2×C17—21no—
231C2×C17—21no—
232C2×C17—82no—
233C2×C17#195411yescharacteristic
234C2×C17#197611yescharacteristic
235C2×C17#197811yescharacteristic
236D17—82no—
237C22×D4—171no—
238C22×D4C4×D1711yescharacteristic
239C23×C4—21no—
240C23×C4—341no—
241C2×D8—174no—
242C2×D8—341no—
243C2×D8—341no—
244C2×D8—342no—
245C22×C8—171no—
246C22×C8—171no—
247C4×D4—21no—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—341no—
252C4×D4—341no—
253C4×D4—341no—
254C4×D4—341no—
255C2×C4⋊C4—171no—
256C2×C4⋊C4C4×D1711yescharacteristic
257C2×C22⋊C4—21no—
258C2×C22⋊C4—341no—
259C2×C42C22×D1711yescharacteristic
260#107—341no—
261#107—341no—
262C4⋊C8—21no—
263C4⋊C8—341no—
264C4⋊C8—341no—
265C4⋊C8C22⋊D1712yes—
266#102—341no—
267#102—341no—
268#102—341no—
269#102—341no—
270C22⋊C8—21no—
271C22⋊C8—21no—
272C22⋊C8—172no—
273C22⋊C8—341no—
274C4×C8—21no—
275C4×C8—21no—
276C4×C8—171no—
277C4×C8—171no—
278C4×C8—171no—
279C4×C8—171no—
280C4×C8—341no—
281C4×C8—341no—
282C17#966811yescharacteristic, complemented, Sylow
283C24—21no—
284C24—341no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—172no—
291C2×D4—341no—
292C2×D4—341no—
293C2×D4—341no—
294C2×D4—341no—
295C2×D4—341no—
296C2×D4C8×D1712yes—
297C22×C4—21no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—82no—
301C22×C4—341no—
302C22×C4—681no—
303C22×C4—681no—
304C22×C4—1362no—
305C22×C4C2×C4×D1711yescharacteristic
306C22×C4D4×D1711yescharacteristic
307C22×C4#6325411yescharacteristic
308D8—344no—
309D8—344no—
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—171no—
313C2×C8—171no—
314C2×C8—172no—
315C2×C8—172no—
316C2×C8—171no—
317C2×C8—171no—
318C2×C8—341no—
319C2×C8—341no—
320C2×C8—342no—
321C2×C8—681no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—341no—
325C4⋊C4—341no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—681no—
329C22⋊C4—681no—
330C42#6325211yescharacteristic
331C42D4×D1711yescharacteristic
332C42D4×D1711yescharacteristic
333C42C2×C22⋊D1711yescharacteristic
334C23—22no—
335C23—41no—
336C23—41no—
337C23—81no—
338C23—81no—
339C23—342no—
340C23—681no—
341C23—681no—
342C23—1361no—
343C23—1361no—
344C23#1058756711yescharacteristic
345D4—22no—
346D4—22no—
347D4—41no—
348D4—41no—
349D4—342no—
350D4—342no—
351D4—681no—
352D4—681no—
353C2×C4—22no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—82no—
357C2×C4—82no—
358C2×C4—81no—
359C2×C4—681no—
360C2×C4—1362no—
361C2×C4—1362no—
362C2×C4—1361no—
363C2×C4C22⋊C4×D1711yescharacteristic
364C2×C4#1058757011yescharacteristic
365C2×C4#1058757111yescharacteristic
366C2×C4C2×C8×D1711yescharacteristic
367C2×C4#1058758711yescharacteristic
368C2×C4M16×D1711yescharacteristic
369C2×C4#1058759311yescharacteristic
370C2×C4C4×C22⋊D1711yescharacteristic
371C2×C4#1058762511yescharacteristic
372C2×C4#1058762611yescharacteristic
373C8—42no—
374C8—81no—
375C8—172no—
376C8—172no—
377C8—341no—
378C8—341no—
379C8—682no—
380C8—1361no—
381C22—21no—
382C22—21no—
383C22—42no—
384C22—82no—
385C22—82no—
386C22—81no—
387C22—81no—
388C22—682no—
389C22—1362no—
390C22—1362no—
391C22—1361no—
392C22—1361no—
393C22#1176270911yescharacteristic
394C22#1176287211yescharacteristic
395C22#1176288411yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—81no—
400C4—1361no—
401C4C22⋊C8×D1711yescharacteristic
402C4#1176277411yescharacteristic
403C4C8×C22⋊D1711yescharacteristic
404C4#1176288511yescharacteristic
405C4#1176307712yes—
406C2—21no—
407C2—21no—
408C2—82no—
409C2—1362no—
410C2#1452957611yescharacteristic
411C2#1452968111yescharacteristic
412C2#1452969311yescharacteristic
subgroupG/H
centerC2×C4#10587625
commutatorC2×C4×C17C22×C8
FrattiniC2×C42C22×D17
FittingC17×#1478C2
socleC22×C17#390
prime radicalC22×#63228C4
cosocleC2×C42×C17C23
hypercenter#1478D17
hypocenterC17#9668
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
2. #14527530C2semidirect
3. #14527174C2semidirect
4. #14527105C2semidirect
5. #14527104C2semidirect
6. #14527068C2semidirect
7. C17×#1478C2semidirect
45. C2×#63228C8semidirect
178. #1478D17semidirect
282. C17#9668semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#632282
#145275302
#145271742
#145271052
#145271042
#145270682
C17×#14782
#966817