Finite Group Databasebeta

← C2×#14528354 #17016990

Subgroups — C2×#14528354 #17016990

Order 4352.

734 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763157C211yesmaximal, characteristic
2C2×#11763009C211yesmaximal, characteristic
3C2×#11762940C211yesmaximal, characteristic, complemented
4#14528354C218yesmaximal, direct product factor
5C2×#11762559C211yesmaximal, characteristic, complemented
6C2×#11762555C211yesmaximal, characteristic, complemented
7C2×#11762552C211yesmaximal, characteristic
8C2×C17×#462C211yesmaximal, characteristic, complemented
9C22×#63230—21no—
10C2×#10587560C2211yescharacteristic
11#11763157—22no—
12#11763157C2214yes—
13#11763009—22no—
14#11763009C2214yes—
15#11762940—22no—
16#11762940C2214yescomplemented
17C2×C4⋊#3622—21no—
18C2×C4⋊#3622C2211yescharacteristic
19C2×C4⋊#3622C2211yescharacteristic
20C2×#10587480—21no—
21C2×#10587480—21no—
22C2×#10587480—21no—
23C2×#10587474—21no—
24C2×C4×#3622C2211yescharacteristic
25#11762559C2214yescomplemented
26#11762555C2214yescomplemented
27#11762552C2214yes—
28C22×Q16×C17—21no—
29C2×C17×C4⋊Q8C2211yescharacteristic
30C2×C4×Q8×C17C2211yescharacteristic
31C17×#462—22no—
32C17×#462C2214yescomplemented
33C2×C17×C4⋊C8C2211yescharacteristic
34C2×C17×#103—21no—
35C22×Q8×C17—21no—
36C22×Q8×C17D411yescharacteristic
37C22×D68—21no—
38C22×D68—21no—
39C22×D68—21no—
40C2×Q16×C17—24no—
41C2×Q16×C17—44no—
42C22×C8×C17—21no—
43C17×C4⋊Q8—21no—
44C17×C4⋊Q8—21no—
45C17×C4⋊Q8—21no—
46C17×C4⋊Q8C2312yes—
47C4×Q8×C17—21no—
48C4×Q8×C17—21no—
49C4×Q8×C17D412yes—
50C4×Q8×C17C2312yes—
51C2×C4⋊C4×C17—21no—
52C2×C4⋊C4×C17—21no—
53C2×C4⋊C4×C17—21no—
54C2×C4⋊C4×C17D411yescharacteristic
55C2×C42×C17—21no—
56C2×C42×C17C2311yescharacteristic
57C2×#63230—24no—
58C2×#63230—44no—
59C22×#3622—21no—
60C22×#3622—21no—
61C22×#3622D411yescharacteristic
62C22×#3622D411yescharacteristic
63#10587560—21no—
64#10587560—21no—
65#10587560—21no—
66#10587560C2312yes—
67C17×C4⋊C8—21no—
68C17×C4⋊C8C2312yes—
69C17×#103—24no—
70#10587480—24no—
71#10587480—24no—
72#10587480—24no—
73C4⋊#3622—24no—
74C4⋊#3622—21no—
75C4⋊#3622—21no—
76C4⋊#3622C2312yes—
77C4⋊#3622C2312yes—
78#10587474—24no—
79C4×#3622D412yes—
80C4×#3622C2312yes—
81C23×D17—41no—
82C2×Q8×C17—21no—
83C2×Q8×C17—22no—
84C2×Q8×C17—22no—
85C2×Q8×C17—22no—
86C2×Q8×C17—41no—
87C2×Q8×C17—42no—
88C2×Q8×C17—42no—
89C2×Q8×C17C2×D412yes—
90C22×C4×C17—21no—
91C22×C4×C17—21no—
92C22×C4×C17—41no—
93C22×C4×C17C2×D411yescharacteristic
94C22×C4×C17C2×D411yescharacteristic
95C22×C4×C17#4111yescharacteristic
96C2×D68—22no—
97C2×D68—22no—
98C2×D68—22no—
99C2×D68—42no—
100C2×D68—42no—
101C2×D68—42no—
102C2×D68—42no—
103C2×D68—41no—
104C2×D68—41no—
105C2×D68—41no—
106C2×D68—82no—
107Q16×C17—48no—
108C2×C8×C17—22no—
109C2×C8×C17—42no—
110C4⋊C4×C17—22no—
111C4⋊C4×C17—21no—
112C4⋊C4×C17—22no—
113C4⋊C4×C17—22no—
114C4⋊C4×C17—22no—
115C4⋊C4×C17—41no—
116C4⋊C4×C17—41no—
117C4⋊C4×C17C2×D412yes—
118C42×C17—22no—
119C42×C17—22no—
120C42×C17C2×D411yescharacteristic
121C42×C17C2×D411yescharacteristic
122C42×C17#4111yescharacteristic
123C42×C17C2411yescharacteristic
124#63230—48no—
125C2×#3622—22no—
126C2×#3622—22no—
127C2×#3622—22no—
128C2×#3622—22no—
129C2×#3622—42no—
130C2×#3622—42no—
131C2×#3622C2×D412yes—
132C2×#3622C2×D412yes—
133C2×#1702—171nomaximal, Sylow
134C23×C17#12111yescharacteristic
135C22×D17—42no—
136C22×D17—82no—
137C22×D17—82no—
138C22×D17—82no—
139Q8×C17—22no—
140Q8×C17—22no—
141Q8×C17—42no—
142Q8×C17—42no—
143Q8×C17—42no—
144Q8×C17—82no—
145C2×C4×C17—22no—
146C2×C4×C17—22no—
147C2×C4×C17—22no—
148C2×C4×C17—42no—
149C2×C4×C17—42no—
150C2×C4×C17—42no—
151C2×C4×C17—82no—
152C2×C4×C17#12111yescharacteristic
153C2×C4×C17#12111yescharacteristic
154C2×C4×C17#12111yescharacteristic
155C2×C4×C17#13512yes—
156C2×C4×C17AGL(1,ℤ/8)12yes—
157C2×C4×C17AGL(1,ℤ/8)12yes—
158C2×C4×C17#13712yes—
159C2×C4×C17C22×D411yescharacteristic
160C2×C4×C17C22×D411yescharacteristic
161C2×C4×C17C2×#4111yescharacteristic
162D68—42no—
163D68—42no—
164D68—42no—
165D68—42no—
166D68—82no—
167D68—82no—
168D68—82no—
169D68—82no—
170C8×C17—42no—
171#3622—22no—
172#3622—22no—
173#3622—42no—
174#3622—42no—
175C2×#486—171no—
176C2×#462D1711yescharacteristic, complemented
177C2×#460—171no—
178C2×#446—171no—
179#1702—178no—
180C2×#334—171no—
181C2×#332—171no—
182C2×#331—171no—
183C22×C17#46412yes—
184C22×C17#46912yes—
185C22×C17#47112yes—
186C22×C17C2×#12111yescharacteristic
187C2×D17—82no—
188C2×D17—82no—
189C2×D17—82no—
190C2×D17—164no—
191C4×C17—21no—
192C4×C17—21no—
193C4×C17—42no—
194C4×C17—42no—
195C4×C17—82no—
196C4×C17#46412yes—
197C4×C17#46912yes—
198C4×C17C2×#13511yescharacteristic
199C4×C17C2×AGL(1,ℤ/8)11yescharacteristic
200C4×C17C2×AGL(1,ℤ/8)11yescharacteristic
201C4×C17C2×#13711yescharacteristic
202C22×Q16—21no—
203C22×SD16—341no—
204C2×C4⋊Q8C2×D1711yescharacteristic
205C2×#127—171no—
206C2×C4×Q8C2×D1711yescharacteristic
207#486—174no—
208#486—342no—
209#462—22no—
210#462C2×D1714yescomplemented
211#460—174no—
212#460—342no—
213#446—174no—
214#446—342no—
215C2×C4⋊C8—171no—
216C2×C4⋊C8—171no—
217C2×C4⋊C8—341no—
218C2×C4⋊C8C2×D1711yescharacteristic
219C2×#103—21no—
220C2×#102—341no—
221C2×#102—341no—
222C2×#102—341no—
223C2×#97—341no—
224C2×C4×C8—171no—
225#334—174no—
226#332—174no—
227#331—174no—
228C2×C17#170214yescomplemented
229C2×C17C2×#46411yescharacteristic
230C2×C17C2×#46911yescharacteristic
231C2×C17C2×#47111yescharacteristic
232D17—162no—
233C22×Q8—21no—
234C22×Q8C22⋊D1711yescharacteristic
235C22×D4—341no—
236C22×D4—341no—
237C22×D4—341no—
238C2×Q16—24no—
239C2×Q16—44no—
240C2×SD16—344no—
241C2×SD16—684no—
242C22×C8—21no—
243C22×C8—171no—
244C22×C8—171no—
245C22×C8—341no—
246C22×C8—341no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8C22×D1712yes—
251#127—172no—
252#127—341no—
253#127—341no—
254#127—341no—
255C4×Q8—21no—
256C4×Q8—21no—
257C4×Q8C22⋊D1712yes—
258C4×Q8C22×D1712yes—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4C22⋊D1711yescharacteristic
263C2×C42—21no—
264C2×C42C22×D1711yescharacteristic
265C4⋊C8—21no—
266C4⋊C8—172no—
267C4⋊C8—172no—
268C4⋊C8—344no—
269C4⋊C8—341no—
270C4⋊C8—341no—
271C4⋊C8C22×D1712yes—
272#103—24no—
273#102—344no—
274#102—344no—
275#102—344no—
276#97—344no—
277C4×C8—172no—
278C4×C8—172no—
279C17C2×#170211yescharacteristic, complemented, Sylow
280C24—681no—
281C2×Q8—21no—
282C2×Q8—22no—
283C2×Q8—22no—
284C2×Q8—22no—
285C2×Q8—41no—
286C2×Q8—42no—
287C2×Q8—42no—
288C2×Q8C2×C22⋊D1712yes—
289C2×D4—342no—
290C2×D4—342no—
291C2×D4—342no—
292C2×D4—682no—
293C2×D4—682no—
294C2×D4—682no—
295C2×D4—681no—
296C2×D4—681no—
297C2×D4—681no—
298C2×D4—682no—
299C2×D4—1362no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—41no—
303C22×C4D4×D1711yescharacteristic
304C22×C4#6325411yescharacteristic
305C22×C4C2×C22⋊D1711yescharacteristic
306Q16—48no—
307SD16—688no—
308C2×C8—22no—
309C2×C8—42no—
310C2×C8—172no—
311C2×C8—172no—
312C2×C8—342no—
313C2×C8—342no—
314C2×C8—342no—
315C2×C8—342no—
316C2×C8—682no—
317C2×C8—682no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—21no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4C2×C22⋊D1712yes—
326C42—22no—
327C42—22no—
328C42D4×D1711yescharacteristic
329C42#6325411yescharacteristic
330C42C2×C22⋊D1711yescharacteristic
331C42C23×D1711yescharacteristic
332C23—682no—
333C23—1362no—
334C23—1362no—
335C23—1362no—
336C23#1058762511yescharacteristic
337Q8—22no—
338Q8—22no—
339Q8—42no—
340Q8—42no—
341Q8—42no—
342Q8—82no—
343D4—682no—
344D4—682no—
345D4—682no—
346D4—682no—
347D4—1362no—
348D4—1362no—
349D4—1362no—
350D4—1362no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—82no—
358C2×C4#1058760412yes—
359C2×C4#1058760512yes—
360C2×C4#1058761812yes—
361C2×C4#1058762511yescharacteristic
362C2×C4#1058762511yescharacteristic
363C2×C4#1058762511yescharacteristic
364C2×C4#1058763512yes—
365C2×C4C2×D4×D1711yescharacteristic
366C2×C4C2×#6325411yescharacteristic
367C2×C4C22×C22⋊D1711yescharacteristic
368C8—42no—
369C8—342no—
370C8—342no—
371C8—682no—
372C8—682no—
373C22—2724no—
374C22—1362no—
375C22—1362no—
376C22—1362no—
377C22#1176303312yes—
378C22#1176306012yes—
379C22#1176307412yes—
380C22C2×#1058762511yescharacteristic
381C4—21no—
382C4—21no—
383C4—42no—
384C4—42no—
385C4—82no—
386C4#1176303312yes—
387C4#1176306012yes—
388C4C2×#1058760511yescharacteristic
389C4C2×#1058763511yescharacteristic
390C4C2×#1058761811yescharacteristic
391C4C2×#1058760411yescharacteristic
392C2—2722no—
393C2#1452835414yesdirect product factor
394C2C2×#1176303311yescharacteristic
395C2C2×#1176306011yescharacteristic
396C2C2×#1176307411yescharacteristic
subgroupG/H
centerC23#10587625
commutator, cosocleC42×C17C24
FrattiniC42C23×D17
FittingC2×C17×#462C2
socleC23×C17#121
prime radicalC2×#10587560C22
hypercenterC2×#462D17
hypocenterC17C2×#1702
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. C2×#11762940C2semidirect
4. #14528354C2direct (N × H)
5. C2×#11762559C2semidirect
6. C2×#11762555C2semidirect
8. C2×C17×#462C2semidirect
16. #11762940C22semidirect
25. #11762559C22semidirect
26. #11762555C22semidirect
32. C17×#462C22semidirect
176. C2×#462D17semidirect
210. #462C2×D17semidirect
228. C2×C17#1702semidirect
279. C17C2×#1702semidirect
393. C2#14528354direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117631572
C2×#117630092
C2×#117629402
#145283542
C2×#117625592
C2×#117625552
C2×#117625522
C2×C17×#4622
C2×#170217