Finite Group Databasebeta

← C2×#14541754 #17914878

Subgroups — C2×#14541754 #17914878

Order 4352.

1746 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×#11763536C212yesmaximal
2#14541754C2116yesmaximal, direct product factor
3C2×#11763216C212yesmaximal
4C2×#11763115C212yesmaximal
5C2×#11763113C212yesmaximal
6C2×#11763103C212yesmaximal
7C2×#11762939C211yesmaximal, characteristic
8C2×#11762915C212yesmaximal
9C2×C4×Dic68C211yesmaximal, characteristic
10C2×C17×#499C211yesmaximal, characteristic
11C22×Dic68C2211yescharacteristic
12#11763536—28no—
13#11763536C22116yes—
14C2×#10587574—22no—
15C2×#10587574C2212yes—
16C2×#10587576C2212yes—
17C2×#10587575—22no—
18C2×#10587575—22no—
19C2×C4×Dic34C2211yescharacteristic
20C2×C4×Dic34C2212yes—
21C2×#10587573—22no—
22C2×#10587573C2212yes—
23C2×#10587573C2212yes—
24#11763216C22116yes—
25#11763115C22116yes—
26#11763113C22116yes—
27#11763103C22116yes—
28#11762939C2218yes—
29#11762915C22116yes—
30C4×Dic68C2218yes—
31C2×#10587489C2211yescharacteristic
32C2×#10587478C2212yes—
33C2×#10587479C2212yes—
34C2×C4⋊#3622C2211yescharacteristic
35C2×#10587485C2212yes—
36C2×#10587487C2212yes—
37C2×#10587481C2212yes—
38C2×#10587481C2212yes—
39C2×#10587486C2212yes—
40C2×C17×#125C2212yes—
41C17×#499C2218yes—
42C2×C17×#107C2211yescharacteristic
43C2×C17×#107C2211yescharacteristic
44C2×C17×#106C2212yes—
45C2×C4×C8×C17C2211yescharacteristic
46C22×Dic34—22no—
47C22×Dic34D411yescharacteristic
48C22×Dic34C2312yes—
49C22×C8×C17C2311yescharacteristic
50C22×C8×C17C2311yescharacteristic
51C17×#125—24no—
52C17×#125C2318yes—
53C2×C4⋊C4×C17—22no—
54C2×C4⋊C4×C17—22no—
55C2×C4⋊C4×C17C2312yes—
56C2×C4⋊C4×C17C2312yes—
57C2×C42×C17C2311yescharacteristic
58C2×C4⋊Dic17—22no—
59C2×C4⋊Dic17D411yescharacteristic
60C2×C4⋊Dic17C2312yes—
61C2×#63225—22no—
62C2×#63225—22no—
63C2×#63225—22no—
64C2×#63225—22no—
65C2×#63225—22no—
66C2×#63225D412yes—
67C2×C4×Dic17—22no—
68C2×C4×Dic17—22no—
69C2×C4×Dic17—22no—
70C2×C4×Dic17C2312yes—
71C22×#3622C2312yes—
72C2×Dic68Q818yescomplemented
73C2×Dic68C2314yes—
74#10587576—24no—
75#10587576C2318yes—
76#10587575—216no—
77#10587575—216no—
78#10587574—24no—
79#10587574—216no—
80#10587574C2318yes—
81#10587573—216no—
82#10587573—24no—
83#10587573—24no—
84#10587573C2318yes—
85#10587573C2318yes—
86C4×Dic34—24no—
87C4×Dic34D414yes—
88C4×Dic34C2314yes—
89C4×Dic34C2318yes—
90C17×#107C2314yes—
91C17×#107C2314yes—
92C17×#106C2318yes—
93C4×C8×C17C2314yes—
94#10587489C2314yes—
95#10587487C2318yes—
96#10587486C2318yes—
97#10587485C2318yes—
98#10587481C2318yes—
99#10587481C2318yes—
100#10587479C2318yes—
101#10587478C2318yes—
102C4⋊#3622C2314yes—
103C22×C4×C17—22no—
104C22×C4×C17—22no—
105C22×C4×C17C2×D411yescharacteristic
106C22×C4×C17C2×D411yescharacteristic
107C22×C4×C17C2411yescharacteristic
108C22×Dic17—22no—
109C22×Dic17—22no—
110C22×Dic17C2×D412yes—
111C22×Dic17C2×D412yes—
112C2×Dic34—22no—
113C2×Dic34—24no—
114C2×Dic34—28no—
115C2×Dic34—42no—
116C2×Dic34—48no—
117C2×Dic34C2×D414yes—
118C2×Dic34C2×Q818yes—
119C2×Dic34C2414yes—
120C2×C8×C17—22no—
121C2×C8×C17C2×Q814yes—
122C2×C8×C17C2412yes—
123C2×C8×C17C2412yes—
124C4⋊C4×C17—22no—
125C4⋊C4×C17—22no—
126C4⋊C4×C17—28no—
127C4⋊C4×C17—28no—
128C4⋊C4×C17C2414yes—
129C4⋊C4×C17C2414yes—
130C42×C17C2×D412yes—
131C42×C17C2412yes—
132C4⋊Dic17—22no—
133C4⋊Dic17—28no—
134C4⋊Dic17C2×D414yes—
135C4⋊Dic17C2414yes—
136#63225—28no—
137#63225—28no—
138#63225—28no—
139#63225—28no—
140#63225—28no—
141#63225C2×D418yes—
142C4×Dic17—28no—
143C4×Dic17—28no—
144C4×Dic17—28no—
145C4×Dic17C2×D414yes—
146C4×Dic17C2414yes—
147C2×#3622—24no—
148C2×#3622C2414yes—
149Dic68C2×Q8116yescomplemented
150C2×#3390—171nomaximal, Sylow
151C23×C17C22×D411yescharacteristic
152C2×C4×C17—22no—
153C2×C4×C17—22no—
154C2×C4×C17—24no—
155C2×C4×C17—24no—
156C2×C4×C17—44no—
157C2×C4×C17—44no—
158C2×C4×C17C22×D412yes—
159C2×C4×C17C22×D412yes—
160C2×C4×C17C22×D411yescharacteristic
161C2×C4×C17C22×Q812yes—
162C2×C4×C172−1+412yes—
163C2×C4×C17C2511yescharacteristic
164C2×Dic17—28no—
165C2×Dic17—24no—
166C2×Dic17—24no—
167C2×Dic17—24no—
168C2×Dic17—24no—
169C2×Dic17—44no—
170C2×Dic17C22×D414yes—
171C2×Dic17C22×D414yes—
172Dic34—28no—
173Dic34—24no—
174Dic34—44no—
175Dic34—416no—
176Dic34C22×Q818yes—
177C8×C17—22no—
178C8×C17C22×Q814yes—
179#3622—24no—
180C2×#557—172no—
181#3390—1716no—
182C2×#501—172no—
183C2×#499D1711yescharacteristic
184C2×#479—172no—
185C2×#479—172no—
186C2×#477—172no—
187C2×#446—171no—
188C2×#441—172no—
189C2×C4×Q16—171no—
190C22×C17D4×Q812yes—
191C22×C17#57512yes—
192C22×C17#57812yes—
193C22×C17C23×D411yescharacteristic
194C4×C17—22no—
195C4×C17—22no—
196C4×C17—44no—
197C4×C17—44no—
198C4×C17D4×Q812yes—
199C4×C17C23×Q811yescharacteristic
200C4×C17C2×2−1+411yescharacteristic
201Dic17—28no—
202Dic17—24no—
203Dic17—24no—
204Dic17—44no—
205C22×Q16—171no—
206#557—1716no—
207#557—348no—
208C2×C4⋊Q8—172no—
209C2×C4⋊Q8—342no—
210C2×#125—172no—
211C2×#125—342no—
212C2×#125—342no—
213C2×#125C2×D1712yes—
214C2×C4×Q8—171no—
215C2×C4×Q8—172no—
216C2×C4×Q8—172no—
217C2×C4×Q8—172no—
218C2×C4×Q8—342no—
219#501—1716no—
220#499C2×D1718yes—
221#479—1716no—
222#479—1716no—
223#477—1716no—
224#446—178no—
225#441—1716no—
226C4×Q16—178no—
227C2×#107—171no—
228C2×#107—172no—
229C2×#107C2×D1711yescharacteristic
230C2×#107C2×D1711yescharacteristic
231C2×#106—172no—
232C2×#106C2×D1712yes—
233C2×C4⋊C8—172no—
234C2×C4⋊C8—171no—
235C2×#103—172no—
236C2×#103—172no—
237C2×#103—172no—
238C2×#97—172no—
239C2×C4×C8C2×D1711yescharacteristic
240C2×C17#339014yescomplemented
241C2×C17C2×D4×Q811yescharacteristic
242C2×C17C2×#57511yescharacteristic
243C2×C17C2×#57811yescharacteristic
244C22×Q8—171no—
245C22×Q8—172no—
246C22×Q8—342no—
247C2×Q16—178no—
248C2×Q16—174no—
249C22×C8—172no—
250C22×C8C22×D1711yescharacteristic
251C22×C8C22×D1711yescharacteristic
252C4⋊Q8—178no—
253C4⋊Q8—344no—
254C4⋊Q8—3416no—
255#125—24no—
256#125—178no—
257#125—344no—
258#125—3416no—
259#125—3416no—
260#125C22×D1718yes—
261C4×Q8—174no—
262C4×Q8—174no—
263C4×Q8—178no—
264C4×Q8—178no—
265C4×Q8—178no—
266C4×Q8—344no—
267C4×Q8—344no—
268C4×Q8—3416no—
269C4×Q8—344no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—172no—
273C2×C4⋊C4—171no—
274C2×C4⋊C4—172no—
275C2×C4⋊C4—342no—
276C2×C4⋊C4—342no—
277C2×C4⋊C4—342no—
278C2×C4⋊C4—342no—
279C2×C4⋊C4—342no—
280C2×C4⋊C4—342no—
281C2×C4⋊C4C22×D1712yes—
282C2×C4⋊C4C22×D1712yes—
283C2×C42—172no—
284C2×C42—342no—
285C2×C42—342no—
286C2×C42—342no—
287C2×C42C22×D1711yescharacteristic
288#107—174no—
289#107—178no—
290#107C22×D1714yes—
291#107C22×D1714yes—
292#106—178no—
293#106C22×D1718yes—
294C4⋊C8—178no—
295C4⋊C8—174no—
296#103—178no—
297#103—178no—
298#103—178no—
299#97—178no—
300C4×C8C22×D1714yes—
301C17C2×#339011yescharacteristic, complemented, Sylow
302C2×Q8—174no—
303C2×Q8—178no—
304C2×Q8—174no—
305C2×Q8—348no—
306C2×Q8—342no—
307C2×Q8—344no—
308C2×Q8—682no—
309C2×Q8—688no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—172no—
313C22×C4—172no—
314C22×C4—342no—
315C22×C4—342no—
316C22×C4D4×D1711yescharacteristic
317C22×C4D4×D1711yescharacteristic
318C22×C4C23×D1711yescharacteristic
319Q16—1716no—
320C2×C8—22no—
321C2×C8—174no—
322C2×C8—344no—
323C2×C8Q8×D1714yes—
324C2×C8C23×D1712yes—
325C2×C8C23×D1712yes—
326C4⋊C4—28no—
327C4⋊C4—28no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—178no—
331C4⋊C4—174no—
332C4⋊C4—174no—
333C4⋊C4—348no—
334C4⋊C4—348no—
335C4⋊C4—348no—
336C4⋊C4—348no—
337C4⋊C4—348no—
338C4⋊C4—342no—
339C4⋊C4—348no—
340C4⋊C4C23×D1714yes—
341C4⋊C4C23×D1714yes—
342C42—174no—
343C42—174no—
344C42—348no—
345C42—348no—
346C42—348no—
347C42D4×D1712yes—
348C42C23×D1712yes—
349C23C2×D4×D1711yescharacteristic
350Q8—178no—
351Q8—348no—
352Q8—344no—
353Q8—684no—
354Q8—6816no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—174no—
362C2×C4—174no—
363C2×C4—348no—
364C2×C4—344no—
365C2×C4—344no—
366C2×C4—344no—
367C2×C4—344no—
368C2×C4—684no—
369C2×C4C2×D4×D1712yes—
370C2×C4C2×D4×D1712yes—
371C2×C4C2×D4×D1711yescharacteristic
372C2×C4C2×Q8×D1712yes—
373C2×C4#1058769412yes—
374C2×C4C24×D1711yescharacteristic
375C8—22no—
376C8—344no—
377C8C2×Q8×D1714yes—
378C22#1176347412yes—
379C22#1176360612yes—
380C22#1176362312yes—
381C22C22×D4×D1711yescharacteristic
382C4—22no—
383C4—22no—
384C4—44no—
385C4—44no—
386C4—344no—
387C4—348no—
388C4—344no—
389C4—684no—
390C4#1176347412yes—
391C4C22×Q8×D1711yescharacteristic
392C4C2×#1058769411yescharacteristic
393C2#1454175414yesdirect product factor
394C2C2×#1176347411yescharacteristic
395C2C2×#1176360611yescharacteristic
396C2C2×#1176362311yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#499C2
socle, prime radicalC23×C17C22×D4
hypercenterC2×#499D17
hypocenterC17C2×#3390
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#499

Complements

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

NH ≅ G/Ntype
2. #14541754C2direct (N × H)
72. C2×Dic68Q8semidirect
149. Dic68C2×Q8semidirect
240. C2×C17#3390semidirect
301. C17C2×#3390semidirect
393. C2#14541754direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635362
#145417542
C2×#117632162
C2×#117631152
C2×#117631132
C2×#117631032
C2×#117629392
C2×#117629152
C2×C4×Dic682
C2×C17×#4992
C2×#339017