Finite Group Databasebeta

← C4×#22576189 #46845178

Subgroups — C4×#22576189 #46845178

Order 34688.

484 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22576189C211yesmaximal, characteristic
2C4×#16864653C211yesmaximal, characteristic
3C4×Q8×D271C211yesmaximal, characteristic, complemented
4#31774003C211yesmaximal, characteristic, complemented
5#31774001C211yesmaximal, characteristic, complemented
6#31773998C211yesmaximal, characteristic, complemented
7#31773994C211yesmaximal, characteristic, complemented
8C4×Dic1084C211yesmaximal, characteristic, complemented
9C4×#16864644C211yesmaximal, characteristic, complemented
10C4×#16864642C211yesmaximal, characteristic, complemented
11#31773936C211yesmaximal, characteristic, complemented
12#31773904C211yesmaximal, characteristic, complemented
13#31773895C211yesmaximal, characteristic
14C4×#16864637C211yesmaximal, characteristic, complemented
15C4×SD16×C271C211yesmaximal, characteristic, complemented
16C2×#16864653C2211yescharacteristic
17C2×Q8×D271C2211yescharacteristic
18#22576189C418yesdirect product factor
19C2×Dic1084C2211yescharacteristic
20C2×#16864644C2211yescharacteristic
21C2×#16864642C2211yescharacteristic
22C2×#16864637C2211yescharacteristic
23C2×#16864637C2211yescharacteristic
24Q8×Dic271C2211yescharacteristic
25C4×Dic542—21no—
26C4×Dic542C2211yescharacteristic
27C4×Dic542C2211yescharacteristic
28#22576125—21no—
29#22576125C2211yescharacteristic
30#22576125C2211yescharacteristic
31D4×Dic271C2211yescharacteristic
32C4×C22⋊D271—21no—
33(C22⋊D271)⋊C4—21no—
34#22576118C2211yescharacteristic
35#22576116—21no—
36C4⋊C4×D271—21no—
37C4⋊C4×D271C2211yescharacteristic
38C2×C4×Dic271—21no—
39C42×D271—21no—
40C42×D271C2211yescharacteristic
41#22576094C2211yescharacteristic
42#22576093C2211yescharacteristic
43#22576091C2211yescharacteristic
44#22576085C2211yescharacteristic
45#22576085C2211yescharacteristic
46#22576084C2211yescharacteristic
47#22576083C2211yescharacteristic
48#22576083C2211yescharacteristic
49#22576081C2211yescharacteristic
50#22576070C2211yescharacteristic
51#22576070C2211yescharacteristic
52C4×C271⋊C8C2211yescharacteristic
53C2×SD16×C271C2211yescharacteristic
54C4×Q8×C271C2211yescharacteristic
55C4×D4×C271C2211yescharacteristic
56#106×C271C2211yescharacteristic
57#103×C271C2211yescharacteristic
58#102×C271C2211yescharacteristic
59C4×C8×C271C2211yescharacteristic
60#16864653—22no—
61#16864653C2×C414yes—
62C2×Dic542—21no—
63C2×Dic542C2311yescharacteristic
64C2×Dic542C2311yescharacteristic
65Q8×D271—22no—
66Q8×D271C2×C414yescomplemented
67C2×C22⋊D271—21no—
68C22×Dic271—21no—
69C22×Dic271—21no—
70C2×C4×D271—21no—
71C2×C4×D271—21no—
72C2×C4×D271D411yescharacteristic
73C2×C4×D271D411yescharacteristic
74C2×C4×D271C2311yescharacteristic
75Dic1084C2×C414yescomplemented
76#16864644C2×C414yescomplemented
77#16864642C2×C414yescomplemented
78#16864637—22no—
79#16864637C2×C414yescomplemented
80C2×C271⋊C8C2311yescharacteristic
81C2×C271⋊C8C2311yescharacteristic
82C4⋊Dic271—21no—
83C4⋊Dic271C2311yescharacteristic
84C4⋊Dic271C2311yescharacteristic
85Dic271⋊C4—21no—
86Dic271⋊C4—21no—
87Dic271⋊C4—21no—
88Dic271⋊C4—21no—
89Dic271⋊C4—21no—
90C22⋊Dic271—21no—
91(C2×D271)⋊C4—21no—
92C4×Dic271—21no—
93C4×Dic271—21no—
94C4×Dic271—21no—
95C4×Dic271—21no—
96C4×Dic271—21no—
97C4×Dic271—21no—
98C4×Dic271D411yescharacteristic
99C4×Dic271D411yescharacteristic
100C4×Dic271C2311yescharacteristic
101C2×Q8×C271C2311yescharacteristic
102C2×D4×C271C2311yescharacteristic
103C22×C4×C271—21no—
104SD16×C271C2×C414yescomplemented
105C2×C8×C271C2311yescharacteristic
106C2×C8×C271C2311yescharacteristic
107C4⋊C4×C271—21no—
108C4⋊C4×C271C2311yescharacteristic
109C4⋊C4×C271C2311yescharacteristic
110C22⋊C4×C271—21no—
111C42×C271—21no—
112C42×C271C2311yescharacteristic
113C22×D271C2×D411yescharacteristic
114Dic542—21no—
115Dic542—21no—
116Dic542—24no—
117Dic542C22×C412yes—
118Dic542C22×C412yes—
119C22⋊D271—24no—
120C2×Dic271—21no—
121C2×Dic271—21no—
122C2×Dic271—24no—
123C2×Dic271—21no—
124C2×Dic271—21no—
125C2×Dic271—42no—
126C2×Dic271C2×D411yescharacteristic
127C2×Dic271C2×D411yescharacteristic
128C2×Dic271C2×D411yescharacteristic
129C4×D271—24no—
130C4×D271—22no—
131C4×D271—41no—
132C4×D271—42no—
133C4×D271C22×C412yes—
134C4×D271#4112yes—
135C271⋊C8—21no—
136C271⋊C8C22×C412yes—
137C23×C271—21no—
138Q8×C271—21no—
139Q8×C271C22×C412yes—
140D4×C271—21no—
141D4×C271C22×C412yes—
142C2×C4×C271—21no—
143C2×C4×C271—21no—
144C2×C4×C271—21no—
145C2×C4×C271—42no—
146C2×C4×C271C2×D411yescharacteristic
147C2×C4×C271C2×D411yescharacteristic
148C2×C4×C271C2411yescharacteristic
149C8×C271—21no—
150C8×C271C22×C412yes—
151C22×C271—22no—
152C22×C271—41no—
153C22×C271—41no—
154C22×C271C22×D411yescharacteristic
155C2×D271—21no—
156C2×D271—21no—
157C2×D271C4×D412yes—
158C4×C271—22no—
159C4×C271—21no—
160C4×C271—41no—
161C4×C271—41no—
162C4×C271#13712yescomplemented
163C4×C271C23×C411yescharacteristic
164C4×C271C2×#4111yescharacteristic
165Dic271—22no—
166Dic271—22no—
167Dic271—21no—
168Dic271—21no—
169Dic271—41no—
170Dic271—41no—
171Dic271C4×D412yes—
172C2×C271—42no—
173C2×C271C2×C4×D411yescharacteristic
174C2×C271C2×#13711yescharacteristic
175C2×C271#57511yescharacteristic
176D271—22no—
177C271C4×#13711yescharacteristic, complemented, Sylow
178C4×#137—2711nomaximal, Sylow
179C2×#137—2711no—
180C4×#41—2711no—
181C2×C4×Q8—2711no—
182#441—2711no—
183#441—2711no—
184#440—2711no—
185#440—2711no—
186C4×Q16—2711no—
187C4×Q16—2711no—
188C4×SD16—2711no—
189C4×SD16D27111yescharacteristic, complemented
190#428—2711no—
191#419—2711no—
192#417—2711no—
193C4×M16—2711no—
194C2×#41—2711no—
195C22×Q8—2711no—
196#137—2718no—
197C2×Q16—2711no—
198C2×Q16—2711no—
199C2×SD16—2711no—
200C2×SD16C2×D27111yescharacteristic
201C2×M16—2711no—
202C2×M16—2711no—
203C4×Q8—2711no—
204C4×Q8—2711no—
205C4×Q8—2711no—
206C4×Q8—2711no—
207C4×Q8—2711no—
208C4×Q8—5421no—
209C4×Q8—5421no—
210C4×Q8C2×D27111yescharacteristic
211C4×D4—2711no—
212C4×D4—5421no—
213C4×D4—5421no—
214C4×D4C2×D27111yescharacteristic
215#117—2711no—
216#117—5421no—
217C2×C4⋊C4—2711no—
218C2×C4⋊C4—5421no—
219C2×C42—2711no—
220C2×C42—5421no—
221C2×C42—5421no—
222#107—2711no—
223#107—2711no—
224#106—2711no—
225#106C2×D27111yescharacteristic
226#103—2711no—
227#103—2711no—
228#103—2711no—
229#103—2711no—
230#103—2711no—
231#103C2×D27111yescharacteristic
232#102—2711no—
233#102C2×D27111yescharacteristic
234#97—2711no—
235#97—2711no—
236C4×C8—2711no—
237C4×C8C2×D27111yescharacteristic
238#41—2714no—
239#41—5422no—
240C2×Q8—2714no—
241C2×Q8—2711no—
242C2×Q8—2711no—
243C2×Q8—5421no—
244C2×Q8—5422no—
245C2×Q8C22×D27111yescharacteristic
246C2×D4—5421no—
247C2×D4C22×D27111yescharacteristic
248C22×C4—21no—
249C22×C4—2711no—
250C22×C4—2711no—
251C22×C4—2711no—
252C22×C4—5421no—
253C22×C4—5421no—
254C22×C4—5421no—
255C22×C4—5421no—
256Q16—2714no—
257Q16—2714no—
258SD16—2714no—
259SD16C4×D27114yescomplemented
260M16—2714no—
261M16—5422no—
262C2×C8—2711no—
263C2×C8—2711no—
264C2×C8C22×D27111yescharacteristic
265C2×C8C22×D27111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—2711no—
268C4⋊C4—2711no—
269C4⋊C4—5421no—
270C4⋊C4—5421no—
271C4⋊C4—5421no—
272C4⋊C4—5421no—
273C4⋊C4—5421no—
274C4⋊C4—5421no—
275C4⋊C4C22×D27111yescharacteristic
276C4⋊C4C22×D27111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—5421no—
279C22⋊C4—5421no—
280C42—21no—
281C42—2711no—
282C42—2711no—
283C42—2711no—
284C42—5421no—
285C42—5421no—
286C42—5421no—
287C42—5421no—
288C42—5421no—
289C42—5421no—
290C42C22×D27111yescharacteristic
291C23—21no—
292C23—2711no—
293Q8—21no—
294Q8—2712no—
295Q8—2712no—
296Q8—5424no—
297Q8—5421no—
298Q8—5421no—
299Q8C2×C4×D27112yes—
300D4—21no—
301D4—5424no—
302D4C2×C4×D27112yes—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—42no—
307C2×C4—2711no—
308C2×C4—2712no—
309C2×C4—2712no—
310C2×C4—2711no—
311C2×C4—2711no—
312C2×C4—5424no—
313C2×C4—5424no—
314C2×C4—5421no—
315C2×C4—5421no—
316C2×C4—5422no—
317C2×C4—5421no—
318C2×C4—5421no—
319C2×C4—10841no—
320C2×C4—10842no—
321C2×C4—10842no—
322C2×C4D4×D27111yescharacteristic
323C2×C4D4×D27111yescharacteristic
324C2×C4C23×D27111yescharacteristic
325C8—21no—
326C8—2712no—
327C8—5421no—
328C8C2×C4×D27112yes—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—2712no—
333C22—5421no—
334C22—5421no—
335C22C2×D4×D27111yescharacteristic
336C4—22no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—2712no—
341C4—5422no—
342C4—5422no—
343C4—5421no—
344C4—5421no—
345C4—10841no—
346C4—10841no—
347C4#2257618912yesdirect product factor
348C4C22×C4×D27111yescharacteristic
349C4#41×D27111yescharacteristic
350C2—42no—
351C2—5422no—
352C2C4×D4×D27111yescharacteristic
353C2C2×#2257618911yescharacteristic
354C2#3177469411yescharacteristic
subgroupG/H
centerC2×C4D4×D271
commutatorC4×C271C23×C4
FrattiniC2×C4C23×D271
FittingC4×SD16×C271C2
socleC22×C271C22×D4
prime radicalC2×#16864653C22
cosocleC2×C4×C271C24
hypercenterC4×SD16D271
hypocenterC271C4×#137
LCSG ▷ C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
3. C4×Q8×D271C2semidirect
4. #31774003C2semidirect
5. #31774001C2semidirect
6. #31773998C2semidirect
7. #31773994C2semidirect
8. C4×Dic1084C2semidirect
9. C4×#16864644C2semidirect
10. C4×#16864642C2semidirect
11. #31773936C2semidirect
12. #31773904C2semidirect
14. C4×#16864637C2semidirect
15. C4×SD16×C271C2semidirect
18. #22576189C4direct (N × H)
66. Q8×D271C2×C4semidirect
75. Dic1084C2×C4semidirect
76. #16864644C2×C4semidirect
77. #16864642C2×C4semidirect
79. #16864637C2×C4semidirect
104. SD16×C271C2×C4semidirect
162. C4×C271#137semidirect
177. C271C4×#137semidirect
189. C4×SD16D271semidirect
259. SD16C4×D271semidirect
347. C4#22576189direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225761892
C4×#168646532
C4×Q8×D2712
#317740032
#317740012
#317739982
#317739942
C4×Dic10842
C4×#168646442
C4×#168646422
#317739362
#317739042
#317738952
C4×#168646372
C4×SD16×C2712
C4×#137271