Finite Group Databasebeta

← C2×#22610046 #33086125

Subgroups — C2×#22610046 #33086125

Order 18688.

1246 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556520C212yesmaximal
2C2×C42×Dic73C211yesmaximal, characteristic
3#22610046C218yesmaximal, direct product factor
4C2×#17988342C211yesmaximal, characteristic
5C2×#17988341C212yesmaximal
6C2×#336×C73C211yesmaximal, characteristic
7C23×#10596831C2212yes—
8C22×C4×Dic73C411yescharacteristic
9C22×C4×Dic73C411yescharacteristic
10C22×C4×Dic73C411yescharacteristic
11C22×C4×Dic73C411yescharacteristic
12C22×C4×Dic73C2211yescharacteristic
13C22×C4×Dic73C2211yescharacteristic
14C2×#14556520—28no—
15C2×#14556520C2218yes—
16C42×Dic73C414yes—
17C42×Dic73C2214yes—
18#17988342C2214yes—
19#17988341C2218yes—
20C23×C8×C73C2212yes—
21C22×C42×C73C2211yescharacteristic
22#336×C73C2214yes—
23C23×Dic73C2×C411yescharacteristic
24C23×Dic73C2×C411yescharacteristic
25C23×Dic73C2×C411yescharacteristic
26C23×Dic73C2×C411yescharacteristic
27C22×#10596831—24no—
28C22×#10596831—24no—
29C22×#10596831—24no—
30C22×#10596831C2314yes—
31C2×C4×Dic73—24no—
32C2×C4×Dic73—24no—
33C2×C4×Dic73—24no—
34C2×C4×Dic73—24no—
35C2×C4×Dic73C818yescomplemented
36C2×C4×Dic73C2×C412yes—
37C2×C4×Dic73C2×C414yes—
38C2×C4×Dic73C2×C414yes—
39C2×C4×Dic73C2×C414yes—
40C2×C4×Dic73C2×C412yes—
41C2×C4×Dic73C2×C414yes—
42C2×C4×Dic73D414yes—
43C2×C4×Dic73Q814yes—
44C2×C4×Dic73C2312yes—
45C2×C4×Dic73C2312yes—
46#14556520—216no—
47C23×C4×C73C2×C411yescharacteristic
48C23×C4×C73C2×C411yescharacteristic
49C23×C4×C73C2311yescharacteristic
50C22×C8×C73—24no—
51C22×C8×C73—24no—
52C22×C8×C73—24no—
53C22×C8×C73C2314yes—
54C2×C42×C73—24no—
55C2×C42×C73C2×C412yes—
56C2×C42×C73C2312yes—
57C22×Dic73—22no—
58C22×Dic73—22no—
59C22×Dic73—22no—
60C22×Dic73—22no—
61C22×Dic73—22no—
62C22×Dic73—22no—
63C22×Dic73C4⋊C414yes—
64C22×Dic73C4⋊C414yes—
65C22×Dic73C2×C814yes—
66C22×Dic73C2×C814yes—
67C22×Dic73M1614yes—
68C22×Dic73M1614yes—
69C22×Dic73C22×C412yes—
70C22×Dic73C22×C412yes—
71C22×Dic73C22×C412yes—
72C22×Dic73C22×C412yes—
73C2×#10596831—24no—
74C2×#10596831—24no—
75C2×#10596831—24no—
76C2×#10596831—48no—
77C4×Dic73—24no—
78C4×Dic73—28no—
79C4×Dic73—24no—
80C4×Dic73—28no—
81C4×Dic73—28no—
82C4×Dic73C4⋊C418yes—
83C4×Dic73C2×C8116yescomplemented
84C4×Dic73C2×D414yes—
85C4×Dic73C2×Q814yes—
86C24×C73C22×C411yescharacteristic
87C22×C4×C73—22no—
88C22×C4×C73—22no—
89C22×C4×C73—22no—
90C22×C4×C73—22no—
91C22×C4×C73C2×C814yes—
92C22×C4×C73M1614yes—
93C22×C4×C73C22×C412yes—
94C22×C4×C73C22×C412yes—
95C22×C4×C73C22×C411yescharacteristic
96C22×C4×C73C2×D412yes—
97C22×C4×C73C2×Q812yes—
98C22×C4×C73#4114yes—
99C22×C4×C73#4114yes—
100C22×C4×C73C2411yescharacteristic
101C2×C8×C73—24no—
102C2×C8×C73—24no—
103C2×C8×C73—24no—
104C2×C8×C73—48no—
105C42×C73—24no—
106C42×C73—24no—
107C23×C73C2×C4⋊C412yes—
108C23×C73#11712yes—
109C23×C73#11712yes—
110C23×C73C22×C812yes—
111C23×C73C2×M1612yes—
112C23×C73C2×M1612yes—
113C23×C73C2×M1612yes—
114C23×C73C23×C411yescharacteristic
115C2×C4×C73—22no—
116C2×C4×C73—22no—
117C2×C4×C73—22no—
118C2×C4×C73—22no—
119C2×C4×C73—28no—
120C2×C4×C73—28no—
121C2×C4×C73C2×C4⋊C412yes—
122C2×C4×C73#11712yes—
123C2×C4×C73#11712yes—
124C2×C4×C73#12418yes—
125C2×C4×C73#12518yes—
126C2×C4×C73C22×C814yes—
127C2×C4×C73C2×M1614yes—
128C2×C4×C73C22×D411yescharacteristic
129C2×C4×C73C22×Q811yescharacteristic
130C2×C4×C73C2×#4112yes—
131C2×C4×C73C2×#4112yes—
132C2×Dic73—22no—
133C2×Dic73—22no—
134C2×Dic73—22no—
135C2×Dic73—22no—
136C2×Dic73—22no—
137C2×Dic73—22no—
138C2×Dic73—28no—
139C2×Dic73—28no—
140C2×Dic73—28no—
141C2×Dic73C4⋊C8116yes—
142C2×Dic73C2×C4⋊C414yes—
143C2×Dic73C2×C4⋊C414yes—
144C2×Dic73C22×C814yes—
145C2×Dic73C22×C814yes—
146C2×Dic73C2×M1614yes—
147C2×Dic73C2×M1614yes—
148C8×C73—44no—
149#10596831—44no—
150C22×C73#38214yes—
151C22×C73C2×C4⋊C814yes—
152C22×C73#42314yes—
153C22×C73#43114yes—
154C22×C73#43114yes—
155C22×C73#43214yes—
156C22×C73#43214yes—
157C22×C73C22×C4⋊C411yescharacteristic
158C22×C73C2×#11711yescharacteristic
159C22×C73C2×#11711yescharacteristic
160C22×C73C23×C811yescharacteristic
161C22×C73C22×M1611yescharacteristic
162C22×C73C22×M1611yescharacteristic
163C22×C73C22×M1611yescharacteristic
164C4×C73—24no—
165C4×C73—24no—
166C4×C73#38214yes—
167C4×C73C2×#12412yes—
168C4×C73C2×#12512yes—
169Dic73—24no—
170Dic73—24no—
171Dic73—24no—
172Dic73C2×C4⋊C818yes—
173C2×#1831—731nomaximal, Sylow
174C2×C73#183118yescomplemented
175C2×C73C2×#38211yescharacteristic
176C2×C73C22×C4⋊C811yescharacteristic
177C2×C73C2×#42311yescharacteristic
178C2×C73C2×#43111yescharacteristic
179C2×C73C2×#43111yescharacteristic
180C2×C73C2×#43211yescharacteristic
181C2×C73C2×#43211yescharacteristic
182C22×C4⋊C8—732no—
183C2×C43—731no—
184#1831—738no—
185C2×#336—731no—
186C2×#336—732no—
187C2×#336D7311yescharacteristic
188C73C2×#183111yescharacteristic, complemented, Sylow
189C23×C8—732no—
190C23×C8C2×D7312yes—
191C22×C42—731no—
192C22×C42—731no—
193C22×C42—731no—
194C22×C42—731no—
195C22×C42—731no—
196C22×C42—731no—
197C22×C42C2×D7311yescharacteristic
198C2×C4⋊C8—738no—
199C2×C4⋊C8—1468no—
200C43—734no—
201C43—734no—
202#336—738no—
203#336—734no—
204#336C2×D7314yes—
205C23×C4—731no—
206C23×C4—731no—
207C23×C4—731no—
208C23×C4—731no—
209C23×C4C4×D7311yescharacteristic
210C23×C4C4×D7311yescharacteristic
211C23×C4C22×D7311yescharacteristic
212C22×C8—24no—
213C22×C8—24no—
214C22×C8—24no—
215C22×C8—734no—
216C22×C8—1464no—
217C22×C8—1464no—
218C22×C8—1464no—
219C22×C8C22×D7314yes—
220C2×C42—24no—
221C2×C42—738no—
222C2×C42—732no—
223C2×C42—734no—
224C2×C42—734no—
225C2×C42—734no—
226C2×C42—732no—
227C2×C42—734no—
228C2×C42—734no—
229C2×C42—732no—
230C2×C42—734no—
231C2×C42—732no—
232C2×C42—1464no—
233C2×C42—1464no—
234C2×C42—1464no—
235C2×C42—1464no—
236C2×C42C4×D7312yes—
237C2×C42C22×D7312yes—
238C4⋊C8—14616no—
239C24C2×C4×D7311yescharacteristic
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—734no—
245C22×C4—734no—
246C22×C4—734no—
247C22×C4—732no—
248C22×C4—734no—
249C22×C4—734no—
250C22×C4—734no—
251C22×C4—732no—
252C22×C4—732no—
253C22×C4—732no—
254C22×C4—1462no—
255C22×C4—1462no—
256C22×C4—1462no—
257C22×C4—1462no—
258C22×C4—1462no—
259C22×C4—1462no—
260C22×C4C8×D7314yes—
261C22×C4#1192401114yes—
262C22×C4C2×C4×D7312yes—
263C22×C4C2×C4×D7312yes—
264C22×C4C2×C4×D7311yescharacteristic
265C22×C4D4×D7312yes—
266C22×C4Q8×D7312yes—
267C22×C4#1192402714yes—
268C22×C4#1192402814yes—
269C22×C4C23×D7311yescharacteristic
270C2×C8—24no—
271C2×C8—24no—
272C2×C8—24no—
273C2×C8—48no—
274C2×C8—2928no—
275C2×C8—1464no—
276C2×C8—1464no—
277C2×C8—1464no—
278C42—24no—
279C42—24no—
280C42—738no—
281C42—7316no—
282C42—734no—
283C42—734no—
284C42—1468no—
285C42—1468no—
286C42—1464no—
287C42—1468no—
288C42—1464no—
289C23C4⋊C4×D7312yes—
290C23#1455654712yes—
291C23#1455654812yes—
292C23C2×C8×D7312yes—
293C23M16×D7312yes—
294C23M16×D7312yes—
295C23C2×#1192401112yes—
296C23C22×C4×D7311yescharacteristic
297C2×C4—28no—
298C2×C4—28no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—734no—
304C2×C4—734no—
305C2×C4—734no—
306C2×C4—7316no—
307C2×C4—734no—
308C2×C4—734no—
309C2×C4—734no—
310C2×C4—1468no—
311C2×C4—1468no—
312C2×C4—1468no—
313C2×C4—1462no—
314C2×C4—1462no—
315C2×C4—1462no—
316C2×C4—1462no—
317C2×C4—1462no—
318C2×C4—1462no—
319C2×C4C4⋊C4×D7312yes—
320C2×C4#1455654712yes—
321C2×C4#1455654812yes—
322C2×C4#1455657718yes—
323C2×C4#1455658118yes—
324C2×C4C2×C8×D7314yes—
325C2×C4C2×#1192401114yes—
326C2×C4C2×D4×D7311yescharacteristic
327C2×C4C2×Q8×D7311yescharacteristic
328C2×C4C2×#1192402712yes—
329C2×C4C2×#1192402812yes—
330C8—44no—
331C8—2924no—
332C22#1798845114yes—
333C22C4⋊C8×D7314yes—
334C22#1798860914yes—
335C22#1798863714yes—
336C22#1798863814yes—
337C22#1798864114yes—
338C22#1798864214yes—
339C22C2×C4⋊C4×D7311yescharacteristic
340C22C2×#1455654711yescharacteristic
341C22C2×#1455654811yescharacteristic
342C22C22×C8×D7311yescharacteristic
343C22C2×M16×D7311yescharacteristic
344C22C2×M16×D7311yescharacteristic
345C22C22×#1192401111yescharacteristic
346C4—24no—
347C4—24no—
348C4—738no—
349C4—1464no—
350C4—1464no—
351C4—1464no—
352C4#1798845114yes—
353C4C2×#1455657712yes—
354C4C2×#1455658112yes—
355C2#2261004618yesdirect product factor
356C2C2×#1798845111yescharacteristic
357C2C2×C4⋊C8×D7311yescharacteristic
358C2C2×#1798860911yescharacteristic
359C2C2×#1798863711yescharacteristic
360C2C2×#1798863811yescharacteristic
361C2C2×#1798864111yescharacteristic
362C2C2×#1798864211yescharacteristic
subgroupG/H
centerC23×C4C22×D73
commutatorC22×C73C23×C8
FrattiniC22×C4C23×D73
FittingC2×#336×C73C2
socle, prime radicalC24×C73C22×C4
cosocleC22×C4×C73C24
hypercenterC2×#336D73
hypocenterC73C2×#1831
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23×C4 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
3. #22610046C2direct (N × H)
35. C2×C4×Dic73C8semidirect
83. C4×Dic73C2×C8semidirect
174. C2×C73#1831semidirect
188. C73C2×#1831semidirect
355. C2#22610046direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145565202
C2×C42×Dic732
#226100462
C2×#179883422
C2×#179883412
C2×#336×C732
C2×#183173