Finite Group Databasebeta

← C2×#22615588 #33256693

Subgroups — C2×#22615588 #33256693

Order 18688.

1966 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22615588C2116yesmaximal, direct product factor
2C2×#17988521C212yesmaximal
3C2×#17988519C212yesmaximal
4C2×#17988485C212yesmaximal
5C2×#17988484C212yesmaximal
6C2×#17988471C212yesmaximal
7C2×#17988470C212yesmaximal
8C2×#17988455C211yesmaximal, characteristic
9C2×C4×C4⋊Dic73C211yesmaximal, characteristic
10C2×#376×C73C211yesmaximal, characteristic
11C22×C4⋊Dic73C2212yes—
12C22×C4⋊Dic73C2212yes—
13C22×C4⋊Dic73C2212yes—
14C22×#11924007C2212yes—
15C22×#11924007C2212yes—
16C22×#11924007C2212yes—
17C22×#11924007C2212yes—
18C22×C4×Dic73C2211yescharacteristic
19C22×C4×Dic73C2211yescharacteristic
20#17988521C22116yes—
21#17988519C22116yes—
22#17988485C22116yes—
23#17988484C22116yes—
24#17988471C22116yes—
25#17988470C22116yes—
26#17988455C2218yes—
27C4×C4⋊Dic73C2218yes—
28C2×#14556498C2212yes—
29C2×#14556498C2212yes—
30C2×#14556498C2211yescharacteristic
31C2×#14556498C2211yescharacteristic
32C2×#14556498C2212yes—
33C2×#14556498C2212yes—
34C2×#14556498C2212yes—
35C22×C42×C73C2212yes—
36C22×C42×C73C2211yescharacteristic
37#376×C73C2218yes—
38C2×#95×C73C2212yes—
39C2×#95×C73C2211yescharacteristic
40C2×#95×C73C2211yescharacteristic
41C23×Dic73C2312yes—
42C23×Dic73C2312yes—
43C23×Dic73C2312yes—
44C23×Dic73C2312yes—
45C2×C4⋊Dic73—28no—
46C2×C4⋊Dic73—28no—
47C2×C4⋊Dic73—28no—
48C2×C4⋊Dic73C2318yes—
49C2×C4⋊Dic73C2318yes—
50C2×C4⋊Dic73C2318yes—
51C2×#11924007—28no—
52C2×#11924007—28no—
53C2×#11924007—44no—
54C2×#11924007—44no—
55C2×#11924007C2318yes—
56C2×#11924007C2318yes—
57C2×#11924007C2318yes—
58C2×#11924007C2318yes—
59C2×C4×Dic73—42no—
60C2×C4×Dic73—42no—
61C2×C4×Dic73C2314yes—
62C2×C4×Dic73C2314yes—
63#14556498C2318yes—
64#14556498C2318yes—
65#14556498C2314yes—
66#14556498C2314yes—
67#14556498C2318yes—
68#14556498C2318yes—
69#14556498C2318yes—
70C23×C4×C73C2312yes—
71C23×C4×C73C2311yescharacteristic
72C23×C4×C73C2311yescharacteristic
73C23×C4×C73C2311yescharacteristic
74C23×C4×C73C2312yes—
75C2×C42×C73—28no—
76C2×C42×C73Q818yes—
77C2×C42×C73C2318yes—
78C2×C42×C73C2314yes—
79#95×C73C2318yes—
80#95×C73C2314yes—
81#95×C73C2314yes—
82C22×Dic73—24no—
83C22×Dic73—24no—
84C22×Dic73—24no—
85C22×Dic73—24no—
86C22×Dic73—24no—
87C22×Dic73—24no—
88C22×Dic73—24no—
89C22×Dic73—24no—
90C22×Dic73—24no—
91C22×Dic73—24no—
92C22×Dic73—24no—
93C22×Dic73#4118yes—
94C22×Dic73C2414yes—
95C22×Dic73C2414yes—
96C22×Dic73C2414yes—
97C22×Dic73C2414yes—
98C4⋊Dic73—216no—
99C4⋊Dic73—216no—
100C4⋊Dic73—216no—
101#11924007—216no—
102#11924007—216no—
103#11924007—48no—
104#11924007—48no—
105C4×Dic73—44no—
106C4×Dic73—44no—
107C24×C73C2411yescharacteristic
108C22×C4×C73—24no—
109C22×C4×C73—24no—
110C22×C4×C73—24no—
111C22×C4×C73—22no—
112C22×C4×C73—22no—
113C22×C4×C73—24no—
114C22×C4×C73—24no—
115C22×C4×C73—24no—
116C22×C4×C73—24no—
117C22×C4×C73C2×Q814yes—
118C22×C4×C73C2×Q814yes—
119C22×C4×C73C2×Q814yes—
120C22×C4×C73#4118yes—
121C22×C4×C73C2414yes—
122C22×C4×C73C2412yes—
123C22×C4×C73C2412yes—
124C22×C4×C73C2412yes—
125C22×C4×C73C2414yes—
126C42×C73—216no—
127C42×C73C2×Q8116yes—
128C23×C73C22×Q812yes—
129C23×C73C2×#4114yes—
130C23×C73C2×#4114yes—
131C23×C73H(5,𝔽2)12yes—
132C23×C732−1+412yes—
133C23×C73C2511yescharacteristic
134C2×C4×C73—28no—
135C2×C4×C73—28no—
136C2×C4×C73—28no—
137C2×C4×C73—216no—
138C2×C4×C73—24no—
139C2×C4×C73—24no—
140C2×C4×C73—24no—
141C2×C4×C73—22no—
142C2×C4×C73—22no—
143C2×C4×C73—24no—
144C2×C4×C73—24no—
145C2×C4×C73—24no—
146C2×C4×C73—24no—
147C2×C4×C73—48no—
148C2×C4×C73C22×Q814yes—
149C2×C4×C73C22×Q814yes—
150C2×C4×C73C22×Q814yes—
151C2×C4×C73C2×#4118yes—
152C2×Dic73—216no—
153C2×Dic73—24no—
154C2×Dic73—24no—
155C2×Dic73—24no—
156C2×Dic73—24no—
157C2×Dic73—24no—
158C2×Dic73—24no—
159C2×Dic73—24no—
160C2×Dic73—24no—
161C2×Dic73—24no—
162C2×Dic73—24no—
163C2×Dic73—24no—
164C2×Dic73—48no—
165C2×Dic73—48no—
166C2×Dic73—48no—
167C2×Dic73C2×#4118yes—
168C22×C73#53314yes—
169C22×C73#53314yes—
170C22×C73#54414yes—
171C22×C73#55218yes—
172C22×C73#55318yes—
173C22×C73C23×Q811yescharacteristic
174C22×C73C22×#4112yes—
175C22×C73C22×#4112yes—
176C22×C73C2×H(5,𝔽2)11yescharacteristic
177C22×C73C2×2−1+411yescharacteristic
178C4×C73—24no—
179C4×C73—24no—
180C4×C73—24no—
181C4×C73—28no—
182C4×C73—44no—
183Dic73—28no—
184Dic73—44no—
185Dic73—44no—
186Dic73—44no—
187C2×#2606—731nomaximal, Sylow
188C2×C73#260618yescomplemented
189C2×C73C2×#53311yescharacteristic
190C2×C73C2×#53311yescharacteristic
191C2×C73C2×#54411yescharacteristic
192C2×C73C2×#55212yes—
193C2×C73C2×#55312yes—
194#2606—7316no—
195C2×#398—732no—
196C2×#398—732no—
197C2×#389—732no—
198C2×#389—732no—
199C2×#387—732no—
200C2×#387—732no—
201C2×#383—731no—
202C2×C4×C4⋊C4—731no—
203C2×#376D7311yescharacteristic
204C73C2×#260611yescharacteristic, complemented, Sylow
205C22×C4⋊C4—732no—
206C22×C4⋊C4—732no—
207C22×C4⋊C4—732no—
208C22×C4⋊C4—732no—
209C22×C4⋊C4—732no—
210C22×C4⋊C4—732no—
211C22×C4⋊C4—732no—
212C22×C42—731no—
213C22×C42—731no—
214C22×C42C2×D7312yes—
215C22×C42C2×D7311yescharacteristic
216#398—7316no—
217#398—7316no—
218#389—7316no—
219#389—7316no—
220#387—7316no—
221#387—7316no—
222#383—738no—
223C4×C4⋊C4—738no—
224#376C2×D7318yes—
225C2×#95—732no—
226C2×#95—732no—
227C2×#95—732no—
228C2×#95—732no—
229C2×#95—731no—
230C2×#95—732no—
231C2×#95—731no—
232C2×#95C2×D7311yescharacteristic
233C2×#95C2×D7311yescharacteristic
234C2×#95C2×D7312yes—
235C23×C4—732no—
236C23×C4—732no—
237C23×C4—732no—
238C23×C4—732no—
239C23×C4C22×D7312yes—
240C23×C4C22×D7311yescharacteristic
241C23×C4C22×D7311yescharacteristic
242C23×C4C22×D7311yescharacteristic
243C23×C4C22×D7312yes—
244C2×C4⋊C4—2924no—
245C2×C4⋊C4—2924no—
246C2×C4⋊C4—738no—
247C2×C4⋊C4—738no—
248C2×C4⋊C4—738no—
249C2×C4⋊C4—738no—
250C2×C4⋊C4—738no—
251C2×C4⋊C4—738no—
252C2×C4⋊C4—738no—
253C2×C4⋊C4—1468no—
254C2×C4⋊C4—1468no—
255C2×C4⋊C4—1468no—
256C2×C4⋊C4—1468no—
257C2×C4⋊C4—1468no—
258C2×C42—28no—
259C2×C42—2922no—
260C2×C42—2922no—
261C2×C42—734no—
262C2×C42—734no—
263C2×C42Dic14618yes—
264C2×C42C22×D7318yes—
265C2×C42C22×D7314yes—
266#95—738no—
267#95—734no—
268#95—738no—
269#95—734no—
270#95—738no—
271#95—738no—
272#95—738no—
273#95C22×D7318yes—
274#95C22×D7314yes—
275#95C22×D7314yes—
276C24C23×D7311yescharacteristic
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—24no—
286C22×C4—738no—
287C22×C4—734no—
288C22×C4—734no—
289C22×C4—734no—
290C22×C4—734no—
291C22×C4—1464no—
292C22×C4—1464no—
293C22×C4—1464no—
294C22×C4—1464no—
295C22×C4—1464no—
296C22×C4—1464no—
297C22×C4—1464no—
298C22×C4—1464no—
299C22×C4—1464no—
300C22×C4—1464no—
301C22×C4—1464no—
302C22×C4C2×Dic14614yes—
303C22×C4C2×Dic14614yes—
304C22×C4C2×Dic14614yes—
305C22×C4#1192402818yes—
306C22×C4C23×D7314yes—
307C22×C4C23×D7312yes—
308C22×C4C23×D7312yes—
309C22×C4C23×D7312yes—
310C22×C4C23×D7314yes—
311C4⋊C4—2928no—
312C4⋊C4—2928no—
313C4⋊C4—14616no—
314C4⋊C4—14616no—
315C4⋊C4—14616no—
316C4⋊C4—14616no—
317C4⋊C4—14616no—
318C42—216no—
319C42—2924no—
320C42—2924no—
321C42C2×Dic146116yes—
322C23C22×Dic14612yes—
323C23#41×D7314yes—
324C23C2×#1192402814yes—
325C23#1455663712yes—
326C23#1455663812yes—
327C23C24×D7311yescharacteristic
328C2×C4—28no—
329C2×C4—28no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—24no—
336C2×C4—28no—
337C2×C4—216no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—48no—
342C2×C4—2928no—
343C2×C4—2928no—
344C2×C4—2928no—
345C2×C4—738no—
346C2×C4—1464no—
347C2×C4—1464no—
348C2×C4—1464no—
349C2×C4—1464no—
350C2×C4—1464no—
351C2×C4—1464no—
352C2×C4—1464no—
353C2×C4—1464no—
354C2×C4—1464no—
355C2×C4—1464no—
356C2×C4—1464no—
357C2×C4—14616no—
358C2×C4C22×Dic14614yes—
359C2×C4C22×Dic14614yes—
360C2×C4C22×Dic14614yes—
361C2×C4C2×#1192402818yes—
362C22#1798914014yes—
363C22#1798914414yes—
364C22#1798921514yes—
365C22#1798927018yes—
366C22#1798928118yes—
367C22C23×Dic14611yescharacteristic
368C22C2×#41×D7312yes—
369C22C22×#1192402812yes—
370C22C2×#1455663711yescharacteristic
371C22C2×#1455663811yescharacteristic
372C4—24no—
373C4—28no—
374C4—24no—
375C4—24no—
376C4—44no—
377C4—2924no—
378C4—2924no—
379C4—2924no—
380C4—1468no—
381C2#2261558818yesdirect product factor
382C2C2×#1798914011yescharacteristic
383C2C2×#1798914411yescharacteristic
384C2C2×#1798921511yescharacteristic
385C2C2×#1798927012yes—
386C2C2×#1798928112yes—
subgroupG/H
centerC24C23×D73
commutator, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC2×#376×C73C2
socle, prime radicalC24×C73C24
hypercenterC2×#376D73
hypocenterC73C2×#2606
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#376

Complements

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

NH ≅ G/Ntype
1. #22615588C2direct (N × H)
188. C2×C73#2606semidirect
204. C73C2×#2606semidirect
381. C2#22615588direct (N × H)

Maximal subgroups

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

subgroupindex
#226155882
C2×#179885212
C2×#179885192
C2×#179884852
C2×#179884842
C2×#179884712
C2×#179884702
C2×#179884552
C2×C4×C4⋊Dic732
C2×#376×C732
C2×#260673