Finite Group Databasebeta

← C2×#22622355 #33964480

Subgroups — C2×#22622355 #33964480

Order 18688.

1982 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989302C212yesmaximal, complemented
2#22622355C2116yesmaximal, direct product factor
3C2×#17988992C211yesmaximal, characteristic, complemented
4C2×#17988909C214yesmaximal, complemented
5C2×#17988877C212yesmaximal, complemented
6C2×#17988820C212yesmaximal, complemented
7C2×C8×D292C211yesmaximal, characteristic, complemented
8C2×#17988624C212yesmaximal, complemented
9C2×C4×D8×C73C211yesmaximal, characteristic, complemented
10C22×C8×D73C2212yes—
11#17989302—28no—
12#17989302C22116yescomplemented
13C2×#14556591C2212yes—
14C2×#14556577—24no—
15C2×#14556565—22no—
16C2×#14556562C2214yes—
17C2×C4×D292C2211yescharacteristic
18C2×#14556550—22no—
19C2×#14556549C2214yes—
20#17988992C2218yescomplemented
21#17988909C22132yescomplemented
22#17988877C22116yescomplemented
23#17988820C22116yescomplemented
24C8×D292C2218yescomplemented
25#17988624C22116yescomplemented
26C2×#14556525C2212yes—
27C2×#14556525C2212yes—
28C2×#14556522C2214yes—
29C2×C4⋊#10596831C2211yescharacteristic
30C2×#14556512C2214yes—
31C2×#14556503C2212yes—
32C22×D8×C73C2211yescharacteristic
33C2×C4×D4×C73C2212yes—
34C4×D8×C73C2218yescomplemented
35C2×#107×C73C2211yescharacteristic
36C2×#102×C73C2212yes—
37C2×C4×C8×C73C2211yescharacteristic
38C22×Dic146—22no—
39C22×D292D411yescharacteristic
40C22×C22⋊D73—24no—
41C22×C4×D73C2312yes—
42C22×#10596831C2312yes—
43C2×C8×D73—28no—
44C2×C8×D73C2318yes—
45#14556591—24no—
46#14556591C2318yes—
47#14556577—232no—
48#14556565—216no—
49#14556562—28no—
50#14556562C23116yes—
51C4×D292D414yes—
52C4×D292C2314yes—
53#14556550—216no—
54#14556549—28no—
55#14556549C23116yes—
56C2×C4⋊Dic73—22no—
57C2×C4⋊Dic73D411yescharacteristic
58C2×C4⋊Dic73C2314yes—
59C2×C22⋊Dic73—24no—
60C2×#11924005—24no—
61C2×#11924005D412yes—
62C2×C4×Dic73—24no—
63#14556525C2318yes—
64#14556525C2318yes—
65#14556522C23116yes—
66C4⋊#10596831C2314yes—
67#14556512C23116yes—
68#14556503C2318yes—
69C22×D4×C73C2312yes—
70C23×C4×C73—22no—
71C2×D8×C73—24no—
72C2×D8×C73C2314yes—
73C22×C8×C73C2311yescharacteristic
74C22×C8×C73C2311yescharacteristic
75C4×D4×C73—24no—
76C4×D4×C73C2318yes—
77C2×C4⋊C4×C73C2312yes—
78C2×C22⋊C4×C73—22no—
79C2×C42×C73C2311yescharacteristic
80#107×C73C2314yes—
81#102×C73C2318yes—
82C4×C8×C73C2314yes—
83C23×D73C2×D412yes—
84C2×Dic146—28no—
85C2×Dic146—84no—
86C2×D292—24no—
87C2×D292C2×D414yes—
88C2×C22⋊D73—216no—
89C2×C22⋊D73—88no—
90C22×Dic73—24no—
91C22×Dic73C2×D412yes—
92C2×C4×D73—24no—
93C2×C4×D73—24no—
94C2×C4×D73C2×D414yes—
95C2×C4×D73C2414yes—
96C2×#10596831—24no—
97C2×#10596831C2414yes—
98C8×D73—216no—
99C4⋊Dic73—28no—
100C4⋊Dic73—24no—
101C4⋊Dic73C2×D414yes—
102C4⋊Dic73C2418yes—
103C22⋊Dic73—216no—
104#11924005—216no—
105#11924005C2×D418yes—
106C4×Dic73—216no—
107C24×C73—22no—
108C2×D4×C73—22no—
109C2×D4×C73—24no—
110C2×D4×C73—24no—
111C2×D4×C73C2414yes—
112C22×C4×C73—22no—
113C22×C4×C73—28no—
114C22×C4×C73—48no—
115C22×C4×C73C2×D411yescharacteristic
116C22×C4×C73C2×D411yescharacteristic
117C22×C4×C73C2411yescharacteristic
118D8×C73—28no—
119C2×C8×C73—22no—
120C2×C8×C73#4114yes—
121C2×C8×C73C2412yes—
122C2×C8×C73C2412yes—
123C4⋊C4×C73—22no—
124C4⋊C4×C73C2414yes—
125C22⋊C4×C73—28no—
126C42×C73C2×D412yes—
127C42×C73C2412yes—
128C23×C73—24no—
129C23×C73—44no—
130C23×C73—44no—
131C23×C73—44no—
132C23×C73C22×D411yescharacteristic
133C22×D73—24no—
134C22×D73—24no—
135C22×D73—24no—
136C22×D73C22×D414yes—
137D4×C73—24no—
138D4×C73—24no—
139D4×C73—44no—
140C2×C4×C73—22no—
141C2×C4×C73—24no—
142C2×C4×C73—44no—
143C2×C4×C73—416no—
144C2×C4×C73#13514yes—
145C2×C4×C73C22×D412yes—
146C2×C4×C73C22×D411yescharacteristic
147C2×C4×C73C22×D412yes—
148C2×C4×C73C2×#4112yes—
149C2×C4×C732−1+412yes—
150C2×C4×C73C2511yescharacteristic
151C22⋊D73—816no—
152C2×Dic73—24no—
153C2×Dic73—28no—
154C2×Dic73—48no—
155C2×Dic73C22×D414yes—
156D292—28no—
157C4×D73—28no—
158C4×D73—24no—
159C4×D73—24no—
160Dic146—88no—
161C8×C73—22no—
162C8×C73C2×#4114yes—
163#10596831—24no—
164C22×C73—44no—
165C22×C73—44no—
166C22×C73—44no—
167C22×C73—88no—
168C22×C73#54712yes—
169C22×C73C2×#13512yes—
170C22×C73#57612yes—
171C22×C73C23×D411yescharacteristic
172C2×D73—24no—
173C2×D73—24no—
174C2×D73—24no—
175C2×D73—48no—
176C4×C73—22no—
177C4×C73—44no—
178C4×C73#54712yes—
179C4×C73C2×#13514yes—
180C4×C73C22×#4111yescharacteristic
181C4×C73C2×2−1+411yescharacteristic
182Dic73—24no—
183Dic73—48no—
184C2×#3341—731nomaximal, Sylow
185C2×C73—84no—
186C2×C73#334114yescomplemented
187C2×C73C2×#54711yescharacteristic
188C2×C73C22×#13511yescharacteristic
189C2×C73C2×#57611yescharacteristic
190D73—44no—
191C2×#555—732no—
192#3341—7316no—
193C2×#500—731no—
194C2×#482—734no—
195C2×#476—732no—
196C2×#466—732no—
197C2×C4×D8D7311yescharacteristic, complemented
198C2×C8×D4—731no—
199C2×#427—732no—
200C73C2×#334111yescharacteristic, complemented, Sylow
201C22×D8C2×D7311yescharacteristic
202C23×C8—732no—
203#555—7316no—
204#555—1468no—
205C2×C4⋊Q8—732no—
206C2×#124—1464no—
207C2×#121—734no—
208C2×#121—1462no—
209C2×C4×D4—731no—
210C2×C4×D4C2×D7312yes—
211C2×#117—734no—
212C2×#117—1462no—
213#500—738no—
214#482—7332no—
215#476—7316no—
216#466—7316no—
217C4×D8C2×D7318yescomplemented
218C8×D4—738no—
219#427—7316no—
220C2×#107—732no—
221C2×#107—732no—
222C2×#107C2×D7311yescharacteristic
223C2×#106—734no—
224C2×C4⋊C8—731no—
225C2×#102—734no—
226C2×#102C2×D7312yes—
227C2×C22⋊C8—732no—
228C2×C4×C8C2×D7311yescharacteristic
229C22×Q8—1462no—
230C22×D4—731no—
231C22×D4—1464no—
232C22×D4C22×D7312yes—
233C23×C4—22no—
234C23×C4—732no—
235C2×D8—24no—
236C2×D8C22×D7314yes—
237C22×C8—732no—
238C22×C8—738no—
239C22×C8—1468no—
240C22×C8C22×D7311yescharacteristic
241C22×C8C22×D7311yescharacteristic
242C4⋊Q8—738no—
243C4⋊Q8—1464no—
244#124—14632no—
245#121—7316no—
246#121—14616no—
247#121—1468no—
248C4×D4—24no—
249C4×D4—734no—
250C4×D4—734no—
251C4×D4C22×D7318yes—
252#117—7316no—
253#117—1468no—
254#117—14616no—
255C2×C4⋊C4—731no—
256C2×C4⋊C4—734no—
257C2×C4⋊C4—1462no—
258C2×C4⋊C4C22×D7312yes—
259C2×C22⋊C4—22no—
260C2×C22⋊C4—732no—
261C2×C22⋊C4—1464no—
262C2×C22⋊C4—1464no—
263C2×C42—1464no—
264C2×C42C22×D7311yescharacteristic
265#107—738no—
266#107—738no—
267#107C22×D7314yes—
268#106—7316no—
269C4⋊C8—734no—
270#102—7316no—
271#102C22×D7318yes—
272C22⋊C8—738no—
273C4×C8C22×D7314yes—
274C24—22no—
275C24—732no—
276C2×Q8—5844no—
277C2×Q8—1468no—
278C2×D4—22no—
279C2×D4—24no—
280C2×D4—24no—
281C2×D4—5848no—
282C2×D4—734no—
283C2×D4—14616no—
284C2×D4—1464no—
285C2×D4C23×D7314yes—
286C22×C4—22no—
287C22×C4—28no—
288C22×C4—48no—
289C22×C4—732no—
290C22×C4—734no—
291C22×C4—734no—
292C22×C4—1464no—
293C22×C4—1464no—
294C22×C4—1464no—
295C22×C4D4×D7311yescharacteristic
296C22×C4D4×D7311yescharacteristic
297C22×C4C23×D7311yescharacteristic
298D8—28no—
299C2×C8—22no—
300C2×C8—734no—
301C2×C8—1464no—
302C2×C8—14616no—
303C2×C8#1192402814yes—
304C2×C8C23×D7312yes—
305C2×C8C23×D7312yes—
306C4⋊C4—22no—
307C4⋊C4—734no—
308C4⋊C4—738no—
309C4⋊C4—1464no—
310C4⋊C4—1468no—
311C4⋊C4C23×D7314yes—
312C22⋊C4—28no—
313C22⋊C4—738no—
314C22⋊C4—14616no—
315C22⋊C4—14616no—
316C42—14616no—
317C42D4×D7312yes—
318C42C23×D7312yes—
319C23—24no—
320C23—44no—
321C23—44no—
322C23—44no—
323C23—734no—
324C23—1464no—
325C23—1464no—
326C23—1464no—
327C23C2×D4×D7311yescharacteristic
328Q8—5848no—
329D4—24no—
330D4—24no—
331D4—44no—
332D4—58416no—
333D4—1468no—
334C2×C4—22no—
335C2×C4—24no—
336C2×C4—44no—
337C2×C4—416no—
338C2×C4—2928no—
339C2×C4—734no—
340C2×C4—1468no—
341C2×C4—1464no—
342C2×C4—1464no—
343C2×C4—1464no—
344C2×C4—1468no—
345C2×C4#1455661014yes—
346C2×C4C2×D4×D7312yes—
347C2×C4C2×D4×D7311yescharacteristic
348C2×C4C2×D4×D7312yes—
349C2×C4C2×#1192402812yes—
350C2×C4#1455663812yes—
351C2×C4C24×D7311yescharacteristic
352C8—22no—
353C8—1464no—
354C8C2×#1192402814yes—
355C22—44no—
356C22—44no—
357C22—44no—
358C22—88no—
359C22—2928no—
360C22—1464no—
361C22—1464no—
362C22—1464no—
363C22#1798924212yes—
364C22C2×#1455661012yes—
365C22#1798938912yes—
366C22C22×D4×D7311yescharacteristic
367C4—22no—
368C4—44no—
369C4—2928no—
370C4—1464no—
371C4#1798924212yes—
372C4C2×#1455661014yes—
373C4C22×#1192402811yescharacteristic
374C4C2×#1455663811yescharacteristic
375C2—84no—
376C2—2924no—
377C2#2262235514yesdirect product factor
378C2C2×#1798924211yescharacteristic
379C2C22×#1455661011yescharacteristic
380C2C2×#1798938911yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×C4×D8×C73C2
socleC23×C73C22×D4
hypercenterC2×C4×D8D73
hypocenterC73C2×#3341
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#17989302C2semidirect
2. #22622355C2direct (N × H)
3. C2×#17988992C2semidirect
4. C2×#17988909C2semidirect
5. C2×#17988877C2semidirect
6. C2×#17988820C2semidirect
7. C2×C8×D292C2semidirect
8. C2×#17988624C2semidirect
9. C2×C4×D8×C73C2semidirect
12. #17989302C22semidirect
20. #17988992C22semidirect
21. #17988909C22semidirect
22. #17988877C22semidirect
23. #17988820C22semidirect
24. C8×D292C22semidirect
25. #17988624C22semidirect
34. C4×D8×C73C22semidirect
186. C2×C73#3341semidirect
197. C2×C4×D8D73semidirect
200. C73C2×#3341semidirect
217. C4×D8C2×D73semidirect
377. C2#22622355direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893022
#226223552
C2×#179889922
C2×#179889092
C2×#179888772
C2×#179888202
C2×C8×D2922
C2×#179886242
C2×C4×D8×C732
C2×#334173