Finite Group Databasebeta

← C2×#22620581 #33955818

Subgroups — C2×#22620581 #33955818

Order 18688.

2098 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989192C212yesmaximal, complemented
2#22620581C2116yesmaximal, direct product factor
3C2×#17988989C211yesmaximal, characteristic, complemented
4C2×#17988964C211yesmaximal, characteristic, complemented
5C2×#17988952C212yesmaximal, complemented
6C2×#17988840C212yesmaximal, complemented
7C2×#17988823C212yesmaximal, complemented
8C2×#17988700C212yesmaximal, complemented
9C2×C4×D584C212yesmaximal, complemented
10C2×#405×C73C211yesmaximal, characteristic, complemented
11C22×D584C2212yes—
12C22×D584C2212yes—
13#17989192—28no—
14#17989192C22116yescomplemented
15C2×#14556588C2212yes—
16C2×#14556583C2212yes—
17C2×#14556576—24no—
18C2×#14556565C2214yes—
19C2×#14556564—24no—
20C2×C4×D292C2214yes—
21#17988989C2218yescomplemented
22#17988964C2218yescomplemented
23#17988952C22116yescomplemented
24#17988840C22116yescomplemented
25#17988823C22116yescomplemented
26#17988700C22116yescomplemented
27C4×D584C22116yescomplemented
28C2×#14556525C2212yes—
29C2×#14556523C2212yes—
30C2×#14556513C2214yes—
31C2×#14556513C2214yes—
32C22×M16×C73C2211yescharacteristic
33C23×C8×C73C2211yescharacteristic
34C2×#117×C73C2211yescharacteristic
35#405×C73C2218yescomplemented
36C2×#97×C73C2211yescharacteristic
37C2×#97×C73C2211yescharacteristic
38C2×C4×C8×C73C2211yescharacteristic
39C2×C4×C8×C73C2211yescharacteristic
40C22×D292—24no—
41C22×D292C2314yes—
42C22×C22⋊D73—24no—
43C22×C4×D73—24no—
44C2×D584—28no—
45C2×D584—28no—
46C2×D584C2318yes—
47C2×D584C2318yes—
48#14556588—24no—
49#14556588C2318yes—
50#14556583—24no—
51#14556583C2318yes—
52#14556576—232no—
53#14556565—28no—
54#14556565C23116yes—
55#14556564—232no—
56C4×D292—28no—
57C4×D292C23116yes—
58C2×C4⋊Dic73C2314yes—
59C2×#11924007—24no—
60C2×#11924005—24no—
61C2×#11924005—24no—
62#14556525C2318yes—
63#14556523C2318yes—
64#14556513C23116yes—
65#14556513C23116yes—
66C23×C4×C73C2311yescharacteristic
67C2×M16×C73—24no—
68C2×M16×C73C2314yes—
69C22×C8×C73—24no—
70C22×C8×C73C2311yescharacteristic
71C22×C8×C73C2311yescharacteristic
72C22×C8×C73C2314yes—
73C22×C8×C73C2311yescharacteristic
74C22×C8×C73C2311yescharacteristic
75#117×C73D414yes—
76#117×C73C2314yes—
77C2×C4⋊C4×C73D412yes—
78C2×C22⋊C4×C73D412yes—
79C2×C42×C73C2311yescharacteristic
80C2×C42×C73C2311yescharacteristic
81#97×C73C2314yes—
82#97×C73C2314yes—
83C4×C8×C73C2314yes—
84C4×C8×C73C2314yes—
85C23×D73—24no—
86C2×D292—28no—
87C2×D292—28no—
88C2×D292—24no—
89C2×D292—216no—
90C2×D292—88no—
91C2×D292C2418yes—
92C2×C22⋊D73—216no—
93C2×C22⋊D73—88no—
94C22×Dic73—24no—
95C2×C4×D73—216no—
96C2×C4×D73—88no—
97D584—216no—
98D584—216no—
99C4⋊Dic73—24no—
100C4⋊Dic73C2418yes—
101#11924007—216no—
102#11924005—216no—
103#11924005—216no—
104C24×C73C2×D411yescharacteristic
105C22×C4×C73—22no—
106C22×C4×C73—22no—
107C22×C4×C73C2×D412yes—
108C22×C4×C73C2×D412yes—
109C22×C4×C73C2×D411yescharacteristic
110C22×C4×C73C2×D412yes—
111C22×C4×C73C2412yes—
112C22×C4×C73C2411yescharacteristic
113M16×C73—28no—
114C2×C8×C73—22no—
115C2×C8×C73—22no—
116C2×C8×C73—28no—
117C2×C8×C73#4114yes—
118C2×C8×C73#4114yes—
119C2×C8×C73C2412yes—
120C2×C8×C73C2412yes—
121C2×C8×C73C2412yes—
122C2×C8×C73C2412yes—
123C4⋊C4×C73C2×D418yes—
124C22⋊C4×C73C2×D418yes—
125C42×C73C2×D412yes—
126C42×C73C2×D412yes—
127C42×C73C2412yes—
128C42×C73C2412yes—
129C23×C73—22no—
130C23×C73—24no—
131C23×C73C22×D412yes—
132C23×C73C22×D411yescharacteristic
133C22×D73—28no—
134C22×D73—48no—
135C22×D73—48no—
136C22×D73—48no—
137C2×C4×C73—22no—
138C2×C4×C73—24no—
139C2×C4×C73—24no—
140C2×C4×C73—24no—
141C2×C4×C73—22no—
142C2×C4×C73—22no—
143C2×C4×C73C22×D414yes—
144C2×C4×C73C22×D414yes—
145C2×C4×C73C22×D412yes—
146C2×C4×C73C22×D411yescharacteristic
147C2×C4×C73C2×#4112yes—
148C2×C4×C73C2×#4112yes—
149C2×C4×C73C2511yescharacteristic
150C22⋊D73—816no—
151C2×Dic73—28no—
152C2×Dic73—48no—
153D292—28no—
154D292—28no—
155D292—48no—
156D292—816no—
157C4×D73—816no—
158C8×C73—22no—
159C8×C73—22no—
160C8×C73C2×#4114yes—
161C8×C73C2×#4114yes—
162C22×C73—22no—
163C22×C73—24no—
164C22×C73—44no—
165C22×C73#53212yes—
166C22×C73#57614yes—
167C22×C73C23×D411yescharacteristic
168C2×D73—48no—
169C2×D73—48no—
170C2×D73—48no—
171C2×D73—816no—
172C4×C73—22no—
173C4×C73—24no—
174C4×C73—24no—
175C4×C73#53212yes—
176C4×C73C22×#4111yescharacteristic
177C4×C73C22×#4111yescharacteristic
178Dic73—48no—
179C2×#3176—731nomaximal, Sylow
180C2×C73—42no—
181C2×C73#317614yescomplemented
182C2×C73C2×#53211yescharacteristic
183C2×C73C2×#57612yes—
184D73—88no—
185C2×#540—732no—
186#3176—7316no—
187C2×#499—731no—
188C2×#493—731no—
189C2×#490—732no—
190C2×#469—732no—
191C2×#466—732no—
192C2×#442—732no—
193C2×C4×D8—732no—
194C2×#405D7311yescharacteristic, complemented
195C73C2×#317611yescharacteristic, complemented, Sylow
196C22×D8—732no—
197C22×D8—732no—
198C22×M16C2×D7311yescharacteristic
199C23×C8C2×D7311yescharacteristic
200#540—7316no—
201#540—1468no—
202C2×#127—732no—
203C2×#125—732no—
204C2×#123—1464no—
205C2×#121—734no—
206C2×#121—1464no—
207C2×C4×D4—734no—
208C2×#117C2×D7311yescharacteristic
209#499—738no—
210#493—738no—
211#490—7316no—
212#469—7316no—
213#466—7316no—
214#442—7316no—
215C4×D8—7316no—
216C2×#107—732no—
217C2×#106—732no—
218C2×#102—734no—
219C2×#102—734no—
220#405C2×D7318yescomplemented
221C2×#97C2×D7311yescharacteristic
222C2×#97C2×D7311yescharacteristic
223C2×C4×C8C2×D7311yescharacteristic
224C2×C4×C8C2×D7311yescharacteristic
225C22×D4—734no—
226C22×D4—1464no—
227C22×D4—1464no—
228C23×C4—1464no—
229C23×C4C22×D7311yescharacteristic
230C2×D8—738no—
231C2×D8—738no—
232C2×D8—1468no—
233C2×D8—1468no—
234C2×M16—24no—
235C2×M16C22×D7314yes—
236C22×C8—24no—
237C22×C8C22×D7311yescharacteristic
238C22×C8C22×D7314yes—
239C22×C8C22×D7311yescharacteristic
240C22×C8C22×D7311yescharacteristic
241C22×C8C22×D7311yescharacteristic
242#127—738no—
243#127—1464no—
244#125—738no—
245#125—1464no—
246#123—14632no—
247#121—7316no—
248#121—1468no—
249#121—14632no—
250C4×D4—7316no—
251C4×D4—1468no—
252#117D29214yes—
253#117C22×D7314yes—
254C2×C4⋊C4—734no—
255C2×C4⋊C4—1464no—
256C2×C4⋊C4D29212yes—
257C2×C22⋊C4—1464no—
258C2×C22⋊C4—1464no—
259C2×C22⋊C4D29212yes—
260C2×C42C22×D7311yescharacteristic
261C2×C42C22×D7311yescharacteristic
262#107—738no—
263#106—738no—
264#102—7316no—
265#102—7316no—
266#97C22×D7314yes—
267#97C22×D7314yes—
268C4×C8C22×D7314yes—
269C4×C8C22×D7314yes—
270C24—1464no—
271C24C2×D29211yescharacteristic
272C2×D4—5848no—
273C2×D4—5848no—
274C2×D4—738no—
275C2×D4—14616no—
276C2×D4—1464no—
277C2×D4—14616no—
278C2×D4—1468no—
279C2×D4—1468no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—5848no—
283C22×C4—1464no—
284C22×C4—14616no—
285C22×C4C2×D29212yes—
286C22×C4C2×D29212yes—
287C22×C4C2×D29212yes—
288C22×C4C2×D29211yescharacteristic
289C22×C4C23×D7312yes—
290C22×C4C23×D7311yescharacteristic
291D8—14616no—
292D8—14616no—
293M16—28no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—28no—
297C2×C8#1192402814yes—
298C2×C8#1192402814yes—
299C2×C8C23×D7312yes—
300C2×C8C23×D7312yes—
301C2×C8C23×D7312yes—
302C2×C8C23×D7312yes—
303C4⋊C4—738no—
304C4⋊C4—14616no—
305C4⋊C4—1464no—
306C4⋊C4C2×D29218yes—
307C22⋊C4—14616no—
308C22⋊C4—14616no—
309C22⋊C4C2×D29218yes—
310C42C2×D29212yes—
311C42C2×D29212yes—
312C42C23×D7312yes—
313C42C23×D7312yes—
314C23—24no—
315C23—22no—
316C23—2928no—
317C23—2928no—
318C23—2928no—
319C23—1468no—
320C23C22×D29212yes—
321C23C22×D29211yescharacteristic
322D4—2928no—
323D4—58416no—
324D4—58416no—
325D4—1468no—
326D4—1468no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—22no—
330C2×C4—24no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—2928no—
334C2×C4—58416no—
335C2×C4—1468no—
336C2×C4C22×D29214yes—
337C2×C4C22×D29214yes—
338C2×C4C22×D29212yes—
339C2×C4C22×D29211yescharacteristic
340C2×C4C2×#1192402812yes—
341C2×C4C2×#1192402812yes—
342C2×C4C24×D7311yescharacteristic
343C8—22no—
344C8—22no—
345C8C2×#1192402814yes—
346C8C2×#1192402814yes—
347C22—24no—
348C22—22no—
349C22—44no—
350C22—2928no—
351C22—2928no—
352C22—2928no—
353C22—58416no—
354C22#1798913712yes—
355C22#1798939214yes—
356C22C23×D29211yescharacteristic
357C4—24no—
358C4—24no—
359C4—22no—
360C4—2928no—
361C4#1798913712yes—
362C4C22×#1192402811yescharacteristic
363C4C22×#1192402811yescharacteristic
364C2—42no—
365C2—5848no—
366C2#2262058114yesdirect product factor
367C2C2×#1798913711yescharacteristic
368C2C2×#1798939212yes—
subgroupG/H
centerC23C22×D292
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#405×C73C2
socleC23×C73C22×D4
hypercenterC2×#405D73
hypocenterC73C2×#3176
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
1. C2×#17989192C2semidirect
2. #22620581C2direct (N × H)
3. C2×#17988989C2semidirect
4. C2×#17988964C2semidirect
5. C2×#17988952C2semidirect
6. C2×#17988840C2semidirect
7. C2×#17988823C2semidirect
8. C2×#17988700C2semidirect
9. C2×C4×D584C2semidirect
10. C2×#405×C73C2semidirect
14. #17989192C22semidirect
21. #17988989C22semidirect
22. #17988964C22semidirect
23. #17988952C22semidirect
24. #17988840C22semidirect
25. #17988823C22semidirect
26. #17988700C22semidirect
27. C4×D584C22semidirect
35. #405×C73C22semidirect
181. C2×C73#3176semidirect
194. C2×#405D73semidirect
195. C73C2×#3176semidirect
220. #405C2×D73semidirect
366. C2#22620581direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891922
#226205812
C2×#179889892
C2×#179889642
C2×#179889522
C2×#179888402
C2×#179888232
C2×#179887002
C2×C4×D5842
C2×#405×C732
C2×#317673