Finite Group Databasebeta

← C2×#22608832 #33055739

Subgroups — C2×#22608832 #33055739

Order 18688.

730 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988714C211yesmaximal, characteristic, complemented
2C2×C4×#11924017C211yesmaximal, characteristic
3C2×#17988664C211yesmaximal, characteristic
4#22608832C218yesmaximal, direct product factor
5C2×#17988317C211yesmaximal, characteristic, complemented
6C2×#17988314C211yesmaximal, characteristic
7C2×#17988308C211yesmaximal, characteristic, complemented
8C2×#335×C73C211yesmaximal, characteristic, complemented
9C22×#11924017C411yescharacteristic
10C22×#11924011—21no—
11C2×C4×Dic146C2211yescharacteristic
12C2×C4×D292C2211yescharacteristic
13#17988714—22no—
14#17988714C2214yescomplemented
15C4×#11924017C414yes—
16C4×#11924017C2214yes—
17#17988664—22no—
18#17988664C2214yes—
19C2×#14556523C411yescharacteristic
20C2×#14556520—21no—
21C2×#14556516C411yescharacteristic
22C2×#14556513C411yescharacteristic
23C2×#14556503—21no—
24C2×#14556501—21no—
25C2×C4×#10596831C2211yescharacteristic
26C2×C4×#10596831C2211yescharacteristic
27#17988317C2214yescomplemented
28#17988314C2214yes—
29#17988308C2214yescomplemented
30C2×C4⋊C8×C73C2211yescharacteristic
31C2×C4⋊C8×C73C2211yescharacteristic
32C2×C4×C8×C73C2211yescharacteristic
33#335×C73C2214yescomplemented
34C22×Dic146C2×C411yescharacteristic
35C22×D292C2×C411yescharacteristic
36C22×C4×D73—21no—
37C2×#11924017—24no—
38C2×#11924017C2×C414yes—
39C2×#11924011—24no—
40C2×#11924011—44no—
41C22×#10596831—21no—
42C22×#10596831D411yescharacteristic
43C22×#10596831D411yescharacteristic
44C4×Dic146—21no—
45C4×Dic146—21no—
46C4×Dic146C2×C412yes—
47C4×Dic146C2312yes—
48C4×D292—21no—
49C4×D292—21no—
50C4×D292C2×C412yes—
51C4×D292C2312yes—
52C2×C4⋊Dic73C2×C411yescharacteristic
53C2×C4⋊Dic73C2×C411yescharacteristic
54C2×#11924007—21no—
55C2×#11924005—21no—
56C2×C4×Dic73—21no—
57#14556523C2×C414yes—
58#14556520—24no—
59#14556516C2×C414yes—
60#14556513C2×C414yes—
61#14556503—24no—
62#14556501—24no—
63C4×#10596831—21no—
64C4×#10596831D412yes—
65C4×#10596831C2312yes—
66C4×#10596831C2312yes—
67C22×C8×C73—21no—
68C22×C8×C73—21no—
69C22×C8×C73C2×C411yescharacteristic
70C22×C8×C73C2×C411yescharacteristic
71C2×C42×C73C2311yescharacteristic
72C4⋊C8×C73—21no—
73C4⋊C8×C73—21no—
74C4⋊C8×C73C2312yes—
75C4⋊C8×C73C2312yes—
76C4×C8×C73C2×C412yes—
77C4×C8×C73C2312yes—
78C23×D73—21no—
79C2×Dic146—22no—
80C2×Dic146—22no—
81C2×Dic146—21no—
82C2×Dic146C22×C412yes—
83C2×D292—22no—
84C2×D292—22no—
85C2×D292—21no—
86C2×D292C22×C412yes—
87C22×Dic73—21no—
88C22×Dic73—21no—
89C22×Dic73—21no—
90C2×C4×D73—22no—
91C2×C4×D73—22no—
92C2×C4×D73—42no—
93C2×C4×D73—42no—
94#11924017—28no—
95#11924011—48no—
96C2×#10596831—22no—
97C2×#10596831—22no—
98C2×#10596831—22no—
99C2×#10596831—42no—
100C2×#10596831C2×D412yes—
101C2×#10596831C2×D412yes—
102C4⋊Dic73—21no—
103C4⋊Dic73—21no—
104C4⋊Dic73C22×C412yes—
105C4⋊Dic73C22×C412yes—
106#11924007—22no—
107#11924007—22no—
108#11924005—22no—
109#11924005—22no—
110C4×Dic73—22no—
111C4×Dic73—22no—
112C22×C4×C73C22×C411yescharacteristic
113C22×C4×C73C2×D411yescharacteristic
114C22×C4×C73#4111yescharacteristic
115C2×C8×C73—22no—
116C2×C8×C73—22no—
117C2×C8×C73—22no—
118C2×C8×C73—42no—
119C2×C8×C73—42no—
120C2×C8×C73M1614yescomplemented
121C2×C8×C73C22×C412yes—
122C2×C8×C73C22×C412yes—
123C42×C73C22×C411yescharacteristic
124C42×C73C2×D411yescharacteristic
125C42×C73#4111yescharacteristic
126C42×C73C2411yescharacteristic
127C23×C73C4×D411yescharacteristic
128C22×D73—22no—
129C22×D73—42no—
130C22×D73—42no—
131C22×D73—42no—
132C2×C4×C73—22no—
133C2×C4×C73C4×D411yescharacteristic
134C2×C4×C73C4×D411yescharacteristic
135C2×C4×C73C4×D411yescharacteristic
136C2×C4×C73C2×M1612yes—
137C2×C4×C73#13112yes—
138C2×C4×C73AGL(1,ℤ/8)12yes—
139C2×C4×C73#13712yes—
140C2×C4×C73C23×C411yescharacteristic
141C2×C4×C73C22×D411yescharacteristic
142C2×C4×C73C2×#4111yescharacteristic
143C2×Dic73—22no—
144C2×Dic73—22no—
145C2×Dic73—22no—
146C2×Dic73—42no—
147C2×Dic73—42no—
148C2×Dic73—42no—
149D292—22no—
150D292—22no—
151D292—42no—
152C4×D73—42no—
153C4×D73—42no—
154C4×D73—44no—
155Dic146—22no—
156Dic146—22no—
157Dic146—42no—
158C8×C73—22no—
159C8×C73—42no—
160C8×C73—42no—
161C8×C73C2×M1614yescomplemented
162#10596831—22no—
163#10596831—22no—
164#10596831—42no—
165C22×C73#43612yes—
166C22×C73#44012yes—
167C22×C73#44412yes—
168C22×C73C2×C4×D411yescharacteristic
169C2×D73—42no—
170C2×D73—42no—
171C2×D73—42no—
172C2×D73—84no—
173C4×C73—21no—
174C4×C73—21no—
175C4×C73#43612yes—
176C4×C73#44012yes—
177C4×C73C22×M1611yescharacteristic
178C4×C73C2×#13111yescharacteristic
179C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
180C4×C73C2×#13711yescharacteristic
181Dic73—42no—
182Dic73—42no—
183Dic73—42no—
184C2×#1592—731nomaximal, Sylow
185C2×C73#159214yescomplemented
186C2×C73C2×#43611yescharacteristic
187C2×C73C2×#44011yescharacteristic
188C2×C73C2×#44411yescharacteristic
189D73—82no—
190C2×#446—731no—
191C2×C4×SD16—731no—
192C2×#436—731no—
193#1592—738no—
194C2×#335D7311yescharacteristic, complemented
195C2×Q8⋊C8—731no—
196C2×D4⋊C8—731no—
197C2×#322—731no—
198C73C2×#159211yescharacteristic, complemented, Sylow
199C22×SD16—731no—
200C22×M16—1461no—
201C2×C4×Q8—731no—
202C2×C4×D4—731no—
203#446—734no—
204#446—1462no—
205C4×SD16—734no—
206C4×SD16—734no—
207#436—734no—
208#436—1462no—
209C2×#106—731no—
210C2×C4⋊C8—1461no—
211C2×C4⋊C8C2×D7311yescharacteristic
212C2×C4⋊C8C2×D7311yescharacteristic
213C2×#103—731no—
214C2×#102—731no—
215C2×C22⋊C8—1461no—
216C2×#97—1461no—
217C2×C4×C8—731no—
218C2×C4×C8—731no—
219C2×C4×C8C2×D7311yescharacteristic
220#335C2×D7314yescomplemented
221Q8⋊C8—734no—
222D4⋊C8—734no—
223#322—734no—
224C22×Q8—731no—
225C22×D4—731no—
226C23×C4—1461no—
227C2×SD16—734no—
228C2×SD16—1464no—
229C2×M16—2924no—
230C2×M16—1464no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—731no—
234C22×C8—731no—
235C22×C8—1461no—
236C22×C8C4×D7311yescharacteristic
237C22×C8C4×D7311yescharacteristic
238C4×Q8—732no—
239C4×Q8—732no—
240C4×Q8—1461no—
241C4×Q8—1461no—
242C4×D4—732no—
243C4×D4—732no—
244C4×D4—1461no—
245C4×D4—1461no—
246C2×C4⋊C4—731no—
247C2×C4⋊C4—731no—
248C2×C4⋊C4—1461no—
249C2×C22⋊C4—1461no—
250C2×C42—1461no—
251C2×C42C22×D7311yescharacteristic
252#106—734no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—1464no—
256C4⋊C8C22×D7312yes—
257C4⋊C8C22×D7312yes—
258#103—734no—
259#102—734no—
260C22⋊C8—1464no—
261#97—1464no—
262C4×C8—732no—
263C4×C8—732no—
264C4×C8—732no—
265C4×C8—1461no—
266C4×C8C4×D7312yes—
267C4×C8C22×D7312yes—
268C24—1461no—
269C2×Q8—732no—
270C2×Q8—1462no—
271C2×Q8—1462no—
272C2×Q8—1461no—
273C2×D4—732no—
274C2×D4—1461no—
275C2×D4—1462no—
276C2×D4—1462no—
277C22×C4—2922no—
278C22×C4—2922no—
279C22×C4—1461no—
280C22×C4—1461no—
281C22×C4—1461no—
282C22×C4—1462no—
283C22×C4—1462no—
284C22×C4C2×C4×D7311yescharacteristic
285C22×C4D4×D7311yescharacteristic
286C22×C4#1192402911yescharacteristic
287SD16—1468no—
288M16—2928no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8—2922no—
295C2×C8—732no—
296C2×C8—732no—
297C2×C8—1462no—
298C2×C8—1462no—
299C2×C8—1462no—
300C2×C8#1192401114yescomplemented
301C2×C8C2×C4×D7312yes—
302C2×C8C2×C4×D7312yes—
303C4⋊C4—732no—
304C4⋊C4—732no—
305C4⋊C4—1462no—
306C4⋊C4—1461no—
307C4⋊C4—1461no—
308C4⋊C4—1462no—
309C22⋊C4—1462no—
310C22⋊C4—1462no—
311C42—1462no—
312C42—1462no—
313C42C2×C4×D7311yescharacteristic
314C42D4×D7311yescharacteristic
315C42#1192402911yescharacteristic
316C42C23×D7311yescharacteristic
317C23—2922no—
318C23—2922no—
319C23—2922no—
320C23—1462no—
321C23#1455655311yescharacteristic
322Q8—2922no—
323Q8—1462no—
324Q8—1462no—
325D4—2922no—
326D4—1462no—
327D4—1462no—
328C2×C4—22no—
329C2×C4—2922no—
330C2×C4—2922no—
331C2×C4—2922no—
332C2×C4—2922no—
333C2×C4—2924no—
334C2×C4—2922no—
335C2×C4—1462no—
336C2×C4—1462no—
337C2×C4—1462no—
338C2×C4#1455655311yescharacteristic
339C2×C4#1455655311yescharacteristic
340C2×C4#1455655311yescharacteristic
341C2×C4C2×#1192401112yes—
342C2×C4#1455659912yes—
343C2×C4#1455661512yes—
344C2×C4#1455662312yes—
345C2×C4C22×C4×D7311yescharacteristic
346C2×C4C2×D4×D7311yescharacteristic
347C2×C4C2×#1192402911yescharacteristic
348C8—22no—
349C8—42no—
350C8—42no—
351C8—2922no—
352C8—1462no—
353C8—1462no—
354C8C2×#1192401114yescomplemented
355C22—2922no—
356C22—2922no—
357C22—2922no—
358C22—5844no—
359C22#1798866412yes—
360C22#1798868612yes—
361C22#1798870812yes—
362C22C2×#1455655311yescharacteristic
363C4—21no—
364C4—21no—
365C4—2922no—
366C4—2922no—
367C4—2922no—
368C4#1798866412yes—
369C4#1798868612yes—
370C4C22×#1192401111yescharacteristic
371C4C2×#1455659911yescharacteristic
372C4C2×#1455661511yescharacteristic
373C4C2×#1455662311yescharacteristic
374C2—5842no—
375C2#2260883214yesdirect product factor
376C2C2×#1798866411yescharacteristic
377C2C2×#1798868611yescharacteristic
378C2C2×#1798870811yescharacteristic
subgroupG/H
centerC22×C4D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC2×#335×C73C2
socleC23×C73C4×D4
prime radicalC22×D292C2×C4
cosocleC42×C73C24
hypercenterC2×#335D73
hypocenterC73C2×#1592
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
1. C2×#17988714C2semidirect
4. #22608832C2direct (N × H)
5. C2×#17988317C2semidirect
7. C2×#17988308C2semidirect
8. C2×#335×C73C2semidirect
14. #17988714C22semidirect
27. #17988317C22semidirect
29. #17988308C22semidirect
33. #335×C73C22semidirect
120. C2×C8×C73M16semidirect
161. C8×C73C2×M16semidirect
185. C2×C73#1592semidirect
194. C2×#335D73semidirect
198. C73C2×#1592semidirect
220. #335C2×D73semidirect
300. C2×C8#11924011semidirect
354. C8C2×#11924011semidirect
375. C2#22608832direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179887142
C2×C4×#119240172
C2×#179886642
#226088322
C2×#179883172
C2×#179883142
C2×#179883082
C2×#335×C732
C2×#159273