Finite Group Databasebeta

← C2×#22611089 #33113347

Subgroups — C2×#22611089 #33113347

Order 18688.

1238 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
1C2×#17988595C212yesmaximal
2C2×#17988492C211yesmaximal, characteristic
3#22611089C218yesmaximal, direct product factor
4C2×#17988356C211yesmaximal, characteristic
5C2×#17988346C212yesmaximal
6C2×#544×C73C211yesmaximal, characteristic
7C23×Dic146C2211yescharacteristic
8C22×#11924012C2212yes—
9C22×C4×Dic73C2211yescharacteristic
10#17988595—24no—
11#17988595C2218yes—
12C2×#14556514—22no—
13C2×#14556514—22no—
14#17988492—22no—
15#17988492C2214yes—
16C2×#14556498—22no—
17#17988356C2214yes—
18#17988346C2218yes—
19#544×C73—24no—
20#544×C73—22no—
21#544×C73C2214yes—
22C2×C4⋊Q8×C73—22no—
23C2×#125×C73—22no—
24C2×C22⋊Q8×C73—22no—
25C2×#117×C73C2212yes—
26C22×C4⋊C4×C73C2211yescharacteristic
27C22×Dic146—21no—
28C22×Dic146—22no—
29C22×Dic146—22no—
30C22×Dic146—22no—
31C22×Dic146—24no—
32C22×Dic146Q814yescomplemented
33C22×Dic146C2312yes—
34C23×Dic73—21no—
35C23×Dic73—21no—
36C2×#11924012—22no—
37C2×#11924012—24no—
38C2×#11924012—24no—
39C2×#11924012C2314yes—
40C22×#10596831—22no—
41C2×C4×Dic73—21no—
42C2×C4×Dic73—24no—
43C2×C4×Dic73C2312yes—
44#14556514—28no—
45#14556514—28no—
46#14556498—28no—
47C22×Q8×C73—22no—
48C23×C4×C73D412yes—
49C23×C4×C73C2311yescharacteristic
50C4⋊Q8×C73—28no—
51C4⋊Q8×C73—28no—
52#125×C73—28no—
53#125×C73—28no—
54C22⋊Q8×C73—28no—
55C22⋊Q8×C73—28no—
56#117×C73—22no—
57#117×C73—22no—
58#117×C73D414yes—
59#117×C73C2314yes—
60C2×C4⋊C4×C73—22no—
61C2×C4⋊C4×C73—24no—
62C2×C4⋊C4×C73—22no—
63C2×C4⋊C4×C73—22no—
64C2×C4⋊C4×C73D412yes—
65C2×C4⋊C4×C73D412yes—
66C2×C4⋊C4×C73D412yes—
67C2×C4⋊C4×C73C2312yes—
68C2×C22⋊C4×C73—22no—
69C2×C42×C73—22no—
70C2×Dic146—28no—
71C2×Dic146—28no—
72C2×Dic146—24no—
73C2×Dic146—24no—
74C2×Dic146—24no—
75C2×Dic146—22no—
76C2×Dic146—42no—
77C2×Dic146—44no—
78C2×Dic146—44no—
79C2×Dic146—42no—
80C2×Dic146C2×Q814yescomplemented
81C22×Dic73—24no—
82C22×Dic73—24no—
83C22×Dic73—22no—
84C22×Dic73—22no—
85C22×Dic73—42no—
86C22×Dic73—41no—
87C22×Dic73—41no—
88C22×Dic73—42no—
89C22×Dic73—42no—
90#11924012—24no—
91#11924012—24no—
92#11924012—44no—
93C2×#10596831—24no—
94C2×#10596831—44no—
95C4×Dic73—24no—
96C4×Dic73—42no—
97C24×C73C2×D411yescharacteristic
98C2×Q8×C73—28no—
99C2×Q8×C73—84no—
100C22×C4×C73—22no—
101C22×C4×C73—22no—
102C22×C4×C73—22no—
103C22×C4×C73—22no—
104C22×C4×C73—44no—
105C22×C4×C73C2×D414yes—
106C22×C4×C73C2×D411yescharacteristic
107C22×C4×C73C2×D412yes—
108C22×C4×C73C2×D412yes—
109C22×C4×C73C2×Q812yes—
110C22×C4×C73#4114yes—
111C22×C4×C73#4112yes—
112C22×C4×C73C2411yescharacteristic
113C4⋊C4×C73—28no—
114C4⋊C4×C73—216no—
115C4⋊C4×C73—24no—
116C4⋊C4×C73—22no—
117C4⋊C4×C73—22no—
118C4⋊C4×C73—24no—
119C4⋊C4×C73C2×D414yes—
120C4⋊C4×C73C2×D414yes—
121C22⋊C4×C73—24no—
122C22⋊C4×C73—24no—
123C42×C73—24no—
124C42×C73—24no—
125C23×C73—22no—
126C23×C73—22no—
127C23×C73#12011yescharacteristic
128C23×C73#12011yescharacteristic
129C23×C73C22⋊Q812yes—
130C23×C73#12412yes—
131C23×C73C22×D411yescharacteristic
132Q8×C73—88no—
133C2×C4×C73—24no—
134C2×C4×C73—24no—
135C2×C4×C73—24no—
136C2×C4×C73—44no—
137C2×C4×C73—44no—
138C2×C4×C73—44no—
139C2×C4×C73—44no—
140C2×C4×C73—82no—
141C2×C4×C73#12012yes—
142C2×C4×C73C22⋊Q814yes—
143C2×C4×C73C22⋊Q814yes—
144C2×C4×C73C22⋊Q812yes—
145C2×C4×C73#12414yes—
146C2×C4×C73#12414yes—
147C2×C4×C73#12412yes—
148C2×C4×C73C22×D412yes—
149C2×C4×C73C22×Q811yescharacteristic
150C2×C4×C73C2×#4112yes—
151C2×C4×C73C2×#4111yescharacteristic
152C2×Dic73—24no—
153C2×Dic73—24no—
154C2×Dic73—42no—
155C2×Dic73—48no—
156C2×Dic73—42no—
157C2×Dic73—42no—
158C2×Dic73—42no—
159C2×Dic73—44no—
160C2×Dic73—44no—
161Dic146—28no—
162Dic146—44no—
163Dic146—48no—
164#10596831—44no—
165C22×C73—21no—
166C22×C73—21no—
167C22×C73—21no—
168C22×C73—21no—
169C22×C73—24no—
170C22×C73—24no—
171C22×C73#39312yes—
172C22×C73#39312yes—
173C22×C73#45512yes—
174C22×C73#45612yes—
175C22×C73C2×#12011yescharacteristic
176C22×C73C2×C22⋊Q811yescharacteristic
177C22×C73C2×#12411yescharacteristic
178C4×C73—44no—
179C4×C73—44no—
180C4×C73—44no—
181C4×C73#39314yes—
182C4×C73C2×C22⋊Q812yes—
183C4×C73C2×#12412yes—
184Dic73—44no—
185Dic73—44no—
186C2×#2028—731nomaximal, Sylow
187C2×C73—21no—
188C2×C73—21no—
189C2×C73—22no—
190C2×C73#202814yescomplemented
191C2×C73C2×#39311yescharacteristic
192C2×C73C2×#45511yescharacteristic
193C2×C73C2×#45611yescharacteristic
194C2×#544D7311yescharacteristic
195C2×#419—732no—
196C2×#391—731no—
197#2028—738no—
198C2×#343—731no—
199C2×#339—732no—
200C73C2×#202811yescharacteristic, complemented, Sylow
201C23×Q8—731no—
202C22×M16—732no—
203#544—24no—
204#544—22no—
205#544C2×D7314yes—
206C2×C4⋊Q8—22no—
207C2×#125—22no—
208C2×C22⋊Q8—22no—
209C2×#117C2×D7312yes—
210C22×C4⋊C4C2×D7311yescharacteristic
211C22×C42—731no—
212#419—738no—
213#419—1464no—
214C2×#103—1462no—
215C2×#103—1462no—
216#391—734no—
217#391—1462no—
218C2×#95—1462no—
219#343—734no—
220#339—738no—
221C22×Q8—22no—
222C22×Q8—734no—
223C22×Q8—732no—
224C22×Q8—1462no—
225C22×Q8—1462no—
226C22×Q8—1464no—
227C22×Q8—1461no—
228C22×Q8—1462no—
229C23×C4—1461no—
230C23×C4—1461no—
231C23×C4C22⋊D7312yes—
232C23×C4C22×D7311yescharacteristic
233C2×M16—734no—
234C2×M16—1464no—
235C2×M16—1464no—
236C2×M16—1462no—
237C22×C8—1462no—
238C4⋊Q8—28no—
239C4⋊Q8—28no—
240#125—28no—
241#125—28no—
242C22⋊Q8—28no—
243C22⋊Q8—28no—
244#117—22no—
245#117—22no—
246#117C22⋊D7314yes—
247#117C22×D7314yes—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4C22⋊D7312yes—
253C2×C4⋊C4C22⋊D7312yes—
254C2×C4⋊C4C22⋊D7312yes—
255C2×C4⋊C4C22×D7312yes—
256C2×C22⋊C4—22no—
257C2×C42—22no—
258C2×C42—732no—
259C2×C42—1461no—
260C2×C42—1464no—
261#103—1468no—
262#103—1468no—
263#95—1468no—
264C24C2×C22⋊D7311yescharacteristic
265C2×Q8—28no—
266C2×Q8—84no—
267C2×Q8—2922no—
268C2×Q8—2924no—
269C2×Q8—2924no—
270C2×Q8—2922no—
271C2×Q8—734no—
272C2×Q8—1468no—
273C2×Q8—1468no—
274C2×Q8—1464no—
275C2×Q8—1464no—
276C2×Q8—1464no—
277C2×Q8—1462no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—44no—
283C22×C4—2922no—
284C22×C4—2921no—
285C22×C4—2921no—
286C22×C4—2922no—
287C22×C4—2922no—
288C22×C4—1464no—
289C22×C4—1464no—
290C22×C4—1462no—
291C22×C4—1462no—
292C22×C4C2×C22⋊D7314yes—
293C22×C4C2×C22⋊D7311yescharacteristic
294C22×C4C2×C22⋊D7312yes—
295C22×C4C2×C22⋊D7312yes—
296C22×C4Q8×D7312yes—
297C22×C4#1192402914yes—
298C22×C4#1192402912yes—
299C22×C4C23×D7311yescharacteristic
300M16—2924no—
301M16—1464no—
302M16—1464no—
303C2×C8—2924no—
304C2×C8—1464no—
305C4⋊C4—28no—
306C4⋊C4—216no—
307C4⋊C4—24no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—24no—
311C4⋊C4C2×C22⋊D7314yes—
312C4⋊C4C2×C22⋊D7314yes—
313C22⋊C4—24no—
314C22⋊C4—24no—
315C42—24no—
316C42—24no—
317C42—2922no—
318C42—1464no—
319C23—22no—
320C23—22no—
321C23#1455656011yescharacteristic
322C23#1455656011yescharacteristic
323C23#1455656712yes—
324C23#1455658012yes—
325C23C22×C22⋊D7311yescharacteristic
326Q8—88no—
327Q8—2928no—
328Q8—2924no—
329Q8—1468no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—44no—
334C2×C4—44no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—82no—
338C2×C4—2922no—
339C2×C4—2928no—
340C2×C4—2924no—
341C2×C4—2924no—
342C2×C4—2922no—
343C2×C4—2922no—
344C2×C4—2922no—
345C2×C4—1464no—
346C2×C4—1464no—
347C2×C4#1455656012yes—
348C2×C4#1455656712yes—
349C2×C4#1455656714yes—
350C2×C4#1455656714yes—
351C2×C4#1455658012yes—
352C2×C4#1455658014yes—
353C2×C4#1455658014yes—
354C2×C4C22×C22⋊D7312yes—
355C2×C4C2×Q8×D7311yescharacteristic
356C2×C4C2×#1192402912yes—
357C2×C4C2×#1192402911yescharacteristic
358C8—2924no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—24no—
364C22—24no—
365C22#1798849812yes—
366C22#1798849812yes—
367C22#1798876512yes—
368C22#1798877012yes—
369C22C2×#1455656011yescharacteristic
370C22C2×#1455656711yescharacteristic
371C22C2×#1455658011yescharacteristic
372C4—44no—
373C4—44no—
374C4—44no—
375C4—2924no—
376C4—2924no—
377C4#1798849814yes—
378C4C2×#1455656712yes—
379C4C2×#1455658012yes—
380C2—21no—
381C2—22no—
382C2—21no—
383C2#2261108914yesdirect product factor
384C2C2×#1798849811yescharacteristic
385C2C2×#1798876511yescharacteristic
386C2C2×#1798877011yescharacteristic
subgroupG/H
centerC23#14556560
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC2×#544×C73C2
socleC23×C73#120
prime radicalC24×C73C2×D4
hypercenterC2×#544D73
hypocenterC73C2×#2028
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
3. #22611089C2direct (N × H)
32. C22×Dic146Q8semidirect
80. C2×Dic146C2×Q8semidirect
190. C2×C73#2028semidirect
200. C73C2×#2028semidirect
383. C2#22611089direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179885952
C2×#179884922
#226110892
C2×#179883562
C2×#179883462
C2×#544×C732
C2×#202873