Finite Group Databasebeta

← C2×#22608939 #33058213

Subgroups — C2×#22608939 #33058213

Order 18688.

1028 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×#17988915C212yesmaximal
2C2×#17988517C211yesmaximal, characteristic
3#22608939C218yesmaximal, direct product factor
4C2×#17988324C212yesmaximal
5C2×#17988313C211yesmaximal, characteristic
6C2×#544×C73C211yesmaximal, characteristic
7C22×C4⋊Dic73C2211yescharacteristic
8C22×#11924007—21no—
9#17988915—24no—
10#17988915C2218yes—
11C2×#14556522—22no—
12C2×#14556515—22no—
13C2×C22⋊#10596831C2212yes—
14#17988517—22no—
15#17988517C2214yes—
16C2×#14556498—21no—
17C2×#14556498C2211yescharacteristic
18#17988324C2218yes—
19#17988313C2214yes—
20#544×C73—24no—
21#544×C73—22no—
22#544×C73C2214yes—
23C2×C4⋊Q8×C73—22no—
24C2×#125×C73—22no—
25C2×C22⋊Q8×C73—21no—
26C2×C22⋊Q8×C73C2212yes—
27C2×#117×C73—21no—
28C22×C4⋊C4×C73C2211yescharacteristic
29C23×Dic73—21no—
30C23×Dic73—21no—
31C22×#10596831—22no—
32C2×C4⋊Dic73—22no—
33C2×C4⋊Dic73—22no—
34C2×C4⋊Dic73—21no—
35C2×C4⋊Dic73C2312yes—
36C2×#11924007—24no—
37C2×#11924007—44no—
38#14556522—28no—
39#14556515—28no—
40C22⋊#10596831—22no—
41C22⋊#10596831C2314yes—
42#14556498—24no—
43#14556498—21no—
44#14556498C2312yes—
45C22×Q8×C73—21no—
46C22×Q8×C73D412yes—
47C23×C4×C73D411yescharacteristic
48C23×C4×C73D411yescharacteristic
49C23×C4×C73C2311yescharacteristic
50C4⋊Q8×C73—28no—
51C4⋊Q8×C73—28no—
52#125×C73—28no—
53#125×C73—28no—
54C22⋊Q8×C73—24no—
55C22⋊Q8×C73—24no—
56C22⋊Q8×C73—22no—
57C22⋊Q8×C73—22no—
58C22⋊Q8×C73D414yes—
59C22⋊Q8×C73C2314yes—
60#117×C73—24no—
61#117×C73—24no—
62C2×C4⋊C4×C73—21no—
63C2×C4⋊C4×C73—21no—
64C2×C4⋊C4×C73—21no—
65C2×C4⋊C4×C73—22no—
66C2×C4⋊C4×C73—22no—
67C2×C4⋊C4×C73—22no—
68C2×C4⋊C4×C73—22no—
69C2×C4⋊C4×C73D412yes—
70C2×C4⋊C4×C73D412yes—
71C2×C4⋊C4×C73C2312yes—
72C2×C22⋊C4×C73—22no—
73C2×C42×C73—22no—
74C22×Dic73—24no—
75C22×Dic73—22no—
76C22×Dic73—22no—
77C22×Dic73—42no—
78C22×Dic73—42no—
79C22×Dic73—41no—
80C22×Dic73—41no—
81C22×Dic73—42no—
82C22×Dic73—42no—
83C2×#10596831—24no—
84C2×#10596831—44no—
85C4⋊Dic73—24no—
86C4⋊Dic73—42no—
87#11924007—48no—
88C24×C73C2×D411yescharacteristic
89C2×Q8×C73—24no—
90C2×Q8×C73—22no—
91C2×Q8×C73—44no—
92C2×Q8×C73—82no—
93C2×Q8×C73C2×D414yes—
94C22×C4×C73—21no—
95C22×C4×C73—21no—
96C22×C4×C73—22no—
97C22×C4×C73—22no—
98C22×C4×C73—22no—
99C22×C4×C73—21no—
100C22×C4×C73—21no—
101C22×C4×C73—42no—
102C22×C4×C73—42no—
103C22×C4×C73SD1614yes—
104C22×C4×C73C2×D412yes—
105C22×C4×C73C2×D412yes—
106C22×C4×C73C2×D412yes—
107C22×C4×C73C2×D411yescharacteristic
108C22×C4×C73C2×D412yes—
109C22×C4×C73C2411yescharacteristic
110C4⋊C4×C73—24no—
111C4⋊C4×C73—24no—
112C4⋊C4×C73—24no—
113C4⋊C4×C73—28no—
114C4⋊C4×C73—24no—
115C4⋊C4×C73—24no—
116C4⋊C4×C73—22no—
117C4⋊C4×C73—24no—
118C4⋊C4×C73—24no—
119C4⋊C4×C73C2×D414yes—
120C22⋊C4×C73—24no—
121C22⋊C4×C73—24no—
122C42×C73—28no—
123C23×C73—22no—
124C23×C73—22no—
125C23×C73#12011yescharacteristic
126C23×C73#12011yescharacteristic
127C23×C73C2×SD1612yes—
128C23×C73#13712yes—
129C23×C73C22×D411yescharacteristic
130Q8×C73—44no—
131Q8×C73—82no—
132Q8×C73—84no—
133C2×C4×C73—22no—
134C2×C4×C73—22no—
135C2×C4×C73—24no—
136C2×C4×C73—24no—
137C2×C4×C73—24no—
138C2×C4×C73—24no—
139C2×C4×C73—24no—
140C2×C4×C73—22no—
141C2×C4×C73—42no—
142C2×C4×C73—41no—
143C2×C4×C73—41no—
144C2×C4×C73—44no—
145C2×C4×C73—42no—
146C2×C4×C73—44no—
147C2×C4×C73—42no—
148C2×C4×C73—81no—
149C2×C4×C73#12012yes—
150C2×C4×C73C2×SD1614yes—
151C2×C4×C73C22×D412yes—
152C2×Dic73—24no—
153C2×Dic73—48no—
154C2×Dic73—42no—
155C2×Dic73—42no—
156C2×Dic73—42no—
157C2×Dic73—42no—
158C2×Dic73—42no—
159C2×Dic73—82no—
160C2×Dic73—82no—
161#10596831—44no—
162C22×C73—24no—
163C22×C73—24no—
164C22×C73—21no—
165C22×C73—21no—
166C22×C73—21no—
167C22×C73—21no—
168C22×C73#44812yes—
169C22×C73#44812yes—
170C22×C73#45612yes—
171C22×C73#45812yes—
172C22×C73C2×#12011yescharacteristic
173C22×C73C22×SD1611yescharacteristic
174C22×C73C2×#13711yescharacteristic
175C4×C73—24no—
176C4×C73—22no—
177C4×C73—22no—
178C4×C73—44no—
179C4×C73—42no—
180C4×C73—44no—
181Dic73—44no—
182Dic73—82no—
183C2×#1611—731nomaximal, Sylow
184C2×C73—21no—
185C2×C73—21no—
186C2×C73—22no—
187C2×C73#161114yescomplemented
188C2×C73C2×#44811yescharacteristic
189C2×C73C2×#45611yescharacteristic
190C2×C73C2×#45811yescharacteristic
191C2×#544D7311yescharacteristic
192C2×#483—732no—
193C2×#398—731no—
194#1611—738no—
195C2×#328—732no—
196C2×#324—731no—
197C73C2×#161111yescharacteristic, complemented, Sylow
198#544—24no—
199#544—22no—
200#544C2×D7314yes—
201C2×C4⋊Q8—22no—
202C2×#125—22no—
203C2×C22⋊Q8—21no—
204C2×C22⋊Q8C2×D7312yes—
205C2×#117—21no—
206C22×C4⋊C4—731no—
207C22×C4⋊C4—1461no—
208C22×C4⋊C4C2×D7311yescharacteristic
209#483—738no—
210#483—1464no—
211C2×#106—1462no—
212C2×#103—1462no—
213C2×C22⋊C8—732no—
214#398—734no—
215#398—1462no—
216C2×#95—731no—
217C2×#95—1461no—
218#328—738no—
219#324—734no—
220C22×Q8—21no—
221C22×Q8C22⋊D7312yes—
222C23×C4—1461no—
223C23×C4—1461no—
224C23×C4C22⋊D7311yescharacteristic
225C23×C4C22⋊D7311yescharacteristic
226C23×C4C22×D7311yescharacteristic
227C22×C8—1462no—
228C4⋊Q8—28no—
229C4⋊Q8—28no—
230#125—28no—
231#125—28no—
232C22⋊Q8—24no—
233C22⋊Q8—24no—
234C22⋊Q8—22no—
235C22⋊Q8—22no—
236C22⋊Q8C22⋊D7314yes—
237C22⋊Q8C22×D7314yes—
238#117—24no—
239#117—24no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—2924no—
248C2×C4⋊C4—732no—
249C2×C4⋊C4—1461no—
250C2×C4⋊C4—1464no—
251C2×C4⋊C4—1462no—
252C2×C4⋊C4—1462no—
253C2×C4⋊C4C22⋊D7312yes—
254C2×C4⋊C4C22⋊D7312yes—
255C2×C4⋊C4C22×D7312yes—
256C2×C22⋊C4—22no—
257C2×C42—22no—
258#106—1468no—
259#103—1468no—
260C22⋊C8—734no—
261C22⋊C8—1462no—
262#95—732no—
263#95—1461no—
264#95—1464no—
265C24C2×C22⋊D7311yescharacteristic
266C2×Q8—24no—
267C2×Q8—22no—
268C2×Q8—44no—
269C2×Q8—82no—
270C2×Q8C2×C22⋊D7314yes—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—2922no—
281C22×C4—2922no—
282C22×C4—2921no—
283C22×C4—2921no—
284C22×C4—2922no—
285C22×C4—2922no—
286C22×C4—1462no—
287C22×C4—1464no—
288C22×C4—1462no—
289C22×C4#1192401514yes—
290C22×C4C2×C22⋊D7312yes—
291C22×C4C2×C22⋊D7312yes—
292C22×C4C2×C22⋊D7312yes—
293C22×C4C2×C22⋊D7311yescharacteristic
294C22×C4C2×C22⋊D7312yes—
295C22×C4C23×D7311yescharacteristic
296C2×C8—2924no—
297C2×C8—1464no—
298C4⋊C4—24no—
299C4⋊C4—24no—
300C4⋊C4—24no—
301C4⋊C4—28no—
302C4⋊C4—24no—
303C4⋊C4—24no—
304C4⋊C4—22no—
305C4⋊C4—24no—
306C4⋊C4—24no—
307C4⋊C4—2922no—
308C4⋊C4—2928no—
309C4⋊C4—1464no—
310C4⋊C4C2×C22⋊D7314yes—
311C22⋊C4—24no—
312C22⋊C4—24no—
313C42—28no—
314C23—22no—
315C23—22no—
316C23#1455656011yescharacteristic
317C23#1455656011yescharacteristic
318C23C2×#1192401512yes—
319C23#1455662212yes—
320C23C22×C22⋊D7311yescharacteristic
321Q8—44no—
322Q8—82no—
323Q8—84no—
324C2×C4—22no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—22no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—22no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—44no—
336C2×C4—42no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—81no—
340C2×C4—2928no—
341C2×C4—2922no—
342C2×C4—2922no—
343C2×C4—2922no—
344C2×C4—2922no—
345C2×C4—2922no—
346C2×C4—5842no—
347C2×C4—5842no—
348C2×C4—1464no—
349C2×C4#1455656012yes—
350C2×C4C2×#1192401514yes—
351C2×C4C22×C22⋊D7312yes—
352C8—2924no—
353C22—24no—
354C22—24no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22#1798872612yes—
360C22#1798872612yes—
361C22#1798877012yes—
362C22#1798877712yes—
363C22C2×#1455656011yescharacteristic
364C22C22×#1192401511yescharacteristic
365C22C2×#1455662211yescharacteristic
366C4—22no—
367C4—22no—
368C4—24no—
369C4—44no—
370C4—42no—
371C4—44no—
372C4—2924no—
373C4—5842no—
374C2—21no—
375C2—21no—
376C2—22no—
377C2#2260893914yesdirect product factor
378C2C2×#1798872611yescharacteristic
379C2C2×#1798877011yescharacteristic
380C2C2×#1798877711yescharacteristic
subgroupG/H
centerC23#14556560
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC2×#544×C73C2
socleC23×C73#120
prime radicalC24×C73C2×D4
hypercenterC2×#544D73
hypocenterC73C2×#1611
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
3. #22608939C2direct (N × H)
187. C2×C73#1611semidirect
197. C73C2×#1611semidirect
377. C2#22608939direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179889152
C2×#179885172
#226089392
C2×#179883242
C2×#179883132
C2×#544×C732
C2×#161173