Finite Group Databasebeta

← C2×#10589702 #11900582

Subgroups — C2×#10589702 #11900582

Order 1152.

1848 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×#121C211yesmaximal, characteristic
2C2×#63498C211yesmaximal, characteristic, complemented
3C2×#63497C212yesmaximal, complemented
4C2×D4×Dic9C211yesmaximal, characteristic, complemented
5C2×D4×Dic9C212yesmaximal, complemented
6C2×#63486C211yesmaximal, characteristic, complemented
7C22×C4×Dic9C211yesmaximal, characteristic, complemented
8#10589702C2116yesmaximal, direct product factor
9C2×#63452C211yesmaximal, characteristic, complemented
10C2×#63449C211yesmaximal, characteristic, complemented
11C2×#63441C212yesmaximal, complemented
12C2×#63439C212yesmaximal, complemented
13C2×#5600—31nomaximal
14C22×D4×C9C2212yes—
15C22×D4×C9C2211yescharacteristic
16C23×C4×C9C2211yescharacteristic
17C23×Dic9C2212yes—
18C23×Dic9C2211yescharacteristic
19C23×Dic9C2211yescharacteristic
20C22×Dic18C2211yescharacteristic
21C9×#121C2218yes—
22C2×C9×C4⋊C4C2211yescharacteristic
23C2×C9×C22⋊C4C2212yes—
24C2×#3676C2212yes—
25C2×#3676C2212yes—
26C2×#3676C2212yes—
27C2×#3676C2212yes—
28#63498C2218yescomplemented
29#63497C22116yescomplemented
30D4×Dic9C22116yescomplemented
31D4×Dic9C2218yescomplemented
32C2×C4⋊Dic9C2212yes—
33C2×C4⋊Dic9C2211yescharacteristic
34#63486C2218yescomplemented
35C2×Dic9⋊C4C2212yes—
36C2×Dic9⋊C4C2212yes—
37C2×Dic9⋊C4C2212yes—
38C2×C4×Dic9C2211yescharacteristic
39C2×C4×Dic9C2212yes—
40C2×C4×Dic9C2211yescharacteristic
41C2×C4×Dic9C2211yescharacteristic
42C2×C4×Dic9C2211yescharacteristic
43C2×C4×Dic9C2218yescomplemented
44#63452C2218yescomplemented
45#63449C2218yescomplemented
46#63441C22116yescomplemented
47#63439C22116yescomplemented
48C2×C3×#121D311yescharacteristic
49C2×#936—31no—
50C2×#935—32no—
51C2×D4×Dic3—32no—
52C2×D4×Dic3—31no—
53C2×#924—31no—
54C22×C4×Dic3—31no—
55#5600—316no—
56C2×#890—31no—
57C2×#887—31no—
58C2×#879—32no—
59C2×#877—32no—
60C24×C9C2312yes—
61C24×C9C2311yescharacteristic
62C2×D4×C9—28no—
63C2×D4×C9—24no—
64C2×D4×C9C2318yes—
65C2×D4×C9C2314yes—
66C22×C4×C9—24no—
67C22×C4×C9C2311yescharacteristic
68C22×C4×C9C2312yes—
69C22×C4×C9C2314yes—
70C22×C4×C9C2311yescharacteristic
71C22×Dic9—24no—
72C22×Dic9—24no—
73C22×Dic9—28no—
74C22×Dic9C2318yes—
75C22×Dic9C2314yes—
76C22×Dic9C2314yes—
77C22×Dic9C2312yes—
78C22×Dic9C2311yescharacteristic
79C22×Dic9C2311yescharacteristic
80C22×Dic9C2311yescharacteristic
81C22×Dic9C2312yes—
82C22×Dic9C2311yescharacteristic
83C2×Dic18—24no—
84C2×Dic18C2314yes—
85C9×C4⋊C4C2314yes—
86C9×C22⋊C4C2318yes—
87#3676C2318yes—
88#3676C2318yes—
89#3676C2318yes—
90#3676C2318yes—
91C4⋊Dic9C2318yes—
92C4⋊Dic9C2314yes—
93Dic9⋊C4C2318yes—
94Dic9⋊C4C2318yes—
95Dic9⋊C4C2318yes—
96C4×Dic9C2318yes—
97C4×Dic9C2314yes—
98C4×Dic9C2314yes—
99C4×Dic9C2314yes—
100C4×Dic9C2314yes—
101C2×#529—91noSylow
102C22×C3×D4C2×D312yes—
103C22×C3×D4C2×D311yescharacteristic
104C23×C3×C4C2×D311yescharacteristic
105C23×Dic3—32no—
106C23×Dic3—31no—
107C23×Dic3—31no—
108C22×Dic6—31no—
109C3×#121C2×D318yes—
110C2×C3×C4⋊C4C2×D311yescharacteristic
111C2×C3×C22⋊C4C2×D312yes—
112C2×#217—32no—
113C2×#217—32no—
114C2×#217—32no—
115C2×#217—32no—
116#936—38no—
117#935—316no—
118D4×Dic3—316no—
119D4×Dic3—38no—
120C2×C4⋊Dic3—32no—
121C2×C4⋊Dic3—31no—
122#924—38no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—32no—
126C2×C4×Dic3—31no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—31no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—31no—
131C2×C4×Dic3—38no—
132#890—38no—
133#887—38no—
134#879—316no—
135#877—316no—
136C23×C9—22no—
137C23×C9—22no—
138C23×C9—24no—
139C23×C9—24no—
140C23×C9—24no—
141C23×C9#4114yes—
142C23×C9C2414yes—
143C23×C9C2412yes—
144C23×C9C2411yescharacteristic
145D4×C9—216no—
146D4×C9—28no—
147C2×C4×C9—22no—
148C2×C4×C9—24no—
149C2×C4×C9—28no—
150C2×C4×C9#4114yes—
151C2×C4×C9C2412yes—
152C2×C4×C9C2414yes—
153C2×C4×C9C2412yes—
154C2×Dic9—24no—
155C2×Dic9—28no—
156C2×Dic9—22no—
157C2×Dic9—22no—
158C2×Dic9—22no—
159C2×Dic9—24no—
160C2×Dic9—28no—
161C2×Dic9—216no—
162C2×Dic9#4114yes—
163C2×Dic9C2412yes—
164C2×Dic9C2412yes—
165C2×Dic9C2412yes—
166C2×Dic9C2414yes—
167C2×Dic9C2414yes—
168C2×Dic9C2412yes—
169Dic18—28no—
170#529—916no—
171C2×#126—92no—
172C2×#125—91no—
173C2×#124—91no—
174C2×#123—92no—
175C2×C22⋊Q8—91no—
176C2×#121D911yescharacteristic
177C2×C4×Q8—91no—
178C2×C4×D4—92no—
179C2×C4×D4—91no—
180C2×#117—92no—
181C22×C42—91no—
182C24×C3C22×D312yes—
183C24×C3C22×D311yescharacteristic
184C2×C3×D4—28no—
185C2×C3×D4—24no—
186C2×C3×D4C22×D318yes—
187C2×C3×D4C22×D314yes—
188C22×C3×C4—24no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D314yes—
191C22×C3×C4C22×D312yes—
192C22×C3×C4C22×D311yescharacteristic
193C22×Dic3—31no—
194C22×Dic3—38no—
195C22×Dic3—31no—
196C22×Dic3—31no—
197C22×Dic3—31no—
198C22×Dic3—34no—
199C22×Dic3—34no—
200C22×Dic3—32no—
201C22×Dic3—32no—
202C22×Dic3—64no—
203C22×Dic3—68no—
204C22×Dic3—64no—
205C2×Dic6—34no—
206C2×Dic6—64no—
207C3×C4⋊C4C22×D314yes—
208C3×C22⋊C4C22×D318yes—
209#217—38no—
210#217—38no—
211#217—38no—
212#217—38no—
213C4⋊Dic3—38no—
214C4⋊Dic3—34no—
215Dic3⋊C4—38no—
216Dic3⋊C4—38no—
217Dic3⋊C4—38no—
218C4×Dic3—34no—
219C4×Dic3—38no—
220C4×Dic3—34no—
221C4×Dic3—34no—
222C4×Dic3—34no—
223C22×C9—28no—
224C22×C9—22no—
225C22×C9—22no—
226C22×C9—24no—
227C22×C9—24no—
228C22×C9—24no—
229C22×C9—48no—
230C22×C9C2×#4114yes—
231C22×C9C2×#4112yes—
232C22×C9C2×#4112yes—
233C22×C9C2×#4112yes—
234C22×C9C2511yescharacteristic
235C4×C9—22no—
236C4×C9—24no—
237C4×C9C2×#4114yes—
238Dic9—24no—
239Dic9—22no—
240Dic9—22no—
241Dic9—22no—
242Dic9—24no—
243Dic9C2×#4114yes—
244C22×Q8—91no—
245C22×D4C2×D912yes—
246C22×D4C2×D911yescharacteristic
247C23×C4—92no—
248C23×C4—91no—
249C23×C4—91no—
250C23×C4C2×D911yescharacteristic
251#126—916no—
252#125—98no—
253#124—98no—
254#123—916no—
255C22⋊Q8—98no—
256#121C2×D918yes—
257C4×Q8—98no—
258C4×D4—98no—
259C4×D4—916no—
260#117—916no—
261C2×C4⋊C4—92no—
262C2×C4⋊C4—92no—
263C2×C4⋊C4—91no—
264C2×C4⋊C4—92no—
265C2×C4⋊C4—92no—
266C2×C4⋊C4C2×D911yescharacteristic
267C2×C22⋊C4—92no—
268C2×C22⋊C4—92no—
269C2×C22⋊C4—92no—
270C2×C22⋊C4—92no—
271C2×C22⋊C4C2×D912yes—
272C2×C42—91no—
273C2×C42—92no—
274C2×C42—91no—
275C2×C42—91no—
276C2×C42—91no—
277C2×C42—98no—
278C23×C3—22no—
279C23×C3—22no—
280C23×C3—24no—
281C23×C3—24no—
282C23×C3—24no—
283C23×C3#23714yes—
284C23×C3C23×D314yes—
285C23×C3C23×D312yes—
286C23×C3C23×D311yescharacteristic
287C3×D4—216no—
288C3×D4—28no—
289C2×C3×C4—22no—
290C2×C3×C4—24no—
291C2×C3×C4—28no—
292C2×C3×C4#23714yes—
293C2×C3×C4C23×D312yes—
294C2×C3×C4C23×D314yes—
295C2×C3×C4C23×D312yes—
296C2×Dic3—34no—
297C2×Dic3—32no—
298C2×Dic3—32no—
299C2×Dic3—32no—
300C2×Dic3—32no—
301C2×Dic3—34no—
302C2×Dic3—34no—
303C2×Dic3—68no—
304C2×Dic3—616no—
305C2×Dic3—64no—
306C2×Dic3—68no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—62no—
310C2×Dic3—64no—
311Dic6—68no—
312C2×C9—24no—
313C2×C9—44no—
314C2×C9#52914yescomplemented
315C2×C9C22×#4111yescharacteristic
316C2×C9C22×#4111yescharacteristic
317C2×C9C22×#4111yescharacteristic
318C24C22×D912yes—
319C24C22×D911yescharacteristic
320C2×Q8—94no—
321C2×Q8—184no—
322C2×D4—28no—
323C2×D4—24no—
324C2×D4C22×D918yes—
325C2×D4C22×D914yes—
326C22×C4—24no—
327C22×C4—91no—
328C22×C4—94no—
329C22×C4—94no—
330C22×C4—98no—
331C22×C4—91no—
332C22×C4—91no—
333C22×C4—91no—
334C22×C4—92no—
335C22×C4—92no—
336C22×C4—184no—
337C22×C4—188no—
338C22×C4—184no—
339C22×C4C22×D914yes—
340C22×C4C22×D911yescharacteristic
341C22×C4C22×D912yes—
342C22×C4C22×D911yescharacteristic
343C4⋊C4—98no—
344C4⋊C4—98no—
345C4⋊C4—94no—
346C4⋊C4—98no—
347C4⋊C4—98no—
348C4⋊C4C22×D914yes—
349C22⋊C4—98no—
350C22⋊C4—98no—
351C22⋊C4—98no—
352C22⋊C4—98no—
353C22⋊C4C22×D918yes—
354C42—94no—
355C42—94no—
356C42—94no—
357C42—94no—
358C42—98no—
359C22×C3—22no—
360C22×C3—22no—
361C22×C3—28no—
362C22×C3—24no—
363C22×C3—24no—
364C22×C3—24no—
365C22×C3—48no—
366C22×C3C2×#23714yes—
367C22×C3C2×#23712yes—
368C22×C3C2×#23712yes—
369C22×C3D3×#4112yes—
370C22×C3C24×D311yescharacteristic
371C3×C4—22no—
372C3×C4—24no—
373C3×C4C2×#23714yes—
374Dic3—34no—
375Dic3—64no—
376Dic3—62no—
377Dic3—62no—
378Dic3—62no—
379Dic3—64no—
380C9C2×#52911yescharacteristic, complemented, Sylow
381C23—22no—
382C23—22no—
383C23—24no—
384C23—24no—
385C23—24no—
386C23#369914yes—
387C23C23×D914yes—
388C23C23×D912yes—
389C23C23×D911yescharacteristic
390Q8—188no—
391D4—216no—
392D4—28no—
393C2×C4—22no—
394C2×C4—24no—
395C2×C4—28no—
396C2×C4—92no—
397C2×C4—94no—
398C2×C4—92no—
399C2×C4—92no—
400C2×C4—92no—
401C2×C4—94no—
402C2×C4—94no—
403C2×C4—188no—
404C2×C4—1816no—
405C2×C4—188no—
406C2×C4—182no—
407C2×C4—182no—
408C2×C4—184no—
409C2×C4—182no—
410C2×C4—184no—
411C2×C4#369914yes—
412C2×C4C23×D912yes—
413C2×C4C23×D914yes—
414C2×C4C23×D912yes—
415C2×C3—24no—
416C2×C3—44no—
417C2×C3#560014yes—
418C2×C3C22×#23711yescharacteristic
419C2×C3C22×#23711yescharacteristic
420C2×C3C2×D3×#4111yescharacteristic
421C22—28no—
422C22—22no—
423C22—22no—
424C22—24no—
425C22—24no—
426C22—24no—
427C22—48no—
428C22C2×#369914yes—
429C22C2×#369912yes—
430C22C2×#369912yes—
431C22#41×D912yes—
432C22C24×D911yescharacteristic
433C4—22no—
434C4—24no—
435C4—94no—
436C4—182no—
437C4—182no—
438C4—184no—
439C4—182no—
440C4—184no—
441C4C2×#369914yes—
442C3C2×#560011yescharacteristic
443C2—24no—
444C2—44no—
445C2#1058970214yesdirect product factor
446C2C22×#369911yescharacteristic
447C2C22×#369911yescharacteristic
448C2C2×#41×D911yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C9×#121C2
socleC23×C3C23×D3
prime radicalC2×C3×#121D3
hypercenterC2×#121D9
hypocenterC9C2×#529
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C2×#63498C2semidirect
3. C2×#63497C2semidirect
4. C2×D4×Dic9C2semidirect
5. C2×D4×Dic9C2semidirect
6. C2×#63486C2semidirect
7. C22×C4×Dic9C2semidirect
8. #10589702C2direct (N × H)
9. C2×#63452C2semidirect
10. C2×#63449C2semidirect
11. C2×#63441C2semidirect
12. C2×#63439C2semidirect
28. #63498C22semidirect
29. #63497C22semidirect
30. D4×Dic9C22semidirect
31. D4×Dic9C22semidirect
34. #63486C22semidirect
43. C2×C4×Dic9C22semidirect
44. #63452C22semidirect
45. #63449C22semidirect
46. #63441C22semidirect
47. #63439C22semidirect
314. C2×C9#529semidirect
380. C9C2×#529semidirect
445. C2#10589702direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×#1212
C2×#634982
C2×#634972
C2×D4×Dic92
C2×#634862
C22×C4×Dic92
#105897022
C2×#634522
C2×#634492
C2×#634412
C2×#634392
C2×#56003