Finite Group Databasebeta

← C2×C4×#3699 #11899945

Subgroups — C2×C4×#3699 #11899945

Order 1152.

2592 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3699C211yesmaximal, characteristic
2C2×C4×D4×C9C211yesmaximal, characteristic, complemented
3C2×D4×Dic9C211yesmaximal, characteristic, complemented
4C2×C4×#611C212yesmaximal, complemented
5C22×C4×Dic9C212yesmaximal, complemented
6C4×#3699C2116yesmaximal, direct product factor
7C2×#63454C211yesmaximal, characteristic, complemented
8C2×#63449C211yesmaximal, characteristic, complemented
9C2×#611⋊C4C212yesmaximal, complemented
10C2×#63439C212yesmaximal, complemented
11C2×C42×D9C211yesmaximal, characteristic, complemented
12C2×C4×Dic18C211yesmaximal, characteristic, complemented
13C2×C4×#237—31nomaximal
14C22×D4×C9C2211yescharacteristic
15C23×C4×C9C2212yes—
16C22×#611C2212yes—
17C23×Dic9C2212yes—
18C23×Dic9C2212yes—
19C2×#3699C4116yesdirect product factor
20C2×#3699C2218yes—
21C22×C4×D9C2211yescharacteristic
22C22×C4×D9C2211yescharacteristic
23C22×C4×D9C2211yescharacteristic
24C22×Dic18C2211yescharacteristic
25C4×D4×C9C2218yescomplemented
26C2×C9×C4⋊C4C2211yescharacteristic
27C2×C9×C22⋊C4C2212yes—
28C2×C42×C9C2211yescharacteristic
29C2×#3676C2212yes—
30D4×Dic9C2218yescomplemented
31C4×#611C22116yescomplemented
32C2×(C2×D9)⋊C4C2212yes—
33C2×C4⋊Dic9C2211yescharacteristic
34C2×Dic9⋊C4C2212yes—
35C2×Dic9⋊C4C2212yes—
36C2×C4×Dic9C2212yes—
37C2×C4×Dic9C2211yescharacteristic
38C2×C4×Dic9C2211yescharacteristic
39C2×C4×Dic9C2211yescharacteristic
40C2×C4×Dic9C2212yes—
41C2×C4×Dic9C2212yes—
42C2×C4×Dic9C22116yescomplemented
43#63454C2218yescomplemented
44#63449C2218yescomplemented
45#611⋊C4C22116yescomplemented
46#63439C22116yescomplemented
47C42×D9C2218yescomplemented
48C4×Dic18C2218yescomplemented
49C22×#237—31no—
50C2×C3×C4×D4D311yescharacteristic
51C2×D4×Dic3—31no—
52C2×C4×#67—32no—
53C22×C4×Dic3—32no—
54C4×#237—316no—
55C2×#892—31no—
56C2×#887—31no—
57C2×#67⋊C4—32no—
58C2×#877—32no—
59C2×C42×D3—31no—
60C2×C4×Dic6—31no—
61C24×C9C2312yes—
62C23×D9C2311yescharacteristic
63C2×D4×C9C2×C418yescomplemented
64C2×D4×C9C2314yes—
65C22×C4×C9—28no—
66C22×C4×C9C2312yes—
67C22×C4×C9C2318yes—
68C22×C4×C9C2311yescharacteristic
69C22×C4×C9C2311yescharacteristic
70C22×C4×C9C2311yescharacteristic
71C2×#611C2×C4116yescomplemented
72C2×#611C2318yes—
73C22×Dic9—28no—
74C22×Dic9C2×C4116yescomplemented
75C22×Dic9C2312yes—
76C22×Dic9C2318yes—
77C22×Dic9C2311yescharacteristic
78C22×Dic9C2312yes—
79C22×Dic9C2311yescharacteristic
80C22×Dic9C2318yes—
81C22×Dic9C2311yescharacteristic
82#3699C2×C4164yesdirect product factor
83C2×C4×D9—24no—
84C2×C4×D9—24no—
85C2×C4×D9C2×C418yescomplemented
86C2×C4×D9C2314yes—
87C2×C4×D9C2314yes—
88C2×C4×D9C2314yes—
89C2×Dic18C2×C418yescomplemented
90C2×Dic18C2314yes—
91C9×C4⋊C4C2314yes—
92C9×C22⋊C4C2318yes—
93C42×C9C2314yes—
94#3676C2318yes—
95(C2×D9)⋊C4C2318yes—
96C4⋊Dic9C2314yes—
97Dic9⋊C4C2318yes—
98Dic9⋊C4C2318yes—
99C4×Dic9C2318yes—
100C4×Dic9C2314yes—
101C4×Dic9C2314yes—
102C4×Dic9C2314yes—
103C4×Dic9C2318yes—
104C4×Dic9C2318yes—
105C2×C4×#41—91noSylow
106C22×C3×D4C2×D311yescharacteristic
107C23×C3×C4C2×D312yes—
108C22×#67—32no—
109C23×Dic3—32no—
110C23×Dic3—32no—
111C2×#237—316no—
112C2×#237—38no—
113C22×C4×D3—31no—
114C22×C4×D3—31no—
115C22×C4×D3—31no—
116C22×Dic6—31no—
117C3×C4×D4C2×D318yes—
118C2×C3×C4⋊C4C2×D311yescharacteristic
119C2×C3×C22⋊C4C2×D312yes—
120C2×C3×C42C2×D311yescharacteristic
121C2×#217—32no—
122D4×Dic3—38no—
123C4×#67—316no—
124C2×(C2×D3)⋊C4—32no—
125C2×C4⋊Dic3—31no—
126C2×Dic3⋊C4—32no—
127C2×Dic3⋊C4—32no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—31no—
131C2×C4×Dic3—31no—
132C2×C4×Dic3—32no—
133C2×C4×Dic3—32no—
134C2×C4×Dic3—316no—
135#892—38no—
136#887—38no—
137#67⋊C4—316no—
138#877—316no—
139C42×D3—38no—
140C4×Dic6—38no—
141C23×C9—24no—
142C23×C9—24no—
143C23×C9C22×C418yes—
144C23×C9C2414yes—
145C23×C9C2411yescharacteristic
146C22×D9—22no—
147C22×D9—22no—
148C22×D9C22×C414yes—
149C22×D9C2412yes—
150D4×C9C22×C4116yescomplemented
151C2×C4×C9—22no—
152C2×C4×C9—24no—
153C2×C4×C9—216no—
154C2×C4×C9C22×C414yes—
155C2×C4×C9#4114yescomplemented
156C2×C4×C9C2414yes—
157C2×C4×C9C2412yes—
158C2×C4×C9C2412yes—
159C2×C4×C9C2412yes—
160#611C22×C4132yescomplemented
161C2×Dic9—22no—
162C2×Dic9—24no—
163C2×Dic9—216no—
164C2×Dic9C22×C418yes—
165C2×Dic9C22×C414yes—
166C2×Dic9C22×C4132yescomplemented
167C2×Dic9#4114yescomplemented
168C2×Dic9C2412yes—
169C2×Dic9C2414yes—
170C2×Dic9C2412yes—
171C2×Dic9C2414yes—
172C2×Dic9C2412yes—
173C4×D9—28no—
174C4×D9—28no—
175C4×D9C22×C4116yescomplemented
176Dic18C22×C4116yescomplemented
177C22×#41—91no—
178C4×#41—916no—
179C2×C4×Q8—91no—
180C2×C4×Q8—91no—
181C2×C4×D4—91no—
182C2×C4×D4—92no—
183C2×C4×D4—92no—
184C2×C4×D4D911yescharacteristic, complemented
185C2×#117—91no—
186C2×#117—92no—
187C22×C42—92no—
188C22×C42—91no—
189C24×C3C22×D312yes—
190C23×D3—31no—
191C2×C3×D4C4×D318yes—
192C2×C3×D4C22×D314yes—
193C22×C3×C4—28no—
194C22×C3×C4C22×D312yes—
195C22×C3×C4C22×D318yes—
196C22×C3×C4C22×D311yescharacteristic
197C22×C3×C4C22×D311yescharacteristic
198C22×C3×C4C22×D311yescharacteristic
199C2×#67—316no—
200C2×#67—38no—
201C22×Dic3—316no—
202C22×Dic3—38no—
203C22×Dic3—31no—
204C22×Dic3—31no—
205C22×Dic3—32no—
206C22×Dic3—38no—
207C22×Dic3—31no—
208C22×Dic3—32no—
209C22×Dic3—68no—
210#237—364no—
211C2×C4×D3—38no—
212C2×C4×D3—34no—
213C2×C4×D3—34no—
214C2×C4×D3—34no—
215C2×C4×D3—64no—
216C2×C4×D3—64no—
217C2×Dic6—38no—
218C2×Dic6—34no—
219C3×C4⋊C4C22×D314yes—
220C3×C22⋊C4C22×D318yes—
221C3×C42C22×D314yes—
222#217—38no—
223(C2×D3)⋊C4—38no—
224C4⋊Dic3—34no—
225Dic3⋊C4—38no—
226Dic3⋊C4—38no—
227C4×Dic3—38no—
228C4×Dic3—34no—
229C4×Dic3—34no—
230C4×Dic3—34no—
231C4×Dic3—38no—
232C4×Dic3—38no—
233C22×C9—216no—
234C22×C9—24no—
235C22×C9—24no—
236C22×C9C23×C418yes—
237C22×C9C23×C412yes—
238C22×C9C2×#4112yes—
239C22×C9C2×#4112yes—
240C22×C9C2511yescharacteristic
241C2×D9—28no—
242C2×D9—22no—
243C2×D9—22no—
244C2×D9C23×C414yes—
245C4×C9—22no—
246C4×C9—24no—
247C4×C9C23×C414yes—
248C4×C9C2×#4114yescomplemented
249Dic9—22no—
250Dic9—24no—
251Dic9C23×C418yes—
252Dic9C23×C414yes—
253Dic9C2×#4114yescomplemented
254C2×#41—916no—
255C2×#41—98no—
256C22×Q8—91no—
257C22×D4—92no—
258C22×D4C2×D911yescharacteristic
259C23×C4—92no—
260C23×C4—91no—
261C23×C4—92no—
262C23×C4—91no—
263C23×C4—91no—
264C23×C4C2×D912yes—
265C4×Q8—98no—
266C4×Q8—98no—
267C4×D4—98no—
268C4×D4—916no—
269C4×D4—916no—
270C4×D4C2×D918yescomplemented
271#117—98no—
272#117—916no—
273C2×C4⋊C4—92no—
274C2×C4⋊C4—92no—
275C2×C4⋊C4—91no—
276C2×C4⋊C4C2×D911yescharacteristic
277C2×C22⋊C4—92no—
278C2×C22⋊C4—92no—
279C2×C22⋊C4C2×D912yes—
280C2×C42—92no—
281C2×C42—91no—
282C2×C42—92no—
283C2×C42—91no—
284C2×C42—916no—
285C2×C42—92no—
286C2×C42—91no—
287C2×C42—98no—
288C2×C42C2×D911yescharacteristic
289C23×C3—24no—
290C23×C3—24no—
291C23×C3C2×C4×D318yes—
292C23×C3C23×D314yes—
293C23×C3C23×D311yescharacteristic
294C22×D3—34no—
295C22×D3—32no—
296C22×D3—62no—
297C22×D3—62no—
298C3×D4C2×C4×D3116yes—
299C2×C3×C4—24no—
300C2×C3×C4—22no—
301C2×C3×C4—216no—
302C2×C3×C4C2×C4×D314yes—
303C2×C3×C4#23714yes—
304C2×C3×C4C23×D314yes—
305C2×C3×C4C23×D312yes—
306C2×C3×C4C23×D312yes—
307C2×C3×C4C23×D312yes—
308#67—332no—
309C2×Dic3—38no—
310C2×Dic3—34no—
311C2×Dic3—332no—
312C2×Dic3—34no—
313C2×Dic3—32no—
314C2×Dic3—32no—
315C2×Dic3—34no—
316C2×Dic3—32no—
317C2×Dic3—34no—
318C2×Dic3—616no—
319C2×Dic3—62no—
320C2×Dic3—64no—
321C4×D3—316no—
322C4×D3—68no—
323C4×D3—68no—
324Dic6—316no—
325C2×C9—28no—
326C2×C9C4×#4114yescomplemented
327C2×C9C24×C411yescharacteristic
328C2×C9C22×#4111yescharacteristic
329C2×C9C22×#4111yescharacteristic
330D9—24no—
331C24—91no—
332C24C22×D912yes—
333#41—964no—
334C2×Q8—98no—
335C2×Q8—94no—
336C2×D4—916no—
337C2×D4—98no—
338C2×D4C4×D918yescomplemented
339C2×D4C22×D914yes—
340C22×C4—28no—
341C22×C4—916no—
342C22×C4—91no—
343C22×C4—91no—
344C22×C4—92no—
345C22×C4—98no—
346C22×C4—98no—
347C22×C4—94no—
348C22×C4—91no—
349C22×C4—92no—
350C22×C4—98no—
351C22×C4—94no—
352C22×C4—94no—
353C22×C4—184no—
354C22×C4—188no—
355C22×C4—184no—
356C22×C4C22×D912yes—
357C22×C4C22×D918yes—
358C22×C4C22×D911yescharacteristic
359C22×C4C22×D911yescharacteristic
360C22×C4C22×D911yescharacteristic
361C4⋊C4—98no—
362C4⋊C4—98no—
363C4⋊C4—94no—
364C4⋊C4C22×D914yes—
365C22⋊C4—98no—
366C22⋊C4—98no—
367C22⋊C4C22×D918yes—
368C42—94no—
369C42—98no—
370C42—94no—
371C42—98no—
372C42—94no—
373C42—98no—
374C42C22×D914yes—
375C22×C3—24no—
376C22×C3—24no—
377C22×C3—216no—
378C22×C3C22×C4×D318yes—
379C22×C3C22×C4×D312yes—
380C22×C3C2×#23712yes—
381C22×C3D3×#4112yes—
382C22×C3C24×D311yescharacteristic
383C2×D3—34no—
384C2×D3—62no—
385C2×D3—62no—
386C2×D3—68no—
387C3×C4—24no—
388C3×C4—22no—
389C3×C4C22×C4×D314yes—
390C3×C4C2×#23714yes—
391Dic3—38no—
392Dic3—34no—
393Dic3—34no—
394Dic3—62no—
395Dic3—64no—
396C9C2×C4×#4111yescharacteristic, complemented, Sylow
397C23—24no—
398C23—24no—
399C23—92no—
400C23—94no—
401C23—182no—
402C23—182no—
403C23C2×C4×D918yes—
404C23C23×D914yes—
405C23C23×D911yescharacteristic
406Q8—916no—
407D4—932no—
408D4C2×C4×D9116yescomplemented
409C2×C4—24no—
410C2×C4—22no—
411C2×C4—216no—
412C2×C4—92no—
413C2×C4—92no—
414C2×C4—94no—
415C2×C4—94no—
416C2×C4—98no—
417C2×C4—932no—
418C2×C4—94no—
419C2×C4—916no—
420C2×C4—92no—
421C2×C4—94no—
422C2×C4—188no—
423C2×C4—1816no—
424C2×C4—182no—
425C2×C4—184no—
426C2×C4—188no—
427C2×C4C2×C4×D914yes—
428C2×C4#369914yesdirect product factor
429C2×C4C23×D914yes—
430C2×C4C23×D912yes—
431C2×C4C23×D912yes—
432C2×C4C23×D912yes—
433C2×C3—28no—
434C2×C3C4×#23714yes—
435C2×C3C23×C4×D311yescharacteristic
436C2×C3C22×#23711yescharacteristic
437C2×C3C2×D3×#4111yescharacteristic
438D3—64no—
439C22—24no—
440C22—24no—
441C22—216no—
442C22—94no—
443C22—182no—
444C22—182no—
445C22—188no—
446C22C22×C4×D918yes—
447C22C22×C4×D912yes—
448C22C2×#369912yes—
449C22#41×D912yes—
450C22C24×D911yescharacteristic
451C4—24no—
452C4—22no—
453C4—94no—
454C4—98no—
455C4—94no—
456C4—182no—
457C4—184no—
458C4C22×C4×D914yes—
459C4C2×#369914yesdirect product factor
460C3C2×C4×#23711yescharacteristic
461C2—28no—
462C2—184no—
463C2C4×#369914yesdirect product factor
464C2C23×C4×D911yescharacteristic
465C2C22×#369911yescharacteristic
466C2C2×#41×D911yescharacteristic
subgroupG/H
centerC22×C4C22×D9
commutatorC2×C9C24×C4
FrattiniC22×C3C24×D3
FittingC2×C4×D4×C9C2
socleC23×C3C23×D3
prime radicalC22×#3699C2
cosocleC22×C9C25
hypercenterC2×C4×D4D9
hypocenterC9C2×C4×#41
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D4×C9C2semidirect
3. C2×D4×Dic9C2semidirect
4. C2×C4×#611C2semidirect
5. C22×C4×Dic9C2semidirect
6. C4×#3699C2direct (N × H)
7. C2×#63454C2semidirect
8. C2×#63449C2semidirect
9. C2×#611⋊C4C2semidirect
10. C2×#63439C2semidirect
11. C2×C42×D9C2semidirect
12. C2×C4×Dic18C2semidirect
19. C2×#3699C4direct (N × H)
25. C4×D4×C9C22semidirect
30. D4×Dic9C22semidirect
31. C4×#611C22semidirect
42. C2×C4×Dic9C22semidirect
43. #63454C22semidirect
44. #63449C22semidirect
45. #611⋊C4C22semidirect
46. #63439C22semidirect
47. C42×D9C22semidirect
48. C4×Dic18C22semidirect
63. C2×D4×C9C2×C4semidirect
71. C2×#611C2×C4semidirect
74. C22×Dic9C2×C4semidirect
82. #3699C2×C4direct (N × H)
85. C2×C4×D9C2×C4semidirect
89. C2×Dic18C2×C4semidirect
150. D4×C9C22×C4semidirect
155. C2×C4×C9#41semidirect
160. #611C22×C4semidirect
166. C2×Dic9C22×C4semidirect
167. C2×Dic9#41semidirect
175. C4×D9C22×C4semidirect
176. Dic18C22×C4semidirect
184. C2×C4×D4D9semidirect
248. C4×C9C2×#41semidirect
253. Dic9C2×#41semidirect
270. C4×D4C2×D9semidirect
326. C2×C9C4×#41semidirect
338. C2×D4C4×D9semidirect
396. C9C2×C4×#41semidirect
408. D4C2×C4×D9semidirect
428. C2×C4#3699direct (N × H)
459. C4C2×#3699direct (N × H)
463. C2C4×#3699direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#36992
C2×C4×D4×C92
C2×D4×Dic92
C2×C4×#6112
C22×C4×Dic92
C4×#36992
C2×#634542
C2×#634492
C2×#611⋊C42
C2×#634392
C2×C42×D92
C2×C4×Dic182
C2×C4×#2373