Finite Group Databasebeta

← C4×#17989017 #33239264

Subgroups — C4×#17989017 #33239264

Order 18688.

690 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989017C211yesmaximal, characteristic
2C4×#14556613C211yesmaximal, characteristic, complemented
3C4×#14556537C212yesmaximal, complemented
4C4×#14556534C212yesmaximal, complemented
5C4×#14556535C212yesmaximal, complemented
6C4×#14556532C212yesmaximal, complemented
7#22611713C211yesmaximal, characteristic, complemented
8#22611638C211yesmaximal, characteristic, complemented
9#22611636C211yesmaximal, characteristic, complemented
10C2×C4×#11924003C211yesmaximal, characteristic, complemented
11C4×#135×C73C211yesmaximal, characteristic, complemented
12C2×#14556613C2211yescharacteristic
13C4×#11924028—21no—
14#17989017C418yesdirect product factor
15C2×#14556537C2211yescharacteristic
16C2×#14556535C2211yescharacteristic
17C2×#14556534C2211yescharacteristic
18C2×#14556532C2211yescharacteristic
19C22×#11924003C2211yescharacteristic
20C22×#11924003C2211yescharacteristic
21C4×Dic292C2212yes—
22C4×#11924017—22no—
23C4×D584C2212yes—
24#17988625C2211yescharacteristic
25#17988584—21no—
26#17988414C2212yes—
27#17988412C2212yes—
28#17988391C2212yes—
29#17988390C2212yes—
30#17988388C2212yes—
31#17988387C2212yes—
32C4×#11924003C2212yes—
33C4×#11924003C2212yes—
34C2×#135×C73C2211yescharacteristic
35C4×#41×C73—21no—
36C4×Q16×C73C2212yes—
37C4×SD16×C73—22no—
38C4×D8×C73C2212yes—
39#427×C73C2211yescharacteristic
40#416×C73—21no—
41C2×C4×C8×C73C2211yescharacteristic
42C2×#11924028—21no—
43#14556613—22no—
44#14556613C2×C414yescomplemented
45C2×Dic292C2311yescharacteristic
46C2×#11924017—21no—
47C2×D584C2311yescharacteristic
48C4×Dic146—22no—
49C4×D292—22no—
50C4×C22⋊D73—42no—
51#14556550—21no—
52#14556548—41no—
53C42×D73—41no—
54#14556537C2×C414yescomplemented
55#14556535C2×C414yescomplemented
56#14556534C2×C414yescomplemented
57#14556532C2×C414yescomplemented
58C2×#11924003—22no—
59C2×#11924003C2×C414yescomplemented
60C2×#11924003C2312yes—
61C2×#11924003C2311yescharacteristic
62C2×#11924003C2311yescharacteristic
63#14556525C2312yes—
64#14556523—21no—
65#14556516—22no—
66#14556513—22no—
67C2×#41×C73—21no—
68#135×C73—22no—
69#135×C73C2×C414yescomplemented
70C2×Q16×C73C2311yescharacteristic
71C2×SD16×C73—21no—
72C2×D8×C73C2311yescharacteristic
73C22×C8×C73D411yescharacteristic
74C22×C8×C73C2311yescharacteristic
75C4×Q8×C73—22no—
76C4×D4×C73—22no—
77C4×D4×C73—42no—
78#117×C73—21no—
79#117×C73—41no—
80C2×C42×C73—41no—
81C2×C42×C73D411yescharacteristic
82#107×C73C2312yes—
83#106×C73—21no—
84#103×C73—22no—
85#102×C73—22no—
86C4×C8×C73D412yes—
87C4×C8×C73C2312yes—
88#11924028—24no—
89#11924028—42no—
90C2×Dic146—21no—
91C2×D292—21no—
92C2×C22⋊D73—41no—
93C2×C4×D73—41no—
94C2×C4×D73—42no—
95Dic292—21no—
96Dic292C22×C412yes—
97#11924017—24no—
98D584—21no—
99D584C22×C412yes—
100C4⋊Dic73—22no—
101#11924007—42no—
102C22⋊Dic73—41no—
103#11924005—42no—
104C4×Dic73—41no—
105C4×Dic73—42no—
106#11924003—22no—
107#11924003C22×C412yes—
108#11924003C22×C412yes—
109#41×C73—24no—
110#41×C73—42no—
111C2×Q8×C73—21no—
112C2×D4×C73—21no—
113C2×D4×C73—41no—
114C22×C4×C73—41no—
115C22×C4×C73—42no—
116C22×C4×C73D812yes—
117C22×C4×C73C2×D411yescharacteristic
118Q16×C73—21no—
119Q16×C73C22×C412yes—
120SD16×C73—24no—
121D8×C73—21no—
122D8×C73C22×C412yes—
123C2×C8×C73—22no—
124C2×C8×C73C22×C412yes—
125C2×C8×C73C2×D412yes—
126C2×C8×C73C2×D411yescharacteristic
127C2×C8×C73#4112yes—
128C2×C8×C73C2411yescharacteristic
129C4⋊C4×C73—22no—
130C4⋊C4×C73—42no—
131C22⋊C4×C73—41no—
132C22⋊C4×C73—42no—
133C42×C73—41no—
134C42×C73—42no—
135C42×C73D811yescharacteristic
136C42×C73D811yescharacteristic
137C42×C73C2×D412yes—
138C23×C73—41no—
139C23×C73C2×D811yescharacteristic
140C22×D73—41no—
141Q8×C73—22no—
142Q8×C73—41no—
143D4×C73—22no—
144D4×C73—44no—
145D4×C73—41no—
146C2×C4×C73—24no—
147C2×C4×C73—41no—
148C2×C4×C73—44no—
149C2×C4×C73—42no—
150C2×C4×C73—84no—
151C2×C4×C73C4×D412yes—
152C2×C4×C73C2×D812yes—
153C2×C4×C73C2×D811yescharacteristic
154C2×C4×C73C2×D812yes—
155C2×C4×C73#13512yes—
156C2×C4×C73C22×D411yescharacteristic
157C22⋊D73—44no—
158C2×Dic73—41no—
159C2×Dic73—42no—
160D292—22no—
161D292—41no—
162C4×D73—44no—
163C4×D73—84no—
164Dic146—22no—
165Dic146—41no—
166C8×C73—22no—
167C8×C73C4×D412yes—
168C8×C73C23×C411yescharacteristic
169C8×C73C2×#4111yescharacteristic
170C22×C73—22no—
171C22×C73—42no—
172C22×C73—82no—
173C22×C73C4×D812yes—
174C22×C73C22×D811yescharacteristic
175C2×D73—42no—
176C2×D73—82no—
177C4×C73—22no—
178C4×C73—42no—
179C4×C73—82no—
180C4×C73C4×D812yes—
181C4×C73#50814yescomplemented
182C4×C73C2×C4×D411yescharacteristic
183C4×C73C2×#13511yescharacteristic
184Dic73—42no—
185Dic73—82no—
186C4×#508—731nomaximal, Sylow
187C2×C73—22no—
188C2×C73—82no—
189C2×C73C2×C4×D811yescharacteristic
190C2×C73C2×#50812yes—
191D73—82no—
192C2×#508—731no—
193C4×#135—731no—
194C4×#135D7311yescharacteristic, complemented
195C4×Q32—732no—
196C4×SD32—732no—
197C4×SD32—732no—
198C4×D16—732no—
199#2158—731no—
200#2138—731no—
201#2138—731no—
202C2×C4×C16—731no—
203C73C4×#50811yescharacteristic, complemented, Sylow
204C2×#135—731no—
205C2×#135C2×D7311yescharacteristic
206C4×#41—21no—
207C4×#41—1461no—
208#508—738no—
209C2×Q32—731no—
210C2×SD32—731no—
211C2×SD32—731no—
212C2×D16—731no—
213C22×C16—731no—
214C22×C16—731no—
215C4×Q16—732no—
216C4×Q16C2×D7312yes—
217C4×SD16—22no—
218C4×SD16—1462no—
219C4×D8—732no—
220C4×D8C2×D7312yes—
221#427—731no—
222#427C2×D7311yescharacteristic
223#416—21no—
224#416—1461no—
225C2×C4×C8C2×D7311yescharacteristic
226#367—732no—
227#366—732no—
228#358—732no—
229#358—732no—
230#357—732no—
231#357—732no—
232C4×C16—732no—
233C4×C16—732no—
234C2×#41—21no—
235C2×#41—1461no—
236#135—22no—
237#135—734no—
238#135—1462no—
239#135C4×D7314yescomplemented
240C2×Q16—731no—
241C2×Q16C22×D7311yescharacteristic
242C2×SD16—21no—
243C2×SD16—1461no—
244C2×D8—731no—
245C2×D8C22×D7311yescharacteristic
246C22×C8C22⋊D7311yescharacteristic
247C22×C8C22×D7311yescharacteristic
248C4×Q8—22no—
249C4×Q8—1462no—
250C4×D4—22no—
251C4×D4—42no—
252C4×D4—2922no—
253C4×D4—1462no—
254#117—21no—
255#117—41no—
256#117—2921no—
257#117—1461no—
258C2×C42—41no—
259C2×C42—2921no—
260C2×C42C22⋊D7311yescharacteristic
261Q32—734no—
262SD32—734no—
263SD32—734no—
264D16—734no—
265C2×C16—734no—
266C2×C16—731no—
267C2×C16—731no—
268C2×C16—732no—
269C2×C16—1462no—
270#107—732no—
271#107C22×D7312yes—
272#106—21no—
273#106—1461no—
274#103—22no—
275#103—1462no—
276#102—22no—
277#102—1462no—
278C4×C8C22⋊D7312yes—
279C4×C8C22×D7312yes—
280#41—24no—
281#41—42no—
282#41—2922no—
283#41—1464no—
284C2×Q8—21no—
285C2×Q8—1461no—
286C2×D4—21no—
287C2×D4—41no—
288C2×D4—2921no—
289C2×D4—1461no—
290C22×C4—41no—
291C22×C4—42no—
292C22×C4—2921no—
293C22×C4—2922no—
294C22×C4#1192401312yes—
295C22×C4C2×C22⋊D7311yescharacteristic
296Q16—21no—
297Q16—732no—
298Q16—1461no—
299Q16C2×C4×D7312yes—
300SD16—24no—
301SD16—1464no—
302D8—21no—
303D8—732no—
304D8—1461no—
305D8C2×C4×D7312yes—
306C2×C8—22no—
307C2×C8C2×C4×D7312yes—
308C2×C8C2×C22⋊D7312yes—
309C2×C8C2×C22⋊D7311yescharacteristic
310C2×C8#1192402812yes—
311C2×C8C23×D7311yescharacteristic
312C4⋊C4—22no—
313C4⋊C4—42no—
314C4⋊C4—2922no—
315C4⋊C4—1462no—
316C22⋊C4—41no—
317C22⋊C4—42no—
318C22⋊C4—2921no—
319C22⋊C4—2922no—
320C42—41no—
321C42—42no—
322C42—2921no—
323C42—2922no—
324C42#1192401311yescharacteristic
325C42#1192401311yescharacteristic
326C42C2×C22⋊D7312yes—
327C16—732no—
328C16—732no—
329C16—1462no—
330C23—41no—
331C23—2921no—
332C23C2×#1192401311yescharacteristic
333Q8—22no—
334Q8—41no—
335Q8—2921no—
336Q8—1462no—
337D4—22no—
338D4—44no—
339D4—41no—
340D4—2924no—
341D4—2921no—
342D4—1462no—
343C2×C4—24no—
344C2×C4—41no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—84no—
348C2×C4—2921no—
349C2×C4—2924no—
350C2×C4—2922no—
351C2×C4—5844no—
352C2×C4C4×C22⋊D7312yes—
353C2×C4C2×#1192401312yes—
354C2×C4C2×#1192401311yescharacteristic
355C2×C4C2×#1192401312yes—
356C2×C4#1455661112yes—
357C2×C4C22×C22⋊D7311yescharacteristic
358C8—22no—
359C8C4×C22⋊D7312yes—
360C8C22×C4×D7311yescharacteristic
361C8C2×#1192402811yescharacteristic
362C22—22no—
363C22—42no—
364C22—82no—
365C22—2922no—
366C22—5842no—
367C22C4×#1192401312yes—
368C22C22×#1192401311yescharacteristic
369C4—22no—
370C4—42no—
371C4—82no—
372C4—2922no—
373C4—5842no—
374C4C4×#1192401312yes—
375C4#1798901714yesdirect product factor
376C4C2×C4×C22⋊D7311yescharacteristic
377C4C2×#1455661111yescharacteristic
378C2—22no—
379C2—82no—
380C2—5842no—
381C2C2×C4×#1192401311yescharacteristic
382C2C2×#1798901712yes—
subgroupG/H
centerC42#11924013
commutatorC8×C73C23×C4
FrattiniC2×C8C23×D73
FittingC4×#135×C73C2
socleC22×C73C22×D8
prime radicalC2×#17989017C2
cosocleC2×C8×C73C24
hypercenterC4×#135D73
hypocenterC73C4×#508
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C42 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
2. C4×#14556613C2semidirect
3. C4×#14556537C2semidirect
4. C4×#14556534C2semidirect
5. C4×#14556535C2semidirect
6. C4×#14556532C2semidirect
7. #22611713C2semidirect
8. #22611638C2semidirect
9. #22611636C2semidirect
10. C2×C4×#11924003C2semidirect
11. C4×#135×C73C2semidirect
14. #17989017C4direct (N × H)
44. #14556613C2×C4semidirect
54. #14556537C2×C4semidirect
55. #14556535C2×C4semidirect
56. #14556534C2×C4semidirect
57. #14556532C2×C4semidirect
59. C2×#11924003C2×C4semidirect
69. #135×C73C2×C4semidirect
181. C4×C73#508semidirect
194. C4×#135D73semidirect
203. C73C4×#508semidirect
239. #135C4×D73semidirect
375. C4#17989017direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179890172
C4×#145566132
C4×#145565372
C4×#145565342
C4×#145565352
C4×#145565322
#226117132
#226116382
#226116362
C2×C4×#119240032
C4×#135×C732
C4×#50873