Finite Group Databasebeta

← C4×#17989022 #33239300

Subgroups — C4×#17989022 #33239300

Order 18688.

738 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989022C211yesmaximal, characteristic
2C2×C4×D584C211yesmaximal, characteristic, complemented
3#22611805C212yesmaximal, complemented
4#22611793C212yesmaximal, complemented
5C4×#14556534C212yesmaximal, complemented
6C4×#14556532C212yesmaximal, complemented
7#22611720C211yesmaximal, characteristic, complemented
8#22611646C211yesmaximal, characteristic, complemented
9#22611643C211yesmaximal, characteristic, complemented
10C4×#14556531C211yesmaximal, characteristic, complemented
11C4×#135×C73C211yesmaximal, characteristic, complemented
12C22×D584C2211yescharacteristic
13C2×C4×D292—21no—
14#17989022C418yesdirect product factor
15C2×#14556534C2212yes—
16C2×#14556532C2212yes—
17C2×#14556531C2211yescharacteristic
18C2×#14556531C2211yescharacteristic
19C4×D584—21no—
20C4×D584—21no—
21C4×D584C2212yes—
22C4×D584C2212yes—
23C2×#14556525C2211yescharacteristic
24C2×#14556513—21no—
25#17988414C2212yescomplemented
26#17988412C2212yescomplemented
27#17988391C2212yescomplemented
28#17988388C2212yescomplemented
29#17988387C2212yes—
30#17988387C2212yes—
31#17988363C2212yescomplemented
32C4×#11924003C2212yescomplemented
33C2×#135×C73C2211yescharacteristic
34C4×#41×C73—21no—
35C4×Q16×C73C2211yescharacteristic, complemented
36C4×Q16×C73C2211yescharacteristic, complemented
37C4×SD16×C73—21no—
38C4×SD16×C73—21no—
39C4×D8×C73C2211yescharacteristic, complemented
40C4×D8×C73C2211yescharacteristic, complemented
41#427×C73C2211yescharacteristic
42#416×C73—21no—
43C2×C4×C8×C73C2211yescharacteristic
44C22×D292—21no—
45C22×C4×D73—41no—
46C2×D584—21no—
47C2×D584—22no—
48C2×D584C2×C414yescomplemented
49C2×D584C2312yes—
50C4×D292—22no—
51C4×D292—22no—
52C4×D292—41no—
53C4×D292—41no—
54C2×C4⋊Dic73—21no—
55C2×#11924005—41no—
56#14556534C2×C418yescomplemented
57#14556532C2×C418yescomplemented
58#14556531—22no—
59#14556531C2×C414yescomplemented
60C2×#11924003C2312yes—
61C2×#11924003C2312yes—
62#14556525—21no—
63#14556525C2312yes—
64#14556513—22no—
65#14556513—22no—
66C2×#41×C73—21no—
67#135×C73—22no—
68#135×C73C2×C414yescomplemented
69C2×Q16×C73C2311yescharacteristic
70C2×SD16×C73—21no—
71C2×D8×C73C2311yescharacteristic
72C22×C8×C73D411yescharacteristic
73C22×C8×C73C2311yescharacteristic
74C4×Q8×C73—21no—
75C4×Q8×C73—21no—
76C4×D4×C73—21no—
77C4×D4×C73—21no—
78C4×D4×C73—41no—
79C4×D4×C73—41no—
80#117×C73—21no—
81#117×C73—41no—
82C2×C42×C73—41no—
83C2×C42×C73D411yescharacteristic
84#107×C73C2311yescharacteristic
85#107×C73C2311yescharacteristic
86#106×C73—21no—
87#103×C73—21no—
88#103×C73—21no—
89#102×C73—21no—
90#102×C73—21no—
91C4×C8×C73D411yescharacteristic
92C4×C8×C73D411yescharacteristic
93C4×C8×C73C2311yescharacteristic
94C4×C8×C73C2311yescharacteristic
95C23×D73—41no—
96C2×D292—24no—
97C2×D292—22no—
98C2×D292—41no—
99C2×D292—42no—
100C22×Dic73—41no—
101C2×C4×D73—42no—
102C2×C4×D73—42no—
103C2×C4×D73—84no—
104D584—24no—
105D584—22no—
106D584C22×C414yes—
107C4⋊Dic73—22no—
108C4⋊Dic73—41no—
109#11924005—42no—
110#11924005—42no—
111#11924003—22no—
112#11924003C22×C414yescomplemented
113#41×C73—24no—
114#41×C73—42no—
115C2×Q8×C73—21no—
116C2×D4×C73—21no—
117C2×D4×C73—41no—
118C22×C4×C73—41no—
119C22×C4×C73—41no—
120C22×C4×C73—41no—
121C22×C4×C73D811yescharacteristic
122C22×C4×C73D811yescharacteristic
123C22×C4×C73C2×D411yescharacteristic
124Q16×C73—21no—
125Q16×C73C22×C412yescomplemented
126SD16×C73—24no—
127D8×C73—21no—
128D8×C73C22×C412yescomplemented
129C2×C8×C73—22no—
130C2×C8×C73C22×C412yes—
131C2×C8×C73C2×D411yescharacteristic
132C2×C8×C73C2×D411yescharacteristic
133C2×C8×C73C2×D411yescharacteristic
134C2×C8×C73#4112yes—
135C2×C8×C73C2411yescharacteristic
136C4⋊C4×C73—21no—
137C4⋊C4×C73—21no—
138C4⋊C4×C73—41no—
139C4⋊C4×C73—41no—
140C22⋊C4×C73—41no—
141C22⋊C4×C73—41no—
142C22⋊C4×C73—41no—
143C42×C73—41no—
144C42×C73—41no—
145C42×C73—41no—
146C42×C73D811yescharacteristic
147C42×C73D811yescharacteristic
148C42×C73C2×D411yescharacteristic
149C42×C73C2×D411yescharacteristic
150C23×C73—41no—
151C23×C73C2×D811yescharacteristic
152C22×D73—42no—
153C22×D73—44no—
154C22×D73—82no—
155C22×D73—82no—
156Q8×C73—22no—
157Q8×C73—41no—
158D4×C73—22no—
159D4×C73—44no—
160D4×C73—41no—
161C2×C4×C73—22no—
162C2×C4×C73—41no—
163C2×C4×C73—41no—
164C2×C4×C73—44no—
165C2×C4×C73—41no—
166C2×C4×C73—41no—
167C2×C4×C73—82no—
168C2×C4×C73—82no—
169C2×C4×C73C4×D412yes—
170C2×C4×C73C2×D811yescharacteristic
171C2×C4×C73C2×D811yescharacteristic
172C2×C4×C73C2×D811yescharacteristic
173C2×C4×C73C2×D811yescharacteristic
174C2×C4×C73C2×D811yescharacteristic
175C2×C4×C73#13512yes—
176C2×C4×C73C22×D411yescharacteristic
177C2×Dic73—42no—
178C2×Dic73—82no—
179D292—24no—
180D292—42no—
181D292—44no—
182C4×D73—84no—
183C4×D73—84no—
184C8×C73—21no—
185C8×C73—21no—
186C8×C73C4×D412yes—
187C8×C73C23×C411yescharacteristic
188C8×C73C2×#4111yescharacteristic
189C22×C73—21no—
190C22×C73—21no—
191C22×C73—42no—
192C22×C73—81no—
193C22×C73—81no—
194C22×C73C4×D812yes—
195C22×C73C22×D811yescharacteristic
196C2×D73—44no—
197C2×D73—88no—
198C2×D73—82no—
199C2×D73—82no—
200C4×C73—21no—
201C4×C73—21no—
202C4×C73—21no—
203C4×C73—42no—
204C4×C73—81no—
205C4×C73—81no—
206C4×C73C4×D812yes—
207C4×C73#50912yescomplemented
208C4×C73C2×C4×D411yescharacteristic
209C4×C73C2×#13511yescharacteristic
210Dic73—82no—
211C4×#509—731nomaximal, Sylow
212C2×C73—22no—
213C2×C73—82no—
214C2×C73C2×C4×D811yescharacteristic
215C2×C73C2×#50911yescharacteristic
216C2×C73#341411yescharacteristic
217D73—84no—
218C2×#509—731no—
219C4×#135D7311yescharacteristic, complemented
220C2×C4×D8—731no—
221#2177—732no—
222#2175—732no—
223C4×SD32—732no—
224C4×D16—732no—
225#2159—731no—
226#2140—731no—
227#2139—731no—
228C4×M32—731no—
229C73C4×#50911yescharacteristic, complemented, Sylow
230C2×#135C2×D7311yescharacteristic
231C22×D8—731no—
232C4×#41—21no—
233C2×C4×D4—1461no—
234#509—738no—
235C2×SD32—732no—
236C2×D16—732no—
237C2×M32—731no—
238C2×M32—731no—
239C4×Q16C2×D7311yescharacteristic, complemented
240C4×Q16C2×D7311yescharacteristic, complemented
241C4×SD16—21no—
242C4×SD16—21no—
243C4×D8—732no—
244C4×D8—732no—
245C4×D8—1461no—
246C4×D8—1461no—
247C4×D8C2×D7311yescharacteristic, complemented
248C4×D8C2×D7311yescharacteristic, complemented
249#427C2×D7311yescharacteristic
250C2×#107—731no—
251#416—21no—
252C2×#102—1461no—
253C2×C4×C8C2×D7311yescharacteristic
254#367—732no—
255#366—732no—
256#358—732no—
257#357—732no—
258#357—732no—
259#357—732no—
260#346—732no—
261C4×C16—732no—
262C2×#41—21no—
263C22×D4—1461no—
264C23×C4—2921no—
265#135—22no—
266#135C4×D7314yescomplemented
267C2×Q16C22×D7311yescharacteristic
268C2×SD16—21no—
269C2×D8—734no—
270C2×D8—732no—
271C2×D8—1461no—
272C2×D8—1462no—
273C2×D8C22×D7311yescharacteristic
274C22×C8C22⋊D7311yescharacteristic
275C22×C8C22×D7311yescharacteristic
276C4×Q8—21no—
277C4×Q8—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4—41no—
281C4×D4—41no—
282C4×D4—2921no—
283C4×D4—2921no—
284C4×D4—1462no—
285C4×D4—1462no—
286#117—21no—
287#117—41no—
288C2×C4⋊C4—1461no—
289C2×C22⋊C4—2921no—
290C2×C42—41no—
291C2×C42C22⋊D7311yescharacteristic
292SD32—738no—
293D16—738no—
294M32—734no—
295M32—1462no—
296C2×C16—732no—
297C2×C16—732no—
298#107—732no—
299#107—1461no—
300#107C22×D7311yescharacteristic
301#107C22×D7311yescharacteristic
302#106—21no—
303#103—21no—
304#103—21no—
305#102—21no—
306#102—21no—
307#102—1462no—
308#102—1462no—
309C4×C8C22⋊D7311yescharacteristic
310C4×C8C22⋊D7311yescharacteristic
311C4×C8C22×D7311yescharacteristic
312C4×C8C22×D7311yescharacteristic
313C24—2921no—
314#41—24no—
315#41—42no—
316C2×Q8—21no—
317C2×D4—21no—
318C2×D4—41no—
319C2×D4—2921no—
320C2×D4—2922no—
321C2×D4—1464no—
322C2×D4—1462no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—2921no—
327C22×C4—2922no—
328C22×C4—2922no—
329C22×C4—5844no—
330C22×C4#1192401311yescharacteristic
331C22×C4#1192401311yescharacteristic
332C22×C4C2×C22⋊D7311yescharacteristic
333Q16—21no—
334Q16C2×C4×D7312yescomplemented
335SD16—24no—
336D8—21no—
337D8—734no—
338D8—1464no—
339D8—1462no—
340D8C2×C4×D7312yescomplemented
341C2×C8—22no—
342C2×C8C2×C4×D7312yes—
343C2×C8C2×C22⋊D7311yescharacteristic
344C2×C8C2×C22⋊D7311yescharacteristic
345C2×C8C2×C22⋊D7311yescharacteristic
346C2×C8#1192402812yes—
347C2×C8C23×D7311yescharacteristic
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—2921no—
353C4⋊C4—1462no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—2922no—
358C22⋊C4—2922no—
359C42—41no—
360C42—41no—
361C42—41no—
362C42#1192401311yescharacteristic
363C42#1192401311yescharacteristic
364C42C2×C22⋊D7311yescharacteristic
365C42C2×C22⋊D7311yescharacteristic
366C16—734no—
367C16—1462no—
368C23—41no—
369C23—2924no—
370C23—2922no—
371C23—5842no—
372C23—5842no—
373C23C2×#1192401311yescharacteristic
374Q8—22no—
375Q8—41no—
376D4—22no—
377D4—44no—
378D4—41no—
379D4—2924no—
380D4—2922no—
381D4—1464no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—44no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—82no—
389C2×C4—82no—
390C2×C4—2922no—
391C2×C4—5844no—
392C2×C4—5842no—
393C2×C4—5844no—
394C2×C4C4×C22⋊D7312yes—
395C2×C4C2×#1192401311yescharacteristic
396C2×C4C2×#1192401311yescharacteristic
397C2×C4C2×#1192401311yescharacteristic
398C2×C4C2×#1192401311yescharacteristic
399C2×C4C2×#1192401311yescharacteristic
400C2×C4#1455661112yes—
401C2×C4C22×C22⋊D7311yescharacteristic
402C8—21no—
403C8—21no—
404C8C4×C22⋊D7312yes—
405C8C22×C4×D7311yescharacteristic
406C8C2×#1192402811yescharacteristic
407C22—21no—
408C22—21no—
409C22—42no—
410C22—81no—
411C22—81no—
412C22—2924no—
413C22—5848no—
414C22—5842no—
415C22—5842no—
416C22C4×#1192401312yes—
417C22C22×#1192401311yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—42no—
422C4—81no—
423C4—81no—
424C4—5842no—
425C4C4×#1192401312yes—
426C4#1798902212yesdirect product factor
427C4C2×C4×C22⋊D7311yescharacteristic
428C4C2×#1455661111yescharacteristic
429C2—22no—
430C2—82no—
431C2—5844no—
432C2C2×C4×#1192401311yescharacteristic
433C2C2×#1798902211yescharacteristic
434C2#2262306511yescharacteristic
subgroupG/H
centerC2×C4C2×#11924013
commutatorC8×C73C23×C4
FrattiniC2×C8C23×D73
FittingC4×#135×C73C2
socleC22×C73C22×D8
prime radicalC2×#17989022C2
cosocleC2×C8×C73C24
hypercenterC4×#135D73
hypocenterC73C4×#509
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
2. C2×C4×D584C2semidirect
3. #22611805C2semidirect
4. #22611793C2semidirect
5. C4×#14556534C2semidirect
6. C4×#14556532C2semidirect
7. #22611720C2semidirect
8. #22611646C2semidirect
9. #22611643C2semidirect
10. C4×#14556531C2semidirect
11. C4×#135×C73C2semidirect
14. #17989022C4direct (N × H)
25. #17988414C22semidirect
26. #17988412C22semidirect
27. #17988391C22semidirect
28. #17988388C22semidirect
31. #17988363C22semidirect
32. C4×#11924003C22semidirect
35. C4×Q16×C73C22semidirect
36. C4×Q16×C73C22semidirect
39. C4×D8×C73C22semidirect
40. C4×D8×C73C22semidirect
48. C2×D584C2×C4semidirect
56. #14556534C2×C4semidirect
57. #14556532C2×C4semidirect
59. #14556531C2×C4semidirect
68. #135×C73C2×C4semidirect
112. #11924003C22×C4semidirect
125. Q16×C73C22×C4semidirect
128. D8×C73C22×C4semidirect
207. C4×C73#509semidirect
219. C4×#135D73semidirect
229. C73C4×#509semidirect
239. C4×Q16C2×D73semidirect
240. C4×Q16C2×D73semidirect
247. C4×D8C2×D73semidirect
248. C4×D8C2×D73semidirect
266. #135C4×D73semidirect
334. Q16C2×C4×D73semidirect
340. D8C2×C4×D73semidirect
426. C4#17989022direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179890222
C2×C4×D5842
#226118052
#226117932
C4×#145565342
C4×#145565322
#226117202
#226116462
#226116432
C4×#145565312
C4×#135×C732
C4×#50973