Finite Group Databasebeta

← C4×#17989023 #33239302

Subgroups — C4×#17989023 #33239302

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×#17989023C211yesmaximal, characteristic
2C4×#14556613C211yesmaximal, characteristic, complemented
3#22611805C212yesmaximal, complemented
4#22611795C212yesmaximal, complemented
5C4×#14556535C212yesmaximal, complemented
6C4×#14556532C212yesmaximal, complemented
7#22611717C211yesmaximal, characteristic, complemented
8#22611647C211yesmaximal, characteristic, complemented
9#22611641C211yesmaximal, characteristic, complemented
10C4×#14556531C211yesmaximal, characteristic, complemented
11C2×C4×D8×C73C211yesmaximal, characteristic, complemented
12C2×#14556613C2211yescharacteristic
13C4×#11924028—21no—
14#17989023C418yesdirect product factor
15C2×#14556535C2212yes—
16C2×#14556532C2212yes—
17C2×#14556531C2211yescharacteristic
18C2×#14556531C2211yescharacteristic
19C4×Dic292C2211yescharacteristic, complemented
20C4×Dic292C2211yescharacteristic, complemented
21C4×#11924017—21no—
22C4×#11924017—21no—
23C4×D584C2211yescharacteristic, complemented
24C4×D584C2211yescharacteristic, complemented
25#17988625C2211yescharacteristic
26#17988584—21no—
27#17988414C2212yescomplemented
28#17988412C2212yescomplemented
29#17988390C2212yescomplemented
30#17988388C2212yes—
31#17988388C2212yes—
32#17988387C2212yescomplemented
33#17988363C2212yescomplemented
34C4×#11924003C2212yescomplemented
35C22×D8×C73C2211yescharacteristic
36C2×C4×D4×C73—21no—
37C4×D8×C73—21no—
38C4×D8×C73—21no—
39C4×D8×C73C2212yes—
40C4×D8×C73C2212yes—
41C2×#107×C73C2211yescharacteristic
42C2×#102×C73—21no—
43C2×C4×C8×C73C2211yescharacteristic
44C2×#11924028—21no—
45#14556613—22no—
46#14556613C2×C414yescomplemented
47C2×Dic292C2311yescharacteristic
48C2×#11924017—21no—
49C2×D584C2311yescharacteristic
50C4×Dic146—21no—
51C4×Dic146—21no—
52C4×D292—21no—
53C4×D292—21no—
54C4×C22⋊D73—41no—
55C4×C22⋊D73—41no—
56#14556550—21no—
57#14556548—41no—
58C42×D73—41no—
59#14556535C2×C418yescomplemented
60#14556532C2×C418yescomplemented
61#14556531—22no—
62#14556531C2×C414yescomplemented
63C2×#11924003C2312yes—
64C2×#11924003C2312yes—
65#14556525C2311yescharacteristic
66#14556525C2311yescharacteristic
67#14556523—21no—
68#14556516—21no—
69#14556516—21no—
70#14556513—21no—
71#14556513—21no—
72C22×D4×C73—21no—
73C23×C4×C73—41no—
74C2×D8×C73—21no—
75C2×D8×C73—22no—
76C2×D8×C73C2×C414yescomplemented
77C2×D8×C73C2312yes—
78C22×C8×C73D411yescharacteristic
79C22×C8×C73C2311yescharacteristic
80C4×D4×C73—22no—
81C4×D4×C73—22no—
82C4×D4×C73—41no—
83C4×D4×C73—41no—
84C2×C4⋊C4×C73—21no—
85C2×C22⋊C4×C73—41no—
86C2×C42×C73D411yescharacteristic
87#107×C73—21no—
88#107×C73C2312yes—
89#102×C73—22no—
90#102×C73—22no—
91C4×C8×C73D411yescharacteristic
92C4×C8×C73D411yescharacteristic
93C4×C8×C73C2311yescharacteristic
94C4×C8×C73C2311yescharacteristic
95#11924028—24no—
96#11924028—42no—
97C2×Dic146—21no—
98C2×D292—21no—
99C2×C22⋊D73—41no—
100C2×C4×D73—41no—
101C2×C4×D73—41no—
102C2×C4×D73—41no—
103Dic292—21no—
104Dic292C22×C412yescomplemented
105#11924017—24no—
106D584—21no—
107D584C22×C412yescomplemented
108C4⋊Dic73—21no—
109C4⋊Dic73—21no—
110#11924007—41no—
111#11924007—41no—
112C22⋊Dic73—41no—
113#11924005—41no—
114#11924005—41no—
115C4×Dic73—41no—
116C4×Dic73—41no—
117C4×Dic73—41no—
118#11924003—22no—
119#11924003C22×C414yescomplemented
120C24×C73—41no—
121C2×D4×C73—24no—
122C2×D4×C73—22no—
123C2×D4×C73—41no—
124C2×D4×C73—42no—
125C22×C4×C73—41no—
126C22×C4×C73—42no—
127C22×C4×C73—42no—
128C22×C4×C73—84no—
129C22×C4×C73D811yescharacteristic
130C22×C4×C73D811yescharacteristic
131C22×C4×C73C2×D411yescharacteristic
132D8×C73—24no—
133D8×C73—22no—
134D8×C73C22×C414yes—
135C2×C8×C73—22no—
136C2×C8×C73C22×C412yes—
137C2×C8×C73C2×D411yescharacteristic
138C2×C8×C73C2×D411yescharacteristic
139C2×C8×C73C2×D411yescharacteristic
140C2×C8×C73#4112yes—
141C2×C8×C73C2411yescharacteristic
142C4⋊C4×C73—22no—
143C4⋊C4×C73—41no—
144C22⋊C4×C73—42no—
145C22⋊C4×C73—42no—
146C42×C73D811yescharacteristic
147C42×C73D811yescharacteristic
148C42×C73C2×D411yescharacteristic
149C42×C73C2×D411yescharacteristic
150C23×C73—42no—
151C23×C73—44no—
152C23×C73—82no—
153C23×C73—82no—
154C23×C73C2×D811yescharacteristic
155C22×D73—41no—
156D4×C73—24no—
157D4×C73—42no—
158D4×C73—44no—
159C2×C4×C73—22no—
160C2×C4×C73—41no—
161C2×C4×C73—42no—
162C2×C4×C73—84no—
163C2×C4×C73—82no—
164C2×C4×C73—84no—
165C2×C4×C73C4×D412yes—
166C2×C4×C73C2×D811yescharacteristic
167C2×C4×C73C2×D811yescharacteristic
168C2×C4×C73C2×D811yescharacteristic
169C2×C4×C73C2×D811yescharacteristic
170C2×C4×C73C2×D811yescharacteristic
171C2×C4×C73#13512yes—
172C2×C4×C73C22×D411yescharacteristic
173C22⋊D73—44no—
174C2×Dic73—41no—
175C2×Dic73—41no—
176C2×Dic73—41no—
177D292—22no—
178D292—41no—
179C4×D73—44no—
180C4×D73—82no—
181C4×D73—82no—
182Dic146—22no—
183Dic146—41no—
184C8×C73—21no—
185C8×C73—21no—
186C8×C73C4×D412yes—
187C8×C73C23×C411yescharacteristic
188C8×C73C2×#4111yescharacteristic
189C22×C73—21no—
190C22×C73—21no—
191C22×C73—44no—
192C22×C73—88no—
193C22×C73—82no—
194C22×C73—82no—
195C22×C73C4×D812yes—
196C22×C73C22×D811yescharacteristic
197C2×D73—42no—
198C2×D73—81no—
199C2×D73—81no—
200C4×C73—21no—
201C4×C73—21no—
202C4×C73—21no—
203C4×C73—82no—
204C4×C73C4×D812yes—
205C4×C73#50912yescomplemented
206C4×C73C2×C4×D411yescharacteristic
207C4×C73C2×#13511yescharacteristic
208Dic73—42no—
209Dic73—81no—
210Dic73—81no—
211C4×#509—731nomaximal, Sylow
212C2×C73—22no—
213C2×C73—84no—
214C2×C73C2×C4×D811yescharacteristic
215C2×C73C2×#50911yescharacteristic
216C2×C73#341411yescharacteristic
217D73—82no—
218C2×#509—731no—
219C4×#135—731no—
220C2×C4×D8D7311yescharacteristic, complemented
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×#135—731no—
231C22×D8C2×D7311yescharacteristic
232C4×#41—1461no—
233C2×C4×D4—21no—
234#509—738no—
235C2×SD32—732no—
236C2×D16—732no—
237C2×M32—731no—
238C2×M32—731no—
239C4×Q16—731no—
240C4×Q16—731no—
241C4×SD16—1461no—
242C4×SD16—1461no—
243C4×D8—21no—
244C4×D8—21no—
245C4×D8—731no—
246C4×D8—731no—
247C4×D8C2×D7312yes—
248C4×D8C2×D7312yes—
249#427—731no—
250C2×#107C2×D7311yescharacteristic
251#416—1461no—
252C2×#102—21no—
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—1461no—
263C22×D4—21no—
264C23×C4—41no—
265#135—734no—
266#135—1462no—
267C2×Q16—731no—
268C2×SD16—1461no—
269C2×D8—21no—
270C2×D8—22no—
271C2×D8—731no—
272C2×D8C4×D7314yescomplemented
273C2×D8C22×D7312yes—
274C22×C8C22⋊D7311yescharacteristic
275C22×C8C22×D7311yescharacteristic
276C4×Q8—1461no—
277C4×Q8—1461no—
278C4×D4—22no—
279C4×D4—22no—
280C4×D4—41no—
281C4×D4—41no—
282C4×D4—2921no—
283C4×D4—2921no—
284C4×D4—1461no—
285C4×D4—1461no—
286#117—2921no—
287#117—1461no—
288C2×C4⋊C4—21no—
289C2×C22⋊C4—41no—
290C2×C42—2921no—
291C2×C42C22⋊D7311yescharacteristic
292SD32—738no—
293D16—738no—
294M32—734no—
295M32—1462no—
296C2×C16—732no—
297C2×C16—732no—
298#107—21no—
299#107—731no—
300#107—731no—
301#107C22×D7312yes—
302#106—1461no—
303#103—1461no—
304#103—1461no—
305#102—22no—
306#102—22no—
307#102—1461no—
308#102—1461no—
309C4×C8C22⋊D7311yescharacteristic
310C4×C8C22⋊D7311yescharacteristic
311C4×C8C22×D7311yescharacteristic
312C4×C8C22×D7311yescharacteristic
313C24—41no—
314#41—2922no—
315#41—1464no—
316C2×Q8—1461no—
317C2×D4—24no—
318C2×D4—22no—
319C2×D4—41no—
320C2×D4—42no—
321C2×D4—2921no—
322C2×D4—1461no—
323C22×C4—41no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—84no—
327C22×C4—2921no—
328C22×C4—2921no—
329C22×C4—2921no—
330C22×C4#1192401311yescharacteristic
331C22×C4#1192401311yescharacteristic
332C22×C4C2×C22⋊D7311yescharacteristic
333Q16—732no—
334Q16—1461no—
335SD16—1464no—
336D8—24no—
337D8—22no—
338D8—732no—
339D8—1461no—
340D8C2×C4×D7314yes—
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—22no—
349C4⋊C4—41no—
350C4⋊C4—2921no—
351C4⋊C4—2921no—
352C4⋊C4—1461no—
353C4⋊C4—1461no—
354C22⋊C4—42no—
355C22⋊C4—42no—
356C22⋊C4—2921no—
357C22⋊C4—2921no—
358C22⋊C4—2921no—
359C42—2921no—
360C42—2921no—
361C42—2921no—
362C42#1192401311yescharacteristic
363C42#1192401311yescharacteristic
364C42C2×C22⋊D7311yescharacteristic
365C42C2×C22⋊D7311yescharacteristic
366C16—734no—
367C16—1462no—
368C23—44no—
369C23—42no—
370C23—82no—
371C23—82no—
372C23—2921no—
373C23C2×#1192401311yescharacteristic
374Q8—2921no—
375Q8—1462no—
376D4—24no—
377D4—44no—
378D4—42no—
379D4—2924no—
380D4—2921no—
381D4—1462no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—84no—
386C2×C4—82no—
387C2×C4—84no—
388C2×C4—2921no—
389C2×C4—2924no—
390C2×C4—2921no—
391C2×C4—2921no—
392C2×C4—5842no—
393C2×C4—5842no—
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—44no—
410C22—88no—
411C22—82no—
412C22—82no—
413C22—2922no—
414C22—5841no—
415C22—5841no—
416C22C4×#1192401312yes—
417C22C22×#1192401311yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—82no—
422C4—2922no—
423C4—5841no—
424C4—5841no—
425C4C4×#1192401312yes—
426C4#1798902312yesdirect product factor
427C4C2×C4×C22⋊D7311yescharacteristic
428C4C2×#1455661111yescharacteristic
429C2—22no—
430C2—84no—
431C2—5842no—
432C2C2×C4×#1192401311yescharacteristic
433C2C2×#1798902311yescharacteristic
434C2#2262306511yescharacteristic
subgroupG/H
centerC2×C4C2×#11924013
commutatorC8×C73C23×C4
FrattiniC2×C8C23×D73
FittingC2×C4×D8×C73C2
socleC22×C73C22×D8
prime radicalC2×#17989023C2
cosocleC2×C8×C73C24
hypercenterC2×C4×D8D73
hypocenterC73C4×#509
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
2. C4×#14556613C2semidirect
3. #22611805C2semidirect
4. #22611795C2semidirect
5. C4×#14556535C2semidirect
6. C4×#14556532C2semidirect
7. #22611717C2semidirect
8. #22611647C2semidirect
9. #22611641C2semidirect
10. C4×#14556531C2semidirect
11. C2×C4×D8×C73C2semidirect
14. #17989023C4direct (N × H)
19. C4×Dic292C22semidirect
20. C4×Dic292C22semidirect
23. C4×D584C22semidirect
24. C4×D584C22semidirect
27. #17988414C22semidirect
28. #17988412C22semidirect
29. #17988390C22semidirect
32. #17988387C22semidirect
33. #17988363C22semidirect
34. C4×#11924003C22semidirect
46. #14556613C2×C4semidirect
59. #14556535C2×C4semidirect
60. #14556532C2×C4semidirect
62. #14556531C2×C4semidirect
76. C2×D8×C73C2×C4semidirect
104. Dic292C22×C4semidirect
107. D584C22×C4semidirect
119. #11924003C22×C4semidirect
205. C4×C73#509semidirect
220. C2×C4×D8D73semidirect
229. C73C4×#509semidirect
272. C2×D8C4×D73semidirect
426. C4#17989023direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179890232
C4×#145566132
#226118052
#226117952
C4×#145565352
C4×#145565322
#226117172
#226116472
#226116412
C4×#145565312
C2×C4×D8×C732
C4×#50973