Finite Group Databasebeta

← C4×#17989198 #33245129

Subgroups — C4×#17989198 #33245129

Order 18688.

2070 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989198C211yesmaximal, characteristic
2#22612729C214yesmaximal, complemented
3#22612699C214yesmaximal
4#22612670C211yesmaximal, characteristic, complemented
5#22612651C211yesmaximal, characteristic, complemented
6#22612616C212yesmaximal
7#22612576C212yesmaximal, complemented
8#22612539C211yesmaximal, characteristic
9C4×#14556583C211yesmaximal, characteristic, complemented
10C4×#14556581C214yesmaximal, complemented
11C4×#14556586C214yesmaximal
12C4×#14556567C212yesmaximal
13C4×Q8×Dic73C212yesmaximal, complemented
14C4×#14556548C211yesmaximal, characteristic
15C4×C4⋊Q8×C73C211yesmaximal, characteristic, complemented
16#17989198C4116yesdirect product factor
17C2×#14556586C2214yes—
18C2×#14556583C2211yescharacteristic
19C2×#14556581C2214yes—
20C2×#14556567C2212yes—
21C2×Q8×Dic73C2212yes—
22C2×Q8×Dic73C2212yes—
23C2×#14556548C2211yescharacteristic
24C2×#14556548C2211yescharacteristic
25C2×C42×D73C2211yescharacteristic
26#17988494C2212yes—
27#17988485C2212yes—
28#17988484C2214yes—
29#17988483C2212yes—
30#17988482C2214yes—
31#17988479C2214yes—
32#17988477C2214yes—
33#17988476C2214yes—
34#17988473C2214yes—
35#17988473C2214yes—
36#17988472C2214yes—
37#17988471C2214yes—
38#17988470C2214yes—
39#17988469C2214yes—
40#17988468C2214yes—
41#17988468C2214yes—
42#17988468C2214yes—
43#17988458C2214yes—
44#17988454C2214yes—
45#17988453C2211yescharacteristic
46#17988451C2214yes—
47#17988444C2212yes—
48C4⋊C4×Dic73C2212yes—
49C4⋊C4×Dic73C2212yes—
50C4⋊C4×Dic73C2214yes—
51C4⋊C4×Dic73C2214yes—
52C4×#11924007C2214yes—
53C4×#11924007C2212yes—
54C4×#11924007C2214yes—
55C4×#11924007C2212yes—
56C4×C4⋊Dic73C2214yes—
57C4×C4⋊Dic73C2212yes—
58C4×#11924005C2212yes—
59C4×#11924005C2214yes—
60C4×#11924005C2212yes—
61#17988433C2211yescharacteristic
62#17988433C2211yescharacteristic
63C42×Dic73C2214yes—
64C42×Dic73C2211yescharacteristic
65C2×C4⋊Q8×C73C2211yescharacteristic
66C2×C4×Q8×C73C2212yes—
67#391×C73C2212yes—
68#389×C73C2214yes—
69#384×C73C2211yescharacteristic
70C4×C4⋊C4×C73C2214yes—
71C43×C73C2211yescharacteristic
72C22×C4×D73C2311yescharacteristic
73C22×C4×D73C2311yescharacteristic
74C22×C4×D73C2311yescharacteristic
75#14556586C2×C4132yes—
76#14556583C2×C418yescomplemented
77#14556581C2×C4132yescomplemented
78#14556567C2×C4116yes—
79Q8×Dic73—28no—
80Q8×Dic73C2×C4116yescomplemented
81#14556548—24no—
82#14556548C2×C418yes—
83C2×C4⋊Dic73C2312yes—
84C2×C4⋊Dic73C2314yes—
85C2×C4⋊Dic73C2314yes—
86C2×C4⋊Dic73C2312yes—
87C2×#11924007C2312yes—
88C2×#11924007C2314yes—
89C2×#11924007C2314yes—
90C2×#11924007C2312yes—
91C2×#11924007C2314yes—
92C2×#11924007C2314yes—
93C2×#11924005C2312yes—
94C2×#11924005C2314yes—
95C2×#11924005C2312yes—
96C2×#11924005C2314yes—
97C2×C4×Dic73C2312yes—
98C2×C4×Dic73C2314yes—
99C2×C4×Dic73C2314yes—
100C2×C4×Dic73C2311yescharacteristic
101C2×C4×Dic73C2311yescharacteristic
102C2×C4×Dic73C2311yescharacteristic
103C2×C4×Dic73C2312yes—
104C2×C4×Dic73C2314yes—
105C2×C4×Dic73C2314yes—
106C2×C4×Dic73C2311yescharacteristic
107C2×C4×Dic73C2314yes—
108C2×C4×Dic73C2311yescharacteristic
109C42×D73—24no—
110#14556498C2312yes—
111#14556498C2312yes—
112#14556498C2312yes—
113#14556498C2312yes—
114#14556498C2314yes—
115#14556498C2314yes—
116#14556498C2314yes—
117#14556498C2314yes—
118#14556498C2314yes—
119#14556498C2314yes—
120#14556498C2314yes—
121#14556498C2314yes—
122#14556498C2314yes—
123C22×Q8×C73C2312yes—
124C4⋊Q8×C73C2×C418yescomplemented
125C4×Q8×C73—28no—
126C2×C4⋊C4×C73C2312yes—
127C2×C4⋊C4×C73C2314yes—
128C2×C4⋊C4×C73C2314yes—
129C2×C4⋊C4×C73C2314yes—
130C2×C42×C73C2314yes—
131C2×C42×C73C2312yes—
132C2×C42×C73C2311yescharacteristic
133C2×C42×C73C2312yes—
134C2×C42×C73C2311yescharacteristic
135C2×C42×C73C2311yescharacteristic
136#95×C73C2314yes—
137#95×C73C2314yes—
138C23×D73C2411yescharacteristic
139C22×Dic73C2411yescharacteristic
140C22×Dic73C2414yes—
141C22×Dic73C2411yescharacteristic
142C22×Dic73C2412yes—
143C22×Dic73C2414yes—
144C22×Dic73C2411yescharacteristic
145C22×Dic73C2412yes—
146C2×C4×D73—22no—
147C2×C4×D73—22no—
148C2×C4×D73—22no—
149C2×C4×D73—22no—
150C2×C4×D73—24no—
151C2×C4×D73—42no—
152C2×C4×D73C22×C414yes—
153C4⋊Dic73—24no—
154C4⋊Dic73—28no—
155C4⋊Dic73C22×C418yes—
156C4⋊Dic73C22×C4116yes—
157#11924007—24no—
158#11924007—44no—
159#11924007—44no—
160#11924007C22×C418yes—
161#11924007C22×C4116yes—
162#11924007C22×C4116yes—
163#11924005—24no—
164#11924005—44no—
165#11924005C22×C418yes—
166#11924005C22×C4116yes—
167C4×Dic73—22no—
168C4×Dic73—22no—
169C4×Dic73—22no—
170C4×Dic73—24no—
171C4×Dic73—28no—
172C4×Dic73—28no—
173C4×Dic73—42no—
174C4×Dic73—44no—
175C4×Dic73—44no—
176C4×Dic73C22×C414yes—
177C4×Dic73C22×C4116yes—
178C4×Dic73#4114yes—
179C2×Q8×C73—24no—
180C2×Q8×C73—24no—
181C2×Q8×C73C22×C418yes—
182C22×C4×C73C2412yes—
183C22×C4×C73C2414yes—
184C22×C4×C73C2414yes—
185C22×C4×C73C2412yes—
186C22×C4×C73C2411yescharacteristic
187C22×C4×C73C2411yescharacteristic
188C22×C4×C73C2411yescharacteristic
189C4⋊C4×C73—28no—
190C4⋊C4×C73—24no—
191C4⋊C4×C73—44no—
192C4⋊C4×C73C22×C4116yes—
193C42×C73—28no—
194C42×C73—22no—
195C42×C73—24no—
196C42×C73—42no—
197C42×C73C22×C414yes—
198C42×C73#4114yes—
199C23×C73C2511yescharacteristic
200C22×D73—21no—
201C22×D73—21no—
202C22×D73—22no—
203C22×D73—22no—
204C22×D73C23×C412yes—
205Q8×C73—216no—
206C2×C4×C73—24no—
207C2×C4×C73—24no—
208C2×C4×C73—22no—
209C2×C4×C73—22no—
210C2×C4×C73—22no—
211C2×C4×C73—24no—
212C2×C4×C73—22no—
213C2×C4×C73—22no—
214C2×C4×C73—22no—
215C2×C4×C73—24no—
216C2×C4×C73—24no—
217C2×C4×C73C23×C414yes—
218C2×C4×C73C23×C418yes—
219C2×C4×C73C23×C412yes—
220C2×C4×C73C2×#4112yes—
221C2×C4×C73C2×#4112yes—
222C2×C4×C73C2×#4112yes—
223C2×C4×C73C2×#4112yes—
224C2×C4×C732−1+414yes—
225C2×Dic73—21no—
226C2×Dic73—21no—
227C2×Dic73—22no—
228C2×Dic73—24no—
229C2×Dic73—22no—
230C2×Dic73—22no—
231C2×Dic73—22no—
232C2×Dic73—24no—
233C2×Dic73—21no—
234C2×Dic73—21no—
235C2×Dic73—24no—
236C2×Dic73—24no—
237C2×Dic73—22no—
238C2×Dic73—24no—
239C2×Dic73—22no—
240C2×Dic73C23×C414yes—
241C2×Dic73C23×C418yes—
242C2×Dic73C23×C412yes—
243C2×Dic73C2×#4114yes—
244C4×D73—28no—
245C4×D73—44no—
246C4×D73—44no—
247C22×C73C24×C411yescharacteristic
248C22×C73C22×#4111yescharacteristic
249C22×C73C22×#4111yescharacteristic
250C22×C73C2×2−1+412yes—
251C22×C73#58512yes—
252C2×D73—22no—
253C2×D73—24no—
254C2×D73—41no—
255C2×D73—41no—
256C2×D73—42no—
257C4×C73—28no—
258C4×C73—24no—
259C4×C73—22no—
260C4×C73—44no—
261C4×C73—42no—
262C4×C73C4×#4114yes—
263C4×C73#54114yescomplemented
264Dic73—22no—
265Dic73—24no—
266Dic73—28no—
267Dic73—24no—
268Dic73—41no—
269Dic73—41no—
270Dic73—44no—
271C4×#541—731nomaximal, Sylow
272C2×C73C2×C4×#4111yescharacteristic
273C2×C73C4×2−1+412yes—
274C2×C73C2×#54111yescharacteristic
275C2×C73#345511yescharacteristic
276C2×C73#346112yes—
277D73—42no—
278C2×#541—731no—
279#2336—734no—
280#2334—734no—
281#2330—731no—
282#2327—731no—
283#2323—732no—
284#2320—732no—
285#2314—731no—
286C4×C4⋊Q8D7311yescharacteristic, complemented
287C4×#125—734no—
288C4×#125—731no—
289C4×#126—734no—
290C4×C22⋊Q8—732no—
291C42×Q8—732no—
292C4×#117—731no—
293C73C4×#54111yescharacteristic, complemented, Sylow
294#541—7316no—
295C2×C4⋊Q8C2×D7311yescharacteristic
296C2×#126—734no—
297C2×#125—734no—
298C2×#125—731no—
299C2×C22⋊Q8—732no—
300C2×C4×Q8—732no—
301C2×C4×Q8—732no—
302C2×C4×Q8C2×D7312yes—
303C2×#117—731no—
304C2×#117—731no—
305C22×C42—731no—
306#391—732no—
307#391C2×D7312yes—
308#389—734no—
309#389—732no—
310#389—732no—
311#389—734no—
312#389C2×D7314yes—
313#388—734no—
314#388—734no—
315#388—734no—
316#387—734no—
317#387—734no—
318#387—734no—
319#387—734no—
320#387—734no—
321#387—734no—
322#387—734no—
323#387—734no—
324#387—734no—
325#385—734no—
326#384C2×D7311yescharacteristic
327#383—734no—
328#382—731no—
329#382—734no—
330#380—732no—
331C4×C4⋊C4—732no—
332C4×C4⋊C4—732no—
333C4×C4⋊C4—734no—
334C4×C4⋊C4—734no—
335C4×C4⋊C4—734no—
336C4×C4⋊C4—734no—
337C4×C4⋊C4—732no—
338C4×C4⋊C4—734no—
339C4×C4⋊C4—732no—
340C4×C4⋊C4—732no—
341C4×C4⋊C4C2×D7314yes—
342C4×C22⋊C4—732no—
343C4×C22⋊C4—734no—
344C4×C22⋊C4—732no—
345#376—731no—
346#376—731no—
347C43—734no—
348C43—731no—
349C43C2×D7311yescharacteristic
350C22×Q8C22×D7312yes—
351C23×C4—731no—
352C23×C4—731no—
353C23×C4—731no—
354C4⋊Q8C4×D7318yescomplemented
355#126—7332no—
356#125—7332no—
357#125—738no—
358C22⋊Q8—7316no—
359C4×Q8—28no—
360C4×Q8—7316no—
361C4×Q8—1468no—
362#117—738no—
363#117—1464no—
364C2×C4⋊C4—734no—
365C2×C4⋊C4—734no—
366C2×C4⋊C4—732no—
367C2×C4⋊C4—732no—
368C2×C4⋊C4—734no—
369C2×C4⋊C4—734no—
370C2×C4⋊C4—734no—
371C2×C4⋊C4—732no—
372C2×C4⋊C4—732no—
373C2×C4⋊C4—734no—
374C2×C4⋊C4C22×D7312yes—
375C2×C4⋊C4C22×D7314yes—
376C2×C4⋊C4C22×D7314yes—
377C2×C4⋊C4C22×D7314yes—
378C2×C22⋊C4—734no—
379C2×C22⋊C4—732no—
380C2×C22⋊C4—734no—
381C2×C22⋊C4—732no—
382C2×C42—732no—
383C2×C42—734no—
384C2×C42—734no—
385C2×C42—731no—
386C2×C42—731no—
387C2×C42—734no—
388C2×C42—734no—
389C2×C42—731no—
390C2×C42—731no—
391C2×C42—732no—
392C2×C42—734no—
393C2×C42—731no—
394C2×C42—1464no—
395C2×C42C22×D7311yescharacteristic
396C2×C42C22×D7314yes—
397C2×C42C22×D7312yes—
398C2×C42C22×D7312yes—
399C2×C42C22×D7311yescharacteristic
400C2×C42C22×D7311yescharacteristic
401#95—732no—
402#95—732no—
403#95—732no—
404#95—732no—
405#95—734no—
406#95—734no—
407#95—734no—
408#95—734no—
409#95—734no—
410#95—734no—
411#95—734no—
412#95—734no—
413#95—734no—
414#95C22×D7314yes—
415#95C22×D7314yes—
416C24—731no—
417C2×Q8—24no—
418C2×Q8—24no—
419C2×Q8C2×C4×D7318yes—
420C22×C4—2922no—
421C22×C4—732no—
422C22×C4—732no—
423C22×C4—734no—
424C22×C4—731no—
425C22×C4—734no—
426C22×C4—731no—
427C22×C4—734no—
428C22×C4—731no—
429C22×C4—1462no—
430C22×C4—1462no—
431C22×C4—1464no—
432C22×C4—1462no—
433C22×C4—1462no—
434C22×C4C23×D7312yes—
435C22×C4C23×D7314yes—
436C22×C4C23×D7312yes—
437C22×C4C23×D7314yes—
438C22×C4C23×D7311yescharacteristic
439C22×C4C23×D7311yescharacteristic
440C22×C4C23×D7311yescharacteristic
441C4⋊C4—28no—
442C4⋊C4—24no—
443C4⋊C4—44no—
444C4⋊C4—2924no—
445C4⋊C4—2924no—
446C4⋊C4—738no—
447C4⋊C4—7316no—
448C4⋊C4—7316no—
449C4⋊C4—738no—
450C4⋊C4—7316no—
451C4⋊C4—1464no—
452C4⋊C4—1468no—
453C4⋊C4—1464no—
454C4⋊C4C2×C4×D73116yes—
455C22⋊C4—2924no—
456C22⋊C4—738no—
457C22⋊C4—7316no—
458C22⋊C4—1464no—
459C42—22no—
460C42—28no—
461C42—24no—
462C42—42no—
463C42—2922no—
464C42—2924no—
465C42—2924no—
466C42—734no—
467C42—7316no—
468C42—734no—
469C42—1468no—
470C42—1462no—
471C42—1462no—
472C42—1462no—
473C42—1468no—
474C42—1464no—
475C42C2×C4×D7314yes—
476C42#1192402714yes—
477C23—732no—
478C23—1461no—
479C23—1461no—
480C23—1462no—
481C23—1462no—
482C23C24×D7311yescharacteristic
483Q8—216no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—2924no—
496C2×C4—2924no—
497C2×C4—734no—
498C2×C4—738no—
499C2×C4—732no—
500C2×C4—734no—
501C2×C4—1464no—
502C2×C4—1461no—
503C2×C4—1461no—
504C2×C4—1464no—
505C2×C4—1462no—
506C2×C4—1464no—
507C2×C4—1462no—
508C2×C4—1461no—
509C2×C4—1461no—
510C2×C4—1462no—
511C2×C4—1462no—
512C2×C4—1464no—
513C2×C4—1462no—
514C2×C4—1462no—
515C2×C4—1464no—
516C2×C4—1468no—
517C2×C4C22×C4×D7318yes—
518C2×C4C22×C4×D7314yes—
519C2×C4C22×C4×D7312yes—
520C2×C4#41×D7312yes—
521C2×C4C2×#1192402712yes—
522C2×C4C2×#1192402712yes—
523C2×C4C2×#1192402712yes—
524C2×C4#1455663914yes—
525C22—2921no—
526C22—2921no—
527C22—2922no—
528C22—1462no—
529C22—1464no—
530C22C23×C4×D7311yescharacteristic
531C22C2×#41×D7311yescharacteristic
532C22C22×#1192402711yescharacteristic
533C22C2×#1455663912yes—
534C22#1798942312yes—
535C4—22no—
536C4—28no—
537C4—24no—
538C4—44no—
539C4—42no—
540C4—2921no—
541C4—2921no—
542C4—2924no—
543C4—1464no—
544C4—1462no—
545C4—1464no—
546C4—1468no—
547C4C4×#1192402714yes—
548C4#1798919814yesdirect product factor
549C2—2922no—
550C2C2×C4×#1192402711yescharacteristic
551C2C4×#1455663912yes—
552C2C2×#1798919811yescharacteristic
553C2#2262332011yescharacteristic
554C2#2262336212yes—
subgroupG/H
centerC22×C4C23×D73
commutatorC22×C73C24×C4
FrattiniC23C24×D73
FittingC4×C4⋊Q8×C73C2
socle, cosocleC23×C73C25
prime radicalC23×D73C24
hypercenterC4×C4⋊Q8D73
hypocenterC73C4×#541
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #22612729C2semidirect
4. #22612670C2semidirect
5. #22612651C2semidirect
7. #22612576C2semidirect
9. C4×#14556583C2semidirect
10. C4×#14556581C2semidirect
13. C4×Q8×Dic73C2semidirect
15. C4×C4⋊Q8×C73C2semidirect
16. #17989198C4direct (N × H)
76. #14556583C2×C4semidirect
77. #14556581C2×C4semidirect
80. Q8×Dic73C2×C4semidirect
124. C4⋊Q8×C73C2×C4semidirect
263. C4×C73#541semidirect
286. C4×C4⋊Q8D73semidirect
293. C73C4×#541semidirect
354. C4⋊Q8C4×D73semidirect
548. C4#17989198direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891982
#226127292
#226126992
#226126702
#226126512
#226126162
#226125762
#226125392
C4×#145565832
C4×#145565812
C4×#145565862
C4×#145565672
C4×Q8×Dic732
C4×#145565482
C4×C4⋊Q8×C732
C4×#54173