Finite Group Databasebeta

← C2×#22623949 #33994250

Subgroups — C2×#22623949 #33994250

Order 18688.

7118 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623949C2132yesmaximal, direct product factor
2C2×#17989311C216yesmaximal, complemented
3C2×#17989310C213yesmaximal, complemented
4C2×#17989303C213yesmaximal, complemented
5C2×Q8×D292C211yesmaximal, characteristic, complemented
6C2×#17989249C212yesmaximal, complemented
7C2×#17989211C216yesmaximal, complemented
8C2×#17989142C213yesmaximal, complemented
9C2×#17989124C213yesmaximal, complemented
10C2×#17989063C212yesmaximal, complemented
11C2×C4×#11924029C211yesmaximal, characteristic, complemented
12C2×Q82×C73C211yesmaximal, characteristic, complemented
13C22×#11924029C2211yescharacteristic
14C22×Q8×D73C2212yes—
15#17989311C22196yescomplemented
16#17989310C22148yescomplemented
17#17989303C22148yescomplemented
18Q8×D292C22116yescomplemented
19#17989249C22132yescomplemented
20#17989211C22196yescomplemented
21#17989142C22148yescomplemented
22C2×#14556591C2213yes—
23#17989124C22148yescomplemented
24C2×#14556586C22112yes—
25C2×#14556586C2216yes—
26C2×#14556582C2213yes—
27C2×#14556580C22112yes—
28C2×#14556580C2211yescharacteristic
29C2×#14556579C2216yes—
30C2×#14556576C2216yes—
31C2×#14556571C2216yes—
32C2×#14556571C2216yes—
33C2×#14556567C2216yes—
34C2×#14556567C2213yes—
35C2×#14556566C2216yes—
36C2×#14556566C2213yes—
37#17989063C22132yescomplemented
38C4×#11924029C22116yescomplemented
39C2×Q8×Dic73C2211yescharacteristic
40C2×Q8×Dic73C2216yes—
41C2×C4×Dic146C2216yes—
42C2×#14556556C2216yes—
43C2×C4×D292C2213yes—
44C2×C4×D292C2216yes—
45C2×C4×D292C2213yes—
46C2×#14556553C2213yes—
47C2×#14556549C2213yes—
48C2×#14556549C2216yes—
49C2×#14556549C2216yes—
50C2×#14556548C2216yes—
51C2×C42×D73C2213yes—
52Q82×C73C22116yescomplemented
53C2×C4⋊Q8×C73C2216yes—
54C2×C4⋊Q8×C73C2213yes—
55C2×C4×Q8×C73C2211yescharacteristic
56C2×C4×Q8×C73C2212yes—
57C2×C4×Q8×C73C2213yes—
58C2×#11924029—28no—
59C2×#11924029C2318yes—
60C22×Dic146C2316yes—
61C2×Q8×D73—216no—
62C2×Q8×D73C23116yes—
63C22×D292C2313yes—
64C22×D292C2311yescharacteristic
65C22×D292C2316yes—
66C22×C4×D73C2316yes—
67C22×C4×D73C2313yes—
68C22×C4×D73C2313yes—
69C22×C4×D73C2313yes—
70#14556591C23124yes—
71#14556586C23148yes—
72#14556586C23196yes—
73#14556582C23124yes—
74#14556580C2318yes—
75#14556580C23196yes—
76#14556579C23148yes—
77#14556576C23148yes—
78#14556571C23148yes—
79#14556571C23148yes—
80#14556567C23124yes—
81#14556567C23148yes—
82#14556566C23124yes—
83#14556566C23148yes—
84Q8×Dic73C23148yes—
85Q8×Dic73C2318yes—
86C4×Dic146C23148yes—
87#14556556C23148yes—
88C4×D292C23148yes—
89C4×D292C23124yes—
90C4×D292C23124yes—
91#14556553C23124yes—
92#14556549C23148yes—
93#14556549C23148yes—
94#14556549C23124yes—
95#14556548C23148yes—
96C2×C4⋊Dic73C2313yes—
97C2×C4⋊Dic73C2316yes—
98C2×C4⋊Dic73C2313yes—
99C2×C4⋊Dic73C2316yes—
100C2×#11924007C2316yes—
101C2×#11924007C2316yes—
102C2×#11924005C2312yes—
103C2×#11924005C2316yes—
104C2×#11924005C2316yes—
105C2×#11924005C23112yes—
106C2×#11924005C2312yes—
107C2×#11924005C2316yes—
108C2×#11924005C2316yes—
109C2×C4×Dic73C2311yescharacteristic
110C2×C4×Dic73C2313yes—
111C2×C4×Dic73C2313yes—
112C2×C4×Dic73C23112yes—
113C42×D73C23124yes—
114C22×Q8×C73C2311yescharacteristic
115C22×Q8×C73C2316yes—
116C22×Q8×C73C2311yescharacteristic
117C4⋊Q8×C73C23124yes—
118C4⋊Q8×C73C23148yes—
119C4×Q8×C73C23124yes—
120C4×Q8×C73C23116yes—
121C4×Q8×C73C2318yes—
122C2×C4⋊C4×C73C2313yes—
123C2×C4⋊C4×C73C2313yes—
124C2×C4⋊C4×C73C2316yes—
125C2×C4⋊C4×C73C2316yes—
126C2×C42×C73C2313yes—
127C2×C42×C73C2316yes—
128C23×D73C2412yes—
129C23×D73C2413yes—
130#11924029—232no—
131C2×Dic146—224no—
132C2×Dic146C24124yes—
133Q8×D73—264no—
134C2×D292—212no—
135C2×D292—24no—
136C2×D292—412no—
137C2×D292C24112yes—
138C2×D292C2414yes—
139C2×D292C24124yes—
140C22×Dic73C2413yes—
141C22×Dic73C2411yescharacteristic
142C22×Dic73C2411yescharacteristic
143C22×Dic73C2416yes—
144C2×C4×D73—224no—
145C2×C4×D73—212no—
146C2×C4×D73—212no—
147C2×C4×D73—46no—
148C2×C4×D73C24112yes—
149C2×C4×D73C24112yes—
150C2×C4×D73C24124yes—
151C2×C4×D73C24112yes—
152C4⋊Dic73C24112yes—
153C4⋊Dic73C24112yes—
154C4⋊Dic73C24124yes—
155C4⋊Dic73C24124yes—
156#11924007C24124yes—
157#11924007C24124yes—
158#11924005C2418yes—
159#11924005C24124yes—
160#11924005C24124yes—
161#11924005C24148yes—
162#11924005C2418yes—
163#11924005C24124yes—
164#11924005C24124yes—
165C4×Dic73C2414yes—
166C4×Dic73C24112yes—
167C4×Dic73C24112yes—
168C4×Dic73C24148yes—
169C2×Q8×C73—24no—
170C2×Q8×C73—412no—
171C2×Q8×C73#4118yes—
172C2×Q8×C73C2414yes—
173C2×Q8×C73C24124yes—
174C2×Q8×C73C2414yes—
175C22×C4×C73C2412yes—
176C22×C4×C73C2416yes—
177C22×C4×C73C2413yes—
178C22×C4×C73C2413yes—
179C22×C4×C73C2411yescharacteristic
180C4⋊C4×C73C24112yes—
181C4⋊C4×C73C24112yes—
182C4⋊C4×C73C24124yes—
183C4⋊C4×C73C24124yes—
184C42×C73C24112yes—
185C42×C73C24124yes—
186C23×C73C2511yescharacteristic
187C22×D73—24no—
188C22×D73—26no—
189C22×D73—26no—
190C22×D73—24no—
191C22×D73—26no—
192C22×D73—24no—
193C22×D73C2514yes—
194C22×D73C2516yes—
195Q8×C73—28no—
196Q8×C73—424no—
197Q8×C73C2×#41116yes—
198C2×C4×C73—24no—
199C2×C4×C73—26no—
200C2×C4×C73—212no—
201C2×C4×C73C2×#41112yes—
202C2×C4×C732−1+414yes—
203C2×C4×C73C2514yes—
204C2×C4×C73C25112yes—
205C2×C4×C73C2516yes—
206C2×C4×C73C2516yes—
207C2×C4×C73C2512yes—
208C2×Dic73—22no—
209C2×Dic73—212no—
210C2×Dic73—26no—
211C2×Dic73—22no—
212C2×Dic73C2516yes—
213C2×Dic73C2512yes—
214C2×Dic73C2512yes—
215C2×Dic73C25112yes—
216D292—224no—
217D292—28no—
218D292—424no—
219C4×D73—248no—
220C4×D73—224no—
221C4×D73—224no—
222C4×D73—412no—
223Dic146—248no—
224C22×C73C22×#4112yes—
225C22×C73C2×2−1+412yes—
226C22×C73#58512yes—
227C22×C73C2611yescharacteristic
228C2×D73—24no—
229C2×D73—26no—
230C2×D73—26no—
231C2×D73—24no—
232C2×D73—26no—
233C2×D73—24no—
234C2×D73—48no—
235C2×D73—412no—
236C4×C73—24no—
237C4×C73—26no—
238C4×C73—212no—
239C4×C73C22×#41112yes—
240C4×C73C2×2−1+414yes—
241Dic73—212no—
242Dic73—22no—
243Dic73—26no—
244Dic73—22no—
245C2×#3518—731nomaximal, Sylow
246C2×C73#351814yescomplemented
247C2×C73C23×#4111yescharacteristic
248C2×C73C22×2−1+411yescharacteristic
249C2×C73C2×#58511yescharacteristic
250D73—44no—
251D73—46no—
252#3518—7332no—
253C2×Q82D7311yescharacteristic, complemented
254C2×#556—736no—
255C2×#556—733no—
256C2×#555—733no—
257C2×D4×Q8—731no—
258C2×#548—732no—
259C2×#542—736no—
260C2×#533—733no—
261C2×#529—733no—
262C2×#519—732no—
263C2×C4×#41—731no—
264C73C2×#351811yescharacteristic, complemented, Sylow
265C22×#41—731no—
266C23×Q8—732no—
267Q82C2×D73116yescomplemented
268#556—7396no—
269#556—7348no—
270#555—7348no—
271D4×Q8—7316no—
272#548—7332no—
273#542—7396no—
274#533—7348no—
275C2×C4⋊Q8—733no—
276C2×C4⋊Q8C2×D7313yes—
277C2×C4⋊Q8C2×D7316yes—
278#529—7348no—
279C2×#126—736no—
280C2×#126—7312no—
281C2×#125—733no—
282C2×#124—731no—
283C2×#124—7312no—
284C2×#124—736no—
285C2×#123—736no—
286C2×C22⋊Q8—733no—
287C2×C22⋊Q8—736no—
288C2×C22⋊Q8—736no—
289C2×C22⋊Q8—736no—
290C2×#121—733no—
291C2×#121—736no—
292#519—7332no—
293C4×#41—7316no—
294C2×C4×Q8—731no—
295C2×C4×Q8—736no—
296C2×C4×Q8—736no—
297C2×C4×Q8—736no—
298C2×C4×Q8C2×D7311yescharacteristic
299C2×C4×Q8C2×D7312yes—
300C2×C4×Q8C2×D7313yes—
301C2×C4×D4—733no—
302C2×C4×D4—733no—
303C2×C4×D4—736no—
304C2×C4×D4—733no—
305C2×#117—733no—
306C2×#117—736no—
307C2×#117—736no—
308C2×#117—736no—
309C22×C42—733no—
310C2×#41—738no—
311C2×#41—1468no—
312C22×Q8—7316no—
313C22×Q8—736no—
314C22×Q8—14616no—
315C22×Q8C22×D7311yescharacteristic
316C22×Q8C22×D7316yes—
317C22×Q8C22×D7311yescharacteristic
318C22×D4—736no—
319C22×D4—731no—
320C22×D4—733no—
321C23×C4—733no—
322C23×C4—736no—
323C23×C4—733no—
324C23×C4—733no—
325C4⋊Q8—7324no—
326C4⋊Q8C22×D73124yes—
327C4⋊Q8C22×D73148yes—
328#126—7348no—
329#126—7396no—
330#125—7324no—
331#124—738no—
332#124—7396no—
333#124—7348no—
334#123—7348no—
335C22⋊Q8—7324no—
336C22⋊Q8—7348no—
337C22⋊Q8—7348no—
338C22⋊Q8—7348no—
339#121—7324no—
340#121—7348no—
341C4×Q8—738no—
342C4×Q8—7348no—
343C4×Q8—7348no—
344C4×Q8—7348no—
345C4×Q8C22×D7318yes—
346C4×Q8C22×D73116yes—
347C4×Q8C22×D73124yes—
348C4×D4—7324no—
349C4×D4—7324no—
350C4×D4—7348no—
351C4×D4—7324no—
352#117—7324no—
353#117—7348no—
354#117—7348no—
355#117—7348no—
356C2×C4⋊C4—733no—
357C2×C4⋊C4—733no—
358C2×C4⋊C4—736no—
359C2×C4⋊C4—736no—
360C2×C4⋊C4—736no—
361C2×C4⋊C4—736no—
362C2×C4⋊C4C22×D7313yes—
363C2×C4⋊C4C22×D7313yes—
364C2×C4⋊C4C22×D7316yes—
365C2×C4⋊C4C22×D7316yes—
366C2×C22⋊C4—736no—
367C2×C22⋊C4—732no—
368C2×C22⋊C4—736no—
369C2×C22⋊C4—7312no—
370C2×C22⋊C4—732no—
371C2×C22⋊C4—736no—
372C2×C22⋊C4—736no—
373C2×C42—733no—
374C2×C42—7312no—
375C2×C42—733no—
376C2×C42—731no—
377C2×C42—7324no—
378C2×C42C22×D7316yes—
379C2×C42C22×D7313yes—
380C24—732no—
381C24—733no—
382#41—14632no—
383C2×Q8—24no—
384C2×Q8—412no—
385C2×Q8—7324no—
386C2×Q8—14664no—
387C2×Q8—14624no—
388C2×Q8#1192402918yes—
389C2×Q8C23×D7314yes—
390C2×Q8C23×D73124yes—
391C2×Q8C23×D7314yes—
392C2×D4—29212no—
393C2×D4—7324no—
394C2×D4—734no—
395C2×D4—7312no—
396C2×D4—14612no—
397C2×D4—1464no—
398C22×C4—2926no—
399C22×C4—7312no—
400C22×C4—733no—
401C22×C4—731no—
402C22×C4—731no—
403C22×C4—736no—
404C22×C4—7312no—
405C22×C4—7312no—
406C22×C4—7324no—
407C22×C4—14624no—
408C22×C4—14612no—
409C22×C4—14612no—
410C22×C4C23×D7316yes—
411C22×C4C23×D7313yes—
412C22×C4C23×D7312yes—
413C22×C4C23×D7313yes—
414C22×C4C23×D7311yescharacteristic
415C4⋊C4—7324no—
416C4⋊C4—7324no—
417C4⋊C4—7312no—
418C4⋊C4—7312no—
419C4⋊C4—7324no—
420C4⋊C4—7324no—
421C4⋊C4C23×D73112yes—
422C4⋊C4C23×D73112yes—
423C4⋊C4C23×D73124yes—
424C4⋊C4C23×D73124yes—
425C22⋊C4—7324no—
426C22⋊C4—738no—
427C22⋊C4—7324no—
428C22⋊C4—7348no—
429C22⋊C4—738no—
430C22⋊C4—7324no—
431C22⋊C4—7324no—
432C42—734no—
433C42—7312no—
434C42—7312no—
435C42—7348no—
436C42C23×D73112yes—
437C42C23×D73124yes—
438C23—734no—
439C23—736no—
440C23—1464no—
441C23—1466no—
442C23—1466no—
443C23—1464no—
444C23—1466no—
445C23—1464no—
446C23C24×D7311yescharacteristic
447Q8—28no—
448Q8—424no—
449Q8—14648no—
450Q8C2×#11924029116yes—
451D4—29224no—
452D4—14624no—
453D4—1468no—
454C2×C4—24no—
455C2×C4—26no—
456C2×C4—212no—
457C2×C4—29212no—
458C2×C4—736no—
459C2×C4—732no—
460C2×C4—732no—
461C2×C4—7312no—
462C2×C4—1462no—
463C2×C4—14612no—
464C2×C4—1466no—
465C2×C4—1462no—
466C2×C4—14648no—
467C2×C4—14624no—
468C2×C4—14624no—
469C2×C4C2×#11924029112yes—
470C2×C4#1455663914yes—
471C2×C4C24×D73112yes—
472C2×C4C24×D7316yes—
473C2×C4C24×D7314yes—
474C2×C4C24×D7316yes—
475C2×C4C24×D7312yes—
476C22—2928no—
477C22—29212no—
478C22—1464no—
479C22—1466no—
480C22—1466no—
481C22—1464no—
482C22—1466no—
483C22—1464no—
484C22C22×#1192402912yes—
485C22C2×#1455663912yes—
486C22#1798942212yes—
487C22C25×D7311yescharacteristic
488C4—24no—
489C4—26no—
490C4—212no—
491C4—1462no—
492C4—14612no—
493C4—1466no—
494C4—1462no—
495C4C22×#11924029112yes—
496C4C2×#1455663914yes—
497C2—2924no—
498C2—2926no—
499C2#2262394914yesdirect product factor
500C2C23×#1192402911yescharacteristic
501C2C22×#1455663911yescharacteristic
502C2C2×#1798942211yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×Q82×C73C2
socleC23×C73C25
hypercenterC2×Q82D73
hypocenterC73C2×#3518
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×Q82

Complements

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

NH ≅ G/Ntype
1. #22623949C2direct (N × H)
2. C2×#17989311C2semidirect
3. C2×#17989310C2semidirect
4. C2×#17989303C2semidirect
5. C2×Q8×D292C2semidirect
6. C2×#17989249C2semidirect
7. C2×#17989211C2semidirect
8. C2×#17989142C2semidirect
9. C2×#17989124C2semidirect
10. C2×#17989063C2semidirect
11. C2×C4×#11924029C2semidirect
12. C2×Q82×C73C2semidirect
15. #17989311C22semidirect
16. #17989310C22semidirect
17. #17989303C22semidirect
18. Q8×D292C22semidirect
19. #17989249C22semidirect
20. #17989211C22semidirect
21. #17989142C22semidirect
23. #17989124C22semidirect
37. #17989063C22semidirect
38. C4×#11924029C22semidirect
52. Q82×C73C22semidirect
246. C2×C73#3518semidirect
253. C2×Q82D73semidirect
264. C73C2×#3518semidirect
267. Q82C2×D73semidirect
499. C2#22623949direct (N × H)

Maximal subgroups

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

subgroupindex
#226239492
C2×#179893112
C2×#179893102
C2×#179893032
C2×Q8×D2922
C2×#179892492
C2×#179892112
C2×#179891422
C2×#179891242
C2×#179890632
C2×C4×#119240292
C2×Q82×C732
C2×#351873