Finite Group Databasebeta

← C2×#22623553 #33993082

Subgroups — C2×#22623553 #33993082

Order 18688.

7706 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623553C2132yesmaximal, direct product factor
2C2×#17989316C211yesmaximal, characteristic, complemented
3C2×#17989307C213yesmaximal, complemented
4C2×#17989276C216yesmaximal, complemented
5C2×Q8×D292C211yesmaximal, characteristic, complemented
6C2×#17989244C212yesmaximal, complemented
7C2×#17989242C213yesmaximal, complemented
8C2×#17989144C213yesmaximal, complemented
9C2×#17989119C216yesmaximal, complemented
10C2×C4×#11924028C213yesmaximal, complemented
11C2×C4×Q8×D73C212yesmaximal, complemented
12C2×C4×#41×C73C211yesmaximal, characteristic, complemented
13C22×#11924028C2213yes—
14C22×Q8×D73C2212yes—
15#17989316C22116yescomplemented
16#17989307C22148yescomplemented
17#17989276C22196yescomplemented
18Q8×D292C22116yescomplemented
19#17989244C22132yescomplemented
20#17989242C22148yescomplemented
21#17989144C22148yescomplemented
22C2×#14556591C2213yes—
23C2×#14556591C2213yes—
24#17989119C22196yescomplemented
25C2×#14556584C22112yes—
26C2×#14556583C2216yes—
27C2×#14556582C2216yes—
28C2×#14556578C2216yes—
29C2×#14556573C22112yes—
30C2×#14556571C2216yes—
31C2×#14556570C2216yes—
32C2×#14556570C2216yes—
33C2×#14556562C2216yes—
34C4×#11924028C22148yescomplemented
35C2×Q8×Dic73C2212yes—
36C2×C4×Dic146C2213yes—
37C2×C4×Dic146C2216yes—
38C2×C4×Dic146C2213yes—
39C2×#14556556C2216yes—
40C4×Q8×D73C22132yescomplemented
41C2×C4×D292C2211yescharacteristic
42C2×C4×D292C2213yes—
43C2×C4×C22⋊D73C2216yes—
44C2×C4×C22⋊D73C2216yes—
45C2×#14556550C2213yes—
46C2×#14556550C2216yes—
47C2×#14556548C2216yes—
48C2×C4⋊C4×D73C2216yes—
49C2×C42×D73C2216yes—
50C22×#41×C73C2211yescharacteristic
51C4×#41×C73C22116yescomplemented
52C2×C4×Q8×C73C2211yescharacteristic
53C2×C4×Q8×C73C2211yescharacteristic
54C2×C4×D4×C73C2213yes—
55C2×C4×D4×C73C2213yes—
56C2×#117×C73C2213yes—
57C22×C42×C73C2213yes—
58C2×#11924028—224no—
59C2×#11924028C23124yes—
60C22×Dic146C2313yes—
61C22×Dic146C2316yes—
62C2×Q8×D73—216no—
63C2×Q8×D73C23116yes—
64C22×D292C2311yescharacteristic
65C22×C22⋊D73C2316yes—
66C22×C4×D73C2316yes—
67C22×C4×D73C2316yes—
68C22×C4×D73C2312yes—
69#14556591C23124yes—
70#14556591C23124yes—
71#14556584C23196yes—
72#14556583C23148yes—
73#14556582C23148yes—
74#14556578C23148yes—
75#14556573C23196yes—
76#14556571C23148yes—
77#14556570C23148yes—
78#14556570C23148yes—
79#14556562C23148yes—
80Q8×Dic73C23116yes—
81C4×Dic146C23124yes—
82C4×Dic146C23148yes—
83C4×Dic146C23124yes—
84#14556556C23148yes—
85C4×D292C23124yes—
86C4×D292C2318yes—
87C4×C22⋊D73C23148yes—
88C4×C22⋊D73C23148yes—
89#14556550C23148yes—
90#14556550C23124yes—
91#14556548C23148yes—
92C2×C4⋊Dic73C2313yes—
93C2×C4⋊Dic73C2316yes—
94C2×C4⋊Dic73C2316yes—
95C2×C4⋊Dic73C2316yes—
96C2×C4⋊Dic73C2311yescharacteristic
97C2×#11924007C23112yes—
98C2×#11924007C2316yes—
99C2×#11924007C2316yes—
100C4⋊C4×D73C23148yes—
101C2×C22⋊Dic73C2316yes—
102C2×C22⋊Dic73C23112yes—
103C2×#11924005C2312yes—
104C2×#11924005C2316yes—
105C2×C4×Dic73C2316yes—
106C2×C4×Dic73C2316yes—
107C2×C4×Dic73C2316yes—
108C42×D73C23148yes—
109C2×#41×C73—28no—
110C2×#41×C73C2318yes—
111C22×Q8×C73C2311yescharacteristic
112C22×D4×C73C2313yes—
113C23×C4×C73C2313yes—
114C23×C4×C73C2313yes—
115C23×C4×C73C2313yes—
116C4×Q8×C73C2318yes—
117C4×Q8×C73C2318yes—
118C4×D4×C73C23124yes—
119C4×D4×C73C23124yes—
120#117×C73C23124yes—
121C2×C4⋊C4×C73C2313yes—
122C2×C4⋊C4×C73C2313yes—
123C2×C22⋊C4×C73C2316yes—
124C2×C42×C73C2313yes—
125C2×C42×C73C23124yes—
126C2×C42×C73C2311yescharacteristic
127C2×C42×C73C2313yes—
128C2×C42×C73C2313yes—
129C23×D73C2412yes—
130#11924028—296no—
131C2×Dic146—224no—
132C2×Dic146—212no—
133C2×Dic146C24124yes—
134C2×Dic146C24112yes—
135Q8×D73—264no—
136C2×D292#4118yescomplemented
137C2×D292C2414yes—
138C2×C22⋊D73—224no—
139C2×C22⋊D73C24124yes—
140C22×Dic73C2412yes—
141C22×Dic73C2416yes—
142C22×Dic73C2416yes—
143C2×C4×D73—224no—
144C2×C4×D73—224no—
145C2×C4×D73—28no—
146C2×C4×D73C2418yes—
147C2×C4×D73C24124yes—
148C2×C4×D73C24124yes—
149C4⋊Dic73C24124yes—
150C4⋊Dic73C2414yes—
151C4⋊Dic73C24112yes—
152C4⋊Dic73C24124yes—
153C4⋊Dic73C24124yes—
154#11924007C24148yes—
155#11924007C24124yes—
156#11924007C24124yes—
157C22⋊Dic73C24124yes—
158C22⋊Dic73C24148yes—
159#11924005C2418yes—
160#11924005C24124yes—
161C4×Dic73C24124yes—
162C4×Dic73C24124yes—
163C4×Dic73C24124yes—
164C24×C73C2413yes—
165#41×C73—232no—
166C2×Q8×C73#4118yescomplemented
167C2×Q8×C73C2414yes—
168C2×D4×C73—212no—
169C2×D4×C73C24112yes—
170C22×C4×C73—212no—
171C22×C4×C73—212no—
172C22×C4×C73—212no—
173C22×C4×C73C2411yescharacteristic
174C22×C4×C73C2413yes—
175C22×C4×C73C2413yes—
176C22×C4×C73C24112yes—
177C22×C4×C73C24112yes—
178C22×C4×C73C24112yes—
179C22×C4×C73C2411yescharacteristic
180C22×C4×C73C2413yes—
181C22×C4×C73C2411yescharacteristic
182C4⋊C4×C73C24112yes—
183C4⋊C4×C73C24112yes—
184C22⋊C4×C73C24124yes—
185C42×C73C2414yes—
186C42×C73C24112yes—
187C42×C73C24112yes—
188C42×C73C24112yes—
189C23×C73—26no—
190C23×C73—26no—
191C23×C73—26no—
192C23×C73C2516yes—
193C23×C73C2511yescharacteristic
194C22×D73—24no—
195C22×D73—24no—
196C22×D73C2×#4118yes—
197C22×D73C2514yes—
198Q8×C73C2×#41116yescomplemented
199D4×C73—224no—
200C2×C4×C73—22no—
201C2×C4×C73—26no—
202C2×C4×C73—26no—
203C2×C4×C73—224no—
204C2×C4×C73—224no—
205C2×C4×C73—224no—
206C2×C4×C73C2×#4114yes—
207C2×C4×C73C2×#41112yes—
208C2×C4×C732−1+414yes—
209C2×C4×C73C2512yes—
210C2×C4×C73C2516yes—
211C2×C4×C73C2516yes—
212C2×C4×C73C2512yes—
213C2×C4×C73C2516yes—
214C2×C4×C73C2512yes—
215C22⋊D73—248no—
216C2×Dic73—212no—
217C2×Dic73—212no—
218C2×Dic73—24no—
219C2×Dic73C2514yes—
220C2×Dic73C25112yes—
221C2×Dic73C25112yes—
222D292C2×#41116yescomplemented
223C4×D73—248no—
224C4×D73—248no—
225C4×D73—216no—
226Dic146—248no—
227Dic146—224no—
228C22×C73—26no—
229C22×C73—26no—
230C22×C73—26no—
231C22×C73—412no—
232C22×C73C22×#4112yes—
233C22×C73C22×#4112yes—
234C22×C73C2×2−1+412yes—
235C22×C73C2611yescharacteristic
236C2×D73—24no—
237C2×D73—24no—
238C2×D73—216no—
239C2×D73C22×#4118yes—
240C4×C73—26no—
241C4×C73—22no—
242C4×C73—26no—
243C4×C73C22×#4114yes—
244C4×C73C22×#41112yes—
245C4×C73C2×2−1+414yes—
246Dic73—212no—
247Dic73—212no—
248Dic73—24no—
249C2×#3482—731nomaximal, Sylow
250C2×C73—46no—
251C2×C73#348214yescomplemented
252C2×C73C23×#4111yescharacteristic
253C2×C73C23×#4111yescharacteristic
254C2×C73C22×2−1+411yescharacteristic
255D73—28no—
256#3482—7332no—
257C2×#557—731no—
258C2×#556—733no—
259C2×#552—736no—
260C2×D4×Q8—731no—
261C2×#548—732no—
262C2×#547—733no—
263C2×#533—733no—
264C2×#529—736no—
265C2×C4×#41—733no—
266C2×C4×#41D7311yescharacteristic, complemented
267C22×C4×Q8—732no—
268C73C2×#348211yescharacteristic, complemented, Sylow
269C22×#41—733no—
270C22×#41C2×D7311yescharacteristic
271C23×Q8—732no—
272#557—7316no—
273#556—7348no—
274#552—7396no—
275D4×Q8—7316no—
276#548—7332no—
277#547—7348no—
278#533—7348no—
279C2×C4⋊Q8—733no—
280C2×C4⋊Q8—733no—
281#529—7396no—
282C2×#126—7312no—
283C2×#125—736no—
284C2×#125—736no—
285C2×#124—736no—
286C2×#123—7312no—
287C2×C22⋊Q8—736no—
288C2×C22⋊Q8—736no—
289C2×C22⋊Q8—736no—
290C2×#121—736no—
291C4×#41—7348no—
292C4×#41C2×D73116yescomplemented
293C2×C4×Q8—732no—
294C2×C4×Q8—7332no—
295C2×C4×Q8—736no—
296C2×C4×Q8—736no—
297C2×C4×Q8—733no—
298C2×C4×Q8—733no—
299C2×C4×Q8C2×D7311yescharacteristic
300C2×C4×Q8C2×D7311yescharacteristic
301C2×C4×D4—736no—
302C2×C4×D4—736no—
303C2×C4×D4—731no—
304C2×C4×D4—733no—
305C2×C4×D4C2×D7313yes—
306C2×C4×D4C2×D7313yes—
307C2×#117—733no—
308C2×#117—736no—
309C2×#117—736no—
310C2×#117C2×D7313yes—
311C22×C4⋊C4—736no—
312C22×C42—736no—
313C22×C42C2×D7313yes—
314C2×#41—28no—
315C2×#41—7324no—
316C2×#41—14624no—
317C2×#41C22×D7318yes—
318C22×Q8—7316no—
319C22×Q8—736no—
320C22×Q8—733no—
321C22×Q8—14616no—
322C22×Q8C22×D7311yescharacteristic
323C22×D4—736no—
324C22×D4—731no—
325C22×D4C22×D7313yes—
326C23×C4—736no—
327C23×C4—736no—
328C23×C4—732no—
329C23×C4C22×D7313yes—
330C23×C4C22×D7313yes—
331C23×C4C22×D7313yes—
332C4⋊Q8—7324no—
333C4⋊Q8—7324no—
334#126—7396no—
335#125—7348no—
336#125—7348no—
337#124—7348no—
338#123—7396no—
339C22⋊Q8—7348no—
340C22⋊Q8—7348no—
341C22⋊Q8—7348no—
342#121—7348no—
343C4×Q8—7316no—
344C4×Q8—7348no—
345C4×Q8—7348no—
346C4×Q8—7324no—
347C4×Q8—7324no—
348C4×Q8C22×D7318yes—
349C4×Q8C22×D7318yes—
350C4×D4—7348no—
351C4×D4—7348no—
352C4×D4—738no—
353C4×D4—7324no—
354C4×D4C22×D73124yes—
355C4×D4C22×D73124yes—
356#117—7324no—
357#117—7348no—
358#117—7348no—
359#117C22×D73124yes—
360C2×C4⋊C4—736no—
361C2×C4⋊C4—7312no—
362C2×C4⋊C4—731no—
363C2×C4⋊C4—736no—
364C2×C4⋊C4—733no—
365C2×C4⋊C4—736no—
366C2×C4⋊C4—736no—
367C2×C4⋊C4—736no—
368C2×C4⋊C4—7348no—
369C2×C4⋊C4C22×D7313yes—
370C2×C4⋊C4C22×D7313yes—
371C2×C22⋊C4—736no—
372C2×C22⋊C4—7312no—
373C2×C22⋊C4—732no—
374C2×C22⋊C4—736no—
375C2×C22⋊C4C22×D7316yes—
376C2×C42—736no—
377C2×C42—736no—
378C2×C42—736no—
379C2×C42—7348no—
380C2×C42C22×D7313yes—
381C2×C42C22×D7313yes—
382C2×C42C22×D73124yes—
383C2×C42C22×D7311yescharacteristic
384C2×C42C22×D7313yes—
385C24—732no—
386C24C23×D7313yes—
387#41—232no—
388#41—14696no—
389C2×Q8—7324no—
390C2×Q8—7312no—
391C2×Q8—14664no—
392C2×Q8—14612no—
393C2×Q8—14624no—
394C2×Q8#1192402818yescomplemented
395C2×Q8C23×D7314yes—
396C2×D4—212no—
397C2×D4—7324no—
398C2×D4—738no—
399C2×D4—734no—
400C2×D4—14624no—
401C2×D4C23×D73112yes—
402C22×C4—212no—
403C22×C4—212no—
404C22×C4—212no—
405C22×C4—732no—
406C22×C4—736no—
407C22×C4—736no—
408C22×C4—738no—
409C22×C4—7324no—
410C22×C4—7324no—
411C22×C4—14624no—
412C22×C4—14624no—
413C22×C4—1468no—
414C22×C4C23×D7313yes—
415C22×C4C23×D7311yescharacteristic
416C22×C4C23×D7313yes—
417C22×C4C23×D73112yes—
418C22×C4C23×D73112yes—
419C22×C4C23×D73112yes—
420C22×C4C23×D7311yescharacteristic
421C22×C4C23×D7313yes—
422C22×C4C23×D7311yescharacteristic
423C4⋊C4—7348no—
424C4⋊C4—7324no—
425C4⋊C4—7324no—
426C4⋊C4—7324no—
427C4⋊C4—734no—
428C4⋊C4—7312no—
429C4⋊C4—7324no—
430C4⋊C4—7324no—
431C4⋊C4C23×D73112yes—
432C4⋊C4C23×D73112yes—
433C22⋊C4—7324no—
434C22⋊C4—7348no—
435C22⋊C4—738no—
436C22⋊C4—7324no—
437C22⋊C4C23×D73124yes—
438C42—7324no—
439C42—7324no—
440C42—7324no—
441C42C23×D73112yes—
442C42C23×D7314yes—
443C42C23×D73112yes—
444C42C23×D73112yes—
445C23—26no—
446C23—26no—
447C23—26no—
448C23—738no—
449C23—734no—
450C23—1464no—
451C23—1464no—
452C23C24×D7316yes—
453C23C24×D7311yescharacteristic
454Q8—14624no—
455Q8—14648no—
456Q8C2×#11924028116yescomplemented
457D4—224no—
458D4—7316no—
459D4—14648no—
460C2×C4—26no—
461C2×C4—22no—
462C2×C4—26no—
463C2×C4—224no—
464C2×C4—224no—
465C2×C4—224no—
466C2×C4—734no—
467C2×C4—7312no—
468C2×C4—7312no—
469C2×C4—14648no—
470C2×C4—14612no—
471C2×C4—14612no—
472C2×C4—1464no—
473C2×C4—14648no—
474C2×C4—14616no—
475C2×C4#41×D7314yes—
476C2×C4C2×#11924028112yes—
477C2×C4#1455663814yes—
478C2×C4C24×D7316yes—
479C2×C4C24×D7312yes—
480C2×C4C24×D7316yes—
481C2×C4C24×D7312yes—
482C2×C4C24×D7316yes—
483C2×C4C24×D7312yes—
484C22—26no—
485C22—26no—
486C22—26no—
487C22—412no—
488C22—738no—
489C22—14616no—
490C22—1464no—
491C22—1464no—
492C22C2×#41×D7312yes—
493C22C22×#1192402812yes—
494C22C2×#1455663812yes—
495C22C25×D7311yescharacteristic
496C4—26no—
497C4—22no—
498C4—26no—
499C4—14612no—
500C4—14612no—
501C4—1464no—
502C4C2×#41×D7314yes—
503C4C22×#11924028112yes—
504C4C2×#1455663814yes—
505C2—46no—
506C2—1468no—
507C2#2262355314yesdirect product factor
508C2C22×#41×D7311yescharacteristic
509C2C23×#1192402811yescharacteristic
510C2C22×#1455663811yescharacteristic
subgroupG/H
centerC22×C4C23×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×C4×#41×C73C2
socleC23×C73C25
hypercenterC2×C4×#41D73
hypocenterC73C2×#3482
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #22623553C2direct (N × H)
2. C2×#17989316C2semidirect
3. C2×#17989307C2semidirect
4. C2×#17989276C2semidirect
5. C2×Q8×D292C2semidirect
6. C2×#17989244C2semidirect
7. C2×#17989242C2semidirect
8. C2×#17989144C2semidirect
9. C2×#17989119C2semidirect
10. C2×C4×#11924028C2semidirect
11. C2×C4×Q8×D73C2semidirect
12. C2×C4×#41×C73C2semidirect
15. #17989316C22semidirect
16. #17989307C22semidirect
17. #17989276C22semidirect
18. Q8×D292C22semidirect
19. #17989244C22semidirect
20. #17989242C22semidirect
21. #17989144C22semidirect
24. #17989119C22semidirect
34. C4×#11924028C22semidirect
40. C4×Q8×D73C22semidirect
51. C4×#41×C73C22semidirect
136. C2×D292#41semidirect
166. C2×Q8×C73#41semidirect
198. Q8×C73C2×#41semidirect
222. D292C2×#41semidirect
251. C2×C73#3482semidirect
266. C2×C4×#41D73semidirect
268. C73C2×#3482semidirect
292. C4×#41C2×D73semidirect
394. C2×Q8#11924028semidirect
456. Q8C2×#11924028semidirect
507. C2#22623553direct (N × H)

Maximal subgroups

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

subgroupindex
#226235532
C2×#179893162
C2×#179893072
C2×#179892762
C2×Q8×D2922
C2×#179892442
C2×#179892422
C2×#179891442
C2×#179891192
C2×C4×#119240282
C2×C4×Q8×D732
C2×C4×#41×C732
C2×#348273