Finite Group Databasebeta

← C2×#22611909 #33239931

Subgroups — C2×#22611909 #33239931

Order 18688.

1078 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989027C211yesmaximal, characteristic, complemented
2C22×#14556537C211yesmaximal, characteristic, complemented
3C2×#17988862C211yesmaximal, characteristic, complemented
4#22611909C218yesmaximal, direct product factor
5C2×#17988403C211yesmaximal, characteristic, complemented
6C2×#17988394C211yesmaximal, characteristic, complemented
7C2×#17988371C211yesmaximal, characteristic, complemented
8C2×#578×C73C211yesmaximal, characteristic
9C2×#14556621—21no—
10C22×Dic292C2211yescharacteristic
11#17989027—22no—
12#17989027C2214yescomplemented
13C2×#14556537—22no—
14C2×#14556537—22no—
15C2×#14556537—21no—
16C2×#14556537C2214yescomplemented
17C2×#14556535—21no—
18C2×#14556531C2211yescharacteristic
19C22×#11924003C2211yescharacteristic
20#17988862—22no—
21#17988862C2214yescomplemented
22C2×#14556527C2211yescharacteristic
23C2×#14556509—21no—
24#17988403C2214yescomplemented
25#17988394C2214yescomplemented
26#17988371C2214yescomplemented
27C2×2−1+4×C73—21no—
28#578×C73—22no—
29#578×C73—22no—
30#578×C73—22no—
31#578×C73C2214yes—
32C2×#137×C73—22no—
33C2×#137×C73—21no—
34C2×#135×C73—21no—
35C2×#135×C73C2211yescharacteristic
36C22×Q16×C73—21no—
37C22×Q16×C73C2211yescharacteristic
38C2×#131×C73C2211yescharacteristic
39C22×Dic146—21no—
40#14556621—24no—
41#14556621—42no—
42C2×Dic292—21no—
43C2×Dic292—21no—
44C2×Dic292—21no—
45C2×Dic292—21no—
46C2×Dic292—21no—
47C2×Dic292C2312yes—
48C2×#11924018—41no—
49C2×#11924016—41no—
50C2×#11924012—21no—
51#14556537—28no—
52#14556537—24no—
53#14556535—24no—
54#14556531—21no—
55#14556531C2312yes—
56C2×#11924003—21no—
57C2×#11924003—21no—
58C2×#11924003—21no—
59C2×#11924003C2312yes—
60#14556527—21no—
61#14556527C2312yes—
62#14556509—24no—
632−1+4×C73—24no—
642−1+4×C73—24no—
652−1+4×C73—42no—
662−1+4×C73—42no—
67C2×#41×C73—22no—
68C2×#41×C73—21no—
69C2×#41×C73—42no—
70C2×#41×C73—41no—
71C2×#41×C73D411yescharacteristic
72C22×Q8×C73—22no—
73C22×Q8×C73—21no—
74C22×Q8×C73—41no—
75#137×C73—24no—
76#137×C73—28no—
77#137×C73—28no—
78#137×C73—24no—
79#135×C73—24no—
80#135×C73—24no—
81#135×C73—21no—
82#135×C73—21no—
83#135×C73D412yes—
84#135×C73C2312yes—
85C2×Q16×C73—22no—
86C2×Q16×C73—24no—
87C2×Q16×C73—24no—
88C2×Q16×C73—21no—
89C2×Q16×C73—21no—
90C2×Q16×C73—21no—
91C2×Q16×C73D411yescharacteristic
92C2×Q16×C73D412yes—
93C2×Q16×C73D412yes—
94C2×Q16×C73C2312yes—
95C2×SD16×C73—22no—
96C2×SD16×C73—21no—
97C2×D8×C73D411yescharacteristic
98#131×C73—21no—
99#131×C73—21no—
100#131×C73D412yes—
101#131×C73C2312yes—
102C2×M16×C73—21no—
103C2×M16×C73D411yescharacteristic
104C22×C8×C73—21no—
105C22×C8×C73C2311yescharacteristic
106C2×Dic146—22no—
107C2×Dic146—41no—
108C2×Dic146—41no—
109C2×Dic146—41no—
110C2×Dic146—41no—
111C2×Dic146—41no—
112C22×Dic73—41no—
113Dic292—22no—
114Dic292—22no—
115Dic292—41no—
116Dic292—41no—
117#11924018—44no—
118#11924016—44no—
119#11924012—22no—
120#11924012—41no—
121C2×#10596831—41no—
122#11924003—22no—
123#11924003—22no—
124#41×C73—21no—
125#41×C73—21no—
126#41×C73—28no—
127#41×C73—22no—
128#41×C73—22no—
129#41×C73—44no—
130#41×C73—48no—
131#41×C73—48no—
132#41×C73—44no—
133#41×C73—44no—
134#41×C73—41no—
135#41×C73—41no—
136#41×C73D812yes—
137#41×C73C2×D412yes—
138C2×Q8×C73—28no—
139C2×Q8×C73—22no—
140C2×Q8×C73—21no—
141C2×Q8×C73—22no—
142C2×Q8×C73—22no—
143C2×Q8×C73—42no—
144C2×Q8×C73—44no—
145C2×Q8×C73—44no—
146C2×Q8×C73—44no—
147C2×Q8×C73—41no—
148C2×Q8×C73—41no—
149C2×Q8×C73—41no—
150C2×Q8×C73D811yescharacteristic
151C2×D4×C73—21no—
152C2×D4×C73—21no—
153C2×D4×C73—42no—
154C2×D4×C73—41no—
155C2×D4×C73D811yescharacteristic
156C22×C4×C73—21no—
157C22×C4×C73—42no—
158C22×C4×C73—42no—
159C22×C4×C73—41no—
160C22×C4×C73—41no—
161C22×C4×C73C2×D411yescharacteristic
162Q16×C73—28no—
163Q16×C73—21no—
164Q16×C73—22no—
165Q16×C73—22no—
166Q16×C73—22no—
167Q16×C73C2×D412yes—
168Q16×C73C2×D414yes—
169SD16×C73—28no—
170SD16×C73—22no—
171SD16×C73—22no—
172D8×C73—21no—
173D8×C73C2×D412yes—
174M16×C73—21no—
175M16×C73—22no—
176M16×C73—22no—
177M16×C73C2×D412yes—
178C2×C8×C73—21no—
179C2×C8×C73—22no—
180C2×C8×C73—22no—
181C2×C8×C73C2×D411yescharacteristic
182C2×C8×C73C2×D411yescharacteristic
183C2×C8×C73C2×D411yescharacteristic
184C2×C8×C73C2×D411yescharacteristic
185C2×C8×C73C2×D411yescharacteristic
186C2×C8×C73C2411yescharacteristic
187C23×C73—21no—
188C23×C73—41no—
189C23×C73AGL(1,ℤ/8)11yescharacteristic
190Q8×C73—21no—
191Q8×C73—24no—
192Q8×C73—22no—
193Q8×C73—48no—
194Q8×C73—42no—
195Q8×C73—41no—
196Q8×C73—42no—
197Q8×C73—42no—
198Q8×C73C2×D812yes—
199D4×C73—22no—
200D4×C73—22no—
201D4×C73—22no—
202D4×C73—21no—
203D4×C73—48no—
204D4×C73—42no—
205D4×C73—42no—
206D4×C73—41no—
207D4×C73C2×D812yes—
208C2×C4×C73—21no—
209C2×C4×C73—22no—
210C2×C4×C73—22no—
211C2×C4×C73—48no—
212C2×C4×C73—48no—
213C2×C4×C73—42no—
214C2×C4×C73—42no—
215C2×C4×C73—41no—
216C2×C4×C73—42no—
217C2×C4×C73—42no—
218C2×C4×C73—42no—
219C2×C4×C73#12011yescharacteristic
220C2×C4×C73#12011yescharacteristic
221C2×C4×C73C2×D811yescharacteristic
222C2×C4×C73C2×D811yescharacteristic
223C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
224C2×C4×C73C22×D411yescharacteristic
225C2×Dic73—42no—
226C2×Dic73—81no—
227C2×Dic73—81no—
228Dic146—42no—
229Dic146—42no—
230Dic146—81no—
231Dic146—81no—
232C8×C73—22no—
233C8×C73#12011yescharacteristic
234C8×C73#12011yescharacteristic
235C8×C73C22×D411yescharacteristic
236C8×C73C22×D411yescharacteristic
237#10596831—42no—
238C22×C73—22no—
239C22×C73—22no—
240C22×C73—42no—
241C22×C73—42no—
242C22×C73—82no—
243C22×C73#44711yescharacteristic
244C22×C73#44711yescharacteristic
245C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
246C4×C73—22no—
247C4×C73—44no—
248C4×C73—42no—
249C4×C73#44711yescharacteristic
250C4×C73#44711yescharacteristic
251C4×C73C2×#12011yescharacteristic
252C4×C73C22×D811yescharacteristic
253Dic73—82no—
254C2×#2195—731nomaximal, Sylow
255C2×C73—21no—
256C2×C73—21no—
257C2×C73—42no—
258C2×C73—82no—
259C2×C73#219512yescomplemented
260C2×C73C2×#44711yescharacteristic
261C2×#578D7311yescharacteristic
262C2×#510—731no—
263C22×Q32—731no—
264C2×#473—731no—
265#2195—738no—
266C2×#362—731no—
267C2×#359—731no—
268C2×#350—731no—
269C73C2×#219511yescharacteristic, complemented, Sylow
270C2×2−1+4—21no—
271#578—22no—
272#578—22no—
273#578—22no—
274#578C2×D7314yes—
275C2×#137—22no—
276C2×#137—21no—
277C2×#137—1461no—
278C2×#135—21no—
279C2×#135C2×D7311yescharacteristic
280C22×Q16—21no—
281C22×Q16—731no—
282C22×Q16C2×D7311yescharacteristic
283C2×#131C2×D7311yescharacteristic
284#510—734no—
285#510—1462no—
286C2×Q32—734no—
287C2×Q32—1462no—
288C2×Q32—1462no—
289C2×Q32—1461no—
290C2×SD32—1461no—
291C2×M32—731no—
292C22×C16—731no—
293#473—734no—
294#473—1462no—
295C2×#108—731no—
296C2×#101—1461no—
297#362—734no—
298#359—734no—
299#350—734no—
3002−1+4—24no—
3012−1+4—24no—
3022−1+4—42no—
3032−1+4—42no—
304C2×#41—22no—
305C2×#41—21no—
306C2×#41—42no—
307C2×#41—41no—
308C2×#41C22⋊D7311yescharacteristic
309C22×Q8—22no—
310C22×Q8—21no—
311C22×Q8—41no—
312C22×Q8—1461no—
313#137—24no—
314#137—28no—
315#137—28no—
316#137—24no—
317#137—2922no—
318#137—1464no—
319#135—24no—
320#135—24no—
321#135—21no—
322#135—21no—
323#135C22⋊D7312yes—
324#135C22×D7312yes—
325C2×Q16—22no—
326C2×Q16—24no—
327C2×Q16—24no—
328C2×Q16—21no—
329C2×Q16—21no—
330C2×Q16—21no—
331C2×Q16—2921no—
332C2×Q16—732no—
333C2×Q16—1461no—
334C2×Q16—1461no—
335C2×Q16—1461no—
336C2×Q16—1461no—
337C2×Q16—1461no—
338C2×Q16C22⋊D7311yescharacteristic
339C2×Q16C22⋊D7312yes—
340C2×Q16C22⋊D7312yes—
341C2×Q16C22×D7312yes—
342C2×SD16—22no—
343C2×SD16—21no—
344C2×SD16—2921no—
345C2×D8C22⋊D7311yescharacteristic
346#131—21no—
347#131—21no—
348#131C22⋊D7312yes—
349#131C22×D7312yes—
350C2×M16—21no—
351C2×M16—1461no—
352C2×M16C22⋊D7311yescharacteristic
353C22×C8—21no—
354C22×C8C22×D7311yescharacteristic
355Q32—1468no—
356Q32—1464no—
357SD32—1464no—
358M32—732no—
359M32—1461no—
360C2×C16—732no—
361C2×C16—1461no—
362C2×C16—1461no—
363C2×C16—1461no—
364#108—732no—
365#108—1461no—
366#101—1464no—
367#41—21no—
368#41—21no—
369#41—28no—
370#41—22no—
371#41—22no—
372#41—44no—
373#41—48no—
374#41—48no—
375#41—44no—
376#41—44no—
377#41—41no—
378#41—41no—
379#41#1192401312yes—
380#41C2×C22⋊D7312yes—
381C2×Q8—28no—
382C2×Q8—22no—
383C2×Q8—21no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—42no—
387C2×Q8—44no—
388C2×Q8—44no—
389C2×Q8—44no—
390C2×Q8—41no—
391C2×Q8—41no—
392C2×Q8—41no—
393C2×Q8—2921no—
394C2×Q8—2921no—
395C2×Q8—2921no—
396C2×Q8—2921no—
397C2×Q8—2921no—
398C2×Q8—1462no—
399C2×Q8#1192401311yescharacteristic
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—42no—
403C2×D4—41no—
404C2×D4#1192401311yescharacteristic
405C22×C4—21no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—2921no—
411C22×C4C2×C22⋊D7311yescharacteristic
412Q16—28no—
413Q16—21no—
414Q16—22no—
415Q16—22no—
416Q16—22no—
417Q16—2924no—
418Q16—2921no—
419Q16—2921no—
420Q16—1462no—
421Q16—1462no—
422Q16C2×C22⋊D7312yes—
423Q16C2×C22⋊D7314yes—
424SD16—28no—
425SD16—22no—
426SD16—22no—
427SD16—2924no—
428D8—21no—
429D8C2×C22⋊D7312yes—
430M16—21no—
431M16—22no—
432M16—22no—
433M16—2921no—
434M16—1462no—
435M16C2×C22⋊D7312yes—
436C2×C8—21no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—2921no—
440C2×C8C2×C22⋊D7311yescharacteristic
441C2×C8C2×C22⋊D7311yescharacteristic
442C2×C8C2×C22⋊D7311yescharacteristic
443C2×C8C2×C22⋊D7311yescharacteristic
444C2×C8C2×C22⋊D7311yescharacteristic
445C2×C8C23×D7311yescharacteristic
446C16—1462no—
447C16—1462no—
448C23—21no—
449C23—41no—
450C23#1455661711yescharacteristic
451Q8—21no—
452Q8—24no—
453Q8—22no—
454Q8—48no—
455Q8—41no—
456Q8—42no—
457Q8—42no—
458Q8—42no—
459Q8—2922no—
460Q8—2922no—
461Q8—5841no—
462Q8—5841no—
463Q8C2×#1192401312yes—
464D4—22no—
465D4—22no—
466D4—21no—
467D4—22no—
468D4—48no—
469D4—42no—
470D4—42no—
471D4—41no—
472D4C2×#1192401312yes—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—48no—
477C2×C4—48no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—2922no—
485C2×C4—5841no—
486C2×C4—5841no—
487C2×C4#1455656011yescharacteristic
488C2×C4#1455656011yescharacteristic
489C2×C4C2×#1192401311yescharacteristic
490C2×C4C2×#1192401311yescharacteristic
491C2×C4#1455661711yescharacteristic
492C2×C4C22×C22⋊D7311yescharacteristic
493C8—22no—
494C8—2922no—
495C8#1455656011yescharacteristic
496C8#1455656011yescharacteristic
497C8C22×C22⋊D7311yescharacteristic
498C8C22×C22⋊D7311yescharacteristic
499C22—22no—
500C22—22no—
501C22—42no—
502C22—42no—
503C22—82no—
504C22#1798872111yescharacteristic
505C22#1798872111yescharacteristic
506C22C2×#1455661711yescharacteristic
507C4—22no—
508C4—44no—
509C4—42no—
510C4—5842no—
511C4#1798872111yescharacteristic
512C4#1798872111yescharacteristic
513C4C2×#1455656011yescharacteristic
514C4C22×#1192401311yescharacteristic
515C2—21no—
516C2—21no—
517C2—42no—
518C2—82no—
519C2#2261190912yesdirect product factor
520C2C2×#1798872111yescharacteristic
subgroupG/H
centerC22#17988721
commutator, cosocleC2×C8×C73C24
FrattiniC2×C8C23×D73
Fitting, prime radicalC2×#578×C73C2
socleC22×C73#447
hypercenterC2×#578D73
hypocenterC73C2×#2195
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#578

Complements

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

NH ≅ G/Ntype
1. C2×#17989027C2semidirect
2. C22×#14556537C2semidirect
3. C2×#17988862C2semidirect
4. #22611909C2direct (N × H)
5. C2×#17988403C2semidirect
6. C2×#17988394C2semidirect
7. C2×#17988371C2semidirect
12. #17989027C22semidirect
16. C2×#14556537C22semidirect
21. #17988862C22semidirect
24. #17988403C22semidirect
25. #17988394C22semidirect
26. #17988371C22semidirect
259. C2×C73#2195semidirect
269. C73C2×#2195semidirect
519. C2#22611909direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179890272
C22×#145565372
C2×#179888622
#226119092
C2×#179884032
C2×#179883942
C2×#179883712
C2×#578×C732
C2×#219573