Finite Group Databasebeta

← C2×#22621102 #33958017

Subgroups — C2×#22621102 #33958017

Order 18688.

1822 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989123C211yesmaximal, characteristic
2C22×#14556582C211yesmaximal, characteristic, complemented
3#22621102C2116yesmaximal, direct product factor
4C2×#17988987C212yesmaximal, complemented
5C2×#17988943C212yesmaximal, complemented
6C2×#17988920C211yesmaximal, characteristic, complemented
7C2×#17988906C211yesmaximal, characteristic
8C2×#17988900C211yesmaximal, characteristic
9C2×#17988892C212yesmaximal, complemented
10C2×#17988886C212yesmaximal, complemented
11C2×#17988637C211yesmaximal, characteristic, complemented
12C2×#483×C73C211yesmaximal, characteristic, complemented
13#17989123—24no—
14#17989123C2218yes—
15C2×#14556586—21no—
16C2×#14556582—24no—
17C2×#14556582—21no—
18C2×#14556582—21no—
19C2×#14556582C2211yescharacteristic
20C2×#14556582C2212yes—
21C2×#14556582C2212yes—
22C2×#14556582C2218yescomplemented
23C2×#14556580C2211yescharacteristic
24C2×#14556575—21no—
25C2×#14556565C2211yescharacteristic
26C2×Q8×Dic73C2211yescharacteristic
27C2×#14556553C2211yescharacteristic
28C2×#14556551—21no—
29C2×#14556549—21no—
30C22×C4⋊Dic73—21no—
31C22×C4⋊Dic73C2211yescharacteristic
32C22×#11924007—21no—
33C22×C4×Dic73C2211yescharacteristic
34#17988987C22116yescomplemented
35#17988943C22116yescomplemented
36#17988920C2218yescomplemented
37#17988906C2218yes—
38#17988900C2218yes—
39#17988892C22116yescomplemented
40#17988886C22116yescomplemented
41#17988637C2218yescomplemented
42C2×#14556524C2212yes—
43C2×#14556524C2212yes—
44C2×#14556523C2212yes—
45C2×#14556520C2212yes—
46C2×#14556515C2212yes—
47C2×#14556513C2212yes—
48C2×#14556511C2212yes—
49C2×C22⋊#10596831C2211yescharacteristic
50C2×C8×Dic73C2212yes—
51C2×C22⋊Q8×C73C2211yescharacteristic
52C22×C4⋊C4×C73C2211yescharacteristic
53#483×C73C2218yescomplemented
54C2×#106×C73C2212yes—
55C2×#103×C73C2212yes—
56C2×C22⋊C8×C73C2211yescharacteristic
57C22×D292C2311yescharacteristic
58C22×C22⋊D73—21no—
59C23×Dic73—21no—
60C23×Dic73D411yescharacteristic
61C23×Dic73D411yescharacteristic
62C22×C4×D73—21no—
63C22×#10596831C2312yes—
64#14556586—28no—
65#14556582—22no—
66#14556582—24no—
67#14556582—24no—
68#14556582—28no—
69#14556582—28no—
70#14556582C2314yes—
71#14556582C2318yes—
72#14556582C2318yes—
73#14556580—22no—
74#14556580C2314yes—
75#14556575—28no—
76#14556565—22no—
77#14556565C2314yes—
78Q8×Dic73—22no—
79Q8×Dic73C2314yes—
80#14556553—22no—
81#14556553C2314yes—
82#14556551—28no—
83#14556549—28no—
84C2×C4⋊Dic73—22no—
85C2×C4⋊Dic73—22no—
86C2×C4⋊Dic73—28no—
87C2×C4⋊Dic73—21no—
88C2×C4⋊Dic73—21no—
89C2×C4⋊Dic73—21no—
90C2×C4⋊Dic73—22no—
91C2×C4⋊Dic73C2311yescharacteristic
92C2×C4⋊Dic73C2312yes—
93C2×C4⋊Dic73C2314yes—
94C2×#11924007—22no—
95C2×#11924007—22no—
96C2×#11924007—28no—
97C2×#11924007—21no—
98C2×#11924005—21no—
99C2×#11924005—21no—
100C2×#11924005—21no—
101C2×#11924005—21no—
102C2×C4×Dic73—21no—
103C2×C4×Dic73D414yes—
104C2×C4×Dic73D411yescharacteristic
105C2×C4×Dic73D411yescharacteristic
106C2×C4×Dic73C2314yes—
107C2×C4×Dic73C2311yescharacteristic
108C2×C4×Dic73C2311yescharacteristic
109#14556524C2318yes—
110#14556524C2318yes—
111#14556523C2318yes—
112#14556520C2318yes—
113#14556515C2318yes—
114#14556513C2318yes—
115#14556511C2318yes—
116C22⋊#10596831C2314yes—
117C8×Dic73C2318yes—
118C22×Q8×C73C2311yescharacteristic
119C23×C4×C73—21no—
120C23×C4×C73C2311yescharacteristic
121C22×C8×C73C2312yes—
122C22⋊Q8×C73—22no—
123C22⋊Q8×C73C2314yes—
124C2×C4⋊C4×C73—21no—
125C2×C4⋊C4×C73—22no—
126C2×C4⋊C4×C73—21no—
127C2×C4⋊C4×C73C2311yescharacteristic
128C2×C4⋊C4×C73C2312yes—
129C2×C4⋊C4×C73C2314yes—
130C2×C22⋊C4×C73—21no—
131#106×C73C2318yes—
132#103×C73C2318yes—
133C22⋊C8×C73C2314yes—
134C23×D73—21no—
135C2×D292—24no—
136C2×D292—21no—
137C2×D292C2412yes—
138C2×C22⋊D73—24no—
139C2×C22⋊D73—44no—
140C22×Dic73—24no—
141C22×Dic73—21no—
142C22×Dic73—24no—
143C22×Dic73—22no—
144C22×Dic73—42no—
145C22×Dic73—44no—
146C22×Dic73C2×D411yescharacteristic
147C22×Dic73C2×D411yescharacteristic
148C22×Dic73C2×D411yescharacteristic
149C22×Dic73C2×D411yescharacteristic
150C22×Dic73C2×D414yes—
151C22×Dic73C2×D414yes—
152C2×C4×D73—24no—
153C2×C4×D73—44no—
154C2×#10596831—24no—
155C2×#10596831C2414yes—
156C4⋊Dic73—24no—
157C4⋊Dic73—22no—
158C4⋊Dic73—21no—
159C4⋊Dic73—28no—
160C4⋊Dic73—28no—
161C4⋊Dic73—24no—
162C4⋊Dic73—24no—
163C4⋊Dic73C2414yes—
164C4⋊Dic73C2412yes—
165#11924007—28no—
166#11924007—28no—
167#11924007—24no—
168#11924005—24no—
169#11924005—24no—
170#11924005—24no—
171#11924005—24no—
172C4×Dic73—24no—
173C4×Dic73C2×D414yes—
174C4×Dic73C2×D412yes—
175C4×Dic73C2×D412yes—
176C4×Dic73C2×D414yes—
177C4×Dic73C2412yes—
178C4×Dic73C2412yes—
179C24×C73C2×D411yescharacteristic
180C2×Q8×C73—21no—
181C2×Q8×C73—24no—
182C2×Q8×C73C2412yes—
183C22×C4×C73—24no—
184C22×C4×C73—21no—
185C22×C4×C73—21no—
186C22×C4×C73—24no—
187C22×C4×C73—22no—
188C22×C4×C73—44no—
189C22×C4×C73C2×D411yescharacteristic
190C22×C4×C73C2×D412yes—
191C22×C4×C73C2412yes—
192C22×C4×C73C2411yescharacteristic
193C2×C8×C73—24no—
194C2×C8×C73C2414yes—
195C4⋊C4×C73—24no—
196C4⋊C4×C73—22no—
197C4⋊C4×C73—24no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73C2414yes—
200C4⋊C4×C73C2412yes—
201C22⋊C4×C73—24no—
202C23×C73—22no—
203C23×C73—22no—
204C23×C73#13514yes—
205C23×C73C22×D412yes—
206C23×C73C22×D411yescharacteristic
207C22×D73—22no—
208C22×D73—42no—
209C22×D73—42no—
210C22×D73—42no—
211Q8×C73—24no—
212Q8×C73—42no—
213C2×C4×C73—22no—
214C2×C4×C73—24no—
215C2×C4×C73—24no—
216C2×C4×C73—22no—
217C2×C4×C73—22no—
218C2×C4×C73—24no—
219C2×C4×C73—42no—
220C2×C4×C73—48no—
221C2×C4×C73—44no—
222C2×C4×C73—42no—
223C2×C4×C73C22×D412yes—
224C2×C4×C73C22×D411yescharacteristic
225C2×C4×C732−1+414yes—
226C2×C4×C73C2511yescharacteristic
227C22⋊D73—48no—
228C2×Dic73—28no—
229C2×Dic73—22no—
230C2×Dic73—22no—
231C2×Dic73—22no—
232C2×Dic73—22no—
233C2×Dic73—22no—
234C2×Dic73—24no—
235C2×Dic73—44no—
236C2×Dic73—48no—
237C2×Dic73—42no—
238C2×Dic73—44no—
239C2×Dic73C22×D412yes—
240C2×Dic73C22×D412yes—
241C2×Dic73C22×D412yes—
242C2×Dic73C22×D412yes—
243D292—24no—
244D292—42no—
245C4×D73—48no—
246C8×C73—24no—
247#10596831—24no—
248C22×C73—22no—
249C22×C73—28no—
250C22×C73—22no—
251C22×C73#53612yes—
252C22×C73C2×#13514yes—
253C22×C73C2×#13512yes—
254C22×C73#57512yes—
255C22×C73C23×D411yescharacteristic
256C2×D73—42no—
257C2×D73—42no—
258C2×D73—42no—
259C2×D73—84no—
260C4×C73—22no—
261C4×C73—42no—
262C4×C73—44no—
263C4×C73—42no—
264C4×C73#53612yes—
265C4×C73C2×2−1+412yes—
266Dic73—22no—
267Dic73—22no—
268Dic73—22no—
269Dic73—22no—
270Dic73—42no—
271Dic73—44no—
272C2×#3232—731nomaximal, Sylow
273C2×C73—24no—
274C2×C73#323214yescomplemented
275C2×C73C2×#53611yescharacteristic
276C2×C73C22×#13511yescharacteristic
277C2×C73C2×#57511yescharacteristic
278D73—82no—
279C2×#529—731no—
280C22×#125—731no—
281#3232—7316no—
282C2×#499—732no—
283C2×#488—732no—
284C2×#484—731no—
285C2×#481—731no—
286C2×#483D7311yescharacteristic, complemented
287C2×#480—731no—
288C2×#479—732no—
289C2×#478—732no—
290C2×#431—731no—
291C73C2×#323211yescharacteristic, complemented, Sylow
292#529—738no—
293#529—1464no—
294C2×#126—1461no—
295C2×#125—732no—
296C2×#125—732no—
297C2×#125—731no—
298C2×#125—738no—
299C2×#125—1461no—
300C2×#125—1461no—
301C2×#125—1464no—
302C2×#124—731no—
303C2×#123—1461no—
304C2×C22⋊Q8C2×D7311yescharacteristic
305C2×#121—731no—
306C2×C4×Q8—731no—
307C2×C4×D4—731no—
308C2×C4×D4—1461no—
309C2×#117—1461no—
310C22×C4⋊C4—731no—
311C22×C4⋊C4—1461no—
312C22×C4⋊C4—1461no—
313C22×C4⋊C4C2×D7311yescharacteristic
314C22×C42—731no—
315#499—7316no—
316#488—7316no—
317#484—738no—
318#483C2×D7318yescomplemented
319#481—738no—
320#480—738no—
321#479—7316no—
322#478—7316no—
323#431—738no—
324C2×#107—732no—
325C2×#107—732no—
326C2×#106—732no—
327C2×#106C2×D7312yes—
328C2×C4⋊C8—732no—
329C2×#103—732no—
330C2×#103C2×D7312yes—
331C2×#102—732no—
332C2×#102—732no—
333C2×C22⋊C8—731no—
334C2×C22⋊C8C2×D7311yescharacteristic
335C2×C4×C8—732no—
336C22×Q8C22×D7311yescharacteristic
337C22×D4—731no—
338C22×D4—1461no—
339C23×C4—21no—
340C23×C4—731no—
341C23×C4—731no—
342C23×C4—1461no—
343C23×C4—1461no—
344C23×C4C22×D7311yescharacteristic
345C22×C8—732no—
346C22×C8C22×D7312yes—
347#126—1468no—
348#125—738no—
349#125—738no—
350#125—734no—
351#125—1468no—
352#125—1464no—
353#125—1464no—
354#125—1468no—
355#125—1462no—
356#124—734no—
357#124—1462no—
358#123—1468no—
359C22⋊Q8—22no—
360C22⋊Q8C22×D7314yes—
361#121—734no—
362#121—1462no—
363C4×Q8—734no—
364C4×Q8—1462no—
365C4×D4—734no—
366C4×D4—1462no—
367C4×D4—1468no—
368#117—1468no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—732no—
373C2×C4⋊C4—734no—
374C2×C4⋊C4—731no—
375C2×C4⋊C4—1468no—
376C2×C4⋊C4—1462no—
377C2×C4⋊C4—1462no—
378C2×C4⋊C4—1468no—
379C2×C4⋊C4—1462no—
380C2×C4⋊C4—1462no—
381C2×C4⋊C4—1461no—
382C2×C4⋊C4—1461no—
383C2×C4⋊C4—1461no—
384C2×C4⋊C4—1462no—
385C2×C4⋊C4—1461no—
386C2×C4⋊C4C22×D7312yes—
387C2×C4⋊C4C22×D7314yes—
388C2×C4⋊C4C22×D7311yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—1461no—
391C2×C22⋊C4—1461no—
392C2×C22⋊C4—1461no—
393C2×C22⋊C4—1461no—
394C2×C42—731no—
395C2×C42—731no—
396C2×C42—734no—
397C2×C42—731no—
398C2×C42—731no—
399C2×C42—734no—
400C2×C42—1461no—
401#107—738no—
402#107—738no—
403#106—738no—
404#106C22×D7318yes—
405C4⋊C8—738no—
406#103—738no—
407#103C22×D7318yes—
408#102—738no—
409#102—738no—
410C22⋊C8—734no—
411C22⋊C8C22×D7314yes—
412C4×C8—738no—
413C24—1461no—
414C24D4×D7311yescharacteristic
415C2×Q8—21no—
416C2×Q8—24no—
417C2×Q8C23×D7312yes—
418C2×D4—2924no—
419C2×D4—732no—
420C2×D4—1464no—
421C2×D4—1461no—
422C2×D4—1464no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—44no—
429C22×C4—2924no—
430C22×C4—2924no—
431C22×C4—2922no—
432C22×C4—734no—
433C22×C4—734no—
434C22×C4—731no—
435C22×C4—731no—
436C22×C4—731no—
437C22×C4—731no—
438C22×C4—1464no—
439C22×C4—1464no—
440C22×C4—1461no—
441C22×C4—1462no—
442C22×C4—1464no—
443C22×C4D4×D7312yes—
444C22×C4D4×D7311yescharacteristic
445C22×C4C23×D7312yes—
446C22×C4C23×D7311yescharacteristic
447C2×C8—24no—
448C2×C8—734no—
449C2×C8—1464no—
450C2×C8C23×D7314yes—
451C4⋊C4—24no—
452C4⋊C4—22no—
453C4⋊C4—24no—
454C4⋊C4—21no—
455C4⋊C4—734no—
456C4⋊C4—732no—
457C4⋊C4—1468no—
458C4⋊C4—1468no—
459C4⋊C4—1464no—
460C4⋊C4—1468no—
461C4⋊C4—1468no—
462C4⋊C4—1464no—
463C4⋊C4—1464no—
464C4⋊C4—1464no—
465C4⋊C4—1462no—
466C4⋊C4—1461no—
467C4⋊C4C23×D7314yes—
468C4⋊C4C23×D7312yes—
469C22⋊C4—24no—
470C22⋊C4—1464no—
471C22⋊C4—1464no—
472C22⋊C4—1464no—
473C22⋊C4—1464no—
474C42—734no—
475C42—732no—
476C42—732no—
477C42—734no—
478C42—732no—
479C42—732no—
480C42—1464no—
481C23—22no—
482C23—22no—
483C23—2922no—
484C23—2922no—
485C23—2922no—
486C23—1462no—
487C23#1455661214yes—
488C23C2×D4×D7312yes—
489C23C2×D4×D7311yescharacteristic
490Q8—24no—
491Q8—42no—
492D4—2928no—
493D4—2922no—
494D4—1464no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—48no—
504C2×C4—44no—
505C2×C4—2928no—
506C2×C4—2928no—
507C2×C4—2924no—
508C2×C4—2922no—
509C2×C4—2924no—
510C2×C4—732no—
511C2×C4—732no—
512C2×C4—732no—
513C2×C4—732no—
514C2×C4—1462no—
515C2×C4—1464no—
516C2×C4—1462no—
517C2×C4—1462no—
518C2×C4—1468no—
519C2×C4—1462no—
520C2×C4—1462no—
521C2×C4C2×D4×D7312yes—
522C2×C4C2×D4×D7311yescharacteristic
523C2×C4#1455663814yes—
524C2×C4C24×D7311yescharacteristic
525C8—24no—
526C8—1464no—
527C22—22no—
528C22—22no—
529C22—28no—
530C22—2922no—
531C22—2922no—
532C22—2922no—
533C22—5844no—
534C22#1798915912yes—
535C22C2×#1455661214yes—
536C22C2×#1455661212yes—
537C22#1798938612yes—
538C22C22×D4×D7311yescharacteristic
539C4—22no—
540C4—42no—
541C4—44no—
542C4—42no—
543C4—2922no—
544C4—2924no—
545C4—1462no—
546C4—1462no—
547C4—1462no—
548C4—1462no—
549C4#1798915912yes—
550C4C2×#1455663812yes—
551C2—24no—
552C2—5842no—
553C2#2262110214yesdirect product factor
554C2C2×#1798915911yescharacteristic
555C2C22×#1455661211yescharacteristic
556C2C2×#1798938611yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#483×C73C2
socleC23×C73C22×D4
prime radicalC2×#14556565C22
hypercenterC2×#483D73
hypocenterC73C2×#3232
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
2. C22×#14556582C2semidirect
3. #22621102C2direct (N × H)
4. C2×#17988987C2semidirect
5. C2×#17988943C2semidirect
6. C2×#17988920C2semidirect
9. C2×#17988892C2semidirect
10. C2×#17988886C2semidirect
11. C2×#17988637C2semidirect
12. C2×#483×C73C2semidirect
22. C2×#14556582C22semidirect
34. #17988987C22semidirect
35. #17988943C22semidirect
36. #17988920C22semidirect
39. #17988892C22semidirect
40. #17988886C22semidirect
41. #17988637C22semidirect
53. #483×C73C22semidirect
274. C2×C73#3232semidirect
286. C2×#483D73semidirect
291. C73C2×#3232semidirect
318. #483C2×D73semidirect
553. C2#22621102direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891232
C22×#145565822
#226211022
C2×#179889872
C2×#179889432
C2×#179889202
C2×#179889062
C2×#179889002
C2×#179888922
C2×#179888862
C2×#179886372
C2×#483×C732
C2×#323273