Finite Group Databasebeta

← C2×#22621174 #33958148

Subgroups — C2×#22621174 #33958148

Order 18688.

1790 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×#17989142C211yesmaximal, characteristic, complemented
2C2×#17989122C211yesmaximal, characteristic
3#22621174C2116yesmaximal, direct product factor
4C2×#17988997C211yesmaximal, characteristic, complemented
5C2×#17988949C211yesmaximal, characteristic, complemented
6C2×#17988947C211yesmaximal, characteristic, complemented
7C2×#17988931C212yesmaximal, complemented
8C2×#17988914C212yesmaximal
9C2×#17988893C212yesmaximal, complemented
10C2×#17988886C212yesmaximal, complemented
11C2×#17988642C211yesmaximal, characteristic, complemented
12C2×#501×C73C211yesmaximal, characteristic, complemented
13#17989142—24no—
14#17989142C2218yescomplemented
15C2×#14556591C2211yescharacteristic
16#17989122—24no—
17#17989122C2218yes—
18C2×#14556586—21no—
19C2×#14556582C2212yes—
20C2×#14556579C2211yescharacteristic
21C2×#14556576—21no—
22C2×#14556571—21no—
23C2×#14556571C2211yescharacteristic
24C2×#14556567—21no—
25C2×#14556566C2211yescharacteristic
26C2×Q8×Dic73—21no—
27C2×#14556556—21no—
28C2×#14556556C2211yescharacteristic
29C2×#14556553—21no—
30C2×#14556553C2211yescharacteristic
31C2×#14556549—21no—
32C2×#14556549C2212yes—
33C2×C42×D73C2211yescharacteristic
34#17988997C2218yescomplemented
35#17988949C2218yescomplemented
36#17988947C2218yescomplemented
37#17988931C22116yescomplemented
38#17988914C22116yes—
39#17988893C22116yescomplemented
40#17988886C22116yescomplemented
41#17988642C2218yescomplemented
42C2×#14556524C2212yes—
43C2×#14556522C2212yes—
44C2×#14556520C2212yes—
45C2×#14556516C2212yes—
46C2×#14556514C2212yes—
47C2×#14556513C2212yes—
48C2×#14556511C2212yes—
49C2×#14556503C2212yes—
50C2×#14556502C2211yescharacteristic
51C2×C4⋊Q8×C73C2211yescharacteristic
52C2×#125×C73C2211yescharacteristic
53#501×C73C2218yescomplemented
54C2×#107×C73C2212yes—
55C2×#106×C73C2212yes—
56C2×#97×C73C2211yescharacteristic
57C22×Dic146—21no—
58C22×Dic146C2311yescharacteristic
59C22×D292—21no—
60C22×D292C2311yescharacteristic
61C22×C4×D73—21no—
62C22×C4×D73D411yescharacteristic
63C22×C4×D73D411yescharacteristic
64C22×C4×D73C2311yescharacteristic
65C22×#10596831C2312yes—
66#14556591—22no—
67#14556591C2314yes—
68#14556586—28no—
69#14556582—24no—
70#14556582C2318yes—
71#14556579—22no—
72#14556579C2314yes—
73#14556576—28no—
74#14556571—22no—
75#14556571—28no—
76#14556571C2314yes—
77#14556567—28no—
78#14556566—22no—
79#14556566C2314yes—
80Q8×Dic73—28no—
81#14556556—22no—
82#14556556—28no—
83#14556556C2314yes—
84#14556553—28no—
85#14556553—22no—
86#14556553C2314yes—
87#14556549—24no—
88#14556549—28no—
89#14556549C2318yes—
90C2×C4⋊Dic73—21no—
91C2×C4⋊Dic73—22no—
92C2×C4⋊Dic73—21no—
93C2×C4⋊Dic73C2312yes—
94C2×#11924007—22no—
95C2×#11924007—21no—
96C2×#11924005—22no—
97C2×#11924005—21no—
98C2×#11924005—21no—
99C2×#11924005—21no—
100C2×#11924005—21no—
101C2×#11924005—21no—
102C2×C4×Dic73—21no—
103C2×C4×Dic73—22no—
104C2×C4×Dic73D411yescharacteristic
105C2×C4×Dic73D411yescharacteristic
106C2×C4×Dic73C2311yescharacteristic
107C42×D73D414yes—
108C42×D73C2314yes—
109#14556524C2318yes—
110#14556522C2318yes—
111#14556520C2318yes—
112#14556516C2318yes—
113#14556514C2318yes—
114#14556513C2318yes—
115#14556511C2318yes—
116#14556503C2318yes—
117#14556502C2314yes—
118C22×Q8×C73—21no—
119C22×C8×C73C2312yes—
120C4⋊Q8×C73—22no—
121C4⋊Q8×C73C2314yes—
122#125×C73—22no—
123#125×C73C2314yes—
124C2×C4⋊C4×C73—21no—
125C2×C4⋊C4×C73—21no—
126C2×C4⋊C4×C73—21no—
127C2×C4⋊C4×C73C2311yescharacteristic
128C2×C4⋊C4×C73C2311yescharacteristic
129C2×C4⋊C4×C73C2312yes—
130C2×C42×C73C2311yescharacteristic
131#107×C73C2318yes—
132#106×C73C2318yes—
133#97×C73C2314yes—
134C23×D73—21no—
135C23×D73C2×D411yescharacteristic
136C2×Dic146—24no—
137C2×Dic146—21no—
138C2×Dic146—24no—
139C2×Dic146—44no—
140C2×Dic146C2412yes—
141C2×D292—24no—
142C2×D292—24no—
143C2×D292—21no—
144C2×D292—44no—
145C2×D292C2412yes—
146C22×Dic73—21no—
147C22×Dic73—22no—
148C22×Dic73C2×D411yescharacteristic
149C22×Dic73C2×D411yescharacteristic
150C22×Dic73C2×D411yescharacteristic
151C2×C4×D73—24no—
152C2×C4×D73—24no—
153C2×C4×D73—42no—
154C2×C4×D73—42no—
155C2×C4×D73—44no—
156C2×C4×D73C2×D412yes—
157C2×C4×D73C2×D414yes—
158C2×C4×D73C2×D414yes—
159C2×C4×D73C2412yes—
160C2×#10596831—24no—
161C2×#10596831C2414yes—
162C4⋊Dic73—24no—
163C4⋊Dic73—22no—
164C4⋊Dic73—24no—
165C4⋊Dic73—28no—
166C4⋊Dic73C2414yes—
167#11924007—28no—
168#11924007—24no—
169#11924005—28no—
170#11924005—24no—
171#11924005—24no—
172#11924005—24no—
173#11924005—24no—
174#11924005—24no—
175C4×Dic73—24no—
176C4×Dic73—28no—
177C4×Dic73C2×D412yes—
178C4×Dic73C2×D414yes—
179C4×Dic73C2×D414yes—
180C4×Dic73C2412yes—
181C2×Q8×C73—24no—
182C2×Q8×C73—44no—
183C22×C4×C73—21no—
184C22×C4×C73—21no—
185C22×C4×C73—22no—
186C22×C4×C73C2×D411yescharacteristic
187C22×C4×C73C2×D411yescharacteristic
188C22×C4×C73C2411yescharacteristic
189C2×C8×C73—24no—
190C2×C8×C73C2414yes—
191C4⋊C4×C73—24no—
192C4⋊C4×C73—24no—
193C4⋊C4×C73—24no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—22no—
197C4⋊C4×C73C2412yes—
198C4⋊C4×C73C2414yes—
199C4⋊C4×C73C2412yes—
200C42×C73C2×D412yes—
201C42×C73C2412yes—
202C23×C73C22×D411yescharacteristic
203C22×D73—22no—
204C22×D73—22no—
205C22×D73—22no—
206C22×D73—22no—
207C22×D73—42no—
208C22×D73—42no—
209C22×D73—42no—
210C22×D73C22×D412yes—
211Q8×C73—48no—
212C2×C4×C73—22no—
213C2×C4×C73—22no—
214C2×C4×C73—22no—
215C2×C4×C73—22no—
216C2×C4×C73—24no—
217C2×C4×C73—44no—
218C2×C4×C73—42no—
219C2×C4×C73—42no—
220C2×C4×C73C22×D412yes—
221C2×C4×C73C22×D412yes—
222C2×C4×C73C22×D411yescharacteristic
223C2×C4×C732−1+414yes—
224C2×C4×C73C2511yescharacteristic
225C2×Dic73—22no—
226C2×Dic73—22no—
227C2×Dic73—22no—
228C2×Dic73—22no—
229C2×Dic73—24no—
230C2×Dic73—42no—
231C2×Dic73—44no—
232C2×Dic73C22×D412yes—
233C2×Dic73C22×D412yes—
234C2×Dic73C22×D412yes—
235D292—24no—
236D292—48no—
237D292—42no—
238C4×D73—24no—
239C4×D73—24no—
240C4×D73—44no—
241C4×D73—44no—
242C4×D73—48no—
243Dic146—24no—
244Dic146—48no—
245Dic146—42no—
246C8×C73—24no—
247#10596831—24no—
248C22×C73#53612yes—
249C22×C73#57512yes—
250C22×C73#57512yes—
251C22×C73C23×D411yescharacteristic
252C2×D73—22no—
253C2×D73—22no—
254C2×D73—22no—
255C2×D73—44no—
256C2×D73—42no—
257C2×D73—42no—
258C2×D73—42no—
259C2×D73—84no—
260C4×C73—22no—
261C4×C73—22no—
262C4×C73—42no—
263C4×C73—42no—
264C4×C73—44no—
265C4×C73#53612yes—
266C4×C73C2×2−1+412yes—
267Dic73—22no—
268Dic73—22no—
269Dic73—22no—
270Dic73—42no—
271Dic73—44no—
272C2×#3240—731nomaximal, Sylow
273C2×C73#324014yescomplemented
274C2×C73C2×#53611yescharacteristic
275C2×C73C2×#57511yescharacteristic
276C2×C73C2×#57511yescharacteristic
277D73—42no—
278D73—82no—
279C2×#533—731no—
280C2×#529—731no—
281#3240—7316no—
282C2×#501—731no—
283C2×#501D7311yescharacteristic, complemented
284C2×#489—731no—
285C2×#489—731no—
286C2×#485—732no—
287C2×#482—732no—
288C2×#479—732no—
289C2×#478—732no—
290C2×#432—731no—
291C73C2×#324011yescharacteristic, complemented, Sylow
292#533—738no—
293#533—1464no—
294C2×C4⋊Q8—731no—
295C2×C4⋊Q8C2×D7311yescharacteristic
296#529—738no—
297#529—1464no—
298C2×#126—1461no—
299C2×#125—732no—
300C2×#125C2×D7311yescharacteristic
301C2×#124—731no—
302C2×#123—1461no—
303C2×C22⋊Q8—731no—
304C2×C22⋊Q8—1461no—
305C2×C22⋊Q8—1461no—
306C2×#121—731no—
307C2×C4×Q8—731no—
308C2×C4×Q8—1461no—
309C2×C4×Q8—1461no—
310C2×C4×D4—731no—
311C2×C4×D4—1461no—
312C2×#117—732no—
313C2×#117—1461no—
314C22×C42—731no—
315#501—738no—
316#501C2×D7318yescomplemented
317#489—738no—
318#489—738no—
319#485—7316no—
320#482—7316no—
321#479—7316no—
322#478—7316no—
323#432—738no—
324C2×#107—732no—
325C2×#107C2×D7312yes—
326C2×#106—732no—
327C2×#106C2×D7312yes—
328C2×C4⋊C8—732no—
329C2×#103—732no—
330C2×#103—732no—
331C2×#102—732no—
332C2×#102—732no—
333C2×C22⋊C8—732no—
334C2×#97—731no—
335C2×#97C2×D7311yescharacteristic
336C22×Q8—21no—
337C22×Q8—731no—
338C22×Q8—1461no—
339C22×D4—731no—
340C22×D4—1461no—
341C23×C4—731no—
342C23×C4—731no—
343C23×C4—731no—
344C23×C4—1461no—
345C22×C8—732no—
346C22×C8C22×D7312yes—
347C4⋊Q8—22no—
348C4⋊Q8—734no—
349C4⋊Q8—1462no—
350C4⋊Q8C22×D7314yes—
351#126—1468no—
352#125—22no—
353#125—738no—
354#125—1464no—
355#125C22×D7314yes—
356#124—734no—
357#124—1462no—
358#123—1468no—
359C22⋊Q8—734no—
360C22⋊Q8—1462no—
361C22⋊Q8—1468no—
362C22⋊Q8—1468no—
363#121—734no—
364#121—1462no—
365C4×Q8—734no—
366C4×Q8—1462no—
367C4×Q8—1468no—
368C4×Q8—1468no—
369C4×D4—734no—
370C4×D4—1462no—
371C4×D4—1468no—
372#117—738no—
373#117—1468no—
374#117—1464no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—732no—
379C2×C4⋊C4—1461no—
380C2×C4⋊C4—1461no—
381C2×C4⋊C4—1462no—
382C2×C4⋊C4—1462no—
383C2×C4⋊C4—1461no—
384C2×C4⋊C4C22×D7312yes—
385C2×C4⋊C4C22×D7311yescharacteristic
386C2×C4⋊C4C22×D7311yescharacteristic
387C2×C22⋊C4—1461no—
388C2×C22⋊C4—1461no—
389C2×C22⋊C4—1462no—
390C2×C22⋊C4—1461no—
391C2×C22⋊C4—1461no—
392C2×C22⋊C4—1461no—
393C2×C42—731no—
394C2×C42—731no—
395C2×C42—731no—
396C2×C42—734no—
397C2×C42—734no—
398C2×C42—1462no—
399C2×C42—1461no—
400C2×C42C22×D7311yescharacteristic
401#107—738no—
402#107C22×D7318yes—
403#106—738no—
404#106C22×D7318yes—
405C4⋊C8—738no—
406#103—738no—
407#103—738no—
408#102—738no—
409#102—738no—
410C22⋊C8—738no—
411#97—734no—
412#97C22×D7314yes—
413C24—731no—
414C24—1461no—
415C2×Q8—24no—
416C2×Q8—44no—
417C2×Q8—2924no—
418C2×Q8—732no—
419C2×Q8—1464no—
420C2×Q8—1461no—
421C2×Q8—1464no—
422C2×D4—2924no—
423C2×D4—732no—
424C2×D4—1464no—
425C2×D4—1461no—
426C2×D4—1464no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—2922no—
431C22×C4—2922no—
432C22×C4—2924no—
433C22×C4—734no—
434C22×C4—734no—
435C22×C4—731no—
436C22×C4—731no—
437C22×C4—731no—
438C22×C4—732no—
439C22×C4—732no—
440C22×C4—1464no—
441C22×C4—1461no—
442C22×C4—1462no—
443C22×C4—1464no—
444C22×C4D4×D7311yescharacteristic
445C22×C4D4×D7311yescharacteristic
446C22×C4C23×D7311yescharacteristic
447C2×C8—24no—
448C2×C8—734no—
449C2×C8—1464no—
450C2×C8C23×D7314yes—
451C4⋊C4—24no—
452C4⋊C4—24no—
453C4⋊C4—24no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—734no—
458C4⋊C4—1464no—
459C4⋊C4—1468no—
460C4⋊C4—1464no—
461C4⋊C4—1468no—
462C4⋊C4—1462no—
463C4⋊C4—1464no—
464C4⋊C4C23×D7314yes—
465C4⋊C4C23×D7312yes—
466C4⋊C4C23×D7312yes—
467C22⋊C4—1464no—
468C22⋊C4—1464no—
469C22⋊C4—1468no—
470C22⋊C4—1464no—
471C22⋊C4—1464no—
472C22⋊C4—1464no—
473C42—734no—
474C42—732no—
475C42—734no—
476C42—732no—
477C42—1468no—
478C42—1464no—
479C42D4×D7312yes—
480C42C23×D7312yes—
481C23—2922no—
482C23—2922no—
483C23—2922no—
484C23—732no—
485C23—1462no—
486C23—1462no—
487C23—1462no—
488C23—1462no—
489C23C2×D4×D7311yescharacteristic
490Q8—48no—
491Q8—2928no—
492Q8—2922no—
493Q8—1464no—
494D4—2928no—
495D4—2922no—
496D4—1464no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—42no—
503C2×C4—44no—
504C2×C4—42no—
505C2×C4—2924no—
506C2×C4—2924no—
507C2×C4—2928no—
508C2×C4—2924no—
509C2×C4—2922no—
510C2×C4—732no—
511C2×C4—732no—
512C2×C4—732no—
513C2×C4—1462no—
514C2×C4—1464no—
515C2×C4—1462no—
516C2×C4—1462no—
517C2×C4—1462no—
518C2×C4—1464no—
519C2×C4—1464no—
520C2×C4C2×D4×D7312yes—
521C2×C4C2×D4×D7312yes—
522C2×C4C2×D4×D7311yescharacteristic
523C2×C4#1455663914yes—
524C2×C4C24×D7311yescharacteristic
525C8—24no—
526C8—1464no—
527C22—2924no—
528C22—2922no—
529C22—2922no—
530C22—2922no—
531C22—5844no—
532C22—1462no—
533C22—1462no—
534C22—1462no—
535C22#1798916212yes—
536C22#1798938312yes—
537C22#1798938612yes—
538C22C22×D4×D7311yescharacteristic
539C4—22no—
540C4—22no—
541C4—42no—
542C4—44no—
543C4—42no—
544C4—2922no—
545C4—2924no—
546C4—1462no—
547C4—1462no—
548C4—1462no—
549C4#1798916212yes—
550C4C2×#1455663912yes—
551C2—2922no—
552C2—5842no—
553C2#2262117414yesdirect product factor
554C2C2×#1798916211yescharacteristic
555C2C2×#1798938311yescharacteristic
556C2C2×#1798938611yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#501×C73C2
socleC23×C73C22×D4
prime radicalC2×#14556566C22
hypercenterC2×#501D73
hypocenterC73C2×#3240
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#17989142C2semidirect
3. #22621174C2direct (N × H)
4. C2×#17988997C2semidirect
5. C2×#17988949C2semidirect
6. C2×#17988947C2semidirect
7. C2×#17988931C2semidirect
9. C2×#17988893C2semidirect
10. C2×#17988886C2semidirect
11. C2×#17988642C2semidirect
12. C2×#501×C73C2semidirect
14. #17989142C22semidirect
34. #17988997C22semidirect
35. #17988949C22semidirect
36. #17988947C22semidirect
37. #17988931C22semidirect
39. #17988893C22semidirect
40. #17988886C22semidirect
41. #17988642C22semidirect
53. #501×C73C22semidirect
273. C2×C73#3240semidirect
283. C2×#501D73semidirect
291. C73C2×#3240semidirect
316. #501C2×D73semidirect
553. C2#22621174direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891422
C2×#179891222
#226211742
C2×#179889972
C2×#179889492
C2×#179889472
C2×#179889312
C2×#179889142
C2×#179888932
C2×#179888862
C2×#179886422
C2×#501×C732
C2×#324073