Finite Group Databasebeta

← C2×#22621098 #33958013

Subgroups — C2×#22621098 #33958013

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×#17989118C211yesmaximal, characteristic
2C22×#14556582C211yesmaximal, characteristic, complemented
3#22621098C2116yesmaximal, direct product factor
4C2×#17988987C212yesmaximal, complemented
5C2×#17988940C212yesmaximal, complemented
6C2×#17988922C211yesmaximal, characteristic, complemented
7C2×#17988918C211yesmaximal, characteristic, complemented
8C2×#17988898C211yesmaximal, characteristic
9C2×#17988897C212yesmaximal, complemented
10C2×#17988889C212yesmaximal, complemented
11C2×#17988637C211yesmaximal, characteristic, complemented
12C2×#481×C73C211yesmaximal, characteristic
13#17989118—24no—
14#17989118C2218yes—
15C2×#14556584—21no—
16C2×#14556582—21no—
17C2×#14556582—21no—
18C2×#14556582—24no—
19C2×#14556582C2211yescharacteristic
20C2×#14556582C2212yes—
21C2×#14556582C2212yes—
22C2×#14556582C2218yescomplemented
23C2×#14556578C2211yescharacteristic
24C2×#14556572—21no—
25C2×#14556570C2211yescharacteristic
26C2×#14556556C2211yescharacteristic
27C2×D4×Dic73—21no—
28C2×D4×Dic73C2211yescharacteristic
29C2×#14556547—21no—
30C22×C4⋊Dic73—21no—
31C22×C4⋊Dic73C2211yescharacteristic
32C22×#11924007—21no—
33C22×C4×Dic73C2211yescharacteristic
34#17988987C22116yescomplemented
35#17988940C22116yescomplemented
36#17988922C2218yescomplemented
37#17988918C2218yescomplemented
38#17988898C2218yes—
39#17988897C22116yescomplemented
40#17988889C22116yescomplemented
41#17988637C2218yescomplemented
42C2×#14556524C2212yes—
43C2×#14556524C2212yes—
44C2×#14556523C2212yes—
45C2×#14556520C2212yes—
46C2×#14556516C2212yes—
47C2×#14556514C2212yes—
48C2×#14556512C2212yes—
49C2×C22⋊#10596831C2211yescharacteristic
50C2×C8×Dic73C2212yes—
51C2×#121×C73C2211yescharacteristic
52C22×C4⋊C4×C73C2211yescharacteristic
53#481×C73C2218yes—
54C2×#106×C73C2212yes—
55C2×#102×C73C2212yes—
56C2×C22⋊C8×C73C2211yescharacteristic
57C22×Dic146C2311yescharacteristic
58C23×Dic73—21no—
59C23×Dic73—21no—
60C23×Dic73D411yescharacteristic
61C23×Dic73D411yescharacteristic
62C22×#10596831C2312yes—
63#14556584—28no—
64#14556582—24no—
65#14556582—24no—
66#14556582—28no—
67#14556582—28no—
68#14556582—22no—
69#14556582C2318yes—
70#14556582C2318yes—
71#14556582C2314yes—
72#14556578—22no—
73#14556578C2314yes—
74#14556572—28no—
75#14556570—22no—
76#14556570C2314yes—
77#14556556—22no—
78#14556556C2314yes—
79D4×Dic73—28no—
80D4×Dic73—22no—
81D4×Dic73C2314yes—
82#14556547—28no—
83C2×C4⋊Dic73—22no—
84C2×C4⋊Dic73—22no—
85C2×C4⋊Dic73—28no—
86C2×C4⋊Dic73—21no—
87C2×C4⋊Dic73—21no—
88C2×C4⋊Dic73—22no—
89C2×C4⋊Dic73C2311yescharacteristic
90C2×C4⋊Dic73C2312yes—
91C2×C4⋊Dic73C2314yes—
92C2×#11924007—22no—
93C2×#11924007—22no—
94C2×#11924007—28no—
95C2×#11924007—21no—
96C2×#11924007—21no—
97C2×#11924007—21no—
98C2×C22⋊Dic73—21no—
99C2×C22⋊Dic73—21no—
100C2×C22⋊Dic73—21no—
101C2×C22⋊Dic73—21no—
102C2×C4×Dic73—21no—
103C2×C4×Dic73D411yescharacteristic
104C2×C4×Dic73D411yescharacteristic
105C2×C4×Dic73D414yes—
106C2×C4×Dic73C2314yes—
107C2×C4×Dic73C2311yescharacteristic
108C2×C4×Dic73C2311yescharacteristic
109#14556524C2318yes—
110#14556524C2318yes—
111#14556523C2318yes—
112#14556520C2318yes—
113#14556516C2318yes—
114#14556514C2318yes—
115#14556512C2318yes—
116C22⋊#10596831C2314yes—
117C8×Dic73C2318yes—
118C22×D4×C73—21no—
119C22×D4×C73C2311yescharacteristic
120C23×C4×C73—21no—
121C23×C4×C73C2311yescharacteristic
122C22×C8×C73C2312yes—
123#121×C73—22no—
124#121×C73C2314yes—
125C2×C4⋊C4×C73—21no—
126C2×C4⋊C4×C73—22no—
127C2×C4⋊C4×C73C2311yescharacteristic
128C2×C4⋊C4×C73C2312yes—
129C2×C4⋊C4×C73C2314yes—
130C2×C22⋊C4×C73—21no—
131#106×C73C2318yes—
132#102×C73C2318yes—
133C22⋊C8×C73C2314yes—
134C2×Dic146—24no—
135C2×Dic146—21no—
136C2×Dic146C2412yes—
137C22×Dic73—24no—
138C22×Dic73—21no—
139C22×Dic73—21no—
140C22×Dic73—24no—
141C22×Dic73—22no—
142C22×Dic73—24no—
143C22×Dic73—42no—
144C22×Dic73—44no—
145C22×Dic73—44no—
146C22×Dic73C2×D411yescharacteristic
147C22×Dic73C2×D411yescharacteristic
148C22×Dic73C2×D411yescharacteristic
149C22×Dic73C2×D411yescharacteristic
150C22×Dic73C2×D414yes—
151C22×Dic73C2×D414yes—
152C2×#10596831—24no—
153C2×#10596831C2414yes—
154C4⋊Dic73—24no—
155C4⋊Dic73—22no—
156C4⋊Dic73—21no—
157C4⋊Dic73—28no—
158C4⋊Dic73—28no—
159C4⋊Dic73—24no—
160C4⋊Dic73C2414yes—
161C4⋊Dic73C2412yes—
162#11924007—24no—
163#11924007—28no—
164#11924007—28no—
165#11924007—24no—
166#11924007—24no—
167C22⋊Dic73—24no—
168C22⋊Dic73—24no—
169C22⋊Dic73—24no—
170C22⋊Dic73—24no—
171C4×Dic73—24no—
172C4×Dic73C2×D414yes—
173C4×Dic73C2×D412yes—
174C4×Dic73C2×D412yes—
175C4×Dic73C2×D414yes—
176C4×Dic73C2412yes—
177C4×Dic73C2412yes—
178C24×C73—21no—
179C24×C73C2×D411yescharacteristic
180C2×D4×C73—24no—
181C2×D4×C73—21no—
182C2×D4×C73—24no—
183C2×D4×C73—44no—
184C2×D4×C73C2412yes—
185C22×C4×C73—24no—
186C22×C4×C73—21no—
187C22×C4×C73—24no—
188C22×C4×C73—22no—
189C22×C4×C73—44no—
190C22×C4×C73C2×D411yescharacteristic
191C22×C4×C73C2×D412yes—
192C22×C4×C73C2412yes—
193C22×C4×C73C2411yescharacteristic
194C2×C8×C73—24no—
195C2×C8×C73C2414yes—
196C4⋊C4×C73—24no—
197C4⋊C4×C73—22no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73C2414yes—
200C4⋊C4×C73C2412yes—
201C22⋊C4×C73—24no—
202C23×C73—22no—
203C23×C73—22no—
204C23×C73—22no—
205C23×C73—42no—
206C23×C73—42no—
207C23×C73—42no—
208C23×C73#13514yes—
209C23×C73C22×D412yes—
210C23×C73C22×D411yescharacteristic
211D4×C73—24no—
212D4×C73—48no—
213D4×C73—42no—
214C2×C4×C73—22no—
215C2×C4×C73—24no—
216C2×C4×C73—24no—
217C2×C4×C73—22no—
218C2×C4×C73—24no—
219C2×C4×C73—48no—
220C2×C4×C73—42no—
221C2×C4×C73—44no—
222C2×C4×C73C22×D412yes—
223C2×C4×C73C22×D411yescharacteristic
224C2×C4×C732−1+414yes—
225C2×C4×C73C2511yescharacteristic
226C2×Dic73—28no—
227C2×Dic73—22no—
228C2×Dic73—22no—
229C2×Dic73—22no—
230C2×Dic73—22no—
231C2×Dic73—22no—
232C2×Dic73—22no—
233C2×Dic73—24no—
234C2×Dic73—44no—
235C2×Dic73—48no—
236C2×Dic73—42no—
237C2×Dic73—48no—
238C2×Dic73—44no—
239C2×Dic73—42no—
240C2×Dic73C22×D412yes—
241C2×Dic73C22×D412yes—
242C2×Dic73C22×D412yes—
243C2×Dic73C22×D412yes—
244Dic146—24no—
245Dic146—42no—
246C8×C73—24no—
247#10596831—24no—
248C22×C73—22no—
249C22×C73—28no—
250C22×C73—22no—
251C22×C73—42no—
252C22×C73—42no—
253C22×C73—42no—
254C22×C73—84no—
255C22×C73#53612yes—
256C22×C73C2×#13514yes—
257C22×C73C2×#13512yes—
258C22×C73#57512yes—
259C22×C73C23×D411yescharacteristic
260C4×C73—22no—
261C4×C73—42no—
262C4×C73—44no—
263C4×C73#53612yes—
264C4×C73C2×2−1+412yes—
265Dic73—22no—
266Dic73—22no—
267Dic73—22no—
268Dic73—22no—
269Dic73—42no—
270Dic73—44no—
271Dic73—42no—
272C2×#3232—731nomaximal, Sylow
273C2×C73—24no—
274C2×C73—82no—
275C2×C73#323214yescomplemented
276C2×C73C2×#53611yescharacteristic
277C2×C73C22×#13511yescharacteristic
278C2×C73C2×#57511yescharacteristic
279C2×#529—731no—
280C22×#125—731no—
281#3232—7316no—
282C2×#499—732no—
283C2×#488—732no—
284C2×#484—731no—
285C2×#481D7311yescharacteristic
286C2×#483—731no—
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⋊Q8—731no—
305C2×#121C2×D7311yescharacteristic
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#483—738no—
319#481C2×D7318yes—
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×#103—732no—
331C2×#102—732no—
332C2×#102C2×D7312yes—
333C2×C22⋊C8—731no—
334C2×C22⋊C8C2×D7311yescharacteristic
335C2×C4×C8—732no—
336C22×Q8—731no—
337C22×D4—21no—
338C22×D4C22×D7311yescharacteristic
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—734no—
360C22⋊Q8—1462no—
361#121—22no—
362#121C22×D7314yes—
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—732no—
372C2×C4⋊C4—734no—
373C2×C4⋊C4—731no—
374C2×C4⋊C4—1468no—
375C2×C4⋊C4—1462no—
376C2×C4⋊C4—1462no—
377C2×C4⋊C4—1468no—
378C2×C4⋊C4—1462no—
379C2×C4⋊C4—1462no—
380C2×C4⋊C4—1461no—
381C2×C4⋊C4—1461no—
382C2×C4⋊C4—1461no—
383C2×C4⋊C4—1462no—
384C2×C4⋊C4—1461no—
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#103—738no—
408#102—738no—
409#102C22×D7318yes—
410C22⋊C8—734no—
411C22⋊C8C22×D7314yes—
412C4×C8—738no—
413C24—21no—
414C24D4×D7311yescharacteristic
415C2×Q8—732no—
416C2×Q8—1464no—
417C2×Q8—1461no—
418C2×D4—24no—
419C2×D4—21no—
420C2×D4—24no—
421C2×D4—44no—
422C2×D4C23×D7312yes—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—44no—
428C22×C4—2924no—
429C22×C4—2924no—
430C22×C4—2922no—
431C22×C4—734no—
432C22×C4—734no—
433C22×C4—731no—
434C22×C4—731no—
435C22×C4—731no—
436C22×C4—731no—
437C22×C4—1464no—
438C22×C4—1464no—
439C22×C4—1461no—
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—21no—
454C4⋊C4—734no—
455C4⋊C4—732no—
456C4⋊C4—1468no—
457C4⋊C4—1468no—
458C4⋊C4—1464no—
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—22no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23#1455661214yes—
488C23C2×D4×D7312yes—
489C23C2×D4×D7311yescharacteristic
490Q8—2922no—
491Q8—1464no—
492D4—24no—
493D4—48no—
494D4—42no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—48no—
501C2×C4—44no—
502C2×C4—42no—
503C2×C4—2922no—
504C2×C4—2922no—
505C2×C4—2928no—
506C2×C4—2924no—
507C2×C4—2928no—
508C2×C4—2924no—
509C2×C4—732no—
510C2×C4—732no—
511C2×C4—732no—
512C2×C4—732no—
513C2×C4—1462no—
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—42no—
531C22—42no—
532C22—42no—
533C22—84no—
534C22#1798915912yes—
535C22C2×#1455661214yes—
536C22C2×#1455661212yes—
537C22#1798938312yes—
538C22C22×D4×D7311yescharacteristic
539C4—22no—
540C4—42no—
541C4—44no—
542C4—2922no—
543C4—2924no—
544C4—2922no—
545C4—1462no—
546C4—1462no—
547C4—1462no—
548C4—1462no—
549C4#1798915912yes—
550C4C2×#1455663812yes—
551C2—24no—
552C2—82no—
553C2#2262109814yesdirect product factor
554C2C2×#1798915911yescharacteristic
555C2C22×#1455661211yescharacteristic
556C2C2×#1798938311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#481×C73C2
socleC23×C73C22×D4
prime radicalC2×#121×C73C22
hypercenterC2×#481D73
hypocenterC73C2×#3232
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
2. C22×#14556582C2semidirect
3. #22621098C2direct (N × H)
4. C2×#17988987C2semidirect
5. C2×#17988940C2semidirect
6. C2×#17988922C2semidirect
7. C2×#17988918C2semidirect
9. C2×#17988897C2semidirect
10. C2×#17988889C2semidirect
11. C2×#17988637C2semidirect
22. C2×#14556582C22semidirect
34. #17988987C22semidirect
35. #17988940C22semidirect
36. #17988922C22semidirect
37. #17988918C22semidirect
39. #17988897C22semidirect
40. #17988889C22semidirect
41. #17988637C22semidirect
275. C2×C73#3232semidirect
291. C73C2×#3232semidirect
553. C2#22621098direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891182
C22×#145565822
#226210982
C2×#179889872
C2×#179889402
C2×#179889222
C2×#179889182
C2×#179888982
C2×#179888972
C2×#179888892
C2×#179886372
C2×#481×C732
C2×#323273