Finite Group Databasebeta

← C2×#22622845 #33966477

Subgroups — C2×#22622845 #33966477

Order 18688.

1854 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989317C211yesmaximal, characteristic, complemented
2C2×#17989294C211yesmaximal, characteristic
3#22622845C2116yesmaximal, direct product factor
4C2×#17988994C212yesmaximal, complemented
5C2×#17988990C211yesmaximal, characteristic, complemented
6C2×#17988897C212yesmaximal, complemented
7C2×#17988883C211yesmaximal, characteristic, complemented
8C2×#17988865C212yesmaximal
9C2×#17988714C211yesmaximal, characteristic, complemented
10C2×#17988684C212yesmaximal
11C2×C4×#11924016C211yesmaximal, characteristic
12C2×#476×C73C211yesmaximal, characteristic
13C22×#11924016C2211yescharacteristic
14#17989317—24no—
15#17989317C2218yescomplemented
16#17989294—24no—
17#17989294C2218yes—
18C2×#14556591C2211yescharacteristic
19C2×#14556590—21no—
20C2×#14556590C2212yes—
21C2×#14556589—22no—
22C2×#14556582C2212yes—
23C2×#14556570—21no—
24C2×#14556568—22no—
25C2×C4×Dic146C2211yescharacteristic
26C2×C4×Dic146C2211yescharacteristic
27C2×#14556556—21no—
28C2×#14556556C2212yes—
29C2×D4×Dic73C2212yes—
30C22×C4⋊Dic73—21no—
31#17988994C22116yescomplemented
32#17988990C2218yescomplemented
33#17988897C22116yescomplemented
34#17988883C2218yescomplemented
35#17988865C22116yes—
36#17988714C2218yescomplemented
37#17988684C22116yes—
38C4×#11924016C2218yes—
39C2×#14556525C2212yes—
40C2×#14556524C2212yes—
41C2×#14556524C2212yes—
42C2×#14556522C2211yescharacteristic
43C2×#14556520C2212yes—
44C2×#14556516C2212yes—
45C2×#14556514C2211yescharacteristic
46C2×#14556512C2211yescharacteristic
47C2×#14556501C2212yes—
48C2×C4×#10596831C2211yescharacteristic
49C2×C4⋊Q8×C73C2211yescharacteristic
50C2×C4×D4×C73C2211yescharacteristic
51#476×C73C2218yes—
52C2×#106×C73C2212yes—
53C2×C4⋊C8×C73C2211yescharacteristic
54C2×#102×C73C2212yes—
55C22×Dic146—22no—
56C22×Dic146—21no—
57C22×Dic146D411yescharacteristic
58C22×Dic146C2311yescharacteristic
59C23×Dic73—22no—
60C2×#11924016Q818yescomplemented
61C2×#11924016C2314yes—
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64#14556591—22no—
65#14556591C2314yes—
66#14556590—28no—
67#14556590—24no—
68#14556590C2318yes—
69#14556589—216no—
70#14556582—24no—
71#14556582C2318yes—
72#14556570—28no—
73#14556568—216no—
74C4×Dic146—22no—
75C4×Dic146D414yes—
76C4×Dic146C2314yes—
77C4×Dic146C2314yes—
78#14556556—28no—
79#14556556—24no—
80#14556556C2318yes—
81D4×Dic73—24no—
82D4×Dic73C2318yes—
83C2×C4⋊Dic73—22no—
84C2×C4⋊Dic73—28no—
85C2×C4⋊Dic73—21no—
86C2×C4⋊Dic73D411yescharacteristic
87C2×C4⋊Dic73C2311yescharacteristic
88C2×C4⋊Dic73C2312yes—
89C2×#11924007—22no—
90C2×#11924007—22no—
91C2×#11924007—22no—
92C2×#11924007—21no—
93C2×#11924007D412yes—
94C2×C22⋊Dic73—22no—
95C2×C4×Dic73—22no—
96C2×C4×Dic73—21no—
97C2×C4×Dic73C2312yes—
98#14556525C2318yes—
99#14556524C2318yes—
100#14556524C2318yes—
101#14556522C2314yes—
102#14556520C2318yes—
103#14556516C2318yes—
104#14556514C2314yes—
105#14556512C2314yes—
106#14556501C2318yes—
107C4×#10596831C2314yes—
108C22×Q8×C73—21no—
109C22×D4×C73C2311yescharacteristic
110C23×C4×C73—21no—
111C22×C8×C73C2312yes—
112C4⋊Q8×C73—22no—
113C4⋊Q8×C73C2314yes—
114C4×D4×C73—22no—
115C4×D4×C73C2314yes—
116C2×C4⋊C4×C73—21no—
117C2×C4⋊C4×C73C2311yescharacteristic
118C2×C4⋊C4×C73C2312yes—
119C2×C22⋊C4×C73—21no—
120C2×C42×C73C2311yescharacteristic
121#106×C73C2318yes—
122C4⋊C8×C73C2314yes—
123#102×C73C2318yes—
124C2×Dic146—24no—
125C2×Dic146—21no—
126C2×Dic146—22no—
127C2×Dic146—24no—
128C2×Dic146—28no—
129C2×Dic146—84no—
130C2×Dic146—82no—
131C2×Dic146C2×D414yes—
132C2×Dic146C2×Q814yes—
133C2×Dic146C2412yes—
134C22×Dic73—21no—
135C22×Dic73—21no—
136C22×Dic73—22no—
137C22×Dic73—28no—
138C22×Dic73—84no—
139C22×Dic73C2×D412yes—
140C22×Dic73C2×D412yes—
141#11924016C2×Q8116yescomplemented
142C2×#10596831—22no—
143C2×#10596831C2×Q814yes—
144C2×#10596831C2412yes—
145C2×#10596831C2412yes—
146C4⋊Dic73—24no—
147C4⋊Dic73—22no—
148C4⋊Dic73—21no—
149C4⋊Dic73—28no—
150C4⋊Dic73C2×D414yes—
151C4⋊Dic73C2412yes—
152C4⋊Dic73C2414yes—
153#11924007—24no—
154#11924007—28no—
155#11924007—28no—
156#11924007—28no—
157#11924007C2×D418yes—
158C22⋊Dic73—28no—
159C4×Dic73—24no—
160C4×Dic73—28no—
161C4×Dic73C2×D414yes—
162C4×Dic73C2414yes—
163C24×C73—21no—
164C2×Q8×C73—24no—
165C2×Q8×C73—82no—
166C2×D4×C73—21no—
167C2×D4×C73—22no—
168C2×D4×C73C2×Q814yes—
169C2×D4×C73C2412yes—
170C22×C4×C73—21no—
171C22×C4×C73—22no—
172C22×C4×C73—24no—
173C22×C4×C73—44no—
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2411yescharacteristic
177C2×C8×C73—24no—
178C2×C8×C73C2414yes—
179C4⋊C4×C73—24no—
180C4⋊C4×C73—21no—
181C4⋊C4×C73—22no—
182C4⋊C4×C73C2414yes—
183C4⋊C4×C73C2412yes—
184C22⋊C4×C73—24no—
185C42×C73C2×D412yes—
186C42×C73C2412yes—
187C23×C73—24no—
188C23×C73—22no—
189C23×C73—42no—
190C23×C73—42no—
191C23×C73C22×D411yescharacteristic
192Q8×C73—84no—
193D4×C73—24no—
194D4×C73—22no—
195D4×C73C22×Q814yes—
196C2×C4×C73—22no—
197C2×C4×C73—22no—
198C2×C4×C73—24no—
199C2×C4×C73—42no—
200C2×C4×C73—44no—
201C2×C4×C73—48no—
202C2×C4×C73#13714yes—
203C2×C4×C73C22×D412yes—
204C2×C4×C73C22×D411yescharacteristic
205C2×C4×C73C22×D412yes—
206C2×C4×C73C22×Q812yes—
207C2×C4×C732−1+412yes—
208C2×C4×C73C2511yescharacteristic
209C2×Dic73—24no—
210C2×Dic73—24no—
211C2×Dic73—24no—
212C2×Dic73—22no—
213C2×Dic73—22no—
214C2×Dic73—24no—
215C2×Dic73—44no—
216C2×Dic73—42no—
217C2×Dic73—88no—
218C2×Dic73C22×D414yes—
219C2×Dic73C22×D414yes—
220Dic146—24no—
221Dic146—28no—
222Dic146—22no—
223Dic146—88no—
224Dic146—84no—
225Dic146C22×Q814yes—
226C8×C73—24no—
227#10596831—22no—
228#10596831C22×Q814yes—
229C22×C73—24no—
230C22×C73—48no—
231C22×C73—42no—
232C22×C73—42no—
233C22×C73D4×Q812yes—
234C22×C73C2×#13712yes—
235C22×C73#57612yes—
236C22×C73C23×D411yescharacteristic
237C4×C73—22no—
238C4×C73—42no—
239C4×C73—44no—
240C4×C73D4×Q812yes—
241C4×C73C2×#13714yes—
242C4×C73C23×Q811yescharacteristic
243C4×C73C2×2−1+411yescharacteristic
244Dic73—24no—
245Dic73—24no—
246Dic73—24no—
247Dic73—42no—
248Dic73—44no—
249C2×#3385—731nomaximal, Sylow
250C2×C73—44no—
251C2×C73#338514yescomplemented
252C2×C73C2×D4×Q811yescharacteristic
253C2×C73C22×#13711yescharacteristic
254C2×C73C2×#57611yescharacteristic
255C2×Q82—731no—
256C2×#554—731no—
257#3385—7316no—
258C2×#501—732no—
259C2×#500—731no—
260C2×#479—732no—
261C2×#477—731no—
262C2×#476D7311yescharacteristic
263C2×#474—732no—
264C2×#446—731no—
265C2×#440—732no—
266C2×C4×SD16—731no—
267C73C2×#338511yescharacteristic, complemented, Sylow
268C22×SD16—731no—
269Q82—738no—
270Q82—1464no—
271#554—738no—
272#554—1464no—
273C2×C4⋊Q8—732no—
274C2×C4⋊Q8—731no—
275C2×C4⋊Q8—1461no—
276C2×C4⋊Q8—1462no—
277C2×C4⋊Q8C2×D7311yescharacteristic
278C2×#125—732no—
279C2×C22⋊Q8—1462no—
280C2×C22⋊Q8—1461no—
281C2×C4×Q8—731no—
282C2×C4×Q8—732no—
283C2×C4×Q8—731no—
284C2×C4×Q8—1461no—
285C2×C4×D4—732no—
286C2×C4×D4C2×D7311yescharacteristic
287C22×C4⋊C4—1461no—
288#501—7316no—
289#500—738no—
290#479—7316no—
291#477—738no—
292#476C2×D7318yes—
293#474—7316no—
294#446—738no—
295#440—7316no—
296C4×SD16—738no—
297C2×#107—732no—
298C2×#107—732no—
299C2×#107—732no—
300C2×#106—731no—
301C2×#106C2×D7312yes—
302C2×C4⋊C8—732no—
303C2×C4⋊C8C2×D7311yescharacteristic
304C2×#103—732no—
305C2×#103—731no—
306C2×#102—731no—
307C2×#102C2×D7312yes—
308C2×#97—732no—
309C2×C4×C8—731no—
310C22×Q8—21no—
311C22×Q8—731no—
312C22×Q8—731no—
313C22×Q8—1462no—
314C22×Q8—1461no—
315C22×D4C22×D7311yescharacteristic
316C23×C4—21no—
317C23×C4—1462no—
318C2×SD16—738no—
319C2×SD16—734no—
320C22×C8—731no—
321C22×C8—731no—
322C22×C8C22×D7312yes—
323C4⋊Q8—22no—
324C4⋊Q8—738no—
325C4⋊Q8—734no—
326C4⋊Q8—1464no—
327C4⋊Q8—1468no—
328C4⋊Q8—14616no—
329C4⋊Q8—1462no—
330C4⋊Q8C22×D7314yes—
331#125—738no—
332#125—1464no—
333C22⋊Q8—14616no—
334C22⋊Q8—1468no—
335C4×Q8—734no—
336C4×Q8—734no—
337C4×Q8—738no—
338C4×Q8—734no—
339C4×Q8—1464no—
340C4×Q8—1468no—
341C4×Q8—1462no—
342C4×D4—22no—
343C4×D4—738no—
344C4×D4—1464no—
345C4×D4C22×D7314yes—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—731no—
348C2×C4⋊C4—732no—
349C2×C4⋊C4—732no—
350C2×C4⋊C4—731no—
351C2×C4⋊C4—1468no—
352C2×C4⋊C4—1462no—
353C2×C4⋊C4—1462no—
354C2×C4⋊C4—1462no—
355C2×C4⋊C4—1462no—
356C2×C4⋊C4—1461no—
357C2×C4⋊C4—1461no—
358C2×C4⋊C4C22×D7311yescharacteristic
359C2×C4⋊C4C22×D7312yes—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—1462no—
362C2×C42—732no—
363C2×C42—1462no—
364C2×C42—1461no—
365C2×C42C22×D7311yescharacteristic
366#107—738no—
367#107—738no—
368#107—738no—
369#106—734no—
370#106C22×D7318yes—
371C4⋊C8—738no—
372C4⋊C8C22×D7314yes—
373#103—738no—
374#103—734no—
375#102—734no—
376#102C22×D7318yes—
377#97—738no—
378C4×C8—734no—
379C24—21no—
380C2×Q8—24no—
381C2×Q8—82no—
382C2×Q8—5842no—
383C2×Q8—5844no—
384C2×Q8—734no—
385C2×Q8—734no—
386C2×Q8—732no—
387C2×Q8—1468no—
388C2×Q8—1464no—
389C2×Q8—1464no—
390C2×Q8—1461no—
391C2×Q8—1462no—
392C2×D4—21no—
393C2×D4—22no—
394C2×D4Q8×D7314yes—
395C2×D4C23×D7312yes—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—24no—
399C22×C4—44no—
400C22×C4—5844no—
401C22×C4—732no—
402C22×C4—732no—
403C22×C4—1461no—
404C22×C4—1462no—
405C22×C4—1468no—
406C22×C4—1461no—
407C22×C4D4×D7311yescharacteristic
408C22×C4D4×D7311yescharacteristic
409C22×C4C23×D7311yescharacteristic
410SD16—7316no—
411C2×C8—24no—
412C2×C8—734no—
413C2×C8—732no—
414C2×C8—732no—
415C2×C8—1462no—
416C2×C8C23×D7314yes—
417C4⋊C4—24no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—738no—
421C4⋊C4—734no—
422C4⋊C4—732no—
423C4⋊C4—734no—
424C4⋊C4—1468no—
425C4⋊C4—1468no—
426C4⋊C4—1468no—
427C4⋊C4—1468no—
428C4⋊C4—1464no—
429C4⋊C4—1462no—
430C4⋊C4—1461no—
431C4⋊C4—1464no—
432C4⋊C4C23×D7314yes—
433C4⋊C4C23×D7312yes—
434C22⋊C4—24no—
435C22⋊C4—1468no—
436C42—734no—
437C42—734no—
438C42—1468no—
439C42—1464no—
440C42D4×D7312yes—
441C42C23×D7312yes—
442C23—22no—
443C23—24no—
444C23—42no—
445C23—42no—
446C23C2×D4×D7311yescharacteristic
447Q8—84no—
448Q8—5844no—
449Q8—5848no—
450Q8—734no—
451Q8—1468no—
452Q8—1462no—
453Q8—1464no—
454D4—22no—
455D4—24no—
456D4C2×Q8×D7314yes—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—42no—
461C2×C4—44no—
462C2×C4—48no—
463C2×C4—2924no—
464C2×C4—2922no—
465C2×C4—5848no—
466C2×C4—734no—
467C2×C4—734no—
468C2×C4—1462no—
469C2×C4—1464no—
470C2×C4—1464no—
471C2×C4—1464no—
472C2×C4—1462no—
473C2×C4—1464no—
474C2×C4#1455662014yes—
475C2×C4C2×D4×D7312yes—
476C2×C4C2×D4×D7312yes—
477C2×C4C2×D4×D7311yescharacteristic
478C2×C4C2×Q8×D7312yes—
479C2×C4#1455663812yes—
480C2×C4C24×D7311yescharacteristic
481C8—24no—
482C8—734no—
483C8—1462no—
484C22—24no—
485C22—48no—
486C22—42no—
487C22—42no—
488C22#1798925012yes—
489C22C2×#1455662012yes—
490C22#1798939112yes—
491C22C22×D4×D7311yescharacteristic
492C4—22no—
493C4—42no—
494C4—44no—
495C4—2924no—
496C4—2922no—
497C4—1464no—
498C4—1464no—
499C4—1464no—
500C4#1798925012yes—
501C4C2×#1455662014yes—
502C4C22×Q8×D7311yescharacteristic
503C4C2×#1455663811yescharacteristic
504C2—44no—
505C2#2262284514yesdirect product factor
506C2C2×#1798925011yescharacteristic
507C2C22×#1455662011yescharacteristic
508C2C2×#1798939111yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#476×C73C2
socleC23×C73C22×D4
prime radicalC22×D4×C73C23
hypercenterC2×#476D73
hypocenterC73C2×#3385
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#17989317C2semidirect
3. #22622845C2direct (N × H)
4. C2×#17988994C2semidirect
5. C2×#17988990C2semidirect
6. C2×#17988897C2semidirect
7. C2×#17988883C2semidirect
9. C2×#17988714C2semidirect
15. #17989317C22semidirect
31. #17988994C22semidirect
32. #17988990C22semidirect
33. #17988897C22semidirect
34. #17988883C22semidirect
36. #17988714C22semidirect
60. C2×#11924016Q8semidirect
141. #11924016C2×Q8semidirect
251. C2×C73#3385semidirect
267. C73C2×#3385semidirect
505. C2#22622845direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893172
C2×#179892942
#226228452
C2×#179889942
C2×#179889902
C2×#179888972
C2×#179888832
C2×#179888652
C2×#179887142
C2×#179886842
C2×C4×#119240162
C2×#476×C732
C2×#338573