Finite Group Databasebeta

← C2×#22622846 #33966478

Subgroups — C2×#22622846 #33966478

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×#17989298C211yesmaximal, characteristic
3#22622846C2116yesmaximal, direct product factor
4C2×#17988995C212yesmaximal, complemented
5C2×#17988893C212yesmaximal, complemented
6C2×#17988879C211yesmaximal, characteristic, complemented
7C2×#17988874C211yesmaximal, characteristic
8C2×#17988866C212yesmaximal
9C2×#17988717C211yesmaximal, characteristic, complemented
10C2×#17988686C212yesmaximal
11C2×C4×#11924017C211yesmaximal, characteristic
12C2×#500×C73C211yesmaximal, characteristic, complemented
13C22×#11924017C2211yescharacteristic
14#17989317—24no—
15#17989317C2218yescomplemented
16#17989298—24no—
17#17989298C2218yes—
18C2×#14556590—21no—
19C2×#14556590C2212yes—
20C2×#14556589—22no—
21C2×#14556582C2212yes—
22C2×#14556571—21no—
23C2×#14556567—22no—
24C2×C4×Dic146C2211yescharacteristic
25C2×C4×Dic146C2211yescharacteristic
26C2×#14556556—21no—
27C2×#14556556C2212yes—
28C2×C4×D292C2211yescharacteristic
29C2×#14556553C2212yes—
30C2×C4⋊C4×D73—21no—
31#17988995C22116yescomplemented
32#17988893C22116yescomplemented
33#17988879C2218yescomplemented
34#17988874C2218yes—
35#17988866C22116yes—
36#17988717C2218yescomplemented
37#17988686C22116yes—
38C4×#11924017C2218yes—
39C2×#14556524C2212yes—
40C2×#14556523C2211yescharacteristic
41C2×#14556522C2212yes—
42C2×C4⋊#10596831C2211yescharacteristic
43C2×#14556520C2212yes—
44C2×#14556516C2211yescharacteristic
45C2×#14556514C2212yes—
46C2×#14556513C2211yescharacteristic
47C2×#14556511C2212yes—
48C2×#14556501C2212yes—
49C2×C4⋊Q8×C73C2211yescharacteristic
50C2×C4⋊Q8×C73C2211yescharacteristic
51#500×C73C2218yescomplemented
52C2×#107×C73C2212yes—
53C2×#107×C73C2212yes—
54C2×C4×C8×C73C2211yescharacteristic
55C22×Dic146—22no—
56C22×Dic146D411yescharacteristic
57C22×Dic146C2311yescharacteristic
58C22×D292C2311yescharacteristic
59C22×C4×D73—22no—
60C22×C4×D73—21no—
61C2×#11924017Q818yescomplemented
62C2×#11924017C2314yes—
63C22×#10596831C2312yes—
64#14556590—28no—
65#14556590—24no—
66#14556590C2318yes—
67#14556589—216no—
68#14556582—24no—
69#14556582C2318yes—
70#14556571—28no—
71#14556567—216no—
72C4×Dic146—22no—
73C4×Dic146D414yes—
74C4×Dic146C2314yes—
75C4×Dic146C2314yes—
76#14556556—28no—
77#14556556—24no—
78#14556556C2318yes—
79C4×D292—22no—
80C4×D292C2314yes—
81#14556553—24no—
82#14556553C2318yes—
83C2×C4⋊Dic73—22no—
84C2×C4⋊Dic73D411yescharacteristic
85C2×C4⋊Dic73C2311yescharacteristic
86C2×C4⋊Dic73C2311yescharacteristic
87C2×#11924007—22no—
88C2×#11924007—22no—
89C2×#11924007—22no—
90C2×#11924007—21no—
91C2×#11924007D412yes—
92C4⋊C4×D73—28no—
93C2×#11924005—22no—
94C2×#11924005—21no—
95C2×C4×Dic73—22no—
96C2×C4×Dic73—21no—
97C2×C4×Dic73C2312yes—
98#14556524C2318yes—
99#14556523C2314yes—
100#14556522C2318yes—
101C4⋊#10596831C2314yes—
102#14556520C2318yes—
103#14556516C2314yes—
104#14556514C2318yes—
105#14556513C2314yes—
106#14556511C2318yes—
107#14556501C2318yes—
108C22×Q8×C73—21no—
109C22×Q8×C73—21no—
110C22×C8×C73C2311yescharacteristic
111C22×C8×C73C2311yescharacteristic
112C4⋊Q8×C73—22no—
113C4⋊Q8×C73—22no—
114C4⋊Q8×C73C2314yes—
115C4⋊Q8×C73C2314yes—
116C2×C4⋊C4×C73—21no—
117C2×C4⋊C4×C73—21no—
118C2×C4⋊C4×C73C2312yes—
119C2×C4⋊C4×C73C2312yes—
120C2×C42×C73C2311yescharacteristic
121#107×C73C2318yes—
122#107×C73C2318yes—
123C4×C8×C73C2314yes—
124C23×D73—21no—
125C2×Dic146—24no—
126C2×Dic146—21no—
127C2×Dic146—22no—
128C2×Dic146—28no—
129C2×Dic146—84no—
130C2×Dic146C2×D414yes—
131C2×Dic146C2×Q814yes—
132C2×Dic146C2412yes—
133C2×D292—21no—
134C2×D292—22no—
135C2×D292C2×Q814yes—
136C2×D292C2412yes—
137C22×Dic73—21no—
138C22×Dic73—21no—
139C22×Dic73—21no—
140C22×Dic73C2×D412yes—
141C22×Dic73C2×D412yes—
142C2×C4×D73—24no—
143C2×C4×D73—28no—
144C2×C4×D73—44no—
145C2×C4×D73—84no—
146#11924017C2×Q8116yescomplemented
147C2×#10596831—24no—
148C2×#10596831C2414yes—
149C4⋊Dic73—21no—
150C4⋊Dic73—21no—
151C4⋊Dic73—28no—
152C4⋊Dic73C2×D414yes—
153C4⋊Dic73C2412yes—
154C4⋊Dic73C2412yes—
155#11924007—24no—
156#11924007—28no—
157#11924007—28no—
158#11924007—28no—
159#11924007C2×D418yes—
160#11924005—24no—
161#11924005—28no—
162C4×Dic73—24no—
163C4×Dic73—28no—
164C4×Dic73C2×D414yes—
165C4×Dic73C2414yes—
166C2×Q8×C73—24no—
167C2×Q8×C73—24no—
168C2×Q8×C73—82no—
169C2×Q8×C73—82no—
170C22×C4×C73—22no—
171C22×C4×C73—22no—
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2411yescharacteristic
175C2×C8×C73—22no—
176C2×C8×C73C2×Q814yes—
177C2×C8×C73C2412yes—
178C2×C8×C73C2412yes—
179C4⋊C4×C73—24no—
180C4⋊C4×C73—24no—
181C4⋊C4×C73—22no—
182C4⋊C4×C73—22no—
183C4⋊C4×C73C2414yes—
184C4⋊C4×C73C2414yes—
185C42×C73C2×D412yes—
186C42×C73C2412yes—
187C23×C73C22×D411yescharacteristic
188C22×D73—24no—
189C22×D73—22no—
190C22×D73—42no—
191C22×D73—42no—
192Q8×C73—84no—
193Q8×C73—84no—
194C2×C4×C73—22no—
195C2×C4×C73—24no—
196C2×C4×C73—24no—
197C2×C4×C73—44no—
198C2×C4×C73—44no—
199C2×C4×C73#13714yes—
200C2×C4×C73C22×D412yes—
201C2×C4×C73C22×D411yescharacteristic
202C2×C4×C73C22×D412yes—
203C2×C4×C73C22×Q812yes—
204C2×C4×C732−1+412yes—
205C2×C4×C73C2511yescharacteristic
206C2×Dic73—24no—
207C2×Dic73—24no—
208C2×Dic73—24no—
209C2×Dic73—22no—
210C2×Dic73—22no—
211C2×Dic73—22no—
212C2×Dic73—42no—
213C2×Dic73—42no—
214C2×Dic73C22×D414yes—
215C2×Dic73C22×D414yes—
216D292—24no—
217D292—22no—
218D292C22×Q814yes—
219C4×D73—48no—
220C4×D73—88no—
221Dic146—24no—
222Dic146—28no—
223Dic146—22no—
224Dic146—88no—
225Dic146C22×Q814yes—
226C8×C73—22no—
227C8×C73C22×Q814yes—
228#10596831—24no—
229C22×C73D4×Q812yes—
230C22×C73C2×#13712yes—
231C22×C73#57612yes—
232C22×C73C23×D411yescharacteristic
233C2×D73—24no—
234C2×D73—48no—
235C2×D73—42no—
236C2×D73—42no—
237C4×C73—22no—
238C4×C73—44no—
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—42no—
249C2×#3385—731nomaximal, Sylow
250C2×C73#338514yescomplemented
251C2×C73C2×D4×Q811yescharacteristic
252C2×C73C22×#13711yescharacteristic
253C2×C73C2×#57611yescharacteristic
254D73—44no—
255C2×Q82—731no—
256C2×#554—731no—
257#3385—7316no—
258C2×#501—732no—
259C2×#500D7311yescharacteristic, complemented
260C2×#479—732no—
261C2×#477—731no—
262C2×#476—731no—
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—1461no—
275C2×C4⋊Q8—1462no—
276C2×C4⋊Q8C2×D7311yescharacteristic
277C2×C4⋊Q8C2×D7311yescharacteristic
278C2×#125—732no—
279C2×C22⋊Q8—1461no—
280C2×C22⋊Q8—1462no—
281C2×C4×Q8—731no—
282C2×C4×Q8—732no—
283C2×C4×Q8—731no—
284C2×C4×Q8—1461no—
285C2×C4×D4—732no—
286C2×C4×D4—731no—
287C22×C4⋊C4—1461no—
288#501—7316no—
289#500C2×D7318yescomplemented
290#479—7316no—
291#477—738no—
292#476—738no—
293#474—7316no—
294#446—738no—
295#440—7316no—
296C4×SD16—738no—
297C2×#107—732no—
298C2×#107C2×D7312yes—
299C2×#107C2×D7312yes—
300C2×#106—731no—
301C2×#106—732no—
302C2×C4⋊C8—732no—
303C2×C4⋊C8—731no—
304C2×#103—731no—
305C2×#103—732no—
306C2×#102—731no—
307C2×#102—732no—
308C2×#97—732no—
309C2×C4×C8C2×D7311yescharacteristic
310C22×Q8—21no—
311C22×Q8—21no—
312C22×Q8—731no—
313C22×Q8—731no—
314C22×Q8—1462no—
315C22×D4—731no—
316C23×C4—1462no—
317C23×C4—1461no—
318C2×SD16—738no—
319C2×SD16—734no—
320C22×C8—732no—
321C22×C8C22×D7311yescharacteristic
322C22×C8C22×D7311yescharacteristic
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325C4⋊Q8—738no—
326C4⋊Q8—1464no—
327C4⋊Q8—1468no—
328C4⋊Q8—14616no—
329C4⋊Q8C22×D7314yes—
330C4⋊Q8C22×D7314yes—
331#125—738no—
332#125—1464no—
333C22⋊Q8—1468no—
334C22⋊Q8—14616no—
335C4×Q8—734no—
336C4×Q8—734no—
337C4×Q8—738no—
338C4×Q8—734no—
339C4×Q8—1464no—
340C4×Q8—1468no—
341C4×Q8—1462no—
342C4×D4—738no—
343C4×D4—734no—
344C4×D4—1464no—
345C4×D4—1462no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—731no—
349C2×C4⋊C4—732no—
350C2×C4⋊C4—731no—
351C2×C4⋊C4—731no—
352C2×C4⋊C4—1468no—
353C2×C4⋊C4—1462no—
354C2×C4⋊C4—1462no—
355C2×C4⋊C4—1462no—
356C2×C4⋊C4—1462no—
357C2×C4⋊C4—1461no—
358C2×C4⋊C4C22×D7312yes—
359C2×C4⋊C4C22×D7312yes—
360C2×C22⋊C4—1462no—
361C2×C22⋊C4—1461no—
362C2×C42—732no—
363C2×C42—1462no—
364C2×C42—1461no—
365C2×C42C22×D7311yescharacteristic
366#107—738no—
367#107C22×D7318yes—
368#107C22×D7318yes—
369#106—734no—
370#106—738no—
371C4⋊C8—738no—
372C4⋊C8—734no—
373#103—734no—
374#103—738no—
375#102—734no—
376#102—738no—
377#97—738no—
378C4×C8C22×D7314yes—
379C24—1461no—
380C2×Q8—24no—
381C2×Q8—24no—
382C2×Q8—82no—
383C2×Q8—82no—
384C2×Q8—5844no—
385C2×Q8—734no—
386C2×Q8—734no—
387C2×Q8—732no—
388C2×Q8—1468no—
389C2×Q8—1464no—
390C2×Q8—1461no—
391C2×Q8—1462no—
392C2×D4—734no—
393C2×D4—732no—
394C2×D4—1461no—
395C2×D4—1462no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—2924no—
399C22×C4—5844no—
400C22×C4—732no—
401C22×C4—732no—
402C22×C4—1468no—
403C22×C4—1461no—
404C22×C4—1461no—
405C22×C4—1464no—
406C22×C4—1461no—
407C22×C4D4×D7311yescharacteristic
408C22×C4D4×D7311yescharacteristic
409C22×C4C23×D7311yescharacteristic
410SD16—7316no—
411C2×C8—22no—
412C2×C8—734no—
413C2×C8—1464no—
414C2×C8Q8×D7314yes—
415C2×C8C23×D7312yes—
416C2×C8C23×D7312yes—
417C4⋊C4—24no—
418C4⋊C4—24no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—738no—
422C4⋊C4—734no—
423C4⋊C4—732no—
424C4⋊C4—732no—
425C4⋊C4—1468no—
426C4⋊C4—1468no—
427C4⋊C4—1468no—
428C4⋊C4—1468no—
429C4⋊C4—1464no—
430C4⋊C4—1461no—
431C4⋊C4—1461no—
432C4⋊C4C23×D7314yes—
433C4⋊C4C23×D7314yes—
434C22⋊C4—1468no—
435C22⋊C4—1464no—
436C42—734no—
437C42—734no—
438C42—1468no—
439C42—1464no—
440C42D4×D7312yes—
441C42C23×D7312yes—
442C23—2922no—
443C23—2922no—
444C23—1462no—
445C23—1464no—
446C23C2×D4×D7311yescharacteristic
447Q8—84no—
448Q8—84no—
449Q8—5848no—
450Q8—734no—
451Q8—1468no—
452Q8—1462no—
453Q8—1464no—
454D4—734no—
455D4—1462no—
456D4—1464no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—44no—
461C2×C4—44no—
462C2×C4—2922no—
463C2×C4—2922no—
464C2×C4—2928no—
465C2×C4—5848no—
466C2×C4—734no—
467C2×C4—734no—
468C2×C4—1462no—
469C2×C4—1462no—
470C2×C4—1464no—
471C2×C4—1464no—
472C2×C4—1462no—
473C2×C4—1464no—
474C2×C4#1455662314yes—
475C2×C4C2×D4×D7312yes—
476C2×C4C2×D4×D7312yes—
477C2×C4C2×D4×D7311yescharacteristic
478C2×C4C2×Q8×D7312yes—
479C2×C4#1455663912yes—
480C2×C4C24×D7311yescharacteristic
481C8—22no—
482C8—1464no—
483C8C2×Q8×D7314yes—
484C22—2928no—
485C22—2922no—
486C22—2922no—
487C22—1464no—
488C22#1798925212yes—
489C22C2×#1455662312yes—
490C22#1798938812yes—
491C22C22×D4×D7311yescharacteristic
492C4—22no—
493C4—44no—
494C4—44no—
495C4—2922no—
496C4—2922no—
497C4—1464no—
498C4—1464no—
499C4—1464no—
500C4#1798925212yes—
501C4C2×#1455662314yes—
502C4C22×Q8×D7311yescharacteristic
503C4C2×#1455663911yescharacteristic
504C2—2924no—
505C2#2262284614yesdirect product factor
506C2C2×#1798925211yescharacteristic
507C2C22×#1455662311yescharacteristic
508C2C2×#1798938811yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#500×C73C2
socleC23×C73C22×D4
prime radicalC22×D292C23
hypercenterC2×#500D73
hypocenterC73C2×#3385
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
1. C2×#17989317C2semidirect
3. #22622846C2direct (N × H)
4. C2×#17988995C2semidirect
5. C2×#17988893C2semidirect
6. C2×#17988879C2semidirect
9. C2×#17988717C2semidirect
12. C2×#500×C73C2semidirect
15. #17989317C22semidirect
31. #17988995C22semidirect
32. #17988893C22semidirect
33. #17988879C22semidirect
36. #17988717C22semidirect
51. #500×C73C22semidirect
61. C2×#11924017Q8semidirect
146. #11924017C2×Q8semidirect
250. C2×C73#3385semidirect
259. C2×#500D73semidirect
267. C73C2×#3385semidirect
289. #500C2×D73semidirect
505. C2#22622846direct (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×#179892982
#226228462
C2×#179889952
C2×#179888932
C2×#179888792
C2×#179888742
C2×#179888662
C2×#179887172
C2×#179886862
C2×C4×#119240172
C2×#500×C732
C2×#338573