Finite Group Databasebeta

← C2×#22622744 #33965718

Subgroups — C2×#22622744 #33965718

Order 18688.

1906 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989322C211yesmaximal, characteristic
2C2×#17989317C211yesmaximal, characteristic, complemented
3#22622744C2116yesmaximal, direct product factor
4C2×#17988948C212yesmaximal, complemented
5C2×#17988935C211yesmaximal, characteristic
6C2×#17988866C212yesmaximal, complemented
7C2×#17988812C212yesmaximal, complemented
8C2×#17988788C211yesmaximal, characteristic
9C2×#17988714C211yesmaximal, characteristic, complemented
10C2×#17988686C212yesmaximal, complemented
11C2×C4×#11924018C211yesmaximal, characteristic, complemented
12C2×#477×C73C211yesmaximal, characteristic, complemented
13C22×#11924018C2211yescharacteristic
14C22×#11924017C2212yes—
15#17989322—24no—
16#17989322C2218yes—
17#17989317—24no—
18#17989317C2218yescomplemented
19C2×#14556590—21no—
20C2×#14556590C2212yes—
21C2×#14556589—22no—
22C2×#14556588C2211yescharacteristic
23C2×#14556580C2212yes—
24C2×#14556579—21no—
25C2×#14556576—22no—
26C2×C4×Dic146C2211yescharacteristic
27C2×C4×Dic146C2211yescharacteristic
28C2×#14556556—21no—
29C2×#14556556C2212yes—
30C2×C4×D292—21no—
31C2×#14556553C2212yes—
32#17988948C22116yescomplemented
33#17988935C2218yes—
34#17988866C22116yescomplemented
35#17988812C22116yescomplemented
36#17988788C2218yes—
37#17988714C2218yescomplemented
38#17988686C22116yescomplemented
39C4×#11924018C2218yescomplemented
40C2×#14556524C2211yescharacteristic
41C2×#14556520C2212yes—
42C2×#14556515C2211yescharacteristic
43C2×#14556514C2211yescharacteristic
44C2×#14556513C2212yes—
45C2×#14556511C2212yes—
46C2×#14556511C2212yes—
47C2×#14556501C2212yes—
48C2×C4×#10596831C2211yescharacteristic
49C2×C4⋊Q8×C73C2211yescharacteristic
50C2×C4×Q8×C73C2211yescharacteristic
51#477×C73C2218yescomplemented
52C2×#107×C73C2212yes—
53C2×C4⋊C8×C73C2211yescharacteristic
54C2×#103×C73C2212yes—
55C22×Dic146—22no—
56C22×Dic146D411yescharacteristic
57C22×Dic146C2311yescharacteristic
58C22×D292—21no—
59C22×D292—21no—
60C22×D292C2312yes—
61C22×C4×D73—22no—
62C2×#11924018—24no—
63C2×#11924018C2314yes—
64C2×#11924017—28no—
65C2×#11924017C2318yes—
66C22×#10596831C2311yescharacteristic
67C22×#10596831C2311yescharacteristic
68#14556590—28no—
69#14556590—24no—
70#14556590C2318yes—
71#14556589—216no—
72#14556588—22no—
73#14556588C2314yes—
74#14556580—24no—
75#14556580C2318yes—
76#14556579—28no—
77#14556576—216no—
78C4×Dic146—22no—
79C4×Dic146D414yes—
80C4×Dic146C2314yes—
81C4×Dic146C2314yes—
82#14556556—28no—
83#14556556—24no—
84#14556556C2318yes—
85C4×D292—28no—
86#14556553—24no—
87#14556553C2318yes—
88C2×C4⋊Dic73D411yescharacteristic
89C2×C4⋊Dic73C2311yescharacteristic
90C2×#11924007—22no—
91C2×#11924007—22no—
92C2×#11924007—21no—
93C2×#11924007D412yes—
94C2×#11924005—22no—
95C2×#11924005—22no—
96C2×#11924005—22no—
97C2×C4×Dic73—22no—
98C2×C4×Dic73—21no—
99C2×C4×Dic73C2312yes—
100#14556524C2314yes—
101#14556520C2318yes—
102#14556515C2314yes—
103#14556514C2314yes—
104#14556513C2318yes—
105#14556511C2318yes—
106#14556511C2318yes—
107#14556501C2318yes—
108C4×#10596831C2314yes—
109C22×Q8×C73—21no—
110C22×Q8×C73C2311yescharacteristic
111C22×C8×C73C2312yes—
112C4⋊Q8×C73—22no—
113C4⋊Q8×C73C2314yes—
114C4×Q8×C73—22no—
115C4×Q8×C73C2314yes—
116C2×C4⋊C4×C73—21no—
117C2×C4⋊C4×C73—21no—
118C2×C4⋊C4×C73C2312yes—
119C2×C4⋊C4×C73C2311yescharacteristic
120C2×C42×C73—21no—
121C2×C42×C73C2311yescharacteristic
122#107×C73C2318yes—
123C4⋊C8×C73C2314yes—
124#103×C73C2318yes—
125C23×D73—22no—
126C2×Dic146—24no—
127C2×Dic146—21no—
128C2×Dic146—22no—
129C2×Dic146—28no—
130C2×Dic146—84no—
131C2×Dic146C2×D414yes—
132C2×Dic146#4114yes—
133C2×Dic146C2412yes—
134C2×D292—24no—
135C2×D292—24no—
136C2×D292—22no—
137C2×D292—24no—
138C2×D292—24no—
139C2×D292—44no—
140C2×D292—82no—
141C2×D292C2414yes—
142C22×Dic73—21no—
143C22×Dic73—21no—
144C22×Dic73C2×D412yes—
145C22×Dic73C2×D412yes—
146C2×C4×D73—28no—
147C2×C4×D73—84no—
148#11924018—28no—
149#11924017—216no—
150C2×#10596831—22no—
151C2×#10596831—22no—
152C2×#10596831C2412yes—
153C2×#10596831C2412yes—
154C4⋊Dic73—21no—
155C4⋊Dic73C2×D414yes—
156C4⋊Dic73C2412yes—
157#11924007—24no—
158#11924007—28no—
159#11924007—28no—
160#11924007C2×D418yes—
161#11924005—28no—
162#11924005—28no—
163#11924005—28no—
164C4×Dic73—24no—
165C4×Dic73—28no—
166C4×Dic73C2×D414yes—
167C4×Dic73C2414yes—
168C2×Q8×C73—21no—
169C2×Q8×C73—24no—
170C2×Q8×C73—22no—
171C2×Q8×C73—22no—
172C2×Q8×C73—82no—
173C2×Q8×C73C2412yes—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—22no—
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2411yescharacteristic
180C2×C8×C73—24no—
181C2×C8×C73C2414yes—
182C4⋊C4×C73—24no—
183C4⋊C4×C73—24no—
184C4⋊C4×C73—21no—
185C4⋊C4×C73—22no—
186C4⋊C4×C73C2414yes—
187C4⋊C4×C73C2412yes—
188C42×C73—24no—
189C42×C73C2×D412yes—
190C42×C73C2412yes—
191C23×C73C22×D411yescharacteristic
192C22×D73—24no—
193C22×D73—44no—
194C22×D73—44no—
195C22×D73—44no—
196Q8×C73—22no—
197Q8×C73—22no—
198Q8×C73—42no—
199Q8×C73—84no—
200C2×C4×C73—22no—
201C2×C4×C73—22no—
202C2×C4×C73—22no—
203C2×C4×C73—24no—
204C2×C4×C73—42no—
205C2×C4×C73—44no—
206C2×C4×C73—42no—
207C2×C4×C73#13714yes—
208C2×C4×C73C22×D412yes—
209C2×C4×C73C22×D411yescharacteristic
210C2×C4×C73C22×D412yes—
211C2×C4×C73C2×#4112yes—
212C2×C4×C732−1+412yes—
213C2×C4×C73C2511yescharacteristic
214C2×Dic73—24no—
215C2×Dic73—24no—
216C2×Dic73—24no—
217C2×Dic73—22no—
218C2×Dic73—22no—
219C2×Dic73—42no—
220C2×Dic73C22×D414yes—
221C2×Dic73C22×D414yes—
222D292—24no—
223D292—24no—
224D292—44no—
225D292—48no—
226D292—84no—
227C4×D73—88no—
228Dic146—24no—
229Dic146—28no—
230Dic146—22no—
231Dic146—88no—
232Dic146C2×#4114yes—
233C8×C73—24no—
234#10596831—22no—
235#10596831—22no—
236C22×C73#54812yes—
237C22×C73C2×#13712yes—
238C22×C73#57612yes—
239C22×C73C23×D411yescharacteristic
240C2×D73—44no—
241C2×D73—44no—
242C2×D73—44no—
243C2×D73—88no—
244C4×C73—22no—
245C4×C73—42no—
246C4×C73—44no—
247C4×C73—42no—
248C4×C73#54812yes—
249C4×C73C2×#13714yes—
250C4×C73C22×#4111yescharacteristic
251C4×C73C2×2−1+411yescharacteristic
252Dic73—24no—
253Dic73—24no—
254Dic73—24no—
255Dic73—42no—
256C2×#3375—731nomaximal, Sylow
257C2×C73#337514yescomplemented
258C2×C73C2×#54811yescharacteristic
259C2×C73C22×#13711yescharacteristic
260C2×C73C2×#57611yescharacteristic
261D73—84no—
262C2×#559—731no—
263C2×Q82—731no—
264#3375—7316no—
265C2×#489—732no—
266C2×#486—731no—
267C2×#477D7311yescharacteristic, complemented
268C2×#474—732no—
269C2×#464—732no—
270C2×#460—731no—
271C2×#446—731no—
272C2×#440—732no—
273C2×C4×Q16—731no—
274C73C2×#337511yescharacteristic, complemented, Sylow
275C22×Q16—731no—
276C22×SD16—732no—
277#559—738no—
278#559—1464no—
279Q82—738no—
280Q82—1464no—
281C2×C4⋊Q8—732no—
282C2×C4⋊Q8—1461no—
283C2×C4⋊Q8—1462no—
284C2×C4⋊Q8C2×D7311yescharacteristic
285C2×#127—731no—
286C2×#124—732no—
287C2×#124—1461no—
288C2×#123—1462no—
289C2×C4×Q8—731no—
290C2×C4×Q8—732no—
291C2×C4×Q8—731no—
292C2×C4×Q8—1461no—
293C2×C4×Q8C2×D7311yescharacteristic
294C2×C4×D4—732no—
295C2×C4×D4—1461no—
296#489—7316no—
297#486—738no—
298#477C2×D7318yescomplemented
299#474—7316no—
300#464—7316no—
301#460—738no—
302#446—738no—
303#440—7316no—
304C4×Q16—738no—
305C2×#107—731no—
306C2×#107C2×D7312yes—
307C2×C4⋊C8—732no—
308C2×C4⋊C8C2×D7311yescharacteristic
309C2×#103—731no—
310C2×#103—731no—
311C2×#103C2×D7312yes—
312C2×#102—732no—
313C2×#102—732no—
314C2×#102—732no—
315C2×#97—732no—
316C2×C4×C8—731no—
317C22×Q8—21no—
318C22×Q8—731no—
319C22×Q8—731no—
320C22×Q8—1462no—
321C22×Q8C22×D7311yescharacteristic
322C22×D4—732no—
323C22×D4—1461no—
324C22×D4—1461no—
325C23×C4—1462no—
326C2×Q16—734no—
327C2×Q16—1464no—
328C2×SD16—738no—
329C2×SD16—1468no—
330C22×C8—731no—
331C22×C8—731no—
332C22×C8C22×D7312yes—
333C4⋊Q8—22no—
334C4⋊Q8—738no—
335C4⋊Q8—1464no—
336C4⋊Q8—1468no—
337C4⋊Q8—14616no—
338C4⋊Q8C22×D7314yes—
339#127—734no—
340#127—1462no—
341#124—738no—
342#124—1468no—
343#124—1464no—
344#123—14616no—
345C4×Q8—22no—
346C4×Q8—734no—
347C4×Q8—734no—
348C4×Q8—738no—
349C4×Q8—734no—
350C4×Q8—1464no—
351C4×Q8—1468no—
352C4×Q8—1462no—
353C4×Q8C22×D7314yes—
354C4×D4—738no—
355C4×D4—1468no—
356C4×D4—1464no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—731no—
360C2×C4⋊C4—732no—
361C2×C4⋊C4—731no—
362C2×C4⋊C4—1462no—
363C2×C4⋊C4—1462no—
364C2×C4⋊C4—1461no—
365C2×C4⋊C4C22×D7311yescharacteristic
366C2×C4⋊C4C22×D7312yes—
367C2×C22⋊C4—1462no—
368C2×C22⋊C4—1462no—
369C2×C22⋊C4—1462no—
370C2×C42—21no—
371C2×C42—732no—
372C2×C42—1462no—
373C2×C42—1461no—
374C2×C42C22×D7311yescharacteristic
375#107—734no—
376#107C22×D7318yes—
377C4⋊C8—738no—
378C4⋊C8C22×D7314yes—
379#103—734no—
380#103—734no—
381#103C22×D7318yes—
382#102—738no—
383#102—738no—
384#102—738no—
385#97—738no—
386C4×C8—734no—
387C24—1462no—
388C2×Q8—21no—
389C2×Q8—24no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—82no—
393C2×Q8—5844no—
394C2×Q8—734no—
395C2×Q8—734no—
396C2×Q8—732no—
397C2×Q8—1468no—
398C2×Q8—1464no—
399C2×Q8—1461no—
400C2×Q8—1462no—
401C2×Q8C23×D7312yes—
402C2×D4—2924no—
403C2×D4—5842no—
404C2×D4—734no—
405C2×D4—1464no—
406C2×D4—1462no—
407C2×D4—1464no—
408C2×D4—1464no—
409C2×D4—1464no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—5844no—
414C22×C4—732no—
415C22×C4—732no—
416C22×C4—1468no—
417C22×C4—1461no—
418C22×C4—1461no—
419C22×C4D4×D7311yescharacteristic
420C22×C4D4×D7311yescharacteristic
421C22×C4C23×D7311yescharacteristic
422Q16—1468no—
423SD16—14616no—
424C2×C8—24no—
425C2×C8—732no—
426C2×C8—732no—
427C2×C8—1462no—
428C2×C8—1462no—
429C2×C8C23×D7314yes—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—21no—
433C4⋊C4—22no—
434C4⋊C4—738no—
435C4⋊C4—734no—
436C4⋊C4—732no—
437C4⋊C4—1468no—
438C4⋊C4—1468no—
439C4⋊C4—1464no—
440C4⋊C4—1461no—
441C4⋊C4C23×D7314yes—
442C4⋊C4C23×D7312yes—
443C22⋊C4—1468no—
444C22⋊C4—1468no—
445C22⋊C4—1468no—
446C42—24no—
447C42—734no—
448C42—734no—
449C42—1468no—
450C42—1464no—
451C42D4×D7312yes—
452C42C23×D7312yes—
453C23—2924no—
454C23—2924no—
455C23—2924no—
456C23—1464no—
457C23C2×D4×D7311yescharacteristic
458Q8—22no—
459Q8—22no—
460Q8—42no—
461Q8—84no—
462Q8—5848no—
463Q8—734no—
464Q8—1468no—
465Q8—1462no—
466Q8—1464no—
467D4—2928no—
468D4—2924no—
469D4—5844no—
470D4—1464no—
471D4—1464no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—42no—
477C2×C4—44no—
478C2×C4—42no—
479C2×C4—2922no—
480C2×C4—5848no—
481C2×C4—734no—
482C2×C4—734no—
483C2×C4—1462no—
484C2×C4—1464no—
485C2×C4—1464no—
486C2×C4—1462no—
487C2×C4—1464no—
488C2×C4#1455662314yes—
489C2×C4C2×D4×D7312yes—
490C2×C4C2×D4×D7312yes—
491C2×C4C2×D4×D7311yescharacteristic
492C2×C4#41×D7312yes—
493C2×C4#1455663912yes—
494C2×C4C24×D7311yescharacteristic
495C8—24no—
496C8—1462no—
497C8—1462no—
498C22—2924no—
499C22—2924no—
500C22—2924no—
501C22—5848no—
502C22#1798924712yes—
503C22C2×#1455662312yes—
504C22#1798939112yes—
505C22C22×D4×D7311yescharacteristic
506C4—22no—
507C4—42no—
508C4—42no—
509C4—44no—
510C4—2922no—
511C4—1464no—
512C4—1464no—
513C4—1464no—
514C4#1798924712yes—
515C4C2×#1455662314yes—
516C4C2×#41×D7311yescharacteristic
517C4C2×#1455663911yescharacteristic
518C2—5844no—
519C2#2262274414yesdirect product factor
520C2C2×#1798924711yescharacteristic
521C2C22×#1455662311yescharacteristic
522C2C2×#1798939111yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#477×C73C2
socleC23×C73C22×D4
prime radicalC2×#14556588C22
hypercenterC2×#477D73
hypocenterC73C2×#3375
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
2. C2×#17989317C2semidirect
3. #22622744C2direct (N × H)
4. C2×#17988948C2semidirect
6. C2×#17988866C2semidirect
7. C2×#17988812C2semidirect
9. C2×#17988714C2semidirect
10. C2×#17988686C2semidirect
11. C2×C4×#11924018C2semidirect
12. C2×#477×C73C2semidirect
18. #17989317C22semidirect
32. #17988948C22semidirect
34. #17988866C22semidirect
35. #17988812C22semidirect
37. #17988714C22semidirect
38. #17988686C22semidirect
39. C4×#11924018C22semidirect
51. #477×C73C22semidirect
257. C2×C73#3375semidirect
267. C2×#477D73semidirect
274. C73C2×#3375semidirect
298. #477C2×D73semidirect
519. C2#22622744direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893222
C2×#179893172
#226227442
C2×#179889482
C2×#179889352
C2×#179888662
C2×#179888122
C2×#179887882
C2×#179887142
C2×#179886862
C2×C4×#119240182
C2×#477×C732
C2×#337573