Finite Group Databasebeta

← C2×#22622344 #33964468

Subgroups — C2×#22622344 #33964468

Order 18688.

1918 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989307C211yesmaximal, characteristic, complemented
2#22622344C2116yesmaximal, direct product factor
3C2×#17988983C211yesmaximal, characteristic, complemented
4C2×#17988928C212yesmaximal, complemented
5C2×#17988908C212yesmaximal, complemented
6C2×#17988879C211yesmaximal, characteristic, complemented
7C2×#17988867C211yesmaximal, characteristic, complemented
8C2×#17988814C212yesmaximal, complemented
9C2×C4×#11924016C211yesmaximal, characteristic, complemented
10C2×D4×#10596831C211yesmaximal, characteristic, complemented
11C2×#17988623C212yesmaximal, complemented
12C2×#555×C73C211yesmaximal, characteristic
13C22×#11924016C2211yescharacteristic
14C23×#10596831C2212yes—
15#17989307—24no—
16#17989307C2218yescomplemented
17C2×#14556591C2211yescharacteristic
18C2×#14556584—22no—
19C2×#14556578—21no—
20C2×#14556570C2212yes—
21C2×C4×Dic146C2211yescharacteristic
22C2×#14556556—21no—
23C2×#14556550C2212yes—
24#17988983C2218yescomplemented
25#17988928C22116yescomplemented
26#17988908C22116yescomplemented
27#17988879C2218yescomplemented
28#17988867C2218yescomplemented
29#17988814C22116yescomplemented
30C4×#11924016C2218yescomplemented
31D4×#10596831C2218yescomplemented
32#17988623C22116yescomplemented
33C2×#14556524C2212yes—
34C2×#14556524C2212yes—
35C2×#14556522C2212yes—
36C2×#14556522C2212yes—
37C2×#14556522C2211yescharacteristic
38C2×C4⋊#10596831C2211yescharacteristic
39C2×#14556514C2212yes—
40C2×#14556514C2211yescharacteristic
41C2×#14556512C2212yes—
42C2×#14556512C2211yescharacteristic
43C2×C22⋊#10596831C2212yes—
44C2×C4×#10596831C2211yescharacteristic
45#555×C73—24no—
46#555×C73C2218yes—
47C2×C4⋊Q8×C73C2211yescharacteristic
48C2×#124×C73—22no—
49C2×#121×C73—21no—
50C2×#121×C73C2212yes—
51C2×C4×D4×C73C2211yescharacteristic
52C2×C4×D4×C73C2211yescharacteristic
53C2×#117×C73—21no—
54C2×#117×C73C2212yes—
55C22×Dic146—21no—
56C22×Dic146C2311yescharacteristic
57C2×#11924016—24no—
58C2×#11924016C2314yes—
59C22×#10596831—28no—
60C22×#10596831C2312yes—
61C22×#10596831C2311yescharacteristic
62C22×#10596831C2318yes—
63C22×#10596831C2311yescharacteristic
64#14556591—22no—
65#14556591C2314yes—
66#14556584—216no—
67#14556578—28no—
68#14556570—24no—
69#14556570C2318yes—
70C4×Dic146—22no—
71C4×Dic146C2314yes—
72#14556556—28no—
73#14556550—24no—
74#14556550C2318yes—
75C2×C4⋊Dic73—21no—
76C2×C4⋊Dic73C2312yes—
77C2×C4⋊Dic73C2311yescharacteristic
78C2×#11924007—22no—
79C2×#11924007—21no—
80C2×C22⋊Dic73—22no—
81C2×C22⋊Dic73—22no—
82C2×C4×Dic73—22no—
83C2×C4×Dic73—21no—
84#14556524C2318yes—
85#14556524C2318yes—
86#14556522C2314yes—
87#14556522C2318yes—
88#14556522C2318yes—
89C4⋊#10596831C2314yes—
90#14556514C2318yes—
91#14556514C2314yes—
92#14556512C2318yes—
93#14556512C2314yes—
94C22⋊#10596831C2318yes—
95C4×#10596831C2314yes—
96C22×Q8×C73—21no—
97C22×D4×C73—22no—
98C22×D4×C73D411yescharacteristic
99C22×D4×C73C2311yescharacteristic
100C23×C4×C73—21no—
101C23×C4×C73C2312yes—
102C4⋊Q8×C73—22no—
103C4⋊Q8×C73C2314yes—
104#124×C73—216no—
105#121×C73—28no—
106#121×C73—24no—
107#121×C73C2318yes—
108C4×D4×C73—22no—
109C4×D4×C73D414yes—
110C4×D4×C73C2314yes—
111C4×D4×C73C2314yes—
112#117×C73—24no—
113#117×C73—28no—
114#117×C73C2318yes—
115C2×C4⋊C4×C73—21no—
116C2×C4⋊C4×C73D411yescharacteristic
117C2×C4⋊C4×C73C2312yes—
118C2×C4⋊C4×C73C2311yescharacteristic
119C2×C22⋊C4×C73—22no—
120C2×C22⋊C4×C73—22no—
121C2×C22⋊C4×C73—21no—
122C2×C22⋊C4×C73D412yes—
123C2×C42×C73—22no—
124C2×C42×C73C2311yescharacteristic
125C2×Dic146—22no—
126C2×Dic146—22no—
127C2×Dic146—24no—
128C2×Dic146—21no—
129C2×Dic146—44no—
130C2×Dic146C2412yes—
131C22×Dic73—21no—
132C22×Dic73—21no—
133C22×Dic73—22no—
134#11924016—28no—
135C2×#10596831—24no—
136C2×#10596831—22no—
137C2×#10596831—216no—
138C2×#10596831#4114yes—
139C2×#10596831C2412yes—
140C2×#10596831C2414yes—
141C2×#10596831C2412yes—
142C4⋊Dic73—24no—
143C4⋊Dic73—21no—
144C4⋊Dic73—22no—
145C4⋊Dic73C2414yes—
146C4⋊Dic73C2412yes—
147#11924007—28no—
148#11924007—24no—
149C22⋊Dic73—28no—
150C22⋊Dic73—28no—
151C4×Dic73—28no—
152C4×Dic73—24no—
153C24×C73—21no—
154C24×C73C2×D412yes—
155C2×Q8×C73—24no—
156C2×Q8×C73—82no—
157C2×D4×C73—28no—
158C2×D4×C73—24no—
159C2×D4×C73—21no—
160C2×D4×C73—22no—
161C2×D4×C73—22no—
162C2×D4×C73—84no—
163C2×D4×C73C2×D414yes—
164C2×D4×C73C2412yes—
165C22×C4×C73—24no—
166C22×C4×C73—24no—
167C22×C4×C73—21no—
168C22×C4×C73—22no—
169C22×C4×C73—24no—
170C22×C4×C73—44no—
171C22×C4×C73C2×D412yes—
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D414yes—
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73C2414yes—
176C22×C4×C73C2411yescharacteristic
177C4⋊C4×C73—24no—
178C4⋊C4×C73—21no—
179C4⋊C4×C73—22no—
180C4⋊C4×C73C2×D414yes—
181C4⋊C4×C73C2412yes—
182C4⋊C4×C73C2414yes—
183C22⋊C4×C73—28no—
184C22⋊C4×C73—28no—
185C22⋊C4×C73—24no—
186C22⋊C4×C73C2×D418yes—
187C42×C73—28no—
188C42×C73C2×D412yes—
189C42×C73C2412yes—
190C23×C73—24no—
191C23×C73—24no—
192C23×C73—24no—
193C23×C73—22no—
194C23×C73—42no—
195C23×C73—42no—
196C23×C73—42no—
197C23×C73C22×D414yes—
198C23×C73C22×D411yescharacteristic
199Q8×C73—84no—
200D4×C73—28no—
201D4×C73—22no—
202D4×C73—22no—
203D4×C73—42no—
204D4×C73—88no—
205C2×C4×C73—24no—
206C2×C4×C73—22no—
207C2×C4×C73—28no—
208C2×C4×C73—24no—
209C2×C4×C73—24no—
210C2×C4×C73—22no—
211C2×C4×C73—24no—
212C2×C4×C73—42no—
213C2×C4×C73—44no—
214C2×C4×C73—48no—
215C2×C4×C73#13514yes—
216C2×C4×C73C22×D414yes—
217C2×C4×C73C22×D412yes—
218C2×C4×C73C22×D411yescharacteristic
219C2×C4×C73C22×D412yes—
220C2×C4×C73C2×#4112yes—
221C2×C4×C732−1+412yes—
222C2×C4×C73C2511yescharacteristic
223C2×Dic73—22no—
224C2×Dic73—22no—
225C2×Dic73—24no—
226C2×Dic73—42no—
227C2×Dic73—44no—
228C2×Dic73—42no—
229Dic146—22no—
230Dic146—22no—
231Dic146—42no—
232Dic146—48no—
233#10596831—24no—
234#10596831—22no—
235#10596831C2×#4114yes—
236C22×C73—24no—
237C22×C73—24no—
238C22×C73—24no—
239C22×C73—48no—
240C22×C73—42no—
241C22×C73—42no—
242C22×C73—42no—
243C22×C73—84no—
244C22×C73#54712yes—
245C22×C73C2×#13512yes—
246C22×C73#57712yes—
247C22×C73C23×D411yescharacteristic
248C4×C73—24no—
249C4×C73—22no—
250C4×C73—42no—
251C4×C73—44no—
252C4×C73#54712yes—
253C4×C73C2×#13514yes—
254C4×C73C22×#4111yescharacteristic
255C4×C73C2×2−1+411yescharacteristic
256Dic73—42no—
257Dic73—44no—
258Dic73—42no—
259C2×#3340—731nomaximal, Sylow
260C2×C73—44no—
261C2×C73—82no—
262C2×C73#334014yescomplemented
263C2×C73C2×#54711yescharacteristic
264C2×C73C22×#13511yescharacteristic
265C2×C73C2×#57711yescharacteristic
266C2×#556—731no—
267C2×#555D7311yescharacteristic
268#3340—7316no—
269C2×#498—731no—
270C2×#485—732no—
271C2×#482—732no—
272C2×#477—731no—
273C2×#474—731no—
274C2×#465—732no—
275C2×C4×SD16—731no—
276C2×C8×D4—731no—
277C2×#427—732no—
278C73C2×#334011yescharacteristic, complemented, Sylow
279C22×SD16—731no—
280C23×C8—732no—
281#556—738no—
282#556—1464no—
283#555—24no—
284#555C2×D7318yes—
285C2×C4⋊Q8—731no—
286C2×C4⋊Q8C2×D7311yescharacteristic
287C2×#126—1462no—
288C2×#124—22no—
289C2×#124—1461no—
290C2×C22⋊Q8—732no—
291C2×#121—21no—
292C2×#121C2×D7312yes—
293C2×C4×Q8—731no—
294C2×C4×Q8—1461no—
295C2×C4×D4C2×D7311yescharacteristic
296C2×C4×D4C2×D7311yescharacteristic
297C2×#117—21no—
298C2×#117—732no—
299C2×#117C2×D7312yes—
300#498—738no—
301#485—7316no—
302#482—7316no—
303#477—738no—
304#474—738no—
305#465—7316no—
306C4×SD16—738no—
307C8×D4—738no—
308#427—7316no—
309C2×#107—732no—
310C2×#107—732no—
311C2×#106—732no—
312C2×#106—732no—
313C2×#106—731no—
314C2×C4⋊C8—731no—
315C2×#103—732no—
316C2×#103—731no—
317C2×#102—731no—
318C2×#102—732no—
319C2×C22⋊C8—732no—
320C2×C4×C8—731no—
321C22×Q8—21no—
322C22×Q8—731no—
323C22×Q8—1461no—
324C22×D4—22no—
325C22×D4C22⋊D7311yescharacteristic
326C22×D4C22×D7311yescharacteristic
327C23×C4—21no—
328C23×C4C22×D7312yes—
329C2×SD16—734no—
330C2×SD16—1464no—
331C22×C8—731no—
332C22×C8—732no—
333C22×C8—738no—
334C22×C8—731no—
335C22×C8—1468no—
336C4⋊Q8—22no—
337C4⋊Q8—734no—
338C4⋊Q8—1462no—
339C4⋊Q8C22×D7314yes—
340#126—14616no—
341#124—216no—
342#124—1468no—
343C22⋊Q8—738no—
344C22⋊Q8—1464no—
345#121—28no—
346#121—24no—
347#121C22×D7318yes—
348C4×Q8—734no—
349C4×Q8—1468no—
350C4×Q8—1462no—
351C4×D4—22no—
352C4×D4C22⋊D7314yes—
353C4×D4C22×D7314yes—
354C4×D4C22×D7314yes—
355#117—24no—
356#117—28no—
357#117—738no—
358#117—1464no—
359#117C22×D7318yes—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—731no—
362C2×C4⋊C4—732no—
363C2×C4⋊C4—1461no—
364C2×C4⋊C4—1462no—
365C2×C4⋊C4—1461no—
366C2×C4⋊C4C22⋊D7311yescharacteristic
367C2×C4⋊C4C22×D7311yescharacteristic
368C2×C4⋊C4C22×D7312yes—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—1462no—
373C2×C22⋊C4—1462no—
374C2×C22⋊C4C22⋊D7312yes—
375C2×C42—22no—
376C2×C42—1462no—
377C2×C42—1461no—
378C2×C42C22×D7311yescharacteristic
379#107—738no—
380#107—738no—
381#106—734no—
382#106—738no—
383#106—738no—
384C4⋊C8—734no—
385#103—734no—
386#103—738no—
387#102—734no—
388#102—738no—
389C22⋊C8—738no—
390C4×C8—734no—
391C24—21no—
392C24C2×C22⋊D7312yes—
393C2×Q8—24no—
394C2×Q8—82no—
395C2×Q8—2924no—
396C2×Q8—732no—
397C2×Q8—1462no—
398C2×Q8—1462no—
399C2×Q8—1461no—
400C2×Q8—1464no—
401C2×D4—28no—
402C2×D4—24no—
403C2×D4—21no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—84no—
407C2×D4C2×C22⋊D7314yes—
408C2×D4C23×D7312yes—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—44no—
415C22×C4—1461no—
416C22×C4—1462no—
417C22×C4—1461no—
418C22×C4C2×C22⋊D7314yes—
419C22×C4C2×C22⋊D7312yes—
420C22×C4C2×C22⋊D7311yescharacteristic
421C22×C4C2×C22⋊D7311yescharacteristic
422C22×C4C23×D7314yes—
423C22×C4C23×D7311yescharacteristic
424SD16—1468no—
425C2×C8—734no—
426C2×C8—732no—
427C2×C8—732no—
428C2×C8—734no—
429C2×C8—14616no—
430C2×C8—1464no—
431C2×C8—1462no—
432C4⋊C4—24no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—734no—
436C4⋊C4—732no—
437C4⋊C4—1464no—
438C4⋊C4—1468no—
439C4⋊C4—1461no—
440C4⋊C4—1462no—
441C4⋊C4—1464no—
442C4⋊C4C2×C22⋊D7314yes—
443C4⋊C4C23×D7314yes—
444C4⋊C4C23×D7312yes—
445C22⋊C4—28no—
446C22⋊C4—28no—
447C22⋊C4—24no—
448C22⋊C4—1468no—
449C22⋊C4—1468no—
450C22⋊C4C2×C22⋊D7318yes—
451C42—28no—
452C42—1468no—
453C42—1464no—
454C42C2×C22⋊D7312yes—
455C42C23×D7312yes—
456C23—24no—
457C23—24no—
458C23—24no—
459C23—22no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23C22×C22⋊D7314yes—
464C23C22×C22⋊D7311yescharacteristic
465Q8—84no—
466Q8—2922no—
467Q8—2928no—
468Q8—1462no—
469Q8—1462no—
470D4—22no—
471D4—22no—
472D4—28no—
473D4—42no—
474D4—88no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—28no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—44no—
483C2×C4—42no—
484C2×C4—48no—
485C2×C4—2922no—
486C2×C4—2922no—
487C2×C4—2924no—
488C2×C4—1462no—
489C2×C4—1464no—
490C2×C4—1462no—
491C2×C4#1455661114yes—
492C2×C4C22×C22⋊D7314yes—
493C2×C4C22×C22⋊D7312yes—
494C2×C4C22×C22⋊D7311yescharacteristic
495C2×C4C22×C22⋊D7312yes—
496C2×C4#41×D7312yes—
497C2×C4#1455663812yes—
498C2×C4C24×D7311yescharacteristic
499C8—734no—
500C8—1464no—
501C8—1462no—
502C22—24no—
503C22—24no—
504C22—24no—
505C22—48no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22—84no—
510C22#1798923612yes—
511C22C2×#1455661112yes—
512C22#1798939812yes—
513C22C23×C22⋊D7311yescharacteristic
514C4—24no—
515C4—22no—
516C4—42no—
517C4—44no—
518C4—2924no—
519C4—2922no—
520C4—2922no—
521C4#1798923612yes—
522C4C2×#1455661114yes—
523C4C2×#41×D7311yescharacteristic
524C4C2×#1455663811yescharacteristic
525C2—44no—
526C2—82no—
527C2#2262234414yesdirect product factor
528C2C2×#1798923611yescharacteristic
529C2C22×#1455661111yescharacteristic
530C2C2×#1798939811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
Fitting, prime radicalC2×#555×C73C2
socleC23×C73C22×D4
hypercenterC2×#555D73
hypocenterC73C2×#3340
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. C2×#17989307C2semidirect
2. #22622344C2direct (N × H)
3. C2×#17988983C2semidirect
4. C2×#17988928C2semidirect
5. C2×#17988908C2semidirect
6. C2×#17988879C2semidirect
7. C2×#17988867C2semidirect
8. C2×#17988814C2semidirect
9. C2×C4×#11924016C2semidirect
10. C2×D4×#10596831C2semidirect
11. C2×#17988623C2semidirect
16. #17989307C22semidirect
24. #17988983C22semidirect
25. #17988928C22semidirect
26. #17988908C22semidirect
27. #17988879C22semidirect
28. #17988867C22semidirect
29. #17988814C22semidirect
30. C4×#11924016C22semidirect
31. D4×#10596831C22semidirect
32. #17988623C22semidirect
262. C2×C73#3340semidirect
278. C73C2×#3340semidirect
527. C2#22622344direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893072
#226223442
C2×#179889832
C2×#179889282
C2×#179889082
C2×#179888792
C2×#179888672
C2×#179888142
C2×C4×#119240162
C2×D4×#105968312
C2×#179886232
C2×#555×C732
C2×#334073