Finite Group Databasebeta

← C2×#11742919 #14262301

Subgroups — C2×#11742919 #14262301

Order 1792.

7238 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×#41C211yesmaximal, characteristic, complemented
2C2×#90524C212yesmaximal, complemented
3#11742919C2132yesmaximal, direct product factor
4C2×#90272C214yesmaximal, complemented
5C2×#90249C214yesmaximal, complemented
6C2×#90231C218yesmaximal, complemented
7C2×#90226C212yesmaximal, complemented
8C2×#90214C212yesmaximal, complemented
9C2×#90209C212yesmaximal, complemented
10C2×#90168C211yesmaximal, characteristic, complemented
11C2×#90170C214yesmaximal, complemented
12C22×#6433C211yesmaximal, characteristic, complemented
13C22×C7×#41C2211yescharacteristic
14C22×#1157C2212yes—
15C4×C7×#41C22116yescomplemented
16C2×C4×C7×Q8C2212yes—
17C2×C4×C7×D4C2214yes—
18C2×C4×C7×D4C2212yes—
19C2×C7×#117C2212yes—
20C2×C7×#117C2211yescharacteristic
21C22×C42×C7C2211yescharacteristic
22C22×C42×C7C2212yes—
23#90524C22132yescomplemented
24C2×#6509C2214yes—
25C2×#6502C2218yes—
26C2×#6501C2214yes—
27C2×#6493C2214yes—
28C2×#6493C2214yes—
29C2×#6492C2218yes—
30C2×C4×C22⋊D7C2218yes—
31C22×C4⋊Dic7C2212yes—
32C2×#6487C2214yes—
33C22×Dic7⋊C4C2214yes—
34#90272C22164yescomplemented
35#90249C22164yescomplemented
36#90231C221128yescomplemented
37#90226C22132yescomplemented
38#90214C22132yescomplemented
39#90209C22132yescomplemented
40C2×#6457C2218yes—
41C2×#6455C2214yes—
42C2×D7×C4⋊C4C2214yes—
43C2×#6452C2218yes—
44C2×#6447C2218yes—
45C2×(C22⋊D7)⋊C4C2218yes—
46C2×#6442C2218yes—
47#90170C22164yescomplemented
48C2×#6439C2218yes—
49#90168C22116yescomplemented
50C2×#6438C2212yes—
51C2×#6437C2211yescharacteristic
52C2×C4×D28C2214yes—
53C2×C4×D28C2214yes—
54C2×#6435C2218yes—
55C2×#6433C2212yes—
56C2×#6433C2212yes—
57C2×#6433C2214yes—
58C2×#6433C22116yescomplemented
59C2×#6432C2211yescharacteristic
60C2×C4×Dic14C2214yes—
61C2×#3512—71nomaximal, Sylow
62C2×C7×#41—28no—
63C2×C7×#41C2318yes—
64C22×C7×Q8C2311yescharacteristic
65C22×C7×D4C2311yescharacteristic
66C22×C7×D4C2312yes—
67C23×C4×C7C2312yes—
68C23×C4×C7C2312yes—
69C23×C4×C7C2314yes—
70C23×C4×C7C2311yescharacteristic
71C22×C22⋊D7C2314yes—
72C22×C22⋊D7C2318yes—
73C23×Dic7C2314yes—
74C2×#1157—216no—
75C2×#1157C23116yes—
76C22×D28C2312yes—
77C22×D28C2314yes—
78C22×C4×D7C2314yes—
79C22×C4×D7C2318yes—
80C22×Dic14C2312yes—
81C4×C7×Q8C23116yes—
82C4×C7×D4C23132yes—
83C4×C7×D4C23116yes—
84C7×#117C23116yes—
85C7×#117C2318yes—
86C2×C7×C4⋊C4C2314yes—
87C2×C7×C4⋊C4C2312yes—
88C2×C7×C22⋊C4C2314yes—
89C2×C7×C22⋊C4C2312yes—
90C2×C42×C7C2312yes—
91C2×C42×C7C2311yescharacteristic
92C2×C42×C7C2312yes—
93C2×C42×C7C2311yescharacteristic
94C2×C42×C7C2318yes—
95C2×C42×C7C2314yes—
96C2×C42×C7C23116yes—
97C2×C22⋊Dic7C2318yes—
98#6509C23132yes—
99#6502C23164yes—
100#6501C23132yes—
101#6493C23132yes—
102#6493C23132yes—
103#6492C23164yes—
104C4×C22⋊D7C23164yes—
105C2×(C2×D7)⋊C4C2314yes—
106C2×(C2×D7)⋊C4C2318yes—
107C2×(C2×D7)⋊C4C2314yes—
108C2×(C2×D7)⋊C4C2318yes—
109C2×C4⋊Dic7C2314yes—
110C2×C4⋊Dic7C2314yes—
111C2×C4⋊Dic7C2314yes—
112C2×C4⋊Dic7C23116yes—
113#6487C23132yes—
114C2×Dic7⋊C4C2318yes—
115C2×Dic7⋊C4C2318yes—
116C2×Dic7⋊C4C2318yes—
117C2×Dic7⋊C4C23132yes—
118C2×Dic7⋊C4C2318yes—
119C2×C4×Dic7C2318yes—
120#6457C23164yes—
121#6455C23132yes—
122D7×C4⋊C4C23132yes—
123#6452C23164yes—
124#6447C23164yes—
125(C22⋊D7)⋊C4C23164yes—
126#6442C23164yes—
127#6439C23164yes—
128#6438C23116yes—
129#6437C2318yes—
130C4×D28C23132yes—
131C4×D28C23132yes—
132#6435C23164yes—
133#6433C23116yes—
134#6433C23116yes—
135#6433C23132yes—
136#6432C2318yes—
137C4×Dic14C23132yes—
138#3512—732no—
139C2×#553—78no—
140C2×#553—74no—
141C2×#552—74no—
142C2×#541—72no—
143C2×#540—72no—
144C2×#537—72no—
145C2×#532—71no—
146C2×#529—74no—
147C22×#125—71no—
148C2×#520—72no—
149C2×C4×#41D711yescharacteristic, complemented
150C24×C7C2412yes—
151C24×C7C2411yescharacteristic
152C23×D7C2414yes—
153C7×#41—232no—
154C2×C7×Q8—24no—
155C2×C7×Q8C2414yes—
156C2×C7×D4—28no—
157C2×C7×D4—24no—
158C2×C7×D4C2414yes—
159C2×C7×D4C2418yes—
160C22×C4×C7—28no—
161C22×C4×C7—48no—
162C22×C4×C7—44no—
163C22×C4×C7#4118yes—
164C22×C4×C7C2414yes—
165C22×C4×C7C2412yes—
166C22×C4×C7C2412yes—
167C22×C4×C7C2412yes—
168C22×C4×C7C2418yes—
169C22×C4×C7C2418yes—
170C22×C4×C7C24116yes—
171C22×C4×C7C2411yescharacteristic
172C22×C4×C7C2411yescharacteristic
173C22×C4×C7C2414yes—
174C2×C22⋊D7—216no—
175C2×C22⋊D7—416no—
176C2×C22⋊D7C24116yes—
177C2×C22⋊D7C24132yes—
178C22×Dic7—48no—
179C22×Dic7C2414yes—
180C22×Dic7C2418yes—
181C22×Dic7C24116yes—
182#1157—264no—
183C2×D28—28no—
184C2×D28—48no—
185C2×D28C2418yes—
186C2×D28C24116yes—
187C2×C4×D7—216no—
188C2×C4×D7—416no—
189C2×C4×D7C24116yes—
190C2×C4×D7C24132yes—
191C2×Dic14—28no—
192C2×Dic14C2418yes—
193C7×C4⋊C4C24116yes—
194C7×C4⋊C4C2418yes—
195C7×C22⋊C4C24116yes—
196C7×C22⋊C4C2418yes—
197C42×C7C2418yes—
198C42×C7C2414yes—
199C42×C7C2418yes—
200C42×C7C2414yes—
201C42×C7C24116yes—
202C22⋊Dic7C24132yes—
203(C2×D7)⋊C4C24116yes—
204(C2×D7)⋊C4C24132yes—
205(C2×D7)⋊C4C24116yes—
206(C2×D7)⋊C4C24132yes—
207C4⋊Dic7C24116yes—
208C4⋊Dic7C24116yes—
209C4⋊Dic7C24116yes—
210Dic7⋊C4C24132yes—
211Dic7⋊C4C24132yes—
212Dic7⋊C4C24132yes—
213Dic7⋊C4C24132yes—
214C4×Dic7C24132yes—
215C22×#41—72no—
216C22×#41C2×D711yescharacteristic
217#553—7128no—
218#553—764no—
219#552—764no—
220#541—732no—
221#540—732no—
222#537—732no—
223#532—716no—
224C2×C4⋊Q8—71no—
225C2×#127—71no—
226#529—764no—
227C2×#126—78no—
228C2×#126—78no—
229C2×#125—78no—
230C2×#125—72no—
231C2×#125—72no—
232C2×#125—74no—
233C2×#125—716no—
234C2×#124—72no—
235C2×#123—78no—
236C2×#123—78no—
237C2×C22⋊Q8—74no—
238C2×C22⋊Q8—74no—
239C2×#121—74no—
240C2×#121—78no—
241C2×#121—74no—
242C2×#121—74no—
243C2×#121—78no—
244#520—732no—
245C4×#41C2×D7116yescomplemented
246C2×C4×Q8—74no—
247C2×C4×Q8C2×D712yes—
248C2×C4×D4—78no—
249C2×C4×D4—78no—
250C2×C4×D4—74no—
251C2×C4×D4—74no—
252C2×C4×D4C2×D714yes—
253C2×C4×D4C2×D712yes—
254C2×#117—74no—
255C2×#117—78no—
256C2×#117C2×D711yescharacteristic
257C2×#117C2×D712yes—
258C22×C4⋊C4—72no—
259C22×C4⋊C4—74no—
260C22×C4⋊C4—74no—
261C22×C42C2×D711yescharacteristic
262C22×C42C2×D712yes—
263C23×C7—24no—
264C23×C7—24no—
265C23×C7—28no—
266C23×C7C2×#4114yes—
267C23×C7C2514yes—
268C23×C7C2512yes—
269C23×C7C2511yescharacteristic
270C22×D7—28no—
271C22×D7—28no—
272C22×D7—28no—
273C22×D7C2518yes—
274C7×Q8—28no—
275C7×D4—216no—
276C7×D4—28no—
277C2×C4×C7—24no—
278C2×C4×C7—28no—
279C2×C4×C7—24no—
280C2×C4×C7—24no—
281C2×C4×C7—216no—
282C2×C4×C7—416no—
283C2×C4×C7—48no—
284C2×C4×C7C2×#4114yes—
285C2×C4×C7C2×#4114yes—
286C2×C4×C7C2×#41116yes—
287C2×C4×C7C2518yes—
288C2×C4×C7C2514yes—
289C2×C4×C7C2514yes—
290C2×C4×C7C2514yes—
291C2×C4×C7C2512yes—
292C2×C4×C7C2512yes—
293C22⋊D7—232no—
294C22⋊D7—432no—
295C2×Dic7—28no—
296C2×Dic7—216no—
297C2×Dic7—416no—
298C2×Dic7C2518yes—
299C2×Dic7C25116yes—
300D28—216no—
301D28—416no—
302C4×D7—232no—
303C4×D7—432no—
304Dic14—216no—
305C2×#41—28no—
306C2×#41—716no—
307C2×#41—1416no—
308C2×#41C22×D718yes—
309C22×Q8—72no—
310C22×Q8C22×D711yescharacteristic
311C22×D4—74no—
312C22×D4—78no—
313C22×D4—72no—
314C22×D4—74no—
315C22×D4C22×D712yes—
316C22×D4C22×D711yescharacteristic
317C23×C4—74no—
318C23×C4—74no—
319C23×C4—78no—
320C23×C4C22×D712yes—
321C23×C4C22×D712yes—
322C23×C4C22×D714yes—
323C23×C4C22×D711yescharacteristic
324C4⋊Q8—78no—
325#127—78no—
326#126—764no—
327#126—764no—
328#125—764no—
329#125—716no—
330#125—716no—
331#125—732no—
332#124—716no—
333#123—764no—
334#123—764no—
335C22⋊Q8—732no—
336C22⋊Q8—732no—
337#121—732no—
338#121—764no—
339#121—732no—
340#121—732no—
341#121—764no—
342C4×Q8—732no—
343C4×Q8C22×D7116yes—
344C4×D4—764no—
345C4×D4—764no—
346C4×D4—732no—
347C4×D4—732no—
348C4×D4C22×D7132yes—
349C4×D4C22×D7116yes—
350#117—732no—
351#117—764no—
352#117C22×D718yes—
353#117C22×D7116yes—
354C2×C4⋊C4—74no—
355C2×C4⋊C4—78no—
356C2×C4⋊C4—74no—
357C2×C4⋊C4—78no—
358C2×C4⋊C4—716no—
359C2×C4⋊C4—78no—
360C2×C4⋊C4—732no—
361C2×C4⋊C4—78no—
362C2×C4⋊C4—74no—
363C2×C4⋊C4—732no—
364C2×C4⋊C4C22×D712yes—
365C2×C4⋊C4C22×D714yes—
366C2×C22⋊C4—78no—
367C2×C22⋊C4—74no—
368C2×C22⋊C4—78no—
369C2×C22⋊C4—78no—
370C2×C22⋊C4—74no—
371C2×C22⋊C4C22×D712yes—
372C2×C22⋊C4C22×D714yes—
373C2×C42—78no—
374C2×C42C22×D714yes—
375C2×C42C22×D712yes—
376C2×C42C22×D711yescharacteristic
377C2×C42C22×D712yes—
378C2×C42C22×D718yes—
379C2×C42C22×D7116yes—
380C2×C42C22×D711yescharacteristic
381C22×C7—24no—
382C22×C7—28no—
383C22×C7—24no—
384C22×C7—28no—
385C22×C7—48no—
386C22×C7C22×#4114yes—
387C22×C7C22×#4112yes—
388C22×C7#58514yes—
389C22×C7C2611yescharacteristic
390C2×D7—28no—
391C2×D7—28no—
392C2×D7—28no—
393C2×D7—416no—
394C4×C7—24no—
395C4×C7—28no—
396C4×C7—24no—
397C4×C7—24no—
398C4×C7C22×#4114yes—
399C4×C7C22×#4114yes—
400Dic7—28no—
401Dic7—216no—
402C24—74no—
403C24C23×D712yes—
404C24C23×D711yescharacteristic
405#41—232no—
406#41—1464no—
407C2×Q8—24no—
408C2×Q8—78no—
409C2×Q8—148no—
410C2×Q8C23×D714yes—
411C2×D4—28no—
412C2×D4—24no—
413C2×D4—716no—
414C2×D4—732no—
415C2×D4—78no—
416C2×D4—716no—
417C2×D4—1416no—
418C2×D4—148no—
419C2×D4—288no—
420C2×D4—2816no—
421C2×D4C23×D718yes—
422C2×D4C23×D714yes—
423C22×C4—28no—
424C22×C4—48no—
425C22×C4—44no—
426C22×C4—74no—
427C22×C4—78no—
428C22×C4—716no—
429C22×C4—716no—
430C22×C4—732no—
431C22×C4—1416no—
432C22×C4—2816no—
433C22×C4—288no—
434C22×C4#115718yes—
435C22×C4C23×D718yes—
436C22×C4C23×D714yes—
437C22×C4C23×D712yes—
438C22×C4C23×D712yes—
439C22×C4C23×D712yes—
440C22×C4C23×D718yes—
441C22×C4C23×D7116yes—
442C22×C4C23×D714yes—
443C22×C4C23×D711yescharacteristic
444C22×C4C23×D711yescharacteristic
445C4⋊C4—732no—
446C4⋊C4—732no—
447C4⋊C4—732no—
448C4⋊C4—732no—
449C4⋊C4—716no—
450C4⋊C4—716no—
451C4⋊C4—716no—
452C4⋊C4C23×D718yes—
453C4⋊C4C23×D7116yes—
454C22⋊C4—732no—
455C22⋊C4—716no—
456C22⋊C4—732no—
457C22⋊C4—732no—
458C22⋊C4—716no—
459C22⋊C4C23×D718yes—
460C22⋊C4C23×D7116yes—
461C42—732no—
462C42C23×D714yes—
463C42C23×D7116yes—
464C42C23×D718yes—
465C42C23×D714yes—
466C42C23×D718yes—
467C2×C7—24no—
468C2×C7—44no—
469C2×C7#351214yescomplemented
470C2×C7C23×#4111yescharacteristic
471C2×C7C2×#58512yes—
472D7—48no—
473C23—24no—
474C23—24no—
475C23—28no—
476C23—78no—
477C23—148no—
478C23—148no—
479C23—148no—
480C23C2×#115714yes—
481C23C24×D714yes—
482C23C24×D712yes—
483C23C24×D711yescharacteristic
484Q8—28no—
485Q8—1416no—
486D4—216no—
487D4—28no—
488D4—1432no—
489D4—1416no—
490D4—2816no—
491D4—2832no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—28no—
495C2×C4—24no—
496C2×C4—216no—
497C2×C4—416no—
498C2×C4—48no—
499C2×C4—78no—
500C2×C4—716no—
501C2×C4—148no—
502C2×C4—1416no—
503C2×C4—1432no—
504C2×C4—2832no—
505C2×C4—2816no—
506C2×C4C2×#115714yes—
507C2×C4C2×#115714yes—
508C2×C4C2×#1157116yes—
509C2×C4C24×D718yes—
510C2×C4C24×D714yes—
511C2×C4C24×D714yes—
512C2×C4C24×D714yes—
513C2×C4C24×D712yes—
514C2×C4C24×D712yes—
515C7C2×#351211yescharacteristic, complemented, Sylow
516C22—24no—
517C22—28no—
518C22—24no—
519C22—28no—
520C22—48no—
521C22—148no—
522C22—148no—
523C22—148no—
524C22—2816no—
525C22C22×#115714yes—
526C22C22×#115712yes—
527C22#9061614yes—
528C22C25×D711yescharacteristic
529C4—24no—
530C4—24no—
531C4—28no—
532C4—24no—
533C4—148no—
534C4—1416no—
535C4C22×#115714yes—
536C4C22×#115714yes—
537C2—24no—
538C2—44no—
539C2—288no—
540C2#1174291914yesdirect product factor
541C2C23×#115711yescharacteristic
542C2C2×#9061612yes—
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC2×C4×C7×#41C2
socleC23×C7C25
hypercenterC2×C4×#41D7
hypocenterC7C2×#3512
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×C4×C7×#41C2semidirect
2. C2×#90524C2semidirect
3. #11742919C2direct (N × H)
4. C2×#90272C2semidirect
5. C2×#90249C2semidirect
6. C2×#90231C2semidirect
7. C2×#90226C2semidirect
8. C2×#90214C2semidirect
9. C2×#90209C2semidirect
10. C2×#90168C2semidirect
11. C2×#90170C2semidirect
12. C22×#6433C2semidirect
15. C4×C7×#41C22semidirect
23. #90524C22semidirect
34. #90272C22semidirect
35. #90249C22semidirect
36. #90231C22semidirect
37. #90226C22semidirect
38. #90214C22semidirect
39. #90209C22semidirect
47. #90170C22semidirect
49. #90168C22semidirect
58. C2×#6433C22semidirect
149. C2×C4×#41D7semidirect
245. C4×#41C2×D7semidirect
469. C2×C7#3512semidirect
515. C7C2×#3512semidirect
540. C2#11742919direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C7×#412
C2×#905242
#117429192
C2×#902722
C2×#902492
C2×#902312
C2×#902262
C2×#902142
C2×#902092
C2×#901682
C2×#901702
C22×#64332
C2×#35127