Finite Group Databasebeta

← C2×#11743155 #14262295

Subgroups — C2×#11743155 #14262295

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
1C22×C7×#125C211yesmaximal, characteristic, complemented
2C2×#90386C214yesmaximal, complemented
3C2×#90385C214yesmaximal, complemented
4C2×#90388C212yesmaximal, complemented
5C2×#90389C212yesmaximal, complemented
6#11743155C2132yesmaximal, direct product factor
7C2×#90382C214yesmaximal, complemented
8C2×#90205C218yesmaximal, complemented
9C2×#90201C212yesmaximal, complemented
10C2×#90195C212yesmaximal, complemented
11C2×#90168C211yesmaximal, characteristic, complemented
12C2×C4×#1157C211yesmaximal, characteristic, complemented
13C22×#1157C2211yescharacteristic
14C22×#1157C2212yes—
15C2×C7×#125C2212yes—
16C2×C7×#125C2212yes—
17C2×C7×#125C2214yes—
18C2×C7×#125C22116yescomplemented
19C22×C7×C4⋊C4C2212yes—
20C22×C7×C4⋊C4C2214yes—
21C22×C42×C7C2211yescharacteristic
22C2×#6493C2214yes—
23C2×#6493C2218yes—
24C2×C4×C22⋊D7C2214yes—
25C2×C4×C22⋊D7C2218yes—
26C2×#6489C2211yescharacteristic
27#90389C22132yescomplemented
28#90388C22132yescomplemented
29#90386C22164yescomplemented
30#90385C22164yescomplemented
31#90382C22164yescomplemented
32#90205C221128yescomplemented
33C2×#6461C2218yes—
34C2×#6461C2218yes—
35#90201C22132yescomplemented
36C2×#6460C2214yes—
37C2×#6460C2214yes—
38C2×#6458C2214yes—
39C2×#6458C2214yes—
40C2×#6458C2218yes—
41C2×#6457C2218yes—
42C2×#6457C2218yes—
43#90195C22132yescomplemented
44C2×#6456C2214yes—
45C2×#6456C2218yes—
46C2×#6455C2214yes—
47C2×#6455C2218yes—
48C2×D7×C4⋊C4C2214yes—
49C2×#6453C2218yes—
50C2×#6450C2214yes—
51#90168C22116yescomplemented
52C2×#6438C2212yes—
53C2×#6437C2211yescharacteristic
54C4×#1157C22116yescomplemented
55C2×C4×D28C2212yes—
56C2×C4×D28C2214yes—
57C2×#6435C2212yes—
58C2×C42×D7C2212yes—
59C2×#6432C2211yescharacteristic
60C2×C4×Dic14C2212yes—
61C2×#3512—71nomaximal, Sylow
62C23×C4×C7C2312yes—
63C23×C4×C7C2314yes—
64C23×C4×C7C2311yescharacteristic
65C22×C22⋊D7C2312yes—
66C22×C22⋊D7C2314yes—
67C2×#1157—28no—
68C2×#1157—216no—
69C2×#1157C2318yes—
70C2×#1157C23116yes—
71C22×D28C2311yescharacteristic
72C22×D28C2312yes—
73C22×D28C2314yes—
74C22×D28C2318yes—
75C22×C4×D7C2312yes—
76C22×C4×D7C2314yes—
77C22×C4×D7C2314yes—
78C22×C4×D7C2318yes—
79C22×Dic14C2311yescharacteristic
80C22×Dic14C2312yes—
81C7×#125C23116yes—
82C7×#125C23132yes—
83C7×#125C23116yes—
84C2×C7×C4⋊C4C2314yes—
85C2×C7×C4⋊C4C2318yes—
86C2×C7×C4⋊C4C2314yes—
87C2×C7×C4⋊C4C2318yes—
88C2×C7×C4⋊C4C23116yes—
89C2×C7×C4⋊C4C23132yes—
90C2×C42×C7C2312yes—
91C2×C42×C7C2311yescharacteristic
92C2×C42×C7C2311yescharacteristic
93C2×C42×C7C2318yes—
94C2×C22⋊Dic7C2312yes—
95#6493C23132yes—
96#6493C23164yes—
97C4×C22⋊D7C23132yes—
98C4×C22⋊D7C23164yes—
99C2×(C2×D7)⋊C4C2314yes—
100C2×(C2×D7)⋊C4C2314yes—
101C2×(C2×D7)⋊C4C2314yes—
102C2×(C2×D7)⋊C4C2318yes—
103C2×(C2×D7)⋊C4C2318yes—
104C2×(C2×D7)⋊C4C2318yes—
105#6489C2318yes—
106C2×C4⋊Dic7C2312yes—
107C2×C4⋊Dic7C2314yes—
108C2×C4⋊Dic7C2318yes—
109C2×Dic7⋊C4C2314yes—
110C2×Dic7⋊C4C2318yes—
111C2×C4×Dic7C2314yes—
112C2×C4×Dic7C2312yes—
113C2×C4×Dic7C2318yes—
114#6461C23164yes—
115#6461C23164yes—
116#6460C23132yes—
117#6460C23132yes—
118#6458C23132yes—
119#6458C23132yes—
120#6458C23164yes—
121#6457C23164yes—
122#6457C23164yes—
123#6456C23164yes—
124#6456C23132yes—
125#6455C23164yes—
126#6455C23132yes—
127D7×C4⋊C4C23132yes—
128#6453C23164yes—
129#6450C23132yes—
130#6438C23116yes—
131#6437C2318yes—
132C4×D28C23132yes—
133C4×D28C23116yes—
134#6435C23116yes—
135C42×D7C23116yes—
136#6432C2318yes—
137C4×Dic14C23116yes—
138#3512—732no—
139C2×#553—74no—
140C2×#553—78no—
141C2×#552—74no—
142C2×#541—72no—
143C2×#540—72no—
144C2×#537—72no—
145C2×#532—71no—
146C2×#529—74no—
147C22×#125D711yescharacteristic, complemented
148C2×#520—72no—
149C2×C4×#41—71no—
150C24×C7C2411yescharacteristic
151C23×D7C2414yes—
152C23×D7C2412yes—
153C22×C4×C7—44no—
154C22×C4×C7—48no—
155C22×C4×C7#4118yes—
156C22×C4×C7C2412yes—
157C22×C4×C7C2418yes—
158C22×C4×C7C2412yes—
159C22×C4×C7C2418yes—
160C22×C4×C7C24116yes—
161C22×C4×C7C2411yescharacteristic
162C22×C4×C7C2411yescharacteristic
163C22×C4×C7C2414yes—
164C2×C22⋊D7—28no—
165C2×C22⋊D7—216no—
166C2×C22⋊D7C2418yes—
167C2×C22⋊D7C24116yes—
168C22×Dic7C2414yes—
169C22×Dic7C2412yes—
170C22×Dic7C2414yes—
171#1157—232no—
172#1157—264no—
173C2×D28—28no—
174C2×D28—24no—
175C2×D28—416no—
176C2×D28—48no—
177C2×D28C2414yes—
178C2×D28C2418yes—
179C2×D28C24116yes—
180C2×D28C24132yes—
181C2×C4×D7—28no—
182C2×C4×D7—216no—
183C2×C4×D7—48no—
184C2×C4×D7—416no—
185C2×C4×D7C2418yes—
186C2×C4×D7C24116yes—
187C2×C4×D7C24116yes—
188C2×C4×D7C24132yes—
189C2×Dic14—28no—
190C2×Dic14—24no—
191C2×Dic14C2414yes—
192C2×Dic14C2418yes—
193C7×C4⋊C4C24116yes—
194C7×C4⋊C4C24132yes—
195C7×C4⋊C4C24116yes—
196C7×C4⋊C4C24132yes—
197C42×C7C2418yes—
198C42×C7C2414yes—
199C42×C7C2414yes—
200C22⋊Dic7C2418yes—
201(C2×D7)⋊C4C24116yes—
202(C2×D7)⋊C4C24116yes—
203(C2×D7)⋊C4C24116yes—
204(C2×D7)⋊C4C24132yes—
205(C2×D7)⋊C4C24132yes—
206(C2×D7)⋊C4C24132yes—
207C4⋊Dic7C2418yes—
208C4⋊Dic7C24116yes—
209C4⋊Dic7C24132yes—
210Dic7⋊C4C24116yes—
211Dic7⋊C4C24132yes—
212C4×Dic7C24116yes—
213C4×Dic7C2418yes—
214C4×Dic7C24132yes—
215C22×#41—71no—
216C22×#41—72no—
217#553—764no—
218#553—7128no—
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×#125C2×D712yes—
231C2×#125C2×D712yes—
232C2×#125C2×D714yes—
233C2×#125C2×D7116yescomplemented
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×#41—716no—
246C2×C4×Q8—74no—
247C2×C4×Q8—72no—
248C2×C4×D4—74no—
249C2×C4×D4—78no—
250C2×C4×D4—74no—
251C2×C4×D4—78no—
252C2×C4×D4—72no—
253C2×C4×D4—74no—
254C2×#117—71no—
255C2×#117—74no—
256C2×#117—78no—
257C2×#117—72no—
258C22×C4⋊C4—74no—
259C22×C4⋊C4C2×D712yes—
260C22×C4⋊C4C2×D714yes—
261C22×C42—72no—
262C22×C42C2×D711yescharacteristic
263C23×C7—24no—
264C23×C7C2×#4114yes—
265C23×C7C2512yes—
266C23×C7C2511yescharacteristic
267C22×D7—28no—
268C22×D7—24no—
269C22×D7—28no—
270C22×D7—28no—
271C22×D7—28no—
272C22×D7C2518yes—
273C22×D7C2514yes—
274C2×C4×C7—24no—
275C2×C4×C7—216no—
276C2×C4×C7—24no—
277C2×C4×C7—48no—
278C2×C4×C7—416no—
279C2×C4×C7C2×#4114yes—
280C2×C4×C7C2×#4114yes—
281C2×C4×C7C2×#41116yes—
282C2×C4×C7C2514yes—
283C2×C4×C7C25116yes—
284C2×C4×C7C2514yes—
285C2×C4×C7C2512yes—
286C2×C4×C7C2512yes—
287C22⋊D7—216no—
288C22⋊D7—232no—
289C2×Dic7—28no—
290C2×Dic7—24no—
291C2×Dic7—28no—
292C2×Dic7C2518yes—
293C2×Dic7C2514yes—
294C2×Dic7C2518yes—
295D28—216no—
296D28—28no—
297D28—432no—
298D28—416no—
299C4×D7—216no—
300C4×D7—232no—
301C4×D7—416no—
302C4×D7—432no—
303Dic14—216no—
304Dic14—28no—
305C2×#41—78no—
306C2×#41—716no—
307C2×#41—148no—
308C2×#41—1416no—
309C22×Q8—71no—
310C22×Q8—72no—
311C22×D4—72no—
312C22×D4—74no—
313C22×D4—71no—
314C22×D4—72no—
315C22×D4—78no—
316C22×D4—74no—
317C23×C4—74no—
318C23×C4—72no—
319C23×C4—78no—
320C23×C4—74no—
321C23×C4C22×D714yes—
322C23×C4C22×D712yes—
323C23×C4C22×D711yescharacteristic
324C4⋊Q8—78no—
325#127—78no—
326#126—764no—
327#126—764no—
328#125—764no—
329#125C22×D7116yes—
330#125C22×D7116yes—
331#125C22×D7132yes—
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×Q8—716no—
344C4×D4—732no—
345C4×D4—764no—
346C4×D4—732no—
347C4×D4—764no—
348C4×D4—716no—
349C4×D4—732no—
350#117—78no—
351#117—732no—
352#117—764no—
353#117—716no—
354C2×C4⋊C4—72no—
355C2×C4⋊C4—78no—
356C2×C4⋊C4—74no—
357C2×C4⋊C4—78no—
358C2×C4⋊C4—74no—
359C2×C4⋊C4—732no—
360C2×C4⋊C4C22×D714yes—
361C2×C4⋊C4C22×D718yes—
362C2×C4⋊C4C22×D714yes—
363C2×C4⋊C4C22×D7116yes—
364C2×C4⋊C4C22×D718yes—
365C2×C4⋊C4C22×D7132yes—
366C2×C22⋊C4—72no—
367C2×C22⋊C4—74no—
368C2×C22⋊C4—74no—
369C2×C22⋊C4—78no—
370C2×C22⋊C4—78no—
371C2×C22⋊C4—74no—
372C2×C22⋊C4—78no—
373C2×C42—72no—
374C2×C42—78no—
375C2×C42—74no—
376C2×C42—716no—
377C2×C42C22×D711yescharacteristic
378C2×C42C22×D712yes—
379C2×C42C22×D718yes—
380C2×C42C22×D711yescharacteristic
381C22×C7—24no—
382C22×C7—28no—
383C22×C7C22×#4114yes—
384C22×C7C22×#4112yes—
385C22×C7#58514yes—
386C22×C7C2611yescharacteristic
387C2×D7—28no—
388C2×D7—24no—
389C2×D7—28no—
390C2×D7—28no—
391C2×D7—28no—
392C2×D7—416no—
393C2×D7—48no—
394C4×C7—24no—
395C4×C7—216no—
396C4×C7—24no—
397C4×C7C22×#4114yes—
398C4×C7C22×#4114yes—
399Dic7—28no—
400Dic7—24no—
401Dic7—28no—
402C24—74no—
403C24—72no—
404C24C23×D711yescharacteristic
405#41—1432no—
406#41—1464no—
407C2×Q8—74no—
408C2×Q8—78no—
409C2×Q8—144no—
410C2×Q8—148no—
411C2×D4—78no—
412C2×D4—716no—
413C2×D4—74no—
414C2×D4—78no—
415C2×D4—732no—
416C2×D4—716no—
417C2×D4—148no—
418C2×D4—1416no—
419C2×D4—144no—
420C2×D4—148no—
421C2×D4—2816no—
422C2×D4—288no—
423C22×C4—44no—
424C22×C4—48no—
425C22×C4—74no—
426C22×C4—74no—
427C22×C4—72no—
428C22×C4—78no—
429C22×C4—716no—
430C22×C4—716no—
431C22×C4—732no—
432C22×C4—1416no—
433C22×C4—148no—
434C22×C4—288no—
435C22×C4—2816no—
436C22×C4#116118yes—
437C22×C4C23×D712yes—
438C22×C4C23×D718yes—
439C22×C4C23×D712yes—
440C22×C4C23×D718yes—
441C22×C4C23×D7116yes—
442C22×C4C23×D714yes—
443C22×C4C23×D711yescharacteristic
444C22×C4C23×D711yescharacteristic
445C4⋊C4—732no—
446C4⋊C4—716no—
447C4⋊C4—78no—
448C4⋊C4—732no—
449C4⋊C4—716no—
450C4⋊C4C23×D7116yes—
451C4⋊C4C23×D7132yes—
452C4⋊C4C23×D7116yes—
453C4⋊C4C23×D7132yes—
454C22⋊C4—78no—
455C22⋊C4—716no—
456C22⋊C4—716no—
457C22⋊C4—732no—
458C22⋊C4—732no—
459C22⋊C4—716no—
460C22⋊C4—732no—
461C42—78no—
462C42—716no—
463C42—732no—
464C42C23×D714yes—
465C42C23×D714yes—
466C42C23×D718yes—
467C2×C7—24no—
468C2×C7#351214yescomplemented
469C2×C7C23×#4111yescharacteristic
470C2×C7C2×#58512yes—
471D7—48no—
472D7—44no—
473C23—24no—
474C23—78no—
475C23—74no—
476C23—148no—
477C23—144no—
478C23—148no—
479C23—148no—
480C23—148no—
481C23C2×#116114yes—
482C23C24×D712yes—
483C23C24×D711yescharacteristic
484Q8—148no—
485Q8—1416no—
486D4—1416no—
487D4—1432no—
488D4—148no—
489D4—1416no—
490D4—2832no—
491D4—2816no—
492C2×C4—24no—
493C2×C4—216no—
494C2×C4—24no—
495C2×C4—48no—
496C2×C4—416no—
497C2×C4—78no—
498C2×C4—74no—
499C2×C4—78no—
500C2×C4—148no—
501C2×C4—144no—
502C2×C4—148no—
503C2×C4—1432no—
504C2×C4—1416no—
505C2×C4—2816no—
506C2×C4—2832no—
507C2×C4C2×#116114yes—
508C2×C4C2×#116114yes—
509C2×C4C2×#1161116yes—
510C2×C4C24×D714yes—
511C2×C4C24×D7116yes—
512C2×C4C24×D714yes—
513C2×C4C24×D712yes—
514C2×C4C24×D712yes—
515C7C2×#351211yescharacteristic, complemented, Sylow
516C22—24no—
517C22—28no—
518C22—148no—
519C22—144no—
520C22—148no—
521C22—148no—
522C22—148no—
523C22—2816no—
524C22—288no—
525C22C22×#116114yes—
526C22C22×#116112yes—
527C22#9061614yes—
528C22C25×D711yescharacteristic
529C4—24no—
530C4—216no—
531C4—24no—
532C4—144no—
533C4—148no—
534C4—148no—
535C4C22×#116114yes—
536C4C22×#116114yes—
537C2—24no—
538C2—288no—
539C2—284no—
540C2#1174315514yesdirect product factor
541C2C23×#116111yescharacteristic
542C2C2×#9061612yes—
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC22×C7×#125C2
socleC23×C7C25
hypercenterC22×#125D7
hypocenterC7C2×#3512
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
1. C22×C7×#125C2semidirect
2. C2×#90386C2semidirect
3. C2×#90385C2semidirect
4. C2×#90388C2semidirect
5. C2×#90389C2semidirect
6. #11743155C2direct (N × H)
7. C2×#90382C2semidirect
8. C2×#90205C2semidirect
9. C2×#90201C2semidirect
10. C2×#90195C2semidirect
11. C2×#90168C2semidirect
12. C2×C4×#1157C2semidirect
18. C2×C7×#125C22semidirect
27. #90389C22semidirect
28. #90388C22semidirect
29. #90386C22semidirect
30. #90385C22semidirect
31. #90382C22semidirect
32. #90205C22semidirect
35. #90201C22semidirect
43. #90195C22semidirect
51. #90168C22semidirect
54. C4×#1157C22semidirect
147. C22×#125D7semidirect
233. C2×#125C2×D7semidirect
468. C2×C7#3512semidirect
515. C7C2×#3512semidirect
540. C2#11743155direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1252
C2×#903862
C2×#903852
C2×#903882
C2×#903892
#117431552
C2×#903822
C2×#902052
C2×#902012
C2×#901952
C2×#901682
C2×C4×#11572
C2×#35127