Finite Group Databasebeta

← C2×#11738432 #14232277

Subgroups — C2×#11738432 #14232277

Order 1792.

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×#90423C211yesmaximal, characteristic, complemented
2C2×#90254C211yesmaximal, characteristic
3C2×C7×#474C211yesmaximal, characteristic, complemented
4C2×#89851C211yesmaximal, characteristic, complemented
5C2×C4×#1142C211yesmaximal, characteristic, complemented
6#11738432C2116yesmaximal, direct product factor
7C2×#89660C212yesmaximal, complemented
8C2×#89652C212yesmaximal, complemented
9C2×#89622C211yesmaximal, characteristic, complemented
10C2×#89606C211yesmaximal, characteristic, complemented
11C2×#89556C212yesmaximal, complemented
12C2×#89550C212yesmaximal, complemented
13C2×C7×C4⋊Q8C2211yescharacteristic
14C2×C4×C7×D4C2211yescharacteristic
15C2×#6510—21no—
16C2×Q8×Dic7—21no—
17C2×#6501C2212yes—
18C22×#1142C2211yescharacteristic
19C2×#6493—21no—
20C2×#6489—21no—
21C22×C8×D7C2212yes—
22#90423—24no—
23#90423C2218yescomplemented
24#90254—24no—
25#90254C2218yes—
26C2×#6461—22no—
27C2×#6460C2212yes—
28C2×#6455C2212yes—
29C2×#6455C2212yes—
30C2×#6448—22no—
31C2×C4×D28C2211yescharacteristic
32C2×#6432C2211yescharacteristic
33C2×C4×Dic14C2211yescharacteristic
34C7×#474C2218yescomplemented
35C2×C7×#107C2212yes—
36C2×C7×C4⋊C8C2211yescharacteristic
37C2×C7×#102C2212yes—
38C2×#6406C2211yescharacteristic
39C2×(C2×D7)⋊C8C2212yes—
40C2×#6392C2212yes—
41C2×#6390C2212yes—
42#89851C2218yescomplemented
43C4×#1142C2218yescomplemented
44C2×#6384C2211yescharacteristic
45C2×#6382C2211yescharacteristic
46C2×#6382C2212yes—
47C2×#6382C2212yes—
48C2×C4×C7⋊C8C2211yescharacteristic
49#89660C22116yescomplemented
50#89652C22116yescomplemented
51#89622C2218yescomplemented
52#89606C2218yescomplemented
53#89556C22116yescomplemented
54#89550C22116yescomplemented
55C2×#3340—71nomaximal, Sylow
56C22×C7×Q8—21no—
57C22×C7×D4C2311yescharacteristic
58C23×C4×C7—21no—
59C22×C22⋊D7—22no—
60C22×D28D411yescharacteristic
61C22×C4×D7C2312yes—
62C22×Dic14—21no—
63C22×Dic14C2311yescharacteristic
64C22×C7×C8C2312yes—
65C7×C4⋊Q8—22no—
66C7×C4⋊Q8C2314yes—
67C4×C7×D4—22no—
68C4×C7×D4C2314yes—
69C2×C7×C4⋊C4—21no—
70C2×C7×C4⋊C4C2311yescharacteristic
71C2×C7×C4⋊C4C2312yes—
72C2×C7×C22⋊C4—21no—
73C2×C42×C7C2311yescharacteristic
74C2×C22⋊Dic7—22no—
75#6510—28no—
76Q8×Dic7—28no—
77#6501—24no—
78#6501C2318yes—
79C2×#1142—24no—
80C2×#1142C2314yes—
81#6493—28no—
82C2×(C2×D7)⋊C4—22no—
83C2×(C2×D7)⋊C4—22no—
84C2×(C2×D7)⋊C4—22no—
85C2×(C2×D7)⋊C4D412yes—
86#6489—28no—
87C2×C4⋊Dic7—21no—
88C2×C4⋊Dic7—22no—
89C2×C4⋊Dic7D411yescharacteristic
90C2×C4⋊Dic7C2312yes—
91C2×C4⋊Dic7C2311yescharacteristic
92C2×Dic7⋊C4—21no—
93C2×C4×Dic7—21no—
94C2×C4×Dic7—22no—
95C2×C4×Dic7—22no—
96C22×C7⋊C8C2311yescharacteristic
97C22×C7⋊C8C2311yescharacteristic
98C2×C8×D7—28no—
99C2×C8×D7C2318yes—
100#6461—216no—
101#6460—24no—
102#6460C2318yes—
103#6455—24no—
104#6455—24no—
105#6455C2318yes—
106#6455C2318yes—
107#6448—216no—
108C4×D28D414yes—
109C4×D28C2314yes—
110#6432—22no—
111#6432C2314yes—
112C4×Dic14—22no—
113C4×Dic14C2314yes—
114C7×#107C2318yes—
115C7×C4⋊C8C2314yes—
116C7×#102C2318yes—
117#6406C2314yes—
118(C2×D7)⋊C8C2318yes—
119#6392C2318yes—
120#6390C2318yes—
121#6384C2314yes—
122#6382C2314yes—
123#6382C2318yes—
124#6382C2318yes—
125C4×C7⋊C8C2314yes—
126C2×#556—71no—
127C2×#555—71no—
128#3340—716no—
129C2×#498—71no—
130C2×#485—72no—
131C2×#482—72no—
132C2×#477—71no—
133C2×#474D711yescharacteristic, complemented
134C2×#465—72no—
135C2×C4×SD16—71no—
136C2×C8×D4—71no—
137C2×#427—72no—
138C24×C7—21no—
139C23×D7C2×D412yes—
140C2×C7×Q8—24no—
141C2×C7×Q8—44no—
142C2×C7×D4—21no—
143C2×C7×D4—22no—
144C2×C7×D4—22no—
145C2×C7×D4C2412yes—
146C22×C4×C7—21no—
147C22×C4×C7—22no—
148C22×C4×C7—24no—
149C22×C4×C7—44no—
150C22×C4×C7C2×D411yescharacteristic
151C22×C4×C7C2×D411yescharacteristic
152C22×C4×C7C2411yescharacteristic
153C2×C22⋊D7—28no—
154C2×C22⋊D7—84no—
155C22×Dic7—21no—
156C22×Dic7—21no—
157C22×Dic7—22no—
158C22×Dic7C2×D412yes—
159C2×D28—24no—
160C2×D28C2×D414yes—
161C2×C4×D7—24no—
162C2×C4×D7—24no—
163C2×C4×D7C2×D414yes—
164C2×C4×D7C2414yes—
165C2×Dic14—22no—
166C2×Dic14—22no—
167C2×Dic14—21no—
168C2×Dic14—24no—
169C2×Dic14—82no—
170C2×Dic14C2412yes—
171C2×C7×C8—24no—
172C2×C7×C8C2414yes—
173C7×C4⋊C4—21no—
174C7×C4⋊C4—22no—
175C7×C4⋊C4—24no—
176C7×C4⋊C4C2414yes—
177C7×C4⋊C4C2412yes—
178C7×C22⋊C4—24no—
179C42×C7C2×D412yes—
180C42×C7C2412yes—
181C22⋊Dic7—28no—
182#1142—28no—
183(C2×D7)⋊C4—28no—
184(C2×D7)⋊C4—28no—
185(C2×D7)⋊C4—28no—
186(C2×D7)⋊C4C2×D418yes—
187C4⋊Dic7—21no—
188C4⋊Dic7—22no—
189C4⋊Dic7—24no—
190C4⋊Dic7—28no—
191C4⋊Dic7C2×D414yes—
192C4⋊Dic7C2412yes—
193C4⋊Dic7C2414yes—
194Dic7⋊C4—24no—
195C4×Dic7—24no—
196C4×Dic7—28no—
197C4×Dic7—28no—
198C2×C7⋊C8—22no—
199C2×C7⋊C8#4114yes—
200C2×C7⋊C8C2412yes—
201C2×C7⋊C8C2412yes—
202C8×D7—216no—
203C22×SD16—71no—
204C23×C8—72no—
205#556—78no—
206#556—144no—
207#555—78no—
208#555—144no—
209C2×C4⋊Q8—71no—
210C2×C4⋊Q8C2×D711yescharacteristic
211C2×#126—142no—
212C2×#124—142no—
213C2×#124—141no—
214C2×C22⋊Q8—72no—
215C2×#121—72no—
216C2×#121—141no—
217C2×C4×Q8—71no—
218C2×C4×Q8—141no—
219C2×C4×D4—71no—
220C2×C4×D4C2×D711yescharacteristic
221C2×#117—72no—
222C2×#117—72no—
223C2×#117—141no—
224#498—78no—
225#485—716no—
226#482—716no—
227#477—78no—
228#474C2×D718yescomplemented
229#465—716no—
230C4×SD16—78no—
231C8×D4—78no—
232#427—716no—
233C2×#107—72no—
234C2×#107C2×D712yes—
235C2×#106—72no—
236C2×#106—72no—
237C2×#106—71no—
238C2×C4⋊C8C2×D711yescharacteristic
239C2×#103—72no—
240C2×#103—71no—
241C2×#102—71no—
242C2×#102C2×D712yes—
243C2×C22⋊C8—72no—
244C2×C4×C8—71no—
245C23×C7—22no—
246C23×C7—42no—
247C23×C7—42no—
248C23×C7—42no—
249C23×C7C22×D411yescharacteristic
250C22×D7—24no—
251C22×D7—24no—
252C22×D7—24no—
253C22×D7C22×D414yes—
254C7×Q8—48no—
255C7×D4—22no—
256C7×D4—22no—
257C7×D4—42no—
258C2×C4×C7—22no—
259C2×C4×C7—22no—
260C2×C4×C7—24no—
261C2×C4×C7—42no—
262C2×C4×C7—44no—
263C2×C4×C7—48no—
264C2×C4×C7#13514yes—
265C2×C4×C7C22×D412yes—
266C2×C4×C7C22×D411yescharacteristic
267C2×C4×C7C22×D412yes—
268C2×C4×C7C2×#4112yes—
269C2×C4×C72−1+412yes—
270C2×C4×C7C2511yescharacteristic
271C22⋊D7—88no—
272C2×Dic7—24no—
273C2×Dic7—22no—
274C2×Dic7—22no—
275C2×Dic7—24no—
276C2×Dic7—42no—
277C2×Dic7—44no—
278C2×Dic7—42no—
279C2×Dic7C22×D414yes—
280D28—28no—
281C4×D7—28no—
282C4×D7—24no—
283C4×D7—24no—
284Dic14—22no—
285Dic14—22no—
286Dic14—42no—
287Dic14—84no—
288C7×C8—24no—
289C7⋊C8—22no—
290C7⋊C8C2×#4114yes—
291C22×Q8—21no—
292C22×Q8—71no—
293C22×Q8—141no—
294C22×D4—71no—
295C22×D4—142no—
296C22×D4C22×D711yescharacteristic
297C23×C4—21no—
298C23×C4—72no—
299C2×SD16—74no—
300C2×SD16—144no—
301C22×C8—71no—
302C22×C8—71no—
303C22×C8—78no—
304C22×C8—148no—
305C22×C8C22×D712yes—
306C4⋊Q8—22no—
307C4⋊Q8—74no—
308C4⋊Q8—142no—
309C4⋊Q8C22×D714yes—
310#126—1416no—
311#124—1416no—
312#124—148no—
313C22⋊Q8—78no—
314C22⋊Q8—144no—
315#121—78no—
316#121—148no—
317#121—144no—
318C4×Q8—74no—
319C4×Q8—148no—
320C4×Q8—142no—
321C4×D4—22no—
322C4×D4—74no—
323C4×D4—74no—
324C4×D4C22×D714yes—
325#117—78no—
326#117—78no—
327#117—144no—
328#117—144no—
329#117—148no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—71no—
332C2×C4⋊C4—71no—
333C2×C4⋊C4—72no—
334C2×C4⋊C4—142no—
335C2×C4⋊C4—141no—
336C2×C4⋊C4—141no—
337C2×C4⋊C4C22×D711yescharacteristic
338C2×C4⋊C4C22×D712yes—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—72no—
341C2×C22⋊C4—142no—
342C2×C22⋊C4—142no—
343C2×C22⋊C4—142no—
344C2×C22⋊C4—142no—
345C2×C42—142no—
346C2×C42—142no—
347C2×C42—141no—
348C2×C42C22×D711yescharacteristic
349#107—78no—
350#107C22×D718yes—
351#106—74no—
352#106—78no—
353#106—78no—
354C4⋊C8C22×D714yes—
355#103—78no—
356#103—74no—
357#102—74no—
358#102C22×D718yes—
359C22⋊C8—78no—
360C4×C8—74no—
361C22×C7—42no—
362C22×C7—42no—
363C22×C7—42no—
364C22×C7—84no—
365C22×C7#54712yes—
366C22×C7C2×#13512yes—
367C22×C7#57712yes—
368C22×C7C23×D411yescharacteristic
369C2×D7—24no—
370C2×D7—24no—
371C2×D7—24no—
372C2×D7—48no—
373C4×C7—22no—
374C4×C7—42no—
375C4×C7—44no—
376C4×C7#54712yes—
377C4×C7C2×#13514yes—
378C4×C7C22×#4111yescharacteristic
379C4×C7C2×2−1+411yescharacteristic
380Dic7—24no—
381Dic7—42no—
382Dic7—44no—
383Dic7—42no—
384C24—21no—
385C24—72no—
386C2×Q8—24no—
387C2×Q8—44no—
388C2×Q8—72no—
389C2×Q8—141no—
390C2×Q8—144no—
391C2×Q8—142no—
392C2×Q8—142no—
393C2×Q8—562no—
394C2×D4—21no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—74no—
398C2×D4—148no—
399C2×D4—144no—
400C2×D4—564no—
401C2×D4C23×D712yes—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—44no—
406C22×C4—72no—
407C22×C4—74no—
408C22×C4—74no—
409C22×C4—144no—
410C22×C4—144no—
411C22×C4—141no—
412C22×C4—142no—
413C22×C4—141no—
414C22×C4D4×D711yescharacteristic
415C22×C4D4×D711yescharacteristic
416C22×C4C23×D711yescharacteristic
417SD16—148no—
418C2×C8—24no—
419C2×C8—74no—
420C2×C8—72no—
421C2×C8—72no—
422C2×C8—1416no—
423C2×C8—142no—
424C2×C8C23×D714yes—
425C4⋊C4—24no—
426C4⋊C4—21no—
427C4⋊C4—22no—
428C4⋊C4—74no—
429C4⋊C4—72no—
430C4⋊C4—74no—
431C4⋊C4—148no—
432C4⋊C4—144no—
433C4⋊C4—141no—
434C4⋊C4—142no—
435C4⋊C4—144no—
436C4⋊C4C23×D714yes—
437C4⋊C4C23×D712yes—
438C22⋊C4—24no—
439C22⋊C4—78no—
440C22⋊C4—148no—
441C22⋊C4—148no—
442C22⋊C4—148no—
443C22⋊C4—148no—
444C42—148no—
445C42—148no—
446C42—144no—
447C42D4×D712yes—
448C42C23×D712yes—
449C2×C7—82no—
450C2×C7#334014yescomplemented
451C2×C7C2×#54711yescharacteristic
452C2×C7C22×#13511yescharacteristic
453C2×C7C2×#57711yescharacteristic
454D7—44no—
455C23—22no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—74no—
460C23—144no—
461C23—144no—
462C23—144no—
463C23C2×D4×D711yescharacteristic
464Q8—48no—
465Q8—142no—
466Q8—142no—
467Q8—282no—
468Q8—564no—
469D4—22no—
470D4—22no—
471D4—42no—
472D4—148no—
473D4—568no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—42no—
478C2×C4—44no—
479C2×C4—48no—
480C2×C4—74no—
481C2×C4—144no—
482C2×C4—148no—
483C2×C4—144no—
484C2×C4—144no—
485C2×C4—142no—
486C2×C4—144no—
487C2×C4—142no—
488C2×C4—282no—
489C2×C4—284no—
490C2×C4—282no—
491C2×C4#647514yes—
492C2×C4C2×D4×D712yes—
493C2×C4C2×D4×D712yes—
494C2×C4C2×D4×D711yescharacteristic
495C2×C4#655112yes—
496C2×C4D7×#4112yes—
497C2×C4C24×D711yescharacteristic
498C8—24no—
499C8—74no—
500C8—142no—
501C7C2×#334011yescharacteristic, complemented, Sylow
502C22—42no—
503C22—42no—
504C22—42no—
505C22—84no—
506C22—144no—
507C22—144no—
508C22—144no—
509C22—288no—
510C22#9032212yes—
511C22C2×#647512yes—
512C22#9046912yes—
513C22C22×D4×D711yescharacteristic
514C4—22no—
515C4—42no—
516C4—44no—
517C4—144no—
518C4—284no—
519C4—282no—
520C4—282no—
521C4#9032212yes—
522C4C2×#647514yes—
523C4C2×#655111yescharacteristic
524C4C2×D7×#4111yescharacteristic
525C2—82no—
526C2—284no—
527C2#1173843214yesdirect product factor
528C2C2×#9032211yescharacteristic
529C2C22×#647511yescharacteristic
530C2C2×#9046911yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#474C2
socleC23×C7C22×D4
prime radicalC2×#90254C2
hypercenterC2×#474D7
hypocenterC7C2×#3340
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#90423C2semidirect
3. C2×C7×#474C2semidirect
4. C2×#89851C2semidirect
5. C2×C4×#1142C2semidirect
6. #11738432C2direct (N × H)
7. C2×#89660C2semidirect
8. C2×#89652C2semidirect
9. C2×#89622C2semidirect
10. C2×#89606C2semidirect
11. C2×#89556C2semidirect
12. C2×#89550C2semidirect
23. #90423C22semidirect
34. C7×#474C22semidirect
42. #89851C22semidirect
43. C4×#1142C22semidirect
49. #89660C22semidirect
50. #89652C22semidirect
51. #89622C22semidirect
52. #89606C22semidirect
53. #89556C22semidirect
54. #89550C22semidirect
133. C2×#474D7semidirect
228. #474C2×D7semidirect
450. C2×C7#3340semidirect
501. C7C2×#3340semidirect
527. C2#11738432direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904232
C2×#902542
C2×C7×#4742
C2×#898512
C2×C4×#11422
#117384322
C2×#896602
C2×#896522
C2×#896222
C2×#896062
C2×#895562
C2×#895502
C2×#33407