Finite Group Databasebeta

← C2×#11741149 #14233519

Subgroups — C2×#11741149 #14233519

Order 1792.

1842 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×Q82C211yesmaximal, characteristic, complemented
2C2×#90275C211yesmaximal, characteristic
3#11741149C2116yesmaximal, direct product factor
4C2×#89866C212yesmaximal, complemented
5C2×#89856C211yesmaximal, characteristic
6C2×#89861C212yesmaximal
7C2×#89865C211yesmaximal, characteristic, complemented
8C2×#89803C211yesmaximal, characteristic, complemented
9C2×#89800C212yesmaximal
10C2×#89796C211yesmaximal, characteristic, complemented
11C2×#89802C212yesmaximal, complemented
12C2×C4×#1143C211yesmaximal, characteristic
13C7×Q82—24no—
14C7×Q82C2218yescomplemented
15C2×C7×C4⋊Q8—21no—
16C2×C7×C4⋊Q8—22no—
17C2×C7×C4⋊Q8C2211yescharacteristic
18C2×C7×C4⋊Q8C2212yes—
19C2×C4×C7×Q8—21no—
20C2×C4×C7×Q8C2211yescharacteristic
21C2×C4×C7×Q8C2212yes—
22C2×C4×C7×Q8C2211yescharacteristic
23C2×#6509—21no—
24C22×#1144C2212yes—
25C22×#1143C2211yescharacteristic
26#90275—24no—
27#90275C2218yes—
28C2×#6461—22no—
29C2×#6455—21no—
30C2×#6438C2212yes—
31C2×C4×D28C2211yescharacteristic
32C2×#6432C2211yescharacteristic
33C2×C4×Dic14C2212yes—
34C2×#6409C2211yescharacteristic
35#89866C22116yescomplemented
36#89865C2218yescomplemented
37#89861C22116yes—
38#89856C2218yes—
39#89803C2218yescomplemented
40#89802C22116yescomplemented
41#89800C22116yes—
42C4×#1143C2218yes—
43#89796C2218yescomplemented
44C2×#6384C2212yes—
45C2×#6384C2212yes—
46C2×#6384C2212yes—
47C2×#6383C2211yescharacteristic
48C2×#6383C2212yes—
49C2×#6382C2211yescharacteristic
50C2×#6382C2212yes—
51C2×C4⋊(C7⋊C8)C2212yes—
52C2×C4⋊(C7⋊C8)C2211yescharacteristic
53C2×#6377C2212yes—
54C2×C4×C7⋊C8C2211yescharacteristic
55C2×#3369—71nomaximal, Sylow
56C22×C7×Q8—22no—
57C22×C7×Q8—21no—
58C22×C7×Q8D411yescharacteristic
59C22×C7×Q8C2311yescharacteristic
60C22×D28C2311yescharacteristic
61C22×C4×D7—21no—
62C22×Dic14C2312yes—
63C7×C4⋊Q8—28no—
64C7×C4⋊Q8—216no—
65C7×C4⋊Q8—24no—
66C7×C4⋊Q8—22no—
67C7×C4⋊Q8C2314yes—
68C7×C4⋊Q8C2318yes—
69C4×C7×Q8—28no—
70C4×C7×Q8—24no—
71C4×C7×Q8—22no—
72C4×C7×Q8D414yes—
73C4×C7×Q8C2314yes—
74C4×C7×Q8C2318yes—
75C4×C7×Q8C2314yes—
76C2×C7×C4⋊C4—22no—
77C2×C7×C4⋊C4—21no—
78C2×C7×C4⋊C4—22no—
79C2×C7×C4⋊C4—21no—
80C2×C7×C4⋊C4D411yescharacteristic
81C2×C7×C4⋊C4D412yes—
82C2×C7×C4⋊C4C2311yescharacteristic
83C2×C7×C4⋊C4C2312yes—
84C2×C42×C7—22no—
85C2×C42×C7—21no—
86C2×C42×C7C2312yes—
87C2×C42×C7C2311yescharacteristic
88#6509—28no—
89C2×#1144—28no—
90C2×#1144C2318yes—
91C2×#1143—24no—
92C2×#1143C2314yes—
93C2×(C2×D7)⋊C4—21no—
94C2×(C2×D7)⋊C4—22no—
95C2×(C2×D7)⋊C4—22no—
96C2×C4⋊Dic7—21no—
97C2×C4⋊Dic7—21no—
98C2×C4⋊Dic7C2311yescharacteristic
99C2×Dic7⋊C4—22no—
100C2×C4×Dic7—22no—
101C22×C7⋊C8C2311yescharacteristic
102C22×C7⋊C8C2311yescharacteristic
103C22×C7⋊C8C2312yes—
104#6461—216no—
105#6455—28no—
106#6438—24no—
107#6438C2318yes—
108C4×D28—22no—
109C4×D28C2314yes—
110#6432—22no—
111#6432C2314yes—
112C4×Dic14—24no—
113C4×Dic14C2318yes—
114#6409C2314yes—
115#6384C2318yes—
116#6384C2318yes—
117#6384C2318yes—
118#6383C2318yes—
119#6383C2314yes—
120#6382C2318yes—
121#6382C2314yes—
122C4⋊(C7⋊C8)C2314yes—
123C4⋊(C7⋊C8)C2318yes—
124#6377C2318yes—
125C4×C7⋊C8C2314yes—
126C2×Q82D711yescharacteristic, complemented
127C2×#556—71no—
128#3369—716no—
129C2×#489—72no—
130C2×#487—71no—
131C2×#475—72no—
132C2×#476—71no—
133C2×#464—72no—
134C2×#462—71no—
135C2×#446—71no—
136C2×#441—72no—
137C2×C4×SD16—71no—
138C23×D7—21no—
139C2×C7×Q8—24no—
140C2×C7×Q8—21no—
141C2×C7×Q8—28no—
142C2×C7×Q8—24no—
143C2×C7×Q8—22no—
144C2×C7×Q8—84no—
145C2×C7×Q8—82no—
146C2×C7×Q8C2×D414yes—
147C2×C7×Q8#4114yes—
148C2×C7×Q8C2412yes—
149C22×C4×C7—21no—
150C22×C4×C7—22no—
151C22×C4×C7—21no—
152C22×C4×C7C2×D412yes—
153C22×C4×C7C2×D412yes—
154C22×C4×C7C2×D411yescharacteristic
155C22×C4×C7C2×D411yescharacteristic
156C22×C4×C7C2411yescharacteristic
157C22×Dic7—21no—
158C22×Dic7—22no—
159C2×D28—22no—
160C2×D28—22no—
161C2×D28—21no—
162C2×D28C2412yes—
163C2×C4×D7—24no—
164C2×C4×D7—44no—
165C2×Dic14—24no—
166C2×Dic14—24no—
167C2×Dic14—22no—
168C2×Dic14C2414yes—
169C7×C4⋊C4—28no—
170C7×C4⋊C4—24no—
171C7×C4⋊C4—28no—
172C7×C4⋊C4—24no—
173C7×C4⋊C4—21no—
174C7×C4⋊C4—22no—
175C7×C4⋊C4C2×D414yes—
176C7×C4⋊C4C2×D418yes—
177C7×C4⋊C4C2412yes—
178C7×C4⋊C4C2414yes—
179C42×C7—28no—
180C42×C7—24no—
181C42×C7C2×D414yes—
182C42×C7C2×D412yes—
183C42×C7C2414yes—
184C42×C7C2412yes—
185#1144—216no—
186#1143—28no—
187(C2×D7)⋊C4—24no—
188(C2×D7)⋊C4—28no—
189(C2×D7)⋊C4—28no—
190C4⋊Dic7—21no—
191C4⋊Dic7—24no—
192C4⋊Dic7—24no—
193C4⋊Dic7C2412yes—
194Dic7⋊C4—28no—
195C4×Dic7—28no—
196C2×C7⋊C8—22no—
197C2×C7⋊C8—24no—
198C2×C7⋊C8—22no—
199C2×C7⋊C8C2412yes—
200C2×C7⋊C8C2412yes—
201C2×C7⋊C8C2414yes—
202C22×Q16—72no—
203C22×SD16—71no—
204Q82—24no—
205Q82C2×D718yescomplemented
206#556—78no—
207#556—144no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8—22no—
210C2×C4⋊Q8—71no—
211C2×C4⋊Q8C2×D712yes—
212C2×C4⋊Q8C2×D711yescharacteristic
213C2×#126—142no—
214C2×#124—72no—
215C2×C22⋊Q8—141no—
216C2×C4×Q8—21no—
217C2×C4×Q8—72no—
218C2×C4×Q8C2×D711yescharacteristic
219C2×C4×Q8C2×D712yes—
220C2×C4×Q8C2×D711yescharacteristic
221C2×C4×D4—71no—
222C2×#117—141no—
223#489—716no—
224#487—78no—
225#476—78no—
226#475—716no—
227#464—716no—
228#462—78no—
229#446—78no—
230#441—716no—
231C4×SD16—78no—
232C2×#106—71no—
233C2×#106—72no—
234C2×C4⋊C8—72no—
235C2×C4⋊C8—71no—
236C2×#103—71no—
237C2×#103—72no—
238C2×#103—72no—
239C2×#103—72no—
240C2×#102—71no—
241C2×#102—72no—
242C2×#97—72no—
243C2×C4×C8—71no—
244C23×C7C22×D411yescharacteristic
245C22×D7—22no—
246C22×D7—42no—
247C22×D7—42no—
248C22×D7—42no—
249C7×Q8—24no—
250C7×Q8—28no—
251C7×Q8—22no—
252C7×Q8—88no—
253C7×Q8—84no—
254C7×Q8C2×#4114yes—
255C2×C4×C7—24no—
256C2×C4×C7—24no—
257C2×C4×C7—24no—
258C2×C4×C7—22no—
259C2×C4×C7—22no—
260C2×C4×C7—24no—
261C2×C4×C7—22no—
262C2×C4×C7—44no—
263C2×C4×C7—42no—
264C2×C4×C7#13714yes—
265C2×C4×C7C22×D414yes—
266C2×C4×C7C22×D414yes—
267C2×C4×C7C22×D412yes—
268C2×C4×C7C22×D411yescharacteristic
269C2×C4×C7C22×D412yes—
270C2×C4×C7C2×#4112yes—
271C2×C4×C72−1+412yes—
272C2×C4×C7C2511yescharacteristic
273C2×Dic7—22no—
274C2×Dic7—24no—
275C2×Dic7—44no—
276C2×Dic7—42no—
277D28—22no—
278D28—22no—
279D28—42no—
280C4×D7—48no—
281Dic14—24no—
282Dic14—24no—
283Dic14—44no—
284C7⋊C8—22no—
285C7⋊C8—24no—
286C7⋊C8—22no—
287C22×Q8—22no—
288C22×Q8—21no—
289C22×Q8—72no—
290C22×Q8C22⋊D711yescharacteristic
291C22×Q8C22×D711yescharacteristic
292C22×D4—71no—
293C23×C4—141no—
294C2×Q16—78no—
295C2×Q16—148no—
296C2×SD16—74no—
297C2×SD16—144no—
298C22×C8—71no—
299C22×C8—72no—
300C22×C8—71no—
301C4⋊Q8—28no—
302C4⋊Q8—216no—
303C4⋊Q8—22no—
304C4⋊Q8—24no—
305C4⋊Q8—74no—
306C4⋊Q8—142no—
307C4⋊Q8C22×D718yes—
308C4⋊Q8C22×D714yes—
309#126—1416no—
310#124—78no—
311#124—144no—
312C22⋊Q8—148no—
313C4×Q8—28no—
314C4×Q8—22no—
315C4×Q8—24no—
316C4×Q8—78no—
317C4×Q8—144no—
318C4×Q8C22⋊D714yes—
319C4×Q8C22×D714yes—
320C4×Q8C22×D718yes—
321C4×Q8C22×D714yes—
322C4×D4—74no—
323C4×D4—142no—
324#117—148no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—71no—
330C2×C4⋊C4—141no—
331C2×C4⋊C4—142no—
332C2×C4⋊C4—141no—
333C2×C4⋊C4C22⋊D711yescharacteristic
334C2×C4⋊C4C22⋊D712yes—
335C2×C4⋊C4C22×D711yescharacteristic
336C2×C4⋊C4C22×D712yes—
337C2×C22⋊C4—142no—
338C2×C22⋊C4—141no—
339C2×C22⋊C4—142no—
340C2×C42—22no—
341C2×C42—21no—
342C2×C42—142no—
343C2×C42C22×D711yescharacteristic
344C2×C42C22×D712yes—
345#106—74no—
346#106—78no—
347C4⋊C8—74no—
348C4⋊C8—78no—
349#103—74no—
350#103—78no—
351#103—78no—
352#103—78no—
353#102—74no—
354#102—78no—
355#97—78no—
356C4×C8—74no—
357C22×C7#54812yes—
358C22×C7C2×#13712yes—
359C22×C7#57712yes—
360C22×C7C23×D411yescharacteristic
361C2×D7—42no—
362C2×D7—42no—
363C2×D7—42no—
364C2×D7—84no—
365C4×C7—24no—
366C4×C7—24no—
367C4×C7—24no—
368C4×C7—22no—
369C4×C7—44no—
370C4×C7—42no—
371C4×C7#54812yes—
372C4×C7C2×#13714yes—
373C4×C7C22×#4111yescharacteristic
374C4×C7C2×2−1+411yescharacteristic
375Dic7—44no—
376Dic7—42no—
377C24—141no—
378C2×Q8—24no—
379C2×Q8—22no—
380C2×Q8—21no—
381C2×Q8—28no—
382C2×Q8—24no—
383C2×Q8—74no—
384C2×Q8—84no—
385C2×Q8—82no—
386C2×Q8—142no—
387C2×Q8—144no—
388C2×Q8—144no—
389C2×Q8#116114yes—
390C2×Q8C2×C22⋊D714yes—
391C2×Q8C23×D712yes—
392C2×D4—72no—
393C2×D4—142no—
394C2×D4—142no—
395C2×D4—141no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—141no—
400C22×C4—142no—
401C22×C4—144no—
402C22×C4—284no—
403C22×C4C2×C22⋊D712yes—
404C22×C4C2×C22⋊D712yes—
405C22×C4C2×C22⋊D711yescharacteristic
406C22×C4C2×C22⋊D711yescharacteristic
407C22×C4C23×D711yescharacteristic
408Q16—1416no—
409SD16—148no—
410C2×C8—72no—
411C2×C8—72no—
412C2×C8—74no—
413C2×C8—142no—
414C2×C8—144no—
415C2×C8—142no—
416C4⋊C4—28no—
417C4⋊C4—24no—
418C4⋊C4—28no—
419C4⋊C4—24no—
420C4⋊C4—21no—
421C4⋊C4—22no—
422C4⋊C4—72no—
423C4⋊C4—148no—
424C4⋊C4—141no—
425C4⋊C4—144no—
426C4⋊C4—144no—
427C4⋊C4C2×C22⋊D714yes—
428C4⋊C4C2×C22⋊D718yes—
429C4⋊C4C23×D712yes—
430C4⋊C4C23×D714yes—
431C22⋊C4—148no—
432C22⋊C4—144no—
433C22⋊C4—148no—
434C42—28no—
435C42—24no—
436C42—148no—
437C42C2×C22⋊D712yes—
438C42C2×C22⋊D714yes—
439C42C23×D712yes—
440C42C23×D714yes—
441C2×C7#336914yescomplemented
442C2×C7C2×#54811yescharacteristic
443C2×C7C22×#13711yescharacteristic
444C2×C7C2×#57711yescharacteristic
445D7—82no—
446C23—142no—
447C23—282no—
448C23—282no—
449C23—282no—
450C23C22×C22⋊D711yescharacteristic
451Q8—28no—
452Q8—24no—
453Q8—22no—
454Q8—88no—
455Q8—84no—
456Q8—144no—
457Q8—144no—
458Q8—284no—
459Q8C2×#116114yes—
460D4—142no—
461D4—142no—
462D4—282no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—44no—
471C2×C4—42no—
472C2×C4—142no—
473C2×C4—144no—
474C2×C4—282no—
475C2×C4—284no—
476C2×C4—288no—
477C2×C4#650514yes—
478C2×C4C2×#116112yes—
479C2×C4#655112yes—
480C2×C4C22×C22⋊D714yes—
481C2×C4C22×C22⋊D714yes—
482C2×C4C22×C22⋊D712yes—
483C2×C4C22×C22⋊D712yes—
484C2×C4C22×C22⋊D711yescharacteristic
485C2×C4C24×D711yescharacteristic
486C8—142no—
487C8—144no—
488C8—142no—
489C7C2×#336911yescharacteristic, complemented, Sylow
490C22—282no—
491C22—282no—
492C22—282no—
493C22—564no—
494C22C2×#650512yes—
495C22#9050812yes—
496C22#9052712yes—
497C22C23×C22⋊D711yescharacteristic
498C4—24no—
499C4—24no—
500C4—24no—
501C4—22no—
502C4—44no—
503C4—42no—
504C4—282no—
505C4—284no—
506C4C2×#650514yes—
507C4#9050812yes—
508C4C22×#116111yescharacteristic
509C4C2×#655111yescharacteristic
510C2—562no—
511C2#1174114914yesdirect product factor
512C2C22×#650511yescharacteristic
513C2C2×#9050811yescharacteristic
514C2C2×#9052711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×Q82C2
socleC23×C7C22×D4
prime radicalC22×D28C23
hypercenterC2×Q82D7
hypocenterC7C2×#3369
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×Q82

Complements

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

NH ≅ G/Ntype
1. C2×C7×Q82C2semidirect
3. #11741149C2direct (N × H)
4. C2×#89866C2semidirect
7. C2×#89865C2semidirect
8. C2×#89803C2semidirect
10. C2×#89796C2semidirect
11. C2×#89802C2semidirect
14. C7×Q82C22semidirect
35. #89866C22semidirect
36. #89865C22semidirect
39. #89803C22semidirect
40. #89802C22semidirect
43. #89796C22semidirect
126. C2×Q82D7semidirect
205. Q82C2×D7semidirect
441. C2×C7#3369semidirect
489. C7C2×#3369semidirect
511. C2#11741149direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×Q822
C2×#902752
#117411492
C2×#898662
C2×#898562
C2×#898612
C2×#898652
C2×#898032
C2×#898002
C2×#897962
C2×#898022
C2×C4×#11432
C2×#33697