Finite Group Databasebeta

← C2×#11741139 #14234293

Subgroups — C2×#11741139 #14234293

Order 1792.

2006 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#557C211yesmaximal, characteristic, complemented
2C2×Q8×D28C211yesmaximal, characteristic
3#11741139C2116yesmaximal, direct product factor
4C2×#89859C211yesmaximal, characteristic
5C2×#89850C211yesmaximal, characteristic, complemented
6C2×#89838C212yesmaximal
7C2×#89837C212yesmaximal, complemented
8C2×#89798C212yesmaximal
9C2×#89796C211yesmaximal, characteristic, complemented
10C2×#89793C212yesmaximal, complemented
11C2×#89792C211yesmaximal, characteristic, complemented
12C2×C4×#1143C211yesmaximal, characteristic
13C22×Q8×D7—21no—
14C7×#557—24no—
15C7×#557C2218yescomplemented
16C2×C7×C4⋊Q8—21no—
17C2×C7×C4⋊Q8C2211yescharacteristic
18C2×C7×#125—22no—
19C2×C7×#125C2212yes—
20C2×C4×C7×Q8—21no—
21C2×C4×C7×Q8C2211yescharacteristic
22C2×C4×C7×Q8C2212yes—
23C2×C4×C7×Q8C2211yescharacteristic
24C22×#1143C2211yescharacteristic
25Q8×D28—24no—
26Q8×D28C2218yes—
27C2×#6460—21no—
28C2×#6460—22no—
29C2×C4×D28C2212yes—
30C2×C4×D28C2211yescharacteristic
31C2×#6432C2212yes—
32C2×#6432C2211yescharacteristic
33C2×#6409C2211yescharacteristic
34C2×#6409C2212yes—
35#89859C2218yes—
36#89850C2218yescomplemented
37#89838C22116yes—
38#89837C22116yescomplemented
39#89798C22116yes—
40C4×#1143C2218yes—
41#89796C2218yescomplemented
42#89793C22116yescomplemented
43#89792C2218yescomplemented
44C2×#6383C2211yescharacteristic
45C2×#6383C2212yes—
46C2×#6382C2211yescharacteristic
47C2×#6382C2212yes—
48C2×#6381C2212yes—
49C2×#6381C2212yes—
50C2×#6381C2212yes—
51C2×C4⋊(C7⋊C8)C2212yes—
52C2×C4⋊(C7⋊C8)C2211yescharacteristic
53C2×#6377C2212yes—
54C2×C4×C7⋊C8C2211yescharacteristic
55C2×#3386—71nomaximal, Sylow
56C22×C7×Q8—21no—
57C22×C7×Q8D411yescharacteristic
58C22×C7×Q8C2311yescharacteristic
59C2×Q8×D7—28no—
60C2×Q8×D7—48no—
61C22×D28C2311yescharacteristic
62C22×C4×D7—22no—
63C22×C4×D7—21no—
64C22×Dic14—22no—
65C22×Dic14—21no—
66C7×C4⋊Q8—28no—
67C7×C4⋊Q8—22no—
68C7×C4⋊Q8C2314yes—
69C7×#125—216no—
70C7×#125—24no—
71C7×#125C2318yes—
72C4×C7×Q8—28no—
73C4×C7×Q8—24no—
74C4×C7×Q8—22no—
75C4×C7×Q8D414yes—
76C4×C7×Q8C2314yes—
77C4×C7×Q8C2318yes—
78C4×C7×Q8C2314yes—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—21no—
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—21no—
83C2×C7×C4⋊C4—22no—
84C2×C7×C4⋊C4D411yescharacteristic
85C2×C7×C4⋊C4D412yes—
86C2×C7×C4⋊C4C2312yes—
87C2×C7×C4⋊C4C2311yescharacteristic
88C2×C42×C7—22no—
89C2×C42×C7—21no—
90C2×C42×C7C2311yescharacteristic
91C2×C42×C7C2312yes—
92C2×#1143Q818yescomplemented
93C2×#1143C2314yes—
94C2×(C2×D7)⋊C4—22no—
95C2×(C2×D7)⋊C4—21no—
96C2×C4⋊Dic7—22no—
97C2×C4⋊Dic7—21no—
98C2×C4⋊Dic7C2311yescharacteristic
99C2×C4⋊Dic7C2312yes—
100C22×C7⋊C8C2311yescharacteristic
101C22×C7⋊C8C2312yes—
102C22×C7⋊C8C2311yescharacteristic
103#6460—28no—
104#6460—216no—
105C4×D28—24no—
106C4×D28—22no—
107C4×D28C2314yes—
108C4×D28C2318yes—
109#6432—24no—
110#6432—22no—
111#6432C2314yes—
112#6432C2318yes—
113#6409C2318yes—
114#6409C2314yes—
115#6383C2318yes—
116#6383C2314yes—
117#6382C2318yes—
118#6382C2314yes—
119#6381C2318yes—
120#6381C2318yes—
121#6381C2318yes—
122C4⋊(C7⋊C8)C2314yes—
123C4⋊(C7⋊C8)C2318yes—
124#6377C2318yes—
125C4×C7⋊C8C2314yes—
126C2×#557D711yescharacteristic, complemented
127C2×D4×Q8—71no—
128#3386—716no—
129C2×#501—72no—
130C2×#500—71no—
131C2×#477—72no—
132C2×#475—71no—
133C2×#478—72no—
134C2×#474—71no—
135C2×#446—71no—
136C2×#440—72no—
137C2×C4×SD16—71no—
138C23×D7—21no—
139C2×C7×Q8—24no—
140C2×C7×Q8—21no—
141C2×C7×Q8—24no—
142C2×C7×Q8—22no—
143C2×C7×Q8—44no—
144C2×C7×Q8C2×D414yes—
145C2×C7×Q8C2×Q814yescomplemented
146C2×C7×Q8C2412yes—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—22no—
150C22×C4×C7C2×D412yes—
151C22×C4×C7C2×D411yescharacteristic
152C22×C4×C7C2×D412yes—
153C22×C4×C7C2×D411yescharacteristic
154C22×C4×C7C2411yescharacteristic
155C22×Dic7—21no—
156C22×Dic7—22no—
157Q8×D7—432no—
158C2×D28—21no—
159C2×D28—22no—
160C2×D28C2×Q814yes—
161C2×D28C2412yes—
162C2×C4×D7—28no—
163C2×C4×D7—24no—
164C2×C4×D7—48no—
165C2×C4×D7—44no—
166C2×Dic14—28no—
167C2×Dic14—24no—
168C2×Dic14—48no—
169C2×Dic14—44no—
170C7×C4⋊C4—28no—
171C7×C4⋊C4—24no—
172C7×C4⋊C4—28no—
173C7×C4⋊C4—24no—
174C7×C4⋊C4—28no—
175C7×C4⋊C4—21no—
176C7×C4⋊C4—22no—
177C7×C4⋊C4C2×D414yes—
178C7×C4⋊C4C2×D418yes—
179C7×C4⋊C4C2412yes—
180C7×C4⋊C4C2414yes—
181C42×C7—28no—
182C42×C7—24no—
183C42×C7C2×D414yes—
184C42×C7C2×D412yes—
185C42×C7C2414yes—
186C42×C7C2412yes—
187#1143C2×Q8116yescomplemented
188(C2×D7)⋊C4—28no—
189(C2×D7)⋊C4—24no—
190C4⋊Dic7—21no—
191C4⋊Dic7—22no—
192C4⋊Dic7—28no—
193C4⋊Dic7—24no—
194C4⋊Dic7C2414yes—
195C4⋊Dic7C2412yes—
196C2×C7⋊C8—22no—
197C2×C7⋊C8—24no—
198C2×C7⋊C8C2×Q814yescomplemented
199C2×C7⋊C8C2412yes—
200C2×C7⋊C8C2414yes—
201C2×C7⋊C8C2412yes—
202C23×Q8—141no—
203C22×SD16—71no—
204#557—24no—
205#557C2×D718yescomplemented
206D4×Q8—78no—
207D4×Q8—144no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8—71no—
210C2×C4⋊Q8—72no—
211C2×C4⋊Q8C2×D711yescharacteristic
212C2×#125—22no—
213C2×#125C2×D712yes—
214C2×C22⋊Q8—141no—
215C2×C22⋊Q8—142no—
216C2×C4×Q8—21no—
217C2×C4×Q8C2×D711yescharacteristic
218C2×C4×Q8C2×D712yes—
219C2×C4×Q8C2×D711yescharacteristic
220C2×C4×D4—72no—
221C2×C4×D4—71no—
222#501—716no—
223#500—78no—
224#478—716no—
225#477—716no—
226#475—78no—
227#474—78no—
228#446—78no—
229#440—716no—
230C4×SD16—78no—
231C2×#107—72no—
232C2×#107—72no—
233C2×#107—72no—
234C2×#106—72no—
235C2×#106—71no—
236C2×C4⋊C8—72no—
237C2×C4⋊C8—71no—
238C2×#103—72no—
239C2×#103—71no—
240C2×#102—71no—
241C2×#102—72no—
242C2×#97—72no—
243C2×C4×C8—71no—
244C23×C7C22×D411yescharacteristic
245C22×D7—24no—
246C22×D7—22no—
247C22×D7—42no—
248C22×D7—42no—
249C7×Q8—24no—
250C7×Q8—28no—
251C7×Q8—22no—
252C7×Q8—48no—
253C7×Q8C22×Q814yescomplemented
254C2×C4×C7—24no—
255C2×C4×C7—24no—
256C2×C4×C7—24no—
257C2×C4×C7—22no—
258C2×C4×C7—22no—
259C2×C4×C7—22no—
260C2×C4×C7—24no—
261C2×C4×C7—44no—
262C2×C4×C7—42no—
263C2×C4×C7AGL(1,ℤ/8)14yes—
264C2×C4×C7C22×D414yes—
265C2×C4×C7C22×D412yes—
266C2×C4×C7C22×D414yes—
267C2×C4×C7C22×D411yescharacteristic
268C2×C4×C7C22×D412yes—
269C2×C4×C7C22×Q812yes—
270C2×C4×C72−1+412yes—
271C2×C4×C7C2511yescharacteristic
272C2×Dic7—22no—
273C2×Dic7—24no—
274C2×Dic7—42no—
275C2×Dic7—44no—
276D28—24no—
277D28—22no—
278D28C22×Q814yes—
279C4×D7—416no—
280C4×D7—48no—
281Dic14—416no—
282Dic14—48no—
283C7⋊C8—22no—
284C7⋊C8—24no—
285C7⋊C8C22×Q814yescomplemented
286C22×Q8—21no—
287C22×Q8—148no—
288C22×Q8—142no—
289C22×Q8—141no—
290C22×Q8—288no—
291C22×Q8C22⋊D711yescharacteristic
292C22×Q8C22×D711yescharacteristic
293C22×D4—71no—
294C23×C4—142no—
295C23×C4—141no—
296C2×SD16—78no—
297C2×SD16—74no—
298C22×C8—71no—
299C22×C8—71no—
300C22×C8—72no—
301C4⋊Q8—28no—
302C4⋊Q8—22no—
303C4⋊Q8—74no—
304C4⋊Q8—78no—
305C4⋊Q8—144no—
306C4⋊Q8—142no—
307C4⋊Q8C22×D714yes—
308#125—216no—
309#125—24no—
310#125C22×D718yes—
311C22⋊Q8—148no—
312C22⋊Q8—1416no—
313C4×Q8—28no—
314C4×Q8—24no—
315C4×Q8—22no—
316C4×Q8C22⋊D714yes—
317C4×Q8C22×D714yes—
318C4×Q8C22×D718yes—
319C4×Q8C22×D714yes—
320C4×D4—74no—
321C4×D4—78no—
322C4×D4—144no—
323C4×D4—142no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—72no—
330C2×C4⋊C4—71no—
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×C42—22no—
340C2×C42—21no—
341C2×C42C22×D712yes—
342C2×C42C22×D711yescharacteristic
343#107—78no—
344#107—78no—
345#107—78no—
346#106—74no—
347#106—78no—
348C4⋊C8—74no—
349C4⋊C8—78no—
350#103—74no—
351#103—78no—
352#102—74no—
353#102—78no—
354#97—78no—
355C4×C8—74no—
356C22×C7D4×Q812yes—
357C22×C7C2×AGL(1,ℤ/8)12yes—
358C22×C7#57812yes—
359C22×C7C23×D411yescharacteristic
360C2×D7—24no—
361C2×D7—48no—
362C2×D7—42no—
363C2×D7—42no—
364C4×C7—24no—
365C4×C7—24no—
366C4×C7—24no—
367C4×C7—22no—
368C4×C7—44no—
369C4×C7—42no—
370C4×C7D4×Q812yes—
371C4×C7C2×AGL(1,ℤ/8)14yes—
372C4×C7C23×Q811yescharacteristic
373C4×C7C2×2−1+411yescharacteristic
374Dic7—42no—
375Dic7—44no—
376C24—141no—
377C2×Q8—24no—
378C2×Q8—22no—
379C2×Q8—21no—
380C2×Q8—24no—
381C2×Q8—44no—
382C2×Q8—148no—
383C2×Q8—144no—
384C2×Q8—288no—
385C2×Q8—2832no—
386C2×Q8—284no—
387C2×Q8Q8×D714yescomplemented
388C2×Q8C2×C22⋊D714yes—
389C2×Q8C23×D712yes—
390C2×D4—74no—
391C2×D4—72no—
392C2×D4—142no—
393C2×D4—141no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—142no—
398C22×C4—141no—
399C22×C4—148no—
400C22×C4—144no—
401C22×C4—288no—
402C22×C4—284no—
403C22×C4C2×C22⋊D712yes—
404C22×C4C2×C22⋊D711yescharacteristic
405C22×C4C2×C22⋊D712yes—
406C22×C4C2×C22⋊D711yescharacteristic
407C22×C4C23×D711yescharacteristic
408SD16—716no—
409C2×C8—74no—
410C2×C8—72no—
411C2×C8—72no—
412C2×C8—74no—
413C2×C8—142no—
414C2×C8—144no—
415C4⋊C4—28no—
416C4⋊C4—24no—
417C4⋊C4—28no—
418C4⋊C4—24no—
419C4⋊C4—28no—
420C4⋊C4—21no—
421C4⋊C4—22no—
422C4⋊C4—72no—
423C4⋊C4—74no—
424C4⋊C4—142no—
425C4⋊C4—141no—
426C4⋊C4—148no—
427C4⋊C4—144no—
428C4⋊C4C2×C22⋊D714yes—
429C4⋊C4C2×C22⋊D718yes—
430C4⋊C4C23×D712yes—
431C4⋊C4C23×D714yes—
432C22⋊C4—148no—
433C22⋊C4—144no—
434C42—28no—
435C42—24no—
436C42C2×C22⋊D714yes—
437C42C2×C22⋊D712yes—
438C42C23×D712yes—
439C42C23×D714yes—
440C2×C7#338614yescomplemented
441C2×C7C2×D4×Q811yescharacteristic
442C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
443C2×C7C2×#57811yescharacteristic
444D7—44no—
445C23—144no—
446C23—142no—
447C23—282no—
448C23—282no—
449C23C22×C22⋊D711yescharacteristic
450Q8—24no—
451Q8—28no—
452Q8—22no—
453Q8—48no—
454Q8—2816no—
455Q8—288no—
456Q8C2×Q8×D714yescomplemented
457D4—74no—
458D4—144no—
459D4—142no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—44no—
468C2×C4—42no—
469C2×C4—144no—
470C2×C4—142no—
471C2×C4—2816no—
472C2×C4—284no—
473C2×C4—282no—
474C2×C4—288no—
475C2×C4#651214yes—
476C2×C4C2×Q8×D712yes—
477C2×C4#655112yes—
478C2×C4C22×C22⋊D714yes—
479C2×C4C22×C22⋊D712yes—
480C2×C4C22×C22⋊D714yes—
481C2×C4C22×C22⋊D711yescharacteristic
482C2×C4C22×C22⋊D712yes—
483C2×C4C24×D711yescharacteristic
484C8—74no—
485C8—142no—
486C8—144no—
487C7C2×#338611yescharacteristic, complemented, Sylow
488C22—144no—
489C22—282no—
490C22—282no—
491C22—288no—
492C22Q8×C22⋊D712yes—
493C22C2×#651212yes—
494C22#9052912yes—
495C22C23×C22⋊D711yescharacteristic
496C4—24no—
497C4—24no—
498C4—24no—
499C4—22no—
500C4—44no—
501C4—42no—
502C4—284no—
503C4—282no—
504C4Q8×C22⋊D712yes—
505C4C2×#651214yes—
506C4C22×Q8×D711yescharacteristic
507C4C2×#655111yescharacteristic
508C2—284no—
509C2#1174113914yesdirect product factor
510C2C2×Q8×C22⋊D711yescharacteristic
511C2C22×#651211yescharacteristic
512C2C2×#9052911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#557C2
socleC23×C7C22×D4
prime radicalC22×D28C23
hypercenterC2×#557D7
hypocenterC7C2×#3386
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. C2×C7×#557C2semidirect
3. #11741139C2direct (N × H)
5. C2×#89850C2semidirect
7. C2×#89837C2semidirect
9. C2×#89796C2semidirect
10. C2×#89793C2semidirect
11. C2×#89792C2semidirect
15. C7×#557C22semidirect
36. #89850C22semidirect
38. #89837C22semidirect
41. #89796C22semidirect
42. #89793C22semidirect
43. #89792C22semidirect
92. C2×#1143Q8semidirect
126. C2×#557D7semidirect
145. C2×C7×Q8C2×Q8semidirect
187. #1143C2×Q8semidirect
198. C2×C7⋊C8C2×Q8semidirect
205. #557C2×D7semidirect
253. C7×Q8C22×Q8semidirect
285. C7⋊C8C22×Q8semidirect
387. C2×Q8Q8×D7semidirect
440. C2×C7#3386semidirect
456. Q8C2×Q8×D7semidirect
487. C7C2×#3386semidirect
509. C2#11741139direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5572
C2×Q8×D282
#117411392
C2×#898592
C2×#898502
C2×#898382
C2×#898372
C2×#897982
C2×#897962
C2×#897932
C2×#897922
C2×C4×#11432
C2×#33867