Finite Group Databasebeta

← C2×#11741151 #14234281

Subgroups — C2×#11741151 #14234281

Order 1792.

1854 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×Q82C211yesmaximal, characteristic, complemented
2C2×#90270C211yesmaximal, characteristic
3#11741151C2116yesmaximal, direct product factor
4C2×#89856C211yesmaximal, characteristic
5C2×#89859C212yesmaximal
6C2×#89852C212yesmaximal, complemented
7C2×#89850C211yesmaximal, characteristic, complemented
8C2×#89798C212yesmaximal
9C2×#89796C211yesmaximal, characteristic, complemented
10C2×#89794C212yesmaximal, complemented
11C2×#89793C211yesmaximal, characteristic, 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×#1143C2211yescharacteristic
25#90270—24no—
26#90270C2218yes—
27C2×#6459—22no—
28C2×D7×C4⋊C4—21no—
29C2×C4×D28C2211yescharacteristic
30C2×C4×D28C2212yes—
31C2×#6433C2212yes—
32C2×#6432C2211yescharacteristic
33C2×#6409C2211yescharacteristic
34C2×#6409C2212yes—
35#89859C22116yes—
36#89856C2218yes—
37#89852C22116yescomplemented
38#89850C2218yescomplemented
39#89798C22116yes—
40C4×#1143C2218yes—
41#89796C2218yescomplemented
42#89794C22116yescomplemented
43#89793C2218yescomplemented
44C2×#6383C2211yescharacteristic
45C2×#6383C2212yes—
46C2×#6382C2211yescharacteristic
47C2×#6382C2212yes—
48C2×#6381C2212yes—
49C2×#6381C2212yes—
50C2×#6381C2212yes—
51C2×C4⋊(C7⋊C8)C2211yescharacteristic
52C2×C4⋊(C7⋊C8)C2212yes—
53C2×#6377C2212yes—
54C2×C4×C7⋊C8C2211yescharacteristic
55C2×#3385—71nomaximal, Sylow
56C22×C7×Q8—22no—
57C22×C7×Q8—21no—
58C22×C7×Q8D411yescharacteristic
59C22×C7×Q8C2311yescharacteristic
60C22×D28C2311yescharacteristic
61C22×C4×D7—21no—
62C22×C4×D7—22no—
63C22×Dic14—21no—
64C7×C4⋊Q8—28no—
65C7×C4⋊Q8—216no—
66C7×C4⋊Q8—22no—
67C7×C4⋊Q8—24no—
68C7×C4⋊Q8C2314yes—
69C7×C4⋊Q8C2318yes—
70C4×C7×Q8—28no—
71C4×C7×Q8—22no—
72C4×C7×Q8—24no—
73C4×C7×Q8D414yes—
74C4×C7×Q8C2314yes—
75C4×C7×Q8C2318yes—
76C4×C7×Q8C2314yes—
77C2×C7×C4⋊C4—22no—
78C2×C7×C4⋊C4—21no—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—21no—
81C2×C7×C4⋊C4D411yescharacteristic
82C2×C7×C4⋊C4D412yes—
83C2×C7×C4⋊C4C2311yescharacteristic
84C2×C7×C4⋊C4C2312yes—
85C2×C42×C7—22no—
86C2×C42×C7—21no—
87C2×C42×C7C2311yescharacteristic
88C2×C42×C7C2312yes—
89#6509—28no—
90C2×#1143Q818yescomplemented
91C2×#1143C2314yes—
92C2×(C2×D7)⋊C4—21no—
93C2×(C2×D7)⋊C4—22no—
94C2×C4⋊Dic7—21no—
95C2×C4⋊Dic7C2312yes—
96C2×C4⋊Dic7C2311yescharacteristic
97C2×Dic7⋊C4—22no—
98C2×Dic7⋊C4—22no—
99C22×C7⋊C8C2311yescharacteristic
100C22×C7⋊C8C2312yes—
101C22×C7⋊C8C2311yescharacteristic
102#6459—216no—
103D7×C4⋊C4—28no—
104C4×D28—24no—
105C4×D28—22no—
106C4×D28C2314yes—
107C4×D28C2318yes—
108#6433—24no—
109#6433C2318yes—
110#6432—22no—
111#6432C2314yes—
112#6409C2318yes—
113#6409C2314yes—
114#6383C2318yes—
115#6383C2314yes—
116#6382C2318yes—
117#6382C2314yes—
118#6381C2318yes—
119#6381C2318yes—
120#6381C2318yes—
121C4⋊(C7⋊C8)C2314yes—
122C4⋊(C7⋊C8)C2318yes—
123#6377C2318yes—
124C4×C7⋊C8C2314yes—
125C2×Q82D711yescharacteristic, complemented
126C2×#554—71no—
127#3385—716no—
128C2×#501—72no—
129C2×#500—71no—
130C2×#479—72no—
131C2×#477—71no—
132C2×#476—71no—
133C2×#474—72no—
134C2×#446—71no—
135C2×#440—72no—
136C2×C4×SD16—71no—
137C23×D7—21no—
138C2×C7×Q8—24no—
139C2×C7×Q8—21no—
140C2×C7×Q8—28no—
141C2×C7×Q8—24no—
142C2×C7×Q8—22no—
143C2×C7×Q8—82no—
144C2×C7×Q8—84no—
145C2×C7×Q8C2×D414yes—
146C2×C7×Q8C2×Q814yes—
147C2×C7×Q8C2412yes—
148C22×C4×C7—21no—
149C22×C4×C7—22no—
150C22×C4×C7—21no—
151C22×C4×C7C2×D412yes—
152C22×C4×C7C2×D412yes—
153C22×C4×C7C2×D411yescharacteristic
154C22×C4×C7C2×D411yescharacteristic
155C22×C4×C7C2411yescharacteristic
156C22×Dic7—21no—
157C22×Dic7—22no—
158C2×D28—21no—
159C2×D28—22no—
160C2×D28C2×Q814yes—
161C2×D28C2412yes—
162C2×C4×D7—24no—
163C2×C4×D7—28no—
164C2×C4×D7—44no—
165C2×C4×D7—84no—
166C2×Dic14—24no—
167C2×Dic14—82no—
168C7×C4⋊C4—28no—
169C7×C4⋊C4—24no—
170C7×C4⋊C4—28no—
171C7×C4⋊C4—24no—
172C7×C4⋊C4—21no—
173C7×C4⋊C4—22no—
174C7×C4⋊C4C2×D414yes—
175C7×C4⋊C4C2×D418yes—
176C7×C4⋊C4C2412yes—
177C7×C4⋊C4C2414yes—
178C42×C7—28no—
179C42×C7—24no—
180C42×C7C2×D412yes—
181C42×C7C2×D414yes—
182C42×C7C2412yes—
183C42×C7C2414yes—
184#1143C2×Q8116yescomplemented
185(C2×D7)⋊C4—24no—
186(C2×D7)⋊C4—28no—
187C4⋊Dic7—22no—
188C4⋊Dic7—24no—
189C4⋊Dic7—21no—
190C4⋊Dic7C2414yes—
191C4⋊Dic7C2412yes—
192Dic7⋊C4—28no—
193Dic7⋊C4—28no—
194C2×C7⋊C8—22no—
195C2×C7⋊C8—24no—
196C2×C7⋊C8C2×Q814yes—
197C2×C7⋊C8C2412yes—
198C2×C7⋊C8C2414yes—
199C2×C7⋊C8C2412yes—
200C22×SD16—71no—
201Q82—24no—
202Q82C2×D718yescomplemented
203#554—78no—
204#554—144no—
205C2×C4⋊Q8—21no—
206C2×C4⋊Q8—22no—
207C2×C4⋊Q8—71no—
208C2×C4⋊Q8C2×D711yescharacteristic
209C2×C4⋊Q8C2×D712yes—
210C2×#125—72no—
211C2×C22⋊Q8—141no—
212C2×C22⋊Q8—142no—
213C2×C4×Q8—21no—
214C2×C4×Q8C2×D711yescharacteristic
215C2×C4×Q8C2×D712yes—
216C2×C4×Q8C2×D711yescharacteristic
217C2×C4×D4—71no—
218C2×C4×D4—72no—
219C22×C4⋊C4—141no—
220#501—716no—
221#500—78no—
222#479—716no—
223#477—78no—
224#476—78no—
225#474—716no—
226#446—78no—
227#440—716no—
228C4×SD16—78no—
229C2×#107—72no—
230C2×#107—72no—
231C2×#107—72no—
232C2×#106—72no—
233C2×#106—71no—
234C2×C4⋊C8—71no—
235C2×C4⋊C8—72no—
236C2×#103—72no—
237C2×#103—71no—
238C2×#102—71no—
239C2×#102—72no—
240C2×#97—72no—
241C2×C4×C8—71no—
242C23×C7C22×D411yescharacteristic
243C22×D7—24no—
244C22×D7—22no—
245C22×D7—42no—
246C22×D7—42no—
247C7×Q8—24no—
248C7×Q8—28no—
249C7×Q8—22no—
250C7×Q8—84no—
251C7×Q8—88no—
252C7×Q8C22×Q814yes—
253C2×C4×C7—24no—
254C2×C4×C7—24no—
255C2×C4×C7—22no—
256C2×C4×C7—24no—
257C2×C4×C7—22no—
258C2×C4×C7—24no—
259C2×C4×C7—22no—
260C2×C4×C7—44no—
261C2×C4×C7—42no—
262C2×C4×C7#13714yes—
263C2×C4×C7C22×D414yes—
264C2×C4×C7C22×D414yes—
265C2×C4×C7C22×D412yes—
266C2×C4×C7C22×D411yescharacteristic
267C2×C4×C7C22×D412yes—
268C2×C4×C7C22×Q812yes—
269C2×C4×C72−1+412yes—
270C2×C4×C7C2511yescharacteristic
271C2×Dic7—22no—
272C2×Dic7—24no—
273C2×Dic7—42no—
274C2×Dic7—44no—
275D28—24no—
276D28—22no—
277D28C22×Q814yes—
278C4×D7—48no—
279C4×D7—88no—
280Dic14—84no—
281C7⋊C8—22no—
282C7⋊C8—24no—
283C7⋊C8C22×Q814yes—
284C22×Q8—21no—
285C22×Q8—22no—
286C22×Q8—141no—
287C22×Q8C22⋊D711yescharacteristic
288C22×Q8C22×D711yescharacteristic
289C22×D4—71no—
290C23×C4—141no—
291C23×C4—142no—
292C2×SD16—78no—
293C2×SD16—74no—
294C22×C8—71no—
295C22×C8—71no—
296C22×C8—72no—
297C4⋊Q8—28no—
298C4⋊Q8—216no—
299C4⋊Q8—24no—
300C4⋊Q8—22no—
301C4⋊Q8—74no—
302C4⋊Q8—142no—
303C4⋊Q8C22×D718yes—
304C4⋊Q8C22×D714yes—
305#125—78no—
306#125—144no—
307C22⋊Q8—148no—
308C22⋊Q8—1416no—
309C4×Q8—28no—
310C4×Q8—24no—
311C4×Q8—22no—
312C4×Q8C22⋊D714yes—
313C4×Q8C22×D714yes—
314C4×Q8C22×D718yes—
315C4×Q8C22×D714yes—
316C4×D4—74no—
317C4×D4—78no—
318C4×D4—144no—
319C4×D4—142no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—71no—
325C2×C4⋊C4—72no—
326C2×C4⋊C4—142no—
327C2×C4⋊C4—141no—
328C2×C4⋊C4—142no—
329C2×C4⋊C4—148no—
330C2×C4⋊C4C22⋊D711yescharacteristic
331C2×C4⋊C4C22⋊D712yes—
332C2×C4⋊C4C22×D711yescharacteristic
333C2×C4⋊C4C22×D712yes—
334C2×C22⋊C4—141no—
335C2×C22⋊C4—142no—
336C2×C42—22no—
337C2×C42—21no—
338C2×C42C22×D712yes—
339C2×C42C22×D711yescharacteristic
340#107—78no—
341#107—78no—
342#107—78no—
343#106—74no—
344#106—78no—
345C4⋊C8—78no—
346C4⋊C8—74no—
347#103—74no—
348#103—78no—
349#102—74no—
350#102—78no—
351#97—78no—
352C4×C8—74no—
353C22×C7D4×Q812yes—
354C22×C7C2×#13712yes—
355C22×C7#57612yes—
356C22×C7C23×D411yescharacteristic
357C2×D7—24no—
358C2×D7—48no—
359C2×D7—42no—
360C2×D7—42no—
361C4×C7—24no—
362C4×C7—24no—
363C4×C7—22no—
364C4×C7—24no—
365C4×C7—44no—
366C4×C7—42no—
367C4×C7D4×Q812yes—
368C4×C7C2×#13714yes—
369C4×C7C23×Q811yescharacteristic
370C4×C7C2×2−1+411yescharacteristic
371Dic7—42no—
372Dic7—44no—
373C24—141no—
374C2×Q8—24no—
375C2×Q8—22no—
376C2×Q8—21no—
377C2×Q8—24no—
378C2×Q8—28no—
379C2×Q8—84no—
380C2×Q8—82no—
381C2×Q8—144no—
382C2×Q8—562no—
383C2×Q8Q8×D714yes—
384C2×Q8C2×C22⋊D714yes—
385C2×Q8C23×D712yes—
386C2×D4—74no—
387C2×D4—72no—
388C2×D4—142no—
389C2×D4—141no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—141no—
394C22×C4—142no—
395C22×C4—144no—
396C22×C4—148no—
397C22×C4—284no—
398C22×C4—564no—
399C22×C4C2×C22⋊D712yes—
400C22×C4C2×C22⋊D711yescharacteristic
401C22×C4C2×C22⋊D712yes—
402C22×C4C2×C22⋊D711yescharacteristic
403C22×C4C23×D711yescharacteristic
404SD16—716no—
405C2×C8—74no—
406C2×C8—72no—
407C2×C8—72no—
408C2×C8—74no—
409C2×C8—142no—
410C2×C8—144no—
411C4⋊C4—28no—
412C4⋊C4—24no—
413C4⋊C4—24no—
414C4⋊C4—28no—
415C4⋊C4—21no—
416C4⋊C4—22no—
417C4⋊C4—72no—
418C4⋊C4—74no—
419C4⋊C4—148no—
420C4⋊C4—148no—
421C4⋊C4—141no—
422C4⋊C4—142no—
423C4⋊C4—144no—
424C4⋊C4C2×C22⋊D714yes—
425C4⋊C4C2×C22⋊D718yes—
426C4⋊C4C23×D712yes—
427C4⋊C4C23×D714yes—
428C22⋊C4—144no—
429C22⋊C4—148no—
430C42—28no—
431C42—24no—
432C42C2×C22⋊D714yes—
433C42C2×C22⋊D712yes—
434C42C23×D712yes—
435C42C23×D714yes—
436C2×C7#338514yescomplemented
437C2×C7C2×D4×Q811yescharacteristic
438C2×C7C22×#13711yescharacteristic
439C2×C7C2×#57611yescharacteristic
440D7—44no—
441C23—144no—
442C23—142no—
443C23—282no—
444C23—282no—
445C23C22×C22⋊D711yescharacteristic
446Q8—28no—
447Q8—24no—
448Q8—22no—
449Q8—88no—
450Q8—84no—
451Q8—564no—
452Q8C2×Q8×D714yes—
453D4—74no—
454D4—144no—
455D4—142no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—22no—
463C2×C4—42no—
464C2×C4—44no—
465C2×C4—142no—
466C2×C4—144no—
467C2×C4—282no—
468C2×C4—284no—
469C2×C4—288no—
470C2×C4—568no—
471C2×C4#650514yes—
472C2×C4C2×Q8×D712yes—
473C2×C4#655112yes—
474C2×C4C22×C22⋊D714yes—
475C2×C4C22×C22⋊D712yes—
476C2×C4C22×C22⋊D714yes—
477C2×C4C22×C22⋊D712yes—
478C2×C4C22×C22⋊D711yescharacteristic
479C2×C4C24×D711yescharacteristic
480C8—74no—
481C8—142no—
482C8—144no—
483C7C2×#338511yescharacteristic, complemented, Sylow
484C22—144no—
485C22—282no—
486C22—282no—
487C22—288no—
488C22C2×#650512yes—
489C22Q8×C22⋊D712yes—
490C22#9052612yes—
491C22C23×C22⋊D711yescharacteristic
492C4—24no—
493C4—24no—
494C4—24no—
495C4—22no—
496C4—42no—
497C4—44no—
498C4—282no—
499C4—284no—
500C4C2×#650514yes—
501C4Q8×C22⋊D712yes—
502C4C22×Q8×D711yescharacteristic
503C4C2×#655111yescharacteristic
504C2—284no—
505C2#1174115114yesdirect product factor
506C2C22×#650511yescharacteristic
507C2C2×Q8×C22⋊D711yescharacteristic
508C2C2×#9052611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×Q82C2
socleC23×C7C22×D4
prime radicalC22×D28C23
hypercenterC2×Q82D7
hypocenterC7C2×#3385
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. #11741151C2direct (N × H)
6. C2×#89852C2semidirect
7. C2×#89850C2semidirect
9. C2×#89796C2semidirect
10. C2×#89794C2semidirect
11. C2×#89793C2semidirect
14. C7×Q82C22semidirect
37. #89852C22semidirect
38. #89850C22semidirect
41. #89796C22semidirect
42. #89794C22semidirect
43. #89793C22semidirect
90. C2×#1143Q8semidirect
125. C2×Q82D7semidirect
184. #1143C2×Q8semidirect
202. Q82C2×D7semidirect
436. C2×C7#3385semidirect
483. C7C2×#3385semidirect
505. C2#11741151direct (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×#902702
#117411512
C2×#898562
C2×#898592
C2×#898522
C2×#898502
C2×#897982
C2×#897962
C2×#897942
C2×#897932
C2×C4×#11432
C2×#33857