Finite Group Databasebeta

← C2×#11725898 #13319635

Subgroups — C2×#11725898 #13319635

Order 1792.

1718 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D7×C4⋊C4C211yesmaximal, characteristic
2C2×#89498C212yesmaximal
3C2×C7×#324C211yesmaximal, characteristic, complemented
4C2×#89323C211yesmaximal, characteristic, complemented
5C2×#89264C212yesmaximal, complemented
6#11725898C218yesmaximal, direct product factor
7C23×C4×D7C411yescharacteristic
8C23×C4×D7C411yescharacteristic
9C23×C4×D7C2211yescharacteristic
10C22×C7×C4⋊C4C2211yescharacteristic
11C22×C4⋊Dic7C411yescharacteristic
12C22×Dic7⋊C4C411yescharacteristic
13C22×Dic7⋊C4C2211yescharacteristic
14C22×#1131—22no—
15C2×D7×C4⋊C4—22no—
16C2×D7×C4⋊C4—22no—
17C2×D7×C4⋊C4—24no—
18C2×D7×C4⋊C4C414yes—
19C2×D7×C4⋊C4C2214yes—
20C2×C7×C22⋊C8C2212yes—
21C2×C22⋊(C7⋊C8)C2212yes—
22C2×(C2×D7)⋊C8—22no—
23#89498—24no—
24#89498C2218yes—
25C7×#324C2214yescomplemented
26#89323C2214yescomplemented
27#89264C2218yescomplemented
28C2×#1463—71nomaximal, Sylow
29C24×D7C2×C411yescharacteristic
30C23×C4×C7C2×C411yescharacteristic
31C23×C4×C7C2×C411yescharacteristic
32C23×C4×C7C2311yescharacteristic
33C23×Dic7C2×C411yescharacteristic
34C23×Dic7C2×C411yescharacteristic
35C23×Dic7C2×C411yescharacteristic
36C22×C4×D7—22no—
37C22×C4×D7—21no—
38C22×C4×D7—21no—
39C22×C4×D7—24no—
40C22×C4×D7—24no—
41C22×C4×D7—22no—
42C22×C4×D7—21no—
43C22×C4×D7—21no—
44C22×C4×D7—44no—
45C22×C4×D7—44no—
46C22×C4×D7C2×C414yes—
47C22×C4×D7C2×C414yes—
48C22×C4×D7C2×C412yes—
49C22×C4×D7D412yes—
50C22×C4×D7D412yes—
51C22×C4×D7D414yes—
52C22×C4×D7C2312yes—
53C22×C7×C8—22no—
54C2×C7×C4⋊C4—22no—
55C2×C7×C4⋊C4—22no—
56C2×C7×C4⋊C4C2×C412yes—
57C2×C7×C4⋊C4C2312yes—
58C2×C4⋊Dic7—22no—
59C2×C4⋊Dic7—22no—
60C2×C4⋊Dic7C2×C414yes—
61C2×Dic7⋊C4—22no—
62C2×Dic7⋊C4—22no—
63C2×Dic7⋊C4—22no—
64C2×Dic7⋊C4—22no—
65C2×Dic7⋊C4C2×C412yes—
66C2×Dic7⋊C4C2×C414yes—
67C2×Dic7⋊C4C2312yes—
68C22×C7⋊C8—22no—
69C2×#1131—28no—
70C2×#1131—48no—
71D7×C4⋊C4—28no—
72D7×C4⋊C4—28no—
73D7×C4⋊C4—28no—
74D7×C4⋊C4—28no—
75C7×C22⋊C8—22no—
76C7×C22⋊C8C2314yes—
77C22⋊(C7⋊C8)—22no—
78C22⋊(C7⋊C8)C2314yes—
79(C2×D7)⋊C8—28no—
80C23×C4⋊C4—71no—
81C2×#407—72no—
82#1463—78no—
83C2×#324—72no—
84C2×#324—71no—
85C2×#324D711yescharacteristic, complemented
86C24×C7C22×C411yescharacteristic
87C23×D7—22no—
88C23×D7—22no—
89C23×D7—24no—
90C23×D7—24no—
91C23×D7C22⋊C412yes—
92C23×D7C22⋊C411yescharacteristic
93C23×D7C22⋊C411yescharacteristic
94C23×D7C22×C412yes—
95C22×C4×C7—21no—
96C22×C4×C7—21no—
97C22×C4×C7—22no—
98C22×C4×C7—21no—
99C22×C4×C7—21no—
100C22×C4×C7—42no—
101C22×C4×C7—42no—
102C22×C4×C7M1614yescomplemented
103C22×C4×C7C22×C412yes—
104C22×C4×C7C22×C412yes—
105C22×C4×C7C22×C411yescharacteristic
106C22×C4×C7C2×D412yes—
107C22×C4×C7C2×D412yes—
108C22×C4×C7C2411yescharacteristic
109C22×Dic7—21no—
110C22×Dic7—21no—
111C22×Dic7—22no—
112C22×Dic7—21no—
113C22×Dic7—21no—
114C22×Dic7—42no—
115C22×Dic7—42no—
116C22×Dic7C22⋊C412yes—
117C22×Dic7C22⋊C412yes—
118C22×Dic7M1614yescomplemented
119C22×Dic7C22×C412yes—
120C22×Dic7C22×C412yes—
121C22×Dic7C22×C412yes—
122C2×C4×D7—216no—
123C2×C4×D7—28no—
124C2×C4×D7—28no—
125C2×C4×D7—28no—
126C2×C4×D7—24no—
127C2×C4×D7—24no—
128C2×C4×D7—28no—
129C2×C4×D7—28no—
130C2×C4×D7—24no—
131C2×C4×D7—24no—
132C2×C4×D7—44no—
133C2×C4×D7—48no—
134C2×C4×D7—44no—
135C2×C4×D7—44no—
136C2×C4×D7—44no—
137C2×C4×D7—48no—
138C2×C4×D7—44no—
139C2×C4×D7—48no—
140C2×C4×D7C22⋊C414yes—
141C2×C4×D7C22⋊C414yes—
142C2×C4×D7C2×D414yes—
143C2×C4×D7C2×D414yes—
144C2×C7×C8—24no—
145C2×C7×C8—44no—
146C7×C4⋊C4—24no—
147C7×C4⋊C4—24no—
148C4⋊Dic7—28no—
149Dic7⋊C4—24no—
150Dic7⋊C4—24no—
151Dic7⋊C4—28no—
152C2×C7⋊C8—24no—
153C2×C7⋊C8—44no—
154#1131—416no—
155C24×C4—71no—
156C24×C4—71no—
157C24×C4—71no—
158C22×M16—142no—
159C22×C4⋊C4—71no—
160C22×C4⋊C4—71no—
161C22×C4⋊C4—71no—
162C22×C4⋊C4—74no—
163C22×C4⋊C4—74no—
164C22×C4⋊C4—142no—
165C22×C4⋊C4—142no—
166C22×C4⋊C4—144no—
167C22×C4⋊C4C2×D711yescharacteristic
168#407—78no—
169#407—144no—
170C2×C22⋊C8—72no—
171C2×C22⋊C8—142no—
172C2×C22⋊C8C2×D712yes—
173#324—74no—
174#324—78no—
175#324C2×D714yescomplemented
176C23×C7—22no—
177C23×C7—22no—
178C23×C7C2×C22⋊C411yescharacteristic
179C23×C7C2×C22⋊C411yescharacteristic
180C23×C7C2×M1612yes—
181C23×C7C2×M1612yes—
182C23×C7C23×C411yescharacteristic
183C22×D7—216no—
184C22×D7—216no—
185C22×D7—22no—
186C22×D7—22no—
187C22×D7—24no—
188C22×D7—22no—
189C22×D7—22no—
190C22×D7—22no—
191C22×D7—22no—
192C22×D7—24no—
193C22×D7—24no—
194C22×D7—24no—
195C22×D7—24no—
196C22×D7#9914yes—
197C22×D7#10114yes—
198C22×D7C2×C22⋊C412yes—
199C22×D7C2×C22⋊C412yes—
200C2×C4×C7—22no—
201C2×C4×C7—22no—
202C2×C4×C7—24no—
203C2×C4×C7—24no—
204C2×C4×C7—24no—
205C2×C4×C7—22no—
206C2×C4×C7—41no—
207C2×C4×C7—42no—
208C2×C4×C7—41no—
209C2×C4×C7—42no—
210C2×C4×C7—42no—
211C2×C4×C7—42no—
212C2×C4×C7C2×C22⋊C412yes—
213C2×C4×C7C2×M1614yescomplemented
214C2×C4×C7C22×D412yes—
215C2×Dic7—22no—
216C2×Dic7—22no—
217C2×Dic7—24no—
218C2×Dic7—24no—
219C2×Dic7—24no—
220C2×Dic7—22no—
221C2×Dic7—42no—
222C2×Dic7—42no—
223C2×Dic7—42no—
224C2×Dic7—42no—
225C2×Dic7—42no—
226C2×Dic7C2×C22⋊C414yes—
227C2×Dic7C2×M1614yescomplemented
228C4×D7—216no—
229C4×D7—216no—
230C4×D7—28no—
231C4×D7—28no—
232C4×D7—44no—
233C4×D7—44no—
234C4×D7—48no—
235C4×D7—48no—
236C7×C8—44no—
237C7⋊C8—44no—
238C25—71no—
239C23×C4—71no—
240C23×C4—71no—
241C23×C4—72no—
242C23×C4—72no—
243C23×C4—72no—
244C23×C4—74no—
245C23×C4—72no—
246C23×C4—71no—
247C23×C4—74no—
248C23×C4—74no—
249C23×C4—144no—
250C23×C4—142no—
251C23×C4—141no—
252C23×C4—141no—
253C23×C4—142no—
254C23×C4—141no—
255C23×C4—141no—
256C23×C4—144no—
257C23×C4—284no—
258C23×C4—284no—
259C23×C4C4×D711yescharacteristic
260C23×C4C4×D711yescharacteristic
261C23×C4C22×D711yescharacteristic
262C2×M16—148no—
263C2×M16—288no—
264C22×C8—22no—
265C22×C8—142no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—74no—
269C2×C4⋊C4—72no—
270C2×C4⋊C4—74no—
271C2×C4⋊C4—72no—
272C2×C4⋊C4—148no—
273C2×C4⋊C4—148no—
274C2×C4⋊C4—148no—
275C2×C4⋊C4—148no—
276C2×C4⋊C4—142no—
277C2×C4⋊C4—142no—
278C2×C4⋊C4—142no—
279C2×C4⋊C4—142no—
280C2×C4⋊C4—142no—
281C2×C4⋊C4—142no—
282C2×C4⋊C4C4×D712yes—
283C2×C4⋊C4C22×D712yes—
284C22⋊C8—22no—
285C22⋊C8—74no—
286C22⋊C8—148no—
287C22⋊C8—142no—
288C22⋊C8C22×D714yes—
289C22×C7—21no—
290C22×C7—21no—
291C22×C7—21no—
292C22×C7—21no—
293C22×C7—24no—
294C22×C7—24no—
295C22×C7#40712yes—
296C22×C7#40712yes—
297C22×C7C2×#9912yes—
298C22×C7C2×#10112yes—
299C22×C7C22×C22⋊C411yescharacteristic
300C22×C7C22×M1611yescharacteristic
301C22×C7C22×M1611yescharacteristic
302C2×D7—28no—
303C2×D7—28no—
304C2×D7—216no—
305C2×D7—22no—
306C2×D7—22no—
307C2×D7—22no—
308C2×D7—22no—
309C2×D7—28no—
310C2×D7—28no—
311C2×D7C2×#9914yes—
312C2×D7C2×#10114yes—
313C4×C7—24no—
314C4×C7—22no—
315C4×C7—22no—
316C4×C7—42no—
317Dic7—24no—
318Dic7—24no—
319Dic7—42no—
320C24—71no—
321C24—71no—
322C24—72no—
323C24—72no—
324C24—144no—
325C24—144no—
326C24—142no—
327C24—142no—
328C24C2×C4×D711yescharacteristic
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—72no—
337C22×C4—74no—
338C22×C4—72no—
339C22×C4—72no—
340C22×C4—72no—
341C22×C4—74no—
342C22×C4—74no—
343C22×C4—74no—
344C22×C4—74no—
345C22×C4—72no—
346C22×C4—148no—
347C22×C4—144no—
348C22×C4—144no—
349C22×C4—148no—
350C22×C4—1416no—
351C22×C4—148no—
352C22×C4—148no—
353C22×C4—144no—
354C22×C4—144no—
355C22×C4—141no—
356C22×C4—141no—
357C22×C4—142no—
358C22×C4—148no—
359C22×C4—141no—
360C22×C4—141no—
361C22×C4—284no—
362C22×C4—284no—
363C22×C4—288no—
364C22×C4—284no—
365C22×C4—284no—
366C22×C4—288no—
367C22×C4—284no—
368C22×C4—288no—
369C22×C4—282no—
370C22×C4—282no—
371C22×C4#113114yescomplemented
372C22×C4C2×C4×D712yes—
373C22×C4C2×C4×D712yes—
374C22×C4C2×C4×D711yescharacteristic
375C22×C4D4×D712yes—
376C22×C4D4×D712yes—
377C22×C4C23×D711yescharacteristic
378M16—2816no—
379C2×C8—24no—
380C2×C8—44no—
381C2×C8—144no—
382C2×C8—284no—
383C4⋊C4—24no—
384C4⋊C4—24no—
385C4⋊C4—148no—
386C4⋊C4—148no—
387C4⋊C4—144no—
388C4⋊C4—144no—
389C2×C7—21no—
390C2×C7—21no—
391C2×C7—22no—
392C2×C7#146314yescomplemented
393C2×C7C2×#40711yescharacteristic
394C2×C7C22×#9911yescharacteristic
395C2×C7C22×#10111yescharacteristic
396D7—24no—
397D7—24no—
398C23—22no—
399C23—22no—
400C23—72no—
401C23—72no—
402C23—74no—
403C23—74no—
404C23—144no—
405C23—144no—
406C23—144no—
407C23—144no—
408C23—1416no—
409C23—1416no—
410C23—142no—
411C23—142no—
412C23—144no—
413C23—142no—
414C23—142no—
415C23—142no—
416C23—142no—
417C23D7×C22⋊C411yescharacteristic
418C23D7×C22⋊C411yescharacteristic
419C23C2×#113112yes—
420C23D7×M1612yes—
421C23C22×C4×D711yescharacteristic
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—22no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—74no—
435C2×C4—74no—
436C2×C4—148no—
437C2×C4—148no—
438C2×C4—1416no—
439C2×C4—1416no—
440C2×C4—142no—
441C2×C4—142no—
442C2×C4—144no—
443C2×C4—144no—
444C2×C4—144no—
445C2×C4—142no—
446C2×C4—284no—
447C2×C4—284no—
448C2×C4—288no—
449C2×C4—288no—
450C2×C4—282no—
451C2×C4—282no—
452C2×C4—282no—
453C2×C4—282no—
454C2×C4—282no—
455C2×C4D7×C22⋊C412yes—
456C2×C4C2×#113114yescomplemented
457C2×C4C2×D4×D712yes—
458C8—44no—
459C8—284no—
460C7C2×#146311yescharacteristic, complemented, Sylow
461C22—21no—
462C22—21no—
463C22—24no—
464C22—24no—
465C22—21no—
466C22—21no—
467C22—74no—
468C22—74no—
469C22—148no—
470C22—148no—
471C22—1416no—
472C22—142no—
473C22—148no—
474C22—148no—
475C22—142no—
476C22—142no—
477C22—142no—
478C22#8949812yes—
479C22#8949812yes—
480C22D7×#9912yes—
481C22D7×#10112yes—
482C22C2×D7×C22⋊C411yescharacteristic
483C22C22×#113111yescharacteristic
484C22C2×D7×M1611yescharacteristic
485C4—22no—
486C4—22no—
487C4—24no—
488C4—42no—
489C4—144no—
490C4—144no—
491C4—282no—
492C2—21no—
493C2—21no—
494C2—22no—
495C2—144no—
496C2—144no—
497C2#1172589814yesdirect product factor
498C2C2×#8949811yescharacteristic
499C2C2×D7×#9911yescharacteristic
500C2C2×D7×#10111yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC23×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#324C2
socleC23×C7C2×C22⋊C4
prime radicalC24×D7C2×C4
cosocleC22×C4×C7C24
hypercenterC2×#324D7
hypocenterC7C2×#1463
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
3. C2×C7×#324C2semidirect
4. C2×#89323C2semidirect
5. C2×#89264C2semidirect
6. #11725898C2direct (N × H)
25. C7×#324C22semidirect
26. #89323C22semidirect
27. #89264C22semidirect
85. C2×#324D7semidirect
102. C22×C4×C7M16semidirect
118. C22×Dic7M16semidirect
175. #324C2×D7semidirect
213. C2×C4×C7C2×M16semidirect
227. C2×Dic7C2×M16semidirect
371. C22×C4#1131semidirect
392. C2×C7#1463semidirect
456. C2×C4C2×#1131semidirect
460. C7C2×#1463semidirect
497. C2#11725898direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D7×C4⋊C42
C2×#894982
C2×C7×#3242
C2×#893232
C2×#892642
#117258982
C2×#14637