Finite Group Databasebeta

← C2×#11727274 #13382624

Subgroups — C2×#11727274 #13382624

Order 1792.

1270 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#380C211yesmaximal, characteristic
2C2×#89984C211yesmaximal, characteristic
3C22×C22⋊(C7⋊C8)C211yesmaximal, characteristic
4C22×#6382C211yesmaximal, characteristic, complemented
5C2×#89324C211yesmaximal, characteristic, complemented
6C2×#89324C211yesmaximal, characteristic, complemented
7C2×#89324C211yesmaximal, characteristic, complemented
8#11727274C218yesmaximal, direct product factor
9C24×C4×C7C2211yescharacteristic
10C22×C7×C4⋊C4C2211yescharacteristic
11C22×C7×C4⋊C4C2211yescharacteristic
12C22×C7×C22⋊C4—21no—
13C22×C22⋊Dic7—21no—
14C22×C4⋊Dic7C2211yescharacteristic
15C22×C4⋊Dic7C2211yescharacteristic
16C23×C7⋊C8C2211yescharacteristic
17C23×C7⋊C8C2211yescharacteristic
18C7×#380—22no—
19C7×#380C2214yes—
20C2×C7×#95—21no—
21#89984—22no—
22#89984C2214yes—
23C2×C7⋊#95—21no—
24C2×C22⋊(C7⋊C8)—24no—
25C2×C22⋊(C7⋊C8)C2214yes—
26C2×#6382—24no—
27C2×#6382C2214yescomplemented
28#89324C2214yescomplemented
29#89324C2214yescomplemented
30#89324C2214yescomplemented
31C2×#2077—71nomaximal, Sylow
32C25×C7D411yescharacteristic
33C23×C4×C7—22no—
34C23×C4×C7—22no—
35C23×C4×C7—22no—
36C23×C4×C7—22no—
37C23×C4×C7—22no—
38C23×C4×C7—22no—
39C23×C4×C7—21no—
40C23×C4×C7—21no—
41C23×C4×C7D411yescharacteristic
42C23×C4×C7D412yes—
43C23×C4×C7C2312yes—
44C23×C4×C7C2311yescharacteristic
45C23×Dic7—21no—
46C23×Dic7—21no—
47C2×C7×C4⋊C4—22no—
48C2×C7×C4⋊C4—22no—
49C2×C7×C4⋊C4—22no—
50C2×C7×C4⋊C4—22no—
51C2×C7×C4⋊C4—21no—
52C2×C7×C4⋊C4—21no—
53C2×C7×C4⋊C4C2312yes—
54C2×C7×C4⋊C4C2312yes—
55C2×C7×C22⋊C4—24no—
56C2×C7×C22⋊C4—44no—
57C2×C22⋊Dic7—24no—
58C2×C22⋊Dic7—44no—
59C2×C4⋊Dic7—22no—
60C2×C4⋊Dic7—22no—
61C2×C4⋊Dic7—22no—
62C2×C4⋊Dic7—22no—
63C2×C4⋊Dic7—21no—
64C2×C4⋊Dic7—21no—
65C2×C4⋊Dic7C2312yes—
66C2×C4⋊Dic7C2312yes—
67C22×C7⋊C8—22no—
68C22×C7⋊C8—22no—
69C22×C7⋊C8—22no—
70C22×C7⋊C8—22no—
71C22×C7⋊C8—22no—
72C22×C7⋊C8D414yes—
73C22×C7⋊C8C2312yes—
74C22×C7⋊C8C2312yes—
75C7×#95—24no—
76C7⋊#95—24no—
77C22⋊(C7⋊C8)—28no—
78#6382—28no—
79C22×#106—71no—
80C22×C22⋊C8—71no—
81C2×#380—71no—
82C2×#380D711yescharacteristic
83#2077—78no—
84C2×#340—71no—
85C2×#340—71no—
86C2×#340—71no—
87C24×C7—22no—
88C24×C7—22no—
89C24×C7—22no—
90C24×C7—22no—
91C24×C7—22no—
92C24×C7—22no—
93C24×C7SD1614yes—
94C24×C7C2×D412yes—
95C24×C7C2×D411yescharacteristic
96C22×C4×C7—22no—
97C22×C4×C7—22no—
98C22×C4×C7—22no—
99C22×C4×C7—24no—
100C22×C4×C7—24no—
101C22×C4×C7—24no—
102C22×C4×C7—22no—
103C22×C4×C7—22no—
104C22×C4×C7—22no—
105C22×C4×C7—22no—
106C22×C4×C7—22no—
107C22×C4×C7—22no—
108C22×C4×C7—22no—
109C22×C4×C7—22no—
110C22×C4×C7—44no—
111C22×C4×C7—44no—
112C22×C4×C7—44no—
113C22×C4×C7—44no—
114C22×C4×C7—42no—
115C22×C4×C7—42no—
116C22×C4×C7—42no—
117C22×C4×C7—42no—
118C22×C4×C7—42no—
119C22×C4×C7—42no—
120C22×C4×C7C2×D412yes—
121C22×C4×C7C2×D411yescharacteristic
122C22×C4×C7C2×D412yes—
123C22×C4×C7#4112yes—
124C22×C4×C7#4112yes—
125C22×C4×C7#4112yes—
126C22×C4×C7#4112yes—
127C22×C4×C7#4112yes—
128C22×C4×C7C2411yescharacteristic
129C22×Dic7—22no—
130C22×Dic7—22no—
131C22×Dic7—42no—
132C22×Dic7—42no—
133C22×Dic7—42no—
134C22×Dic7—42no—
135C22×Dic7—42no—
136C22×Dic7—42no—
137C7×C4⋊C4—22no—
138C7×C4⋊C4—22no—
139C7×C4⋊C4—22no—
140C7×C4⋊C4—22no—
141C7×C4⋊C4—42no—
142C7×C4⋊C4—42no—
143C7×C22⋊C4—48no—
144C22⋊Dic7—48no—
145C4⋊Dic7—22no—
146C4⋊Dic7—22no—
147C4⋊Dic7—22no—
148C4⋊Dic7—22no—
149C4⋊Dic7—42no—
150C4⋊Dic7—42no—
151C2×C7⋊C8—28no—
152C2×C7⋊C8—22no—
153C2×C7⋊C8—22no—
154C2×C7⋊C8—22no—
155C2×C7⋊C8—22no—
156C2×C7⋊C8—22no—
157C2×C7⋊C8—44no—
158C2×C7⋊C8C2×D414yes—
159C24×C4C2×D711yescharacteristic
160C23×C8—71no—
161C23×C8—71no—
162C22×C4⋊C4—71no—
163C22×C4⋊C4—71no—
164C22×C4⋊C4C2×D711yescharacteristic
165C22×C4⋊C4C2×D711yescharacteristic
166C22×C22⋊C4—21no—
167C22×C22⋊C4—141no—
168C2×#106—74no—
169C2×#106—144no—
170C2×C22⋊C8—74no—
171C2×C22⋊C8—144no—
172#380—22no—
173#380—74no—
174#380—142no—
175#380C2×D714yes—
176C2×#95—21no—
177C2×#95—141no—
178#340—74no—
179#340—74no—
180#340—74no—
181C23×C7—22no—
182C23×C7—22no—
183C23×C7—22no—
184C23×C7—22no—
185C23×C7—22no—
186C23×C7—22no—
187C23×C7—28no—
188C23×C7—28no—
189C23×C7—28no—
190C23×C7—44no—
191C23×C7—44no—
192C23×C7—44no—
193C23×C7—44no—
194C23×C7#12112yes—
195C23×C7#12312yes—
196C23×C7#12312yes—
197C23×C7C2×SD1614yes—
198C23×C7C2×SD1612yes—
199C23×C7#13512yes—
200C23×C7AGL(1,ℤ/8)12yes—
201C23×C7#13712yes—
202C23×C7C22×D411yescharacteristic
203C2×C4×C7—22no—
204C2×C4×C7—22no—
205C2×C4×C7—22no—
206C2×C4×C7—44no—
207C2×C4×C7—42no—
208C2×C4×C7—42no—
209C2×C4×C7—42no—
210C2×C4×C7—42no—
211C2×C4×C7—48no—
212C2×C4×C7—42no—
213C2×C4×C7—42no—
214C2×C4×C7—42no—
215C2×C4×C7—42no—
216C2×C4×C7—42no—
217C2×C4×C7—42no—
218C2×C4×C7—84no—
219C2×C4×C7—84no—
220C2×C4×C7#12112yes—
221C2×C4×C7#12314yes—
222C2×C4×C7#12312yes—
223C2×C4×C7#12312yes—
224C2×C4×C7#12414yes—
225C2×C4×C7#12614yes—
226C2×C4×C7#12614yes—
227C2×C4×C7C22×D411yescharacteristic
228C2×C4×C7C2×#4111yescharacteristic
229C2×C4×C7C2×#4111yescharacteristic
230C2×C4×C7C2×#4111yescharacteristic
231C2×C4×C7C2×#4111yescharacteristic
232C2×C4×C7C2×#4111yescharacteristic
233C2×Dic7—42no—
234C2×Dic7—42no—
235C2×Dic7—42no—
236C2×Dic7—42no—
237C2×Dic7—42no—
238C2×Dic7—42no—
239C2×Dic7—84no—
240C2×Dic7—84no—
241C7⋊C8—24no—
242C7⋊C8—42no—
243C25C22⋊D711yescharacteristic
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—141no—
253C23×C4—141no—
254C23×C4C22⋊D712yes—
255C23×C4C22⋊D711yescharacteristic
256C23×C4C22×D712yes—
257C23×C4C22×D711yescharacteristic
258C22×C8—74no—
259C22×C8—72no—
260C22×C8—72no—
261C22×C8—142no—
262C22×C8—142no—
263C22×C8—142no—
264C22×C8—142no—
265C22×C8—142no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—72no—
273C2×C4⋊C4—72no—
274C2×C4⋊C4—142no—
275C2×C4⋊C4—142no—
276C2×C4⋊C4—142no—
277C2×C4⋊C4—142no—
278C2×C4⋊C4—141no—
279C2×C4⋊C4—141no—
280C2×C4⋊C4C22×D712yes—
281C2×C4⋊C4C22×D712yes—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—44no—
284C2×C22⋊C4—144no—
285C2×C22⋊C4—284no—
286#106—148no—
287C22⋊C8—148no—
288#95—24no—
289#95—144no—
290C22×C7—24no—
291C22×C7—24no—
292C22×C7—24no—
293C22×C7—42no—
294C22×C7—42no—
295C22×C7—416no—
296C22×C7—42no—
297C22×C7—42no—
298C22×C7#39714yes—
299C22×C7#46514yes—
300C22×C7#46814yes—
301C22×C7#48114yes—
302C22×C7#48214yes—
303C22×C7#48314yes—
304C22×C7#48514yes—
305C22×C7C2×#12111yescharacteristic
306C22×C7C2×#12311yescharacteristic
307C22×C7C2×#12311yescharacteristic
308C22×C7C22×SD1611yescharacteristic
309C22×C7C2×#13511yescharacteristic
310C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
311C22×C7C2×#13711yescharacteristic
312C4×C7—42no—
313C4×C7—82no—
314C4×C7—82no—
315C4×C7#39714yes—
316C4×C7C2×#12311yescharacteristic
317C4×C7C2×#12411yescharacteristic
318C4×C7C2×#12611yescharacteristic
319C4×C7C2×#12611yescharacteristic
320Dic7—82no—
321Dic7—82no—
322C24—22no—
323C24—22no—
324C24—22no—
325C24—22no—
326C24—22no—
327C24—22no—
328C24#114214yes—
329C24C2×C22⋊D712yes—
330C24C2×C22⋊D711yescharacteristic
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—24no—
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—44no—
346C22×C4—44no—
347C22×C4—44no—
348C22×C4—44no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—142no—
356C22×C4—142no—
357C22×C4—282no—
358C22×C4—282no—
359C22×C4—282no—
360C22×C4—282no—
361C22×C4—282no—
362C22×C4—282no—
363C22×C4#115712yes—
364C22×C4#115712yes—
365C22×C4D4×D712yes—
366C22×C4#115912yes—
367C22×C4#115912yes—
368C22×C4#115912yes—
369C22×C4C2×C22⋊D712yes—
370C22×C4C2×C22⋊D711yescharacteristic
371C22×C4C23×D711yescharacteristic
372C2×C8—74no—
373C2×C8—148no—
374C2×C8—142no—
375C2×C8—142no—
376C2×C8—142no—
377C2×C8—142no—
378C2×C8—142no—
379C2×C8—284no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—42no—
385C4⋊C4—42no—
386C4⋊C4—142no—
387C4⋊C4—142no—
388C4⋊C4—142no—
389C4⋊C4—142no—
390C4⋊C4—282no—
391C4⋊C4—282no—
392C22⋊C4—48no—
393C22⋊C4—288no—
394C2×C7—44no—
395C2×C7#207718yescomplemented
396C2×C7C2×#39711yescharacteristic
397C2×C7C2×#46511yescharacteristic
398C2×C7C2×#46811yescharacteristic
399C2×C7C2×#48311yescharacteristic
400C2×C7C2×#48211yescharacteristic
401C2×C7C2×#48511yescharacteristic
402C2×C7C2×#48111yescharacteristic
403C23—22no—
404C23—22no—
405C23—22no—
406C23—22no—
407C23—28no—
408C23—22no—
409C23—22no—
410C23—28no—
411C23—28no—
412C23—44no—
413C23—44no—
414C23—44no—
415C23—44no—
416C23#649212yes—
417C23C2×#114214yes—
418C23C2×#114212yes—
419C23#649812yes—
420C23#650212yes—
421C23#650512yes—
422C23#651212yes—
423C23#651312yes—
424C23C22×C22⋊D711yescharacteristic
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—44no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—48no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—84no—
441C2×C4—84no—
442C2×C4—282no—
443C2×C4—282no—
444C2×C4—282no—
445C2×C4—282no—
446C2×C4—282no—
447C2×C4—282no—
448C2×C4—564no—
449C2×C4—564no—
450C2×C4#644214yes—
451C2×C4#644214yes—
452C2×C4#644614yes—
453C2×C4#644814yes—
454C2×C4#649212yes—
455C2×C4#649812yes—
456C2×C4#650212yes—
457C2×C4C2×#115711yescharacteristic
458C2×C4C2×#115711yescharacteristic
459C2×C4C2×D4×D711yescharacteristic
460C2×C4C2×#115911yescharacteristic
461C2×C4C2×#115911yescharacteristic
462C2×C4C2×#115911yescharacteristic
463C8—144no—
464C8—282no—
465C7C2×#207711yescharacteristic, complemented, Sylow
466C22—24no—
467C22—24no—
468C22—24no—
469C22—42no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—416no—
474C22#8972414yes—
475C22#8974314yes—
476C22#8977514yes—
477C22#8980614yes—
478C22#8981314yes—
479C22#8981714yes—
480C22#8982114yes—
481C22C2×#649211yescharacteristic
482C22C22×#114211yescharacteristic
483C22C2×#649811yescharacteristic
484C22C2×#650211yescharacteristic
485C22C2×#650511yescharacteristic
486C22C2×#651211yescharacteristic
487C22C2×#651311yescharacteristic
488C4—42no—
489C4—82no—
490C4—82no—
491C4—562no—
492C4—562no—
493C4#8972414yes—
494C4C2×#644211yescharacteristic
495C4C2×#644211yescharacteristic
496C4C2×#644611yescharacteristic
497C4C2×#644811yescharacteristic
498C2—44no—
499C2#1172727418yesdirect product factor
500C2C2×#8972411yescharacteristic
501C2C2×#8974311yescharacteristic
502C2C2×#8977511yescharacteristic
503C2C2×#8980611yescharacteristic
504C2C2×#8981311yescharacteristic
505C2C2×#8981711yescharacteristic
506C2C2×#8982111yescharacteristic
subgroupG/H
centerC24C2×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#380C2
socleC24×C7C2×D4
prime radicalC25×C7D4
hypercenterC2×#380D7
hypocenterC7C2×#2077
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C24 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
4. C22×#6382C2semidirect
5. C2×#89324C2semidirect
6. C2×#89324C2semidirect
7. C2×#89324C2semidirect
8. #11727274C2direct (N × H)
27. C2×#6382C22semidirect
28. #89324C22semidirect
29. #89324C22semidirect
30. #89324C22semidirect
395. C2×C7#2077semidirect
465. C7C2×#2077semidirect
499. C2#11727274direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3802
C2×#899842
C22×C22⋊(C7⋊C8)2
C22×#63822
C2×#893242
#117272742
C2×#20777