Finite Group Databasebeta

← #13256136

Subgroups — #13256136

Order 1792.

712 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#476C211yesmaximal, characteristic, complemented
2C2×#89856C211yesmaximal, characteristic, complemented
3#11739862C211yesmaximal, characteristic
4#11729539C211yesmaximal, characteristic, complemented
5C2×D4⋊(C7⋊C8)C211yesmaximal, characteristic, complemented
6C2×#89278C211yesmaximal, characteristic, complemented
7#11725508C211yesmaximal, characteristic, complemented
8C2×C7×C4⋊Q8C2211yescharacteristic
9C2×C4×C7×D4C2211yescharacteristic
10C2×#6501—21no—
11C2×#6493—21no—
12C2×C4×D28C2211yescharacteristic
13C7×#476—22no—
14C7×#476—22no—
15C2×C7×#106—21no—
16C2×C7×C4⋊C8C2211yescharacteristic
17C2×C7×#102—21no—
18C2×#6409—22no—
19#89984—21no—
20#89856—22no—
21#89856—22no—
22#89759—21no—
23C2×#6383—21no—
24C2×#6382—21no—
25#89733—22no—
26#89707C2211yescharacteristic
27C2×C4⋊(C7⋊C8)C2211yescharacteristic
28C2×C4×C7⋊C8C2211yescharacteristic
29D4⋊(C7⋊C8)—22no—
30#89278—22no—
31#10235—71nomaximal, Sylow
32C22×C7×Q8—21no—
33C22×C7×D4D411yescharacteristic
34C23×C4×C7—21no—
35C22×C22⋊D7—22no—
36C22×D28D411yescharacteristic
37C22×C4×D7—21no—
38C22×C7×C8—21no—
39C7×C4⋊Q8—21no—
40C7×C4⋊Q8—21no—
41C7×C4⋊Q8—21no—
42C7×C4⋊Q8D412yescomplemented
43C4×C7×D4—21no—
44C4×C7×D4—21no—
45C4×C7×D4—21no—
46C4×C7×D4—21no—
47C2×C7×C4⋊C4—21no—
48C2×C7×C4⋊C4—21no—
49C2×C7×C4⋊C4D411yescharacteristic
50C2×C7×C22⋊C4—21no—
51C2×C42×C7C2311yescharacteristic
52C2×C22⋊Dic7—22no—
53#6501—42no—
54#6501—42no—
55#6493—42no—
56#6493—42no—
57C2×(C2×D7)⋊C4—22no—
58C2×(C2×D7)⋊C4—21no—
59C2×C4⋊Dic7—21no—
60C2×C4⋊Dic7—21no—
61C2×C4⋊Dic7D411yescharacteristic
62C2×C4⋊Dic7D412yes—
63C22×C7⋊C8—21no—
64C22×C7⋊C8—21no—
65C4×D28—21no—
66C4×D28—21no—
67C4×D28—21no—
68C4×D28—21no—
69C7×#106—24no—
70C7×C4⋊C8—21no—
71C7×C4⋊C8D412yescomplemented
72C7×#102—24no—
73#6409—44no—
74C7⋊#95—22no—
75#6383—24no—
76#6382—24no—
77C4⋊(C7⋊C8)—21no—
78C4⋊(C7⋊C8)D412yescomplemented
79C4×C7⋊C8—21no—
80C4×C7⋊C8—21no—
81C2×#476—71no—
82C2×#476D711yescharacteristic, complemented
83#2537—71no—
84#1956—71no—
85C2×D4⋊C8—71no—
86C2×D4⋊C8—71no—
87#1296—71no—
88C24×C7—21no—
89C23×D7—21no—
90C2×C7×Q8—22no—
91C2×C7×Q8—42no—
92C2×C7×Q8—42no—
93C2×C7×Q8—41no—
94C2×C7×D4—21no—
95C2×C7×D4—21no—
96C2×C7×D4—21no—
97C2×C7×D4—21no—
98C2×C7×D4—21no—
99C2×C7×D4SD1612yes—
100C22×C4×C7—21no—
101C22×C4×C7—41no—
102C22×C4×C7—41no—
103C22×C4×C7—41no—
104C22×C4×C7—41no—
105C22×C4×C7—41no—
106C22×C4×C7—41no—
107C22×C4×C7—41no—
108C22×C4×C7C2×D411yescharacteristic
109C22×C4×C7C2×D411yescharacteristic
110C22×C4×C7C2×D411yescharacteristic
111C2×C22⋊D7—44no—
112C2×C22⋊D7—44no—
113C2×C22⋊D7—82no—
114C22×Dic7—21no—
115C22×Dic7—22no—
116C2×D28—21no—
117C2×D28—21no—
118C2×D28—21no—
119C2×D28—21no—
120C2×D28—21no—
121C2×D28SD1612yes—
122C2×C4×D7—41no—
123C2×C4×D7—41no—
124C2×C4×D7—41no—
125C2×C4×D7—41no—
126C2×C4×D7—41no—
127C2×C4×D7—41no—
128C2×C7×C8—22no—
129C2×C7×C8—41no—
130C2×C7×C8—41no—
131C7×C4⋊C4—22no—
132C7×C4⋊C4—21no—
133C7×C4⋊C4—22no—
134C7×C4⋊C4—21no—
135C7×C4⋊C4—41no—
136C7×C4⋊C4—41no—
137C7×C22⋊C4—41no—
138C7×C22⋊C4—41no—
139C42×C7C2×D411yescharacteristic
140C42×C7C2×D411yescharacteristic
141C42×C7C2×D411yescharacteristic
142C42×C7#4111yescharacteristic
143C22⋊Dic7—44no—
144(C2×D7)⋊C4—44no—
145(C2×D7)⋊C4—41no—
146(C2×D7)⋊C4—41no—
147C4⋊Dic7—21no—
148C4⋊Dic7—21no—
149C4⋊Dic7—41no—
150C4⋊Dic7—41no—
151C4⋊Dic7—41no—
152C4⋊Dic7—41no—
153C4⋊Dic7—42no—
154C2×C7⋊C8—22no—
155C2×C7⋊C8—22no—
156C2×C7⋊C8—41no—
157C2×C7⋊C8—41no—
158C2×C7⋊C8—41no—
159C2×C7⋊C8—41no—
160C2×C4⋊Q8C2×D711yescharacteristic
161C2×#121—141no—
162C2×#121—141no—
163C2×C4×D4—71no—
164C2×C4×D4C2×D711yescharacteristic
165#476—22no—
166#476—22no—
167#476—142no—
168#476—142no—
169C2×#106—21no—
170C2×#106—141no—
171C2×C4⋊C8—71no—
172C2×C4⋊C8C2×D711yescharacteristic
173C2×#103—142no—
174C2×#102—21no—
175C2×#102—141no—
176C2×C4×C8—71no—
177#394—142no—
178#384—71no—
179#380—141no—
180#380—141no—
181D4⋊C8—142no—
182D4⋊C8—142no—
183C23×C7—22no—
184C23×C7—41no—
185C23×C7—41no—
186C23×C7—41no—
187C23×C7—41no—
188C23×C7—41no—
189C23×C7—41no—
190C23×C7#12011yescharacteristic
191C22×D7—22no—
192C22×D7—41no—
193C22×D7—41no—
194C22×D7—41no—
195C22×D7—41no—
196C22×D7—41no—
197C22×D7—41no—
198C7×Q8—44no—
199C7×Q8—82no—
200C7×D4—22no—
201C7×D4—22no—
202C7×D4—41no—
203C7×D4—41no—
204C2×C4×C7—21no—
205C2×C4×C7—21no—
206C2×C4×C7—41no—
207C2×C4×C7—42no—
208C2×C4×C7—41no—
209C2×C4×C7—41no—
210C2×C4×C7—81no—
211C2×C4×C7—81no—
212C2×C4×C7—81no—
213C2×C4×C7—81no—
214C2×C4×C7—81no—
215C2×C4×C7—81no—
216C2×C4×C7#12011yescharacteristic
217C2×C4×C7#12011yescharacteristic
218C2×C4×C7#12111yescharacteristic
219C2×C4×C7#12111yescharacteristic
220C2×C4×C7#12111yescharacteristic
221C2×C4×C7#12711yescharacteristic
222C2×C4×C7C2×SD1611yescharacteristic
223C2×C4×C7C2×SD1611yescharacteristic
224C2×C4×C7#13511yescharacteristic
225C2×C4×C7#13511yescharacteristic
226C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
227C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
228C2×C4×C7#13711yescharacteristic
229C2×C4×C7#13711yescharacteristic
230C22⋊D7—88no—
231C2×Dic7—41no—
232C2×Dic7—42no—
233C2×Dic7—42no—
234C2×Dic7—41no—
235C2×Dic7—41no—
236C2×Dic7—42no—
237D28—22no—
238D28—22no—
239D28—41no—
240D28—41no—
241C4×D7—81no—
242C4×D7—81no—
243C4×D7—81no—
244C4×D7—81no—
245C7×C8—42no—
246C7⋊C8—42no—
247C7⋊C8—42no—
248C22×Q8—21no—
249C22×D4—71no—
250C22×D4—142no—
251C22×D4C22⋊D711yescharacteristic
252C23×C4—21no—
253C23×C4—141no—
254C22×C8—21no—
255C22×C8—141no—
256C22×C8—141no—
257C4⋊Q8—21no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8C22⋊D712yescomplemented
261#121—282no—
262#121—282no—
263#121—282no—
264#121—282no—
265C4×D4—21no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4—141no—
270C4×D4—141no—
271C4×D4—141no—
272C4×D4—141no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—71no—
276C2×C4⋊C4—72no—
277C2×C4⋊C4—141no—
278C2×C4⋊C4—141no—
279C2×C4⋊C4C22⋊D711yescharacteristic
280C2×C22⋊C4—21no—
281C2×C22⋊C4—142no—
282C2×C22⋊C4—142no—
283C2×C22⋊C4—141no—
284C2×C42C22×D711yescharacteristic
285#106—24no—
286#106—144no—
287C4⋊C8—21no—
288C4⋊C8—72no—
289C4⋊C8—141no—
290C4⋊C8C22⋊D712yescomplemented
291#103—284no—
292#102—24no—
293#102—144no—
294C4×C8—141no—
295C4×C8—141no—
296#95—142no—
297C22×C7—42no—
298C22×C7—42no—
299C22×C7—42no—
300C22×C7—81no—
301C22×C7—81no—
302C22×C7—81no—
303C22×C7—81no—
304C22×C7#39211yescharacteristic
305C22×C7#45011yescharacteristic
306C22×C7#45011yescharacteristic
307C22×C7#45211yescharacteristic
308C22×C7#45211yescharacteristic
309C22×C7#45311yescharacteristic
310C22×C7#45411yescharacteristic
311C2×D7—42no—
312C2×D7—42no—
313C2×D7—42no—
314C2×D7—81no—
315C2×D7—81no—
316C2×D7—81no—
317C2×D7—81no—
318C4×C7—21no—
319C4×C7—21no—
320C4×C7—81no—
321C4×C7—82no—
322C4×C7#44811yescharacteristic
323C4×C7#44811yescharacteristic
324C4×C7#44911yescharacteristic
325C4×C7#44911yescharacteristic
326C4×C7#46511yescharacteristic
327C4×C7#46511yescharacteristic
328C4×C7#46811yescharacteristic
329C4×C7#46811yescharacteristic
330Dic7—82no—
331Dic7—81no—
332C24—21no—
333C24—141no—
334C2×Q8—22no—
335C2×Q8—42no—
336C2×Q8—42no—
337C2×Q8—41no—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—72no—
344C2×D4—141no—
345C2×D4—141no—
346C2×D4—141no—
347C2×D4—141no—
348C2×D4—141no—
349C2×D4—284no—
350C2×D4—284no—
351C2×D4—562no—
352C2×D4#114312yes—
353C22×C4—21no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—141no—
362C22×C4—142no—
363C22×C4—281no—
364C22×C4—281no—
365C22×C4—281no—
366C22×C4—281no—
367C22×C4—281no—
368C22×C4—281no—
369C22×C4D4×D711yescharacteristic
370C22×C4D4×D711yescharacteristic
371C22×C4C2×C22⋊D711yescharacteristic
372C2×C8—22no—
373C2×C8—41no—
374C2×C8—41no—
375C2×C8—142no—
376C2×C8—142no—
377C2×C8—281no—
378C2×C8—281no—
379C2×C8—281no—
380C2×C8—281no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—21no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—141no—
388C4⋊C4—141no—
389C4⋊C4—282no—
390C4⋊C4—281no—
391C4⋊C4—281no—
392C4⋊C4—281no—
393C4⋊C4—281no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—284no—
397C22⋊C4—284no—
398C22⋊C4—281no—
399C22⋊C4—281no—
400C42D4×D711yescharacteristic
401C42#115911yescharacteristic
402C42C2×C22⋊D711yescharacteristic
403C42C2×C22⋊D711yescharacteristic
404C2×C7—82no—
405C2×C7#162911yescharacteristic
406C2×C7#163411yescharacteristic
407C2×C7#163511yescharacteristic
408C2×C7#163511yescharacteristic
409C2×C7#200011yescharacteristic
410C2×C7#200011yescharacteristic
411C2×C7#200611yescharacteristic
412D7—82no—
413C23—22no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—142no—
421C23—281no—
422C23—281no—
423C23—281no—
424C23—281no—
425C23—281no—
426C23—281no—
427C23#650011yescharacteristic
428Q8—44no—
429Q8—82no—
430D4—22no—
431D4—22no—
432D4—41no—
433D4—41no—
434D4—142no—
435D4—142no—
436D4—281no—
437D4—281no—
438D4—568no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4—81no—
450C2×C4—81no—
451C2×C4—282no—
452C2×C4—282no—
453C2×C4—281no—
454C2×C4—281no—
455C2×C4—282no—
456C2×C4—281no—
457C2×C4—561no—
458C2×C4—561no—
459C2×C4—561no—
460C2×C4—561no—
461C2×C4D7×SD1611yescharacteristic
462C2×C4#647711yescharacteristic
463C2×C4#647811yescharacteristic
464C2×C4#647911yescharacteristic
465C2×C4#650011yescharacteristic
466C2×C4#650111yescharacteristic
467C2×C4#650211yescharacteristic
468C2×C4#650211yescharacteristic
469C2×C4#650311yescharacteristic
470C2×C4C2×#114311yescharacteristic
471C2×C4#650511yescharacteristic
472C2×C4#651211yescharacteristic
473C2×C4#651311yescharacteristic
474C2×C4#651611yescharacteristic
475C8—42no—
476C8—282no—
477C8—282no—
478C7#1023511yescharacteristic, complemented, Sylow
479C22—42no—
480C22—42no—
481C22—42no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22—282no—
487C22—282no—
488C22—282no—
489C22—561no—
490C22—561no—
491C22—561no—
492C22—561no—
493C22#8981811yescharacteristic
494C22#8981911yescharacteristic
495C22#8994111yescharacteristic
496C22#8994511yescharacteristic
497C22#8997011yescharacteristic
498C22#8997311yescharacteristic
499C22#8999511yescharacteristic
500C4—21no—
501C4—21no—
502C4—81no—
503C4—82no—
504C4—562no—
505C4—561no—
506C4#8982011yescharacteristic
507C4#8982111yescharacteristic
508C4#8994211yescharacteristic
509C4#8994311yescharacteristic
510C4#8994411yescharacteristic
511C4#8994611yescharacteristic
512C4#8999911yescharacteristic
513C4#9001011yescharacteristic
514C2—82no—
515C2—562no—
516C2#1172889411yescharacteristic
517C2#1172889711yescharacteristic
518C2#1172889911yescharacteristic
519C2#1172890011yescharacteristic
520C2#1172945311yescharacteristic
521C2#1172980811yescharacteristic
522C2#1172985211yescharacteristic
subgroupG/H
centerC23#6500
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC2×C7×#476C2
socleC23×C7#120
prime radical#11739862C2
hypercenterC2×#476D7
hypocenterC7#10235
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×C7×#476C2semidirect
2. C2×#89856C2semidirect
4. #11729539C2semidirect
5. C2×D4⋊(C7⋊C8)C2semidirect
6. C2×#89278C2semidirect
7. #11725508C2semidirect
42. C7×C4⋊Q8D4semidirect
71. C7×C4⋊C8D4semidirect
78. C4⋊(C7⋊C8)D4semidirect
82. C2×#476D7semidirect
260. C4⋊Q8C22⋊D7semidirect
290. C4⋊C8C22⋊D7semidirect
478. C7#10235semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4762
C2×#898562
#117398622
#117295392
C2×D4⋊(C7⋊C8)2
C2×#892782
#117255082
#102357