Finite Group Databasebeta

← #13370977

Subgroups — #13370977

Order 1792.

1190 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×D4×C22⋊C4C211yesmaximal, characteristic
2C22×#6406C211yesmaximal, characteristic
3#11730902C211yesmaximal, characteristic, complemented
4#11729882C211yesmaximal, characteristic
5C4×#6406C212yesmaximal, complemented
6#11729361C212yesmaximal, complemented
7#11727398C212yesmaximal, complemented
8#11727391C212yesmaximal, complemented
9#11727265C211yesmaximal, characteristic, complemented
10#11727256C211yesmaximal, characteristic, complemented
11C22⋊C4×C7⋊C8C211yesmaximal, characteristic, complemented
12C23×C7×D4C2211yescharacteristic
13C2×C4×C7×D4C2212yes—
14C22×C7×C22⋊C4—21no—
15C22×C4⋊Dic7C2211yescharacteristic
16C23×C7⋊C8C2211yescharacteristic
17C7×#390C2212yes—
18C7×#386—22no—
19C7×#380C2211yescharacteristic
20C7×#379—21no—
21C4×C7×C22⋊C4C2211yescharacteristic
22C2×#6406C418yescomplemented
23C2×#6406C2212yes—
24C2×#6406C2212yes—
25C2×#6406C2211yescharacteristic
26C2×#6406C2211yescharacteristic
27C2×#6406C2211yescharacteristic
28C2×#6406C2211yescharacteristic
29#89984C2211yescharacteristic
30C2×C22⋊(C7⋊C8)C2211yescharacteristic
31C2×#6382C2212yescomplemented
32#89714—21no—
33C22⋊C4×Dic7—21no—
34C4×C4⋊Dic7C2212yescomplemented
35#89700C2212yescomplemented
36C2×C4×C7⋊C8C2212yescomplemented
37#89426—22no—
38#89324C2212yescomplemented
39#89324C2212yescomplemented
40#89324C2212yescomplemented
41#89319C2212yescomplemented
42#22574—71nomaximal, Sylow
43C25×C7—21no—
44C22×C7×D4—24no—
45C22×C7×D4—21no—
46C22×C7×D4—22no—
47C22×C7×D4—42no—
48C22×C7×D4C2×C414yes—
49C22×C7×D4C2311yescharacteristic
50C22×C7×D4C2311yescharacteristic
51C23×C4×C7—22no—
52C23×C4×C7C2311yescharacteristic
53C23×Dic7—21no—
54C4×C7×D4—24no—
55C4×C7×D4—42no—
56C2×C7×C4⋊C4C2312yes—
57C2×C7×C22⋊C4—21no—
58C2×C7×C22⋊C4—22no—
59C2×C7×C22⋊C4—22no—
60C2×C7×C22⋊C4—22no—
61C2×C7×C22⋊C4—44no—
62C2×C7×C22⋊C4D411yescharacteristic
63C2×C7×C22⋊C4D411yescharacteristic
64C2×C42×C7C2312yes—
65C2×C22⋊Dic7—21no—
66C2×C4⋊Dic7—21no—
67C2×C4⋊Dic7—22no—
68C2×C4⋊Dic7C2×C414yescomplemented
69C2×C4⋊Dic7C2312yes—
70C2×C4⋊Dic7C2311yescharacteristic
71C2×C4⋊Dic7C2311yescharacteristic
72C2×Dic7⋊C4—22no—
73C2×C4×Dic7—22no—
74C22×C7⋊C8—42no—
75C22×C7⋊C8C2×C414yescomplemented
76C22×C7⋊C8C2312yes—
77C22×C7⋊C8C2311yescharacteristic
78C22×C7⋊C8C2311yescharacteristic
79C7×#95—21no—
80C7×#95D412yes—
81#6406—24no—
82#6406—42no—
83#6406C2×C414yes—
84#6406C2×C414yes—
85#6406C2×C414yescomplemented
86#6406C2×C414yescomplemented
87C7⋊#95—21no—
88C7⋊#95—22no—
89C7⋊#95—22no—
90C22⋊(C7⋊C8)—22no—
91#6382—42no—
92C4×C7⋊C8—42no—
93C22×#102—71no—
94#2345—71no—
95D4×C22⋊C4D711yescharacteristic
96#1934—72no—
97#1926—72no—
98#1864—72no—
99#1824—71no—
100#1807—71no—
101#1786—71no—
102C4×#102—72no—
103C8×C22⋊C4—71no—
104C24×C7—21no—
105C24×C7—21no—
106C24×C7—24no—
107C24×C7—44no—
108C24×C7—42no—
109C24×C7—42no—
110C24×C7—82no—
111C24×C7C2×D411yescharacteristic
112C2×C7×D4—28no—
113C2×C7×D4—24no—
114C2×C7×D4—21no—
115C2×C7×D4—22no—
116C2×C7×D4—21no—
117C2×C7×D4—22no—
118C2×C7×D4—22no—
119C2×C7×D4—44no—
120C2×C7×D4—48no—
121C2×C7×D4—44no—
122C2×C7×D4C22×C412yes—
123C2×C7×D4C22×C412yes—
124C2×C7×D4#4114yes—
125C22×C4×C7—22no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7—44no—
129C22×C4×C7—44no—
130C22×C4×C7—82no—
131C22×C4×C7C22×C412yes—
132C22×C4×C7C2×D412yes—
133C22×C4×C7C2×D411yescharacteristic
134C22×C4×C7C2×D412yes—
135C22×C4×C7#4112yes—
136C22×C4×C7C2411yescharacteristic
137C22×Dic7—21no—
138C22×Dic7—21no—
139C22×Dic7—24no—
140C22×Dic7—22no—
141C22×Dic7—82no—
142C7×C4⋊C4—22no—
143C7×C4⋊C4—22no—
144C7×C22⋊C4—22no—
145C7×C22⋊C4—44no—
146C7×C22⋊C4—42no—
147C7×C22⋊C4—44no—
148C7×C22⋊C4—82no—
149C7×C22⋊C4SD1614yes—
150C42×C7—22no—
151C42×C7—22no—
152C22⋊Dic7—42no—
153C4⋊Dic7—24no—
154C4⋊Dic7—21no—
155C4⋊Dic7—21no—
156C4⋊Dic7—22no—
157C4⋊Dic7—22no—
158C4⋊Dic7C22×C412yes—
159C4⋊Dic7C22×C412yes—
160Dic7⋊C4—82no—
161C4×Dic7—82no—
162C2×C7⋊C8—22no—
163C2×C7⋊C8—22no—
164C2×C7⋊C8—22no—
165C2×C7⋊C8—22no—
166C2×C7⋊C8—22no—
167C2×C7⋊C8—44no—
168C2×C7⋊C8C22×C412yes—
169C2×C7⋊C8C22×C412yes—
170C23×D4C2×D711yescharacteristic
171C23×C8—71no—
172C2×C4×D4C2×D712yes—
173C22×C4⋊C4—71no—
174C22×C22⋊C4—21no—
175C2×#106—72no—
176C2×#102—78no—
177C2×#102—71no—
178C2×#102—71no—
179C2×#102—71no—
180C2×#102—71no—
181C2×#102—72no—
182C2×#102—72no—
183C2×C22⋊C8—71no—
184C2×C4×C8—72no—
185#390C2×D712yes—
186#389—72no—
187#387—142no—
188#386—22no—
189#380—71no—
190#380—141no—
191#380C2×D711yescharacteristic
192#379—21no—
193C4×C4⋊C4—72no—
194C4×C22⋊C4—141no—
195C4×C22⋊C4C2×D711yescharacteristic
196#340—72no—
197#340—72no—
198#340—72no—
199#336—72no—
200C23×C7—22no—
201C23×C7—22no—
202C23×C7—22no—
203C23×C7—24no—
204C23×C7—22no—
205C23×C7—48no—
206C23×C7—41no—
207C23×C7—41no—
208C23×C7—42no—
209C23×C7—42no—
210C23×C7—41no—
211C23×C7—41no—
212C23×C7—42no—
213C23×C7—48no—
214C23×C7—84no—
215C23×C7—88no—
216C23×C7—88no—
217C23×C7C4×D412yes—
218C23×C7C2×SD1612yes—
219C23×C7#13512yes—
220C23×C7C22×D411yescharacteristic
221C7×D4—22no—
222C7×D4—22no—
223C7×D4—22no—
224C7×D4—24no—
225C7×D4—48no—
226C7×D4—42no—
227C7×D4#11714yes—
228C2×C4×C7—22no—
229C2×C4×C7—22no—
230C2×C4×C7—22no—
231C2×C4×C7—22no—
232C2×C4×C7—22no—
233C2×C4×C7—24no—
234C2×C4×C7—22no—
235C2×C4×C7—22no—
236C2×C4×C7—22no—
237C2×C4×C7—42no—
238C2×C4×C7—42no—
239C2×C4×C7—42no—
240C2×C4×C7—88no—
241C2×C4×C7C4×D412yes—
242C2×C4×C7C2×SD1614yes—
243C2×C4×C7C23×C411yescharacteristic
244C2×C4×C7C2×#4111yescharacteristic
245C2×C4×C7C2×#4112yes—
246C2×C4×C7H(5,𝔽2)12yes—
247C2×Dic7—22no—
248C2×Dic7—22no—
249C2×Dic7—42no—
250C2×Dic7—42no—
251C2×Dic7—42no—
252C2×Dic7—42no—
253C2×Dic7—42no—
254C2×Dic7—84no—
255C7⋊C8—22no—
256C7⋊C8—22no—
257C7⋊C8—42no—
258C25—21no—
259C22×D4—24no—
260C22×D4—22no—
261C22×D4—21no—
262C22×D4—42no—
263C22×D4C4×D714yes—
264C22×D4C22×D711yescharacteristic
265C22×D4C22×D711yescharacteristic
266C23×C4—22no—
267C23×C4—141no—
268C23×C4C22×D711yescharacteristic
269C22×C8—71no—
270C22×C8—71no—
271C22×C8—74no—
272C22×C8—72no—
273C22×C8—282no—
274C4×D4—24no—
275C4×D4—42no—
276C2×C4⋊C4—74no—
277C2×C4⋊C4—71no—
278C2×C4⋊C4—71no—
279C2×C4⋊C4—72no—
280C2×C4⋊C4—142no—
281C2×C4⋊C4—141no—
282C2×C4⋊C4—142no—
283C2×C4⋊C4C22×D712yes—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—44no—
289C2×C22⋊C4—141no—
290C2×C22⋊C4C22⋊D711yescharacteristic
291C2×C22⋊C4C22⋊D711yescharacteristic
292C2×C42—142no—
293C2×C42C22×D712yes—
294#106—282no—
295#102—74no—
296#102—74no—
297#102—74no—
298#102—74no—
299#102—144no—
300#102—282no—
301C22⋊C8—142no—
302C4×C8—282no—
303#95—21no—
304#95—142no—
305#95—142no—
306#95—141no—
307#95C22⋊D712yes—
308C22×C7—22no—
309C22×C7—22no—
310C22×C7—24no—
311C22×C7—24no—
312C22×C7—24no—
313C22×C7—42no—
314C22×C7—42no—
315C22×C7—44no—
316C22×C7—44no—
317C22×C7—42no—
318C22×C7—42no—
319C22×C7—42no—
320C22×C7—816no—
321C22×C7—82no—
322C22×C7—82no—
323C22×C7C4×SD1614yes—
324C22×C7C2×C4×D411yescharacteristic
325C22×C7#54612yes—
326C22×C7C22×SD1611yescharacteristic
327C22×C7C2×#13511yescharacteristic
328C22×C7#57612yes—
329C4×C7—22no—
330C4×C7—24no—
331C4×C7—42no—
332C4×C7—82no—
333C4×C7C2×#11711yescharacteristic
334C4×C7#51811yescharacteristic
335C4×C7#55112yes—
336Dic7—42no—
337Dic7—42no—
338Dic7—82no—
339C24—21no—
340C24—21no—
341C24—24no—
342C24—44no—
343C24—42no—
344C24—42no—
345C24—82no—
346C24C2×C22⋊D711yescharacteristic
347C2×D4—28no—
348C2×D4—24no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4—44no—
355C2×D4—48no—
356C2×D4—44no—
357C2×D4C2×C4×D712yes—
358C2×D4C2×C4×D712yes—
359C2×D4#115914yes—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—44no—
364C22×C4—44no—
365C22×C4—82no—
366C22×C4—141no—
367C22×C4—141no—
368C22×C4—144no—
369C22×C4—142no—
370C22×C4—562no—
371C22×C4C2×C4×D712yes—
372C22×C4#115712yes—
373C22×C4C2×C22⋊D712yes—
374C22×C4C2×C22⋊D711yescharacteristic
375C22×C4C2×C22⋊D712yes—
376C22×C4C23×D711yescharacteristic
377C2×C8—72no—
378C2×C8—72no—
379C2×C8—142no—
380C2×C8—142no—
381C2×C8—142no—
382C2×C8—142no—
383C2×C8—142no—
384C2×C8—284no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—72no—
388C4⋊C4—72no—
389C4⋊C4—144no—
390C4⋊C4—141no—
391C4⋊C4—141no—
392C4⋊C4—142no—
393C4⋊C4—142no—
394C4⋊C4—562no—
395C22⋊C4—22no—
396C22⋊C4—44no—
397C22⋊C4—42no—
398C22⋊C4—44no—
399C22⋊C4—82no—
400C22⋊C4—282no—
401C22⋊C4#114214yes—
402C42—22no—
403C42—22no—
404C42—562no—
405C2×C7—24no—
406C2×C7—44no—
407C2×C7—82no—
408C2×C7#234211yescharacteristic
409C2×C7C2×C4×SD1611yescharacteristic
410C2×C7#294811yescharacteristic
411C2×C7#329512yes—
412C2×C7#329712yes—
413C23—22no—
414C23—22no—
415C23—22no—
416C23—24no—
417C23—22no—
418C23—48no—
419C23—41no—
420C23—41no—
421C23—42no—
422C23—41no—
423C23—42no—
424C23—41no—
425C23—42no—
426C23—48no—
427C23—84no—
428C23—88no—
429C23—88no—
430C23C4×C22⋊D712yes—
431C23C2×#114212yes—
432C23#651312yes—
433C23C22×C22⋊D711yescharacteristic
434D4—22no—
435D4—22no—
436D4—22no—
437D4—24no—
438D4—48no—
439D4—42no—
440D4#644014yes—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—24no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—88no—
454C2×C4—142no—
455C2×C4—142no—
456C2×C4—282no—
457C2×C4—282no—
458C2×C4—282no—
459C2×C4—282no—
460C2×C4—282no—
461C2×C4—564no—
462C2×C4C4×C22⋊D712yes—
463C2×C4C2×#114214yes—
464C2×C4C22×C4×D711yescharacteristic
465C2×C4C2×#115711yescharacteristic
466C2×C4C2×#115912yes—
467C2×C4#654812yes—
468C8—142no—
469C8—142no—
470C8—282no—
471C7#2257411yescharacteristic, complemented, Sylow
472C22—24no—
473C22—24no—
474C22—22no—
475C22—22no—
476C22—24no—
477C22—44no—
478C22—44no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—816no—
485C22—82no—
486C22—82no—
487C22C4×#114214yes—
488C22C2×C4×C22⋊D711yescharacteristic
489C22C22×#114211yescharacteristic
490C22#9049712yes—
491C22C2×#651311yescharacteristic
492C22#9052612yes—
493C4—24no—
494C4—22no—
495C4—42no—
496C4—82no—
497C4—282no—
498C4—282no—
499C4—562no—
500C4C2×#644011yescharacteristic
501C4#9017711yescharacteristic
502C4#9018612yes—
503C2—24no—
504C2—44no—
505C2—82no—
506C2#1173954311yescharacteristic
507C2C2×C4×#114211yescharacteristic
508C2#1173998311yescharacteristic
509C2#1174092812yes—
510C2#1174094012yes—
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×D4×C22⋊C4C2
socleC23×C7C22×D4
prime radicalC23×C7×D4C22
cosocleC22×C4×C7C24
hypercenterD4×C22⋊C4D7
hypocenterC7#22574
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #11730902C2semidirect
5. C4×#6406C2semidirect
6. #11729361C2semidirect
7. #11727398C2semidirect
8. #11727391C2semidirect
9. #11727265C2semidirect
10. #11727256C2semidirect
11. C22⋊C4×C7⋊C8C2semidirect
22. C2×#6406C4semidirect
31. C2×#6382C22semidirect
34. C4×C4⋊Dic7C22semidirect
35. #89700C22semidirect
36. C2×C4×C7⋊C8C22semidirect
38. #89324C22semidirect
39. #89324C22semidirect
40. #89324C22semidirect
41. #89319C22semidirect
68. C2×C4⋊Dic7C2×C4semidirect
75. C22×C7⋊C8C2×C4semidirect
85. #6406C2×C4semidirect
86. #6406C2×C4semidirect
471. C7#22574semidirect

Maximal subgroups

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

subgroupindex
C7×D4×C22⋊C42
C22×#64062
#117309022
#117298822
C4×#64062
#117293612
#117273982
#117273912
#117272652
#117272562
C22⋊C4×C7⋊C82
#225747