Finite Group Databasebeta

← #13338971

Subgroups — #13338971

Order 1792.

792 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#459C211yesmaximal, characteristic, complemented
2#11740611C211yesmaximal, characteristic, complemented
3#11739752C211yesmaximal, characteristic, complemented
4#11739746C211yesmaximal, characteristic, complemented
5#11729513C211yesmaximal, characteristic, complemented
6#11728761C214yesmaximal, complemented
7#11728759C214yesmaximal, complemented
8#11728185C211yesmaximal, characteristic, complemented
9#11728176C211yesmaximal, characteristic, complemented
10C22×C7×D8—21no—
11C2×C7×#127C2211yescharacteristic
12C2×C4×C7×D4C2211yescharacteristic
13C2×#6495—21no—
14#90168C2211yescharacteristic
15C7×#459—22no—
16C7×#459C2214yes—
17C2×C7×C4⋊C8C2211yescharacteristic
18C2×C7×#102—21no—
19#89989—22no—
20C2×C22⋊(C7⋊C8)—22no—
21#89845C2212yescomplemented
22#89844—22no—
23#89842C2212yescomplemented
24#89791C2212yescomplemented
25#89788—22no—
26#89787C2212yescomplemented
27D4×C7⋊C8—22no—
28D4×C7⋊C8C2214yescomplemented
29#89738—21no—
30#89697C2211yescharacteristic
31#89697C2211yescharacteristic
32#89696C2211yescharacteristic
33#89339C2214yescomplemented
34#89280C2212yescomplemented
35#89277C2212yescomplemented
36#89274C2214yescomplemented
37#19386—71nomaximal, Sylow
38C22×C7×D4—21no—
39C22×C7×D4—21no—
40C22×C7×D4—21no—
41C22×C7×D4D411yescharacteristic
42C23×C4×C7—21no—
43C2×#1157—21no—
44C2×C7×D8—24no—
45C2×C7×D8—44no—
46C22×C7×C8—21no—
47C7×#127—21no—
48C7×#127—21no—
49C7×#127—21no—
50C7×#127C2312yes—
51C4×C7×D4—21no—
52C4×C7×D4—21no—
53C4×C7×D4D412yes—
54C4×C7×D4C2312yes—
55C2×C7×C4⋊C4D411yescharacteristic
56C2×C7×C22⋊C4—21no—
57C2×C42×C7C2311yescharacteristic
58C2×#1142—22no—
59#6495—44no—
60C2×#1141—22no—
61C2×#1141—24no—
62#6493—21no—
63#6493—21no—
64C2×#1136—21no—
65C22×C7⋊C8—24no—
66#6438—21no—
67#6437C2311yescharacteristic
68C4×D28—21no—
69C4×D28—21no—
70#6432C2311yescharacteristic
71C7×C4⋊C8—21no—
72C7×C4⋊C8C2312yes—
73C7×#102—24no—
74#6406—24no—
75C22⋊(C7⋊C8)—21no—
76C22⋊(C7⋊C8)—24no—
77C22⋊(C7⋊C8)D412yes—
78#6384—22no—
79#6383—22no—
80C4⋊(C7⋊C8)—21no—
81C4⋊(C7⋊C8)D412yes—
82C4⋊(C7⋊C8)C2312yes—
83C4⋊(C7⋊C8)C2312yes—
84C4×C7⋊C8—21no—
85C4×C7⋊C8C2312yes—
86#3205—71no—
87#3036—71no—
88C2×#459D711yescharacteristic, complemented
89#2972—71no—
90#1681—74no—
91#1667—74no—
92#1571—71no—
93#1545—71no—
94#1540—71no—
95C24×C7—21no—
96C24×C7—41no—
97C2×C7×D4—21no—
98C2×C7×D4—22no—
99C2×C7×D4—22no—
100C2×C7×D4—22no—
101C2×C7×D4—22no—
102C2×C7×D4—41no—
103C2×C7×D4—41no—
104C2×C7×D4—41no—
105C2×C7×D4—42no—
106C2×C7×D4—42no—
107C2×C7×D4—82no—
108C2×C7×D4—82no—
109C2×C7×D4D814yescomplemented
110C2×C7×D4C2×D412yes—
111C22×C4×C7—21no—
112C22×C4×C7—22no—
113C22×C4×C7—22no—
114C22×C4×C7—82no—
115C22×C4×C7C2×D411yescharacteristic
116C22×C4×C7C2×D411yescharacteristic
117C22×C4×C7#4111yescharacteristic
118C2×C22⋊D7—41no—
119#1157—42no—
120#1157—42no—
121C2×D28—21no—
122C2×D28—21no—
123C2×D28—21no—
124C2×C4×D7—41no—
125C2×Dic14—21no—
126C7×D8—48no—
127C2×C7×C8—22no—
128C2×C7×C8—42no—
129C7×C4⋊C4—21no—
130C7×C4⋊C4C2×D412yes—
131C7×C22⋊C4—22no—
132C7×C22⋊C4—22no—
133C42×C7C2×D411yescharacteristic
134C42×C7C2×D411yescharacteristic
135C42×C7#4111yescharacteristic
136C42×C7C2411yescharacteristic
137#1142—44no—
138#1141—44no—
139#1141—84no—
140(C2×D7)⋊C4—41no—
141(C2×D7)⋊C4—41no—
142C4⋊Dic7—21no—
143C4⋊Dic7—21no—
144#1136—42no—
145C2×C7⋊C8—22no—
146C2×C7⋊C8—22no—
147C2×C7⋊C8—84no—
148C2×C7⋊C8C2×D414yes—
149C2×AGL(1,ℤ/8)—141no—
150C22×D8—21no—
151#532—71no—
152C2×#127C2×D711yescharacteristic
153C2×C4×D4C2×D711yescharacteristic
154#493—72no—
155#486—72no—
156#463—142no—
157#461—72no—
158#459—22no—
159#459—72no—
160#459—142no—
161#459C2×D714yes—
162#447—142no—
163C8×D4—74no—
164C8×D4—142no—
165#431—71no—
166#431—71no—
167#423—71no—
168C2×C4⋊C8C2×D711yescharacteristic
169#417—141no—
170C2×#102—21no—
171C2×C22⋊C8—142no—
172#335—74no—
173#332—72no—
174#331—74no—
175#331—72no—
176C23×C7—22no—
177C23×C7—24no—
178C23×C7—42no—
179C23×C7—81no—
180C23×C7—81no—
181C23×C7—82no—
182C23×C7—82no—
183C23×C7—82no—
184C23×C7#12111yescharacteristic
185C22×D7—41no—
186C7×D4—22no—
187C7×D4—24no—
188C7×D4—42no—
189C7×D4—42no—
190C7×D4—44no—
191C7×D4—82no—
192C7×D4—82no—
193C7×D4—82no—
194C7×D4—82no—
195C7×D4C2×D814yes—
196C2×C4×C7—22no—
197C2×C4×C7—22no—
198C2×C4×C7—41no—
199C2×C4×C7—44no—
200C2×C4×C7—82no—
201C2×C4×C7—81no—
202C2×C4×C7#12111yescharacteristic
203C2×C4×C7#12111yescharacteristic
204C2×C4×C7#12111yescharacteristic
205C2×C4×C7C2×D812yes—
206C2×C4×C7#13512yes—
207C2×C4×C7C22×D411yescharacteristic
208C2×C4×C7C22×D411yescharacteristic
209C2×C4×C7C2×#4111yescharacteristic
210C22⋊D7—82no—
211C2×Dic7—41no—
212D28—41no—
213D28—41no—
214D28—42no—
215D28—81no—
216C4×D7—82no—
217Dic14—41no—
218Dic14—41no—
219C7×C8—42no—
220C7⋊C8—24no—
221C7⋊C8—42no—
222C7⋊C8—42no—
223C2×#41—141no—
224C22×D4—21no—
225C22×D4—21no—
226C22×D4—21no—
227C22×D4C22⋊D711yescharacteristic
228C23×C4—21no—
229AGL(1,ℤ/8)—284no—
230C2×SD16—142no—
231C2×D8—24no—
232C2×D8—44no—
233C2×D8—144no—
234C2×D8—142no—
235C2×M16—141no—
236C22×C8—21no—
237C22×C8—144no—
238C4⋊Q8—71no—
239#127—21no—
240#127—21no—
241#127—21no—
242#127—71no—
243#127C22×D712yes—
244#124—141no—
245#121—141no—
246#121—141no—
247C4×D4—21no—
248C4×D4—21no—
249C4×D4—141no—
250C4×D4—141no—
251C4×D4C22⋊D712yes—
252C4×D4C22×D712yes—
253C2×C4⋊C4C22⋊D711yescharacteristic
254C2×C22⋊C4—21no—
255C2×C42C22×D711yescharacteristic
256C4⋊C8—21no—
257C4⋊C8—72no—
258C4⋊C8—72no—
259C4⋊C8—72no—
260C4⋊C8—141no—
261C4⋊C8C22×D712yes—
262#103—142no—
263#102—24no—
264#102—144no—
265#102—142no—
266C22⋊C8—72no—
267C22⋊C8—144no—
268C22⋊C8—141no—
269C4×C8—72no—
270C4×C8—141no—
271C22×C7—21no—
272C22×C7—21no—
273C22×C7—24no—
274C22×C7—42no—
275C22×C7—42no—
276C22×C7—84no—
277C22×C7—82no—
278C22×C7—82no—
279C22×C7—82no—
280C22×C7—164no—
281C22×C7#46612yes—
282C22×C7C2×#12111yescharacteristic
283C2×D7—81no—
284C2×D7—81no—
285C2×D7—81no—
286C4×C7—21no—
287C4×C7—21no—
288C4×C7—21no—
289C4×C7—42no—
290C4×C7#46612yes—
291C4×C7C22×D811yescharacteristic
292C4×C7C2×#13511yescharacteristic
293C4×C7#57612yes—
294Dic7—81no—
295C24—21no—
296C24—41no—
297#41—282no—
298#41—282no—
299C2×Q8—141no—
300C2×D4—21no—
301C2×D4—22no—
302C2×D4—22no—
303C2×D4—22no—
304C2×D4—22no—
305C2×D4—42no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—42no—
310C2×D4—82no—
311C2×D4—82no—
312C2×D4—141no—
313C2×D4—141no—
314C2×D4—141no—
315C2×D4—281no—
316C2×D4#114114yescomplemented
317C2×D4C2×C22⋊D712yes—
318C22×C4—21no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—82no—
322C22×C4—281no—
323C22×C4D4×D711yescharacteristic
324C22×C4#115911yescharacteristic
325C22×C4C2×C22⋊D711yescharacteristic
326SD16—284no—
327D8—48no—
328D8—284no—
329D8—564no—
330M16—282no—
331C2×C8—22no—
332C2×C8—42no—
333C2×C8—74no—
334C2×C8—142no—
335C2×C8—142no—
336C2×C8—564no—
337C4⋊C4—21no—
338C4⋊C4—141no—
339C4⋊C4—141no—
340C4⋊C4C2×C22⋊D712yes—
341C22⋊C4—22no—
342C22⋊C4—22no—
343C22⋊C4—281no—
344C22⋊C4—281no—
345C42D4×D711yescharacteristic
346C42#115911yescharacteristic
347C42C2×C22⋊D711yescharacteristic
348C42C23×D711yescharacteristic
349C2×C7—22no—
350C2×C7—44no—
351C2×C7—162no—
352C2×C7#304111yescharacteristic
353C2×C7C2×#46611yescharacteristic
354C2×C7#306811yescharacteristic
355D7—161no—
356C23—22no—
357C23—24no—
358C23—42no—
359C23—81no—
360C23—81no—
361C23—82no—
362C23—82no—
363C23—82no—
364C23—281no—
365C23#650211yescharacteristic
366Q8—281no—
367Q8—281no—
368D4—22no—
369D4—24no—
370D4—44no—
371D4—42no—
372D4—42no—
373D4—82no—
374D4—82no—
375D4—82no—
376D4—82no—
377D4—282no—
378D4—281no—
379D4—281no—
380D4—561no—
381D4—562no—
382D4C2×#114114yes—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—44no—
387C2×C4—82no—
388C2×C4—81no—
389C2×C4—281no—
390C2×C4—562no—
391C2×C4C2×#114112yes—
392C2×C4#650211yescharacteristic
393C2×C4#650211yescharacteristic
394C2×C4#650211yescharacteristic
395C2×C4#651312yes—
396C2×C4C2×D4×D711yescharacteristic
397C2×C4C2×#115911yescharacteristic
398C2×C4C22×C22⋊D711yescharacteristic
399C8—42no—
400C8—144no—
401C8—282no—
402C8—282no—
403C7#1938611yescharacteristic, complemented, Sylow
404C22—21no—
405C22—21no—
406C22—24no—
407C22—42no—
408C22—42no—
409C22—84no—
410C22—82no—
411C22—82no—
412C22—82no—
413C22—164no—
414C22—561no—
415C22—561no—
416C22—561no—
417C22#8981012yes—
418C22C2×#650211yescharacteristic
419C4—21no—
420C4—21no—
421C4—21no—
422C4—42no—
423C4—561no—
424C4#8981012yes—
425C4#9044812yes—
426C4C22×#114111yescharacteristic
427C4C2×#651311yescharacteristic
428C2—22no—
429C2—44no—
430C2—162no—
431C2—1121no—
432C2C2×#8981011yescharacteristic
433C2#1174127111yescharacteristic
434C2#1174138811yescharacteristic
subgroupG/H
centerC22C2×#6502
commutator, cosocleC42×C7C24
FrattiniC42C23×D7
FittingC2×C7×#459C2
socleC22×C7C2×#121
hypercenterC2×#459D7
hypocenterC7#19386
LCSG ▷ C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×C7×#459C2semidirect
2. #11740611C2semidirect
3. #11739752C2semidirect
4. #11739746C2semidirect
5. #11729513C2semidirect
6. #11728761C2semidirect
7. #11728759C2semidirect
8. #11728185C2semidirect
9. #11728176C2semidirect
21. #89845C22semidirect
23. #89842C22semidirect
24. #89791C22semidirect
26. #89787C22semidirect
28. D4×C7⋊C8C22semidirect
33. #89339C22semidirect
34. #89280C22semidirect
35. #89277C22semidirect
36. #89274C22semidirect
88. C2×#459D7semidirect
109. C2×C7×D4D8semidirect
316. C2×D4#1141semidirect
403. C7#19386semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4592
#117406112
#117397522
#117397462
#117295132
#117287612
#117287592
#117281852
#117281762
#193867