Finite Group Databasebeta

← #13273148

Subgroups — #13273148

Order 1792.

482 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89468C211yesmaximal, characteristic
2C2×#89298C211yesmaximal, characteristic, complemented
3C2×#89298C211yesmaximal, characteristic, complemented
4C2×#89304C211yesmaximal, characteristic
5C2×#89304C211yesmaximal, characteristic
6#11727524C211yesmaximal, characteristic, complemented
7C7×#1374C211yesmaximal, characteristic, complemented
8C22×Dic28C2211yescharacteristic
9C22×D56C2211yescharacteristic
10C22×#1132—21no—
11C2×#6438—21no—
12C22×C7×C16C2211yescharacteristic
13C22×C7×C16C2211yescharacteristic
14C2×C4×C7×C8C2211yescharacteristic
15C2×#6392C2211yescharacteristic
16C2×#6392C2211yescharacteristic
17#89700—21no—
18#89468—22no—
19#89468—22no—
20#89346—21no—
21#89304—22no—
22#89304—22no—
23#89298—22no—
24#89298—22no—
25#13408—71nomaximal, Sylow
26C22×D28—21no—
27C22×Dic14—21no—
28C22×C7×C8D411yescharacteristic
29C22×C7×C8C2311yescharacteristic
30C2×C42×C7D411yescharacteristic
31C2×(C2×D7)⋊C4—41no—
32C2×(C2×D7)⋊C4—41no—
33C2×C4⋊Dic7—21no—
34C2×C4⋊Dic7—21no—
35C2×Dic7⋊C4—41no—
36C2×Dic28—21no—
37C2×Dic28—21no—
38C2×Dic28—21no—
39C2×Dic28—21no—
40C2×Dic28—21no—
41C2×Dic28D412yes—
42C2×D56—21no—
43C2×D56—21no—
44C2×D56—21no—
45C2×D56—21no—
46C2×D56—21no—
47C2×D56D412yes—
48C2×#1132—24no—
49C2×#1132—42no—
50C2×#1132—42no—
51#6438—24no—
52#6438—42no—
53C2×C7×C16—21no—
54C2×C7×C16—21no—
55C2×C7×C16—21no—
56C2×C7×C16—21no—
57C2×C7×C16—21no—
58C2×C7×C16—21no—
59C4×C7×C8—21no—
60C4×C7×C8—21no—
61C7⋊#95—41no—
62#6392—21no—
63#6392—21no—
64#6392—21no—
65#6392D412yes—
66C2×#495—71no—
67C2×#358—71no—
68C2×#358—71no—
69C2×#357—71no—
70C2×#357—71no—
71#1942—71no—
72#1374D711yescharacteristic, complemented
73C23×D7—41no—
74C22×C4×C7D811yescharacteristic
75C22×C4×C7D811yescharacteristic
76C22×C4×C7C2×D411yescharacteristic
77C22×Dic7—41no—
78C22×Dic7—41no—
79C22×Dic7—41no—
80C2×D28—22no—
81C2×D28—41no—
82C2×D28—41no—
83C2×D28—41no—
84C2×D28—41no—
85C2×D28—41no—
86C2×Dic14—22no—
87C2×Dic14—41no—
88C2×Dic14—41no—
89C2×Dic14—41no—
90C2×Dic14—41no—
91C2×Dic14—41no—
92C2×C7×C8—21no—
93C2×C7×C8—21no—
94C2×C7×C8SD1612yes—
95C2×C7×C8C2×D411yescharacteristic
96C2×C7×C8C2×D411yescharacteristic
97C2×C7×C8C2×D411yescharacteristic
98C2×C7×C8#4111yescharacteristic
99C2×C7×C8#4111yescharacteristic
100C2×C7×C8#4111yescharacteristic
101C42×C7—21no—
102C42×C7—21no—
103(C2×D7)⋊C4—44no—
104(C2×D7)⋊C4—44no—
105C4⋊Dic7—22no—
106C4⋊Dic7—41no—
107C4⋊Dic7—41no—
108C4⋊Dic7—41no—
109Dic7⋊C4—82no—
110Dic28—22no—
111Dic28—22no—
112Dic28—41no—
113Dic28—41no—
114D56—22no—
115D56—22no—
116D56—41no—
117D56—41no—
118#1132—48no—
119C7×C16—41no—
120C7×C16—41no—
121C22×Q16—71no—
122C22×SD16—141no—
123C22×D8—71no—
124C2×#124—141no—
125C22×C16C2×D711yescharacteristic
126C22×C16C2×D711yescharacteristic
127#495—142no—
128#495—142no—
129C2×#107—71no—
130C2×#107—71no—
131C2×C4×C8C2×D711yescharacteristic
132#389—141no—
133#358—142no—
134#358—142no—
135#357—142no—
136#357—142no—
137#340—141no—
138C23×C7C2×D811yescharacteristic
139C22×D7—42no—
140C22×D7—81no—
141C22×D7—81no—
142C22×D7—81no—
143C22×D7—81no—
144C22×D7—81no—
145C22×D7—81no—
146C2×C4×C7—21no—
147C2×C4×C7—21no—
148C2×C4×C7—21no—
149C2×C4×C7—21no—
150C2×C4×C7—21no—
151C2×C4×C7—21no—
152C2×C4×C7#12011yescharacteristic
153C2×C4×C7#12111yescharacteristic
154C2×C4×C7#12411yescharacteristic
155C2×C4×C7C2×SD1611yescharacteristic
156C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
158C2×Dic7—42no—
159C2×Dic7—42no—
160C2×Dic7—81no—
161C2×Dic7—81no—
162C2×Dic7—81no—
163C2×Dic7—81no—
164C2×Dic7—81no—
165C2×Dic7—81no—
166C2×Dic7—81no—
167D28—42no—
168D28—42no—
169D28—81no—
170D28—81no—
171Dic14—42no—
172Dic14—42no—
173Dic14—81no—
174Dic14—81no—
175C7×C8—22no—
176C7×C8#12111yescharacteristic
177C7×C8#12111yescharacteristic
178C7×C8#12311yescharacteristic
179C7×C8#12311yescharacteristic
180C22×Q8—141no—
181C22×D4—141no—
182C2×Q16—72no—
183C2×Q16—141no—
184C2×Q16—141no—
185C2×Q16—141no—
186C2×Q16—141no—
187C2×Q16—141no—
188C2×SD16—144no—
189C2×SD16—282no—
190C2×SD16—282no—
191C2×D8—72no—
192C2×D8—141no—
193C2×D8—141no—
194C2×D8—141no—
195C2×D8—141no—
196C2×D8—141no—
197C22×C8D2811yescharacteristic
198C22×C8C22×D711yescharacteristic
199#124—144no—
200#124—282no—
201C2×C4⋊C4—141no—
202C2×C4⋊C4—141no—
203C2×C4⋊C4—281no—
204C2×C22⋊C4—281no—
205C2×C22⋊C4—281no—
206C2×C42D2811yescharacteristic
207C2×C16—21no—
208C2×C16—21no—
209C2×C16—21no—
210C2×C16—21no—
211C2×C16—21no—
212C2×C16—21no—
213#107—72no—
214#107—141no—
215#107—141no—
216#107—141no—
217C4×C8—21no—
218C4×C8—21no—
219#95—281no—
220C22×C7#44711yescharacteristic
221C22×C7#45911yescharacteristic
222C22×C7#48611yescharacteristic
223C22×C7#50811yescharacteristic
224C22×C7#50811yescharacteristic
225C22×C7#50911yescharacteristic
226C22×C7#51011yescharacteristic
227C2×D7—82no—
228C2×D7—82no—
229C2×D7—82no—
230C2×D7—161no—
231C2×D7—161no—
232C2×D7—161no—
233C2×D7—161no—
234C4×C7—41no—
235C4×C7—41no—
236C4×C7#39411yescharacteristic
237C4×C7#45011yescharacteristic
238C4×C7#46011yescharacteristic
239C4×C7#49011yescharacteristic
240Dic7—82no—
241Dic7—82no—
242Dic7—161no—
243C24—281no—
244C2×Q8—142no—
245C2×Q8—281no—
246C2×Q8—281no—
247C2×Q8—281no—
248C2×Q8—281no—
249C2×Q8—281no—
250C2×D4—142no—
251C2×D4—281no—
252C2×D4—281no—
253C2×D4—281no—
254C2×D4—281no—
255C2×D4—281no—
256C22×C4—281no—
257C22×C4—281no—
258C22×C4—281no—
259C22×C4D5611yescharacteristic
260C22×C4D5611yescharacteristic
261C22×C4C2×D2811yescharacteristic
262Q16—142no—
263Q16—142no—
264Q16—281no—
265Q16—281no—
266SD16—288no—
267D8—142no—
268D8—142no—
269D8—281no—
270D8—281no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8#113212yes—
274C2×C8#115711yescharacteristic
275C2×C8#115711yescharacteristic
276C2×C8D4×D711yescharacteristic
277C2×C8D4×D711yescharacteristic
278C2×C8D4×D711yescharacteristic
279C2×C8#116111yescharacteristic
280C4⋊C4—142no—
281C4⋊C4—281no—
282C4⋊C4—281no—
283C4⋊C4—281no—
284C4⋊C4—562no—
285C22⋊C4—284no—
286C22⋊C4—284no—
287C42—21no—
288C42—21no—
289C16—41no—
290C16—41no—
291C2×C7#204111yescharacteristic
292C2×C7#218611yescharacteristic
293C2×C7#218911yescharacteristic
294C2×C7#221011yescharacteristic
295C2×C7#221111yescharacteristic
296C2×C7#224211yescharacteristic
297C2×C7#224311yescharacteristic
298D7—162no—
299C23—282no—
300C23—561no—
301C23—561no—
302C23—561no—
303C23—561no—
304C23—561no—
305C23—561no—
306C23C2×D5611yescharacteristic
307Q8—282no—
308Q8—282no—
309Q8—561no—
310Q8—561no—
311D4—282no—
312D4—282no—
313D4—561no—
314D4—561no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—282no—
322C2×C4—282no—
323C2×C4—561no—
324C2×C4—561no—
325C2×C4—561no—
326C2×C4—561no—
327C2×C4—561no—
328C2×C4—561no—
329C2×C4—561no—
330C2×C4#643811yescharacteristic
331C2×C4#644511yescharacteristic
332C2×C4#645811yescharacteristic
333C2×C4C2×#113211yescharacteristic
334C2×C4#647111yescharacteristic
335C2×C4#647111yescharacteristic
336C8—22no—
337C8#644711yescharacteristic
338C8#644711yescharacteristic
339C8#645711yescharacteristic
340C8#645711yescharacteristic
341C7#1340811yescharacteristic, complemented, Sylow
342C22—562no—
343C22—562no—
344C22—562no—
345C22—1121no—
346C22—1121no—
347C22—1121no—
348C22—1121no—
349C22#8946611yescharacteristic
350C22#8950411yescharacteristic
351C22#8961511yescharacteristic
352C22#8967611yescharacteristic
353C22#8967611yescharacteristic
354C22#8968011yescharacteristic
355C22#8968111yescharacteristic
356C4—41no—
357C4—41no—
358C4—562no—
359C4—562no—
360C4—1121no—
361C4#8944411yescharacteristic
362C4#8948511yescharacteristic
363C4#8950311yescharacteristic
364C4#8962011yescharacteristic
365C2—1122no—
366C2#1172638311yescharacteristic
367C2#1172681311yescharacteristic
368C2#1172683311yescharacteristic
369C2#1172686311yescharacteristic
370C2#1172686511yescharacteristic
371C2#1172704211yescharacteristic
372C2#1172704811yescharacteristic
subgroupG/H
centerC23C2×D56
commutator, cosocleC22×C7×C8C23
FrattiniC22×C8C22×D7
FittingC7×#1374C2
socleC23×C7C2×D8
prime radicalC22×D56C22
hypercenter#1374D7
hypocenterC7#13408
LCSG ▷ C22×C7×C8 ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1374

Complements

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

NH ≅ G/Ntype
2. C2×#89298C2semidirect
3. C2×#89298C2semidirect
6. #11727524C2semidirect
7. C7×#1374C2semidirect
72. #1374D7semidirect
341. C7#13408semidirect

Maximal subgroups

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

subgroupindex
C2×#894682
C2×#892982
C2×#893042
#117275242
C7×#13742
#134087