Finite Group Databasebeta

← #13060574

Subgroups — #13060574

Order 1344.

496 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#1010C211yesmaximal, characteristic, complemented
2#10621548C211yesmaximal, characteristic, complemented
3#10621434C211yesmaximal, characteristic, complemented
4C3×#6513C211yesmaximal, characteristic, complemented
5#10621080C212yesmaximal, complemented
6D3×#1144C212yesmaximal, complemented
7#10621055C212yesmaximal, complemented
8#10621048C212yesmaximal, complemented
9C2×#66571C211yesmaximal, characteristic, complemented
10#10620869C211yesmaximal, characteristic, complemented
11#10620848C211yesmaximal, characteristic, complemented
12#90529—31nomaximal, Hall
13C3×C7×#41C2211yescharacteristic
14C2×Dic42C2211yescharacteristic
15D3×C7×Q8C2212yes—
16C7×#237—22no—
17C7×#237C2212yes—
18C7×#235—21no—
19C7×#235C2211yescharacteristic
20C2×C7×Dic6—21no—
21C2×C7×Dic6C2211yescharacteristic
22C3×#1157C2211yescharacteristic
23#66684—22no—
24#66676—21no—
25D3×Dic14C2212yes—
26#66669C2212yes—
27D7×Dic6—21no—
28#66635C2212yes—
29#66633C2212yes—
30#66627C2211yescharacteristic
31C3×#1144C2211yescharacteristic
32C3×#1143C2211yescharacteristic
33C3×#1142C2211yescharacteristic
34C3×#1141C2211yescharacteristic
35C2×C3×C7⋊C8C2211yescharacteristic
36#66571C2212yes—
37#66571C2212yes—
38#66569C2212yes—
39#66563C2212yes—
40#66558C2212yes—
41D3×C7⋊C8C2212yes—
42C7×2−1+4—31no—
43#6554—31no—
44#6514—31no—
45#6514—32no—
46#6513—32no—
47#6513D311yescharacteristic, complemented
48#6511—31no—
49C2×#1144—32no—
50C2×#1144—31no—
51#6505—31no—
52#6505—32no—
53#5771—71nomaximal, Hall
54C3×C7×Q8C2311yescharacteristic
55C3×C7×D4—21no—
56C3×C7×D4C2311yescharacteristic
57C2×C3×C4×C7—21no—
58C2×C3×C4×C7C2311yescharacteristic
59C2×Dic21—21no—
60Dic42—21no—
61Dic42C2312yes—
62C7×#67—22no—
63C7×#67D412yes—
64C2×C7×Dic3—21no—
65C2×C7×Dic3—22no—
66C7×D12D411yescharacteristic
67C4×D3×C7—22no—
68C4×D3×C7C2312yes—
69C7×Dic6—21no—
70C7×Dic6—22no—
71C7×Dic6D411yescharacteristic
72C7×Dic6C2312yes—
73C3×C22⋊D7—21no—
74C3×D28C2311yescharacteristic
75C3×C4×D7—21no—
76C3×Dic14C2311yescharacteristic
77#4248—22no—
78#4245—22no—
79D3×Dic7—22no—
80Dic3×D7—22no—
81C3⋊(C7⋊C8)C2312yes—
82C3×C7⋊C8C2311yescharacteristic
83C3×C7⋊C8C2311yescharacteristic
84C7×#41—31no—
85C7×#41—32no—
86C7×#41—61no—
87C7×#41—62no—
88C7×#41C2×D311yescharacteristic
89C2×C7×Q8—32no—
90C2×C7×Q8—31no—
91C2×C7×Q8—61no—
92Q8×D7—61no—
93#1159—61no—
94#1159—62no—
95#1157—32no—
96#1157C2×D311yescharacteristic
97C2×Dic14—31no—
98C2×Dic14—32no—
99#1144—32no—
100#1144—32no—
101#1144—32no—
102#1144—32no—
103#1144C2×D311yescharacteristic
104#1143—32no—
105#1143C2×D311yescharacteristic
106#1142—32no—
107#1142C2×D311yescharacteristic
108#1141C2×D311yescharacteristic
109#1136—31no—
110#1136—32no—
111C2×C7⋊C8—32no—
112C2×C7⋊C8C2×D311yescharacteristic
113#1010—71no—
114#1010D711yescharacteristic, complemented
115C3×#135—71no—
116#951—71no—
117#951—71no—
118D3×Q16—72no—
119#915—72no—
120#915—72no—
121#912—72no—
122C2×Dic12—71no—
123#901—71no—
124C22×C3×C7—21no—
125C22×C3×C7C2×D411yescharacteristic
126C2×D3×C7C2×D412yes—
127C2×C3×D7—21no—
128C3×C4×C7—21no—
129C3×C4×C7C2×D411yescharacteristic
130C3×C4×C7C2411yescharacteristic
131Dic21—22no—
132C3×Dic7—21no—
133C7×Dic3—22no—
134C7×Dic3C2×D412yes—
135#578—211noSylow
136C7×Q8—31no—
137C7×Q8—32no—
138C7×Q8—62no—
139C7×Q8—61no—
140C7×Q8C22×D311yescharacteristic
141C7×D4—21no—
142C7×D4—32no—
143C7×D4—31no—
144C7×D4—62no—
145C7×D4C22×D311yescharacteristic
146C2×C4×C7—21no—
147C2×C4×C7—32no—
148C2×C4×C7—62no—
149C2×C4×C7—62no—
150C2×C4×C7—61no—
151C2×C4×C7C22×D311yescharacteristic
152C22⋊D7—21no—
153C22⋊D7—62no—
154C2×Dic7—62no—
155C2×Dic7—61no—
156D28C22×D311yescharacteristic
157C4×D7—21no—
158C4×D7—62no—
159Dic14—32no—
160Dic14—62no—
161Dic14—61no—
162Dic14C22×D311yescharacteristic
163C7⋊C8—32no—
164C7⋊C8C22×D311yescharacteristic
165C7⋊C8C22×D311yescharacteristic
166C3×#41—71no—
167C3×#41C2×D711yescharacteristic
168D3×Q8—72no—
169D3×Q8C2×D712yes—
170#237—22no—
171#237—72no—
172#237—142no—
173#237C2×D712yes—
174#235—21no—
175#235—141no—
176#235C2×D711yescharacteristic
177C2×Dic6—21no—
178C2×Dic6—71no—
179C2×Dic6—141no—
180C2×Dic6C2×D711yescharacteristic
181C3×Q16—71no—
182C3×SD16—71no—
183C3×SD16—71no—
184C3×D8—71no—
185C2×C3×C8—71no—
186#216—72no—
187#216—72no—
188#214—72no—
189#214—72no—
190#208—71no—
191Dic12—72no—
192Dic12—72no—
193ΓL(1,𝔽25)—72no—
194D3×C8—72no—
195C2×C3×C7—21no—
196C2×C3×C7—41no—
197C2×C3×C7C22×D411yescharacteristic
198C3×D7—41no—
199D3×C7—22no—
2002−1+4—31no—
2012−1+4—211no—
202#137—212no—
203#137—212no—
204#137—211no—
205#137—211no—
206#135—71no—
207#135—212no—
208C2×Q16—211no—
209C2×Q16—212no—
210#131—211no—
211C22×C7—21no—
212C22×C7—32no—
213C22×C7D3×D411yescharacteristic
214C2×D7—21no—
215C4×C7—21no—
216C4×C7—32no—
217C4×C7—62no—
218C4×C7D3×D411yescharacteristic
219C4×C7C23×D311yescharacteristic
220Dic7—21no—
221Dic7—62no—
222C3×Q8—71no—
223C3×Q8C22×D711yescharacteristic
224C3×D4—21no—
225C3×D4—71no—
226C3×D4—141no—
227C3×D4C22×D711yescharacteristic
228C2×C3×C4—21no—
229C2×C3×C4—141no—
230C2×C3×C4C22×D711yescharacteristic
231#67—22no—
232#67—142no—
233#67C22⋊D712yes—
234C2×Dic3—21no—
235C2×Dic3—22no—
236C2×Dic3—141no—
237C2×Dic3—142no—
238D12C22⋊D711yescharacteristic
239C4×D3—22no—
240C4×D3—142no—
241C4×D3C22×D712yes—
242Dic6—21no—
243Dic6—22no—
244Dic6—72no—
245Dic6—141no—
246Dic6—142no—
247Dic6C22⋊D711yescharacteristic
248Dic6C22×D712yes—
249C3×C8—71no—
250C3×C8—71no—
251C3⋊C8—72no—
252C3×C7#57811yescharacteristic, complemented, Hall
253#41—31no—
254#41—32no—
255#41—61no—
256#41—62no—
257#41—71no—
258#41—212no—
259#41—421no—
260#41—422no—
261#41D3×D711yescharacteristic
262C2×Q8—32no—
263C2×Q8—31no—
264C2×Q8—61no—
265C2×Q8—212no—
266C2×Q8—211no—
267C2×Q8—421no—
268Q16—71no—
269Q16—212no—
270Q16—212no—
271Q16—212no—
272Q16—212no—
273SD16—71no—
274SD16—71no—
275SD16—212no—
276SD16—212no—
277D8—71no—
278M16—212no—
279M16—211no—
280C2×C8—71no—
281C2×C8—212no—
282C2×C7—21no—
283C2×C7—41no—
284C2×C7—62no—
285C2×C7C2×D3×D411yescharacteristic
286D7—41no—
287C22×C3—21no—
288C22×C3—141no—
289C22×C3C2×C22⋊D711yescharacteristic
290C2×D3C2×C22⋊D712yes—
291C3×C4—21no—
292C3×C4—141no—
293C3×C4C2×C22⋊D711yescharacteristic
294C3×C4C23×D711yescharacteristic
295Dic3—22no—
296Dic3—142no—
297Dic3C2×C22⋊D712yes—
298Q8—31no—
299Q8—32no—
300Q8—62no—
301Q8—61no—
302Q8—71no—
303Q8—212no—
304Q8—422no—
305Q8—421no—
306Q8C2×D3×D711yescharacteristic
307D4—21no—
308D4—32no—
309D4—31no—
310D4—62no—
311D4—71no—
312D4—141no—
313D4—422no—
314D4C2×D3×D711yescharacteristic
315C2×C4—21no—
316C2×C4—32no—
317C2×C4—62no—
318C2×C4—62no—
319C2×C4—61no—
320C2×C4—141no—
321C2×C4—422no—
322C2×C4—422no—
323C2×C4—421no—
324C2×C4C2×D3×D711yescharacteristic
325C8—71no—
326C8—71no—
327C8—212no—
328C7#577111yescharacteristic, complemented, Sylow
329C2×C3—21no—
330C2×C3—41no—
331C2×C3—281no—
332C2×C3C22×C22⋊D711yescharacteristic
333D3—22no—
334C22—21no—
335C22—32no—
336C22—141no—
337C22D3×C22⋊D711yescharacteristic
338C4—21no—
339C4—32no—
340C4—62no—
341C4—141no—
342C4—422no—
343C4D3×C22⋊D711yescharacteristic
344C4C22×D3×D711yescharacteristic
345C3#9052911yescharacteristic, complemented, Sylow
346C2—21no—
347C2—41no—
348C2—62no—
349C2—281no—
350C2C2×D3×C22⋊D711yescharacteristic
subgroupG/H
centerC2C2×D3×C22⋊D7
commutator, cosocleC3×C4×C7C24
FrattiniC4C22×D3×D7
FittingC3×C7×#41C22
socleC2×C3×C7C22×D4
hypercenter#41D3×D7
hypocenterC3×C7#578
LCSG ▷ C3×C4×C7 ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C2 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. C7×#1010C2semidirect
2. #10621548C2semidirect
3. #10621434C2semidirect
4. C3×#6513C2semidirect
5. #10621080C2semidirect
6. D3×#1144C2semidirect
7. #10621055C2semidirect
8. #10621048C2semidirect
9. C2×#66571C2semidirect
10. #10620869C2semidirect
11. #10620848C2semidirect
47. #6513D3semidirect
114. #1010D7semidirect
252. C3×C7#578semidirect
328. C7#5771semidirect
345. C3#90529semidirect

Maximal subgroups

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

subgroupindex
C7×#10102
#106215482
#106214342
C3×#65132
#106210802
D3×#11442
#106210552
#106210482
C2×#665712
#106208692
#106208482
#905293
#57717