Finite Group Databasebeta

← #13054897

Subgroups — #13054897

Order 1344.

572 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊D7C211yesmaximal, characteristic
2C22×Dic3×D7C211yesmaximal, characteristic, complemented
3C2×#66636C211yesmaximal, characteristic, complemented
4C2×C7×#217C211yesmaximal, characteristic, complemented
5C2×(C2×D7)⋊Dic3C211yesmaximal, characteristic, complemented
6#10620529C211yesmaximal, characteristic, complemented
7#10620529C211yesmaximal, characteristic, complemented
8#89728—31nomaximal, Hall
9C24×C3×C7C2211yescharacteristic
10C23×C3×D7C2211yescharacteristic
11C22×Dic21C2211yescharacteristic
12C22×Dic21C2211yescharacteristic
13C22×C7×Dic3C2211yescharacteristic
14C22×C7×Dic3C2211yescharacteristic
15C2×C3×C22⋊D7—22no—
16C2×C3×C22⋊D7—22no—
17C2×C3×C22⋊D7C414yescomplemented
18C22×C3×Dic7C2211yescharacteristic
19C2×Dic3×D7—22no—
20C2×Dic3×D7—22no—
21C2×Dic3×D7—22no—
22#66636—22no—
23C7×#217—22no—
24(C2×D7)⋊Dic3—22no—
25C22×C22⋊D7D311yescharacteristic
26C22×C4×D7—31no—
27C2×C7×C22⋊C4—31no—
28C2×C22⋊Dic7—31no—
29C2×(C2×D7)⋊C4—31no—
30C7⋊#95—31no—
31C7⋊#95—31no—
32#5220—71nomaximal, Hall
33C23×C3×C7—21no—
34C23×C3×C7—21no—
35C23×C3×C7—21no—
36C23×C3×C7—21no—
37C23×C3×C7—21no—
38C23×C3×C7—21no—
39C23×C3×C7C2×C412yescomplemented
40C23×C3×C7C2311yescharacteristic
41C22×C3×D7—21no—
42C22×C3×D7—21no—
43C22×C3×D7—21no—
44C22×C3×D7—21no—
45C22×C3×D7C2×C412yes—
46C22×C3×D7D412yes—
47C22×C3×D7D412yes—
48C2×Dic21—21no—
49C2×Dic21—21no—
50C2×Dic21—21no—
51C2×Dic21—21no—
52C2×Dic21—21no—
53C2×Dic21D412yescomplemented
54C2×C7×Dic3—21no—
55C2×C7×Dic3—21no—
56C2×C7×Dic3—21no—
57C2×C7×Dic3—21no—
58C2×C7×Dic3—21no—
59C2×C7×Dic3D412yescomplemented
60C3×C22⋊D7—28no—
61C2×C3×Dic7—21no—
62C2×C3×Dic7—21no—
63C2×C3×Dic7C2×C412yescomplemented
64Dic3×D7—28no—
65C24×C7C2×D311yescharacteristic
66C23×D7C2×D311yescharacteristic
67C22×C4×C7—31no—
68C22×C4×C7—31no—
69C2×C22⋊D7—22no—
70C2×C22⋊D7—22no—
71C2×C22⋊D7Dic314yescomplemented
72C22×Dic7—31no—
73C22×Dic7—31no—
74C22×Dic7C2×D311yescharacteristic
75C2×C4×D7—62no—
76C2×C4×D7—62no—
77C2×C4×D7—62no—
78C7×C22⋊C4—62no—
79C22⋊Dic7—62no—
80(C2×D7)⋊C4—62no—
81C22×C3×D4—71no—
82C23×Dic3—71no—
83C2×#217—71no—
84C2×#217—71no—
85C2×#217D711yescharacteristic, complemented
86C3⋊#95—71no—
87C3⋊#95—71no—
88C22×C3×C7—22no—
89C22×C3×C7—22no—
90C22×C3×C7—22no—
91C22×C3×C7—41no—
92C22×C3×C7—41no—
93C22×C3×C7—41no—
94C22×C3×C7—41no—
95C22×C3×C7C22×C411yescharacteristic
96C22×C3×C7C2×D411yescharacteristic
97C22×C3×C7C2×D411yescharacteristic
98C22×C3×C7C2×D411yescharacteristic
99C22×C3×C7C2×D411yescharacteristic
100C22×C3×C7#4111yescharacteristic
101C22×C3×C7#4111yescharacteristic
102C2×C3×D7—22no—
103C2×C3×D7—22no—
104C2×C3×D7—22no—
105C2×C3×D7—22no—
106C2×C3×D7—22no—
107C2×C3×D7—22no—
108C2×C3×D7C22⋊C414yescomplemented
109Dic21—22no—
110Dic21—41no—
111C3×Dic7—22no—
112C7×Dic3—22no—
113C7×Dic3—41no—
114#386—211noSylow
115C23×C7—21no—
116C23×C7—21no—
117C23×C7—21no—
118C23×C7—21no—
119C23×C7—21no—
120C23×C7—21no—
121C23×C7C2×Dic312yescomplemented
122C23×C7C22×D311yescharacteristic
123C22×D7—21no—
124C22×D7—21no—
125C22×D7—21no—
126C22×D7—21no—
127C22×D7C2×Dic312yes—
128C22×D7#6712yes—
129C22×D7#6712yes—
130C2×C4×C7—32no—
131C2×C4×C7—61no—
132C2×C4×C7—61no—
133C2×C4×C7—61no—
134C2×C4×C7—61no—
135C2×C4×C7—61no—
136C22⋊D7—28no—
137C2×Dic7—21no—
138C2×Dic7—21no—
139C2×Dic7—32no—
140C2×Dic7—61no—
141C2×Dic7—61no—
142C2×Dic7—61no—
143C2×Dic7—61no—
144C2×Dic7—61no—
145C2×Dic7C2×Dic312yescomplemented
146C4×D7—68no—
147C24×C3—71no—
148C24×C3C2×D711yescharacteristic
149C2×C3×D4—74no—
150C2×C3×D4—142no—
151C2×C3×D4—142no—
152C22×C3×C4—71no—
153C22×Dic3—71no—
154C22×Dic3—71no—
155C22×Dic3—142no—
156C22×Dic3—142no—
157C22×Dic3—142no—
158C22×Dic3C2×D711yescharacteristic
159C22×Dic3C2×D711yescharacteristic
160#217—22no—
161#217—142no—
162#217—142no—
163C2×C3×C7—42no—
164C2×C3×C7C2×C22⋊C411yescharacteristic
165C2×C3×C7C4×D411yescharacteristic
166C2×C3×C7C4×D411yescharacteristic
167C2×C3×C7#12011yescharacteristic
168C2×C3×C7#12111yescharacteristic
169C2×C3×C7#12111yescharacteristic
170C2×C3×C7#12311yescharacteristic
171C3×D7—24no—
172C22×D4—71no—
173C23×C4—211no—
174C2×C22⋊C4—31no—
175C2×C22⋊C4—211no—
176C2×C22⋊C4—211no—
177#95—211no—
178#95—211no—
179C22×C7—22no—
180C22×C7—22no—
181C22×C7—22no—
182C22×C7—41no—
183C22×C7—41no—
184C22×C7—41no—
185C22×C7—41no—
186C22×C7D3×D411yescharacteristic
187C22×C7D3×D411yescharacteristic
188C22×C7#23711yescharacteristic
189C22×C7#23711yescharacteristic
190C22×C7C22×Dic311yescharacteristic
191C22×C7C2×#6711yescharacteristic
192C22×C7C2×#6711yescharacteristic
193C2×D7—22no—
194C2×D7—22no—
195C2×D7—22no—
196C2×D7—22no—
197C2×D7—22no—
198C2×D7—22no—
199C2×D7#21714yescomplemented
200C4×C7—62no—
201C4×C7—121no—
202Dic7—22no—
203Dic7—62no—
204Dic7—121no—
205C23×C3—21no—
206C23×C3—21no—
207C23×C3—21no—
208C23×C3—21no—
209C23×C3—21no—
210C23×C3—21no—
211C23×C3—72no—
212C23×C3—72no—
213C23×C3—72no—
214C23×C3—141no—
215C23×C3—141no—
216C23×C3—141no—
217C23×C3—141no—
218C23×C3C4×D712yescomplemented
219C23×C3C22×D711yescharacteristic
220C3×D4—148no—
221C2×C3×C4—72no—
222C2×C3×C4—141no—
223C2×C3×C4—141no—
224C2×Dic3—21no—
225C2×Dic3—21no—
226C2×Dic3—21no—
227C2×Dic3—21no—
228C2×Dic3—21no—
229C2×Dic3—72no—
230C2×Dic3—148no—
231C2×Dic3—141no—
232C2×Dic3—141no—
233C2×Dic3—141no—
234C2×Dic3—141no—
235C2×Dic3—141no—
236C2×Dic3C22⋊D712yescomplemented
237C3×C7#38611yescharacteristic, complemented, Hall
238C24—71no—
239C24D3×D711yescharacteristic
240C2×D4—74no—
241C2×D4—142no—
242C2×D4—142no—
243C22×C4—31no—
244C22×C4—31no—
245C22×C4—71no—
246C22×C4—211no—
247C22×C4—211no—
248C22×C4—422no—
249C22×C4—422no—
250C22×C4—422no—
251C22⋊C4—62no—
252C22⋊C4—422no—
253C22⋊C4—422no—
254C2×C7—42no—
255C2×C7D4×Dic311yescharacteristic
256C2×C7D4×Dic311yescharacteristic
257C2×C7#93511yescharacteristic
258C2×C7#93711yescharacteristic
259C2×C7#93911yescharacteristic
260C2×C7#93911yescharacteristic
261C2×C7C2×#21711yescharacteristic
262D7—24no—
263C22×C3—22no—
264C22×C3—22no—
265C22×C3—22no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3—74no—
271C22×C3—142no—
272C22×C3—142no—
273C22×C3—142no—
274C22×C3—142no—
275C22×C3—142no—
276C22×C3—142no—
277C22×C3C2×C4×D711yescharacteristic
278C22×C3#115711yescharacteristic
279C22×C3D4×D711yescharacteristic
280C22×C3D4×D711yescharacteristic
281C22×C3D4×D711yescharacteristic
282C22×C3#115911yescharacteristic
283C22×C3C2×C22⋊D711yescharacteristic
284C3×C4—142no—
285Dic3—22no—
286Dic3—41no—
287Dic3—142no—
288Dic3—281no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—72no—
296C23—72no—
297C23—72no—
298C23—141no—
299C23—141no—
300C23—141no—
301C23—141no—
302C23Dic3×D712yescomplemented
303C23C2×D3×D711yescharacteristic
304D4—148no—
305C2×C4—32no—
306C2×C4—61no—
307C2×C4—61no—
308C2×C4—61no—
309C2×C4—61no—
310C2×C4—61no—
311C2×C4—72no—
312C2×C4—141no—
313C2×C4—141no—
314C2×C4—212no—
315C2×C4—428no—
316C2×C4—421no—
317C2×C4—421no—
318C2×C4—421no—
319C2×C4—421no—
320C2×C4—421no—
321C7#522011yescharacteristic, complemented, Sylow
322C2×C3—42no—
323C2×C3—144no—
324C2×C3D7×C22⋊C411yescharacteristic
325C2×C3(C22⋊D7)⋊C411yescharacteristic
326C2×C3#644611yescharacteristic
327C2×C3#644711yescharacteristic
328C2×C3C4×C22⋊D711yescharacteristic
329C2×C3#650011yescharacteristic
330C2×C3#650111yescharacteristic
331C22—22no—
332C22—22no—
333C22—22no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—74no—
339C22—142no—
340C22—142no—
341C22—142no—
342C22—142no—
343C22—142no—
344C22—142no—
345C22C2×Dic3×D711yescharacteristic
346C22#6668311yescharacteristic
347C22#6668411yescharacteristic
348C22D7×#6711yescharacteristic
349C22D7×#6711yescharacteristic
350C22D3×C22⋊D711yescharacteristic
351C22#6669411yescharacteristic
352C4—62no—
353C4—121no—
354C4—142no—
355C4—422no—
356C4—841no—
357C3#8972811yescharacteristic, complemented, Sylow
358C2—42no—
359C2—144no—
360C2D7×#21711yescharacteristic
361C2#1062111011yescharacteristic
362C2#1062111111yescharacteristic
363C2#1062111211yescharacteristic
364C2Dic3×C22⋊D711yescharacteristic
365C2(C22⋊D7)⋊Dic311yescharacteristic
366C2#1062113911yescharacteristic
subgroupG/H
center, FrattiniC23C2×D3×D7
commutatorC22×C3×C7C22×C4
FittingC24×C3×C7C22
socle, cosocleC23×C3×C7C23
prime radicalC22×C3×C22⋊D7C2
hypercenterC24D3×D7
hypocenterC3×C7#386
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C22×Dic3×D7C2semidirect
3. C2×#66636C2semidirect
4. C2×C7×#217C2semidirect
5. C2×(C2×D7)⋊Dic3C2semidirect
6. #10620529C2semidirect
7. #10620529C2semidirect
17. C2×C3×C22⋊D7C4semidirect
39. C23×C3×C7C2×C4semidirect
53. C2×Dic21D4semidirect
59. C2×C7×Dic3D4semidirect
63. C2×C3×Dic7C2×C4semidirect
71. C2×C22⋊D7Dic3semidirect
85. C2×#217D7semidirect
108. C2×C3×D7C22⋊C4semidirect
121. C23×C7C2×Dic3semidirect
145. C2×Dic7C2×Dic3semidirect
199. C2×D7#217semidirect
218. C23×C3C4×D7semidirect
236. C2×Dic3C22⋊D7semidirect
237. C3×C7#386semidirect
302. C23Dic3×D7semidirect
321. C7#5220semidirect
357. C3#89728semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊D72
C22×Dic3×D72
C2×#666362
C2×C7×#2172
C2×(C2×D7)⋊Dic32
#106205292
#897283
#52207