Finite Group Databasebeta

← #13058625

Subgroups — #13058625

Order 1344.

424 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10621381C211yesmaximal, characteristic, complemented
2C7×#898C211yesmaximal, characteristic, complemented
3C3×#6450C211yesmaximal, characteristic, complemented
4#10621030C211yesmaximal, characteristic, complemented
5C4×#4248C211yesmaximal, characteristic, complemented
6#10620973C211yesmaximal, characteristic, complemented
7#10620972C211yesmaximal, characteristic, complemented
8#10620967C211yesmaximal, characteristic
9#10620965C211yesmaximal, characteristic, complemented
10#10620962C211yesmaximal, characteristic, complemented
11#10620912C211yesmaximal, characteristic
12#10620912C211yesmaximal, characteristic
13#10620904C211yesmaximal, characteristic, complemented
14#10620899C211yesmaximal, characteristic, complemented
15#10620885C211yesmaximal, characteristic, complemented
16#90393—31nomaximal, Hall
17C2×C3×Dic14C2211yescharacteristic
18C2×#4248C2211yescharacteristic
19C2×#4248C2211yescharacteristic
20C2×#4247C2211yescharacteristic
21C2×D21⋊C4C2211yescharacteristic
22C2×D3×Dic7C2211yescharacteristic
23C3×C7×C4⋊C4C2211yescharacteristic
24#66631C2211yescharacteristic
25#66631C2211yescharacteristic
26#66631C2211yescharacteristic
27C4⋊Dic21C2211yescharacteristic
28#66629C2211yescharacteristic
29C4×Dic21C2211yescharacteristic
30C7×(C2×D3)⋊C4C2211yescharacteristic
31C7×(C2×D3)⋊C4C2211yescharacteristic
32C7×(C2×D3)⋊C4C2211yescharacteristic
33C7×C4⋊Dic3C2211yescharacteristic
34C7×Dic3⋊C4C2211yescharacteristic
35C4×C7×Dic3C2211yescharacteristic
36C3×Dic7⋊C4C2211yescharacteristic
37C3×Dic7⋊C4C2211yescharacteristic
38C3×C4×Dic7C2211yescharacteristic
39C3×C4×Dic7C2211yescharacteristic
40C3×C4×Dic7C2211yescharacteristic
41Dic3⋊Dic7C2211yescharacteristic
42#66577C2211yescharacteristic
43Dic7⋊Dic3C2211yescharacteristic
44Dic7⋊Dic3C2211yescharacteristic
45Dic7⋊Dic3C2211yescharacteristic
46#66575C2211yescharacteristic
47#66575C2211yescharacteristic
48(C2×D3)⋊Dic7C2211yescharacteristic
49(C2×D3)⋊Dic7C2211yescharacteristic
50Dic3×Dic7C2211yescharacteristic
51Dic3×Dic7C2211yescharacteristic
52C7×#126—31no—
53#6461—31no—
54#6461—31no—
55#6459—31no—
56#6451—31no—
57#6450—31no—
58#6450D311yescharacteristic, complemented
59#6448—31no—
60#6448—31no—
61(C22⋊D7)⋊C4—31no—
62#6442—31no—
63#6441—31no—
64#6440—31no—
65#6435—31no—
66C4×Dic14—31no—
67#5584—71nomaximal, Hall
68C22×D21C2311yescharacteristic
69C22×D3×C7C2311yescharacteristic
70C2×C3×C4×C7C2311yescharacteristic
71C2×C3×C4×C7C2311yescharacteristic
72C2×C3×C4×C7C2311yescharacteristic
73C2×Dic21C2311yescharacteristic
74C2×Dic21C2311yescharacteristic
75C2×Dic21C2311yescharacteristic
76C2×C7×Dic3C2311yescharacteristic
77C2×C7×Dic3C2311yescharacteristic
78C2×C7×Dic3C2311yescharacteristic
79C2×C3×Dic7C2311yescharacteristic
80C2×C3×Dic7C2311yescharacteristic
81C2×C3×Dic7C2311yescharacteristic
82C2×C3×Dic7C2311yescharacteristic
83C3×Dic14—22no—
84#4248—22no—
85#4248—22no—
86#4247—22no—
87D21⋊C4—22no—
88D3×Dic7—22no—
89C2×C22⋊D7—31no—
90C22×Dic7—31no—
91C2×C4×D7—31no—
92C2×Dic14—31no—
93C2×Dic14—31no—
94C2×Dic14C2×D311yescharacteristic
95C7×C4⋊C4—31no—
96C7×C4⋊C4—31no—
97C7×C4⋊C4C2×D311yescharacteristic
98C7×C22⋊C4—31no—
99C7×C22⋊C4—31no—
100C7×C22⋊C4—31no—
101C42×C7—31no—
102C22⋊Dic7—31no—
103C22⋊Dic7—31no—
104(C2×D7)⋊C4—31no—
105(C2×D7)⋊C4—31no—
106(C2×D7)⋊C4—31no—
107(C2×D7)⋊C4—31no—
108(C2×D7)⋊C4—31no—
109C4⋊Dic7—31no—
110C4⋊Dic7—31no—
111Dic7⋊C4—31no—
112Dic7⋊C4—31no—
113Dic7⋊C4—31no—
114Dic7⋊C4—31no—
115Dic7⋊C4—31no—
116Dic7⋊C4C2×D311yescharacteristic
117Dic7⋊C4C2×D311yescharacteristic
118C4×Dic7—31no—
119C4×Dic7—31no—
120C4×Dic7—31no—
121C4×Dic7C2×D311yescharacteristic
122C4×Dic7C2×D311yescharacteristic
123C4×Dic7C2×D311yescharacteristic
124C3×C4×Q8—71no—
125#946—71no—
126#946—71no—
127#898—71no—
128#898—71no—
129#898—71no—
130#898D711yescharacteristic, complemented
131#892—71no—
132#892—71no—
133#875—71no—
134#875—71no—
135C4×D12—71no—
136#869—71no—
137C4×Dic6—71no—
138C4×Dic6—71no—
139C22×C3×C7C2411yescharacteristic
140C2×D21—21no—
141C2×D21—21no—
142C2×D21—21no—
143C2×D3×C7—21no—
144C2×D3×C7—21no—
145C2×D3×C7—21no—
146C3×C4×C7—21no—
147C3×C4×C7—21no—
148C3×C4×C7—21no—
149Dic21—21no—
150Dic21—21no—
151Dic21—21no—
152C3×Dic7—21no—
153C3×Dic7—21no—
154C3×Dic7#4112yes—
155C3×Dic7#4112yes—
156C7×Dic3—21no—
157C7×Dic3—21no—
158C7×Dic3—21no—
159#556—211noSylow
160C23×C7—31no—
161C22×D7—31no—
162C2×C4×C7—31no—
163C2×C4×C7—31no—
164C2×C4×C7—31no—
165C2×C4×C7C22×D311yescharacteristic
166C2×C4×C7C22×D311yescharacteristic
167C2×C4×C7C22×D311yescharacteristic
168C22⋊D7—62no—
169C2×Dic7—31no—
170C2×Dic7—31no—
171C2×Dic7—31no—
172C2×Dic7—62no—
173C2×Dic7C22×D311yescharacteristic
174C2×Dic7C22×D311yescharacteristic
175C2×Dic7C22×D311yescharacteristic
176C2×Dic7C22×D311yescharacteristic
177C4×D7—62no—
178Dic14—22no—
179Dic14—62no—
180Dic14—62no—
181C2×C3×Q8—71no—
182C2×D12—71no—
183C2×C4×D3—71no—
184C2×C4×D3—71no—
185C2×Dic6—71no—
186C2×Dic6—71no—
187C3×C4⋊C4—71no—
188C3×C4⋊C4—71no—
189C3×C4⋊C4C2×D711yescharacteristic
190C3×C42—71no—
191C3×C42—71no—
192C3×C42—71no—
193(C2×D3)⋊C4—71no—
194(C2×D3)⋊C4—71no—
195(C2×D3)⋊C4—71no—
196(C2×D3)⋊C4—71no—
197(C2×D3)⋊C4—71no—
198(C2×D3)⋊C4—71no—
199(C2×D3)⋊C4—71no—
200(C2×D3)⋊C4C2×D711yescharacteristic
201(C2×D3)⋊C4C2×D711yescharacteristic
202(C2×D3)⋊C4C2×D711yescharacteristic
203C4⋊Dic3—71no—
204C4⋊Dic3—71no—
205C4⋊Dic3—71no—
206C4⋊Dic3—71no—
207C4⋊Dic3C2×D711yescharacteristic
208Dic3⋊C4—71no—
209Dic3⋊C4—71no—
210Dic3⋊C4—71no—
211Dic3⋊C4C2×D711yescharacteristic
212C4×Dic3—71no—
213C4×Dic3—71no—
214C4×Dic3—71no—
215C4×Dic3C2×D711yescharacteristic
216C2×C3×C7C2×#4111yescharacteristic
217C2×C3×C7C2×#4111yescharacteristic
218C2×C3×C72−1+411yescharacteristic
219D21—41no—
220D3×C7—41no—
221C4⋊Q8—211no—
222#126—31no—
223#126—211no—
224#126—211no—
225#126—211no—
226#124—211no—
227#124—211no—
228C22⋊Q8—211no—
229C22⋊Q8—211no—
230C4×Q8—71no—
231C4×Q8—211no—
232C4×Q8—211no—
233C4×D4—211no—
234#117—211no—
235#117—211no—
236C22×C7—61no—
237C22×C7—61no—
238C22×C7—61no—
239C22×C7C23×D311yescharacteristic
240C2×D7—61no—
241C2×D7—61no—
242C2×D7—61no—
243C4×C7—21no—
244C4×C7—21no—
245C4×C7—21no—
246C4×C7—61no—
247C4×C7—61no—
248C4×C7—61no—
249Dic7—21no—
250Dic7—21no—
251Dic7—61no—
252Dic7—61no—
253Dic7—61no—
254Dic7#23512yes—
255Dic7#23912yes—
256C22×D3—71no—
257C22×D3C22×D711yescharacteristic
258C3×Q8—142no—
259C2×C3×C4—71no—
260C2×C3×C4—71no—
261C2×C3×C4—71no—
262C2×C3×C4—71no—
263C2×C3×C4C22×D711yescharacteristic
264C2×C3×C4C22×D711yescharacteristic
265C2×C3×C4C22×D711yescharacteristic
266C2×Dic3—71no—
267C2×Dic3—71no—
268C2×Dic3—71no—
269C2×Dic3C22×D711yescharacteristic
270C2×Dic3C22×D711yescharacteristic
271C2×Dic3C22×D711yescharacteristic
272D12—142no—
273C4×D3—142no—
274C4×D3—142no—
275Dic6—142no—
276Dic6—142no—
277C3×C7#55611yescharacteristic, complemented, Hall
278C2×Q8—71no—
279C2×Q8—211no—
280C2×Q8—211no—
281C2×D4—211no—
282C22×C4—211no—
283C22×C4—211no—
284C4⋊C4—31no—
285C4⋊C4—31no—
286C4⋊C4—71no—
287C4⋊C4—71no—
288C4⋊C4—211no—
289C4⋊C4—211no—
290C4⋊C4—211no—
291C4⋊C4—211no—
292C4⋊C4—211no—
293C4⋊C4—211no—
294C4⋊C4—211no—
295C4⋊C4D3×D711yescharacteristic
296C22⋊C4—31no—
297C22⋊C4—31no—
298C22⋊C4—31no—
299C22⋊C4—211no—
300C22⋊C4—211no—
301C22⋊C4—211no—
302C22⋊C4—211no—
303C22⋊C4—211no—
304C22⋊C4—211no—
305C22⋊C4—211no—
306C42—31no—
307C42—71no—
308C42—71no—
309C42—71no—
310C42—211no—
311C42—211no—
312C42—211no—
313C2×C7—121no—
314C2×C7C2×#23511yescharacteristic
315C2×C7C2×#23911yescharacteristic
316C2×C7#101011yescharacteristic
317D7—121no—
318C22×C3C23×D711yescharacteristic
319C2×D3—21no—
320C2×D3—21no—
321C2×D3—21no—
322C2×D3—141no—
323C2×D3—141no—
324C2×D3—141no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—72no—
329C3×C4—72no—
330C3×C4—141no—
331C3×C4—141no—
332Dic3—21no—
333Dic3—21no—
334Dic3—21no—
335Dic3—141no—
336Dic3—141no—
337Dic3—141no—
338C23—31no—
339C23—211no—
340Q8—142no—
341Q8—422no—
342Q8—422no—
343D4—422no—
344C2×C4—31no—
345C2×C4—31no—
346C2×C4—31no—
347C2×C4—71no—
348C2×C4—71no—
349C2×C4—71no—
350C2×C4—71no—
351C2×C4—211no—
352C2×C4—211no—
353C2×C4—211no—
354C2×C4—422no—
355C2×C4—422no—
356C2×C4C2×D3×D711yescharacteristic
357C2×C4C2×D3×D711yescharacteristic
358C2×C4C2×D3×D711yescharacteristic
359C7#558411yescharacteristic, complemented, Sylow
360C2×C3D7×#4111yescharacteristic
361C2×C3D7×#4111yescharacteristic
362C2×C3#655411yescharacteristic
363D3—41no—
364D3—281no—
365C22—61no—
366C22—61no—
367C22—61no—
368C22—421no—
369C22—421no—
370C22—421no—
371C22C22×D3×D711yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—61no—
376C4—61no—
377C4—61no—
378C4—72no—
379C4—72no—
380C4—141no—
381C4—141no—
382C4—421no—
383C4—421no—
384C4—421no—
385C3#9039311yescharacteristic, complemented, Sylow
386C2—121no—
387C2—841no—
388C2D7×#23511yescharacteristic
389C2#1062156711yescharacteristic
390C2D7×#23911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×C4⋊C4C22
prime radicalC2×#4247C22
hypercenterC4⋊C4D3×D7
hypocenterC3×C7#556
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #10621381C2semidirect
2. C7×#898C2semidirect
3. C3×#6450C2semidirect
4. #10621030C2semidirect
5. C4×#4248C2semidirect
6. #10620973C2semidirect
7. #10620972C2semidirect
9. #10620965C2semidirect
10. #10620962C2semidirect
13. #10620904C2semidirect
14. #10620899C2semidirect
15. #10620885C2semidirect
58. #6450D3semidirect
130. #898D7semidirect
277. C3×C7#556semidirect
359. C7#5584semidirect
385. C3#90393semidirect

Maximal subgroups

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

subgroupindex
#106213812
C7×#8982
C3×#64502
#106210302
C4×#42482
#106209732
#106209722
#106209672
#106209652
#106209622
#106209122
#106209042
#106208992
#106208852
#903933
#55847