Finite Group Databasebeta

← #13058596

Subgroups — #13058596

Order 1344.

444 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10621370C211yesmaximal, characteristic, complemented
2C7×#889C211yesmaximal, characteristic, complemented
3C3×#6459C211yesmaximal, characteristic
4#10620993C211yesmaximal, characteristic
5#10620992C211yesmaximal, characteristic
6#10620956C211yesmaximal, characteristic
7#10620956C211yesmaximal, characteristic
8C4×Dic3×D7C211yesmaximal, characteristic
9#10620941C211yesmaximal, characteristic, complemented
10#10620911C211yesmaximal, characteristic
11#10620893C211yesmaximal, characteristic, complemented
12#10620890C211yesmaximal, characteristic, complemented
13#10620889C211yesmaximal, characteristic, complemented
14#10620887C211yesmaximal, characteristic, complemented
15#10620887C211yesmaximal, characteristic, complemented
16#90379—31nomaximal, Hall
17C2×Dic42C2211yescharacteristic
18C2×C3×C4×D7C2211yescharacteristic
19C2×C3×Dic14C2211yescharacteristic
20C2×#4248C2211yescharacteristic
21C2×#4248C2211yescharacteristic
22C2×Dic3×D7C2211yescharacteristic
23C2×Dic3×D7C2211yescharacteristic
24C3×C7×C4⋊C4C2211yescharacteristic
25#66629C2211yescharacteristic
26#66629C2211yescharacteristic
27C4×Dic21C2211yescharacteristic
28C4×Dic21C2211yescharacteristic
29C4×Dic21C2211yescharacteristic
30C7×C4⋊Dic3C2211yescharacteristic
31C7×Dic3⋊C4C2211yescharacteristic
32C7×Dic3⋊C4C2211yescharacteristic
33C7×Dic3⋊C4C2211yescharacteristic
34C7×Dic3⋊C4C2211yescharacteristic
35C4×C7×Dic3C2211yescharacteristic
36C3×(C2×D7)⋊C4C2211yescharacteristic
37C3×(C2×D7)⋊C4C2211yescharacteristic
38C3×Dic7⋊C4C2211yescharacteristic
39C3×Dic7⋊C4C2211yescharacteristic
40Dic3⋊Dic7C2211yescharacteristic
41Dic3⋊Dic7C2211yescharacteristic
42#66577C2211yescharacteristic
43#66577C2211yescharacteristic
44Dic7⋊Dic3C2211yescharacteristic
45Dic7⋊Dic3C2211yescharacteristic
46(C2×D7)⋊Dic3C2211yescharacteristic
47(C2×D7)⋊Dic3C2211yescharacteristic
48Dic3×Dic7C2211yescharacteristic
49Dic3×Dic7C2211yescharacteristic
50Dic3×Dic7C2211yescharacteristic
51Dic3×Dic7C2211yescharacteristic
52C7×#125—31no—
53#6459—31no—
54#6459—31no—
55#6459—31no—
56#6459D311yescharacteristic
57#6455—31no—
58#6455—31no—
59#6451—31no—
60#6451—31no—
61#6450—31no—
62#6450—31no—
63#6450—31no—
64#6450—31no—
65C42×D7—31no—
66#6433—31no—
67#5622—71nomaximal, Hall
68C22×C3×D7C2311yescharacteristic
69C2×C3×C4×C7C2311yescharacteristic
70C2×C3×C4×C7C2311yescharacteristic
71C2×C3×C4×C7C2311yescharacteristic
72C2×Dic21C2311yescharacteristic
73C2×Dic21C2311yescharacteristic
74C2×Dic21C2311yescharacteristic
75C2×Dic21C2311yescharacteristic
76Dic42—22no—
77C2×C7×Dic3C2311yescharacteristic
78C2×C7×Dic3C2311yescharacteristic
79C2×C7×Dic3C2311yescharacteristic
80C2×C7×Dic3C2311yescharacteristic
81C2×C3×Dic7C2311yescharacteristic
82C2×C3×Dic7C2311yescharacteristic
83C2×C3×Dic7C2311yescharacteristic
84C3×C4×D7—22no—
85C3×Dic14—22no—
86#4248—22no—
87#4248—22no—
88Dic3×D7—22no—
89Dic3×D7Q814yescomplemented
90C2×C4×D7—31no—
91C2×C4×D7—31no—
92C2×C4×D7C2×D311yescharacteristic
93C2×Dic14—31no—
94C2×Dic14—31no—
95C2×Dic14—31no—
96C2×Dic14C2×D311yescharacteristic
97C7×C4⋊C4—31no—
98C7×C4⋊C4—31no—
99C7×C4⋊C4—31no—
100C7×C4⋊C4—31no—
101C7×C4⋊C4—31no—
102C7×C4⋊C4C2×D311yescharacteristic
103C42×C7—31no—
104(C2×D7)⋊C4—31no—
105(C2×D7)⋊C4—31no—
106(C2×D7)⋊C4C2×D311yescharacteristic
107(C2×D7)⋊C4C2×D311yescharacteristic
108C4⋊Dic7—31no—
109C4⋊Dic7—31no—
110Dic7⋊C4—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×Dic7—31no—
122C4×Dic7—31no—
123C4×Dic7—31no—
124C4×Dic7—31no—
125C3×C22⋊Q8—71no—
126Q8×Dic3—71no—
127#944—71no—
128#924—71no—
129C2×C4×Dic3—71no—
130#889—71no—
131#889D711yescharacteristic, complemented
132#888—71no—
133#887—71no—
134#887—71no—
135#887—71no—
136#878—71no—
137#878—71no—
138#877—71no—
139#877—71no—
140C22×C3×C7C2411yescharacteristic
141C2×C3×D7—21no—
142C2×C3×D7—21no—
143C2×C3×D7C2×Q812yes—
144C3×C4×C7—21no—
145C3×C4×C7—21no—
146C3×C4×C7—21no—
147Dic21—21no—
148Dic21—21no—
149Dic21C2×Q812yes—
150Dic21#4112yes—
151C3×Dic7—21no—
152C3×Dic7—21no—
153C3×Dic7#4112yes—
154C7×Dic3—21no—
155C7×Dic3—21no—
156C7×Dic3—21no—
157C7×Dic3C2×Q812yes—
158#533—211noSylow
159C22×D7C22×D311yescharacteristic
160C2×C4×C7—31no—
161C2×C4×C7—31no—
162C2×C4×C7—31no—
163C2×C4×C7—31no—
164C2×C4×C7C22×D311yescharacteristic
165C2×C4×C7C22×D311yescharacteristic
166C2×C4×C7C22×D311yescharacteristic
167C2×Dic7—31no—
168C2×Dic7—31no—
169C2×Dic7—31no—
170C2×Dic7—31no—
171C2×Dic7C22×D311yescharacteristic
172C2×Dic7C22×D311yescharacteristic
173C2×Dic7C22×D311yescharacteristic
174C4×D7—22no—
175C4×D7—34no—
176C4×D7—62no—
177Dic14—22no—
178Dic14—62no—
179Dic14—62no—
180Dic14—62no—
181C2×C3×Q8—71no—
182C22×C3×C4—71no—
183C22×Dic3—71no—
184C22×Dic3—71no—
185C2×Dic6—71no—
186C2×Dic6—71no—
187C2×Dic6—71no—
188C3×C4⋊C4—71no—
189C3×C4⋊C4—71no—
190C3×C4⋊C4C2×D711yescharacteristic
191C3×C22⋊C4—71no—
192C3×C22⋊C4—71no—
193#217—71no—
194#217—71no—
195C4⋊Dic3—71no—
196C4⋊Dic3—71no—
197C4⋊Dic3C2×D711yescharacteristic
198Dic3⋊C4—71no—
199Dic3⋊C4—71no—
200Dic3⋊C4—71no—
201Dic3⋊C4—71no—
202Dic3⋊C4—71no—
203Dic3⋊C4—71no—
204Dic3⋊C4C2×D711yescharacteristic
205Dic3⋊C4C2×D711yescharacteristic
206Dic3⋊C4C2×D711yescharacteristic
207Dic3⋊C4C2×D711yescharacteristic
208C4×Dic3—71no—
209C4×Dic3—71no—
210C4×Dic3—71no—
211C4×Dic3—71no—
212C4×Dic3—71no—
213C4×Dic3—71no—
214C4×Dic3—71no—
215C4×Dic3C2×D711yescharacteristic
216C2×C3×C7C22×Q811yescharacteristic
217C2×C3×C7C2×#4111yescharacteristic
218C2×C3×C7C2×#4111yescharacteristic
219C3×D7—22no—
220C4⋊Q8—211no—
221C4⋊Q8—211no—
222#125—31no—
223#125—211no—
224C22⋊Q8—71no—
225C22⋊Q8—211no—
226C22⋊Q8—211no—
227C22⋊Q8—211no—
228C4×Q8—211no—
229C4×Q8—211no—
230C4×Q8—211no—
231C4×Q8—211no—
232#117—211no—
233#117—211no—
234C2×C42—211no—
235C22×C7C23×D311yescharacteristic
236C2×D7—21no—
237C2×D7—21no—
238C2×D7D3×Q812yes—
239C4×C7—21no—
240C4×C7—21no—
241C4×C7—21no—
242C4×C7—32no—
243C4×C7—61no—
244C4×C7—61no—
245C4×C7—61no—
246Dic7—21no—
247Dic7—21no—
248Dic7—32no—
249Dic7—32no—
250Dic7—61no—
251Dic7—61no—
252Dic7#23712yes—
253C23×C3—71no—
254C3×Q8—142no—
255C2×C3×C4—71no—
256C2×C3×C4—71no—
257C2×C3×C4—71no—
258C2×C3×C4—142no—
259C2×C3×C4C22×D711yescharacteristic
260C2×C3×C4C22×D711yescharacteristic
261C2×C3×C4C22×D711yescharacteristic
262C2×Dic3—71no—
263C2×Dic3—71no—
264C2×Dic3—74no—
265C2×Dic3—71no—
266C2×Dic3—71no—
267C2×Dic3—142no—
268C2×Dic3C22×D711yescharacteristic
269C2×Dic3C22×D711yescharacteristic
270C2×Dic3C22×D711yescharacteristic
271C2×Dic3C22×D711yescharacteristic
272Dic6—142no—
273Dic6—142no—
274Dic6—142no—
275C3×C7#53311yescharacteristic, complemented, Hall
276C2×Q8—71no—
277C2×Q8—211no—
278C2×Q8—211no—
279C2×Q8—211no—
280C22×C4—71no—
281C22×C4—211no—
282C22×C4—211no—
283C4⋊C4—31no—
284C4⋊C4—31no—
285C4⋊C4—31no—
286C4⋊C4—31no—
287C4⋊C4—31no—
288C4⋊C4—71no—
289C4⋊C4—71no—
290C4⋊C4—211no—
291C4⋊C4—211no—
292C4⋊C4—211no—
293C4⋊C4—211no—
294C4⋊C4—211no—
295C4⋊C4—211no—
296C4⋊C4—211no—
297C4⋊C4—211no—
298C4⋊C4D3×D711yescharacteristic
299C22⋊C4—71no—
300C22⋊C4—71no—
301C22⋊C4—211no—
302C22⋊C4—211no—
303C42—31no—
304C42—211no—
305C42—211no—
306C42—211no—
307C42—211no—
308C42—211no—
309C42—211no—
310C42—211no—
311C2×C7C2×#23711yescharacteristic
312C2×C7C2×D3×Q811yescharacteristic
313C2×C7D3×#4111yescharacteristic
314D7—22no—
315C22×C3—72no—
316C22×C3—141no—
317C22×C3—141no—
318C22×C3C23×D711yescharacteristic
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—72no—
323C3×C4—141no—
324C3×C4—141no—
325Dic3—21no—
326Dic3—21no—
327Dic3—21no—
328Dic3—72no—
329Dic3—72no—
330Dic3—141no—
331Dic3—141no—
332Dic3Q8×D712yes—
333C23—71no—
334Q8—142no—
335Q8—422no—
336Q8—422no—
337Q8—422no—
338C2×C4—31no—
339C2×C4—31no—
340C2×C4—31no—
341C2×C4—31no—
342C2×C4—71no—
343C2×C4—71no—
344C2×C4—71no—
345C2×C4—142no—
346C2×C4—214no—
347C2×C4—211no—
348C2×C4—211no—
349C2×C4—211no—
350C2×C4—211no—
351C2×C4—422no—
352C2×C4C2×D3×D711yescharacteristic
353C2×C4C2×D3×D711yescharacteristic
354C2×C4C2×D3×D711yescharacteristic
355C7#562211yescharacteristic, complemented, Sylow
356C2×C3—142no—
357C2×C3C2×Q8×D711yescharacteristic
358C2×C3D7×#4111yescharacteristic
359C2×C3D7×#4111yescharacteristic
360C22—72no—
361C22—141no—
362C22—141no—
363C22C22×D3×D711yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—32no—
368C4—61no—
369C4—61no—
370C4—61no—
371C4—72no—
372C4—141no—
373C4—141no—
374C4—212no—
375C4—212no—
376C4—421no—
377C4—421no—
378C3#9037911yescharacteristic, complemented, Sylow
379C2—142no—
380C2#1062156311yescharacteristic
381C2D7×#23711yescharacteristic
382C2D3×Q8×D711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×C4⋊C4C22
prime radicalC22×C3×D7C23
hypercenterC4⋊C4D3×D7
hypocenterC3×C7#533
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. #10621370C2semidirect
2. C7×#889C2semidirect
9. #10620941C2semidirect
11. #10620893C2semidirect
12. #10620890C2semidirect
13. #10620889C2semidirect
14. #10620887C2semidirect
15. #10620887C2semidirect
89. Dic3×D7Q8semidirect
131. #889D7semidirect
275. C3×C7#533semidirect
355. C7#5622semidirect
378. C3#90379semidirect

Maximal subgroups

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

subgroupindex
#106213702
C7×#8892
C3×#64592
#106209932
#106209922
#106209562
C4×Dic3×D72
#106209412
#106209112
#106208932
#106208902
#106208892
#106208872
#903793
#56227