Finite Group Databasebeta

← #13058570

Subgroups — #13058570

Order 1344.

540 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66672C211yesmaximal, characteristic
2C2×D3×Dic14C211yesmaximal, characteristic, complemented
3#10621379C211yesmaximal, characteristic, complemented
4C7×#894C211yesmaximal, characteristic, complemented
5C3×#6451C211yesmaximal, characteristic, complemented
6#10620998C211yesmaximal, characteristic, complemented
7#10620994C211yesmaximal, characteristic, complemented
8#10620989C211yesmaximal, characteristic, complemented
9#10620985C211yesmaximal, characteristic, complemented
10#10620960C211yesmaximal, characteristic, complemented
11#10620939C211yesmaximal, characteristic, complemented
12#10620913C211yesmaximal, characteristic, complemented
13#10620912C211yesmaximal, characteristic, complemented
14#10620889C211yesmaximal, characteristic, complemented
15#10620888C211yesmaximal, characteristic, complemented
16#90339—31nomaximal, Hall
17C2×C4×D21C2211yescharacteristic
18C2×Dic42C2211yescharacteristic
19C2×C7×D12C2211yescharacteristic
20C2×C4×D3×C7C2211yescharacteristic
21C2×C3×Dic14C2211yescharacteristic
22C2×C3×Dic14C2211yescharacteristic
23C2×#4248C2211yescharacteristic
24C2×#4248C2211yescharacteristic
25C2×#4247C2211yescharacteristic
26C2×#4247C2211yescharacteristic
27C2×D3×Dic7C2211yescharacteristic
28C2×D3×Dic7C2211yescharacteristic
29C2×D3×Dic7C2211yescharacteristic
30#66672—24no—
31D3×Dic14—24no—
32C3×C7×C4⋊C4C2211yescharacteristic
33#66631C2211yescharacteristic
34#66631C2211yescharacteristic
35#66629C2211yescharacteristic
36#66629C2211yescharacteristic
37C7×(C2×D3)⋊C4C2211yescharacteristic
38C7×(C2×D3)⋊C4C2211yescharacteristic
39C7×(C2×D3)⋊C4C2211yescharacteristic
40C7×Dic3⋊C4C2211yescharacteristic
41C3×C4⋊Dic7C2211yescharacteristic
42C3×Dic7⋊C4C2211yescharacteristic
43C3×Dic7⋊C4C2211yescharacteristic
44C3×C4×Dic7C2211yescharacteristic
45Dic3⋊Dic7C2211yescharacteristic
46#66577C2211yescharacteristic
47#66577C2211yescharacteristic
48#66575C2211yescharacteristic
49#66575C2211yescharacteristic
50(C2×D3)⋊Dic7C2211yescharacteristic
51(C2×D3)⋊Dic7C2211yescharacteristic
52(C2×D3)⋊Dic7C2211yescharacteristic
53Dic3×Dic7C2211yescharacteristic
54C2×#1159—31no—
55C22×Dic14—31no—
56C7×#123—31no—
57#6498—31no—
58#6492—31no—
59#6459—31no—
60#6459—31no—
61#6451—31no—
62#6451D311yescharacteristic, complemented
63#6449—31no—
64#6448—31no—
65#6448—31no—
66#6441—31no—
67#6441—31no—
68#6440—31no—
69#5724—71nomaximal, Hall
70C22×D21C2311yescharacteristic
71C22×D3×C7C2311yescharacteristic
72C22×D3×C7C2311yescharacteristic
73C2×C3×C4×C7C2311yescharacteristic
74C2×C3×C4×C7C2311yescharacteristic
75C2×C3×C4×C7C2311yescharacteristic
76C2×Dic21C2311yescharacteristic
77C2×Dic21C2311yescharacteristic
78C2×Dic21C2311yescharacteristic
79C4×D21—22no—
80Dic42—22no—
81C2×C7×Dic3C2311yescharacteristic
82C2×C7×Dic3C2311yescharacteristic
83C7×D12—22no—
84C4×D3×C7—22no—
85C2×C3×Dic7C2311yescharacteristic
86C2×C3×Dic7C2311yescharacteristic
87C2×C3×Dic7C2311yescharacteristic
88C2×C3×Dic7C2311yescharacteristic
89C3×Dic14—22no—
90C3×Dic14—22no—
91#4248—22no—
92#4248—22no—
93#4247—22no—
94#4247—22no—
95D3×Dic7—22no—
96D3×Dic7—22no—
97D3×Dic7D414yes—
98C2×C7×D4—31no—
99C22×C4×C7—31no—
100C2×C22⋊D7—31no—
101C2×C22⋊D7—31no—
102C22×Dic7—31no—
103C22×Dic7—31no—
104C22×Dic7—31no—
105#1159—64no—
106C2×C4×D7—31no—
107C2×Dic14—31no—
108C2×Dic14—31no—
109C2×Dic14—31no—
110C2×Dic14—64no—
111C2×Dic14C2×D311yescharacteristic
112C2×Dic14C2×D311yescharacteristic
113C7×C4⋊C4—31no—
114C7×C4⋊C4C2×D311yescharacteristic
115C7×C22⋊C4—31no—
116C7×C22⋊C4—31no—
117C7×C22⋊C4—31no—
118C22⋊Dic7—31no—
119C22⋊Dic7—31no—
120C22⋊Dic7—31no—
121(C2×D7)⋊C4—31no—
122(C2×D7)⋊C4—31no—
123(C2×D7)⋊C4—31no—
124(C2×D7)⋊C4—31no—
125C4⋊Dic7—31no—
126C4⋊Dic7C2×D311yescharacteristic
127Dic7⋊C4—31no—
128Dic7⋊C4—31no—
129Dic7⋊C4—31no—
130Dic7⋊C4—31no—
131Dic7⋊C4C2×D311yescharacteristic
132Dic7⋊C4C2×D311yescharacteristic
133C4×Dic7—31no—
134C4×Dic7C2×D311yescharacteristic
135C2×#239—71no—
136C2×D3×Q8—71no—
137C3×C4⋊Q8—71no—
138#947—71no—
139#944—71no—
140#896—71no—
141#896—71no—
142#896—71no—
143#896—71no—
144#894—71no—
145#894—71no—
146#894—71no—
147#894D711yescharacteristic, complemented
148#875—71no—
149#872—71no—
150C22×C3×C7C2411yescharacteristic
151C2×D21—21no—
152C2×D21—21no—
153C2×D21—21no—
154C2×D3×C7—21no—
155C2×D3×C7—21no—
156C2×D3×C7—21no—
157C2×D3×C7—21no—
158C2×D3×C7—21no—
159C2×D3×C7C2×D412yes—
160C3×C4×C7—21no—
161C3×C4×C7—21no—
162C3×C4×C7—21no—
163Dic21—21no—
164Dic21—21no—
165Dic21C2×D412yes—
166C3×Dic7—21no—
167C3×Dic7—21no—
168C3×Dic7—21no—
169C3×Dic7C2×D412yes—
170C7×Dic3—21no—
171C7×Dic3—21no—
172#536—211noSylow
173C23×C7—31no—
174C23×C7—31no—
175C22×D7—31no—
176C7×D4—62no—
177C2×C4×C7—31no—
178C2×C4×C7—31no—
179C2×C4×C7—62no—
180C2×C4×C7C22×D311yescharacteristic
181C2×C4×C7C22×D311yescharacteristic
182C2×C4×C7C22×D311yescharacteristic
183C22⋊D7—62no—
184C22⋊D7—62no—
185C2×Dic7—31no—
186C2×Dic7—34no—
187C2×Dic7—31no—
188C2×Dic7—31no—
189C2×Dic7—62no—
190C2×Dic7—62no—
191C2×Dic7C22×D311yescharacteristic
192C2×Dic7C22×D311yescharacteristic
193C2×Dic7C22×D311yescharacteristic
194C2×Dic7C22×D311yescharacteristic
195C4×D7—62no—
196Dic14—22no—
197Dic14—22no—
198Dic14—62no—
199Dic14—62no—
200Dic14—62no—
201C2×C3×Q8—71no—
202C2×C3×Q8—71no—
203#239—144no—
204D3×Q8—144no—
205C2×D12—71no—
206C2×D12—71no—
207C2×D12C2×D711yescharacteristic
208C2×C4×D3—71no—
209C2×C4×D3—71no—
210C2×C4×D3—71no—
211C2×C4×D3—71no—
212C2×C4×D3C2×D711yescharacteristic
213C2×Dic6—71no—
214C2×Dic6—71no—
215C2×Dic6—71no—
216C3×C4⋊C4—71no—
217C3×C4⋊C4—71no—
218C3×C4⋊C4—71no—
219C3×C4⋊C4C2×D711yescharacteristic
220C3×C42—71no—
221(C2×D3)⋊C4—71no—
222(C2×D3)⋊C4—71no—
223(C2×D3)⋊C4—71no—
224(C2×D3)⋊C4—71no—
225(C2×D3)⋊C4—71no—
226(C2×D3)⋊C4—71no—
227(C2×D3)⋊C4—71no—
228(C2×D3)⋊C4C2×D711yescharacteristic
229(C2×D3)⋊C4C2×D711yescharacteristic
230(C2×D3)⋊C4C2×D711yescharacteristic
231Dic3⋊C4—71no—
232Dic3⋊C4—71no—
233Dic3⋊C4—71no—
234Dic3⋊C4—71no—
235Dic3⋊C4—71no—
236Dic3⋊C4C2×D711yescharacteristic
237C4×Dic3—71no—
238C2×C3×C7C22×D411yescharacteristic
239C2×C3×C72−1+411yescharacteristic
240C2×C3×C72−1+411yescharacteristic
241D21—41no—
242D3×C7—22no—
243D3×C7—41no—
244C2×#41—211no—
245C22×Q8—211no—
246C4⋊Q8—71no—
247C4⋊Q8—211no—
248#124—211no—
249#124—211no—
250#123—31no—
251#123—211no—
252#123—211no—
253#123—211no—
254C22⋊Q8—211no—
255C22⋊Q8—211no—
256C22⋊Q8—211no—
257C22⋊Q8—211no—
258#117—211no—
259C22×C7—32no—
260C22×C7—61no—
261C22×C7—61no—
262C22×C7—61no—
263C22×C7—61no—
264C22×C7—61no—
265C22×C7C23×D311yescharacteristic
266C2×D7—61no—
267C2×D7—61no—
268C2×D7—61no—
269C4×C7—21no—
270C4×C7—21no—
271C4×C7—21no—
272C4×C7—61no—
273C4×C7—61no—
274Dic7—21no—
275Dic7—21no—
276Dic7—21no—
277Dic7—32no—
278Dic7—61no—
279Dic7—61no—
280Dic7D3×D412yes—
281C22×D3—71no—
282C22×D3C22×D711yescharacteristic
283C22×D3C22×D711yescharacteristic
284C3×Q8—142no—
285C3×Q8—142no—
286C2×C3×C4—71no—
287C2×C3×C4—71no—
288C2×C3×C4—71no—
289C2×C3×C4—71no—
290C2×C3×C4C22×D711yescharacteristic
291C2×C3×C4C22×D711yescharacteristic
292C2×C3×C4C22×D711yescharacteristic
293C2×Dic3—71no—
294C2×Dic3—71no—
295C2×Dic3—71no—
296C2×Dic3C22×D711yescharacteristic
297C2×Dic3C22×D711yescharacteristic
298D12—22no—
299D12—142no—
300D12—142no—
301C4×D3—22no—
302C4×D3—74no—
303C4×D3—142no—
304C4×D3—142no—
305C4×D3—142no—
306Dic6—142no—
307Dic6—142no—
308Dic6—142no—
309C3×C7#53611yescharacteristic, complemented, Hall
310#41—424no—
311C2×Q8—71no—
312C2×Q8—71no—
313C2×Q8—211no—
314C2×Q8—211no—
315C2×Q8—211no—
316C2×Q8—424no—
317C2×D4—31no—
318C2×D4—211no—
319C2×D4—211no—
320C22×C4—31no—
321C22×C4—211no—
322C22×C4—211no—
323C22×C4—211no—
324C22×C4—211no—
325C4⋊C4—31no—
326C4⋊C4—71no—
327C4⋊C4—71no—
328C4⋊C4—71no—
329C4⋊C4—211no—
330C4⋊C4—211no—
331C4⋊C4—211no—
332C4⋊C4—211no—
333C4⋊C4—211no—
334C4⋊C4D3×D711yescharacteristic
335C22⋊C4—31no—
336C22⋊C4—31no—
337C22⋊C4—31no—
338C22⋊C4—211no—
339C22⋊C4—211no—
340C22⋊C4—211no—
341C22⋊C4—211no—
342C22⋊C4—211no—
343C22⋊C4—211no—
344C22⋊C4—211no—
345C42—71no—
346C42—211no—
347C2×C7—62no—
348C2×C7—121no—
349C2×C7C2×D3×D411yescharacteristic
350C2×C7#100711yescharacteristic
351C2×C7#100711yescharacteristic
352D7—121no—
353C22×C3C23×D711yescharacteristic
354C2×D3—21no—
355C2×D3—21no—
356C2×D3—21no—
357C2×D3—21no—
358C2×D3—21no—
359C2×D3—141no—
360C2×D3—141no—
361C2×D3—141no—
362C2×D3D4×D712yes—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—72no—
367C3×C4—141no—
368C3×C4—141no—
369C3×C4—141no—
370Dic3—21no—
371Dic3—21no—
372Dic3—72no—
373Dic3—141no—
374Dic3—141no—
375C23—31no—
376C23—31no—
377C23—211no—
378Q8—142no—
379Q8—142no—
380Q8—422no—
381Q8—422no—
382Q8—422no—
383D4—62no—
384D4—422no—
385D4—422no—
386C2×C4—31no—
387C2×C4—31no—
388C2×C4—62no—
389C2×C4—71no—
390C2×C4—71no—
391C2×C4—71no—
392C2×C4—71no—
393C2×C4—214no—
394C2×C4—211no—
395C2×C4—211no—
396C2×C4—211no—
397C2×C4—422no—
398C2×C4—422no—
399C2×C4—422no—
400C2×C4C2×D3×D711yescharacteristic
401C2×C4C2×D3×D711yescharacteristic
402C2×C4C2×D3×D711yescharacteristic
403C7#572411yescharacteristic, complemented, Sylow
404C2×C3C2×D4×D711yescharacteristic
405C2×C3#655411yescharacteristic
406C2×C3#655411yescharacteristic
407D3—22no—
408D3—41no—
409D3—281no—
410C22—32no—
411C22—61no—
412C22—61no—
413C22—61no—
414C22—61no—
415C22—61no—
416C22—421no—
417C22—421no—
418C22—421no—
419C22C22×D3×D711yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—61no—
424C4—61no—
425C4—72no—
426C4—141no—
427C4—141no—
428C4—141no—
429C4—212no—
430C4—421no—
431C4—421no—
432C3#9033911yescharacteristic, complemented, Sylow
433C2—62no—
434C2—121no—
435C2—841no—
436C2#1062155111yescharacteristic
437C2D3×D4×D711yescharacteristic
438C2#1062157711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×C4⋊C4C22
prime radicalC2×#66672C2
hypercenterC4⋊C4D3×D7
hypocenterC3×C7#536
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×D3×Dic14C2semidirect
3. #10621379C2semidirect
4. C7×#894C2semidirect
5. C3×#6451C2semidirect
6. #10620998C2semidirect
7. #10620994C2semidirect
8. #10620989C2semidirect
9. #10620985C2semidirect
10. #10620960C2semidirect
11. #10620939C2semidirect
12. #10620913C2semidirect
13. #10620912C2semidirect
14. #10620889C2semidirect
15. #10620888C2semidirect
62. #6451D3semidirect
147. #894D7semidirect
309. C3×C7#536semidirect
403. C7#5724semidirect
432. C3#90339semidirect

Maximal subgroups

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

subgroupindex
C2×#666722
C2×D3×Dic142
#106213792
C7×#8942
C3×#64512
#106209982
#106209942
#106209892
#106209852
#106209602
#106209392
#106209132
#106209122
#106208892
#106208882
#903393
#57247