Finite Group Databasebeta

← #13057995

Subgroups — #13057995

Order 1344.

496 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D84C211yesmaximal, characteristic, complemented
2C7×#872C211yesmaximal, characteristic, complemented
3C3×#6439C211yesmaximal, characteristic, complemented
4#10621038C211yesmaximal, characteristic
5#10621035C211yesmaximal, characteristic, complemented
6D3×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
7#10620995C211yesmaximal, characteristic, complemented
8#10620979C211yesmaximal, characteristic, complemented
9#10620968C211yesmaximal, characteristic, complemented
10#10620965C211yesmaximal, characteristic, complemented
11#10620939C211yesmaximal, characteristic, complemented
12#10620924C211yesmaximal, characteristic, complemented
13#10620916C211yesmaximal, characteristic, complemented
14#10620915C211yesmaximal, characteristic, complemented
15#10620913C211yesmaximal, characteristic, complemented
16#90218—31nomaximal, Hall
17C22×D3×D7C2211yescharacteristic
18C2×D84C2211yescharacteristic
19C2×C4×D21C2211yescharacteristic
20C2×C4×D21C2211yescharacteristic, complemented
21C2×C4×D3×C7C2211yescharacteristic
22C2×#4248C2211yescharacteristic, complemented
23C2×#4247C2211yescharacteristic
24C2×#4246C2211yescharacteristic
25C2×D21⋊C4C2211yescharacteristic
26C2×D3×Dic7C2211yescharacteristic
27C3×C42×C7C2211yescharacteristic, complemented
28#66631C2211yescharacteristic
29#66631C2211yescharacteristic, complemented
30C4⋊Dic21C2211yescharacteristic, complemented
31C7×(C2×D3)⋊C4C2211yescharacteristic
32C7×(C2×D3)⋊C4C2211yescharacteristic
33C7×Dic3⋊C4C2211yescharacteristic, complemented
34C7×Dic3⋊C4C2211yescharacteristic, complemented
35C4×C7×Dic3C2211yescharacteristic, complemented
36C3×(C2×D7)⋊C4C2211yescharacteristic
37C3×(C2×D7)⋊C4C2211yescharacteristic
38C3×(C2×D7)⋊C4C2211yescharacteristic
39C3×Dic7⋊C4C2211yescharacteristic, complemented
40C3×Dic7⋊C4C2211yescharacteristic, complemented
41C3×Dic7⋊C4C2211yescharacteristic, complemented
42#66577C2211yescharacteristic, complemented
43Dic7⋊Dic3C2211yescharacteristic, complemented
44#66575C2211yescharacteristic
45#66575C2211yescharacteristic
46#66575C2211yescharacteristic, complemented
47#66575C2211yescharacteristic, complemented
48(C2×D3)⋊Dic7C2211yescharacteristic
49(C2×D7)⋊Dic3C2211yescharacteristic
50(C2×D7)⋊Dic3C2211yescharacteristic
51Dic3×Dic7C2211yescharacteristic, complemented
52C7×#117—31no—
53#6492—31no—
54C2×(C2×D7)⋊C4—31no—
55#6461—31no—
56#6459—31no—
57#6457—31no—
58#6457—31no—
59#6445—31no—
60(C22⋊D7)⋊C4—31no—
61D7×C22⋊C4—31no—
62#6441—31no—
63#6439D311yescharacteristic, complemented
64#6438—31no—
65C4×D28—31no—
66#6435—31no—
67#5705—71nomaximal, Hall
68C22×D21C2311yescharacteristic
69C22×D21C2311yescharacteristic
70C22×D3×C7C2311yescharacteristic
71C22×C3×D7C2311yescharacteristic
72C2×D3×D7—22no—
73C2×D3×D7—22no—
74C2×D3×D7—41no—
75C2×C3×C4×C7C2311yescharacteristic
76C2×C3×C4×C7C2311yescharacteristic
77C2×C3×C4×C7C2311yescharacteristic
78C2×Dic21C2311yescharacteristic
79C2×Dic21C2311yescharacteristic
80D84—22no—
81C4×D21—41no—
82C4×D21—41no—
83C2×C7×Dic3C2311yescharacteristic
84C2×C7×Dic3C2311yescharacteristic
85C2×C7×Dic3C2311yescharacteristic
86C4×D3×C7—22no—
87C2×C3×Dic7C2311yescharacteristic
88C2×C3×Dic7C2311yescharacteristic
89C2×C3×Dic7C2311yescharacteristic
90#4248—41no—
91#4247—22no—
92#4246—41no—
93D21⋊C4—22no—
94D3×Dic7—41no—
95C23×D7—31no—
96C22×C4×C7—31no—
97C2×C22⋊D7—31no—
98C22×Dic7—31no—
99C2×D28—31no—
100C2×D28—31no—
101C2×C4×D7—31no—
102C2×C4×D7—31no—
103C2×C4×D7—31no—
104C2×Dic14—31no—
105C7×C4⋊C4—31no—
106C7×C4⋊C4—31no—
107C7×C22⋊C4—31no—
108C7×C22⋊C4—31no—
109C42×C7—31no—
110C42×C7C2×D311yescharacteristic, complemented
111C22⋊Dic7—31no—
112(C2×D7)⋊C4—31no—
113(C2×D7)⋊C4—31no—
114(C2×D7)⋊C4—31no—
115(C2×D7)⋊C4—31no—
116(C2×D7)⋊C4—31no—
117(C2×D7)⋊C4—31no—
118(C2×D7)⋊C4—31no—
119(C2×D7)⋊C4—31no—
120(C2×D7)⋊C4C2×D311yescharacteristic
121(C2×D7)⋊C4C2×D311yescharacteristic
122(C2×D7)⋊C4C2×D311yescharacteristic
123C4⋊Dic7—31no—
124Dic7⋊C4—31no—
125Dic7⋊C4—31no—
126Dic7⋊C4C2×D311yescharacteristic, complemented
127Dic7⋊C4C2×D311yescharacteristic, complemented
128Dic7⋊C4C2×D311yescharacteristic, complemented
129C4×Dic7—31no—
130C3×#126—71no—
131#897—71no—
132#896—71no—
133#894—71no—
134#894—71no—
135#893—71no—
136#892—71no—
137#885—71no—
138#883—71no—
139#882—71no—
140D3×C22⋊C4—71no—
141D3×C22⋊C4—71no—
142#879—71no—
143C4×D12—71no—
144#872D711yescharacteristic, complemented
145C22×C3×C7C2411yescharacteristic
146C2×D21—21no—
147C2×D21—21no—
148C2×D21—21no—
149C2×D21—21no—
150C2×D21—21no—
151C2×D21#4112yes—
152C2×D3×C7—21no—
153C2×D3×C7—21no—
154C2×D3×C7#4112yes—
155C2×C3×D7—21no—
156C2×C3×D7—21no—
157C2×C3×D7—21no—
158D3×D7—44no—
159C3×C4×C7—21no—
160C3×C4×C7—21no—
161C3×C4×C7—21no—
162Dic21—21no—
163Dic21—21no—
164C3×Dic7—21no—
165C3×Dic7—21no—
166C3×Dic7—21no—
167C7×Dic3—21no—
168C7×Dic3—21no—
169C7×Dic3—21no—
170#551—211noSylow
171C23×C7—31no—
172C22×D7—31no—
173C22×D7—31no—
174C22×D7—62no—
175C22×D7—62no—
176C22×D7—121no—
177C22×D7C22×D311yescharacteristic
178C2×C4×C7—31no—
179C2×C4×C7—31no—
180C2×C4×C7—31no—
181C2×C4×C7—62no—
182C2×C4×C7C22×D311yescharacteristic
183C2×C4×C7C22×D311yescharacteristic
184C2×C4×C7C22×D311yescharacteristic
185C22⋊D7—62no—
186C2×Dic7—31no—
187C2×Dic7—31no—
188C2×Dic7—121no—
189C2×Dic7C22×D311yescharacteristic
190C2×Dic7C22×D311yescharacteristic
191C2×Dic7C22×D311yescharacteristic
192D28—62no—
193D28—121no—
194C4×D7—62no—
195C4×D7—121no—
196C4×D7—121no—
197Dic14—121no—
198C23×D3—71no—
199C2×#67—71no—
200C2×D12—71no—
201C2×D12—71no—
202C2×C4×D3—71no—
203C2×C4×D3—71no—
204C2×C4×D3—71no—
205C2×C4×D3—71no—
206C2×C4×D3C2×D711yescharacteristic
207C2×Dic6—71no—
208C3×C4⋊C4—71no—
209C3×C4⋊C4—71no—
210C3×C4⋊C4—71no—
211C3×C22⋊C4—71no—
212C3×C22⋊C4—71no—
213C3×C22⋊C4—71no—
214C3×C42C2×D711yescharacteristic, complemented
215#217—71no—
216#217—71no—
217(C2×D3)⋊C4—71no—
218(C2×D3)⋊C4—71no—
219(C2×D3)⋊C4—71no—
220(C2×D3)⋊C4—71no—
221(C2×D3)⋊C4—71no—
222(C2×D3)⋊C4—71no—
223(C2×D3)⋊C4—71no—
224(C2×D3)⋊C4C2×D711yescharacteristic
225(C2×D3)⋊C4C2×D711yescharacteristic
226C4⋊Dic3—71no—
227C4⋊Dic3—71no—
228Dic3⋊C4—71no—
229Dic3⋊C4C2×D711yescharacteristic, complemented
230Dic3⋊C4C2×D711yescharacteristic, complemented
231C4×Dic3—71no—
232C4×Dic3C2×D711yescharacteristic, complemented
233C2×C3×C7C2×#4111yescharacteristic
234C2×C3×C7C2×#4111yescharacteristic
235C2×C3×C7H(5,𝔽2)11yescharacteristic
236D21—22no—
237D21—41no—
238C3×D7—41no—
239D3×C7—22no—
240#126—71no—
241#126—211no—
242#124—211no—
243#123—211no—
244#123—211no—
245#123—211no—
246C22⋊Q8—211no—
247C22⋊Q8—211no—
248#120—211no—
249C4×D4—211no—
250C4×D4—211no—
251#117—31no—
252#117—211no—
253C2×C22⋊C4—211no—
254C2×C22⋊C4—211no—
255C22×C7—32no—
256C22×C7—61no—
257C22×C7—61no—
258C22×C7C23×D311yescharacteristic
259C2×D7—21no—
260C2×D7—21no—
261C2×D7—21no—
262C2×D7—32no—
263C2×D7—61no—
264C2×D7—61no—
265C2×D7—61no—
266C2×D7—61no—
267C2×D7—61no—
268C2×D7—124no—
269C4×C7—21no—
270C4×C7—21no—
271C4×C7—21no—
272C4×C7—61no—
273C4×C7—61no—
274C4×C7—61no—
275Dic7—21no—
276Dic7—21no—
277Dic7—21no—
278Dic7—61no—
279Dic7—61no—
280C23×C3—71no—
281C22×D3—71no—
282C22×D3—71no—
283C22×D3—142no—
284C22×D3—142no—
285C22×D3—281no—
286C22×D3C22×D711yescharacteristic
287C2×C3×C4—71no—
288C2×C3×C4—71no—
289C2×C3×C4—71no—
290C2×C3×C4C22×D711yescharacteristic
291C2×C3×C4C22×D711yescharacteristic
292C2×C3×C4C22×D711yescharacteristic
293#67—281no—
294C2×Dic3—71no—
295C2×Dic3—71no—
296C2×Dic3C22×D711yescharacteristic
297C2×Dic3C22×D711yescharacteristic
298C2×Dic3C22×D711yescharacteristic
299D12—142no—
300D12—142no—
301C4×D3—22no—
302C4×D3—142no—
303C4×D3—281no—
304C4×D3—281no—
305C4×D3—281no—
306Dic6—281no—
307C3×C7#55111yescharacteristic, complemented, Hall
308C24—211no—
309C2×Q8—211no—
310C2×D4—211no—
311C2×D4—211no—
312C2×D4—211no—
313C22×C4—31no—
314C22×C4—211no—
315C22×C4—211no—
316C22×C4—211no—
317C22×C4—211no—
318C4⋊C4—31no—
319C4⋊C4—31no—
320C4⋊C4—71no—
321C4⋊C4—71no—
322C4⋊C4—71no—
323C4⋊C4—211no—
324C4⋊C4—211no—
325C4⋊C4—211no—
326C22⋊C4—31no—
327C22⋊C4—31no—
328C22⋊C4—71no—
329C22⋊C4—71no—
330C22⋊C4—71no—
331C22⋊C4—211no—
332C22⋊C4—211no—
333C22⋊C4—211no—
334C22⋊C4—211no—
335C22⋊C4—211no—
336C22⋊C4—211no—
337C22⋊C4—211no—
338C22⋊C4—211no—
339C22⋊C4—211no—
340C42—31no—
341C42—211no—
342C42D3×D711yescharacteristic, complemented
343C2×C7—62no—
344C2×C7D3×#4111yescharacteristic
345C2×C7D3×#4111yescharacteristic
346C2×C7#100911yescharacteristic
347D7—41no—
348D7—62no—
349D7—121no—
350C22×C3—141no—
351C22×C3—141no—
352C22×C3—141no—
353C22×C3C23×D711yescharacteristic
354C2×D3—21no—
355C2×D3—21no—
356C2×D3—72no—
357C2×D3—141no—
358C2×D3—141no—
359C2×D3—141no—
360C2×D3—141no—
361C2×D3—141no—
362C2×D3—284no—
363C2×D3#115712yes—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—141no—
368C3×C4—141no—
369C3×C4—141no—
370Dic3—21no—
371Dic3—21no—
372Dic3—21no—
373Dic3—141no—
374Dic3—141no—
375C23—31no—
376C23—71no—
377C23—211no—
378C23—211no—
379C23—422no—
380C23—422no—
381C23—841no—
382Q8—841no—
383D4—422no—
384D4—422no—
385D4—841no—
386C2×C4—31no—
387C2×C4—31no—
388C2×C4—31no—
389C2×C4—62no—
390C2×C4—71no—
391C2×C4—71no—
392C2×C4—71no—
393C2×C4—211no—
394C2×C4—211no—
395C2×C4—422no—
396C2×C4—841no—
397C2×C4—841no—
398C2×C4—841no—
399C2×C4C2×D3×D711yescharacteristic
400C2×C4C2×D3×D711yescharacteristic
401C2×C4C2×D3×D711yescharacteristic
402C7#570511yescharacteristic, complemented, Sylow
403C2×C3—281no—
404C2×C3C2×#115711yescharacteristic
405C2×C3D7×#4111yescharacteristic
406C2×C3#655311yescharacteristic
407D3—22no—
408D3—142no—
409D3—281no—
410C22—32no—
411C22—61no—
412C22—61no—
413C22—141no—
414C22—141no—
415C22—141no—
416C22—212no—
417C22—421no—
418C22—421no—
419C22—421no—
420C22—421no—
421C22—421no—
422C22—844no—
423C22C22×D3×D711yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—61no—
428C4—61no—
429C4—61no—
430C4—141no—
431C4—141no—
432C4—141no—
433C4—421no—
434C4—421no—
435C3#9021811yescharacteristic, complemented, Sylow
436C2—62no—
437C2—281no—
438C2—422no—
439C2—841no—
440C2D3×#115711yescharacteristic
441C2#1062156311yescharacteristic
442C2#1062156611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C42×C7C22
prime radical#10621038C2
hypercenterC42D3×D7
hypocenterC3×C7#551
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C4×D84C2semidirect
2. C7×#872C2semidirect
3. C3×#6439C2semidirect
5. #10621035C2semidirect
6. D3×(C2×D7)⋊C4C2semidirect
7. #10620995C2semidirect
8. #10620979C2semidirect
9. #10620968C2semidirect
10. #10620965C2semidirect
11. #10620939C2semidirect
12. #10620924C2semidirect
13. #10620916C2semidirect
14. #10620915C2semidirect
15. #10620913C2semidirect
20. C2×C4×D21C22semidirect
22. C2×#4248C22semidirect
27. C3×C42×C7C22semidirect
29. #66631C22semidirect
30. C4⋊Dic21C22semidirect
33. C7×Dic3⋊C4C22semidirect
34. C7×Dic3⋊C4C22semidirect
35. C4×C7×Dic3C22semidirect
39. C3×Dic7⋊C4C22semidirect
40. C3×Dic7⋊C4C22semidirect
41. C3×Dic7⋊C4C22semidirect
42. #66577C22semidirect
43. Dic7⋊Dic3C22semidirect
46. #66575C22semidirect
47. #66575C22semidirect
51. Dic3×Dic7C22semidirect
63. #6439D3semidirect
110. C42×C7C2×D3semidirect
126. Dic7⋊C4C2×D3semidirect
127. Dic7⋊C4C2×D3semidirect
128. Dic7⋊C4C2×D3semidirect
144. #872D7semidirect
214. C3×C42C2×D7semidirect
229. Dic3⋊C4C2×D7semidirect
230. Dic3⋊C4C2×D7semidirect
232. C4×Dic3C2×D7semidirect
307. C3×C7#551semidirect
342. C42D3×D7semidirect
402. C7#5705semidirect
435. C3#90218semidirect

Maximal subgroups

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

subgroupindex
C4×D842
C7×#8722
C3×#64392
#106210382
#106210352
D3×(C2×D7)⋊C42
#106209952
#106209792
#106209682
#106209652
#106209392
#106209242
#106209162
#106209152
#106209132
#902183
#57057