Finite Group Databasebeta

← #13058104

Subgroups — #13058104

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
1#10621361C211yesmaximal, characteristic, complemented
2C7×#877C211yesmaximal, characteristic, complemented
3C3×#6445C211yesmaximal, characteristic
4(C22⋊D7)⋊Dic3C211yesmaximal, characteristic, complemented
5D7×#217C211yesmaximal, characteristic, complemented
6#10621098C211yesmaximal, characteristic, complemented
7C2×(C2×D7)⋊Dic3C211yesmaximal, characteristic, complemented
8#10620993C211yesmaximal, characteristic, complemented
9Dic3×D28C211yesmaximal, characteristic, complemented
10#10620969C211yesmaximal, characteristic, complemented
11#10620969C211yesmaximal, characteristic, complemented
12#10620955C211yesmaximal, characteristic, complemented
13#10620926C211yesmaximal, characteristic, complemented
14#10620925C211yesmaximal, characteristic, complemented
15#10620924C211yesmaximal, characteristic, complemented
16#90218—31nomaximal, Hall
17C23×C3×D7C2211yescharacteristic
18C22×Dic21C2211yescharacteristic
19C2×Dic42C2211yescharacteristic, complemented
20C22×C7×Dic3C2211yescharacteristic
21C2×C3×C22⋊D7C2211yescharacteristic
22C2×C3×D28C2211yescharacteristic
23C2×C3×D28C2211yescharacteristic
24C2×Dic3×D7C2211yescharacteristic
25C2×Dic3×D7C2211yescharacteristic
26C2×Dic3×D7C2211yescharacteristic, complemented
27C3×C7×C22⋊C4C2211yescharacteristic
28#66636C2211yescharacteristic
29C4⋊Dic21C2211yescharacteristic, complemented
30#66629C2211yescharacteristic, complemented
31#66629C2211yescharacteristic, complemented
32C7×#217C2211yescharacteristic
33C7×Dic3⋊C4C2211yescharacteristic, complemented
34C7×Dic3⋊C4C2211yescharacteristic, complemented
35C4×C7×Dic3C2211yescharacteristic, complemented
36C4×C7×Dic3C2211yescharacteristic, complemented
37C3×(C2×D7)⋊C4C2211yescharacteristic
38C3×(C2×D7)⋊C4C2211yescharacteristic
39#66577C2211yescharacteristic, complemented
40#66577C2211yescharacteristic, complemented
41Dic7⋊Dic3C2211yescharacteristic, complemented
42(C2×D7)⋊Dic3C2211yescharacteristic
43(C2×D7)⋊Dic3C2211yescharacteristic
44(C2×D7)⋊Dic3C2211yescharacteristic
45(C2×D7)⋊Dic3C2211yescharacteristic
46(C2×D7)⋊Dic3C2211yescharacteristic
47(C2×D7)⋊Dic3C2211yescharacteristic
48(C2×D7)⋊Dic3C2211yescharacteristic, complemented
49(C2×D7)⋊Dic3C2211yescharacteristic, complemented
50(C2×D7)⋊Dic3C2211yescharacteristic, complemented
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#6445D311yescharacteristic
60(C22⋊D7)⋊C4—31no—
61D7×C22⋊C4—31no—
62#6441—31no—
63#6439—31no—
64#6438—31no—
65C4×D28—31no—
66#6435—31no—
67#5587—71nomaximal, Hall
68C23×C3×C7C2311yescharacteristic
69C22×C3×D7—22no—
70C22×C3×D7—22no—
71C22×C3×D7—41no—
72C22×C3×D7C2311yescharacteristic
73C22×C3×D7C2311yescharacteristic
74C22×C3×D7C2311yescharacteristic
75C2×C3×C4×C7C2311yescharacteristic
76C2×C3×C4×C7C2311yescharacteristic
77C2×Dic21—41no—
78C2×Dic21C2311yescharacteristic
79C2×Dic21C2311yescharacteristic
80C2×Dic21C2311yescharacteristic
81C2×Dic21C2311yescharacteristic
82Dic42—41no—
83C2×C7×Dic3—22no—
84C2×C7×Dic3C2311yescharacteristic
85C2×C7×Dic3C2311yescharacteristic
86C2×C7×Dic3C2311yescharacteristic
87C2×C7×Dic3C2311yescharacteristic
88C3×C22⋊D7—22no—
89C2×C3×Dic7C2311yescharacteristic
90C3×D28—22no—
91C3×D28—41no—
92Dic3×D7—22no—
93Dic3×D7—41no—
94Dic3×D7—41no—
95C23×D7C2×D311yescharacteristic
96C22×C4×C7—31no—
97C2×C22⋊D7C2×D311yescharacteristic
98C22×Dic7—31no—
99C2×D28C2×D311yescharacteristic
100C2×D28C2×D311yescharacteristic
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⋊C4C2×D311yescharacteristic
109C42×C7—31no—
110C42×C7—31no—
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)⋊C4—31no—
121(C2×D7)⋊C4C2×D311yescharacteristic
122(C2×D7)⋊C4C2×D311yescharacteristic
123C4⋊Dic7—31no—
124Dic7⋊C4—31no—
125Dic7⋊C4—31no—
126Dic7⋊C4—31no—
127Dic7⋊C4—31no—
128Dic7⋊C4—31no—
129C4×Dic7—31no—
130C3×#120—71no—
131C2×#217—71no—
132C2×#217—71no—
133#936—71no—
134#935—71no—
135#935—71no—
136#935—71no—
137D4×Dic3—71no—
138D4×Dic3—71no—
139#879—71no—
140#879—71no—
141#878—71no—
142#878—71no—
143#877—71no—
144#877D711yescharacteristic, complemented
145C22×C3×C7—21no—
146C22×C3×C7—21no—
147C22×C3×C7#4112yes—
148C22×C3×C7C2411yescharacteristic
149C2×C3×D7—21no—
150C2×C3×D7—21no—
151C2×C3×D7—21no—
152C2×C3×D7—21no—
153C2×C3×D7—21no—
154C2×C3×D7—21no—
155C2×C3×D7—21no—
156C2×C3×D7—21no—
157C2×C3×D7—44no—
158C2×C3×D7#4112yes—
159C3×C4×C7—21no—
160C3×C4×C7—21no—
161Dic21—21no—
162Dic21—21no—
163Dic21—21no—
164Dic21—21no—
165C3×Dic7—21no—
166C7×Dic3—21no—
167C7×Dic3—21no—
168C7×Dic3—21no—
169C7×Dic3—21no—
170#551—211noSylow
171C23×C7C22×D311yescharacteristic
172C22×D7—22no—
173C22×D7—22no—
174C22×D7—41no—
175C22×D7C22×D311yescharacteristic
176C22×D7C22×D311yescharacteristic
177C22×D7C22×D311yescharacteristic
178C2×C4×C7—31no—
179C2×C4×C7—31no—
180C2×C4×C7—31no—
181C2×C4×C7—31no—
182C2×C4×C7—62no—
183C2×C4×C7C22×D311yescharacteristic
184C2×C4×C7C22×D311yescharacteristic
185C22⋊D7—22no—
186C2×Dic7—31no—
187C2×Dic7—31no—
188C2×Dic7—31no—
189C2×Dic7—31no—
190C2×Dic7—121no—
191C2×Dic7C22×D311yescharacteristic
192D28—22no—
193D28—41no—
194C4×D7—62no—
195C4×D7—121no—
196C4×D7—121no—
197Dic14—121no—
198C24×C3—71no—
199C2×C3×D4—71no—
200C2×C3×D4—71no—
201C2×C3×D4—71no—
202C22×Dic3—71no—
203C22×Dic3—71no—
204C22×Dic3—71no—
205C22×Dic3—71no—
206C22×Dic3C2×D711yescharacteristic
207C2×Dic6—71no—
208C3×C22⋊C4—71no—
209C3×C22⋊C4—71no—
210C3×C22⋊C4C2×D711yescharacteristic
211#217—71no—
212#217—71no—
213#217—71no—
214#217—71no—
215#217—71no—
216#217—71no—
217#217—71no—
218#217—71no—
219#217—71no—
220#217—71no—
221#217C2×D711yescharacteristic
222C4⋊Dic3—71no—
223C4⋊Dic3—71no—
224Dic3⋊C4—71no—
225Dic3⋊C4—71no—
226Dic3⋊C4—71no—
227Dic3⋊C4—71no—
228Dic3⋊C4C2×D711yescharacteristic, complemented
229Dic3⋊C4C2×D711yescharacteristic, complemented
230C4×Dic3—71no—
231C4×Dic3C2×D711yescharacteristic, complemented
232C4×Dic3C2×D711yescharacteristic, complemented
233C2×C3×C7—22no—
234C2×C3×C7C2×#4111yescharacteristic
235C2×C3×C7C2×#4111yescharacteristic
236C2×C3×C7H(5,𝔽2)11yescharacteristic
237C3×D7—22no—
238C3×D7—41no—
239C3×D7—41no—
240#126—211no—
241#126—211no—
242#124—211no—
243#123—211no—
244#123—211no—
245#123—211no—
246C22⋊Q8—211no—
247C22⋊Q8—211no—
248#120—71no—
249C4×D4—211no—
250C4×D4—211no—
251#117—31no—
252#117—211no—
253C2×C22⋊C4—211no—
254C2×C22⋊C4—211no—
255C22×C7—21no—
256C22×C7—21no—
257C22×C7#23712yes—
258C22×C7C23×D311yescharacteristic
259C2×D7—21no—
260C2×D7—21no—
261C2×D7—21no—
262C2×D7—21no—
263C2×D7—21no—
264C2×D7—21no—
265C2×D7—21no—
266C2×D7—21no—
267C2×D7—44no—
268C2×D7#23712yes—
269C4×C7—21no—
270C4×C7—21no—
271C4×C7—61no—
272C4×C7—61no—
273C4×C7—61no—
274C4×C7—61no—
275Dic7—21no—
276Dic7—61no—
277Dic7—61no—
278Dic7—61no—
279Dic7—61no—
280C23×C3—71no—
281C23×C3—71no—
282C23×C3—71no—
283C23×C3—142no—
284C23×C3—142no—
285C23×C3—281no—
286C23×C3C22×D711yescharacteristic
287C3×D4—142no—
288C3×D4—142no—
289C3×D4—281no—
290C2×C3×C4—71no—
291C2×C3×C4C22×D711yescharacteristic
292C2×C3×C4C22×D711yescharacteristic
293C2×Dic3—22no—
294C2×Dic3—71no—
295C2×Dic3—71no—
296C2×Dic3—71no—
297C2×Dic3—71no—
298C2×Dic3—142no—
299C2×Dic3—281no—
300C2×Dic3—281no—
301C2×Dic3—281no—
302C2×Dic3C22×D711yescharacteristic
303C2×Dic3C22×D711yescharacteristic
304C2×Dic3C22×D711yescharacteristic
305C2×Dic3C22×D711yescharacteristic
306Dic6—281no—
307C3×C7#55111yescharacteristic, complemented, Hall
308C24—71no—
309C2×Q8—211no—
310C2×D4—71no—
311C2×D4—71no—
312C2×D4—71no—
313C22×C4—31no—
314C22×C4—211no—
315C22×C4—211no—
316C22×C4—211no—
317C22×C4—211no—
318C4⋊C4—31no—
319C4⋊C4—31no—
320C4⋊C4—211no—
321C4⋊C4—211no—
322C4⋊C4—211no—
323C4⋊C4—211no—
324C4⋊C4—211no—
325C4⋊C4—211no—
326C22⋊C4—31no—
327C22⋊C4—71no—
328C22⋊C4—71no—
329C22⋊C4—211no—
330C22⋊C4—211no—
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⋊C4D3×D711yescharacteristic
340C42—31no—
341C42—31no—
342C42—211no—
343C2×C7—22no—
344C2×C7C2×#23711yescharacteristic
345C2×C7C2×#23711yescharacteristic
346C2×C7#100411yescharacteristic
347D7—22no—
348D7—41no—
349D7—41no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—72no—
353C22×C3—141no—
354C22×C3—141no—
355C22×C3—141no—
356C22×C3—141no—
357C22×C3—141no—
358C22×C3—141no—
359C22×C3—141no—
360C22×C3—141no—
361C22×C3—284no—
362C22×C3#115712yes—
363C22×C3C23×D711yescharacteristic
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—141no—
367Dic3—21no—
368Dic3—21no—
369Dic3—21no—
370Dic3—21no—
371Dic3—141no—
372Dic3—141no—
373Dic3—141no—
374Dic3—141no—
375C23—71no—
376C23—71no—
377C23—71no—
378C23—142no—
379C23—142no—
380C23—281no—
381C23C2×D3×D711yescharacteristic
382Q8—841no—
383D4—142no—
384D4—142no—
385D4—281no—
386C2×C4—31no—
387C2×C4—31no—
388C2×C4—31no—
389C2×C4—31no—
390C2×C4—62no—
391C2×C4—71no—
392C2×C4—211no—
393C2×C4—211no—
394C2×C4—211no—
395C2×C4—211no—
396C2×C4—422no—
397C2×C4—841no—
398C2×C4—841no—
399C2×C4—841no—
400C2×C4C2×D3×D711yescharacteristic
401C2×C4C2×D3×D711yescharacteristic
402C7#558711yescharacteristic, complemented, Sylow
403C2×C3—22no—
404C2×C3—142no—
405C2×C3—281no—
406C2×C3—281no—
407C2×C3C2×#115711yescharacteristic
408C2×C3D7×#4111yescharacteristic
409C2×C3#655311yescharacteristic
410C22—21no—
411C22—21no—
412C22—72no—
413C22—141no—
414C22—141no—
415C22—141no—
416C22—141no—
417C22—141no—
418C22—141no—
419C22—141no—
420C22—141no—
421C22—284no—
422C22#6666912yes—
423C22C22×D3×D711yescharacteristic
424C4—21no—
425C4—21no—
426C4—61no—
427C4—61no—
428C4—61no—
429C4—61no—
430C4—141no—
431C4—421no—
432C4—421no—
433C4—421no—
434C4—421no—
435C3#9021811yescharacteristic, complemented, Sylow
436C2—22no—
437C2—142no—
438C2—281no—
439C2—281no—
440C2C2×#6666911yescharacteristic
441C2D7×#23711yescharacteristic
442C2#1062157311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×C22⋊C4C22
prime radicalC3×#6445C2
hypercenterC22⋊C4D3×D7
hypocenterC3×C7#551
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #10621361C2semidirect
2. C7×#877C2semidirect
4. (C22⋊D7)⋊Dic3C2semidirect
5. D7×#217C2semidirect
6. #10621098C2semidirect
7. C2×(C2×D7)⋊Dic3C2semidirect
8. #10620993C2semidirect
9. Dic3×D28C2semidirect
10. #10620969C2semidirect
11. #10620969C2semidirect
12. #10620955C2semidirect
13. #10620926C2semidirect
14. #10620925C2semidirect
15. #10620924C2semidirect
19. C2×Dic42C22semidirect
26. C2×Dic3×D7C22semidirect
29. C4⋊Dic21C22semidirect
30. #66629C22semidirect
31. #66629C22semidirect
33. C7×Dic3⋊C4C22semidirect
34. C7×Dic3⋊C4C22semidirect
35. C4×C7×Dic3C22semidirect
36. C4×C7×Dic3C22semidirect
39. #66577C22semidirect
40. #66577C22semidirect
41. Dic7⋊Dic3C22semidirect
48. (C2×D7)⋊Dic3C22semidirect
49. (C2×D7)⋊Dic3C22semidirect
50. (C2×D7)⋊Dic3C22semidirect
51. Dic3×Dic7C22semidirect
144. #877D7semidirect
228. Dic3⋊C4C2×D7semidirect
229. Dic3⋊C4C2×D7semidirect
231. C4×Dic3C2×D7semidirect
232. C4×Dic3C2×D7semidirect
307. C3×C7#551semidirect
402. C7#5587semidirect
435. C3#90218semidirect

Maximal subgroups

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

subgroupindex
#106213612
C7×#8772
C3×#64452
(C22⋊D7)⋊Dic32
D7×#2172
#106210982
C2×(C2×D7)⋊Dic32
#106209932
Dic3×D282
#106209692
#106209552
#106209262
#106209252
#106209242
#902183
#55877