Finite Group Databasebeta

← #13058749

Subgroups — #13058749

Order 1344.

440 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
1#10621372C211yesmaximal, characteristic, complemented
2C7×#896C211yesmaximal, characteristic, complemented
3C3×#6458C211yesmaximal, characteristic, complemented
4#10621026C211yesmaximal, characteristic, complemented
5#10621018C211yesmaximal, characteristic, complemented
6#10621014C211yesmaximal, characteristic, complemented
7#10621009C211yesmaximal, characteristic, complemented
8#10620984C211yesmaximal, characteristic, complemented
9#10620983C211yesmaximal, characteristic, complemented
10#10620970C211yesmaximal, characteristic, complemented
11#10620970C211yesmaximal, characteristic, complemented
12#10620969C211yesmaximal, characteristic, complemented
13#10620969C211yesmaximal, characteristic, complemented
14#10620930C211yesmaximal, characteristic, complemented
15#10620911C211yesmaximal, characteristic, complemented
16#90338—31nomaximal, Hall
17C2×C4×D3×C7C2211yescharacteristic
18C2×C7×Dic6C2211yescharacteristic
19C2×C3×D28C2211yescharacteristic
20C2×C3×D28C2211yescharacteristic
21C2×C3×D28C2211yescharacteristic
22C2×C3×C4×D7C2211yescharacteristic
23C2×#4248C2211yescharacteristic
24C2×#4245C2211yescharacteristic
25C2×#4245C2211yescharacteristic
26C2×#4245C2211yescharacteristic
27C2×Dic3×D7C2211yescharacteristic
28C2×Dic3×D7C2211yescharacteristic
29C3×C7×C4⋊C4C2211yescharacteristic
30C4⋊Dic21C2211yescharacteristic
31#66629C2211yescharacteristic
32#66629C2211yescharacteristic
33#66629C2211yescharacteristic
34#66629C2211yescharacteristic
35C4×Dic21C2211yescharacteristic
36C7×(C2×D3)⋊C4C2211yescharacteristic
37C7×(C2×D3)⋊C4C2211yescharacteristic
38C7×Dic3⋊C4C2211yescharacteristic
39C7×Dic3⋊C4C2211yescharacteristic
40C3×(C2×D7)⋊C4C2211yescharacteristic
41C3×(C2×D7)⋊C4C2211yescharacteristic
42Dic3⋊Dic7C2211yescharacteristic
43Dic7⋊Dic3C2211yescharacteristic
44(C2×D3)⋊Dic7C2211yescharacteristic
45(C2×D7)⋊Dic3C2211yescharacteristic
46(C2×D7)⋊Dic3C2211yescharacteristic
47(C2×D7)⋊Dic3C2211yescharacteristic
48(C2×D7)⋊Dic3C2211yescharacteristic
49(C2×D7)⋊Dic3C2211yescharacteristic
50(C2×D7)⋊Dic3C2211yescharacteristic
51(C2×D7)⋊Dic3C2211yescharacteristic
52C7×C22⋊Q8—31no—
53#6510—31no—
54#6509—31no—
55#6493—31no—
56#6492—31no—
57#6460—31no—
58#6459—31no—
59#6458D311yescharacteristic, complemented
60#6457—31no—
61#6457—31no—
62#6452—31no—
63#6448—31no—
64#6447—31no—
65#6447—31no—
66#6446—31no—
67#5621—71nomaximal, Hall
68C22×D3×C7C2311yescharacteristic
69C22×C3×D7C2311yescharacteristic
70C22×C3×D7C2311yescharacteristic
71C22×C3×D7C2311yescharacteristic
72C2×C3×C4×C7C2311yescharacteristic
73C2×C3×C4×C7C2311yescharacteristic
74C2×C3×C4×C7C2311yescharacteristic
75C2×Dic21C2311yescharacteristic
76C2×Dic21C2311yescharacteristic
77C2×Dic21C2311yescharacteristic
78C2×Dic21C2311yescharacteristic
79C2×C7×Dic3C2311yescharacteristic
80C2×C7×Dic3C2311yescharacteristic
81C2×C7×Dic3C2311yescharacteristic
82C4×D3×C7—41no—
83C7×Dic6—41no—
84C2×C3×Dic7C2311yescharacteristic
85C3×D28—41no—
86C3×D28—41no—
87C3×D28—41no—
88C3×C4×D7—41no—
89#4248—41no—
90#4245—41no—
91#4245—41no—
92#4245—41no—
93Dic3×D7—41no—
94Dic3×D7—41no—
95C2×C7×Q8—31no—
96C22×C4×C7—31no—
97C2×C22⋊D7—31no—
98C2×C22⋊D7—31no—
99C2×C22⋊D7—31no—
100C2×D28C2×D311yescharacteristic
101C2×D28C2×D311yescharacteristic
102C2×D28C2×D311yescharacteristic
103C2×C4×D7—31no—
104C2×C4×D7—31no—
105C2×C4×D7C2×D311yescharacteristic
106C2×Dic14—31no—
107C7×C4⋊C4—31no—
108C7×C4⋊C4—31no—
109C7×C4⋊C4C2×D311yescharacteristic
110C7×C22⋊C4—31no—
111C7×C22⋊C4—31no—
112C22⋊Dic7—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
122C4⋊Dic7—31no—
123C4⋊Dic7—31no—
124Dic7⋊C4—31no—
125Dic7⋊C4—31no—
126Dic7⋊C4—31no—
127Dic7⋊C4—31no—
128Dic7⋊C4—31no—
129C4×Dic7—31no—
130C3×#121—71no—
131#939—71no—
132#939—71no—
133#938—71no—
134#936—71no—
135#935—71no—
136#935—71no—
137#929—71no—
138#924—71no—
139#896D711yescharacteristic, complemented
140#889—71no—
141#885—71no—
142#883—71no—
143#878—71no—
144#878—71no—
145C22×C3×C7C2411yescharacteristic
146C2×D3×C7—21no—
147C2×D3×C7—21no—
148C2×D3×C7—21no—
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—21no—
158C3×C4×C7—21no—
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—
169#562—211noSylow
170C23×C7—31no—
171C22×D7C22×D311yescharacteristic
172C22×D7C22×D311yescharacteristic
173C22×D7C22×D311yescharacteristic
174C7×Q8—121no—
175C2×C4×C7—31no—
176C2×C4×C7—31no—
177C2×C4×C7—31no—
178C2×C4×C7—121no—
179C2×C4×C7C22×D311yescharacteristic
180C2×C4×C7C22×D311yescharacteristic
181C2×C4×C7C22×D311yescharacteristic
182C22⋊D7—121no—
183C22⋊D7—121no—
184C22⋊D7—121no—
185C2×Dic7—31no—
186C2×Dic7—31no—
187C2×Dic7—31no—
188C2×Dic7—31no—
189C2×Dic7C22×D311yescharacteristic
190D28—41no—
191D28—41no—
192D28—41no—
193C4×D7—41no—
194C4×D7—121no—
195C4×D7—121no—
196Dic14—121no—
197C2×C3×D4—71no—
198C2×C3×D4—71no—
199C2×C3×D4—71no—
200C22×C3×C4—71no—
201C2×#67—71no—
202C2×#67—71no—
203C2×#67—71no—
204C22×Dic3—71no—
205C22×Dic3—71no—
206C2×C4×D3C2×D711yescharacteristic
207C2×Dic6—71no—
208C2×Dic6C2×D711yescharacteristic
209C3×C4⋊C4C2×D711yescharacteristic
210C3×C22⋊C4—71no—
211C3×C22⋊C4—71no—
212#217—71no—
213#217—71no—
214#217—71no—
215#217—71no—
216#217—71no—
217#217—71no—
218#217—71no—
219(C2×D3)⋊C4—71no—
220(C2×D3)⋊C4C2×D711yescharacteristic
221(C2×D3)⋊C4C2×D711yescharacteristic
222C4⋊Dic3—71no—
223C4⋊Dic3—71no—
224Dic3⋊C4—71no—
225Dic3⋊C4—71no—
226Dic3⋊C4—71no—
227Dic3⋊C4—71no—
228Dic3⋊C4—71no—
229Dic3⋊C4C2×D711yescharacteristic
230Dic3⋊C4C2×D711yescharacteristic
231C4×Dic3—71no—
232C2×C3×C7H(5,𝔽2)11yescharacteristic
233C2×C3×C7H(5,𝔽2)11yescharacteristic
234C2×C3×C72−1+411yescharacteristic
235C3×D7—41no—
236C3×D7—41no—
237C3×D7—41no—
238D3×C7—41no—
239#125—211no—
240#124—211no—
241#124—211no—
242#123—211no—
243#123—211no—
244#123—211no—
245#123—211no—
246C22⋊Q8—31no—
247C22⋊Q8—211no—
248C22⋊Q8—211no—
249C22⋊Q8—211no—
250#121—71no—
251#121—211no—
252#121—211no—
253#121—211no—
254C22×C7—61no—
255C22×C7—61no—
256C22×C7—61no—
257C22×C7C23×D311yescharacteristic
258C2×D7—21no—
259C2×D7—21no—
260C2×D7—21no—
261C2×D7—21no—
262C2×D7—21no—
263C2×D7—21no—
264C2×D7—21no—
265C2×D7—21no—
266C2×D7—21no—
267C4×C7—21no—
268C4×C7—21no—
269C4×C7—21no—
270C4×C7—61no—
271C4×C7—61no—
272C4×C7—61no—
273Dic7—21no—
274Dic7—61no—
275Dic7—61no—
276Dic7—61no—
277Dic7—61no—
278C23×C3—71no—
279C23×C3—71no—
280C23×C3—71no—
281C22×D3C22×D711yescharacteristic
282C3×D4—281no—
283C3×D4—281no—
284C3×D4—281no—
285C2×C3×C4—71no—
286C2×C3×C4—281no—
287C2×C3×C4C22×D711yescharacteristic
288C2×C3×C4C22×D711yescharacteristic
289C2×C3×C4C22×D711yescharacteristic
290#67—281no—
291#67—281no—
292#67—281no—
293C2×Dic3—71no—
294C2×Dic3—71no—
295C2×Dic3—71no—
296C2×Dic3—71no—
297C2×Dic3—281no—
298C2×Dic3—281no—
299C2×Dic3C22×D711yescharacteristic
300C2×Dic3C22×D711yescharacteristic
301C2×Dic3C22×D711yescharacteristic
302C4×D3—41no—
303Dic6—41no—
304Dic6—281no—
305C3×C7#56211yescharacteristic, complemented, Hall
306C2×Q8—31no—
307C2×Q8—211no—
308C2×D4—71no—
309C2×D4—71no—
310C2×D4—71no—
311C2×D4—211no—
312C2×D4—211no—
313C2×D4—211no—
314C22×C4—31no—
315C22×C4—71no—
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—
326C4⋊C4—211no—
327C4⋊C4D3×D711yescharacteristic
328C22⋊C4—31no—
329C22⋊C4—31no—
330C22⋊C4—71no—
331C22⋊C4—71no—
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—211no—
341C2×C7—121no—
342C2×C7#100411yescharacteristic
343C2×C7#100411yescharacteristic
344C2×C7#101011yescharacteristic
345D7—41no—
346D7—41no—
347D7—41no—
348C22×C3—141no—
349C22×C3—141no—
350C22×C3—141no—
351C22×C3—141no—
352C22×C3—141no—
353C22×C3—141no—
354C22×C3—141no—
355C22×C3—141no—
356C22×C3—141no—
357C22×C3C23×D711yescharacteristic
358C2×D3—21no—
359C2×D3—21no—
360C2×D3—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—141no—
365Dic3—21no—
366Dic3—21no—
367Dic3—21no—
368Dic3—141no—
369Dic3—141no—
370Dic3—141no—
371Dic3—141no—
372C23—31no—
373C23—71no—
374C23—71no—
375C23—71no—
376Q8—121no—
377Q8—841no—
378D4—281no—
379D4—281no—
380D4—281no—
381D4—841no—
382D4—841no—
383D4—841no—
384C2×C4—31no—
385C2×C4—31no—
386C2×C4—31no—
387C2×C4—71no—
388C2×C4—121no—
389C2×C4—211no—
390C2×C4—211no—
391C2×C4—211no—
392C2×C4—211no—
393C2×C4—281no—
394C2×C4—841no—
395C2×C4—841no—
396C2×C4C2×D3×D711yescharacteristic
397C2×C4C2×D3×D711yescharacteristic
398C2×C4C2×D3×D711yescharacteristic
399C7#562111yescharacteristic, complemented, Sylow
400C2×C3—281no—
401C2×C3—281no—
402C2×C3—281no—
403C2×C3#654811yescharacteristic
404C2×C3#655111yescharacteristic
405C2×C3#655311yescharacteristic
406D3—41no—
407C22—61no—
408C22—61no—
409C22—61no—
410C22—141no—
411C22—141no—
412C22—141no—
413C22—141no—
414C22—141no—
415C22—141no—
416C22—141no—
417C22—141no—
418C22—141no—
419C22C22×D3×D711yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—61no—
424C4—61no—
425C4—61no—
426C4—141no—
427C4—421no—
428C4—421no—
429C4—421no—
430C4—421no—
431C3#9033811yescharacteristic, complemented, Sylow
432C2—121no—
433C2—281no—
434C2—281no—
435C2—281no—
436C2#1062156411yescharacteristic
437C2#1062157211yescharacteristic
438C2#1062157511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×C4⋊C4C22
hypercenterC4⋊C4D3×D7
hypocenterC3×C7#562
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. #10621372C2semidirect
2. C7×#896C2semidirect
3. C3×#6458C2semidirect
4. #10621026C2semidirect
5. #10621018C2semidirect
6. #10621014C2semidirect
7. #10621009C2semidirect
8. #10620984C2semidirect
9. #10620983C2semidirect
10. #10620970C2semidirect
11. #10620970C2semidirect
12. #10620969C2semidirect
13. #10620969C2semidirect
14. #10620930C2semidirect
15. #10620911C2semidirect
59. #6458D3semidirect
139. #896D7semidirect
305. C3×C7#562semidirect
399. C7#5621semidirect
431. C3#90338semidirect

Maximal subgroups

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

subgroupindex
#106213722
C7×#8962
C3×#64582
#106210262
#106210182
#106210142
#106210092
#106209842
#106209832
#106209702
#106209692
#106209302
#106209112
#903383
#56217