Finite Group Databasebeta

← #13058750

Subgroups — #13058750

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#10621379C211yesmaximal, characteristic, complemented
2C7×#889C211yesmaximal, characteristic, complemented
3C3×#6458C211yesmaximal, characteristic, complemented
4#10621027C211yesmaximal, characteristic, complemented
5#10620993C211yesmaximal, characteristic, complemented
6#10620992C211yesmaximal, characteristic, complemented
7#10620971C211yesmaximal, characteristic, complemented
8#10620971C211yesmaximal, characteristic, complemented
9#10620969C211yesmaximal, characteristic, complemented
10#10620969C211yesmaximal, characteristic, complemented
11#10620926C211yesmaximal, characteristic, complemented
12#10620916C211yesmaximal, characteristic, complemented
13#10620915C211yesmaximal, characteristic, complemented
14#10620911C211yesmaximal, characteristic, complemented
15#10620910C211yesmaximal, characteristic, complemented
16#90391—31nomaximal, Hall
17C2×C4×D21C2211yescharacteristic
18C2×Dic42C2211yescharacteristic
19C2×C3×D28C2211yescharacteristic
20C2×C3×D28C2211yescharacteristic
21C2×C3×D28C2211yescharacteristic
22C2×C3×C4×D7C2211yescharacteristic
23C2×#4248C2211yescharacteristic
24C2×#4246C2211yescharacteristic
25C2×#4246C2211yescharacteristic
26C2×#4246C2211yescharacteristic
27C2×Dic3×D7C2211yescharacteristic
28C2×Dic3×D7C2211yescharacteristic
29C3×C7×C4⋊C4C2211yescharacteristic
30#66631C2211yescharacteristic
31#66631C2211yescharacteristic
32#66629C2211yescharacteristic
33#66629C2211yescharacteristic
34C7×C4⋊Dic3C2211yescharacteristic
35C7×Dic3⋊C4C2211yescharacteristic
36C7×Dic3⋊C4C2211yescharacteristic
37C7×Dic3⋊C4C2211yescharacteristic
38C7×Dic3⋊C4C2211yescharacteristic
39C4×C7×Dic3C2211yescharacteristic
40C3×(C2×D7)⋊C4C2211yescharacteristic
41C3×(C2×D7)⋊C4C2211yescharacteristic
42#66577C2211yescharacteristic
43Dic7⋊Dic3C2211yescharacteristic
44#66575C2211yescharacteristic
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×#125—31no—
53#6459—31no—
54#6459—31no—
55#6459—31no—
56#6459—31no—
57#6458—31no—
58#6458—31no—
59#6458—31no—
60#6458D311yescharacteristic, complemented
61#6457—31no—
62#6457—31no—
63#6457—31no—
64#6457—31no—
65#6438—31no—
66#6438—31no—
67#5621—71nomaximal, Hall
68C22×D21C2311yescharacteristic
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
78C4×D21—41no—
79Dic42—41no—
80C2×C7×Dic3C2311yescharacteristic
81C2×C7×Dic3C2311yescharacteristic
82C2×C7×Dic3C2311yescharacteristic
83C2×C7×Dic3C2311yescharacteristic
84C2×C3×Dic7C2311yescharacteristic
85C3×D28—41no—
86C3×D28—41no—
87C3×D28—41no—
88C3×C4×D7—41no—
89#4248—41no—
90#4246—41no—
91#4246—41no—
92#4246—41no—
93Dic3×D7—41no—
94Dic3×D7—41no—
95C2×D28—31no—
96C2×D28—31no—
97C2×D28—31no—
98C2×D28C2×D311yescharacteristic
99C2×D28C2×D311yescharacteristic
100C2×D28C2×D311yescharacteristic
101C2×C4×D7—31no—
102C2×C4×D7—31no—
103C2×C4×D7—31no—
104C2×C4×D7C2×D311yescharacteristic
105C2×Dic14—31no—
106C2×Dic14—31no—
107C7×C4⋊C4—31no—
108C7×C4⋊C4—31no—
109C7×C4⋊C4—31no—
110C7×C4⋊C4—31no—
111C7×C4⋊C4—31no—
112C7×C4⋊C4C2×D311yescharacteristic
113C42×C7—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)⋊C4—31no—
122(C2×D7)⋊C4—31no—
123(C2×D7)⋊C4—31no—
124(C2×D7)⋊C4C2×D311yescharacteristic
125(C2×D7)⋊C4C2×D311yescharacteristic
126Dic7⋊C4—31no—
127Dic7⋊C4—31no—
128Dic7⋊C4—31no—
129Dic7⋊C4—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#896—71no—
140#889D711yescharacteristic, complemented
141#885—71no—
142#883—71no—
143#878—71no—
144#878—71no—
145C22×C3×C7C2411yescharacteristic
146C2×D21—21no—
147C2×D21—21no—
148C2×D21—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—
164C3×Dic7—21no—
165C7×Dic3—21no—
166C7×Dic3—21no—
167C7×Dic3—21no—
168C7×Dic3—21no—
169#562—211noSylow
170C22×D7—31no—
171C22×D7C22×D311yescharacteristic
172C22×D7C22×D311yescharacteristic
173C22×D7C22×D311yescharacteristic
174C2×C4×C7—31no—
175C2×C4×C7—31no—
176C2×C4×C7—31no—
177C2×C4×C7—31no—
178C2×C4×C7C22×D311yescharacteristic
179C2×C4×C7C22×D311yescharacteristic
180C2×C4×C7C22×D311yescharacteristic
181C2×Dic7—31no—
182C2×Dic7—31no—
183C2×Dic7—31no—
184C2×Dic7C22×D311yescharacteristic
185D28—41no—
186D28—41no—
187D28—41no—
188D28—121no—
189D28—121no—
190D28—121no—
191C4×D7—41no—
192C4×D7—121no—
193C4×D7—121no—
194C4×D7—121no—
195Dic14—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×D3—71no—
207C2×Dic6—71no—
208C2×Dic6—71no—
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)⋊C4—71no—
221(C2×D3)⋊C4—71no—
222C4⋊Dic3—71no—
223C4⋊Dic3C2×D711yescharacteristic
224Dic3⋊C4—71no—
225Dic3⋊C4—71no—
226Dic3⋊C4—71no—
227Dic3⋊C4C2×D711yescharacteristic
228Dic3⋊C4C2×D711yescharacteristic
229Dic3⋊C4C2×D711yescharacteristic
230Dic3⋊C4C2×D711yescharacteristic
231C4×Dic3C2×D711yescharacteristic
232C2×C3×C7H(5,𝔽2)11yescharacteristic
233C2×C3×C7H(5,𝔽2)11yescharacteristic
234C2×C3×C72−1+411yescharacteristic
235D21—41no—
236C3×D7—41no—
237C3×D7—41no—
238C3×D7—41no—
239#125—31no—
240#124—211no—
241#124—211no—
242#123—211no—
243#123—211no—
244#123—211no—
245#123—211no—
246C22⋊Q8—211no—
247C22⋊Q8—211no—
248C22⋊Q8—211no—
249C22⋊Q8—211no—
250#121—71no—
251#121—211no—
252#121—211no—
253#121—211no—
254C22×C7C23×D311yescharacteristic
255C2×D7—21no—
256C2×D7—21no—
257C2×D7—21no—
258C2×D7—21no—
259C2×D7—21no—
260C2×D7—21no—
261C2×D7—21no—
262C2×D7—21no—
263C2×D7—21no—
264C2×D7—61no—
265C2×D7—61no—
266C2×D7—61no—
267C4×C7—21no—
268C4×C7—21no—
269C4×C7—21no—
270C4×C7—61no—
271C4×C7—61no—
272C4×C7—61no—
273C4×C7—61no—
274Dic7—21no—
275Dic7—61no—
276Dic7—61no—
277Dic7—61no—
278C23×C3—71no—
279C23×C3—71no—
280C23×C3—71no—
281C22×D3—71no—
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—281no—
297C2×Dic3—281no—
298C2×Dic3C22×D711yescharacteristic
299C2×Dic3C22×D711yescharacteristic
300C2×Dic3C22×D711yescharacteristic
301C2×Dic3C22×D711yescharacteristic
302C4×D3—281no—
303Dic6—281no—
304Dic6—281no—
305C3×C7#56211yescharacteristic, complemented, Hall
306C2×Q8—211no—
307C2×Q8—211no—
308C2×D4—71no—
309C2×D4—71no—
310C2×D4—71no—
311C2×D4—211no—
312C2×D4—211no—
313C2×D4—211no—
314C22×C4—71no—
315C22×C4—211no—
316C22×C4—211no—
317C22×C4—211no—
318C4⋊C4—31no—
319C4⋊C4—31no—
320C4⋊C4—31no—
321C4⋊C4—31no—
322C4⋊C4—31no—
323C4⋊C4—211no—
324C4⋊C4—211no—
325C4⋊C4—211no—
326C4⋊C4—211no—
327C4⋊C4D3×D711yescharacteristic
328C22⋊C4—71no—
329C22⋊C4—71no—
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⋊C4—211no—
340C42—31no—
341C2×C7#100411yescharacteristic
342C2×C7#100411yescharacteristic
343C2×C7#101011yescharacteristic
344D7—41no—
345D7—41no—
346D7—41no—
347D7—121no—
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—141no—
359C2×D3—141no—
360C2×D3—141no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—141no—
365Dic3—21no—
366Dic3—21no—
367Dic3—21no—
368Dic3—21no—
369Dic3—141no—
370Dic3—141no—
371Dic3—141no—
372C23—71no—
373C23—71no—
374C23—71no—
375C23—211no—
376Q8—841no—
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—31no—
388C2×C4—71no—
389C2×C4—211no—
390C2×C4—211no—
391C2×C4—211no—
392C2×C4—281no—
393C2×C4—841no—
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#655111yescharacteristic
404C2×C3#655311yescharacteristic
405C2×C3#655311yescharacteristic
406D3—281no—
407C22—141no—
408C22—141no—
409C22—141no—
410C22—141no—
411C22—141no—
412C22—141no—
413C22—141no—
414C22—141no—
415C22—141no—
416C22—421no—
417C22—421no—
418C22—421no—
419C22C22×D3×D711yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—61no—
424C4—61no—
425C4—61no—
426C4—61no—
427C4—141no—
428C4—421no—
429C4—421no—
430C4—421no—
431C3#9039111yescharacteristic, complemented, Sylow
432C2—281no—
433C2—281no—
434C2—281no—
435C2—841no—
436C2#1062156411yescharacteristic
437C2#1062157311yescharacteristic
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. #10621379C2semidirect
2. C7×#889C2semidirect
3. C3×#6458C2semidirect
4. #10621027C2semidirect
5. #10620993C2semidirect
6. #10620992C2semidirect
7. #10620971C2semidirect
8. #10620971C2semidirect
9. #10620969C2semidirect
10. #10620969C2semidirect
11. #10620926C2semidirect
12. #10620916C2semidirect
13. #10620915C2semidirect
14. #10620911C2semidirect
15. #10620910C2semidirect
60. #6458D3semidirect
140. #889D7semidirect
305. C3×C7#562semidirect
399. C7#5621semidirect
431. C3#90391semidirect

Maximal subgroups

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

subgroupindex
#106213792
C7×#8892
C3×#64582
#106210272
#106209932
#106209922
#106209712
#106209692
#106209262
#106209162
#106209152
#106209112
#106209102
#903913
#56217