Finite Group Databasebeta

← #13059474

Subgroups — #13059474

Order 1344.

588 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66686C211yesmaximal, characteristic
2C4×#4268C211yesmaximal, characteristic, complemented
3C4×C7×#67C211yesmaximal, characteristic, complemented
4C2×C3×Dic7⋊C4C211yesmaximal, characteristic, complemented
5#10621114C211yesmaximal, characteristic, complemented
6#67×Dic7C211yesmaximal, characteristic, complemented
7#10621090C211yesmaximal, characteristic, complemented
8#10621008C211yesmaximal, characteristic, complemented
9#10620968C211yesmaximal, characteristic, complemented
10#10620966C211yesmaximal, characteristic, complemented
11#10620965C211yesmaximal, characteristic, complemented
12#10620962C211yesmaximal, characteristic, complemented
13D3×Dic7⋊C4C211yesmaximal, characteristic, complemented
14#10620887C211yesmaximal, characteristic, complemented
15#10620886C211yesmaximal, characteristic, complemented
16#90237—31nomaximal, Hall
17C22×C3×C4×C7C2211yescharacteristic
18C2×#4268C2211yescharacteristic
19C2×C4×D21C2211yescharacteristic
20C2×C7×#67C2211yescharacteristic
21C2×C4×D3×C7C2211yescharacteristic
22C22×C3×Dic7C2211yescharacteristic
23C22×C3×Dic7C2211yescharacteristic
24C2×#4248C2211yescharacteristic
25C2×#4247C2211yescharacteristic
26C2×D21⋊C4C2211yescharacteristic
27C2×D21⋊C4C2211yescharacteristic
28#66686C418yescomplemented
29C2×D3×Dic7C2211yescharacteristic
30C2×D3×Dic7C2211yescharacteristic
31#66636C2211yescharacteristic
32#66631C2211yescharacteristic
33#66629C2211yescharacteristic
34C4×Dic21C2211yescharacteristic
35C7×#217C2211yescharacteristic
36C7×(C2×D3)⋊C4C2211yescharacteristic
37C7×Dic3⋊C4C2211yescharacteristic
38C4×C7×Dic3C2211yescharacteristic
39C3×Dic7⋊C4C2211yescharacteristic
40C3×Dic7⋊C4C2211yescharacteristic
41C3×Dic7⋊C4C2211yescharacteristic
42C3×Dic7⋊C4C2211yescharacteristic
43Dic3⋊Dic7C2211yescharacteristic
44#66577C2211yescharacteristic
45Dic7⋊Dic3C2211yescharacteristic
46Dic7⋊Dic3C2211yescharacteristic
47#66575C2211yescharacteristic
48(C2×D3)⋊Dic7C2211yescharacteristic
49Dic3×Dic7C2211yescharacteristic
50Dic3×Dic7C2211yescharacteristic
51Dic3×Dic7C2211yescharacteristic
52Dic3×Dic7C2211yescharacteristic
53C2×#1159—31no—
54C4×C7×D4—31no—
55D4×Dic7—31no—
56C4×C22⋊D7—31no—
57C4×C22⋊D7—31no—
58C2×Dic7⋊C4—31no—
59C2×Dic7⋊C4D311yescharacteristic, complemented
60D7×C4⋊C4—31no—
61#6450—31no—
62(C22⋊D7)⋊C4—31no—
63(C22⋊D7)⋊C4—31no—
64#6440—31no—
65#6440—31no—
66#6435—31no—
67C4×Dic14—31no—
68#5504—71nomaximal, Hall
69C23×C3×C7C2311yescharacteristic
70C22×D21C2311yescharacteristic
71C22×D3×C7C2311yescharacteristic
72C2×C3×C4×C7—41no—
73C2×C3×C4×C7C2311yescharacteristic
74C2×C3×C4×C7C2311yescharacteristic
75#4268C2×C414yescomplemented
76C2×Dic21C2311yescharacteristic
77C2×Dic21C2311yescharacteristic
78C2×Dic21C2311yescharacteristic
79C4×D21—41no—
80C7×#67C2×C414yescomplemented
81C2×C7×Dic3C2311yescharacteristic
82C2×C7×Dic3C2311yescharacteristic
83C2×C7×Dic3C2311yescharacteristic
84C4×D3×C7—41no—
85C2×C3×Dic7—41no—
86C2×C3×Dic7C2×C414yescomplemented
87C2×C3×Dic7C2311yescharacteristic
88C2×C3×Dic7C2311yescharacteristic
89C2×C3×Dic7C2311yescharacteristic
90C2×C3×Dic7C2311yescharacteristic
91#4248C2×C414yescomplemented
92#4247C2×C414yescomplemented
93D21⋊C4—41no—
94D21⋊C4C2×C414yescomplemented
95D3×Dic7—41no—
96D3×Dic7C2×C414yescomplemented
97C2×C7×D4—31no—
98C22×C4×C7—31no—
99C22×C4×C7C2×D311yescharacteristic
100C2×C22⋊D7—31no—
101C2×C22⋊D7—31no—
102C22×Dic7—31no—
103C22×Dic7—31no—
104C22×Dic7C2×D311yescharacteristic
105C22×Dic7C2×D311yescharacteristic
106#1159—38no—
107C2×C4×D7—31no—
108C2×C4×D7—31no—
109C2×C4×D7—31no—
110C2×Dic14—31no—
111C7×C4⋊C4—31no—
112C7×C22⋊C4—31no—
113C7×C22⋊C4—31no—
114C42×C7—31no—
115C22⋊Dic7—31no—
116C22⋊Dic7—31no—
117(C2×D7)⋊C4—31no—
118(C2×D7)⋊C4—31no—
119C4⋊Dic7—31no—
120Dic7⋊C4—31no—
121Dic7⋊C4—31no—
122Dic7⋊C4—31no—
123Dic7⋊C4—31no—
124Dic7⋊C4C2×D311yescharacteristic
125Dic7⋊C4C2×D311yescharacteristic
126Dic7⋊C4C2×D311yescharacteristic
127Dic7⋊C4C2×D311yescharacteristic
128C4×Dic7—31no—
129C4×Dic7—31no—
130C4×Dic7—31no—
131C4×Dic7—31no—
132C4×Dic7—31no—
133C2×#235—71no—
134C2×C3×C4⋊C4—71no—
135C4×#67—71no—
136C4×#67—71no—
137C4×#67—71no—
138C4×#67D711yescharacteristic, complemented
139#926—71no—
140#893—71no—
141#893—71no—
142#892—71no—
143#892—71no—
144D3×C4⋊C4—71no—
145D3×C4⋊C4—71no—
146#887—71no—
147#887—71no—
148C22×C3×C7—21no—
149C22×C3×C7—21no—
150C22×C3×C7C22×C412yes—
151C22×C3×C7C2411yescharacteristic
152C2×D21—21no—
153C2×D21—21no—
154C2×D21C22×C412yes—
155C2×D3×C7—21no—
156C2×D3×C7—21no—
157C2×D3×C7C22×C412yes—
158C3×C4×C7—21no—
159C3×C4×C7—21no—
160Dic21—21no—
161Dic21—21no—
162Dic21C22×C412yes—
163C3×Dic7—21no—
164C3×Dic7—21no—
165C3×Dic7C22×C412yes—
166C3×Dic7C22×C412yes—
167C7×Dic3—21no—
168C7×Dic3—21no—
169C7×Dic3C22×C412yes—
170#520—211noSylow
171C23×C7—31no—
172C23×C7C22×D311yescharacteristic
173C22×D7—31no—
174C7×D4—34no—
175C2×C4×C7—31no—
176C2×C4×C7—31no—
177C2×C4×C7—31no—
178C2×C4×C7—41no—
179C2×C4×C7—121no—
180C2×C4×C7C22×D311yescharacteristic
181C2×C4×C7C22×D311yescharacteristic
182C22⋊D7—34no—
183C22⋊D7—34no—
184C2×Dic7—31no—
185C2×Dic7—34no—
186C2×Dic7—31no—
187C2×Dic7—31no—
188C2×Dic7—41no—
189C2×Dic7—121no—
190C2×Dic7C4×D314yescomplemented
191C2×Dic7C22×D311yescharacteristic
192C2×Dic7C22×D311yescharacteristic
193C2×Dic7C22×D311yescharacteristic
194C2×Dic7C22×D311yescharacteristic
195C4×D7—34no—
196C4×D7—121no—
197C4×D7—121no—
198Dic14—34no—
199C22×C3×C4—71no—
200C22×C3×C4—71no—
201C22×C3×C4C2×D711yescharacteristic
202C2×#67—71no—
203C2×#67C2×D711yescharacteristic
204#235—78no—
205C2×D12—71no—
206C2×C4×D3—71no—
207C2×C4×D3—71no—
208C2×C4×D3—71no—
209C2×C4×D3—71no—
210C2×C4×D3—71no—
211C2×C4×D3C2×D711yescharacteristic
212C2×Dic6—71no—
213C3×C4⋊C4—71no—
214C3×C4⋊C4—71no—
215C3×C4⋊C4—71no—
216C3×C4⋊C4—71no—
217#217—71no—
218#217C2×D711yescharacteristic
219(C2×D3)⋊C4—71no—
220(C2×D3)⋊C4—71no—
221(C2×D3)⋊C4—71no—
222(C2×D3)⋊C4C2×D711yescharacteristic
223C4⋊Dic3—71no—
224C4⋊Dic3—71no—
225Dic3⋊C4—71no—
226Dic3⋊C4—71no—
227Dic3⋊C4—71no—
228Dic3⋊C4C2×D711yescharacteristic
229C4×Dic3—71no—
230C4×Dic3—71no—
231C4×Dic3—71no—
232C4×Dic3—71no—
233C4×Dic3—71no—
234C4×Dic3C2×D711yescharacteristic
235C2×C3×C7—22no—
236C2×C3×C7C23×C411yescharacteristic
237C2×C3×C7H(5,𝔽2)11yescharacteristic
238C2×C3×C72−1+411yescharacteristic
239D21—22no—
240D3×C7—22no—
241C2×#41—211no—
242C4×Q8—211no—
243C4×Q8—211no—
244C4×D4—31no—
245C4×D4—211no—
246C4×D4—211no—
247C4×D4—211no—
248C4×D4—211no—
249C4×D4—211no—
250#117—211no—
251#117—211no—
252#117—211no—
253C2×C4⋊C4—71no—
254C2×C4⋊C4—211no—
255C2×C4⋊C4—211no—
256C22×C7—21no—
257C22×C7—21no—
258C22×C7—32no—
259C22×C7—61no—
260C22×C7—61no—
261C22×C7C2×C4×D312yes—
262C22×C7C23×D311yescharacteristic
263C2×D7—32no—
264C2×D7—61no—
265C2×D7—61no—
266C4×C7—21no—
267C4×C7—21no—
268C4×C7—32no—
269C4×C7—61no—
270C4×C7—61no—
271Dic7—21no—
272Dic7—21no—
273Dic7—32no—
274Dic7—61no—
275Dic7—61no—
276Dic7C2×C4×D312yes—
277Dic7C2×C4×D312yes—
278C23×C3C22×D711yescharacteristic
279C22×D3—71no—
280C22×D3C22×D711yescharacteristic
281C2×C3×C4—41no—
282C2×C3×C4—74no—
283C2×C3×C4—71no—
284C2×C3×C4—71no—
285C2×C3×C4—71no—
286C2×C3×C4—71no—
287C2×C3×C4—281no—
288C2×C3×C4C22×D711yescharacteristic
289C2×C3×C4C22×D711yescharacteristic
290#67—74no—
291#67C4×D714yescomplemented
292C2×Dic3—71no—
293C2×Dic3—71no—
294C2×Dic3—71no—
295C2×Dic3C22×D711yescharacteristic
296C2×Dic3C22×D711yescharacteristic
297C2×Dic3C22×D711yescharacteristic
298D12—74no—
299C4×D3—41no—
300C4×D3—74no—
301C4×D3—74no—
302C4×D3—281no—
303C4×D3—281no—
304C4×D3—281no—
305Dic6—74no—
306C3×C7#52011yescharacteristic, complemented, Hall
307#41—218no—
308C2×Q8—211no—
309C2×D4—31no—
310C2×D4—211no—
311C2×D4—211no—
312C22×C4—31no—
313C22×C4—71no—
314C22×C4—71no—
315C22×C4—211no—
316C22×C4—211no—
317C22×C4—211no—
318C22×C4—211no—
319C22×C4—211no—
320C22×C4D3×D711yescharacteristic
321C4⋊C4—31no—
322C4⋊C4—71no—
323C4⋊C4—71no—
324C4⋊C4—71no—
325C4⋊C4—71no—
326C4⋊C4—211no—
327C4⋊C4—211no—
328C4⋊C4—211no—
329C4⋊C4—211no—
330C4⋊C4—211no—
331C22⋊C4—31no—
332C22⋊C4—31no—
333C22⋊C4—211no—
334C22⋊C4—211no—
335C22⋊C4—211no—
336C22⋊C4—211no—
337C42—31no—
338C42—211no—
339C42—211no—
340C42—211no—
341C42—211no—
342C42—211no—
343C2×C7—22no—
344C2×C7—62no—
345C2×C7C22×C4×D311yescharacteristic
346C2×C7#100411yescharacteristic
347C2×C7#100711yescharacteristic
348D7—62no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3C2×C4×D712yes—
352C22×C3C23×D711yescharacteristic
353C2×D3—21no—
354C2×D3—21no—
355C2×D3—72no—
356C2×D3—141no—
357C2×D3—141no—
358C2×D3C2×C4×D712yes—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—72no—
362C3×C4—72no—
363C3×C4—141no—
364C3×C4—141no—
365Dic3—21no—
366Dic3—21no—
367Dic3—72no—
368Dic3—141no—
369Dic3—141no—
370Dic3C2×C4×D712yes—
371C23—31no—
372C23—211no—
373C23C2×D3×D711yescharacteristic
374Q8—214no—
375D4—34no—
376D4—214no—
377D4—214no—
378C2×C4—31no—
379C2×C4—31no—
380C2×C4—31no—
381C2×C4—41no—
382C2×C4—74no—
383C2×C4—71no—
384C2×C4—71no—
385C2×C4—71no—
386C2×C4—71no—
387C2×C4—121no—
388C2×C4—214no—
389C2×C4—214no—
390C2×C4—211no—
391C2×C4—211no—
392C2×C4—211no—
393C2×C4—281no—
394C2×C4—841no—
395C2×C4—841no—
396C2×C4—841no—
397C2×C4C2×D3×D711yescharacteristic
398C2×C4C2×D3×D711yescharacteristic
399C7#550411yescharacteristic, complemented, Sylow
400C2×C3—22no—
401C2×C3C22×C4×D711yescharacteristic
402C2×C3#654811yescharacteristic
403C2×C3#655411yescharacteristic
404D3—22no—
405D3—142no—
406C22—21no—
407C22—21no—
408C22—32no—
409C22—61no—
410C22—61no—
411C22—212no—
412C22—421no—
413C22—421no—
414C22C4×D3×D712yes—
415C22C22×D3×D711yescharacteristic
416C4—21no—
417C4—21no—
418C4—32no—
419C4—61no—
420C4—61no—
421C4—72no—
422C4—72no—
423C4—141no—
424C4—141no—
425C4—212no—
426C4—421no—
427C4—421no—
428C3#9023711yescharacteristic, complemented, Sylow
429C2—22no—
430C2—62no—
431C2—422no—
432C2#1062155111yescharacteristic
433C2C2×C4×D3×D711yescharacteristic
434C2#1062159611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutatorC2×C3×C7C23×C4
FittingC22×C3×C4×C7C22
socle, cosocleC22×C3×C7C24
prime radicalC2×#66686C2
hypercenterC22×C4D3×D7
hypocenterC3×C7#520
LCSG ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C4×#4268C2semidirect
3. C4×C7×#67C2semidirect
4. C2×C3×Dic7⋊C4C2semidirect
5. #10621114C2semidirect
6. #67×Dic7C2semidirect
7. #10621090C2semidirect
8. #10621008C2semidirect
9. #10620968C2semidirect
10. #10620966C2semidirect
11. #10620965C2semidirect
12. #10620962C2semidirect
13. D3×Dic7⋊C4C2semidirect
14. #10620887C2semidirect
15. #10620886C2semidirect
28. #66686C4semidirect
59. C2×Dic7⋊C4D3semidirect
75. #4268C2×C4semidirect
80. C7×#67C2×C4semidirect
86. C2×C3×Dic7C2×C4semidirect
91. #4248C2×C4semidirect
92. #4247C2×C4semidirect
94. D21⋊C4C2×C4semidirect
96. D3×Dic7C2×C4semidirect
138. C4×#67D7semidirect
190. C2×Dic7C4×D3semidirect
291. #67C4×D7semidirect
306. C3×C7#520semidirect
399. C7#5504semidirect
428. C3#90237semidirect

Maximal subgroups

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

subgroupindex
C2×#666862
C4×#42682
C4×C7×#672
C2×C3×Dic7⋊C42
#106211142
#67×Dic72
#106210902
#106210082
#106209682
#106209662
#106209652
#106209622
D3×Dic7⋊C42
#106208872
#106208862
#902373
#55047