Finite Group Databasebeta

← #13059485

Subgroups — #13059485

Order 1344.

584 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1157C211yesmaximal, characteristic, complemented
2C2×#66684C211yesmaximal, characteristic, complemented
3C2×#66629C211yesmaximal, characteristic, complemented
4C7×#929C211yesmaximal, characteristic, complemented
5#10621133C211yesmaximal, characteristic, complemented
6(C22⋊D7)⋊Dic3C211yesmaximal, characteristic, complemented
7#10621099C211yesmaximal, characteristic, complemented
8#10621009C211yesmaximal, characteristic, complemented
9#10621002C211yesmaximal, characteristic, complemented
10#10620972C211yesmaximal, characteristic, complemented
11#10620970C211yesmaximal, characteristic, complemented
12#10620969C211yesmaximal, characteristic, complemented
13D7×Dic3⋊C4C211yesmaximal, characteristic, complemented
14#10620911C211yesmaximal, characteristic, complemented
15#10620889C211yesmaximal, characteristic, complemented
16#90346—31nomaximal, Hall
17C22×C3×C4×C7C2211yescharacteristic
18C22×Dic21C2211yescharacteristic
19C22×Dic21C2211yescharacteristic
20C2×C7×#67C2211yescharacteristic
21C2×C3×C22⋊D7C2211yescharacteristic
22C2×C3×C22⋊D7C2211yescharacteristic
23C3×#1157—24no—
24C2×C3×D28C2211yescharacteristic
25C2×C3×C4×D7C2211yescharacteristic
26C2×C3×C4×D7C2211yescharacteristic
27C2×C3×Dic14C2211yescharacteristic
28C2×#4248C2211yescharacteristic
29C2×#4245C2211yescharacteristic
30C2×#4245C2211yescharacteristic
31C2×D3×Dic7C2211yescharacteristic
32#66684—24no—
33C2×Dic3×D7C2211yescharacteristic
34C2×Dic3×D7C2211yescharacteristic
35#66629C2211yescharacteristic
36#66629C2211yescharacteristic
37#66629C2211yescharacteristic
38#66629C2211yescharacteristic
39C7×#217C2211yescharacteristic
40C7×(C2×D3)⋊C4C2211yescharacteristic
41C7×(C2×D3)⋊C4C2211yescharacteristic
42C7×Dic3⋊C4C2211yescharacteristic
43C7×Dic3⋊C4C2211yescharacteristic
44Dic3⋊Dic7C2211yescharacteristic
45Dic3⋊Dic7C2211yescharacteristic
46#66577C2211yescharacteristic
47Dic7⋊Dic3C2211yescharacteristic
48(C2×D3)⋊Dic7C2211yescharacteristic
49(C2×D7)⋊Dic3C2211yescharacteristic
50(C2×D7)⋊Dic3C2211yescharacteristic
51(C2×D7)⋊Dic3C2211yescharacteristic
52(C2×D7)⋊Dic3C2211yescharacteristic
53Dic3×Dic7C2211yescharacteristic
54C2×#1159—31no—
55C2×#1157D311yescharacteristic, complemented
56C7×#123—31no—
57#6502—31no—
58C2×Dic7⋊C4—31no—
59#6459—31no—
60#6457—31no—
61D7×C4⋊C4—31no—
62#6451—31no—
63#6449—31no—
64#6447—31no—
65#6446—31no—
66(C22⋊D7)⋊C4—31no—
67(C22⋊D7)⋊C4—31no—
68#6441—31no—
69#5824—71nomaximal, Hall
70C23×C3×C7C2311yescharacteristic
71C22×D3×C7C2311yescharacteristic
72C22×C3×D7C2311yescharacteristic
73C22×C3×D7C2311yescharacteristic
74C2×C3×C4×C7—22no—
75C2×C3×C4×C7C2311yescharacteristic
76C2×C3×C4×C7C2311yescharacteristic
77C2×Dic21—22no—
78C2×Dic21—22no—
79C2×Dic21C2311yescharacteristic
80C2×Dic21C2311yescharacteristic
81C2×Dic21C2311yescharacteristic
82C2×Dic21C2311yescharacteristic
83C7×#67—22no—
84C2×C7×Dic3C2311yescharacteristic
85C2×C7×Dic3C2311yescharacteristic
86C2×C7×Dic3C2311yescharacteristic
87C3×C22⋊D7—22no—
88C3×C22⋊D7D414yescomplemented
89C2×C3×Dic7C2311yescharacteristic
90C2×C3×Dic7C2311yescharacteristic
91C3×D28—22no—
92C3×C4×D7—22no—
93C3×C4×D7—22no—
94C3×Dic14—22no—
95#4248—22no—
96#4245—22no—
97#4245—22no—
98D3×Dic7—22no—
99Dic3×D7—22no—
100Dic3×D7—22no—
101C2×C7×D4—31no—
102C22×C4×C7C2×D311yescharacteristic
103C2×C22⋊D7—31no—
104C2×C22⋊D7—31no—
105C2×C22⋊D7C2×D311yescharacteristic
106C2×C22⋊D7C2×D311yescharacteristic
107C22×Dic7—31no—
108C22×Dic7—31no—
109C22×Dic7—31no—
110#1159—64no—
111#1157—24no—
112C2×D28C2×D311yescharacteristic
113C2×C4×D7—31no—
114C2×C4×D7—31no—
115C2×C4×D7C2×D311yescharacteristic
116C2×C4×D7C2×D311yescharacteristic
117C2×Dic14—31no—
118C2×Dic14C2×D311yescharacteristic
119C7×C4⋊C4—31no—
120C7×C4⋊C4—31no—
121C7×C22⋊C4—31no—
122C7×C22⋊C4—31no—
123C7×C22⋊C4—31no—
124C22⋊Dic7—31no—
125(C2×D7)⋊C4—31no—
126(C2×D7)⋊C4—31no—
127(C2×D7)⋊C4—31no—
128(C2×D7)⋊C4—31no—
129C4⋊Dic7—31no—
130C4⋊Dic7—31no—
131Dic7⋊C4—31no—
132Dic7⋊C4—31no—
133Dic7⋊C4—31no—
134Dic7⋊C4—31no—
135Dic7⋊C4—31no—
136Dic7⋊C4—31no—
137C4×Dic7—31no—
138C2×C3×#41—71no—
139C2×#237—71no—
140#946—71no—
141#944—71no—
142#939—71no—
143#939—71no—
144#935—71no—
145#935—71no—
146D4×Dic3—71no—
147#929—71no—
148#929D711yescharacteristic, complemented
149C4×#67—71no—
150#924—71no—
151C2×Dic3⋊C4—71no—
152C2×Dic3⋊C4—71no—
153C22×C3×C7—21no—
154C22×C3×C7—21no—
155C22×C3×C7C2×D412yes—
156C22×C3×C7C2411yescharacteristic
157C2×D3×C7—21no—
158C2×D3×C7—21no—
159C2×D3×C7—21no—
160C2×C3×D7—21no—
161C2×C3×D7—21no—
162C2×C3×D7—21no—
163C2×C3×D7—21no—
164C2×C3×D7—21no—
165C2×C3×D7C2×D412yes—
166C3×C4×C7—21no—
167C3×C4×C7—21no—
168Dic21—21no—
169Dic21—21no—
170Dic21—21no—
171Dic21#4112yescomplemented
172C3×Dic7—21no—
173C3×Dic7C2×D412yes—
174C7×Dic3—21no—
175C7×Dic3—21no—
176C7×Dic3—21no—
177#547—211noSylow
178C23×C7—31no—
179C23×C7C22×D311yescharacteristic
180C22×D7C22×D311yescharacteristic
181C22×D7C22×D311yescharacteristic
182C7×D4—62no—
183C2×C4×C7—22no—
184C2×C4×C7—31no—
185C2×C4×C7—31no—
186C2×C4×C7—31no—
187C2×C4×C7C22×D311yescharacteristic
188C2×C4×C7C22×D311yescharacteristic
189C22⋊D7—22no—
190C22⋊D7—62no—
191C22⋊D7—62no—
192C22⋊D7#6714yescomplemented
193C2×Dic7—31no—
194C2×Dic7—31no—
195C2×Dic7—31no—
196C2×Dic7—31no—
197C2×Dic7—62no—
198C2×Dic7—62no—
199C2×Dic7—62no—
200C2×Dic7C22×D311yescharacteristic
201C2×Dic7C22×D311yescharacteristic
202D28—22no—
203C4×D7—22no—
204C4×D7—22no—
205C4×D7—62no—
206C4×D7—62no—
207Dic14—22no—
208Dic14—62no—
209C3×#41—144no—
210C2×C3×Q8—71no—
211C2×C3×D4—71no—
212C2×C3×D4—71no—
213C2×C3×D4—71no—
214C22×C3×C4—71no—
215C22×C3×C4—71no—
216C22×C3×C4C2×D711yescharacteristic
217C2×#67—71no—
218C2×#67—71no—
219C2×#67C2×D711yescharacteristic
220C22×Dic3—71no—
221C22×Dic3—71no—
222C22×Dic3—71no—
223C22×Dic3—71no—
224#237—144no—
225C2×C4×D3—71no—
226C2×Dic6—71no—
227#217—71no—
228#217—71no—
229#217—71no—
230#217—71no—
231#217C2×D711yescharacteristic
232(C2×D3)⋊C4—71no—
233(C2×D3)⋊C4C2×D711yescharacteristic
234(C2×D3)⋊C4C2×D711yescharacteristic
235C4⋊Dic3—71no—
236Dic3⋊C4—71no—
237Dic3⋊C4—71no—
238Dic3⋊C4—71no—
239Dic3⋊C4—71no—
240Dic3⋊C4—71no—
241Dic3⋊C4—71no—
242Dic3⋊C4—71no—
243Dic3⋊C4C2×D711yescharacteristic
244Dic3⋊C4C2×D711yescharacteristic
245C4×Dic3—71no—
246C2×C3×C7—22no—
247C2×C3×C7C22×D411yescharacteristic
248C2×C3×C7C2×#4111yescharacteristic
249C2×C3×C72−1+411yescharacteristic
250C3×D7—22no—
251C3×D7—41no—
252D3×C7—41no—
253C2×#41—71no—
254C2×#41—211no—
255C4⋊Q8—211no—
256#123—31no—
257#123—211no—
258#123—211no—
259#123—211no—
260C22⋊Q8—211no—
261C22⋊Q8—211no—
262#121—211no—
263#121—211no—
264C4×D4—211no—
265C4×D4—211no—
266C2×C4⋊C4—211no—
267C2×C4⋊C4—211no—
268C22×C7—21no—
269C22×C7—21no—
270C22×C7—61no—
271C22×C7—61no—
272C22×C7—61no—
273C22×C7C2×#6712yes—
274C22×C7C23×D311yescharacteristic
275C2×D7—21no—
276C2×D7—21no—
277C2×D7—21no—
278C2×D7—21no—
279C2×D7—21no—
280C2×D7C2×#6712yes—
281C4×C7—21no—
282C4×C7—21no—
283C4×C7—61no—
284C4×C7—61no—
285C4×C7—61no—
286Dic7—21no—
287Dic7—32no—
288Dic7—61no—
289Dic7—61no—
290Dic7—61no—
291Dic7C2×#6712yes—
292C23×C3—71no—
293C23×C3—71no—
294C23×C3C22×D711yescharacteristic
295C22×D3C22×D711yescharacteristic
296C3×Q8—142no—
297C3×D4—74no—
298C3×D4—142no—
299C3×D4—142no—
300C2×C3×C4—22no—
301C2×C3×C4—71no—
302C2×C3×C4—71no—
303C2×C3×C4—142no—
304C2×C3×C4—142no—
305C2×C3×C4C22×D711yescharacteristic
306C2×C3×C4C22×D711yescharacteristic
307#67—22no—
308#67—142no—
309#67—142no—
310C2×Dic3—71no—
311C2×Dic3—71no—
312C2×Dic3—71no—
313C2×Dic3—71no—
314C2×Dic3—142no—
315C2×Dic3—142no—
316C2×Dic3—142no—
317C2×Dic3—142no—
318C2×Dic3C22×D711yescharacteristic
319C2×Dic3C22×D711yescharacteristic
320C2×Dic3C22×D711yescharacteristic
321C4×D3—142no—
322Dic6—142no—
323C3×C7#54711yescharacteristic, complemented, Hall
324#41—144no—
325#41—424no—
326C2×Q8—71no—
327C2×Q8—211no—
328C2×D4—31no—
329C2×D4—71no—
330C2×D4—71no—
331C2×D4—71no—
332C2×D4—211no—
333C2×D4—211no—
334C22×C4—71no—
335C22×C4—71no—
336C22×C4—211no—
337C22×C4—211no—
338C22×C4—211no—
339C22×C4—211no—
340C22×C4—211no—
341C22×C4D3×D711yescharacteristic
342C4⋊C4—31no—
343C4⋊C4—31no—
344C4⋊C4—211no—
345C4⋊C4—211no—
346C4⋊C4—211no—
347C4⋊C4—211no—
348C4⋊C4—211no—
349C4⋊C4—211no—
350C4⋊C4—211no—
351C4⋊C4—211no—
352C22⋊C4—31no—
353C22⋊C4—31no—
354C22⋊C4—31no—
355C22⋊C4—211no—
356C22⋊C4—211no—
357C22⋊C4—211no—
358C22⋊C4—211no—
359C22⋊C4—211no—
360C42—211no—
361C2×C7—22no—
362C2×C7—121no—
363C2×C7D3×#4111yescharacteristic
364C2×C7#101011yescharacteristic
365C2×C7C22×#6711yescharacteristic
366D7—22no—
367D7—41no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—72no—
371C22×C3—141no—
372C22×C3—141no—
373C22×C3—141no—
374C22×C3—141no—
375C22×C3—141no—
376C22×C3D4×D712yes—
377C22×C3C23×D711yescharacteristic
378C2×D3—21no—
379C2×D3—21no—
380C2×D3—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—72no—
384C3×C4—141no—
385Dic3—21no—
386Dic3—21no—
387Dic3—21no—
388Dic3—72no—
389Dic3—141no—
390Dic3—141no—
391Dic3—141no—
392C23—31no—
393C23—71no—
394C23—71no—
395C23C2×D3×D711yescharacteristic
396Q8—142no—
397Q8—422no—
398D4—62no—
399D4—74no—
400D4—142no—
401D4—142no—
402D4—422no—
403D4—422no—
404C2×C4—22no—
405C2×C4—31no—
406C2×C4—31no—
407C2×C4—31no—
408C2×C4—71no—
409C2×C4—71no—
410C2×C4—142no—
411C2×C4—142no—
412C2×C4—211no—
413C2×C4—211no—
414C2×C4—211no—
415C2×C4—211no—
416C2×C4—422no—
417C2×C4—422no—
418C2×C4—422no—
419C2×C4—422no—
420C2×C4—422no—
421C2×C4C2×D3×D711yescharacteristic
422C2×C4C2×D3×D711yescharacteristic
423C7#582411yescharacteristic, complemented, Sylow
424C2×C3—22no—
425C2×C3—142no—
426C2×C3—281no—
427C2×C3C2×D4×D711yescharacteristic
428C2×C3D7×#4111yescharacteristic
429C2×C3#655411yescharacteristic
430D3—41no—
431C22—21no—
432C22—21no—
433C22—61no—
434C22—61no—
435C22—61no—
436C22—72no—
437C22—141no—
438C22—141no—
439C22—141no—
440C22—141no—
441C22—141no—
442C22D7×#6712yes—
443C22C22×D3×D711yescharacteristic
444C4—21no—
445C4—21no—
446C4—61no—
447C4—61no—
448C4—61no—
449C4—72no—
450C4—141no—
451C4—212no—
452C4—421no—
453C4—421no—
454C4—421no—
455C3#9034611yescharacteristic, complemented, Sylow
456C2—22no—
457C2—121no—
458C2—142no—
459C2—281no—
460C2#1062154811yescharacteristic
461C2#1062156311yescharacteristic
462C2C2×D7×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC22×C3×C4×C7C22
hypercenterC22×C4D3×D7
hypocenterC3×C7#547
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. C2×C3×#1157C2semidirect
2. C2×#66684C2semidirect
3. C2×#66629C2semidirect
4. C7×#929C2semidirect
5. #10621133C2semidirect
6. (C22⋊D7)⋊Dic3C2semidirect
7. #10621099C2semidirect
8. #10621009C2semidirect
9. #10621002C2semidirect
10. #10620972C2semidirect
11. #10620970C2semidirect
12. #10620969C2semidirect
13. D7×Dic3⋊C4C2semidirect
14. #10620911C2semidirect
15. #10620889C2semidirect
55. C2×#1157D3semidirect
88. C3×C22⋊D7D4semidirect
148. #929D7semidirect
171. Dic21#41semidirect
192. C22⋊D7#67semidirect
323. C3×C7#547semidirect
423. C7#5824semidirect
455. C3#90346semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#11572
C2×#666842
C2×#666292
C7×#9292
#106211332
(C22⋊D7)⋊Dic32
#106210992
#106210092
#106210022
#106209722
#106209702
#106209692
D7×Dic3⋊C42
#106209112
#106208892
#903463
#58247