Finite Group Databasebeta

← #13058531

Subgroups — #13058531

Order 1344.

504 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10621367C211yesmaximal, characteristic, complemented
2C7×#886C211yesmaximal, characteristic, complemented
3C3×#6447C211yesmaximal, characteristic, complemented
4#10621139C211yesmaximal, characteristic, complemented
5#10621131C211yesmaximal, characteristic, complemented
6#10621131C211yesmaximal, characteristic, complemented
7#10621129C211yesmaximal, characteristic, complemented
8#10621038C211yesmaximal, characteristic, complemented
9#10621036C211yesmaximal, characteristic, complemented
10#10621027C211yesmaximal, characteristic, complemented
11#10621012C211yesmaximal, characteristic, complemented
12#10621009C211yesmaximal, characteristic, complemented
13#10620923C211yesmaximal, characteristic, complemented
14#10620917C211yesmaximal, characteristic, complemented
15#10620899C211yesmaximal, characteristic, complemented
16#90357—31nomaximal, Hall
17C22×D3×D7C2211yescharacteristic
18C2×#4268C2211yescharacteristic
19C2×#4268C2211yescharacteristic, complemented
20C2×D84C2211yescharacteristic
21C2×C4×D21C2211yescharacteristic, complemented
22C2×C7×#67C2211yescharacteristic
23C22×C7×Dic3C2211yescharacteristic, complemented
24C2×C3×C22⋊D7C2211yescharacteristic
25C2×C3×C22⋊D7C2211yescharacteristic, complemented
26C2×C3×D28C2211yescharacteristic
27C2×C3×C4×D7C2211yescharacteristic, complemented
28C2×#4247C2211yescharacteristic
29C2×#4246C2211yescharacteristic
30C2×#4246C2211yescharacteristic
31C2×#4246C2211yescharacteristic, complemented
32C2×#4245C2211yescharacteristic
33C3×C7×C22⋊C4C2211yescharacteristic, complemented
34#66631C2211yescharacteristic
35#66629C2211yescharacteristic, complemented
36C7×(C2×D3)⋊C4C2211yescharacteristic
37C7×(C2×D3)⋊C4C2211yescharacteristic
38C7×C4⋊Dic3C2211yescharacteristic, complemented
39C7×C4⋊Dic3C2211yescharacteristic, complemented
40C3×(C2×D7)⋊C4C2211yescharacteristic
41C3×Dic7⋊C4C2211yescharacteristic, complemented
42Dic3⋊Dic7C2211yescharacteristic, complemented
43Dic3⋊Dic7C2211yescharacteristic, complemented
44#66575C2211yescharacteristic
45#66575C2211yescharacteristic
46#66575C2211yescharacteristic, complemented
47(C2×D3)⋊Dic7C2211yescharacteristic
48(C2×D7)⋊Dic3C2211yescharacteristic
49(C2×D7)⋊Dic3C2211yescharacteristic
50(C2×D7)⋊Dic3C2211yescharacteristic, complemented
51Dic3×Dic7C2211yescharacteristic, complemented
52C7×#123—31no—
53#6503—31no—
54#6500—31no—
55#6493—31no—
56#6493—31no—
57#6461—31no—
58#6461—31no—
59#6458—31no—
60#6458—31no—
61#6447—31no—
62#6447D311yescharacteristic, complemented
63#6446—31no—
64#6446—31no—
65#6445—31no—
66#6445—31no—
67#5620—71nomaximal, Hall
68C23×C3×C7C2311yescharacteristic
69C22×D21C2311yescharacteristic
70C22×D21C2311yescharacteristic
71C22×D3×C7C2311yescharacteristic
72C22×C3×D7C2311yescharacteristic
73C22×C3×D7C2311yescharacteristic
74C2×D3×D7—41no—
75C2×D3×D7—41no—
76C2×D3×D7—41no—
77C2×C3×C4×C7C2311yescharacteristic
78C2×C3×C4×C7C2311yescharacteristic
79#4268—41no—
80#4268—41no—
81C2×Dic21C2311yescharacteristic
82C2×Dic21C2311yescharacteristic
83D84—41no—
84C4×D21—41no—
85C7×#67—41no—
86C2×C7×Dic3—41no—
87C2×C7×Dic3C2311yescharacteristic
88C2×C7×Dic3C2311yescharacteristic
89C2×C7×Dic3C2311yescharacteristic
90C3×C22⋊D7—41no—
91C3×C22⋊D7—41no—
92C2×C3×Dic7C2311yescharacteristic
93C2×C3×Dic7C2311yescharacteristic
94C3×D28—41no—
95C3×C4×D7—41no—
96#4247—41no—
97#4246—41no—
98#4246—41no—
99#4246—41no—
100#4245—41no—
101C23×D7—31no—
102C2×C7×D4—31no—
103C22×C4×C7—31no—
104C2×C22⋊D7—31no—
105C2×C22⋊D7—31no—
106C2×C22⋊D7—31no—
107C2×C22⋊D7—31no—
108C2×C22⋊D7C2×D311yescharacteristic
109C2×C22⋊D7C2×D311yescharacteristic, complemented
110C2×D28—31no—
111C2×D28—31no—
112C2×D28—31no—
113C2×D28—31no—
114C2×D28C2×D311yescharacteristic
115C2×C4×D7—31no—
116C2×C4×D7C2×D311yescharacteristic, complemented
117C7×C4⋊C4—31no—
118C7×C4⋊C4—31no—
119C7×C22⋊C4—31no—
120C7×C22⋊C4—31no—
121C7×C22⋊C4C2×D311yescharacteristic, complemented
122C22⋊Dic7—31no—
123(C2×D7)⋊C4—31no—
124(C2×D7)⋊C4—31no—
125(C2×D7)⋊C4—31no—
126(C2×D7)⋊C4—31no—
127(C2×D7)⋊C4—31no—
128(C2×D7)⋊C4—31no—
129(C2×D7)⋊C4—31no—
130(C2×D7)⋊C4C2×D311yescharacteristic
131C4⋊Dic7—31no—
132C4⋊Dic7—31no—
133Dic7⋊C4—31no—
134Dic7⋊C4C2×D311yescharacteristic, complemented
135C4×Dic7—31no—
136C3×#121—71no—
137#940—71no—
138#939—71no—
139#939—71no—
140#938—71no—
141#937—71no—
142#937—71no—
143#930—71no—
144#929—71no—
145#898—71no—
146#894—71no—
147#886D711yescharacteristic, complemented
148#884—71no—
149#882—71no—
150#879—71no—
151C22×C3×C7—21no—
152C22×C3×C7—21no—
153C22×C3×C7—21no—
154C22×C3×C7C2411yescharacteristic
155C2×D21—21no—
156C2×D21—21no—
157C2×D21—21no—
158C2×D21—21no—
159C2×D21—21no—
160C2×D21—21no—
161C2×D3×C7—21no—
162C2×D3×C7—21no—
163C2×D3×C7—21no—
164C2×C3×D7—21no—
165C2×C3×D7—21no—
166C2×C3×D7—21no—
167C2×C3×D7—21no—
168C2×C3×D7—21no—
169C2×C3×D7—21no—
170D3×D7—44no—
171C3×C4×C7—21no—
172C3×C4×C7—21no—
173Dic21—21no—
174Dic21—21no—
175C3×Dic7—21no—
176C3×Dic7—21no—
177C7×Dic3—21no—
178C7×Dic3—21no—
179C7×Dic3—21no—
180#560—211noSylow
181C23×C7—31no—
182C23×C7C22×D311yescharacteristic
183C22×D7—31no—
184C22×D7—31no—
185C22×D7—121no—
186C22×D7—121no—
187C22×D7—121no—
188C22×D7C22×D311yescharacteristic
189C22×D7C22×D311yescharacteristic
190C7×D4—121no—
191C2×C4×C7—31no—
192C2×C4×C7—31no—
193C2×C4×C7—31no—
194C2×C4×C7—121no—
195C2×C4×C7C22×D311yescharacteristic
196C2×C4×C7C22×D311yescharacteristic
197C22⋊D7—41no—
198C22⋊D7—41no—
199C22⋊D7—121no—
200C22⋊D7—121no—
201C22⋊D7—121no—
202C22⋊D7—121no—
203C2×Dic7—31no—
204C2×Dic7—31no—
205C2×Dic7C22×D311yescharacteristic
206C2×Dic7C22×D311yescharacteristic
207D28—41no—
208D28—121no—
209D28—121no—
210D28—121no—
211D28—121no—
212C4×D7—41no—
213C4×D7—121no—
214C23×D3—71no—
215C2×C3×D4—71no—
216C2×C3×D4—71no—
217C2×C3×D4—71no—
218C22×C3×C4—71no—
219C2×#67—71no—
220C2×#67—71no—
221C2×#67—71no—
222C2×#67—71no—
223C2×#67—71no—
224C2×#67—71no—
225C2×#67C2×D711yescharacteristic
226C22×Dic3C2×D711yescharacteristic, complemented
227C2×D12—71no—
228C2×D12—71no—
229C2×C4×D3—71no—
230C3×C4⋊C4—71no—
231C3×C22⋊C4—71no—
232C3×C22⋊C4C2×D711yescharacteristic, complemented
233#217—71no—
234#217—71no—
235#217—71no—
236(C2×D3)⋊C4—71no—
237(C2×D3)⋊C4—71no—
238(C2×D3)⋊C4—71no—
239(C2×D3)⋊C4—71no—
240(C2×D3)⋊C4—71no—
241(C2×D3)⋊C4C2×D711yescharacteristic
242(C2×D3)⋊C4C2×D711yescharacteristic
243C4⋊Dic3C2×D711yescharacteristic, complemented
244C4⋊Dic3C2×D711yescharacteristic, complemented
245Dic3⋊C4—71no—
246Dic3⋊C4—71no—
247Dic3⋊C4—71no—
248C4×Dic3—71no—
249C2×C3×C7—41no—
250C2×C3×C7H(5,𝔽2)11yescharacteristic
251C2×C3×C7H(5,𝔽2)11yescharacteristic
252C2×C3×C7H(5,𝔽2)11yescharacteristic
253D21—41no—
254D21—41no—
255C3×D7—41no—
256C3×D7—41no—
257D3×C7—41no—
258#127—211no—
259#126—211no—
260#126—211no—
261#123—31no—
262#123—211no—
263#123—211no—
264#121—71no—
265#121—211no—
266#121—211no—
267#121—211no—
268#121—211no—
269#121—211no—
270#120—211no—
271#120—211no—
272#120—211no—
273C22×C7—21no—
274C22×C7—21no—
275C22×C7—21no—
276C22×C7—61no—
277C22×C7—61no—
278C22×C7—61no—
279C22×C7C23×D311yescharacteristic
280C2×D7—21no—
281C2×D7—21no—
282C2×D7—21no—
283C2×D7—21no—
284C2×D7—21no—
285C2×D7—21no—
286C2×D7—61no—
287C2×D7—61no—
288C2×D7—61no—
289C2×D7—61no—
290C2×D7—61no—
291C2×D7—61no—
292C2×D7—124no—
293C4×C7—21no—
294C4×C7—21no—
295C4×C7—61no—
296C4×C7—61no—
297C4×C7—61no—
298Dic7—21no—
299Dic7—21no—
300Dic7—61no—
301Dic7—61no—
302C23×C3—71no—
303C23×C3—71no—
304C23×C3C22×D711yescharacteristic
305C22×D3—71no—
306C22×D3—71no—
307C22×D3—281no—
308C22×D3—281no—
309C22×D3—281no—
310C22×D3C22×D711yescharacteristic
311C3×D4—281no—
312C3×D4—281no—
313C3×D4—281no—
314C2×C3×C4—71no—
315C2×C3×C4—71no—
316C2×C3×C4—281no—
317C2×C3×C4C22×D711yescharacteristic
318C2×C3×C4C22×D711yescharacteristic
319#67—41no—
320#67—281no—
321#67—281no—
322#67—281no—
323#67—281no—
324#67—281no—
325#67—281no—
326C2×Dic3—41no—
327C2×Dic3—71no—
328C2×Dic3—71no—
329C2×Dic3C22×D711yescharacteristic
330C2×Dic3C22×D711yescharacteristic
331C2×Dic3C22×D711yescharacteristic
332D12—281no—
333D12—281no—
334C4×D3—281no—
335C3×C7#56011yescharacteristic, complemented, Hall
336C24—211no—
337C2×D4—31no—
338C2×D4—71no—
339C2×D4—71no—
340C2×D4—71no—
341C2×D4—211no—
342C2×D4—211no—
343C2×D4—211no—
344C2×D4—211no—
345C2×D4—211no—
346C2×D4—211no—
347C2×D4—211no—
348C2×D4—211no—
349C22×C4—31no—
350C22×C4—71no—
351C22×C4—211no—
352C4⋊C4—31no—
353C4⋊C4—31no—
354C4⋊C4—71no—
355C4⋊C4—211no—
356C4⋊C4—211no—
357C4⋊C4—211no—
358C22⋊C4—31no—
359C22⋊C4—31no—
360C22⋊C4—71no—
361C22⋊C4—211no—
362C22⋊C4—211no—
363C22⋊C4—211no—
364C22⋊C4—211no—
365C22⋊C4—211no—
366C22⋊C4—211no—
367C22⋊C4—211no—
368C22⋊C4—211no—
369C22⋊C4D3×D711yescharacteristic, complemented
370C42—211no—
371C2×C7—41no—
372C2×C7—121no—
373C2×C7#100411yescharacteristic
374C2×C7#100411yescharacteristic
375C2×C7#100911yescharacteristic
376D7—41no—
377D7—41no—
378D7—121no—
379D7—121no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—141no—
384C22×C3—141no—
385C22×C3—141no—
386C22×C3—141no—
387C22×C3—141no—
388C22×C3—141no—
389C22×C3C23×D711yescharacteristic
390C2×D3—21no—
391C2×D3—21no—
392C2×D3—21no—
393C2×D3—141no—
394C2×D3—141no—
395C2×D3—141no—
396C2×D3—141no—
397C2×D3—141no—
398C2×D3—141no—
399C2×D3—284no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—141no—
403C3×C4—141no—
404Dic3—21no—
405Dic3—21no—
406Dic3—21no—
407Dic3—141no—
408Dic3—141no—
409C23—31no—
410C23—71no—
411C23—71no—
412C23—211no—
413C23—211no—
414C23—841no—
415C23—841no—
416C23—841no—
417C23C2×D3×D711yescharacteristic
418D4—121no—
419D4—281no—
420D4—281no—
421D4—281no—
422D4—841no—
423D4—841no—
424D4—841no—
425D4—841no—
426D4—841no—
427D4—841no—
428D4—841no—
429D4—841no—
430C2×C4—31no—
431C2×C4—31no—
432C2×C4—31no—
433C2×C4—71no—
434C2×C4—71no—
435C2×C4—121no—
436C2×C4—211no—
437C2×C4—211no—
438C2×C4—281no—
439C2×C4—841no—
440C2×C4C2×D3×D711yescharacteristic
441C2×C4C2×D3×D711yescharacteristic
442C7#562011yescharacteristic, complemented, Sylow
443C2×C3—41no—
444C2×C3—281no—
445C2×C3—281no—
446C2×C3#654811yescharacteristic
447C2×C3#655311yescharacteristic
448C2×C3#655311yescharacteristic
449D3—41no—
450D3—281no—
451D3—281no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—61no—
456C22—61no—
457C22—61no—
458C22—141no—
459C22—141no—
460C22—141no—
461C22—141no—
462C22—141no—
463C22—141no—
464C22—421no—
465C22—421no—
466C22—421no—
467C22—421no—
468C22—421no—
469C22—421no—
470C22—844no—
471C22C22×D3×D711yescharacteristic
472C4—21no—
473C4—21no—
474C4—61no—
475C4—61no—
476C4—61no—
477C4—141no—
478C4—141no—
479C4—421no—
480C4—421no—
481C3#9035711yescharacteristic, complemented, Sylow
482C2—41no—
483C2—121no—
484C2—281no—
485C2—281no—
486C2—841no—
487C2—841no—
488C2#1062156511yescharacteristic
489C2#1062157311yescharacteristic
490C2#1062157311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×C22⋊C4C22
hypercenterC22⋊C4D3×D7
hypocenterC3×C7#560
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. #10621367C2semidirect
2. C7×#886C2semidirect
3. C3×#6447C2semidirect
4. #10621139C2semidirect
5. #10621131C2semidirect
6. #10621131C2semidirect
7. #10621129C2semidirect
8. #10621038C2semidirect
9. #10621036C2semidirect
10. #10621027C2semidirect
11. #10621012C2semidirect
12. #10621009C2semidirect
13. #10620923C2semidirect
14. #10620917C2semidirect
15. #10620899C2semidirect
19. C2×#4268C22semidirect
21. C2×C4×D21C22semidirect
23. C22×C7×Dic3C22semidirect
25. C2×C3×C22⋊D7C22semidirect
27. C2×C3×C4×D7C22semidirect
31. C2×#4246C22semidirect
33. C3×C7×C22⋊C4C22semidirect
35. #66629C22semidirect
38. C7×C4⋊Dic3C22semidirect
39. C7×C4⋊Dic3C22semidirect
41. C3×Dic7⋊C4C22semidirect
42. Dic3⋊Dic7C22semidirect
43. Dic3⋊Dic7C22semidirect
46. #66575C22semidirect
50. (C2×D7)⋊Dic3C22semidirect
51. Dic3×Dic7C22semidirect
62. #6447D3semidirect
109. C2×C22⋊D7C2×D3semidirect
116. C2×C4×D7C2×D3semidirect
121. C7×C22⋊C4C2×D3semidirect
134. Dic7⋊C4C2×D3semidirect
147. #886D7semidirect
226. C22×Dic3C2×D7semidirect
232. C3×C22⋊C4C2×D7semidirect
243. C4⋊Dic3C2×D7semidirect
244. C4⋊Dic3C2×D7semidirect
335. C3×C7#560semidirect
369. C22⋊C4D3×D7semidirect
442. C7#5620semidirect
481. C3#90357semidirect

Maximal subgroups

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

subgroupindex
#106213672
C7×#8862
C3×#64472
#106211392
#106211312
#106211292
#106210382
#106210362
#106210272
#106210122
#106210092
#106209232
#106209172
#106208992
#903573
#56207