Finite Group Databasebeta

← #13058562

Subgroups — #13058562

Order 1344.

588 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66670C211yesmaximal, characteristic, complemented
2C2×#66669C211yesmaximal, characteristic, complemented
3#10621379C211yesmaximal, characteristic, complemented
4C7×#896C211yesmaximal, characteristic, complemented
5C3×#6458C211yesmaximal, characteristic, complemented
6#10621023C211yesmaximal, characteristic, complemented
7#10621016C211yesmaximal, characteristic, complemented
8#10621010C211yesmaximal, characteristic, complemented
9#10620993C211yesmaximal, characteristic, complemented
10#10620983C211yesmaximal, characteristic, complemented
11#10620971C211yesmaximal, characteristic, complemented
12#10620971C211yesmaximal, characteristic, complemented
13#10620970C211yesmaximal, characteristic, complemented
14#10620970C211yesmaximal, characteristic, complemented
15D7×Dic3⋊C4C211yesmaximal, characteristic, complemented
16#90320—31nomaximal, Hall
17C2×C4×D21C2211yescharacteristic
18C2×Dic42C2211yescharacteristic
19C2×C4×D3×C7C2211yescharacteristic
20C2×C7×Dic6C2211yescharacteristic
21C2×C3×D28C2211yescharacteristic
22C2×C3×D28C2211yescharacteristic
23C2×C3×D28C2211yescharacteristic
24C2×C3×C4×D7C2211yescharacteristic
25C2×#4247C2211yescharacteristic
26C2×#4246C2211yescharacteristic
27C2×#4246C2211yescharacteristic
28C2×#4246C2211yescharacteristic
29C2×#4245C2211yescharacteristic
30C2×#4245C2211yescharacteristic
31C2×#4245C2211yescharacteristic
32C2×Dic3×D7C2211yescharacteristic
33C2×Dic3×D7C2211yescharacteristic
34C2×Dic3×D7C2211yescharacteristic
35C2×Dic3×D7C2211yescharacteristic
36#66670—24no—
37#66669—24no—
38C3×C7×C4⋊C4C2211yescharacteristic
39#66631C2211yescharacteristic
40#66631C2211yescharacteristic
41#66629C2211yescharacteristic
42#66629C2211yescharacteristic
43C7×(C2×D3)⋊C4C2211yescharacteristic
44C7×(C2×D3)⋊C4C2211yescharacteristic
45C7×Dic3⋊C4C2211yescharacteristic
46C7×Dic3⋊C4C2211yescharacteristic
47C3×(C2×D7)⋊C4C2211yescharacteristic
48C3×(C2×D7)⋊C4C2211yescharacteristic
49Dic3⋊Dic7C2211yescharacteristic
50#66577C2211yescharacteristic
51Dic7⋊Dic3C2211yescharacteristic
52(C2×D7)⋊Dic3C2211yescharacteristic
53(C2×D7)⋊Dic3C2211yescharacteristic
54C2×#1161—31no—
55C2×#1157—31no—
56C7×C22⋊Q8—31no—
57#6509—31no—
58#6493—31no—
59#6459—31no—
60#6459—31no—
61#6458—31no—
62#6458—31no—
63#6458D311yescharacteristic, complemented
64D7×C4⋊C4—31no—
65#6447—31no—
66#6447—31no—
67#6447—31no—
68#6447—31no—
69#5597—71nomaximal, Hall
70C22×D21C2311yescharacteristic
71C22×D3×C7C2311yescharacteristic
72C22×C3×D7C2311yescharacteristic
73C22×C3×D7C2311yescharacteristic
74C22×C3×D7C2311yescharacteristic
75C2×C3×C4×C7C2311yescharacteristic
76C2×C3×C4×C7C2311yescharacteristic
77C2×C3×C4×C7C2311yescharacteristic
78C2×Dic21C2311yescharacteristic
79C2×Dic21C2311yescharacteristic
80C2×Dic21C2311yescharacteristic
81C4×D21—22no—
82Dic42—22no—
83C2×C7×Dic3C2311yescharacteristic
84C2×C7×Dic3C2311yescharacteristic
85C2×C7×Dic3C2311yescharacteristic
86C4×D3×C7—22no—
87C7×Dic6—22no—
88C2×C3×Dic7C2311yescharacteristic
89C3×D28—22no—
90C3×D28—22no—
91C3×D28—41no—
92C3×C4×D7—41no—
93#4247—41no—
94#4246—22no—
95#4246—22no—
96#4246—41no—
97#4245—22no—
98#4245—22no—
99#4245—41no—
100Dic3×D7—22no—
101Dic3×D7—22no—
102Dic3×D7—41no—
103Dic3×D7D414yescomplemented
104C2×C7×Q8—31no—
105C22×C4×C7—31no—
106C2×C22⋊D7—31no—
107C2×C22⋊D7—31no—
108C2×C22⋊D7—31no—
109C2×C22⋊D7—31no—
110#1161—64no—
111#1157—64no—
112C2×D28—31no—
113C2×D28—31no—
114C2×D28—31no—
115C2×D28C2×D311yescharacteristic
116C2×D28C2×D311yescharacteristic
117C2×D28C2×D311yescharacteristic
118C2×C4×D7—31no—
119C2×C4×D7—31no—
120C2×C4×D7—31no—
121C2×C4×D7—31no—
122C2×C4×D7—31no—
123C2×C4×D7C2×D311yescharacteristic
124C2×Dic14—31no—
125C7×C4⋊C4—31no—
126C7×C4⋊C4—31no—
127C7×C4⋊C4C2×D311yescharacteristic
128C7×C22⋊C4—31no—
129C7×C22⋊C4—31no—
130(C2×D7)⋊C4—31no—
131(C2×D7)⋊C4—31no—
132(C2×D7)⋊C4—31no—
133(C2×D7)⋊C4—31no—
134(C2×D7)⋊C4C2×D311yescharacteristic
135(C2×D7)⋊C4C2×D311yescharacteristic
136C4⋊Dic7—31no—
137Dic7⋊C4—31no—
138Dic7⋊C4—31no—
139Dic7⋊C4—31no—
140Dic7⋊C4—31no—
141C2×#237—71no—
142C2×#237—71no—
143C3×#121—71no—
144#939—71no—
145#939—71no—
146#939—71no—
147#939—71no—
148#930—71no—
149C2×Dic3⋊C4—71no—
150#896—71no—
151#896D711yescharacteristic, complemented
152#884—71no—
153#884—71no—
154#878—71no—
155#878—71no—
156C22×C3×C7C2411yescharacteristic
157C2×D21—21no—
158C2×D21—21no—
159C2×D21—21no—
160C2×D3×C7—21no—
161C2×D3×C7—21no—
162C2×D3×C7—21no—
163C2×C3×D7—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—
170C2×C3×D7—21no—
171C2×C3×D7C2×D412yes—
172C3×C4×C7—21no—
173C3×C4×C7—21no—
174C3×C4×C7—21no—
175Dic21—21no—
176Dic21—21no—
177Dic21C2×D412yes—
178C3×Dic7—21no—
179C7×Dic3—21no—
180C7×Dic3—21no—
181C7×Dic3C2×D412yes—
182#537—211noSylow
183C23×C7—31no—
184C22×D7—31no—
185C22×D7C22×D311yescharacteristic
186C22×D7C22×D311yescharacteristic
187C22×D7C22×D311yescharacteristic
188C7×Q8—62no—
189C2×C4×C7—31no—
190C2×C4×C7—31no—
191C2×C4×C7—31no—
192C2×C4×C7—62no—
193C2×C4×C7C22×D311yescharacteristic
194C2×C4×C7C22×D311yescharacteristic
195C2×C4×C7C22×D311yescharacteristic
196C22⋊D7—62no—
197C22⋊D7—62no—
198C22⋊D7—121no—
199C22⋊D7—121no—
200C2×Dic7—31no—
201C2×Dic7—31no—
202C2×Dic7—31no—
203C2×Dic7C22×D311yescharacteristic
204D28—22no—
205D28—22no—
206D28—41no—
207D28—62no—
208D28—62no—
209D28—121no—
210C4×D7—34no—
211C4×D7—41no—
212C4×D7—62no—
213C4×D7—62no—
214C4×D7—62no—
215C4×D7—121no—
216Dic14—62no—
217C2×C3×D4—71no—
218C2×C3×D4—71no—
219C2×C3×D4—71no—
220C22×C3×C4—71no—
221C2×#67—71no—
222C2×#67—71no—
223C2×#67—71no—
224C2×#67—71no—
225C2×#67—71no—
226C2×#67—71no—
227C22×Dic3—71no—
228C22×Dic3—71no—
229C22×Dic3—71no—
230C22×Dic3—71no—
231#237—144no—
232#237—144no—
233C2×D12—71no—
234C2×C4×D3—71no—
235C2×C4×D3C2×D711yescharacteristic
236C2×Dic6—71no—
237C2×Dic6C2×D711yescharacteristic
238C3×C4⋊C4C2×D711yescharacteristic
239C3×C22⋊C4—71no—
240C3×C22⋊C4—71no—
241#217—71no—
242#217—71no—
243(C2×D3)⋊C4—71no—
244(C2×D3)⋊C4—71no—
245(C2×D3)⋊C4C2×D711yescharacteristic
246(C2×D3)⋊C4C2×D711yescharacteristic
247C4⋊Dic3—71no—
248Dic3⋊C4—71no—
249Dic3⋊C4—71no—
250Dic3⋊C4—71no—
251Dic3⋊C4—71no—
252Dic3⋊C4C2×D711yescharacteristic
253Dic3⋊C4C2×D711yescharacteristic
254C2×C3×C7C22×D411yescharacteristic
255C2×C3×C7H(5,𝔽2)11yescharacteristic
256C2×C3×C72−1+411yescharacteristic
257D21—41no—
258C3×D7—22no—
259C3×D7—41no—
260C3×D7—41no—
261D3×C7—41no—
262C2×#41—211no—
263C2×#41—211no—
264C22⋊Q8—31no—
265C22⋊Q8—211no—
266C22⋊Q8—211no—
267C22⋊Q8—211no—
268#121—71no—
269#121—211no—
270#121—211no—
271#121—211no—
272#121—211no—
273#121—211no—
274#121—211no—
275#121—211no—
276C2×C4⋊C4—211no—
277C22×C7—61no—
278C22×C7—61no—
279C22×C7—61no—
280C22×C7C23×D311yescharacteristic
281C2×D7—21no—
282C2×D7—21no—
283C2×D7—21no—
284C2×D7—21no—
285C2×D7—21no—
286C2×D7—21no—
287C2×D7—21no—
288C2×D7—21no—
289C2×D7—61no—
290C2×D7—61no—
291C2×D7—61no—
292C2×D7D3×D412yes—
293C4×C7—21no—
294C4×C7—21no—
295C4×C7—21no—
296C4×C7—32no—
297C4×C7—61no—
298C4×C7—61no—
299Dic7—21no—
300Dic7—32no—
301Dic7—61no—
302Dic7—61no—
303C23×C3—71no—
304C23×C3—71no—
305C23×C3—71no—
306C22×D3—71no—
307C22×D3C22×D711yescharacteristic
308C3×D4—142no—
309C3×D4—142no—
310C3×D4—281no—
311C2×C3×C4—71no—
312C2×C3×C4—281no—
313C2×C3×C4C22×D711yescharacteristic
314C2×C3×C4C22×D711yescharacteristic
315C2×C3×C4C22×D711yescharacteristic
316#67—142no—
317#67—142no—
318#67—142no—
319#67—142no—
320#67—281no—
321#67—281no—
322C2×Dic3—71no—
323C2×Dic3—74no—
324C2×Dic3—71no—
325C2×Dic3—71no—
326C2×Dic3—142no—
327C2×Dic3—142no—
328C2×Dic3—281no—
329C2×Dic3C22×D711yescharacteristic
330C2×Dic3C22×D711yescharacteristic
331C2×Dic3C22×D711yescharacteristic
332D12—281no—
333C4×D3—22no—
334C4×D3—142no—
335Dic6—22no—
336Dic6—142no—
337C3×C7#53711yescharacteristic, complemented, Hall
338#41—424no—
339#41—424no—
340C2×Q8—31no—
341C2×Q8—211no—
342C2×D4—71no—
343C2×D4—71no—
344C2×D4—71no—
345C2×D4—211no—
346C2×D4—211no—
347C2×D4—211no—
348C2×D4—211no—
349C2×D4—211no—
350C2×D4—211no—
351C2×D4—211no—
352C22×C4—31no—
353C22×C4—71no—
354C22×C4—211no—
355C22×C4—211no—
356C22×C4—211no—
357C22×C4—211no—
358C22×C4—211no—
359C4⋊C4—31no—
360C4⋊C4—31no—
361C4⋊C4—211no—
362C4⋊C4—211no—
363C4⋊C4—211no—
364C4⋊C4—211no—
365C4⋊C4—211no—
366C4⋊C4D3×D711yescharacteristic
367C22⋊C4—31no—
368C22⋊C4—31no—
369C22⋊C4—71no—
370C22⋊C4—71no—
371C22⋊C4—211no—
372C22⋊C4—211no—
373C22⋊C4—211no—
374C22⋊C4—211no—
375C2×C7—121no—
376C2×C7C2×D3×D411yescharacteristic
377C2×C7#100411yescharacteristic
378C2×C7#101011yescharacteristic
379D7—22no—
380D7—41no—
381D7—41no—
382D7—121no—
383C22×C3—72no—
384C22×C3—141no—
385C22×C3—141no—
386C22×C3—141no—
387C22×C3—141no—
388C22×C3—141no—
389C22×C3—141no—
390C22×C3—141no—
391C22×C3—141no—
392C22×C3C23×D711yescharacteristic
393C2×D3—21no—
394C2×D3—21no—
395C2×D3—21no—
396C2×D3—141no—
397C2×D3—141no—
398C2×D3—141no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—141no—
403Dic3—21no—
404Dic3—21no—
405Dic3—72no—
406Dic3—141no—
407Dic3—141no—
408Dic3D4×D712yes—
409C23—31no—
410C23—71no—
411C23—71no—
412C23—71no—
413C23—211no—
414Q8—62no—
415Q8—422no—
416D4—142no—
417D4—142no—
418D4—281no—
419D4—422no—
420D4—422no—
421D4—422no—
422D4—422no—
423D4—841no—
424D4—841no—
425D4—841no—
426C2×C4—31no—
427C2×C4—31no—
428C2×C4—31no—
429C2×C4—62no—
430C2×C4—71no—
431C2×C4—214no—
432C2×C4—211no—
433C2×C4—211no—
434C2×C4—211no—
435C2×C4—281no—
436C2×C4—422no—
437C2×C4—422no—
438C2×C4—422no—
439C2×C4—841no—
440C2×C4C2×D3×D711yescharacteristic
441C2×C4C2×D3×D711yescharacteristic
442C2×C4C2×D3×D711yescharacteristic
443C7#559711yescharacteristic, complemented, Sylow
444C2×C3—142no—
445C2×C3—281no—
446C2×C3—281no—
447C2×C3C2×D4×D711yescharacteristic
448C2×C3#655111yescharacteristic
449C2×C3#655311yescharacteristic
450D3—41no—
451D3—281no—
452C22—61no—
453C22—61no—
454C22—61no—
455C22—72no—
456C22—141no—
457C22—141no—
458C22—141no—
459C22—141no—
460C22—141no—
461C22—141no—
462C22—141no—
463C22—141no—
464C22—421no—
465C22—421no—
466C22—421no—
467C22C22×D3×D711yescharacteristic
468C4—21no—
469C4—21no—
470C4—21no—
471C4—32no—
472C4—61no—
473C4—61no—
474C4—141no—
475C4—212no—
476C4—421no—
477C4—421no—
478C3#9032011yescharacteristic, complemented, Sylow
479C2—121no—
480C2—142no—
481C2—281no—
482C2—281no—
483C2—841no—
484C2#1062156411yescharacteristic
485C2D3×D4×D711yescharacteristic
486C2#1062157511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×C4⋊C4C22
hypercenterC4⋊C4D3×D7
hypocenterC3×C7#537
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. C2×#66670C2semidirect
2. C2×#66669C2semidirect
3. #10621379C2semidirect
4. C7×#896C2semidirect
5. C3×#6458C2semidirect
6. #10621023C2semidirect
7. #10621016C2semidirect
8. #10621010C2semidirect
9. #10620993C2semidirect
10. #10620983C2semidirect
11. #10620971C2semidirect
12. #10620971C2semidirect
13. #10620970C2semidirect
14. #10620970C2semidirect
15. D7×Dic3⋊C4C2semidirect
63. #6458D3semidirect
103. Dic3×D7D4semidirect
151. #896D7semidirect
337. C3×C7#537semidirect
443. C7#5597semidirect
478. C3#90320semidirect

Maximal subgroups

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

subgroupindex
C2×#666702
C2×#666692
#106213792
C7×#8962
C3×#64582
#106210232
#106210162
#106210102
#106209932
#106209832
#106209712
#106209702
D7×Dic3⋊C42
#903203
#55977