Finite Group Databasebeta

← #13061749

Subgroups — #13061749

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×#66730C211yesmaximal, characteristic, complemented
2C2×#66728C211yesmaximal, characteristic, complemented
3C3×C7×#123C211yesmaximal, characteristic, complemented
4#10621422C211yesmaximal, characteristic, complemented
5C2×#66629C211yesmaximal, characteristic, complemented
6#10621379C211yesmaximal, characteristic, complemented
7#10621377C211yesmaximal, characteristic, complemented
8C4⋊C4×D21C211yesmaximal, characteristic, complemented
9#10621371C211yesmaximal, characteristic, complemented
10#10621369C211yesmaximal, characteristic, complemented
11#10621367C211yesmaximal, characteristic, complemented
12#10621366C211yesmaximal, characteristic, complemented
13#10621364C211yesmaximal, characteristic, complemented
14#10621364C211yesmaximal, characteristic, complemented
15#10621361C211yesmaximal, characteristic, complemented
16#90346—31nomaximal, Hall
17C2×C3×C7×D4C2211yescharacteristic
18C22×C3×C4×C7C2211yescharacteristic
19C2×#4268C2211yescharacteristic
20C2×#4268C2211yescharacteristic
21C2×#4268C2211yescharacteristic
22C2×#4268C2211yescharacteristic
23C22×Dic21C2211yescharacteristic
24C22×Dic21C2211yescharacteristic
25C22×Dic21C2211yescharacteristic
26#66730—24no—
27#66728—24no—
28C2×D84C2211yescharacteristic
29C2×C4×D21C2211yescharacteristic
30C2×C4×D21C2211yescharacteristic
31C2×C4×D21C2211yescharacteristic
32C2×C4×D21C2211yescharacteristic
33C2×Dic42C2211yescharacteristic
34C2×Dic42C2211yescharacteristic
35C3×C7×C4⋊C4C2211yescharacteristic
36C3×C7×C4⋊C4C2211yescharacteristic
37C3×C7×C22⋊C4C2211yescharacteristic
38C3×C7×C22⋊C4C2211yescharacteristic
39C3×C7×C22⋊C4C2211yescharacteristic
40#66636C2211yescharacteristic
41#66631C2211yescharacteristic
42#66631C2211yescharacteristic
43#66631C2211yescharacteristic
44#66631C2211yescharacteristic
45C4⋊Dic21C2211yescharacteristic
46C4⋊Dic21C2211yescharacteristic
47#66629C2211yescharacteristic
48#66629C2211yescharacteristic
49#66629C2211yescharacteristic
50#66629C2211yescharacteristic
51#66629C2211yescharacteristic
52#66629C2211yescharacteristic
53C4×Dic21C2211yescharacteristic
54C2×#1159—31no—
55C2×#1157—31no—
56C7×#123D311yescharacteristic, complemented
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#5655—71nomaximal, Hall
70C23×C3×C7C2311yescharacteristic
71C23×C3×C7C2311yescharacteristic
72C22×D21C2311yescharacteristic
73C22×D21C2311yescharacteristic
74C3×C7×D4—22no—
75C2×C3×C4×C7—22no—
76C2×C3×C4×C7C2311yescharacteristic
77C2×C3×C4×C7C2311yescharacteristic
78C2×C3×C4×C7C2311yescharacteristic
79C2×C3×C4×C7C2311yescharacteristic
80C2×C3×C4×C7C2311yescharacteristic
81#4268—22no—
82#4268—22no—
83#4268—22no—
84#4268D414yescomplemented
85C2×Dic21—22no—
86C2×Dic21—22no—
87C2×Dic21—22no—
88C2×Dic21C2311yescharacteristic
89C2×Dic21C2311yescharacteristic
90C2×Dic21C2311yescharacteristic
91C2×Dic21C2311yescharacteristic
92C2×Dic21C2311yescharacteristic
93C2×Dic21C2311yescharacteristic
94D84—22no—
95C4×D21—22no—
96C4×D21—22no—
97C4×D21—22no—
98C4×D21—22no—
99Dic42—22no—
100Dic42—22no—
101C2×C7×D4C2×D311yescharacteristic
102C22×C4×C7C2×D311yescharacteristic
103C2×C22⋊D7—31no—
104C2×C22⋊D7—31no—
105C2×C22⋊D7—31no—
106C2×C22⋊D7—31no—
107C22×Dic7—31no—
108C22×Dic7—31no—
109C22×Dic7—31no—
110#1159—64no—
111#1157—64no—
112C2×D28—31no—
113C2×C4×D7—31no—
114C2×C4×D7—31no—
115C2×C4×D7—31no—
116C2×C4×D7—31no—
117C2×Dic14—31no—
118C2×Dic14—31no—
119C7×C4⋊C4C2×D311yescharacteristic
120C7×C4⋊C4C2×D311yescharacteristic
121C7×C22⋊C4C2×D311yescharacteristic
122C7×C22⋊C4C2×D311yescharacteristic
123C7×C22⋊C4C2×D311yescharacteristic
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×#237—71no—
139C2×#235—71no—
140C3×#123D711yescharacteristic, complemented
141#939—71no—
142C2×Dic3⋊C4—71no—
143#896—71no—
144#894—71no—
145D3×C4⋊C4—71no—
146#888—71no—
147#886—71no—
148#884—71no—
149#883—71no—
150#67⋊C4—71no—
151#67⋊C4—71no—
152#878—71no—
153C22×C3×C7—21no—
154C22×C3×C7—21no—
155C22×C3×C7—21no—
156C22×C3×C7—21no—
157C22×C3×C7—21no—
158C22×C3×C7C2×D412yes—
159C22×C3×C7C2411yescharacteristic
160C2×D21—21no—
161C2×D21—21no—
162C2×D21—21no—
163C2×D21—21no—
164C2×D21—21no—
165C2×D21C2×D412yes—
166C3×C4×C7—21no—
167C3×C4×C7—21no—
168C3×C4×C7—21no—
169C3×C4×C7—21no—
170C3×C4×C7—21no—
171Dic21—21no—
172Dic21—21no—
173Dic21—21no—
174Dic21—21no—
175Dic21C2×D412yes—
176Dic21#4112yescomplemented
177#547—211noSylow
178C23×C7C22×D311yescharacteristic
179C23×C7C22×D311yescharacteristic
180C22×D7—31no—
181C22×D7—31no—
182C7×D4—22no—
183C2×C4×C7—22no—
184C2×C4×C7C22×D311yescharacteristic
185C2×C4×C7C22×D311yescharacteristic
186C2×C4×C7C22×D311yescharacteristic
187C2×C4×C7C22×D311yescharacteristic
188C2×C4×C7C22×D311yescharacteristic
189C22⋊D7—34no—
190C22⋊D7—62no—
191C22⋊D7—62no—
192C22⋊D7—62no—
193C2×Dic7—31no—
194C2×Dic7—31no—
195C2×Dic7—31no—
196C2×Dic7—31no—
197C2×Dic7—31no—
198C2×Dic7—31no—
199C2×Dic7—62no—
200C2×Dic7—62no—
201C2×Dic7—62no—
202D28—62no—
203C4×D7—62no—
204C4×D7—62no—
205C4×D7—62no—
206C4×D7—62no—
207Dic14—62no—
208Dic14—62no—
209C2×C3×D4C2×D711yescharacteristic
210C22×C3×C4C2×D711yescharacteristic
211C2×#67—71no—
212C2×#67—71no—
213C2×#67—71no—
214C2×#67—71no—
215C22×Dic3—71no—
216C22×Dic3—71no—
217C22×Dic3—71no—
218#237—144no—
219#235—144no—
220C2×D12—71no—
221C2×C4×D3—71no—
222C2×C4×D3—71no—
223C2×C4×D3—71no—
224C2×C4×D3—71no—
225C2×Dic6—71no—
226C2×Dic6—71no—
227C3×C4⋊C4C2×D711yescharacteristic
228C3×C4⋊C4C2×D711yescharacteristic
229C3×C22⋊C4C2×D711yescharacteristic
230C3×C22⋊C4C2×D711yescharacteristic
231C3×C22⋊C4C2×D711yescharacteristic
232#217—71no—
233(C2×D3)⋊C4—71no—
234(C2×D3)⋊C4—71no—
235(C2×D3)⋊C4—71no—
236(C2×D3)⋊C4—71no—
237C4⋊Dic3—71no—
238C4⋊Dic3—71no—
239Dic3⋊C4—71no—
240Dic3⋊C4—71no—
241Dic3⋊C4—71no—
242Dic3⋊C4—71no—
243Dic3⋊C4—71no—
244Dic3⋊C4—71no—
245C4×Dic3—71no—
246C2×C3×C7—22no—
247C2×C3×C7—41no—
248C2×C3×C7C22×D411yescharacteristic
249C2×C3×C7C2×#4111yescharacteristic
250C2×C3×C72−1+411yescharacteristic
251D21—22no—
252D21—41no—
253C2×#41—211no—
254C2×#41—211no—
255C4⋊Q8—211no—
256#123—211no—
257#123—211no—
258#123—211no—
259#123D2111yescharacteristic, complemented
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—21no—
271C22×C7—21no—
272C22×C7—21no—
273C22×C7D3×D412yes—
274C22×C7C23×D311yescharacteristic
275C2×D7—32no—
276C2×D7—61no—
277C2×D7—61no—
278C2×D7—61no—
279C2×D7—61no—
280C2×D7—61no—
281C4×C7—21no—
282C4×C7—21no—
283C4×C7—21no—
284C4×C7—21no—
285C4×C7—21no—
286Dic7—32no—
287Dic7—32no—
288Dic7—61no—
289Dic7—61no—
290Dic7—61no—
291Dic7—61no—
292C23×C3C22×D711yescharacteristic
293C23×C3C22×D711yescharacteristic
294C22×D3—71no—
295C22×D3—71no—
296C3×D4—22no—
297C2×C3×C4—22no—
298C2×C3×C4C22×D711yescharacteristic
299C2×C3×C4C22×D711yescharacteristic
300C2×C3×C4C22×D711yescharacteristic
301C2×C3×C4C22×D711yescharacteristic
302C2×C3×C4C22×D711yescharacteristic
303#67—74no—
304#67—142no—
305#67—142no—
306#67—142no—
307C2×Dic3—71no—
308C2×Dic3—71no—
309C2×Dic3—71no—
310C2×Dic3—71no—
311C2×Dic3—71no—
312C2×Dic3—71no—
313C2×Dic3—142no—
314C2×Dic3—142no—
315C2×Dic3—142no—
316D12—142no—
317C4×D3—142no—
318C4×D3—142no—
319C4×D3—142no—
320C4×D3—142no—
321Dic6—142no—
322Dic6—142no—
323C3×C7#54711yescharacteristic, complemented, Hall
324#41—424no—
325#41—424no—
326C2×Q8—211no—
327C2×Q8—211no—
328C2×D4—211no—
329C2×D4—211no—
330C2×D4—211no—
331C2×D4—211no—
332C2×D4—211no—
333C2×D4C2×D2111yescharacteristic
334C22×C4—211no—
335C22×C4—211no—
336C22×C4—211no—
337C22×C4—211no—
338C22×C4—211no—
339C22×C4—211no—
340C22×C4—211no—
341C22×C4C2×D2111yescharacteristic
342C4⋊C4—211no—
343C4⋊C4—211no—
344C4⋊C4—211no—
345C4⋊C4—211no—
346C4⋊C4—211no—
347C4⋊C4—211no—
348C4⋊C4—211no—
349C4⋊C4—211no—
350C4⋊C4C2×D2111yescharacteristic
351C4⋊C4C2×D2111yescharacteristic
352C22⋊C4—211no—
353C22⋊C4—211no—
354C22⋊C4—211no—
355C22⋊C4—211no—
356C22⋊C4—211no—
357C22⋊C4C2×D2111yescharacteristic
358C22⋊C4C2×D2111yescharacteristic
359C22⋊C4C2×D2111yescharacteristic
360C42—211no—
361C2×C7—22no—
362C2×C7—41no—
363C2×C7C2×D3×D411yescharacteristic
364C2×C7D3×#4111yescharacteristic
365C2×C7#101011yescharacteristic
366D7—62no—
367D7—121no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3D4×D712yes—
374C22×C3C23×D711yescharacteristic
375C2×D3—72no—
376C2×D3—141no—
377C2×D3—141no—
378C2×D3—141no—
379C2×D3—141no—
380C2×D3—141no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—21no—
386Dic3—72no—
387Dic3—72no—
388Dic3—141no—
389Dic3—141no—
390Dic3—141no—
391Dic3—141no—
392C23—211no—
393C23—211no—
394C23C22×D2111yescharacteristic
395C23C22×D2111yescharacteristic
396Q8—422no—
397Q8—422no—
398D4—22no—
399D4—214no—
400D4—422no—
401D4—422no—
402D4—422no—
403D4—422no—
404C2×C4—22no—
405C2×C4—211no—
406C2×C4—211no—
407C2×C4—211no—
408C2×C4—211no—
409C2×C4—211no—
410C2×C4—211no—
411C2×C4—422no—
412C2×C4—422no—
413C2×C4—422no—
414C2×C4—422no—
415C2×C4—422no—
416C2×C4—422no—
417C2×C4—422no—
418C2×C4C22×D2111yescharacteristic
419C2×C4C22×D2111yescharacteristic
420C2×C4C22×D2111yescharacteristic
421C2×C4C22×D2111yescharacteristic
422C2×C4C22×D2111yescharacteristic
423C7#565511yescharacteristic, complemented, Sylow
424C2×C3—22no—
425C2×C3—41no—
426C2×C3C2×D4×D711yescharacteristic
427C2×C3D7×#4111yescharacteristic
428C2×C3#655411yescharacteristic
429D3—142no—
430D3—281no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—212no—
437C22—421no—
438C22—421no—
439C22—421no—
440C22—421no—
441C22—421no—
442C22D4×D2112yes—
443C22C23×D2111yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—212no—
450C4—212no—
451C4—421no—
452C4—421no—
453C4—421no—
454C4—421no—
455C3#9034611yescharacteristic, complemented, Sylow
456C2—22no—
457C2—41no—
458C2—422no—
459C2—841no—
460C2C2×D4×D2111yescharacteristic
461C2#41×D2111yescharacteristic
462C2#1062166311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D21
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×#123C2
hypercenter#123D21
hypocenterC3×C7#547
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#66730C2semidirect
2. C2×#66728C2semidirect
3. C3×C7×#123C2semidirect
4. #10621422C2semidirect
5. C2×#66629C2semidirect
6. #10621379C2semidirect
7. #10621377C2semidirect
8. C4⋊C4×D21C2semidirect
9. #10621371C2semidirect
10. #10621369C2semidirect
11. #10621367C2semidirect
12. #10621366C2semidirect
13. #10621364C2semidirect
14. #10621364C2semidirect
15. #10621361C2semidirect
56. C7×#123D3semidirect
84. #4268D4semidirect
140. C3×#123D7semidirect
176. Dic21#41semidirect
259. #123D21semidirect
323. C3×C7#547semidirect
423. C7#5655semidirect
455. C3#90346semidirect

Maximal subgroups

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

subgroupindex
C2×#667302
C2×#667282
C3×C7×#1232
#106214222
C2×#666292
#106213792
#106213772
C4⋊C4×D212
#106213712
#106213692
#106213672
#106213662
#106213642
#106213612
#903463
#56557