Finite Group Databasebeta

← #13061654

Subgroups — #13061654

Order 1344.

436 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×C7×D4C211yesmaximal, characteristic, complemented
2#10621422C211yesmaximal, characteristic
3#10621418C211yesmaximal, characteristic, complemented
4#10621412C211yesmaximal, characteristic, complemented
5C4×#4268C211yesmaximal, characteristic, complemented
6#10621407C211yesmaximal, characteristic, complemented
7C2×#66629C211yesmaximal, characteristic, complemented
8#10621379C211yesmaximal, characteristic, complemented
9#10621372C211yesmaximal, characteristic, complemented
10#10621369C211yesmaximal, characteristic, complemented
11#10621366C211yesmaximal, characteristic, complemented
12#10621362C211yesmaximal, characteristic, complemented
13#10621361C211yesmaximal, characteristic, complemented
14#10621359C211yesmaximal, characteristic, complemented
15#10621353C211yesmaximal, characteristic, complemented
16#90255—31nomaximal, Hall
17C2×C3×C7×D4C2211yescharacteristic
18C22×C3×C4×C7C2211yescharacteristic
19C22×C3×C4×C7C2211yescharacteristic
20C2×#4268C2211yescharacteristic
21C2×#4268C2211yescharacteristic
22C22×Dic21C2211yescharacteristic
23C22×Dic21C2211yescharacteristic
24C2×C4×D21C2211yescharacteristic
25C2×Dic42C2211yescharacteristic
26C3×C7×C4⋊C4C2211yescharacteristic
27C3×C7×C22⋊C4C2211yescharacteristic
28C3×C7×C22⋊C4C2211yescharacteristic
29C3×C42×C7C2211yescharacteristic
30#66636C2211yescharacteristic
31#66636C2211yescharacteristic
32#66636C2211yescharacteristic
33#66636C2211yescharacteristic
34#66631C2211yescharacteristic
35#66631C2211yescharacteristic
36#66631C2211yescharacteristic
37#66631C2211yescharacteristic
38C4⋊Dic21C2211yescharacteristic
39C4⋊Dic21C2211yescharacteristic
40C4⋊Dic21C2211yescharacteristic
41#66629C2211yescharacteristic
42#66629C2211yescharacteristic
43#66629C2211yescharacteristic
44#66629C2211yescharacteristic
45#66629C2211yescharacteristic
46#66629C2211yescharacteristic
47#66629C2211yescharacteristic
48#66629C2211yescharacteristic
49#66629C2211yescharacteristic
50#66629C2211yescharacteristic
51C4×Dic21C2211yescharacteristic
52C4×C7×D4D311yescharacteristic, complemented
53#6502—31no—
54#6498—31no—
55#6492—31no—
56C4×C22⋊D7—31no—
57#6487—31no—
58C2×Dic7⋊C4—31no—
59#6459—31no—
60#6452—31no—
61#6449—31no—
62#6446—31no—
63#6442—31no—
64#6441—31no—
65#6439—31no—
66#6433—31no—
67#5564—71nomaximal, Hall
68C23×C3×C7C2311yescharacteristic
69C23×C3×C7C2311yescharacteristic
70C22×D21C2311yescharacteristic
71C3×C7×D4—22no—
72C2×C3×C4×C7—41no—
73C2×C3×C4×C7—41no—
74C2×C3×C4×C7C2311yescharacteristic
75C2×C3×C4×C7C2311yescharacteristic
76C2×C3×C4×C7C2311yescharacteristic
77C2×C3×C4×C7C2311yescharacteristic
78C2×C3×C4×C7C2311yescharacteristic
79#4268—22no—
80#4268—41no—
81C2×Dic21—22no—
82C2×Dic21—41no—
83C2×Dic21C2311yescharacteristic
84C2×Dic21C2311yescharacteristic
85C2×Dic21C2311yescharacteristic
86C2×Dic21C2311yescharacteristic
87C2×Dic21C2311yescharacteristic
88C2×Dic21C2311yescharacteristic
89C2×Dic21C2311yescharacteristic
90C4×D21—41no—
91Dic42—41no—
92C2×C7×D4C2×D311yescharacteristic
93C22×C4×C7C2×D311yescharacteristic
94C22×C4×C7C2×D311yescharacteristic
95C2×C22⋊D7—31no—
96C2×C22⋊D7—31no—
97C22×Dic7—31no—
98C22×Dic7—31no—
99C2×C4×D7—31no—
100C2×Dic14—31no—
101C7×C4⋊C4C2×D311yescharacteristic
102C7×C22⋊C4C2×D311yescharacteristic
103C7×C22⋊C4C2×D311yescharacteristic
104C42×C7C2×D311yescharacteristic
105C22⋊Dic7—31no—
106C22⋊Dic7—31no—
107C22⋊Dic7—31no—
108C22⋊Dic7—31no—
109(C2×D7)⋊C4—31no—
110(C2×D7)⋊C4—31no—
111(C2×D7)⋊C4—31no—
112(C2×D7)⋊C4—31no—
113C4⋊Dic7—31no—
114C4⋊Dic7—31no—
115C4⋊Dic7—31no—
116Dic7⋊C4—31no—
117Dic7⋊C4—31no—
118Dic7⋊C4—31no—
119Dic7⋊C4—31no—
120Dic7⋊C4—31no—
121Dic7⋊C4—31no—
122Dic7⋊C4—31no—
123Dic7⋊C4—31no—
124Dic7⋊C4—31no—
125Dic7⋊C4—31no—
126C4×Dic7—31no—
127C3×C4×D4D711yescharacteristic, complemented
128#939—71no—
129#935—71no—
130#929—71no—
131C4×#67—71no—
132#924—71no—
133C2×Dic3⋊C4—71no—
134#896—71no—
135#889—71no—
136#886—71no—
137#883—71no—
138#879—71no—
139#878—71no—
140#876—71no—
141#870—71no—
142C22×C3×C7—21no—
143C22×C3×C7—21no—
144C22×C3×C7—21no—
145C22×C3×C7—21no—
146C22×C3×C7—21no—
147C22×C3×C7#4112yes—
148C22×C3×C7C2411yescharacteristic
149C2×D21—21no—
150C2×D21—21no—
151C2×D21—21no—
152C3×C4×C7—21no—
153C3×C4×C7—21no—
154C3×C4×C7—21no—
155C3×C4×C7—21no—
156C3×C4×C7—21no—
157Dic21—21no—
158Dic21—21no—
159Dic21—21no—
160Dic21—21no—
161Dic21—21no—
162Dic21—21no—
163Dic21—21no—
164#539—211noSylow
165C23×C7C22×D311yescharacteristic
166C23×C7C22×D311yescharacteristic
167C22×D7—31no—
168C7×D4—22no—
169C2×C4×C7—41no—
170C2×C4×C7—41no—
171C2×C4×C7C22×D311yescharacteristic
172C2×C4×C7C22×D311yescharacteristic
173C2×C4×C7C22×D311yescharacteristic
174C2×C4×C7C22×D311yescharacteristic
175C2×C4×C7C22×D311yescharacteristic
176C22⋊D7—62no—
177C22⋊D7—121no—
178C2×Dic7—31no—
179C2×Dic7—31no—
180C2×Dic7—31no—
181C2×Dic7—31no—
182C2×Dic7—31no—
183C2×Dic7—31no—
184C2×Dic7—31no—
185C2×Dic7—62no—
186C2×Dic7—121no—
187C4×D7—121no—
188Dic14—121no—
189C2×C3×D4C2×D711yescharacteristic
190C22×C3×C4C2×D711yescharacteristic
191C22×C3×C4C2×D711yescharacteristic
192C2×#67—71no—
193C2×#67—71no—
194C22×Dic3—71no—
195C22×Dic3—71no—
196C2×C4×D3—71no—
197C2×Dic6—71no—
198C3×C4⋊C4C2×D711yescharacteristic
199C3×C22⋊C4C2×D711yescharacteristic
200C3×C22⋊C4C2×D711yescharacteristic
201C3×C42C2×D711yescharacteristic
202#217—71no—
203#217—71no—
204#217—71no—
205#217—71no—
206(C2×D3)⋊C4—71no—
207(C2×D3)⋊C4—71no—
208(C2×D3)⋊C4—71no—
209(C2×D3)⋊C4—71no—
210C4⋊Dic3—71no—
211C4⋊Dic3—71no—
212C4⋊Dic3—71no—
213Dic3⋊C4—71no—
214Dic3⋊C4—71no—
215Dic3⋊C4—71no—
216Dic3⋊C4—71no—
217Dic3⋊C4—71no—
218Dic3⋊C4—71no—
219Dic3⋊C4—71no—
220Dic3⋊C4—71no—
221Dic3⋊C4—71no—
222Dic3⋊C4—71no—
223C4×Dic3—71no—
224C2×C3×C7—22no—
225C2×C3×C7—41no—
226C2×C3×C7C2×#4111yescharacteristic
227C2×C3×C7H(5,𝔽2)11yescharacteristic
228C2×C3×C72−1+411yescharacteristic
229D21—41no—
230#126—211no—
231#126—211no—
232#125—211no—
233#125—211no—
234#123—211no—
235#123—211no—
236#123—211no—
237#123—211no—
238C22⋊Q8—211no—
239C22⋊Q8—211no—
240C22⋊Q8—211no—
241#121—211no—
242C4×D4—211no—
243C4×D4D2111yescharacteristic, complemented
244C2×C4⋊C4—211no—
245C22×C7—21no—
246C22×C7—21no—
247C22×C7—21no—
248C22×C7—21no—
249C22×C7—21no—
250C22×C7#23512yes—
251C22×C7C23×D311yescharacteristic
252C2×D7—61no—
253C2×D7—61no—
254C2×D7—61no—
255C4×C7—21no—
256C4×C7—21no—
257C4×C7—21no—
258C4×C7—21no—
259C4×C7—21no—
260Dic7—61no—
261Dic7—61no—
262Dic7—61no—
263Dic7—61no—
264Dic7—61no—
265Dic7—61no—
266Dic7—61no—
267C23×C3C22×D711yescharacteristic
268C23×C3C22×D711yescharacteristic
269C22×D3—71no—
270C3×D4—22no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4C22×D711yescharacteristic
274C2×C3×C4C22×D711yescharacteristic
275C2×C3×C4C22×D711yescharacteristic
276C2×C3×C4C22×D711yescharacteristic
277C2×C3×C4C22×D711yescharacteristic
278#67—142no—
279#67—281no—
280C2×Dic3—71no—
281C2×Dic3—71no—
282C2×Dic3—71no—
283C2×Dic3—71no—
284C2×Dic3—71no—
285C2×Dic3—71no—
286C2×Dic3—71no—
287C2×Dic3—142no—
288C2×Dic3—281no—
289C4×D3—281no—
290Dic6—281no—
291C3×C7#53911yescharacteristic, complemented, Hall
292C2×Q8—211no—
293C2×D4—211no—
294C2×D4—211no—
295C2×D4C2×D2111yescharacteristic
296C22×C4—211no—
297C22×C4—211no—
298C22×C4—211no—
299C22×C4C2×D2111yescharacteristic
300C22×C4C2×D2111yescharacteristic
301C4⋊C4—211no—
302C4⋊C4—211no—
303C4⋊C4—211no—
304C4⋊C4—211no—
305C4⋊C4—211no—
306C4⋊C4—211no—
307C4⋊C4—211no—
308C4⋊C4—211no—
309C4⋊C4—211no—
310C4⋊C4—211no—
311C4⋊C4—211no—
312C4⋊C4—211no—
313C4⋊C4—211no—
314C4⋊C4C2×D2111yescharacteristic
315C22⋊C4—211no—
316C22⋊C4—211no—
317C22⋊C4—211no—
318C22⋊C4—211no—
319C22⋊C4—211no—
320C22⋊C4—211no—
321C22⋊C4—211no—
322C22⋊C4—211no—
323C22⋊C4C2×D2111yescharacteristic
324C22⋊C4C2×D2111yescharacteristic
325C42—211no—
326C42C2×D2111yescharacteristic
327C2×C7—22no—
328C2×C7—41no—
329C2×C7C2×#23511yescharacteristic
330C2×C7#100411yescharacteristic
331C2×C7#101011yescharacteristic
332D7—121no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3#115712yes—
339C22×C3C23×D711yescharacteristic
340C2×D3—141no—
341C2×D3—141no—
342C2×D3—141no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348Dic3—141no—
349Dic3—141no—
350Dic3—141no—
351Dic3—141no—
352Dic3—141no—
353Dic3—141no—
354Dic3—141no—
355C23—211no—
356C23C22×D2111yescharacteristic
357C23C22×D2111yescharacteristic
358Q8—841no—
359D4—22no—
360D4—422no—
361D4—841no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—211no—
365C2×C4—211no—
366C2×C4—211no—
367C2×C4—211no—
368C2×C4—211no—
369C2×C4—211no—
370C2×C4—211no—
371C2×C4—422no—
372C2×C4—841no—
373C2×C4—841no—
374C2×C4C22×D2111yescharacteristic
375C2×C4C22×D2111yescharacteristic
376C2×C4C22×D2111yescharacteristic
377C2×C4C22×D2111yescharacteristic
378C2×C4C22×D2111yescharacteristic
379C7#556411yescharacteristic, complemented, Sylow
380C2×C3—22no—
381C2×C3—41no—
382C2×C3C2×#115711yescharacteristic
383C2×C3#654811yescharacteristic
384C2×C3#655411yescharacteristic
385D3—281no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—421no—
392C22—421no—
393C22—421no—
394C22#6672812yes—
395C22C23×D2111yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—421no—
402C4—421no—
403C4—421no—
404C4—421no—
405C4—421no—
406C4—421no—
407C4—421no—
408C3#9025511yescharacteristic, complemented, Sylow
409C2—22no—
410C2—41no—
411C2—841no—
412C2C2×#6672811yescharacteristic
413C2#1062165711yescharacteristic
414C2#1062166311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D21
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C4×C7×D4C2
prime radical#10621422C2
hypercenterC4×D4D21
hypocenterC3×C7#539
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×C4×C7×D4C2semidirect
3. #10621418C2semidirect
4. #10621412C2semidirect
5. C4×#4268C2semidirect
6. #10621407C2semidirect
7. C2×#66629C2semidirect
8. #10621379C2semidirect
9. #10621372C2semidirect
10. #10621369C2semidirect
11. #10621366C2semidirect
12. #10621362C2semidirect
13. #10621361C2semidirect
14. #10621359C2semidirect
15. #10621353C2semidirect
52. C4×C7×D4D3semidirect
127. C3×C4×D4D7semidirect
243. C4×D4D21semidirect
291. C3×C7#539semidirect
379. C7#5564semidirect
408. C3#90255semidirect

Maximal subgroups

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

subgroupindex
C3×C4×C7×D42
#106214222
#106214182
#106214122
C4×#42682
#106214072
C2×#666292
#106213792
#106213722
#106213692
#106213662
#106213622
#106213612
#106213592
#106213532
#902553
#55647