Finite Group Databasebeta

← #13061621

Subgroups — #13061621

Order 1344.

468 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×C7×#117C211yesmaximal, characteristic, complemented
2C4×#4268C211yesmaximal, characteristic, complemented
3C4×#4268C211yesmaximal, characteristic, complemented
4#10621381C211yesmaximal, characteristic, complemented
5#10621379C211yesmaximal, characteristic, complemented
6#10621377C211yesmaximal, characteristic, complemented
7#10621372C211yesmaximal, characteristic, complemented
8#10621368C211yesmaximal, characteristic, complemented
9#10621367C211yesmaximal, characteristic
10#10621366C211yesmaximal, characteristic, complemented
11#10621362C211yesmaximal, characteristic, complemented
12C4×D84C211yesmaximal, characteristic, complemented
13#10621355C211yesmaximal, characteristic, complemented
14C42×D21C211yesmaximal, characteristic, complemented
15C4×Dic42C211yesmaximal, characteristic, complemented
16#90219—31nomaximal, Hall
17C22×C3×C4×C7C2211yescharacteristic
18C2×#4268C2211yescharacteristic
19C2×#4268C2211yescharacteristic
20C2×D84C2211yescharacteristic
21C2×C4×D21C2211yescharacteristic
22C2×C4×D21C2211yescharacteristic
23C2×C4×D21C2211yescharacteristic
24C2×C4×D21C2211yescharacteristic
25C2×Dic42C2211yescharacteristic
26C3×C7×C4⋊C4C2211yescharacteristic
27C3×C7×C4⋊C4C2211yescharacteristic
28C3×C7×C22⋊C4C2211yescharacteristic
29C3×C7×C22⋊C4C2211yescharacteristic
30C3×C42×C7C2211yescharacteristic
31C3×C42×C7C2211yescharacteristic
32#66636C2211yescharacteristic
33#66636C2211yescharacteristic
34#66631C2211yescharacteristic
35#66631C2211yescharacteristic
36#66631C2211yescharacteristic
37#66631C2211yescharacteristic
38#66631C2211yescharacteristic
39#66631C2211yescharacteristic
40C4⋊Dic21C2211yescharacteristic
41C4⋊Dic21C2211yescharacteristic
42#66629C2211yescharacteristic
43#66629C2211yescharacteristic
44#66629C2211yescharacteristic
45#66629C2211yescharacteristic
46#66629C2211yescharacteristic
47#66629C2211yescharacteristic
48C4×Dic21C2211yescharacteristic
49C4×Dic21C2211yescharacteristic
50C4×Dic21C2211yescharacteristic
51C4×Dic21C2211yescharacteristic
52C7×#117D311yescharacteristic, complemented
53C4×C22⋊D7—31no—
54C4×C22⋊D7—31no—
55#6461—31no—
56#6459—31no—
57#6457—31no—
58#6452—31no—
59#6448—31no—
60#6447—31no—
61#6446—31no—
62#6442—31no—
63C4×D28—31no—
64#6435—31no—
65C42×D7—31no—
66C4×Dic14—31no—
67#5528—71nomaximal, Hall
68C23×C3×C7C2311yescharacteristic
69C22×D21C2311yescharacteristic
70C22×D21C2311yescharacteristic
71C2×C3×C4×C7—22no—
72C2×C3×C4×C7C2311yescharacteristic
73C2×C3×C4×C7C2311yescharacteristic
74C2×C3×C4×C7C2311yescharacteristic
75C2×C3×C4×C7C2311yescharacteristic
76C2×C3×C4×C7C2311yescharacteristic
77C2×C3×C4×C7C2311yescharacteristic
78#4268—22no—
79#4268—22no—
80C2×Dic21C2311yescharacteristic
81C2×Dic21C2311yescharacteristic
82C2×Dic21C2311yescharacteristic
83C2×Dic21C2311yescharacteristic
84C2×Dic21C2311yescharacteristic
85C2×Dic21C2311yescharacteristic
86D84—22no—
87C4×D21—22no—
88C4×D21—22no—
89C4×D21—22no—
90C4×D21—22no—
91Dic42—22no—
92C22×C4×C7C2×D311yescharacteristic
93C2×C22⋊D7—31no—
94C2×C22⋊D7—31no—
95C2×D28—31no—
96C2×C4×D7—31no—
97C2×C4×D7—31no—
98C2×C4×D7—31no—
99C2×C4×D7—31no—
100C2×Dic14—31no—
101C7×C4⋊C4C2×D311yescharacteristic
102C7×C4⋊C4C2×D311yescharacteristic
103C7×C22⋊C4C2×D311yescharacteristic
104C7×C22⋊C4C2×D311yescharacteristic
105C42×C7C2×D311yescharacteristic
106C42×C7C2×D311yescharacteristic
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—
113(C2×D7)⋊C4—31no—
114(C2×D7)⋊C4—31no—
115C4⋊Dic7—31no—
116C4⋊Dic7—31no—
117Dic7⋊C4—31no—
118Dic7⋊C4—31no—
119Dic7⋊C4—31no—
120Dic7⋊C4—31no—
121Dic7⋊C4—31no—
122Dic7⋊C4—31no—
123C4×Dic7—31no—
124C4×Dic7—31no—
125C4×Dic7—31no—
126C4×Dic7—31no—
127C3×#117D711yescharacteristic, complemented
128C4×#67—71no—
129C4×#67—71no—
130#898—71no—
131#896—71no—
132#894—71no—
133#889—71no—
134#885—71no—
135#884—71no—
136#883—71no—
137#879—71no—
138C4×D12—71no—
139#872—71no—
140C42×D3—71no—
141C4×Dic6—71no—
142C22×C3×C7—21no—
143C22×C3×C7—21no—
144C22×C3×C7—21no—
145C22×C3×C7C2411yescharacteristic
146C2×D21—21no—
147C2×D21—21no—
148C2×D21—21no—
149C2×D21—21no—
150C2×D21—21no—
151C2×D21#4112yes—
152C3×C4×C7—21no—
153C3×C4×C7—21no—
154C3×C4×C7—21no—
155C3×C4×C7—21no—
156C3×C4×C7—21no—
157C3×C4×C7#4112yes—
158Dic21—21no—
159Dic21—21no—
160Dic21—21no—
161Dic21—21no—
162Dic21—21no—
163Dic21#4112yes—
164#529—211noSylow
165C23×C7C22×D311yescharacteristic
166C22×D7—31no—
167C22×D7—31no—
168C2×C4×C7—22no—
169C2×C4×C7C22×D311yescharacteristic
170C2×C4×C7C22×D311yescharacteristic
171C2×C4×C7C22×D311yescharacteristic
172C2×C4×C7C22×D311yescharacteristic
173C2×C4×C7C22×D311yescharacteristic
174C2×C4×C7C22×D311yescharacteristic
175C22⋊D7—62no—
176C22⋊D7—62no—
177C2×Dic7—31no—
178C2×Dic7—31no—
179C2×Dic7—31no—
180C2×Dic7—31no—
181C2×Dic7—31no—
182C2×Dic7—31no—
183D28—62no—
184C4×D7—62no—
185C4×D7—62no—
186C4×D7—62no—
187C4×D7—62no—
188Dic14—62no—
189C22×C3×C4C2×D711yescharacteristic
190C2×#67—71no—
191C2×#67—71no—
192C2×D12—71no—
193C2×C4×D3—71no—
194C2×C4×D3—71no—
195C2×C4×D3—71no—
196C2×C4×D3—71no—
197C2×Dic6—71no—
198C3×C4⋊C4C2×D711yescharacteristic
199C3×C4⋊C4C2×D711yescharacteristic
200C3×C22⋊C4C2×D711yescharacteristic
201C3×C22⋊C4C2×D711yescharacteristic
202C3×C42C2×D711yescharacteristic
203C3×C42C2×D711yescharacteristic
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—
210(C2×D3)⋊C4—71no—
211(C2×D3)⋊C4—71no—
212C4⋊Dic3—71no—
213C4⋊Dic3—71no—
214Dic3⋊C4—71no—
215Dic3⋊C4—71no—
216Dic3⋊C4—71no—
217Dic3⋊C4—71no—
218Dic3⋊C4—71no—
219Dic3⋊C4—71no—
220C4×Dic3—71no—
221C4×Dic3—71no—
222C4×Dic3—71no—
223C4×Dic3—71no—
224C2×C3×C7—41no—
225C2×C3×C7C2×#4111yescharacteristic
226C2×C3×C7C2×#4111yescharacteristic
227C2×C3×C7C2×#4111yescharacteristic
228D21—22no—
229D21—41no—
230#126—211no—
231#126—211no—
232#125—211no—
233#124—211no—
234#123—211no—
235#123—211no—
236C22⋊Q8—211no—
237#121—211no—
238C4×Q8—211no—
239C4×D4—211no—
240C4×D4—211no—
241C4×D4—211no—
242#117—211no—
243#117D2111yescharacteristic, complemented
244C2×C42—211no—
245C22×C7—21no—
246C22×C7—21no—
247C22×C7—21no—
248C22×C7C23×D311yescharacteristic
249C2×D7—32no—
250C2×D7—61no—
251C2×D7—61no—
252C2×D7—61no—
253C2×D7—61no—
254C2×D7—61no—
255C4×C7—21no—
256C4×C7—21no—
257C4×C7—21no—
258C4×C7—21no—
259C4×C7—21no—
260C4×C7#23512yes—
261Dic7—32no—
262Dic7—61no—
263Dic7—61no—
264Dic7—61no—
265Dic7—61no—
266Dic7—61no—
267C23×C3C22×D711yescharacteristic
268C22×D3—71no—
269C22×D3—71no—
270C2×C3×C4—22no—
271C2×C3×C4C22×D711yescharacteristic
272C2×C3×C4C22×D711yescharacteristic
273C2×C3×C4C22×D711yescharacteristic
274C2×C3×C4C22×D711yescharacteristic
275C2×C3×C4C22×D711yescharacteristic
276C2×C3×C4C22×D711yescharacteristic
277#67—142no—
278#67—142no—
279C2×Dic3—71no—
280C2×Dic3—71no—
281C2×Dic3—71no—
282C2×Dic3—71no—
283C2×Dic3—71no—
284C2×Dic3—71no—
285D12—142no—
286C4×D3—142no—
287C4×D3—142no—
288C4×D3—142no—
289C4×D3—142no—
290Dic6—142no—
291C3×C7#52911yescharacteristic, complemented, Hall
292C2×Q8—211no—
293C2×D4—211no—
294C2×D4—211no—
295C2×D4—211no—
296C22×C4—211no—
297C22×C4—211no—
298C22×C4—211no—
299C22×C4—211no—
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⋊C4C2×D2111yescharacteristic
310C4⋊C4C2×D2111yescharacteristic
311C22⋊C4—211no—
312C22⋊C4—211no—
313C22⋊C4—211no—
314C22⋊C4—211no—
315C22⋊C4—211no—
316C22⋊C4—211no—
317C22⋊C4—211no—
318C22⋊C4—211no—
319C22⋊C4C2×D2111yescharacteristic
320C22⋊C4C2×D2111yescharacteristic
321C42—211no—
322C42—211no—
323C42—211no—
324C42—211no—
325C42C2×D2111yescharacteristic
326C42C2×D2111yescharacteristic
327C2×C7—41no—
328C2×C7C2×#23511yescharacteristic
329C2×C7D3×#4111yescharacteristic
330C2×C7D3×#4111yescharacteristic
331D7—62no—
332D7—121no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3C23×D711yescharacteristic
337C2×D3—72no—
338C2×D3—141no—
339C2×D3—141no—
340C2×D3—141no—
341C2×D3—141no—
342C2×D3—141no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4#115712yes—
349Dic3—72no—
350Dic3—141no—
351Dic3—141no—
352Dic3—141no—
353Dic3—141no—
354Dic3—141no—
355C23—211no—
356C23—211no—
357C23C22×D2111yescharacteristic
358Q8—422no—
359D4—422no—
360D4—422no—
361D4—422no—
362C2×C4—22no—
363C2×C4—211no—
364C2×C4—211no—
365C2×C4—211no—
366C2×C4—211no—
367C2×C4—211no—
368C2×C4—211no—
369C2×C4—422no—
370C2×C4—422no—
371C2×C4—422no—
372C2×C4—422no—
373C2×C4C22×D2111yescharacteristic
374C2×C4C22×D2111yescharacteristic
375C2×C4C22×D2111yescharacteristic
376C2×C4C22×D2111yescharacteristic
377C2×C4C22×D2111yescharacteristic
378C2×C4C22×D2111yescharacteristic
379C7#552811yescharacteristic, complemented, Sylow
380C2×C3—41no—
381C2×C3C2×#115711yescharacteristic
382C2×C3D7×#4111yescharacteristic
383C2×C3D7×#4111yescharacteristic
384D3—142no—
385D3—281no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—212no—
390C22—421no—
391C22—421no—
392C22—421no—
393C22—421no—
394C22—421no—
395C22C23×D2111yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—212no—
402C4—421no—
403C4—421no—
404C4—421no—
405C4—421no—
406C4—421no—
407C4#6672812yes—
408C3#9021911yescharacteristic, complemented, Sylow
409C2—41no—
410C2—422no—
411C2—841no—
412C2C2×#6672811yescharacteristic
413C2#41×D2111yescharacteristic
414C2#41×D2111yescharacteristic
subgroupG/H
centerC2×C4C22×D21
commutator, socle, cosocleC22×C3×C7C24
FrattiniC22C23×D21
FittingC3×C7×#117C2
prime radical#10621367C2
hypercenter#117D21
hypocenterC3×C7#529
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C2×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×C7×#117C2semidirect
2. C4×#4268C2semidirect
3. C4×#4268C2semidirect
4. #10621381C2semidirect
5. #10621379C2semidirect
6. #10621377C2semidirect
7. #10621372C2semidirect
8. #10621368C2semidirect
10. #10621366C2semidirect
11. #10621362C2semidirect
12. C4×D84C2semidirect
13. #10621355C2semidirect
14. C42×D21C2semidirect
15. C4×Dic42C2semidirect
52. C7×#117D3semidirect
127. C3×#117D7semidirect
243. #117D21semidirect
291. C3×C7#529semidirect
379. C7#5528semidirect
408. C3#90219semidirect

Maximal subgroups

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

subgroupindex
C3×C7×#1172
C4×#42682
#106213812
#106213792
#106213772
#106213722
#106213682
#106213672
#106213662
#106213622
C4×D842
#106213552
C42×D212
C4×Dic422
#902193
#55287