Finite Group Databasebeta

← #13057789

Subgroups — #13057789

Order 1344.

472 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10621358C211yesmaximal, characteristic, complemented
2C7×#872C211yesmaximal, characteristic, complemented
3C3×#6435C211yesmaximal, characteristic, complemented
4#10621024C211yesmaximal, characteristic, complemented
5#10621021C211yesmaximal, characteristic, complemented
6#10621016C211yesmaximal, characteristic, complemented
7#10621010C211yesmaximal, characteristic, complemented
8#10621008C211yesmaximal, characteristic, complemented
9#10621006C211yesmaximal, characteristic, complemented
10#10620982C211yesmaximal, characteristic, complemented
11#10620965C211yesmaximal, characteristic, complemented
12#10620964C211yesmaximal, characteristic, complemented
13#10620915C211yesmaximal, characteristic, complemented
14#10620912C211yesmaximal, characteristic, complemented
15#10620890C211yesmaximal, characteristic, complemented
16#90223—31nomaximal, Hall
17C2×D84C2211yescharacteristic
18C2×Dic42C2211yescharacteristic
19C2×C4×D3×C7C2211yescharacteristic
20C2×C3×C4×D7C2211yescharacteristic
21C2×#4248C2211yescharacteristic
22C2×#4247C2211yescharacteristic
23C2×#4247C2211yescharacteristic
24C2×#4246C2211yescharacteristic
25C2×#4246C2211yescharacteristic
26C2×#4245C2211yescharacteristic
27C2×D21⋊C4C2211yescharacteristic
28C2×D21⋊C4C2211yescharacteristic
29C3×C42×C7C2211yescharacteristic
30#66631C2211yescharacteristic
31#66631C2211yescharacteristic
32#66631C2211yescharacteristic
33#66631C2211yescharacteristic
34C7×(C2×D3)⋊C4C2211yescharacteristic
35C7×(C2×D3)⋊C4C2211yescharacteristic
36C7×Dic3⋊C4C2211yescharacteristic
37C7×Dic3⋊C4C2211yescharacteristic
38C4×C7×Dic3C2211yescharacteristic
39C3×(C2×D7)⋊C4C2211yescharacteristic
40C3×(C2×D7)⋊C4C2211yescharacteristic
41C3×Dic7⋊C4C2211yescharacteristic
42C3×Dic7⋊C4C2211yescharacteristic
43C3×C4×Dic7C2211yescharacteristic
44Dic3⋊Dic7C2211yescharacteristic
45Dic7⋊Dic3C2211yescharacteristic
46#66575C2211yescharacteristic
47#66575C2211yescharacteristic
48(C2×D3)⋊Dic7C2211yescharacteristic
49(C2×D7)⋊Dic3C2211yescharacteristic
50Dic3×Dic7C2211yescharacteristic
51Dic3×Dic7C2211yescharacteristic
52C7×#117—31no—
53#6493—31no—
54C4×C22⋊D7—31no—
55#6458—31no—
56#6456—31no—
57#6455—31no—
58#6451—31no—
59#6448—31no—
60#6448—31no—
61#6447—31no—
62#6447—31no—
63#6438—31no—
64#6438—31no—
65#6435—31no—
66#6435D311yescharacteristic, complemented
67#5532—71nomaximal, Hall
68C22×D21C2311yescharacteristic
69C22×D21C2311yescharacteristic
70C22×D3×C7C2311yescharacteristic
71C22×C3×D7C2311yescharacteristic
72C2×C3×C4×C7C2311yescharacteristic
73C2×C3×C4×C7C2311yescharacteristic
74C2×C3×C4×C7C2311yescharacteristic
75C2×Dic21C2311yescharacteristic
76C2×Dic21C2311yescharacteristic
77D84—41no—
78Dic42—41no—
79C2×C7×Dic3C2311yescharacteristic
80C2×C7×Dic3C2311yescharacteristic
81C2×C7×Dic3C2311yescharacteristic
82C4×D3×C7—22no—
83C2×C3×Dic7C2311yescharacteristic
84C2×C3×Dic7C2311yescharacteristic
85C2×C3×Dic7C2311yescharacteristic
86C3×C4×D7—22no—
87#4248—41no—
88#4247—22no—
89#4247—41no—
90#4246—22no—
91#4246—41no—
92#4245—41no—
93D21⋊C4—22no—
94D21⋊C4—22no—
95C22×C4×C7—31no—
96C2×C22⋊D7—31no—
97C2×C22⋊D7—31no—
98C2×C22⋊D7—31no—
99C2×D28—31no—
100C2×D28—31no—
101C2×D28—31no—
102C2×C4×D7—31no—
103C2×C4×D7—31no—
104C2×C4×D7C2×D311yescharacteristic
105C2×Dic14—31no—
106C2×Dic14—31no—
107C7×C4⋊C4—31no—
108C7×C4⋊C4—31no—
109C7×C22⋊C4—31no—
110C7×C22⋊C4—31no—
111C42×C7—31no—
112C42×C7C2×D311yescharacteristic
113C22⋊Dic7—31no—
114(C2×D7)⋊C4—31no—
115(C2×D7)⋊C4—31no—
116(C2×D7)⋊C4—31no—
117(C2×D7)⋊C4—31no—
118(C2×D7)⋊C4—31no—
119(C2×D7)⋊C4—31no—
120(C2×D7)⋊C4—31no—
121(C2×D7)⋊C4C2×D311yescharacteristic
122(C2×D7)⋊C4C2×D311yescharacteristic
123C4⋊Dic7—31no—
124Dic7⋊C4—31no—
125Dic7⋊C4C2×D311yescharacteristic
126Dic7⋊C4C2×D311yescharacteristic
127C4×Dic7—31no—
128C4×Dic7—31no—
129C4×Dic7C2×D311yescharacteristic
130C3×#117—71no—
131#930—71no—
132C4×#67—71no—
133#895—71no—
134#893—71no—
135#892—71no—
136#888—71no—
137#885—71no—
138#885—71no—
139#884—71no—
140#884—71no—
141#875—71no—
142#875—71no—
143#872—71no—
144#872D711yescharacteristic, complemented
145C22×C3×C7C2411yescharacteristic
146C2×D21—21no—
147C2×D21—21no—
148C2×D21—21no—
149C2×D21—21no—
150C2×D21—21no—
151C2×D21—21no—
152C2×D3×C7—21no—
153C2×D3×C7—21no—
154C2×D3×C7—21no—
155C2×C3×D7—21no—
156C2×C3×D7—21no—
157C2×C3×D7—21no—
158C3×C4×C7—21no—
159C3×C4×C7—21no—
160C3×C4×C7—21no—
161Dic21—21no—
162Dic21—21no—
163C3×Dic7—21no—
164C3×Dic7—21no—
165C3×Dic7#4112yes—
166C7×Dic3—21no—
167C7×Dic3—21no—
168C7×Dic3#4112yes—
169#555—211noSylow
170C23×C7—31no—
171C22×D7—31no—
172C22×D7—31no—
173C22×D7C22×D311yescharacteristic
174C2×C4×C7—31no—
175C2×C4×C7—31no—
176C2×C4×C7—31no—
177C2×C4×C7—62no—
178C2×C4×C7C22×D311yescharacteristic
179C2×C4×C7C22×D311yescharacteristic
180C2×C4×C7C22×D311yescharacteristic
181C22⋊D7—62no—
182C22⋊D7—121no—
183C22⋊D7—121no—
184C2×Dic7—31no—
185C2×Dic7—31no—
186C2×Dic7C22×D311yescharacteristic
187C2×Dic7C22×D311yescharacteristic
188C2×Dic7C22×D311yescharacteristic
189D28—62no—
190D28—121no—
191D28—121no—
192C4×D7—22no—
193C4×D7—62no—
194C4×D7—62no—
195Dic14—121no—
196Dic14—121no—
197C22×C3×C4—71no—
198C2×#67—71no—
199C2×#67—71no—
200C2×#67—71no—
201C2×D12—71no—
202C2×D12—71no—
203C2×D12—71no—
204C2×C4×D3—71no—
205C2×C4×D3—71no—
206C2×C4×D3C2×D711yescharacteristic
207C2×Dic6—71no—
208C2×Dic6—71no—
209C3×C4⋊C4—71no—
210C3×C4⋊C4—71no—
211C3×C22⋊C4—71no—
212C3×C22⋊C4—71no—
213C3×C42—71no—
214C3×C42C2×D711yescharacteristic
215#217—71no—
216(C2×D3)⋊C4—71no—
217(C2×D3)⋊C4—71no—
218(C2×D3)⋊C4—71no—
219(C2×D3)⋊C4—71no—
220(C2×D3)⋊C4—71no—
221(C2×D3)⋊C4—71no—
222(C2×D3)⋊C4—71no—
223(C2×D3)⋊C4C2×D711yescharacteristic
224(C2×D3)⋊C4C2×D711yescharacteristic
225C4⋊Dic3—71no—
226Dic3⋊C4—71no—
227Dic3⋊C4C2×D711yescharacteristic
228Dic3⋊C4C2×D711yescharacteristic
229C4×Dic3—71no—
230C4×Dic3—71no—
231C4×Dic3C2×D711yescharacteristic
232C2×C3×C7C2×#4111yescharacteristic
233C2×C3×C7C2×#4111yescharacteristic
234C2×C3×C7H(5,𝔽2)11yescharacteristic
235D21—41no—
236D21—41no—
237C3×D7—41no—
238D3×C7—41no—
239C4⋊Q8—211no—
240#124—211no—
241#124—211no—
242#124—211no—
243#124—211no—
244#121—211no—
245#121—211no—
246#121—211no—
247#121—211no—
248C4×D4—211no—
249C4×D4—211no—
250#117—31no—
251#117—71no—
252#117—211no—
253#117—211no—
254C22×C7—61no—
255C22×C7—61no—
256C22×C7—61no—
257C22×C7C23×D311yescharacteristic
258C2×D7—21no—
259C2×D7—21no—
260C2×D7—21no—
261C2×D7—61no—
262C2×D7—61no—
263C2×D7—61no—
264C2×D7—61no—
265C2×D7—61no—
266C2×D7—61no—
267C4×C7—21no—
268C4×C7—21no—
269C4×C7—21no—
270C4×C7—32no—
271C4×C7—61no—
272C4×C7—61no—
273Dic7—21no—
274Dic7—21no—
275Dic7—61no—
276Dic7—61no—
277Dic7#23512yes—
278C23×C3—71no—
279C22×D3—71no—
280C22×D3—71no—
281C22×D3C22×D711yescharacteristic
282C2×C3×C4—71no—
283C2×C3×C4—71no—
284C2×C3×C4—71no—
285C2×C3×C4—142no—
286C2×C3×C4C22×D711yescharacteristic
287C2×C3×C4C22×D711yescharacteristic
288C2×C3×C4C22×D711yescharacteristic
289#67—142no—
290#67—281no—
291#67—281no—
292C2×Dic3—71no—
293C2×Dic3—71no—
294C2×Dic3C22×D711yescharacteristic
295C2×Dic3C22×D711yescharacteristic
296C2×Dic3C22×D711yescharacteristic
297D12—142no—
298D12—281no—
299D12—281no—
300C4×D3—22no—
301C4×D3—142no—
302C4×D3—142no—
303Dic6—281no—
304Dic6—281no—
305C3×C7#55511yescharacteristic, complemented, Hall
306C2×Q8—211no—
307C2×Q8—211no—
308C2×D4—211no—
309C2×D4—211no—
310C2×D4—211no—
311C2×D4—211no—
312C2×D4—211no—
313C2×D4—211no—
314C22×C4—31no—
315C22×C4—71no—
316C22×C4—211no—
317C22×C4—211no—
318C4⋊C4—31no—
319C4⋊C4—31no—
320C4⋊C4—71no—
321C4⋊C4—71no—
322C4⋊C4—211no—
323C4⋊C4—211no—
324C22⋊C4—31no—
325C22⋊C4—31no—
326C22⋊C4—71no—
327C22⋊C4—71no—
328C22⋊C4—211no—
329C22⋊C4—211no—
330C22⋊C4—211no—
331C22⋊C4—211no—
332C22⋊C4—211no—
333C22⋊C4—211no—
334C22⋊C4—211no—
335C22⋊C4—211no—
336C42—31no—
337C42—71no—
338C42—211no—
339C42—211no—
340C42D3×D711yescharacteristic
341C2×C7—121no—
342C2×C7C2×#23511yescharacteristic
343C2×C7D3×#4111yescharacteristic
344C2×C7#100911yescharacteristic
345D7—41no—
346D7—121no—
347D7—121no—
348C22×C3—141no—
349C22×C3—141no—
350C22×C3—141no—
351C22×C3C23×D711yescharacteristic
352C2×D3—21no—
353C2×D3—21no—
354C2×D3—21no—
355C2×D3—141no—
356C2×D3—141no—
357C2×D3—141no—
358C2×D3—141no—
359C2×D3—141no—
360C2×D3—141no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—72no—
365C3×C4—141no—
366C3×C4—141no—
367Dic3—21no—
368Dic3—21no—
369Dic3—141no—
370Dic3—141no—
371Dic3#115712yes—
372C23—31no—
373C23—71no—
374C23—211no—
375C23—211no—
376Q8—841no—
377Q8—841no—
378D4—422no—
379D4—422no—
380D4—841no—
381D4—841no—
382D4—841no—
383D4—841no—
384C2×C4—31no—
385C2×C4—31no—
386C2×C4—31no—
387C2×C4—62no—
388C2×C4—71no—
389C2×C4—71no—
390C2×C4—71no—
391C2×C4—142no—
392C2×C4—211no—
393C2×C4—211no—
394C2×C4—422no—
395C2×C4—422no—
396C2×C4C2×D3×D711yescharacteristic
397C2×C4C2×D3×D711yescharacteristic
398C2×C4C2×D3×D711yescharacteristic
399C7#553211yescharacteristic, complemented, Sylow
400C2×C3—281no—
401C2×C3C2×#115711yescharacteristic
402C2×C3D7×#4111yescharacteristic
403C2×C3#655311yescharacteristic
404D3—41no—
405D3—281no—
406D3—281no—
407C22—61no—
408C22—61no—
409C22—61no—
410C22—141no—
411C22—141no—
412C22—141no—
413C22—421no—
414C22—421no—
415C22—421no—
416C22—421no—
417C22—421no—
418C22—421no—
419C22C22×D3×D711yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—32no—
424C4—61no—
425C4—61no—
426C4—72no—
427C4—141no—
428C4—141no—
429C4—421no—
430C4—421no—
431C3#9022311yescharacteristic, complemented, Sylow
432C2—121no—
433C2—281no—
434C2—841no—
435C2—841no—
436C2D7×#23511yescharacteristic
437C2D3×#115711yescharacteristic
438C2#1062156611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C42×C7C22
hypercenterC42D3×D7
hypocenterC3×C7#555
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. #10621358C2semidirect
2. C7×#872C2semidirect
3. C3×#6435C2semidirect
4. #10621024C2semidirect
5. #10621021C2semidirect
6. #10621016C2semidirect
7. #10621010C2semidirect
8. #10621008C2semidirect
9. #10621006C2semidirect
10. #10620982C2semidirect
11. #10620965C2semidirect
12. #10620964C2semidirect
13. #10620915C2semidirect
14. #10620912C2semidirect
15. #10620890C2semidirect
66. #6435D3semidirect
144. #872D7semidirect
305. C3×C7#555semidirect
399. C7#5532semidirect
431. C3#90223semidirect

Maximal subgroups

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

subgroupindex
#106213582
C7×#8722
C3×#64352
#106210242
#106210212
#106210162
#106210102
#106210082
#106210062
#106209822
#106209652
#106209642
#106209152
#106209122
#106208902
#902233
#55327