Finite Group Databasebeta

← #13252892

Subgroups — #13252892

Order 1792.

850 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11740630C211yesmaximal, characteristic
2C2×C7×#331C211yesmaximal, characteristic, complemented
3C2×#89339C211yesmaximal, characteristic, complemented
4#11728197C211yesmaximal, characteristic, complemented
5#11728195C211yesmaximal, characteristic, complemented
6C2×#89280C211yesmaximal, characteristic, complemented
7C2×#89280C211yesmaximal, characteristic, complemented
8C2×C7×#127C2211yescharacteristic
9C2×#6503—21no—
10C2×#6503—22no—
11C2×#6503—21no—
12C2×#6503C414yes—
13C2×#6437C2211yescharacteristic
14C2×C7×C4⋊C8C2211yescharacteristic
15C2×C7×C4⋊C8C2211yescharacteristic
16C2×#6389—21no—
17C42×Dic7C2211yescharacteristic
18C2×C4⋊(C7⋊C8)C2211yescharacteristic
19C2×C4⋊(C7⋊C8)C2211yescharacteristic
20C7×#331—22no—
21#89345—21no—
22#89345—22no—
23#89339—22no—
24#89280—22no—
25#89280—22no—
26#9706—71nomaximal, Sylow
27C22×C7×D4—21no—
28C22×C7×D4—21no—
29C22×C7×D4C2×C412yes—
30C22×C22⋊D7—24no—
31C22×C22⋊D7—24no—
32C22×D28—21no—
33C22×D28—21no—
34C22×D28C2×C412yes—
35C22×C7×C8—21no—
36C22×C7×C8—21no—
37C7×#127—21no—
38C7×#127—21no—
39C7×#127—21no—
40C7×#127—21no—
41C2×C42×C7C2311yescharacteristic
42#6503—42no—
43#6503—44no—
44#6503—42no—
45#6503—44no—
46#6503—48no—
47#6503—42no—
48#6503—42no—
49C2×C4×Dic7C2×C412yes—
50C2×C4×Dic7D411yescharacteristic
51C2×C4×Dic7D412yes—
52C2×C4×Dic7D411yescharacteristic
53C22×C7⋊C8—21no—
54C22×C7⋊C8—21no—
55#6437—21no—
56#6437—21no—
57#6437—21no—
58#6437—21no—
59C7×C4⋊C8—21no—
60C7×C4⋊C8—21no—
61C7×C4⋊C8—21no—
62C7×C4⋊C8D412yescomplemented
63#6389—42no—
64C4⋊(C7⋊C8)—21no—
65C4⋊(C7⋊C8)—21no—
66C4⋊(C7⋊C8)—21no—
67C4⋊(C7⋊C8)D412yescomplemented
68#2867—71no—
69#1831—71no—
70#1767—71no—
71C2×#331—71no—
72C2×#331—71no—
73C2×#331—71no—
74C2×#331D711yescharacteristic, complemented
75C24×C7—22no—
76C23×D7—22no—
77C2×C7×D4—22no—
78C2×C7×D4—22no—
79C2×C7×D4—44no—
80C2×C7×D4—41no—
81C2×C7×D4—41no—
82C2×C7×D4—41no—
83C2×C7×D4—41no—
84C2×C7×D4—41no—
85C2×C7×D4—41no—
86C2×C7×D4—41no—
87C2×C7×D4—42no—
88C2×C7×D4—41no—
89C2×C7×D4—42no—
90C22×C4×C7C22×C411yescharacteristic
91C22×C4×C7C2×D411yescharacteristic
92C22×C4×C7C2×D411yescharacteristic
93C2×C22⋊D7—48no—
94C2×C22⋊D7—48no—
95C2×C22⋊D7—48no—
96C2×C22⋊D7—48no—
97C2×C22⋊D7—48no—
98C2×C22⋊D7—48no—
99C22×Dic7C22⋊C412yes—
100C22×Dic7C22⋊C412yes—
101C2×D28—22no—
102C2×D28—22no—
103C2×D28—44no—
104C2×D28—41no—
105C2×D28—41no—
106C2×D28—41no—
107C2×D28—41no—
108C2×D28—41no—
109C2×D28—41no—
110C2×D28—41no—
111C2×D28—41no—
112C2×D28—42no—
113C2×D28—42no—
114C2×C7×C8—22no—
115C2×C7×C8—41no—
116C2×C7×C8—41no—
117C2×C7×C8—41no—
118C2×C7×C8—42no—
119C42×C7C2×D411yescharacteristic
120C42×C7C2×D411yescharacteristic
121C42×C7#4111yescharacteristic
122C42×C7#4111yescharacteristic
123C4×Dic7—21no—
124C4×Dic7—22no—
125C4×Dic7—21no—
126C4×Dic7—22no—
127C4×Dic7—24no—
128C4×Dic7D812yes—
129C4×Dic7SD1612yes—
130C2×C7⋊C8—22no—
131C2×C7⋊C8—41no—
132C2×C7⋊C8—41no—
133C2×C7⋊C8—41no—
134C2×C7⋊C8—42no—
135C2×#127—74no—
136C2×#127—71no—
137C2×#127—141no—
138C2×#127—141no—
139C2×#127—142no—
140C2×#127C2×D711yescharacteristic
141C2×C4⋊C8—71no—
142C2×C4⋊C8—71no—
143C2×C4⋊C8C2×D711yescharacteristic
144C2×C4⋊C8C2×D711yescharacteristic
145C2×#97—141no—
146C43—71no—
147#336—142no—
148#336—141no—
149#331—22no—
150#331—142no—
151#331—142no—
152#331—142no—
153C23×C7—42no—
154C23×C7—44no—
155C23×C7—42no—
156C23×C7—44no—
157C23×C7—42no—
158C23×C7C2×C22⋊C411yescharacteristic
159C22×D7—42no—
160C22×D7—44no—
161C22×D7—42no—
162C22×D7—44no—
163C22×D7—42no—
164C7×D4—82no—
165C7×D4—82no—
166C7×D4—81no—
167C7×D4—81no—
168C7×D4—81no—
169C7×D4—81no—
170C7×D4—82no—
171C7×D4—81no—
172C7×D4—81no—
173C2×C4×C7—22no—
174C2×C4×C7C4×D411yescharacteristic
175C2×C4×C7C4×D411yescharacteristic
176C2×C4×C7#12111yescharacteristic
177C2×C4×C7#12111yescharacteristic
178C2×C4×C7#12411yescharacteristic
179C2×C4×C7#12711yescharacteristic
180C2×C4×C7C2×D811yescharacteristic
181C2×C4×C7C2×SD1611yescharacteristic
182C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C7AGL(1,ℤ/8)12yes—
184C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C7AGL(1,ℤ/8)12yes—
186C22⋊D7—816no—
187C22⋊D7—816no—
188C2×Dic7—22no—
189C2×Dic7—22no—
190C2×Dic7—22no—
191C2×Dic7—22no—
192C2×Dic7#10014yes—
193C2×Dic7#10214yes—
194D28—82no—
195D28—82no—
196D28—81no—
197D28—81no—
198D28—81no—
199D28—81no—
200D28—82no—
201D28—81no—
202D28—81no—
203C7×C8—42no—
204C7×C8—81no—
205C7⋊C8—42no—
206C7⋊C8—81no—
207C22×D4—21no—
208C22×D4—21no—
209C22×D4—72no—
210C22×D4—144no—
211C22×D4—144no—
212C22×D4—141no—
213C22×D4—141no—
214C22×D4C4×D712yes—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—141no—
218C22×C8—141no—
219#127—21no—
220#127—21no—
221#127—21no—
222#127—21no—
223#127—141no—
224#127—141no—
225#127—141no—
226#127—141no—
227#127—282no—
228#127—282no—
229#127—288no—
230#127—282no—
231#127—284no—
232#127—282no—
233#127—284no—
234C2×C42—71no—
235C2×C42—72no—
236C2×C42—71no—
237C2×C42—72no—
238C2×C42C22×D711yescharacteristic
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—72no—
243C4⋊C8—141no—
244C4⋊C8—141no—
245C4⋊C8—141no—
246C4⋊C8C22⋊D712yescomplemented
247#97—282no—
248C22×C7—84no—
249C22×C7—84no—
250C22×C7—82no—
251C22×C7—82no—
252C22×C7—82no—
253C22×C7#39011yescharacteristic
254C22×C7C2×#10012yes—
255C22×C7C2×#10211yescharacteristic
256C22×C7#41812yes—
257C22×C7#41811yescharacteristic
258C2×D7—84no—
259C2×D7—84no—
260C2×D7—82no—
261C2×D7—82no—
262C2×D7—82no—
263C4×C7—21no—
264C4×C7—21no—
265C4×C7#45911yescharacteristic
266C4×C7#45911yescharacteristic
267C4×C7#46011yescharacteristic
268C4×C7#46011yescharacteristic
269C4×C7#49012yes—
270C4×C7#49611yescharacteristic
271C4×C7#49611yescharacteristic
272Dic7—24no—
273Dic7—24no—
274C24—22no—
275C24—142no—
276C2×D4—22no—
277C2×D4—22no—
278C2×D4—44no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—42no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—42no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—142no—
290C2×D4—142no—
291C2×D4—284no—
292C2×D4—288no—
293C2×D4—288no—
294C2×D4—288no—
295C2×D4—288no—
296C2×D4—288no—
297C2×D4—288no—
298C2×D4—281no—
299C2×D4—281no—
300C2×D4—281no—
301C2×D4—281no—
302C2×D4—282no—
303C2×D4—281no—
304C2×D4—281no—
305C2×D4—282no—
306C2×D4—281no—
307C2×D4—281no—
308C22×C4—72no—
309C22×C4—72no—
310C22×C4C2×C4×D711yescharacteristic
311C22×C4D4×D711yescharacteristic
312C22×C4D4×D711yescharacteristic
313C2×C8—22no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—42no—
317C2×C8—41no—
318C2×C8—142no—
319C2×C8—281no—
320C2×C8—281no—
321C2×C8—282no—
322C2×C8—281no—
323C42—72no—
324C42—72no—
325C42—144no—
326C42—141no—
327C42—142no—
328C42—141no—
329C42—142no—
330C42#115711yescharacteristic
331C42D4×D711yescharacteristic
332C42#115911yescharacteristic
333C42C2×C22⋊D711yescharacteristic
334C2×C7—162no—
335C2×C7#154512yes—
336C2×C7#155512yes—
337C2×C7#196111yescharacteristic
338C2×C7#196511yescharacteristic
339C2×C7#198211yescharacteristic
340D7—162no—
341C23—42no—
342C23—44no—
343C23—42no—
344C23—44no—
345C23—42no—
346C23—282no—
347C23—284no—
348C23—282no—
349C23—284no—
350C23—282no—
351C23D7×C22⋊C411yescharacteristic
352D4—82no—
353D4—82no—
354D4—81no—
355D4—81no—
356D4—81no—
357D4—81no—
358D4—81no—
359D4—82no—
360D4—81no—
361D4—562no—
362D4—562no—
363D4—5616no—
364D4—5616no—
365D4—561no—
366D4—561no—
367D4—561no—
368D4—561no—
369D4—561no—
370D4—562no—
371D4—561no—
372C2×C4—22no—
373C2×C4—74no—
374C2×C4—74no—
375C2×C4—142no—
376C2×C4—142no—
377C2×C4—142no—
378C2×C4—142no—
379C2×C4(C22⋊D7)⋊C411yescharacteristic
380C2×C4#644711yescharacteristic
381C2×C4#644811yescharacteristic
382C2×C4D7×D811yescharacteristic
383C2×C4#647411yescharacteristic
384C2×C4#647412yes—
385C2×C4D7×SD1611yescharacteristic
386C2×C4#647711yescharacteristic
387C2×C4#647712yes—
388C2×C4C4×C22⋊D711yescharacteristic
389C2×C4#650211yescharacteristic
390C2×C4#650311yescharacteristic
391C8—42no—
392C8—81no—
393C8—282no—
394C8—561no—
395C7#970611yescharacteristic, complemented, Sylow
396C22—82no—
397C22—82no—
398C22—84no—
399C22—84no—
400C22—82no—
401C22—562no—
402C22—562no—
403C22—564no—
404C22—564no—
405C22—562no—
406C22D7×#10012yes—
407C22D7×#10211yescharacteristic
408C22#8954212yes—
409C22#8954211yescharacteristic
410C22#8972911yescharacteristic
411C4—21no—
412C4—21no—
413C4—144no—
414C4—144no—
415C4#8953411yescharacteristic
416C4#8953612yes—
417C4#8955811yescharacteristic
418C4#8992211yescharacteristic
419C4#8992611yescharacteristic
420C4#8993511yescharacteristic
421C4#8994811yescharacteristic
422C2—162no—
423C2—1122no—
424C2#1172613712yes—
425C2#1172614112yes—
426C2#1172781811yescharacteristic
427C2#1172791411yescharacteristic
428C2#1172791511yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC2×C7×#331C2
socleC23×C7C2×C22⋊C4
prime radical#11740630C2
cosocleC2×C42×C7C23
hypercenterC2×#331D7
hypocenterC7#9706
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
2. C2×C7×#331C2semidirect
3. C2×#89339C2semidirect
4. #11728197C2semidirect
5. #11728195C2semidirect
6. C2×#89280C2semidirect
7. C2×#89280C2semidirect
62. C7×C4⋊C8D4semidirect
67. C4⋊(C7⋊C8)D4semidirect
74. C2×#331D7semidirect
246. C4⋊C8C22⋊D7semidirect
395. C7#9706semidirect

Maximal subgroups

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

subgroupindex
#117406302
C2×C7×#3312
C2×#893392
#117281972
#117281952
C2×#892802
#97067