Finite Group Databasebeta

← C7×#13395 #13190611

Subgroups — C7×#13395 #13190611

Order 1792.

422 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3050C211yesmaximal, characteristic
2C7×#2155C211yesmaximal, characteristic, complemented
3C7×#2148C211yesmaximal, characteristic, complemented
4C7×#2143C211yesmaximal, characteristic, complemented
5C7×#2112C211yesmaximal, characteristic, complemented
6C7×#1810C211yesmaximal, characteristic, complemented
7C7×#1389C211yesmaximal, characteristic, complemented
8C2×C7×#135C2211yescharacteristic
9C23×C7×C8C2211yescharacteristic
10C7×#525—21no—
11C2×C7×M32C2211yescharacteristic
12C2×C7×M32C2211yescharacteristic
13C7×#467—21no—
14C7×#466—21no—
15C7×#465—22no—
16C2×C7×#108C2211yescharacteristic
17C2×C7×#108C2211yescharacteristic
18C7×#427C2211yescharacteristic
19C7×#416—21no—
20C7×#407—21no—
21C7×#365—22no—
22C7×#362—21no—
23C7×#361—21no—
24C7×#359—22no—
25C7×C22⋊C16—22no—
26C7×#341—21no—
27#13395C711yesmaximal, characteristic, direct product factor, Sylow
28C2×C7×#41—21no—
29C23×C4×C7D411yescharacteristic
30C7×#135—21no—
31C7×#135—21no—
32C7×#135—21no—
33C7×#135—21no—
34C2×C7×Q16D411yescharacteristic
35C2×C7×SD16—21no—
36C2×C7×D8D411yescharacteristic
37C2×C7×M16—21no—
38C2×C7×M16—21no—
39C22×C7×C8—21no—
40C22×C7×C8—21no—
41C22×C7×C8—21no—
42C22×C7×C8—21no—
43C22×C7×C8—21no—
44C22×C7×C8—21no—
45C22×C7×C8D411yescharacteristic
46C22×C7×C8C2311yescharacteristic
47C7×#123—41no—
48C7×C22⋊Q8—22no—
49C7×#121—22no—
50C7×#120—41no—
51C4×C7×D4—42no—
52C7×#117—21no—
53C7×M32—21no—
54C7×M32—21no—
55C7×M32—21no—
56C7×M32—21no—
57C2×C7×C16—21no—
58C2×C7×C16D412yescomplemented
59C7×#108—21no—
60C7×#108—21no—
61C7×#108—21no—
62C7×#108—21no—
63C7×#107—21no—
64C7×#106D412yes—
65C7×#103—22no—
66C7×#102—22no—
67C7×C22⋊C8—42no—
68#3050C2×C711yescharacteristic
69#2155C2×C711yescharacteristic, complemented
70#2148C2×C711yescharacteristic, complemented
71#2143C2×C711yescharacteristic, complemented
72#2112C2×C711yescharacteristic, complemented
73#1810C2×C711yescharacteristic, complemented
74#1389C2×C711yescharacteristic, complemented
75C24×C7SD1611yescharacteristic
76C7×#41—41no—
77C7×#41—41no—
78C7×#41—41no—
79C7×#41—41no—
80C2×C7×Q8—21no—
81C2×C7×D4—21no—
82C2×C7×D4—42no—
83C2×C7×D4—41no—
84C22×C4×C7—21no—
85C22×C4×C7—21no—
86C22×C4×C7—21no—
87C22×C4×C7—21no—
88C22×C4×C7—21no—
89C22×C4×C7—21no—
90C22×C4×C7—41no—
91C22×C4×C7SD1611yescharacteristic
92C22×C4×C7C2×D411yescharacteristic
93C7×Q16—21no—
94C7×Q16—21no—
95C7×SD16—41no—
96C7×SD16—41no—
97C7×D8—21no—
98C7×D8—21no—
99C7×M16—41no—
100C7×M16—41no—
101C7×M16—41no—
102C7×M16—41no—
103C2×C7×C8—21no—
104C2×C7×C8—21no—
105C2×C7×C8—21no—
106C2×C7×C8—41no—
107C2×C7×C8—41no—
108C2×C7×C8—41no—
109C2×C7×C8—41no—
110C2×C7×C8—41no—
111C2×C7×C8—41no—
112C2×C7×C8C2×D411yescharacteristic
113C2×C7×C8C2×D411yescharacteristic
114C2×C7×C8C2×D411yescharacteristic
115C2×C7×C8#4111yescharacteristic
116C2×C7×C8#4111yescharacteristic
117C2×C7×C8#4111yescharacteristic
118C7×C4⋊C4—22no—
119C7×C4⋊C4—42no—
120C7×C22⋊C4—42no—
121C7×C22⋊C4—42no—
122C7×C22⋊C4—41no—
123C42×C7—41no—
124C7×C16—22no—
125C7×C16—41no—
126C2×#135C22×C711yescharacteristic
127C23×C8C22×C711yescharacteristic
128#525—21no—
129C2×M32C22×C711yescharacteristic
130C2×M32C22×C711yescharacteristic
131#467—21no—
132#466—21no—
133#465—22no—
134C2×#108C22×C711yescharacteristic
135C2×#108C22×C711yescharacteristic
136#427C22×C711yescharacteristic
137#416—21no—
138#407—21no—
139#365—22no—
140#362—21no—
141#361—21no—
142#359—22no—
143C22⋊C16—22no—
144#341—21no—
145C23×C7—21no—
146C23×C7—21no—
147C23×C7—21no—
148C23×C7—42no—
149C23×C7—41no—
150C23×C7C2×SD1611yescharacteristic
151C7×Q8—41no—
152C7×Q8—41no—
153C7×D4—41no—
154C7×D4—41no—
155C7×D4—84no—
156C7×D4—81no—
157C7×D4—81no—
158C2×C4×C7—21no—
159C2×C4×C7—21no—
160C2×C4×C7—21no—
161C2×C4×C7—41no—
162C2×C4×C7—41no—
163C2×C4×C7—41no—
164C2×C4×C7—41no—
165C2×C4×C7—42no—
166C2×C4×C7—41no—
167C2×C4×C7—81no—
168C2×C4×C7—81no—
169C2×C4×C7#12011yescharacteristic
170C2×C4×C7#12111yescharacteristic
171C2×C4×C7#12311yescharacteristic
172C2×C4×C7#13511yescharacteristic
173C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
175C7×C8—41no—
176C7×C8—81no—
177C7×C8—81no—
178C7×C8#12111yescharacteristic
179C7×C8#12111yescharacteristic
180C7×C8#12311yescharacteristic
181C7×C8#12411yescharacteristic
182C2×#41—21no—
183C23×C4C7×D411yescharacteristic
184#135—21no—
185#135—21no—
186#135—21no—
187#135—21no—
188C2×Q16C7×D411yescharacteristic
189C2×SD16—21no—
190C2×D8C7×D411yescharacteristic
191C2×M16—21no—
192C2×M16—21no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8C7×D411yescharacteristic
200C22×C8C23×C711yescharacteristic
201#123—41no—
202C22⋊Q8—22no—
203#121—22no—
204#120—41no—
205C4×D4—42no—
206#117—21no—
207M32—21no—
208M32—21no—
209M32—21no—
210M32—21no—
211C2×C16—21no—
212C2×C16C7×D412yescomplemented
213#108—21no—
214#108—21no—
215#108—21no—
216#108—21no—
217#107—21no—
218#106C7×D412yes—
219#103—22no—
220#102—22no—
221C22⋊C8—42no—
222C22×C7—22no—
223C22×C7—22no—
224C22×C7—22no—
225C22×C7—41no—
226C22×C7—41no—
227C22×C7—41no—
228C22×C7—41no—
229C22×C7—41no—
230C22×C7—82no—
231C22×C7—81no—
232C22×C7#45011yescharacteristic
233C22×C7#46511yescharacteristic
234C22×C7#48111yescharacteristic
235C4×C7—41no—
236C4×C7—82no—
237C4×C7—81no—
238C4×C7#39411yescharacteristic
239C4×C7#44911yescharacteristic
240C4×C7#46911yescharacteristic
241C4×C7#48211yescharacteristic
242C24C7×SD1611yescharacteristic
243#41—41no—
244#41—41no—
245#41—41no—
246#41—41no—
247C2×Q8—21no—
248C2×D4—21no—
249C2×D4—42no—
250C2×D4—41no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—41no—
258C22×C4C7×SD1611yescharacteristic
259C22×C4C2×C7×D411yescharacteristic
260Q16—21no—
261Q16—21no—
262SD16—41no—
263SD16—41no—
264D8—21no—
265D8—21no—
266M16—41no—
267M16—41no—
268M16—41no—
269M16—41no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8C2×C7×D411yescharacteristic
280C2×C8C2×C7×D411yescharacteristic
281C2×C8C2×C7×D411yescharacteristic
282C2×C8C7×#4111yescharacteristic
283C2×C8C7×#4111yescharacteristic
284C2×C8C7×#4111yescharacteristic
285C4⋊C4—22no—
286C4⋊C4—42no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C22⋊C4—41no—
290C42—41no—
291C16—22no—
292C16—41no—
293C2×C7—21no—
294C2×C7—21no—
295C2×C7—21no—
296C2×C7—42no—
297C2×C7—161no—
298C2×C7#203411yescharacteristic
299C23—21no—
300C23—21no—
301C23—21no—
302C23—42no—
303C23—41no—
304C23C2×C7×SD1611yescharacteristic
305Q8—41no—
306Q8—41no—
307D4—41no—
308D4—41no—
309D4—84no—
310D4—81no—
311D4—81no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4C7×#12011yescharacteristic
324C2×C4C7×#12111yescharacteristic
325C2×C4C7×#12311yescharacteristic
326C2×C4C7×#13511yescharacteristic
327C2×C4C7×AGL(1,ℤ/8)11yescharacteristic
328C2×C4C7×AGL(1,ℤ/8)11yescharacteristic
329C8—41no—
330C8—81no—
331C8—81no—
332C8C7×#12111yescharacteristic
333C8C7×#12111yescharacteristic
334C8C7×#12311yescharacteristic
335C8C7×#12411yescharacteristic
336C7#1339511yescharacteristic, direct product factor, Sylow
337C22—22no—
338C22—22no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—82no—
346C22—81no—
347C22C7×#45011yescharacteristic
348C22C7×#46511yescharacteristic
349C22C7×#48111yescharacteristic
350C4—41no—
351C4—82no—
352C4—81no—
353C4C7×#39411yescharacteristic
354C4C7×#44911yescharacteristic
355C4C7×#46911yescharacteristic
356C4C7×#48211yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—42no—
361C2—161no—
362C2C7×#203411yescharacteristic
subgroupG/H
centerC4×C7#469
commutator, Frattini, cosocleC22×C8C23×C7
socleC2×C7#2034
prime radicalC7×#3050C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C7 ◁ C22×C4×C7 ◁ C23×C7×C8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C7×#2155C2semidirect
3. C7×#2148C2semidirect
4. C7×#2143C2semidirect
5. C7×#2112C2semidirect
6. C7×#1810C2semidirect
7. C7×#1389C2semidirect
27. #13395C7direct (N × H)
58. C2×C7×C16D4semidirect
69. #2155C2×C7semidirect
70. #2148C2×C7semidirect
71. #2143C2×C7semidirect
72. #2112C2×C7semidirect
73. #1810C2×C7semidirect
74. #1389C2×C7semidirect
212. C2×C16C7×D4semidirect
336. C7#13395direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#30502
C7×#21552
C7×#21482
C7×#21432
C7×#21122
C7×#18102
C7×#13892
#133957