Finite Group Databasebeta

← C7×#13445 #13190661

Subgroups — C7×#13445 #13190661

Order 1792.

432 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#509C211yesmaximal, characteristic
2C2×C7×#364C211yesmaximal, characteristic, complemented
3C2×C7×#361C211yesmaximal, characteristic, complemented
4C7×#2139C211yesmaximal, characteristic, complemented
5C7×#1974C211yesmaximal, characteristic, complemented
6C7×#1970C211yesmaximal, characteristic, complemented
7C7×#1387C211yesmaximal, characteristic, complemented
8C2×C7×#135C2211yescharacteristic
9C22×C7×D8C2211yescharacteristic
10C7×#509—22no—
11C7×#509—22no—
12C2×C7×SD32—21no—
13C2×C7×D16—21no—
14C2×C7×M32C2211yescharacteristic
15C2×C7×M32C2211yescharacteristic
16C2×C7×#108C2211yescharacteristic
17C2×C7×#107C2211yescharacteristic
18C2×C7×#104—21no—
19C2×C7×#102—21no—
20C7×#408—21no—
21C2×C4×C7×C8C2211yescharacteristic
22C7×#390—21no—
23C7×#364—22no—
24C7×#361—22no—
25C7×#358—21no—
26C7×#357—21no—
27#13445C711yesmaximal, characteristic, direct product factor, Sylow
28C2×C7×#41—21no—
29C22×C7×D4—21no—
30C7×#135—21no—
31C7×#135—21no—
32C7×#135—21no—
33C7×#135—21no—
34C2×C7×Q16D411yescharacteristic
35C2×C7×SD16—21no—
36C2×C7×D8—21no—
37C2×C7×D8—21no—
38C2×C7×D8—21no—
39C2×C7×D8—21no—
40C2×C7×D8—21no—
41C2×C7×D8D411yescharacteristic
42C2×C7×D8D412yes—
43C2×C7×M16—21no—
44C22×C7×C8D411yescharacteristic
45C22×C7×C8C2311yescharacteristic
46C2×C7×C4⋊C4—21no—
47C2×C7×C22⋊C4—42no—
48C2×C42×C7D411yescharacteristic
49C7×SD32—24no—
50C7×D16—24no—
51C7×M32—21no—
52C7×M32—21no—
53C7×M32—21no—
54C7×M32D412yes—
55C2×C7×C16—21no—
56C2×C7×C16—21no—
57C7×#108—21no—
58C7×#108—21no—
59C7×#107—21no—
60C7×#107—21no—
61C7×#104—42no—
62C7×#102—42no—
63C7×C22⋊C8—42no—
64C4×C7×C8—21no—
65C4×C7×C8—21no—
66C2×#509C2×C711yescharacteristic
67C2×#364C2×C711yescharacteristic, complemented
68C2×#361C2×C711yescharacteristic, complemented
69#2139C2×C711yescharacteristic, complemented
70#1974C2×C711yescharacteristic, complemented
71#1970C2×C711yescharacteristic, complemented
72#1387C2×C711yescharacteristic, complemented
73C24×C7—41no—
74C7×#41—41no—
75C7×#41—41no—
76C7×#41—41no—
77C7×#41—41no—
78C2×C7×Q8—21no—
79C2×C7×D4—22no—
80C2×C7×D4—21no—
81C2×C7×D4—41no—
82C2×C7×D4—41no—
83C2×C7×D4—41no—
84C2×C7×D4—41no—
85C2×C7×D4—41no—
86C2×C7×D4—41no—
87C22×C4×C7—21no—
88C22×C4×C7—41no—
89C22×C4×C7—41no—
90C22×C4×C7C2×D411yescharacteristic
91C7×Q16—21no—
92C7×Q16—21no—
93C7×SD16—41no—
94C7×SD16—41no—
95C7×D8—21no—
96C7×D8—22no—
97C7×D8—22no—
98C7×D8—21no—
99C7×D8—41no—
100C7×D8—41no—
101C7×M16—41no—
102C7×M16—41no—
103C2×C7×C8—21no—
104C2×C7×C8—21no—
105C2×C7×C8—41no—
106C2×C7×C8D812yes—
107C2×C7×C8C2×D411yescharacteristic
108C2×C7×C8C2×D411yescharacteristic
109C2×C7×C8C2×D411yescharacteristic
110C2×C7×C8#4111yescharacteristic
111C2×C7×C8#4111yescharacteristic
112C2×C7×C8#4111yescharacteristic
113C7×C4⋊C4—41no—
114C7×C4⋊C4—41no—
115C7×C22⋊C4—84no—
116C42×C7—21no—
117C42×C7—21no—
118C7×C16—22no—
119C7×C16—41no—
120C2×#135C22×C711yescharacteristic
121C22×D8C22×C711yescharacteristic
122#509—22no—
123#509—22no—
124C2×SD32—21no—
125C2×D16—21no—
126C2×M32C22×C711yescharacteristic
127C2×M32C22×C711yescharacteristic
128C2×#108C22×C711yescharacteristic
129C2×#107C22×C711yescharacteristic
130C2×#104—21no—
131C2×#102—21no—
132#408—21no—
133C2×C4×C8C22×C711yescharacteristic
134#390—21no—
135#364—22no—
136#361—22no—
137#358—21no—
138#357—21no—
139C23×C7—41no—
140C23×C7—42no—
141C23×C7—82no—
142C23×C7—82no—
143C23×C7—81no—
144C23×C7—81no—
145C23×C7AGL(1,ℤ/8)11yescharacteristic
146C7×Q8—41no—
147C7×Q8—41no—
148C7×D4—42no—
149C7×D4—41no—
150C7×D4—42no—
151C7×D4—41no—
152C7×D4—81no—
153C7×D4—81no—
154C7×D4—81no—
155C7×D4—81no—
156C2×C4×C7—22no—
157C2×C4×C7—41no—
158C2×C4×C7—41no—
159C2×C4×C7—41no—
160C2×C4×C7—81no—
161C2×C4×C7—81no—
162C2×C4×C7—82no—
163C2×C4×C7—81no—
164C2×C4×C7#12111yescharacteristic
165C2×C4×C7#12111yescharacteristic
166C2×C4×C7#12111yescharacteristic
167C2×C4×C7C2×D811yescharacteristic
168C2×C4×C7#13511yescharacteristic
169C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
170C7×C8—22no—
171C7×C8—81no—
172C7×C8#12011yescharacteristic
173C7×C8#12311yescharacteristic
174C7×C8#12311yescharacteristic
175C7×C8#12411yescharacteristic
176C2×#41—21no—
177C22×D4—21no—
178#135—21no—
179#135—21no—
180#135—21no—
181#135—21no—
182C2×Q16C7×D411yescharacteristic
183C2×SD16—21no—
184C2×D8—21no—
185C2×D8—21no—
186C2×D8—21no—
187C2×D8—21no—
188C2×D8—21no—
189C2×D8C7×D412yes—
190C2×D8C7×D411yescharacteristic
191C2×M16—21no—
192C22×C8C7×D411yescharacteristic
193C22×C8C23×C711yescharacteristic
194C2×C4⋊C4—21no—
195C2×C22⋊C4—42no—
196C2×C42C7×D411yescharacteristic
197SD32—24no—
198D16—24no—
199M32—21no—
200M32—21no—
201M32—21no—
202M32C7×D412yes—
203C2×C16—21no—
204C2×C16—21no—
205#108—21no—
206#108—21no—
207#107—21no—
208#107—21no—
209#104—42no—
210#102—42no—
211C22⋊C8—42no—
212C4×C8—21no—
213C4×C8—21no—
214C22×C7—21no—
215C22×C7—21no—
216C22×C7—84no—
217C22×C7—81no—
218C22×C7—82no—
219C22×C7—81no—
220C22×C7—81no—
221C22×C7—162no—
222C22×C7—161no—
223C22×C7—161no—
224C22×C7#45911yescharacteristic
225C22×C7#46311yescharacteristic
226C22×C7#46911yescharacteristic
227C4×C7—42no—
228C4×C7—81no—
229C4×C7—161no—
230C4×C7#39411yescharacteristic
231C4×C7#45911yescharacteristic
232C4×C7#46311yescharacteristic
233C4×C7#46611yescharacteristic
234C24—41no—
235#41—41no—
236#41—41no—
237#41—41no—
238#41—41no—
239C2×Q8—21no—
240C2×D4—22no—
241C2×D4—21no—
242C2×D4—41no—
243C2×D4—41no—
244C2×D4—41no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—41no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4C2×C7×D411yescharacteristic
252Q16—21no—
253Q16—21no—
254SD16—41no—
255SD16—41no—
256D8—21no—
257D8—22no—
258D8—22no—
259D8—21no—
260D8—41no—
261D8—41no—
262M16—41no—
263M16—41no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—41no—
267C2×C8C7×D812yes—
268C2×C8C2×C7×D411yescharacteristic
269C2×C8C2×C7×D411yescharacteristic
270C2×C8C2×C7×D411yescharacteristic
271C2×C8C7×#4111yescharacteristic
272C2×C8C7×#4111yescharacteristic
273C2×C8C7×#4111yescharacteristic
274C4⋊C4—41no—
275C4⋊C4—41no—
276C22⋊C4—84no—
277C42—21no—
278C42—21no—
279C16—22no—
280C16—41no—
281C2×C7—21no—
282C2×C7—21no—
283C2×C7—161no—
284C2×C7—162no—
285C2×C7#205411yescharacteristic
286C2×C7#221211yescharacteristic
287C2×C7#221311yescharacteristic
288C23—41no—
289C23—42no—
290C23—82no—
291C23—82no—
292C23—81no—
293C23—81no—
294C23C7×AGL(1,ℤ/8)11yescharacteristic
295Q8—41no—
296Q8—41no—
297D4—42no—
298D4—41no—
299D4—42no—
300D4—41no—
301D4—81no—
302D4—81no—
303D4—81no—
304D4—81no—
305C2×C4—22no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—82no—
312C2×C4—81no—
313C2×C4C7×#12111yescharacteristic
314C2×C4C7×#12111yescharacteristic
315C2×C4C7×#12111yescharacteristic
316C2×C4C2×C7×D811yescharacteristic
317C2×C4C7×#13511yescharacteristic
318C2×C4C7×AGL(1,ℤ/8)11yescharacteristic
319C8—22no—
320C8—81no—
321C8C7×#12011yescharacteristic
322C8C7×#12311yescharacteristic
323C8C7×#12311yescharacteristic
324C8C7×#12411yescharacteristic
325C7#1344511yescharacteristic, direct product factor, Sylow
326C22—21no—
327C22—21no—
328C22—84no—
329C22—81no—
330C22—82no—
331C22—81no—
332C22—81no—
333C22—162no—
334C22—161no—
335C22—161no—
336C22C7×#45911yescharacteristic
337C22C7×#46311yescharacteristic
338C22C7×#46911yescharacteristic
339C4—42no—
340C4—81no—
341C4—161no—
342C4C7×#39411yescharacteristic
343C4C7×#45911yescharacteristic
344C4C7×#46311yescharacteristic
345C4C7×#46611yescharacteristic
346C2—21no—
347C2—21no—
348C2—162no—
349C2—161no—
350C2C7×#205411yescharacteristic
351C2C7×#221211yescharacteristic
352C2C7×#221311yescharacteristic
subgroupG/H
center, socleC22×C7#459
commutator, Frattini, cosocleC22×C8C23×C7
prime radicalC2×C7×#509C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C2×C4×C7×C8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#364C2semidirect
3. C2×C7×#361C2semidirect
4. C7×#2139C2semidirect
5. C7×#1974C2semidirect
6. C7×#1970C2semidirect
7. C7×#1387C2semidirect
27. #13445C7direct (N × H)
67. C2×#364C2×C7semidirect
68. C2×#361C2×C7semidirect
69. #2139C2×C7semidirect
70. #1974C2×C7semidirect
71. #1970C2×C7semidirect
72. #1387C2×C7semidirect
325. C7#13445direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5092
C2×C7×#3642
C2×C7×#3612
C7×#21392
C7×#19742
C7×#19702
C7×#13872
#134457