Finite Group Databasebeta

← D7×#1347 #13264013

Subgroups — D7×#1347 #13264013

Order 1792.

558 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D7×#466C211yesmaximal, characteristic
2D7×C22⋊C16C211yesmaximal, characteristic, complemented
3D7×#340C211yesmaximal, characteristic, complemented
4C7×#1347C211yesmaximal, characteristic, complemented
5#11725580C211yesmaximal, characteristic, complemented
6#11725332C211yesmaximal, characteristic, complemented
7#11725291C211yesmaximal, characteristic, complemented
8C2×D7×D8C411yescharacteristic, complemented
9C22×C8×D7C2211yescharacteristic
10D7×#121—21no—
11C2×D7×C4⋊C4—21no—
12C7×#466C2211yescharacteristic
13#89929C411yescharacteristic, complemented
14#89887C2211yescharacteristic
15#89810—21no—
16C2×D7×C16—21no—
17#89655C411yescharacteristic, complemented
18D7×#107C411yescharacteristic, complemented
19#89547—21no—
20D7×#102—21no—
21C7×C22⋊C16C2211yescharacteristic, complemented
22C7×#340C2211yescharacteristic, complemented
23#89346C2211yescharacteristic, complemented
24C22⋊(C7⋊C16)C2211yescharacteristic, complemented
25#89324—21no—
26(C2×D7)⋊C16—21no—
27C2×#1347—71nomaximal, Sylow
28C2×D4×D7—21no—
29C2×D4×D7—41no—
30C22×C4×D7—41no—
31C22×C4×D7D411yescharacteristic
32C2×C7×D8C2×C411yescharacteristic, complemented
33C22×C7×C8C2311yescharacteristic
34C7×#121—21no—
35C2×C7×C4⋊C4—21no—
36#6502—41no—
37#6501—21no—
38C2×#1141—21no—
39#6493—21no—
40C2×C4⋊Dic7—21no—
41C2×Dic7⋊C4—41no—
42C22×C7⋊C8D411yescharacteristic
43D7×D8—42no—
44C2×D56C2×C411yescharacteristic, complemented
45C2×C8×D7—42no—
46C2×C8×D7C2×C411yescharacteristic
47C2×C8×D7C2×C411yescharacteristic
48C2×C8×D7D411yescharacteristic
49C2×C8×D7D411yescharacteristic
50#6458—21no—
51D7×C4⋊C4—24no—
52D7×C4⋊C4—21no—
53D7×C4⋊C4—42no—
54#6447—41no—
55D7×C22⋊C4—41no—
56C2×C7×C16—21no—
57C7×#107C2×C411yescharacteristic, complemented
58C7×#102—21no—
59#6406—21no—
60#6395—21no—
61#6392C2×C411yescharacteristic, complemented
62C2×C7⋊C16—21no—
63#6383—21no—
64#6381—21no—
65D7×C16—42no—
66C2×#466—71no—
67C2×C22⋊C16—71no—
68C2×#340—71no—
69#1347—71no—
70#1347—71no—
71#1347—71no—
72#1347D711yescharacteristic, direct product factor
73C23×D7—41no—
74C23×D7D811yescharacteristic
75C2×C7×D4—21no—
76C2×C7×D4—41no—
77C22×C4×C7—41no—
78C22×C4×C7C2×D411yescharacteristic
79C2×C22⋊D7—41no—
80C2×C22⋊D7—41no—
81C2×C22⋊D7—41no—
82C22×Dic7—41no—
83C22×Dic7D811yescharacteristic
84D4×D7—42no—
85D4×D7—42no—
86D4×D7—82no—
87D4×D7—82no—
88C2×D28—21no—
89C2×D28—41no—
90C2×C4×D7—22no—
91C2×C4×D7—22no—
92C2×C4×D7—44no—
93C2×C4×D7—41no—
94C2×C4×D7—82no—
95C2×C4×D7—82no—
96C2×C4×D7C22⋊C411yescharacteristic
97C2×C4×D7C22⋊C411yescharacteristic
98C2×C4×D7SD1611yescharacteristic
99C2×C4×D7SD1611yescharacteristic
100C7×D8—41no—
101C2×C7×C8—41no—
102C2×C7×C8C22×C411yescharacteristic
103C2×C7×C8C2×D411yescharacteristic
104C7×C4⋊C4—22no—
105C7×C4⋊C4—21no—
106C7×C4⋊C4—41no—
107C7×C22⋊C4—41no—
108C22⋊Dic7—41no—
109#1141—42no—
110(C2×D7)⋊C4—41no—
111(C2×D7)⋊C4—41no—
112C4⋊Dic7—22no—
113C4⋊Dic7—21no—
114C4⋊Dic7—41no—
115Dic7⋊C4—44no—
116Dic7⋊C4—41no—
117C2×C7⋊C8—41no—
118C2×C7⋊C8C22⋊C411yescharacteristic
119C2×C7⋊C8C22⋊C411yescharacteristic
120D56—41no—
121C8×D7—22no—
122C8×D7—22no—
123C8×D7—41no—
124C8×D7—41no—
125C7×C16—41no—
126C7⋊C16—41no—
127C22×D8—71no—
128C23×C8—71no—
129C2×#121—141no—
130C22×C4⋊C4—141no—
131C22×C16—141no—
132#466—71no—
133#466—71no—
134#466—71no—
135#466—141no—
136#466—141no—
137#466C2×D711yescharacteristic
138C2×#107—71no—
139C2×#102—141no—
140C22⋊C16—71no—
141C22⋊C16—141no—
142C22⋊C16C2×D711yescharacteristic, complemented
143#340—71no—
144#340—141no—
145#340C2×D711yescharacteristic, complemented
146C23×C7—41no—
147C23×C7C2×D811yescharacteristic
148C22×D7—22no—
149C22×D7—22no—
150C22×D7—41no—
151C22×D7—82no—
152C22×D7—82no—
153C22×D7—82no—
154C22×D7#10211yescharacteristic
155C22×D7#10211yescharacteristic
156C22×D7D1612yes—
157C22×D7SD3212yes—
158C7×D4—41no—
159C7×D4—41no—
160C7×D4—81no—
161C7×D4—81no—
162C2×C4×C7—21no—
163C2×C4×C7—21no—
164C2×C4×C7—42no—
165C2×C4×C7—41no—
166C2×C4×C7—81no—
167C2×C4×C7—81no—
168C2×C4×C7C2×C22⋊C411yescharacteristic
169C2×C4×C7C2×SD1611yescharacteristic
170C22⋊D7—81no—
171C22⋊D7—81no—
172C22⋊D7—82no—
173C22⋊D7—82no—
174C2×Dic7—22no—
175C2×Dic7—42no—
176C2×Dic7—41no—
177C2×Dic7—81no—
178C2×Dic7—81no—
179C2×Dic7#10211yescharacteristic
180C2×Dic7#10211yescharacteristic
181D28—41no—
182D28—41no—
183D28—82no—
184C4×D7—22no—
185C4×D7—21no—
186C4×D7—21no—
187C4×D7—22no—
188C4×D7—88no—
189C4×D7—82no—
190C4×D7#9912yes—
191C4×D7#10412yes—
192C7×C8—21no—
193C7×C8—21no—
194C7⋊C8—21no—
195C7⋊C8—21no—
196C22×D4—141no—
197C22×D4—281no—
198C23×C4—71no—
199C23×C4—281no—
200C2×D8—71no—
201C2×D8—141no—
202C2×D8—282no—
203C2×D8C4×D711yescharacteristic, complemented
204C22×C8—71no—
205C22×C8—71no—
206C22×C8—71no—
207C22×C8—71no—
208C22×C8—71no—
209C22×C8—282no—
210C22×C8C22×D711yescharacteristic
211#121—21no—
212#121—141no—
213#121—141no—
214#121—141no—
215#121—281no—
216#121—281no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—141no—
219C2×C4⋊C4—144no—
220C2×C4⋊C4—141no—
221C2×C4⋊C4—282no—
222C2×C4⋊C4—281no—
223C2×C22⋊C4—281no—
224C2×C16—21no—
225C2×C16—141no—
226C2×C16—282no—
227#107—71no—
228#107—141no—
229#107C4×D711yescharacteristic, complemented
230#102—21no—
231#102—141no—
232#102—141no—
233#102—141no—
234C22×C7—21no—
235C22×C7—21no—
236C22×C7—81no—
237C22×C7—81no—
238C22×C7—81no—
239C22×C7C2×#10211yescharacteristic
240C22×C7C2×D1611yescharacteristic
241C22×C7C2×SD3211yescharacteristic
242C2×D7—21no—
243C2×D7—21no—
244C2×D7—24no—
245C2×D7—24no—
246C2×D7—81no—
247C2×D7—81no—
248C2×D7—81no—
249C2×D7—164no—
250C2×D7#32712yes—
251C2×D7#35712yes—
252C2×D7#35712yes—
253C2×D7#36012yes—
254C4×C7—21no—
255C4×C7—82no—
256C4×C7—81no—
257C4×C7C2×#9911yescharacteristic
258C4×C7C2×#10411yescharacteristic
259Dic7—21no—
260Dic7—82no—
261Dic7—81no—
262Dic7#32712yes—
263C24—71no—
264C24—281no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—141no—
268C2×D4—281no—
269C2×D4—282no—
270C2×D4—282no—
271C2×D4—281no—
272C2×D4—281no—
273C2×D4—281no—
274C2×D4—562no—
275C2×D4—562no—
276C22×C4—41no—
277C22×C4—71no—
278C22×C4—71no—
279C22×C4—71no—
280C22×C4—71no—
281C22×C4—71no—
282C22×C4—142no—
283C22×C4—142no—
284C22×C4—281no—
285C22×C4—284no—
286C22×C4—281no—
287C22×C4—562no—
288C22×C4—562no—
289C22×C4D4×D711yescharacteristic
290D8—41no—
291D8—281no—
292D8—282no—
293C2×C8—41no—
294C2×C8—71no—
295C2×C8—71no—
296C2×C8—142no—
297C2×C8—142no—
298C2×C8—281no—
299C2×C8—281no—
300C2×C8—281no—
301C2×C8C2×C4×D711yescharacteristic
302C2×C8D4×D711yescharacteristic
303C4⋊C4—22no—
304C4⋊C4—21no—
305C4⋊C4—41no—
306C4⋊C4—142no—
307C4⋊C4—141no—
308C4⋊C4—281no—
309C4⋊C4—281no—
310C4⋊C4—284no—
311C22⋊C4—41no—
312C22⋊C4—281no—
313C22⋊C4—281no—
314C22⋊C4—281no—
315C16—41no—
316C16—281no—
317C2×C7—21no—
318C2×C7—21no—
319C2×C7—161no—
320C2×C7C2×#32711yescharacteristic
321C2×C7C2×#35711yescharacteristic
322C2×C7C2×#36011yescharacteristic
323D7—22no—
324D7—161no—
325D7#134714yesdirect product factor
326C23—41no—
327C23—71no—
328C23—72no—
329C23—72no—
330C23—71no—
331C23—142no—
332C23—142no—
333C23—281no—
334C23—562no—
335C23—562no—
336C23—562no—
337C23D7×D811yescharacteristic
338D4—41no—
339D4—41no—
340D4—81no—
341D4—81no—
342D4—281no—
343D4—281no—
344D4—562no—
345D4—562no—
346D4—562no—
347D4—561no—
348D4—561no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—71no—
354C2×C4—72no—
355C2×C4—72no—
356C2×C4—71no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—142no—
360C2×C4—142no—
361C2×C4—142no—
362C2×C4—141no—
363C2×C4—141no—
364C2×C4—282no—
365C2×C4—281no—
366C2×C4—562no—
367C2×C4—568no—
368C2×C4—561no—
369C2×C4—561no—
370C2×C4D7×C22⋊C411yescharacteristic
371C2×C4D7×SD1611yescharacteristic
372C8—21no—
373C8—21no—
374C8—141no—
375C8—141no—
376C7C2×#134711yescharacteristic, complemented, Sylow
377C22—21no—
378C22—21no—
379C22—72no—
380C22—72no—
381C22—72no—
382C22—72no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22—144no—
387C22—144no—
388C22—141no—
389C22—141no—
390C22—561no—
391C22—561no—
392C22—561no—
393C22—1124no—
394C22D7×#10211yescharacteristic
395C22D7×D1611yescharacteristic
396C22D7×SD3211yescharacteristic
397C4—21no—
398C4—72no—
399C4—82no—
400C4—81no—
401C4—141no—
402C4—562no—
403C4—561no—
404C4D7×#9911yescharacteristic
405C4D7×#10411yescharacteristic
406C2—21no—
407C2—21no—
408C2—74no—
409C2—142no—
410C2—161no—
411C2—1121no—
412C2D7×#32711yescharacteristic
413C2D7×#35711yescharacteristic
414C2D7×#36011yescharacteristic
subgroupG/H
centerC22D7×#102
commutatorC2×C7×C8C22×C4
FrattiniC22×C8C22×D7
FittingC7×#1347C2
socleC22×C7C2×#102
prime radicalD7×#466C2
cosocleC22×C7×C8C23
hypercenter#1347D7
hypocenterC7C2×#1347
LCSG ▷ C2×C7×C8 ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1347

Complements

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

NH ≅ G/Ntype
2. D7×C22⋊C16C2semidirect
3. D7×#340C2semidirect
4. C7×#1347C2semidirect
5. #11725580C2semidirect
6. #11725332C2semidirect
7. #11725291C2semidirect
8. C2×D7×D8C4semidirect
13. #89929C4semidirect
17. #89655C4semidirect
18. D7×#107C4semidirect
21. C7×C22⋊C16C22semidirect
22. C7×#340C22semidirect
23. #89346C22semidirect
24. C22⋊(C7⋊C16)C22semidirect
32. C2×C7×D8C2×C4semidirect
44. C2×D56C2×C4semidirect
57. C7×#107C2×C4semidirect
61. #6392C2×C4semidirect
72. #1347D7direct (N × H)
142. C22⋊C16C2×D7semidirect
145. #340C2×D7semidirect
203. C2×D8C4×D7semidirect
229. #107C4×D7semidirect
325. D7#1347direct (N × H)
376. C7C2×#1347semidirect

Maximal subgroups

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

subgroupindex
D7×#4662
D7×C22⋊C162
D7×#3402
C7×#13472
#117255802
#117253322
#117252912
C2×#13477