Finite Group Databasebeta

← #13249586

Subgroups — #13249586

Order 1792.

980 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 980 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C2×C7×#381C211yesmaximal, characteristic, complemented
2#11741477C211yesmaximal, characteristic
3#11729880C211yesmaximal, characteristic, complemented
4C2×#89246C212yesmaximal, complemented
5#11725418C212yesmaximal, complemented
6C24×C4×C7C2211yescharacteristic
7C22×C7×C22⋊C4—21no—
8C2×#6516—21no—
9C2×#6493C412yescomplemented
10C2×#6493C2211yescharacteristic
11C7×#381—24no—
12C2×C7×#95—21no—
13C2×C7×#95C2212yes—
14#89985—21no—
15#89985—22no—
16#89984C412yescomplemented
17#89984C2211yescharacteristic
18C2×C22⋊(C7⋊C8)—22no—
19C2×C22⋊(C7⋊C8)C2212yes—
20#89246—24no—
21#9158—71nomaximal, Sylow
22C25×C7D411yescharacteristic
23C23×C4×C7—22no—
24C23×C4×C7—22no—
25C23×C4×C7—22no—
26C23×C4×C7—44no—
27C23×C4×C7C2×C412yes—
28C23×C4×C7D412yes—
29C23×C4×C7D411yescharacteristic
30C23×C4×C7C2311yescharacteristic
31C22×C22⋊D7—22no—
32C22×C22⋊D7—21no—
33C22×D28C2×C411yescharacteristic
34C2×C7×C22⋊C4—24no—
35C2×C7×C22⋊C4—44no—
36#6516—44no—
37C2×C22⋊Dic7—22no—
38C2×C22⋊Dic7—21no—
39#6493—22no—
40#6493—22no—
41#6493—44no—
42C2×(C2×D7)⋊C4—22no—
43C2×(C2×D7)⋊C4—21no—
44C2×C4⋊Dic7C2×C411yescharacteristic
45C2×C4⋊Dic7C2×C412yes—
46C22×C7⋊C8—22no—
47C7×#95—24no—
48C7×#95—22no—
49C7×#95D414yescomplemented
50C7⋊#95—22no—
51C7⋊#95—21no—
52C22⋊(C7⋊C8)—22no—
53C22⋊(C7⋊C8)—22no—
54C22⋊(C7⋊C8)—44no—
55#2847—71no—
56C2×#381D711yescharacteristic, complemented
57#1779—71no—
58C2×#327—72no—
59#1294—72no—
60C24×C7—24no—
61C24×C7—21no—
62C24×C7—21no—
63C24×C7—22no—
64C24×C7—22no—
65C24×C7—42no—
66C24×C7C22⋊C412yes—
67C24×C7C2×D411yescharacteristic
68C23×D7—21no—
69C22×C4×C7—24no—
70C22×C4×C7—24no—
71C22×C4×C7—21no—
72C22×C4×C7—21no—
73C22×C4×C7—24no—
74C22×C4×C7—24no—
75C22×C4×C7—24no—
76C22×C4×C7—42no—
77C22×C4×C7—42no—
78C22×C4×C7—42no—
79C22×C4×C7—42no—
80C22×C4×C7—48no—
81C22×C4×C7—48no—
82C22×C4×C7—44no—
83C22×C4×C7—44no—
84C22×C4×C7—42no—
85C22×C4×C7—42no—
86C22×C4×C7C22⋊C412yes—
87C22×C4×C7C22×C411yescharacteristic
88C22×C4×C7C2×D411yescharacteristic
89C22×C4×C7C2×D412yes—
90C22×C4×C7#4112yes—
91C2×C22⋊D7—44no—
92C2×C22⋊D7—44no—
93C2×C22⋊D7—44no—
94C2×C22⋊D7—41no—
95C2×C22⋊D7—41no—
96C2×C22⋊D7—42no—
97C2×C22⋊D7—42no—
98C22×Dic7—21no—
99C22×Dic7—22no—
100C2×D28—22no—
101C2×D28—42no—
102C7×C22⋊C4—48no—
103C22⋊Dic7—44no—
104C22⋊Dic7—42no—
105(C2×D7)⋊C4—44no—
106(C2×D7)⋊C4—42no—
107C4⋊Dic7—22no—
108C4⋊Dic7—42no—
109C2×C7⋊C8—44no—
110C2×C7⋊C8—42no—
111C24×C4C2×D711yescharacteristic
112C2×#121—71no—
113C2×#121—72no—
114C2×#120—141no—
115C22×C22⋊C4—21no—
116C2×C22⋊C8—72no—
117C2×C22⋊C8—142no—
118#386—142no—
119#386—141no—
120#381—24no—
121#380—72no—
122#380—71no—
123C2×#95—21no—
124C2×#95C2×D712yes—
125#327—144no—
126C23×C7—22no—
127C23×C7—22no—
128C23×C7—24no—
129C23×C7—24no—
130C23×C7—22no—
131C23×C7—22no—
132C23×C7—22no—
133C23×C7—22no—
134C23×C7—22no—
135C23×C7—22no—
136C23×C7—48no—
137C23×C7—48no—
138C23×C7—42no—
139C23×C7—42no—
140C23×C7—42no—
141C23×C7—42no—
142C23×C7#9914yes—
143C23×C7C2×C22⋊C411yescharacteristic
144C23×C7#12011yescharacteristic
145C23×C7#12311yescharacteristic
146C23×C7#13512yes—
147C23×C7AGL(1,ℤ/8)12yes—
148C22×D7—41no—
149C22×D7—42no—
150C22×D7—41no—
151C22×D7—41no—
152C22×D7—42no—
153C2×C4×C7—22no—
154C2×C4×C7—22no—
155C2×C4×C7—22no—
156C2×C4×C7—22no—
157C2×C4×C7—22no—
158C2×C4×C7—42no—
159C2×C4×C7—42no—
160C2×C4×C7—48no—
161C2×C4×C7—48no—
162C2×C4×C7—42no—
163C2×C4×C7—42no—
164C2×C4×C7—44no—
165C2×C4×C7—44no—
166C2×C4×C7—44no—
167C2×C4×C7—84no—
168C2×C4×C7—84no—
169C2×C4×C7C4×D412yes—
170C2×C4×C7#12112yes—
171C22⋊D7—88no—
172C22⋊D7—82no—
173C22⋊D7—82no—
174C2×Dic7—41no—
175C2×Dic7—42no—
176C2×Dic7—41no—
177C2×Dic7—41no—
178C2×Dic7—42no—
179C2×Dic7—42no—
180D28—82no—
181C7⋊C8—82no—
182C25C22⋊D711yescharacteristic
183C22×D4—71no—
184C22×D4—142no—
185C22×D4—141no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—44no—
190C23×C4C4×D712yes—
191C23×C4D2812yes—
192C23×C4C22⋊D711yescharacteristic
193C23×C4C22×D711yescharacteristic
194C22×C8—142no—
195#121—142no—
196#121—142no—
197#121—284no—
198#120—284no—
199C2×C4⋊C4—71no—
200C2×C4⋊C4—72no—
201C2×C22⋊C4—24no—
202C2×C22⋊C4—44no—
203C2×C22⋊C4—142no—
204C2×C22⋊C4—141no—
205C2×C22⋊C4—142no—
206C2×C22⋊C4—141no—
207C22⋊C8—142no—
208C22⋊C8—142no—
209C22⋊C8—284no—
210#95—24no—
211#95—22no—
212#95—142no—
213#95—141no—
214#95C22⋊D714yescomplemented
215C22×C7—21no—
216C22×C7—21no—
217C22×C7—21no—
218C22×C7—21no—
219C22×C7—24no—
220C22×C7—24no—
221C22×C7—24no—
222C22×C7—24no—
223C22×C7—24no—
224C22×C7—48no—
225C22×C7—48no—
226C22×C7—42no—
227C22×C7—42no—
228C22×C7—42no—
229C22×C7—42no—
230C22×C7#38611yescharacteristic
231C22×C7C2×#9912yes—
232C22×C7#41611yescharacteristic
233C22×C7#41811yescharacteristic
234C22×C7#42112yes—
235C22×C7#44912yes—
236C22×C7#48212yes—
237C2×D7—81no—
238C2×D7—81no—
239C2×D7—81no—
240C2×D7—82no—
241C2×D7—82no—
242C4×C7—22no—
243C4×C7—22no—
244C4×C7—42no—
245C4×C7—84no—
246Dic7—81no—
247Dic7—82no—
248C24—21no—
249C24—21no—
250C24—24no—
251C24—22no—
252C24—22no—
253C24—42no—
254C24—141no—
255C24(C2×D7)⋊C412yes—
256C24C2×C22⋊D711yescharacteristic
257C2×D4—142no—
258C2×D4—282no—
259C2×D4—284no—
260C2×D4—284no—
261C2×D4—281no—
262C2×D4—282no—
263C2×D4—282no—
264C2×D4—281no—
265C2×D4—284no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—24no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—24no—
272C22×C4—24no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—48no—
278C22×C4—48no—
279C22×C4—44no—
280C22×C4—44no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—142no—
284C22×C4—141no—
285C22×C4(C2×D7)⋊C412yes—
286C22×C4C2×C4×D711yescharacteristic
287C22×C4C2×D2811yescharacteristic
288C22×C4#115712yes—
289C22×C4C2×C22⋊D712yes—
290C2×C8—284no—
291C2×C8—282no—
292C4⋊C4—142no—
293C4⋊C4—282no—
294C22⋊C4—48no—
295C22⋊C4—284no—
296C22⋊C4—284no—
297C22⋊C4—282no—
298C22⋊C4—282no—
299C2×C7—22no—
300C2×C7—22no—
301C2×C7—44no—
302C2×C7#151012yes—
303C2×C7#151612yes—
304C2×C7#187511yescharacteristic
305C2×C7#189711yescharacteristic
306C2×C7#189811yescharacteristic
307D7—161no—
308C23—22no—
309C23—22no—
310C23—24no—
311C23—24no—
312C23—22no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—22no—
318C23—48no—
319C23—48no—
320C23—42no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23—282no—
325C23—281no—
326C23—281no—
327C23—281no—
328C23—282no—
329C23#638014yes—
330C23C2×(C2×D7)⋊C411yescharacteristic
331C23#649211yescharacteristic
332C23#651212yes—
333C23#651312yes—
334C23#651611yescharacteristic
335D4—562no—
336D4—568no—
337D4—562no—
338D4—562no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—48no—
347C2×C4—48no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4—84no—
354C2×C4—84no—
355C2×C4—282no—
356C2×C4—281no—
357C2×C4—282no—
358C2×C4—281no—
359C2×C4—281no—
360C2×C4—282no—
361C2×C4C4×C22⋊D712yes—
362C2×C4#649312yes—
363C8—562no—
364C7#915811yescharacteristic, complemented, Sylow
365C22—21no—
366C22—21no—
367C22—24no—
368C22—24no—
369C22—21no—
370C22—21no—
371C22—24no—
372C22—24no—
373C22—24no—
374C22—48no—
375C22—48no—
376C22—42no—
377C22—42no—
378C22—42no—
379C22—42no—
380C22—561no—
381C22—562no—
382C22—562no—
383C22—561no—
384C22—561no—
385C22C2×#638012yes—
386C22#8977311yescharacteristic
387C22#8977411yescharacteristic
388C22#8977512yes—
389C22#8977712yes—
390C22#8998511yescharacteristic
391C22#9001012yes—
392C4—22no—
393C4—22no—
394C4—42no—
395C4—84no—
396C4—562no—
397C4—561no—
398C2—22no—
399C2—22no—
400C2—44no—
401C2—1121no—
402C2#1172728512yes—
403C2#1172728612yes—
404C2#1172929711yescharacteristic
405C2#1172934011yescharacteristic
406C2#1172934511yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC2×C7×#381C2
socleC23×C7C2×C22⋊C4
prime radical#11741477C2
cosocleC23×C4×C7C23
hypercenterC2×#381D7
hypocenterC7#9158
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
1. C2×C7×#381C2semidirect
3. #11729880C2semidirect
4. C2×#89246C2semidirect
5. #11725418C2semidirect
9. C2×#6493C4semidirect
16. #89984C4semidirect
49. C7×#95D4semidirect
56. C2×#381D7semidirect
214. #95C22⋊D7semidirect
364. C7#9158semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3812
#117414772
#117298802
C2×#892462
#117254182
#91587