Finite Group Databasebeta

← #13249546

Subgroups — #13249546

Order 1792.

1088 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 147 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×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
2#11741477C211yesmaximal, characteristic
3#11729880C211yesmaximal, characteristic, complemented
4C2×#89246C212yesmaximal, complemented
5#11725418C212yesmaximal, complemented
6C24×C4×C7C2211yescharacteristic
7C22×C7×C22⋊C4—21no—
8C22×C42×C7—21no—
9C2×#6516—21no—
10C2×#6493C412yescomplemented
11C2×#6493C2211yescharacteristic
12C4×C7×C22⋊C4—24no—
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#9150—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—28no—
35C2×C7×C22⋊C4—24no—
36C2×C42×C7—24no—
37C2×C42×C7—44no—
38#6516—44no—
39C2×C22⋊Dic7—22no—
40C2×C22⋊Dic7—21no—
41#6493—22no—
42#6493—22no—
43#6493—44no—
44C2×(C2×D7)⋊C4—22no—
45C2×(C2×D7)⋊C4—21no—
46C2×C4⋊Dic7C2×C411yescharacteristic
47C2×C4⋊Dic7C2×C412yes—
48C22×C7⋊C8—22no—
49C7×#95—22no—
50C7×#95D414yescomplemented
51C7⋊#95—22no—
52C7⋊#95—21no—
53C22⋊(C7⋊C8)—22no—
54C22⋊(C7⋊C8)—22no—
55C22⋊(C7⋊C8)—44no—
56#2847—71no—
57C2×C4×C22⋊C4D711yescharacteristic, complemented
58#1779—71no—
59C2×#327—72no—
60#1294—72no—
61C24×C7—24no—
62C24×C7—21no—
63C24×C7—21no—
64C24×C7—22no—
65C24×C7—22no—
66C24×C7—42no—
67C24×C7C22⋊C412yes—
68C24×C7C2×D411yescharacteristic
69C23×D7—21no—
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7—24no—
73C22×C4×C7—28no—
74C22×C4×C7—24no—
75C22×C4×C7—24no—
76C22×C4×C7—24no—
77C22×C4×C7—24no—
78C22×C4×C7—24no—
79C22×C4×C7—42no—
80C22×C4×C7—42no—
81C22×C4×C7—42no—
82C22×C4×C7—48no—
83C22×C4×C7—48no—
84C22×C4×C7—44no—
85C22×C4×C7—42no—
86C22×C4×C7—42no—
87C22×C4×C7C22⋊C412yes—
88C22×C4×C7C22×C411yescharacteristic
89C22×C4×C7C2×D411yescharacteristic
90C22×C4×C7C2×D412yes—
91C22×C4×C7#4112yes—
92C2×C22⋊D7—44no—
93C2×C22⋊D7—44no—
94C2×C22⋊D7—44no—
95C2×C22⋊D7—41no—
96C2×C22⋊D7—41no—
97C2×C22⋊D7—42no—
98C2×C22⋊D7—42no—
99C22×Dic7—21no—
100C22×Dic7—22no—
101C2×D28—22no—
102C2×D28—42no—
103C7×C22⋊C4—216no—
104C42×C7—48no—
105C22⋊Dic7—44no—
106C22⋊Dic7—42no—
107(C2×D7)⋊C4—44no—
108(C2×D7)⋊C4—42no—
109C4⋊Dic7—22no—
110C4⋊Dic7—42no—
111C2×C7⋊C8—44no—
112C2×C7⋊C8—42no—
113C24×C4C2×D711yescharacteristic
114C2×#121—71no—
115C2×#121—72no—
116C2×#120—141no—
117C22×C22⋊C4—21no—
118C22×C42—21no—
119C2×C22⋊C8—72no—
120C2×C22⋊C8—142no—
121#386—142no—
122#386—141no—
123#380—72no—
124#380—71no—
125C4×C22⋊C4—24no—
126C2×#95C2×D712yes—
127#327—144no—
128C23×C7—22no—
129C23×C7—22no—
130C23×C7—24no—
131C23×C7—24no—
132C23×C7—22no—
133C23×C7—22no—
134C23×C7—22no—
135C23×C7—22no—
136C23×C7—22no—
137C23×C7—22no—
138C23×C7—48no—
139C23×C7—48no—
140C23×C7—42no—
141C23×C7—42no—
142C23×C7—42no—
143C23×C7—42no—
144C23×C7#10414yes—
145C23×C7C2×C22⋊C411yescharacteristic
146C23×C7#12011yescharacteristic
147C23×C7#12311yescharacteristic
148C23×C7#13512yes—
149C23×C7AGL(1,ℤ/8)12yes—
150C22×D7—41no—
151C22×D7—42no—
152C22×D7—41no—
153C22×D7—41no—
154C22×D7—42no—
155C2×C4×C7—24no—
156C2×C4×C7—24no—
157C2×C4×C7—22no—
158C2×C4×C7—22no—
159C2×C4×C7—22no—
160C2×C4×C7—22no—
161C2×C4×C7—28no—
162C2×C4×C7—42no—
163C2×C4×C7—42no—
164C2×C4×C7—48no—
165C2×C4×C7—48no—
166C2×C4×C7—44no—
167C2×C4×C7—48no—
168C2×C4×C7—48no—
169C2×C4×C7—44no—
170C2×C4×C7#9914yes—
171C2×C4×C7C4×D412yes—
172C2×C4×C7#12112yes—
173C22⋊D7—88no—
174C22⋊D7—82no—
175C22⋊D7—82no—
176C2×Dic7—41no—
177C2×Dic7—42no—
178C2×Dic7—41no—
179C2×Dic7—41no—
180C2×Dic7—42no—
181C2×Dic7—42no—
182D28—82no—
183C7⋊C8—82no—
184C25C22⋊D711yescharacteristic
185C22×D4—71no—
186C22×D4—142no—
187C22×D4—141no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—44no—
192C23×C4C4×D712yes—
193C23×C4D2812yes—
194C23×C4C22⋊D711yescharacteristic
195C23×C4C22×D711yescharacteristic
196C22×C8—142no—
197#121—142no—
198#121—142no—
199#121—284no—
200#120—284no—
201C2×C4⋊C4—71no—
202C2×C4⋊C4—72no—
203C2×C22⋊C4—28no—
204C2×C22⋊C4—24no—
205C2×C22⋊C4—142no—
206C2×C22⋊C4—141no—
207C2×C22⋊C4—142no—
208C2×C22⋊C4—141no—
209C2×C42—24no—
210C2×C42—44no—
211C22⋊C8—142no—
212C22⋊C8—142no—
213C22⋊C8—284no—
214#95—22no—
215#95—142no—
216#95—141no—
217#95C22⋊D714yescomplemented
218C22×C7—21no—
219C22×C7—21no—
220C22×C7—21no—
221C22×C7—21no—
222C22×C7—24no—
223C22×C7—24no—
224C22×C7—24no—
225C22×C7—24no—
226C22×C7—24no—
227C22×C7—48no—
228C22×C7—48no—
229C22×C7—42no—
230C22×C7—42no—
231C22×C7—42no—
232C22×C7—42no—
233C22×C7#38611yescharacteristic
234C22×C7C2×#9912yes—
235C22×C7#41611yescharacteristic
236C22×C7#41811yescharacteristic
237C22×C7C2×#10412yes—
238C22×C7#44912yes—
239C22×C7#48212yes—
240C2×D7—81no—
241C2×D7—81no—
242C2×D7—81no—
243C2×D7—82no—
244C2×D7—82no—
245C4×C7—22no—
246C4×C7—22no—
247C4×C7—24no—
248C4×C7—48no—
249Dic7—81no—
250Dic7—82no—
251C24—21no—
252C24—21no—
253C24—24no—
254C24—22no—
255C24—22no—
256C24—42no—
257C24—141no—
258C24(C2×D7)⋊C412yes—
259C24C2×C22⋊D711yescharacteristic
260C2×D4—142no—
261C2×D4—282no—
262C2×D4—284no—
263C2×D4—284no—
264C2×D4—281no—
265C2×D4—282no—
266C2×D4—282no—
267C2×D4—281no—
268C2×D4—284no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—24no—
272C22×C4—28no—
273C22×C4—24no—
274C22×C4—24no—
275C22×C4—24no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—48no—
282C22×C4—48no—
283C22×C4—44no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—142no—
287C22×C4—141no—
288C22×C4(C2×D7)⋊C412yes—
289C22×C4C2×C4×D711yescharacteristic
290C22×C4C2×D2811yescharacteristic
291C22×C4#115712yes—
292C22×C4C2×C22⋊D712yes—
293C2×C8—284no—
294C2×C8—282no—
295C4⋊C4—142no—
296C4⋊C4—282no—
297C22⋊C4—216no—
298C22⋊C4—284no—
299C22⋊C4—282no—
300C22⋊C4—282no—
301C22⋊C4—284no—
302C42—48no—
303C2×C7—22no—
304C2×C7—22no—
305C2×C7—44no—
306C2×C7#150112yes—
307C2×C7#150712yes—
308C2×C7#187511yescharacteristic
309C2×C7#189611yescharacteristic
310C2×C7#189811yescharacteristic
311D7—161no—
312C23—22no—
313C23—22no—
314C23—24no—
315C23—24no—
316C23—22no—
317C23—22no—
318C23—22no—
319C23—22no—
320C23—22no—
321C23—22no—
322C23—48no—
323C23—48no—
324C23—42no—
325C23—42no—
326C23—42no—
327C23—42no—
328C23—282no—
329C23—282no—
330C23—281no—
331C23—281no—
332C23—281no—
333C23#637914yes—
334C23C2×(C2×D7)⋊C411yescharacteristic
335C23#649211yescharacteristic
336C23#651212yes—
337C23#651312yes—
338C23#651611yescharacteristic
339D4—562no—
340D4—568no—
341D4—562no—
342D4—562no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—28no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—48no—
353C2×C4—48no—
354C2×C4—44no—
355C2×C4—48no—
356C2×C4—48no—
357C2×C4—44no—
358C2×C4—282no—
359C2×C4—282no—
360C2×C4—281no—
361C2×C4—282no—
362C2×C4—281no—
363C2×C4—281no—
364C2×C4#638014yes—
365C2×C4C4×C22⋊D712yes—
366C2×C4#649312yes—
367C8—562no—
368C7#915011yescharacteristic, complemented, Sylow
369C22—24no—
370C22—24no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—24no—
376C22—24no—
377C22—24no—
378C22—48no—
379C22—48no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—42no—
384C22—562no—
385C22—562no—
386C22—561no—
387C22—561no—
388C22—561no—
389C22C2×#637912yes—
390C22C2×#638012yes—
391C22#8977311yescharacteristic
392C22#8977411yescharacteristic
393C22#8977512yes—
394C22#8998511yescharacteristic
395C22#9001012yes—
396C4—22no—
397C4—24no—
398C4—22no—
399C4—48no—
400C4—562no—
401C4—561no—
402C2—22no—
403C2—22no—
404C2—44no—
405C2—1121no—
406C2#1172719712yes—
407C2#1172719812yes—
408C2#1172928611yescharacteristic
409C2#1172929711yescharacteristic
410C2#1172934011yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC2×C4×C7×C22⋊C4C2
socleC23×C7C2×C22⋊C4
prime radical#11741477C2
cosocleC23×C4×C7C23
hypercenterC2×C4×C22⋊C4D7
hypocenterC7#9150
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C7×C22⋊C4C2semidirect
3. #11729880C2semidirect
4. C2×#89246C2semidirect
5. #11725418C2semidirect
10. C2×#6493C4semidirect
16. #89984C4semidirect
50. C7×#95D4semidirect
57. C2×C4×C22⋊C4D7semidirect
217. #95C22⋊D7semidirect
368. C7#9150semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C7×C22⋊C42
#117414772
#117298802
C2×#892462
#117254182
#91507