Finite Group Databasebeta

← #13249536

Subgroups — #13249536

Order 1792.

800 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
2#11739525C211yesmaximal, characteristic
3#11729285C211yesmaximal, characteristic, complemented
4C2×#89246C212yesmaximal
5#11725418C212yesmaximal, complemented
6C22×C7×C4⋊C4—21no—
7C22×C42×C7—21no—
8C22×C42×C7C2211yescharacteristic
9C2×#6493C2211yescharacteristic
10C2×#6492—21no—
11C4×C7×C4⋊C4—24no—
12C2×C7×#95C2212yes—
13#89985—21no—
14#89984C2211yescharacteristic
15C2×C22⋊(C7⋊C8)C2212yes—
16#89712—22no—
17#89711C412yescomplemented
18#89700C412yescomplemented
19#89319—22no—
20#89246—24no—
21#9148—71nomaximal, Sylow
22C23×C4×C7—22no—
23C23×C4×C7D411yescharacteristic
24C23×C4×C7D411yescharacteristic
25C23×C4×C7C2311yescharacteristic
26C22×C22⋊D7—21no—
27C22×D28C2×C411yescharacteristic
28C2×C7×C4⋊C4—28no—
29C2×C7×C4⋊C4—24no—
30C2×C42×C7—22no—
31C2×C42×C7—22no—
32C2×C42×C7—24no—
33C2×C42×C7—42no—
34C2×C42×C7—42no—
35C2×C42×C7C2×C412yes—
36C2×C42×C7D412yes—
37C2×C22⋊Dic7—21no—
38#6493—22no—
39#6493—22no—
40#6492—42no—
41#6492—42no—
42C2×(C2×D7)⋊C4—22no—
43C2×(C2×D7)⋊C4—22no—
44C2×(C2×D7)⋊C4—21no—
45C2×C4⋊Dic7C2×C411yescharacteristic
46C2×C4⋊Dic7C2×C412yes—
47C2×Dic7⋊C4—22no—
48C22×C7⋊C8—22no—
49C7×#95—22no—
50C7×#95D414yes—
51C7⋊#95—22no—
52C7⋊#95—21no—
53C22⋊(C7⋊C8)—22no—
54C22⋊(C7⋊C8)—22no—
55#2854—71no—
56C2×C4×C4⋊C4D711yescharacteristic, complemented
57#1817—71no—
58C2×#327—72no—
59#1294—72no—
60C24×C7C2×D411yescharacteristic
61C23×D7—21no—
62C22×C4×C7—21no—
63C22×C4×C7—21no—
64C22×C4×C7—21no—
65C22×C4×C7—21no—
66C22×C4×C7—21no—
67C22×C4×C7—21no—
68C22×C4×C7—24no—
69C22×C4×C7—28no—
70C22×C4×C7—24no—
71C22×C4×C7—42no—
72C22×C4×C7—44no—
73C22×C4×C7—42no—
74C22×C4×C7—42no—
75C22×C4×C7C22⋊C412yes—
76C22×C4×C7C22⋊C412yes—
77C22×C4×C7D812yes—
78C22×C4×C7SD1612yes—
79C22×C4×C7C22×C411yescharacteristic
80C22×C4×C7C2×D411yescharacteristic
81C22×C4×C7C2×D412yes—
82C22×C4×C7#4112yes—
83C2×C22⋊D7—41no—
84C2×C22⋊D7—41no—
85C2×C22⋊D7—41no—
86C2×C22⋊D7—41no—
87C2×C22⋊D7—41no—
88C2×C22⋊D7—41no—
89C22×Dic7—21no—
90C22×Dic7—22no—
91C2×D28—22no—
92C2×D28—42no—
93C7×C4⋊C4—216no—
94C42×C7—24no—
95C42×C7—24no—
96C42×C7—48no—
97C22⋊Dic7—41no—
98C22⋊Dic7—41no—
99(C2×D7)⋊C4—44no—
100(C2×D7)⋊C4—44no—
101(C2×D7)⋊C4—42no—
102C4⋊Dic7—22no—
103C4⋊Dic7—42no—
104Dic7⋊C4—44no—
105C2×C7⋊C8—44no—
106C2×C7⋊C8—42no—
107C2×#123—141no—
108C2×#121—71no—
109C22×C4⋊C4—21no—
110C22×C42—21no—
111C22×C42C2×D711yescharacteristic
112C2×C22⋊C8—72no—
113#390—72no—
114#389—72no—
115#388—142no—
116#386—141no—
117#380—71no—
118C4×C4⋊C4—24no—
119C2×#95C2×D712yes—
120#336—142no—
121#327—144no—
122C23×C7—22no—
123C23×C7—22no—
124C23×C7C2×C22⋊C411yescharacteristic
125C23×C7#12011yescharacteristic
126C23×C7#12311yescharacteristic
127C23×C7C2×D811yescharacteristic
128C23×C7C2×SD1611yescharacteristic
129C23×C7AGL(1,ℤ/8)11yescharacteristic
130C23×C7#13711yescharacteristic
131C22×D7—41no—
132C22×D7—42no—
133C22×D7—41no—
134C22×D7—41no—
135C22×D7—42no—
136C2×C4×C7—24no—
137C2×C4×C7—24no—
138C2×C4×C7—22no—
139C2×C4×C7—22no—
140C2×C4×C7—22no—
141C2×C4×C7—22no—
142C2×C4×C7—22no—
143C2×C4×C7—22no—
144C2×C4×C7—22no—
145C2×C4×C7—22no—
146C2×C4×C7—22no—
147C2×C4×C7—22no—
148C2×C4×C7—28no—
149C2×C4×C7—42no—
150C2×C4×C7—42no—
151C2×C4×C7—44no—
152C2×C4×C7—48no—
153C2×C4×C7—48no—
154C2×C4×C7—44no—
155C2×C4×C7#10214yes—
156C2×C4×C7#10414yes—
157C2×C4×C7C4×D412yes—
158C2×C4×C7#12112yes—
159C22⋊D7—81no—
160C22⋊D7—81no—
161C22⋊D7—81no—
162C22⋊D7—81no—
163C2×Dic7—41no—
164C2×Dic7—42no—
165C2×Dic7—41no—
166C2×Dic7—42no—
167C2×Dic7—41no—
168C2×Dic7—42no—
169D28—82no—
170C7⋊C8—82no—
171C22×D4—71no—
172C22×D4—141no—
173C23×C4—22no—
174C23×C4C22⋊D711yescharacteristic
175C23×C4C22⋊D711yescharacteristic
176C23×C4C22×D711yescharacteristic
177C22×C8—142no—
178#123—282no—
179#123—282no—
180#121—142no—
181#121—142no—
182C2×C4⋊C4—28no—
183C2×C4⋊C4—24no—
184C2×C4⋊C4—71no—
185C2×C4⋊C4—72no—
186C2×C4⋊C4—142no—
187C2×C22⋊C4—141no—
188C2×C22⋊C4—142no—
189C2×C22⋊C4—142no—
190C2×C22⋊C4—141no—
191C2×C42—22no—
192C2×C42—22no—
193C2×C42—24no—
194C2×C42—42no—
195C2×C42—42no—
196C2×C42C4×D712yes—
197C2×C42D2812yes—
198C22⋊C8—142no—
199C22⋊C8—142no—
200#95—22no—
201#95—142no—
202#95—141no—
203#95C22⋊D714yes—
204C22×C7—21no—
205C22×C7—21no—
206C22×C7—21no—
207C22×C7—21no—
208C22×C7—22no—
209C22×C7—22no—
210C22×C7—22no—
211C22×C7—22no—
212C22×C7#38611yescharacteristic
213C22×C7#41012yes—
214C22×C7C2×#10211yescharacteristic
215C22×C7#41711yescharacteristic
216C22×C7C2×#10412yes—
217C22×C7#44711yescharacteristic
218C22×C7#44811yescharacteristic
219C22×C7#48011yescharacteristic
220C22×C7#48111yescharacteristic
221C2×D7—81no—
222C2×D7—81no—
223C2×D7—81no—
224C2×D7—82no—
225C2×D7—82no—
226C4×C7—24no—
227C4×C7—24no—
228C4×C7—22no—
229C4×C7—22no—
230C4×C7—48no—
231Dic7—81no—
232Dic7—82no—
233C24—141no—
234C24C2×C22⋊D711yescharacteristic
235C2×D4—142no—
236C2×D4—282no—
237C2×D4—281no—
238C2×D4—281no—
239C2×D4—281no—
240C2×D4—281no—
241C2×D4—281no—
242C2×D4—281no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—24no—
250C22×C4—28no—
251C22×C4—24no—
252C22×C4—42no—
253C22×C4—44no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—142no—
257C22×C4—141no—
258C22×C4(C2×D7)⋊C412yes—
259C22×C4(C2×D7)⋊C412yes—
260C22×C4#114112yes—
261C22×C4#114312yes—
262C22×C4C2×C4×D711yescharacteristic
263C22×C4C2×D2811yescharacteristic
264C22×C4#115712yes—
265C22×C4C2×C22⋊D712yes—
266C2×C8—284no—
267C2×C8—282no—
268C4⋊C4—216no—
269C4⋊C4—142no—
270C4⋊C4—282no—
271C4⋊C4—284no—
272C22⋊C4—281no—
273C22⋊C4—281no—
274C22⋊C4—282no—
275C22⋊C4—284no—
276C22⋊C4—284no—
277C42—24no—
278C42—24no—
279C42—48no—
280C2×C7—21no—
281C2×C7—21no—
282C2×C7—21no—
283C2×C7—21no—
284C2×C7#150212yes—
285C2×C7#150912yes—
286C2×C7#187411yescharacteristic
287C2×C7#189611yescharacteristic
288C2×C7#189911yescharacteristic
289D7—161no—
290C23—22no—
291C23—22no—
292C23—282no—
293C23—281no—
294C23—281no—
295C23—281no—
296C23—282no—
297C23C2×(C2×D7)⋊C411yescharacteristic
298C23#649211yescharacteristic
299C23C2×#114111yescharacteristic
300C23#649511yescharacteristic
301C23C2×#114311yescharacteristic
302C23#650511yescharacteristic
303C23#651611yescharacteristic
304D4—562no—
305D4—561no—
306D4—561no—
307D4—561no—
308D4—561no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—28no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—48no—
325C2×C4—48no—
326C2×C4—44no—
327C2×C4—44no—
328C2×C4—282no—
329C2×C4—281no—
330C2×C4—282no—
331C2×C4—281no—
332C2×C4—281no—
333C2×C4—282no—
334C2×C4#637914yes—
335C2×C4#638314yes—
336C2×C4C4×C22⋊D712yes—
337C2×C4#649312yes—
338C8—562no—
339C7#914811yescharacteristic, complemented, Sylow
340C22—22no—
341C22—22no—
342C22—22no—
343C22—22no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—562no—
349C22—562no—
350C22—561no—
351C22—561no—
352C22—561no—
353C22C2×#637912yes—
354C22C2×#638311yescharacteristic
355C22#8973811yescharacteristic
356C22#8973911yescharacteristic
357C22#8974011yescharacteristic
358C22#8977812yes—
359C22#8998511yescharacteristic
360C22#8998911yescharacteristic
361C22#8999911yescharacteristic
362C4—24no—
363C4—24no—
364C4—22no—
365C4—22no—
366C4—48no—
367C4—562no—
368C4—561no—
369C2—21no—
370C2—21no—
371C2—21no—
372C2—21no—
373C2—1121no—
374C2#1172722312yes—
375C2#1172722412yes—
376C2#1172928611yescharacteristic
377C2#1172931411yescharacteristic
378C2#1172934911yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC2×C4×C7×C4⋊C4C2
socleC23×C7C2×C22⋊C4
prime radicalC2×#6493C22
cosocleC23×C4×C7C23
hypercenterC2×C4×C4⋊C4D7
hypocenterC7#9148
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C7×C4⋊C4C2semidirect
3. #11729285C2semidirect
5. #11725418C2semidirect
17. #89711C4semidirect
18. #89700C4semidirect
56. C2×C4×C4⋊C4D7semidirect
339. C7#9148semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C7×C4⋊C42
#117395252
#117292852
C2×#892462
#117254182
#91487