Finite Group Databasebeta

← #13249576

Subgroups — #13249576

Order 1792.

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

normal subgroups only

This group has 692 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×C7×#382C211yesmaximal, characteristic, complemented
2#11739525C211yesmaximal, characteristic
3#11729285C211yesmaximal, characteristic, complemented
4C2×#89246C212yesmaximal
5#11725418C212yesmaximal, complemented
6C22×C7×C4⋊C4—21no—
7C22×C42×C7C2211yescharacteristic
8C2×#6493C2211yescharacteristic
9C2×#6492—21no—
10C7×#382—24no—
11C2×C7×#95—21no—
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#9156—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—24no—
29C2×C7×C4⋊C4—42no—
30C2×C7×C4⋊C4—42no—
31C2×C42×C7—22no—
32C2×C42×C7—22no—
33C2×C42×C7C2×C412yes—
34C2×C42×C7D412yes—
35C2×C22⋊Dic7—21no—
36#6493—22no—
37#6493—22no—
38#6492—42no—
39#6492—42no—
40C2×(C2×D7)⋊C4—22no—
41C2×(C2×D7)⋊C4—22no—
42C2×(C2×D7)⋊C4—21no—
43C2×C4⋊Dic7C2×C411yescharacteristic
44C2×C4⋊Dic7C2×C412yes—
45C2×Dic7⋊C4—22no—
46C22×C7⋊C8—22no—
47C7×#95—24no—
48C7×#95—22no—
49C7×#95D414yes—
50C7⋊#95—22no—
51C7⋊#95—21no—
52C22⋊(C7⋊C8)—22no—
53C22⋊(C7⋊C8)—22no—
54#2854—71no—
55C2×#382D711yescharacteristic, complemented
56#1817—71no—
57C2×#327—72no—
58#1294—72no—
59C24×C7C2×D411yescharacteristic
60C23×D7—21no—
61C22×C4×C7—21no—
62C22×C4×C7—21no—
63C22×C4×C7—21no—
64C22×C4×C7—21no—
65C22×C4×C7—21no—
66C22×C4×C7—21no—
67C22×C4×C7—24no—
68C22×C4×C7—42no—
69C22×C4×C7—42no—
70C22×C4×C7—44no—
71C22×C4×C7—44no—
72C22×C4×C7—42no—
73C22×C4×C7—42no—
74C22×C4×C7C22⋊C412yes—
75C22×C4×C7C22⋊C412yes—
76C22×C4×C7D812yes—
77C22×C4×C7SD1612yes—
78C22×C4×C7C22×C411yescharacteristic
79C22×C4×C7C2×D411yescharacteristic
80C22×C4×C7C2×D412yes—
81C22×C4×C7#4112yes—
82C2×C22⋊D7—41no—
83C2×C22⋊D7—41no—
84C2×C22⋊D7—41no—
85C2×C22⋊D7—41no—
86C2×C22⋊D7—41no—
87C2×C22⋊D7—41no—
88C22×Dic7—21no—
89C22×Dic7—22no—
90C2×D28—22no—
91C2×D28—42no—
92C7×C4⋊C4—48no—
93C42×C7—24no—
94C42×C7—24no—
95C22⋊Dic7—41no—
96C22⋊Dic7—41no—
97(C2×D7)⋊C4—44no—
98(C2×D7)⋊C4—44no—
99(C2×D7)⋊C4—42no—
100C4⋊Dic7—22no—
101C4⋊Dic7—42no—
102Dic7⋊C4—44no—
103C2×C7⋊C8—44no—
104C2×C7⋊C8—42no—
105C2×#123—141no—
106C2×#121—71no—
107C22×C4⋊C4—21no—
108C22×C42C2×D711yescharacteristic
109C2×C22⋊C8—72no—
110#390—72no—
111#389—72no—
112#388—142no—
113#386—141no—
114#382—24no—
115#380—71no—
116C2×#95—21no—
117C2×#95C2×D712yes—
118#336—142no—
119#327—144no—
120C23×C7—22no—
121C23×C7—22no—
122C23×C7C2×C22⋊C411yescharacteristic
123C23×C7#12011yescharacteristic
124C23×C7#12311yescharacteristic
125C23×C7C2×D811yescharacteristic
126C23×C7C2×SD1611yescharacteristic
127C23×C7AGL(1,ℤ/8)11yescharacteristic
128C23×C7#13711yescharacteristic
129C22×D7—41no—
130C22×D7—42no—
131C22×D7—41no—
132C22×D7—41no—
133C22×D7—42no—
134C2×C4×C7—22no—
135C2×C4×C7—22no—
136C2×C4×C7—22no—
137C2×C4×C7—22no—
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—42no—
146C2×C4×C7—42no—
147C2×C4×C7—42no—
148C2×C4×C7—42no—
149C2×C4×C7—44no—
150C2×C4×C7—44no—
151C2×C4×C7—44no—
152C2×C4×C7—84no—
153C2×C4×C7—84no—
154C2×C4×C7#10214yes—
155C2×C4×C7C4×D412yes—
156C2×C4×C7#12112yes—
157C22⋊D7—81no—
158C22⋊D7—81no—
159C22⋊D7—81no—
160C22⋊D7—81no—
161C2×Dic7—41no—
162C2×Dic7—42no—
163C2×Dic7—41no—
164C2×Dic7—42no—
165C2×Dic7—41no—
166C2×Dic7—42no—
167D28—82no—
168C7⋊C8—82no—
169C22×D4—71no—
170C22×D4—141no—
171C23×C4—22no—
172C23×C4C22⋊D711yescharacteristic
173C23×C4C22⋊D711yescharacteristic
174C23×C4C22×D711yescharacteristic
175C22×C8—142no—
176#123—282no—
177#123—282no—
178#121—142no—
179#121—142no—
180C2×C4⋊C4—24no—
181C2×C4⋊C4—42no—
182C2×C4⋊C4—42no—
183C2×C4⋊C4—71no—
184C2×C4⋊C4—72no—
185C2×C4⋊C4—142no—
186C2×C22⋊C4—141no—
187C2×C22⋊C4—142no—
188C2×C22⋊C4—142no—
189C2×C22⋊C4—141no—
190C2×C42—22no—
191C2×C42—22no—
192C2×C42C4×D712yes—
193C2×C42D2812yes—
194C22⋊C8—142no—
195C22⋊C8—142no—
196#95—24no—
197#95—22no—
198#95—142no—
199#95—141no—
200#95C22⋊D714yes—
201C22×C7—21no—
202C22×C7—21no—
203C22×C7—21no—
204C22×C7—21no—
205C22×C7—22no—
206C22×C7—22no—
207C22×C7—22no—
208C22×C7—22no—
209C22×C7#38611yescharacteristic
210C22×C7#41012yes—
211C22×C7C2×#10211yescharacteristic
212C22×C7#41711yescharacteristic
213C22×C7#42112yes—
214C22×C7#44711yescharacteristic
215C22×C7#44811yescharacteristic
216C22×C7#48011yescharacteristic
217C22×C7#48111yescharacteristic
218C2×D7—81no—
219C2×D7—81no—
220C2×D7—81no—
221C2×D7—82no—
222C2×D7—82no—
223C4×C7—24no—
224C4×C7—22no—
225C4×C7—22no—
226C4×C7—42no—
227C4×C7—84no—
228Dic7—81no—
229Dic7—82no—
230C24—141no—
231C24C2×C22⋊D711yescharacteristic
232C2×D4—142no—
233C2×D4—282no—
234C2×D4—281no—
235C2×D4—281no—
236C2×D4—281no—
237C2×D4—281no—
238C2×D4—281no—
239C2×D4—281no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—24no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—44no—
250C22×C4—44no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—142no—
254C22×C4—141no—
255C22×C4(C2×D7)⋊C412yes—
256C22×C4(C2×D7)⋊C412yes—
257C22×C4#114112yes—
258C22×C4#114312yes—
259C22×C4C2×C4×D711yescharacteristic
260C22×C4C2×D2811yescharacteristic
261C22×C4#115712yes—
262C22×C4C2×C22⋊D712yes—
263C2×C8—284no—
264C2×C8—282no—
265C4⋊C4—48no—
266C4⋊C4—142no—
267C4⋊C4—282no—
268C4⋊C4—284no—
269C22⋊C4—284no—
270C22⋊C4—281no—
271C22⋊C4—281no—
272C22⋊C4—282no—
273C22⋊C4—284no—
274C42—24no—
275C42—24no—
276C2×C7—21no—
277C2×C7—21no—
278C2×C7—21no—
279C2×C7—21no—
280C2×C7#151212yes—
281C2×C7#151712yes—
282C2×C7#187411yescharacteristic
283C2×C7#189711yescharacteristic
284C2×C7#189911yescharacteristic
285D7—161no—
286C23—22no—
287C23—22no—
288C23—281no—
289C23—281no—
290C23—281no—
291C23—282no—
292C23—282no—
293C23C2×(C2×D7)⋊C411yescharacteristic
294C23#649211yescharacteristic
295C23C2×#114111yescharacteristic
296C23#649511yescharacteristic
297C23C2×#114311yescharacteristic
298C23#650511yescharacteristic
299C23#651611yescharacteristic
300D4—562no—
301D4—561no—
302D4—561no—
303D4—561no—
304D4—561no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—44no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—84no—
324C2×C4—84no—
325C2×C4—281no—
326C2×C4—282no—
327C2×C4—281no—
328C2×C4—281no—
329C2×C4—282no—
330C2×C4—282no—
331C2×C4#638314yes—
332C2×C4C4×C22⋊D712yes—
333C2×C4#649312yes—
334C8—562no—
335C7#915611yescharacteristic, complemented, Sylow
336C22—21no—
337C22—21no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—21no—
343C22—21no—
344C22—561no—
345C22—561no—
346C22—562no—
347C22—562no—
348C22—561no—
349C22C2×#638311yescharacteristic
350C22#8973811yescharacteristic
351C22#8973911yescharacteristic
352C22#8974011yescharacteristic
353C22#8977712yes—
354C22#8977812yes—
355C22#8998511yescharacteristic
356C22#8998911yescharacteristic
357C22#8999911yescharacteristic
358C4—24no—
359C4—22no—
360C4—22no—
361C4—42no—
362C4—84no—
363C4—561no—
364C4—562no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—1121no—
370C2#1172729812yes—
371C2#1172729912yes—
372C2#1172931411yescharacteristic
373C2#1172934511yescharacteristic
374C2#1172934911yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC2×C7×#382C2
socleC23×C7C2×C22⋊C4
prime radicalC2×#6493C22
cosocleC23×C4×C7C23
hypercenterC2×#382D7
hypocenterC7#9156
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
1. C2×C7×#382C2semidirect
3. #11729285C2semidirect
5. #11725418C2semidirect
17. #89711C4semidirect
18. #89700C4semidirect
55. C2×#382D7semidirect
335. C7#9156semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3822
#117395252
#117292852
C2×#892462
#117254182
#91567