Finite Group Databasebeta

← #13252815

Subgroups — #13252815

Order 1792.

482 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2861C211yesmaximal, characteristic
2C2×#89338C212yesmaximal, complemented
3C2×#89335C212yesmaximal
4#11727145C211yesmaximal, characteristic, complemented
5#11727143C211yesmaximal, characteristic, complemented
6C2×C7×#125C2211yescharacteristic
7C2×C7×#124C2211yescharacteristic
8C7×#391C411yescharacteristic
9C7×#391C411yescharacteristic
10C7×#390C411yescharacteristic
11C7×#390C411yescharacteristic
12C7×#388—21no—
13C7×#388—21no—
14C7×#388—21no—
15C7×#388—21no—
16C43×C7C2211yescharacteristic
17C2×C4⋊(C7⋊C8)—21no—
18C2×#6377C2212yes—
19C2×#6377C2212yes—
20#89338—24no—
21#89335—24no—
22#89319—21no—
23#89319—21no—
24#89319—21no—
25#9688—71nomaximal, Sylow
26C22×C7×Q8C2×C411yescharacteristic
27C22×C7×D4C2×C411yescharacteristic
28C7×#125—22no—
29C7×#125—22no—
30C7×#124—22no—
31C7×#124—22no—
32C2×C7×C4⋊C4—21no—
33C2×C7×C4⋊C4—21no—
34C2×C7×C4⋊C4C2×C411yescharacteristic
35C2×C7×C4⋊C4C2×C411yescharacteristic
36C2×C7×C22⋊C4—21no—
37C2×C7×C22⋊C4—21no—
38C2×C7×C22⋊C4—21no—
39C2×C7×C22⋊C4—21no—
40C2×C7×C22⋊C4—21no—
41C2×C7×C22⋊C4—21no—
42C2×C42×C7C2×C411yescharacteristic
43C2×C42×C7C2×C411yescharacteristic
44C2×C42×C7D411yescharacteristic
45C2×C42×C7D411yescharacteristic
46C2×C42×C7D411yescharacteristic
47C2×C42×C7D411yescharacteristic
48C2×C42×C7C2311yescharacteristic
49C22×C7⋊C8—22no—
50C22×C7⋊C8—22no—
51C7×#95—21no—
52C7×#95—21no—
53C7×#95—21no—
54C7×#95—21no—
55C4⋊(C7⋊C8)—24no—
56#6377—22no—
57#6377—22no—
58#6377—22no—
59#6377D414yes—
60#2861D711yescharacteristic
61#1767—71no—
62#1745—71no—
63C2×#330—72no—
64C2×#329—72no—
65C24×C7—21no—
66C2×C7×Q8—22no—
67C2×C7×Q8—41no—
68C2×C7×Q8—41no—
69C2×C7×D4—22no—
70C2×C7×D4—41no—
71C2×C7×D4—41no—
72C22×C4×C7—21no—
73C22×C4×C7—21no—
74C22×C4×C7—21no—
75C22×C4×C7C22⋊C411yescharacteristic
76C22×C4×C7C22⋊C411yescharacteristic
77C22×C4×C7C22⋊C411yescharacteristic
78C22×C4×C7C22⋊C411yescharacteristic
79C22×C4×C7C22×C411yescharacteristic
80C22×C4×C7C2×D411yescharacteristic
81C22×C4×C7C2×D411yescharacteristic
82C7×C4⋊C4—22no—
83C7×C4⋊C4—22no—
84C7×C4⋊C4—42no—
85C7×C4⋊C4—41no—
86C7×C4⋊C4—41no—
87C7×C22⋊C4—42no—
88C7×C22⋊C4—42no—
89C7×C22⋊C4—42no—
90C7×C22⋊C4—42no—
91C7×C22⋊C4—42no—
92C7×C22⋊C4—41no—
93C7×C22⋊C4—41no—
94C42×C7—22no—
95C42×C7—41no—
96C42×C7—41no—
97C42×C7—41no—
98C42×C7—41no—
99C42×C7—41no—
100C42×C7C2×D412yes—
101C42×C7#4112yes—
102C2×C7⋊C8—24no—
103C2×C7⋊C8—24no—
104C2×C7⋊C8—42no—
105C2×C7⋊C8—42no—
106C2×C7⋊C8—42no—
107C2×C7⋊C8—42no—
108C2×#125C2×D711yescharacteristic
109C2×#124C2×D711yescharacteristic
110C2×C4⋊C8—141no—
111C2×#97—72no—
112C2×#97—72no—
113#391Dic711yescharacteristic
114#391Dic711yescharacteristic
115#390Dic711yescharacteristic
116#390Dic711yescharacteristic
117#388—21no—
118#388—21no—
119#388—21no—
120#388—21no—
121C43C2×D711yescharacteristic
122#336—141no—
123#336—141no—
124#336—141no—
125#330—144no—
126#329—144no—
127C23×C7—41no—
128C23×C7—41no—
129C23×C7—41no—
130C23×C7—41no—
131C23×C7—41no—
132C23×C7—41no—
133C23×C7—41no—
134C23×C7C2×C22⋊C411yescharacteristic
135C7×Q8—82no—
136C7×D4—82no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—21no—
140C2×C4×C7—21no—
141C2×C4×C7—21no—
142C2×C4×C7—21no—
143C2×C4×C7—21no—
144C2×C4×C7—21no—
145C2×C4×C7—21no—
146C2×C4×C7—21no—
147C2×C4×C7—21no—
148C2×C4×C7—21no—
149C2×C4×C7—21no—
150C2×C4×C7—21no—
151C2×C4×C7—21no—
152C2×C4×C7—21no—
153C2×C4×C7—21no—
154C2×C4×C7—41no—
155C2×C4×C7—41no—
156C2×C4×C7—41no—
157C2×C4×C7—41no—
158C2×C4×C7—41no—
159C2×C4×C7—41no—
160C2×C4×C7—41no—
161C2×C4×C7—41no—
162C2×C4×C7—41no—
163C2×C4×C7#10412yes—
164C2×C4×C7C4×D412yes—
165C2×C4×C7#12112yes—
166C2×C4×C7#12411yescharacteristic
167C2×C4×C7#12711yescharacteristic
168C7⋊C8—44no—
169C7⋊C8—44no—
170C22×Q8C2×Dic711yescharacteristic
171C22×D4C2×Dic711yescharacteristic
172C22×C8—142no—
173C22×C8—142no—
174#125—22no—
175#125—22no—
176#124—22no—
177#124—22no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4C2×Dic711yescharacteristic
181C2×C4⋊C4C2×Dic711yescharacteristic
182C2×C22⋊C4—21no—
183C2×C22⋊C4—21no—
184C2×C22⋊C4—21no—
185C2×C22⋊C4—21no—
186C2×C22⋊C4—21no—
187C2×C22⋊C4—21no—
188C2×C42C2×Dic711yescharacteristic
189C2×C42C2×Dic711yescharacteristic
190C2×C42C22⋊D711yescharacteristic
191C2×C42C22⋊D711yescharacteristic
192C2×C42C22⋊D711yescharacteristic
193C2×C42C22⋊D711yescharacteristic
194C2×C42C22×D711yescharacteristic
195C4⋊C8—144no—
196#97—74no—
197#97—142no—
198#97—142no—
199#97—142no—
200#95—21no—
201#95—21no—
202#95—21no—
203#95—21no—
204C22×C7—81no—
205C22×C7—81no—
206C22×C7—81no—
207C22×C7—81no—
208C22×C7—81no—
209C22×C7—81no—
210C22×C7—81no—
211C22×C7#39011yescharacteristic
212C22×C7#41311yescharacteristic
213C22×C7#41311yescharacteristic
214C22×C7C2×#10411yescharacteristic
215C22×C7#42111yescharacteristic
216C22×C7#42111yescharacteristic
217C22×C7#42111yescharacteristic
218C4×C7—22no—
219C4×C7—22no—
220C4×C7—21no—
221C4×C7—21no—
222C4×C7—22no—
223C4×C7—41no—
224C4×C7—41no—
225C4×C7—41no—
226C4×C7—81no—
227C4×C7—81no—
228C4×C7—81no—
229C24—21no—
230C2×Q8—22no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×D4—22no—
234C2×D4—41no—
235C2×D4—41no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4C22⋊Dic711yescharacteristic
240C22×C4C22⋊Dic711yescharacteristic
241C22×C4C22⋊Dic711yescharacteristic
242C22×C4C22⋊Dic711yescharacteristic
243C22×C4C22×Dic711yescharacteristic
244C22×C4C2×C22⋊D711yescharacteristic
245C22×C4C2×C22⋊D711yescharacteristic
246C2×C8—144no—
247C2×C8—144no—
248C2×C8—282no—
249C2×C8—282no—
250C2×C8—282no—
251C2×C8—282no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—41no—
255C4⋊C4—42no—
256C4⋊C4—41no—
257C22⋊C4—42no—
258C22⋊C4—42no—
259C22⋊C4—42no—
260C22⋊C4—42no—
261C22⋊C4—41no—
262C22⋊C4—42no—
263C22⋊C4—41no—
264C42—22no—
265C42—41no—
266C42—41no—
267C42—41no—
268C42—41no—
269C42—41no—
270C42D4×D712yes—
271C42#115912yes—
272C2×C7—161no—
273C2×C7#152911yescharacteristic
274C2×C7#153211yescharacteristic
275C2×C7#153511yescharacteristic
276C2×C7#153511yescharacteristic
277C2×C7#196311yescharacteristic
278C2×C7#196711yescharacteristic
279C2×C7#198011yescharacteristic
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23C2×C22⋊Dic711yescharacteristic
288Q8—82no—
289D4—82no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4#641112yes—
317C2×C4D4×Dic712yes—
318C2×C4#649911yescharacteristic
319C2×C4#650112yes—
320C2×C4#650311yescharacteristic
321C8—284no—
322C8—284no—
323C7#968811yescharacteristic, complemented, Sylow
324C22—81no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22#8999311yescharacteristic
332C22C2×#641111yescharacteristic
333C22#9000811yescharacteristic
334C22#9000811yescharacteristic
335C22#9000811yescharacteristic
336C22#9000911yescharacteristic
337C22#9000911yescharacteristic
338C4—22no—
339C4—22no—
340C4—22no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—81no—
347C4—81no—
348C4—81no—
349C2—161no—
350C2#1172948111yescharacteristic
351C2#1172950111yescharacteristic
352C2#1172950211yescharacteristic
353C2#1172950311yescharacteristic
354C2#1172950311yescharacteristic
355C2#1172957011yescharacteristic
356C2#1172957211yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic7
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#2861C2
socleC23×C7C2×C22⋊C4
prime radicalC22×C7×D4C2×C4
cosocleC2×C42×C7C23
hypercenter#2861D7
hypocenterC7#9688
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C43 ◁ #2861

Complements

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

NH ≅ G/Ntype
2. C2×#89338C2semidirect
4. #11727145C2semidirect
5. #11727143C2semidirect
323. C7#9688semidirect

Maximal subgroups

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

subgroupindex
C7×#28612
C2×#893382
C2×#893352
#117271452
#117271432
#96887