Finite Group Databasebeta

← #13242159

Subgroups — #13242159

Order 1792.

482 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11739520C211yesmaximal, characteristic
2C4×C7×C22⋊C8C211yesmaximal, characteristic
3#11729284C211yesmaximal, characteristic
4#11725286C212yesmaximal, complemented
5#11725284C212yesmaximal, complemented
6C22×C42×C7C2211yescharacteristic
7C2×#6487C411yescharacteristic
8C2×C7×C22⋊C8—21no—
9C2×C4×C7×C8—21no—
10#89984C411yescharacteristic
11#89983—21no—
12#89982—21no—
13C2×C22⋊(C7⋊C8)—21no—
14#89705—21no—
15#89705—21no—
16#89701C411yescharacteristic
17#89701C2211yescharacteristic
18#89700C411yescharacteristic
19#89700C2211yescharacteristic
20C2×C4⋊(C7⋊C8)—21no—
21C7×#336C2212yes—
22#89319C2212yes—
23#7661—71nomaximal, Sylow
24C23×C4×C7C2×C411yescharacteristic
25C23×C4×C7D411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C22×Dic14C2×C411yescharacteristic
28C22×C7×C8—22no—
29C2×C42×C7—42no—
30C2×C42×C7C2×C411yescharacteristic
31C2×C42×C7D411yescharacteristic
32C2×C42×C7D411yescharacteristic
33C2×C42×C7C2311yescharacteristic
34C2×C22⋊Dic7—21no—
35C2×C22⋊Dic7—21no—
36C2×C4⋊Dic7C2×C411yescharacteristic
37C2×C4⋊Dic7C2×C411yescharacteristic
38C2×C4⋊Dic7C2×C411yescharacteristic
39#6487—42no—
40C2×Dic7⋊C4—21no—
41C2×Dic7⋊C4—21no—
42C2×Dic7⋊C4—21no—
43C22×C7⋊C8—22no—
44C7×C22⋊C8—24no—
45C4×C7×C8—42no—
46C7⋊#95—21no—
47C7⋊#95—21no—
48C7⋊#95—21no—
49C7⋊#95—21no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C22⋊(C7⋊C8)—42no—
54C4⋊(C7⋊C8)—42no—
55#2855—71no—
56#1797—71no—
57C4×C22⋊C8D711yescharacteristic
58#1272—72no—
59#1271—72no—
60C24×C7C22⋊C411yescharacteristic
61C22×C4×C7—22no—
62C22×C4×C7—22no—
63C22×C4×C7—22no—
64C22×C4×C7—22no—
65C22×C4×C7—41no—
66C22×C4×C7—41no—
67C22×C4×C7—41no—
68C22×C4×C7—41no—
69C22×C4×C7C22⋊C411yescharacteristic
70C22×C4×C7C22⋊C411yescharacteristic
71C22×C4×C7C22⋊C411yescharacteristic
72C22×C4×C7SD1612yes—
73C22×C4×C7Q1612yes—
74C22×C4×C7C22×C411yescharacteristic
75C22×C4×C7C2×D411yescharacteristic
76C22×C4×C7C2×D411yescharacteristic
77C22×Dic7—21no—
78C22×Dic7—21no—
79C22×Dic7—21no—
80C22×Dic7—21no—
81C2×Dic14—22no—
82C2×Dic14—41no—
83C2×Dic14—41no—
84C2×C7×C8—24no—
85C2×C7×C8—42no—
86C2×C7×C8—42no—
87C42×C7—22no—
88C42×C7—22no—
89C42×C7—41no—
90C42×C7—41no—
91C22⋊Dic7—42no—
92C22⋊Dic7—42no—
93C4⋊Dic7—22no—
94C4⋊Dic7—41no—
95C4⋊Dic7—41no—
96Dic7⋊C4—42no—
97Dic7⋊C4—42no—
98Dic7⋊C4—42no—
99C2×C7⋊C8—42no—
100C2×C7⋊C8—42no—
101C2×C7⋊C8—42no—
102C2×C22⋊Q8—71no—
103C22×C42C2×D711yescharacteristic
104C2×C4⋊C8—141no—
105C2×C22⋊C8—21no—
106C2×C22⋊C8—141no—
107C2×C4×C8—21no—
108#391—71no—
109#391—71no—
110#389—71no—
111#389—71no—
112#387—141no—
113#387—141no—
114#385—141no—
115#381—141no—
116#380—71no—
117#336—72no—
118#336C2×D712yes—
119C23×C7—21no—
120C23×C7—21no—
121C23×C7—21no—
122C23×C7—21no—
123C23×C7—21no—
124C23×C7—21no—
125C23×C7#10312yes—
126C23×C7C2×C22⋊C411yescharacteristic
127C2×C4×C7—21no—
128C2×C4×C7—21no—
129C2×C4×C7—21no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—21no—
134C2×C4×C7—21no—
135C2×C4×C7—21no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—42no—
140C2×C4×C7—42no—
141C2×C4×C7—44no—
142C2×C4×C7—44no—
143C2×C4×C7#9912yes—
144C2×C4×C7#10312yes—
145C2×C4×C7#10412yes—
146C2×C4×C7#13112yes—
147C2×C4×C7C2×SD1611yescharacteristic
148C2×C4×C7C2×Q1611yescharacteristic
149C2×C4×C7#13512yes—
150C2×Dic7—41no—
151C2×Dic7—41no—
152C2×Dic7—41no—
153C2×Dic7—41no—
154C2×Dic7—41no—
155C2×Dic7—41no—
156C2×Dic7—41no—
157C2×Dic7—41no—
158C2×Dic7—41no—
159C2×Dic7—41no—
160C2×Dic7—41no—
161C2×Dic7—41no—
162Dic14—82no—
163C7×C8—44no—
164C7⋊C8—82no—
165C22×Q8—71no—
166C23×C4C4×D711yescharacteristic
167C23×C4D2811yescharacteristic
168C23×C4C22⋊D711yescharacteristic
169C22×C8—22no—
170C22×C8—142no—
171C22⋊Q8—282no—
172C2×C4⋊C4—71no—
173C2×C4⋊C4—71no—
174C2×C4⋊C4—71no—
175C2×C4⋊C4—141no—
176C2×C4⋊C4—141no—
177C2×C4⋊C4—141no—
178C2×C22⋊C4—141no—
179C2×C22⋊C4—141no—
180C2×C42—42no—
181C2×C42C4×D711yescharacteristic
182C2×C42D2811yescharacteristic
183C2×C42C22⋊D711yescharacteristic
184C2×C42C22×D711yescharacteristic
185C4⋊C8—282no—
186C22⋊C8—24no—
187C22⋊C8—282no—
188C4×C8—42no—
189#95—141no—
190#95—141no—
191#95—141no—
192#95—141no—
193#95—141no—
194#95—141no—
195#95—141no—
196C22×C7—22no—
197C22×C7—22no—
198C22×C7—22no—
199C22×C7—41no—
200C22×C7—41no—
201C22×C7—41no—
202C22×C7—41no—
203C22×C7#40811yescharacteristic
204C22×C7C2×#9911yescharacteristic
205C22×C7#41311yescharacteristic
206C22×C7C2×#10311yescharacteristic
207C22×C7#41611yescharacteristic
208C22×C7C2×#10411yescharacteristic
209C22×C7#42111yescharacteristic
210C4×C7—22no—
211C4×C7—22no—
212C4×C7—22no—
213C4×C7—22no—
214C4×C7—21no—
215C4×C7—22no—
216C4×C7—21no—
217Dic7—81no—
218Dic7—81no—
219Dic7—81no—
220Dic7—81no—
221C24(C2×D7)⋊C411yescharacteristic
222C2×Q8—142no—
223C2×Q8—281no—
224C2×Q8—281no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—141no—
234C22×C4—141no—
235C22×C4—141no—
236C22×C4—141no—
237C22×C4#113212yes—
238C22×C4Dic2812yes—
239C22×C4(C2×D7)⋊C411yescharacteristic
240C22×C4(C2×D7)⋊C411yescharacteristic
241C22×C4(C2×D7)⋊C411yescharacteristic
242C22×C4C2×C4×D711yescharacteristic
243C22×C4C2×D2811yescharacteristic
244C22×C4C2×C22⋊D711yescharacteristic
245C2×C8—24no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—282no—
249C2×C8—282no—
250C2×C8—282no—
251C4⋊C4—142no—
252C4⋊C4—281no—
253C4⋊C4—281no—
254C4⋊C4—282no—
255C4⋊C4—282no—
256C4⋊C4—282no—
257C22⋊C4—282no—
258C22⋊C4—282no—
259C42—22no—
260C42—22no—
261C42—41no—
262C42—41no—
263C2×C7—42no—
264C2×C7#146811yescharacteristic
265C2×C7#148211yescharacteristic
266C2×C7#149311yescharacteristic
267C2×C7#150111yescharacteristic
268C2×C7#152011yescharacteristic
269C2×C7#152911yescharacteristic
270C2×C7#154211yescharacteristic
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23#639012yes—
278C23C2×(C2×D7)⋊C411yescharacteristic
279Q8—562no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4—281no—
297C2×C4—281no—
298C2×C4—281no—
299C2×C4—281no—
300C2×C4—281no—
301C2×C4—281no—
302C2×C4—281no—
303C2×C4—281no—
304C2×C4—281no—
305C2×C4—281no—
306C2×C4—281no—
307C2×C4—281no—
308C2×C4#637912yes—
309C2×C4#638012yes—
310C2×C4#639012yes—
311C2×C4#646412yes—
312C2×C4C2×#113211yescharacteristic
313C2×C4C2×Dic2811yescharacteristic
314C2×C4#651312yes—
315C8—44no—
316C8—562no—
317C7#766111yescharacteristic, complemented, Sylow
318C22—22no—
319C22—22no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22C2×#637911yescharacteristic
326C22C2×#638011yescharacteristic
327C22#8977411yescharacteristic
328C22C2×#639011yescharacteristic
329C22#8988211yescharacteristic
330C22#8990411yescharacteristic
331C22#8991111yescharacteristic
332C4—22no—
333C4—22no—
334C4—21no—
335C4—21no—
336C4—22no—
337C4—22no—
338C4—22no—
339C4—561no—
340C4—561no—
341C4—561no—
342C4—561no—
343C2—42no—
344C2#1172719711yescharacteristic
345C2#1172749211yescharacteristic
346C2#1172761511yescharacteristic
347C2#1172767411yescharacteristic
348C2#1172770011yescharacteristic
349C2#1172851311yescharacteristic
350C2#1172853011yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC4×C7×C22⋊C8C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C22⋊C4
cosocleC2×C42×C7C23
hypercenterC4×C22⋊C8D7
hypocenterC7#7661
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
4. #11725286C2semidirect
5. #11725284C2semidirect
317. C7#7661semidirect

Maximal subgroups

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

subgroupindex
#117395202
C4×C7×C22⋊C82
#117292842
#117252862
#117252842
#76617