Finite Group Databasebeta

← #13242005

Subgroups — #13242005

Order 1792.

506 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C4×#6487C211yesmaximal, characteristic
2C7×#1749C211yesmaximal, characteristic
3#11729285C211yesmaximal, characteristic
4#11725286C212yesmaximal, complemented
5#11725284C212yesmaximal, complemented
6C22×C42×C7C2211yescharacteristic
7C2×#6487C411yescharacteristic
8C2×C4×Dic14C411yescharacteristic
9C2×C7×C22⋊C8—21no—
10C2×C7×#97—21no—
11#89984C411yescharacteristic
12#89982—21no—
13C4×C22⋊Dic7—21no—
14C2×C22⋊(C7⋊C8)—21no—
15C4×C4⋊Dic7C411yescharacteristic
16#89705—21no—
17C4×Dic7⋊C4—21no—
18#89701C2211yescharacteristic
19#89700C2211yescharacteristic
20C7×#336C2212yes—
21#89319—21no—
22#89319C2212yes—
23#7623—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—22no—
40#6487—22no—
41C2×Dic7⋊C4—21no—
42C2×Dic7⋊C4—21no—
43C2×Dic7⋊C4—21no—
44C2×C4×Dic7—21no—
45C2×C4×Dic7—21no—
46C22×C7⋊C8—22no—
47C4×Dic14—42no—
48C7×C22⋊C8—24no—
49C7×#97—42no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95—21no—
55C22⋊(C7⋊C8)—42no—
56C4×C22⋊Q8—71no—
57#1817—71no—
58#1749D711yescharacteristic
59#1272—72no—
60#1271—72no—
61C24×C7C22⋊C411yescharacteristic
62C22×C4×C7—22no—
63C22×C4×C7—22no—
64C22×C4×C7—21no—
65C22×C4×C7—21no—
66C22×C4×C7—22no—
67C22×C4×C7—22no—
68C22×C4×C7—41no—
69C22×C4×C7—41no—
70C22×C4×C7—41no—
71C22×C4×C7—41no—
72C22×C4×C7C22⋊C411yescharacteristic
73C22×C4×C7C22⋊C411yescharacteristic
74C22×C4×C7C22⋊C411yescharacteristic
75C22×C4×C7C22×C411yescharacteristic
76C22×C4×C7C2×D411yescharacteristic
77C22×C4×C7C2×D411yescharacteristic
78C22×Dic7—21no—
79C22×Dic7—21no—
80C22×Dic7—21no—
81C22×Dic7—21no—
82C2×Dic14—21no—
83C2×Dic14—41no—
84C2×Dic14—41no—
85C2×Dic14M1612yes—
86C2×C7×C8—24no—
87C2×C7×C8—42no—
88C2×C7×C8—42no—
89C42×C7—22no—
90C42×C7—22no—
91C42×C7—41no—
92C42×C7—41no—
93C22⋊Dic7—24no—
94C22⋊Dic7—42no—
95C4⋊Dic7—21no—
96C4⋊Dic7—41no—
97C4⋊Dic7—41no—
98C4⋊Dic7M1612yes—
99Dic7⋊C4—24no—
100Dic7⋊C4—42no—
101Dic7⋊C4—42no—
102C4×Dic7—42no—
103C4×Dic7—42no—
104C2×C7⋊C8—42no—
105C2×C7⋊C8—42no—
106C2×C7⋊C8—42no—
107C2×C22⋊Q8—71no—
108C2×C4×Q8—71no—
109C22×C42C2×D711yescharacteristic
110C2×C22⋊C8—21no—
111C2×C22⋊C8—141no—
112C2×#97—21no—
113#391—71no—
114#389—71no—
115#387—141no—
116#385—141no—
117#380—71no—
118C4×C4⋊C4—71no—
119C4×C4⋊C4—141no—
120C4×C22⋊C4—141no—
121#336—72no—
122#336—141no—
123#336C2×D712yes—
124C23×C7—21no—
125C23×C7—21no—
126C23×C7—21no—
127C23×C7—21no—
128C23×C7—21no—
129C23×C7—21no—
130C23×C7#10412yes—
131C23×C7C2×C22⋊C411yescharacteristic
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—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—44no—
147C2×C4×C7—44no—
148C2×C4×C7—42no—
149C2×C4×C7—42no—
150C2×C4×C7#9912yes—
151C2×C4×C7C2×M1611yescharacteristic
152C2×C4×C7C2×M1611yescharacteristic
153C2×C4×C7#13512yes—
154C2×C4×C7#13712yes—
155C2×Dic7—22no—
156C2×Dic7—22no—
157C2×Dic7—41no—
158C2×Dic7—41no—
159C2×Dic7—41no—
160C2×Dic7—41no—
161C2×Dic7—41no—
162C2×Dic7—41no—
163C2×Dic7—41no—
164C2×Dic7—41no—
165C2×Dic7—41no—
166C2×Dic7—41no—
167Dic14—42no—
168Dic14—42no—
169C7×C8—44no—
170C7⋊C8—82no—
171C22×Q8—71no—
172C23×C4C4×D711yescharacteristic
173C23×C4D2811yescharacteristic
174C23×C4C22⋊D711yescharacteristic
175C22×C8—22no—
176C22×C8—142no—
177C22⋊Q8—142no—
178C22⋊Q8—142no—
179C4×Q8—282no—
180C2×C4⋊C4—71no—
181C2×C4⋊C4—71no—
182C2×C4⋊C4—71no—
183C2×C4⋊C4—141no—
184C2×C4⋊C4—141no—
185C2×C4⋊C4—141no—
186C2×C22⋊C4—141no—
187C2×C22⋊C4—141no—
188C2×C42—42no—
189C2×C42—141no—
190C2×C42—141no—
191C2×C42C4×D711yescharacteristic
192C2×C42D2811yescharacteristic
193C2×C42C22⋊D711yescharacteristic
194C2×C42C22×D711yescharacteristic
195C22⋊C8—24no—
196C22⋊C8—282no—
197#97—42no—
198#95—141no—
199#95—141no—
200#95—141no—
201#95—141no—
202#95—141no—
203C22×C7—22no—
204C22×C7—22no—
205C22×C7—22no—
206C22×C7—41no—
207C22×C7—41no—
208C22×C7—41no—
209C22×C7—41no—
210C22×C7#40711yescharacteristic
211C22×C7C2×#9911yescharacteristic
212C22×C7#41311yescharacteristic
213C22×C7#41611yescharacteristic
214C22×C7#41911yescharacteristic
215C22×C7C2×#10411yescharacteristic
216C22×C7#42111yescharacteristic
217C4×C7—21no—
218C4×C7—21no—
219C4×C7—22no—
220C4×C7—22no—
221C4×C7—22no—
222C4×C7—41no—
223C4×C7—41no—
224Dic7—42no—
225Dic7—42no—
226Dic7—81no—
227Dic7—81no—
228C24(C2×D7)⋊C411yescharacteristic
229C2×Q8—72no—
230C2×Q8—141no—
231C2×Q8—281no—
232C2×Q8—281no—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—141no—
244C22×C4—141no—
245C22×C4—141no—
246C22×C4—141no—
247C22×C4(C2×D7)⋊C411yescharacteristic
248C22×C4(C2×D7)⋊C411yescharacteristic
249C22×C4(C2×D7)⋊C411yescharacteristic
250C22×C4C2×C4×D711yescharacteristic
251C22×C4C2×D2811yescharacteristic
252C22×C4C2×C22⋊D711yescharacteristic
253C2×C8—24no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—282no—
257C2×C8—282no—
258C2×C8—282no—
259C4⋊C4—72no—
260C4⋊C4—144no—
261C4⋊C4—141no—
262C4⋊C4—281no—
263C4⋊C4—281no—
264C4⋊C4—282no—
265C4⋊C4—282no—
266C22⋊C4—144no—
267C22⋊C4—282no—
268C42—22no—
269C42—22no—
270C42—41no—
271C42—41no—
272C42—282no—
273C42—282no—
274C2×C7—42no—
275C2×C7#146511yescharacteristic
276C2×C7#148811yescharacteristic
277C2×C7#149111yescharacteristic
278C2×C7#150111yescharacteristic
279C2×C7#151111yescharacteristic
280C2×C7#153211yescharacteristic
281C2×C7#155411yescharacteristic
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23#637912yes—
289C23C2×(C2×D7)⋊C411yescharacteristic
290Q8—282no—
291Q8—282no—
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—44no—
307C2×C4—44no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—142no—
311C2×C4—142no—
312C2×C4—281no—
313C2×C4—281no—
314C2×C4—281no—
315C2×C4—281no—
316C2×C4—281no—
317C2×C4—281no—
318C2×C4—281no—
319C2×C4—281no—
320C2×C4—281no—
321C2×C4—281no—
322C2×C4#638012yes—
323C2×C4D7×M1611yescharacteristic
324C2×C4D7×M1611yescharacteristic
325C2×C4#647212yes—
326C2×C4#651312yes—
327C8—44no—
328C8—562no—
329C7#762311yescharacteristic, complemented, Sylow
330C22—22no—
331C22—22no—
332C22—22no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22C2×#637911yescharacteristic
338C22C2×#638011yescharacteristic
339C22#8977411yescharacteristic
340C22#8989211yescharacteristic
341C22#8989811yescharacteristic
342C22#8990411yescharacteristic
343C22#8991111yescharacteristic
344C4—22no—
345C4—21no—
346C4—21no—
347C4—22no—
348C4—22no—
349C4—41no—
350C4—41no—
351C4—282no—
352C4—282no—
353C4—561no—
354C4—561no—
355C2—42no—
356C2#1172719711yescharacteristic
357C2#1172755311yescharacteristic
358C2#1172761111yescharacteristic
359C2#1172772211yescharacteristic
360C2#1172773511yescharacteristic
361C2#1172855211yescharacteristic
362C2#1172857511yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#1749C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C22⋊C4
cosocleC2×C42×C7C23
hypercenter#1749D7
hypocenterC7#7623
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
4. #11725286C2semidirect
5. #11725284C2semidirect
329. C7#7623semidirect

Maximal subgroups

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

subgroupindex
C4×#64872
C7×#17492
#117292852
#117252862
#117252842
#76237