Finite Group Databasebeta

← #13263155

Subgroups — #13263155

Order 1792.

706 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 706 conjugacy classes of subgroups — too many to draw. Only its 95 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×#89715C211yesmaximal, characteristic
2C7×#1462C211yesmaximal, characteristic
3#11729293C211yesmaximal, characteristic
4#11725251C214yesmaximal, complemented
5C24×Dic7C411yescharacteristic
6C22×C7×C22⋊C4C2211yescharacteristic
7C22×C22⋊Dic7C411yescharacteristic
8C7×#407—21no—
9C2×C7⋊#95—21no—
10C2×C7⋊#95—21no—
11#89979—21no—
12#89715—21no—
13#89715—21no—
14#89715C412yes—
15#89715C2212yes—
16C7×#323—21no—
17C7×#323C2212yes—
18#89320—21no—
19#89320C2212yes—
20#11500—71nomaximal, Sylow
21C25×C7C2×C411yescharacteristic
22C23×C4×C7D411yescharacteristic
23C23×C4×C7D411yescharacteristic
24C23×Dic7—21no—
25C23×Dic7—21no—
26C23×Dic7—24no—
27C23×Dic7—21no—
28C23×Dic7—41no—
29C23×Dic7—41no—
30C23×Dic7—42no—
31C23×Dic7C2×C412yes—
32C2×C7×M16—41no—
33C2×C7×C22⋊C4—41no—
34C2×C7×C22⋊C4—41no—
35C2×C7×C22⋊C4C2×C411yescharacteristic
36C2×C7×C22⋊C4D411yescharacteristic
37C2×C7×C22⋊C4D411yescharacteristic
38C2×C7×C22⋊C4C2311yescharacteristic
39C2×C22⋊Dic7—21no—
40C2×C22⋊Dic7—42no—
41C2×C22⋊Dic7C2×C412yes—
42C2×#1136—41no—
43C7×C22⋊C8—22no—
44C7×C22⋊C8—41no—
45C7⋊#95—22no—
46C7⋊#95—22no—
47C7⋊#95—22no—
48C7⋊#95—22no—
49C22⋊(C7⋊C8)—22no—
50C22⋊(C7⋊C8)—41no—
51C2×#381—71no—
52#1462—71no—
53#1462D711yescharacteristic
54#1317—74no—
55C24×C7—21no—
56C24×C7—21no—
57C24×C7—22no—
58C24×C7—22no—
59C24×C7—42no—
60C24×C7—42no—
61C24×C7C22⋊C411yescharacteristic
62C24×C7C22⋊C411yescharacteristic
63C24×C7C22×C411yescharacteristic
64C22×C4×C7—21no—
65C22×C4×C7—21no—
66C22×C4×C7—21no—
67C22×C4×C7—21no—
68C22×C4×C7—42no—
69C22×C4×C7—42no—
70C22×C4×C7C22⋊C411yescharacteristic
71C22×C4×C7C22⋊C411yescharacteristic
72C22×C4×C7C2×D411yescharacteristic
73C22×C4×C7C2×D411yescharacteristic
74C22×Dic7—24no—
75C22×Dic7—24no—
76C22×Dic7—22no—
77C22×Dic7—22no—
78C22×Dic7—22no—
79C22×Dic7—48no—
80C22×Dic7—48no—
81C22×Dic7—42no—
82C22×Dic7—42no—
83C22×Dic7—41no—
84C22×Dic7—41no—
85C22×Dic7—42no—
86C22×Dic7—42no—
87C22×Dic7—42no—
88C22×Dic7—42no—
89C22×Dic7—42no—
90C22×Dic7—42no—
91C22×Dic7M1614yescomplemented
92C7×M16—82no—
93C2×C7×C8—42no—
94C7×C22⋊C4—41no—
95C7×C22⋊C4—41no—
96C7×C22⋊C4—41no—
97C7×C22⋊C4—41no—
98C22⋊Dic7—42no—
99C22⋊Dic7—42no—
100#1136—82no—
101C2×C7⋊C8—42no—
102C24×C4—71no—
103C22×C22⋊C4—71no—
104C22×C22⋊C4C2×D711yescharacteristic
105#407—21no—
106#407—141no—
107#381—72no—
108#381—72no—
109#381—141no—
110#381—141no—
111C2×#95—141no—
112C2×#95—141no—
113#323—21no—
114#323—72no—
115#323—141no—
116#323C2×D712yes—
117C23×C7—22no—
118C23×C7—22no—
119C23×C7—21no—
120C23×C7—21no—
121C23×C7—24no—
122C23×C7—24no—
123C23×C7—21no—
124C23×C7—21no—
125C23×C7—21no—
126C23×C7—21no—
127C23×C7—41no—
128C23×C7—41no—
129C23×C7—41no—
130C23×C7—41no—
131C23×C7—48no—
132C23×C7—48no—
133C23×C7—42no—
134C23×C7—42no—
135C23×C7—42no—
136C23×C7—42no—
137C23×C7#9911yescharacteristic
138C23×C7#9911yescharacteristic
139C23×C7#10012yes—
140C23×C7C2×C22⋊C411yescharacteristic
141C23×C7C2×M1612yes—
142C2×C4×C7—21no—
143C2×C4×C7—21no—
144C2×C4×C7—21no—
145C2×C4×C7—21no—
146C2×C4×C7—42no—
147C2×C4×C7—42no—
148C2×C4×C7—41no—
149C2×C4×C7—41no—
150C2×C4×C7—41no—
151C2×C4×C7—41no—
152C2×C4×C7—81no—
153C2×C4×C7—81no—
154C2×Dic7—24no—
155C2×Dic7—44no—
156C2×Dic7—44no—
157C2×Dic7—48no—
158C2×Dic7—44no—
159C2×Dic7—42no—
160C2×Dic7—42no—
161C2×Dic7—44no—
162C2×Dic7—42no—
163C2×Dic7—42no—
164C2×Dic7—42no—
165C2×Dic7—84no—
166C7×C8—82no—
167C7⋊C8—82no—
168C25C4×D711yescharacteristic
169C23×C4—72no—
170C23×C4—144no—
171C23×C4—141no—
172C23×C4—141no—
173C23×C4—141no—
174C23×C4—281no—
175C23×C4—281no—
176C23×C4—282no—
177C23×C4D2811yescharacteristic
178C23×C4C22⋊D711yescharacteristic
179C2×M16—41no—
180C2×M16—281no—
181C2×C22⋊C4—41no—
182C2×C22⋊C4—41no—
183C2×C22⋊C4—72no—
184C2×C22⋊C4—141no—
185C2×C22⋊C4—282no—
186C2×C22⋊C4C4×D711yescharacteristic
187C2×C22⋊C4D2811yescharacteristic
188C2×C22⋊C4C22⋊D711yescharacteristic
189C2×C22⋊C4C22×D711yescharacteristic
190C22⋊C8—22no—
191C22⋊C8—41no—
192C22⋊C8—142no—
193C22⋊C8—281no—
194#95—142no—
195#95—142no—
196#95—142no—
197#95—142no—
198C22×C7—24no—
199C22×C7—24no—
200C22×C7—21no—
201C22×C7—21no—
202C22×C7—21no—
203C22×C7—21no—
204C22×C7—21no—
205C22×C7—21no—
206C22×C7—22no—
207C22×C7—22no—
208C22×C7—42no—
209C22×C7—42no—
210C22×C7—42no—
211C22×C7—48no—
212C22×C7—48no—
213C22×C7—42no—
214C22×C7—41no—
215C22×C7—41no—
216C22×C7—41no—
217C22×C7—41no—
218C22×C7#35212yes—
219C22×C7#35212yes—
220C22×C7#40711yescharacteristic
221C22×C7C2×#9911yescharacteristic
222C22×C7C2×#10011yescharacteristic
223C4×C7—41no—
224C4×C7—41no—
225C4×C7—41no—
226C4×C7—41no—
227Dic7—44no—
228Dic7—82no—
229C24—22no—
230C24—21no—
231C24—21no—
232C24—22no—
233C24—42no—
234C24—42no—
235C24(C2×D7)⋊C411yescharacteristic
236C24(C2×D7)⋊C411yescharacteristic
237C24C2×C4×D711yescharacteristic
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—74no—
245C22×C4—144no—
246C22×C4—144no—
247C22×C4—142no—
248C22×C4—142no—
249C22×C4—142no—
250C22×C4—288no—
251C22×C4—288no—
252C22×C4—282no—
253C22×C4—282no—
254C22×C4—281no—
255C22×C4—281no—
256C22×C4—282no—
257C22×C4—282no—
258C22×C4—282no—
259C22×C4—282no—
260C22×C4—282no—
261C22×C4—282no—
262C22×C4(C2×D7)⋊C411yescharacteristic
263C22×C4(C2×D7)⋊C411yescharacteristic
264C22×C4C2×D2811yescharacteristic
265C22×C4C2×C22⋊D711yescharacteristic
266M16—82no—
267M16—562no—
268C2×C8—42no—
269C2×C8—282no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—282no—
275C22⋊C4—282no—
276C2×C7—21no—
277C2×C7—22no—
278C2×C7—22no—
279C2×C7—21no—
280C2×C7—42no—
281C2×C7—42no—
282C2×C7#146211yescharacteristic
283C2×C7C2×#35211yescharacteristic
284C2×C7C2×#35211yescharacteristic
285C23—21no—
286C23—21no—
287C23—22no—
288C23—22no—
289C23—24no—
290C23—24no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—48no—
300C23—48no—
301C23—42no—
302C23—42no—
303C23—42no—
304C23—42no—
305C23#638011yescharacteristic
306C23#638011yescharacteristic
307C23#639712yes—
308C23D7×M1612yes—
309C23C2×(C2×D7)⋊C411yescharacteristic
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—144no—
323C2×C4—284no—
324C2×C4—284no—
325C2×C4—284no—
326C2×C4—288no—
327C2×C4—282no—
328C2×C4—282no—
329C2×C4—284no—
330C2×C4—282no—
331C2×C4—282no—
332C2×C4—282no—
333C2×C4—564no—
334C8—82no—
335C8—562no—
336C7#1150011yescharacteristic, complemented, Sylow
337C22—24no—
338C22—24no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—22no—
347C22—42no—
348C22—42no—
349C22—42no—
350C22—42no—
351C22—48no—
352C22—48no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22#8926712yes—
358C22#8927112yes—
359C22C2×#638011yescharacteristic
360C22#8989811yescharacteristic
361C22C2×#639711yescharacteristic
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—284no—
367C4—562no—
368C2—21no—
369C2—21no—
370C2—22no—
371C2—22no—
372C2—42no—
373C2—42no—
374C2#1172772111yescharacteristic
375C2C2×#8926711yescharacteristic
376C2C2×#8927111yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC24×C7C22×C4
FrattiniC2×C22⋊C4C22×D7
FittingC7×#1462C2
socleC22×C7C2×#99
prime radicalC25×C7C2×C4
cosocleC2×C7×C22⋊C4C23
hypercenter#1462D7
hypocenterC7#11500
LCSG ▷ C24×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
4. #11725251C2semidirect
91. C22×Dic7M16semidirect
336. C7#11500semidirect

Maximal subgroups

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

subgroupindex
C2×#897152
C7×#14622
#117292932
#117252512
#115007