Finite Group Databasebeta

← #13264628

Subgroups — #13264628

Order 1792.

400 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 79 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
1#11739837C211yesmaximal, characteristic
2C7×#1465C211yesmaximal, characteristic
3#11729371C211yesmaximal, characteristic
4#11725264C212yesmaximal, complemented
5#11725263C212yesmaximal, complemented
6C2×C4×C7×D4C2211yescharacteristic
7C2×#6487C411yescharacteristic
8C7×#407—21no—
9#89994—21no—
10C2×#6407—21no—
11#89983C411yescharacteristic
12#89982—21no—
13#89755C2211yescharacteristic
14#89751C2211yescharacteristic
15#89725C411yescharacteristic
16#89724—21no—
17#89719C411yescharacteristic
18#89705—21no—
19#89696—21no—
20C7×#324C2212yes—
21C7×#323—21no—
22#89325C2212yes—
23#11834—71nomaximal, Sylow
24C22×C7×D4D411yescharacteristic
25C23×C4×C7C2×C411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C22×Dic14C2×C411yescharacteristic
28C2×C7×M16—41no—
29C4×C7×D4—41no—
30C4×C7×D4—41no—
31C2×C7×C4⋊C4C2311yescharacteristic
32C2×C7×C22⋊C4C2×C411yescharacteristic
33C2×C7×C22⋊C4D411yescharacteristic
34C2×C42×C7D411yescharacteristic
35C2×C22⋊Dic7—21no—
36C2×C22⋊Dic7—21no—
37C2×C22⋊Dic7—21no—
38C2×C22⋊Dic7—21no—
39C2×C4⋊Dic7C2×C411yescharacteristic
40#6487—41no—
41#6487—41no—
42C2×Dic7⋊C4—21no—
43C2×Dic7⋊C4—21no—
44C2×Dic7⋊C4—21no—
45C2×#1136—22no—
46C7×C22⋊C8—22no—
47C7×C22⋊C8—41no—
48#6407—42no—
49C7⋊#95—21no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95C2×C411yescharacteristic
55C7⋊#95C2×C411yescharacteristic
56C4⋊(C7⋊C8)—41no—
57C4⋊(C7⋊C8)—41no—
58#2638—71no—
59#1800—71no—
60#1465D711yescharacteristic
61#1354—72no—
62#1346—72no—
63C24×C7C22⋊C411yescharacteristic
64C24×C7C22⋊C411yescharacteristic
65C2×C7×D4—21no—
66C2×C7×D4—21no—
67C2×C7×D4—41no—
68C2×C7×D4—41no—
69C22×C4×C7—21no—
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7—21no—
73C22×C4×C7—81no—
74C22×C4×C7—81no—
75C22×C4×C7C22⋊C411yescharacteristic
76C22×C4×C7C22⋊C411yescharacteristic
77C22×C4×C7C22×C411yescharacteristic
78C22×C4×C7C2×D411yescharacteristic
79C22×C4×C7C2×D411yescharacteristic
80C22×Dic7—21no—
81C22×Dic7—21no—
82C22×Dic7—21no—
83C22×Dic7—21no—
84C2×Dic14—41no—
85C2×Dic14—81no—
86C7×M16—82no—
87C2×C7×C8—42no—
88C7×C4⋊C4—41no—
89C7×C22⋊C4—41no—
90C7×C22⋊C4—41no—
91C42×C7—21no—
92C42×C7—21no—
93C22⋊Dic7—42no—
94C22⋊Dic7—42no—
95C22⋊Dic7—81no—
96C22⋊Dic7—81no—
97C4⋊Dic7—41no—
98Dic7⋊C4—41no—
99Dic7⋊C4—41no—
100Dic7⋊C4—41no—
101Dic7⋊C4—41no—
102Dic7⋊C4—81no—
103#1136—42no—
104#1136—42no—
105C2×C7⋊C8—42no—
106C2×C22⋊Q8—71no—
107C2×C4×D4C2×D711yescharacteristic
108#423—141no—
109C2×#100—141no—
110#407—21no—
111#398—71no—
112#397—71no—
113#397—141no—
114#395—71no—
115#394—141no—
116#393—71no—
117#387—141no—
118#385—141no—
119#381—71no—
120#343—72no—
121#324C2×D712yes—
122#323—21no—
123C23×C7—21no—
124C23×C7—21no—
125C23×C7—21no—
126C23×C7—21no—
127C23×C7—21no—
128C23×C7—21no—
129C23×C7—41no—
130C23×C7—41no—
131C23×C7—41no—
132C23×C7—41no—
133C23×C7C2×C22⋊C411yescharacteristic
134C7×D4—42no—
135C7×D4—42no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—21no—
140C2×C4×C7—21no—
141C2×C4×C7—41no—
142C2×C4×C7—42no—
143C2×C4×C7—41no—
144C2×C4×C7—41no—
145C2×C4×C7—41no—
146C2×C4×C7—81no—
147C2×C4×C7—81no—
148C2×C4×C7—81no—
149C2×C4×C7#9911yescharacteristic
150C2×C4×C7#9911yescharacteristic
151C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C7#13711yescharacteristic
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—
162C2×Dic7—41no—
163C2×Dic7—41no—
164C2×Dic7—41no—
165Dic14—82no—
166C7×C8—82no—
167C7⋊C8—82no—
168C22×Q8—71no—
169C22×D4D2811yescharacteristic
170C23×C4C4×D711yescharacteristic
171C23×C4C22⋊D711yescharacteristic
172C2×M16—41no—
173C2×M16—142no—
174C22⋊Q8—281no—
175C22⋊Q8—281no—
176C4×D4—41no—
177C4×D4—41no—
178C2×C4⋊C4—71no—
179C2×C4⋊C4—141no—
180C2×C4⋊C4—141no—
181C2×C4⋊C4—141no—
182C2×C4⋊C4C22×D711yescharacteristic
183C2×C22⋊C4—141no—
184C2×C22⋊C4—141no—
185C2×C22⋊C4—141no—
186C2×C22⋊C4—141no—
187C2×C22⋊C4C4×D711yescharacteristic
188C2×C22⋊C4C22⋊D711yescharacteristic
189C2×C42D2811yescharacteristic
190C4⋊C8—281no—
191C4⋊C8—281no—
192#100—282no—
193C22⋊C8—22no—
194C22⋊C8—41no—
195#95—71no—
196#95—71no—
197#95—141no—
198#95—141no—
199#95—141no—
200#95—141no—
201#95—141no—
202C22×C7—21no—
203C22×C7—21no—
204C22×C7—42no—
205C22×C7—41no—
206C22×C7—41no—
207C22×C7—41no—
208C22×C7—41no—
209C22×C7—41no—
210C22×C7—41no—
211C22×C7—81no—
212C22×C7—81no—
213C22×C7—81no—
214C22×C7C2×#9911yescharacteristic
215C22×C7#41711yescharacteristic
216C22×C7#42111yescharacteristic
217C4×C7—21no—
218C4×C7—21no—
219C4×C7—21no—
220C4×C7—21no—
221C4×C7—41no—
222C4×C7—41no—
223C4×C7—41no—
224Dic7—81no—
225Dic7—81no—
226Dic7—81no—
227Dic7—81no—
228C24(C2×D7)⋊C411yescharacteristic
229C24(C2×D7)⋊C411yescharacteristic
230C2×Q8—281no—
231C2×Q8—561no—
232C2×D4—21no—
233C2×D4—21no—
234C2×D4—41no—
235C2×D4—41no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—81no—
241C22×C4—81no—
242C22×C4—141no—
243C22×C4—141no—
244C22×C4—141no—
245C22×C4—141no—
246C22×C4(C2×D7)⋊C411yescharacteristic
247C22×C4(C2×D7)⋊C411yescharacteristic
248C22×C4C2×C4×D711yescharacteristic
249C22×C4C2×D2811yescharacteristic
250C22×C4C2×C22⋊D711yescharacteristic
251M16—82no—
252M16—282no—
253M16—282no—
254C2×C8—42no—
255C2×C8—282no—
256C4⋊C4—41no—
257C4⋊C4—281no—
258C4⋊C4—281no—
259C4⋊C4—281no—
260C4⋊C4—281no—
261C4⋊C4—281no—
262C4⋊C4—561no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—282no—
266C22⋊C4—282no—
267C22⋊C4—561no—
268C22⋊C4—561no—
269C42—21no—
270C42—21no—
271C2×C7—21no—
272C2×C7—21no—
273C2×C7—81no—
274C2×C7—81no—
275C2×C7#151311yescharacteristic
276C2×C7#212111yescharacteristic
277C2×C7#213511yescharacteristic
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23C2×(C2×D7)⋊C411yescharacteristic
289Q8—562no—
290D4—42no—
291D4—42no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—281no—
306C2×C4—281no—
307C2×C4—281no—
308C2×C4—281no—
309C2×C4—281no—
310C2×C4—281no—
311C2×C4—281no—
312C2×C4—281no—
313C2×C4—281no—
314C2×C4—281no—
315C2×C4—281no—
316C2×C4—281no—
317C2×C4#638011yescharacteristic
318C2×C4#638011yescharacteristic
319C2×C4#647111yescharacteristic
320C2×C4#647211yescharacteristic
321C8—82no—
322C8—562no—
323C7#1183411yescharacteristic, complemented, Sylow
324C22—21no—
325C22—21no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—81no—
334C22—81no—
335C22—81no—
336C22C2×#638011yescharacteristic
337C22#8990511yescharacteristic
338C22#8991111yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—561no—
347C4—561no—
348C4—561no—
349C4—561no—
350C2—21no—
351C2—21no—
352C2—81no—
353C2—81no—
354C2#1172773311yescharacteristic
355C2#1172776911yescharacteristic
356C2#1172790411yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1465C2
socleC22×C7C2×#99
prime radicalC22×C7×D4D4
cosocleC2×C7×C4⋊C4C23
hypercenter#1465D7
hypocenterC7#11834
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
4. #11725264C2semidirect
5. #11725263C2semidirect
323. C7#11834semidirect

Maximal subgroups

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

subgroupindex
#117398372
C7×#14652
#117293712
#117252642
#117252632
#118347