Finite Group Databasebeta

← #13272054

Subgroups — #13272054

Order 1792.

574 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89923C211yesmaximal, characteristic
2C2×C7×#361C211yesmaximal, characteristic, complemented
3C2×#89358C211yesmaximal, characteristic, complemented
4C2×#89311C211yesmaximal, characteristic, complemented
5Dic7×M32C211yesmaximal, characteristic, complemented
6#11728447C211yesmaximal, characteristic, complemented
7C2×#89290C211yesmaximal, characteristic, complemented
8C22×C7×D8C2211yescharacteristic
9C2×#6503—21no—
10C22×#1141—21no—
11C22×D56C2211yescharacteristic
12C2×C7×M32C2211yescharacteristic
13C2×C7×#108C2211yescharacteristic
14#89923—21no—
15#89923—21no—
16#89923C412yes—
17#89923C412yes—
18C2×#6396—21no—
19#89890—21no—
20C2×#6393C2211yescharacteristic
21C2×C8×Dic7C2211yescharacteristic
22C2×#6386C2211yescharacteristic
23C7×#361—22no—
24#89358—22no—
25#89311—22no—
26#89297—21no—
27C16×Dic7—21no—
28#89290—22no—
29#13213—71nomaximal, Sylow
30C22×C7×D4—21no—
31C22×C22⋊D7—42no—
32C22×D28—21no—
33C2×C7×D8—21no—
34C2×C7×D8—21no—
35C2×C7×D8—21no—
36C2×C7×D8—21no—
37C2×C7×D8—21no—
38C2×C7×D8C2×C412yes—
39C2×C7×M16—21no—
40C22×C7×C8C2311yescharacteristic
41#6503—22no—
42#6503—22no—
43#6503—42no—
44C2×#1141—22no—
45C2×#1141—22no—
46C2×#1141—42no—
47C2×#1141—42no—
48C2×C4×Dic7D411yescharacteristic
49C2×#1136—21no—
50C22×C7⋊C8D411yescharacteristic
51C2×D56—21no—
52C2×D56—21no—
53C2×D56—21no—
54C2×D56—21no—
55C2×D56—21no—
56C2×D56C2×C412yes—
57C7×M32—21no—
58C7×M32D412yescomplemented
59C2×C7×C16—21no—
60C7×#108—21no—
61C7×#108—21no—
62#6396—42no—
63#6393—21no—
64#6393—21no—
65Dic7⋊C8—42no—
66C8×Dic7C2×C411yescharacteristic
67C8×Dic7C2×C411yescharacteristic
68C8×Dic7D411yescharacteristic
69C8×Dic7D411yescharacteristic
70#6386—21no—
71#6386D412yescomplemented
72C2×C7⋊C16—21no—
73C2×#493—71no—
74C2×#361—71no—
75C2×#361—71no—
76C2×#361—71no—
77C2×#361D711yescharacteristic, complemented
78C4×M32—71no—
79#1848—71no—
80C24×C7—41no—
81C23×D7—41no—
82C2×C7×D4—22no—
83C2×C7×D4—41no—
84C2×C7×D4—41no—
85C2×C7×D4—41no—
86C2×C7×D4—41no—
87C2×C7×D4—41no—
88C22×C4×C7C2×D411yescharacteristic
89C2×C22⋊D7—44no—
90C2×C22⋊D7—44no—
91C2×C22⋊D7—88no—
92C22×Dic7SD1612yes—
93C2×D28—22no—
94C2×D28—41no—
95C2×D28—41no—
96C2×D28—41no—
97C2×D28—41no—
98C2×D28—41no—
99C7×D8—22no—
100C7×D8—22no—
101C7×D8—41no—
102C7×D8—41no—
103C7×M16—41no—
104C7×M16—41no—
105C2×C7×C8—41no—
106C2×C7×C8C22×C411yescharacteristic
107C2×C7×C8C2×D411yescharacteristic
108C2×C7×C8C2×D411yescharacteristic
109C2×C7×C8C2×D411yescharacteristic
110C2×C7×C8#4111yescharacteristic
111C2×C7×C8#4111yescharacteristic
112#1141—44no—
113#1141—44no—
114C4×Dic7C22⋊C411yescharacteristic
115C4×Dic7C22⋊C411yescharacteristic
116C4×Dic7D812yes—
117#1136—41no—
118#1136—41no—
119C2×C7⋊C8—41no—
120C2×C7⋊C8C22⋊C411yescharacteristic
121C2×C7⋊C8C22⋊C411yescharacteristic
122C2×C7⋊C8D812yes—
123C2×C7⋊C8SD1612yes—
124D56—22no—
125D56—22no—
126D56—41no—
127D56—41no—
128C7×C16—22no—
129C7⋊C16—22no—
130C22×D8—71no—
131C22×D8—141no—
132C22×D8C2×D711yescharacteristic
133C2×#127—141no—
134C2×M32—71no—
135C2×M32C2×D711yescharacteristic
136#493—72no—
137#493—72no—
138#493—141no—
139#493—141no—
140C2×#108—71no—
141C2×#108—141no—
142C2×#108C2×D711yescharacteristic
143#423—141no—
144C2×C4×C8—71no—
145#361—22no—
146#361—142no—
147#361—142no—
148#361—142no—
149#346—141no—
150C4×C16—141no—
151C23×C7—42no—
152C23×C7—84no—
153C23×C7—81no—
154C23×C7—81no—
155C23×C7C2×SD1611yescharacteristic
156C22×D7—42no—
157C22×D7—84no—
158C22×D7—81no—
159C22×D7—81no—
160C7×D4—42no—
161C7×D4—42no—
162C7×D4—81no—
163C7×D4—81no—
164C2×C4×C7C2×C22⋊C411yescharacteristic
165C2×C4×C7#12411yescharacteristic
166C2×C4×C7#12711yescharacteristic
167C2×C4×C7C2×D811yescharacteristic
168C2×C4×C7C2×D811yescharacteristic
169C2×C4×C7C2×SD1611yescharacteristic
170C22⋊D7—88no—
171C22⋊D7—88no—
172C2×Dic7—24no—
173C2×Dic7#10212yes—
174C2×Dic7#10212yes—
175D28—42no—
176D28—42no—
177D28—81no—
178D28—81no—
179C7×C8—81no—
180C7×C8C4×D411yescharacteristic
181C7×C8C4×D411yescharacteristic
182C7×C8#12111yescharacteristic
183C7×C8#12111yescharacteristic
184C7⋊C8—81no—
185C7⋊C8#10212yes—
186C7⋊C8#10212yes—
187C22×D4—21no—
188C22×D4—141no—
189C22×D4—282no—
190C2×D8—21no—
191C2×D8—21no—
192C2×D8—21no—
193C2×D8—21no—
194C2×D8—21no—
195C2×D8—72no—
196C2×D8—142no—
197C2×D8—142no—
198C2×D8—141no—
199C2×D8—141no—
200C2×D8—141no—
201C2×D8—141no—
202C2×D8—141no—
203C2×D8—282no—
204C2×D8—282no—
205C2×D8C4×D712yes—
206C2×M16—21no—
207C2×M16—141no—
208C22×C8—71no—
209C22×C8C22×D711yescharacteristic
210#127—142no—
211#127—142no—
212#127—282no—
213C2×C42—71no—
214M32—21no—
215M32—72no—
216M32—141no—
217M32C22⋊D712yescomplemented
218C2×C16—21no—
219C2×C16—141no—
220#108—21no—
221#108—21no—
222#108—141no—
223#108—141no—
224#108—282no—
225C4⋊C8—282no—
226C4×C8—71no—
227C4×C8—71no—
228C4×C8—71no—
229C4×C8—71no—
230C22×C7—22no—
231C22×C7—84no—
232C22×C7—82no—
233C22×C7—162no—
234C22×C7—162no—
235C22×C7C2×#10211yescharacteristic
236C22×C7#48611yescharacteristic
237C22×C7#49211yescharacteristic
238C2×D7—84no—
239C2×D7—82no—
240C2×D7—162no—
241C2×D7—162no—
242C4×C7#39011yescharacteristic
243C4×C7C2×#10211yescharacteristic
244C4×C7#48611yescharacteristic
245C4×C7#49311yescharacteristic
246Dic7—22no—
247Dic7#36114yescomplemented
248C24—41no—
249C24—281no—
250C2×D4—22no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—142no—
257C2×D4—284no—
258C2×D4—284no—
259C2×D4—281no—
260C2×D4—281no—
261C2×D4—281no—
262C2×D4—281no—
263C2×D4—281no—
264C2×D4—568no—
265C22×C4—72no—
266C22×C4D4×D711yescharacteristic
267D8—22no—
268D8—22no—
269D8—41no—
270D8—41no—
271D8—142no—
272D8—142no—
273D8—284no—
274D8—284no—
275D8—281no—
276D8—281no—
277M16—41no—
278M16—41no—
279M16—281no—
280M16—281no—
281C2×C8—41no—
282C2×C8—71no—
283C2×C8—71no—
284C2×C8—72no—
285C2×C8—72no—
286C2×C8—281no—
287C2×C8C2×C4×D711yescharacteristic
288C2×C8#115711yescharacteristic
289C2×C8D4×D711yescharacteristic
290C2×C8D4×D711yescharacteristic
291C2×C8#115911yescharacteristic
292C2×C8C2×C22⋊D711yescharacteristic
293C42—71no—
294C42—71no—
295C42—72no—
296C16—22no—
297C16—142no—
298C2×C7—21no—
299C2×C7—21no—
300C2×C7—162no—
301C2×C7#195711yescharacteristic
302C2×C7C2×#36112yes—
303D7—162no—
304C23—42no—
305C23—84no—
306C23—81no—
307C23—81no—
308C23—282no—
309C23—564no—
310C23—561no—
311C23—561no—
312C23D7×SD1611yescharacteristic
313D4—42no—
314D4—42no—
315D4—81no—
316D4—81no—
317D4—282no—
318D4—282no—
319D4—568no—
320D4—568no—
321D4—561no—
322D4—561no—
323C2×C4—72no—
324C2×C4—72no—
325C2×C4—144no—
326C2×C4D7×C22⋊C411yescharacteristic
327C2×C4#644811yescharacteristic
328C2×C4D7×D811yescharacteristic
329C2×C4D7×D811yescharacteristic
330C2×C4D7×SD1611yescharacteristic
331C2×C4#650311yescharacteristic
332C8—72no—
333C8—72no—
334C8—81no—
335C8—561no—
336C8(C22⋊D7)⋊C411yescharacteristic
337C8#644711yescharacteristic
338C8C4×C22⋊D711yescharacteristic
339C8#650211yescharacteristic
340C7#1321311yescharacteristic, complemented, Sylow
341C22—22no—
342C22—82no—
343C22—84no—
344C22—162no—
345C22—162no—
346C22—562no—
347C22—564no—
348C22—1122no—
349C22—1122no—
350C22#8953211yescharacteristic
351C22D7×#10211yescharacteristic
352C22#8994711yescharacteristic
353C4—74no—
354C4—142no—
355C4#8953211yescharacteristic
356C4D7×#10211yescharacteristic
357C4#8972911yescharacteristic
358C4#8992311yescharacteristic
359C2—21no—
360C2—21no—
361C2—162no—
362C2—1122no—
363C2D7×#36112yes—
364C2#1172791111yescharacteristic
subgroupG/H
centerC22D7×#102
commutatorC2×C7×C8C22×C4
FrattiniC22×C8C22×D7
FittingC2×C7×#361C2
socleC22×C7C2×#102
prime radicalC2×#89923C2
cosocleC22×C7×C8C23
hypercenterC2×#361D7
hypocenterC7#13213
LCSG ▷ C2×C7×C8 ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

Complements

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

NH ≅ G/Ntype
2. C2×C7×#361C2semidirect
3. C2×#89358C2semidirect
4. C2×#89311C2semidirect
5. Dic7×M32C2semidirect
6. #11728447C2semidirect
7. C2×#89290C2semidirect
58. C7×M32D4semidirect
71. #6386D4semidirect
77. C2×#361D7semidirect
217. M32C22⋊D7semidirect
247. Dic7#361semidirect
340. C7#13213semidirect

Maximal subgroups

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

subgroupindex
C2×#899232
C2×C7×#3612
C2×#893582
C2×#893112
Dic7×M322
#117284472
C2×#892902
#132137