Finite Group Databasebeta

← #13253147

Subgroups — #13253147

Order 1792.

428 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11735908C211yesmaximal, characteristic
2C7×C8×C4⋊C4C211yesmaximal, characteristic, complemented
3#11728183C211yesmaximal, characteristic, complemented
4#11728180C211yesmaximal, characteristic
5#11727483C211yesmaximal, characteristic, complemented
6#11727225C211yesmaximal, characteristic, complemented
7#11727223C211yesmaximal, characteristic
8#90168C2211yescharacteristic
9#90161C2211yescharacteristic
10C2×C7×C4⋊C8C2211yescharacteristic
11C2×C4×C7×C8—21no—
12C2×C4×C7×C8C2211yescharacteristic
13C4×C7×C4⋊C4C2211yescharacteristic
14#89885—21no—
15#89885—21no—
16#89697C2211yescharacteristic
17#89697C2211yescharacteristic
18#89469—21no—
19#89469—21no—
20#89466C411yescharacteristic, complemented
21#89466C411yescharacteristic, complemented
22#89453C411yescharacteristic, complemented
23#89453C411yescharacteristic, complemented
24C7×#336—21no—
25#89279—22no—
26#89278—22no—
27#89253—21no—
28#89252—21no—
29#89247—22no—
30#89246—22no—
31#9751—71nomaximal, Sylow
32C2×#1157—21no—
33C22×C7×C8—21no—
34C22×C7×C8D411yescharacteristic
35C22×C7×C8D411yescharacteristic
36C2×C7×C4⋊C4—21no—
37C2×C42×C7—21no—
38C2×C42×C7C2311yescharacteristic
39#6493—21no—
40#6493—21no—
41#6489—21no—
42#6487—21no—
43#6487—21no—
44#6438—21no—
45#6437C2×C411yescharacteristic
46C4×D28—21no—
47C4×D28—21no—
48#6433—21no—
49#6432C2×C411yescharacteristic
50#6432C2×C411yescharacteristic
51#6432C2×C411yescharacteristic
52C4×Dic14—21no—
53C4×Dic14—21no—
54C7×C4⋊C8—21no—
55C7×C4⋊C8D412yes—
56C4×C7×C8—42no—
57C4×C7×C8C2×C411yescharacteristic
58C4×C7×C8C2×C411yescharacteristic
59C4×C7×C8D411yescharacteristic
60C4×C7×C8D411yescharacteristic
61C7×#95D412yes—
62C22⋊(C7⋊C8)—21no—
63C22⋊(C7⋊C8)—21no—
64#6395—21no—
65#6395—21no—
66#6395—21no—
67#6395—21no—
68#6390—21no—
69#6390—21no—
70#6390—21no—
71#6390—21no—
72C4⋊(C7⋊C8)—21no—
73C4⋊(C7⋊C8)—21no—
74C4×C7⋊C8—21no—
75C4×C7⋊C8—21no—
76#3131—71no—
77C8×C4⋊C4D711yescharacteristic, complemented
78#1564—71no—
79#1503—71no—
80#1502—71no—
81#1481—71no—
82#1480—71no—
83C22×C4×C7—22no—
84C22×C4×C7C2×D411yescharacteristic
85C22×C4×C7C2×D411yescharacteristic
86C22×C4×C7#4111yescharacteristic
87C2×C22⋊D7—41no—
88#1157—41no—
89#1157—41no—
90#1157—41no—
91#1157—41no—
92C2×D28—21no—
93C2×D28—21no—
94C2×D28—21no—
95C2×C4×D7—41no—
96C2×Dic14—21no—
97C2×Dic14—21no—
98C2×Dic14—21no—
99C2×C7×C8—21no—
100C2×C7×C8—21no—
101C2×C7×C8—21no—
102C2×C7×C8—21no—
103C2×C7×C8—22no—
104C2×C7×C8—41no—
105C2×C7×C8—41no—
106C2×C7×C8C22⋊C411yescharacteristic
107C2×C7×C8C22⋊C411yescharacteristic
108C2×C7×C8C22⋊C411yescharacteristic
109C2×C7×C8C22⋊C411yescharacteristic
110C7×C4⋊C4—24no—
111C42×C7—41no—
112C42×C7—41no—
113C42×C7C22×C411yescharacteristic
114C42×C7C2×D411yescharacteristic
115C42×C7C2×D411yescharacteristic
116C42×C7#4111yescharacteristic
117C22⋊Dic7—41no—
118(C2×D7)⋊C4—41no—
119(C2×D7)⋊C4—41no—
120C4⋊Dic7—21no—
121C4⋊Dic7—21no—
122C4⋊Dic7—21no—
123C4⋊Dic7—21no—
124C4⋊Dic7—21no—
125C4⋊Dic7—21no—
126Dic7⋊C4—41no—
127Dic7⋊C4—41no—
128C4×Dic7—41no—
129C2×C7⋊C8—41no—
130C2×C7⋊C8—41no—
131#533—71no—
132#532—71no—
133#488—141no—
134#488—141no—
135#487—71no—
136#487—71no—
137#486—71no—
138#486—71no—
139#431—71no—
140#431—71no—
141C2×C4⋊C8C2×D711yescharacteristic
142#416—141no—
143#416—141no—
144C2×C4×C8—21no—
145C2×C4×C8C2×D711yescharacteristic
146C4×C4⋊C4C2×D711yescharacteristic
147#336—21no—
148#335—141no—
149#334—141no—
150#328—142no—
151#327—142no—
152Q8⋊C8—142no—
153D4⋊C8—142no—
154C23×C7#12111yescharacteristic
155C22×D7—41no—
156C2×C4×C7—22no—
157C2×C4×C7—24no—
158C2×C4×C7—41no—
159C2×C4×C7—42no—
160C2×C4×C7—42no—
161C2×C4×C7C2×C22⋊C411yescharacteristic
162C2×C4×C7C4×D411yescharacteristic
163C2×C4×C7C4×D411yescharacteristic
164C2×C4×C7#12111yescharacteristic
165C2×C4×C7#12411yescharacteristic
166C2×C4×C7#12711yescharacteristic
167C2×C4×C7#13511yescharacteristic
168C2×C4×C7#13511yescharacteristic
169C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C7#13711yescharacteristic
171C22⋊D7—81no—
172C22⋊D7—81no—
173C2×Dic7—41no—
174C2×Dic7—41no—
175C2×Dic7—41no—
176D28—41no—
177D28—41no—
178D28—42no—
179D28—81no—
180C4×D7—81no—
181C4×D7—81no—
182Dic14—41no—
183Dic14—41no—
184Dic14—42no—
185Dic14—81no—
186C7×C8—21no—
187C7×C8—21no—
188C7×C8—21no—
189C7×C8—21no—
190C7×C8—42no—
191C7⋊C8—81no—
192C7⋊C8—81no—
193C2×#41—141no—
194C22×C8—21no—
195C22×C8C22⋊D711yescharacteristic
196C22×C8C22⋊D711yescharacteristic
197C4⋊Q8—71no—
198C4⋊Q8—71no—
199C4⋊Q8—71no—
200#127—71no—
201#125—141no—
202#124—141no—
203C22⋊Q8—141no—
204C22⋊Q8—141no—
205#121—141no—
206#121—141no—
207C4×Q8—141no—
208C4×Q8—141no—
209C4×D4—141no—
210C4×D4—141no—
211#117—141no—
212C2×C4⋊C4—21no—
213C2×C42—21no—
214C2×C42C22×D711yescharacteristic
215C4⋊C8—21no—
216C4⋊C8—141no—
217C4⋊C8—141no—
218C4⋊C8D2812yes—
219#103—141no—
220#103—141no—
221#103—141no—
222#103—141no—
223#102—141no—
224#102—141no—
225#102—141no—
226#102—141no—
227C22⋊C8—141no—
228C22⋊C8—141no—
229C4×C8—42no—
230C4×C8—141no—
231C4×C8—141no—
232C4×C8C4×D711yescharacteristic
233C4×C8C4×D711yescharacteristic
234C4×C8D2811yescharacteristic
235C4×C8D2811yescharacteristic
236#95D2812yes—
237C22×C7—21no—
238C22×C7—21no—
239C22×C7#39011yescharacteristic
240C22×C7#46311yescharacteristic
241C22×C7#46411yescharacteristic
242C2×D7—81no—
243C2×D7—81no—
244C2×D7—81no—
245C4×C7—21no—
246C4×C7—21no—
247C4×C7—21no—
248C4×C7—44no—
249C4×C7#41611yescharacteristic
250C4×C7#41711yescharacteristic
251C4×C7#44312yes—
252C4×C7#46311yescharacteristic
253C4×C7#46411yescharacteristic
254Dic7—81no—
255Dic7—81no—
256Dic7—81no—
257#41—281no—
258#41—281no—
259#41—281no—
260#41—281no—
261C2×Q8—141no—
262C2×Q8—141no—
263C2×Q8—141no—
264C2×D4—141no—
265C2×D4—141no—
266C2×D4—141no—
267C2×D4—281no—
268C22×C4—22no—
269C22×C4—281no—
270C22×C4C2×D2811yescharacteristic
271C22×C4#115711yescharacteristic
272C22×C4C2×C22⋊D711yescharacteristic
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—22no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—281no—
281C2×C8—281no—
282C2×C8(C2×D7)⋊C411yescharacteristic
283C2×C8(C2×D7)⋊C411yescharacteristic
284C2×C8(C2×D7)⋊C411yescharacteristic
285C2×C8(C2×D7)⋊C411yescharacteristic
286C4⋊C4—24no—
287C4⋊C4—141no—
288C4⋊C4—141no—
289C4⋊C4—141no—
290C4⋊C4—141no—
291C4⋊C4—141no—
292C4⋊C4—141no—
293C4⋊C4—281no—
294C4⋊C4—281no—
295C22⋊C4—281no—
296C22⋊C4—281no—
297C22⋊C4—281no—
298C42—41no—
299C42—41no—
300C42—281no—
301C42C2×C4×D711yescharacteristic
302C42C2×D2811yescharacteristic
303C42C2×D2811yescharacteristic
304C42#115711yescharacteristic
305C2×C7—21no—
306C2×C7—21no—
307C2×C7#197411yescharacteristic
308C2×C7#197611yescharacteristic
309C2×C7#198311yescharacteristic
310D7—161no—
311C23—281no—
312C23#649311yescharacteristic
313Q8—282no—
314Q8—281no—
315Q8—281no—
316Q8—561no—
317D4—282no—
318D4—281no—
319D4—281no—
320D4—561no—
321D4—561no—
322D4—561no—
323C2×C4—22no—
324C2×C4—24no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—281no—
329C2×C4—281no—
330C2×C4—281no—
331C2×C4—561no—
332C2×C4—561no—
333C2×C4C4×D2811yescharacteristic
334C2×C4C4×D2811yescharacteristic
335C2×C4#643711yescharacteristic
336C2×C4#643811yescharacteristic
337C2×C4C2×(C2×D7)⋊C411yescharacteristic
338C2×C4#649311yescharacteristic
339C2×C4#649511yescharacteristic
340C2×C4#650511yescharacteristic
341C2×C4#651311yescharacteristic
342C2×C4#651311yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C8—42no—
348C8—561no—
349C8—561no—
350C7#975111yescharacteristic, complemented, Sylow
351C22—21no—
352C22—21no—
353C22—561no—
354C22—561no—
355C22—561no—
356C22#8971111yescharacteristic
357C22#8978811yescharacteristic
358C22#8980011yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—44no—
363C4—561no—
364C4—561no—
365C4—561no—
366C4#8947212yes—
367C4#8973811yescharacteristic
368C4#8977411yescharacteristic
369C4#8978811yescharacteristic
370C4#8980011yescharacteristic
371C2—21no—
372C2—21no—
373C2—1121no—
374C2#1172724211yescharacteristic
375C2#1172754911yescharacteristic
376C2#1172765111yescharacteristic
subgroupG/H
centerC2×C4#6493
commutatorC42×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×C8×C4⋊C4C2
socleC22×C7#390
prime radical#90168C22
cosocleC2×C42×C7C23
hypercenterC8×C4⋊C4D7
hypocenterC7#9751
LCSG ▷ C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C8×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C7×C8×C4⋊C4C2semidirect
3. #11728183C2semidirect
5. #11727483C2semidirect
6. #11727225C2semidirect
20. #89466C4semidirect
21. #89466C4semidirect
22. #89453C4semidirect
23. #89453C4semidirect
77. C8×C4⋊C4D7semidirect
350. C7#9751semidirect

Maximal subgroups

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

subgroupindex
#117359082
C7×C8×C4⋊C42
#117281832
#117281802
#117274832
#117272252
#117272232
#97517