Finite Group Databasebeta

← #13250068

Subgroups — #13250068

Order 1792.

604 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C42×C7×Q8C211yesmaximal, characteristic, complemented
2#11739887C211yesmaximal, characteristic
3#11729376C211yesmaximal, characteristic, complemented
4#11727223C211yesmaximal, characteristic
5#11727149C211yesmaximal, characteristic
6#11725426C211yesmaximal, characteristic, complemented
7#11725417C211yesmaximal, characteristic, complemented
8C2×C4×C7×Q8—21no—
9C2×C4×C7×Q8C2211yescharacteristic
10#90168C2211yescharacteristic
11C4×C7×C4⋊C4—21no—
12C4×C7×C4⋊C4—21no—
13C4×C7×C4⋊C4—22no—
14C4×C7×C4⋊C4C2211yescharacteristic
15C43×C7—21no—
16C43×C7C2211yescharacteristic
17#89999—21no—
18#89799C412yescomplemented
19C4×#1143—22no—
20#89792C412yescomplemented
21#89740—21no—
22C2×#6379—21no—
23C2×#6379—21no—
24#89697C2211yescharacteristic
25#89697C2211yescharacteristic
26#89696C2211yescharacteristic
27Q8⋊(C7⋊C8)—22no—
28#89246—22no—
29#9234—71nomaximal, Sylow
30C22×C7×Q8D411yescharacteristic
31C2×#1157—21no—
32C4×C7×Q8—28no—
33C4×C7×Q8—21no—
34C4×C7×Q8—21no—
35C4×C7×Q8C2×C412yes—
36C4×C7×Q8D412yes—
37C2×C7×C4⋊C4—22no—
38C2×C7×C4⋊C4—21no—
39C2×C7×C4⋊C4—21no—
40C2×C7×C4⋊C4D411yescharacteristic
41C2×C42×C7—22no—
42C2×C42×C7—21no—
43C2×C42×C7—21no—
44C2×C42×C7—22no—
45C2×C42×C7—21no—
46C2×C42×C7—21no—
47C2×C42×C7D411yescharacteristic
48C2×C42×C7D411yescharacteristic
49C2×C42×C7C2311yescharacteristic
50C2×#1143—22no—
51#6493—21no—
52#6493—21no—
53C2×#1136—21no—
54#6438—21no—
55#6437C2×C411yescharacteristic
56C4×D28—21no—
57C4×D28—21no—
58#6432C2×C411yescharacteristic
59C7×#95—22no—
60C7×#95D412yes—
61#6409—22no—
62C22⋊(C7⋊C8)—21no—
63C22⋊(C7⋊C8)—21no—
64#6383—22no—
65#6382—22no—
66#6379—42no—
67#6379—42no—
68C4⋊(C7⋊C8)—21no—
69C4⋊(C7⋊C8)—21no—
70C4⋊(C7⋊C8)—21no—
71C4⋊(C7⋊C8)C2×C412yes—
72C4×C7⋊C8—21no—
73C4×C7⋊C8—21no—
74#3103—71no—
75C42×Q8D711yescharacteristic, complemented
76#1962—71no—
77#1502—71no—
78#1487—71no—
79#1303—71no—
80#1276—71no—
81C2×C7×Q8—24no—
82C2×C7×Q8—21no—
83C2×C7×Q8C22⋊C412yes—
84C22×C4×C7—21no—
85C22×C4×C7—21no—
86C22×C4×C7—21no—
87C22×C4×C7—21no—
88C22×C4×C7—22no—
89C22×C4×C7C2×D411yescharacteristic
90C22×C4×C7C2×D411yescharacteristic
91C22×C4×C7C2×D411yescharacteristic
92C2×C22⋊D7—41no—
93#1157—41no—
94#1157—41no—
95#1157—41no—
96#1157—41no—
97C2×D28—21no—
98C2×D28—21no—
99C2×D28—21no—
100C2×C4×D7—41no—
101C2×Dic14—21no—
102C7×C4⋊C4—28no—
103C7×C4⋊C4—24no—
104C7×C4⋊C4—22no—
105C7×C4⋊C4—22no—
106C7×C4⋊C4—21no—
107C7×C4⋊C4C22⋊C412yes—
108C42×C7—28no—
109C42×C7—24no—
110C42×C7—22no—
111C42×C7—22no—
112C42×C7—21no—
113C42×C7—21no—
114C42×C7—21no—
115C42×C7—42no—
116C42×C7—44no—
117C42×C7—41no—
118C42×C7—41no—
119C42×C7SD1612yescomplemented
120C42×C7C22×C411yescharacteristic
121C42×C7C2×D411yescharacteristic
122C42×C7#4111yescharacteristic
123C42×C7#4111yescharacteristic
124#1143—44no—
125(C2×D7)⋊C4—41no—
126(C2×D7)⋊C4—41no—
127C4⋊Dic7—21no—
128C4⋊Dic7—21no—
129#1136—41no—
130#1136—41no—
131C2×C7⋊C8—22no—
132C2×C7⋊C8—41no—
133C2×C7⋊C8—41no—
134#532—71no—
135C2×C4×Q8—21no—
136C2×C4×Q8C2×D711yescharacteristic
137#481—141no—
138#475—72no—
139#460—72no—
140#448—141no—
141C4×SD16—142no—
142#431—71no—
143#431—71no—
144#423—71no—
145C2×#104—141no—
146C2×#104—141no—
147C4×C4⋊C4—21no—
148C4×C4⋊C4—21no—
149C4×C4⋊C4—22no—
150C4×C4⋊C4C2×D711yescharacteristic
151C43—21no—
152C43C2×D711yescharacteristic
153#327—142no—
154Q8⋊C8—142no—
155C23×C7#12011yescharacteristic
156C22×D7—41no—
157C7×Q8—24no—
158C7×Q8—22no—
159C7×Q8#10414yescomplemented
160C2×C4×C7—22no—
161C2×C4×C7—24no—
162C2×C4×C7—22no—
163C2×C4×C7—22no—
164C2×C4×C7—22no—
165C2×C4×C7—22no—
166C2×C4×C7—22no—
167C2×C4×C7—24no—
168C2×C4×C7—22no—
169C2×C4×C7—41no—
170C2×C4×C7—41no—
171C2×C4×C7—42no—
172C2×C4×C7—42no—
173C2×C4×C7—41no—
174C2×C4×C7—42no—
175C2×C4×C7C2×C22⋊C411yescharacteristic
176C2×C4×C7C4×D411yescharacteristic
177C2×C4×C7C4×D411yescharacteristic
178C2×C4×C7#12111yescharacteristic
179C2×C4×C7#12111yescharacteristic
180C2×C4×C7#12311yescharacteristic
181C2×C4×C7C2×SD1611yescharacteristic
182C2×C4×C7#13511yescharacteristic
183C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C7#13711yescharacteristic
185C22⋊D7—81no—
186C22⋊D7—81no—
187C2×Dic7—41no—
188D28—42no—
189D28—41no—
190D28—41no—
191D28—81no—
192C4×D7—81no—
193C4×D7—81no—
194Dic14—41no—
195Dic14—41no—
196C7⋊C8—42no—
197C7⋊C8—81no—
198C7⋊C8—81no—
199C2×#41—141no—
200C22×Q8C22⋊D711yescharacteristic
201C2×SD16—142no—
202C2×M16—141no—
203C4⋊Q8—71no—
204#127—71no—
205#124—141no—
206#121—141no—
207#121—141no—
208C4×Q8—28no—
209C4×Q8—21no—
210C4×Q8—21no—
211C4×Q8C4×D712yes—
212C4×Q8D2812yes—
213C4×D4—141no—
214C4×D4—141no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4C22⋊D711yescharacteristic
219C2×C42—22no—
220C2×C42—21no—
221C2×C42—21no—
222C2×C42—22no—
223C2×C42—21no—
224C2×C42—21no—
225C2×C42C22⋊D711yescharacteristic
226C2×C42C22⋊D711yescharacteristic
227C2×C42C22×D711yescharacteristic
228#106—142no—
229C4⋊C8—72no—
230C4⋊C8—141no—
231C4⋊C8—141no—
232C4⋊C8—141no—
233#104—282no—
234#104—282no—
235#103—142no—
236#102—142no—
237C22⋊C8—141no—
238C22⋊C8—141no—
239C4×C8—141no—
240C4×C8—141no—
241#95—22no—
242#95C22⋊D712yes—
243C22×C7—21no—
244C22×C7—21no—
245C22×C7#38611yescharacteristic
246C22×C7#44811yescharacteristic
247C22×C7#44911yescharacteristic
248C2×D7—81no—
249C2×D7—81no—
250C2×D7—81no—
251C4×C7—24no—
252C4×C7—24no—
253C4×C7—21no—
254C4×C7—21no—
255C4×C7—21no—
256C4×C7—42no—
257C4×C7—44no—
258C4×C7—42no—
259C4×C7C2×#10412yes—
260C4×C7C4×SD1611yescharacteristic
261C4×C7#44011yescharacteristic
262C4×C7#46011yescharacteristic
263C4×C7#46411yescharacteristic
264Dic7—81no—
265#41—281no—
266#41—281no—
267#41—281no—
268#41—281no—
269C2×Q8—24no—
270C2×Q8—21no—
271C2×Q8—141no—
272C2×Q8(C2×D7)⋊C412yes—
273C2×D4—141no—
274C2×D4—141no—
275C2×D4—141no—
276C2×D4—281no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—22no—
282C22×C4—281no—
283C22×C4C2×C22⋊D711yescharacteristic
284C22×C4C2×C22⋊D711yescharacteristic
285C22×C4C2×C22⋊D711yescharacteristic
286SD16—284no—
287M16—281no—
288M16—281no—
289C2×C8—142no—
290C2×C8—281no—
291C2×C8—281no—
292C4⋊C4—28no—
293C4⋊C4—24no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—22no—
297C4⋊C4—141no—
298C4⋊C4—141no—
299C4⋊C4(C2×D7)⋊C412yes—
300C22⋊C4—281no—
301C22⋊C4—281no—
302C42—28no—
303C42—24no—
304C42—22no—
305C42—22no—
306C42—21no—
307C42—21no—
308C42—21no—
309C42—42no—
310C42—44no—
311C42—41no—
312C42—41no—
313C42#114312yescomplemented
314C42C2×C4×D711yescharacteristic
315C42C2×D2811yescharacteristic
316C42#115711yescharacteristic
317C42#115711yescharacteristic
318C2×C7—21no—
319C2×C7—21no—
320C2×C7#188011yescharacteristic
321C2×C7#189611yescharacteristic
322C2×C7#190611yescharacteristic
323D7—161no—
324C23—281no—
325C23#651611yescharacteristic
326Q8—24no—
327Q8—22no—
328Q8—281no—
329Q8—281no—
330Q8#637914yescomplemented
331D4—282no—
332D4—281no—
333D4—281no—
334D4—561no—
335D4—561no—
336D4—561no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—24no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—281no—
353C2×C4—561no—
354C2×C4—561no—
355C2×C4C2×(C2×D7)⋊C411yescharacteristic
356C2×C4C4×C22⋊D711yescharacteristic
357C2×C4C4×C22⋊D711yescharacteristic
358C2×C4#649211yescharacteristic
359C2×C4#649311yescharacteristic
360C2×C4#649311yescharacteristic
361C2×C4C2×#114311yescharacteristic
362C2×C4#650511yescharacteristic
363C2×C4#651211yescharacteristic
364C2×C4#651311yescharacteristic
365C8—282no—
366C8—561no—
367C8—561no—
368C7#923411yescharacteristic, complemented, Sylow
369C22—21no—
370C22—21no—
371C22—561no—
372C22—561no—
373C22—561no—
374C22#8998511yescharacteristic
375C22#8999911yescharacteristic
376C22#9001011yescharacteristic
377C4—24no—
378C4—24no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—42no—
383C4—44no—
384C4—42no—
385C4—561no—
386C4C2×#637912yes—
387C4C4×#114311yescharacteristic
388C4#8979811yescharacteristic
389C4#8979911yescharacteristic
390C4#8980011yescharacteristic
391C2—21no—
392C2—21no—
393C2—1121no—
394C2#1172928611yescharacteristic
395C2#1172938711yescharacteristic
396C2#1172939911yescharacteristic
subgroupG/H
centerC2×C4#6493
commutatorC42×C7C22×C4
FrattiniC2×C42C22×D7
FittingC42×C7×Q8C2
socleC22×C7#386
prime radical#90168C22
cosocleC2×C42×C7C23
hypercenterC42×Q8D7
hypocenterC7#9234
LCSG ▷ C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C42×Q8

Complements

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

NH ≅ G/Ntype
1. C42×C7×Q8C2semidirect
3. #11729376C2semidirect
6. #11725426C2semidirect
7. #11725417C2semidirect
18. #89799C4semidirect
20. #89792C4semidirect
75. C42×Q8D7semidirect
119. C42×C7SD16semidirect
159. C7×Q8#104semidirect
313. C42#1143semidirect
330. Q8#6379semidirect
368. C7#9234semidirect

Maximal subgroups

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

subgroupindex
C42×C7×Q82
#117398872
#117293762
#117272232
#117271492
#117254262
#117254172
#92347