Finite Group Databasebeta

← #13250096

Subgroups — #13250096

Order 1792.

512 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2295C211yesmaximal, 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×Q8C2211yescharacteristic
9#90168C2211yescharacteristic
10C7×#391—21no—
11C7×#389—21no—
12C7×#387—22no—
13C4×C7×C4⋊C4—21no—
14C4×C7×C4⋊C4C2211yescharacteristic
15C7×#376—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#9238—71nomaximal, Sylow
30C22×C7×Q8D411yescharacteristic
31C2×#1157—21no—
32C4×C7×Q8—21no—
33C4×C7×Q8—21no—
34C4×C7×Q8C2×C412yes—
35C4×C7×Q8D412yes—
36C2×C7×C4⋊C4—21no—
37C2×C7×C4⋊C4—22no—
38C2×C7×C4⋊C4—21no—
39C2×C7×C4⋊C4D411yescharacteristic
40C2×C42×C7—21no—
41C2×C42×C7—21no—
42C2×C42×C7—21no—
43C2×C42×C7—21no—
44C2×C42×C7D411yescharacteristic
45C2×C42×C7D411yescharacteristic
46C2×C42×C7C2311yescharacteristic
47C2×#1143—22no—
48#6493—21no—
49#6493—21no—
50C2×#1136—21no—
51#6438—21no—
52#6437C2×C411yescharacteristic
53C4×D28—21no—
54C4×D28—21no—
55#6432C2×C411yescharacteristic
56C7×#95—22no—
57C7×#95—22no—
58C7×#95—22no—
59C7×#95D412yes—
60#6409—22no—
61C22⋊(C7⋊C8)—21no—
62C22⋊(C7⋊C8)—21no—
63#6383—22no—
64#6382—22no—
65#6379—42no—
66#6379—42no—
67C4⋊(C7⋊C8)—21no—
68C4⋊(C7⋊C8)—21no—
69C4⋊(C7⋊C8)—21no—
70C4⋊(C7⋊C8)C2×C412yes—
71C4×C7⋊C8—21no—
72C4×C7⋊C8—21no—
73#3103—71no—
74#2295D711yescharacteristic, complemented
75#1962—71no—
76#1502—71no—
77#1487—71no—
78#1303—71no—
79#1276—71no—
80C2×C7×Q8—21no—
81C2×C7×Q8—42no—
82C2×C7×Q8C22⋊C412yes—
83C22×C4×C7—21no—
84C22×C4×C7—21no—
85C22×C4×C7—21no—
86C22×C4×C7—21no—
87C22×C4×C7—22no—
88C22×C4×C7C2×D411yescharacteristic
89C22×C4×C7C2×D411yescharacteristic
90C22×C4×C7C2×D411yescharacteristic
91C2×C22⋊D7—41no—
92#1157—41no—
93#1157—41no—
94#1157—41no—
95#1157—41no—
96C2×D28—21no—
97C2×D28—21no—
98C2×D28—21no—
99C2×C4×D7—41no—
100C2×Dic14—21no—
101C7×C4⋊C4—22no—
102C7×C4⋊C4—22no—
103C7×C4⋊C4—21no—
104C7×C4⋊C4—42no—
105C7×C4⋊C4—44no—
106C7×C4⋊C4C22⋊C412yes—
107C42×C7—22no—
108C42×C7—22no—
109C42×C7—21no—
110C42×C7—21no—
111C42×C7—21no—
112C42×C7—42no—
113C42×C7—42no—
114C42×C7—41no—
115C42×C7—41no—
116C42×C7SD1612yescomplemented
117C42×C7C22×C411yescharacteristic
118C42×C7C2×D411yescharacteristic
119C42×C7#4111yescharacteristic
120C42×C7#4111yescharacteristic
121#1143—44no—
122(C2×D7)⋊C4—41no—
123(C2×D7)⋊C4—41no—
124C4⋊Dic7—21no—
125C4⋊Dic7—21no—
126#1136—41no—
127#1136—41no—
128C2×C7⋊C8—22no—
129C2×C7⋊C8—41no—
130C2×C7⋊C8—41no—
131#532—71no—
132C2×C4×Q8C2×D711yescharacteristic
133#481—141no—
134#475—72no—
135#460—72no—
136#448—141no—
137C4×SD16—142no—
138#431—71no—
139#431—71no—
140#423—71no—
141C2×#104—141no—
142C2×#104—141no—
143#391—21no—
144#389—21no—
145#387—22no—
146C4×C4⋊C4—21no—
147C4×C4⋊C4C2×D711yescharacteristic
148#376—21no—
149C43C2×D711yescharacteristic
150#327—142no—
151Q8⋊C8—142no—
152C23×C7#12011yescharacteristic
153C22×D7—41no—
154C7×Q8—22no—
155C7×Q8—22no—
156C7×Q8—42no—
157C2×C4×C7—22no—
158C2×C4×C7—22no—
159C2×C4×C7—22no—
160C2×C4×C7—22no—
161C2×C4×C7—22no—
162C2×C4×C7—41no—
163C2×C4×C7—41no—
164C2×C4×C7—41no—
165C2×C4×C7—41no—
166C2×C4×C7—42no—
167C2×C4×C7—42no—
168C2×C4×C7—41no—
169C2×C4×C7—42no—
170C2×C4×C7—42no—
171C2×C4×C7—42no—
172C2×C4×C7C2×C22⋊C411yescharacteristic
173C2×C4×C7C4×D411yescharacteristic
174C2×C4×C7C4×D411yescharacteristic
175C2×C4×C7#12111yescharacteristic
176C2×C4×C7#12111yescharacteristic
177C2×C4×C7#12311yescharacteristic
178C2×C4×C7C2×SD1611yescharacteristic
179C2×C4×C7#13511yescharacteristic
180C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C7#13711yescharacteristic
182C22⋊D7—81no—
183C22⋊D7—81no—
184C2×Dic7—41no—
185D28—42no—
186D28—41no—
187D28—41no—
188D28—81no—
189C4×D7—81no—
190C4×D7—81no—
191Dic14—41no—
192Dic14—41no—
193C7⋊C8—42no—
194C7⋊C8—81no—
195C7⋊C8—81no—
196C2×#41—141no—
197C22×Q8C22⋊D711yescharacteristic
198C2×SD16—142no—
199C2×M16—141no—
200C4⋊Q8—71no—
201#127—71no—
202#124—141no—
203#121—141no—
204#121—141no—
205C4×Q8—21no—
206C4×Q8—21no—
207C4×Q8C4×D712yes—
208C4×Q8D2812yes—
209C4×D4—141no—
210C4×D4—141no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4C22⋊D711yescharacteristic
215C2×C42—21no—
216C2×C42—21no—
217C2×C42—21no—
218C2×C42—21no—
219C2×C42C22⋊D711yescharacteristic
220C2×C42C22⋊D711yescharacteristic
221C2×C42C22×D711yescharacteristic
222#106—142no—
223C4⋊C8—72no—
224C4⋊C8—141no—
225C4⋊C8—141no—
226C4⋊C8—141no—
227#104—282no—
228#104—282no—
229#103—142no—
230#102—142no—
231C22⋊C8—141no—
232C22⋊C8—141no—
233C4×C8—141no—
234C4×C8—141no—
235#95—22no—
236#95—22no—
237#95—22no—
238#95C22⋊D712yes—
239C22×C7—21no—
240C22×C7—21no—
241C22×C7#38611yescharacteristic
242C22×C7#44811yescharacteristic
243C22×C7#44911yescharacteristic
244C2×D7—81no—
245C2×D7—81no—
246C2×D7—81no—
247C4×C7—21no—
248C4×C7—21no—
249C4×C7—21no—
250C4×C7—42no—
251C4×C7—42no—
252C4×C7—42no—
253C4×C7—42no—
254C4×C7—82no—
255C4×C7#42112yes—
256C4×C7C4×SD1611yescharacteristic
257C4×C7#44011yescharacteristic
258C4×C7#46011yescharacteristic
259C4×C7#46411yescharacteristic
260Dic7—81no—
261#41—281no—
262#41—281no—
263#41—281no—
264#41—281no—
265C2×Q8—21no—
266C2×Q8—42no—
267C2×Q8—141no—
268C2×Q8(C2×D7)⋊C412yes—
269C2×D4—141no—
270C2×D4—141no—
271C2×D4—141no—
272C2×D4—281no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—281no—
279C22×C4C2×C22⋊D711yescharacteristic
280C22×C4C2×C22⋊D711yescharacteristic
281C22×C4C2×C22⋊D711yescharacteristic
282SD16—284no—
283M16—281no—
284M16—281no—
285C2×C8—142no—
286C2×C8—281no—
287C2×C8—281no—
288C4⋊C4—22no—
289C4⋊C4—21no—
290C4⋊C4—22no—
291C4⋊C4—42no—
292C4⋊C4—44no—
293C4⋊C4—141no—
294C4⋊C4—141no—
295C4⋊C4(C2×D7)⋊C412yes—
296C22⋊C4—281no—
297C22⋊C4—281no—
298C42—22no—
299C42—22no—
300C42—21no—
301C42—21no—
302C42—21no—
303C42—42no—
304C42—42no—
305C42—41no—
306C42—41no—
307C42#114312yescomplemented
308C42C2×C4×D711yescharacteristic
309C42C2×D2811yescharacteristic
310C42#115711yescharacteristic
311C42#115711yescharacteristic
312C2×C7—21no—
313C2×C7—21no—
314C2×C7#188011yescharacteristic
315C2×C7#189711yescharacteristic
316C2×C7#190611yescharacteristic
317D7—161no—
318C23—281no—
319C23#651611yescharacteristic
320Q8—22no—
321Q8—22no—
322Q8—42no—
323Q8—281no—
324Q8—281no—
325D4—282no—
326D4—281no—
327D4—281no—
328D4—561no—
329D4—561no—
330D4—561no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—281no—
347C2×C4—561no—
348C2×C4—561no—
349C2×C4C2×(C2×D7)⋊C411yescharacteristic
350C2×C4C4×C22⋊D711yescharacteristic
351C2×C4C4×C22⋊D711yescharacteristic
352C2×C4#649211yescharacteristic
353C2×C4#649311yescharacteristic
354C2×C4#649311yescharacteristic
355C2×C4C2×#114311yescharacteristic
356C2×C4#650511yescharacteristic
357C2×C4#651211yescharacteristic
358C2×C4#651311yescharacteristic
359C8—282no—
360C8—561no—
361C8—561no—
362C7#923811yescharacteristic, complemented, Sylow
363C22—21no—
364C22—21no—
365C22—561no—
366C22—561no—
367C22—561no—
368C22#8998511yescharacteristic
369C22#8999911yescharacteristic
370C22#9001011yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—42no—
375C4—42no—
376C4—42no—
377C4—42no—
378C4—82no—
379C4—561no—
380C4#8977712yes—
381C4C4×#114311yescharacteristic
382C4#8979811yescharacteristic
383C4#8979911yescharacteristic
384C4#8980011yescharacteristic
385C2—21no—
386C2—21no—
387C2—1121no—
388C2#1172934511yescharacteristic
389C2#1172938711yescharacteristic
390C2#1172939911yescharacteristic
subgroupG/H
centerC2×C4#6493
commutatorC42×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#2295C2
socleC22×C7#386
prime radical#90168C22
cosocleC2×C42×C7C23
hypercenter#2295D7
hypocenterC7#9238
LCSG ▷ C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2295

Complements

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

NH ≅ G/Ntype
1. C7×#2295C2semidirect
3. #11729376C2semidirect
6. #11725426C2semidirect
7. #11725417C2semidirect
18. #89799C4semidirect
20. #89792C4semidirect
74. #2295D7semidirect
116. C42×C7SD16semidirect
307. C42#1143semidirect
362. C7#9238semidirect

Maximal subgroups

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

subgroupindex
C7×#22952
#117398872
#117293762
#117272232
#117271492
#117254262
#117254172
#92387