Finite Group Databasebeta

← #13339145

Subgroups — #13339145

Order 1792.

676 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#462C211yesmaximal, characteristic, complemented
2#11740660C211yesmaximal, characteristic
3#11739886C211yesmaximal, characteristic
4#11739880C211yesmaximal, characteristic, complemented
5#11729527C211yesmaximal, characteristic, complemented
6#11728809C214yesmaximal, complemented
7#11728807C214yesmaximal, complemented
8#11728185C211yesmaximal, characteristic
9#11728176C211yesmaximal, characteristic, complemented
10C22×C7×Q16—21no—
11C2×C7×C4⋊Q8C2211yescharacteristic
12C2×C4×C7×Q8C2211yescharacteristic
13C2×#6505—21no—
14#90168C2211yescharacteristic
15C7×#462—22no—
16C7×#462C2214yes—
17C2×C7×C4⋊C8C2211yescharacteristic
18C2×C7×#103—21no—
19#89860C2212yes—
20#89859—22no—
21#89850C2212yes—
22#89803C2212yes—
23#89800—22no—
24#89799C2212yes—
25Q8×C7⋊C8—22no—
26Q8×C7⋊C8C2214yes—
27#89739—22no—
28#89738—21no—
29#89697—22no—
30#89697C2211yescharacteristic
31#89697C2211yescharacteristic
32#89696C2211yescharacteristic
33#89342C2214yes—
34#89280C2212yes—
35#89277C2212yes—
36#89274C2214yes—
37#19404—71nomaximal, Sylow
38C22×C7×Q8—21no—
39C22×C7×Q8D411yescharacteristic
40C2×#1157—21no—
41C2×C7×Q16—24no—
42C2×C7×Q16—44no—
43C22×C7×C8—21no—
44C7×C4⋊Q8—21no—
45C7×C4⋊Q8—21no—
46C7×C4⋊Q8—21no—
47C7×C4⋊Q8C2312yes—
48C4×C7×Q8—21no—
49C4×C7×Q8—21no—
50C4×C7×Q8D412yes—
51C4×C7×Q8C2312yes—
52C2×C7×C4⋊C4—21no—
53C2×C7×C4⋊C4—21no—
54C2×C7×C4⋊C4—21no—
55C2×C7×C4⋊C4D411yescharacteristic
56C2×C42×C7—21no—
57C2×C42×C7C2311yescharacteristic
58C2×#1144—22no—
59#6505—44no—
60C2×#1143—22no—
61#6493—21no—
62#6493—21no—
63C2×#1136—21no—
64#6438—21no—
65#6437C2311yescharacteristic
66C4×D28—21no—
67C4×D28—21no—
68#6432C2311yescharacteristic
69C7×C4⋊C8—21no—
70C7×C4⋊C8C2312yes—
71C7×#103—24no—
72C22⋊(C7⋊C8)—21no—
73C22⋊(C7⋊C8)D412yes—
74#6384—22no—
75#6383—22no—
76#6383—24no—
77#6381—24no—
78C4⋊(C7⋊C8)—21no—
79C4⋊(C7⋊C8)—24no—
80C4⋊(C7⋊C8)D412yes—
81C4⋊(C7⋊C8)C2312yes—
82C4⋊(C7⋊C8)C2312yes—
83C4×C7⋊C8—21no—
84C4×C7⋊C8—24no—
85C4×C7⋊C8C2312yes—
86#3226—71no—
87#3037—71no—
88C2×#462D711yescharacteristic, complemented
89#2982—71no—
90#1682—74no—
91#1674—74no—
92#1571—71no—
93#1546—71no—
94#1540—71no—
95C2×C7×Q8—21no—
96C2×C7×Q8—22no—
97C2×C7×Q8—22no—
98C2×C7×Q8—41no—
99C2×C7×Q8—42no—
100C2×C7×Q8—42no—
101C2×C7×Q8D814yes—
102C2×C7×Q8C2×D412yes—
103C22×C4×C7—21no—
104C22×C4×C7—21no—
105C22×C4×C7—41no—
106C22×C4×C7C2×D411yescharacteristic
107C22×C4×C7C2×D411yescharacteristic
108C22×C4×C7#4111yescharacteristic
109C2×C22⋊D7—41no—
110#1157—42no—
111#1157—42no—
112C2×D28—21no—
113C2×D28—21no—
114C2×D28—21no—
115C2×C4×D7—41no—
116C2×Dic14—21no—
117C7×Q16—48no—
118C2×C7×C8—22no—
119C2×C7×C8—42no—
120C7×C4⋊C4—22no—
121C7×C4⋊C4—21no—
122C7×C4⋊C4—22no—
123C7×C4⋊C4—22no—
124C7×C4⋊C4—22no—
125C7×C4⋊C4—41no—
126C7×C4⋊C4—41no—
127C7×C4⋊C4C2×D412yes—
128C42×C7—22no—
129C42×C7—22no—
130C42×C7C2×D411yescharacteristic
131C42×C7C2×D411yescharacteristic
132C42×C7#4111yescharacteristic
133C42×C7C2411yescharacteristic
134#1144—44no—
135#1143—44no—
136(C2×D7)⋊C4—41no—
137(C2×D7)⋊C4—41no—
138C4⋊Dic7—21no—
139C4⋊Dic7—21no—
140#1136—42no—
141C2×C7⋊C8—22no—
142C2×C7⋊C8—22no—
143C2×C7⋊C8C2×D414yes—
144C2×#137—141no—
145C22×Q16—21no—
146#532—71no—
147C2×C4⋊Q8C2×D711yescharacteristic
148C2×C4×Q8C2×D711yescharacteristic
149#500—72no—
150#486—72no—
151#480—142no—
152#474—142no—
153#464—142no—
154#462—22no—
155#462—72no—
156#462C2×D714yes—
157#460—72no—
158C8×Q8—74no—
159C8×Q8—142no—
160#431—71no—
161#431—71no—
162#431—142no—
163#423—71no—
164C2×C4⋊C8C2×D711yescharacteristic
165#417—141no—
166C2×#103—21no—
167#335—74no—
168#332—74no—
169#332—72no—
170#331—72no—
171C23×C7#12111yescharacteristic
172C22×D7—41no—
173C7×Q8—22no—
174C7×Q8—24no—
175C7×Q8—42no—
176C7×Q8—42no—
177C7×Q8—82no—
178C7×Q8C2×D814yes—
179C2×C4×C7—22no—
180C2×C4×C7—24no—
181C2×C4×C7—22no—
182C2×C4×C7—22no—
183C2×C4×C7—41no—
184C2×C4×C7—42no—
185C2×C4×C7—81no—
186C2×C4×C7—82no—
187C2×C4×C7#12111yescharacteristic
188C2×C4×C7#12111yescharacteristic
189C2×C4×C7#12111yescharacteristic
190C2×C4×C7C2×D812yes—
191C2×C4×C7#13512yes—
192C2×C4×C7C22×D411yescharacteristic
193C2×C4×C7C22×D411yescharacteristic
194C2×C4×C7C2×#4111yescharacteristic
195C22⋊D7—82no—
196C2×Dic7—41no—
197D28—41no—
198D28—41no—
199D28—42no—
200D28—81no—
201C4×D7—82no—
202Dic14—41no—
203Dic14—41no—
204C7×C8—42no—
205C7⋊C8—24no—
206C7⋊C8—42no—
207C7⋊C8—42no—
208C2×#41—141no—
209C22×Q8—21no—
210C22×Q8C22⋊D711yescharacteristic
211#137—284no—
212C2×Q16—24no—
213C2×Q16—44no—
214C2×Q16—142no—
215C2×SD16—142no—
216C2×M16—141no—
217C22×C8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—71no—
222C4⋊Q8C22×D712yes—
223#127—71no—
224#124—141no—
225#121—141no—
226#121—141no—
227C4×Q8—21no—
228C4×Q8—21no—
229C4×Q8C22⋊D712yes—
230C4×Q8C22×D712yes—
231C4×D4—141no—
232C4×D4—141no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4C22⋊D711yescharacteristic
237C2×C42—21no—
238C2×C42C22×D711yescharacteristic
239#107—144no—
240C4⋊C8—21no—
241C4⋊C8—72no—
242C4⋊C8—72no—
243C4⋊C8—72no—
244C4⋊C8—144no—
245C4⋊C8—141no—
246C4⋊C8C22×D712yes—
247#103—24no—
248#103—142no—
249#102—144no—
250#102—142no—
251C22⋊C8—72no—
252C22⋊C8—141no—
253C4×C8—72no—
254C4×C8—144no—
255C4×C8—141no—
256C22×C7—21no—
257C22×C7—21no—
258C22×C7#46612yes—
259C22×C7C2×#12111yescharacteristic
260C2×D7—81no—
261C2×D7—81no—
262C2×D7—81no—
263C4×C7—21no—
264C4×C7—24no—
265C4×C7—21no—
266C4×C7—21no—
267C4×C7—42no—
268C4×C7—82no—
269C4×C7#46612yes—
270C4×C7C22×D811yescharacteristic
271C4×C7C2×#13511yescharacteristic
272C4×C7#57812yes—
273Dic7—81no—
274#41—282no—
275#41—282no—
276C2×Q8—21no—
277C2×Q8—22no—
278C2×Q8—22no—
279C2×Q8—41no—
280C2×Q8—42no—
281C2×Q8—42no—
282C2×Q8—141no—
283C2×Q8#114114yes—
284C2×Q8C2×C22⋊D712yes—
285C2×D4—141no—
286C2×D4—141no—
287C2×D4—141no—
288C2×D4—281no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—41no—
292C22×C4—281no—
293C22×C4D4×D711yescharacteristic
294C22×C4#115911yescharacteristic
295C22×C4C2×C22⋊D711yescharacteristic
296Q16—48no—
297Q16—284no—
298SD16—284no—
299M16—282no—
300C2×C8—22no—
301C2×C8—42no—
302C2×C8—74no—
303C2×C8—142no—
304C2×C8—142no—
305C4⋊C4—22no—
306C4⋊C4—21no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—141no—
313C4⋊C4—141no—
314C4⋊C4C2×C22⋊D712yes—
315C22⋊C4—281no—
316C22⋊C4—281no—
317C42—22no—
318C42—22no—
319C42D4×D711yescharacteristic
320C42#115911yescharacteristic
321C42C2×C22⋊D711yescharacteristic
322C42C23×D711yescharacteristic
323C2×C7—22no—
324C2×C7#304411yescharacteristic
325C2×C7C2×#46611yescharacteristic
326C2×C7#306911yescharacteristic
327D7—161no—
328C23—281no—
329C23#650211yescharacteristic
330Q8—22no—
331Q8—24no—
332Q8—42no—
333Q8—42no—
334Q8—82no—
335Q8—281no—
336Q8—281no—
337Q8C2×#114114yes—
338D4—282no—
339D4—281no—
340D4—281no—
341D4—561no—
342D4—562no—
343C2×C4—22no—
344C2×C4—24no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—81no—
350C2×C4—82no—
351C2×C4—281no—
352C2×C4—562no—
353C2×C4C2×#114112yes—
354C2×C4#650211yescharacteristic
355C2×C4#650211yescharacteristic
356C2×C4#650211yescharacteristic
357C2×C4#651312yes—
358C2×C4C2×D4×D711yescharacteristic
359C2×C4C2×#115911yescharacteristic
360C2×C4C22×C22⋊D711yescharacteristic
361C8—42no—
362C8—144no—
363C8—282no—
364C8—282no—
365C7#1940411yescharacteristic, complemented, Sylow
366C22—21no—
367C22—21no—
368C22—561no—
369C22—561no—
370C22—561no—
371C22#8981012yes—
372C22C2×#650211yescharacteristic
373C4—21no—
374C4—24no—
375C4—21no—
376C4—21no—
377C4—42no—
378C4—82no—
379C4—561no—
380C4#8981012yes—
381C4#9045712yes—
382C4C22×#114111yescharacteristic
383C4C2×#651311yescharacteristic
384C2—22no—
385C2—1121no—
386C2C2×#8981011yescharacteristic
387C2#1174132211yescharacteristic
388C2#1174142311yescharacteristic
subgroupG/H
centerC22C2×#6502
commutator, cosocleC42×C7C24
FrattiniC42C23×D7
FittingC2×C7×#462C2
socleC22×C7C2×#121
prime radical#90168C22
hypercenterC2×#462D7
hypocenterC7#19404
LCSG ▷ C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
1. C2×C7×#462C2semidirect
4. #11739880C2semidirect
5. #11729527C2semidirect
6. #11728809C2semidirect
7. #11728807C2semidirect
9. #11728176C2semidirect
88. C2×#462D7semidirect
365. C7#19404semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4622
#117406602
#117398862
#117398802
#117295272
#117288092
#117288072
#117281852
#117281762
#194047