Finite Group Databasebeta

← #13330010

Subgroups — #13330010

Order 1792.

886 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#557C211yesmaximal, characteristic
2#11740652C211yesmaximal, characteristic
3#11739893C211yesmaximal, characteristic
4#11739893C211yesmaximal, characteristic
5#11729692C214yesmaximal, complemented
6#11729691C214yesmaximal, complemented
7#11729530C211yesmaximal, characteristic
8#11729377C211yesmaximal, characteristic
9#11729377C211yesmaximal, characteristic
10C7×#557—22no—
11C7×#557—22no—
12C7×#557—22no—
13C7×#557C2214yes—
14C2×C7×C4⋊Q8—21no—
15C2×C7×C4⋊Q8C2211yescharacteristic
16C2×C7×#125—22no—
17C2×C7×#125—21no—
18C2×C4×C7×Q8—21no—
19C2×C4×C7×Q8—21no—
20C2×C4×C7×Q8C2211yescharacteristic
21C2×C4×C7×Q8C2211yescharacteristic
22#90161C2211yescharacteristic
23#90000—21no—
24#90000—21no—
25#89852—22no—
26#89851C2212yes—
27#89850C2212yes—
28#89803C2212yes—
29#89803C2212yes—
30#89802—22no—
31#89802—22no—
32#89792C2212yes—
33#89792C2212yes—
34#89743—21no—
35#89743—21no—
36#89736—22no—
37#89698C2211yescharacteristic
38#89698C2211yescharacteristic
39C4×#1136C2211yescharacteristic
40#89342C2214yes—
41Q8⋊(C7⋊C8)C2214yes—
42Q8⋊(C7⋊C8)C2214yes—
43#18541—71nomaximal, Sylow
44C22×C7×Q8—21no—
45C22×C7×Q8D411yescharacteristic
46C22×C7×Q8D411yescharacteristic
47C7×C4⋊Q8—24no—
48C7×C4⋊Q8—24no—
49C7×C4⋊Q8—21no—
50C7×C4⋊Q8—21no—
51C7×C4⋊Q8D412yes—
52C7×C4⋊Q8C2312yes—
53C7×#125—28no—
54C7×#125—24no—
55C7×#125—28no—
56C7×#125—24no—
57C4×C7×Q8—24no—
58C4×C7×Q8—24no—
59C4×C7×Q8—24no—
60C4×C7×Q8—24no—
61C4×C7×Q8—21no—
62C4×C7×Q8—21no—
63C4×C7×Q8—21no—
64C4×C7×Q8—21no—
65C4×C7×Q8D412yes—
66C4×C7×Q8D412yes—
67C4×C7×Q8C2312yes—
68C4×C7×Q8C2312yes—
69C2×C7×C4⋊C4—22no—
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4—21no—
73C2×C7×C4⋊C4—21no—
74C2×C7×C4⋊C4—21no—
75C2×C7×C4⋊C4D412yes—
76C2×C7×C4⋊C4D411yescharacteristic
77C2×C7×C4⋊C4D411yescharacteristic
78C2×C42×C7—22no—
79C2×C42×C7—21no—
80C2×C42×C7—21no—
81C2×C42×C7C2311yescharacteristic
82C2×#1144—22no—
83C2×#1144—22no—
84#6489—21no—
85#6487—21no—
86#6487—21no—
87C2×#1136—21no—
88#6433—21no—
89#6432C2311yescharacteristic
90#6432C2311yescharacteristic
91C4×Dic14—21no—
92C4×Dic14—21no—
93#6409—22no—
94#6409—22no—
95C22⋊(C7⋊C8)—21no—
96C22⋊(C7⋊C8)—21no—
97#6384—22no—
98#6384—22no—
99#6382—24no—
100#6382—22no—
101#6382—22no—
102#6381—24no—
103C4⋊(C7⋊C8)C2312yes—
104C4⋊(C7⋊C8)C2312yes—
105#6377—21no—
106#6377—21no—
107#6377—21no—
108C4×C7⋊C8C2312yes—
109C2×#557D711yescharacteristic
110#3165—71no—
111#3113—71no—
112#3113—71no—
113#1653—74no—
114#1648—74no—
115#1556—71no—
116#1491—71no—
117#1491—71no—
118C2×C7×Q8—24no—
119C2×C7×Q8—21no—
120C2×C7×Q8—21no—
121C2×C7×Q8—22no—
122C2×C7×Q8—22no—
123C2×C7×Q8—42no—
124C2×C7×Q8—44no—
125C2×C7×Q8C2×D412yes—
126C2×C7×Q8C2×D412yes—
127C22×C4×C7—21no—
128C22×C4×C7—21no—
129C22×C4×C7—21no—
130C22×C4×C7—21no—
131C22×C4×C7—22no—
132C22×C4×C7C2×D411yescharacteristic
133C22×C4×C7C2×D411yescharacteristic
134C22×C4×C7C2×D411yescharacteristic
135C2×Dic14—21no—
136C2×Dic14—21no—
137C7×C4⋊C4—28no—
138C7×C4⋊C4—28no—
139C7×C4⋊C4—28no—
140C7×C4⋊C4—22no—
141C7×C4⋊C4—22no—
142C7×C4⋊C4—22no—
143C7×C4⋊C4—21no—
144C7×C4⋊C4—21no—
145C7×C4⋊C4—22no—
146C7×C4⋊C4—22no—
147C7×C4⋊C4—22no—
148C7×C4⋊C4—22no—
149C7×C4⋊C4C2×D412yes—
150C7×C4⋊C4C2×D412yes—
151C7×C4⋊C4C2×D414yes—
152C42×C7—28no—
153C42×C7—22no—
154C42×C7—22no—
155C42×C7—22no—
156C42×C7—22no—
157C42×C7C2×D411yescharacteristic
158C42×C7C2×D411yescharacteristic
159C42×C7C2×D411yescharacteristic
160C42×C7C2411yescharacteristic
161C22⋊Dic7—41no—
162#1144—44no—
163#1144—44no—
164C4⋊Dic7—21no—
165C4⋊Dic7—21no—
166C4⋊Dic7—21no—
167C4⋊Dic7—21no—
168Dic7⋊C4—41no—
169Dic7⋊C4—41no—
170C4×Dic7—41no—
171#1136—24no—
172C2×C7⋊C8—22no—
173C2×C7⋊C8—22no—
174C2×C7⋊C8—22no—
175#557—22no—
176#557—22no—
177#557—22no—
178#557C2×D714yes—
179#533—71no—
180C2×C4⋊Q8—21no—
181C2×C4⋊Q8C2×D711yescharacteristic
182C2×#125—22no—
183C2×#125—21no—
184C2×C4×Q8—21no—
185C2×C4×Q8—21no—
186C2×C4×Q8C2×D711yescharacteristic
187C2×C4×Q8C2×D711yescharacteristic
188#501—142no—
189#500—72no—
190#498—72no—
191#483—141no—
192#483—141no—
193#475—72no—
194#475—72no—
195#462—72no—
196#462—72no—
197#451—141no—
198#451—141no—
199#441—142no—
200#441—142no—
201#432—71no—
202#432—71no—
203#428—142no—
204C4×M16—71no—
205#332—74no—
206Q8⋊C8—74no—
207Q8⋊C8—74no—
208C23×C7#12011yescharacteristic
209C7×Q8—24no—
210C7×Q8—22no—
211C7×Q8—22no—
212C7×Q8—22no—
213C7×Q8—42no—
214C7×Q8—44no—
215C7×Q8—44no—
216C7×Q8#13714yes—
217C2×C4×C7—24no—
218C2×C4×C7—22no—
219C2×C4×C7—22no—
220C2×C4×C7—22no—
221C2×C4×C7—22no—
222C2×C4×C7—22no—
223C2×C4×C7—22no—
224C2×C4×C7—22no—
225C2×C4×C7—24no—
226C2×C4×C7—42no—
227C2×C4×C7—44no—
228C2×C4×C7—42no—
229C2×C4×C7—42no—
230C2×C4×C7#12011yescharacteristic
231C2×C4×C7#12011yescharacteristic
232C2×C4×C7#12011yescharacteristic
233C2×C4×C7C22×D411yescharacteristic
234C2×C4×C7C22×D411yescharacteristic
235C2×C4×C7C22×D411yescharacteristic
236C2×Dic7—41no—
237C2×Dic7—41no—
238Dic14—42no—
239Dic14—42no—
240C7⋊C8—24no—
241C7⋊C8—42no—
242C7⋊C8—42no—
243C22×Q8—21no—
244C22×Q8C22⋊D711yescharacteristic
245C22×Q8C22⋊D711yescharacteristic
246C2×Q16—142no—
247C2×Q16—142no—
248C2×M16—141no—
249C4⋊Q8—24no—
250C4⋊Q8—24no—
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8—71no—
254C4⋊Q8—71no—
255C4⋊Q8C22⋊D712yes—
256C4⋊Q8C22×D712yes—
257#125—28no—
258#125—24no—
259#125—28no—
260#125—24no—
261#125—141no—
262C22⋊Q8—141no—
263C22⋊Q8—141no—
264C4×Q8—24no—
265C4×Q8—24no—
266C4×Q8—24no—
267C4×Q8—24no—
268C4×Q8—21no—
269C4×Q8—21no—
270C4×Q8—21no—
271C4×Q8—21no—
272C4×Q8—141no—
273C4×Q8—141no—
274C4×Q8C22⋊D712yes—
275C4×Q8C22⋊D712yes—
276C4×Q8C22×D712yes—
277C4×Q8C22×D712yes—
278#117—141no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4C22⋊D711yescharacteristic
286C2×C4⋊C4C22⋊D711yescharacteristic
287C2×C4⋊C4C22⋊D712yes—
288C2×C42—22no—
289C2×C42—21no—
290C2×C42—21no—
291C2×C42C22×D711yescharacteristic
292#107—144no—
293#106—144no—
294#106—142no—
295#106—142no—
296C4⋊C8—72no—
297C4⋊C8—72no—
298#103—142no—
299#103—142no—
300#103—142no—
301#103—142no—
302C22⋊C8—141no—
303C22⋊C8—141no—
304#97—141no—
305#97—141no—
306#97—141no—
307C4×C8—72no—
308C22×C7—21no—
309C22×C7—21no—
310C22×C7#45612yes—
311C22×C7C2×#12011yescharacteristic
312C4×C7—24no—
313C4×C7—21no—
314C4×C7—21no—
315C4×C7—21no—
316C4×C7—21no—
317C4×C7—42no—
318C4×C7—44no—
319C4×C7—42no—
320C4×C7—42no—
321C4×C7C2×#13712yes—
322C4×C7#57512yes—
323Dic7—81no—
324Dic7—81no—
325C2×Q8—24no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8—22no—
329C2×Q8—22no—
330C2×Q8—42no—
331C2×Q8—44no—
332C2×Q8—141no—
333C2×Q8—141no—
334C2×Q8C2×C22⋊D712yes—
335C2×Q8C2×C22⋊D712yes—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4C2×C22⋊D711yescharacteristic
342C22×C4C2×C22⋊D711yescharacteristic
343C22×C4C2×C22⋊D711yescharacteristic
344Q16—284no—
345Q16—284no—
346M16—144no—
347C2×C8—142no—
348C2×C8—142no—
349C2×C8—142no—
350C4⋊C4—28no—
351C4⋊C4—28no—
352C4⋊C4—28no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—141no—
363C4⋊C4—141no—
364C4⋊C4—141no—
365C4⋊C4—141no—
366C4⋊C4—281no—
367C4⋊C4—281no—
368C4⋊C4C2×C22⋊D712yes—
369C4⋊C4C2×C22⋊D712yes—
370C4⋊C4C2×C22⋊D714yes—
371C22⋊C4—281no—
372C42—28no—
373C42—22no—
374C42—22no—
375C42—22no—
376C42—22no—
377C42—281no—
378C42C2×C22⋊D711yescharacteristic
379C42C2×C22⋊D711yescharacteristic
380C42C2×C22⋊D711yescharacteristic
381C42C23×D711yescharacteristic
382C2×C7—22no—
383C2×C7#300411yescharacteristic
384C2×C7#300511yescharacteristic
385C2×C7C2×#45611yescharacteristic
386C23#651611yescharacteristic
387Q8—24no—
388Q8—22no—
389Q8—22no—
390Q8—22no—
391Q8—42no—
392Q8—44no—
393Q8—44no—
394Q8—282no—
395Q8—282no—
396Q8#650514yes—
397C2×C4—24no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—24no—
406C2×C4—42no—
407C2×C4—44no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—281no—
411C2×C4—281no—
412C2×C4#651611yescharacteristic
413C2×C4#651611yescharacteristic
414C2×C4#651611yescharacteristic
415C2×C4C22×C22⋊D711yescharacteristic
416C2×C4C22×C22⋊D711yescharacteristic
417C2×C4C22×C22⋊D711yescharacteristic
418C8—144no—
419C8—282no—
420C8—282no—
421C7#1854111yescharacteristic, complemented, Sylow
422C22—21no—
423C22—21no—
424C22#9001812yes—
425C22C2×#651611yescharacteristic
426C4—24no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—42no—
432C4—44no—
433C4—42no—
434C4—42no—
435C4—561no—
436C4—561no—
437C4C2×#650512yes—
438C4#9051312yes—
439C2—22no—
440C2#1174150411yescharacteristic
441C2#1174152611yescharacteristic
442C2C2×#9001811yescharacteristic
subgroupG/H
centerC22C2×#6516
commutator, cosocleC42×C7C24
FrattiniC42C23×D7
FittingC2×C7×#557C2
socleC22×C7C2×#120
prime radicalC23×C7#120
hypercenterC2×#557D7
hypocenterC7#18541
LCSG ▷ C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
5. #11729692C2semidirect
6. #11729691C2semidirect
421. C7#18541semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5572
#117406522
#117398932
#117296922
#117296912
#117295302
#117293772
#185417