Finite Group Databasebeta

← #13329952

Subgroups — #13329952

Order 1792.

908 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#557C211yesmaximal, characteristic, complemented
2#11740644C211yesmaximal, characteristic
3#11739889C211yesmaximal, characteristic
4#11739889C211yesmaximal, characteristic
5#11729690C214yesmaximal, complemented
6#11729689C214yesmaximal, complemented
7#11729530C211yesmaximal, characteristic, complemented
8#11729377C211yesmaximal, characteristic, complemented
9#11729377C211yesmaximal, characteristic, complemented
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#90168C2211yescharacteristic
23#89999—21no—
24#89999—21no—
25#89865C2212yes—
26#89861—22no—
27#89860C2212yes—
28#89799C2212yes—
29#89799C2212yes—
30#89798—22no—
31#89798—22no—
32#89793C2212yes—
33#89793C2212yes—
34#89739—21no—
35#89739—21no—
36#89738—22no—
37#89698C2211yescharacteristic
38#89698C2211yescharacteristic
39C4×#1136C2211yescharacteristic
40#89342C2214yes—
41Q8⋊(C7⋊C8)C2214yes—
42Q8⋊(C7⋊C8)C2214yes—
43#18535—71nomaximal, Sylow
44C22×C7×Q8—21no—
45C22×C7×Q8D411yescharacteristic
46C22×C7×Q8D411yescharacteristic
47C2×#1157—21no—
48C7×C4⋊Q8—24no—
49C7×C4⋊Q8—24no—
50C7×C4⋊Q8—21no—
51C7×C4⋊Q8—21no—
52C7×C4⋊Q8D412yes—
53C7×C4⋊Q8C2312yes—
54C7×#125—28no—
55C7×#125—24no—
56C7×#125—28no—
57C7×#125—24no—
58C4×C7×Q8—24no—
59C4×C7×Q8—24no—
60C4×C7×Q8—24no—
61C4×C7×Q8—24no—
62C4×C7×Q8—21no—
63C4×C7×Q8—21no—
64C4×C7×Q8—21no—
65C4×C7×Q8—21no—
66C4×C7×Q8D412yes—
67C4×C7×Q8D412yes—
68C4×C7×Q8C2312yes—
69C4×C7×Q8C2312yes—
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—21no—
74C2×C7×C4⋊C4—21no—
75C2×C7×C4⋊C4—21no—
76C2×C7×C4⋊C4D412yes—
77C2×C7×C4⋊C4D411yescharacteristic
78C2×C7×C4⋊C4D411yescharacteristic
79C2×C42×C7—22no—
80C2×C42×C7—21no—
81C2×C42×C7—21no—
82C2×C42×C7C2311yescharacteristic
83C2×#1143—22no—
84C2×#1143—22no—
85#6493—21no—
86#6493—21no—
87C2×#1136—21no—
88#6438—21no—
89#6437C2311yescharacteristic
90C4×D28—21no—
91C4×D28—21no—
92#6432C2311yescharacteristic
93#6409—22no—
94#6409—22no—
95C22⋊(C7⋊C8)—21no—
96C22⋊(C7⋊C8)—21no—
97#6384—24no—
98#6383—24no—
99#6383—22no—
100#6383—22no—
101#6381—22no—
102#6381—22no—
103C4⋊(C7⋊C8)C2312yes—
104C4⋊(C7⋊C8)C2312yes—
105#6377—21no—
106#6377—21no—
107#6377—21no—
108C4×C7⋊C8C2312yes—
109C2×#557D711yescharacteristic, complemented
110#3141—71no—
111#3112—71no—
112#3112—71no—
113#1636—74no—
114#1626—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×C22⋊D7—41no—
136#1157—44no—
137C2×D28—21no—
138C2×D28—21no—
139C2×D28—21no—
140C2×C4×D7—41no—
141C2×Dic14—21no—
142C7×C4⋊C4—28no—
143C7×C4⋊C4—28no—
144C7×C4⋊C4—28no—
145C7×C4⋊C4—22no—
146C7×C4⋊C4—22no—
147C7×C4⋊C4—22no—
148C7×C4⋊C4—21no—
149C7×C4⋊C4—21no—
150C7×C4⋊C4—22no—
151C7×C4⋊C4—22no—
152C7×C4⋊C4—22no—
153C7×C4⋊C4—22no—
154C7×C4⋊C4C2×D412yes—
155C7×C4⋊C4C2×D412yes—
156C7×C4⋊C4C2×D414yes—
157C42×C7—28no—
158C42×C7—22no—
159C42×C7—22no—
160C42×C7—22no—
161C42×C7—22no—
162C42×C7C2×D411yescharacteristic
163C42×C7C2×D411yescharacteristic
164C42×C7C2×D411yescharacteristic
165C42×C7C2411yescharacteristic
166#1143—44no—
167#1143—44no—
168(C2×D7)⋊C4—41no—
169(C2×D7)⋊C4—41no—
170C4⋊Dic7—21no—
171C4⋊Dic7—21no—
172#1136—42no—
173C2×C7⋊C8—22no—
174C2×C7⋊C8—22no—
175C2×C7⋊C8—22no—
176#557—22no—
177#557—22no—
178#557—22no—
179#557C2×D714yes—
180#532—71no—
181C2×C4⋊Q8—21no—
182C2×C4⋊Q8C2×D711yescharacteristic
183C2×#125—22no—
184C2×#125—21no—
185C2×C4×Q8—21no—
186C2×C4×Q8—21no—
187C2×C4×Q8C2×D711yescharacteristic
188C2×C4×Q8C2×D711yescharacteristic
189#489—142no—
190#487—72no—
191#486—72no—
192#480—141no—
193#480—141no—
194#477—72no—
195#477—72no—
196#460—72no—
197#460—72no—
198#448—141no—
199#448—141no—
200#440—142no—
201#440—142no—
202#432—71no—
203#432—71no—
204#417—142no—
205C4×M16—71no—
206#332—74no—
207Q8⋊C8—74no—
208Q8⋊C8—74no—
209C23×C7#12011yescharacteristic
210C22×D7—41no—
211C7×Q8—24no—
212C7×Q8—22no—
213C7×Q8—22no—
214C7×Q8—22no—
215C7×Q8—42no—
216C7×Q8—44no—
217C7×Q8—44no—
218C7×Q8#13714yes—
219C2×C4×C7—24no—
220C2×C4×C7—22no—
221C2×C4×C7—22no—
222C2×C4×C7—22no—
223C2×C4×C7—22no—
224C2×C4×C7—22no—
225C2×C4×C7—22no—
226C2×C4×C7—22no—
227C2×C4×C7—24no—
228C2×C4×C7—42no—
229C2×C4×C7—44no—
230C2×C4×C7—42no—
231C2×C4×C7—42no—
232C2×C4×C7#12011yescharacteristic
233C2×C4×C7#12011yescharacteristic
234C2×C4×C7#12011yescharacteristic
235C2×C4×C7C22×D411yescharacteristic
236C2×C4×C7C22×D411yescharacteristic
237C2×C4×C7C22×D411yescharacteristic
238C22⋊D7—82no—
239C2×Dic7—41no—
240D28—42no—
241D28—42no—
242D28—42no—
243C4×D7—82no—
244Dic14—42no—
245C7⋊C8—42no—
246C7⋊C8—42no—
247C7⋊C8—42no—
248C2×#41—141no—
249C22×Q8—21no—
250C22×Q8C22⋊D711yescharacteristic
251C22×Q8C22⋊D711yescharacteristic
252C2×SD16—142no—
253C2×SD16—142no—
254C2×M16—141no—
255C4⋊Q8—24no—
256C4⋊Q8—24no—
257C4⋊Q8—21no—
258C4⋊Q8—21no—
259C4⋊Q8—71no—
260C4⋊Q8C22⋊D712yes—
261C4⋊Q8C22×D712yes—
262#127—71no—
263#125—28no—
264#125—24no—
265#125—28no—
266#125—24no—
267#124—141no—
268#121—141no—
269#121—141no—
270C4×Q8—24no—
271C4×Q8—24no—
272C4×Q8—24no—
273C4×Q8—24no—
274C4×Q8—21no—
275C4×Q8—21no—
276C4×Q8—21no—
277C4×Q8—21no—
278C4×Q8C22⋊D712yes—
279C4×Q8C22⋊D712yes—
280C4×Q8C22×D712yes—
281C4×Q8C22×D712yes—
282C4×D4—141no—
283C4×D4—141no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4C22⋊D711yescharacteristic
291C2×C4⋊C4C22⋊D711yescharacteristic
292C2×C4⋊C4C22⋊D712yes—
293C2×C42—22no—
294C2×C42—21no—
295C2×C42—21no—
296C2×C42C22×D711yescharacteristic
297#107—142no—
298#107—142no—
299C4⋊C8—72no—
300C4⋊C8—72no—
301#103—142no—
302#103—142no—
303#103—144no—
304#102—144no—
305#102—142no—
306#102—142no—
307C22⋊C8—141no—
308C22⋊C8—141no—
309#97—141no—
310#97—141no—
311#97—141no—
312C4×C8—72no—
313C22×C7—21no—
314C22×C7—21no—
315C22×C7#45412yes—
316C22×C7C2×#12011yescharacteristic
317C2×D7—81no—
318C2×D7—81no—
319C2×D7—81no—
320C4×C7—24no—
321C4×C7—21no—
322C4×C7—21no—
323C4×C7—21no—
324C4×C7—21no—
325C4×C7—42no—
326C4×C7—44no—
327C4×C7—42no—
328C4×C7—42no—
329C4×C7C2×#13712yes—
330C4×C7#57512yes—
331Dic7—81no—
332#41—284no—
333C2×Q8—24no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8—22no—
337C2×Q8—22no—
338C2×Q8—42no—
339C2×Q8—44no—
340C2×Q8—141no—
341C2×Q8C2×C22⋊D712yes—
342C2×Q8C2×C22⋊D712yes—
343C2×D4—141no—
344C2×D4—141no—
345C2×D4—141no—
346C2×D4—281no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—281no—
353C22×C4C2×C22⋊D711yescharacteristic
354C22×C4C2×C22⋊D711yescharacteristic
355C22×C4C2×C22⋊D711yescharacteristic
356SD16—284no—
357SD16—284no—
358M16—282no—
359C2×C8—142no—
360C2×C8—142no—
361C2×C8—142no—
362C4⋊C4—28no—
363C4⋊C4—28no—
364C4⋊C4—28no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—141no—
375C4⋊C4—141no—
376C4⋊C4C2×C22⋊D714yes—
377C4⋊C4C2×C22⋊D712yes—
378C4⋊C4C2×C22⋊D712yes—
379C22⋊C4—281no—
380C22⋊C4—281no—
381C42—28no—
382C42—22no—
383C42—22no—
384C42—22no—
385C42—22no—
386C42C2×C22⋊D711yescharacteristic
387C42C2×C22⋊D711yescharacteristic
388C42C2×C22⋊D711yescharacteristic
389C42C23×D711yescharacteristic
390C2×C7—22no—
391C2×C7#300411yescharacteristic
392C2×C7#300511yescharacteristic
393C2×C7C2×#45411yescharacteristic
394D7—161no—
395C23—281no—
396C23#651611yescharacteristic
397Q8—24no—
398Q8—22no—
399Q8—22no—
400Q8—22no—
401Q8—42no—
402Q8—44no—
403Q8—44no—
404Q8—282no—
405Q8#650514yes—
406D4—282no—
407D4—282no—
408D4—282no—
409D4—562no—
410C2×C4—24no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—24no—
419C2×C4—42no—
420C2×C4—44no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—281no—
424C2×C4—562no—
425C2×C4#651611yescharacteristic
426C2×C4#651611yescharacteristic
427C2×C4#651611yescharacteristic
428C2×C4C22×C22⋊D711yescharacteristic
429C2×C4C22×C22⋊D711yescharacteristic
430C2×C4C22×C22⋊D711yescharacteristic
431C8—282no—
432C8—282no—
433C8—282no—
434C7#1853511yescharacteristic, complemented, Sylow
435C22—21no—
436C22—21no—
437C22—561no—
438C22—561no—
439C22—561no—
440C22#9001712yes—
441C22C2×#651611yescharacteristic
442C4—24no—
443C4—21no—
444C4—21no—
445C4—21no—
446C4—21no—
447C4—42no—
448C4—44no—
449C4—42no—
450C4—42no—
451C4—561no—
452C4C2×#650512yes—
453C4#9051312yes—
454C2—22no—
455C2—1121no—
456C2#1174150411yescharacteristic
457C2#1174152611yescharacteristic
458C2C2×#9001711yescharacteristic
subgroupG/H
centerC22C2×#6516
commutator, cosocleC42×C7C24
FrattiniC42C23×D7
FittingC2×C7×#557C2
socleC22×C7C2×#120
prime radical#90168C22
hypercenterC2×#557D7
hypocenterC7#18535
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
1. C2×C7×#557C2semidirect
5. #11729690C2semidirect
6. #11729689C2semidirect
7. #11729530C2semidirect
8. #11729377C2semidirect
9. #11729377C2semidirect
109. C2×#557D7semidirect
434. C7#18535semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5572
#117406442
#117398892
#117296902
#117296892
#117295302
#117293772
#185357