Finite Group Databasebeta

← #13360984

Subgroups — #13360984

Order 1792.

964 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C7×C22⋊Q8C211yesmaximal, characteristic
2C2×#89815C211yesmaximal, characteristic
3C2×C4×C4⋊Dic7C211yesmaximal, characteristic
4#11729446C211yesmaximal, characteristic
5#11729385C212yesmaximal, complemented
6#11729283C211yesmaximal, characteristic
7#11727421C212yesmaximal, complemented
8#11727355C212yesmaximal, complemented
9#11727258C211yesmaximal, characteristic
10#11727255C211yesmaximal, characteristic
11#11727235C212yesmaximal, complemented
12C2×C7×C22⋊Q8C2211yescharacteristic
13C2×C4×C7×Q8C2211yescharacteristic
14C22×C42×C7C2211yescharacteristic
15C22×C4⋊Dic7C2211yescharacteristic
16C22×C4⋊Dic7C2211yescharacteristic
17C22×C4×Dic7—21no—
18C7×#391C2211yescharacteristic
19C7×#389C2211yescharacteristic
20C7×#387—21no—
21C7×#385—21no—
22C7×#380C2211yescharacteristic
23C4×C7×C4⋊C4—21no—
24C4×C7×C4⋊C4C2211yescharacteristic
25C4×C7×C22⋊C4—21no—
26C2×#6409C2212yes—
27C2×#6409C2212yes—
28C2×C7⋊#95—21no—
29C2×C22⋊(C7⋊C8)C2211yescharacteristic
30C2×C22⋊(C7⋊C8)C2211yescharacteristic
31#89815C418yescomplemented
32C2×#6382C2212yes—
33C2×#6381C2212yes—
34C4×C4⋊Dic7—21no—
35C4×C4⋊Dic7—21no—
36C4×C4⋊Dic7C2212yes—
37C4×C4⋊Dic7C2212yes—
38C2×#6377C2212yes—
39#89324C2212yes—
40#89324C2212yes—
41#89324C2212yes—
42#89324C2212yes—
43#89319C2212yes—
44#21579—71nomaximal, Sylow
45C22×C7×Q8C2311yescharacteristic
46C23×C4×C7D411yescharacteristic
47C23×C4×C7D411yescharacteristic
48C23×C4×C7C2311yescharacteristic
49C23×Dic7—21no—
50C23×Dic7—21no—
51C7×C22⋊Q8—22no—
52C7×C22⋊Q8C2×C414yes—
53C4×C7×Q8—24no—
54C2×C7×C4⋊C4—21no—
55C2×C7×C4⋊C4—21no—
56C2×C7×C4⋊C4—21no—
57C2×C7×C4⋊C4C2311yescharacteristic
58C2×C7×C4⋊C4C2311yescharacteristic
59C2×C7×C4⋊C4C2311yescharacteristic
60C2×C7×C22⋊C4—21no—
61C2×C7×C22⋊C4—21no—
62C2×C42×C7—24no—
63C2×C42×C7—21no—
64C2×C42×C7—21no—
65C2×C42×C7D411yescharacteristic
66C2×C42×C7D411yescharacteristic
67C2×C42×C7C2311yescharacteristic
68C2×C42×C7C2311yescharacteristic
69C2×C4⋊Dic7—21no—
70C2×C4⋊Dic7—21no—
71C2×C4⋊Dic7—22no—
72C2×C4⋊Dic7—24no—
73C2×C4⋊Dic7C2×C414yes—
74C2×C4⋊Dic7C2312yes—
75C2×C4⋊Dic7C2312yes—
76C2×C4×Dic7—22no—
77C2×C4×Dic7—22no—
78C2×C4×Dic7—44no—
79C22×C7⋊C8C2312yes—
80C22×C7⋊C8C2312yes—
81C7×#95—21no—
82C7×#95—21no—
83C7×#95—21no—
84C7×#95—21no—
85C7×#95—21no—
86#6409—24no—
87#6409C2×C418yescomplemented
88C7⋊#95—22no—
89C7⋊#95—22no—
90C22⋊(C7⋊C8)—22no—
91C22⋊(C7⋊C8)C2×C414yes—
92#6382C2×C418yescomplemented
93#6381—24no—
94#6377—24no—
95C2×#483—71no—
96C4×C22⋊Q8D711yescharacteristic
97C2×C4×C4⋊C4—71no—
98#1928—72no—
99#1919—72no—
100#1872—71no—
101#1852—71no—
102#1823—71no—
103#1776—72no—
104#1763—72no—
105#1749—71no—
106C24×C7C2×D411yescharacteristic
107C2×C7×Q8—21no—
108C2×C7×Q8—22no—
109C2×C7×Q8—22no—
110C2×C7×Q8C22×C412yes—
111C22×C4×C7—22no—
112C22×C4×C7—22no—
113C22×C4×C7—22no—
114C22×C4×C7—22no—
115C22×C4×C7—22no—
116C22×C4×C7—22no—
117C22×C4×C7—21no—
118C22×C4×C7—21no—
119C22×C4×C7—22no—
120C22×C4×C7—21no—
121C22×C4×C7—21no—
122C22×C4×C7—41no—
123C22×C4×C7C22×C412yes—
124C22×C4×C7C2×D411yescharacteristic
125C22×C4×C7C2×D411yescharacteristic
126C22×C4×C7C2×D411yescharacteristic
127C22×C4×C7C2×D411yescharacteristic
128C22×C4×C7C2×D411yescharacteristic
129C22×C4×C7#4112yes—
130C22×C4×C7C2411yescharacteristic
131C22×Dic7—24no—
132C22×Dic7—24no—
133C22×Dic7—22no—
134C22×Dic7—22no—
135C22×Dic7—42no—
136C22×Dic7—42no—
137C22×Dic7—42no—
138C22×Dic7—42no—
139C7×C4⋊C4—24no—
140C7×C4⋊C4—21no—
141C7×C4⋊C4—22no—
142C7×C4⋊C4—22no—
143C7×C4⋊C4—42no—
144C7×C4⋊C4—42no—
145C7×C4⋊C4C22×C412yes—
146C7×C22⋊C4—24no—
147C7×C22⋊C4—42no—
148C42×C7—22no—
149C42×C7—22no—
150C42×C7—22no—
151C42×C7—42no—
152C42×C7—42no—
153C42×C7#4114yes—
154C4⋊Dic7—24no—
155C4⋊Dic7—24no—
156C4⋊Dic7—22no—
157C4⋊Dic7—22no—
158C4⋊Dic7C22×C414yes—
159C4⋊Dic7#4114yes—
160C4×Dic7—44no—
161C4×Dic7—44no—
162C2×C7⋊C8—22no—
163C2×C7⋊C8—22no—
164C2×C7⋊C8—22no—
165C2×C7⋊C8—22no—
166C2×C7⋊C8—22no—
167C2×C7⋊C8C22×C414yes—
168C2×C22⋊Q8C2×D711yescharacteristic
169C2×C4×Q8C2×D711yescharacteristic
170C22×C4⋊C4—71no—
171C22×C4⋊C4—71no—
172C22×C42—141no—
173C22×C42C2×D711yescharacteristic
174#483—78no—
175C2×#107—72no—
176C2×#106—72no—
177C2×#103—72no—
178C2×#103—72no—
179C2×C22⋊C8—71no—
180C2×C22⋊C8—71no—
181C2×#97—72no—
182#391C2×D711yescharacteristic
183#389C2×D711yescharacteristic
184#387—21no—
185#385—21no—
186#380C2×D711yescharacteristic
187C4×C4⋊C4—21no—
188C4×C4⋊C4—72no—
189C4×C4⋊C4—72no—
190C4×C4⋊C4—141no—
191C4×C4⋊C4—141no—
192C4×C4⋊C4C2×D711yescharacteristic
193C4×C22⋊C4—21no—
194C2×#95—141no—
195#340—72no—
196#340—72no—
197#340—72no—
198#340—72no—
199#336—72no—
200C23×C7—21no—
201C23×C7—21no—
202C23×C7—21no—
203C23×C7—21no—
204C23×C7C4×D412yes—
205C23×C7AGL(1,ℤ/8)12yes—
206C23×C7#13712yes—
207C23×C7C22×D411yescharacteristic
208C7×Q8—24no—
209C7×Q8—42no—
210C2×C4×C7—28no—
211C2×C4×C7—21no—
212C2×C4×C7—21no—
213C2×C4×C7—21no—
214C2×C4×C7—21no—
215C2×C4×C7—21no—
216C2×C4×C7—21no—
217C2×C4×C7—21no—
218C2×C4×C7—21no—
219C2×C4×C7—24no—
220C2×C4×C7—24no—
221C2×C4×C7—22no—
222C2×C4×C7—22no—
223C2×C4×C7—21no—
224C2×C4×C7—21no—
225C2×C4×C7—21no—
226C2×C4×C7—44no—
227C2×C4×C7—41no—
228C2×C4×C7—41no—
229C2×C4×C7—41no—
230C2×C4×C7—41no—
231C2×C4×C7—41no—
232C2×C4×C7—41no—
233C2×C4×C7—41no—
234C2×C4×C7—41no—
235C2×C4×C7—41no—
236C2×C4×C7—41no—
237C2×C4×C7C4×D412yes—
238C2×C4×C7#12312yes—
239C2×C4×C7#12312yes—
240C2×C4×C7#13712yes—
241C2×C4×C7C23×C411yescharacteristic
242C2×C4×C7C2×#4111yescharacteristic
243C2×C4×C7C2×#4112yes—
244C2×C4×C7C2×#4112yes—
245C2×Dic7—24no—
246C2×Dic7—24no—
247C2×Dic7—48no—
248C2×Dic7—42no—
249C2×Dic7—42no—
250C2×Dic7—42no—
251C2×Dic7—42no—
252C2×Dic7—48no—
253C7⋊C8—24no—
254C7⋊C8—42no—
255C22×Q8C22×D711yescharacteristic
256C23×C4—141no—
257C23×C4—141no—
258C23×C4C22⋊D711yescharacteristic
259C23×C4C22⋊D711yescharacteristic
260C23×C4C22×D711yescharacteristic
261C22×C8—72no—
262C22×C8—72no—
263C22⋊Q8—22no—
264C22⋊Q8C4×D714yes—
265C4×Q8—24no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—74no—
270C2×C4⋊C4—72no—
271C2×C4⋊C4—72no—
272C2×C4⋊C4—144no—
273C2×C4⋊C4—142no—
274C2×C4⋊C4—141no—
275C2×C4⋊C4—141no—
276C2×C4⋊C4C22×D711yescharacteristic
277C2×C4⋊C4C22×D711yescharacteristic
278C2×C4⋊C4C22×D711yescharacteristic
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C42—24no—
282C2×C42—21no—
283C2×C42—21no—
284C2×C42—142no—
285C2×C42—142no—
286C2×C42—284no—
287C2×C42C22⋊D711yescharacteristic
288C2×C42C22⋊D711yescharacteristic
289C2×C42C22×D711yescharacteristic
290C2×C42C22×D711yescharacteristic
291#107—144no—
292#106—78no—
293#103—78no—
294#103—144no—
295C22⋊C8—74no—
296C22⋊C8—142no—
297#97—144no—
298#95—21no—
299#95—21no—
300#95—21no—
301#95—21no—
302#95—21no—
303#95—142no—
304#95—142no—
305C22×C7—22no—
306C22×C7—22no—
307C22×C7—22no—
308C22×C7—22no—
309C22×C7—22no—
310C22×C7—22no—
311C22×C7#44014yes—
312C22×C7C2×C4×D411yescharacteristic
313C22×C7C2×#12311yescharacteristic
314C22×C7#52511yescharacteristic
315C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
316C22×C7C2×#13711yescharacteristic
317C22×C7C2×#13711yescharacteristic
318C22×C7#57511yescharacteristic
319C4×C7—22no—
320C4×C7—22no—
321C4×C7—22no—
322C4×C7—22no—
323C4×C7—41no—
324C4×C7—42no—
325C4×C7—42no—
326C4×C7—81no—
327C4×C7—81no—
328C4×C7C4×#4112yes—
329C4×C7#52912yes—
330Dic7—44no—
331Dic7—44no—
332C24C2×C22⋊D711yescharacteristic
333C2×Q8—21no—
334C2×Q8—22no—
335C2×Q8—22no—
336C2×Q8C2×C4×D712yes—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—41no—
349C22×C4—144no—
350C22×C4—144no—
351C22×C4—142no—
352C22×C4—142no—
353C22×C4—282no—
354C22×C4—282no—
355C22×C4—282no—
356C22×C4—282no—
357C22×C4C2×C4×D712yes—
358C22×C4#115712yes—
359C22×C4C2×C22⋊D711yescharacteristic
360C22×C4C2×C22⋊D711yescharacteristic
361C22×C4C2×C22⋊D711yescharacteristic
362C22×C4C2×C22⋊D711yescharacteristic
363C22×C4C2×C22⋊D711yescharacteristic
364C22×C4C23×D711yescharacteristic
365C2×C8—74no—
366C2×C8—142no—
367C2×C8—142no—
368C2×C8—142no—
369C2×C8—142no—
370C2×C8—142no—
371C4⋊C4—24no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—42no—
376C4⋊C4—42no—
377C4⋊C4—74no—
378C4⋊C4—74no—
379C4⋊C4—144no—
380C4⋊C4—144no—
381C4⋊C4—142no—
382C4⋊C4—142no—
383C4⋊C4C2×C4×D712yes—
384C22⋊C4—24no—
385C22⋊C4—42no—
386C42—22no—
387C42—22no—
388C42—22no—
389C42—42no—
390C42—42no—
391C42—284no—
392C42—284no—
393C42#115914yes—
394C2×C7—24no—
395C2×C7C4×#12311yescharacteristic
396C2×C7C2×#44011yescharacteristic
397C2×C7C4×#13711yescharacteristic
398C2×C7#309211yescharacteristic
399C2×C7#309511yescharacteristic
400C2×C7#311311yescharacteristic
401C2×C7#311411yescharacteristic
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23C4×C22⋊D712yes—
407C23#650512yes—
408C23#651212yes—
409C23C22×C22⋊D711yescharacteristic
410Q8—24no—
411Q8—42no—
412C2×C4—28no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—44no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—144no—
440C2×C4—144no—
441C2×C4—288no—
442C2×C4—282no—
443C2×C4—282no—
444C2×C4—282no—
445C2×C4—282no—
446C2×C4—288no—
447C2×C4C4×C22⋊D712yes—
448C2×C4#649812yes—
449C2×C4#649812yes—
450C2×C4#651412yes—
451C2×C4C22×C4×D711yescharacteristic
452C2×C4C2×#115711yescharacteristic
453C2×C4C2×#115912yes—
454C2×C4D7×#4112yes—
455C8—144no—
456C8—282no—
457C7#2157911yescharacteristic, complemented, Sylow
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22#8979814yes—
465C22C2×C4×C22⋊D711yescharacteristic
466C22C2×#649811yescharacteristic
467C22C2×#650511yescharacteristic
468C22C2×#651211yescharacteristic
469C22#9051311yescharacteristic
470C22C2×#651411yescharacteristic
471C22#9051911yescharacteristic
472C4—22no—
473C4—22no—
474C4—22no—
475C4—22no—
476C4—41no—
477C4—42no—
478C4—42no—
479C4—81no—
480C4—81no—
481C4—284no—
482C4—284no—
483C4C4×#115912yes—
484C4#9022912yes—
485C2—24no—
486C2C4×#649811yescharacteristic
487C2C2×#8979811yescharacteristic
488C2C4×#651411yescharacteristic
489C2#1174017211yescharacteristic
490C2#1174035911yescharacteristic
491C2#1174058811yescharacteristic
492C2#1174081411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC4×C7×C22⋊Q8C2
socleC23×C7C22×D4
prime radicalC24×C7C2×D4
cosocleC22×C4×C7C24
hypercenterC4×C22⋊Q8D7
hypocenterC7#21579
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
5. #11729385C2semidirect
7. #11727421C2semidirect
8. #11727355C2semidirect
11. #11727235C2semidirect
31. #89815C4semidirect
87. #6409C2×C4semidirect
92. #6382C2×C4semidirect
457. C7#21579semidirect

Maximal subgroups

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

subgroupindex
C4×C7×C22⋊Q82
C2×#898152
C2×C4×C4⋊Dic72
#117294462
#117293852
#117292832
#117274212
#117273552
#117272582
#117272552
#117272352
#215797