Finite Group Databasebeta

← #13404535

Subgroups — #13404535

Order 1792.

1018 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#462C211yesmaximal, characteristic, complemented
2C2×#89960C212yesmaximal, complemented
3#11740704C211yesmaximal, characteristic
4#11739945C211yesmaximal, characteristic
5C2×#89606C211yesmaximal, characteristic
6#11729825C212yesmaximal, complemented
7#11729539C211yesmaximal, characteristic, complemented
8C4×#6409C211yesmaximal, characteristic, complemented
9#11728207C211yesmaximal, characteristic, complemented
10#11728024C212yesmaximal, complemented
11#11727998C212yesmaximal, complemented
12C22×C7×Q16C2212yes—
13C2×C7×C4⋊Q8C2211yescharacteristic
14C2×C4×C7×Q8C2211yescharacteristic
15C2×#6509C2212yes—
16C2×#6509C2212yes—
17C2×#6509C2212yes—
18C22×C8×D7C2212yes—
19C2×C4×D28C2211yescharacteristic
20C7×#462—24no—
21C2×C7×C4⋊C8C2211yescharacteristic
22C2×C7×#103C2212yes—
23C2×#6409C2212yes—
24C2×#6409C2211yescharacteristic
25C2×#6409C2212yes—
26C2×#6409C2211yescharacteristic
27#89960—28no—
28C2×(C2×D7)⋊C8C2212yes—
29C2×#6392C2212yes—
30#89766—22no—
31#89764—22no—
32#89760—21no—
33#89759C2212yes—
34#89748—21no—
35#89711—21no—
36#89707C2211yescharacteristic
37C4×C4⋊Dic7C2211yescharacteristic
38#89700—21no—
39C2×C4×C7⋊C8C2211yescharacteristic
40#89606—24no—
41#89346C2212yes—
42#89324C2211yescharacteristic
43#89324C2211yescharacteristic
44#25386—71nomaximal, Sylow
45C22×C7×Q8C2312yes—
46C22×C7×Q8C2311yescharacteristic
47C22×D28D411yescharacteristic
48C22×C4×D7C2312yes—
49C2×C7×Q16—24no—
50C2×C7×Q16—24no—
51C2×C7×Q16—42no—
52C22×C7×C8C2312yes—
53C7×C4⋊Q8—22no—
54C7×C4⋊Q8—22no—
55C4×C7×Q8—22no—
56C4×C7×Q8—22no—
57C2×C7×C4⋊C4—21no—
58C2×C7×C4⋊C4—21no—
59C2×C7×C4⋊C4—21no—
60C2×C7×C4⋊C4C2311yescharacteristic
61C2×C42×C7—21no—
62C2×C42×C7C2311yescharacteristic
63#6509—24no—
64#6509—24no—
65#6509—24no—
66#6509—42no—
67#6509—42no—
68#6509—42no—
69C2×(C2×D7)⋊C4—22no—
70C2×(C2×D7)⋊C4—22no—
71C2×(C2×D7)⋊C4—22no—
72C2×(C2×D7)⋊C4—22no—
73C2×(C2×D7)⋊C4D412yes—
74C2×C4⋊Dic7—21no—
75C2×C4⋊Dic7—21no—
76C2×C4⋊Dic7D411yescharacteristic
77C2×C4⋊Dic7C2312yes—
78C2×C4⋊Dic7C2311yescharacteristic
79C2×C4⋊Dic7C2311yescharacteristic
80C2×Dic7⋊C4—22no—
81C2×Dic7⋊C4—22no—
82C2×Dic7⋊C4—22no—
83C2×C4×Dic7—21no—
84C22×C7⋊C8C2311yescharacteristic
85C22×C7⋊C8C2311yescharacteristic
86C2×C8×D7—24no—
87C2×C8×D7—24no—
88C2×C8×D7—42no—
89C4×D28—22no—
90C4×D28—22no—
91C7×C4⋊C8D414yes—
92C7×#103—24no—
93#6409—22no—
94#6409—24no—
95#6409—42no—
96#6409D414yescomplemented
97C7⋊#95—21no—
98C7⋊#95—22no—
99(C2×D7)⋊C8—24no—
100#6392—24no—
101C4×C7⋊C8—22no—
102C2×#467—72no—
103C2×#462D711yescharacteristic, complemented
104C2×C8×D4—71no—
105#2542—71no—
106#2538—71no—
107#2036—72no—
108#2001—72no—
109#1956—71no—
110#1947—71no—
111#1892—72no—
112C4×#103—71no—
113C23×D7C2×D412yes—
114C2×C7×Q8—21no—
115C2×C7×Q8—21no—
116C2×C7×Q8—22no—
117C2×C7×Q8—22no—
118C2×C7×Q8—21no—
119C2×C7×Q8—21no—
120C2×C7×Q8—22no—
121C2×C7×Q8—22no—
122C2×C7×Q8—21no—
123C2×C7×Q8—22no—
124C2×C7×Q8—22no—
125C2×C7×Q8C2×D412yes—
126C22×C4×C7—21no—
127C22×C4×C7—21no—
128C22×C4×C7—22no—
129C22×C4×C7C2×D411yescharacteristic
130C22×C4×C7C2×D411yescharacteristic
131C22×C4×C7C2411yescharacteristic
132C22×Dic7—21no—
133C22×Dic7—21no—
134C22×Dic7—22no—
135C22×Dic7C2×D412yes—
136C2×D28—22no—
137C2×D28—22no—
138C2×D28Q1614yescomplemented
139C2×C4×D7—22no—
140C2×C4×D7—22no—
141C2×C4×D7—22no—
142C2×C4×D7—22no—
143C2×C4×D7—22no—
144C2×C4×D7—22no—
145C7×Q16—48no—
146C2×C7×C8—22no—
147C2×C7×C8—22no—
148C2×C7×C8C2×D414yes—
149C7×C4⋊C4—21no—
150C7×C4⋊C4—21no—
151C7×C4⋊C4—42no—
152C7×C4⋊C4—42no—
153C7×C4⋊C4—42no—
154C42×C7—42no—
155C42×C7C2×D412yes—
156C42×C7#4112yes—
157(C2×D7)⋊C4—24no—
158(C2×D7)⋊C4—44no—
159(C2×D7)⋊C4—44no—
160(C2×D7)⋊C4—44no—
161(C2×D7)⋊C4—82no—
162C4⋊Dic7—22no—
163C4⋊Dic7—21no—
164C4⋊Dic7—21no—
165C4⋊Dic7—22no—
166C4⋊Dic7—22no—
167C4⋊Dic7—42no—
168C4⋊Dic7—81no—
169C4⋊Dic7C2×D412yes—
170C4⋊Dic7#4112yes—
171Dic7⋊C4—44no—
172Dic7⋊C4—44no—
173Dic7⋊C4—44no—
174C4×Dic7—42no—
175C2×C7⋊C8—21no—
176C2×C7⋊C8—21no—
177C2×C7⋊C8—21no—
178C2×C7⋊C8—21no—
179C2×C7⋊C8—21no—
180C2×C7⋊C8C2×D412yes—
181C8×D7—48no—
182C22×Q16C2×D712yes—
183C23×C8—72no—
184C2×C4⋊Q8C2×D711yescharacteristic
185C2×C22⋊Q8—72no—
186C2×C22⋊Q8—72no—
187C2×C22⋊Q8—72no—
188C2×C4×Q8C2×D711yescharacteristic
189C2×C4×D4—71no—
190#467—148no—
191#462—24no—
192C8×D4—144no—
193C2×#107—72no—
194C2×C4⋊C8C2×D711yescharacteristic
195C2×#103—71no—
196C2×#103—72no—
197C2×#103—71no—
198C2×#103—72no—
199C2×#103C2×D712yes—
200C2×C22⋊C8—72no—
201C2×C4×C8—71no—
202#399—142no—
203#396—142no—
204#390—141no—
205#390—141no—
206#389—141no—
207#384—71no—
208#384—141no—
209#380—72no—
210C4×C4⋊C4—71no—
211#340—72no—
212#340—71no—
213#340—71no—
214C23×C7C22×D411yescharacteristic
215C22×D7—22no—
216C22×D7—22no—
217C22×D7—22no—
218C22×D7—22no—
219C22×D7—22no—
220C22×D7—22no—
221C22×D7C2×Q1614yes—
222C7×Q8—22no—
223C7×Q8—22no—
224C7×Q8—41no—
225C7×Q8—41no—
226C7×Q8—42no—
227C7×Q8—42no—
228C7×Q8—42no—
229C7×Q8—42no—
230C2×C4×C7—21no—
231C2×C4×C7—21no—
232C2×C4×C7—22no—
233C2×C4×C7—41no—
234C2×C4×C7—41no—
235C2×C4×C7—41no—
236C2×C4×C7—42no—
237C2×C4×C7—42no—
238C2×C4×C7—42no—
239C2×C4×C7—41no—
240C2×C4×C7—41no—
241C2×C4×C7#12112yes—
242C2×C4×C7#12112yes—
243C2×C4×C7C2×Q1612yes—
244C2×C4×C7#13512yes—
245C2×C4×C7C22×D411yescharacteristic
246C2×C4×C7C22×D411yescharacteristic
247C2×C4×C7C2×#4111yescharacteristic
248C2×C4×C7C2×#4111yescharacteristic
249C2×C4×C7H(5,𝔽2)11yescharacteristic
250C2×C4×C7H(5,𝔽2)11yescharacteristic
251C2×Dic7—22no—
252C2×Dic7—22no—
253C2×Dic7—22no—
254C2×Dic7—22no—
255C2×Dic7—22no—
256C2×Dic7—41no—
257C2×Dic7—41no—
258C2×Dic7—41no—
259C2×Dic7—41no—
260C2×Dic7—42no—
261C2×Dic7—42no—
262C2×Dic7—42no—
263D28—28no—
264C4×D7—42no—
265C4×D7—42no—
266C4×D7—42no—
267C4×D7—42no—
268C7×C8—24no—
269C7⋊C8—22no—
270C7⋊C8—41no—
271C22×Q8C22×D712yes—
272C22×Q8C22×D711yescharacteristic
273C22×D4—71no—
274C23×C4—72no—
275C2×Q16—24no—
276C2×Q16—24no—
277C2×Q16—42no—
278C22×C8—71no—
279C22×C8—71no—
280C22×C8—144no—
281C22×C8—144no—
282C22×C8—282no—
283C22×C8C22×D712yes—
284C4⋊Q8—22no—
285C4⋊Q8—22no—
286C22⋊Q8—144no—
287C22⋊Q8—144no—
288C22⋊Q8—144no—
289C22⋊Q8—282no—
290C22⋊Q8—282no—
291C22⋊Q8—282no—
292C4×Q8—22no—
293C4×Q8—22no—
294C4×D4—142no—
295C4×D4—142no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—71no—
300C2×C4⋊C4—71no—
301C2×C4⋊C4—71no—
302C2×C4⋊C4—72no—
303C2×C4⋊C4—142no—
304C2×C4⋊C4—142no—
305C2×C4⋊C4—142no—
306C2×C4⋊C4—141no—
307C2×C4⋊C4—141no—
308C2×C4⋊C4C22×D711yescharacteristic
309C2×C22⋊C4—72no—
310C2×C22⋊C4—142no—
311C2×C22⋊C4—142no—
312C2×C22⋊C4—142no—
313C2×C22⋊C4—142no—
314C2×C42—21no—
315C2×C42—141no—
316C2×C42C22×D711yescharacteristic
317#107—144no—
318C4⋊C8C22⋊D714yes—
319#103—24no—
320#103—74no—
321#103—142no—
322#103—144no—
323#103—282no—
324C22⋊C8—144no—
325C4×C8—142no—
326#95—142no—
327#95—141no—
328C22×C7C2×#12111yescharacteristic
329C22×C7D4211yescharacteristic
330C22×C7#54611yescharacteristic
331C22×C7C22×Q1611yescharacteristic
332C22×C7C2×#13511yescharacteristic
333C22×C7#57711yescharacteristic
334C22×C7#57811yescharacteristic
335C2×D7—24no—
336C2×D7—24no—
337C2×D7—24no—
338C2×D7—42no—
339C2×D7—42no—
340C2×D7—42no—
341C2×D7—42no—
342C4×C7—22no—
343C4×C7—42no—
344C4×C7—82no—
345C4×C7—81no—
346C4×C7#46714yescomplemented
347C4×C7#53211yescharacteristic
348C4×C7#54011yescharacteristic
349C4×C7D4211yescharacteristic
350C4×C7#55011yescharacteristic
351Dic7—42no—
352Dic7—42no—
353Dic7—42no—
354Dic7—82no—
355C24—72no—
356C2×Q8—21no—
357C2×Q8—22no—
358C2×Q8—21no—
359C2×Q8—22no—
360C2×Q8—21no—
361C2×Q8—22no—
362C2×Q8—21no—
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8—21no—
366C2×Q8—22no—
367C2×Q8D4×D712yes—
368C2×D4—74no—
369C2×D4—142no—
370C2×D4—142no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—72no—
375C22×C4—141no—
376C22×C4—141no—
377C22×C4—142no—
378C22×C4—142no—
379C22×C4—142no—
380C22×C4—142no—
381C22×C4—142no—
382C22×C4—142no—
383C22×C4—142no—
384C22×C4D4×D711yescharacteristic
385C22×C4D4×D711yescharacteristic
386C22×C4C23×D711yescharacteristic
387Q16—48no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—72no—
391C2×C8—141no—
392C2×C8—141no—
393C2×C8—141no—
394C2×C8—141no—
395C2×C8—141no—
396C2×C8—288no—
397C2×C8C2×C22⋊D714yes—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—42no—
401C4⋊C4—42no—
402C4⋊C4—42no—
403C4⋊C4—72no—
404C4⋊C4—72no—
405C4⋊C4—142no—
406C4⋊C4—141no—
407C4⋊C4—141no—
408C4⋊C4—142no—
409C4⋊C4—142no—
410C4⋊C4—284no—
411C4⋊C4—284no—
412C4⋊C4—284no—
413C4⋊C4—282no—
414C4⋊C4—561no—
415C22⋊C4—144no—
416C22⋊C4—284no—
417C22⋊C4—284no—
418C22⋊C4—284no—
419C22⋊C4—562no—
420C42—42no—
421C42—282no—
422C42#115912yes—
423C42C2×C22⋊D712yes—
424C2×C7#242811yescharacteristic
425C2×C7C2×#46711yescharacteristic
426C2×C7#306311yescharacteristic
427C2×C7#328411yescharacteristic
428C2×C7D4×Q1611yescharacteristic
429C2×C7#329911yescharacteristic
430C2×C7#330211yescharacteristic
431D7—44no—
432C23—74no—
433C23—142no—
434C23—142no—
435C23—142no—
436C23—142no—
437C23—142no—
438C23—142no—
439C23C2×D4×D711yescharacteristic
440Q8—22no—
441Q8—22no—
442Q8—41no—
443Q8—41no—
444Q8—42no—
445Q8—42no—
446Q8—42no—
447Q8—42no—
448D4—148no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—142no—
461C2×C4—142no—
462C2×C4—142no—
463C2×C4—142no—
464C2×C4—142no—
465C2×C4—281no—
466C2×C4—281no—
467C2×C4—281no—
468C2×C4—281no—
469C2×C4—282no—
470C2×C4—282no—
471C2×C4—282no—
472C2×C4—282no—
473C2×C4—282no—
474C2×C4—282no—
475C2×C4—282no—
476C2×C4D7×Q1612yes—
477C2×C4#648212yes—
478C2×C4#650112yes—
479C2×C4#650112yes—
480C2×C4C2×D4×D711yescharacteristic
481C2×C4C2×#115911yescharacteristic
482C2×C4#654811yescharacteristic
483C2×C4D7×#4111yescharacteristic
484C2×C4#655311yescharacteristic
485C2×C4C22×C22⋊D711yescharacteristic
486C8—24no—
487C8—142no—
488C8—281no—
489C7#2538611yescharacteristic, complemented, Sylow
490C22—144no—
491C22—144no—
492C22—144no—
493C22—282no—
494C22—282no—
495C22—282no—
496C22—282no—
497C22#9030011yescharacteristic
498C22#9030311yescharacteristic
499C22C2×D7×Q1611yescharacteristic
500C22C2×#648211yescharacteristic
501C22#9046911yescharacteristic
502C22#9047011yescharacteristic
503C22C2×#650111yescharacteristic
504C4—22no—
505C4—42no—
506C4—82no—
507C4—81no—
508C4—282no—
509C4—282no—
510C4—282no—
511C4—562no—
512C4#8996014yescomplemented
513C4#9028711yescharacteristic
514C4#9031011yescharacteristic
515C4D4×C22⋊D711yescharacteristic
516C4#9052511yescharacteristic
517C2—284no—
518C2#1173793511yescharacteristic
519C2#1173793611yescharacteristic
520C2#1173793711yescharacteristic
521C2#1173794711yescharacteristic
522C2#1174009311yescharacteristic
523C2C2×#8996011yescharacteristic
524C2#1174143111yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#462C2
socleC23×C7C22×D4
prime radicalC22×D28D4
hypercenterC2×#462D7
hypocenterC7#25386
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
1. C2×C7×#462C2semidirect
2. C2×#89960C2semidirect
6. #11729825C2semidirect
7. #11729539C2semidirect
8. C4×#6409C2semidirect
9. #11728207C2semidirect
10. #11728024C2semidirect
11. #11727998C2semidirect
96. #6409D4semidirect
103. C2×#462D7semidirect
138. C2×D28Q16semidirect
346. C4×C7#467semidirect
489. C7#25386semidirect
512. C4#89960semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4622
C2×#899602
#117407042
#117399452
C2×#896062
#117298252
#117295392
C4×#64092
#117282072
#117280242
#117279982
#253867