Finite Group Databasebeta

← #13395361

Subgroups — #13395361

Order 1792.

946 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#462C211yesmaximal, characteristic, complemented
2C2×#89957C212yesmaximal
3#11740685C211yesmaximal, characteristic
4Q8×C4⋊Dic7C211yesmaximal, characteristic, complemented
5C2×C4×#1143C211yesmaximal, characteristic
6#11729819C212yesmaximal, complemented
7#11729539C211yesmaximal, characteristic, complemented
8#11728233C211yesmaximal, characteristic
9#11728222C211yesmaximal, characteristic, complemented
10#11728015C212yesmaximal, complemented
11#11727999C212yesmaximal
12C22×C7×Q16C2212yes—
13C2×C7×C4⋊Q8C2211yescharacteristic
14C2×C4×C7×Q8C2211yescharacteristic
15C2×#6510C2212yes—
16C2×Q8×Dic7C2212yes—
17C22×#1143C2211yescharacteristic
18C2×C4×D28C2211yescharacteristic
19C7×#462—24no—
20C2×C7×C4⋊C8C2211yescharacteristic
21C2×C7×#103C2212yes—
22#90002C2212yes—
23C2×#6409C2212yes—
24C2×#6409C2211yescharacteristic
25C2×#6409C2212yes—
26#89957—28no—
27C2×#6395C2212yes—
28C2×Dic7⋊C8C2212yes—
29C4×#1143—24no—
30#89765—22no—
31#89759—21no—
32#89759—21no—
33#89757—22no—
34#89757C2212yes—
35C2×#6383C2211yescharacteristic
36C2×#6382C2211yescharacteristic
37#89707—21no—
38#89707C2211yescharacteristic
39C4×C4⋊Dic7—21no—
40C4×C4⋊Dic7C2211yescharacteristic
41C2×C4×C7⋊C8C2211yescharacteristic
42#89346C2212yes—
43#89345C2212yes—
44#24729—71nomaximal, Sylow
45C22×C7×Q8C2312yes—
46C22×C7×Q8C2311yescharacteristic
47C22×D28C2311yescharacteristic
48C22×C4×D7—21no—
49C2×C7×Q16—24no—
50C2×C7×Q16—24no—
51C2×C7×Q16—24no—
52C22×C7×C8C2312yes—
53C7×C4⋊Q8—22no—
54C7×C4⋊Q8—22no—
55C4×C7×Q8—22no—
56C4×C7×Q8D414yes—
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#6510—24no—
64#6510—42no—
65Q8×Dic7—24no—
66Q8×Dic7—42no—
67C2×#1143—22no—
68C2×#1143—22no—
69C2×#1143D414yes—
70C2×(C2×D7)⋊C4—21no—
71C2×(C2×D7)⋊C4—22no—
72C2×(C2×D7)⋊C4—22no—
73C2×C4⋊Dic7—21no—
74C2×C4⋊Dic7—22no—
75C2×C4⋊Dic7—21no—
76C2×C4⋊Dic7—22no—
77C2×C4⋊Dic7D411yescharacteristic
78C2×C4⋊Dic7D411yescharacteristic
79C2×C4⋊Dic7C2311yescharacteristic
80C2×C4⋊Dic7C2312yes—
81C2×C4×Dic7—22no—
82C2×C4×Dic7C2312yes—
83C22×C7⋊C8C2311yescharacteristic
84C22×C7⋊C8C2311yescharacteristic
85C4×D28—22no—
86C4×D28—22no—
87C7×C4⋊C8—22no—
88C7×#103—24no—
89#6409—22no—
90#6409—24no—
91#6409—42no—
92C7⋊#95—22no—
93C7⋊#95—22no—
94C7⋊#95—22no—
95C7⋊#95D412yes—
96#6395—24no—
97Dic7⋊C8—24no—
98#6383—22no—
99#6382—22no—
100C4×C7⋊C8—22no—
101C2×#464—72no—
102C2×#462D711yescharacteristic, complemented
103C2×C4×SD16—71no—
104#2547—71no—
105Q8×C4⋊C4—71no—
106#2066—72no—
107#2042—72no—
108#1956—71no—
109#1939—71no—
110#1878—72no—
111#1802—71no—
112C23×D7—21no—
113C2×C7×Q8—21no—
114C2×C7×Q8—21no—
115C2×C7×Q8—21no—
116C2×C7×Q8—22no—
117C2×C7×Q8—22no—
118C2×C7×Q8—22no—
119C2×C7×Q8—22no—
120C2×C7×Q8—22no—
121C2×C7×Q8—22no—
122C2×C7×Q8C2×D412yes—
123C2×C7×Q8C2×D412yes—
124C2×C7×Q8#4112yes—
125C22×C4×C7—21no—
126C22×C4×C7—21no—
127C22×C4×C7—22no—
128C22×C4×C7C2×D411yescharacteristic
129C22×C4×C7C2×D411yescharacteristic
130C22×C4×C7C2411yescharacteristic
131C22×Dic7—21no—
132C22×Dic7—22no—
133C22×Dic7C2×D412yes—
134C22×Dic7C2×D412yes—
135C2×D28—21no—
136C2×D28—21no—
137C2×D28—21no—
138C2×D28—21no—
139C2×D28—21no—
140C2×D28C2×D412yes—
141C2×C4×D7—42no—
142C2×C4×D7—42no—
143C2×C4×D7—42no—
144C7×Q16—48no—
145C2×C7×C8—22no—
146C2×C7×C8—22no—
147C2×C7×C8—22no—
148C7×C4⋊C4—24no—
149C7×C4⋊C4—21no—
150C7×C4⋊C4—42no—
151C7×C4⋊C4—42no—
152C7×C4⋊C4C2×D412yes—
153C42×C7—24no—
154C42×C7C2×D412yes—
155C42×C7#4112yes—
156#1143—28no—
157(C2×D7)⋊C4—44no—
158(C2×D7)⋊C4—44no—
159(C2×D7)⋊C4—42no—
160C4⋊Dic7—22no—
161C4⋊Dic7—22no—
162C4⋊Dic7—21no—
163C4⋊Dic7—22no—
164C4⋊Dic7—21no—
165C4⋊Dic7—22no—
166C4⋊Dic7—44no—
167C4⋊Dic7—42no—
168C4⋊Dic7—82no—
169C4⋊Dic7—81no—
170C4×Dic7—22no—
171C4×Dic7—22no—
172C4×Dic7—44no—
173C2×C7⋊C8—21no—
174C2×C7⋊C8—21no—
175C2×C7⋊C8—21no—
176C2×C7⋊C8—21no—
177C2×C7⋊C8—21no—
178C2×C7⋊C8C2×D412yes—
179C22×Q16C2×D712yes—
180C22×SD16—71no—
181C2×C4⋊Q8C2×D711yescharacteristic
182C2×#124—72no—
183C2×C4×Q8—72no—
184C2×C4×Q8C2×D711yescharacteristic
185C2×C4×D4—71no—
186#464—148no—
187#462—24no—
188C4×SD16—144no—
189C2×#106—71no—
190C2×C4⋊C8—72no—
191C2×C4⋊C8C2×D711yescharacteristic
192C2×#103—72no—
193C2×#103—71no—
194C2×#103—72no—
195C2×#103C2×D712yes—
196C2×#102—72no—
197C2×#102—71no—
198C2×C4×C8—71no—
199#397—142no—
200#391—72no—
201#389—72no—
202#389—142no—
203#384—71no—
204#384—141no—
205#380—141no—
206#380—141no—
207C4×C4⋊C4—71no—
208C4×C4⋊C4—141no—
209#340—72no—
210#336—72no—
211C23×C7C22×D411yescharacteristic
212C22×D7—22no—
213C22×D7—41no—
214C22×D7—41no—
215C22×D7—41no—
216C22×D7—41no—
217C22×D7—41no—
218C22×D7—41no—
219C7×Q8—22no—
220C7×Q8—22no—
221C7×Q8—22no—
222C7×Q8—42no—
223C7×Q8—42no—
224C7×Q8—42no—
225C7×Q8—42no—
226C7×Q8#12114yes—
227C2×C4×C7—22no—
228C2×C4×C7—22no—
229C2×C4×C7—22no—
230C2×C4×C7—21no—
231C2×C4×C7—21no—
232C2×C4×C7—22no—
233C2×C4×C7—41no—
234C2×C4×C7—41no—
235C2×C4×C7—42no—
236C2×C4×C7—42no—
237C2×C4×C7—42no—
238C2×C4×C7#12112yes—
239C2×C4×C7#12112yes—
240C2×C4×C7#13512yes—
241C2×C4×C7#13712yes—
242C2×C4×C7C22×D411yescharacteristic
243C2×C4×C7C22×D411yescharacteristic
244C2×C4×C7C2×#4111yescharacteristic
245C2×C4×C7C2×#4111yescharacteristic
246C2×C4×C7H(5,𝔽2)11yescharacteristic
247C2×C4×C72−1+411yescharacteristic
248C2×Dic7—22no—
249C2×Dic7—22no—
250C2×Dic7—22no—
251C2×Dic7—22no—
252C2×Dic7—22no—
253C2×Dic7—22no—
254C2×Dic7—41no—
255C2×Dic7—42no—
256C2×Dic7—42no—
257C2×Dic7—41no—
258C2×Dic7—41no—
259C2×Dic7—42no—
260D28—22no—
261D28—22no—
262D28—41no—
263D28—41no—
264C4×D7—84no—
265C7×C8—42no—
266C7⋊C8—22no—
267C7⋊C8—41no—
268C22×Q8C22×D712yes—
269C22×Q8C22×D711yescharacteristic
270C22×D4—71no—
271C23×C4—141no—
272C2×Q16—24no—
273C2×Q16—24no—
274C2×Q16—24no—
275C2×SD16—74no—
276C2×SD16—142no—
277C2×SD16—142no—
278C22×C8—71no—
279C22×C8—71no—
280C22×C8C22×D712yes—
281C4⋊Q8—22no—
282C4⋊Q8—22no—
283#124—144no—
284#124—282no—
285C4×Q8—22no—
286C4×Q8—144no—
287C4×Q8—282no—
288C4×Q8C22⋊D714yes—
289C4×D4—142no—
290C4×D4—142no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—71no—
295C2×C4⋊C4—71no—
296C2×C4⋊C4—71no—
297C2×C4⋊C4—72no—
298C2×C4⋊C4—142no—
299C2×C4⋊C4—141no—
300C2×C4⋊C4—142no—
301C2×C4⋊C4—141no—
302C2×C4⋊C4C22×D711yescharacteristic
303C2×C22⋊C4—142no—
304C2×C22⋊C4—142no—
305C2×C22⋊C4—141no—
306C2×C42—21no—
307C2×C42—72no—
308C2×C42—142no—
309C2×C42C22×D711yescharacteristic
310#106—142no—
311C4⋊C8—22no—
312C4⋊C8—144no—
313#103—24no—
314#103—144no—
315#103—142no—
316#103—282no—
317#102—144no—
318#102—142no—
319C4×C8—142no—
320#95—72no—
321#95—142no—
322#95—142no—
323#95—142no—
324C22×C7C2×#12111yescharacteristic
325C22×C7D4211yescharacteristic
326C22×C7#54811yescharacteristic
327C22×C7C2×#13511yescharacteristic
328C22×C7C2×#13711yescharacteristic
329C22×C7#57711yescharacteristic
330C22×C7#57811yescharacteristic
331C2×D7—42no—
332C2×D7—42no—
333C2×D7—42no—
334C2×D7—81no—
335C2×D7—81no—
336C2×D7—81no—
337C2×D7—81no—
338C4×C7—24no—
339C4×C7—22no—
340C4×C7—42no—
341C4×C7—82no—
342C4×C7#46414yescomplemented
343C4×C7C2×#12111yescharacteristic
344C4×C7#53711yescharacteristic
345C4×C7#54711yescharacteristic
346C4×C7#55311yescharacteristic
347Dic7—42no—
348Dic7—42no—
349Dic7—82no—
350Dic7—81no—
351C24—141no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8D4×D712yes—
362C2×Q8#115912yes—
363C2×Q8C2×C22⋊D712yes—
364C2×D4—72no—
365C2×D4—141no—
366C2×D4—141no—
367C2×D4—141no—
368C2×D4—141no—
369C2×D4—141no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—72no—
374C22×C4—72no—
375C22×C4—141no—
376C22×C4—142no—
377C22×C4—282no—
378C22×C4—282no—
379C22×C4—282no—
380C22×C4D4×D711yescharacteristic
381C22×C4D4×D711yescharacteristic
382C22×C4C23×D711yescharacteristic
383Q16—48no—
384SD16—148no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—72no—
389C2×C8—141no—
390C2×C8—141no—
391C2×C8—141no—
392C2×C8—141no—
393C2×C8—141no—
394C4⋊C4—24no—
395C4⋊C4—21no—
396C4⋊C4—42no—
397C4⋊C4—42no—
398C4⋊C4—142no—
399C4⋊C4—142no—
400C4⋊C4—142no—
401C4⋊C4—141no—
402C4⋊C4—142no—
403C4⋊C4—141no—
404C4⋊C4—284no—
405C4⋊C4—282no—
406C4⋊C4—561no—
407C4⋊C4—562no—
408C4⋊C4C2×C22⋊D712yes—
409C22⋊C4—284no—
410C22⋊C4—284no—
411C22⋊C4—282no—
412C42—24no—
413C42—142no—
414C42—142no—
415C42—284no—
416C42#115912yes—
417C42C2×C22⋊D712yes—
418C2×C7#241611yescharacteristic
419C2×C7C2×#46411yescharacteristic
420C2×C7#304611yescharacteristic
421C2×C7#327611yescharacteristic
422C2×C7#328411yescharacteristic
423C2×C7#336411yescharacteristic
424C2×C7#336911yescharacteristic
425D7—82no—
426C23—142no—
427C23—281no—
428C23—281no—
429C23—281no—
430C23—281no—
431C23—281no—
432C23—281no—
433C23C2×D4×D711yescharacteristic
434Q8—22no—
435Q8—22no—
436Q8—22no—
437Q8—42no—
438Q8—42no—
439Q8—42no—
440Q8—42no—
441Q8#650114yes—
442D4—142no—
443D4—142no—
444D4—281no—
445D4—281no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—142no—
458C2×C4—142no—
459C2×C4—142no—
460C2×C4—142no—
461C2×C4—142no—
462C2×C4—142no—
463C2×C4—281no—
464C2×C4—282no—
465C2×C4—281no—
466C2×C4—282no—
467C2×C4—281no—
468C2×C4—282no—
469C2×C4—564no—
470C2×C4#648112yes—
471C2×C4#648212yes—
472C2×C4#650212yes—
473C2×C4#650212yes—
474C2×C4C2×D4×D711yescharacteristic
475C2×C4C2×#115911yescharacteristic
476C2×C4C2×#115911yescharacteristic
477C2×C4#655311yescharacteristic
478C2×C4#655411yescharacteristic
479C2×C4C22×C22⋊D711yescharacteristic
480C8—42no—
481C8—142no—
482C8—281no—
483C7#2472911yescharacteristic, complemented, Sylow
484C22—282no—
485C22—282no—
486C22—282no—
487C22—561no—
488C22—561no—
489C22—561no—
490C22—561no—
491C22#9028911yescharacteristic
492C22#9030011yescharacteristic
493C22C2×#648111yescharacteristic
494C22C2×#648211yescharacteristic
495C22#9046911yescharacteristic
496C22#9047011yescharacteristic
497C22C2×#650211yescharacteristic
498C4—22no—
499C4—24no—
500C4—42no—
501C4—82no—
502C4—282no—
503C4—282no—
504C4—562no—
505C4—561no—
506C4#8995714yescomplemented
507C4#9030211yescharacteristic
508C4#9030911yescharacteristic
509C4C2×#650111yescharacteristic
510C4#9052411yescharacteristic
511C2—562no—
512C2#1173790811yescharacteristic
513C2#1173790911yescharacteristic
514C2#1173794611yescharacteristic
515C2#1173794711yescharacteristic
516C2#1174015011yescharacteristic
517C2C2×#8995711yescharacteristic
518C2#1174141611yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#462C2
socleC23×C7C22×D4
prime radicalC22×D28C23
hypercenterC2×#462D7
hypocenterC7#24729
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
4. Q8×C4⋊Dic7C2semidirect
6. #11729819C2semidirect
7. #11729539C2semidirect
9. #11728222C2semidirect
10. #11728015C2semidirect
102. C2×#462D7semidirect
342. C4×C7#464semidirect
483. C7#24729semidirect
506. C4#89957semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4622
C2×#899572
#117406852
Q8×C4⋊Dic72
C2×C4×#11432
#117298192
#117295392
#117282332
#117282222
#117280152
#117279992
#247297