Finite Group Databasebeta

← #13280792

Subgroups — #13280792

Order 1792.

1318 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89701C211yesmaximal, characteristic
2C2×C4×Dic7⋊C4C211yesmaximal, characteristic
3C2×#89428C211yesmaximal, characteristic
4C7×#1434C211yesmaximal, characteristic
5#11727178C211yesmaximal, characteristic
6#11727176C212yesmaximal
7#11727167C212yesmaximal
8#11727166C211yesmaximal, characteristic
9#11727164C211yesmaximal, characteristic
10#11727161C212yesmaximal
11#11727156C212yesmaximal
12C23×Dic14C2211yescharacteristic
13C22×C42×C7C2211yescharacteristic
14C22×C4⋊Dic7C2211yescharacteristic
15C22×C4⋊Dic7C2212yes—
16C22×Dic7⋊C4C2211yescharacteristic
17C22×Dic7⋊C4C2211yescharacteristic
18C22×C4×Dic7C2211yescharacteristic
19C22×C4×Dic7C2211yescharacteristic
20C2×C7×#95C2212yes—
21C2×C7×#95C2211yescharacteristic
22C2×C7×#95C2212yes—
23C2×C7×#95C2211yescharacteristic
24C2×C7⋊#95C2212yes—
25C2×C7⋊#95C2212yes—
26C2×C7⋊#95C2212yes—
27C2×C7⋊#95C2211yescharacteristic
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2211yescharacteristic
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C4×Dic7⋊C4—24no—
36#89701—24no—
37#89428C418yescomplemented
38#14320—71nomaximal, Sylow
39C23×C4×C7C2312yes—
40C23×C4×C7C2312yes—
41C23×C4×C7C2311yescharacteristic
42C23×C4×C7C2311yescharacteristic
43C23×C4×C7C2311yescharacteristic
44C23×Dic7C2312yes—
45C23×Dic7C2311yescharacteristic
46C23×Dic7C2312yes—
47C23×Dic7C2311yescharacteristic
48C23×Dic7C2311yescharacteristic
49C23×Dic7C2311yescharacteristic
50C22×Dic14—22no—
51C22×Dic14—22no—
52C22×Dic14—42no—
53C22×Dic14—42no—
54C22×Dic14C2×C414yes—
55C2×C42×C7—42no—
56C2×C42×C7D414yes—
57C2×C4⋊Dic7—22no—
58C2×C4⋊Dic7—42no—
59C2×C4⋊Dic7—42no—
60C2×C4⋊Dic7—42no—
61C2×C4⋊Dic7C2×C418yes—
62C2×Dic7⋊C4—22no—
63C2×Dic7⋊C4—22no—
64C2×Dic7⋊C4—22no—
65C2×Dic7⋊C4—22no—
66C2×Dic7⋊C4—22no—
67C2×Dic7⋊C4C2×C414yes—
68C2×C4×Dic7—22no—
69C2×C4×Dic7—22no—
70C2×C4×Dic7—22no—
71C2×C4×Dic7—42no—
72C2×C4×Dic7Q814yescomplemented
73C7×#95—22no—
74C7×#95—24no—
75C7×#95—42no—
76C7×#95C2×C414yes—
77C7⋊#95—24no—
78C7⋊#95—24no—
79C7⋊#95—22no—
80C7⋊#95—22no—
81C7⋊#95—24no—
82C7⋊#95—24no—
83C7⋊#95—42no—
84C7⋊#95—42no—
85C7⋊#95—42no—
86C7⋊#95—42no—
87C7⋊#95C2×C418yes—
88C2×#395—71no—
89C2×#391—71no—
90C2×C4×C4⋊C4—71no—
91#1446—71no—
92#1445—72no—
93#1442—71no—
94#1442—72no—
95#1441—71no—
96#1436—72no—
97#1434—72no—
98#1434D711yescharacteristic
99C24×C7C2411yescharacteristic
100C22×C4×C7—22no—
101C22×C4×C7—22no—
102C22×C4×C7—22no—
103C22×C4×C7—22no—
104C22×C4×C7—22no—
105C22×C4×C7—22no—
106C22×C4×C7—21no—
107C22×C4×C7—21no—
108C22×C4×C7—22no—
109C22×C4×C7—22no—
110C22×C4×C7—22no—
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—22no—
118C22×C4×C7—22no—
119C22×C4×C7—22no—
120C22×C4×C7—22no—
121C22×C4×C7C22×C414yes—
122C22×C4×C7C22×C412yes—
123C22×C4×C7C2×D412yes—
124C22×C4×C7C2×D412yes—
125C22×C4×C7C2×D412yes—
126C22×C4×C7C2×Q812yes—
127C22×C4×C7#4112yes—
128C22×C4×C7#4112yes—
129C22×Dic7—21no—
130C22×Dic7—21no—
131C22×Dic7—21no—
132C22×Dic7—21no—
133C22×Dic7—21no—
134C22×Dic7—22no—
135C22×Dic7—21no—
136C22×Dic7—21no—
137C22×Dic7—21no—
138C22×Dic7—21no—
139C22×Dic7—21no—
140C22×Dic7—22no—
141C22×Dic7—22no—
142C22×Dic7—22no—
143C22×Dic7—22no—
144C22×Dic7—22no—
145C22×Dic7—22no—
146C22×Dic7—22no—
147C22×Dic7—22no—
148C22×Dic7—22no—
149C22×Dic7—22no—
150C22×Dic7—22no—
151C22×Dic7—22no—
152C22×Dic7—22no—
153C22×Dic7—22no—
154C22×Dic7—22no—
155C22×Dic7—22no—
156C22×Dic7—22no—
157C22×Dic7—22no—
158C22×Dic7C22×C414yes—
159C22×Dic7C22×C412yes—
160C22×Dic7C22×C412yes—
161C22×Dic7C2×Q812yes—
162C22×Dic7C2×Q812yes—
163C22×Dic7#4112yes—
164C22×Dic7#4112yes—
165C2×Dic14—28no—
166C2×Dic14—48no—
167C2×Dic14—44no—
168C2×Dic14—44no—
169C2×Dic14—48no—
170C42×C7—44no—
171C4⋊Dic7—48no—
172C4⋊Dic7—44no—
173Dic7⋊C4—28no—
174Dic7⋊C4—28no—
175C4×Dic7—28no—
176C4×Dic7—44no—
177C23×Q8—71no—
178C22×C4⋊C4—71no—
179C22×C4⋊C4—72no—
180C22×C4⋊C4—71no—
181C22×C4⋊C4—71no—
182C22×C42—71no—
183C22×C42—71no—
184C22×C42C2×D711yescharacteristic
185#395—78no—
186#391—144no—
187C4×C4⋊C4—144no—
188C2×#95—72no—
189C2×#95—72no—
190C2×#95—72no—
191C2×#95—72no—
192C2×#95—72no—
193C2×#95—71no—
194C2×#95—71no—
195C2×#95—72no—
196C2×#95—72no—
197C2×#95—72no—
198C2×#95—72no—
199C2×#95C2×D712yes—
200C2×#95C2×D711yescharacteristic
201C2×#95C2×D712yes—
202C2×#95C2×D711yescharacteristic
203C23×C7C23×C411yescharacteristic
204C23×C7C22×D411yescharacteristic
205C23×C7C22×Q811yescharacteristic
206C23×C7C2×#4111yescharacteristic
207C23×C7C2×#4111yescharacteristic
208C23×C7C2×#4111yescharacteristic
209C23×C7C2×#4111yescharacteristic
210C23×C7H(5,𝔽2)12yes—
211C23×C7H(5,𝔽2)12yes—
212C23×C72−1+412yes—
213C23×C72−1+412yes—
214C2×C4×C7—24no—
215C2×C4×C7—22no—
216C2×C4×C7—22no—
217C2×C4×C7—22no—
218C2×C4×C7—22no—
219C2×C4×C7—24no—
220C2×C4×C7—24no—
221C2×C4×C7—24no—
222C2×C4×C7—24no—
223C2×C4×C7—24no—
224C2×C4×C7—24no—
225C2×C4×C7—22no—
226C2×C4×C7—22no—
227C2×C4×C7—22no—
228C2×C4×C7—42no—
229C2×C4×C7—42no—
230C2×C4×C7—42no—
231C2×C4×C7—42no—
232C2×C4×C7—42no—
233C2×C4×C7—42no—
234C2×C4×C7—42no—
235C2×C4×C7—42no—
236C2×C4×C7—42no—
237C2×C4×C7—42no—
238C2×C4×C7—42no—
239C2×C4×C7—42no—
240C2×C4×C7—42no—
241C2×C4×C7C4×D414yes—
242C2×C4×C7C22⋊Q814yes—
243C2×Dic7—22no—
244C2×Dic7—22no—
245C2×Dic7—22no—
246C2×Dic7—22no—
247C2×Dic7—22no—
248C2×Dic7—22no—
249C2×Dic7—22no—
250C2×Dic7—24no—
251C2×Dic7—24no—
252C2×Dic7—24no—
253C2×Dic7—24no—
254C2×Dic7—22no—
255C2×Dic7—22no—
256C2×Dic7—24no—
257C2×Dic7—24no—
258C2×Dic7—41no—
259C2×Dic7—41no—
260C2×Dic7—42no—
261C2×Dic7—42no—
262C2×Dic7—41no—
263C2×Dic7—41no—
264C2×Dic7—41no—
265C2×Dic7—41no—
266C2×Dic7—42no—
267C2×Dic7—42no—
268C2×Dic7—42no—
269C2×Dic7—42no—
270C2×Dic7—42no—
271C2×Dic7—42no—
272C2×Dic7—42no—
273C2×Dic7—42no—
274C2×Dic7—42no—
275C2×Dic7—42no—
276C2×Dic7—42no—
277C2×Dic7—42no—
278C2×Dic7C4×Q814yes—
279Dic14—416no—
280C22×Q8—74no—
281C22×Q8—142no—
282C22×Q8—142no—
283C22×Q8—282no—
284C22×Q8—282no—
285C23×C4—71no—
286C23×C4—71no—
287C23×C4—72no—
288C23×C4—71no—
289C23×C4—71no—
290C23×C4—72no—
291C23×C4C22×D712yes—
292C23×C4C22×D712yes—
293C23×C4C22×D711yescharacteristic
294C23×C4C22×D711yescharacteristic
295C23×C4C22×D711yescharacteristic
296C2×C4⋊C4—74no—
297C2×C4⋊C4—78no—
298C2×C4⋊C4—142no—
299C2×C4⋊C4—142no—
300C2×C4⋊C4—142no—
301C2×C4⋊C4—142no—
302C2×C4⋊C4—142no—
303C2×C4⋊C4—142no—
304C2×C4⋊C4—282no—
305C2×C4⋊C4—282no—
306C2×C4⋊C4—282no—
307C2×C42—42no—
308C2×C42—74no—
309C2×C42—142no—
310C2×C42—142no—
311C2×C42—142no—
312C2×C42—282no—
313C2×C42D2814yes—
314#95—22no—
315#95—24no—
316#95—42no—
317#95—78no—
318#95—144no—
319#95—144no—
320#95—142no—
321#95—142no—
322#95—144no—
323#95—144no—
324#95—282no—
325#95—282no—
326#95—282no—
327#95—282no—
328#95C4×D714yes—
329C22×C7C2×C4×D411yescharacteristic
330C22×C7C2×C4×Q811yescharacteristic
331C22×C7C4×#4111yescharacteristic
332C22×C7#51812yes—
333C22×C7#51912yes—
334C22×C7C2×C22⋊Q811yescharacteristic
335C22×C7#52511yescharacteristic
336C22×C7#52911yescharacteristic
337C22×C7#53311yescharacteristic
338C22×C7#53411yescharacteristic
339C22×C7#53511yescharacteristic
340C22×C7#53611yescharacteristic
341C22×C7#53611yescharacteristic
342C22×C7#53812yes—
343C22×C7#53912yes—
344C22×C7#53912yes—
345C22×C7#54112yes—
346C22×C7#54212yes—
347C22×C7#54212yes—
348C22×C7#54212yes—
349C22×C7#54212yes—
350C22×C7#54412yes—
351C22×C7#54412yes—
352C4×C7—24no—
353C4×C7—24no—
354C4×C7—44no—
355C4×C7—42no—
356C4×C7—82no—
357Dic7—24no—
358Dic7—44no—
359Dic7—42no—
360Dic7—42no—
361Dic7—42no—
362Dic7—82no—
363C24C23×D711yescharacteristic
364C2×Q8—148no—
365C2×Q8—288no—
366C2×Q8—284no—
367C2×Q8—284no—
368C2×Q8—288no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—72no—
391C22×C4—72no—
392C22×C4—72no—
393C22×C4—74no—
394C22×C4—72no—
395C22×C4—72no—
396C22×C4—72no—
397C22×C4—141no—
398C22×C4—141no—
399C22×C4—141no—
400C22×C4—141no—
401C22×C4—141no—
402C22×C4—142no—
403C22×C4—141no—
404C22×C4—141no—
405C22×C4—141no—
406C22×C4—142no—
407C22×C4—141no—
408C22×C4—142no—
409C22×C4—142no—
410C22×C4—142no—
411C22×C4—142no—
412C22×C4—141no—
413C22×C4—142no—
414C22×C4—142no—
415C22×C4—142no—
416C22×C4—142no—
417C22×C4—142no—
418C22×C4—142no—
419C22×C4—142no—
420C22×C4—142no—
421C22×C4—142no—
422C22×C4—142no—
423C22×C4—142no—
424C22×C4—142no—
425C22×C4—142no—
426C22×C4C2×C4×D714yes—
427C22×C4C2×C4×D712yes—
428C22×C4C2×D2812yes—
429C22×C4C2×D2812yes—
430C22×C4C2×D2812yes—
431C22×C4#115712yes—
432C22×C4#115912yes—
433C22×C4Q8×D712yes—
434C4⋊C4—148no—
435C4⋊C4—148no—
436C4⋊C4—288no—
437C4⋊C4—284no—
438C42—44no—
439C42—148no—
440C42—284no—
441C2×C7C4×C22⋊Q811yescharacteristic
442C2×C7#232111yescharacteristic
443C2×C7#232711yescharacteristic
444C2×C7#233112yes—
445C2×C7#233212yes—
446C2×C7#262711yescharacteristic
447C2×C7#262811yescharacteristic
448C2×C7#263211yescharacteristic
449C2×C7#263811yescharacteristic
450C2×C7#265012yes—
451C2×C7#266612yes—
452C23C22×C4×D711yescharacteristic
453C23C22×D2811yescharacteristic
454C23C2×#115711yescharacteristic
455C23C2×#115911yescharacteristic
456C23#654812yes—
457C23C2×Q8×D711yescharacteristic
458C23D7×#4111yescharacteristic
459C23D7×#4111yescharacteristic
460C23#655312yes—
461C23#655412yes—
462C23#655412yes—
463Q8—2816no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—74no—
492C2×C4—142no—
493C2×C4—142no—
494C2×C4—142no—
495C2×C4—142no—
496C2×C4—142no—
497C2×C4—142no—
498C2×C4—144no—
499C2×C4—142no—
500C2×C4—144no—
501C2×C4—142no—
502C2×C4—142no—
503C2×C4—144no—
504C2×C4—144no—
505C2×C4—144no—
506C2×C4—144no—
507C2×C4—282no—
508C2×C4—281no—
509C2×C4—281no—
510C2×C4—282no—
511C2×C4—281no—
512C2×C4—281no—
513C2×C4—282no—
514C2×C4—281no—
515C2×C4—281no—
516C2×C4—282no—
517C2×C4—282no—
518C2×C4—282no—
519C2×C4—282no—
520C2×C4—282no—
521C2×C4—282no—
522C2×C4—282no—
523C2×C4—282no—
524C2×C4—282no—
525C2×C4—282no—
526C2×C4—282no—
527C2×C4C4×D2814yes—
528C2×C4#646014yes—
529C7#1432011yescharacteristic, complemented, Sylow
530C22C2×C4×D2811yescharacteristic
531C22#9018411yescharacteristic
532C22C2×#646011yescharacteristic
533C22#9020712yes—
534C22#9020912yes—
535C22#9021511yescharacteristic
536C22#9021611yescharacteristic
537C22#9021711yescharacteristic
538C22#9021711yescharacteristic
539C22C4×#115911yescharacteristic
540C22#9023612yes—
541C22#9024811yescharacteristic
542C22#9025112yes—
543C22C4×Q8×D711yescharacteristic
544C22#9026911yescharacteristic
545C22#9029312yes—
546C22#9031412yes—
547C22#9035112yes—
548C22#9035312yes—
549C22#9037312yes—
550C22#9038012yes—
551C22#9040112yes—
552C22#9040112yes—
553C4—24no—
554C4—24no—
555C4—42no—
556C4—44no—
557C4—82no—
558C4—144no—
559C4—284no—
560C4—282no—
561C4—282no—
562C4—282no—
563C4—562no—
564C2#1173083311yescharacteristic
565C2#1173101411yescharacteristic
566C2C4×#646011yescharacteristic
567C2#1173139811yescharacteristic
568C2#1173153611yescharacteristic
569C2#1173163911yescharacteristic
570C2#1173175511yescharacteristic
571C2#1173239512yes—
572C2#1173259212yes—
573C2#1173290812yes—
574C2#1173310112yes—
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1434C2
socle, prime radical, cosocleC24×C7C24
hypercenter#1434D7
hypocenterC7#14320
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
37. #89428C4semidirect
72. C2×C4×Dic7Q8semidirect
529. C7#14320semidirect

Maximal subgroups

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

subgroupindex
C2×#897012
C2×C4×Dic7⋊C42
C2×#894282
C7×#14342
#117271782
#117271762
#117271672
#117271662
#117271642
#117271612
#117271562
#143207