Finite Group Databasebeta

← #13282921

Subgroups — #13282921

Order 1792.

1310 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#391C211yesmaximal, characteristic
2C2×#90002C211yesmaximal, characteristic
3C2×#90002C211yesmaximal, characteristic
4#11729321C212yesmaximal
5#11729290C212yesmaximal
6#11727169C212yesmaximal
7#11727165C212yesmaximal
8#11727160C212yesmaximal
9#11727157C212yesmaximal
10C23×C7×Q8C2211yescharacteristic
11C22×C7×C4⋊C4C2211yescharacteristic
12C22×C42×C7C2211yescharacteristic
13C22×C4⋊Dic7C2211yescharacteristic
14C22×C4⋊Dic7C2211yescharacteristic
15C22×Dic7⋊C4C2212yes—
16C22×C4×Dic7C2211yescharacteristic
17C22×C4×Dic7C2211yescharacteristic
18C7×#391—24no—
19C2×C7×#95C2212yes—
20C2×C7×#95C2212yes—
21#90002—24no—
22#90002C418yescomplemented
23C2×C7⋊#95C2212yes—
24C2×C7⋊#95C2212yes—
25C2×C7⋊#95C2212yes—
26C2×C7⋊#95C2212yes—
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34#14501—71nomaximal, Sylow
35C22×C7×Q8—41no—
36C22×C7×Q8—41no—
37C22×C7×Q8—41no—
38C22×C7×Q8—41no—
39C22×C7×Q8C2×C414yes—
40C22×C7×Q8D414yes—
41C22×C7×Q8Q814yes—
42C23×C4×C7C2312yes—
43C23×C4×C7C2312yes—
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2311yescharacteristic
47C23×Dic7C2312yes—
48C23×Dic7C2312yes—
49C23×Dic7C2312yes—
50C23×Dic7C2312yes—
51C2×C7×C4⋊C4—22no—
52C2×C7×C4⋊C4—41no—
53C2×C7×C4⋊C4—41no—
54C2×C42×C7—22no—
55C2×C42×C7—41no—
56C2×C42×C7—41no—
57C2×C4⋊Dic7—22no—
58C2×C4⋊Dic7—41no—
59C2×C4⋊Dic7—41no—
60C2×C4⋊Dic7—41no—
61C2×C4⋊Dic7—41no—
62C2×C4⋊Dic7C2×C414yes—
63C2×Dic7⋊C4—24no—
64C2×Dic7⋊C4—24no—
65C2×Dic7⋊C4—42no—
66C2×C4×Dic7—22no—
67C2×C4×Dic7—41no—
68C2×C4×Dic7—41no—
69C2×C4×Dic7—41no—
70C2×C4×Dic7—41no—
71C2×C4×Dic7C2×C414yes—
72C7×#95—24no—
73C7×#95—24no—
74C7⋊#95—24no—
75C7⋊#95—24no—
76C7⋊#95—24no—
77C7⋊#95—24no—
78C7⋊#95—24no—
79C7⋊#95—24no—
80C7⋊#95—42no—
81C7⋊#95—42no—
82C7⋊#95—42no—
83C7⋊#95C2×C418yes—
84C7⋊#95C2×C418yes—
85C2×#391—71no—
86C2×#391—71no—
87C2×#391D711yescharacteristic
88#1442—72no—
89#1442—72no—
90#1441—72no—
91#1436—72no—
92#1436—72no—
93#1434—72no—
94C24×C7C2411yescharacteristic
95C2×C7×Q8—44no—
96C2×C7×Q8—44no—
97C2×C7×Q8—44no—
98C2×C7×Q8—44no—
99C2×C7×Q8—44no—
100C2×C7×Q8—44no—
101C2×C7×Q8C4⋊C4116yescomplemented
102C22×C4×C7—21no—
103C22×C4×C7—21no—
104C22×C4×C7—21no—
105C22×C4×C7—21no—
106C22×C4×C7—21no—
107C22×C4×C7—21no—
108C22×C4×C7—21no—
109C22×C4×C7—21no—
110C22×C4×C7—21no—
111C22×C4×C7—21no—
112C22×C4×C7—21no—
113C22×C4×C7—21no—
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×C7—22no—
122C22×C4×C7—22no—
123C22×C4×C7—22no—
124C22×C4×C7—22no—
125C22×C4×C7—22no—
126C22×C4×C7—22no—
127C22×C4×C7C22×C412yes—
128C22×C4×C7C22×C412yes—
129C22×C4×C7C22×C412yes—
130C22×C4×C7C2×D412yes—
131C22×C4×C7C2×D412yes—
132C22×C4×C7C2×D412yes—
133C22×C4×C7C2×Q812yes—
134C22×C4×C7C2×Q812yes—
135C22×C4×C7C2×Q812yes—
136C22×C4×C7#4114yes—
137C22×Dic7—22no—
138C22×Dic7—22no—
139C22×Dic7—22no—
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×Dic7—22no—
159C22×Dic7—22no—
160C22×Dic7—22no—
161C22×Dic7—22no—
162C22×Dic7C22×C414yes—
163C22×Dic7C22×C414yes—
164C22×Dic7#4114yes—
165C7×C4⋊C4—44no—
166C42×C7—44no—
167C4⋊Dic7—44no—
168C4⋊Dic7—44no—
169Dic7⋊C4—48no—
170C4×Dic7—44no—
171C4×Dic7—44no—
172C23×Q8C2×D711yescharacteristic
173C22×C4⋊C4—71no—
174C22×C4⋊C4—72no—
175C22×C4⋊C4—71no—
176C22×C4⋊C4C2×D711yescharacteristic
177C22×C42—71no—
178C22×C42—71no—
179C22×C42C2×D711yescharacteristic
180#391—24no—
181#391—78no—
182#391—144no—
183C2×#95—72no—
184C2×#95—72no—
185C2×#95—72no—
186C2×#95—72no—
187C2×#95—72no—
188C2×#95—72no—
189C2×#95—72no—
190C2×#95—72no—
191C2×#95—72no—
192C2×#95—72no—
193C2×#95—72no—
194C2×#95C2×D712yes—
195C2×#95C2×D712yes—
196C23×C7C23×C411yescharacteristic
197C23×C7C22×D411yescharacteristic
198C23×C7C22×Q811yescharacteristic
199C23×C7C2×#4112yes—
200C23×C7C2×#4112yes—
201C23×C7H(5,𝔽2)11yescharacteristic
202C23×C7H(5,𝔽2)11yescharacteristic
203C23×C7H(5,𝔽2)11yescharacteristic
204C23×C7H(5,𝔽2)11yescharacteristic
205C23×C72−1+412yes—
206C23×C72−1+412yes—
207C7×Q8—416no—
208C2×C4×C7—22no—
209C2×C4×C7—22no—
210C2×C4×C7—22no—
211C2×C4×C7—22no—
212C2×C4×C7—22no—
213C2×C4×C7—22no—
214C2×C4×C7—22no—
215C2×C4×C7—22no—
216C2×C4×C7—22no—
217C2×C4×C7—22no—
218C2×C4×C7—22no—
219C2×C4×C7—22no—
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—24no—
227C2×C4×C7—24no—
228C2×C4×C7—24no—
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×C7C2×C4⋊C414yes—
241C2×C4×C7C2×C4⋊C414yes—
242C2×C4×C7C2×C4⋊C414yes—
243C2×Dic7—24no—
244C2×Dic7—24no—
245C2×Dic7—24no—
246C2×Dic7—24no—
247C2×Dic7—24no—
248C2×Dic7—24no—
249C2×Dic7—24no—
250C2×Dic7—24no—
251C2×Dic7—24no—
252C2×Dic7—42no—
253C2×Dic7—42no—
254C2×Dic7—42no—
255C2×Dic7—42no—
256C2×Dic7—42no—
257C2×Dic7—42no—
258C2×Dic7—42no—
259C2×Dic7—42no—
260C2×Dic7—42no—
261C2×Dic7—42no—
262C2×Dic7—42no—
263C2×Dic7—42no—
264C2×Dic7—42no—
265C2×Dic7—42no—
266C2×Dic7—42no—
267C2×Dic7—42no—
268C2×Dic7—42no—
269C2×Dic7—42no—
270C2×Dic7—42no—
271C22×Q8—41no—
272C22×Q8—41no—
273C22×Q8—41no—
274C22×Q8—41no—
275C22×Q8Dic1414yes—
276C22×Q8C4×D714yes—
277C22×Q8C22⋊D714yes—
278C23×C4—72no—
279C23×C4—72no—
280C23×C4—72no—
281C23×C4—72no—
282C23×C4C22×D712yes—
283C23×C4C22×D712yes—
284C23×C4C22×D711yescharacteristic
285C23×C4C22×D711yescharacteristic
286C23×C4C22×D711yescharacteristic
287C2×C4⋊C4—22no—
288C2×C4⋊C4—41no—
289C2×C4⋊C4—41no—
290C2×C4⋊C4—74no—
291C2×C4⋊C4—144no—
292C2×C4⋊C4—144no—
293C2×C4⋊C4—142no—
294C2×C4⋊C4—282no—
295C2×C4⋊C4—281no—
296C2×C4⋊C4—281no—
297C2×C4⋊C4—281no—
298C2×C4⋊C4—281no—
299C2×C42—22no—
300C2×C42—41no—
301C2×C42—41no—
302C2×C42—74no—
303C2×C42—142no—
304C2×C42—281no—
305C2×C42—281no—
306C2×C42—281no—
307C2×C42—281no—
308#95—24no—
309#95—24no—
310#95—78no—
311#95—78no—
312#95—144no—
313#95—144no—
314#95—144no—
315#95—144no—
316#95—144no—
317#95—144no—
318#95—282no—
319#95—282no—
320#95—282no—
321C22×C7C22×C4⋊C411yescharacteristic
322C22×C7C4×#4112yes—
323C22×C7#51811yescharacteristic
324C22×C7#51811yescharacteristic
325C22×C7#51912yes—
326C22×C7#53411yescharacteristic
327C22×C7#53411yescharacteristic
328C22×C7#53912yes—
329C22×C7#53912yes—
330C22×C7#54212yes—
331C22×C7#54212yes—
332C22×C7#54311yescharacteristic
333C22×C7#54311yescharacteristic
334C22×C7#54812yes—
335C22×C7#54812yes—
336C22×C7#55112yes—
337C22×C7#55511yescharacteristic
338C22×C7#55511yescharacteristic
339C22×C7#55712yes—
340C22×C7#55712yes—
341C22×C7#56311yescharacteristic
342C22×C7#56312yes—
343C22×C7#56311yescharacteristic
344C4×C7—24no—
345C4×C7—24no—
346C4×C7—24no—
347C4×C7—44no—
348C4×C7—82no—
349Dic7—44no—
350Dic7—44no—
351Dic7—44no—
352Dic7—82no—
353C24C23×D711yescharacteristic
354C2×Q8—44no—
355C2×Q8—44no—
356C2×Q8—44no—
357C2×Q8—44no—
358C2×Q8—44no—
359C2×Q8—44no—
360C2×Q8Dic7⋊C4116yescomplemented
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—74no—
387C22×C4—74no—
388C22×C4—74no—
389C22×C4—142no—
390C22×C4—142no—
391C22×C4—142no—
392C22×C4—142no—
393C22×C4—142no—
394C22×C4—142no—
395C22×C4—142no—
396C22×C4—142no—
397C22×C4—142no—
398C22×C4—142no—
399C22×C4—142no—
400C22×C4—142no—
401C22×C4—142no—
402C22×C4—142no—
403C22×C4—142no—
404C22×C4—142no—
405C22×C4—142no—
406C22×C4—142no—
407C22×C4—142no—
408C22×C4—142no—
409C22×C4—142no—
410C22×C4—142no—
411C22×C4—142no—
412C22×C4—142no—
413C22×C4—142no—
414C22×C4C2×Dic1412yes—
415C22×C4C2×Dic1412yes—
416C22×C4C2×Dic1412yes—
417C22×C4C2×C4×D712yes—
418C22×C4C2×C4×D712yes—
419C22×C4C2×C4×D712yes—
420C22×C4#116114yes—
421C22×C4C2×C22⋊D712yes—
422C22×C4C2×C22⋊D712yes—
423C22×C4C2×C22⋊D712yes—
424C4⋊C4—44no—
425C4⋊C4—284no—
426C4⋊C4—288no—
427C4⋊C4—284no—
428C42—44no—
429C42—284no—
430C42—284no—
431C2×C7#231511yescharacteristic
432C2×C7#233212yes—
433C2×C7#235112yes—
434C2×C7#237211yescharacteristic
435C2×C7#238111yescharacteristic
436C2×C7#272812yes—
437C2×C7#273111yescharacteristic
438C2×C7#273111yescharacteristic
439C2×C7#279912yes—
440C2×C7#280911yescharacteristic
441C2×C7#280911yescharacteristic
442C23C22×Dic1411yescharacteristic
443C23C22×C4×D711yescharacteristic
444C23#654811yescharacteristic
445C23#654811yescharacteristic
446C23#654811yescharacteristic
447C23#654811yescharacteristic
448C23C2×#116112yes—
449C23#655112yes—
450C23D7×#4112yes—
451C23#655412yes—
452C23C22×C22⋊D711yescharacteristic
453Q8—416no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
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—144no—
487C2×C4—144no—
488C2×C4—144no—
489C2×C4—144no—
490C2×C4—144no—
491C2×C4—144no—
492C2×C4—144no—
493C2×C4—144no—
494C2×C4—144no—
495C2×C4—282no—
496C2×C4—282no—
497C2×C4—282no—
498C2×C4—282no—
499C2×C4—282no—
500C2×C4—282no—
501C2×C4—282no—
502C2×C4—282no—
503C2×C4—282no—
504C2×C4—282no—
505C2×C4—282no—
506C2×C4—282no—
507C2×C4—282no—
508C2×C4—282no—
509C2×C4—282no—
510C2×C4—282no—
511C2×C4—282no—
512C2×C4—282no—
513C2×C4—282no—
514C2×C4C2×Dic7⋊C414yes—
515C2×C4C2×Dic7⋊C414yes—
516C2×C4C2×Dic7⋊C414yes—
517C7#1450111yescharacteristic, complemented, Sylow
518C22#9017411yescharacteristic
519C22#9017411yescharacteristic
520C22#9017711yescharacteristic
521C22#9017711yescharacteristic
522C22#9026012yes—
523C22#9026112yes—
524C22#9026312yes—
525C22C4×#116112yes—
526C22#9032812yes—
527C22#9032912yes—
528C22#9033612yes—
529C22#9033712yes—
530C22#9036012yes—
531C22#9036111yescharacteristic
532C22#9036311yescharacteristic
533C22#9042412yes—
534C22#9042511yescharacteristic
535C22#9042611yescharacteristic
536C22C22×Dic7⋊C411yescharacteristic
537C22#9049511yescharacteristic
538C22#9049511yescharacteristic
539C22#9050812yes—
540C22#9052212yes—
541C4—24no—
542C4—24no—
543C4—24no—
544C4—44no—
545C4—82no—
546C4—284no—
547C4—284no—
548C4—284no—
549C4—562no—
550C2#1173393212yes—
551C2#1173394011yescharacteristic
552C2#1173394211yescharacteristic
553C2#1173404012yes—
554C2#1173404711yescharacteristic
555C2#1173404811yescharacteristic
556C2#1173954011yescharacteristic
557C2#1173990612yes—
558C2#1174027612yes—
559C2#1174043511yescharacteristic
560C2#1174069411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#391C2
socle, prime radical, cosocleC24×C7C24
hypercenterC2×#391D7
hypocenterC7#14501
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
22. #90002C4semidirect
101. C2×C7×Q8C4⋊C4semidirect
360. C2×Q8Dic7⋊C4semidirect
517. C7#14501semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3912
C2×#900022
#117293212
#117292902
#117271692
#117271652
#117271602
#117271572
#145017