Finite Group Databasebeta

← #13243458

Subgroups — #13243458

Order 1792.

954 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89498C211yesmaximal, characteristic
2C2×D7×C22⋊C8C211yesmaximal, characteristic
3#11731006C211yesmaximal, characteristic
4C7×#1282C211yesmaximal, characteristic, complemented
5#11725484C211yesmaximal, characteristic, complemented
6#11725483C211yesmaximal, characteristic, complemented
7#11725423C211yesmaximal, characteristic, complemented
8C23×C4×D7C2211yescharacteristic
9C22×#1131—21no—
10C22×C8×D7C412yescomplemented
11C2×#6435—21no—
12C2×C7×C22⋊C8C2211yescharacteristic
13C2×C7×C22⋊C8C2211yescharacteristic
14C4×C7×C22⋊C4C2211yescharacteristic
15C4×C22⋊Dic7C2211yescharacteristic
16C2×C22⋊(C7⋊C8)C2211yescharacteristic
17C2×C22⋊(C7⋊C8)C2211yescharacteristic
18C2×(C2×D7)⋊C8—21no—
19C2×(C2×D7)⋊C8C412yescomplemented
20#89727C412yes—
21#89714C412yes—
22C4×(C2×D7)⋊C4—21no—
23#89498—21no—
24#89498—21no—
25#89498C412yescomplemented
26#89498C412yescomplemented
27D7×C22⋊C8—21no—
28D7×C22⋊C8—21no—
29D7×C22⋊C8—21no—
30D7×C22⋊C8—21no—
31#89439—21no—
32#89436—21no—
33#7927—71nomaximal, Sylow
34C24×D7C2×C411yescharacteristic
35C23×C4×C7C2311yescharacteristic
36C23×Dic7C2×C411yescharacteristic
37C22×C4×D7—44no—
38C22×C4×D7C2×C411yescharacteristic
39C22×C4×D7C2×C411yescharacteristic
40C22×C4×D7C2×C411yescharacteristic
41C22×C4×D7C2×C411yescharacteristic
42C22×C4×D7D411yescharacteristic
43C22×C4×D7D411yescharacteristic
44C22×C4×D7D411yescharacteristic
45C22×C4×D7D411yescharacteristic
46C22×C4×D7D411yescharacteristic
47C22×C4×D7D411yescharacteristic
48C22×C4×D7Q811yescharacteristic
49C22×C4×D7Q811yescharacteristic
50C22×C7×C8—21no—
51C22×C7×C8C2×C412yes—
52C2×C7×C22⋊C4C2×C412yes—
53C2×C42×C7—21no—
54C2×C22⋊Dic7C2×C412yes—
55C2×(C2×D7)⋊C4—22no—
56C2×(C2×D7)⋊C4—22no—
57C2×Dic7⋊C4—22no—
58C2×C4×Dic7—21no—
59C22×C7⋊C8—21no—
60C22×C7⋊C8C2×C412yes—
61C2×#1131—22no—
62C2×#1131—22no—
63C2×#1131—44no—
64C2×C8×D7—22no—
65C2×C8×D7—22no—
66C2×C8×D7—44no—
67#6435—44no—
68C7×C22⋊C8—21no—
69C7×C22⋊C8—21no—
70C7×C22⋊C8—21no—
71C7×C22⋊C8C2×C412yes—
72C7×#95—21no—
73C7⋊#95—21no—
74C7⋊#95—22no—
75C22⋊(C7⋊C8)—21no—
76C22⋊(C7⋊C8)—21no—
77C22⋊(C7⋊C8)—21no—
78C22⋊(C7⋊C8)C2×C412yes—
79(C2×D7)⋊C8—22no—
80(C2×D7)⋊C8—22no—
81(C2×D7)⋊C8—22no—
82(C2×D7)⋊C8—22no—
83C2×#407—71no—
84C22×C22⋊C8—71no—
85#2280—71no—
86#1282—71no—
87#1282—71no—
88#1282—71no—
89#1282D711yescharacteristic, complemented
90C24×C7C22×C411yescharacteristic
91C23×D7—22no—
92C23×D7—22no—
93C23×D7—42no—
94C23×D7—42no—
95C23×D7C4211yescharacteristic
96C23×D7C4211yescharacteristic
97C23×D7C22⋊C411yescharacteristic
98C23×D7C22⋊C411yescharacteristic
99C23×D7C4⋊C411yescharacteristic
100C23×D7C4⋊C411yescharacteristic
101C22×C4×C7—22no—
102C22×C4×C7—42no—
103C22×C4×C7C22×C411yescharacteristic
104C22×C4×C7C22×C411yescharacteristic
105C22×C4×C7C2×D411yescharacteristic
106C22×C4×C7C2×D411yescharacteristic
107C22×C4×C7C2×D411yescharacteristic
108C22×C4×C7C2×Q811yescharacteristic
109C22×Dic7—22no—
110C22×Dic7—42no—
111C22×Dic7C4211yescharacteristic
112C22×Dic7C4211yescharacteristic
113C22×Dic7C22⋊C411yescharacteristic
114C22×Dic7C22⋊C411yescharacteristic
115C22×Dic7C4⋊C411yescharacteristic
116C22×Dic7C4⋊C411yescharacteristic
117C2×C4×D7—24no—
118C2×C4×D7—24no—
119C2×C4×D7—24no—
120C2×C4×D7—42no—
121C2×C4×D7—42no—
122C2×C4×D7—42no—
123C2×C4×D7—42no—
124C2×C4×D7—42no—
125C2×C4×D7—42no—
126C2×C4×D7—42no—
127C2×C4×D7—42no—
128C2×C4×D7—42no—
129C2×C4×D7C22⋊C411yescharacteristic
130C2×C4×D7C22⋊C411yescharacteristic
131C2×C4×D7C22⋊C411yescharacteristic
132C2×C4×D7C22⋊C411yescharacteristic
133C2×C4×D7C22⋊C411yescharacteristic
134C2×C4×D7C22⋊C411yescharacteristic
135C2×C4×D7C22⋊C411yescharacteristic
136C2×C4×D7C22⋊C411yescharacteristic
137C2×C4×D7C4⋊C411yescharacteristic
138C2×C4×D7C4⋊C411yescharacteristic
139C2×C4×D7C4⋊C411yescharacteristic
140C2×C4×D7C4⋊C411yescharacteristic
141C2×C4×D7C4⋊C411yescharacteristic
142C2×C4×D7C4⋊C411yescharacteristic
143C2×C4×D7C4⋊C411yescharacteristic
144C2×C4×D7C4⋊C411yescharacteristic
145C2×C7×C8—22no—
146C2×C7×C8—22no—
147C2×C7×C8—42no—
148C2×C7×C8—42no—
149C7×C22⋊C4—22no—
150C7×C22⋊C4—22no—
151C42×C7—42no—
152C22⋊Dic7—22no—
153C22⋊Dic7—22no—
154(C2×D7)⋊C4—44no—
155(C2×D7)⋊C4—44no—
156Dic7⋊C4—44no—
157C4×Dic7—42no—
158C2×C7⋊C8—22no—
159C2×C7⋊C8—22no—
160C2×C7⋊C8—42no—
161C2×C7⋊C8—42no—
162#1131—44no—
163#1131—44no—
164C8×D7—44no—
165C8×D7—44no—
166C24×C4—71no—
167C22×M16—141no—
168C23×C8—72no—
169C2×#117—141no—
170#407—72no—
171#407—72no—
172#407—141no—
173#407—141no—
174C2×C22⋊C8—71no—
175C2×C22⋊C8—71no—
176C2×C22⋊C8—72no—
177C2×C22⋊C8—141no—
178C2×C22⋊C8—141no—
179C2×C22⋊C8—141no—
180C2×C22⋊C8—141no—
181C2×C22⋊C8—141no—
182C2×C22⋊C8C2×D711yescharacteristic
183C2×C22⋊C8C2×D711yescharacteristic
184#381—141no—
185#380—72no—
186#380—141no—
187#379—72no—
188C4×C22⋊C4—71no—
189C4×C22⋊C4—141no—
190C4×C22⋊C4C2×D711yescharacteristic
191C23×C7—41no—
192C23×C7—41no—
193C23×C7C2×C4211yescharacteristic
194C23×C7C2×C22⋊C411yescharacteristic
195C23×C7C2×C4⋊C411yescharacteristic
196C23×C7#13112yes—
197C23×C7#13112yes—
198C22×D7—21no—
199C22×D7—21no—
200C22×D7—22no—
201C22×D7—22no—
202C22×D7—21no—
203C22×D7—21no—
204C22×D7—22no—
205C22×D7—22no—
206C22×D7—22no—
207C22×D7—22no—
208C22×D7—22no—
209C22×D7—22no—
210C22×D7—22no—
211C22×D7—22no—
212C22×D7—41no—
213C22×D7—41no—
214C22×D7—41no—
215C22×D7—41no—
216C22×D7—41no—
217C22×D7—41no—
218C22×D7—48no—
219C22×D7—48no—
220C22×D7#9511yescharacteristic
221C22×D7#9511yescharacteristic
222C22×D7#9511yescharacteristic
223C22×D7#9511yescharacteristic
224C2×C4×C7—22no—
225C2×C4×C7—22no—
226C2×C4×C7—22no—
227C2×C4×C7—41no—
228C2×C4×C7—41no—
229C2×C4×C7—41no—
230C2×C4×C7—42no—
231C2×C4×C7—42no—
232C2×C4×C7—42no—
233C2×C4×C7C2×C22⋊C411yescharacteristic
234C2×C4×C7C2×C22⋊C411yescharacteristic
235C2×C4×C7C2×C4⋊C411yescharacteristic
236C2×C4×C7C2×C4⋊C411yescharacteristic
237C2×Dic7—22no—
238C2×Dic7—22no—
239C2×Dic7—22no—
240C2×Dic7—41no—
241C2×Dic7—41no—
242C2×Dic7—41no—
243C2×Dic7—42no—
244C2×Dic7—42no—
245C2×Dic7—42no—
246C2×Dic7#9511yescharacteristic
247C2×Dic7#9511yescharacteristic
248C2×Dic7#9511yescharacteristic
249C2×Dic7#9511yescharacteristic
250C4×D7—22no—
251C4×D7—22no—
252C4×D7—22no—
253C4×D7—22no—
254C4×D7—22no—
255C4×D7—22no—
256C4×D7—22no—
257C4×D7—22no—
258C4×D7—22no—
259C4×D7—41no—
260C4×D7—41no—
261C4×D7—41no—
262C4×D7—41no—
263C4×D7—41no—
264C4×D7—41no—
265C4×D7#9914yes—
266C7×C8—42no—
267C7×C8—42no—
268C7⋊C8—42no—
269C7⋊C8—42no—
270C25—71no—
271C23×C4—71no—
272C23×C4—71no—
273C23×C4—71no—
274C23×C4—71no—
275C23×C4—71no—
276C23×C4—71no—
277C23×C4—71no—
278C23×C4—71no—
279C23×C4—71no—
280C23×C4—71no—
281C23×C4—71no—
282C23×C4—71no—
283C23×C4—71no—
284C23×C4—284no—
285C23×C4C22×D711yescharacteristic
286C2×M16—142no—
287C2×M16—142no—
288C2×M16—284no—
289C22×C8—21no—
290C22×C8—72no—
291C22×C8—142no—
292C22×C8—142no—
293C22×C8—141no—
294C22×C8—284no—
295C22×C8C4×D712yes—
296#117—284no—
297C2×C4⋊C4—142no—
298C2×C22⋊C4—72no—
299C2×C22⋊C4—142no—
300C2×C22⋊C4—142no—
301C2×C22⋊C4C4×D712yes—
302C2×C42—21no—
303C2×C42—141no—
304C22⋊C8—21no—
305C22⋊C8—21no—
306C22⋊C8—21no—
307C22⋊C8—72no—
308C22⋊C8—142no—
309C22⋊C8—142no—
310C22⋊C8—142no—
311C22⋊C8—142no—
312C22⋊C8—141no—
313C22⋊C8—141no—
314C22⋊C8—141no—
315C22⋊C8C4×D712yes—
316#95—21no—
317#95—142no—
318#95—141no—
319C22×C7—21no—
320C22×C7—21no—
321C22×C7—21no—
322C22×C7—21no—
323C22×C7—21no—
324C22×C7—21no—
325C22×C7—42no—
326C22×C7—42no—
327C22×C7C2×#9511yescharacteristic
328C22×C7#40511yescharacteristic
329C22×C7#40511yescharacteristic
330C22×C7#40812yes—
331C22×C7#42412yes—
332C2×D7—24no—
333C2×D7—24no—
334C2×D7—21no—
335C2×D7—21no—
336C2×D7—21no—
337C2×D7—21no—
338C2×D7—21no—
339C2×D7—21no—
340C2×D7—21no—
341C2×D7—21no—
342C2×D7—21no—
343C2×D7—21no—
344C2×D7—44no—
345C2×D7—44no—
346C2×D7—44no—
347C2×D7—44no—
348C2×D7—42no—
349C2×D7—42no—
350C2×D7#34212yes—
351C2×D7#34412yes—
352C4×C7—21no—
353C4×C7—21no—
354C4×C7—21no—
355C4×C7—82no—
356C4×C7C2×#9912yes—
357Dic7—21no—
358Dic7—21no—
359Dic7—21no—
360Dic7—82no—
361Dic7#34212yes—
362C24—71no—
363C24—71no—
364C24—71no—
365C24—71no—
366C24—71no—
367C24—71no—
368C24—142no—
369C24—142no—
370C24—282no—
371C24—282no—
372C24C2×C4×D711yescharacteristic
373C22×C4—22no—
374C22×C4—42no—
375C22×C4—71no—
376C22×C4—71no—
377C22×C4—71no—
378C22×C4—71no—
379C22×C4—71no—
380C22×C4—71no—
381C22×C4—71no—
382C22×C4—71no—
383C22×C4—71no—
384C22×C4—71no—
385C22×C4—71no—
386C22×C4—71no—
387C22×C4—71no—
388C22×C4—71no—
389C22×C4—71no—
390C22×C4—71no—
391C22×C4—71no—
392C22×C4—71no—
393C22×C4—71no—
394C22×C4—71no—
395C22×C4—71no—
396C22×C4—71no—
397C22×C4—144no—
398C22×C4—144no—
399C22×C4—144no—
400C22×C4—142no—
401C22×C4—282no—
402C22×C4—282no—
403C22×C4—282no—
404C22×C4—282no—
405C22×C4—282no—
406C22×C4—282no—
407C22×C4—282no—
408C22×C4—282no—
409C22×C4—282no—
410C22×C4—282no—
411C22×C4C2×C4×D711yescharacteristic
412C22×C4C2×C4×D711yescharacteristic
413C22×C4D4×D711yescharacteristic
414C22×C4D4×D711yescharacteristic
415C22×C4D4×D711yescharacteristic
416C22×C4Q8×D711yescharacteristic
417M16—284no—
418M16—284no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—42no—
422C2×C8—42no—
423C2×C8—142no—
424C2×C8—142no—
425C2×C8—284no—
426C2×C8—284no—
427C2×C8—282no—
428C2×C8—282no—
429C4⋊C4—284no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—142no—
433C22⋊C4—142no—
434C22⋊C4—284no—
435C22⋊C4—284no—
436C42—42no—
437C42—282no—
438C2×C7—22no—
439C2×C7—21no—
440C2×C7—21no—
441C2×C7—22no—
442C2×C7#172911yescharacteristic
443C2×C7C2×#34211yescharacteristic
444C2×C7C2×#34411yescharacteristic
445D7—22no—
446D7—22no—
447D7—41no—
448D7—41no—
449C23—41no—
450C23—41no—
451C23—71no—
452C23—71no—
453C23—71no—
454C23—71no—
455C23—142no—
456C23—142no—
457C23—142no—
458C23—142no—
459C23—142no—
460C23—142no—
461C23—141no—
462C23—141no—
463C23—142no—
464C23—142no—
465C23—141no—
466C23—141no—
467C23—142no—
468C23—142no—
469C23—281no—
470C23—281no—
471C23—281no—
472C23—281no—
473C23—281no—
474C23—281no—
475C23—288no—
476C23—288no—
477C23C42×D711yescharacteristic
478C23D7×C22⋊C411yescharacteristic
479C23D7×C4⋊C411yescharacteristic
480C23#646412yes—
481C23#647012yes—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—71no—
492C2×C4—74no—
493C2×C4—71no—
494C2×C4—71no—
495C2×C4—71no—
496C2×C4—142no—
497C2×C4—142no—
498C2×C4—142no—
499C2×C4—142no—
500C2×C4—142no—
501C2×C4—142no—
502C2×C4—142no—
503C2×C4—142no—
504C2×C4—142no—
505C2×C4—142no—
506C2×C4—142no—
507C2×C4—142no—
508C2×C4—281no—
509C2×C4—281no—
510C2×C4—281no—
511C2×C4—281no—
512C2×C4—281no—
513C2×C4—281no—
514C2×C4—281no—
515C2×C4—281no—
516C2×C4—281no—
517C2×C4—282no—
518C2×C4—282no—
519C2×C4—282no—
520C2×C4D7×C22⋊C411yescharacteristic
521C2×C4D7×C22⋊C411yescharacteristic
522C2×C4D7×C4⋊C411yescharacteristic
523C2×C4D7×C4⋊C411yescharacteristic
524C8—42no—
525C8—42no—
526C8—282no—
527C8—282no—
528C7#792711yescharacteristic, complemented, Sylow
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—42no—
536C22—42no—
537C22—72no—
538C22—72no—
539C22—144no—
540C22—144no—
541C22—141no—
542C22—141no—
543C22—141no—
544C22—141no—
545C22—141no—
546C22—141no—
547C22—141no—
548C22—141no—
549C22—141no—
550C22—141no—
551C22—284no—
552C22—284no—
553C22—284no—
554C22—284no—
555C22—282no—
556C22—282no—
557C22D7×#9511yescharacteristic
558C22#8946111yescharacteristic
559C22#8948011yescharacteristic
560C22#8949912yes—
561C22#8961112yes—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—72no—
566C4—82no—
567C4—141no—
568C4—141no—
569C4—141no—
570C4—562no—
571C4D7×#9912yes—
572C2—22no—
573C2—21no—
574C2—21no—
575C2—22no—
576C2—142no—
577C2—142no—
578C2—281no—
579C2—281no—
580C2#1172641511yescharacteristic
581C2D7×#34211yescharacteristic
582C2D7×#34411yescharacteristic
subgroupG/H
centerC2×C4D7×C22⋊C4
commutatorC23×C7C2×C42
FrattiniC23×C4C22×D7
FittingC7×#1282C2
socleC22×C7C2×#95
prime radicalC24×D7C2×C4
cosocleC23×C4×C7C23
hypercenter#1282D7
hypocenterC7#7927
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
4. C7×#1282C2semidirect
5. #11725484C2semidirect
6. #11725483C2semidirect
7. #11725423C2semidirect
10. C22×C8×D7C4semidirect
19. C2×(C2×D7)⋊C8C4semidirect
25. #89498C4semidirect
26. #89498C4semidirect
89. #1282D7semidirect
528. C7#7927semidirect

Maximal subgroups

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

subgroupindex
C2×#894982
C2×D7×C22⋊C82
#117310062
C7×#12822
#117254842
#117254832
#117254232
#79277