Finite Group Databasebeta

← #13320931

Subgroups — #13320931

Order 1792.

1116 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90170C211yesmaximal, characteristic
2C7×#2920C211yesmaximal, characteristic, complemented
3C4×#6489C211yesmaximal, characteristic, complemented
4#11728587C214yesmaximal, complemented
5#11728542C214yesmaximal, complemented
6#11727734C212yesmaximal, complemented
7#11727731C212yesmaximal
8C22×C42×C7C2211yescharacteristic
9C2×#6493C2211yescharacteristic
10C2×#6492—21no—
11C2×C4×C22⋊D7—21no—
12C2×#6489—21no—
13C2×#6487C2211yescharacteristic
14#90170—21no—
15#90170—21no—
16#90170—21no—
17#90170—21no—
18#90170C412yescomplemented
19#90170C412yescomplemented
20#90170C2212yes—
21#90170C2212yes—
22C2×#6439—21no—
23C2×#6438C411yescharacteristic, complemented
24C2×C4×D28C411yescharacteristic, complemented
25C2×#6435—21no—
26C2×#6433C411yescharacteristic, complemented
27C2×C4×Dic14C411yescharacteristic, complemented
28C7×#432—21no—
29C7×#432C2212yescomplemented
30C7×#431—21no—
31C7×#431C2212yescomplemented
32C7×#423—21no—
33C7×#407C2212yes—
34C4×C7×M16—21no—
35C4×C22⋊Dic7—21no—
36C4×C22⋊Dic7C2212yes—
37C4×C4⋊Dic7—21no—
38C4×C4⋊Dic7C2212yescomplemented
39#89704C2212yescomplemented
40C42×Dic7—21no—
41#89265C2218yes—
42#89262C2218yescomplemented
43#17537—71nomaximal, Sylow
44C23×C4×C7D411yescharacteristic
45C23×C4×C7D411yescharacteristic
46C23×C4×C7C2311yescharacteristic
47C22×C22⋊D7—21no—
48C22×D28C2×C411yescharacteristic
49C22×C4×D7—21no—
50C22×Dic14C2×C411yescharacteristic
51C2×C7×M16—22no—
52C2×C42×C7C2×C411yescharacteristic
53C2×C42×C7C2×C411yescharacteristic
54C2×C42×C7C2×C411yescharacteristic
55C2×C42×C7C2×C411yescharacteristic
56C2×C42×C7D411yescharacteristic
57C2×C42×C7D411yescharacteristic
58C2×C42×C7D411yescharacteristic
59C2×C42×C7D411yescharacteristic
60C2×C42×C7D411yescharacteristic
61C2×C42×C7D411yescharacteristic
62C2×C42×C7C2311yescharacteristic
63C2×C42×C7C2311yescharacteristic
64C2×C22⋊Dic7—21no—
65C2×C22⋊Dic7—22no—
66#6493—21no—
67#6493—21no—
68#6493C2×C412yes—
69#6493C2312yes—
70#6492—22no—
71#6492—22no—
72#6492—22no—
73#6492—22no—
74C4×C22⋊D7—22no—
75C4×C22⋊D7—22no—
76C4×C22⋊D7—22no—
77C4×C22⋊D7—22no—
78C2×(C2×D7)⋊C4—21no—
79C2×(C2×D7)⋊C4—21no—
80C2×(C2×D7)⋊C4—21no—
81C2×(C2×D7)⋊C4—21no—
82#6489—28no—
83C2×C4⋊Dic7—22no—
84C2×C4⋊Dic7C2×C411yescharacteristic
85C2×C4⋊Dic7C2×C411yescharacteristic
86#6487—21no—
87#6487—21no—
88#6487C2×C412yes—
89#6487C2312yes—
90C2×Dic7⋊C4—21no—
91C2×Dic7⋊C4—21no—
92C2×Dic7⋊C4—21no—
93C2×Dic7⋊C4—21no—
94C2×C4×Dic7—21no—
95C2×C4×Dic7—22no—
96C2×C4×Dic7—22no—
97C2×C4×Dic7—22no—
98#6439—22no—
99#6439—22no—
100#6439—22no—
101#6439—22no—
102#6438—21no—
103#6438—21no—
104#6438C2×C412yes—
105#6438C2×C412yes—
106C4×D28—21no—
107C4×D28—21no—
108C4×D28C2×C412yes—
109C4×D28C2×C412yes—
110#6435—22no—
111#6435—22no—
112#6435—22no—
113#6435—22no—
114#6433—21no—
115#6433—21no—
116#6433C2×C412yes—
117#6433C2×C412yes—
118C4×Dic14—21no—
119C4×Dic14—21no—
120C4×Dic14C2×C412yes—
121C4×Dic14C2×C412yes—
122C7×C4⋊C8—22no—
123C7×C4⋊C8—22no—
124C7×C22⋊C8—22no—
125C7×C22⋊C8C2314yes—
126C7×#97—22no—
127C4×C7×C8—22no—
128C7⋊#95—22no—
129C7⋊#95C2314yes—
130C2×#529—71no—
131#2920D711yescharacteristic, complemented
132C4×#117—71no—
133#1509—74no—
134#1508—72no—
135#1507—72no—
136#1500—74no—
137C24×C7C2×D411yescharacteristic
138C23×D7—21no—
139C22×C4×C7—24no—
140C22×C4×C7—42no—
141C22×C4×C7—42no—
142C22×C4×C7C22⋊C411yescharacteristic
143C22×C4×C7C22⋊C411yescharacteristic
144C22×C4×C7C22⋊C411yescharacteristic
145C22×C4×C7C22⋊C411yescharacteristic
146C22×C4×C7C22⋊C411yescharacteristic
147C22×C4×C7C22⋊C411yescharacteristic
148C22×C4×C7C22⋊C411yescharacteristic
149C22×C4×C7C22⋊C411yescharacteristic
150C22×C4×C7C22×C411yescharacteristic
151C22×C4×C7C22×C411yescharacteristic
152C22×C4×C7C2×D411yescharacteristic
153C22×C4×C7C2×D411yescharacteristic
154C22×C4×C7C2×D411yescharacteristic
155C22×C4×C7C2×D411yescharacteristic
156C22×C4×C7C2×D411yescharacteristic
157C22×C4×C7C2×D411yescharacteristic
158C22×C4×C7C2×D411yescharacteristic
159C22×C4×C7C2411yescharacteristic
160C2×C22⋊D7—22no—
161C2×C22⋊D7—22no—
162C2×C22⋊D7—44no—
163C22×Dic7—21no—
164C22×Dic7—21no—
165C22×Dic7—21no—
166C22×Dic7—24no—
167C2×D28—21no—
168C2×D28—42no—
169C2×D28C22×C412yes—
170C2×C4×D7—22no—
171C2×C4×D7—22no—
172C2×C4×D7—44no—
173C2×Dic14—21no—
174C2×Dic14—42no—
175C2×Dic14C22×C412yes—
176C7×M16—44no—
177C2×C7×C8—24no—
178C42×C7C22⋊C411yescharacteristic
179C42×C7C22⋊C411yescharacteristic
180C42×C7C22⋊C411yescharacteristic
181C42×C7C22⋊C411yescharacteristic
182C42×C7C22⋊C411yescharacteristic
183C42×C7C22⋊C411yescharacteristic
184C42×C7C22⋊C411yescharacteristic
185C42×C7C22⋊C411yescharacteristic
186C42×C7C22×C411yescharacteristic
187C42×C7C22×C411yescharacteristic
188C42×C7C22×C411yescharacteristic
189C42×C7C22×C411yescharacteristic
190C42×C7C2×D411yescharacteristic
191C42×C7C2×D411yescharacteristic
192C42×C7C2×D411yescharacteristic
193C42×C7C2×D411yescharacteristic
194C22⋊Dic7—28no—
195C22⋊Dic7—22no—
196C22⋊Dic7—22no—
197(C2×D7)⋊C4—22no—
198(C2×D7)⋊C4—22no—
199(C2×D7)⋊C4—22no—
200(C2×D7)⋊C4—22no—
201(C2×D7)⋊C4—22no—
202(C2×D7)⋊C4—22no—
203(C2×D7)⋊C4—22no—
204(C2×D7)⋊C4—22no—
205C4⋊Dic7—28no—
206C4⋊Dic7—21no—
207C4⋊Dic7—21no—
208C4⋊Dic7C22×C412yes—
209C4⋊Dic7C22×C412yes—
210Dic7⋊C4—22no—
211Dic7⋊C4—22no—
212Dic7⋊C4—22no—
213Dic7⋊C4—22no—
214Dic7⋊C4—22no—
215Dic7⋊C4—22no—
216Dic7⋊C4—22no—
217Dic7⋊C4—22no—
218C4×Dic7—28no—
219C4×Dic7—22no—
220C4×Dic7—22no—
221C4×Dic7—44no—
222C4×Dic7—44no—
223#529—72no—
224#529—72no—
225#529—72no—
226#529—72no—
227#529—141no—
228#529—141no—
229#529—141no—
230#529—141no—
231C2×#126—141no—
232C2×#125—71no—
233C2×#124—71no—
234C2×#123—141no—
235C2×C22⋊Q8—71no—
236C2×#121—71no—
237C2×C4×Q8—71no—
238C2×C4×D4—71no—
239C2×C4×D4—141no—
240C2×#117—141no—
241C2×#117—141no—
242C22×C42C2×D711yescharacteristic
243#432—21no—
244#432C2×D712yescomplemented
245#431—21no—
246#431C2×D712yescomplemented
247#423—21no—
248#407C2×D712yes—
249C4×M16—21no—
250C4×C4⋊C4—72no—
251C4×C4⋊C4—141no—
252C4×C22⋊C4—72no—
253C4×C22⋊C4—141no—
254#376—72no—
255C43—141no—
256#328—78no—
257#327—78no—
258C23×C7—22no—
259C23×C7—22no—
260C23×C7—41no—
261C23×C7C2×C22⋊C411yescharacteristic
262C23×C7C2×C22⋊C411yescharacteristic
263C23×C7C22×D411yescharacteristic
264C22×D7—22no—
265C22×D7—42no—
266C22×D7—42no—
267C22×D7—42no—
268C2×C4×C7—22no—
269C2×C4×C7—22no—
270C2×C4×C7—22no—
271C2×C4×C7—22no—
272C2×C4×C7—22no—
273C2×C4×C7—22no—
274C2×C4×C7—22no—
275C2×C4×C7—22no—
276C2×C4×C7—22no—
277C2×C4×C7—22no—
278C2×C4×C7—41no—
279C2×C4×C7—41no—
280C2×C4×C7—41no—
281C2×C4×C7—41no—
282C2×C4×C7—41no—
283C2×C4×C7—41no—
284C2×C4×C7—41no—
285C2×C4×C7#10414yes—
286C2×C4×C7C2×C22⋊C411yescharacteristic
287C2×C4×C7C2×C22⋊C411yescharacteristic
288C2×C4×C7C2×C22⋊C411yescharacteristic
289C2×C4×C7C2×C22⋊C411yescharacteristic
290C2×C4×C7C2×C22⋊C411yescharacteristic
291C2×C4×C7C2×C22⋊C411yescharacteristic
292C2×C4×C7C2×C22⋊C411yescharacteristic
293C2×C4×C7C2×C22⋊C411yescharacteristic
294C2×C4×C7C2×C22⋊C411yescharacteristic
295C2×C4×C7C2×C22⋊C411yescharacteristic
296C2×C4×C7C23×C411yescharacteristic
297C2×C4×C7C22×D411yescharacteristic
298C22⋊D7—44no—
299C22⋊D7—44no—
300C2×Dic7—28no—
301C2×Dic7—22no—
302C2×Dic7—22no—
303C2×Dic7—22no—
304C2×Dic7—44no—
305C2×Dic7—42no—
306C2×Dic7—42no—
307C2×Dic7—44no—
308C2×Dic7—42no—
309D28—42no—
310D28—42no—
311C4×D7—44no—
312C4×D7—44no—
313Dic14—42no—
314Dic14—42no—
315C7×C8—44no—
316C22×Q8—71no—
317C22×D4—71no—
318C22×D4—141no—
319C23×C4—141no—
320C23×C4D2811yescharacteristic
321C23×C4D2811yescharacteristic
322C23×C4C22×D711yescharacteristic
323C2×M16—22no—
324#126—142no—
325#126—142no—
326#126—142no—
327#126—142no—
328#125—72no—
329#125—72no—
330#125—141no—
331#125—141no—
332#124—72no—
333#124—72no—
334#124—141no—
335#124—141no—
336#123—142no—
337#123—142no—
338#123—142no—
339#123—142no—
340C22⋊Q8—72no—
341C22⋊Q8—72no—
342C22⋊Q8—141no—
343C22⋊Q8—141no—
344#121—72no—
345#121—72no—
346#121—141no—
347#121—141no—
348C4×Q8—72no—
349C4×Q8—72no—
350C4×Q8—141no—
351C4×Q8—141no—
352C4×D4—72no—
353C4×D4—72no—
354C4×D4—142no—
355C4×D4—142no—
356C4×D4—142no—
357C4×D4—142no—
358C4×D4—141no—
359C4×D4—141no—
360#117—148no—
361#117—142no—
362#117—142no—
363#117—142no—
364#117—142no—
365C2×C4⋊C4—71no—
366C2×C4⋊C4—71no—
367C2×C4⋊C4—141no—
368C2×C4⋊C4—141no—
369C2×C4⋊C4—141no—
370C2×C4⋊C4—142no—
371C2×C4⋊C4—141no—
372C2×C22⋊C4—142no—
373C2×C22⋊C4—141no—
374C2×C22⋊C4—141no—
375C2×C22⋊C4—141no—
376C2×C22⋊C4—141no—
377C2×C22⋊C4—141no—
378C2×C42—141no—
379C2×C42—142no—
380C2×C42—142no—
381C2×C42—142no—
382C2×C42C4×D711yescharacteristic
383C2×C42C4×D711yescharacteristic
384C2×C42C4×D711yescharacteristic
385C2×C42C4×D711yescharacteristic
386C2×C42D2811yescharacteristic
387C2×C42D2811yescharacteristic
388C2×C42C22⋊D711yescharacteristic
389C2×C42C22⋊D711yescharacteristic
390C2×C42C22⋊D711yescharacteristic
391C2×C42C22⋊D711yescharacteristic
392C2×C42C22×D711yescharacteristic
393C2×C42C22×D711yescharacteristic
394C4⋊C8—22no—
395C4⋊C8—22no—
396C22⋊C8—22no—
397C22⋊C8C22×D714yes—
398#97—22no—
399C4×C8—22no—
400#95—74no—
401#95—142no—
402C22×C7—21no—
403C22×C7—21no—
404C22×C7—21no—
405C22×C7—21no—
406C22×C7—21no—
407C22×C7—21no—
408C22×C7—21no—
409C22×C7—44no—
410C22×C7C2×#10412yes—
411C22×C7C22×C22⋊C411yescharacteristic
412C22×C7#57512yes—
413C2×D7—42no—
414C2×D7—42no—
415C2×D7—42no—
416C2×D7—84no—
417C4×C7—21no—
418C4×C7—21no—
419C4×C7—21no—
420C4×C7—21no—
421C4×C7—21no—
422C4×C7—21no—
423C4×C7—21no—
424C4×C7—21no—
425C4×C7—21no—
426C4×C7#41012yes—
427C4×C7C2×#10412yes—
428C4×C7C2×#10412yes—
429Dic7—48no—
430Dic7—42no—
431Dic7—42no—
432Dic7—42no—
433C24—141no—
434C24C2×D2811yescharacteristic
435C2×Q8—72no—
436C2×Q8—141no—
437C2×Q8—282no—
438C2×D4—72no—
439C2×D4—142no—
440C2×D4—142no—
441C2×D4—141no—
442C2×D4—282no—
443C2×D4—284no—
444C22×C4—24no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—141no—
448C22×C4—141no—
449C22×C4—141no—
450C22×C4—144no—
451C22×C4—142no—
452C22×C4—142no—
453C22×C4—284no—
454C22×C4(C2×D7)⋊C411yescharacteristic
455C22×C4(C2×D7)⋊C411yescharacteristic
456C22×C4(C2×D7)⋊C411yescharacteristic
457C22×C4(C2×D7)⋊C411yescharacteristic
458C22×C4(C2×D7)⋊C411yescharacteristic
459C22×C4(C2×D7)⋊C411yescharacteristic
460C22×C4(C2×D7)⋊C411yescharacteristic
461C22×C4(C2×D7)⋊C411yescharacteristic
462C22×C4C2×C4×D711yescharacteristic
463C22×C4C2×C4×D711yescharacteristic
464C22×C4C2×D2811yescharacteristic
465C22×C4C2×D2811yescharacteristic
466C22×C4C2×D2811yescharacteristic
467C22×C4C2×D2811yescharacteristic
468C22×C4C2×D2811yescharacteristic
469C22×C4C2×C22⋊D711yescharacteristic
470C22×C4C2×C22⋊D711yescharacteristic
471C22×C4C23×D711yescharacteristic
472M16—44no—
473C2×C8—24no—
474C4⋊C4—72no—
475C4⋊C4—72no—
476C4⋊C4—148no—
477C4⋊C4—142no—
478C4⋊C4—142no—
479C4⋊C4—142no—
480C4⋊C4—142no—
481C4⋊C4—142no—
482C4⋊C4—142no—
483C4⋊C4—142no—
484C4⋊C4—141no—
485C4⋊C4—141no—
486C4⋊C4—142no—
487C22⋊C4—148no—
488C22⋊C4—142no—
489C22⋊C4—142no—
490C22⋊C4—142no—
491C22⋊C4—142no—
492C22⋊C4—142no—
493C22⋊C4—142no—
494C22⋊C4—142no—
495C22⋊C4—142no—
496C22⋊C4—142no—
497C22⋊C4—142no—
498C42—148no—
499C42—142no—
500C42—142no—
501C42—284no—
502C42—284no—
503C42(C2×D7)⋊C411yescharacteristic
504C42(C2×D7)⋊C411yescharacteristic
505C42(C2×D7)⋊C411yescharacteristic
506C42(C2×D7)⋊C411yescharacteristic
507C42(C2×D7)⋊C411yescharacteristic
508C42(C2×D7)⋊C411yescharacteristic
509C42(C2×D7)⋊C411yescharacteristic
510C42(C2×D7)⋊C411yescharacteristic
511C42C2×C4×D711yescharacteristic
512C42C2×C4×D711yescharacteristic
513C42C2×C4×D711yescharacteristic
514C42C2×C4×D711yescharacteristic
515C42C2×C22⋊D711yescharacteristic
516C42C2×C22⋊D711yescharacteristic
517C42C2×C22⋊D711yescharacteristic
518C42C2×C22⋊D711yescharacteristic
519C2×C7—22no—
520C2×C7—22no—
521C2×C7—41no—
522C2×C7C2×#41011yescharacteristic
523C2×C7#289611yescharacteristic
524C2×C7C22×#10411yescharacteristic
525D7—82no—
526C23—22no—
527C23—22no—
528C23—41no—
529C23—142no—
530C23—282no—
531C23—282no—
532C23—282no—
533C23C2×(C2×D7)⋊C411yescharacteristic
534C23C2×(C2×D7)⋊C411yescharacteristic
535C23C22×D2811yescharacteristic
536Q8—282no—
537Q8—282no—
538D4—282no—
539D4—284no—
540D4—284no—
541D4—282no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—148no—
560C2×C4—142no—
561C2×C4—142no—
562C2×C4—142no—
563C2×C4—284no—
564C2×C4—282no—
565C2×C4—282no—
566C2×C4—282no—
567C2×C4—284no—
568C2×C4—284no—
569C2×C4—284no—
570C2×C4#639914yes—
571C2×C4C2×(C2×D7)⋊C411yescharacteristic
572C2×C4C2×(C2×D7)⋊C411yescharacteristic
573C2×C4C2×(C2×D7)⋊C411yescharacteristic
574C2×C4C2×(C2×D7)⋊C411yescharacteristic
575C2×C4C2×(C2×D7)⋊C411yescharacteristic
576C2×C4C2×(C2×D7)⋊C411yescharacteristic
577C2×C4C2×(C2×D7)⋊C411yescharacteristic
578C2×C4C2×(C2×D7)⋊C411yescharacteristic
579C2×C4C2×(C2×D7)⋊C411yescharacteristic
580C2×C4C2×(C2×D7)⋊C411yescharacteristic
581C2×C4C22×C4×D711yescharacteristic
582C2×C4C22×C22⋊D711yescharacteristic
583C8—44no—
584C7#1753711yescharacteristic, complemented, Sylow
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—44no—
593C22—282no—
594C22—282no—
595C22—282no—
596C22—564no—
597C22C2×#639912yes—
598C22#9043912yes—
599C22C22×(C2×D7)⋊C411yescharacteristic
600C4—21no—
601C4—21no—
602C4—21no—
603C4—21no—
604C4—21no—
605C4—21no—
606C4—21no—
607C4—21no—
608C4—21no—
609C4—288no—
610C4—282no—
611C4—282no—
612C4—282no—
613C4#8977812yes—
614C4C2×#639912yes—
615C4C2×#639912yes—
616C2—22no—
617C2—22no—
618C2—41no—
619C2—562no—
620C2C2×#8977811yescharacteristic
621C2#1174121311yescharacteristic
622C2C22×#639911yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D7)⋊C4
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2920C2
socleC22×C7C22×C22⋊C4
prime radicalC2×#6493C22
cosocleC22×C4×C7C24
hypercenter#2920D7
hypocenterC7#17537
LCSG ▷ C2×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
2. C7×#2920C2semidirect
3. C4×#6489C2semidirect
4. #11728587C2semidirect
5. #11728542C2semidirect
6. #11727734C2semidirect
18. #90170C4semidirect
19. #90170C4semidirect
23. C2×#6438C4semidirect
24. C2×C4×D28C4semidirect
26. C2×#6433C4semidirect
27. C2×C4×Dic14C4semidirect
29. C7×#432C22semidirect
31. C7×#431C22semidirect
38. C4×C4⋊Dic7C22semidirect
39. #89704C22semidirect
42. #89262C22semidirect
131. #2920D7semidirect
244. #432C2×D7semidirect
246. #431C2×D7semidirect
584. C7#17537semidirect

Maximal subgroups

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

subgroupindex
C2×#901702
C7×#29202
C4×#64892
#117285872
#117285422
#117277342
#117277312
#175377