Finite Group Databasebeta

← #13320984

Subgroups — #13320984

Order 1792.

1194 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11742748C211yesmaximal, characteristic
2C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
3#11739494C211yesmaximal, characteristic, complemented
4#11727225C212yesmaximal, complemented
5#11727224C214yesmaximal, complemented
6#11727223C212yesmaximal, complemented
7#11727152C214yesmaximal, complemented
8C22×C7×C4⋊C4—21no—
9C22×C42×C7—21no—
10C22×C42×C7C2211yescharacteristic
11#90482—21no—
12#90482—21no—
13#90482C2212yes—
14#90170—21no—
15#90170—21no—
16#90170—21no—
17#90170—21no—
18#90170C412yescomplemented
19#90170C2212yes—
20#90168C411yescharacteristic, complemented
21#90168C411yescharacteristic, complemented
22#90168C2211yescharacteristic
23C4×#1157—21no—
24C4×#1157—21no—
25C4×#1157C412yescomplemented
26#90161C411yescharacteristic, complemented
27#90161C411yescharacteristic, complemented
28#90161C2211yescharacteristic
29C4×C7×C4⋊C4—21no—
30C4×C7×C4⋊C4—21no—
31C4×C7×C4⋊C4C2212yes—
32C4×C7×C4⋊C4C2212yes—
33C2×C7×#95C2212yes—
34#89979C2212yes—
35#89698—21no—
36#89698C2212yes—
37#89697—21no—
38#89697C2212yes—
39#89696—21no—
40C4×#1136—21no—
41#89247C2218yes—
42#89246C2218yes—
43#17546—71nomaximal, Sylow
44C23×C4×C7—22no—
45C23×C4×C7D411yescharacteristic
46C23×C4×C7D411yescharacteristic
47C23×C4×C7C2311yescharacteristic
48C2×#1157—21no—
49C2×#1157—21no—
50C2×#1157C2×C412yes—
51C2×C7×C4⋊C4—28no—
52C2×C7×C4⋊C4—22no—
53C2×C7×C4⋊C4—22no—
54C2×C42×C7—22no—
55C2×C42×C7—22no—
56C2×C42×C7—44no—
57C2×C42×C7C2×C411yescharacteristic
58C2×C42×C7C2×C411yescharacteristic
59C2×C42×C7C2×C411yescharacteristic
60C2×C42×C7C2×C411yescharacteristic
61C2×C42×C7D411yescharacteristic
62C2×C42×C7D411yescharacteristic
63C2×C42×C7D411yescharacteristic
64C2×C42×C7D411yescharacteristic
65C2×C42×C7D411yescharacteristic
66C2×C42×C7D411yescharacteristic
67C2×C42×C7C2311yescharacteristic
68C2×C42×C7C2311yescharacteristic
69#6516—22no—
70#6493—21no—
71#6493—21no—
72#6493—21no—
73#6493—21no—
74#6493C2×C412yes—
75#6493C2312yes—
76#6492—22no—
77#6492—22no—
78#6492—22no—
79C4×C22⋊D7—22no—
80C4×C22⋊D7—22no—
81C4×C22⋊D7—22no—
82C4×C22⋊D7—22no—
83C4×C22⋊D7—22no—
84C4×C22⋊D7—22no—
85#6489—21no—
86#6489—21no—
87#6489C2×C412yes—
88#6487—21no—
89#6487—21no—
90#6487—21no—
91#6487—21no—
92#6487C2×C412yes—
93#6487C2312yes—
94C2×#1136—22no—
95#6439—22no—
96#6439—22no—
97#6438—21no—
98#6438—21no—
99#6438C2×C412yescomplemented
100#6437C2×C411yescharacteristic, complemented
101C4×D28—21no—
102C4×D28—21no—
103C4×D28—21no—
104C4×D28—21no—
105C4×D28C2×C412yescomplemented
106C4×D28C2×C412yescomplemented
107#6435—22no—
108#6435—22no—
109#6435—22no—
110C42×D7—22no—
111#6433—21no—
112#6433—21no—
113#6433C2×C412yescomplemented
114#6432C2×C411yescharacteristic, complemented
115#6432C2×C411yescharacteristic, complemented
116#6432C2×C411yescharacteristic, complemented
117C4×Dic14—21no—
118C4×Dic14—21no—
119C4×Dic14—21no—
120C4×Dic14—21no—
121C4×Dic14C2×C412yescomplemented
122C4×Dic14C2×C412yescomplemented
123C7×#95—22no—
124C7×#95C2314yes—
125C22⋊(C7⋊C8)—22no—
126C22⋊(C7⋊C8)C2314yes—
127C4⋊(C7⋊C8)—22no—
128C4⋊(C7⋊C8)—22no—
129#6377—22no—
130C4×C7⋊C8—22no—
131#3444—71no—
132#2920—71no—
133C2×C4×C4⋊C4D711yescharacteristic, complemented
134#1509—74no—
135#1504—74no—
136#1503—72no—
137#1502—72no—
138C24×C7C2×D411yescharacteristic
139C22×C4×C7—24no—
140C22×C4×C7—22no—
141C22×C4×C7—22no—
142C22×C4×C7—28no—
143C22×C4×C7—24no—
144C22×C4×C7—42no—
145C22×C4×C7—44no—
146C22×C4×C7—44no—
147C22×C4×C7C22⋊C411yescharacteristic
148C22×C4×C7C22⋊C411yescharacteristic
149C22×C4×C7C22⋊C411yescharacteristic
150C22×C4×C7C22⋊C411yescharacteristic
151C22×C4×C7C22⋊C411yescharacteristic
152C22×C4×C7C22⋊C411yescharacteristic
153C22×C4×C7C22⋊C411yescharacteristic
154C22×C4×C7C22⋊C411yescharacteristic
155C22×C4×C7C22×C411yescharacteristic
156C22×C4×C7C22×C411yescharacteristic
157C22×C4×C7C2×D411yescharacteristic
158C22×C4×C7C2×D411yescharacteristic
159C22×C4×C7C2×D411yescharacteristic
160C22×C4×C7C2×D411yescharacteristic
161C22×C4×C7C2×D411yescharacteristic
162C22×C4×C7C2×D411yescharacteristic
163C22×C4×C7C2×D411yescharacteristic
164C22×C4×C7C2411yescharacteristic
165C2×C22⋊D7—22no—
166C2×C22⋊D7—22no—
167C2×C22⋊D7—22no—
168#1157—44no—
169#1157—42no—
170#1157—42no—
171#1157—44no—
172C2×D28—21no—
173C2×D28—21no—
174C2×D28C22×C412yes—
175C2×C4×D7—22no—
176C2×C4×D7—22no—
177C2×C4×D7—22no—
178C2×Dic14—21no—
179C2×Dic14—21no—
180C2×Dic14C22×C412yes—
181C7×C4⋊C4—28no—
182C7×C4⋊C4—28no—
183C42×C7—44no—
184C42×C7—44no—
185C42×C7C22⋊C411yescharacteristic
186C42×C7C22⋊C411yescharacteristic
187C42×C7C22⋊C411yescharacteristic
188C42×C7C22⋊C411yescharacteristic
189C42×C7C22⋊C411yescharacteristic
190C42×C7C22⋊C411yescharacteristic
191C42×C7C22⋊C411yescharacteristic
192C42×C7C22⋊C411yescharacteristic
193C42×C7C22×C411yescharacteristic
194C42×C7C22×C411yescharacteristic
195C42×C7C22×C411yescharacteristic
196C42×C7C22×C411yescharacteristic
197C42×C7C2×D411yescharacteristic
198C42×C7C2×D411yescharacteristic
199C42×C7C2×D411yescharacteristic
200C42×C7C2×D411yescharacteristic
201C22⋊Dic7—22no—
202C22⋊Dic7—22no—
203C22⋊Dic7—22no—
204(C2×D7)⋊C4—22no—
205(C2×D7)⋊C4—22no—
206(C2×D7)⋊C4—22no—
207(C2×D7)⋊C4—22no—
208(C2×D7)⋊C4—22no—
209(C2×D7)⋊C4—22no—
210C4⋊Dic7—21no—
211C4⋊Dic7—21no—
212C4⋊Dic7—21no—
213C4⋊Dic7—21no—
214C4⋊Dic7C22×C412yes—
215C4⋊Dic7C22×C412yes—
216Dic7⋊C4—22no—
217Dic7⋊C4—22no—
218Dic7⋊C4—22no—
219Dic7⋊C4—22no—
220Dic7⋊C4—22no—
221Dic7⋊C4—22no—
222C4×Dic7—22no—
223C4×Dic7—22no—
224C4×Dic7—22no—
225#1136—44no—
226C2×C7⋊C8—24no—
227#533—71no—
228#533—71no—
229#533—71no—
230#532—71no—
231#532—71no—
232#532—71no—
233#529—72no—
234#529—72no—
235#529—141no—
236#529—141no—
237#529—141no—
238#529—141no—
239#525—72no—
240#525—141no—
241#525—141no—
242C4×#41—72no—
243C4×#41—141no—
244C4×#41—141no—
245C22×C4⋊C4—21no—
246C22×C42—21no—
247C22×C42C2×D711yescharacteristic
248#432—72no—
249#432—141no—
250#431—72no—
251#431—141no—
252#423—141no—
253#407—72no—
254C4×M16—141no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4—21no—
257C4×C4⋊C4C2×D712yes—
258C4×C4⋊C4C2×D712yes—
259C2×#95C2×D712yes—
260#328—78no—
261#327—78no—
262C23×C7—21no—
263C23×C7—21no—
264C23×C7—22no—
265C23×C7—22no—
266C23×C7C2×C22⋊C411yescharacteristic
267C23×C7C2×C22⋊C411yescharacteristic
268C23×C7C22×D411yescharacteristic
269C22×D7—22no—
270C2×C4×C7—21no—
271C2×C4×C7—21no—
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—22no—
279C2×C4×C7—22no—
280C2×C4×C7—22no—
281C2×C4×C7—22no—
282C2×C4×C7—22no—
283C2×C4×C7—28no—
284C2×C4×C7—41no—
285C2×C4×C7—41no—
286C2×C4×C7—41no—
287C2×C4×C7—41no—
288C2×C4×C7—416no—
289C2×C4×C7—44no—
290C2×C4×C7—44no—
291C2×C4×C7#10414yes—
292C2×C4×C7C2×C22⋊C411yescharacteristic
293C2×C4×C7C2×C22⋊C411yescharacteristic
294C2×C4×C7C2×C22⋊C411yescharacteristic
295C2×C4×C7C2×C22⋊C411yescharacteristic
296C2×C4×C7C2×C22⋊C411yescharacteristic
297C2×C4×C7C2×C22⋊C411yescharacteristic
298C2×C4×C7C2×C22⋊C411yescharacteristic
299C2×C4×C7C2×C22⋊C411yescharacteristic
300C2×C4×C7C2×C22⋊C411yescharacteristic
301C2×C4×C7C2×C22⋊C411yescharacteristic
302C2×C4×C7AGL(1,ℤ/8)12yes—
303C2×C4×C7#13712yes—
304C2×C4×C7C23×C411yescharacteristic
305C2×C4×C7C22×D411yescharacteristic
306C22⋊D7—42no—
307C22⋊D7—42no—
308C22⋊D7—44no—
309C22⋊D7—44no—
310C2×Dic7—22no—
311C2×Dic7—22no—
312C2×Dic7—22no—
313D28—42no—
314D28—42no—
315D28—42no—
316C4×D7—44no—
317C4×D7—44no—
318C4×D7—44no—
319Dic14—42no—
320Dic14—42no—
321Dic14—42no—
322C7⋊C8—44no—
323C2×#41—72no—
324C2×#41—141no—
325C2×#41—141no—
326C23×C4—22no—
327C23×C4C22⋊D711yescharacteristic
328C23×C4C22⋊D711yescharacteristic
329C23×C4C22×D711yescharacteristic
330C2×M16—142no—
331C4⋊Q8—71no—
332C4⋊Q8—71no—
333C4⋊Q8—71no—
334#127—71no—
335#126—142no—
336#126—142no—
337#125—72no—
338#125—141no—
339#125—141no—
340#124—72no—
341#124—141no—
342#124—141no—
343#123—142no—
344#123—142no—
345#123—142no—
346C22⋊Q8—72no—
347C22⋊Q8—72no—
348C22⋊Q8—141no—
349C22⋊Q8—141no—
350C22⋊Q8—141no—
351C22⋊Q8—141no—
352#121—72no—
353#121—72no—
354#121—141no—
355#121—141no—
356#121—141no—
357#121—141no—
358#120—142no—
359C4×Q8—72no—
360C4×Q8—72no—
361C4×Q8—141no—
362C4×Q8—141no—
363C4×Q8—141no—
364C4×Q8—141no—
365C4×D4—72no—
366C4×D4—72no—
367C4×D4—142no—
368C4×D4—142no—
369C4×D4—142no—
370C4×D4—142no—
371C4×D4—142no—
372C4×D4—142no—
373C4×D4—141no—
374C4×D4—141no—
375C4×D4—141no—
376C4×D4—141no—
377#117—72no—
378#117—141no—
379#117—141no—
380#117—142no—
381#117—142no—
382#117—142no—
383C2×C4⋊C4—28no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—44no—
389C2×C42—142no—
390C2×C42C4×D711yescharacteristic
391C2×C42C4×D711yescharacteristic
392C2×C42C4×D711yescharacteristic
393C2×C42C4×D711yescharacteristic
394C2×C42D2811yescharacteristic
395C2×C42D2811yescharacteristic
396C2×C42D2811yescharacteristic
397C2×C42D2811yescharacteristic
398C2×C42C22⋊D711yescharacteristic
399C2×C42C22⋊D711yescharacteristic
400C2×C42C22×D711yescharacteristic
401C2×C42C22×D711yescharacteristic
402C4⋊C8—142no—
403C4⋊C8—142no—
404C22⋊C8—74no—
405C22⋊C8—142no—
406#97—142no—
407C4×C8—142no—
408#95—22no—
409#95C22×D714yes—
410C22×C7—24no—
411C22×C7—24no—
412C22×C7—21no—
413C22×C7—21no—
414C22×C7—21no—
415C22×C7—21no—
416C22×C7—21no—
417C22×C7—21no—
418C22×C7#41012yes—
419C22×C7C2×#10412yes—
420C22×C7C22×C22⋊C411yescharacteristic
421C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
422C22×C7C2×#13711yescharacteristic
423C2×D7—42no—
424C2×D7—42no—
425C2×D7—42no—
426C4×C7—21no—
427C4×C7—21no—
428C4×C7—21no—
429C4×C7—21no—
430C4×C7—21no—
431C4×C7—21no—
432C4×C7—21no—
433C4×C7—21no—
434C4×C7—48no—
435C4×C7#41712yes—
436C4×C7#41712yes—
437C4×C7C2×#10412yes—
438C4×C7C2×#10412yes—
439Dic7—42no—
440Dic7—42no—
441Dic7—42no—
442C24C2×C22⋊D711yescharacteristic
443#41—284no—
444#41—282no—
445#41—282no—
446#41—284no—
447C2×Q8—72no—
448C2×Q8—141no—
449C2×Q8—141no—
450C2×D4—72no—
451C2×D4—142no—
452C2×D4—142no—
453C2×D4—142no—
454C2×D4—141no—
455C2×D4—141no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—28no—
460C22×C4—24no—
461C22×C4—42no—
462C22×C4—44no—
463C22×C4—44no—
464C22×C4—142no—
465C22×C4—142no—
466C22×C4—142no—
467C22×C4(C2×D7)⋊C411yescharacteristic
468C22×C4(C2×D7)⋊C411yescharacteristic
469C22×C4(C2×D7)⋊C411yescharacteristic
470C22×C4(C2×D7)⋊C411yescharacteristic
471C22×C4(C2×D7)⋊C411yescharacteristic
472C22×C4(C2×D7)⋊C411yescharacteristic
473C22×C4(C2×D7)⋊C411yescharacteristic
474C22×C4(C2×D7)⋊C411yescharacteristic
475C22×C4C2×C4×D711yescharacteristic
476C22×C4C2×C4×D711yescharacteristic
477C22×C4C2×D2811yescharacteristic
478C22×C4C2×D2811yescharacteristic
479C22×C4C2×C22⋊D711yescharacteristic
480C22×C4C2×C22⋊D711yescharacteristic
481C22×C4C2×C22⋊D711yescharacteristic
482C22×C4C2×C22⋊D711yescharacteristic
483C22×C4C2×C22⋊D711yescharacteristic
484C22×C4C23×D711yescharacteristic
485M16—284no—
486C2×C8—144no—
487C4⋊C4—28no—
488C4⋊C4—28no—
489C4⋊C4—72no—
490C4⋊C4—72no—
491C4⋊C4—142no—
492C4⋊C4—142no—
493C4⋊C4—142no—
494C4⋊C4—142no—
495C4⋊C4—142no—
496C4⋊C4—141no—
497C4⋊C4—141no—
498C4⋊C4—141no—
499C4⋊C4—141no—
500C4⋊C4—142no—
501C22⋊C4—142no—
502C22⋊C4—142no—
503C22⋊C4—142no—
504C22⋊C4—142no—
505C22⋊C4—142no—
506C22⋊C4—142no—
507C22⋊C4—142no—
508C22⋊C4—142no—
509C22⋊C4—142no—
510C42—44no—
511C42—44no—
512C42—142no—
513C42—142no—
514C42—142no—
515C42(C2×D7)⋊C411yescharacteristic
516C42(C2×D7)⋊C411yescharacteristic
517C42(C2×D7)⋊C411yescharacteristic
518C42(C2×D7)⋊C411yescharacteristic
519C42(C2×D7)⋊C411yescharacteristic
520C42(C2×D7)⋊C411yescharacteristic
521C42(C2×D7)⋊C411yescharacteristic
522C42(C2×D7)⋊C411yescharacteristic
523C42C2×C4×D711yescharacteristic
524C42C2×C4×D711yescharacteristic
525C42C2×C4×D711yescharacteristic
526C42C2×C4×D711yescharacteristic
527C42C2×D2811yescharacteristic
528C42C2×D2811yescharacteristic
529C42C2×D2811yescharacteristic
530C42C2×D2811yescharacteristic
531C2×C7—21no—
532C2×C7—21no—
533C2×C7—22no—
534C2×C7—22no—
535C2×C7C2×#41011yescharacteristic
536C2×C7C2×#41711yescharacteristic
537C2×C7C22×#10411yescharacteristic
538D7—82no—
539C23—22no—
540C23—21no—
541C23—21no—
542C23—22no—
543C23—142no—
544C23C2×(C2×D7)⋊C411yescharacteristic
545C23C2×(C2×D7)⋊C411yescharacteristic
546C23C22×C22⋊D711yescharacteristic
547Q8—282no—
548Q8—282no—
549Q8—282no—
550D4—282no—
551D4—284no—
552D4—282no—
553D4—282no—
554D4—284no—
555D4—282no—
556D4—282no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—28no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—416no—
576C2×C4—44no—
577C2×C4—44no—
578C2×C4—142no—
579C2×C4—142no—
580C2×C4—142no—
581C2×C4—284no—
582C2×C4—284no—
583C2×C4—284no—
584C2×C4#637914yes—
585C2×C4C2×(C2×D7)⋊C411yescharacteristic
586C2×C4C2×(C2×D7)⋊C411yescharacteristic
587C2×C4C2×(C2×D7)⋊C411yescharacteristic
588C2×C4C2×(C2×D7)⋊C411yescharacteristic
589C2×C4C2×(C2×D7)⋊C411yescharacteristic
590C2×C4C2×(C2×D7)⋊C411yescharacteristic
591C2×C4C2×(C2×D7)⋊C411yescharacteristic
592C2×C4C2×(C2×D7)⋊C411yescharacteristic
593C2×C4C2×(C2×D7)⋊C411yescharacteristic
594C2×C4C2×(C2×D7)⋊C411yescharacteristic
595C2×C4#649512yes—
596C2×C4#650512yes—
597C2×C4C22×C4×D711yescharacteristic
598C2×C4C22×D2811yescharacteristic
599C8—284no—
600C7#1754611yescharacteristic, complemented, Sylow
601C22—24no—
602C22—24no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—282no—
610C22—282no—
611C22—282no—
612C22C2×#637912yes—
613C22#8977812yes—
614C22C22×(C2×D7)⋊C411yescharacteristic
615C22C2×#649511yescharacteristic
616C22C2×#650511yescharacteristic
617C4—21no—
618C4—21no—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—21no—
623C4—21no—
624C4—21no—
625C4—48no—
626C4—282no—
627C4—282no—
628C4—282no—
629C4C2×#637912yes—
630C4C2×#637912yes—
631C4#8973812yes—
632C4#8973812yes—
633C2—21no—
634C2—22no—
635C2—21no—
636C2—22no—
637C2—562no—
638C2C22×#637911yescharacteristic
639C2C2×#8973811yescharacteristic
640C2C2×#8977811yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D7)⋊C4
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C4×C7×C4⋊C4C2
socleC22×C7C22×C22⋊C4
prime radical#11742748C2
cosocleC22×C4×C7C24
hypercenterC2×C4×C4⋊C4D7
hypocenterC7#17546
LCSG ▷ C2×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C7×C4⋊C4C2semidirect
3. #11739494C2semidirect
4. #11727225C2semidirect
5. #11727224C2semidirect
6. #11727223C2semidirect
7. #11727152C2semidirect
18. #90170C4semidirect
20. #90168C4semidirect
21. #90168C4semidirect
25. C4×#1157C4semidirect
26. #90161C4semidirect
27. #90161C4semidirect
99. #6438C2×C4semidirect
100. #6437C2×C4semidirect
105. C4×D28C2×C4semidirect
106. C4×D28C2×C4semidirect
113. #6433C2×C4semidirect
114. #6432C2×C4semidirect
115. #6432C2×C4semidirect
116. #6432C2×C4semidirect
121. C4×Dic14C2×C4semidirect
122. C4×Dic14C2×C4semidirect
133. C2×C4×C4⋊C4D7semidirect
600. C7#17546semidirect

Maximal subgroups

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

subgroupindex
#117427482
C2×C4×C7×C4⋊C42
#117394942
#117272252
#117272242
#117272232
#117271522
#175467