Finite Group Databasebeta

← #13320102

Subgroups — #13320102

Order 1792.

996 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90202C211yesmaximal, characteristic
2#11736078C212yesmaximal
3C7×#1463C211yesmaximal, characteristic, complemented
4C2×#89323C211yesmaximal, characteristic, complemented
5#11727726C212yesmaximal, complemented
6#11725901C212yesmaximal, complemented
7#11725898C211yesmaximal, characteristic, complemented
8D7×#324C211yesmaximal, characteristic, complemented
9#11725882C212yesmaximal, complemented
10#11725881C211yesmaximal, characteristic, complemented
11#11725879C211yesmaximal, characteristic, complemented
12C22×C7×C4⋊C4C2211yescharacteristic
13C2×C4×C22⋊D7C411yescharacteristic
14C2×C4×C22⋊D7C411yescharacteristic
15C2×C4×C22⋊D7C2211yescharacteristic
16C2×#6487C411yescharacteristic
17C2×#6487C411yescharacteristic
18C2×#6487C2211yescharacteristic
19#90202—22no—
20#90202—22no—
21#90202—22no—
22#90202—22no—
23C2×#6460C411yescharacteristic
24C2×#6459C411yescharacteristic
25C2×#6459C2211yescharacteristic
26C2×D7×C4⋊C4C2211yescharacteristic
27C2×#6452C411yescharacteristic
28C2×#6452C2211yescharacteristic
29C2×#6451C411yescharacteristic
30C2×#6450C2211yescharacteristic
31C7×#407C2212yes—
32C2×C22⋊(C7⋊C8)C2212yes—
33#89900—22no—
34#89899—22no—
35#89502—22no—
36#89498C2212yes—
37(C22⋊D7)⋊C8—22no—
38D7×C22⋊C8C2212yes—
39#89491C2212yes—
40#89490C2212yes—
41C7×#324C2211yescharacteristic
42C7×#324C2211yescharacteristic
43C7×#324C2212yes—
44#89323C2211yescharacteristic
45#89323C2211yescharacteristic
46#89323C2212yes—
47#89264C2212yes—
48#89264C2212yes—
49#89264C2212yes—
50#89264C2212yes—
51#17426—71nomaximal, Sylow
52C23×C4×C7C2×C411yescharacteristic
53C23×C4×C7C2×C411yescharacteristic
54C23×C4×C7C2311yescharacteristic
55C22×C22⋊D7C2×C411yescharacteristic
56C22×C4×D7C2×C411yescharacteristic
57C22×C4×D7C2×C411yescharacteristic
58C22×C4×D7C2311yescharacteristic
59C22×Dic14C2×C411yescharacteristic
60C22×Dic14C2×C411yescharacteristic
61C22×Dic14C2×C411yescharacteristic
62C2×C7×M16—22no—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4—22no—
65C2×C7×C4⋊C4C2×C411yescharacteristic
66C2×C7×C4⋊C4C2×C411yescharacteristic
67C2×C7×C4⋊C4C2311yescharacteristic
68C2×C7×C4⋊C4C2311yescharacteristic
69C2×C22⋊Dic7C2×C411yescharacteristic
70C2×C22⋊Dic7C2×C411yescharacteristic
71C2×C22⋊Dic7C2×C411yescharacteristic
72C4×C22⋊D7—21no—
73C4×C22⋊D7—21no—
74C4×C22⋊D7—21no—
75C4×C22⋊D7—21no—
76C4×C22⋊D7—21no—
77C4×C22⋊D7—21no—
78C4×C22⋊D7—21no—
79C4×C22⋊D7—21no—
80C4×C22⋊D7D412yes—
81C4×C22⋊D7D412yes—
82C4×C22⋊D7D412yes—
83C4×C22⋊D7D412yes—
84C2×(C2×D7)⋊C4C2×C411yescharacteristic
85C2×(C2×D7)⋊C4C2×C411yescharacteristic
86C2×(C2×D7)⋊C4C2×C411yescharacteristic
87C2×C4⋊Dic7C2×C411yescharacteristic
88C2×C4⋊Dic7C2×C411yescharacteristic
89C2×C4⋊Dic7C2×C411yescharacteristic
90#6487—22no—
91#6487—22no—
92#6487—22no—
93#6487—22no—
94#6487—22no—
95#6487—22no—
96C2×Dic7⋊C4C2×C411yescharacteristic
97C2×Dic7⋊C4C2×C411yescharacteristic
98C2×Dic7⋊C4C2×C411yescharacteristic
99C2×Dic7⋊C4C2×C411yescharacteristic
100C2×Dic7⋊C4C2×C411yescharacteristic
101C2×Dic7⋊C4C2×C411yescharacteristic
102C2×Dic7⋊C4C2×C411yescharacteristic
103C2×Dic7⋊C4C2311yescharacteristic
104C2×Dic7⋊C4C2311yescharacteristic
105C2×C4×Dic7C2×C411yescharacteristic
106C2×C4×Dic7C2×C411yescharacteristic
107C2×C4×Dic7C2311yescharacteristic
108C22×C7⋊C8—22no—
109C2×#1131—22no—
110C2×C8×D7—22no—
111#6460—22no—
112#6460—22no—
113#6459—22no—
114#6459—22no—
115#6459—22no—
116#6459—22no—
117D7×C4⋊C4—22no—
118D7×C4⋊C4—22no—
119#6452—22no—
120#6452—22no—
121#6452—22no—
122#6452—22no—
123#6451—22no—
124#6451—22no—
125#6450—22no—
126#6450—22no—
127C7×C22⋊C8—22no—
128C7×C22⋊C8C2312yes—
129C7×C22⋊C8C2312yes—
130C22⋊(C7⋊C8)—22no—
131C22⋊(C7⋊C8)C2312yes—
132C22⋊(C7⋊C8)C2312yes—
133(C2×D7)⋊C8—22no—
134(C2×D7)⋊C8—22no—
135#6389—22no—
136Dic7⋊C8—22no—
137Dic7⋊C8—22no—
138C8×Dic7—22no—
139C2×#554—71no—
140#2974—72no—
141#1472—72no—
142#1472—72no—
143#1470—72no—
144#1467—71no—
145#1463—71no—
146#1463D711yescharacteristic, complemented
147#1461—71no—
148C2×#324—71no—
149C2×#324—71no—
150C24×C7C22×C411yescharacteristic
151C23×D7C22×C411yescharacteristic
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—22no—
157C22×C4×C7—41no—
158C22×C4×C7—81no—
159C22×C4×C7—81no—
160C22×C4×C7C22×C411yescharacteristic
161C22×C4×C7C22×C411yescharacteristic
162C22×C4×C7C22×C411yescharacteristic
163C22×C4×C7C22×C411yescharacteristic
164C22×C4×C7C22×C411yescharacteristic
165C22×C4×C7C2×D412yes—
166C22×C4×C7C2×D412yes—
167C22×C4×C7C2411yescharacteristic
168C2×C22⋊D7—24no—
169C2×C22⋊D7C22⋊C411yescharacteristic
170C2×C22⋊D7C22⋊C411yescharacteristic
171C2×C22⋊D7C22⋊C411yescharacteristic
172C2×C22⋊D7C22⋊C411yescharacteristic
173C22×Dic7C22×C411yescharacteristic
174C22×Dic7C22×C411yescharacteristic
175C22×Dic7C22×C411yescharacteristic
176C22×Dic7C22×C411yescharacteristic
177C22×Dic7C22×C411yescharacteristic
178C22×Dic7C22×C411yescharacteristic
179C22×Dic7C22×C411yescharacteristic
180C2×C4×D7—21no—
181C2×C4×D7—21no—
182C2×C4×D7—22no—
183C2×C4×D7—21no—
184C2×C4×D7—21no—
185C2×C4×D7—41no—
186C2×C4×D7—81no—
187C2×C4×D7—81no—
188C2×C4×D7C2×D412yes—
189C2×C4×D7C2×D412yes—
190C2×Dic14—22no—
191C2×Dic14—22no—
192C2×Dic14—22no—
193C2×Dic14—22no—
194C2×Dic14—41no—
195C2×Dic14—81no—
196C2×Dic14—81no—
197C7×M16—82no—
198C2×C7×C8—22no—
199C2×C7×C8—22no—
200C7×C4⋊C4—22no—
201C7×C4⋊C4—22no—
202C7×C4⋊C4—22no—
203C7×C4⋊C4—22no—
204C22⋊Dic7—21no—
205C22⋊Dic7—21no—
206C22⋊Dic7—21no—
207C22⋊Dic7—21no—
208C22⋊Dic7C22⋊C412yes—
209C22⋊Dic7C22⋊C412yes—
210(C2×D7)⋊C4—21no—
211(C2×D7)⋊C4—21no—
212(C2×D7)⋊C4—21no—
213(C2×D7)⋊C4—21no—
214(C2×D7)⋊C4C22⋊C412yes—
215(C2×D7)⋊C4C22⋊C412yes—
216C4⋊Dic7—22no—
217C4⋊Dic7—22no—
218C4⋊Dic7—22no—
219Dic7⋊C4—22no—
220Dic7⋊C4—22no—
221Dic7⋊C4—22no—
222Dic7⋊C4—21no—
223Dic7⋊C4—21no—
224Dic7⋊C4—21no—
225Dic7⋊C4—21no—
226Dic7⋊C4—22no—
227Dic7⋊C4—22no—
228Dic7⋊C4—22no—
229Dic7⋊C4C22⋊C412yes—
230Dic7⋊C4C22⋊C412yes—
231C4×Dic7—21no—
232C4×Dic7—21no—
233C4×Dic7—21no—
234C4×Dic7—21no—
235C4×Dic7C2×D412yes—
236C4×Dic7C2×D412yes—
237C2×C7⋊C8—22no—
238C2×C7⋊C8—22no—
239C2×C7⋊C8—82no—
240#1131—82no—
241C8×D7—82no—
242#554—142no—
243#554—142no—
244#554—142no—
245#554—142no—
246C2×C4⋊Q8—71no—
247C2×#125—71no—
248C2×#125—71no—
249C2×C22⋊Q8—71no—
250C2×C22⋊Q8—71no—
251C2×C22⋊Q8—71no—
252C2×C22⋊Q8—71no—
253C2×C22⋊Q8—71no—
254C2×C22⋊Q8—71no—
255C2×C4×Q8—71no—
256C2×C4×D4—71no—
257C2×C4×D4—71no—
258C2×C4×D4—71no—
259C22×C4⋊C4—71no—
260C22×C4⋊C4C2×D711yescharacteristic
261#436—142no—
262#435—142no—
263#435—142no—
264C8×D4—142no—
265#432—72no—
266#431—72no—
267#407—72no—
268#407C2×D712yes—
269C2×C22⋊C8—72no—
270C2×C22⋊C8—72no—
271#324—71no—
272#324—71no—
273#324—72no—
274#324—72no—
275#324—72no—
276#324—72no—
277#324—72no—
278#324C2×D711yescharacteristic
279#324C2×D711yescharacteristic
280#324C2×D712yes—
281C23×C7—21no—
282C23×C7—21no—
283C23×C7—22no—
284C23×C7—41no—
285C23×C7C2×C22⋊C411yescharacteristic
286C23×C7C2×C22⋊C411yescharacteristic
287C23×C7C23×C411yescharacteristic
288C22×D7—21no—
289C22×D7—21no—
290C22×D7—22no—
291C22×D7—41no—
292C22×D7C2×C22⋊C411yescharacteristic
293C22×D7C2×C22⋊C411yescharacteristic
294C2×C4×C7—21no—
295C2×C4×C7—21no—
296C2×C4×C7—21no—
297C2×C4×C7—21no—
298C2×C4×C7—21no—
299C2×C4×C7—21no—
300C2×C4×C7—21no—
301C2×C4×C7—42no—
302C2×C4×C7—42no—
303C2×C4×C7—41no—
304C2×C4×C7—41no—
305C2×C4×C7—42no—
306C2×C4×C7—42no—
307C2×C4×C7—41no—
308C2×C4×C7—41no—
309C2×C4×C7—81no—
310C2×C4×C7—81no—
311C2×C4×C7C2×C22⋊C412yes—
312C2×C4×C7#13112yes—
313C2×C4×C7C22×D412yes—
314C22⋊D7—22no—
315C22⋊D7—22no—
316C22⋊D7—22no—
317C22⋊D7#10114yes—
318C2×Dic7—21no—
319C2×Dic7—21no—
320C2×Dic7—22no—
321C2×Dic7—21no—
322C2×Dic7—21no—
323C2×Dic7—21no—
324C2×Dic7—21no—
325C2×Dic7—21no—
326C2×Dic7—21no—
327C2×Dic7—21no—
328C2×Dic7—21no—
329C2×Dic7—41no—
330C2×Dic7—41no—
331C2×Dic7—41no—
332C2×Dic7C2×C22⋊C411yescharacteristic
333C2×Dic7C2×C22⋊C412yes—
334C2×Dic7C2×C22⋊C412yes—
335C2×Dic7C2×C22⋊C411yescharacteristic
336C4×D7—42no—
337C4×D7—42no—
338C4×D7—42no—
339C4×D7—42no—
340C4×D7—81no—
341C4×D7—81no—
342Dic14—44no—
343Dic14—82no—
344Dic14—82no—
345C7×C8—42no—
346C7×C8—42no—
347C7⋊C8—42no—
348C7⋊C8—42no—
349C22×Q8—71no—
350C22×Q8—71no—
351C22×Q8—71no—
352C22×D4—71no—
353C23×C4—71no—
354C23×C4—71no—
355C23×C4—71no—
356C23×C4C4×D711yescharacteristic
357C23×C4C4×D711yescharacteristic
358C23×C4C22×D711yescharacteristic
359C2×M16—22no—
360C2×M16—142no—
361C22×C8—142no—
362C22×C8—142no—
363C4⋊Q8—142no—
364C4⋊Q8—142no—
365#125—142no—
366#125—142no—
367#125—142no—
368#125—142no—
369C22⋊Q8—142no—
370C22⋊Q8—142no—
371C22⋊Q8—142no—
372C22⋊Q8—142no—
373C22⋊Q8—142no—
374C22⋊Q8—142no—
375C22⋊Q8—142no—
376C22⋊Q8—142no—
377C22⋊Q8—142no—
378C22⋊Q8—142no—
379C22⋊Q8—142no—
380C22⋊Q8—142no—
381C4×Q8—142no—
382C4×Q8—142no—
383C4×D4—72no—
384C4×D4—72no—
385C4×D4—72no—
386C4×D4—72no—
387C4×D4—141no—
388C4×D4—141no—
389C4×D4—141no—
390C4×D4—141no—
391C4×D4—141no—
392C4×D4—141no—
393C4×D4—141no—
394C4×D4—141no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—71no—
398C2×C4⋊C4—71no—
399C2×C4⋊C4—71no—
400C2×C4⋊C4—71no—
401C2×C4⋊C4—71no—
402C2×C4⋊C4—71no—
403C2×C4⋊C4—71no—
404C2×C4⋊C4—71no—
405C2×C4⋊C4—71no—
406C2×C4⋊C4—71no—
407C2×C4⋊C4—71no—
408C2×C4⋊C4—71no—
409C2×C4⋊C4—142no—
410C2×C4⋊C4—142no—
411C2×C4⋊C4C4×D711yescharacteristic
412C2×C4⋊C4C4×D711yescharacteristic
413C2×C4⋊C4C22×D711yescharacteristic
414C2×C4⋊C4C22×D711yescharacteristic
415C2×C22⋊C4—71no—
416C2×C22⋊C4—71no—
417C2×C22⋊C4—71no—
418C2×C22⋊C4—71no—
419C2×C22⋊C4—71no—
420C2×C22⋊C4—71no—
421C2×C42—71no—
422C2×C42—71no—
423C2×C42—71no—
424C4⋊C8—142no—
425C4⋊C8—142no—
426C22⋊C8—22no—
427C22⋊C8—72no—
428C22⋊C8—72no—
429C22⋊C8—142no—
430C22⋊C8—142no—
431C22⋊C8—142no—
432C22⋊C8C22×D712yes—
433C22⋊C8C22×D712yes—
434#97—142no—
435C4×C8—142no—
436C22×C7—21no—
437C22×C7—21no—
438C22×C7—21no—
439C22×C7—21no—
440C22×C7—21no—
441C22×C7—21no—
442C22×C7—21no—
443C22×C7—42no—
444C22×C7—42no—
445C22×C7C2×#10112yes—
446C22×C7C22×C22⋊C411yescharacteristic
447C22×C7C2×#13111yescharacteristic
448C22×C7#56811yescharacteristic
449C2×D7—21no—
450C2×D7—21no—
451C2×D7—21no—
452C2×D7—21no—
453C2×D7—21no—
454C2×D7—42no—
455C2×D7—42no—
456C2×D7C2×#10112yes—
457C4×C7—22no—
458C4×C7—22no—
459C4×C7—22no—
460C4×C7—41no—
461C4×C7—41no—
462C4×C7—41no—
463Dic7—22no—
464Dic7—22no—
465Dic7—21no—
466Dic7—41no—
467Dic7—41no—
468Dic7—41no—
469Dic7—41no—
470Dic7C2×#10112yes—
471C24—71no—
472C24C2×C4×D711yescharacteristic
473C2×Q8—142no—
474C2×Q8—142no—
475C2×Q8—142no—
476C2×Q8—142no—
477C2×Q8—281no—
478C2×Q8—561no—
479C2×Q8—561no—
480C2×D4—71no—
481C2×D4—71no—
482C2×D4—71no—
483C2×D4—71no—
484C2×D4—144no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—41no—
491C22×C4—71no—
492C22×C4—71no—
493C22×C4—71no—
494C22×C4—72no—
495C22×C4—72no—
496C22×C4—71no—
497C22×C4—71no—
498C22×C4—71no—
499C22×C4—71no—
500C22×C4—81no—
501C22×C4—81no—
502C22×C4—141no—
503C22×C4—141no—
504C22×C4—141no—
505C22×C4—141no—
506C22×C4—142no—
507C22×C4—281no—
508C22×C4—561no—
509C22×C4—561no—
510C22×C4C2×C4×D711yescharacteristic
511C22×C4C2×C4×D711yescharacteristic
512C22×C4C2×C4×D711yescharacteristic
513C22×C4C2×C4×D711yescharacteristic
514C22×C4C2×C4×D711yescharacteristic
515C22×C4D4×D712yes—
516C22×C4D4×D712yes—
517C22×C4C23×D711yescharacteristic
518M16—82no—
519M16—562no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—142no—
523C2×C8—142no—
524C2×C8—562no—
525C2×C8—562no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—72no—
531C4⋊C4—72no—
532C4⋊C4—142no—
533C4⋊C4—141no—
534C4⋊C4—141no—
535C4⋊C4—141no—
536C4⋊C4—141no—
537C4⋊C4—142no—
538C4⋊C4—142no—
539C4⋊C4—142no—
540C4⋊C4—142no—
541C4⋊C4—142no—
542C4⋊C4—142no—
543C4⋊C4—142no—
544C4⋊C4—142no—
545C22⋊C4—72no—
546C22⋊C4—72no—
547C22⋊C4—72no—
548C22⋊C4—72no—
549C22⋊C4—141no—
550C22⋊C4—141no—
551C22⋊C4—141no—
552C22⋊C4—141no—
553C22⋊C4—141no—
554C22⋊C4—141no—
555C22⋊C4—141no—
556C22⋊C4—141no—
557C42—72no—
558C42—72no—
559C42—141no—
560C42—141no—
561C42—141no—
562C42—141no—
563C2×C7—21no—
564C2×C7—21no—
565C2×C7—22no—
566C2×C7—41no—
567C2×C7#288011yescharacteristic
568C2×C7#288311yescharacteristic
569C2×C7C22×#10111yescharacteristic
570D7—22no—
571D7—41no—
572C23—21no—
573C23—21no—
574C23—22no—
575C23—41no—
576C23—71no—
577C23—71no—
578C23—142no—
579C23—141no—
580C23—141no—
581C23—281no—
582C23D7×C22⋊C411yescharacteristic
583C23D7×C22⋊C411yescharacteristic
584C23C22×C4×D711yescharacteristic
585Q8—284no—
586Q8—562no—
587Q8—562no—
588D4—74no—
589D4—142no—
590D4—142no—
591D4—142no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—71no—
608C2×C4—71no—
609C2×C4—72no—
610C2×C4—72no—
611C2×C4—81no—
612C2×C4—81no—
613C2×C4—142no—
614C2×C4—141no—
615C2×C4—141no—
616C2×C4—141no—
617C2×C4—141no—
618C2×C4—141no—
619C2×C4—141no—
620C2×C4—141no—
621C2×C4—141no—
622C2×C4—141no—
623C2×C4—141no—
624C2×C4—282no—
625C2×C4—282no—
626C2×C4—282no—
627C2×C4—282no—
628C2×C4—281no—
629C2×C4—281no—
630C2×C4—281no—
631C2×C4—561no—
632C2×C4—561no—
633C2×C4D7×C22⋊C412yes—
634C2×C4#647012yes—
635C2×C4C2×D4×D712yes—
636C8—42no—
637C8—42no—
638C8—282no—
639C8—282no—
640C7#1742611yescharacteristic, complemented, Sylow
641C22—21no—
642C22—21no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—21no—
647C22—21no—
648C22—42no—
649C22—42no—
650C22—72no—
651C22—141no—
652C22—141no—
653C22—141no—
654C22—141no—
655C22—141no—
656C22—282no—
657C22—282no—
658C22D7×#10112yes—
659C22C2×D7×C22⋊C411yescharacteristic
660C22C2×#647011yescharacteristic
661C22#9043611yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—41no—
666C4—41no—
667C4—41no—
668C4—72no—
669C4—142no—
670C4—142no—
671C4—141no—
672C4—281no—
673C4—281no—
674C4—281no—
675C4—281no—
676C2—21no—
677C2—21no—
678C2—22no—
679C2—41no—
680C2—142no—
681C2—281no—
682C2#1173607611yescharacteristic
683C2#1173613311yescharacteristic
684C2C2×D7×#10111yescharacteristic
subgroupG/H
centerC22C2×D7×C22⋊C4
commutatorC23×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1463C2
socleC22×C7C22×C22⋊C4
prime radicalC22×C22⋊D7C2×C4
cosocleC22×C4×C7C24
hypercenter#1463D7
hypocenterC7#17426
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
3. C7×#1463C2semidirect
4. C2×#89323C2semidirect
5. #11727726C2semidirect
6. #11725901C2semidirect
7. #11725898C2semidirect
8. D7×#324C2semidirect
9. #11725882C2semidirect
10. #11725881C2semidirect
11. #11725879C2semidirect
146. #1463D7semidirect
640. C7#17426semidirect

Maximal subgroups

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

subgroupindex
C2×#902022
#117360782
C7×#14632
C2×#893232
#117277262
#117259012
#117258982
D7×#3242
#117258822
#117258812
#117258792
#174267