Finite Group Databasebeta

← #13321866

Subgroups — #13321866

Order 1792.

962 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D7×#125C211yesmaximal, characteristic
2#11736776C211yesmaximal, characteristic
3#11735962C211yesmaximal, characteristic
4C7×#1528C211yesmaximal, characteristic, complemented
5#11729489C211yesmaximal, characteristic, complemented
6#11728566C211yesmaximal, characteristic, complemented
7#11727617C211yesmaximal, characteristic, complemented
8#11726121C214yesmaximal, complemented
9#11726117C214yesmaximal, complemented
10C2×C7×#125C2211yescharacteristic
11D7×#125—21no—
12D7×#125—21no—
13D7×#125—21no—
14D7×#125—21no—
15D7×#125C412yes—
16D7×#125C412yes—
17D7×#125C2212yes—
18D7×#125C2212yes—
19C2×D7×C4⋊C4—21no—
20C2×D7×C4⋊C4—21no—
21C2×D7×C4⋊C4C411yescharacteristic
22C2×D7×C4⋊C4C411yescharacteristic
23C2×#6453C411yescharacteristic
24C2×#6453C411yescharacteristic
25C2×#6452—21no—
26C2×#6452—21no—
27C2×C42×D7C2211yescharacteristic
28C2×#6433C2211yescharacteristic
29C7×#432C2211yescharacteristic
30C4×C7×M16C2211yescharacteristic
31#89898—21no—
32#89890—21no—
33#89698C2211yescharacteristic
34C4×#1136C2211yescharacteristic
35#89609—21no—
36#89605—21no—
37#89498—21no—
38#89490—21no—
39#89479C2212yes—
40#89477C2212yes—
41#89477C2212yes—
42#89477C2212yes—
43#89457—21no—
44#89457—21no—
45C7×#330C2214yescomplemented
46#89338C2214yescomplemented
47#89260C2214yescomplemented
48#89260C2214yescomplemented
49#17667—71nomaximal, Sylow
50C22×C4×D7—21no—
51C22×C4×D7—21no—
52C22×C4×D7C2×C411yescharacteristic
53C22×C4×D7D411yescharacteristic
54C22×C4×D7D411yescharacteristic
55C2×C7×M16—21no—
56C7×#125—21no—
57C7×#125—21no—
58C7×#125C2×C412yes—
59C7×#125C2312yes—
60C2×C7×C4⋊C4—21no—
61C2×C7×C4⋊C4—21no—
62C2×C7×C4⋊C4C2×C411yescharacteristic
63C2×C7×C4⋊C4C2×C411yescharacteristic
64C2×C42×C7C2311yescharacteristic
65C2×C4⋊Dic7—21no—
66C2×C4⋊Dic7—21no—
67C2×C4⋊Dic7C2×C411yescharacteristic
68C2×C4⋊Dic7C2×C411yescharacteristic
69C2×Dic7⋊C4—21no—
70C2×Dic7⋊C4—21no—
71C2×Dic7⋊C4—21no—
72C2×Dic7⋊C4—21no—
73C2×Dic7⋊C4—21no—
74C2×Dic7⋊C4—21no—
75C2×C4×Dic7C2×C411yescharacteristic
76C2×C4×Dic7D411yescharacteristic
77C2×C4×Dic7D411yescharacteristic
78C2×#1136—21no—
79C2×#1131—22no—
80D7×C4⋊C4—21no—
81D7×C4⋊C4—21no—
82D7×C4⋊C4—21no—
83D7×C4⋊C4—21no—
84D7×C4⋊C4—22no—
85D7×C4⋊C4—22no—
86D7×C4⋊C4—22no—
87D7×C4⋊C4—22no—
88D7×C4⋊C4—22no—
89D7×C4⋊C4—22no—
90D7×C4⋊C4—22no—
91D7×C4⋊C4—22no—
92D7×C4⋊C4C2×C412yes—
93D7×C4⋊C4C2×C412yes—
94D7×C4⋊C4C2×C412yes—
95D7×C4⋊C4C2×C412yes—
96#6453—21no—
97#6453—21no—
98#6453—21no—
99#6453—21no—
100#6453C2×C412yes—
101#6453C2×C412yes—
102#6453C2×C412yes—
103#6453C2×C412yes—
104#6452—22no—
105#6452—22no—
106#6452—22no—
107#6452—22no—
108#6452—22no—
109#6452—22no—
110#6452—22no—
111#6452—22no—
112C42×D7C2×C411yescharacteristic
113C42×D7C2×C411yescharacteristic
114C42×D7D411yescharacteristic
115C42×D7D411yescharacteristic
116C42×D7D411yescharacteristic
117C42×D7D411yescharacteristic
118C42×D7C2311yescharacteristic
119C42×D7C2311yescharacteristic
120#6433—21no—
121#6433—21no—
122#6433C2×C412yes—
123#6433C2312yes—
124C7×C4⋊C8—21no—
125C7×C22⋊C8—21no—
126C7×#97C2312yes—
127C7×#97C2312yes—
128C4×C7×C8—21no—
129C22⋊(C7⋊C8)—21no—
130(C2×D7)⋊C8—22no—
131(C2×D7)⋊C8—22no—
132(C2×D7)⋊C8—22no—
133Dic7⋊C8—22no—
134Dic7⋊C8—22no—
135Dic7⋊C8—22no—
136C8×Dic7—22no—
137C4⋊(C7⋊C8)—21no—
138#6377C2312yes—
139#6377C2312yes—
140C4×C7⋊C8—21no—
141C22×#125—71no—
142#2920—71no—
143#2920—71no—
144#1534—74no—
145#1528—71no—
146#1528—71no—
147#1528—74no—
148#1528—71no—
149#1528D711yescharacteristic, complemented
150C23×D7C22⋊C411yescharacteristic
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7C22×C411yescharacteristic
154C22×C4×C7C2×D411yescharacteristic
155C22×C4×C7C2×D411yescharacteristic
156C22×Dic7—21no—
157C22×Dic7—21no—
158C22×Dic7C22⋊C411yescharacteristic
159C22×Dic7C22⋊C411yescharacteristic
160C22×Dic7C22⋊C411yescharacteristic
161C2×C4×D7—24no—
162C2×C4×D7—22no—
163C2×C4×D7—22no—
164C2×C4×D7—22no—
165C2×C4×D7—22no—
166C2×C4×D7—42no—
167C2×C4×D7—42no—
168C2×C4×D7—44no—
169C2×C4×D7—44no—
170C2×C4×D7C22⋊C411yescharacteristic
171C2×C4×D7C22⋊C411yescharacteristic
172C2×C4×D7C22⋊C411yescharacteristic
173C2×C4×D7C22⋊C411yescharacteristic
174C2×C4×D7C22⋊C411yescharacteristic
175C2×C4×D7C22⋊C411yescharacteristic
176C2×C4×D7C22×C411yescharacteristic
177C2×C4×D7C22×C411yescharacteristic
178C2×C4×D7C2×D411yescharacteristic
179C2×C4×D7C2×D411yescharacteristic
180C2×C4×D7C2×D411yescharacteristic
181C2×C4×D7C2×D411yescharacteristic
182C7×M16—42no—
183C2×C7×C8—22no—
184C2×C7×C8—22no—
185C7×C4⋊C4—22no—
186C7×C4⋊C4—22no—
187C7×C4⋊C4—21no—
188C7×C4⋊C4—21no—
189C7×C4⋊C4—22no—
190C7×C4⋊C4—22no—
191C7×C4⋊C4C22×C412yes—
192C7×C4⋊C4C22×C412yes—
193C42×C7C22×C411yescharacteristic
194C42×C7C2×D411yescharacteristic
195C42×C7C2×D411yescharacteristic
196C42×C7C2411yescharacteristic
197C4⋊Dic7—21no—
198C4⋊Dic7—21no—
199C4⋊Dic7—22no—
200C4⋊Dic7—22no—
201C4⋊Dic7—22no—
202C4⋊Dic7—22no—
203C4⋊Dic7C22×C412yes—
204C4⋊Dic7C22×C412yes—
205Dic7⋊C4—22no—
206Dic7⋊C4—22no—
207Dic7⋊C4—22no—
208Dic7⋊C4—22no—
209Dic7⋊C4—22no—
210Dic7⋊C4—22no—
211Dic7⋊C4—22no—
212Dic7⋊C4—22no—
213Dic7⋊C4—22no—
214Dic7⋊C4—22no—
215Dic7⋊C4—22no—
216Dic7⋊C4—22no—
217C4×Dic7C22⋊C411yescharacteristic
218C4×Dic7C22⋊C411yescharacteristic
219C4×Dic7C22⋊C411yescharacteristic
220C4×Dic7C22⋊C411yescharacteristic
221C4×Dic7C22⋊C411yescharacteristic
222C4×Dic7C22⋊C411yescharacteristic
223C4×Dic7C22×C411yescharacteristic
224C4×Dic7C22×C411yescharacteristic
225C4×Dic7C2×D411yescharacteristic
226C4×Dic7C2×D411yescharacteristic
227C4×Dic7C2×D411yescharacteristic
228C4×Dic7C2×D411yescharacteristic
229#1136—42no—
230C2×C7⋊C8—22no—
231C2×C7⋊C8—22no—
232#1131—44no—
233C2×#125—72no—
234C2×#125—72no—
235C2×#125—72no—
236C2×#125—72no—
237C2×#125—71no—
238C2×#125—71no—
239C2×#125—71no—
240C2×#125—141no—
241C2×#125—141no—
242C2×#125—141no—
243C2×#125—141no—
244C2×#125—141no—
245C2×#125—141no—
246C2×#125C2×D711yescharacteristic
247C22×C4⋊C4—71no—
248C22×C4⋊C4—71no—
249C22×C4⋊C4—141no—
250C22×C4⋊C4—141no—
251C22×C42—71no—
252#432—71no—
253#432—72no—
254#432—72no—
255#432—72no—
256#432C2×D711yescharacteristic
257#431—141no—
258#431—141no—
259#431—141no—
260#431—141no—
261#423—141no—
262#423—141no—
263#407—141no—
264#407—141no—
265C4×M16—71no—
266C4×M16—72no—
267C4×M16C2×D711yescharacteristic
268#330—74no—
269#330—74no—
270#330—74no—
271#330C2×D714yescomplemented
272C23×C7C2×C22⋊C411yescharacteristic
273C22×D7—22no—
274C22×D7—22no—
275C22×D7—22no—
276C22×D7C2×C22⋊C411yescharacteristic
277C22×D7C2×C22⋊C411yescharacteristic
278C2×C4×C7—22no—
279C2×C4×C7—22no—
280C2×C4×C7—22no—
281C2×C4×C7—22no—
282C2×C4×C7—41no—
283C2×C4×C7—42no—
284C2×C4×C7—42no—
285C2×C4×C7C2×C22⋊C411yescharacteristic
286C2×C4×C7C2×C22⋊C411yescharacteristic
287C2×C4×C7C2×C22⋊C411yescharacteristic
288C2×C4×C7C23×C411yescharacteristic
289C2×C4×C7C22×D411yescharacteristic
290C2×C4×C7C22×D411yescharacteristic
291C2×Dic7—22no—
292C2×Dic7—22no—
293C2×Dic7—22no—
294C2×Dic7—22no—
295C2×Dic7—41no—
296C2×Dic7—42no—
297C2×Dic7—42no—
298C2×Dic7C2×C22⋊C411yescharacteristic
299C2×Dic7C2×C22⋊C411yescharacteristic
300C2×Dic7C2×C22⋊C411yescharacteristic
301C2×Dic7C2×C22⋊C411yescharacteristic
302C2×Dic7C2×C22⋊C411yescharacteristic
303C2×Dic7C2×C22⋊C411yescharacteristic
304C4×D7—22no—
305C4×D7—22no—
306C4×D7—22no—
307C4×D7—22no—
308C4×D7—22no—
309C4×D7—41no—
310C4×D7—41no—
311C4×D7—41no—
312C4×D7—41no—
313C4×D7—41no—
314C4×D7—41no—
315C4×D7—44no—
316C4×D7—44no—
317C4×D7—44no—
318C4×D7—44no—
319C4×D7#10114yes—
320C7×C8—42no—
321C7×C8—42no—
322C7⋊C8—42no—
323C7⋊C8—42no—
324C23×C4—71no—
325C23×C4—71no—
326C23×C4—71no—
327C23×C4—141no—
328C23×C4—141no—
329C2×M16—21no—
330C2×M16—142no—
331C2×M16—141no—
332#125—21no—
333#125—21no—
334#125—72no—
335#125—72no—
336#125—72no—
337#125—72no—
338#125—72no—
339#125—72no—
340#125—142no—
341#125—142no—
342#125—142no—
343#125—142no—
344#125—142no—
345#125—142no—
346#125—142no—
347#125—142no—
348#125—141no—
349#125—141no—
350#125—141no—
351#125—141no—
352#125—141no—
353#125—141no—
354#125C4×D712yes—
355#125C22×D712yes—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—71no—
359C2×C4⋊C4—71no—
360C2×C4⋊C4—72no—
361C2×C4⋊C4—72no—
362C2×C4⋊C4—72no—
363C2×C4⋊C4—72no—
364C2×C4⋊C4—141no—
365C2×C4⋊C4—141no—
366C2×C4⋊C4—141no—
367C2×C4⋊C4—141no—
368C2×C4⋊C4—142no—
369C2×C4⋊C4—142no—
370C2×C4⋊C4—142no—
371C2×C4⋊C4—142no—
372C2×C4⋊C4—142no—
373C2×C4⋊C4—142no—
374C2×C4⋊C4—142no—
375C2×C4⋊C4—142no—
376C2×C4⋊C4—141no—
377C2×C4⋊C4—141no—
378C2×C4⋊C4—141no—
379C2×C4⋊C4—141no—
380C2×C4⋊C4—141no—
381C2×C4⋊C4—141no—
382C2×C4⋊C4—141no—
383C2×C4⋊C4—141no—
384C2×C4⋊C4C4×D711yescharacteristic
385C2×C4⋊C4C4×D711yescharacteristic
386C2×C42—71no—
387C2×C42—71no—
388C2×C42—71no—
389C2×C42—71no—
390C2×C42—71no—
391C2×C42—71no—
392C2×C42—71no—
393C2×C42—71no—
394C2×C42—71no—
395C2×C42—71no—
396C2×C42—71no—
397C2×C42C22×D711yescharacteristic
398C4⋊C8—21no—
399C4⋊C8—142no—
400C4⋊C8—142no—
401C4⋊C8—142no—
402C4⋊C8—141no—
403C22⋊C8—21no—
404C22⋊C8—142no—
405C22⋊C8—142no—
406C22⋊C8—142no—
407C22⋊C8—141no—
408#97—72no—
409#97—72no—
410#97C22×D712yes—
411#97C22×D712yes—
412C4×C8—21no—
413C4×C8—142no—
414C4×C8—141no—
415C22×C7—21no—
416C22×C7—21no—
417C22×C7#42112yes—
418C22×C7C22×C22⋊C411yescharacteristic
419C2×D7—28no—
420C2×D7—21no—
421C2×D7—21no—
422C2×D7—21no—
423C2×D7—21no—
424C2×D7C2×#10112yes—
425C2×D7#42112yes—
426C4×C7—21no—
427C4×C7—21no—
428C4×C7—21no—
429C4×C7—21no—
430C4×C7—21no—
431C4×C7—42no—
432C4×C7—42no—
433C4×C7C2×#10112yes—
434Dic7—21no—
435Dic7—21no—
436Dic7—21no—
437Dic7—21no—
438Dic7—21no—
439Dic7—42no—
440Dic7—42no—
441Dic7C2×#10112yes—
442C24—71no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—71no—
446C22×C4—71no—
447C22×C4—71no—
448C22×C4—71no—
449C22×C4—71no—
450C22×C4—71no—
451C22×C4—71no—
452C22×C4—71no—
453C22×C4—71no—
454C22×C4—71no—
455C22×C4—71no—
456C22×C4—71no—
457C22×C4—71no—
458C22×C4—71no—
459C22×C4—71no—
460C22×C4—144no—
461C22×C4—142no—
462C22×C4—142no—
463C22×C4—142no—
464C22×C4—142no—
465C22×C4—141no—
466C22×C4—141no—
467C22×C4—282no—
468C22×C4—282no—
469C22×C4—284no—
470C22×C4—284no—
471C22×C4C2×C4×D711yescharacteristic
472C22×C4D4×D711yescharacteristic
473C22×C4D4×D711yescharacteristic
474M16—42no—
475M16—284no—
476M16—282no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—142no—
480C2×C8—142no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—72no—
488C4⋊C4—72no—
489C4⋊C4—142no—
490C4⋊C4—142no—
491C4⋊C4—142no—
492C4⋊C4—142no—
493C4⋊C4—142no—
494C4⋊C4—142no—
495C4⋊C4—142no—
496C4⋊C4—142no—
497C4⋊C4—142no—
498C4⋊C4—142no—
499C4⋊C4—142no—
500C4⋊C4—142no—
501C4⋊C4—142no—
502C4⋊C4—142no—
503C4⋊C4—141no—
504C4⋊C4—141no—
505C4⋊C4—142no—
506C4⋊C4—142no—
507C4⋊C4C2×C4×D712yes—
508C4⋊C4C2×C4×D712yes—
509C42—71no—
510C42—71no—
511C42—71no—
512C42—71no—
513C42—71no—
514C42—71no—
515C42—71no—
516C42—71no—
517C42—71no—
518C42—71no—
519C42—71no—
520C42—71no—
521C42C2×C4×D711yescharacteristic
522C42D4×D711yescharacteristic
523C42D4×D711yescharacteristic
524C42C23×D711yescharacteristic
525C2×C7—22no—
526C2×C7C22×#10111yescharacteristic
527C2×C7C2×#42111yescharacteristic
528C2×C7C2×#42111yescharacteristic
529D7—22no—
530D7—22no—
531C23—71no—
532C23—71no—
533C23—142no—
534C23—142no—
535C23—142no—
536C23D7×C22⋊C411yescharacteristic
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—71no—
545C2×C4—74no—
546C2×C4—71no—
547C2×C4—71no—
548C2×C4—71no—
549C2×C4—71no—
550C2×C4—71no—
551C2×C4—142no—
552C2×C4—142no—
553C2×C4—142no—
554C2×C4—142no—
555C2×C4—142no—
556C2×C4—142no—
557C2×C4—142no—
558C2×C4—142no—
559C2×C4—142no—
560C2×C4—281no—
561C2×C4—281no—
562C2×C4—281no—
563C2×C4—281no—
564C2×C4—281no—
565C2×C4—281no—
566C2×C4—284no—
567C2×C4—284no—
568C2×C4—284no—
569C2×C4—284no—
570C2×C4—281no—
571C2×C4—282no—
572C2×C4—282no—
573C2×C4D7×C22⋊C411yescharacteristic
574C2×C4D7×C22⋊C411yescharacteristic
575C2×C4D7×C22⋊C411yescharacteristic
576C2×C4C22×C4×D711yescharacteristic
577C2×C4C2×D4×D711yescharacteristic
578C2×C4C2×D4×D711yescharacteristic
579C8—42no—
580C8—42no—
581C8—282no—
582C8—282no—
583C7#1766711yescharacteristic, complemented, Sylow
584C22—21no—
585C22—21no—
586C22—72no—
587C22—72no—
588C22—148no—
589C22—141no—
590C22—141no—
591C22—141no—
592C22—141no—
593C22#8959312yes—
594C22C2×D7×C22⋊C411yescharacteristic
595C4—21no—
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—42no—
601C4—42no—
602C4—72no—
603C4—141no—
604C4—141no—
605C4—141no—
606C4—141no—
607C4—141no—
608C4—282no—
609C4—282no—
610C4D7×#10112yes—
611C2—22no—
612C2—142no—
613C2—142no—
614C2C2×D7×#10111yescharacteristic
615C2C2×#8959311yescharacteristic
616C2D7×#42111yescharacteristic
subgroupG/H
centerC22C2×D7×C22⋊C4
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
FittingC7×#1528C2
socleC22×C7C22×C22⋊C4
prime radicalC23×D7C22⋊C4
cosocleC42×C7C24
hypercenter#1528D7
hypocenterC7#17667
LCSG ▷ C2×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1528

Complements

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

NH ≅ G/Ntype
4. C7×#1528C2semidirect
5. #11729489C2semidirect
6. #11728566C2semidirect
7. #11727617C2semidirect
8. #11726121C2semidirect
9. #11726117C2semidirect
45. C7×#330C22semidirect
46. #89338C22semidirect
47. #89260C22semidirect
48. #89260C22semidirect
149. #1528D7semidirect
271. #330C2×D7semidirect
583. C7#17667semidirect

Maximal subgroups

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

subgroupindex
C2×D7×#1252
#117367762
#117359622
C7×#15282
#117294892
#117285662
#117276172
#117261212
#117261172
#176677