Finite Group Databasebeta

← #14217786

Subgroups — #14217786

Order 1792.

2742 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#568C211yesmaximal, characteristic, complemented
2#41×C22⋊D7C211yesmaximal, characteristic
3C2×#90441C211yesmaximal, characteristic, complemented
4#11741520C211yesmaximal, characteristic, complemented
5#11741241C213yesmaximal, complemented
6#11741240C213yesmaximal, complemented
7#11741238C211yesmaximal, characteristic, complemented
8#11741233C213yesmaximal, complemented
9#11741231C213yesmaximal, complemented
10#11741228C211yesmaximal, characteristic, complemented
11Dic7×#131C211yesmaximal, characteristic, complemented
12M16×C22⋊D7C213yesmaximal, complemented
13#11741202C213yesmaximal, complemented
14#11741201C213yesmaximal, complemented
15C2×#89900C213yesmaximal, complemented
16C22×C7×#41C2211yescharacteristic
17C2×D7×#41C2211yescharacteristic
18C7×#568—28no—
19C2×C7×#131C2211yescharacteristic
20C2×C7×#131C2211yescharacteristic
21C2×C7×#131C2213yescomplemented
22C2×C7×#131C2213yescomplemented
23C22×C7×M16C2213yescomplemented
24C22×C7×M16C2213yescomplemented
25#90525C411yescharacteristic
26#90523C2213yes—
27#90522C411yescharacteristic
28#90520C413yes—
29#90519C2213yes—
30#41×Dic7C2211yescharacteristic
31#90515C413yes—
32C2×#6511C2211yescharacteristic
33C2×#6511C2211yescharacteristic
34#90508C411yescharacteristic
35Q8×C22⋊D7C411yescharacteristic
36#90497C413yes—
37D4×C22⋊D7C413yes—
38#90482C2213yes—
39C2×C4×C22⋊D7C2213yes—
40#90441—28no—
41C2×#6470C2213yescomplemented
42C2×D7×M16C2213yescomplemented
43C2×#6464C2213yescomplemented
44C22×#1131C2213yescomplemented
45#90006C2213yescomplemented
46#90006C2213yescomplemented
47#89979C2213yescomplemented
48C2×C22⋊(C7⋊C8)C2213yescomplemented
49#89901C2213yescomplemented
50#89900C2211yescharacteristic
51#89900C2213yes—
52#89900C2213yescomplemented
53#89900C2213yescomplemented
54#89900C2213yescomplemented
55#89900C2213yescomplemented
56#89900C2213yescomplemented
57#89900C2213yescomplemented
58#89900C2216yescomplemented
59#89899C2216yescomplemented
60#89899C2216yescomplemented
61#89898C2213yescomplemented
62#89894C2213yescomplemented
63#89891C2213yescomplemented
64#89890C2213yescomplemented
65M16×Dic7C2213yescomplemented
66#89883C2216yescomplemented
67#89883C2216yescomplemented
68#89882C2213yescomplemented
69C8×C22⋊D7C2216yescomplemented
70C8×C22⋊D7C2216yescomplemented
71C2×(C2×D7)⋊C8C2213yescomplemented
72#89874C2213yescomplemented
73#89873C2213yescomplemented
74C2×Dic7⋊C8C2213yescomplemented
75C2×C8×Dic7C2213yescomplemented
76#60147—71nomaximal, Sylow
77C2×C7×#41—24no—
78C2×C7×#41—24no—
79C2×C7×#41C2×C413yes—
80C2×C7×#41C2×C411yescharacteristic
81C2×C7×#41C2313yes—
82C2×C7×#41C2311yescharacteristic
83C22×C7×Q8C2×C411yescharacteristic
84C22×C7×D4C2×C413yes—
85C23×C4×C7C2313yes—
86C22×C22⋊D7C2×C413yes—
87D7×#41—24no—
88D7×#41—24no—
89C2×#1161C2×C411yescharacteristic
90C2×Q8×D7C2×C411yescharacteristic
91C2×#1159C2×C413yes—
92C2×D4×D7C2×C413yes—
93C2×#1157C2313yes—
94C22×C4×D7C2313yes—
95C7×#131—24no—
96C7×#131—212no—
97C7×#131—212no—
98C7×#131D418yescomplemented
99C2×C7×M16—212no—
100C2×C7×M16—212no—
101C2×C7×M16C2313yes—
102C2×C7×M16C2313yes—
103C2×C7×M16C2313yes—
104C2×C7×M16C2311yescharacteristic
105C2×C7×M16C2313yes—
106C2×C7×M16C2313yes—
107C22×C7×C8C2313yes—
108C22×C7×C8C2316yes—
109C22×C7×C8C2313yes—
110#6516C2×C416yes—
111C2×C22⋊Dic7C2×C413yes—
112#6511—24no—
113#6511—24no—
114#6510C2×C413yes—
115#6509C2×C413yes—
116#6509C2×C413yes—
117Q8×Dic7C2×C411yescharacteristic
118Q8×Dic7C2×C411yescharacteristic
119#6507C2×C413yes—
120#6503C2×C413yes—
121#6502C2×C416yes—
122#6502C2×C416yes—
123#6501C2×C413yes—
124#6501C2×C413yes—
125#6500C2×C416yes—
126#6499C2×C413yes—
127#6498C2×C416yes—
128D4×Dic7C2×C413yes—
129D4×Dic7C2×C413yes—
130#6493C2×C413yes—
131#6493C2×C413yes—
132#6492C2×C416yes—
133C4×C22⋊D7C2×C413yes—
134C4×C22⋊D7C2×C413yes—
135C4×C22⋊D7C2×C413yes—
136C4×C22⋊D7C2×C413yes—
137C4×C22⋊D7C2313yes—
138C4×C22⋊D7C2316yes—
139C4×C22⋊D7C2313yes—
140C4×C22⋊D7C2313yes—
141C4×C22⋊D7C2311yescharacteristic
142C2×(C2×D7)⋊C4C2×C413yes—
143#6489C2313yes—
144#6487C2×C413yes—
145#6487C2×C413yes—
146C2×Dic7⋊C4C2×C413yes—
147C2×C4×Dic7C2313yes—
148C2×#1136C2313yes—
149C2×#1136C2313yes—
150C22×C7⋊C8C2313yes—
151C22×C7⋊C8C2313yes—
152#6470—212no—
153D7×M16—212no—
154#6464—212no—
155C2×#1131—212no—
156C2×#1131C2313yes—
157C2×#1131C2313yes—
158C2×#1131C2311yescharacteristic
159C2×#1131C2313yes—
160C2×C8×D7C2316yes—
161C22⋊(C7⋊C8)C2313yes—
162C22⋊(C7⋊C8)C2316yes—
163C22⋊(C7⋊C8)C2313yes—
164C22⋊(C7⋊C8)C2313yes—
165C22⋊(C7⋊C8)C2311yescharacteristic
166(C2×D7)⋊C8C2311yescharacteristic
167(C2×D7)⋊C8C2313yes—
168(C2×D7)⋊C8C2313yes—
169(C2×D7)⋊C8C2313yes—
170(C2×D7)⋊C8C2316yes—
171#6389C2316yes—
172Dic7⋊C8C2311yescharacteristic
173Dic7⋊C8C2313yes—
174Dic7⋊C8C2313yes—
175Dic7⋊C8C2313yes—
176Dic7⋊C8C2316yes—
177C8×Dic7C2311yescharacteristic
178C8×Dic7C2313yes—
179C8×Dic7C2313yes—
180C8×Dic7C2313yes—
181C2×#568—71no—
182C2×#568D711yescharacteristic, complemented
183D4×#41—71no—
184#2935—73no—
185D4×M16—73no—
186#2933—73no—
187#2933—73no—
188#2931—73no—
189#2930—73no—
190#2930—73no—
191C2×#436—73no—
192#2906—71no—
193#2880—71no—
194#2880—71no—
195C4×#131—71no—
196C24×C7C22×C413yes—
197C23×D7C22×C413yes—
198C7×#41—24no—
199C7×#41—212no—
200C7×#41—26no—
201C7×#41—26no—
202C7×#41C2×D414yes—
203C7×#41#4114yes—
204C2×C7×Q8—24no—
205C2×C7×Q8C22×C413yes—
206C2×C7×Q8C22×C411yescharacteristic
207C2×C7×D4—212no—
208C2×C7×D4C22×C416yes—
209C2×C7×D4C22×C413yes—
210C2×C7×D4C22×C413yes—
211C22×C4×C7—26no—
212C22×C4×C7—26no—
213C22×C4×C7C22×C413yes—
214C22×C4×C7C22×C413yes—
215C22×C4×C7C22×C413yes—
216C22×C4×C7C2413yes—
217C22×C4×C7C2411yescharacteristic
218C22×C4×C7C2413yes—
219C2×C22⋊D7—46no—
220C2×C22⋊D7C22×C411yescharacteristic
221C2×C22⋊D7C22×C413yes—
222C2×C22⋊D7C22×C416yes—
223C2×C22⋊D7C22×C413yes—
224C2×C22⋊D7C22×C413yes—
225C2×C22⋊D7C22×C416yes—
226C22×Dic7C22×C413yes—
227C22×Dic7C22×C413yes—
228C22×Dic7C22×C413yes—
229#1161—24no—
230Q8×D7—24no—
231#1159—212no—
232D4×D7—212no—
233#1157—26no—
234#1157—26no—
235C2×D28C22×C413yes—
236C2×C4×D7—26no—
237C2×C4×D7—26no—
238C2×C4×D7C22×C413yes—
239C2×C4×D7C22×C413yes—
240C2×C4×D7C2413yes—
241C2×C4×D7C2411yescharacteristic
242C2×Dic14C22×C413yes—
243C7×M16—26no—
244C7×M16—26no—
245C7×M16—22no—
246C7×M16—26no—
247C7×M16—26no—
248C7×M16C2×D4112yescomplemented
249C2×C7×C8—26no—
250C2×C7×C8—212no—
251C2×C7×C8C2×D4112yescomplemented
252C2×C7×C8C2411yescharacteristic
253C2×C7×C8C2413yes—
254C2×C7×C8C2413yes—
255C2×C7×C8C2411yescharacteristic
256C22⋊Dic7C22×C413yes—
257C22⋊Dic7C22×C416yes—
258C22⋊Dic7C22×C416yes—
259C22⋊Dic7C22×C411yescharacteristic
260C22⋊Dic7C22×C413yes—
261C22⋊Dic7C22×C413yes—
262(C2×D7)⋊C4C22×C411yescharacteristic
263(C2×D7)⋊C4C22×C413yes—
264(C2×D7)⋊C4C22×C413yes—
265(C2×D7)⋊C4C22×C413yes—
266(C2×D7)⋊C4C22×C416yes—
267C4⋊Dic7C22×C413yes—
268C4⋊Dic7C22×C413yes—
269Dic7⋊C4C22×C411yescharacteristic
270Dic7⋊C4C22×C413yes—
271Dic7⋊C4C22×C413yes—
272Dic7⋊C4C22×C413yes—
273Dic7⋊C4C22×C416yes—
274C4×Dic7C22×C413yes—
275C4×Dic7C22×C413yes—
276C4×Dic7C2411yescharacteristic
277C4×Dic7C2413yes—
278#1136—26no—
279#1136—26no—
280C2×C7⋊C8—26no—
281C2×C7⋊C8—26no—
282C2×C7⋊C8C2413yes—
283C2×C7⋊C8C2411yescharacteristic
284C2×C7⋊C8C2411yescharacteristic
285C2×C7⋊C8C2413yes—
286#1131—22no—
287#1131—26no—
288#1131—26no—
289#1131—26no—
290C8×D7—212no—
291C22×#41—71no—
292C22×#41C2×D711yescharacteristic
293#568—28no—
294#568—148no—
295C2×#131—71no—
296C2×#131—71no—
297C2×#131—73no—
298C2×#131—73no—
299C2×#131C2×D711yescharacteristic
300C2×#131C2×D711yescharacteristic
301C2×#131C2×D713yescomplemented
302C2×#131C2×D713yescomplemented
303C22×M16—73no—
304C22×M16—73no—
305C22×M16C2×D713yescomplemented
306C22×M16C2×D713yescomplemented
307#550—71no—
308D4×Q8—71no—
309#548—71no—
310#548—71no—
311#547—73no—
312#546—73no—
313#546—73no—
314D42—73no—
315#532—73no—
316#525—73no—
317#525—73no—
318C4×#41—71no—
319C2×C4×D4—73no—
320#436—71no—
321#436—73no—
322#436—73no—
323#436—73no—
324#436—73no—
325#436—73no—
326#436—73no—
327#436—73no—
328#436—76no—
329#435—76no—
330#435—76no—
331#435—76no—
332#435—76no—
333C8×D4—76no—
334C8×D4—76no—
335#424—73no—
336#424—73no—
337#423—73no—
338C2×C4⋊C8—73no—
339#408—73no—
340#408—73no—
341#408—73no—
342#408—73no—
343#407—73no—
344#407—73no—
345C2×C22⋊C8—73no—
346C2×C22⋊C8—73no—
347#405—73no—
348#405—73no—
349C4×M16—73no—
350C2×C4×C8—73no—
351C23×C7—26no—
352C23×C7—43no—
353C23×C7—43no—
354C23×C7C23×C411yescharacteristic
355C23×C7C23×C413yes—
356C23×C7C23×C413yes—
357C22×D7—26no—
358C22×D7—43no—
359C22×D7—43no—
360C22×D7C23×C411yescharacteristic
361C22×D7C23×C413yes—
362C7×Q8—26no—
363C7×Q8C4×D414yes—
364C7×D4—212no—
365C7×D4—26no—
366C7×D4C4×D4112yes—
367C2×C4×C7—26no—
368C2×C4×C7—26no—
369C2×C4×C7—26no—
370C2×C4×C7—23no—
371C2×C4×C7—21no—
372C2×C4×C7—21no—
373C2×C4×C7—23no—
374C2×C4×C7C23×C411yescharacteristic
375C2×C4×C7C23×C413yes—
376C2×C4×C7C23×C413yes—
377C2×C4×C7C22×D416yes—
378C2×C4×C7C2×#4116yes—
379C2×C4×C7C2511yescharacteristic
380C22⋊D7—212no—
381C22⋊D7—22no—
382C22⋊D7—26no—
383C22⋊D7—43no—
384C22⋊D7—43no—
385C22⋊D7—46no—
386C2×Dic7—26no—
387C2×Dic7—26no—
388C2×Dic7—43no—
389C2×Dic7C23×C411yescharacteristic
390C2×Dic7C23×C413yes—
391C2×Dic7C23×C413yes—
392C2×Dic7C23×C413yes—
393C2×Dic7C23×C411yescharacteristic
394C2×Dic7C23×C411yescharacteristic
395D28—26no—
396C4×D7—26no—
397C4×D7—26no—
398C4×D7—23no—
399C4×D7—21no—
400C4×D7—21no—
401C4×D7—23no—
402Dic14—26no—
403C7×C8—21no—
404C7×C8—23no—
405C7×C8C22×D416yes—
406C7×C8C22×D412yes—
407C7⋊C8—23no—
408C7⋊C8—21no—
409C7⋊C8—21no—
410C7⋊C8—23no—
411C2×#41—24no—
412C2×#41—24no—
413C2×#41—71no—
414C2×#41—73no—
415C2×#41—73no—
416C2×#41—144no—
417C2×#41—144no—
418C2×#41C4×D713yes—
419C2×#41C4×D711yescharacteristic
420C2×#41C22×D713yes—
421C2×#41C22×D711yescharacteristic
422C22×Q8—71no—
423C22×Q8C4×D711yescharacteristic
424C22×D4—73no—
425C22×D4—73no—
426C22×D4C4×D713yes—
427C23×C4—73no—
428C23×C4C22×D713yes—
429#131—24no—
430#131—212no—
431#131—212no—
432#131—144no—
433#131—144no—
434#131—1412no—
435#131—1412no—
436#131C22⋊D718yescomplemented
437C2×M16—212no—
438C2×M16—212no—
439C2×M16—73no—
440C2×M16—73no—
441C2×M16—73no—
442C2×M16—71no—
443C2×M16—73no—
444C2×M16—73no—
445C2×M16—1412no—
446C2×M16—1412no—
447C2×M16C22×D713yes—
448C2×M16C22×D711yescharacteristic
449C2×M16C22×D713yes—
450C2×M16C22×D713yes—
451C2×M16C22×D713yes—
452C2×M16C22×D713yes—
453C22×C8—73no—
454C22×C8—73no—
455C22×C8—76no—
456C22×C8C22×D713yes—
457C22×C8C22×D716yes—
458C22×C8C22×D713yes—
459C4⋊Q8—73no—
460#127—73no—
461#124—73no—
462#124—73no—
463#123—76no—
464#123—76no—
465C22⋊Q8—73no—
466C22⋊Q8—73no—
467C22⋊Q8—73no—
468C22⋊Q8—73no—
469#121—73no—
470#121—73no—
471#121—76no—
472#121—76no—
473#121—73no—
474#121—73no—
475#120—76no—
476#120—76no—
477C4×Q8—71no—
478C4×Q8—71no—
479C4×D4—73no—
480C4×D4—73no—
481C4×D4—73no—
482C4×D4—73no—
483C4×D4—73no—
484C4×D4—73no—
485C4×D4—71no—
486C4×D4—73no—
487C4×D4—73no—
488C4×D4—73no—
489C4×D4—76no—
490#117—73no—
491C2×C4⋊C4—73no—
492C2×C22⋊C4—73no—
493C2×C22⋊C4—73no—
494C2×C42—73no—
495C4⋊C8—71no—
496C4⋊C8—73no—
497C4⋊C8—73no—
498C4⋊C8—73no—
499C4⋊C8—76no—
500C22⋊C8—71no—
501C22⋊C8—73no—
502C22⋊C8—73no—
503C22⋊C8—73no—
504C22⋊C8—76no—
505C22⋊C8—71no—
506C22⋊C8—73no—
507C22⋊C8—73no—
508C22⋊C8—73no—
509C22⋊C8—76no—
510#97—76no—
511C4×C8—71no—
512C4×C8—73no—
513C4×C8—73no—
514C4×C8—73no—
515C22×C7—23no—
516C22×C7—23no—
517C22×C7—21no—
518C22×C7—23no—
519C22×C7—21no—
520C22×C7—23no—
521C22×C7—23no—
522C22×C7—21no—
523C22×C7—86no—
524C22×C7C2×C4×D416yes—
525C22×C7C24×C411yescharacteristic
526C2×D7—21no—
527C2×D7—23no—
528C2×D7—21no—
529C2×D7—23no—
530C2×D7—23no—
531C2×D7—21no—
532C2×D7—86no—
533C4×C7—21no—
534C4×C7—23no—
535C4×C7C2×C4×D416yes—
536C4×C7C23×D411yescharacteristic
537C4×C7C22×#4111yescharacteristic
538Dic7—23no—
539Dic7—21no—
540Dic7—23no—
541Dic7—21no—
542Dic7—23no—
543Dic7#56812yescomplemented
544C24—73no—
545C24C2×C4×D713yes—
546#41—24no—
547#41—212no—
548#41—26no—
549#41—26no—
550#41—144no—
551#41—1412no—
552#41—146no—
553#41—146no—
554#41#115714yes—
555#41C2×C22⋊D714yes—
556C2×Q8—24no—
557C2×Q8—73no—
558C2×Q8—144no—
559C2×Q8C2×C4×D713yes—
560C2×Q8C2×C4×D711yescharacteristic
561C2×D4—212no—
562C2×D4—71no—
563C2×D4—73no—
564C2×D4—76no—
565C2×D4—73no—
566C2×D4—73no—
567C2×D4—76no—
568C2×D4—73no—
569C2×D4—1412no—
570C2×D4—286no—
571C2×D4C2×C4×D716yes—
572C2×D4C2×C4×D713yes—
573C2×D4C2×C4×D713yes—
574C22×C4—26no—
575C22×C4—26no—
576C22×C4—73no—
577C22×C4—73no—
578C22×C4—73no—
579C22×C4—73no—
580C22×C4—73no—
581C22×C4—73no—
582C22×C4—71no—
583C22×C4—146no—
584C22×C4—146no—
585C22×C4C2×C4×D713yes—
586C22×C4C2×C4×D713yes—
587C22×C4C2×C4×D713yes—
588C22×C4C23×D713yes—
589C22×C4C23×D711yescharacteristic
590C22×C4C23×D713yes—
591M16—26no—
592M16—26no—
593M16—22no—
594M16—26no—
595M16—26no—
596M16—146no—
597M16—146no—
598M16—146no—
599M16—142no—
600M16—146no—
601M16—146no—
602M16C2×C22⋊D7112yescomplemented
603C2×C8—26no—
604C2×C8—212no—
605C2×C8—71no—
606C2×C8—73no—
607C2×C8—71no—
608C2×C8—73no—
609C2×C8—146no—
610C2×C8—146no—
611C2×C8—1412no—
612C2×C8C2×C22⋊D7112yescomplemented
613C2×C8C23×D711yescharacteristic
614C2×C8C23×D713yes—
615C2×C8C23×D711yescharacteristic
616C2×C8C23×D713yes—
617C4⋊C4—71no—
618C4⋊C4—73no—
619C4⋊C4—73no—
620C4⋊C4—73no—
621C4⋊C4—76no—
622C4⋊C4—73no—
623C4⋊C4—73no—
624C22⋊C4—71no—
625C22⋊C4—73no—
626C22⋊C4—73no—
627C22⋊C4—73no—
628C22⋊C4—76no—
629C22⋊C4—76no—
630C22⋊C4—71no—
631C22⋊C4—73no—
632C22⋊C4—73no—
633C22⋊C4—73no—
634C22⋊C4—76no—
635C42—73no—
636C42—73no—
637C42—71no—
638C42—73no—
639C2×C7—26no—
640C2×C7—43no—
641C2×C7—41no—
642C2×C7C22×C4×D411yescharacteristic
643C2×C7C2×#56811yescharacteristic
644C2×C7#357311yescharacteristic
645D7—43no—
646D7—41no—
647C23—26no—
648C23—43no—
649C23—43no—
650C23—71no—
651C23—73no—
652C23—146no—
653C23—283no—
654C23—283no—
655C23C22×C4×D711yescharacteristic
656C23C22×C4×D713yes—
657C23C22×C4×D713yes—
658Q8—26no—
659Q8—146no—
660Q8C4×C22⋊D714yes—
661D4—212no—
662D4—26no—
663D4—146no—
664D4—142no—
665D4—1412no—
666D4—146no—
667D4—286no—
668D4—283no—
669D4—283no—
670D4C4×C22⋊D7112yes—
671C2×C4—26no—
672C2×C4—26no—
673C2×C4—26no—
674C2×C4—21no—
675C2×C4—23no—
676C2×C4—23no—
677C2×C4—21no—
678C2×C4—71no—
679C2×C4—71no—
680C2×C4—73no—
681C2×C4—73no—
682C2×C4—71no—
683C2×C4—73no—
684C2×C4—146no—
685C2×C4—146no—
686C2×C4—146no—
687C2×C4—146no—
688C2×C4—141no—
689C2×C4—143no—
690C2×C4—143no—
691C2×C4—141no—
692C2×C4—283no—
693C2×C4C22×C4×D711yescharacteristic
694C2×C4C22×C4×D713yes—
695C2×C4C22×C4×D713yes—
696C2×C4C2×#115716yes—
697C2×C4C22×C22⋊D716yes—
698C2×C4C24×D711yescharacteristic
699C8—21no—
700C8—23no—
701C8—141no—
702C8—143no—
703C8—143no—
704C8—141no—
705C8C22×C22⋊D716yes—
706C8C22×C22⋊D712yes—
707C7#6014711yescharacteristic, complemented, Sylow
708C22—23no—
709C22—23no—
710C22—21no—
711C22—23no—
712C22—21no—
713C22—23no—
714C22—23no—
715C22—21no—
716C22—86no—
717C22—141no—
718C22—143no—
719C22—141no—
720C22—143no—
721C22—143no—
722C22—141no—
723C22—566no—
724C22C2×C4×C22⋊D716yes—
725C22C23×C4×D711yescharacteristic
726C4—21no—
727C4—23no—
728C4—72no—
729C4—141no—
730C4—143no—
731C4—143no—
732C4—141no—
733C4—143no—
734C4C2×C4×C22⋊D716yes—
735C4C22×#115711yescharacteristic
736C4C23×C22⋊D711yescharacteristic
737C2—26no—
738C2—41no—
739C2—43no—
740C2—281no—
741C2—283no—
742C2D7×#56811yescharacteristic
743C2#1174423411yescharacteristic
744C2C22×C4×C22⋊D711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D7
commutator, socleC22×C7C24×C4
FittingC2×C7×#568C2
prime radical#41×C22⋊D7C2
cosocleC2×C4×C7C25
hypercenterC2×#568D7
hypocenterC7#60147
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×#568

Complements

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

NH ≅ G/Ntype
1. C2×C7×#568C2semidirect
3. C2×#90441C2semidirect
4. #11741520C2semidirect
5. #11741241C2semidirect
6. #11741240C2semidirect
7. #11741238C2semidirect
8. #11741233C2semidirect
9. #11741231C2semidirect
10. #11741228C2semidirect
11. Dic7×#131C2semidirect
12. M16×C22⋊D7C2semidirect
13. #11741202C2semidirect
14. #11741201C2semidirect
15. C2×#89900C2semidirect
21. C2×C7×#131C22semidirect
22. C2×C7×#131C22semidirect
23. C22×C7×M16C22semidirect
24. C22×C7×M16C22semidirect
41. C2×#6470C22semidirect
42. C2×D7×M16C22semidirect
43. C2×#6464C22semidirect
44. C22×#1131C22semidirect
45. #90006C22semidirect
46. #90006C22semidirect
47. #89979C22semidirect
48. C2×C22⋊(C7⋊C8)C22semidirect
49. #89901C22semidirect
52. #89900C22semidirect
53. #89900C22semidirect
54. #89900C22semidirect
55. #89900C22semidirect
56. #89900C22semidirect
57. #89900C22semidirect
58. #89900C22semidirect
59. #89899C22semidirect
60. #89899C22semidirect
61. #89898C22semidirect
62. #89894C22semidirect
63. #89891C22semidirect
64. #89890C22semidirect
65. M16×Dic7C22semidirect
66. #89883C22semidirect
67. #89883C22semidirect
68. #89882C22semidirect
69. C8×C22⋊D7C22semidirect
70. C8×C22⋊D7C22semidirect
71. C2×(C2×D7)⋊C8C22semidirect
72. #89874C22semidirect
73. #89873C22semidirect
74. C2×Dic7⋊C8C22semidirect
75. C2×C8×Dic7C22semidirect
98. C7×#131D4semidirect
182. C2×#568D7semidirect
248. C7×M16C2×D4semidirect
251. C2×C7×C8C2×D4semidirect
301. C2×#131C2×D7semidirect
302. C2×#131C2×D7semidirect
305. C22×M16C2×D7semidirect
306. C22×M16C2×D7semidirect
436. #131C22⋊D7semidirect
543. Dic7#568semidirect
602. M16C2×C22⋊D7semidirect
612. C2×C8C2×C22⋊D7semidirect
707. C7#60147semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5682
#41×C22⋊D72
C2×#904412
#117415202
#117412412
#117412402
#117412382
#117412332
#117412312
#117412282
Dic7×#1312
M16×C22⋊D72
#117412022
#117412012
C2×#899002
#601477