Finite Group Databasebeta

← #13259167

Subgroups — #13259167

Order 1792.

1254 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90436C211yesmaximal, characteristic
2C2×#89778C211yesmaximal, characteristic
3#11739673C211yesmaximal, characteristic
4C7×#1733C211yesmaximal, characteristic, complemented
5C2×#89350C211yesmaximal, characteristic, complemented
6#11729328C211yesmaximal, characteristic, complemented
7C2×#89327C211yesmaximal, characteristic, complemented
8C22×#1157C2211yescharacteristic
9C22×C7×M16C2211yescharacteristic
10C2×C7×#117C2211yescharacteristic
11C2×C7×#117C2211yescharacteristic
12C2×#6489C2211yescharacteristic
13C22×C4×Dic7C2211yescharacteristic
14C22×#1136C2211yescharacteristic
15#90436—22no—
16#90436—22no—
17#90436—22no—
18#90436C414yescomplemented
19C2×#6470—22no—
20C2×D7×M16—22no—
21C2×#6464—22no—
22#89778—22no—
23#89778C414yescomplemented
24#89760C412yescomplemented
25#89746C412yescomplemented
26#89730—22no—
27C2×#6380—22no—
28C4×(C2×D7)⋊C4—22no—
29C7×#339—22no—
30#89350—22no—
31#89327—22no—
32#89327—22no—
33#10751—71nomaximal, Sylow
34C23×C4×C7C2311yescharacteristic
35C22×C22⋊D7D412yes—
36C23×Dic7—21no—
37C2×#1157—21no—
38C2×#1157—21no—
39C2×#1157—21no—
40C2×#1157—21no—
41C2×#1157—21no—
42C2×#1157—21no—
43C2×#1157—21no—
44C2×#1157—21no—
45C2×#1157C2×C412yes—
46C2×#1157C2×C412yes—
47C2×#1157D412yes—
48C2×#1157Q812yes—
49C22×D28C2×C411yescharacteristic
50C22×C4×D7D412yes—
51C22×Dic14C2×C411yescharacteristic
52C2×C7×M16—21no—
53C2×C7×M16—21no—
54C2×C7×M16—21no—
55C2×C7×M16C2×C412yes—
56C2×C7×M16D412yes—
57C2×C7×M16D412yes—
58C22×C7×C8—21no—
59C7×#117—21no—
60C7×#117—21no—
61C7×#117—21no—
62C7×#117—21no—
63C7×#117—21no—
64C7×#117—21no—
65C7×#117—21no—
66C7×#117C2×C412yes—
67C2×C7×C4⋊C4—21no—
68C2×C7×C4⋊C4C2×C412yes—
69C2×C7×C22⋊C4—21no—
70C2×C7×C22⋊C4—21no—
71C2×C42×C7—21no—
72C2×C42×C7—21no—
73C2×C22⋊Dic7—21no—
74C2×(C2×D7)⋊C4—24no—
75#6489—21no—
76#6489—21no—
77#6489—21no—
78#6489C2×C412yes—
79C2×C4⋊Dic7—21no—
80C2×C4×Dic7—21no—
81C2×C4×Dic7—21no—
82C2×C4×Dic7—21no—
83C2×C4×Dic7—21no—
84C2×C4×Dic7—21no—
85C2×C4×Dic7—21no—
86C2×C4×Dic7C2×C412yes—
87C2×#1136—21no—
88C2×#1136—21no—
89C2×#1136—21no—
90C2×#1136C2×C412yes—
91C2×#1136D412yes—
92C2×#1136D412yes—
93C22×C7⋊C8—21no—
94#6470—28no—
95#6470—28no—
96D7×M16—28no—
97D7×M16—28no—
98#6464—28no—
99#6464—28no—
100C2×#1131—24no—
101C2×C8×D7—24no—
102C7⋊#95—24no—
103#6380—28no—
104C2×#568—71no—
105C2×#410—71no—
106#2297—71no—
107#1733—71no—
108#1733D711yescharacteristic, complemented
109C2×#339—71no—
110C2×#339—71no—
111C24×C7C2×D411yescharacteristic
112C23×D7C22⋊C412yes—
113C22×C4×C7—22no—
114C22×C4×C7—41no—
115C22×C4×C7C22×C411yescharacteristic
116C22×C4×C7C22×C411yescharacteristic
117C22×C4×C7C22×C411yescharacteristic
118C22×C4×C7C2×D411yescharacteristic
119C22×C4×C7C2×D411yescharacteristic
120C22×C4×C7C2×D411yescharacteristic
121C22×C4×C7C2×D411yescharacteristic
122C22×C4×C7C2×D411yescharacteristic
123C22×C4×C7C2×D411yescharacteristic
124C22×C4×C7C2×Q811yescharacteristic
125C22×C4×C7#4111yescharacteristic
126C22×C4×C7#4111yescharacteristic
127C22×C4×C7#4111yescharacteristic
128C22×C4×C7#4111yescharacteristic
129C2×C22⋊D7—22no—
130C2×C22⋊D7—22no—
131C2×C22⋊D7—22no—
132C2×C22⋊D7—22no—
133C2×C22⋊D7C22⋊C414yes—
134C2×C22⋊D7C4⋊C414yes—
135C22×Dic7—22no—
136C22×Dic7—44no—
137C22×Dic7—41no—
138C22×Dic7—41no—
139C22×Dic7—41no—
140C22×Dic7C22⋊C412yes—
141#1157—22no—
142#1157—22no—
143#1157—22no—
144#1157—22no—
145#1157—22no—
146#1157—22no—
147#1157—22no—
148#1157—22no—
149#1157—22no—
150#1157—22no—
151#1157—22no—
152#1157—22no—
153#1157—22no—
154#1157—22no—
155#1157—22no—
156#1157—22no—
157C2×D28—21no—
158C2×D28—21no—
159C2×D28—21no—
160C2×D28—21no—
161C2×D28C4212yes—
162C2×D28C4⋊C412yes—
163C2×C4×D7—22no—
164C2×C4×D7—22no—
165C2×C4×D7—22no—
166C2×C4×D7—22no—
167C2×C4×D7C22⋊C414yes—
168C2×C4×D7C4⋊C414yes—
169C2×Dic14—21no—
170C2×Dic14—21no—
171C2×Dic14—21no—
172C2×Dic14—21no—
173C2×Dic14C4212yes—
174C2×Dic14C4⋊C412yes—
175C7×M16—22no—
176C7×M16—22no—
177C7×M16—22no—
178C7×M16C22⋊C414yescomplemented
179C2×C7×C8—22no—
180C2×C7×C8—22no—
181C2×C7×C8—22no—
182C7×C4⋊C4—22no—
183C7×C4⋊C4—22no—
184C7×C4⋊C4—22no—
185C7×C4⋊C4—41no—
186C7×C22⋊C4—22no—
187C7×C22⋊C4—41no—
188C7×C22⋊C4—41no—
189C7×C22⋊C4—41no—
190C42×C7—22no—
191C42×C7—41no—
192C42×C7—41no—
193C42×C7—41no—
194C22⋊Dic7—22no—
195C22⋊Dic7—41no—
196(C2×D7)⋊C4—48no—
197C4⋊Dic7—22no—
198C4⋊Dic7—41no—
199C4×Dic7—22no—
200C4×Dic7—22no—
201C4×Dic7—22no—
202C4×Dic7—41no—
203C4×Dic7—41no—
204C4×Dic7—41no—
205#1136—22no—
206#1136—22no—
207#1136—22no—
208#1136C22⋊C414yescomplemented
209C2×C7⋊C8—22no—
210C2×C7⋊C8—22no—
211C2×C7⋊C8—22no—
212#1131—216no—
213C8×D7—216no—
214C22×#41—71no—
215#568—74no—
216#568—142no—
217#568—142no—
218#568—142no—
219C2×#131—142no—
220C2×#131—142no—
221C22×M16—71no—
222C22×M16—142no—
223C22×M16C2×D711yescharacteristic
224C2×#117—71no—
225C2×#117C2×D711yescharacteristic
226C2×#117C2×D711yescharacteristic
227C22×C42—71no—
228#410—74no—
229#410—142no—
230C2×#99—142no—
231#391—72no—
232#390—72no—
233#386—142no—
234C4×C22⋊C4—142no—
235#339—22no—
236#339—142no—
237#339—142no—
238#339—142no—
239C23×C7—42no—
240C23×C7C2×C22⋊C411yescharacteristic
241C23×C7C2×C22⋊C411yescharacteristic
242C23×C7C2×C4⋊C411yescharacteristic
243C23×C7#12111yescharacteristic
244C23×C7#12111yescharacteristic
245C23×C7#12111yescharacteristic
246C23×C7#12111yescharacteristic
247C22×D7—22no—
248C22×D7—22no—
249C22×D7—44no—
250C22×D7#9514yes—
251C2×C4×C7—44no—
252C2×C4×C7—42no—
253C2×C4×C7—42no—
254C2×C4×C7—82no—
255C2×C4×C7C2×C4211yescharacteristic
256C2×C4×C7C2×C22⋊C411yescharacteristic
257C2×C4×C7C2×C22⋊C411yescharacteristic
258C2×C4×C7C2×C22⋊C411yescharacteristic
259C2×C4×C7C2×C4⋊C411yescharacteristic
260C2×C4×C7C2×C4⋊C411yescharacteristic
261C2×C4×C7#11711yescharacteristic
262C2×C4×C7#11711yescharacteristic
263C2×C4×C7C4×D411yescharacteristic
264C2×C4×C7C4×D411yescharacteristic
265C2×C4×C7C4×D411yescharacteristic
266C2×C4×C7C4×D411yescharacteristic
267C2×C4×C7C4×D411yescharacteristic
268C2×C4×C7C4×D411yescharacteristic
269C2×C4×C7C4×D411yescharacteristic
270C2×C4×C7C4×D411yescharacteristic
271C2×C4×C7#12011yescharacteristic
272C2×C4×C7#12011yescharacteristic
273C2×C4×C7#12011yescharacteristic
274C2×C4×C7#12011yescharacteristic
275C2×C4×C7C22⋊Q811yescharacteristic
276C2×C4×C7C22⋊Q811yescharacteristic
277C2×C4×C7C22⋊Q811yescharacteristic
278C2×C4×C7C22⋊Q811yescharacteristic
279C2×C4×C7#12311yescharacteristic
280C2×C4×C7#12311yescharacteristic
281C2×C4×C7#12311yescharacteristic
282C2×C4×C7#12311yescharacteristic
283C22⋊D7—24no—
284C22⋊D7—24no—
285C22⋊D7—24no—
286C22⋊D7—24no—
287C2×Dic7—22no—
288C2×Dic7—22no—
289C2×Dic7—24no—
290C2×Dic7—42no—
291C2×Dic7—44no—
292C2×Dic7—44no—
293C2×Dic7—42no—
294C2×Dic7—42no—
295C2×Dic7—82no—
296C2×Dic7#9514yes—
297D28—22no—
298D28—22no—
299D28—22no—
300D28—22no—
301C4×D7—24no—
302C4×D7—24no—
303C4×D7—24no—
304C4×D7—24no—
305Dic14—22no—
306Dic14—22no—
307Dic14—22no—
308Dic14—22no—
309C7×C8—24no—
310C7⋊C8—24no—
311C2×#41—72no—
312C2×#41—72no—
313C2×#41—72no—
314C2×#41—72no—
315C2×#41—141no—
316C2×#41—141no—
317C2×#41—141no—
318C2×#41—141no—
319C2×#41—141no—
320C2×#41—141no—
321C2×#41—141no—
322C2×#41—141no—
323C22×Q8—71no—
324C22×D4—72no—
325C22×D4—71no—
326C23×C4—72no—
327C23×C4—141no—
328C23×C4C22×D711yescharacteristic
329#131—148no—
330#131—148no—
331#131—148no—
332#131—148no—
333C2×M16—21no—
334C2×M16—21no—
335C2×M16—21no—
336C2×M16—72no—
337C2×M16—72no—
338C2×M16—72no—
339C2×M16—144no—
340C2×M16—148no—
341C2×M16—148no—
342C2×M16—141no—
343C2×M16—141no—
344C2×M16—141no—
345C2×M16C4×D712yes—
346C2×M16D2812yes—
347C2×M16C22⋊D712yes—
348C22×C8—21no—
349C22×C8—144no—
350C22×C8—141no—
351#117—21no—
352#117—21no—
353#117—21no—
354#117—21no—
355#117—21no—
356#117—21no—
357#117—21no—
358#117—72no—
359#117—141no—
360#117—141no—
361#117—141no—
362#117C4×D712yes—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—141no—
365C2×C4⋊C4C4×D712yes—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—141no—
369C2×C22⋊C4—144no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—72no—
373C2×C42—141no—
374C2×C42—141no—
375C2×C42—141no—
376C2×C42—141no—
377C2×C42—141no—
378C2×C42—141no—
379#99—148no—
380#95—144no—
381C22×C7—22no—
382C22×C7—22no—
383C22×C7—22no—
384C22×C7—41no—
385C22×C7—41no—
386C22×C7—41no—
387C22×C7—41no—
388C22×C7C2×#9511yescharacteristic
389C22×C7#38011yescharacteristic
390C22×C7#38011yescharacteristic
391C22×C7#38611yescharacteristic
392C22×C7#38611yescharacteristic
393C22×C7#38611yescharacteristic
394C22×C7#38611yescharacteristic
395C2×D7—24no—
396C2×D7—44no—
397C2×D7—44no—
398C2×D7—82no—
399C4×C7—82no—
400C4×C7—82no—
401C4×C7C4×C22⋊C411yescharacteristic
402C4×C7C4×C22⋊C411yescharacteristic
403C4×C7#37911yescharacteristic
404C4×C7#38111yescharacteristic
405C4×C7#38511yescharacteristic
406C4×C7#38511yescharacteristic
407C4×C7#38511yescharacteristic
408C4×C7#38511yescharacteristic
409Dic7—24no—
410Dic7—44no—
411Dic7—82no—
412C24—72no—
413C24D4×D711yescharacteristic
414#41—142no—
415#41—142no—
416#41—142no—
417#41—142no—
418#41—142no—
419#41—142no—
420#41—142no—
421#41—142no—
422#41—142no—
423#41—142no—
424#41—142no—
425#41—142no—
426#41—142no—
427#41—142no—
428#41—142no—
429#41—142no—
430C2×Q8—72no—
431C2×Q8—72no—
432C2×Q8—141no—
433C2×Q8—141no—
434C2×Q8—141no—
435C2×Q8—141no—
436C2×D4—74no—
437C2×D4—74no—
438C2×D4—72no—
439C2×D4—72no—
440C2×D4—142no—
441C2×D4—142no—
442C2×D4—142no—
443C2×D4—142no—
444C2×D4—141no—
445C2×D4—141no—
446C2×D4—141no—
447C2×D4—141no—
448C22×C4—22no—
449C22×C4—41no—
450C22×C4—72no—
451C22×C4—74no—
452C22×C4—74no—
453C22×C4—142no—
454C22×C4—142no—
455C22×C4—142no—
456C22×C4—142no—
457C22×C4—142no—
458C22×C4—284no—
459C22×C4—281no—
460C22×C4—281no—
461C22×C4—281no—
462C22×C4C2×C4×D711yescharacteristic
463C22×C4C2×C4×D711yescharacteristic
464C22×C4C2×C4×D711yescharacteristic
465C22×C4C2×D2811yescharacteristic
466C22×C4#115711yescharacteristic
467C22×C4#115711yescharacteristic
468C22×C4D4×D711yescharacteristic
469C22×C4D4×D711yescharacteristic
470C22×C4D4×D711yescharacteristic
471C22×C4D4×D711yescharacteristic
472C22×C4#115911yescharacteristic
473C22×C4Q8×D711yescharacteristic
474C22×C4#116111yescharacteristic
475C22×C4C2×C22⋊D711yescharacteristic
476M16—22no—
477M16—22no—
478M16—22no—
479M16—74no—
480M16—1416no—
481M16—142no—
482M16—142no—
483M16—142no—
484M16(C2×D7)⋊C414yescomplemented
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—1416no—
489C2×C8—142no—
490C2×C8—142no—
491C2×C8—142no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—41no—
496C4⋊C4—142no—
497C4⋊C4—281no—
498C22⋊C4—22no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—142no—
503C22⋊C4—288no—
504C22⋊C4—281no—
505C42—22no—
506C42—41no—
507C42—41no—
508C42—41no—
509C42—142no—
510C42—142no—
511C42—142no—
512C42—281no—
513C42—281no—
514C42—281no—
515C2×C7—21no—
516C2×C7—21no—
517C2×C7—21no—
518C2×C7—21no—
519C2×C7—21no—
520C2×C7—21no—
521C2×C7C22⋊#9511yescharacteristic
522C2×C7#188412yes—
523D7—44no—
524C23—42no—
525C23—74no—
526C23—142no—
527C23—142no—
528C23—284no—
529C23D7×C22⋊C411yescharacteristic
530C23D7×C22⋊C411yescharacteristic
531C23#644711yescharacteristic
532C23#644711yescharacteristic
533C23D7×C4⋊C411yescharacteristic
534C23#645811yescharacteristic
535C23#650111yescharacteristic
536Q8—142no—
537Q8—142no—
538Q8—142no—
539Q8—142no—
540D4—144no—
541D4—144no—
542D4—144no—
543D4—144no—
544D4—142no—
545D4—142no—
546D4—142no—
547D4—142no—
548C2×C4—44no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—74no—
552C2×C4—82no—
553C2×C4—142no—
554C2×C4—142no—
555C2×C4—144no—
556C2×C4—144no—
557C2×C4—144no—
558C2×C4—144no—
559C2×C4—144no—
560C2×C4—282no—
561C2×C4—284no—
562C2×C4—284no—
563C2×C4—282no—
564C2×C4—282no—
565C2×C4—562no—
566C2×C4C42×D711yescharacteristic
567C2×C4#643511yescharacteristic
568C2×C4C4×D2811yescharacteristic
569C2×C4C4×D2811yescharacteristic
570C2×C4D7×C22⋊C411yescharacteristic
571C2×C4D7×C22⋊C411yescharacteristic
572C2×C4(C22⋊D7)⋊C411yescharacteristic
573C2×C4(C22⋊D7)⋊C411yescharacteristic
574C2×C4#644511yescharacteristic
575C2×C4#644511yescharacteristic
576C2×C4#644611yescharacteristic
577C2×C4#644611yescharacteristic
578C2×C4D7×C4⋊C411yescharacteristic
579C2×C4D7×C4⋊C411yescharacteristic
580C2×C4#645511yescharacteristic
581C2×C4#645611yescharacteristic
582C2×C4#645611yescharacteristic
583C2×C4#645711yescharacteristic
584C2×C4#645711yescharacteristic
585C2×C4#645911yescharacteristic
586C2×C4#645911yescharacteristic
587C2×C4#646011yescharacteristic
588C2×C4C2×(C2×D7)⋊C411yescharacteristic
589C2×C4C4×C22⋊D711yescharacteristic
590C2×C4C4×C22⋊D711yescharacteristic
591C2×C4#650011yescharacteristic
592C2×C4#650011yescharacteristic
593C2×C4#650911yescharacteristic
594C8—24no—
595C8—144no—
596C7#1075111yescharacteristic, complemented, Sylow
597C22—22no—
598C22—22no—
599C22—22no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—144no—
605C22—284no—
606C22—284no—
607C22—562no—
608C22D7×#9511yescharacteristic
609C22#8943711yescharacteristic
610C22#8943711yescharacteristic
611C22#8943911yescharacteristic
612C22#8972811yescharacteristic
613C22#8972811yescharacteristic
614C22#8975911yescharacteristic
615C4—82no—
616C4—82no—
617C4—144no—
618C4—284no—
619C4—562no—
620C4#8943611yescharacteristic
621C4#8943811yescharacteristic
622C4#8944011yescharacteristic
623C4#8944011yescharacteristic
624C4C4×(C2×D7)⋊C411yescharacteristic
625C4#8972711yescharacteristic
626C4#8976111yescharacteristic
627C4#8976111yescharacteristic
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—21no—
634C2—284no—
635C2(C2×D7)⋊#9511yescharacteristic
636C2#1172817112yes—
subgroupG/H
centerC2×C4#6500
commutatorC2×C4×C7C2×C42
FrattiniC23×C4C22×D7
FittingC7×#1733C2
socleC22×C7#386
prime radicalC22×#1157C22
cosocleC23×C4×C7C23
hypercenter#1733D7
hypocenterC7#10751
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1733

Complements

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

NH ≅ G/Ntype
4. C7×#1733C2semidirect
5. C2×#89350C2semidirect
6. #11729328C2semidirect
7. C2×#89327C2semidirect
18. #90436C4semidirect
23. #89778C4semidirect
24. #89760C4semidirect
25. #89746C4semidirect
108. #1733D7semidirect
178. C7×M16C22⋊C4semidirect
208. #1136C22⋊C4semidirect
484. M16(C2×D7)⋊C4semidirect
596. C7#10751semidirect

Maximal subgroups

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

subgroupindex
C2×#904362
C2×#897782
#117396732
C7×#17332
C2×#893502
#117293282
C2×#893272
#107517