Finite Group Databasebeta

← #13259172

Subgroups — #13259172

Order 1792.

1222 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11742799C211yesmaximal, characteristic
2C2×#89901C211yesmaximal, characteristic
3C2×#89778C211yesmaximal, characteristic
4C7×#1733C211yesmaximal, characteristic, complemented
5#11729736C211yesmaximal, characteristic, complemented
6#11729334C211yesmaximal, characteristic, complemented
7#11729334C211yesmaximal, characteristic, complemented
8C22×#1157C2211yescharacteristic
9C22×C7×M16C2211yescharacteristic
10C2×C7×#117C2211yescharacteristic
11C2×C7×#117C2211yescharacteristic
12C2×#6489C2211yescharacteristic
13C2×#6489C2211yescharacteristic
14C23×C7⋊C8C2211yescharacteristic
15#90214—22no—
16#90213—22no—
17#90212C412yescomplemented
18D7×#117—22no—
19#90207C412yescomplemented
20#90195—22no—
21#90177—22no—
22C4×#1157—22no—
23#89901—22no—
24#89901C414yescomplemented
25C2×(C2×D7)⋊C8—22no—
26#89778—22no—
27#89778C414yescomplemented
28C2×#6380—22no—
29C7×#339—22no—
30#89350—22no—
31#89324—22no—
32#89324—22no—
33#10752—71nomaximal, Sylow
34C23×C4×C7C2311yescharacteristic
35C22×C22⋊D7D412yes—
36C2×#1157—21no—
37C2×#1157—21no—
38C2×#1157—21no—
39C2×#1157—21no—
40C2×#1157—21no—
41C2×#1157—21no—
42C2×#1157—21no—
43C2×#1157—21no—
44C2×#1157C2×C412yes—
45C2×#1157C2×C412yes—
46C2×#1157D412yes—
47C2×#1157Q812yes—
48C22×D28C2×C411yescharacteristic
49C22×C4×D7D412yes—
50C22×Dic14C2×C411yescharacteristic
51C2×C7×M16—21no—
52C2×C7×M16—21no—
53C2×C7×M16—21no—
54C2×C7×M16—21no—
55C2×C7×M16—21no—
56C2×C7×M16C2×C412yescomplemented
57C22×C7×C8—21no—
58C7×#117—21no—
59C7×#117—21no—
60C7×#117—21no—
61C7×#117—21no—
62C7×#117—21no—
63C7×#117C2×C412yes—
64C7×#117C2×C412yescomplemented
65C7×#117D412yes—
66C2×C7×C4⋊C4—21no—
67C2×C7×C4⋊C4D412yes—
68C2×C7×C22⋊C4—21no—
69C2×C7×C22⋊C4—21no—
70C2×C42×C7—21no—
71C2×C42×C7—21no—
72C2×C22⋊Dic7—21no—
73C2×C22⋊Dic7—21no—
74C4×C22⋊D7—28no—
75#6489—21no—
76#6489—21no—
77#6489—21no—
78#6489—21no—
79#6489—21no—
80#6489C2×C412yes—
81#6489C2×C412yescomplemented
82#6489D412yes—
83C2×C4⋊Dic7—21no—
84C2×C4⋊Dic7D412yes—
85C2×C4×Dic7—21no—
86C2×C4×Dic7—21no—
87C22×C7⋊C8—21no—
88C22×C7⋊C8—21no—
89C22×C7⋊C8—21no—
90C22×C7⋊C8—21no—
91C22×C7⋊C8—21no—
92C22×C7⋊C8—21no—
93C22×C7⋊C8C2×C412yescomplemented
94#6456—24no—
95#6455—24no—
96D7×C4⋊C4—24no—
97#6450—24no—
98(C22⋊D7)⋊C4—28no—
99D7×C22⋊C4—24no—
100#6440—24no—
101C4×D28—24no—
102#6435—24no—
103C42×D7—24no—
104C4×Dic14—24no—
105(C2×D7)⋊C8—28no—
106#6380—28no—
107#3428—71no—
108C2×#410—71no—
109C2×#408—71no—
110#1735—71no—
111#1735—71no—
112#1733—71no—
113#1733D711yescharacteristic, complemented
114C24×C7C2×D411yescharacteristic
115C23×D7C22⋊C412yes—
116C22×C4×C7—22no—
117C22×C4×C7—41no—
118C22×C4×C7C22×C411yescharacteristic
119C22×C4×C7C22×C411yescharacteristic
120C22×C4×C7C22×C411yescharacteristic
121C22×C4×C7C2×D411yescharacteristic
122C22×C4×C7C2×D411yescharacteristic
123C22×C4×C7C2×D411yescharacteristic
124C22×C4×C7C2×D411yescharacteristic
125C22×C4×C7C2×D411yescharacteristic
126C22×C4×C7C2×D411yescharacteristic
127C22×C4×C7C2×Q811yescharacteristic
128C22×C4×C7#4111yescharacteristic
129C22×C4×C7#4111yescharacteristic
130C22×C4×C7#4111yescharacteristic
131C22×C4×C7#4111yescharacteristic
132C2×C22⋊D7—22no—
133C2×C22⋊D7—22no—
134C2×C22⋊D7—22no—
135C2×C22⋊D7—22no—
136C2×C22⋊D7C22⋊C414yes—
137C2×C22⋊D7C4⋊C414yes—
138C22×Dic7—22no—
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×D7—28no—
168C2×C4×D7C22⋊C414yes—
169C2×C4×D7C4⋊C414yes—
170C2×Dic14—21no—
171C2×Dic14—21no—
172C2×Dic14—21no—
173C2×Dic14—21no—
174C2×Dic14C4212yes—
175C2×Dic14C4⋊C412yes—
176C7×M16—22no—
177C7×M16—22no—
178C7×M16—41no—
179C7×M16—41no—
180C2×C7×C8—22no—
181C2×C7×C8—41no—
182C2×C7×C8—41no—
183C7×C4⋊C4—22no—
184C7×C4⋊C4—22no—
185C7×C4⋊C4—41no—
186C7×C4⋊C4C22⋊C414yes—
187C7×C22⋊C4—22no—
188C7×C22⋊C4—22no—
189C7×C22⋊C4—22no—
190C7×C22⋊C4—41no—
191C42×C7—22no—
192C42×C7—22no—
193C42×C7—22no—
194C42×C7—41no—
195C22⋊Dic7—22no—
196C22⋊Dic7—22no—
197C22⋊Dic7—22no—
198C22⋊Dic7—41no—
199(C2×D7)⋊C4—28no—
200C4⋊Dic7—22no—
201C4⋊Dic7—22no—
202C4⋊Dic7—41no—
203C4⋊Dic7C22⋊C414yes—
204Dic7⋊C4—28no—
205C4×Dic7—28no—
206C4×Dic7—22no—
207C4×Dic7—22no—
208C4×Dic7—22no—
209C4×Dic7—41no—
210C2×C7⋊C8—22no—
211C2×C7⋊C8—22no—
212C2×C7⋊C8—22no—
213C2×C7⋊C8—41no—
214C2×C7⋊C8—41no—
215C2×C7⋊C8—41no—
216C2×C7⋊C8—41no—
217C22×#41—71no—
218C22×M16C2×D711yescharacteristic
219C23×C8—71no—
220#520—142no—
221#520—142no—
222#519—72no—
223#518—72no—
224#518—142no—
225C4×#41—142no—
226C4×#41—142no—
227C2×#117—71no—
228C2×#117—71no—
229C2×#117—142no—
230C2×#117C2×D711yescharacteristic
231C2×#117C2×D711yescharacteristic
232#410—74no—
233#410—142no—
234C2×#99—142no—
235#408—74no—
236#408—142no—
237C2×C22⋊C8—142no—
238#340—142no—
239#340—142no—
240#339—22no—
241#339—142no—
242C23×C7—42no—
243C23×C7C2×C22⋊C411yescharacteristic
244C23×C7C2×C22⋊C411yescharacteristic
245C23×C7C2×C4⋊C411yescharacteristic
246C23×C7#12011yescharacteristic
247C23×C7#12011yescharacteristic
248C23×C7#12311yescharacteristic
249C23×C7#12311yescharacteristic
250C22×D7—22no—
251C22×D7—22no—
252C22×D7—44no—
253C22×D7#9514yes—
254C2×C4×C7—24no—
255C2×C4×C7—42no—
256C2×C4×C7—82no—
257C2×C4×C7—82no—
258C2×C4×C7C2×C4211yescharacteristic
259C2×C4×C7C2×C22⋊C411yescharacteristic
260C2×C4×C7C2×C22⋊C411yescharacteristic
261C2×C4×C7C2×C22⋊C411yescharacteristic
262C2×C4×C7C2×C4⋊C411yescharacteristic
263C2×C4×C7C2×C4⋊C411yescharacteristic
264C2×C4×C7#11711yescharacteristic
265C2×C4×C7#11711yescharacteristic
266C2×C4×C7C4×D411yescharacteristic
267C2×C4×C7C4×D411yescharacteristic
268C2×C4×C7C4×D411yescharacteristic
269C2×C4×C7C4×D411yescharacteristic
270C2×C4×C7C4×D411yescharacteristic
271C2×C4×C7C4×D411yescharacteristic
272C2×C4×C7C4×D411yescharacteristic
273C2×C4×C7C4×D411yescharacteristic
274C2×C4×C7#12011yescharacteristic
275C2×C4×C7#12011yescharacteristic
276C2×C4×C7#12111yescharacteristic
277C2×C4×C7#12111yescharacteristic
278C2×C4×C7#12111yescharacteristic
279C2×C4×C7#12111yescharacteristic
280C2×C4×C7C22⋊Q811yescharacteristic
281C2×C4×C7C22⋊Q811yescharacteristic
282C2×C4×C7C22⋊Q811yescharacteristic
283C2×C4×C7C22⋊Q811yescharacteristic
284C2×C4×C7#12311yescharacteristic
285C2×C4×C7#12311yescharacteristic
286C22⋊D7—24no—
287C22⋊D7—24no—
288C22⋊D7—24no—
289C22⋊D7—24no—
290C2×Dic7—22no—
291C2×Dic7—22no—
292C2×Dic7—24no—
293C2×Dic7—42no—
294C2×Dic7—82no—
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—
305C4×D7—88no—
306Dic14—22no—
307Dic14—22no—
308Dic14—22no—
309Dic14—22no—
310C7×C8—42no—
311C7⋊C8—42no—
312C2×#41—72no—
313C2×#41—72no—
314C2×#41—72no—
315C2×#41—72no—
316C2×#41—141no—
317C2×#41—141no—
318C2×#41—141no—
319C2×#41—141no—
320C2×#41—141no—
321C2×#41—141no—
322C2×#41—141no—
323C2×#41—141no—
324C22×Q8—71no—
325C22×D4—72no—
326C22×D4—71no—
327C23×C4—72no—
328C23×C4C22×D711yescharacteristic
329C2×M16—21no—
330C2×M16—21no—
331C2×M16—21no—
332C2×M16—21no—
333C2×M16—21no—
334C2×M16C4×D712yescomplemented
335C22×C8—21no—
336C22×C8—72no—
337C22×C8—141no—
338C22×C8—141no—
339C22×C8—141no—
340C22×C8—141no—
341C22×C8—141no—
342C22×C8—141no—
343C4×Q8—144no—
344C4×Q8—144no—
345C4×D4—144no—
346C4×D4—148no—
347C4×D4—148no—
348C4×D4—144no—
349#117—21no—
350#117—21no—
351#117—21no—
352#117—21no—
353#117—21no—
354#117—72no—
355#117—72no—
356#117—72no—
357#117—144no—
358#117—144no—
359#117—144no—
360#117—141no—
361#117—141no—
362#117—141no—
363#117—141no—
364#117—141no—
365#117C4×D712yes—
366#117C4×D712yescomplemented
367#117C22⋊D712yes—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—72no—
370C2×C4⋊C4—144no—
371C2×C4⋊C4—141no—
372C2×C4⋊C4D2812yes—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—144no—
376C2×C22⋊C4—141no—
377C2×C22⋊C4—141no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—144no—
381C2×C42—141no—
382C2×C42—141no—
383#99—148no—
384C22⋊C8—148no—
385C22×C7—22no—
386C22×C7—22no—
387C22×C7—22no—
388C22×C7—41no—
389C22×C7—41no—
390C22×C7—41no—
391C22×C7—41no—
392C22×C7C2×#9511yescharacteristic
393C22×C7#37911yescharacteristic
394C22×C7#38111yescharacteristic
395C22×C7#38511yescharacteristic
396C22×C7#38511yescharacteristic
397C22×C7#38611yescharacteristic
398C22×C7#38611yescharacteristic
399C2×D7—24no—
400C2×D7—44no—
401C2×D7—44no—
402C2×D7—82no—
403C4×C7—44no—
404C4×C7—82no—
405C4×C7C4×C22⋊C411yescharacteristic
406C4×C7C4×C22⋊C411yescharacteristic
407C4×C7#38011yescharacteristic
408C4×C7#38011yescharacteristic
409C4×C7#38511yescharacteristic
410C4×C7#38511yescharacteristic
411C4×C7#38611yescharacteristic
412C4×C7#38611yescharacteristic
413Dic7—24no—
414Dic7—44no—
415Dic7—82no—
416C24—72no—
417C24D4×D711yescharacteristic
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—
430#41—142no—
431#41—142no—
432#41—142no—
433#41—142no—
434C2×Q8—72no—
435C2×Q8—72no—
436C2×Q8—141no—
437C2×Q8—141no—
438C2×Q8—141no—
439C2×Q8—141no—
440C2×D4—74no—
441C2×D4—74no—
442C2×D4—72no—
443C2×D4—72no—
444C2×D4—142no—
445C2×D4—142no—
446C2×D4—142no—
447C2×D4—142no—
448C2×D4—141no—
449C2×D4—141no—
450C2×D4—141no—
451C2×D4—141no—
452C22×C4—22no—
453C22×C4—41no—
454C22×C4—72no—
455C22×C4—74no—
456C22×C4—74no—
457C22×C4—148no—
458C22×C4—142no—
459C22×C4—142no—
460C22×C4—142no—
461C22×C4—142no—
462C22×C4—142no—
463C22×C4—281no—
464C22×C4C2×C4×D711yescharacteristic
465C22×C4C2×C4×D711yescharacteristic
466C22×C4C2×C4×D711yescharacteristic
467C22×C4C2×D2811yescharacteristic
468C22×C4#115711yescharacteristic
469C22×C4#115711yescharacteristic
470C22×C4D4×D711yescharacteristic
471C22×C4D4×D711yescharacteristic
472C22×C4D4×D711yescharacteristic
473C22×C4D4×D711yescharacteristic
474C22×C4#115911yescharacteristic
475C22×C4Q8×D711yescharacteristic
476C22×C4#116111yescharacteristic
477C22×C4C2×C22⋊D711yescharacteristic
478M16—22no—
479M16—22no—
480M16—41no—
481M16—41no—
482C2×C8—22no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—142no—
486C2×C8—142no—
487C2×C8—142no—
488C2×C8—281no—
489C2×C8—281no—
490C2×C8—281no—
491C2×C8—281no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—41no—
495C4⋊C4—74no—
496C4⋊C4—148no—
497C4⋊C4—142no—
498C4⋊C4—142no—
499C4⋊C4—281no—
500C4⋊C4(C2×D7)⋊C414yes—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—41no—
505C22⋊C4—148no—
506C22⋊C4—142no—
507C22⋊C4—142no—
508C22⋊C4—142no—
509C22⋊C4—281no—
510C42—22no—
511C42—22no—
512C42—22no—
513C42—41no—
514C42—148no—
515C42—142no—
516C42—142no—
517C42—142no—
518C42—281no—
519C2×C7—21no—
520C2×C7—21no—
521C2×C7—21no—
522C2×C7—21no—
523C2×C7—21no—
524C2×C7—21no—
525C2×C7C22⋊#9511yescharacteristic
526C2×C7#179412yes—
527D7—44no—
528C23—42no—
529C23—74no—
530C23—142no—
531C23—142no—
532C23—284no—
533C23D7×C22⋊C411yescharacteristic
534C23D7×C22⋊C411yescharacteristic
535C23#644511yescharacteristic
536C23#644611yescharacteristic
537C23D7×C4⋊C411yescharacteristic
538C23#645711yescharacteristic
539C23#650011yescharacteristic
540Q8—142no—
541Q8—142no—
542Q8—142no—
543Q8—142no—
544D4—144no—
545D4—144no—
546D4—144no—
547D4—144no—
548D4—142no—
549D4—142no—
550D4—142no—
551D4—142no—
552C2×C4—24no—
553C2×C4—42no—
554C2×C4—74no—
555C2×C4—82no—
556C2×C4—82no—
557C2×C4—142no—
558C2×C4—142no—
559C2×C4—144no—
560C2×C4—144no—
561C2×C4—144no—
562C2×C4—144no—
563C2×C4—144no—
564C2×C4—282no—
565C2×C4—568no—
566C2×C4—562no—
567C2×C4—562no—
568C2×C4C42×D711yescharacteristic
569C2×C4#643511yescharacteristic
570C2×C4C4×D2811yescharacteristic
571C2×C4C4×D2811yescharacteristic
572C2×C4D7×C22⋊C411yescharacteristic
573C2×C4D7×C22⋊C411yescharacteristic
574C2×C4(C22⋊D7)⋊C411yescharacteristic
575C2×C4(C22⋊D7)⋊C411yescharacteristic
576C2×C4#644511yescharacteristic
577C2×C4#644611yescharacteristic
578C2×C4#644711yescharacteristic
579C2×C4#644711yescharacteristic
580C2×C4D7×C4⋊C411yescharacteristic
581C2×C4D7×C4⋊C411yescharacteristic
582C2×C4#645511yescharacteristic
583C2×C4#645611yescharacteristic
584C2×C4#645611yescharacteristic
585C2×C4#645711yescharacteristic
586C2×C4#645811yescharacteristic
587C2×C4#645911yescharacteristic
588C2×C4#645911yescharacteristic
589C2×C4#646011yescharacteristic
590C2×C4C2×(C2×D7)⋊C411yescharacteristic
591C2×C4C4×C22⋊D711yescharacteristic
592C2×C4C4×C22⋊D711yescharacteristic
593C2×C4#650011yescharacteristic
594C2×C4#650111yescharacteristic
595C2×C4#650911yescharacteristic
596C8—42no—
597C8—282no—
598C7#1075211yescharacteristic, complemented, Sylow
599C22—22no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—144no—
607C22—284no—
608C22—284no—
609C22—562no—
610C22D7×#9511yescharacteristic
611C22#8943611yescharacteristic
612C22#8943711yescharacteristic
613C22#8944011yescharacteristic
614C22#8972711yescharacteristic
615C22#8972811yescharacteristic
616C22#8976111yescharacteristic
617C4—44no—
618C4—82no—
619C4—144no—
620C4—284no—
621C4—562no—
622C4#8943711yescharacteristic
623C4#8943811yescharacteristic
624C4#8943911yescharacteristic
625C4#8944011yescharacteristic
626C4C4×(C2×D7)⋊C411yescharacteristic
627C4#8972811yescharacteristic
628C4#8975911yescharacteristic
629C4#8976111yescharacteristic
630C2—21no—
631C2—21no—
632C2—21no—
633C2—21no—
634C2—21no—
635C2—21no—
636C2—284no—
637C2(C2×D7)⋊#9511yescharacteristic
638C2#1172816712yes—
subgroupG/H
centerC2×C4#6500
commutatorC2×C4×C7C2×C42
FrattiniC23×C4C22×D7
FittingC7×#1733C2
socleC22×C7#379
prime radicalC22×#1157C22
cosocleC23×C4×C7C23
hypercenter#1733D7
hypocenterC7#10752
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. #11729736C2semidirect
6. #11729334C2semidirect
7. #11729334C2semidirect
17. #90212C4semidirect
19. #90207C4semidirect
24. #89901C4semidirect
27. #89778C4semidirect
56. C2×C7×M16C2×C4semidirect
64. C7×#117C2×C4semidirect
81. #6489C2×C4semidirect
93. C22×C7⋊C8C2×C4semidirect
113. #1733D7semidirect
334. C2×M16C4×D7semidirect
366. #117C4×D7semidirect
598. C7#10752semidirect

Maximal subgroups

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

subgroupindex
#117427992
C2×#899012
C2×#897782
C7×#17332
#117297362
#117293342
#107527