Finite Group Databasebeta

← #13259232

Subgroups — #13259232

Order 1792.

1254 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90195C211yesmaximal, characteristic
2C2×#89904C211yesmaximal, characteristic
3C2×#89778C211yesmaximal, characteristic
4C7×#1736C211yesmaximal, characteristic, complemented
5#11729736C211yesmaximal, characteristic, complemented
6#11729332C211yesmaximal, characteristic, complemented
7#11729312C211yesmaximal, characteristic, complemented
8C22×#1157C2211yescharacteristic
9C22×C7×M16C2211yescharacteristic
10C2×C7×#117C2211yescharacteristic
11C22×C7×C4⋊C4C2211yescharacteristic
12C2×C4×C22⋊D7—22no—
13C2×#6489C2211yescharacteristic
14C2×#6489C2211yescharacteristic
15C22×#1136C2211yescharacteristic
16#90195—22no—
17#90195—22no—
18#90195—22no—
19#90195—22no—
20C2×#6456—21no—
21C2×#6455C412yescomplemented
22C2×D7×C4⋊C4C412yescomplemented
23C2×#6450—21no—
24C2×#6398—21no—
25#89904—22no—
26#89904C414yescomplemented
27C2×#6397—21no—
28#89778—22no—
29#89778C414yescomplemented
30C2×#6380—22no—
31C7×#340—22no—
32#89350—22no—
33#89324—22no—
34#89318—22no—
35#10765—71nomaximal, Sylow
36C23×C4×C7—21no—
37C23×C4×C7C2311yescharacteristic
38C22×C22⋊D7D412yes—
39C2×#1157—21no—
40C2×#1157—21no—
41C2×#1157—21no—
42C2×#1157—21no—
43C2×#1157—21no—
44C2×#1157—21no—
45C2×#1157—21no—
46C2×#1157—21no—
47C2×#1157C2×C412yes—
48C2×#1157C2×C412yes—
49C2×#1157D412yes—
50C2×#1157Q812yes—
51C22×D28D411yescharacteristic
52C22×C4×D7—22no—
53C22×C4×D7C2×C412yes—
54C22×Dic14D411yescharacteristic
55C2×C7×M16—21no—
56C2×C7×M16—21no—
57C2×C7×M16—21no—
58C2×C7×M16—21no—
59C2×C7×M16—21no—
60C2×C7×M16C2×C412yescomplemented
61C22×C7×C8—21no—
62C7×#117—21no—
63C7×#117—21no—
64C7×#117—21no—
65C7×#117C2×C412yescomplemented
66C2×C7×C4⋊C4—21no—
67C2×C7×C4⋊C4—21no—
68C2×C7×C4⋊C4—21no—
69C2×C7×C4⋊C4—21no—
70C2×C7×C4⋊C4C2×C412yes—
71C2×C7×C4⋊C4D412yes—
72C2×C7×C4⋊C4D412yes—
73C2×C7×C22⋊C4—21no—
74C2×C42×C7—21no—
75C2×C22⋊Dic7—21no—
76C2×C22⋊Dic7—21no—
77C4×C22⋊D7—28no—
78C4×C22⋊D7—28no—
79C2×(C2×D7)⋊C4—22no—
80#6489—21no—
81#6489—21no—
82#6489—21no—
83#6489—21no—
84#6489—21no—
85#6489C2×C412yescomplemented
86#6489D412yes—
87#6489D412yes—
88C2×C4⋊Dic7—21no—
89C2×C4⋊Dic7C2×C411yescharacteristic
90C2×C4⋊Dic7C2×C411yescharacteristic
91C2×Dic7⋊C4—22no—
92C2×C4×Dic7—21no—
93C2×C4×Dic7—22no—
94C2×C4×Dic7—21no—
95C2×#1136—21no—
96C2×#1136—21no—
97C2×#1136—21no—
98C2×#1136—21no—
99C2×#1136—21no—
100C2×#1136C2×C412yescomplemented
101C22×C7⋊C8—21no—
102#6456—24no—
103#6456—24no—
104#6455—24no—
105#6455—24no—
106D7×C4⋊C4—24no—
107D7×C4⋊C4—24no—
108#6450—24no—
109#6450—24no—
110#6398—24no—
111#6397—24no—
112#6380—28no—
113C2×#520—71no—
114C2×#413—71no—
115C2×#410—71no—
116#1736—71no—
117#1736D711yescharacteristic, complemented
118#1733—71no—
119#1733—71no—
120C24×C7C2×D411yescharacteristic
121C23×D7C22⋊C412yes—
122C22×C4×C7—22no—
123C22×C4×C7—22no—
124C22×C4×C7—22no—
125C22×C4×C7—41no—
126C22×C4×C7—82no—
127C22×C4×C7C22×C411yescharacteristic
128C22×C4×C7C22×C411yescharacteristic
129C22×C4×C7C22×C411yescharacteristic
130C22×C4×C7C2×D411yescharacteristic
131C22×C4×C7C2×D411yescharacteristic
132C22×C4×C7C2×D411yescharacteristic
133C22×C4×C7C2×D411yescharacteristic
134C22×C4×C7C2×D411yescharacteristic
135C22×C4×C7C2×D411yescharacteristic
136C22×C4×C7C2×Q811yescharacteristic
137C22×C4×C7#4111yescharacteristic
138C22×C4×C7#4111yescharacteristic
139C22×C4×C7#4111yescharacteristic
140C22×C4×C7#4111yescharacteristic
141C2×C22⋊D7—22no—
142C2×C22⋊D7—22no—
143C2×C22⋊D7—22no—
144C2×C22⋊D7—22no—
145C2×C22⋊D7C22⋊C414yes—
146C2×C22⋊D7C4⋊C414yes—
147C22×Dic7—21no—
148C22×Dic7—21no—
149C22×Dic7—41no—
150C22×Dic7C22⋊C412yes—
151#1157—22no—
152#1157—22no—
153#1157—22no—
154#1157—22no—
155#1157—22no—
156#1157—22no—
157#1157—22no—
158#1157—22no—
159#1157—22no—
160#1157—22no—
161#1157—22no—
162#1157—22no—
163#1157—22no—
164#1157—22no—
165#1157—22no—
166#1157—22no—
167C2×D28—21no—
168C2×D28—21no—
169C2×D28—21no—
170C2×D28—21no—
171C2×D28C22⋊C412yes—
172C2×D28C4⋊C412yes—
173C2×C4×D7—22no—
174C2×C4×D7—22no—
175C2×C4×D7—22no—
176C2×C4×D7—22no—
177C2×C4×D7—28no—
178C2×C4×D7—84no—
179C2×C4×D7C4214yes—
180C2×C4×D7C4⋊C414yes—
181C2×Dic14—21no—
182C2×Dic14—21no—
183C2×Dic14—21no—
184C2×Dic14—21no—
185C2×Dic14C22⋊C412yes—
186C2×Dic14C4⋊C412yes—
187C7×M16—22no—
188C7×M16—22no—
189C7×M16—41no—
190C7×M16—41no—
191C2×C7×C8—22no—
192C2×C7×C8—41no—
193C2×C7×C8—41no—
194C7×C4⋊C4—22no—
195C7×C4⋊C4—22no—
196C7×C4⋊C4—22no—
197C7×C4⋊C4—22no—
198C7×C4⋊C4—41no—
199C7×C4⋊C4C22⋊C414yes—
200C7×C22⋊C4—22no—
201C7×C22⋊C4—41no—
202C42×C7—22no—
203C42×C7—41no—
204C22⋊Dic7—22no—
205C22⋊Dic7—22no—
206C22⋊Dic7—22no—
207C22⋊Dic7—41no—
208(C2×D7)⋊C4—28no—
209C4⋊Dic7—21no—
210C4⋊Dic7—21no—
211C4⋊Dic7—22no—
212C4⋊Dic7—41no—
213C4⋊Dic7C22⋊C412yes—
214C4⋊Dic7C22⋊C412yes—
215Dic7⋊C4—28no—
216C4×Dic7—28no—
217C4×Dic7—22no—
218C4×Dic7—22no—
219C4×Dic7—22no—
220C4×Dic7—41no—
221#1136—22no—
222#1136—22no—
223#1136—41no—
224#1136—41no—
225C2×C7⋊C8—22no—
226C2×C7⋊C8—41no—
227C2×C7⋊C8—41no—
228C22×#41—71no—
229C22×M16—71no—
230C22×M16C2×D711yescharacteristic
231#520—142no—
232#520—142no—
233#520—142no—
234#520—142no—
235C2×C4×Q8—141no—
236C2×C4×D4—141no—
237C2×C4×D4—142no—
238C2×#117—71no—
239C2×#117—72no—
240C2×#117—71no—
241C2×#117C2×D711yescharacteristic
242C22×C4⋊C4—72no—
243C22×C4⋊C4C2×D711yescharacteristic
244#413—74no—
245#413—142no—
246C2×#101—141no—
247C2×#100—141no—
248#410—74no—
249#410—142no—
250C2×#99—142no—
251#340—22no—
252#340—142no—
253#339—142no—
254#339—142no—
255C23×C7—41no—
256C23×C7—41no—
257C23×C7C2×C22⋊C411yescharacteristic
258C23×C7C2×C22⋊C411yescharacteristic
259C23×C7C2×C4⋊C411yescharacteristic
260C23×C7#12011yescharacteristic
261C23×C7#12011yescharacteristic
262C23×C7#12311yescharacteristic
263C23×C7#12311yescharacteristic
264C22×D7—22no—
265C22×D7—22no—
266C22×D7—42no—
267C22×D7—42no—
268C22×D7#9514yes—
269C2×C4×C7—24no—
270C2×C4×C7—44no—
271C2×C4×C7—42no—
272C2×C4×C7—82no—
273C2×C4×C7—82no—
274C2×C4×C7—81no—
275C2×C4×C7—81no—
276C2×C4×C7C2×C4211yescharacteristic
277C2×C4×C7C2×C22⋊C411yescharacteristic
278C2×C4×C7C2×C22⋊C411yescharacteristic
279C2×C4×C7C2×C22⋊C411yescharacteristic
280C2×C4×C7C2×C4⋊C411yescharacteristic
281C2×C4×C7C2×C4⋊C411yescharacteristic
282C2×C4×C7#11711yescharacteristic
283C2×C4×C7#11711yescharacteristic
284C2×C4×C7C4×D411yescharacteristic
285C2×C4×C7C4×D411yescharacteristic
286C2×C4×C7C4×D411yescharacteristic
287C2×C4×C7C4×D411yescharacteristic
288C2×C4×C7C4×D411yescharacteristic
289C2×C4×C7C4×D411yescharacteristic
290C2×C4×C7C4×D411yescharacteristic
291C2×C4×C7C4×D411yescharacteristic
292C2×C4×C7#12011yescharacteristic
293C2×C4×C7#12011yescharacteristic
294C2×C4×C7#12111yescharacteristic
295C2×C4×C7#12111yescharacteristic
296C2×C4×C7#12111yescharacteristic
297C2×C4×C7#12111yescharacteristic
298C2×C4×C7C22⋊Q811yescharacteristic
299C2×C4×C7C22⋊Q811yescharacteristic
300C2×C4×C7C22⋊Q811yescharacteristic
301C2×C4×C7C22⋊Q811yescharacteristic
302C2×C4×C7#12311yescharacteristic
303C2×C4×C7#12311yescharacteristic
304C22⋊D7—24no—
305C22⋊D7—24no—
306C22⋊D7—24no—
307C22⋊D7—24no—
308C2×Dic7—22no—
309C2×Dic7—22no—
310C2×Dic7—22no—
311C2×Dic7—22no—
312C2×Dic7—42no—
313C2×Dic7—42no—
314C2×Dic7—42no—
315C2×Dic7—81no—
316C2×Dic7—81no—
317C2×Dic7#9514yes—
318D28—22no—
319D28—22no—
320D28—22no—
321D28—22no—
322C4×D7—24no—
323C4×D7—24no—
324C4×D7—24no—
325C4×D7—24no—
326C4×D7—88no—
327Dic14—22no—
328Dic14—22no—
329Dic14—22no—
330Dic14—22no—
331C7×C8—42no—
332C7⋊C8—42no—
333C2×#41—72no—
334C2×#41—72no—
335C2×#41—72no—
336C2×#41—72no—
337C2×#41—141no—
338C2×#41—141no—
339C2×#41—141no—
340C2×#41—141no—
341C2×#41—141no—
342C2×#41—141no—
343C2×#41—141no—
344C2×#41—141no—
345C22×Q8—71no—
346C22×D4—72no—
347C22×D4—71no—
348C23×C4—21no—
349C23×C4—72no—
350C23×C4—142no—
351C23×C4C22×D711yescharacteristic
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—72no—
358C2×M16—141no—
359C2×M16—141no—
360C2×M16—141no—
361C2×M16—141no—
362C2×M16—141no—
363C2×M16C4×D712yescomplemented
364C22×C8—21no—
365C22×C8—141no—
366C4×Q8—144no—
367C4×Q8—144no—
368C4×D4—144no—
369C4×D4—144no—
370C4×D4—148no—
371C4×D4—148no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—72no—
376#117—72no—
377#117—72no—
378#117—144no—
379#117—141no—
380#117—141no—
381#117—144no—
382#117—141no—
383#117—141no—
384#117—141no—
385#117C4×D712yescomplemented
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—71no—
391C2×C4⋊C4—71no—
392C2×C4⋊C4—144no—
393C2×C4⋊C4—142no—
394C2×C4⋊C4—144no—
395C2×C4⋊C4—141no—
396C2×C4⋊C4C4×D712yes—
397C2×C4⋊C4D2812yes—
398C2×C4⋊C4C22⋊D712yes—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—142no—
401C2×C22⋊C4—141no—
402C2×C22⋊C4—141no—
403C2×C42—21no—
404C2×C42—142no—
405C2×C42—141no—
406C2×C42—141no—
407#101—144no—
408#100—144no—
409#99—148no—
410C22×C7—21no—
411C22×C7—21no—
412C22×C7—21no—
413C22×C7—21no—
414C22×C7—21no—
415C22×C7—21no—
416C22×C7—41no—
417C22×C7—41no—
418C22×C7—41no—
419C22×C7—41no—
420C22×C7C2×#9511yescharacteristic
421C22×C7#37911yescharacteristic
422C22×C7#38111yescharacteristic
423C22×C7#38511yescharacteristic
424C22×C7#38511yescharacteristic
425C22×C7#38611yescharacteristic
426C22×C7#38611yescharacteristic
427C2×D7—24no—
428C2×D7—44no—
429C2×D7—42no—
430C2×D7—42no—
431C2×D7—44no—
432C4×C7—44no—
433C4×C7—82no—
434C4×C7C4×C22⋊C411yescharacteristic
435C4×C7C4×C22⋊C411yescharacteristic
436C4×C7#38011yescharacteristic
437C4×C7#38011yescharacteristic
438C4×C7#38511yescharacteristic
439C4×C7#38511yescharacteristic
440C4×C7#38611yescharacteristic
441C4×C7#38611yescharacteristic
442Dic7—24no—
443Dic7—42no—
444Dic7—42no—
445Dic7—82no—
446C24—72no—
447C24D4×D711yescharacteristic
448#41—142no—
449#41—142no—
450#41—142no—
451#41—142no—
452#41—142no—
453#41—142no—
454#41—142no—
455#41—142no—
456#41—142no—
457#41—142no—
458#41—142no—
459#41—142no—
460#41—142no—
461#41—142no—
462#41—142no—
463#41—142no—
464C2×Q8—72no—
465C2×Q8—72no—
466C2×Q8—141no—
467C2×Q8—141no—
468C2×Q8—141no—
469C2×Q8—141no—
470C2×D4—74no—
471C2×D4—74no—
472C2×D4—72no—
473C2×D4—72no—
474C2×D4—142no—
475C2×D4—142no—
476C2×D4—142no—
477C2×D4—142no—
478C2×D4—141no—
479C2×D4—141no—
480C2×D4—141no—
481C2×D4—141no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—41no—
486C22×C4—72no—
487C22×C4—74no—
488C22×C4—74no—
489C22×C4—82no—
490C22×C4—148no—
491C22×C4—142no—
492C22×C4—142no—
493C22×C4—142no—
494C22×C4—142no—
495C22×C4—141no—
496C22×C4—141no—
497C22×C4—281no—
498C22×C4—564no—
499C22×C4C2×C4×D711yescharacteristic
500C22×C4C2×C4×D711yescharacteristic
501C22×C4C2×C4×D711yescharacteristic
502C22×C4C2×D2811yescharacteristic
503C22×C4#115711yescharacteristic
504C22×C4#115711yescharacteristic
505C22×C4D4×D711yescharacteristic
506C22×C4D4×D711yescharacteristic
507C22×C4D4×D711yescharacteristic
508C22×C4D4×D711yescharacteristic
509C22×C4#115911yescharacteristic
510C22×C4Q8×D711yescharacteristic
511C22×C4#116111yescharacteristic
512C22×C4C2×C22⋊D711yescharacteristic
513M16—22no—
514M16—22no—
515M16—41no—
516M16—41no—
517M16—142no—
518M16—142no—
519M16—281no—
520M16—281no—
521C2×C8—22no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—142no—
525C2×C8—281no—
526C2×C8—281no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—41no—
532C4⋊C4—72no—
533C4⋊C4—72no—
534C4⋊C4—148no—
535C4⋊C4—141no—
536C4⋊C4—141no—
537C4⋊C4—142no—
538C4⋊C4—281no—
539C4⋊C4(C2×D7)⋊C414yes—
540C22⋊C4—22no—
541C22⋊C4—41no—
542C22⋊C4—148no—
543C22⋊C4—142no—
544C22⋊C4—142no—
545C22⋊C4—142no—
546C22⋊C4—281no—
547C42—22no—
548C42—41no—
549C42—148no—
550C42—142no—
551C42—142no—
552C42—142no—
553C42—281no—
554C2×C7—21no—
555C2×C7—21no—
556C2×C7—21no—
557C2×C7—21no—
558C2×C7—21no—
559C2×C7—21no—
560C2×C7C22⋊#9511yescharacteristic
561C2×C7#179511yescharacteristic
562C2×C7#179611yescharacteristic
563D7—44no—
564C23—41no—
565C23—41no—
566C23—74no—
567C23—142no—
568C23—142no—
569C23—282no—
570C23—282no—
571C23D7×C22⋊C411yescharacteristic
572C23D7×C22⋊C411yescharacteristic
573C23#644511yescharacteristic
574C23#644611yescharacteristic
575C23D7×C4⋊C411yescharacteristic
576C23#645711yescharacteristic
577C23#650011yescharacteristic
578Q8—142no—
579Q8—142no—
580Q8—142no—
581Q8—142no—
582D4—144no—
583D4—144no—
584D4—144no—
585D4—144no—
586D4—142no—
587D4—142no—
588D4—142no—
589D4—142no—
590C2×C4—24no—
591C2×C4—44no—
592C2×C4—42no—
593C2×C4—74no—
594C2×C4—82no—
595C2×C4—82no—
596C2×C4—81no—
597C2×C4—81no—
598C2×C4—142no—
599C2×C4—142no—
600C2×C4—144no—
601C2×C4—144no—
602C2×C4—144no—
603C2×C4—144no—
604C2×C4—142no—
605C2×C4—142no—
606C2×C4—282no—
607C2×C4—282no—
608C2×C4—282no—
609C2×C4—568no—
610C2×C4—561no—
611C2×C4—561no—
612C2×C4C42×D711yescharacteristic
613C2×C4#643511yescharacteristic
614C2×C4C4×D2811yescharacteristic
615C2×C4C4×D2811yescharacteristic
616C2×C4D7×C22⋊C411yescharacteristic
617C2×C4D7×C22⋊C411yescharacteristic
618C2×C4(C22⋊D7)⋊C411yescharacteristic
619C2×C4(C22⋊D7)⋊C411yescharacteristic
620C2×C4#644511yescharacteristic
621C2×C4#644611yescharacteristic
622C2×C4#644711yescharacteristic
623C2×C4#644711yescharacteristic
624C2×C4D7×C4⋊C411yescharacteristic
625C2×C4D7×C4⋊C411yescharacteristic
626C2×C4#645511yescharacteristic
627C2×C4#645611yescharacteristic
628C2×C4#645611yescharacteristic
629C2×C4#645711yescharacteristic
630C2×C4#645811yescharacteristic
631C2×C4#645911yescharacteristic
632C2×C4#645911yescharacteristic
633C2×C4#646011yescharacteristic
634C2×C4C2×(C2×D7)⋊C411yescharacteristic
635C2×C4C4×C22⋊D711yescharacteristic
636C2×C4C4×C22⋊D711yescharacteristic
637C2×C4#650011yescharacteristic
638C2×C4#650111yescharacteristic
639C2×C4#650911yescharacteristic
640C8—42no—
641C8—282no—
642C7#1076511yescharacteristic, complemented, Sylow
643C22—21no—
644C22—21no—
645C22—21no—
646C22—21no—
647C22—21no—
648C22—21no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—144no—
654C22—284no—
655C22—284no—
656C22—282no—
657C22—282no—
658C22D7×#9511yescharacteristic
659C22#8943611yescharacteristic
660C22#8943711yescharacteristic
661C22#8944011yescharacteristic
662C22#8972711yescharacteristic
663C22#8972811yescharacteristic
664C22#8976111yescharacteristic
665C4—44no—
666C4—82no—
667C4—144no—
668C4—282no—
669C4—282no—
670C4—562no—
671C4#8943711yescharacteristic
672C4#8943811yescharacteristic
673C4#8943911yescharacteristic
674C4#8944011yescharacteristic
675C4C4×(C2×D7)⋊C411yescharacteristic
676C4#8972811yescharacteristic
677C4#8975911yescharacteristic
678C4#8976111yescharacteristic
679C2—21no—
680C2—21no—
681C2—21no—
682C2—21no—
683C2—21no—
684C2—21no—
685C2—284no—
686C2(C2×D7)⋊#9511yescharacteristic
687C2#1172808111yescharacteristic
688C2#1172810111yescharacteristic
subgroupG/H
centerC22#89727
commutatorC2×C4×C7C2×C42
FrattiniC23×C4C22×D7
FittingC7×#1736C2
socleC22×C7#379
prime radicalC22×#1157C22
cosocleC23×C4×C7C23
hypercenter#1736D7
hypocenterC7#10765
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. C7×#1736C2semidirect
5. #11729736C2semidirect
6. #11729332C2semidirect
7. #11729312C2semidirect
21. C2×#6455C4semidirect
22. C2×D7×C4⋊C4C4semidirect
26. #89904C4semidirect
29. #89778C4semidirect
60. C2×C7×M16C2×C4semidirect
65. C7×#117C2×C4semidirect
85. #6489C2×C4semidirect
100. C2×#1136C2×C4semidirect
117. #1736D7semidirect
363. C2×M16C4×D7semidirect
385. #117C4×D7semidirect
642. C7#10765semidirect

Maximal subgroups

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

subgroupindex
C2×#901952
C2×#899042
C2×#897782
C7×#17362
#117297362
#117293322
#117293122
#107657