Finite Group Databasebeta

← #13259261

Subgroups — #13259261

Order 1792.

1298 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#1157C211yesmaximal, characteristic
2C2×#89911C211yesmaximal, characteristic
3#11739658C211yesmaximal, characteristic
4C2×C7×#339C211yesmaximal, characteristic, complemented
5C2×#89351C211yesmaximal, characteristic, complemented
6#11729346C211yesmaximal, characteristic, complemented
7C2×#89318C211yesmaximal, characteristic, complemented
8C22×#1157C2211yescharacteristic
9C22×C7×M16C2211yescharacteristic
10C2×C7×#117C2211yescharacteristic
11C22×C42×C7C2211yescharacteristic
12C2×C4×C22⋊D7—22no—
13C2×#6489C2211yescharacteristic
14C2×#6489C2211yescharacteristic
15C22×#1136C2211yescharacteristic
16C4×#1157—22no—
17C4×#1157—22no—
18C4×#1157—22no—
19C4×#1157C414yescomplemented
20C2×C4×D28—21no—
21C2×#6435—21no—
22C2×C42×D7—21no—
23C2×C4×Dic14—21no—
24#89911—22no—
25#89911C414yescomplemented
26C2×#6399—22no—
27#89776—21no—
28#89774—22no—
29#89773—21no—
30#89738C414yescomplemented
31C7×#339—21no—
32C7×#339—21no—
33#89351—22no—
34#89321—22no—
35#89318—22no—
36#10772—71nomaximal, Sylow
37C23×C4×C7—21no—
38C23×C4×C7C2311yescharacteristic
39C22×C22⋊D7—21no—
40C2×#1157—21no—
41C2×#1157—21no—
42C2×#1157—21no—
43C2×#1157—21no—
44C2×#1157—21no—
45C2×#1157—21no—
46C2×#1157C2×C412yes—
47C2×#1157C2×C412yes—
48C2×#1157C2×C412yes—
49C2×#1157D412yes—
50C2×#1157D412yes—
51C2×#1157Q812yes—
52C22×D28D411yescharacteristic
53C22×C4×D7—21no—
54C22×C4×D7—22no—
55C22×Dic14D411yescharacteristic
56C2×C7×M16—21no—
57C2×C7×M16—21no—
58C2×C7×M16—21no—
59C2×C7×M16—21no—
60C2×C7×M16—21no—
61C2×C7×M16C2×C412yescomplemented
62C22×C7×C8—21no—
63C7×#117—21no—
64C7×#117—21no—
65C7×#117—21no—
66C7×#117—21no—
67C2×C7×C4⋊C4C2×C412yescomplemented
68C2×C7×C22⋊C4—21no—
69C2×C42×C7—21no—
70C2×C42×C7—21no—
71C2×C42×C7—21no—
72C2×C42×C7—21no—
73C2×C42×C7C2×C412yes—
74C2×C42×C7D412yes—
75C2×C42×C7D411yescharacteristic
76C2×C42×C7D411yescharacteristic
77C2×C22⋊Dic7—21no—
78C2×C22⋊Dic7D412yes—
79C4×C22⋊D7—28no—
80C4×C22⋊D7—28no—
81C2×(C2×D7)⋊C4—22no—
82#6489—21no—
83#6489—21no—
84#6489—21no—
85#6489—21no—
86#6489—21no—
87#6489C2×C412yes—
88#6489C2×C412yescomplemented
89#6489D412yes—
90C2×C4⋊Dic7—21no—
91C2×C4⋊Dic7—21no—
92C2×Dic7⋊C4—22no—
93C2×C4×Dic7—22no—
94C2×C4×Dic7—21no—
95C2×C4×Dic7—21no—
96C2×#1136—21no—
97C2×#1136—21no—
98C2×#1136—21no—
99C2×#1136—21no—
100C2×#1136—21no—
101C2×#1136C2×C412yescomplemented
102C22×C7⋊C8—21no—
103C4×D28—24no—
104C4×D28—24no—
105#6435—24no—
106#6435—24no—
107C42×D7—24no—
108C42×D7—24no—
109C4×Dic14—24no—
110C4×Dic14—24no—
111#6399—28no—
112#6384—24no—
113#6383—24no—
114C2×C4×#41—71no—
115C2×#421—71no—
116#2896—71no—
117C2×#344—71no—
118#1740—71no—
119C2×#339—71no—
120C2×#339D711yescharacteristic, complemented
121C24×C7C2×D411yescharacteristic
122C23×D7—21no—
123C22×C4×C7—21no—
124C22×C4×C7—22no—
125C22×C4×C7—21no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7—44no—
129C22×C4×C7C22×C411yescharacteristic
130C22×C4×C7C22×C411yescharacteristic
131C22×C4×C7C22×C411yescharacteristic
132C22×C4×C7C2×D411yescharacteristic
133C22×C4×C7C2×D411yescharacteristic
134C22×C4×C7C2×D411yescharacteristic
135C22×C4×C7C2×D411yescharacteristic
136C22×C4×C7C2×D411yescharacteristic
137C22×C4×C7C2×D411yescharacteristic
138C22×C4×C7C2×Q811yescharacteristic
139C22×C4×C7#4111yescharacteristic
140C22×C4×C7#4111yescharacteristic
141C22×C4×C7#4111yescharacteristic
142C22×C4×C7#4111yescharacteristic
143C2×C22⋊D7—22no—
144C2×C22⋊D7—22no—
145C2×C22⋊D7—22no—
146C2×C22⋊D7—22no—
147C2×C22⋊D7—22no—
148C2×C22⋊D7—22no—
149C22×Dic7—21no—
150C22×Dic7—22no—
151C22×Dic7—41no—
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#1157C4214yes—
165#1157C22⋊C414yes—
166#1157C4⋊C414yes—
167#1157C4⋊C414yes—
168C2×D28—21no—
169C2×D28—21no—
170C2×D28—21no—
171C2×D28C22⋊C412yes—
172C2×D28C22⋊C412yes—
173C2×D28C4⋊C412yes—
174C2×C4×D7—22no—
175C2×C4×D7—22no—
176C2×C4×D7—22no—
177C2×C4×D7—22no—
178C2×C4×D7—22no—
179C2×C4×D7—22no—
180C2×C4×D7—28no—
181C2×C4×D7—48no—
182C2×Dic14—21no—
183C2×Dic14—21no—
184C2×Dic14—21no—
185C2×Dic14C22⋊C412yes—
186C2×Dic14C22⋊C412yes—
187C2×Dic14C4⋊C412yes—
188C7×M16—22no—
189C7×M16—22no—
190C7×M16—41no—
191C7×M16—41no—
192C2×C7×C8—22no—
193C2×C7×C8—41no—
194C2×C7×C8—41no—
195C7×C4⋊C4—22no—
196C7×C4⋊C4—22no—
197C7×C22⋊C4—41no—
198C7×C22⋊C4—41no—
199C42×C7—22no—
200C42×C7—22no—
201C42×C7—21no—
202C42×C7—21no—
203C42×C7—41no—
204C42×C7—41no—
205C42×C7C22⋊C412yes—
206C42×C7C22⋊C412yes—
207C22⋊Dic7—22no—
208C22⋊Dic7—22no—
209C22⋊Dic7—41no—
210C22⋊Dic7C22⋊C414yes—
211(C2×D7)⋊C4—28no—
212C4⋊Dic7—22no—
213C4⋊Dic7—22no—
214C4⋊Dic7—22no—
215C4⋊Dic7—41no—
216Dic7⋊C4—28no—
217C4×Dic7—28no—
218C4×Dic7—22no—
219C4×Dic7—22no—
220C4×Dic7—22no—
221C4×Dic7—41no—
222#1136—22no—
223#1136—22no—
224#1136—41no—
225#1136—41no—
226C2×C7⋊C8—22no—
227C2×C7⋊C8—41no—
228C2×C7⋊C8—41no—
229C22×#41—71no—
230C22×M16—71no—
231C22×M16C2×D711yescharacteristic
232C4×#41—74no—
233C4×#41—142no—
234C4×#41—142no—
235C4×#41—142no—
236C2×C4×Q8—141no—
237C2×C4×D4—141no—
238C2×C4×D4—142no—
239C2×#117—71no—
240C2×#117—71no—
241C2×#117—141no—
242C2×#117C2×D711yescharacteristic
243C22×C42—141no—
244C22×C42C2×D711yescharacteristic
245#421—74no—
246#421—142no—
247C2×#104—142no—
248#419—141no—
249#418—141no—
250#417—74no—
251#416—142no—
252#344—142no—
253#342—142no—
254#339—21no—
255#339—21no—
256#339—142no—
257C23×C7—42no—
258C23×C7C2×C22⋊C411yescharacteristic
259C23×C7C4×D411yescharacteristic
260C23×C7C4×D411yescharacteristic
261C23×C7#12011yescharacteristic
262C23×C7#12011yescharacteristic
263C23×C7#12111yescharacteristic
264C23×C7C22⋊Q811yescharacteristic
265C22×D7—22no—
266C22×D7—22no—
267C22×D7—22no—
268C22×D7—44no—
269C2×C4×C7—24no—
270C2×C4×C7—22no—
271C2×C4×C7—22no—
272C2×C4×C7—44no—
273C2×C4×C7—44no—
274C2×C4×C7—42no—
275C2×C4×C7—42no—
276C2×C4×C7—82no—
277C2×C4×C7C2×C4211yescharacteristic
278C2×C4×C7C2×C22⋊C411yescharacteristic
279C2×C4×C7C2×C22⋊C411yescharacteristic
280C2×C4×C7C2×C22⋊C411yescharacteristic
281C2×C4×C7C2×C22⋊C411yescharacteristic
282C2×C4×C7C2×C4⋊C411yescharacteristic
283C2×C4×C7C2×C4⋊C411yescharacteristic
284C2×C4×C7C2×C4⋊C411yescharacteristic
285C2×C4×C7#11711yescharacteristic
286C2×C4×C7#11711yescharacteristic
287C2×C4×C7C4×D411yescharacteristic
288C2×C4×C7C4×D411yescharacteristic
289C2×C4×C7C4×D411yescharacteristic
290C2×C4×C7C4×D411yescharacteristic
291C2×C4×C7C4×D411yescharacteristic
292C2×C4×C7C4×D411yescharacteristic
293C2×C4×C7#12011yescharacteristic
294C2×C4×C7#12011yescharacteristic
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×C7#12311yescharacteristic
302C2×C4×C7#12311yescharacteristic
303C2×C4×C7#12311yescharacteristic
304C2×C4×C7#12311yescharacteristic
305C22⋊D7—24no—
306C22⋊D7—24no—
307C22⋊D7—24no—
308C22⋊D7—24no—
309C2×Dic7—22no—
310C2×Dic7—22no—
311C2×Dic7—22no—
312C2×Dic7—24no—
313C2×Dic7—44no—
314C2×Dic7—42no—
315C2×Dic7—82no—
316D28—22no—
317D28—22no—
318D28—22no—
319D28#9514yes—
320C4×D7—24no—
321C4×D7—24no—
322C4×D7—24no—
323C4×D7—24no—
324C4×D7—416no—
325Dic14—22no—
326Dic14—22no—
327Dic14—22no—
328Dic14#9514yes—
329C7×C8—42no—
330C7⋊C8—42no—
331C2×#41—72no—
332C2×#41—72no—
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—
343C22×Q8—71no—
344C22×D4—71no—
345C22×D4—141no—
346C23×C4—21no—
347C23×C4—142no—
348C23×C4—141no—
349C23×C4C22×D711yescharacteristic
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—72no—
356C2×M16—141no—
357C2×M16—141no—
358C2×M16—141no—
359C2×M16—141no—
360C2×M16—141no—
361C2×M16C4×D712yescomplemented
362C22×C8—21no—
363C22×C8—141no—
364C4×Q8—144no—
365C4×Q8—144no—
366C4×D4—144no—
367C4×D4—144no—
368C4×D4—148no—
369C4×D4—148no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—72no—
375#117—72no—
376#117—72no—
377#117—144no—
378#117—141no—
379#117—141no—
380#117—141no—
381#117—144no—
382#117—141no—
383#117—141no—
384C2×C4⋊C4—142no—
385C2×C4⋊C4—141no—
386C2×C4⋊C4—141no—
387C2×C4⋊C4C4×D712yescomplemented
388C2×C22⋊C4—21no—
389C2×C22⋊C4—72no—
390C2×C22⋊C4—142no—
391C2×C22⋊C4—141no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—144no—
397C2×C42—142no—
398C2×C42—141no—
399C2×C42—144no—
400C2×C42—141no—
401C2×C42C4×D712yes—
402C2×C42D2812yes—
403C2×C42C22⋊D711yescharacteristic
404C2×C42C22⋊D711yescharacteristic
405#104—148no—
406#103—144no—
407#102—144no—
408C22×C7—22no—
409C22×C7—22no—
410C22×C7—22no—
411C22×C7—41no—
412C22×C7—41no—
413C22×C7—41no—
414C22×C7—41no—
415C22×C7C4×C22⋊C411yescharacteristic
416C22×C7#37911yescharacteristic
417C22×C7#38011yescharacteristic
418C22×C7#38511yescharacteristic
419C22×C7#38511yescharacteristic
420C22×C7#38611yescharacteristic
421C22×C7#38611yescharacteristic
422C2×D7—24no—
423C2×D7—44no—
424C2×D7—44no—
425C2×D7—44no—
426C4×C7—24no—
427C4×C7—42no—
428C4×C7—82no—
429C4×C7C2×#9511yescharacteristic
430C4×C7C4×C22⋊C411yescharacteristic
431C4×C7#38011yescharacteristic
432C4×C7#38111yescharacteristic
433C4×C7#38511yescharacteristic
434C4×C7#38511yescharacteristic
435C4×C7#38611yescharacteristic
436C4×C7#38611yescharacteristic
437Dic7—24no—
438Dic7—44no—
439Dic7—82no—
440C24—141no—
441C24D4×D711yescharacteristic
442#41—74no—
443#41—74no—
444#41—74no—
445#41—74no—
446#41—142no—
447#41—142no—
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—
458C2×Q8—72no—
459C2×Q8—72no—
460C2×Q8—72no—
461C2×Q8—141no—
462C2×Q8—141no—
463C2×Q8—141no—
464C2×D4—72no—
465C2×D4—72no—
466C2×D4—72no—
467C2×D4—142no—
468C2×D4—142no—
469C2×D4—142no—
470C2×D4—142no—
471C2×D4—142no—
472C2×D4—142no—
473C2×D4—141no—
474C2×D4—141no—
475C2×D4—141no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—44no—
482C22×C4—148no—
483C22×C4—141no—
484C22×C4—142no—
485C22×C4—142no—
486C22×C4—142no—
487C22×C4—142no—
488C22×C4—142no—
489C22×C4—142no—
490C22×C4—142no—
491C22×C4—288no—
492C22×C4—281no—
493C22×C4C2×C4×D711yescharacteristic
494C22×C4C2×C4×D711yescharacteristic
495C22×C4C2×C4×D711yescharacteristic
496C22×C4C2×D2811yescharacteristic
497C22×C4#115711yescharacteristic
498C22×C4#115711yescharacteristic
499C22×C4D4×D711yescharacteristic
500C22×C4D4×D711yescharacteristic
501C22×C4D4×D711yescharacteristic
502C22×C4D4×D711yescharacteristic
503C22×C4#115911yescharacteristic
504C22×C4Q8×D711yescharacteristic
505C22×C4#116111yescharacteristic
506C22×C4C2×C22⋊D711yescharacteristic
507M16—22no—
508M16—22no—
509M16—41no—
510M16—41no—
511M16—142no—
512M16—142no—
513M16—281no—
514M16—281no—
515C2×C8—22no—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—142no—
519C2×C8—281no—
520C2×C8—281no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—148no—
524C4⋊C4—142no—
525C4⋊C4—142no—
526C4⋊C4—142no—
527C4⋊C4—281no—
528C22⋊C4—41no—
529C22⋊C4—41no—
530C22⋊C4—74no—
531C22⋊C4—148no—
532C22⋊C4—142no—
533C22⋊C4—142no—
534C22⋊C4—281no—
535C42—22no—
536C42—22no—
537C42—21no—
538C42—21no—
539C42—41no—
540C42—41no—
541C42—148no—
542C42—142no—
543C42—142no—
544C42—142no—
545C42—281no—
546C42(C2×D7)⋊C412yes—
547C42(C2×D7)⋊C412yes—
548C2×C7—21no—
549C2×C7—21no—
550C2×C7—21no—
551C2×C7—21no—
552C2×C7—21no—
553C2×C7—21no—
554C2×C7C22⋊#9511yescharacteristic
555C2×C7#190612yes—
556D7—44no—
557C23—42no—
558C23—142no—
559C23—142no—
560C23—142no—
561C23—284no—
562C23D7×C22⋊C411yescharacteristic
563C23(C22⋊D7)⋊C411yescharacteristic
564C23#644511yescharacteristic
565C23#644711yescharacteristic
566C23#645611yescharacteristic
567C23#645911yescharacteristic
568C23#650011yescharacteristic
569Q8—74no—
570Q8—142no—
571Q8—142no—
572Q8—142no—
573D4—74no—
574D4—144no—
575D4—144no—
576D4—144no—
577D4—144no—
578D4—142no—
579D4—142no—
580D4—142no—
581C2×C4—24no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—44no—
585C2×C4—44no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—82no—
589C2×C4—142no—
590C2×C4—142no—
591C2×C4—142no—
592C2×C4—144no—
593C2×C4—144no—
594C2×C4—144no—
595C2×C4—144no—
596C2×C4—144no—
597C2×C4—2816no—
598C2×C4—284no—
599C2×C4—282no—
600C2×C4—562no—
601C2×C4C42×D711yescharacteristic
602C2×C4#643511yescharacteristic
603C2×C4C4×D2811yescharacteristic
604C2×C4C4×D2811yescharacteristic
605C2×C4D7×C22⋊C411yescharacteristic
606C2×C4D7×C22⋊C411yescharacteristic
607C2×C4D7×C22⋊C411yescharacteristic
608C2×C4(C22⋊D7)⋊C411yescharacteristic
609C2×C4#644511yescharacteristic
610C2×C4#644611yescharacteristic
611C2×C4#644611yescharacteristic
612C2×C4#644711yescharacteristic
613C2×C4D7×C4⋊C411yescharacteristic
614C2×C4D7×C4⋊C411yescharacteristic
615C2×C4D7×C4⋊C411yescharacteristic
616C2×C4#645511yescharacteristic
617C2×C4#645611yescharacteristic
618C2×C4#645711yescharacteristic
619C2×C4#645711yescharacteristic
620C2×C4#645811yescharacteristic
621C2×C4#645911yescharacteristic
622C2×C4#646011yescharacteristic
623C2×C4C2×(C2×D7)⋊C411yescharacteristic
624C2×C4C4×C22⋊D711yescharacteristic
625C2×C4C4×C22⋊D711yescharacteristic
626C2×C4#650011yescharacteristic
627C2×C4#650111yescharacteristic
628C2×C4#650911yescharacteristic
629C8—42no—
630C8—282no—
631C7#1077211yescharacteristic, complemented, Sylow
632C22—22no—
633C22—22no—
634C22—22no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—144no—
640C22—284no—
641C22—284no—
642C22—284no—
643C22#8943711yescharacteristic
644C22#8943811yescharacteristic
645C22#8943911yescharacteristic
646C22#8944011yescharacteristic
647C22#8972711yescharacteristic
648C22#8972811yescharacteristic
649C22#8976111yescharacteristic
650C4—24no—
651C4—42no—
652C4—82no—
653C4—144no—
654C4—284no—
655C4—562no—
656C4D7×#9511yescharacteristic
657C4#8943611yescharacteristic
658C4#8943711yescharacteristic
659C4#8944011yescharacteristic
660C4C4×(C2×D7)⋊C411yescharacteristic
661C4#8972811yescharacteristic
662C4#8975911yescharacteristic
663C4#8976111yescharacteristic
664C2—21no—
665C2—21no—
666C2—21no—
667C2—21no—
668C2—21no—
669C2—21no—
670C2—284no—
671C2(C2×D7)⋊#9511yescharacteristic
672C2#1172814512yes—
subgroupG/H
centerC2×C4#6501
commutatorC2×C4×C7C2×C42
FrattiniC23×C4C22×D7
FittingC2×C7×#339C2
socleC22×C7#386
prime radicalC22×#1157C22
cosocleC23×C4×C7C23
hypercenterC2×#339D7
hypocenterC7#10772
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. C2×C7×#339C2semidirect
5. C2×#89351C2semidirect
6. #11729346C2semidirect
7. C2×#89318C2semidirect
19. C4×#1157C4semidirect
25. #89911C4semidirect
30. #89738C4semidirect
61. C2×C7×M16C2×C4semidirect
67. C2×C7×C4⋊C4C2×C4semidirect
88. #6489C2×C4semidirect
101. C2×#1136C2×C4semidirect
120. C2×#339D7semidirect
361. C2×M16C4×D7semidirect
387. C2×C4⋊C4C4×D7semidirect
631. C7#10772semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#11572
C2×#899112
#117396582
C2×C7×#3392
C2×#893512
#117293462
C2×#893182
#107727