Finite Group Databasebeta

← #13277291

Subgroups — #13277291

Order 1792.

2574 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6499C211yesmaximal, characteristic
2C22×D4×Dic7C211yesmaximal, characteristic
3C2×C7×#390C211yesmaximal, characteristic
4C2×#89746C211yesmaximal, characteristic, complemented
5C2×#89701C211yesmaximal, characteristic, complemented
6#11729317C211yesmaximal, characteristic, complemented
7#11729303C214yesmaximal, complemented
8#11729298C214yesmaximal, complemented
9C4×C7⋊#95C211yesmaximal, characteristic, complemented
10C23×C7×D4C2211yescharacteristic
11C24×Dic7C2212yes—
12C23×Dic14C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C22⋊C4C2214yes—
15C22×C42×C7C2211yescharacteristic
16C22×C22⋊Dic7C2212yes—
17C22×C22⋊Dic7C2214yes—
18C2×#6499—24no—
19C2×#6499—24no—
20C2×#6499C418yescomplemented
21C2×D4×Dic7—24no—
22C2×D4×Dic7—24no—
23C2×D4×Dic7—24no—
24C22×C4⋊Dic7C2211yescharacteristic
25C22×C4×Dic7C2211yescharacteristic
26C22×C4×Dic7C2211yescharacteristic
27C7×#390—24no—
28C2×C7⋊#95C2214yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2214yes—
34#89746—24no—
35#89701—24no—
36#14027—71nomaximal, Sylow
37C25×C7C2312yes—
38C22×C7×D4—22no—
39C22×C7×D4—22no—
40C22×C7×D4—22no—
41C22×C7×D4—22no—
42C22×C7×D4C2×C414yes—
43C22×C7×D4D414yes—
44C22×C7×D4D414yes—
45C23×C4×C7C2312yes—
46C23×C4×C7C2312yes—
47C23×C4×C7C2311yescharacteristic
48C23×Dic7—24no—
49C23×Dic7—24no—
50C23×Dic7—24no—
51C23×Dic7—28no—
52C23×Dic7—44no—
53C23×Dic7C2312yes—
54C23×Dic7C2312yes—
55C23×Dic7C2311yescharacteristic
56C23×Dic7C2312yes—
57C23×Dic7C2311yescharacteristic
58C22×Dic14—22no—
59C22×Dic14—22no—
60C22×Dic14—22no—
61C22×Dic14—22no—
62C22×Dic14—22no—
63C22×Dic14—22no—
64C22×Dic14C2×C414yescomplemented
65C2×C7×C4⋊C4—22no—
66C2×C7×C4⋊C4—22no—
67C2×C7×C4⋊C4—22no—
68C2×C7×C22⋊C4—28no—
69C2×C7×C22⋊C4—28no—
70C2×C7×C22⋊C4—44no—
71C2×C42×C7—22no—
72C2×C42×C7—22no—
73C2×C42×C7—22no—
74C2×C22⋊Dic7—24no—
75C2×C22⋊Dic7—28no—
76C2×C22⋊Dic7—28no—
77C2×C22⋊Dic7—24no—
78C2×C22⋊Dic7—24no—
79C2×C22⋊Dic7C2×C4116yescomplemented
80#6499—232no—
81D4×Dic7—232no—
82C2×C4⋊Dic7—22no—
83C2×C4⋊Dic7—22no—
84C2×C4⋊Dic7D414yes—
85C2×C4×Dic7—22no—
86C2×C4×Dic7—22no—
87C2×C4×Dic7—22no—
88C2×C4×Dic7—22no—
89C2×C4×Dic7C2×C414yescomplemented
90C2×C4×Dic7D414yes—
91C7⋊#95—24no—
92C7⋊#95—28no—
93C7⋊#95—24no—
94C7⋊#95—24no—
95C7⋊#95—24no—
96C7⋊#95—44no—
97C22×#124—71no—
98C22×C4×D4—71no—
99C2×#391—71no—
100C2×#391—71no—
101C2×#390D711yescharacteristic
102#1440—74no—
103C4⋊#95—71no—
104C22⋊#95—74no—
105C4×#95—71no—
106C24×C7—22no—
107C24×C7—22no—
108C24×C7—24no—
109C24×C7—24no—
110C24×C7—22no—
111C24×C7—22no—
112C24×C7—24no—
113C24×C7—24no—
114C24×C7C22×C414yes—
115C24×C7C2×D414yes—
116C24×C7C2×D414yes—
117C24×C7C2411yescharacteristic
118C2×C7×D4—28no—
119C2×C7×D4—28no—
120C2×C7×D4—28no—
121C2×C7×D4—28no—
122C2×C7×D4—28no—
123C2×C7×D4—28no—
124C2×C7×D4C22⋊C4116yes—
125C22×C4×C7—22no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7—22no—
129C22×C4×C7—22no—
130C22×C4×C7—22no—
131C22×C4×C7—22no—
132C22×C4×C7—22no—
133C22×C4×C7—24no—
134C22×C4×C7—22no—
135C22×C4×C7—24no—
136C22×C4×C7C22×C412yes—
137C22×C4×C7C2×D412yes—
138C22×C4×C7C2×D412yes—
139C22×C4×C7C2×D412yes—
140C22×C4×C7C2×D412yes—
141C22×C4×C7#4114yes—
142C22×C4×C7#4112yes—
143C22×C4×C7#4112yes—
144C22×Dic7—21no—
145C22×Dic7—21no—
146C22×Dic7—22no—
147C22×Dic7—216no—
148C22×Dic7—22no—
149C22×Dic7—22no—
150C22×Dic7—22no—
151C22×Dic7—22no—
152C22×Dic7—21no—
153C22×Dic7—21no—
154C22×Dic7—22no—
155C22×Dic7—22no—
156C22×Dic7—22no—
157C22×Dic7—22no—
158C22×Dic7—22no—
159C22×Dic7—22no—
160C22×Dic7—22no—
161C22×Dic7—22no—
162C22×Dic7—22no—
163C22×Dic7—24no—
164C22×Dic7—22no—
165C22×Dic7—24no—
166C22×Dic7—22no—
167C22×Dic7—22no—
168C22×Dic7—416no—
169C22×Dic7—416no—
170C22×Dic7—48no—
171C22×Dic7—48no—
172C22×Dic7C22×C414yes—
173C22×Dic7C22×C414yes—
174C22×Dic7C2×D412yes—
175C22×Dic7C2×D414yes—
176C22×Dic7C2×D412yes—
177C22×Dic7#4114yes—
178C2×Dic14—28no—
179C2×Dic14—28no—
180C2×Dic14—28no—
181C2×Dic14—44no—
182C2×Dic14—44no—
183C2×Dic14—44no—
184C2×Dic14—44no—
185C7×C4⋊C4—44no—
186C7×C22⋊C4—416no—
187C42×C7—44no—
188C22⋊Dic7—216no—
189C22⋊Dic7—232no—
190C4⋊Dic7—28no—
191C4×Dic7—28no—
192C4×Dic7—28no—
193C23×Q8—71no—
194C23×D4C2×D711yescharacteristic
195C24×C4—72no—
196C2×#124—78no—
197C2×#124—144no—
198C2×#124—144no—
199C2×C4×D4—144no—
200C2×C4×D4—144no—
201C2×C4×D4—144no—
202C22×C4⋊C4—71no—
203C22×C4⋊C4C2×D711yescharacteristic
204C22×C22⋊C4—74no—
205C22×C22⋊C4—72no—
206C22×C22⋊C4C2×D714yes—
207C22×C42—71no—
208C22×C42—71no—
209C22×C42C2×D711yescharacteristic
210#391—144no—
211#391—144no—
212#390—24no—
213C2×#95—72no—
214C2×#95—72no—
215C2×#95—72no—
216C2×#95—74no—
217C2×#95—72no—
218C2×#95—74no—
219C23×C7—24no—
220C23×C7—24no—
221C23×C7—28no—
222C23×C7—28no—
223C23×C7—24no—
224C23×C7—24no—
225C23×C7—24no—
226C23×C7—24no—
227C23×C7—28no—
228C23×C7—28no—
229C23×C7—28no—
230C23×C7—28no—
231C23×C7—42no—
232C23×C7—44no—
233C23×C7—42no—
234C23×C7—42no—
235C23×C7—42no—
236C23×C7—44no—
237C23×C7—44no—
238C23×C7—44no—
239C23×C7—44no—
240C23×C7—44no—
241C23×C7C2×C22⋊C418yes—
242C23×C7C23×C411yescharacteristic
243C23×C7C22×D411yescharacteristic
244C23×C7C22×D411yescharacteristic
245C23×C7C22×D411yescharacteristic
246C23×C7C22×D411yescharacteristic
247C23×C7C2×#4111yescharacteristic
248C23×C7C2×#4111yescharacteristic
249C23×C7C2×#4112yes—
250C23×C7C2×#4112yes—
251C23×C7H(5,𝔽2)12yes—
252C23×C72−1+412yes—
253C7×D4—232no—
254C2×C4×C7—24no—
255C2×C4×C7—24no—
256C2×C4×C7—24no—
257C2×C4×C7—42no—
258C2×C4×C7—42no—
259C2×C4×C7—42no—
260C2×C4×C7—42no—
261C2×C4×C7—42no—
262C2×C4×C7—42no—
263C2×C4×C7—42no—
264C2×C4×C7—44no—
265C2×C4×C7—44no—
266C2×C4×C7C2×C22⋊C414yes—
267C2×C4×C7C4×D414yes—
268C2×C4×C7C4×D414yes—
269C2×C4×C7#12014yes—
270C2×C4×C7#12114yes—
271C2×C4×C7#12114yes—
272C2×C4×C7#12314yes—
273C2×Dic7—22no—
274C2×Dic7—22no—
275C2×Dic7—24no—
276C2×Dic7—24no—
277C2×Dic7—24no—
278C2×Dic7—24no—
279C2×Dic7—24no—
280C2×Dic7—24no—
281C2×Dic7—24no—
282C2×Dic7—24no—
283C2×Dic7—22no—
284C2×Dic7—24no—
285C2×Dic7—22no—
286C2×Dic7—22no—
287C2×Dic7—28no—
288C2×Dic7—432no—
289C2×Dic7—42no—
290C2×Dic7—42no—
291C2×Dic7—42no—
292C2×Dic7—42no—
293C2×Dic7—42no—
294C2×Dic7—42no—
295C2×Dic7—42no—
296C2×Dic7—42no—
297C2×Dic7—44no—
298C2×Dic7—42no—
299C2×Dic7—42no—
300C2×Dic7—42no—
301C2×Dic7—42no—
302C2×Dic7#12414yescomplemented
303Dic14—416no—
304C25C22×D712yes—
305C22×Q8—74no—
306C22×Q8—142no—
307C22×Q8—142no—
308C22×Q8—142no—
309C22×Q8—142no—
310C22×Q8—142no—
311C22×Q8—142no—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4—22no—
316C22×D4C4×D714yes—
317C22×D4D2814yes—
318C22×D4C22⋊D714yes—
319C23×C4—71no—
320C23×C4—72no—
321C23×C4—72no—
322C23×C4—71no—
323C23×C4—72no—
324C23×C4—144no—
325C23×C4—144no—
326C23×C4—148no—
327C23×C4—144no—
328C23×C4—284no—
329C23×C4C22×D712yes—
330C23×C4C22×D712yes—
331C23×C4C22×D711yescharacteristic
332#124—1432no—
333C4×D4—1432no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—74no—
338C2×C4⋊C4—142no—
339C2×C4⋊C4—142no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—716no—
344C2×C22⋊C4—144no—
345C2×C22⋊C4—144no—
346C2×C22⋊C4—144no—
347C2×C22⋊C4—148no—
348C2×C22⋊C4—148no—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—74no—
353C2×C42—74no—
354C2×C42—142no—
355C2×C42—142no—
356C2×C42—142no—
357C2×C42—142no—
358#95—144no—
359#95—148no—
360#95—144no—
361#95—144no—
362#95—144no—
363#95—284no—
364C22×C7—216no—
365C22×C7—28no—
366C22×C7—44no—
367C22×C7—48no—
368C22×C7—48no—
369C22×C7—44no—
370C22×C7—44no—
371C22×C7—48no—
372C22×C7—44no—
373C22×C7—44no—
374C22×C7—44no—
375C22×C7C22×C22⋊C411yescharacteristic
376C22×C7C2×C4×D411yescharacteristic
377C22×C7C2×C4×D411yescharacteristic
378C22×C7C4×#4112yes—
379C22×C7#52012yes—
380C22×C7C2×#12011yescharacteristic
381C22×C7C2×#12111yescharacteristic
382C22×C7C2×#12111yescharacteristic
383C22×C7C2×#12311yescharacteristic
384C22×C7C2×#12411yescharacteristic
385C22×C7#52912yes—
386C22×C7#53211yescharacteristic
387C22×C7#53511yescharacteristic
388C22×C7#53611yescharacteristic
389C22×C7#54212yes—
390C22×C7#54612yes—
391C22×C7#54612yes—
392C22×C7#54612yes—
393C22×C7#54712yes—
394C22×C7#54712yes—
395C22×C7#54812yes—
396C22×C7#55612yes—
397C22×C7#55912yes—
398C4×C7—44no—
399C4×C7—82no—
400C4×C7#38618yes—
401Dic7—24no—
402Dic7—44no—
403Dic7—42no—
404Dic7—44no—
405Dic7—44no—
406C24—22no—
407C24—22no—
408C24—24no—
409C24—22no—
410C24—22no—
411C24—24no—
412C24—24no—
413C24—24no—
414C24C2×C4×D714yes—
415C24C2×D2814yes—
416C24C2×C22⋊D714yes—
417C24C23×D711yescharacteristic
418C2×Q8—148no—
419C2×Q8—148no—
420C2×Q8—148no—
421C2×Q8—284no—
422C2×Q8—284no—
423C2×Q8—284no—
424C2×Q8—284no—
425C2×D4—28no—
426C2×D4—28no—
427C2×D4—28no—
428C2×D4—28no—
429C2×D4—28no—
430C2×D4—28no—
431C2×D4(C2×D7)⋊C4116yes—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—24no—
442C22×C4—22no—
443C22×C4—72no—
444C22×C4—74no—
445C22×C4—74no—
446C22×C4—74no—
447C22×C4—72no—
448C22×C4—74no—
449C22×C4—141no—
450C22×C4—141no—
451C22×C4—142no—
452C22×C4—1416no—
453C22×C4—141no—
454C22×C4—142no—
455C22×C4—142no—
456C22×C4—142no—
457C22×C4—142no—
458C22×C4—142no—
459C22×C4—141no—
460C22×C4—142no—
461C22×C4—142no—
462C22×C4—142no—
463C22×C4—142no—
464C22×C4—142no—
465C22×C4—142no—
466C22×C4—144no—
467C22×C4—142no—
468C22×C4—144no—
469C22×C4—142no—
470C22×C4—142no—
471C22×C4—142no—
472C22×C4—142no—
473C22×C4—288no—
474C22×C4—2816no—
475C22×C4—2816no—
476C22×C4—288no—
477C22×C4C2×C4×D712yes—
478C22×C4C2×D2812yes—
479C22×C4D4×D712yes—
480C22×C4D4×D712yes—
481C22×C4#115914yes—
482C22×C4#115912yes—
483C22×C4#115912yes—
484C22×C4C2×C22⋊D712yes—
485C4⋊C4—44no—
486C4⋊C4—148no—
487C22⋊C4—416no—
488C22⋊C4—1416no—
489C22⋊C4—1432no—
490C42—44no—
491C42—148no—
492C42—148no—
493C2×C7—48no—
494C2×C7C2×#38611yescharacteristic
495C2×C7C4×#12411yescharacteristic
496C2×C7#232611yescharacteristic
497C2×C7#233912yes—
498C2×C7#236712yes—
499C2×C7#242712yes—
500C2×C7#243211yescharacteristic
501C2×C7#243511yescharacteristic
502C2×C7#244712yes—
503C2×C7#254411yescharacteristic
504C2×C7#254711yescharacteristic
505C23—24no—
506C23—24no—
507C23—24no—
508C23—24no—
509C23—28no—
510C23—28no—
511C23—24no—
512C23—24no—
513C23—28no—
514C23—28no—
515C23—28no—
516C23—28no—
517C23—44no—
518C23—42no—
519C23—42no—
520C23—44no—
521C23—44no—
522C23—44no—
523C23—44no—
524C23—44no—
525C23—42no—
526C23—42no—
527C23C2×(C2×D7)⋊C418yes—
528C23C22×C4×D711yescharacteristic
529C23C22×D2811yescharacteristic
530C23C2×D4×D711yescharacteristic
531C23C2×D4×D711yescharacteristic
532C23C2×#115911yescharacteristic
533C23C2×#115912yes—
534C23C2×#115911yescharacteristic
535C23#654812yes—
536C23D7×#4112yes—
537C23#655412yes—
538C23C22×C22⋊D711yescharacteristic
539Q8—2816no—
540D4—232no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—44no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—44no—
553C2×C4—74no—
554C2×C4—142no—
555C2×C4—142no—
556C2×C4—144no—
557C2×C4—144no—
558C2×C4—142no—
559C2×C4—144no—
560C2×C4—144no—
561C2×C4—142no—
562C2×C4—144no—
563C2×C4—144no—
564C2×C4—144no—
565C2×C4—144no—
566C2×C4—144no—
567C2×C4—148no—
568C2×C4—142no—
569C2×C4—2832no—
570C2×C4—282no—
571C2×C4—282no—
572C2×C4—282no—
573C2×C4—282no—
574C2×C4—282no—
575C2×C4—282no—
576C2×C4—282no—
577C2×C4—284no—
578C2×C4—282no—
579C2×C4—282no—
580C2×C4—282no—
581C2×C4—282no—
582C2×C4—282no—
583C2×C4(C22⋊D7)⋊C414yes—
584C2×C4(C22⋊D7)⋊C414yes—
585C2×C4#644514yes—
586C2×C4#644914yes—
587C2×C4C2×(C2×D7)⋊C414yes—
588C2×C4#650214yes—
589C2×C4#650214yes—
590C7#1402711yescharacteristic, complemented, Sylow
591C22—216no—
592C22—28no—
593C22—44no—
594C22—44no—
595C22—48no—
596C22—44no—
597C22—48no—
598C22—44no—
599C22—44no—
600C22—44no—
601C22—48no—
602C22C2×(C22⋊D7)⋊C411yescharacteristic
603C22C2×(C22⋊D7)⋊C411yescharacteristic
604C22C2×#644511yescharacteristic
605C22C2×#644911yescharacteristic
606C22C4×#115912yes—
607C22#9023712yes—
608C22#9024512yes—
609C22#9024612yes—
610C22#9028912yes—
611C22#9029112yes—
612C22#9029412yes—
613C22#9030312yes—
614C22#9036212yes—
615C22D7×#12411yescharacteristic
616C22#9036611yescharacteristic
617C22#9040412yes—
618C22#9040611yescharacteristic
619C22#9040711yescharacteristic
620C22C22×(C2×D7)⋊C411yescharacteristic
621C22C2×#650211yescharacteristic
622C22C2×#650211yescharacteristic
623C22#9049712yes—
624C22#9051512yes—
625C4—44no—
626C4—82no—
627C4—144no—
628C4—284no—
629C4—284no—
630C4—282no—
631C4—284no—
632C4#8973018yes—
633C2—48no—
634C2#1173373711yescharacteristic
635C2#1173374211yescharacteristic
636C2#1173375212yes—
637C2#1173376011yescharacteristic
638C2#1173376412yes—
639C2#1173389011yescharacteristic
640C2C2×#8973011yescharacteristic
641C2#1173977512yes—
642C2#1174009212yes—
643C2#1174041811yescharacteristic
644C2#1174062311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#390C2
socle, cosocleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC2×#390D7
hypocenterC7#14027
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
4. C2×#89746C2semidirect
5. C2×#89701C2semidirect
6. #11729317C2semidirect
7. #11729303C2semidirect
8. #11729298C2semidirect
9. C4×C7⋊#95C2semidirect
20. C2×#6499C4semidirect
64. C22×Dic14C2×C4semidirect
79. C2×C22⋊Dic7C2×C4semidirect
89. C2×C4×Dic7C2×C4semidirect
302. C2×Dic7#124semidirect
590. C7#14027semidirect

Maximal subgroups

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

subgroupindex
C22×#64992
C22×D4×Dic72
C2×C7×#3902
C2×#897462
C2×#897012
#117293172
#117293032
#117292982
C4×C7⋊#952
#140277