Finite Group Databasebeta

← #13388141

Subgroups — #13388141

Order 1792.

1394 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#532C211yesmaximal, characteristic
2C2×#89866C211yesmaximal, characteristic, complemented
3C2×#89847C211yesmaximal, characteristic, complemented
4C4×#6487C211yesmaximal, characteristic, complemented
5#11729534C211yesmaximal, characteristic, complemented
6#11729515C211yesmaximal, characteristic, complemented
7#11729439C212yesmaximal, complemented
8#11729434C212yesmaximal, complemented
9#11729366C212yesmaximal, complemented
10#11729361C212yesmaximal, complemented
11#11729284C211yesmaximal, characteristic, complemented
12C22×C7×#41—21no—
13C7×#532—24no—
14C7×#532—24no—
15C2×C7×C4⋊Q8C2211yescharacteristic
16C2×C7×#127C2211yescharacteristic
17C2×C7×#124—21no—
18C2×C7×#121—21no—
19C2×C7×#121C2212yes—
20C2×C4×C7×D4—21no—
21C2×C4×C7×D4C2212yes—
22C22×C42×C7C2211yescharacteristic
23C22×#1142C2212yes—
24C2×#6487C2211yescharacteristic
25C2×C4×Dic14C2211yescharacteristic
26C2×#6406C2212yes—
27C2×#6406C2212yes—
28C2×#6406C2212yes—
29#89984C2211yescharacteristic
30#89982—21no—
31C4×C22⋊Dic7—21no—
32C2×C22⋊(C7⋊C8)C2212yes—
33#89866—24no—
34#89847—24no—
35C2×#6384C2212yes—
36C2×#6382C2212yes—
37C4×C4⋊Dic7C2211yescharacteristic
38#89705—21no—
39C4×Dic7⋊C4—21no—
40#89701C2211yescharacteristic
41#89700C2211yescharacteristic
42C2×C4⋊(C7⋊C8)C2211yescharacteristic
43C2×C4⋊(C7⋊C8)C2211yescharacteristic
44#89324C2212yes—
45#89324C2212yes—
46#89319C2212yes—
47#24154—71nomaximal, Sylow
48C2×C7×#41—28no—
49C2×C7×#41—44no—
50C2×C7×#41—44no—
51C22×C7×Q8—21no—
52C22×C7×D4—22no—
53C22×C7×D4—21no—
54C22×C7×D4—21no—
55C22×C7×D4C2312yes—
56C23×C4×C7—22no—
57C23×C4×C7D411yescharacteristic
58C23×C4×C7D411yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C22×Dic14C2311yescharacteristic
61C7×C4⋊Q8—22no—
62C7×C4⋊Q8D414yes—
63C7×#127—22no—
64C7×#127D414yes—
65C7×#124—28no—
66C7×#121—28no—
67C7×#121—24no—
68C7×#121—24no—
69C4×C7×D4—28no—
70C4×C7×D4—24no—
71C4×C7×D4—24no—
72C2×C7×C4⋊C4—21no—
73C2×C7×C4⋊C4C2312yes—
74C2×C7×C22⋊C4—22no—
75C2×C7×C22⋊C4—22no—
76C2×C42×C7—22no—
77C2×C42×C7—22no—
78C2×C42×C7D411yescharacteristic
79C2×C42×C7D411yescharacteristic
80C2×C42×C7C2311yescharacteristic
81C2×C42×C7C2311yescharacteristic
82C2×C22⋊Dic7—21no—
83C2×C22⋊Dic7—21no—
84C2×#1142—24no—
85C2×#1142—24no—
86C2×#1142—42no—
87C2×C4⋊Dic7C2311yescharacteristic
88C2×C4⋊Dic7C2311yescharacteristic
89C2×C4⋊Dic7C2311yescharacteristic
90#6487—22no—
91#6487—22no—
92C2×Dic7⋊C4—21no—
93C2×Dic7⋊C4—21no—
94C2×Dic7⋊C4—21no—
95C2×C4×Dic7—21no—
96C2×C4×Dic7—21no—
97C22×C7⋊C8C2312yes—
98C22×C7⋊C8C2312yes—
99C4×Dic14—22no—
100C4×Dic14—22no—
101#6406—24no—
102#6406—24no—
103#6406—42no—
104C7⋊#95—21no—
105C7⋊#95—21no—
106C7⋊#95—21no—
107C7⋊#95—21no—
108C7⋊#95—21no—
109C22⋊(C7⋊C8)—42no—
110#6384—24no—
111#6382—24no—
112C4⋊(C7⋊C8)—22no—
113C4⋊(C7⋊C8)—22no—
114C2×#532D711yescharacteristic
115C2×#475—71no—
116C2×#460—71no—
117C4×C22⋊Q8—71no—
118#2034—72no—
119#2000—72no—
120#1988—71no—
121#1982—71no—
122#1877—72no—
123#1864—72no—
124#1797—71no—
125C24×C7—22no—
126C24×C7C2×D411yescharacteristic
127C7×#41—432no—
128C2×C7×Q8—24no—
129C2×C7×Q8—42no—
130C2×C7×Q8—42no—
131C2×C7×D4—28no—
132C2×C7×D4—24no—
133C2×C7×D4—24no—
134C2×C7×D4—22no—
135C2×C7×D4—22no—
136C2×C7×D4—22no—
137C2×C7×D4—22no—
138C2×C7×D4—22no—
139C2×C7×D4—42no—
140C2×C7×D4—42no—
141C2×C7×D4—44no—
142C2×C7×D4—44no—
143C2×C7×D4—42no—
144C2×C7×D4—42no—
145C2×C7×D4C2×D414yes—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—28no—
149C22×C4×C7—22no—
150C22×C4×C7—22no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7—41no—
158C22×C4×C7—41no—
159C22×C4×C7—44no—
160C22×C4×C7—44no—
161C22×C4×C7SD1614yescomplemented
162C22×C4×C7C2×D411yescharacteristic
163C22×C4×C7C2×D411yescharacteristic
164C22×C4×C7C2×D411yescharacteristic
165C22×C4×C7C2×D411yescharacteristic
166C22×C4×C7C2×D411yescharacteristic
167C22×C4×C7C2411yescharacteristic
168C22×Dic7—21no—
169C22×Dic7—21no—
170C22×Dic7—21no—
171C22×Dic7—21no—
172C2×Dic14—21no—
173C2×Dic14—21no—
174C2×Dic14—21no—
175C2×Dic14—21no—
176C2×Dic14—21no—
177C2×Dic14#4112yescomplemented
178C7×C4⋊C4—24no—
179C7×C4⋊C4—22no—
180C7×C4⋊C4C2×D414yes—
181C7×C22⋊C4—28no—
182C7×C22⋊C4—28no—
183C42×C7—22no—
184C42×C7—22no—
185C42×C7—21no—
186C42×C7—21no—
187C42×C7C2×D412yes—
188C42×C7C2×D412yes—
189C22⋊Dic7—24no—
190C22⋊Dic7—42no—
191#1142—48no—
192C4⋊Dic7—21no—
193C4⋊Dic7—21no—
194C4⋊Dic7—21no—
195C4⋊Dic7—21no—
196C4⋊Dic7—21no—
197C4⋊Dic7#4112yescomplemented
198Dic7⋊C4—24no—
199Dic7⋊C4—42no—
200Dic7⋊C4—42no—
201C4×Dic7—42no—
202C4×Dic7—42no—
203C2×C7⋊C8—22no—
204C2×C7⋊C8—22no—
205C2×C7⋊C8—22no—
206C2×C7⋊C8—22no—
207C2×C7⋊C8—22no—
208C2×C7⋊C8—22no—
209C22×#41—21no—
210C22×SD16—72no—
211#532—24no—
212#532—24no—
213C2×C4⋊Q8C2×D711yescharacteristic
214C2×#127C2×D711yescharacteristic
215C2×#124—21no—
216C2×C22⋊Q8—71no—
217C2×#121—21no—
218C2×#121C2×D712yes—
219C2×C4×Q8—71no—
220C2×C4×D4—21no—
221C2×C4×D4C2×D712yes—
222C22×C42C2×D711yescharacteristic
223#475—144no—
224#460—144no—
225C2×#106—72no—
226C2×C4⋊C8—71no—
227C2×C4⋊C8—71no—
228C2×#103—72no—
229C2×#102—72no—
230C2×#102—72no—
231C2×#102—72no—
232C2×C22⋊C8—72no—
233#391—71no—
234#389—71no—
235#387—141no—
236#385—141no—
237#380—71no—
238C4×C4⋊C4—71no—
239C4×C4⋊C4—141no—
240C4×C22⋊C4—141no—
241#340—72no—
242#340—72no—
243#336—72no—
244C23×C7—21no—
245C23×C7—21no—
246C23×C7—21no—
247C23×C7—21no—
248C23×C7—21no—
249C23×C7—21no—
250C23×C7—24no—
251C23×C7—42no—
252C23×C7—42no—
253C23×C7—42no—
254C23×C7—42no—
255C23×C7—42no—
256C23×C7—42no—
257C23×C7C2×SD1612yes—
258C23×C7C22×D411yescharacteristic
259C7×Q8—48no—
260C7×D4—24no—
261C7×D4—24no—
262C7×D4—48no—
263C7×D4—416no—
264C7×D4—42no—
265C7×D4—42no—
266C7×D4—48no—
267C2×C4×C7—21no—
268C2×C4×C7—21no—
269C2×C4×C7—21no—
270C2×C4×C7—21no—
271C2×C4×C7—28no—
272C2×C4×C7—21no—
273C2×C4×C7—21no—
274C2×C4×C7—24no—
275C2×C4×C7—21no—
276C2×C4×C7—21no—
277C2×C4×C7—21no—
278C2×C4×C7—21no—
279C2×C4×C7—44no—
280C2×C4×C7—416no—
281C2×C4×C7—42no—
282C2×C4×C7—42no—
283C2×C4×C7—41no—
284C2×C4×C7—41no—
285C2×C4×C7—41no—
286C2×C4×C7—41no—
287C2×C4×C7#12012yes—
288C2×C4×C7#12012yes—
289C2×C4×C7C2×SD1612yes—
290C2×C4×C7C2×SD1612yes—
291C2×C4×C7AGL(1,ℤ/8)12yes—
292C2×C4×C7C22×D411yescharacteristic
293C2×C4×C7C22×D411yescharacteristic
294C2×C4×C7C2×#4111yescharacteristic
295C2×C4×C7C2×#4111yescharacteristic
296C2×C4×C7H(5,𝔽2)11yescharacteristic
297C2×C4×C72−1+411yescharacteristic
298C2×Dic7—22no—
299C2×Dic7—22no—
300C2×Dic7—41no—
301C2×Dic7—41no—
302C2×Dic7—41no—
303C2×Dic7—41no—
304C2×Dic7—41no—
305C2×Dic7—41no—
306C2×Dic7—41no—
307C2×Dic7—41no—
308C2×Dic7—41no—
309C2×Dic7—41no—
310Dic14—22no—
311Dic14—22no—
312Dic14—41no—
313Dic14—41no—
314C7⋊C8—42no—
315C7⋊C8—42no—
316C2×#41—28no—
317C2×#41—44no—
318C2×#41—44no—
319C22×Q8—21no—
320C22×Q8—71no—
321C22×D4—22no—
322C22×D4—21no—
323C22×D4—21no—
324C22×D4C22×D712yes—
325C23×C4—22no—
326C23×C4C22⋊D711yescharacteristic
327C23×C4C22⋊D711yescharacteristic
328C23×C4C22×D711yescharacteristic
329C2×SD16—144no—
330C2×SD16—144no—
331C2×SD16—282no—
332C22×C8—72no—
333C22×C8—72no—
334C4⋊Q8—22no—
335C4⋊Q8C22⋊D714yes—
336#127—22no—
337#127C22⋊D714yes—
338#124—28no—
339C22⋊Q8—142no—
340C22⋊Q8—142no—
341#121—28no—
342#121—24no—
343#121—24no—
344C4×Q8—142no—
345C4×Q8—142no—
346C4×D4—28no—
347C4×D4—24no—
348C4×D4—24no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—71no—
351C2×C4⋊C4—71no—
352C2×C4⋊C4—71no—
353C2×C4⋊C4—141no—
354C2×C4⋊C4—141no—
355C2×C4⋊C4—141no—
356C2×C4⋊C4C22×D712yes—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—141no—
360C2×C22⋊C4—141no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—141no—
364C2×C42—141no—
365C2×C42C22⋊D711yescharacteristic
366C2×C42C22⋊D711yescharacteristic
367C2×C42C22×D711yescharacteristic
368C2×C42C22×D711yescharacteristic
369#106—144no—
370C4⋊C8—142no—
371C4⋊C8—142no—
372#103—144no—
373#102—144no—
374#102—144no—
375#102—282no—
376C22⋊C8—282no—
377#95—141no—
378#95—141no—
379#95—141no—
380#95—141no—
381#95—141no—
382C22×C7—22no—
383C22×C7—22no—
384C22×C7—22no—
385C22×C7—41no—
386C22×C7—41no—
387C22×C7—41no—
388C22×C7—41no—
389C22×C7—44no—
390C22×C7—44no—
391C22×C7—44no—
392C22×C7—82no—
393C22×C7—82no—
394C22×C7—82no—
395C22×C7—82no—
396C22×C7C2×#12011yescharacteristic
397C22×C7#52511yescharacteristic
398C22×C7#53711yescharacteristic
399C22×C7C22×SD1611yescharacteristic
400C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
401C22×C7#57511yescharacteristic
402C22×C7#57511yescharacteristic
403C4×C7—22no—
404C4×C7—22no—
405C4×C7—41no—
406C4×C7—44no—
407C4×C7—41no—
408C4×C7#45014yes—
409C4×C7#54611yescharacteristic
410C4×C7#54711yescharacteristic
411C4×C7#54811yescharacteristic
412C4×C7#55011yescharacteristic
413Dic7—42no—
414Dic7—42no—
415Dic7—81no—
416Dic7—81no—
417C24—22no—
418C24C2×C22⋊D711yescharacteristic
419#41—432no—
420C2×Q8—24no—
421C2×Q8—42no—
422C2×Q8—42no—
423C2×Q8—72no—
424C2×Q8—141no—
425C2×Q8—141no—
426C2×Q8—141no—
427C2×Q8—141no—
428C2×Q8—141no—
429C2×D4—28no—
430C2×D4—24no—
431C2×D4—24no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—44no—
440C2×D4—44no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4C2×C22⋊D714yes—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—28no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4—141no—
460C22×C4—141no—
461C22×C4—141no—
462C22×C4—141no—
463C22×C4#114214yescomplemented
464C22×C4C2×C22⋊D711yescharacteristic
465C22×C4C2×C22⋊D711yescharacteristic
466C22×C4C2×C22⋊D711yescharacteristic
467C22×C4C2×C22⋊D711yescharacteristic
468C22×C4C2×C22⋊D711yescharacteristic
469C22×C4C23×D711yescharacteristic
470SD16—288no—
471C2×C8—142no—
472C2×C8—142no—
473C2×C8—142no—
474C2×C8—142no—
475C2×C8—142no—
476C2×C8—142no—
477C4⋊C4—24no—
478C4⋊C4—22no—
479C4⋊C4—72no—
480C4⋊C4—144no—
481C4⋊C4—141no—
482C4⋊C4—141no—
483C4⋊C4—141no—
484C4⋊C4—141no—
485C4⋊C4—141no—
486C4⋊C4—282no—
487C4⋊C4—282no—
488C4⋊C4C2×C22⋊D714yes—
489C22⋊C4—28no—
490C22⋊C4—28no—
491C22⋊C4—144no—
492C22⋊C4—282no—
493C42—22no—
494C42—22no—
495C42—21no—
496C42—21no—
497C42—282no—
498C42—282no—
499C42C2×C22⋊D712yes—
500C42C2×C22⋊D712yes—
501C2×C7—42no—
502C2×C7—84no—
503C2×C7#240711yescharacteristic
504C2×C7C2×#45011yescharacteristic
505C2×C7#300511yescharacteristic
506C2×C7#310311yescharacteristic
507C2×C7#311511yescharacteristic
508C2×C7#324611yescharacteristic
509C2×C7#325111yescharacteristic
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—24no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23C2×#114212yes—
524C23C22×C22⋊D711yescharacteristic
525Q8—48no—
526Q8—142no—
527Q8—142no—
528Q8—281no—
529Q8—281no—
530D4—24no—
531D4—24no—
532D4—48no—
533D4—416no—
534D4—48no—
535D4—42no—
536D4—42no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—28no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—24no—
549C2×C4—44no—
550C2×C4—416no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—142no—
558C2×C4—142no—
559C2×C4—281no—
560C2×C4—281no—
561C2×C4—281no—
562C2×C4—281no—
563C2×C4—281no—
564C2×C4—281no—
565C2×C4—281no—
566C2×C4—281no—
567C2×C4—281no—
568C2×C4—281no—
569C2×C4#649512yes—
570C2×C4C2×#114212yes—
571C2×C4C2×#114212yes—
572C2×C4#651612yes—
573C2×C4#651612yes—
574C2×C4D7×#4111yescharacteristic
575C2×C4D7×#4111yescharacteristic
576C2×C4#655311yescharacteristic
577C2×C4#655411yescharacteristic
578C2×C4C22×C22⋊D711yescharacteristic
579C2×C4C22×C22⋊D711yescharacteristic
580C8—282no—
581C8—282no—
582C7#2415411yescharacteristic, complemented, Sylow
583C22—22no—
584C22—22no—
585C22—22no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—44no—
591C22—44no—
592C22—44no—
593C22—82no—
594C22—82no—
595C22—82no—
596C22—82no—
597C22C2×#649511yescharacteristic
598C22C22×#114211yescharacteristic
599C22#9051311yescharacteristic
600C22#9051311yescharacteristic
601C22#9051911yescharacteristic
602C22#9052411yescharacteristic
603C22C2×#651611yescharacteristic
604C4—22no—
605C4—22no—
606C4—44no—
607C4—41no—
608C4—41no—
609C4—282no—
610C4—282no—
611C4—561no—
612C4—561no—
613C4#8999014yes—
614C4#9051511yescharacteristic
615C4#9052011yescharacteristic
616C4#9052211yescharacteristic
617C4#9052511yescharacteristic
618C2—42no—
619C2—84no—
620C2#1174074611yescharacteristic
621C2#1174075711yescharacteristic
622C2#1174076011yescharacteristic
623C2#1174076511yescharacteristic
624C2C2×#8999011yescharacteristic
625C2#1174152611yescharacteristic
626C2#1174154211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
Fitting, prime radicalC2×C7×#532C2
socleC23×C7C22×D4
hypercenterC2×#532D7
hypocenterC7#24154
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
2. C2×#89866C2semidirect
3. C2×#89847C2semidirect
4. C4×#6487C2semidirect
5. #11729534C2semidirect
6. #11729515C2semidirect
7. #11729439C2semidirect
8. #11729434C2semidirect
9. #11729366C2semidirect
10. #11729361C2semidirect
11. #11729284C2semidirect
161. C22×C4×C7SD16semidirect
177. C2×Dic14#41semidirect
197. C4⋊Dic7#41semidirect
463. C22×C4#1142semidirect
582. C7#24154semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5322
C2×#898662
C2×#898472
C4×#64872
#117295342
#117295152
#117294392
#117294342
#117293662
#117293612
#117292842
#241547