Finite Group Databasebeta

← #13388147

Subgroups — #13388147

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×#90168C211yesmaximal, characteristic
2C4×C7×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×#89799C211yesmaximal, characteristic, complemented
4C2×#89792C211yesmaximal, characteristic, complemented
5#11729453C212yesmaximal, complemented
6#11729284C211yesmaximal, characteristic, complemented
7#11727441C212yesmaximal, complemented
8#11727380C212yesmaximal, complemented
9#11727278C212yesmaximal, complemented
10#11727244C211yesmaximal, characteristic, complemented
11#11727241C211yesmaximal, characteristic, complemented
12C22×#1157—21no—
13C2×C7×C22⋊Q8C2211yescharacteristic
14C2×C4×C7×Q8C2211yescharacteristic
15C22×C42×C7C2211yescharacteristic
16C22×#1143C2212yes—
17C2×#6493—21no—
18C2×#6493C2212yes—
19#90168—24no—
20#90168—24no—
21C2×#6438—21no—
22C2×#6437C2211yescharacteristic
23C2×C4×D28—21no—
24C2×C4×D28C2212yes—
25C2×#6432C2211yescharacteristic
26C7×#391C2211yescharacteristic
27C7×#389C2211yescharacteristic
28C7×#387—21no—
29C7×#385—21no—
30C7×#380C2211yescharacteristic
31C4×C7×C4⋊C4—21no—
32C4×C7×C4⋊C4C2211yescharacteristic
33C4×C7×C22⋊C4—21no—
34C2×#6409C2212yes—
35C2×C22⋊(C7⋊C8)C2212yes—
36#89799—24no—
37#89792—24no—
38C2×#6383C2212yes—
39C2×#6383C2212yes—
40C2×#6383C2212yes—
41C2×#6382C2212yes—
42C2×C4⋊(C7⋊C8)C2211yescharacteristic
43C2×C4⋊(C7⋊C8)C2211yescharacteristic
44#89324C2212yes—
45#89324C2212yes—
46#89319C2212yes—
47#24154—71nomaximal, Sylow
48C22×C7×Q8C2311yescharacteristic
49C23×C4×C7D411yescharacteristic
50C23×C4×C7D411yescharacteristic
51C23×C4×C7C2311yescharacteristic
52C22×C22⋊D7—22no—
53C2×#1157—28no—
54C2×#1157—44no—
55C2×#1157—44no—
56C22×D28—21no—
57C22×D28—21no—
58C22×D28C2312yes—
59C22×C4×D7—22no—
60C22×Dic14—21no—
61C7×C22⋊Q8—22no—
62C7×C22⋊Q8—22no—
63C4×C7×Q8—22no—
64C4×C7×Q8—22no—
65C2×C7×C4⋊C4—21no—
66C2×C7×C4⋊C4—21no—
67C2×C7×C4⋊C4—21no—
68C2×C7×C4⋊C4C2311yescharacteristic
69C2×C7×C4⋊C4C2311yescharacteristic
70C2×C7×C4⋊C4C2311yescharacteristic
71C2×C7×C22⋊C4—21no—
72C2×C7×C22⋊C4—21no—
73C2×C42×C7—22no—
74C2×C42×C7—22no—
75C2×C42×C7—21no—
76C2×C42×C7—21no—
77C2×C42×C7D411yescharacteristic
78C2×C42×C7D411yescharacteristic
79C2×C42×C7C2311yescharacteristic
80C2×C42×C7C2311yescharacteristic
81C2×#1143—24no—
82C2×#1143—24no—
83C2×#1143—42no—
84#6493—28no—
85#6493—24no—
86#6493—24no—
87C2×(C2×D7)⋊C4—22no—
88C2×(C2×D7)⋊C4—22no—
89C2×C4⋊Dic7—21no—
90C2×C4⋊Dic7C2312yes—
91C22×C7⋊C8C2312yes—
92C22×C7⋊C8C2312yes—
93#6438—28no—
94#6437—22no—
95#6437D414yes—
96C4×D28—28no—
97C4×D28—24no—
98C4×D28—24no—
99#6432—22no—
100#6432D414yes—
101C7×#95—21no—
102C7×#95—21no—
103C7×#95—21no—
104C7×#95—21no—
105C7×#95—21no—
106#6409—24no—
107C22⋊(C7⋊C8)—42no—
108#6383—24no—
109#6383—24no—
110#6383—42no—
111#6382—24no—
112C4⋊(C7⋊C8)—22no—
113C4⋊(C7⋊C8)—22no—
114C2×#532—71no—
115C2×#475—71no—
116C2×#460—71no—
117C4×C22⋊Q8D711yescharacteristic, complemented
118#2034—72no—
119#2000—72no—
120#1988—71no—
121#1982—71no—
122#1877—72no—
123#1864—72no—
124#1797—71no—
125C24×C7C2×D411yescharacteristic
126C23×D7—22no—
127C2×C7×Q8—21no—
128C2×C7×Q8—21no—
129C2×C7×Q8—21no—
130C2×C7×Q8—21no—
131C2×C7×Q8—21no—
132C2×C7×Q8#4112yescomplemented
133C22×C4×C7—22no—
134C22×C4×C7—22no—
135C22×C4×C7—21no—
136C22×C4×C7—21no—
137C22×C4×C7—22no—
138C22×C4×C7—21no—
139C22×C4×C7—21no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7—21no—
145C22×C4×C7—21no—
146C22×C4×C7—41no—
147C22×C4×C7—41no—
148C22×C4×C7SD1614yescomplemented
149C22×C4×C7C2×D411yescharacteristic
150C22×C4×C7C2×D411yescharacteristic
151C22×C4×C7C2×D411yescharacteristic
152C22×C4×C7C2×D411yescharacteristic
153C22×C4×C7C2×D411yescharacteristic
154C22×C4×C7C2411yescharacteristic
155C2×C22⋊D7—28no—
156C2×C22⋊D7—44no—
157C2×C22⋊D7—44no—
158C22×Dic7—22no—
159#1157—432no—
160C2×D28—22no—
161C2×D28—22no—
162C2×D28—22no—
163C2×D28—22no—
164C2×D28—24no—
165C2×D28—24no—
166C2×D28—22no—
167C2×D28—42no—
168C2×D28—42no—
169C2×D28—42no—
170C2×D28—42no—
171C2×D28C2×D414yes—
172C2×C4×D7—28no—
173C2×C4×D7—44no—
174C2×C4×D7—44no—
175C2×Dic14—24no—
176C2×Dic14—42no—
177C2×Dic14—42no—
178C7×C4⋊C4—24no—
179C7×C4⋊C4—21no—
180C7×C4⋊C4—21no—
181C7×C4⋊C4—21no—
182C7×C4⋊C4—21no—
183C7×C4⋊C4—21no—
184C7×C4⋊C4—42no—
185C7×C4⋊C4—42no—
186C7×C4⋊C4#4112yescomplemented
187C7×C22⋊C4—24no—
188C7×C22⋊C4—42no—
189C42×C7—22no—
190C42×C7—22no—
191C42×C7—21no—
192C42×C7—21no—
193C42×C7—42no—
194C42×C7—42no—
195C42×C7C2×D412yes—
196C42×C7C2×D412yes—
197#1143—48no—
198(C2×D7)⋊C4—28no—
199(C2×D7)⋊C4—28no—
200C4⋊Dic7—24no—
201C4⋊Dic7—22no—
202C4⋊Dic7C2×D414yes—
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—141no—
210C22×SD16—72no—
211#532—144no—
212#532—144no—
213C2×C4⋊Q8—71no—
214C2×#127—71no—
215C2×#124—141no—
216C2×C22⋊Q8C2×D711yescharacteristic
217C2×#121—72no—
218C2×#121—141no—
219C2×C4×Q8C2×D711yescharacteristic
220C2×C4×D4—72no—
221C2×C4×D4—141no—
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#391C2×D711yescharacteristic
234#389C2×D711yescharacteristic
235#387—21no—
236#385—21no—
237#380C2×D711yescharacteristic
238C4×C4⋊C4—21no—
239C4×C4⋊C4C2×D711yescharacteristic
240C4×C22⋊C4—21no—
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×C7C2×SD1612yes—
251C23×C7C22×D411yescharacteristic
252C22×D7—24no—
253C22×D7—42no—
254C22×D7—42no—
255C22×D7—42no—
256C22×D7—42no—
257C22×D7—42no—
258C22×D7—42no—
259C7×Q8—22no—
260C7×Q8—22no—
261C7×Q8—41no—
262C7×Q8—41no—
263C2×C4×C7—21no—
264C2×C4×C7—21no—
265C2×C4×C7—21no—
266C2×C4×C7—21no—
267C2×C4×C7—28no—
268C2×C4×C7—21no—
269C2×C4×C7—21no—
270C2×C4×C7—22no—
271C2×C4×C7—22no—
272C2×C4×C7—21no—
273C2×C4×C7—21no—
274C2×C4×C7—21no—
275C2×C4×C7—21no—
276C2×C4×C7—44no—
277C2×C4×C7—41no—
278C2×C4×C7—41no—
279C2×C4×C7—41no—
280C2×C4×C7—41no—
281C2×C4×C7—41no—
282C2×C4×C7—41no—
283C2×C4×C7—41no—
284C2×C4×C7—41no—
285C2×C4×C7—41no—
286C2×C4×C7—41no—
287C2×C4×C7—41no—
288C2×C4×C7—41no—
289C2×C4×C7—41no—
290C2×C4×C7—41no—
291C2×C4×C7#12012yes—
292C2×C4×C7#12012yes—
293C2×C4×C7C2×SD1612yes—
294C2×C4×C7C2×SD1612yes—
295C2×C4×C7AGL(1,ℤ/8)12yes—
296C2×C4×C7C22×D411yescharacteristic
297C2×C4×C7C22×D411yescharacteristic
298C2×C4×C7C2×#4111yescharacteristic
299C2×C4×C7C2×#4111yescharacteristic
300C2×C4×C7H(5,𝔽2)11yescharacteristic
301C2×C4×C72−1+411yescharacteristic
302C22⋊D7—416no—
303C2×Dic7—24no—
304C2×Dic7—42no—
305C2×Dic7—42no—
306D28—24no—
307D28—24no—
308D28—48no—
309D28—42no—
310D28—42no—
311D28—48no—
312C4×D7—416no—
313Dic14—48no—
314C7⋊C8—42no—
315C7⋊C8—42no—
316C2×#41—148no—
317C2×#41—284no—
318C2×#41—284no—
319C22×Q8—141no—
320C22×Q8C22×D711yescharacteristic
321C22×D4—72no—
322C22×D4—142no—
323C22×D4—141no—
324C22×D4—141no—
325C23×C4—142no—
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—74no—
335C4⋊Q8—142no—
336#127—74no—
337#127—142no—
338#124—148no—
339C22⋊Q8—22no—
340C22⋊Q8—22no—
341#121—144no—
342#121—144no—
343#121—148no—
344C4×Q8—22no—
345C4×Q8—22no—
346C4×D4—144no—
347C4×D4—144no—
348C4×D4—148no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—72no—
353C2×C4⋊C4—141no—
354C2×C4⋊C4C22×D711yescharacteristic
355C2×C4⋊C4C22×D711yescharacteristic
356C2×C4⋊C4C22×D711yescharacteristic
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—142no—
360C2×C22⋊C4—142no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—21no—
364C2×C42—21no—
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—21no—
378#95—21no—
379#95—21no—
380#95—21no—
381#95—21no—
382C22×C7—22no—
383C22×C7—22no—
384C22×C7—22no—
385C22×C7—41no—
386C22×C7—41no—
387C22×C7—41no—
388C22×C7—41no—
389C22×C7C2×#12011yescharacteristic
390C22×C7#52511yescharacteristic
391C22×C7#53711yescharacteristic
392C22×C7C22×SD1611yescharacteristic
393C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
394C22×C7#57511yescharacteristic
395C22×C7#57511yescharacteristic
396C2×D7—44no—
397C2×D7—44no—
398C2×D7—44no—
399C2×D7—82no—
400C2×D7—82no—
401C2×D7—82no—
402C2×D7—82no—
403C4×C7—22no—
404C4×C7—22no—
405C4×C7—42no—
406C4×C7—41no—
407C4×C7—42no—
408C4×C7—41no—
409C4×C7—81no—
410C4×C7—81no—
411C4×C7#45014yes—
412C4×C7#54611yescharacteristic
413C4×C7#54711yescharacteristic
414C4×C7#54811yescharacteristic
415C4×C7#55011yescharacteristic
416Dic7—44no—
417C24—142no—
418C24C2×C22⋊D711yescharacteristic
419#41—2832no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—144no—
426C2×Q8—282no—
427C2×Q8—282no—
428C2×Q8#115712yescomplemented
429C2×D4—74no—
430C2×D4—148no—
431C2×D4—144no—
432C2×D4—144no—
433C2×D4—142no—
434C2×D4—142no—
435C2×D4—142no—
436C2×D4—142no—
437C2×D4—142no—
438C2×D4—282no—
439C2×D4—282no—
440C2×D4—284no—
441C2×D4—284no—
442C2×D4—282no—
443C2×D4—282no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—148no—
460C22×C4—142no—
461C22×C4—284no—
462C22×C4—284no—
463C22×C4#114314yescomplemented
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—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—42no—
484C4⋊C4—42no—
485C4⋊C4—74no—
486C4⋊C4—144no—
487C4⋊C4—142no—
488C4⋊C4#115712yescomplemented
489C22⋊C4—24no—
490C22⋊C4—42no—
491C22⋊C4—148no—
492C22⋊C4—148no—
493C42—22no—
494C42—22no—
495C42—21no—
496C42—21no—
497C42—42no—
498C42—42no—
499C42D4×D712yes—
500C42D4×D712yes—
501C2×C7—42no—
502C2×C7#240711yescharacteristic
503C2×C7C2×#45011yescharacteristic
504C2×C7#300511yescharacteristic
505C2×C7#310311yescharacteristic
506C2×C7#311511yescharacteristic
507C2×C7#324611yescharacteristic
508C2×C7#325111yescharacteristic
509D7—84no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—144no—
517C23—282no—
518C23—282no—
519C23—282no—
520C23—282no—
521C23—282no—
522C23—282no—
523C23C2×#114312yes—
524C23C22×C22⋊D711yescharacteristic
525Q8—22no—
526Q8—22no—
527Q8—41no—
528Q8—41no—
529Q8—288no—
530D4—144no—
531D4—144no—
532D4—288no—
533D4—2816no—
534D4—282no—
535D4—282no—
536D4—288no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—28no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—44no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—144no—
566C2×C4—2816no—
567C2×C4—282no—
568C2×C4—282no—
569C2×C4#650012yes—
570C2×C4#650012yes—
571C2×C4C2×#114312yes—
572C2×C4C2×#114312yes—
573C2×C4#651212yes—
574C2×C4C2×#115711yescharacteristic
575C2×C4C2×#115711yescharacteristic
576C2×C4C2×D4×D711yescharacteristic
577C2×C4C2×D4×D711yescharacteristic
578C2×C4#655311yescharacteristic
579C2×C4#655411yescharacteristic
580C8—282no—
581C8—282no—
582C7#2415411yescharacteristic, complemented, Sylow
583C22—22no—
584C22—22no—
585C22—22no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—284no—
591C22—284no—
592C22—284no—
593C22—562no—
594C22—562no—
595C22—562no—
596C22—562no—
597C22#9048211yescharacteristic
598C22C2×#650011yescharacteristic
599C22C22×#114311yescharacteristic
600C22C2×#651211yescharacteristic
601C22#9051311yescharacteristic
602C22#9051311yescharacteristic
603C22#9052411yescharacteristic
604C4—22no—
605C4—22no—
606C4—42no—
607C4—41no—
608C4—42no—
609C4—41no—
610C4—81no—
611C4—81no—
612C4—284no—
613C4#8981814yes—
614C4#9024111yescharacteristic
615C4#9024211yescharacteristic
616C4#9024311yescharacteristic
617C4#9024411yescharacteristic
618C2—42no—
619C2—564no—
620C2#1173984711yescharacteristic
621C2#1173988711yescharacteristic
622C2#1173997611yescharacteristic
623C2C2×#8981811yescharacteristic
624C2#1174037311yescharacteristic
625C2#1174059511yescharacteristic
626C2#1174080811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC4×C7×C22⋊Q8C2
socleC23×C7C22×D4
prime radicalC2×#90168C2
hypercenterC4×C22⋊Q8D7
hypocenterC7#24154
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C4×C7×C22⋊Q8C2semidirect
3. C2×#89799C2semidirect
4. C2×#89792C2semidirect
5. #11729453C2semidirect
6. #11729284C2semidirect
7. #11727441C2semidirect
8. #11727380C2semidirect
9. #11727278C2semidirect
10. #11727244C2semidirect
11. #11727241C2semidirect
117. C4×C22⋊Q8D7semidirect
132. C2×C7×Q8#41semidirect
148. C22×C4×C7SD16semidirect
186. C7×C4⋊C4#41semidirect
428. C2×Q8#1157semidirect
463. C22×C4#1143semidirect
488. C4⋊C4#1157semidirect
582. C7#24154semidirect

Maximal subgroups

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

subgroupindex
C2×#901682
C4×C7×C22⋊Q82
C2×#897992
C2×#897922
#117294532
#117292842
#117274412
#117273802
#117272782
#117272442
#117272412
#241547