Finite Group Databasebeta

← #13388103

Subgroups — #13388103

Order 1792.

1478 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90168C211yesmaximal, characteristic, complemented
2C4×C7×#121C211yesmaximal, characteristic, complemented
3C2×#89787C211yesmaximal, characteristic, complemented
4C2×#89779C211yesmaximal, characteristic, complemented
5#11729438C212yesmaximal, complemented
6#11729284C211yesmaximal, characteristic, complemented
7#11727411C212yesmaximal, complemented
8#11727379C212yesmaximal, complemented
9#11727277C212yesmaximal, complemented
10#11727244C211yesmaximal, characteristic, complemented
11#11727241C211yesmaximal, characteristic, complemented
12C22×#1157—21no—
13C2×C7×#121C2211yescharacteristic
14C2×C4×C7×D4—21no—
15C2×C4×C7×D4C2211yescharacteristic
16C22×C42×C7C2211yescharacteristic
17C22×#1141C2212yes—
18C2×#6493—21no—
19C2×#6493C2212yes—
20#90168—24no—
21#90168—24no—
22C2×#6438—21no—
23C2×#6437C2211yescharacteristic
24C2×C4×D28—21no—
25C2×C4×D28C2212yes—
26C2×#6432C2211yescharacteristic
27C7×#390C2211yescharacteristic
28C7×#389C2211yescharacteristic
29C7×#388—21no—
30C7×#386—21no—
31C7×#380C2211yescharacteristic
32C4×C7×C4⋊C4C2211yescharacteristic
33C4×C7×C22⋊C4—21no—
34C2×#6406C2212yes—
35C2×C22⋊(C7⋊C8)C2212yes—
36#89787—24no—
37#89779—24no—
38C2×#6383C2212yes—
39C2×#6383C2212yes—
40C2×#6383C2212yes—
41C2×#6381C2212yes—
42C2×C4⋊(C7⋊C8)C2211yescharacteristic
43C2×C4⋊(C7⋊C8)C2211yescharacteristic
44#89324C2212yes—
45#89324C2212yes—
46#89319C2212yes—
47#24150—71nomaximal, Sylow
48C22×C7×D4—21no—
49C22×C7×D4C2311yescharacteristic
50C23×C4×C7—21no—
51C23×C4×C7D411yescharacteristic
52C23×C4×C7D411yescharacteristic
53C23×C4×C7C2311yescharacteristic
54C22×C22⋊D7—22no—
55C2×#1157—28no—
56C2×#1157—44no—
57C2×#1157—44no—
58C22×D28—21no—
59C22×D28—21no—
60C22×D28C2312yes—
61C22×C4×D7—22no—
62C22×Dic14—21no—
63C7×#121—22no—
64C7×#121—22no—
65C4×C7×D4—22no—
66C4×C7×D4—22no—
67C4×C7×D4—44no—
68C2×C7×C4⋊C4—21no—
69C2×C7×C4⋊C4C2311yescharacteristic
70C2×C7×C4⋊C4C2311yescharacteristic
71C2×C7×C4⋊C4C2311yescharacteristic
72C2×C7×C22⋊C4—21no—
73C2×C7×C22⋊C4—21no—
74C2×C7×C22⋊C4—21no—
75C2×C7×C22⋊C4—21no—
76C2×C7×C22⋊C4—21no—
77C2×C42×C7—22no—
78C2×C42×C7—22no—
79C2×C42×C7—21no—
80C2×C42×C7D411yescharacteristic
81C2×C42×C7D411yescharacteristic
82C2×C42×C7C2311yescharacteristic
83C2×C42×C7C2311yescharacteristic
84C2×#1141—24no—
85C2×#1141—24no—
86C2×#1141—42no—
87#6493—28no—
88#6493—24no—
89#6493—24no—
90C2×(C2×D7)⋊C4—22no—
91C2×(C2×D7)⋊C4—22no—
92C2×C4⋊Dic7—21no—
93C2×C4⋊Dic7C2312yes—
94C22×C7⋊C8C2312yes—
95C22×C7⋊C8C2312yes—
96#6438—28no—
97#6437—22no—
98#6437D414yescomplemented
99C4×D28—28no—
100C4×D28—24no—
101C4×D28—24no—
102#6432—22no—
103#6432D414yescomplemented
104C7×#95—21no—
105C7×#95—21no—
106C7×#95—21no—
107#6406—24no—
108C22⋊(C7⋊C8)—42no—
109#6383—24no—
110#6383—24no—
111#6383—42no—
112#6381—24no—
113C4⋊(C7⋊C8)—22no—
114C4⋊(C7⋊C8)—22no—
115C2×#532—71no—
116C2×#474—71no—
117C2×#459—71no—
118C4×#121D711yescharacteristic, complemented
119#2033—72no—
120#1999—72no—
121#1988—71no—
122#1982—71no—
123#1879—72no—
124#1862—72no—
125#1797—71no—
126C24×C7—21no—
127C24×C7C2×D411yescharacteristic
128C23×D7—22no—
129C2×C7×D4—24no—
130C2×C7×D4—21no—
131C2×C7×D4—21no—
132C2×C7×D4—21no—
133C2×C7×D4—21no—
134C2×C7×D4—21no—
135C2×C7×D4—42no—
136C2×C7×D4—42no—
137C2×C7×D4#4112yescomplemented
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—21no—
141C22×C4×C7—22no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7—21no—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—41no—
151C22×C4×C7—41no—
152C22×C4×C7—42no—
153C22×C4×C7—42no—
154C22×C4×C7—42no—
155C22×C4×C7D814yescomplemented
156C22×C4×C7C2×D411yescharacteristic
157C22×C4×C7C2×D411yescharacteristic
158C22×C4×C7C2×D411yescharacteristic
159C22×C4×C7C2×D411yescharacteristic
160C22×C4×C7C2×D411yescharacteristic
161C22×C4×C7C2411yescharacteristic
162C2×C22⋊D7—28no—
163C2×C22⋊D7—44no—
164C2×C22⋊D7—44no—
165C22×Dic7—22no—
166#1157—432no—
167C2×D28—22no—
168C2×D28—22no—
169C2×D28—22no—
170C2×D28—22no—
171C2×D28—24no—
172C2×D28—24no—
173C2×D28—22no—
174C2×D28—42no—
175C2×D28—42no—
176C2×D28—42no—
177C2×D28—42no—
178C2×D28C2×D414yes—
179C2×C4×D7—28no—
180C2×C4×D7—44no—
181C2×C4×D7—44no—
182C2×Dic14—24no—
183C2×Dic14—42no—
184C2×Dic14—42no—
185C7×C4⋊C4—21no—
186C7×C4⋊C4—21no—
187C7×C4⋊C4—21no—
188C7×C4⋊C4—21no—
189C7×C4⋊C4—21no—
190C7×C4⋊C4—42no—
191C7×C4⋊C4#4112yescomplemented
192C7×C22⋊C4—24no—
193C7×C22⋊C4—42no—
194C7×C22⋊C4—42no—
195C7×C22⋊C4—42no—
196C7×C22⋊C4—42no—
197C42×C7—22no—
198C42×C7—22no—
199C42×C7—21no—
200C42×C7—21no—
201C42×C7—42no—
202C42×C7C2×D412yes—
203C42×C7C2×D412yes—
204#1141—48no—
205(C2×D7)⋊C4—28no—
206(C2×D7)⋊C4—28no—
207C4⋊Dic7—24no—
208C4⋊Dic7—22no—
209C4⋊Dic7C2×D414yes—
210C2×C7⋊C8—22no—
211C2×C7⋊C8—22no—
212C2×C7⋊C8—22no—
213C2×C7⋊C8—22no—
214C2×C7⋊C8—22no—
215C2×C7⋊C8—22no—
216C22×#41—141no—
217C22×D8—72no—
218#532—144no—
219#532—144no—
220C2×C4⋊Q8—71no—
221C2×#127—71no—
222C2×#124—141no—
223C2×#121—72no—
224C2×#121—141no—
225C2×#121C2×D711yescharacteristic
226C2×C4×D4—21no—
227C2×C4×D4—72no—
228C2×C4×D4—141no—
229C2×C4×D4C2×D711yescharacteristic
230C22×C42C2×D711yescharacteristic
231#474—144no—
232#459—144no—
233C2×#107—72no—
234C2×C4⋊C8—71no—
235C2×C4⋊C8—71no—
236C2×#102—72no—
237C2×#102—72no—
238C2×#102—72no—
239C2×#102—72no—
240C2×C22⋊C8—72no—
241#390C2×D711yescharacteristic
242#389C2×D711yescharacteristic
243#388—21no—
244#386—21no—
245#380C2×D711yescharacteristic
246C4×C4⋊C4C2×D711yescharacteristic
247C4×C22⋊C4—21no—
248#340—72no—
249#340—72no—
250#336—72no—
251C23×C7—21no—
252C23×C7—21no—
253C23×C7—21no—
254C23×C7—21no—
255C23×C7—21no—
256C23×C7—21no—
257C23×C7—22no—
258C23×C7—41no—
259C23×C7—41no—
260C23×C7—41no—
261C23×C7—41no—
262C23×C7—41no—
263C23×C7—41no—
264C23×C7C2×D812yes—
265C23×C7C22×D411yescharacteristic
266C22×D7—24no—
267C22×D7—42no—
268C22×D7—42no—
269C22×D7—42no—
270C22×D7—42no—
271C22×D7—42no—
272C22×D7—42no—
273C7×D4—22no—
274C7×D4—22no—
275C7×D4—48no—
276C7×D4—41no—
277C7×D4—41no—
278C2×C4×C7—21no—
279C2×C4×C7—21no—
280C2×C4×C7—21no—
281C2×C4×C7—21no—
282C2×C4×C7—28no—
283C2×C4×C7—21no—
284C2×C4×C7—21no—
285C2×C4×C7—21no—
286C2×C4×C7—22no—
287C2×C4×C7—21no—
288C2×C4×C7—21no—
289C2×C4×C7—21no—
290C2×C4×C7—44no—
291C2×C4×C7—41no—
292C2×C4×C7—41no—
293C2×C4×C7—41no—
294C2×C4×C7—41no—
295C2×C4×C7—41no—
296C2×C4×C7—41no—
297C2×C4×C7—41no—
298C2×C4×C7—41no—
299C2×C4×C7—41no—
300C2×C4×C7—41no—
301C2×C4×C7—41no—
302C2×C4×C7—41no—
303C2×C4×C7—84no—
304C2×C4×C7#12012yes—
305C2×C4×C7#12012yes—
306C2×C4×C7C2×D812yes—
307C2×C4×C7C2×D812yes—
308C2×C4×C7AGL(1,ℤ/8)12yes—
309C2×C4×C7C22×D411yescharacteristic
310C2×C4×C7C22×D411yescharacteristic
311C2×C4×C7C2×#4111yescharacteristic
312C2×C4×C7C2×#4111yescharacteristic
313C2×C4×C7H(5,𝔽2)11yescharacteristic
314C2×C4×C72−1+411yescharacteristic
315C22⋊D7—416no—
316C2×Dic7—24no—
317C2×Dic7—42no—
318C2×Dic7—42no—
319D28—24no—
320D28—24no—
321D28—48no—
322D28—42no—
323D28—42no—
324D28—48no—
325C4×D7—416no—
326Dic14—48no—
327C7⋊C8—42no—
328C7⋊C8—42no—
329C2×#41—148no—
330C2×#41—284no—
331C2×#41—284no—
332C22×Q8—141no—
333C22×D4—21no—
334C22×D4—72no—
335C22×D4—142no—
336C22×D4—141no—
337C22×D4—141no—
338C22×D4C22×D711yescharacteristic
339C23×C4—21no—
340C23×C4—142no—
341C23×C4C22⋊D711yescharacteristic
342C23×C4C22⋊D711yescharacteristic
343C23×C4C22×D711yescharacteristic
344C2×D8—144no—
345C2×D8—144no—
346C2×D8—282no—
347C22×C8—72no—
348C22×C8—72no—
349C4⋊Q8—74no—
350C4⋊Q8—142no—
351#127—74no—
352#127—142no—
353#124—148no—
354#121—22no—
355#121—22no—
356#121—144no—
357#121—144no—
358#121—148no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—44no—
362C4×D4—144no—
363C4×D4—144no—
364C4×D4—148no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—72no—
367C2×C4⋊C4—141no—
368C2×C4⋊C4C22×D711yescharacteristic
369C2×C4⋊C4C22×D711yescharacteristic
370C2×C4⋊C4C22×D711yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—142no—
377C2×C22⋊C4—142no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—21no—
381C2×C42C22⋊D711yescharacteristic
382C2×C42C22⋊D711yescharacteristic
383C2×C42C22×D711yescharacteristic
384C2×C42C22×D711yescharacteristic
385#107—144no—
386C4⋊C8—142no—
387C4⋊C8—142no—
388#102—144no—
389#102—144no—
390#102—144no—
391#102—282no—
392C22⋊C8—282no—
393#95—21no—
394#95—21no—
395#95—21no—
396C22×C7—22no—
397C22×C7—22no—
398C22×C7—22no—
399C22×C7—41no—
400C22×C7—41no—
401C22×C7—41no—
402C22×C7—41no—
403C22×C7—42no—
404C22×C7—42no—
405C22×C7—42no—
406C22×C7—81no—
407C22×C7—81no—
408C22×C7—81no—
409C22×C7—81no—
410C22×C7C2×#12011yescharacteristic
411C22×C7#52511yescharacteristic
412C22×C7#53711yescharacteristic
413C22×C7C22×D811yescharacteristic
414C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
415C22×C7#57511yescharacteristic
416C22×C7#57511yescharacteristic
417C2×D7—44no—
418C2×D7—44no—
419C2×D7—44no—
420C2×D7—82no—
421C2×D7—82no—
422C2×D7—82no—
423C2×D7—82no—
424C4×C7—22no—
425C4×C7—22no—
426C4×C7—42no—
427C4×C7—41no—
428C4×C7—41no—
429C4×C7—81no—
430C4×C7—81no—
431C4×C7#44714yes—
432C4×C7#54611yescharacteristic
433C4×C7#54711yescharacteristic
434C4×C7#54811yescharacteristic
435C4×C7#55011yescharacteristic
436Dic7—44no—
437C24—21no—
438C24—142no—
439C24C2×C22⋊D711yescharacteristic
440#41—2832no—
441C2×Q8—144no—
442C2×Q8—282no—
443C2×Q8—282no—
444C2×D4—24no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—42no—
451C2×D4—42no—
452C2×D4—74no—
453C2×D4—148no—
454C2×D4—144no—
455C2×D4—144no—
456C2×D4—142no—
457C2×D4—142no—
458C2×D4—142no—
459C2×D4—142no—
460C2×D4—142no—
461C2×D4—282no—
462C2×D4—282no—
463C2×D4—284no—
464C2×D4—284no—
465C2×D4—282no—
466C2×D4—282no—
467C2×D4#115712yescomplemented
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—148no—
486C22×C4—142no—
487C22×C4—284no—
488C22×C4—284no—
489C22×C4#114114yescomplemented
490C22×C4C2×C22⋊D711yescharacteristic
491C22×C4C2×C22⋊D711yescharacteristic
492C22×C4C2×C22⋊D711yescharacteristic
493C22×C4C2×C22⋊D711yescharacteristic
494C22×C4C2×C22⋊D711yescharacteristic
495C22×C4C23×D711yescharacteristic
496D8—288no—
497C2×C8—142no—
498C2×C8—142no—
499C2×C8—142no—
500C2×C8—142no—
501C2×C8—142no—
502C2×C8—142no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—42no—
509C4⋊C4—74no—
510C4⋊C4—144no—
511C4⋊C4—142no—
512C4⋊C4#115712yescomplemented
513C22⋊C4—24no—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—148no—
519C22⋊C4—148no—
520C42—22no—
521C42—22no—
522C42—21no—
523C42—21no—
524C42—42no—
525C42D4×D712yes—
526C42D4×D712yes—
527C2×C7—42no—
528C2×C7—82no—
529C2×C7#240711yescharacteristic
530C2×C7C2×#44711yescharacteristic
531C2×C7#300511yescharacteristic
532C2×C7#310011yescharacteristic
533C2×C7#311511yescharacteristic
534C2×C7#324511yescharacteristic
535C2×C7#325111yescharacteristic
536D7—84no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—22no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—144no—
551C23—282no—
552C23—282no—
553C23—282no—
554C23—282no—
555C23—282no—
556C23—282no—
557C23C2×#114112yes—
558C23C22×C22⋊D711yescharacteristic
559Q8—288no—
560D4—22no—
561D4—22no—
562D4—48no—
563D4—41no—
564D4—41no—
565D4—144no—
566D4—144no—
567D4—288no—
568D4—2816no—
569D4—282no—
570D4—282no—
571D4—288no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—28no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—44no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—84no—
598C2×C4—144no—
599C2×C4—2816no—
600C2×C4—282no—
601C2×C4—282no—
602C2×C4C2×#114112yes—
603C2×C4C2×#114112yes—
604C2×C4#650012yes—
605C2×C4#650012yes—
606C2×C4#651212yes—
607C2×C4C2×#115711yescharacteristic
608C2×C4C2×#115711yescharacteristic
609C2×C4C2×D4×D711yescharacteristic
610C2×C4C2×D4×D711yescharacteristic
611C2×C4#655311yescharacteristic
612C2×C4#655411yescharacteristic
613C8—282no—
614C8—282no—
615C7#2415011yescharacteristic, complemented, Sylow
616C22—22no—
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—42no—
624C22—42no—
625C22—42no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—284no—
631C22—284no—
632C22—284no—
633C22—562no—
634C22—562no—
635C22—562no—
636C22—562no—
637C22#9048211yescharacteristic
638C22C22×#114111yescharacteristic
639C22C2×#650011yescharacteristic
640C22C2×#651211yescharacteristic
641C22#9051311yescharacteristic
642C22#9051311yescharacteristic
643C22#9052411yescharacteristic
644C4—22no—
645C4—22no—
646C4—42no—
647C4—41no—
648C4—41no—
649C4—81no—
650C4—81no—
651C4—284no—
652C4#8980814yes—
653C4#9024111yescharacteristic
654C4#9024211yescharacteristic
655C4#9024311yescharacteristic
656C4#9024411yescharacteristic
657C2—42no—
658C2—82no—
659C2—564no—
660C2#1173975311yescharacteristic
661C2#1173984711yescharacteristic
662C2#1173997611yescharacteristic
663C2C2×#8980811yescharacteristic
664C2#1174037311yescharacteristic
665C2#1174059511yescharacteristic
666C2#1174075511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC4×C7×#121C2
socleC23×C7C22×D4
hypercenterC4×#121D7
hypocenterC7#24150
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#90168C2semidirect
2. C4×C7×#121C2semidirect
3. C2×#89787C2semidirect
4. C2×#89779C2semidirect
5. #11729438C2semidirect
6. #11729284C2semidirect
7. #11727411C2semidirect
8. #11727379C2semidirect
9. #11727277C2semidirect
10. #11727244C2semidirect
11. #11727241C2semidirect
98. #6437D4semidirect
103. #6432D4semidirect
118. C4×#121D7semidirect
137. C2×C7×D4#41semidirect
155. C22×C4×C7D8semidirect
191. C7×C4⋊C4#41semidirect
467. C2×D4#1157semidirect
489. C22×C4#1141semidirect
512. C4⋊C4#1157semidirect
615. C7#24150semidirect

Maximal subgroups

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

subgroupindex
C2×#901682
C4×C7×#1212
C2×#897872
C2×#897792
#117294382
#117292842
#117274112
#117273792
#117272772
#117272442
#117272412
#241507