Finite Group Databasebeta

← #13280839

Subgroups — #13280839

Order 1792.

1650 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#387C211yesmaximal, characteristic, complemented
2C2×#89763C211yesmaximal, characteristic
3C2×#89711C211yesmaximal, characteristic
4#11729324C212yesmaximal, complemented
5#11729319C211yesmaximal, characteristic, complemented
6C4×C7⋊#95C211yesmaximal, characteristic, complemented
7#11727183C212yesmaximal, complemented
8#11727180C211yesmaximal, characteristic
9#11727169C211yesmaximal, characteristic, complemented
10#11727162C212yesmaximal, complemented
11#11727162C212yesmaximal, complemented
12C23×D28C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C42×C7C2211yescharacteristic
16C22×(C2×D7)⋊C4C2212yes—
17C22×(C2×D7)⋊C4C2212yes—
18C22×(C2×D7)⋊C4C2212yes—
19C22×(C2×D7)⋊C4C2212yes—
20C22×(C2×D7)⋊C4C2212yes—
21C22×(C2×D7)⋊C4C2212yes—
22C22×C4⋊Dic7C2211yescharacteristic
23C22×C4×Dic7C2212yes—
24C7×#387—24no—
25C2×C7×#95C2211yescharacteristic
26C2×C7×#95C2211yescharacteristic
27C2×C7×#95C2211yescharacteristic
28C2×C7×#95C2211yescharacteristic
29C2×C7⋊#95C2211yescharacteristic
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2211yescharacteristic
36#89763C418yescomplemented
37#89711—24no—
38#14325—71nomaximal, Sylow
39C24×D7C2312yes—
40C23×C4×C7C2311yescharacteristic
41C23×C4×C7C2311yescharacteristic
42C23×C4×C7C2311yescharacteristic
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2311yescharacteristic
47C23×Dic7C2312yes—
48C23×Dic7C2312yes—
49C23×Dic7C2312yes—
50C22×D28—22no—
51C22×D28—22no—
52C22×D28—42no—
53C22×D28—42no—
54C22×D28C2×C414yes—
55C2×C7×C4⋊C4—22no—
56C2×C7×C4⋊C4—22no—
57C2×C7×C4⋊C4—22no—
58C2×C7×C4⋊C4—42no—
59C2×C7×C4⋊C4C2×C414yes—
60C2×C42×C7—42no—
61C2×C42×C7D414yes—
62C2×(C2×D7)⋊C4—24no—
63C2×(C2×D7)⋊C4—24no—
64C2×(C2×D7)⋊C4—24no—
65C2×(C2×D7)⋊C4—24no—
66C2×(C2×D7)⋊C4—24no—
67C2×(C2×D7)⋊C4—24no—
68C2×(C2×D7)⋊C4—42no—
69C2×(C2×D7)⋊C4—42no—
70C2×(C2×D7)⋊C4—42no—
71C2×(C2×D7)⋊C4—42no—
72C2×(C2×D7)⋊C4—42no—
73C2×(C2×D7)⋊C4—42no—
74C2×(C2×D7)⋊C4—42no—
75C2×(C2×D7)⋊C4—42no—
76C2×(C2×D7)⋊C4—42no—
77C2×(C2×D7)⋊C4—42no—
78C2×(C2×D7)⋊C4C2×C418yes—
79C2×(C2×D7)⋊C4C2×C418yes—
80C2×C4⋊Dic7—22no—
81C2×C4⋊Dic7—42no—
82C2×C4×Dic7—24no—
83C2×C4×Dic7—42no—
84C2×C4×Dic7—42no—
85C7×#95—22no—
86C7×#95—22no—
87C7×#95—22no—
88C7×#95—22no—
89C7⋊#95—22no—
90C7⋊#95—24no—
91C7⋊#95—42no—
92C7⋊#95—42no—
93C7⋊#95—42no—
94C7⋊#95—42no—
95C7⋊#95C2×C414yes—
96C2×#394—71no—
97C2×#390—71no—
98C2×#387D711yescharacteristic, complemented
99#1442—71no—
100#1441—71no—
101#1440—72no—
102#1439—72no—
103#1438—71no—
104#1437—72no—
105#1437—72no—
106C4×#95—71no—
107C24×C7C2411yescharacteristic
108C23×D7—22no—
109C23×D7—22no—
110C23×D7—22no—
111C23×D7—22no—
112C23×D7—22no—
113C23×D7—22no—
114C23×D7—22no—
115C23×D7—22no—
116C23×D7—22no—
117C23×D7—22no—
118C23×D7—22no—
119C23×D7—22no—
120C23×D7—22no—
121C23×D7—22no—
122C23×D7C22×C414yes—
123C22×C4×C7—21no—
124C22×C4×C7—22no—
125C22×C4×C7—22no—
126C22×C4×C7—22no—
127C22×C4×C7—21no—
128C22×C4×C7—21no—
129C22×C4×C7—21no—
130C22×C4×C7—22no—
131C22×C4×C7—21no—
132C22×C4×C7—21no—
133C22×C4×C7—21no—
134C22×C4×C7—22no—
135C22×C4×C7—21no—
136C22×C4×C7—21no—
137C22×C4×C7—21no—
138C22×C4×C7—21no—
139C22×C4×C7—22no—
140C22×C4×C7—22no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7—22no—
145C22×C4×C7—22no—
146C22×C4×C7—21no—
147C22×C4×C7—22no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—22no—
151C22×C4×C7—21no—
152C22×C4×C7C22×C412yes—
153C22×C4×C7C22×C412yes—
154C22×C4×C7C22×C412yes—
155C22×C4×C7C2×D412yes—
156C22×C4×C7C2×D412yes—
157C22×C4×C7C2×D412yes—
158C22×C4×C7#4112yes—
159C22×C4×C7#4114yes—
160C22×Dic7—22no—
161C22×Dic7—22no—
162C22×Dic7—22no—
163C22×Dic7—22no—
164C22×Dic7—22no—
165C22×Dic7—22no—
166C22×Dic7—22no—
167C22×Dic7—22no—
168C22×Dic7—22no—
169C22×Dic7—22no—
170C22×Dic7—22no—
171C22×Dic7—22no—
172C22×Dic7—22no—
173C22×Dic7—22no—
174C22×Dic7—22no—
175C22×Dic7—22no—
176C22×Dic7—22no—
177C22×Dic7—22no—
178C22×Dic7—22no—
179C22×Dic7C22×C414yes—
180C22×Dic7#4114yes—
181C2×D28—28no—
182C2×D28—48no—
183C2×D28—44no—
184C2×D28—44no—
185C2×D28—48no—
186C7×C4⋊C4—28no—
187C7×C4⋊C4—44no—
188C42×C7—44no—
189(C2×D7)⋊C4—48no—
190(C2×D7)⋊C4—48no—
191(C2×D7)⋊C4—48no—
192(C2×D7)⋊C4—48no—
193(C2×D7)⋊C4—48no—
194(C2×D7)⋊C4—48no—
195C4⋊Dic7—44no—
196C4×Dic7—48no—
197C23×D4—71no—
198C22×C4⋊C4—71no—
199C22×C4⋊C4C2×D711yescharacteristic
200C22×C4⋊C4C2×D711yescharacteristic
201C22×C22⋊C4—72no—
202C22×C22⋊C4—72no—
203C22×C22⋊C4—72no—
204C22×C22⋊C4—72no—
205C22×C22⋊C4—72no—
206C22×C22⋊C4—72no—
207C22×C42—72no—
208C22×C42C2×D711yescharacteristic
209#394—78no—
210#390—144no—
211#387—24no—
212C2×#95—71no—
213C2×#95—71no—
214C2×#95—72no—
215C2×#95—72no—
216C2×#95—72no—
217C2×#95—72no—
218C2×#95—72no—
219C2×#95C2×D711yescharacteristic
220C2×#95C2×D711yescharacteristic
221C2×#95C2×D711yescharacteristic
222C2×#95C2×D711yescharacteristic
223C23×C7C23×C411yescharacteristic
224C23×C7C22×D411yescharacteristic
225C23×C7C2×#4111yescharacteristic
226C23×C7C2×#4112yes—
227C23×C7C2×#4112yes—
228C23×C7H(5,𝔽2)12yes—
229C23×C7H(5,𝔽2)12yes—
230C23×C7H(5,𝔽2)11yescharacteristic
231C23×C7H(5,𝔽2)11yescharacteristic
232C23×C7H(5,𝔽2)11yescharacteristic
233C23×C72−1+411yescharacteristic
234C22×D7—24no—
235C22×D7—24no—
236C22×D7—24no—
237C22×D7—24no—
238C22×D7—24no—
239C22×D7—24no—
240C22×D7—24no—
241C22×D7—42no—
242C22×D7—42no—
243C22×D7—42no—
244C22×D7—42no—
245C22×D7—42no—
246C22×D7—42no—
247C22×D7—42no—
248C22×D7—42no—
249C22×D7—42no—
250C22×D7—42no—
251C22×D7—42no—
252C22×D7—42no—
253C22×D7—42no—
254C22×D7—42no—
255C22×D7—42no—
256C22×D7—42no—
257C22×D7—42no—
258C22×D7—42no—
259C22×D7—42no—
260C22×D7—42no—
261C22×D7—42no—
262C22×D7—42no—
263C22×D7—42no—
264C22×D7—42no—
265C22×D7—42no—
266C22×D7—42no—
267C22×D7—42no—
268C22×D7—42no—
269C2×C4×C7—24no—
270C2×C4×C7—22no—
271C2×C4×C7—22no—
272C2×C4×C7—22no—
273C2×C4×C7—22no—
274C2×C4×C7—24no—
275C2×C4×C7—24no—
276C2×C4×C7—24no—
277C2×C4×C7—22no—
278C2×C4×C7—22no—
279C2×C4×C7—22no—
280C2×C4×C7—24no—
281C2×C4×C7—22no—
282C2×C4×C7—22no—
283C2×C4×C7—22no—
284C2×C4×C7—22no—
285C2×C4×C7—41no—
286C2×C4×C7—41no—
287C2×C4×C7—41no—
288C2×C4×C7—41no—
289C2×C4×C7—42no—
290C2×C4×C7—42no—
291C2×C4×C7—41no—
292C2×C4×C7—42no—
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—42no—
301C2×C4×C7—42no—
302C2×C4×C7—42no—
303C2×C4×C7—42no—
304C2×C4×C7C4×D414yes—
305C2×C4×C7#12414yes—
306C2×Dic7—24no—
307C2×Dic7—24no—
308C2×Dic7—24no—
309C2×Dic7—24no—
310C2×Dic7—24no—
311C2×Dic7—24no—
312C2×Dic7—42no—
313C2×Dic7—42no—
314C2×Dic7—42no—
315C2×Dic7—42no—
316C2×Dic7—42no—
317C2×Dic7—42no—
318C2×Dic7—42no—
319C2×Dic7—42no—
320C2×Dic7—42no—
321C2×Dic7—42no—
322C2×Dic7—42no—
323C2×Dic7—42no—
324C2×Dic7—42no—
325C2×Dic7—42no—
326C2×Dic7—42no—
327D28—416no—
328C25—72no—
329C22×D4—74no—
330C22×D4—142no—
331C22×D4—142no—
332C22×D4—282no—
333C22×D4—282no—
334C23×C4—72no—
335C23×C4—72no—
336C23×C4—72no—
337C23×C4C22×D711yescharacteristic
338C23×C4C22×D711yescharacteristic
339C23×C4C22×D711yescharacteristic
340C23×C4C22×D711yescharacteristic
341C23×C4C22×D711yescharacteristic
342C23×C4C22×D711yescharacteristic
343C23×C4C22×D711yescharacteristic
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—142no—
349C2×C4⋊C4—282no—
350C2×C4⋊C4C4×D714yes—
351C2×C22⋊C4—78no—
352C2×C22⋊C4—78no—
353C2×C22⋊C4—144no—
354C2×C22⋊C4—144no—
355C2×C22⋊C4—144no—
356C2×C22⋊C4—144no—
357C2×C22⋊C4—144no—
358C2×C22⋊C4—144no—
359C2×C22⋊C4—282no—
360C2×C22⋊C4—282no—
361C2×C22⋊C4—282no—
362C2×C22⋊C4—282no—
363C2×C22⋊C4—282no—
364C2×C22⋊C4—282no—
365C2×C22⋊C4—282no—
366C2×C22⋊C4—282no—
367C2×C22⋊C4—282no—
368C2×C22⋊C4—282no—
369C2×C42—42no—
370C2×C42—144no—
371C2×C42—282no—
372C2×C42—282no—
373C2×C42C22⋊D714yes—
374#95—22no—
375#95—22no—
376#95—22no—
377#95—22no—
378#95—74no—
379#95—144no—
380#95—142no—
381#95—282no—
382#95—282no—
383#95—282no—
384#95—282no—
385C22×C7C2×C4×D411yescharacteristic
386C22×C7C4×#4112yes—
387C22×C7#51811yescharacteristic
388C22×C7#51812yes—
389C22×C7#52011yescharacteristic
390C22×C7C2×#12411yescharacteristic
391C22×C7#52912yes—
392C22×C7#53211yescharacteristic
393C22×C7#53411yescharacteristic
394C22×C7#53511yescharacteristic
395C22×C7#53511yescharacteristic
396C22×C7#53711yescharacteristic
397C22×C7#53812yes—
398C22×C7#53812yes—
399C22×C7#53812yes—
400C22×C7#53812yes—
401C22×C7#53912yes—
402C22×C7#54012yes—
403C22×C7#54012yes—
404C22×C7#54011yescharacteristic
405C22×C7#54012yes—
406C22×C7#54212yes—
407C22×C7#54211yescharacteristic
408C2×D7—44no—
409C2×D7—44no—
410C2×D7—44no—
411C2×D7—44no—
412C2×D7—44no—
413C2×D7—44no—
414C2×D7—44no—
415C2×D7—82no—
416C2×D7—82no—
417C2×D7—82no—
418C2×D7—82no—
419C2×D7—82no—
420C2×D7—82no—
421C2×D7—82no—
422C2×D7—82no—
423C4×C7—24no—
424C4×C7—24no—
425C4×C7—42no—
426C4×C7—42no—
427C4×C7—42no—
428C4×C7—81no—
429C4×C7—81no—
430Dic7—44no—
431Dic7—44no—
432Dic7—82no—
433C24—74no—
434C24—142no—
435C24—142no—
436C24—142no—
437C24—142no—
438C24—142no—
439C24—142no—
440C24—142no—
441C24—142no—
442C24—142no—
443C24—142no—
444C24—142no—
445C24—142no—
446C24—142no—
447C24—142no—
448C24C23×D711yescharacteristic
449C2×D4—148no—
450C2×D4—288no—
451C2×D4—284no—
452C2×D4—288no—
453C2×D4—284no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—74no—
484C22×C4—74no—
485C22×C4—142no—
486C22×C4—142no—
487C22×C4—142no—
488C22×C4—142no—
489C22×C4—142no—
490C22×C4—142no—
491C22×C4—142no—
492C22×C4—142no—
493C22×C4—142no—
494C22×C4—142no—
495C22×C4—142no—
496C22×C4—142no—
497C22×C4—142no—
498C22×C4—142no—
499C22×C4—142no—
500C22×C4—142no—
501C22×C4—142no—
502C22×C4—142no—
503C22×C4—142no—
504C22×C4C2×C4×D712yes—
505C22×C4C2×C4×D712yes—
506C22×C4C2×C4×D712yes—
507C22×C4#115712yes—
508C22×C4#116114yes—
509C22×C4C2×C22⋊D712yes—
510C22×C4C2×C22⋊D712yes—
511C22×C4C2×C22⋊D712yes—
512C4⋊C4—28no—
513C4⋊C4—44no—
514C4⋊C4—284no—
515C22⋊C4—288no—
516C22⋊C4—288no—
517C22⋊C4—288no—
518C22⋊C4—288no—
519C22⋊C4—288no—
520C22⋊C4—288no—
521C42—44no—
522C42—288no—
523C2×C7C4×#12411yescharacteristic
524C2×C7#232111yescharacteristic
525C2×C7#232411yescharacteristic
526C2×C7#233312yes—
527C2×C7#233512yes—
528C2×C7#263911yescharacteristic
529C2×C7#264111yescharacteristic
530C2×C7#264812yes—
531C2×C7#265112yes—
532C2×C7#266111yescharacteristic
533C2×C7#266211yescharacteristic
534D7—84no—
535C23—144no—
536C23—144no—
537C23—144no—
538C23—144no—
539C23—144no—
540C23—144no—
541C23—144no—
542C23—282no—
543C23—282no—
544C23—282no—
545C23—282no—
546C23—282no—
547C23—282no—
548C23—282no—
549C23—282no—
550C23—282no—
551C23—282no—
552C23—282no—
553C23—282no—
554C23—282no—
555C23—282no—
556C23—282no—
557C23—282no—
558C23—282no—
559C23—282no—
560C23—282no—
561C23—282no—
562C23—282no—
563C23—282no—
564C23—282no—
565C23—282no—
566C23—282no—
567C23—282no—
568C23—282no—
569C23—282no—
570C23C22×C4×D711yescharacteristic
571C23C2×#115711yescharacteristic
572C23#654812yes—
573C23C2×#116112yes—
574C23D7×#4112yes—
575C23#655312yes—
576C23#655311yescharacteristic
577C23#655311yescharacteristic
578C23#655311yescharacteristic
579C23#655411yescharacteristic
580C23C22×C22⋊D711yescharacteristic
581D4—2816no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—144no—
618C2×C4—144no—
619C2×C4—144no—
620C2×C4—144no—
621C2×C4—144no—
622C2×C4—144no—
623C2×C4—282no—
624C2×C4—282no—
625C2×C4—282no—
626C2×C4—282no—
627C2×C4—282no—
628C2×C4—282no—
629C2×C4—282no—
630C2×C4—282no—
631C2×C4—282no—
632C2×C4—282no—
633C2×C4—282no—
634C2×C4—282no—
635C2×C4—282no—
636C2×C4—282no—
637C2×C4—282no—
638C2×C4C4×C22⋊D714yes—
639C2×C4#651014yes—
640C7#1432511yescharacteristic, complemented, Sylow
641C22—284no—
642C22—284no—
643C22—284no—
644C22—284no—
645C22—284no—
646C22—284no—
647C22—284no—
648C22—562no—
649C22—562no—
650C22—562no—
651C22—562no—
652C22—562no—
653C22—562no—
654C22—562no—
655C22—562no—
656C22#9021211yescharacteristic
657C22#9021411yescharacteristic
658C22#9022511yescharacteristic
659C22#9022611yescharacteristic
660C22#9023612yes—
661C22#9025112yes—
662C22C4×#116112yes—
663C22#9027112yes—
664C22#9033512yes—
665C22#9033612yes—
666C22#9034812yes—
667C22#9035412yes—
668C22#9038912yes—
669C22#9038912yes—
670C22#9039512yes—
671C22#9040112yes—
672C22C2×C4×C22⋊D711yescharacteristic
673C22#9049511yescharacteristic
674C22C2×#651011yescharacteristic
675C22#9052111yescharacteristic
676C22#9052111yescharacteristic
677C22#9052311yescharacteristic
678C22#9052411yescharacteristic
679C4—24no—
680C4—24no—
681C4—42no—
682C4—42no—
683C4—42no—
684C4—81no—
685C4—81no—
686C4—284no—
687C4—284no—
688C4—562no—
689C2—564no—
690C2#1173239712yes—
691C2#1173240112yes—
692C2#1173282512yes—
693C2#1173282912yes—
694C2#1173968111yescharacteristic
695C2#1173984011yescharacteristic
696C2C4×#651011yescharacteristic
697C2#1174026911yescharacteristic
698C2#1174031211yescharacteristic
699C2#1174051211yescharacteristic
700C2#1174055811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#387C2
socle, cosocleC24×C7C24
prime radicalC23×D28C22
hypercenterC2×#387D7
hypocenterC7#14325
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C2×C7×#387C2semidirect
4. #11729324C2semidirect
5. #11729319C2semidirect
6. C4×C7⋊#95C2semidirect
7. #11727183C2semidirect
9. #11727169C2semidirect
10. #11727162C2semidirect
11. #11727162C2semidirect
36. #89763C4semidirect
98. C2×#387D7semidirect
640. C7#14325semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3872
C2×#897632
C2×#897112
#117293242
#117293192
C4×C7⋊#952
#117271832
#117271802
#117271692
#117271622
#143257