Finite Group Databasebeta

← #13280838

Subgroups — #13280838

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×#390C211yesmaximal, characteristic
2C2×#89994C211yesmaximal, characteristic
3C2×#89705C211yesmaximal, characteristic, complemented
4#11729885C211yesmaximal, characteristic
5#11729321C211yesmaximal, characteristic, complemented
6#11729320C211yesmaximal, characteristic, complemented
7#11729303C212yesmaximal, complemented
8#11729301C212yesmaximal, complemented
9#11729299C212yesmaximal, complemented
10#11729299C212yesmaximal, complemented
11C4×C7⋊#95C211yesmaximal, characteristic, complemented
12C23×C7×D4C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C22⋊C4C2212yes—
15C22×C7×C22⋊C4C2212yes—
16C22×C42×C7C2211yescharacteristic
17C22×C22⋊Dic7C2212yes—
18C22×C22⋊Dic7C2212yes—
19C22×C22⋊Dic7C2212yes—
20C22×C22⋊Dic7C2212yes—
21C22×Dic7⋊C4C2211yescharacteristic
22C22×Dic7⋊C4C2211yescharacteristic
23C22×C4×Dic7C2212yes—
24C7×#390—24no—
25#89994C418yescomplemented
26C2×C7⋊#95C2211yescharacteristic
27C2×C7⋊#95C2211yescharacteristic
28C2×C7⋊#95C2211yescharacteristic
29C2×C7⋊#95C2211yescharacteristic
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2211yescharacteristic
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2211yescharacteristic
37#89705—24no—
38#14325—71nomaximal, Sylow
39C25×C7C2312yes—
40C22×C7×D4—22no—
41C22×C7×D4—22no—
42C22×C7×D4—42no—
43C22×C7×D4—42no—
44C22×C7×D4C2×C414yes—
45C23×C4×C7C2312yes—
46C23×C4×C7C2311yescharacteristic
47C23×C4×C7C2311yescharacteristic
48C23×C4×C7C2311yescharacteristic
49C23×Dic7C2311yescharacteristic
50C23×Dic7C2311yescharacteristic
51C23×Dic7C2312yes—
52C23×Dic7C2311yescharacteristic
53C23×Dic7C2311yescharacteristic
54C23×Dic7C2312yes—
55C2×C7×C4⋊C4—22no—
56C2×C7×C4⋊C4—42no—
57C2×C7×C22⋊C4—24no—
58C2×C7×C22⋊C4—24no—
59C2×C7×C22⋊C4—24no—
60C2×C7×C22⋊C4—24no—
61C2×C7×C22⋊C4—42no—
62C2×C7×C22⋊C4—42no—
63C2×C42×C7—42no—
64C2×C42×C7D414yes—
65C2×C22⋊Dic7—24no—
66C2×C22⋊Dic7—24no—
67C2×C22⋊Dic7—42no—
68C2×C22⋊Dic7—42no—
69C2×C22⋊Dic7—42no—
70C2×C22⋊Dic7—42no—
71C2×C22⋊Dic7—42no—
72C2×C22⋊Dic7—42no—
73C2×C22⋊Dic7—42no—
74C2×C22⋊Dic7—42no—
75C2×C22⋊Dic7C2×C418yes—
76C2×C22⋊Dic7C2×C418yes—
77C2×Dic7⋊C4—22no—
78C2×Dic7⋊C4—22no—
79C2×Dic7⋊C4—22no—
80C2×Dic7⋊C4—42no—
81C2×Dic7⋊C4C2×C414yes—
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×#390D711yescharacteristic
98C2×#387—71no—
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×C7—22no—
108C24×C7—22no—
109C24×C7—22no—
110C24×C7—22no—
111C24×C7—22no—
112C24×C7—22no—
113C24×C7—22no—
114C24×C7—22no—
115C24×C7—22no—
116C24×C7—22no—
117C24×C7—22no—
118C24×C7—22no—
119C24×C7—22no—
120C24×C7—22no—
121C24×C7C22×C414yes—
122C24×C7C2411yescharacteristic
123C2×C7×D4—28no—
124C2×C7×D4—48no—
125C2×C7×D4—44no—
126C2×C7×D4—44no—
127C2×C7×D4—48no—
128C22×C4×C7—21no—
129C22×C4×C7—22no—
130C22×C4×C7—22no—
131C22×C4×C7—22no—
132C22×C4×C7—21no—
133C22×C4×C7—22no—
134C22×C4×C7—22no—
135C22×C4×C7—21no—
136C22×C4×C7—21no—
137C22×C4×C7—22no—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—22no—
141C22×C4×C7—22no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7C22×C412yes—
145C22×C4×C7C2×D412yes—
146C22×C4×C7C2×D412yes—
147C22×C4×C7C2×D412yes—
148C22×C4×C7#4112yes—
149C22×C4×C7#4114yes—
150C22×Dic7—21no—
151C22×Dic7—21no—
152C22×Dic7—22no—
153C22×Dic7—22no—
154C22×Dic7—22no—
155C22×Dic7—22no—
156C22×Dic7—21no—
157C22×Dic7—21no—
158C22×Dic7—21no—
159C22×Dic7—22no—
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—21no—
170C22×Dic7—21no—
171C22×Dic7—21no—
172C22×Dic7—21no—
173C22×Dic7—21no—
174C22×Dic7—22no—
175C22×Dic7—22no—
176C22×Dic7—21no—
177C22×Dic7—22no—
178C22×Dic7—22no—
179C22×Dic7—21no—
180C22×Dic7—21no—
181C22×Dic7—21no—
182C22×Dic7C22×C414yes—
183C22×Dic7C22×C412yes—
184C22×Dic7C22×C412yes—
185C22×Dic7#4114yes—
186C7×C4⋊C4—44no—
187C7×C22⋊C4—48no—
188C7×C22⋊C4—48no—
189C42×C7—44no—
190C22⋊Dic7—48no—
191C22⋊Dic7—48no—
192C22⋊Dic7—48no—
193C22⋊Dic7—48no—
194Dic7⋊C4—28no—
195Dic7⋊C4—44no—
196C4×Dic7—48no—
197C23×D4C2×D711yescharacteristic
198C22×C4⋊C4—71no—
199C22×C4⋊C4—71no—
200C22×C4⋊C4C2×D711yescharacteristic
201C22×C22⋊C4—72no—
202C22×C22⋊C4—72no—
203C22×C22⋊C4—72no—
204C22×C22⋊C4—72no—
205C22×C22⋊C4C2×D712yes—
206C22×C22⋊C4C2×D712yes—
207C22×C42—72no—
208C22×C42C2×D711yescharacteristic
209#394—78no—
210#390—24no—
211#387—144no—
212C2×#95—71no—
213C2×#95—71no—
214C2×#95—72no—
215C2×#95—71no—
216C2×#95—71no—
217C2×#95—71no—
218C2×#95—71no—
219C2×#95—72no—
220C2×#95—72no—
221C2×#95—72no—
222C2×#95—72no—
223C23×C7—24no—
224C23×C7—24no—
225C23×C7—24no—
226C23×C7—24no—
227C23×C7—24no—
228C23×C7—24no—
229C23×C7—24no—
230C23×C7—42no—
231C23×C7—42no—
232C23×C7—42no—
233C23×C7—42no—
234C23×C7—42no—
235C23×C7—42no—
236C23×C7—42no—
237C23×C7—42no—
238C23×C7—42no—
239C23×C7—42no—
240C23×C7—42no—
241C23×C7—42no—
242C23×C7—42no—
243C23×C7—42no—
244C23×C7—42no—
245C23×C7—42no—
246C23×C7—42no—
247C23×C7—42no—
248C23×C7—42no—
249C23×C7—42no—
250C23×C7—42no—
251C23×C7—42no—
252C23×C7—42no—
253C23×C7—42no—
254C23×C7—42no—
255C23×C7—42no—
256C23×C7—42no—
257C23×C7—42no—
258C23×C7C23×C411yescharacteristic
259C23×C7C22×D411yescharacteristic
260C23×C7C2×#4111yescharacteristic
261C23×C7C2×#4112yes—
262C23×C7C2×#4112yes—
263C23×C7H(5,𝔽2)12yes—
264C23×C7H(5,𝔽2)12yes—
265C23×C7H(5,𝔽2)11yescharacteristic
266C23×C7H(5,𝔽2)11yescharacteristic
267C23×C7H(5,𝔽2)11yescharacteristic
268C23×C72−1+411yescharacteristic
269C7×D4—416no—
270C2×C4×C7—24no—
271C2×C4×C7—22no—
272C2×C4×C7—22no—
273C2×C4×C7—22no—
274C2×C4×C7—22no—
275C2×C4×C7—24no—
276C2×C4×C7—24no—
277C2×C4×C7—24no—
278C2×C4×C7—22no—
279C2×C4×C7—22no—
280C2×C4×C7—22no—
281C2×C4×C7—42no—
282C2×C4×C7—42no—
283C2×C4×C7—42no—
284C2×C4×C7—42no—
285C2×C4×C7—42no—
286C2×C4×C7—42no—
287C2×C4×C7—42no—
288C2×C4×C7—42no—
289C2×C4×C7—42no—
290C2×C4×C7C4×D414yes—
291C2×C4×C7#12414yes—
292C2×Dic7—22no—
293C2×Dic7—22no—
294C2×Dic7—24no—
295C2×Dic7—22no—
296C2×Dic7—24no—
297C2×Dic7—24no—
298C2×Dic7—24no—
299C2×Dic7—22no—
300C2×Dic7—24no—
301C2×Dic7—24no—
302C2×Dic7—24no—
303C2×Dic7—41no—
304C2×Dic7—41no—
305C2×Dic7—41no—
306C2×Dic7—41no—
307C2×Dic7—42no—
308C2×Dic7—42no—
309C2×Dic7—42no—
310C2×Dic7—42no—
311C2×Dic7—42no—
312C2×Dic7—42no—
313C2×Dic7—42no—
314C2×Dic7—41no—
315C2×Dic7—42no—
316C2×Dic7—42no—
317C2×Dic7—41no—
318C2×Dic7—41no—
319C2×Dic7—41no—
320C2×Dic7—41no—
321C2×Dic7—41no—
322C2×Dic7—41no—
323C2×Dic7—41no—
324C2×Dic7—42no—
325C2×Dic7—42no—
326C2×Dic7—42no—
327C2×Dic7—42no—
328C25C22×D712yes—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—42no—
332C22×D4—42no—
333C22×D4C4×D714yes—
334C23×C4—71no—
335C23×C4—71no—
336C23×C4—72no—
337C23×C4—72no—
338C23×C4—71no—
339C23×C4—71no—
340C23×C4C22×D712yes—
341C23×C4C22×D711yescharacteristic
342C23×C4C22×D711yescharacteristic
343C23×C4C22×D711yescharacteristic
344C2×C4⋊C4—22no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—74no—
347C2×C4⋊C4—142no—
348C2×C4⋊C4—142no—
349C2×C4⋊C4—142no—
350C2×C4⋊C4—282no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—78no—
358C2×C22⋊C4—78no—
359C2×C22⋊C4—144no—
360C2×C22⋊C4—144no—
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—74no—
375#95—144no—
376#95—142no—
377#95—142no—
378#95—142no—
379#95—142no—
380#95—142no—
381#95—282no—
382#95—282no—
383#95—282no—
384#95—282no—
385C22×C7—44no—
386C22×C7—44no—
387C22×C7—44no—
388C22×C7—44no—
389C22×C7—44no—
390C22×C7—44no—
391C22×C7—44no—
392C22×C7—82no—
393C22×C7—82no—
394C22×C7—82no—
395C22×C7—82no—
396C22×C7—82no—
397C22×C7—82no—
398C22×C7—82no—
399C22×C7—82no—
400C22×C7C2×C4×D411yescharacteristic
401C22×C7C4×#4112yes—
402C22×C7#51812yes—
403C22×C7#51811yescharacteristic
404C22×C7#52011yescharacteristic
405C22×C7C2×#12411yescharacteristic
406C22×C7#52912yes—
407C22×C7#53211yescharacteristic
408C22×C7#53411yescharacteristic
409C22×C7#53511yescharacteristic
410C22×C7#53511yescharacteristic
411C22×C7#53711yescharacteristic
412C22×C7#53812yes—
413C22×C7#53812yes—
414C22×C7#53812yes—
415C22×C7#53812yes—
416C22×C7#53912yes—
417C22×C7#54012yes—
418C22×C7#54012yes—
419C22×C7#54011yescharacteristic
420C22×C7#54012yes—
421C22×C7#54211yescharacteristic
422C22×C7#54212yes—
423C4×C7—24no—
424C4×C7—24no—
425C4×C7—42no—
426C4×C7—82no—
427Dic7—42no—
428Dic7—42no—
429Dic7—44no—
430Dic7—44no—
431Dic7—81no—
432Dic7—81no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24C2×C4×D714yes—
448C24C23×D711yescharacteristic
449C2×D4—28no—
450C2×D4—48no—
451C2×D4—48no—
452C2×D4—44no—
453C2×D4—44no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—74no—
471C22×C4—72no—
472C22×C4—72no—
473C22×C4—74no—
474C22×C4—142no—
475C22×C4—141no—
476C22×C4—141no—
477C22×C4—142no—
478C22×C4—142no—
479C22×C4—141no—
480C22×C4—142no—
481C22×C4—142no—
482C22×C4—142no—
483C22×C4—142no—
484C22×C4—142no—
485C22×C4—142no—
486C22×C4—142no—
487C22×C4—141no—
488C22×C4—142no—
489C22×C4—142no—
490C22×C4—142no—
491C22×C4—142no—
492C22×C4—141no—
493C22×C4—141no—
494C22×C4—141no—
495C22×C4—141no—
496C22×C4—141no—
497C22×C4—142no—
498C22×C4—141no—
499C22×C4—142no—
500C22×C4—142no—
501C22×C4—142no—
502C22×C4—141no—
503C22×C4—141no—
504C22×C4—141no—
505C22×C4—141no—
506C22×C4C2×C4×D712yes—
507C22×C4#115712yes—
508C22×C4#115914yes—
509C22×C4C2×C22⋊D712yes—
510C22×C4C2×C22⋊D712yes—
511C22×C4C2×C22⋊D712yes—
512C4⋊C4—44no—
513C4⋊C4—148no—
514C4⋊C4—284no—
515C22⋊C4—48no—
516C22⋊C4—48no—
517C22⋊C4—288no—
518C22⋊C4—288no—
519C22⋊C4—288no—
520C22⋊C4—288no—
521C42—44no—
522C42—288no—
523C2×C7—84no—
524C2×C7C4×#12411yescharacteristic
525C2×C7#232111yescharacteristic
526C2×C7#232411yescharacteristic
527C2×C7#233312yes—
528C2×C7#233512yes—
529C2×C7#263911yescharacteristic
530C2×C7#264111yescharacteristic
531C2×C7#264812yes—
532C2×C7#265112yes—
533C2×C7#266111yescharacteristic
534C2×C7#266211yescharacteristic
535C23—24no—
536C23—24no—
537C23—24no—
538C23—24no—
539C23—24no—
540C23—24no—
541C23—24no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23C22×C4×D711yescharacteristic
571C23C2×#115711yescharacteristic
572C23C2×#115912yes—
573C23#654812yes—
574C23#654811yescharacteristic
575C23#654811yescharacteristic
576C23#654812yes—
577C23D7×#4112yes—
578C23#655311yescharacteristic
579C23#655411yescharacteristic
580C23C22×C22⋊D711yescharacteristic
581D4—416no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—144no—
603C2×C4—144no—
604C2×C4—144no—
605C2×C4—142no—
606C2×C4—142no—
607C2×C4—144no—
608C2×C4—142no—
609C2×C4—144no—
610C2×C4—142no—
611C2×C4—144no—
612C2×C4—144no—
613C2×C4—282no—
614C2×C4—282no—
615C2×C4—282no—
616C2×C4—282no—
617C2×C4—282no—
618C2×C4—281no—
619C2×C4—281no—
620C2×C4—281no—
621C2×C4—281no—
622C2×C4—282no—
623C2×C4—281no—
624C2×C4—281no—
625C2×C4—282no—
626C2×C4—282no—
627C2×C4—282no—
628C2×C4—282no—
629C2×C4—281no—
630C2×C4—281no—
631C2×C4—281no—
632C2×C4—281no—
633C2×C4—281no—
634C2×C4—281no—
635C2×C4—282no—
636C2×C4—282no—
637C2×C4—282no—
638C2×C4C4×C22⋊D714yes—
639C2×C4#649914yes—
640C7#1432511yescharacteristic, complemented, Sylow
641C22—44no—
642C22—44no—
643C22—44no—
644C22—44no—
645C22—44no—
646C22—44no—
647C22—44no—
648C22—82no—
649C22—82no—
650C22—82no—
651C22—82no—
652C22—82no—
653C22—82no—
654C22—82no—
655C22—82no—
656C22#9017712yes—
657C22#9018512yes—
658C22C4×#115912yes—
659C22#9023611yescharacteristic
660C22#9023711yescharacteristic
661C22#9024812yes—
662C22#9025211yescharacteristic
663C22#9025311yescharacteristic
664C22#9029312yes—
665C22#9030412yes—
666C22#9030612yes—
667C22#9030812yes—
668C22#9036012yes—
669C22#9036912yes—
670C22#9041012yes—
671C22#9041012yes—
672C22C2×C4×C22⋊D711yescharacteristic
673C22C2×#649911yescharacteristic
674C22#9049511yescharacteristic
675C22#9049611yescharacteristic
676C22#9049611yescharacteristic
677C22#9052311yescharacteristic
678C22#9052411yescharacteristic
679C4—24no—
680C4—24no—
681C4—42no—
682C4—82no—
683C4—284no—
684C4—282no—
685C4—282no—
686C4—284no—
687C4—561no—
688C4—561no—
689C2—84no—
690C2#1173374412yes—
691C2#1173374512yes—
692C2#1173382112yes—
693C2#1173390412yes—
694C2#1173954111yescharacteristic
695C2C4×#649911yescharacteristic
696C2#1173984111yescharacteristic
697C2#1174012411yescharacteristic
698C2#1174015711yescharacteristic
699C2#1174042611yescharacteristic
700C2#1174062511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#390C2
socle, cosocleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC2×#390D7
hypocenterC7#14325
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
3. C2×#89705C2semidirect
5. #11729321C2semidirect
6. #11729320C2semidirect
7. #11729303C2semidirect
8. #11729301C2semidirect
9. #11729299C2semidirect
10. #11729299C2semidirect
11. C4×C7⋊#95C2semidirect
25. #89994C4semidirect
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×#3902
C2×#899942
C2×#897052
#117298852
#117293212
#117293202
#117293032
#117293012
#117292992
C4×C7⋊#952
#143257