Finite Group Databasebeta

← #13276891

Subgroups — #13276891

Order 1792.

1802 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#89759C211yesmaximal, characteristic
3C2×#89759C211yesmaximal, characteristic
4C2×#89745C211yesmaximal, characteristic, complemented
5C2×#89712C212yesmaximal
6C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic
7#11729317C211yesmaximal, characteristic, complemented
8#11729289C211yesmaximal, characteristic, complemented
9#11729288C212yesmaximal, complemented
10#11727183C212yesmaximal
11#11727167C212yesmaximal, complemented
12C23×C4×D7C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C42×C7C2212yes—
16C22×C42×C7C2211yescharacteristic
17C22×(C2×D7)⋊C4C2211yescharacteristic
18C22×(C2×D7)⋊C4C2212yes—
19C22×(C2×D7)⋊C4C2212yes—
20C22×(C2×D7)⋊C4C2211yescharacteristic
21C22×C4⋊Dic7C2211yescharacteristic
22C22×C4⋊Dic7C2211yescharacteristic
23C22×Dic7⋊C4C2212yes—
24C22×C4×Dic7C2211yescharacteristic
25C4×C7×C4⋊C4—24no—
26C2×C7×#95C2212yes—
27C2×C7⋊#95C2211yescharacteristic
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2211yescharacteristic
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36#89759—24no—
37#89759C418yescomplemented
38#89745—24no—
39#89712—28no—
40C4×(C2×D7)⋊C4—24no—
41#13994—71nomaximal, Sylow
42C24×D7C2311yescharacteristic
43C23×C4×C7C2312yes—
44C23×C4×C7C2312yes—
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2311yescharacteristic
47C23×C4×C7C2311yescharacteristic
48C23×Dic7C2312yes—
49C23×Dic7C2312yes—
50C23×Dic7C2311yescharacteristic
51C23×Dic7C2311yescharacteristic
52C23×Dic7C2311yescharacteristic
53C22×C4×D7—22no—
54C22×C4×D7—22no—
55C22×C4×D7—22no—
56C22×C4×D7—22no—
57C22×C4×D7—22no—
58C22×C4×D7—22no—
59C22×C4×D7C2×C414yes—
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4C2×C414yes—
65C2×C7×C4⋊C4D414yes—
66C2×C42×C7—22no—
67C2×C42×C7—22no—
68C2×C42×C7—24no—
69C2×C42×C7—24no—
70C2×C42×C7—24no—
71C2×C42×C7D414yes—
72C2×(C2×D7)⋊C4—24no—
73C2×(C2×D7)⋊C4—22no—
74C2×(C2×D7)⋊C4—24no—
75C2×(C2×D7)⋊C4—22no—
76C2×(C2×D7)⋊C4—22no—
77C2×(C2×D7)⋊C4—22no—
78C2×(C2×D7)⋊C4—22no—
79C2×(C2×D7)⋊C4—24no—
80C2×(C2×D7)⋊C4—24no—
81C2×(C2×D7)⋊C4—42no—
82C2×(C2×D7)⋊C4C2×C418yes—
83C2×(C2×D7)⋊C4D414yes—
84C2×C4⋊Dic7—22no—
85C2×C4⋊Dic7—22no—
86C2×C4⋊Dic7—22no—
87C2×C4⋊Dic7—22no—
88C2×C4⋊Dic7—22no—
89C2×C4⋊Dic7C2×C414yes—
90C2×Dic7⋊C4—24no—
91C2×Dic7⋊C4—24no—
92C2×Dic7⋊C4—42no—
93C2×C4×Dic7—22no—
94C2×C4×Dic7—22no—
95C2×C4×Dic7—22no—
96C7×#95—24no—
97C7⋊#95—22no—
98C7⋊#95—22no—
99C7⋊#95—24no—
100C7⋊#95—24no—
101C7⋊#95—24no—
102C7⋊#95—24no—
103C7⋊#95—24no—
104C7⋊#95—42no—
105C7⋊#95C2×C418yes—
106C2×#389—71no—
107C2×#388—72no—
108C2×#380—71no—
109C2×#380—71no—
110C2×C4×C4⋊C4D711yescharacteristic, complemented
111C2×C4×C22⋊C4—71no—
112#1442—72no—
113#1440—72no—
114C4⋊#95—71no—
115C4⋊#95—71no—
116#1434—72no—
117C24×C7C2411yescharacteristic
118C23×D7—21no—
119C23×D7—21no—
120C23×D7—21no—
121C23×D7—21no—
122C23×D7—21no—
123C23×D7—21no—
124C23×D7—21no—
125C23×D7—21no—
126C23×D7—21no—
127C23×D7—21no—
128C23×D7—21no—
129C23×D7—21no—
130C23×D7C22×C412yes—
131C23×D7C2×D412yes—
132C23×D7#4112yes—
133C22×C4×C7—21no—
134C22×C4×C7—21no—
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—21no—
144C22×C4×C7—21no—
145C22×C4×C7—22no—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—22no—
149C22×C4×C7—22no—
150C22×C4×C7—22no—
151C22×C4×C7—21no—
152C22×C4×C7—22no—
153C22×C4×C7—21no—
154C22×C4×C7—22no—
155C22×C4×C7C22×C414yes—
156C22×C4×C7C22×C412yes—
157C22×C4×C7C2×D414yes—
158C22×C4×C7C2×D412yes—
159C22×C4×C7C2×D412yes—
160C22×C4×C7C2×D412yes—
161C22×C4×C7C2×D412yes—
162C22×C4×C7C2×D412yes—
163C22×C4×C7#4112yes—
164C22×C4×C7#4112yes—
165C22×C4×C7#4112yes—
166C22×C4×C7#4112yes—
167C22×C4×C7#4112yes—
168C22×Dic7—21no—
169C22×Dic7—21no—
170C22×Dic7—21no—
171C22×Dic7—21no—
172C22×Dic7—21no—
173C22×Dic7—22no—
174C22×Dic7—22no—
175C22×Dic7—21no—
176C22×Dic7—21no—
177C22×Dic7—21no—
178C22×Dic7—22no—
179C22×Dic7—22no—
180C22×Dic7—21no—
181C22×Dic7—21no—
182C22×Dic7—21no—
183C22×Dic7—21no—
184C22×Dic7—21no—
185C22×Dic7—21no—
186C22×Dic7—22no—
187C22×Dic7—21no—
188C22×Dic7—22no—
189C22×Dic7—21no—
190C22×Dic7—21no—
191C22×Dic7—21no—
192C22×Dic7—22no—
193C22×Dic7—22no—
194C22×Dic7—22no—
195C22×Dic7—22no—
196C22×Dic7—22no—
197C22×Dic7—22no—
198C22×Dic7—22no—
199C22×Dic7C22×C412yes—
200C22×Dic7C22×C414yes—
201C22×Dic7C2×D412yes—
202C22×Dic7#4112yes—
203C2×C4×D7—28no—
204C2×C4×D7—28no—
205C2×C4×D7—28no—
206C2×C4×D7—44no—
207C2×C4×D7—44no—
208C2×C4×D7—44no—
209C2×C4×D7—44no—
210C7×C4⋊C4—28no—
211C7×C4⋊C4—28no—
212C42×C7—28no—
213C42×C7—48no—
214(C2×D7)⋊C4—28no—
215(C2×D7)⋊C4—216no—
216(C2×D7)⋊C4—28no—
217(C2×D7)⋊C4—48no—
218C4⋊Dic7—28no—
219C4⋊Dic7—44no—
220Dic7⋊C4—48no—
221C4×Dic7—44no—
222C24×C4—71no—
223C22×C4⋊C4—71no—
224C22×C4⋊C4—71no—
225C22×C4⋊C4—72no—
226C22×C4⋊C4C2×D711yescharacteristic
227C22×C4⋊C4C2×D711yescharacteristic
228C22×C22⋊C4—72no—
229C22×C22⋊C4—71no—
230C22×C22⋊C4—71no—
231C22×C22⋊C4—72no—
232C22×C42—71no—
233C22×C42C2×D712yes—
234C22×C42C2×D711yescharacteristic
235#389—144no—
236#388—148no—
237#380—78no—
238#380—144no—
239C4×C4⋊C4—24no—
240C4×C22⋊C4—144no—
241C2×#95—72no—
242C2×#95—71no—
243C2×#95—72no—
244C2×#95—72no—
245C2×#95—72no—
246C2×#95—72no—
247C2×#95—72no—
248C2×#95—71no—
249C2×#95—72no—
250C2×#95C2×D712yes—
251C23×C7C23×C411yescharacteristic
252C23×C7C22×D411yescharacteristic
253C23×C7C22×D411yescharacteristic
254C23×C7C22×D411yescharacteristic
255C23×C7C2×#4111yescharacteristic
256C23×C7C2×#4111yescharacteristic
257C23×C7C2×#4111yescharacteristic
258C23×C7C2×#4111yescharacteristic
259C23×C7C2×#4111yescharacteristic
260C23×C7C2×#4111yescharacteristic
261C23×C7C2×#4111yescharacteristic
262C23×C7H(5,𝔽2)11yescharacteristic
263C23×C72−1+411yescharacteristic
264C23×C72−1+411yescharacteristic
265C23×C72−1+411yescharacteristic
266C22×D7—22no—
267C22×D7—22no—
268C22×D7—22no—
269C22×D7—22no—
270C22×D7—22no—
271C22×D7—22no—
272C22×D7—22no—
273C22×D7—22no—
274C22×D7—22no—
275C22×D7—22no—
276C22×D7—22no—
277C22×D7—22no—
278C22×D7—22no—
279C22×D7—22no—
280C22×D7—22no—
281C22×D7—22no—
282C22×D7—22no—
283C22×D7—22no—
284C22×D7—41no—
285C22×D7—41no—
286C22×D7—41no—
287C22×D7—41no—
288C22×D7—41no—
289C22×D7—41no—
290C22×D7—41no—
291C22×D7—41no—
292C22×D7—41no—
293C22×D7—41no—
294C22×D7—41no—
295C22×D7—41no—
296C22×D7—41no—
297C22×D7—41no—
298C22×D7—41no—
299C22×D7—41no—
300C22×D7C4×D414yes—
301C2×C4×C7—22no—
302C2×C4×C7—22no—
303C2×C4×C7—22no—
304C2×C4×C7—22no—
305C2×C4×C7—22no—
306C2×C4×C7—22no—
307C2×C4×C7—24no—
308C2×C4×C7—24no—
309C2×C4×C7—24no—
310C2×C4×C7—24no—
311C2×C4×C7—22no—
312C2×C4×C7—22no—
313C2×C4×C7—22no—
314C2×C4×C7—24no—
315C2×C4×C7—24no—
316C2×C4×C7—42no—
317C2×C4×C7—42no—
318C2×C4×C7—42no—
319C2×C4×C7—42no—
320C2×C4×C7—42no—
321C2×C4×C7—42no—
322C2×C4×C7—42no—
323C2×C4×C7—41no—
324C2×C4×C7—41no—
325C2×C4×C7—41no—
326C2×C4×C7—42no—
327C2×C4×C7—41no—
328C2×C4×C7#11714yes—
329C2×C4×C7C4×D414yes—
330C2×C4×C7C4×D414yes—
331C2×C4×C7#12114yes—
332C2×C4×C7#12114yes—
333C2×C4×C7#12314yes—
334C2×C4×C7#12414yes—
335C2×C4×C7#12614yes—
336C2×Dic7—22no—
337C2×Dic7—24no—
338C2×Dic7—24no—
339C2×Dic7—22no—
340C2×Dic7—22no—
341C2×Dic7—24no—
342C2×Dic7—22no—
343C2×Dic7—22no—
344C2×Dic7—22no—
345C2×Dic7—22no—
346C2×Dic7—22no—
347C2×Dic7—22no—
348C2×Dic7—41no—
349C2×Dic7—41no—
350C2×Dic7—41no—
351C2×Dic7—41no—
352C2×Dic7—41no—
353C2×Dic7—41no—
354C2×Dic7—41no—
355C2×Dic7—41no—
356C2×Dic7—42no—
357C2×Dic7—42no—
358C2×Dic7—41no—
359C2×Dic7—42no—
360C2×Dic7—41no—
361C2×Dic7—41no—
362C2×Dic7—42no—
363C2×Dic7—41no—
364C2×Dic7—42no—
365C2×Dic7—42no—
366C2×Dic7—42no—
367C2×Dic7—42no—
368C2×Dic7—42no—
369C2×Dic7—42no—
370C2×Dic7—42no—
371C4×D7—416no—
372C25—71no—
373C23×C4—72no—
374C23×C4—71no—
375C23×C4—71no—
376C23×C4—71no—
377C23×C4—74no—
378C23×C4—72no—
379C23×C4—142no—
380C23×C4—142no—
381C23×C4—142no—
382C23×C4—142no—
383C23×C4—142no—
384C23×C4—142no—
385C23×C4C22×D712yes—
386C23×C4C22×D712yes—
387C23×C4C22×D711yescharacteristic
388C23×C4C22×D711yescharacteristic
389C23×C4C22×D711yescharacteristic
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—74no—
395C2×C4⋊C4—142no—
396C2×C4⋊C4—142no—
397C2×C4⋊C4—144no—
398C2×C4⋊C4—144no—
399C2×C4⋊C4—142no—
400C2×C4⋊C4—142no—
401C2×C4⋊C4—142no—
402C2×C4⋊C4—282no—
403C2×C4⋊C4C4×D714yes—
404C2×C4⋊C4D2814yes—
405C2×C22⋊C4—78no—
406C2×C22⋊C4—74no—
407C2×C22⋊C4—142no—
408C2×C22⋊C4—144no—
409C2×C22⋊C4—142no—
410C2×C22⋊C4—144no—
411C2×C22⋊C4—142no—
412C2×C22⋊C4—142no—
413C2×C22⋊C4—142no—
414C2×C22⋊C4—144no—
415C2×C22⋊C4—144no—
416C2×C22⋊C4—282no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—24no—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—142no—
423C2×C42—142no—
424C2×C42—142no—
425C2×C42C22⋊D714yes—
426#95—24no—
427#95—78no—
428#95—144no—
429#95—144no—
430#95—144no—
431#95—144no—
432#95—144no—
433#95—142no—
434#95—142no—
435#95—282no—
436C22×C7C2×#11711yescharacteristic
437C22×C7C2×C4×D411yescharacteristic
438C22×C7C2×C4×D411yescharacteristic
439C22×C7C2×C4×D411yescharacteristic
440C22×C7C4×#4111yescharacteristic
441C22×C7#51911yescharacteristic
442C22×C7#52011yescharacteristic
443C22×C7C2×#12111yescharacteristic
444C22×C7C2×#12111yescharacteristic
445C22×C7C2×#12311yescharacteristic
446C22×C7#52511yescharacteristic
447C22×C7C2×#12411yescharacteristic
448C22×C7C2×#12611yescharacteristic
449C22×C7#52911yescharacteristic
450C22×C7#53211yescharacteristic
451C22×C7#53611yescharacteristic
452C22×C7#53711yescharacteristic
453C22×C7#54111yescharacteristic
454C22×C7#54211yescharacteristic
455C22×C7D4211yescharacteristic
456C22×C7#54711yescharacteristic
457C22×C7#54711yescharacteristic
458C22×C7#54711yescharacteristic
459C22×C7#54711yescharacteristic
460C22×C7#54811yescharacteristic
461C22×C7#54811yescharacteristic
462C22×C7#55211yescharacteristic
463C22×C7#55211yescharacteristic
464C22×C7#55211yescharacteristic
465C22×C7#55211yescharacteristic
466C22×C7#55211yescharacteristic
467C22×C7#55311yescharacteristic
468C22×C7#55511yescharacteristic
469C22×C7#55511yescharacteristic
470C22×C7#55611yescharacteristic
471C2×D7—24no—
472C2×D7—24no—
473C2×D7—24no—
474C2×D7—42no—
475C2×D7—42no—
476C2×D7—42no—
477C2×D7—42no—
478C2×D7—42no—
479C2×D7—42no—
480C2×D7—42no—
481C2×D7—42no—
482C2×D7—42no—
483C2×D7—42no—
484C2×D7—42no—
485C2×D7—42no—
486C4×C7—24no—
487C4×C7—42no—
488C4×C7—44no—
489C4×C7—44no—
490C4×C7#38818yescomplemented
491Dic7—44no—
492Dic7—42no—
493Dic7—42no—
494Dic7—42no—
495Dic7—82no—
496C24—72no—
497C24—72no—
498C24—72no—
499C24—141no—
500C24—141no—
501C24—141no—
502C24—141no—
503C24—141no—
504C24—141no—
505C24—141no—
506C24—141no—
507C24—141no—
508C24—141no—
509C24—141no—
510C24—141no—
511C24C23×D711yescharacteristic
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—72no—
535C22×C4—74no—
536C22×C4—72no—
537C22×C4—72no—
538C22×C4—141no—
539C22×C4—141no—
540C22×C4—142no—
541C22×C4—141no—
542C22×C4—141no—
543C22×C4—141no—
544C22×C4—142no—
545C22×C4—141no—
546C22×C4—141no—
547C22×C4—141no—
548C22×C4—141no—
549C22×C4—142no—
550C22×C4—141no—
551C22×C4—142no—
552C22×C4—141no—
553C22×C4—141no—
554C22×C4—142no—
555C22×C4—141no—
556C22×C4—142no—
557C22×C4—141no—
558C22×C4—141no—
559C22×C4—141no—
560C22×C4—141no—
561C22×C4—141no—
562C22×C4—148no—
563C22×C4—148no—
564C22×C4—148no—
565C22×C4—142no—
566C22×C4—142no—
567C22×C4—142no—
568C22×C4—142no—
569C22×C4—142no—
570C22×C4—142no—
571C22×C4—142no—
572C22×C4—284no—
573C22×C4—284no—
574C22×C4—284no—
575C22×C4—284no—
576C22×C4C2×C4×D714yes—
577C22×C4C2×C4×D712yes—
578C22×C4C2×D2814yes—
579C22×C4C2×D2812yes—
580C22×C4#115712yes—
581C22×C4#115712yes—
582C22×C4#115712yes—
583C22×C4#115712yes—
584C22×C4D4×D712yes—
585C22×C4#115912yes—
586C22×C4C2×C22⋊D712yes—
587C22×C4C2×C22⋊D712yes—
588C22×C4C2×C22⋊D712yes—
589C4⋊C4—28no—
590C4⋊C4—28no—
591C4⋊C4—148no—
592C4⋊C4—288no—
593C4⋊C4—284no—
594C22⋊C4—1416no—
595C22⋊C4—148no—
596C22⋊C4—148no—
597C22⋊C4—288no—
598C42—28no—
599C42—48no—
600C42—284no—
601C2×C7C2×#38811yescharacteristic
602C2×C7C4×#12111yescharacteristic
603C2×C7#232311yescharacteristic
604C2×C7#234411yescharacteristic
605C2×C7#234611yescharacteristic
606C2×C7#236111yescharacteristic
607C2×C7#236211yescharacteristic
608C2×C7#248511yescharacteristic
609C2×C7#248611yescharacteristic
610C2×C7#248911yescharacteristic
611C2×C7#249111yescharacteristic
612C2×C7#249511yescharacteristic
613C2×C7#249611yescharacteristic
614C2×C7#253611yescharacteristic
615C2×C7#253711yescharacteristic
616D7—44no—
617C23—74no—
618C23—142no—
619C23—142no—
620C23—142no—
621C23—142no—
622C23—142no—
623C23—142no—
624C23—142no—
625C23—142no—
626C23—142no—
627C23—142no—
628C23—142no—
629C23—142no—
630C23—142no—
631C23—142no—
632C23—142no—
633C23—142no—
634C23—142no—
635C23—142no—
636C23—281no—
637C23—281no—
638C23—281no—
639C23—281no—
640C23—281no—
641C23—281no—
642C23—281no—
643C23—281no—
644C23—281no—
645C23—281no—
646C23—281no—
647C23—281no—
648C23—281no—
649C23—281no—
650C23—281no—
651C23—281no—
652C23C22×C4×D711yescharacteristic
653C23C22×D2811yescharacteristic
654C23C2×#115711yescharacteristic
655C23C2×#115711yescharacteristic
656C23C2×#115711yescharacteristic
657C23C2×#115711yescharacteristic
658C23C2×D4×D711yescharacteristic
659C23C2×#115911yescharacteristic
660C23#655111yescharacteristic
661C23#655111yescharacteristic
662C23D7×#4111yescharacteristic
663C23D7×#4111yescharacteristic
664C23#655311yescharacteristic
665C23#655411yescharacteristic
666C23C22×C22⋊D711yescharacteristic
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—142no—
695C2×C4—144no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—144no—
699C2×C4—142no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—142no—
703C2×C4—144no—
704C2×C4—142no—
705C2×C4—142no—
706C2×C4—281no—
707C2×C4—281no—
708C2×C4—282no—
709C2×C4—282no—
710C2×C4—281no—
711C2×C4—281no—
712C2×C4—281no—
713C2×C4—281no—
714C2×C4—282no—
715C2×C4—281no—
716C2×C4—281no—
717C2×C4—281no—
718C2×C4—282no—
719C2×C4—281no—
720C2×C4—281no—
721C2×C4—281no—
722C2×C4—2816no—
723C2×C4—282no—
724C2×C4—282no—
725C2×C4—282no—
726C2×C4—282no—
727C2×C4—282no—
728C2×C4—282no—
729C2×C4—282no—
730C2×C4#643514yes—
731C2×C4C4×D2814yes—
732C2×C4#643814yes—
733C2×C4#643914yes—
734C2×C4C4×C22⋊D714yes—
735C2×C4#649214yes—
736C2×C4#649314yes—
737C2×C4#650114yes—
738C7#1399411yescharacteristic, complemented, Sylow
739C22—144no—
740C22—144no—
741C22—144no—
742C22—282no—
743C22—282no—
744C22—282no—
745C22—282no—
746C22—282no—
747C22—282no—
748C22—282no—
749C22—282no—
750C22—282no—
751C22—282no—
752C22—282no—
753C22—282no—
754C22C2×#643511yescharacteristic
755C22C2×C4×D2811yescharacteristic
756C22C2×#643811yescharacteristic
757C22C2×#643911yescharacteristic
758C22#9019811yescharacteristic
759C22#9019811yescharacteristic
760C22#9020411yescharacteristic
761C22#9020411yescharacteristic
762C22#9022011yescharacteristic
763C22#9022111yescharacteristic
764C22#9022311yescharacteristic
765C22#9022411yescharacteristic
766C22C4×#115911yescharacteristic
767C22C4×D4×D711yescharacteristic
768C22#9023911yescharacteristic
769C22D4×D2811yescharacteristic
770C22#9024211yescharacteristic
771C22#9024611yescharacteristic
772C22#9024811yescharacteristic
773C22#9025411yescharacteristic
774C22#9026311yescharacteristic
775C22#9026511yescharacteristic
776C22#9026711yescharacteristic
777C22#9026711yescharacteristic
778C22#9027211yescharacteristic
779C22#9027211yescharacteristic
780C22#9027311yescharacteristic
781C22#9027411yescharacteristic
782C22C2×C4×C22⋊D711yescharacteristic
783C22C2×#649211yescharacteristic
784C22C2×#649311yescharacteristic
785C22C2×#650111yescharacteristic
786C22#9050711yescharacteristic
787C22#9051911yescharacteristic
788C22#9052411yescharacteristic
789C4—24no—
790C4—42no—
791C4—44no—
792C4—44no—
793C4—284no—
794C4—282no—
795C4—282no—
796C4—282no—
797C4—562no—
798C4#8971218yescomplemented
799C2—284no—
800C2#1173107811yescharacteristic
801C2#1173109211yescharacteristic
802C2#1173121211yescharacteristic
803C2#1173121911yescharacteristic
804C2#1173123111yescharacteristic
805C2#1173123311yescharacteristic
806C2#1173123611yescharacteristic
807C2#1173123711yescharacteristic
808C2C2×#8971211yescharacteristic
809C2#1173964111yescharacteristic
810C2#1173972811yescharacteristic
811C2C4×#650111yescharacteristic
812C2#1173986211yescharacteristic
813C2#1173993311yescharacteristic
814C2#1173994411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C4×C7×C4⋊C4C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×C4×C4⋊C4D7
hypocenterC7#13994
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C7×C4⋊C4C2semidirect
4. C2×#89745C2semidirect
7. #11729317C2semidirect
8. #11729289C2semidirect
9. #11729288C2semidirect
11. #11727167C2semidirect
37. #89759C4semidirect
110. C2×C4×C4⋊C4D7semidirect
490. C4×C7#388semidirect
738. C7#13994semidirect
798. C4#89712semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C7×C4⋊C42
C2×#897592
C2×#897452
C2×#897122
C2×C4×(C2×D7)⋊C42
#117293172
#117292892
#117292882
#117271832
#117271672
#139947