Finite Group Databasebeta

← #13276636

Subgroups — #13276636

Order 1792.

1746 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#380C211yesmaximal, characteristic
2C2×#89984C211yesmaximal, characteristic
3C2×C4×C22⋊Dic7C211yesmaximal, characteristic
4C2×#89757C211yesmaximal, characteristic, complemented
5C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
6#11729317C211yesmaximal, characteristic, complemented
7#11729317C211yesmaximal, characteristic, complemented
8#11729300C212yesmaximal
9#11729299C212yesmaximal
10#11727166C212yesmaximal, complemented
11#11727155C212yesmaximal, complemented
12C24×C4×C7C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C22⋊C4C2212yes—
16C22×C22⋊Dic7C2211yescharacteristic
17C22×C22⋊Dic7C2212yes—
18C22×C22⋊Dic7C2211yescharacteristic
19C22×C4⋊Dic7C2211yescharacteristic
20C22×C4⋊Dic7C2211yescharacteristic
21C22×C4⋊Dic7C2212yes—
22C22×C4×Dic7C2211yescharacteristic
23C22×C4×Dic7C2212yes—
24C22×C4×Dic7C2211yescharacteristic
25C7×#380C418yescomplemented
26C2×C7×#95C2212yes—
27#89984—24no—
28C4×C22⋊Dic7—24no—
29C2×C7⋊#95C2211yescharacteristic
30C2×C7⋊#95C2211yescharacteristic
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38#89757—24no—
39C4⋊C4×Dic7—24no—
40#13973—71nomaximal, Sylow
41C25×C7C2311yescharacteristic
42C23×C4×C7—22no—
43C23×C4×C7—22no—
44C23×C4×C7—22no—
45C23×C4×C7—22no—
46C23×C4×C7—22no—
47C23×C4×C7—22no—
48C23×C4×C7C2×C414yes—
49C23×C4×C7C2312yes—
50C23×C4×C7C2312yes—
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2311yescharacteristic
53C23×Dic7C2312yes—
54C23×Dic7C2311yescharacteristic
55C23×Dic7C2312yes—
56C23×Dic7C2311yescharacteristic
57C23×Dic7C2311yescharacteristic
58C23×Dic7C2311yescharacteristic
59C2×C7×C4⋊C4—22no—
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4C2×C414yes—
64C2×C7×C4⋊C4C2×C414yes—
65C2×C7×C22⋊C4—42no—
66C2×C7×C22⋊C4—42no—
67C2×C7×C22⋊C4C2×C418yes—
68C2×C22⋊Dic7—22no—
69C2×C22⋊Dic7—22no—
70C2×C22⋊Dic7—22no—
71C2×C22⋊Dic7—22no—
72C2×C22⋊Dic7—22no—
73C2×C22⋊Dic7—24no—
74C2×C22⋊Dic7—24no—
75C2×C22⋊Dic7—42no—
76C2×C22⋊Dic7Q814yes—
77C2×C4⋊Dic7—22no—
78C2×C4⋊Dic7—22no—
79C2×C4⋊Dic7—22no—
80C2×C4⋊Dic7—22no—
81C2×C4⋊Dic7—22no—
82C2×C4⋊Dic7—24no—
83C2×C4⋊Dic7—42no—
84C2×C4⋊Dic7—42no—
85C2×C4⋊Dic7D414yes—
86C2×C4×Dic7—22no—
87C2×C4×Dic7—22no—
88C2×C4×Dic7—22no—
89C2×C4×Dic7—22no—
90C2×C4×Dic7—22no—
91C2×C4×Dic7—24no—
92C2×C4×Dic7—24no—
93C2×C4×Dic7—42no—
94C2×C4×Dic7D414yes—
95C7×#95C2×C418yes—
96C7⋊#95—22no—
97C7⋊#95—22no—
98C7⋊#95—24no—
99C7⋊#95—24no—
100C7⋊#95—24no—
101C7⋊#95—24no—
102C7⋊#95—42no—
103C7⋊#95—42no—
104C7⋊#95—42no—
105C2×#389—71no—
106C2×#380—71no—
107C2×#380D711yescharacteristic
108C2×C4×C4⋊C4—71no—
109C2×C4×C22⋊C4—71no—
110#1442—72no—
111#1439—72no—
112#1437—72no—
113C4⋊#95—71no—
114C4⋊#95—71no—
115#1434—72no—
116C24×C7—21no—
117C24×C7—21no—
118C24×C7—21no—
119C24×C7—21no—
120C24×C7—21no—
121C24×C7—21no—
122C24×C7—21no—
123C24×C7—21no—
124C24×C7—21no—
125C24×C7—21no—
126C24×C7—21no—
127C24×C7—21no—
128C24×C7C22×C412yes—
129C24×C7C2×Q812yes—
130C24×C7#4112yes—
131C24×C7C2411yescharacteristic
132C22×C4×C7—21no—
133C22×C4×C7—21no—
134C22×C4×C7—22no—
135C22×C4×C7—22no—
136C22×C4×C7—22no—
137C22×C4×C7—22no—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7—22no—
145C22×C4×C7—22no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—22no—
150C22×C4×C7—28no—
151C22×C4×C7—28no—
152C22×C4×C7—28no—
153C22×C4×C7—44no—
154C22×C4×C7—44no—
155C22×C4×C7—44no—
156C22×C4×C7—44no—
157C22×C4×C7C22×C412yes—
158C22×C4×C7C22×C414yes—
159C22×C4×C7C22×C414yes—
160C22×C4×C7C22×C412yes—
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×Dic7—21no—
168C22×Dic7—21no—
169C22×Dic7—21no—
170C22×Dic7—21no—
171C22×Dic7—21no—
172C22×Dic7—21no—
173C22×Dic7—21no—
174C22×Dic7—21no—
175C22×Dic7—22no—
176C22×Dic7—21no—
177C22×Dic7—21no—
178C22×Dic7—21no—
179C22×Dic7—21no—
180C22×Dic7—22no—
181C22×Dic7—22no—
182C22×Dic7—21no—
183C22×Dic7—21no—
184C22×Dic7—21no—
185C22×Dic7—21no—
186C22×Dic7—22no—
187C22×Dic7—21no—
188C22×Dic7—21no—
189C22×Dic7—21no—
190C22×Dic7—22no—
191C22×Dic7—22no—
192C22×Dic7—21no—
193C22×Dic7—21no—
194C22×Dic7—21no—
195C22×Dic7—22no—
196C22×Dic7—22no—
197C22×Dic7—22no—
198C22×Dic7—22no—
199C22×Dic7—22no—
200C22×Dic7—22no—
201C22×Dic7—22no—
202C22×Dic7C2×D414yes—
203C22×Dic7C2×D412yes—
204C22×Dic7C2×D412yes—
205C22×Dic7C2×Q812yes—
206C22×Dic7C2×Q812yes—
207C22×Dic7#4112yes—
208C22×Dic7#4112yes—
209C7×C4⋊C4—28no—
210C7×C4⋊C4—28no—
211C7×C22⋊C4—48no—
212C22⋊Dic7—28no—
213C22⋊Dic7—28no—
214C22⋊Dic7—48no—
215C4⋊Dic7—28no—
216C4⋊Dic7—48no—
217C4⋊Dic7—44no—
218C4×Dic7—28no—
219C4×Dic7—48no—
220C4×Dic7—44no—
221C24×C4C2×D711yescharacteristic
222C22×C4⋊C4—71no—
223C22×C4⋊C4—71no—
224C22×C4⋊C4—72no—
225C22×C4⋊C4C2×D711yescharacteristic
226C22×C4⋊C4C2×D711yescharacteristic
227C22×C22⋊C4—71no—
228C22×C22⋊C4—71no—
229C22×C22⋊C4—72no—
230C22×C22⋊C4C2×D712yes—
231C22×C42—71no—
232C22×C42—71no—
233C22×C42—72no—
234#389—144no—
235#380—144no—
236#380Dic718yescomplemented
237C4×C4⋊C4—144no—
238C4×C22⋊C4—144no—
239C2×#95—71no—
240C2×#95—72no—
241C2×#95—72no—
242C2×#95—72no—
243C2×#95—72no—
244C2×#95—71no—
245C2×#95—72no—
246C2×#95—72no—
247C2×#95—72no—
248C2×#95C2×D712yes—
249C23×C7—22no—
250C23×C7—22no—
251C23×C7—22no—
252C23×C7—22no—
253C23×C7—22no—
254C23×C7—22no—
255C23×C7—22no—
256C23×C7—22no—
257C23×C7—22no—
258C23×C7—22no—
259C23×C7—22no—
260C23×C7—22no—
261C23×C7—22no—
262C23×C7—22no—
263C23×C7—22no—
264C23×C7—22no—
265C23×C7—22no—
266C23×C7—22no—
267C23×C7—41no—
268C23×C7—41no—
269C23×C7—41no—
270C23×C7—41no—
271C23×C7—41no—
272C23×C7—41no—
273C23×C7—41no—
274C23×C7—41no—
275C23×C7—41no—
276C23×C7—41no—
277C23×C7—41no—
278C23×C7—41no—
279C23×C7—41no—
280C23×C7—41no—
281C23×C7—41no—
282C23×C7—41no—
283C23×C7C4×Q814yes—
284C23×C7C23×C411yescharacteristic
285C23×C7C22×D411yescharacteristic
286C23×C7C22×D411yescharacteristic
287C23×C7C22×Q811yescharacteristic
288C23×C7C2×#4111yescharacteristic
289C23×C7C2×#4111yescharacteristic
290C23×C7C2×#4111yescharacteristic
291C23×C7C2×#4111yescharacteristic
292C23×C7C2×#4111yescharacteristic
293C23×C7C2×#4111yescharacteristic
294C23×C7C2×#4111yescharacteristic
295C23×C7H(5,𝔽2)11yescharacteristic
296C23×C7H(5,𝔽2)11yescharacteristic
297C23×C7H(5,𝔽2)11yescharacteristic
298C23×C72−1+411yescharacteristic
299C2×C4×C7—22no—
300C2×C4×C7—24no—
301C2×C4×C7—24no—
302C2×C4×C7—22no—
303C2×C4×C7—22no—
304C2×C4×C7—24no—
305C2×C4×C7—24no—
306C2×C4×C7—24no—
307C2×C4×C7—24no—
308C2×C4×C7—41no—
309C2×C4×C7—41no—
310C2×C4×C7—41no—
311C2×C4×C7—41no—
312C2×C4×C7—42no—
313C2×C4×C7—42no—
314C2×C4×C7—42no—
315C2×C4×C7—42no—
316C2×C4×C7—42no—
317C2×C4×C7—42no—
318C2×C4×C7—42no—
319C2×C4×C7—42no—
320C2×C4×C7—416no—
321C2×C4×C7#11714yes—
322C2×C4×C7C4×D414yes—
323C2×C4×C7C4×D414yes—
324C2×C4×C7#12114yes—
325C2×C4×C7#12314yes—
326C2×C4×C7#12414yes—
327C2×C4×C7#12614yes—
328C2×Dic7—22no—
329C2×Dic7—22no—
330C2×Dic7—22no—
331C2×Dic7—22no—
332C2×Dic7—22no—
333C2×Dic7—22no—
334C2×Dic7—22no—
335C2×Dic7—22no—
336C2×Dic7—24no—
337C2×Dic7—22no—
338C2×Dic7—22no—
339C2×Dic7—22no—
340C2×Dic7—24no—
341C2×Dic7—24no—
342C2×Dic7—22no—
343C2×Dic7—22no—
344C2×Dic7—22no—
345C2×Dic7—22no—
346C2×Dic7—41no—
347C2×Dic7—41no—
348C2×Dic7—42no—
349C2×Dic7—41no—
350C2×Dic7—41no—
351C2×Dic7—42no—
352C2×Dic7—41no—
353C2×Dic7—41no—
354C2×Dic7—41no—
355C2×Dic7—41no—
356C2×Dic7—41no—
357C2×Dic7—42no—
358C2×Dic7—41no—
359C2×Dic7—41no—
360C2×Dic7—42no—
361C2×Dic7—41no—
362C2×Dic7—42no—
363C2×Dic7—42no—
364C2×Dic7—42no—
365C2×Dic7—42no—
366C2×Dic7—42no—
367C2×Dic7—42no—
368C2×Dic7—42no—
369C2×Dic7C22⋊Q814yes—
370C25C22×D711yescharacteristic
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—71no—
378C23×C4—71no—
379C23×C4—72no—
380C23×C4—71no—
381C23×C4—71no—
382C23×C4—72no—
383C23×C4C2×Dic714yes—
384C23×C4C22×D712yes—
385C23×C4C22×D712yes—
386C23×C4C22×D711yescharacteristic
387C23×C4C22×D711yescharacteristic
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—74no—
393C2×C4⋊C4—142no—
394C2×C4⋊C4—142no—
395C2×C4⋊C4—144no—
396C2×C4⋊C4—142no—
397C2×C4⋊C4—142no—
398C2×C4⋊C4—142no—
399C2×C4⋊C4—282no—
400C2×C4⋊C4—282no—
401C2×C4⋊C4C2×Dic714yes—
402C2×C4⋊C4C2×Dic714yes—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—74no—
406C2×C22⋊C4—142no—
407C2×C22⋊C4—142no—
408C2×C22⋊C4—142no—
409C2×C22⋊C4—142no—
410C2×C22⋊C4—142no—
411C2×C22⋊C4—144no—
412C2×C22⋊C4—144no—
413C2×C22⋊C4—282no—
414C2×C22⋊C4C2×Dic718yes—
415C2×C42—74no—
416C2×C42—142no—
417C2×C42—142no—
418C2×C42—144no—
419C2×C42—144no—
420C2×C42—142no—
421C2×C42—142no—
422C2×C42—142no—
423C2×C42—282no—
424#95—144no—
425#95—142no—
426#95—142no—
427#95—144no—
428#95—144no—
429#95—144no—
430#95—282no—
431#95—282no—
432#95—282no—
433#95C2×Dic718yes—
434C22×C7—24no—
435C22×C7—24no—
436C22×C7—24no—
437C22×C7—42no—
438C22×C7—42no—
439C22×C7—42no—
440C22×C7—42no—
441C22×C7—42no—
442C22×C7—42no—
443C22×C7—42no—
444C22×C7—42no—
445C22×C7—42no—
446C22×C7—42no—
447C22×C7—42no—
448C22×C7—42no—
449C22×C7C2×#11711yescharacteristic
450C22×C7C2×C4×D411yescharacteristic
451C22×C7C2×C4×D411yescharacteristic
452C22×C7C2×C4×Q811yescharacteristic
453C22×C7C4×#4111yescharacteristic
454C22×C7#51811yescharacteristic
455C22×C7#52011yescharacteristic
456C22×C7C2×#12111yescharacteristic
457C22×C7C2×C22⋊Q811yescharacteristic
458C22×C7C2×#12311yescharacteristic
459C22×C7#52511yescharacteristic
460C22×C7C2×#12411yescharacteristic
461C22×C7C2×#12611yescharacteristic
462C22×C7#52911yescharacteristic
463C22×C7#53311yescharacteristic
464C22×C7#53511yescharacteristic
465C22×C7#53711yescharacteristic
466C22×C7#54011yescharacteristic
467C22×C7#54211yescharacteristic
468C22×C7#54611yescharacteristic
469C22×C7#54611yescharacteristic
470C22×C7D4×Q811yescharacteristic
471C22×C7#55011yescharacteristic
472C22×C7#55211yescharacteristic
473C22×C7#55211yescharacteristic
474C22×C7#55211yescharacteristic
475C22×C7#55311yescharacteristic
476C22×C7#55311yescharacteristic
477C22×C7#55311yescharacteristic
478C22×C7#55411yescharacteristic
479C22×C7#55411yescharacteristic
480C22×C7#55411yescharacteristic
481C22×C7#55511yescharacteristic
482C22×C7#55511yescharacteristic
483C22×C7#55511yescharacteristic
484C4×C7—44no—
485C4×C7—44no—
486C4×C7—42no—
487C4×C7#38818yes—
488Dic7—24no—
489Dic7—42no—
490Dic7—42no—
491Dic7—42no—
492Dic7—44no—
493Dic7—82no—
494C24—21no—
495C24—21no—
496C24—21no—
497C24—21no—
498C24—21no—
499C24—21no—
500C24—21no—
501C24—21no—
502C24—21no—
503C24—21no—
504C24—21no—
505C24—21no—
506C24Q8×D712yes—
507C24#116112yes—
508C24C22×Dic712yes—
509C24C23×D711yescharacteristic
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—28no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—72no—
536C22×C4—72no—
537C22×C4—72no—
538C22×C4—74no—
539C22×C4—72no—
540C22×C4—72no—
541C22×C4—72no—
542C22×C4—141no—
543C22×C4—141no—
544C22×C4—141no—
545C22×C4—141no—
546C22×C4—141no—
547C22×C4—141no—
548C22×C4—141no—
549C22×C4—142no—
550C22×C4—141no—
551C22×C4—141no—
552C22×C4—141no—
553C22×C4—141no—
554C22×C4—141no—
555C22×C4—142no—
556C22×C4—141no—
557C22×C4—141no—
558C22×C4—142no—
559C22×C4—141no—
560C22×C4—141no—
561C22×C4—141no—
562C22×C4—142no—
563C22×C4—142no—
564C22×C4—141no—
565C22×C4—141no—
566C22×C4—141no—
567C22×C4—142no—
568C22×C4—141no—
569C22×C4—141no—
570C22×C4—142no—
571C22×C4—142no—
572C22×C4—142no—
573C22×C4—142no—
574C22×C4—142no—
575C22×C4—142no—
576C22×C4—142no—
577C22×C4#115712yes—
578C22×C4#115712yes—
579C22×C4D4×D712yes—
580C22×C4D4×D712yes—
581C22×C4#115912yes—
582C22×C4#115912yes—
583C22×C4C22×Dic712yes—
584C22×C4C22×Dic714yes—
585C22×C4C22×Dic714yes—
586C22×C4C22×Dic712yes—
587C4⋊C4—28no—
588C4⋊C4—28no—
589C4⋊C4—148no—
590C4⋊C4—288no—
591C4⋊C4—284no—
592C22⋊C4—48no—
593C22⋊C4—148no—
594C22⋊C4—148no—
595C22⋊C4—288no—
596C42—148no—
597C42—288no—
598C42—284no—
599C2×C7—44no—
600C2×C7C2×#38811yescharacteristic
601C2×C7C4×C22⋊Q811yescharacteristic
602C2×C7#232411yescharacteristic
603C2×C7#234511yescharacteristic
604C2×C7#234611yescharacteristic
605C2×C7#236011yescharacteristic
606C2×C7#236311yescharacteristic
607C2×C7#241411yescharacteristic
608C2×C7#241711yescharacteristic
609C2×C7#242011yescharacteristic
610C2×C7#242311yescharacteristic
611C2×C7#249511yescharacteristic
612C2×C7#249711yescharacteristic
613C2×C7#256211yescharacteristic
614C2×C7#256311yescharacteristic
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23Q8×Dic714yes—
650C23C2×#115711yescharacteristic
651C23C2×#115711yescharacteristic
652C23C2×D4×D711yescharacteristic
653C23C2×D4×D711yescharacteristic
654C23C2×#115911yescharacteristic
655C23C2×#115911yescharacteristic
656C23#654811yescharacteristic
657C23#654811yescharacteristic
658C23C2×Q8×D711yescharacteristic
659C23C2×#116111yescharacteristic
660C23D7×#4111yescharacteristic
661C23D7×#4111yescharacteristic
662C23#655311yescharacteristic
663C23#655411yescharacteristic
664C23C23×Dic711yescharacteristic
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—416no—
687C2×C4—74no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—142no—
693C2×C4—142no—
694C2×C4—144no—
695C2×C4—142no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—142no—
699C2×C4—144no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—142no—
703C2×C4—142no—
704C2×C4—144no—
705C2×C4—142no—
706C2×C4—281no—
707C2×C4—281no—
708C2×C4—281no—
709C2×C4—282no—
710C2×C4—281no—
711C2×C4—281no—
712C2×C4—282no—
713C2×C4—281no—
714C2×C4—281no—
715C2×C4—281no—
716C2×C4—281no—
717C2×C4—281no—
718C2×C4—282no—
719C2×C4—282no—
720C2×C4—281no—
721C2×C4—281no—
722C2×C4—282no—
723C2×C4—282no—
724C2×C4—282no—
725C2×C4—282no—
726C2×C4—282no—
727C2×C4—282no—
728C2×C4—282no—
729C2×C4#644214yes—
730C2×C4#644614yes—
731C2×C4#644714yes—
732C2×C4#644814yes—
733C2×C4#648914yes—
734C2×C4D4×Dic714yes—
735C2×C4D4×Dic714yes—
736C7#1397311yescharacteristic, complemented, Sylow
737C22—24no—
738C22—24no—
739C22—24no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22C2×#644211yescharacteristic
753C22C2×#644611yescharacteristic
754C22C2×#644711yescharacteristic
755C22C2×#644811yescharacteristic
756C22#9020211yescharacteristic
757C22#9020211yescharacteristic
758C22#9020511yescharacteristic
759C22#9020511yescharacteristic
760C22#9022011yescharacteristic
761C22#9022011yescharacteristic
762C22#9022311yescharacteristic
763C22#9022311yescharacteristic
764C22#9029011yescharacteristic
765C22#9029411yescharacteristic
766C22#9029811yescharacteristic
767C22#9029911yescharacteristic
768C22#9030311yescharacteristic
769C22#9030511yescharacteristic
770C22#9030711yescharacteristic
771C22#9031011yescharacteristic
772C22#9031311yescharacteristic
773C22#9031511yescharacteristic
774C22D7×C22⋊Q811yescharacteristic
775C22#9031811yescharacteristic
776C22#9032111yescharacteristic
777C22#9032311yescharacteristic
778C22#9032611yescharacteristic
779C22#9033311yescharacteristic
780C22C2×#648911yescharacteristic
781C22C2×D4×Dic711yescharacteristic
782C22C2×D4×Dic711yescharacteristic
783C22#9048911yescharacteristic
784C22C2×Q8×Dic711yescharacteristic
785C22#41×Dic711yescharacteristic
786C22#9051811yescharacteristic
787C4—42no—
788C4—44no—
789C4—44no—
790C4—144no—
791C4—282no—
792C4—284no—
793C4—282no—
794C4—282no—
795C4—562no—
796C4#8972318yes—
797C2—44no—
798C2#1173133311yescharacteristic
799C2#1173133611yescharacteristic
800C2#1173133911yescharacteristic
801C2#1173136511yescharacteristic
802C2#1173136911yescharacteristic
803C2#1173138611yescharacteristic
804C2#1173138711yescharacteristic
805C2#1173146411yescharacteristic
806C2C2×#8972311yescharacteristic
807C2#1173960511yescharacteristic
808C2#1173968411yescharacteristic
809C2#1174007811yescharacteristic
810C2#1174008211yescharacteristic
811C2Dic7×C22⋊Q811yescharacteristic
812C2#1174019211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#380C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#380D7
hypocenterC7#13973
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
4. C2×#89757C2semidirect
5. C2×C4⋊C4×Dic7C2semidirect
6. #11729317C2semidirect
7. #11729317C2semidirect
10. #11727166C2semidirect
11. #11727155C2semidirect
25. C7×#380C4semidirect
236. #380Dic7semidirect
736. C7#13973semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3802
C2×#899842
C2×C4×C22⋊Dic72
C2×#897572
C2×C4⋊C4×Dic72
#117293172
#117293002
#117292992
#117271662
#117271552
#139737