Finite Group Databasebeta

← #13276884

Subgroups — #13276884

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×#389C211yesmaximal, characteristic, complemented
2C2×#89759C211yesmaximal, characteristic
3C2×#89759C211yesmaximal, characteristic
4C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic
6#11729324C212yesmaximal
7#11729318C212yesmaximal, complemented
8#11729317C211yesmaximal, characteristic, complemented
9#11729289C211yesmaximal, characteristic, complemented
10#11727171C212yesmaximal, complemented
11#11727162C212yesmaximal
12C23×C4×D7C2211yescharacteristic
13C22×C7×C4⋊C4C2212yes—
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C42×C7C2211yescharacteristic
17C22×(C2×D7)⋊C4C2211yescharacteristic
18C22×(C2×D7)⋊C4C2212yes—
19C22×(C2×D7)⋊C4C2211yescharacteristic
20C22×(C2×D7)⋊C4C2212yes—
21C22×C4⋊Dic7C2211yescharacteristic
22C22×C4⋊Dic7C2211yescharacteristic
23C22×C4×Dic7C2211yescharacteristic
24C22×C4×Dic7C2212yes—
25C7×#389—24no—
26C2×C7×#95C2212yes—
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2211yescharacteristic
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2211yescharacteristic
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36#89759—24no—
37#89759C418yescomplemented
38C4⋊C4×Dic7—24no—
39C4×(C2×D7)⋊C4—24no—
40#13993—71nomaximal, Sylow
41C24×D7C2311yescharacteristic
42C23×C4×C7C2312yes—
43C23×C4×C7C2312yes—
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2311yescharacteristic
47C23×Dic7C2312yes—
48C23×Dic7C2312yes—
49C23×Dic7C2311yescharacteristic
50C23×Dic7C2311yescharacteristic
51C23×Dic7C2311yescharacteristic
52C22×C4×D7—22no—
53C22×C4×D7—22no—
54C22×C4×D7—22no—
55C22×C4×D7—22no—
56C22×C4×D7—22no—
57C22×C4×D7—22no—
58C22×C4×D7C2×C414yes—
59C2×C7×C4⋊C4—22no—
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—24no—
64C2×C7×C4⋊C4—24no—
65C2×C7×C4⋊C4—42no—
66C2×C7×C4⋊C4C2×C414yes—
67C2×C7×C4⋊C4D414yes—
68C2×C42×C7—22no—
69C2×C42×C7—22no—
70C2×C42×C7—22no—
71C2×(C2×D7)⋊C4—22no—
72C2×(C2×D7)⋊C4—22no—
73C2×(C2×D7)⋊C4—22no—
74C2×(C2×D7)⋊C4—22no—
75C2×(C2×D7)⋊C4—22no—
76C2×(C2×D7)⋊C4—24no—
77C2×(C2×D7)⋊C4—24no—
78C2×(C2×D7)⋊C4—42no—
79C2×(C2×D7)⋊C4—42no—
80C2×(C2×D7)⋊C4—42no—
81C2×(C2×D7)⋊C4C2×C418yes—
82C2×(C2×D7)⋊C4Q814yes—
83C2×C4⋊Dic7—22no—
84C2×C4⋊Dic7—22no—
85C2×C4⋊Dic7—22no—
86C2×C4⋊Dic7—22no—
87C2×C4⋊Dic7—22no—
88C2×C4⋊Dic7C2×C414yes—
89C2×C4×Dic7—22no—
90C2×C4×Dic7—22no—
91C2×C4×Dic7—24no—
92C2×C4×Dic7—42no—
93C2×C4×Dic7—42no—
94C2×C4×Dic7D414yes—
95C7×#95—24no—
96C7⋊#95—24no—
97C7⋊#95—22no—
98C7⋊#95—22no—
99C7⋊#95—24no—
100C7⋊#95—24no—
101C7⋊#95—42no—
102C7⋊#95—42no—
103C7⋊#95—42no—
104C7⋊#95C2×C418yes—
105C2×#389D711yescharacteristic, complemented
106C2×#380—71no—
107C2×#380—71no—
108C2×C4×C4⋊C4—71no—
109C2×C4×C22⋊C4—71no—
110#1443—72no—
111#1439—72no—
112#1437—72no—
113#1436—72no—
114C4⋊#95—71no—
115C4⋊#95—71no—
116C24×C7C2411yescharacteristic
117C23×D7—21no—
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×D7C22×C412yes—
130C23×D7C2×Q812yes—
131C23×D7#4112yes—
132C22×C4×C7—22no—
133C22×C4×C7—21no—
134C22×C4×C7—21no—
135C22×C4×C7—21no—
136C22×C4×C7—22no—
137C22×C4×C7—21no—
138C22×C4×C7—22no—
139C22×C4×C7—21no—
140C22×C4×C7—21no—
141C22×C4×C7—22no—
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—21no—
149C22×C4×C7—21no—
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7C22×C414yes—
157C22×C4×C7C22×C412yes—
158C22×C4×C7C2×D414yes—
159C22×C4×C7C2×D412yes—
160C22×C4×C7C2×D412yes—
161C22×C4×C7C2×Q812yes—
162C22×C4×C7#4112yes—
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—22no—
174C22×Dic7—21no—
175C22×Dic7—21no—
176C22×Dic7—22no—
177C22×Dic7—21no—
178C22×Dic7—21no—
179C22×Dic7—21no—
180C22×Dic7—21no—
181C22×Dic7—21no—
182C22×Dic7—21no—
183C22×Dic7—21no—
184C22×Dic7—22no—
185C22×Dic7—22no—
186C22×Dic7—22no—
187C22×Dic7—22no—
188C22×Dic7—21no—
189C22×Dic7—22no—
190C22×Dic7—22no—
191C22×Dic7—22no—
192C22×Dic7—22no—
193C22×Dic7—22no—
194C22×Dic7—22no—
195C22×Dic7—22no—
196C22×Dic7C22×C412yes—
197C22×Dic7C22×C414yes—
198C22×Dic7C2×D412yes—
199C22×Dic7C2×D412yes—
200C22×Dic7C2×Q812yes—
201C22×Dic7#4112yes—
202C2×C4×D7—28no—
203C2×C4×D7—28no—
204C2×C4×D7—28no—
205C2×C4×D7—44no—
206C2×C4×D7—44no—
207C2×C4×D7—44no—
208C2×C4×D7—44no—
209C7×C4⋊C4—28no—
210C7×C4⋊C4—28no—
211C7×C4⋊C4—48no—
212C42×C7—44no—
213(C2×D7)⋊C4—28no—
214(C2×D7)⋊C4—28no—
215(C2×D7)⋊C4—48no—
216(C2×D7)⋊C4—48no—
217C4⋊Dic7—28no—
218C4⋊Dic7—44no—
219C4×Dic7—28no—
220C4×Dic7—48no—
221C24×C4—71no—
222C22×C4⋊C4—71no—
223C22×C4⋊C4—71no—
224C22×C4⋊C4C2×D712yes—
225C22×C4⋊C4C2×D711yescharacteristic
226C22×C4⋊C4C2×D711yescharacteristic
227C22×C22⋊C4—71no—
228C22×C22⋊C4—72no—
229C22×C22⋊C4—71no—
230C22×C22⋊C4—72no—
231C22×C42—71no—
232C22×C42—72no—
233C22×C42C2×D711yescharacteristic
234#389—24no—
235#380—78no—
236#380—144no—
237C4×C4⋊C4—144no—
238C4×C22⋊C4—144no—
239C2×#95—72no—
240C2×#95—72no—
241C2×#95—71no—
242C2×#95—72no—
243C2×#95—72no—
244C2×#95—71no—
245C2×#95—72no—
246C2×#95—72no—
247C2×#95—72no—
248C2×#95C2×D712yes—
249C23×C7C23×C411yescharacteristic
250C23×C7C22×D411yescharacteristic
251C23×C7C22×D411yescharacteristic
252C23×C7C22×Q811yescharacteristic
253C23×C7C2×#4111yescharacteristic
254C23×C7C2×#4111yescharacteristic
255C23×C7C2×#4111yescharacteristic
256C23×C7C2×#4111yescharacteristic
257C23×C7C2×#4111yescharacteristic
258C23×C7C2×#4111yescharacteristic
259C23×C7C2×#4111yescharacteristic
260C23×C7H(5,𝔽2)11yescharacteristic
261C23×C7H(5,𝔽2)11yescharacteristic
262C23×C7H(5,𝔽2)11yescharacteristic
263C23×C72−1+411yescharacteristic
264C22×D7—22no—
265C22×D7—22no—
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—41no—
283C22×D7—41no—
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×D7C4×Q814yes—
299C2×C4×C7—24no—
300C2×C4×C7—24no—
301C2×C4×C7—24no—
302C2×C4×C7—24no—
303C2×C4×C7—22no—
304C2×C4×C7—22no—
305C2×C4×C7—24no—
306C2×C4×C7—22no—
307C2×C4×C7—24no—
308C2×C4×C7—22no—
309C2×C4×C7—22no—
310C2×C4×C7—22no—
311C2×C4×C7—41no—
312C2×C4×C7—41no—
313C2×C4×C7—42no—
314C2×C4×C7—42no—
315C2×C4×C7—41no—
316C2×C4×C7—41no—
317C2×C4×C7—42no—
318C2×C4×C7—41no—
319C2×C4×C7—42no—
320C2×C4×C7—41no—
321C2×C4×C7—42no—
322C2×C4×C7—41no—
323C2×C4×C7—42no—
324C2×C4×C7—42no—
325C2×C4×C7—42no—
326C2×C4×C7—41no—
327C2×C4×C7#11714yes—
328C2×C4×C7C4×D414yes—
329C2×C4×C7C4×D414yes—
330C2×C4×C7#12114yes—
331C2×C4×C7#12314yes—
332C2×C4×C7#12414yes—
333C2×C4×C7#12614yes—
334C2×Dic7—22no—
335C2×Dic7—22no—
336C2×Dic7—22no—
337C2×Dic7—22no—
338C2×Dic7—22no—
339C2×Dic7—22no—
340C2×Dic7—22no—
341C2×Dic7—24no—
342C2×Dic7—22no—
343C2×Dic7—22no—
344C2×Dic7—24no—
345C2×Dic7—24no—
346C2×Dic7—22no—
347C2×Dic7—22no—
348C2×Dic7—22no—
349C2×Dic7—41no—
350C2×Dic7—41no—
351C2×Dic7—41no—
352C2×Dic7—41no—
353C2×Dic7—42no—
354C2×Dic7—42no—
355C2×Dic7—42no—
356C2×Dic7—42no—
357C2×Dic7—41no—
358C2×Dic7—41no—
359C2×Dic7—41no—
360C2×Dic7—41no—
361C2×Dic7—42no—
362C2×Dic7—42no—
363C2×Dic7—42no—
364C2×Dic7—42no—
365C2×Dic7—42no—
366C2×Dic7—42no—
367C2×Dic7—42no—
368C2×Dic7C22⋊Q814yes—
369C4×D7—416no—
370C25—71no—
371C23×C4—71no—
372C23×C4—72no—
373C23×C4—71no—
374C23×C4—71no—
375C23×C4—74no—
376C23×C4—72no—
377C23×C4—142no—
378C23×C4—142no—
379C23×C4—142no—
380C23×C4—142no—
381C23×C4—142no—
382C23×C4—142no—
383C23×C4C22×D712yes—
384C23×C4C22×D711yescharacteristic
385C23×C4C22×D711yescharacteristic
386C23×C4C22×D712yes—
387C23×C4C22×D711yescharacteristic
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4—74no—
396C2×C4⋊C4—142no—
397C2×C4⋊C4—142no—
398C2×C4⋊C4—142no—
399C2×C4⋊C4—142no—
400C2×C4⋊C4—142no—
401C2×C4⋊C4C4×D714yes—
402C2×C4⋊C4C22⋊D714yes—
403C2×C22⋊C4—74no—
404C2×C22⋊C4—78no—
405C2×C22⋊C4—142no—
406C2×C22⋊C4—142no—
407C2×C22⋊C4—142no—
408C2×C22⋊C4—142no—
409C2×C22⋊C4—142no—
410C2×C22⋊C4—144no—
411C2×C22⋊C4—144no—
412C2×C22⋊C4—282no—
413C2×C22⋊C4—282no—
414C2×C22⋊C4—282no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—74no—
419C2×C42—142no—
420C2×C42—142no—
421C2×C42—144no—
422C2×C42—282no—
423C2×C42—282no—
424#95—24no—
425#95—78no—
426#95—144no—
427#95—142no—
428#95—142no—
429#95—144no—
430#95—144no—
431#95—282no—
432#95—282no—
433#95—282no—
434C22×C7C2×#11711yescharacteristic
435C22×C7C2×C4×D411yescharacteristic
436C22×C7C2×C4×D411yescharacteristic
437C22×C7C2×C4×Q811yescharacteristic
438C22×C7C4×#4111yescharacteristic
439C22×C7#51811yescharacteristic
440C22×C7#52011yescharacteristic
441C22×C7C2×#12111yescharacteristic
442C22×C7C2×C22⋊Q811yescharacteristic
443C22×C7C2×#12311yescharacteristic
444C22×C7#52511yescharacteristic
445C22×C7C2×#12411yescharacteristic
446C22×C7C2×#12611yescharacteristic
447C22×C7#52911yescharacteristic
448C22×C7#53311yescharacteristic
449C22×C7#53511yescharacteristic
450C22×C7#53711yescharacteristic
451C22×C7#54011yescharacteristic
452C22×C7#54211yescharacteristic
453C22×C7#54611yescharacteristic
454C22×C7#54611yescharacteristic
455C22×C7D4×Q811yescharacteristic
456C22×C7#55011yescharacteristic
457C22×C7#55211yescharacteristic
458C22×C7#55311yescharacteristic
459C22×C7#55311yescharacteristic
460C22×C7#55311yescharacteristic
461C22×C7#55311yescharacteristic
462C22×C7#55311yescharacteristic
463C22×C7#55411yescharacteristic
464C22×C7#55411yescharacteristic
465C22×C7#55411yescharacteristic
466C22×C7#55511yescharacteristic
467C22×C7#55611yescharacteristic
468C22×C7#55611yescharacteristic
469C2×D7—24no—
470C2×D7—24no—
471C2×D7—24no—
472C2×D7—42no—
473C2×D7—42no—
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—
484C4×C7—44no—
485C4×C7—44no—
486C4×C7—42no—
487C4×C7—42no—
488C4×C7#38818yes—
489Dic7—24no—
490Dic7—44no—
491Dic7—42no—
492Dic7—42no—
493Dic7—82no—
494C24—72no—
495C24—72no—
496C24—72no—
497C24—141no—
498C24—141no—
499C24—141no—
500C24—141no—
501C24—141no—
502C24—141no—
503C24—141no—
504C24—141no—
505C24—141no—
506C24—141no—
507C24—141no—
508C24—141no—
509C24C23×D711yescharacteristic
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—72no—
535C22×C4—72no—
536C22×C4—72no—
537C22×C4—72no—
538C22×C4—74no—
539C22×C4—72no—
540C22×C4—141no—
541C22×C4—141no—
542C22×C4—141no—
543C22×C4—141no—
544C22×C4—141no—
545C22×C4—141no—
546C22×C4—141no—
547C22×C4—142no—
548C22×C4—141no—
549C22×C4—141no—
550C22×C4—142no—
551C22×C4—141no—
552C22×C4—142no—
553C22×C4—141no—
554C22×C4—141no—
555C22×C4—142no—
556C22×C4—141no—
557C22×C4—141no—
558C22×C4—141no—
559C22×C4—142no—
560C22×C4—142no—
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×C4#115712yes—
579C22×C4D4×D712yes—
580C22×C4#115912yes—
581C22×C4#115912yes—
582C22×C4Q8×D712yes—
583C22×C4#116112yes—
584C22×C4#116112yes—
585C22×C4C2×C22⋊D714yes—
586C22×C4C2×C22⋊D712yes—
587C4⋊C4—28no—
588C4⋊C4—28no—
589C4⋊C4—48no—
590C4⋊C4—148no—
591C4⋊C4—284no—
592C22⋊C4—148no—
593C22⋊C4—148no—
594C22⋊C4—288no—
595C22⋊C4—288no—
596C42—44no—
597C42—148no—
598C42—288no—
599C2×C7C2×#38811yescharacteristic
600C2×C7C4×C22⋊Q811yescharacteristic
601C2×C7#232411yescharacteristic
602C2×C7#234511yescharacteristic
603C2×C7#234711yescharacteristic
604C2×C7#236011yescharacteristic
605C2×C7#236311yescharacteristic
606C2×C7#248511yescharacteristic
607C2×C7#248711yescharacteristic
608C2×C7#249011yescharacteristic
609C2×C7#249211yescharacteristic
610C2×C7#249411yescharacteristic
611C2×C7#249711yescharacteristic
612C2×C7#253511yescharacteristic
613C2×C7#253811yescharacteristic
614D7—44no—
615C23—74no—
616C23—142no—
617C23—142no—
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—281no—
635C23—281no—
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—
650C23C22×C4×D711yescharacteristic
651C23C2×#115711yescharacteristic
652C23C2×D4×D711yescharacteristic
653C23C2×#115911yescharacteristic
654C23C2×#115911yescharacteristic
655C23#654811yescharacteristic
656C23C2×Q8×D711yescharacteristic
657C23C2×#116111yescharacteristic
658C23C2×#116111yescharacteristic
659C23#655111yescharacteristic
660C23D7×#4111yescharacteristic
661C23D7×#4111yescharacteristic
662C23#655311yescharacteristic
663C23#655311yescharacteristic
664C23C22×C22⋊D711yescharacteristic
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—74no—
694C2×C4—142no—
695C2×C4—142no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—142no—
699C2×C4—142no—
700C2×C4—142no—
701C2×C4—144no—
702C2×C4—142no—
703C2×C4—142no—
704C2×C4—142no—
705C2×C4—144no—
706C2×C4—144no—
707C2×C4—142no—
708C2×C4—142no—
709C2×C4—281no—
710C2×C4—282no—
711C2×C4—281no—
712C2×C4—282no—
713C2×C4—281no—
714C2×C4—281no—
715C2×C4—281no—
716C2×C4—281no—
717C2×C4—281no—
718C2×C4—281no—
719C2×C4—282no—
720C2×C4—282no—
721C2×C4—2816no—
722C2×C4—282no—
723C2×C4—282no—
724C2×C4—282no—
725C2×C4—282no—
726C2×C4—282no—
727C2×C4—282no—
728C2×C4—282no—
729C2×C4#645514yes—
730C2×C4#645614yes—
731C2×C4#645714yes—
732C2×C4#646114yes—
733C2×C4C4×C22⋊D714yes—
734C2×C4#650214yes—
735C2×C4#651014yes—
736C7#1399311yescharacteristic, complemented, Sylow
737C22—144no—
738C22—144no—
739C22—144no—
740C22—282no—
741C22—282no—
742C22—282no—
743C22—282no—
744C22—282no—
745C22—282no—
746C22—282no—
747C22—282no—
748C22—282no—
749C22—282no—
750C22—282no—
751C22—282no—
752C22C2×#645511yescharacteristic
753C22C2×#645611yescharacteristic
754C22C2×#645711yescharacteristic
755C22C2×#646111yescharacteristic
756C22C4×#115911yescharacteristic
757C22#9023611yescharacteristic
758C22#9024911yescharacteristic
759C22#9025411yescharacteristic
760C22C4×Q8×D711yescharacteristic
761C22#9026511yescharacteristic
762C22#9027011yescharacteristic
763C22#9027211yescharacteristic
764C22#9029711yescharacteristic
765C22#9029811yescharacteristic
766C22#9030511yescharacteristic
767C22#9030911yescharacteristic
768C22D7×C22⋊Q811yescharacteristic
769C22#9032011yescharacteristic
770C22#9032611yescharacteristic
771C22#9033211yescharacteristic
772C22#9038211yescharacteristic
773C22#9038611yescharacteristic
774C22#9038611yescharacteristic
775C22#9038911yescharacteristic
776C22#9041911yescharacteristic
777C22#9042111yescharacteristic
778C22#9042311yescharacteristic
779C22#9042411yescharacteristic
780C22C2×C4×C22⋊D711yescharacteristic
781C22C2×#650211yescharacteristic
782C22#9049711yescharacteristic
783C22C2×#651011yescharacteristic
784C22Q8×C22⋊D711yescharacteristic
785C22#9052011yescharacteristic
786C22#9052511yescharacteristic
787C4—42no—
788C4—44no—
789C4—44no—
790C4—42no—
791C4—144no—
792C4—284no—
793C4—282no—
794C4—282no—
795C4—562no—
796C4#8976218yes—
797C2—284no—
798C2#1173341011yescharacteristic
799C2#1173342511yescharacteristic
800C2#1173364311yescharacteristic
801C2#1173364611yescharacteristic
802C2#1173367411yescharacteristic
803C2#1173367711yescharacteristic
804C2#1173367911yescharacteristic
805C2#1173368511yescharacteristic
806C2C2×#8976211yescharacteristic
807C2#1173978611yescharacteristic
808C2#1173993511yescharacteristic
809C2#1174011111yescharacteristic
810C2#1174022311yescharacteristic
811C2#1174050611yescharacteristic
812C2#1174070311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#389C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×#389D7
hypocenterC7#13993
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C2×C7×#389C2semidirect
4. C2×C4⋊C4×Dic7C2semidirect
7. #11729318C2semidirect
8. #11729317C2semidirect
9. #11729289C2semidirect
10. #11727171C2semidirect
37. #89759C4semidirect
105. C2×#389D7semidirect
736. C7#13993semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3892
C2×#897592
C2×C4⋊C4×Dic72
C2×C4×(C2×D7)⋊C42
#117293242
#117293182
#117293172
#117292892
#117271712
#117271622
#139937