Finite Group Databasebeta

← #13276886

Subgroups — #13276886

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×C4×C7×C22⋊C4C211yesmaximal, characteristic
2C2×#89984C211yesmaximal, characteristic
3C2×#89984C211yesmaximal, characteristic
4C2×#89700C211yesmaximal, characteristic, complemented
5C2×C4×C4⋊Dic7C211yesmaximal, characteristic, complemented
6#11729301C212yesmaximal
7#11729299C212yesmaximal
8#11729289C211yesmaximal, characteristic, complemented
9#11729289C211yesmaximal, characteristic, complemented
10#11727171C212yesmaximal, complemented
11#11727160C212yesmaximal, complemented
12C24×C4×C7C2211yescharacteristic
13C22×C7×C22⋊C4C2211yescharacteristic
14C22×C7×C22⋊C4C2211yescharacteristic
15C22×C42×C7C2211yescharacteristic
16C22×C42×C7C2211yescharacteristic
17C22×C22⋊Dic7C2212yes—
18C22×C22⋊Dic7C2212yes—
19C22×C4⋊Dic7C2211yescharacteristic
20C22×C4⋊Dic7C2211yescharacteristic
21C22×C4⋊Dic7C2211yescharacteristic
22C22×C4⋊Dic7C2211yescharacteristic
23C22×Dic7⋊C4C2212yes—
24C22×C4×Dic7C2212yes—
25C4×C7×C22⋊C4—24no—
26C2×C7×#95C2211yescharacteristic
27C2×C7×#95C2211yescharacteristic
28#89984—24no—
29#89984C418yescomplemented
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38C4×C4⋊Dic7—24no—
39#89700—24no—
40#13993—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×C7C2311yescharacteristic
50C23×C4×C7C2311yescharacteristic
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2311yescharacteristic
53C23×C4×C7C2311yescharacteristic
54C23×C4×C7C2311yescharacteristic
55C23×Dic7C2312yes—
56C23×Dic7C2312yes—
57C23×Dic7C2312yes—
58C23×Dic7C2312yes—
59C2×C7×C22⋊C4—22no—
60C2×C7×C22⋊C4—22no—
61C2×C7×C22⋊C4—22no—
62C2×C7×C22⋊C4—22no—
63C2×C7×C22⋊C4—22no—
64C2×C7×C22⋊C4Q814yes—
65C2×C42×C7—22no—
66C2×C42×C7—22no—
67C2×C42×C7—22no—
68C2×C42×C7—22no—
69C2×C42×C7—22no—
70C2×C42×C7D414yes—
71C2×C22⋊Dic7—24no—
72C2×C22⋊Dic7—24no—
73C2×C22⋊Dic7—42no—
74C2×C22⋊Dic7—42no—
75C2×C22⋊Dic7—42no—
76C2×C22⋊Dic7C2×C418yes—
77C2×C4⋊Dic7—22no—
78C2×C4⋊Dic7—22no—
79C2×C4⋊Dic7—22no—
80C2×C4⋊Dic7—22no—
81C2×C4⋊Dic7—22no—
82C2×C4⋊Dic7—22no—
83C2×C4⋊Dic7—22no—
84C2×C4⋊Dic7—22no—
85C2×C4⋊Dic7—22no—
86C2×C4⋊Dic7C2×C414yes—
87C2×C4⋊Dic7C2×C414yes—
88C2×C4⋊Dic7D414yes—
89C2×Dic7⋊C4—24no—
90C2×Dic7⋊C4—24no—
91C2×Dic7⋊C4—42no—
92C2×C4×Dic7—24no—
93C2×C4×Dic7—42no—
94C2×C4×Dic7—42no—
95C7×#95—22no—
96C7×#95—22no—
97C7⋊#95—24no—
98C7⋊#95—24no—
99C7⋊#95—24no—
100C7⋊#95—24no—
101C7⋊#95—42no—
102C7⋊#95—42no—
103C7⋊#95—42no—
104C7⋊#95C2×C418yes—
105C2×#389—71no—
106C2×#380—71no—
107C2×#380—71no—
108C2×C4×C4⋊C4—71no—
109C2×C4×C22⋊C4D711yescharacteristic
110#1443—72no—
111#1439—72no—
112#1437—72no—
113#1436—72no—
114C4⋊#95—71no—
115C4⋊#95—71no—
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—21no—
135C22×C4×C7—21no—
136C22×C4×C7—21no—
137C22×C4×C7—21no—
138C22×C4×C7—21no—
139C22×C4×C7—21no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7—21no—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
160C22×C4×C7—28no—
161C22×C4×C7—28no—
162C22×C4×C7—28no—
163C22×C4×C7—44no—
164C22×C4×C7—44no—
165C22×C4×C7—44no—
166C22×C4×C7—44no—
167C22×C4×C7C22×C412yes—
168C22×C4×C7C22×C412yes—
169C22×C4×C7C2×D412yes—
170C22×C4×C7C2×D412yes—
171C22×C4×C7C2×D412yes—
172C22×C4×C7C2×D412yes—
173C22×C4×C7C2×Q812yes—
174C22×C4×C7C2×Q812yes—
175C22×C4×C7#4112yes—
176C22×C4×C7#4112yes—
177C22×C4×C7#4112yes—
178C22×C4×C7#4112yes—
179C22×C4×C7#4112yes—
180C22×C4×C7#4112yes—
181C22×Dic7—22no—
182C22×Dic7—22no—
183C22×Dic7—22no—
184C22×Dic7—22no—
185C22×Dic7—22no—
186C22×Dic7—22no—
187C22×Dic7—22no—
188C22×Dic7—22no—
189C22×Dic7—22no—
190C22×Dic7—22no—
191C22×Dic7—22no—
192C22×Dic7—22no—
193C22×Dic7—22no—
194C22×Dic7—22no—
195C22×Dic7—22no—
196C22×Dic7—22no—
197C22×Dic7—22no—
198C22×Dic7—22no—
199C22×Dic7—22no—
200C22×Dic7—22no—
201C22×Dic7—22no—
202C22×Dic7—22no—
203C22×Dic7—22no—
204C22×Dic7—22no—
205C22×Dic7—22no—
206C22×Dic7C22×C414yes—
207C22×Dic7C22×C414yes—
208C22×Dic7C2×D414yes—
209C7×C22⋊C4—28no—
210C7×C22⋊C4—28no—
211C42×C7—28no—
212C42×C7—44no—
213C22⋊Dic7—48no—
214C22⋊Dic7—48no—
215C4⋊Dic7—28no—
216C4⋊Dic7—28no—
217C4⋊Dic7—28no—
218C4⋊Dic7—44no—
219Dic7⋊C4—48no—
220C4×Dic7—48no—
221C24×C4C2×D711yescharacteristic
222C22×C4⋊C4—71no—
223C22×C4⋊C4—71no—
224C22×C4⋊C4—71no—
225C22×C4⋊C4—71no—
226C22×C4⋊C4—72no—
227C22×C22⋊C4—72no—
228C22×C22⋊C4—72no—
229C22×C22⋊C4C2×D711yescharacteristic
230C22×C22⋊C4C2×D711yescharacteristic
231C22×C42—72no—
232C22×C42C2×D711yescharacteristic
233C22×C42C2×D711yescharacteristic
234#389—144no—
235#380—78no—
236#380—144no—
237C4×C4⋊C4—144no—
238C4×C22⋊C4—24no—
239C2×#95—72no—
240C2×#95—72no—
241C2×#95—72no—
242C2×#95—72no—
243C2×#95—72no—
244C2×#95—72no—
245C2×#95—72no—
246C2×#95—72no—
247C2×#95C2×D711yescharacteristic
248C2×#95C2×D711yescharacteristic
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—22no—
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—22no—
308C2×C4×C7—22no—
309C2×C4×C7—22no—
310C2×C4×C7—22no—
311C2×C4×C7—22no—
312C2×C4×C7—22no—
313C2×C4×C7—22no—
314C2×C4×C7—22no—
315C2×C4×C7—22no—
316C2×C4×C7—22no—
317C2×C4×C7—41no—
318C2×C4×C7—41no—
319C2×C4×C7—41no—
320C2×C4×C7—41no—
321C2×C4×C7—41no—
322C2×C4×C7—41no—
323C2×C4×C7—41no—
324C2×C4×C7—41no—
325C2×C4×C7—41no—
326C2×C4×C7—41no—
327C2×C4×C7—41no—
328C2×C4×C7—41no—
329C2×C4×C7—41no—
330C2×C4×C7—41no—
331C2×C4×C7—41no—
332C2×C4×C7—41no—
333C2×C4×C7—416no—
334C2×C4×C7#11714yes—
335C2×C4×C7C4×D414yes—
336C2×C4×C7C4×D414yes—
337C2×C4×C7#12114yes—
338C2×C4×C7C22⋊Q814yes—
339C2×C4×C7#12314yes—
340C2×C4×C7#12414yes—
341C2×C4×C7#12614yes—
342C2×Dic7—24no—
343C2×Dic7—24no—
344C2×Dic7—24no—
345C2×Dic7—24no—
346C2×Dic7—24no—
347C2×Dic7—24no—
348C2×Dic7—24no—
349C2×Dic7—24no—
350C2×Dic7—24no—
351C2×Dic7—42no—
352C2×Dic7—42no—
353C2×Dic7—42no—
354C2×Dic7—42no—
355C2×Dic7—42no—
356C2×Dic7—42no—
357C2×Dic7—42no—
358C2×Dic7—42no—
359C2×Dic7—42no—
360C2×Dic7—42no—
361C2×Dic7—42no—
362C2×Dic7—42no—
363C2×Dic7—42no—
364C2×Dic7—42no—
365C2×Dic7—42no—
366C2×Dic7—42no—
367C2×Dic7—42no—
368C2×Dic7—42no—
369C2×Dic7—42no—
370C25C22×D711yescharacteristic
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—72no—
378C23×C4—72no—
379C23×C4—72no—
380C23×C4—72no—
381C23×C4C4×D714yes—
382C23×C4C22×D711yescharacteristic
383C23×C4C22×D711yescharacteristic
384C23×C4C22×D711yescharacteristic
385C23×C4C22×D711yescharacteristic
386C23×C4C22×D711yescharacteristic
387C23×C4C22×D711yescharacteristic
388C2×C4⋊C4—74no—
389C2×C4⋊C4—74no—
390C2×C4⋊C4—74no—
391C2×C4⋊C4—142no—
392C2×C4⋊C4—142no—
393C2×C4⋊C4—142no—
394C2×C4⋊C4—142no—
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×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—78no—
409C2×C22⋊C4—144no—
410C2×C22⋊C4—144no—
411C2×C22⋊C4—282no—
412C2×C22⋊C4—282no—
413C2×C22⋊C4—282no—
414C2×C22⋊C4Dic1414yes—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—144no—
421C2×C42—282no—
422C2×C42—282no—
423C2×C42C22⋊D714yes—
424#95—22no—
425#95—22no—
426#95—78no—
427#95—144no—
428#95—144no—
429#95—144no—
430#95—144no—
431#95—282no—
432#95—282no—
433#95—282no—
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#55311yescharacteristic
474C22×C7#55311yescharacteristic
475C22×C7#55311yescharacteristic
476C22×C7#55311yescharacteristic
477C22×C7#55311yescharacteristic
478C22×C7#55411yescharacteristic
479C22×C7#55411yescharacteristic
480C22×C7#55411yescharacteristic
481C22×C7#55511yescharacteristic
482C22×C7#55611yescharacteristic
483C22×C7#55611yescharacteristic
484C4×C7—24no—
485C4×C7—42no—
486C4×C7—42no—
487C4×C7—42no—
488C4×C7—42no—
489C4×C7#38818yes—
490Dic7—44no—
491Dic7—44no—
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—
506C24C2×Dic1412yes—
507C24C2×C4×D712yes—
508C24#115712yes—
509C24C23×D711yescharacteristic
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—74no—
546C22×C4—74no—
547C22×C4—74no—
548C22×C4—142no—
549C22×C4—142no—
550C22×C4—142no—
551C22×C4—142no—
552C22×C4—142no—
553C22×C4—142no—
554C22×C4—142no—
555C22×C4—142no—
556C22×C4—142no—
557C22×C4—142no—
558C22×C4—142no—
559C22×C4—142no—
560C22×C4—142no—
561C22×C4—142no—
562C22×C4—142no—
563C22×C4—142no—
564C22×C4—142no—
565C22×C4—142no—
566C22×C4—142no—
567C22×C4—142no—
568C22×C4—142no—
569C22×C4—142no—
570C22×C4—142no—
571C22×C4—142no—
572C22×C4—142no—
573C22×C4C2×Dic1412yes—
574C22×C4C2×Dic1412yes—
575C22×C4C2×C4×D712yes—
576C22×C4C2×C4×D712yes—
577C22×C4#115712yes—
578C22×C4#115712yes—
579C22×C4#115712yes—
580C22×C4D4×D712yes—
581C22×C4#115912yes—
582C22×C4#115912yes—
583C22×C4#115912yes—
584C22×C4C2×C22⋊D712yes—
585C22×C4C2×C22⋊D712yes—
586C22×C4C2×C22⋊D712yes—
587C4⋊C4—148no—
588C4⋊C4—148no—
589C4⋊C4—148no—
590C4⋊C4—288no—
591C4⋊C4—284no—
592C22⋊C4—28no—
593C22⋊C4—28no—
594C22⋊C4—288no—
595C22⋊C4—288no—
596C42—28no—
597C42—44no—
598C42—288no—
599C2×C7—44no—
600C2×C7C2×#38811yescharacteristic
601C2×C7C4×C22⋊Q811yescharacteristic
602C2×C7#232411yescharacteristic
603C2×C7#234511yescharacteristic
604C2×C7#234711yescharacteristic
605C2×C7#236011yescharacteristic
606C2×C7#236311yescharacteristic
607C2×C7#248511yescharacteristic
608C2×C7#248711yescharacteristic
609C2×C7#249011yescharacteristic
610C2×C7#249211yescharacteristic
611C2×C7#249411yescharacteristic
612C2×C7#249711yescharacteristic
613C2×C7#253511yescharacteristic
614C2×C7#253811yescharacteristic
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—
649C23C4×Dic1414yes—
650C23C22×Dic1411yescharacteristic
651C23C22×C4×D711yescharacteristic
652C23C2×#115711yescharacteristic
653C23C2×#115711yescharacteristic
654C23C2×#115711yescharacteristic
655C23C2×#115711yescharacteristic
656C23C2×D4×D711yescharacteristic
657C23C2×#115911yescharacteristic
658C23C2×#115911yescharacteristic
659C23C2×#115911yescharacteristic
660C23#655311yescharacteristic
661C23#655311yescharacteristic
662C23#655311yescharacteristic
663C23#655411yescharacteristic
664C23C22×C22⋊D711yescharacteristic
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—416no—
700C2×C4—144no—
701C2×C4—144no—
702C2×C4—144no—
703C2×C4—144no—
704C2×C4—144no—
705C2×C4—144no—
706C2×C4—144no—
707C2×C4—144no—
708C2×C4—144no—
709C2×C4—282no—
710C2×C4—282no—
711C2×C4—282no—
712C2×C4—282no—
713C2×C4—282no—
714C2×C4—282no—
715C2×C4—282no—
716C2×C4—282no—
717C2×C4—282no—
718C2×C4—282no—
719C2×C4—282no—
720C2×C4—282no—
721C2×C4—282no—
722C2×C4—282no—
723C2×C4—282no—
724C2×C4—282no—
725C2×C4—282no—
726C2×C4—282no—
727C2×C4—282no—
728C2×C4#644014yes—
729C2×C4#644214yes—
730C2×C4(C22⋊D7)⋊C414yes—
731C2×C4#644814yes—
732C2×C4#648714yes—
733C2×C4C4×C22⋊D714yes—
734C2×C4#649814yes—
735C2×C4#650114yes—
736C7#1399311yescharacteristic, 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×C4×Dic1411yescharacteristic
753C22#9016111yescharacteristic
754C22C4×#115711yescharacteristic
755C22#9017011yescharacteristic
756C22C2×#644011yescharacteristic
757C22C2×#644211yescharacteristic
758C22C2×(C22⋊D7)⋊C411yescharacteristic
759C22C2×#644811yescharacteristic
760C22#9021211yescharacteristic
761C22#9021411yescharacteristic
762C22#9022511yescharacteristic
763C22#9022611yescharacteristic
764C22D4×Dic1411yescharacteristic
765C22#9023211yescharacteristic
766C22#9023311yescharacteristic
767C22#9023311yescharacteristic
768C22#9023411yescharacteristic
769C22#9023411yescharacteristic
770C22#9023411yescharacteristic
771C22#9024111yescharacteristic
772C22#9024111yescharacteristic
773C22#9024411yescharacteristic
774C22#9025411yescharacteristic
775C22#9025611yescharacteristic
776C22#9025611yescharacteristic
777C22#9025611yescharacteristic
778C22#9025611yescharacteristic
779C22#9025611yescharacteristic
780C22C2×#648711yescharacteristic
781C22C2×C4×C22⋊D711yescharacteristic
782C22#9048211yescharacteristic
783C22C2×#649811yescharacteristic
784C22C2×#650111yescharacteristic
785C22#9052111yescharacteristic
786C22#9052411yescharacteristic
787C4—24no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—42no—
792C4—284no—
793C4—284no—
794C4—284no—
795C4—562no—
796C4#8971618yes—
797C2—44no—
798C2#1173090211yescharacteristic
799C2#1173090511yescharacteristic
800C2#1173091011yescharacteristic
801C2#1173091411yescharacteristic
802C2#1173095111yescharacteristic
803C2#1173095311yescharacteristic
804C2#1173095511yescharacteristic
805C2#1173095811yescharacteristic
806C2C4×#648711yescharacteristic
807C2C2×#8971611yescharacteristic
808C2#1173968111yescharacteristic
809C2#1173981711yescharacteristic
810C2#1173981911yescharacteristic
811C2#1173982111yescharacteristic
812C2#1173986011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C4×C7×C22⋊C4C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×C4×C22⋊C4D7
hypocenterC7#13993
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#89700C2semidirect
5. C2×C4×C4⋊Dic7C2semidirect
8. #11729289C2semidirect
9. #11729289C2semidirect
10. #11727171C2semidirect
11. #11727160C2semidirect
29. #89984C4semidirect
736. C7#13993semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C7×C22⋊C42
C2×#899842
C2×#897002
C2×C4×C4⋊Dic72
#117293012
#117292992
#117292892
#117271712
#117271602
#139937