Finite Group Databasebeta

← #13276897

Subgroups — #13276897

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×C22⋊C4C211yesmaximal, characteristic
2C2×#89984C211yesmaximal, characteristic
3C2×#89984C211yesmaximal, characteristic
4C2×#89716C212yesmaximal
5C2×#89700C211yesmaximal, characteristic, complemented
6C2×C4×C4⋊Dic7C211yesmaximal, characteristic, complemented
7#11729303C212yesmaximal
8#11729289C211yesmaximal, characteristic, complemented
9#11729289C211yesmaximal, characteristic, complemented
10#11727167C212yesmaximal, complemented
11#11727156C212yesmaximal, 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—
38#89716—28no—
39C4×C4⋊Dic7—24no—
40#89700—24no—
41#13994—71nomaximal, Sylow
42C25×C7C2311yescharacteristic
43C23×C4×C7—22no—
44C23×C4×C7—22no—
45C23×C4×C7—22no—
46C23×C4×C7—22no—
47C23×C4×C7—22no—
48C23×C4×C7—22no—
49C23×C4×C7C2×C414yes—
50C23×C4×C7C2311yescharacteristic
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2311yescharacteristic
53C23×C4×C7C2311yescharacteristic
54C23×C4×C7C2311yescharacteristic
55C23×C4×C7C2311yescharacteristic
56C23×Dic7C2312yes—
57C23×Dic7C2312yes—
58C23×Dic7C2312yes—
59C23×Dic7C2312yes—
60C2×C7×C22⋊C4—22no—
61C2×C7×C22⋊C4—22no—
62C2×C7×C22⋊C4—22no—
63C2×C7×C22⋊C4—22no—
64C2×C7×C22⋊C4—22no—
65C2×C7×C22⋊C4D414yes—
66C2×C42×C7—22no—
67C2×C42×C7—22no—
68C2×C42×C7—22no—
69C2×C42×C7—22no—
70C2×C42×C7—22no—
71C2×C42×C7D414yes—
72C2×C22⋊Dic7—24no—
73C2×C22⋊Dic7—24no—
74C2×C22⋊Dic7—24no—
75C2×C22⋊Dic7—24no—
76C2×C22⋊Dic7—42no—
77C2×C22⋊Dic7C2×C418yes—
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⋊Dic7—22no—
87C2×C4⋊Dic7C2×C414yes—
88C2×C4⋊Dic7C2×C414yes—
89C2×C4⋊Dic7D414yes—
90C2×Dic7⋊C4—24no—
91C2×Dic7⋊C4—24no—
92C2×Dic7⋊C4—42no—
93C2×C4×Dic7—24no—
94C2×C4×Dic7—24no—
95C2×C4×Dic7—24no—
96C7×#95—22no—
97C7×#95—22no—
98C7⋊#95—24no—
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⋊C4—71no—
111C2×C4×C22⋊C4D711yescharacteristic
112#1442—72no—
113#1440—72no—
114C4⋊#95—71no—
115C4⋊#95—71no—
116#1434—72no—
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×C7—21no—
129C24×C7C22×C412yes—
130C24×C7C2×D412yes—
131C24×C7#4112yes—
132C24×C7C2411yescharacteristic
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—21no—
161C22×C4×C7—28no—
162C22×C4×C7—28no—
163C22×C4×C7—28no—
164C22×C4×C7—44no—
165C22×C4×C7—44no—
166C22×C4×C7—44no—
167C22×C4×C7—44no—
168C22×C4×C7C22×C412yes—
169C22×C4×C7C22×C412yes—
170C22×C4×C7C2×D412yes—
171C22×C4×C7C2×D412yes—
172C22×C4×C7C2×D412yes—
173C22×C4×C7C2×D412yes—
174C22×C4×C7C2×D412yes—
175C22×C4×C7C2×D412yes—
176C22×C4×C7#4112yes—
177C22×C4×C7#4112yes—
178C22×C4×C7#4112yes—
179C22×C4×C7#4112yes—
180C22×C4×C7#4112yes—
181C22×C4×C7#4112yes—
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×Dic7—22no—
207C22×Dic7C22×C414yes—
208C22×Dic7C22×C414yes—
209C22×Dic7C2×D414yes—
210C7×C22⋊C4—28no—
211C7×C22⋊C4—28no—
212C42×C7—28no—
213C42×C7—44no—
214C22⋊Dic7—216no—
215C22⋊Dic7—48no—
216C4⋊Dic7—28no—
217C4⋊Dic7—28no—
218C4⋊Dic7—28no—
219C4⋊Dic7—44no—
220Dic7⋊C4—48no—
221C4×Dic7—48no—
222C24×C4C2×D711yescharacteristic
223C22×C4⋊C4—71no—
224C22×C4⋊C4—71no—
225C22×C4⋊C4—71no—
226C22×C4⋊C4—71no—
227C22×C4⋊C4—72no—
228C22×C22⋊C4—72no—
229C22×C22⋊C4—72no—
230C22×C22⋊C4C2×D711yescharacteristic
231C22×C22⋊C4C2×D711yescharacteristic
232C22×C42—72no—
233C22×C42C2×D711yescharacteristic
234C22×C42C2×D711yescharacteristic
235#389—144no—
236#388—148no—
237#380—78no—
238#380—144no—
239C4×C4⋊C4—144no—
240C4×C22⋊C4—24no—
241C2×#95—72no—
242C2×#95—72no—
243C2×#95—72no—
244C2×#95—72no—
245C2×#95—72no—
246C2×#95—72no—
247C2×#95—72no—
248C2×#95—72no—
249C2×#95C2×D711yescharacteristic
250C2×#95C2×D711yescharacteristic
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—22no—
268C23×C7—22no—
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×C7—41no—
284C23×C7—41no—
285C23×C7C4×D414yes—
286C23×C7C23×C411yescharacteristic
287C23×C7C22×D411yescharacteristic
288C23×C7C22×D411yescharacteristic
289C23×C7C22×D411yescharacteristic
290C23×C7C2×#4111yescharacteristic
291C23×C7C2×#4111yescharacteristic
292C23×C7C2×#4111yescharacteristic
293C23×C7C2×#4111yescharacteristic
294C23×C7C2×#4111yescharacteristic
295C23×C7C2×#4111yescharacteristic
296C23×C7C2×#4111yescharacteristic
297C23×C7H(5,𝔽2)11yescharacteristic
298C23×C72−1+411yescharacteristic
299C23×C72−1+411yescharacteristic
300C23×C72−1+411yescharacteristic
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—22no—
318C2×C4×C7—22no—
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—41no—
334C2×C4×C7—41no—
335C2×C4×C7—416no—
336C2×C4×C7#11714yes—
337C2×C4×C7C4×D414yes—
338C2×C4×C7C4×D414yes—
339C2×C4×C7#12114yes—
340C2×C4×C7#12114yes—
341C2×C4×C7#12314yes—
342C2×C4×C7#12414yes—
343C2×C4×C7#12614yes—
344C2×Dic7—24no—
345C2×Dic7—24no—
346C2×Dic7—24no—
347C2×Dic7—24no—
348C2×Dic7—24no—
349C2×Dic7—24no—
350C2×Dic7—24no—
351C2×Dic7—24no—
352C2×Dic7—24no—
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—
370C2×Dic7—42no—
371C2×Dic7—42no—
372C25C22×D711yescharacteristic
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—72no—
380C23×C4—72no—
381C23×C4—72no—
382C23×C4—72no—
383C23×C4C4×D714yes—
384C23×C4C22×D711yescharacteristic
385C23×C4C22×D711yescharacteristic
386C23×C4C22×D711yescharacteristic
387C23×C4C22×D711yescharacteristic
388C23×C4C22×D711yescharacteristic
389C23×C4C22×D711yescharacteristic
390C2×C4⋊C4—74no—
391C2×C4⋊C4—74no—
392C2×C4⋊C4—74no—
393C2×C4⋊C4—142no—
394C2×C4⋊C4—142no—
395C2×C4⋊C4—142no—
396C2×C4⋊C4—142no—
397C2×C4⋊C4—142no—
398C2×C4⋊C4—142no—
399C2×C4⋊C4—144no—
400C2×C4⋊C4—144no—
401C2×C4⋊C4—142no—
402C2×C4⋊C4—142no—
403C2×C4⋊C4—142no—
404C2×C4⋊C4—282no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—78no—
411C2×C22⋊C4—144no—
412C2×C22⋊C4—144no—
413C2×C22⋊C4—144no—
414C2×C22⋊C4—144no—
415C2×C22⋊C4—282no—
416C2×C22⋊C4D2814yes—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—144no—
423C2×C42—144no—
424C2×C42—144no—
425C2×C42C22⋊D714yes—
426#95—22no—
427#95—22no—
428#95—78no—
429#95—144no—
430#95—144no—
431#95—144no—
432#95—144no—
433#95—144no—
434#95—144no—
435#95—282no—
436C22×C7—24no—
437C22×C7—24no—
438C22×C7—24no—
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×C7—42no—
450C22×C7—42no—
451C22×C7C2×#11711yescharacteristic
452C22×C7C2×C4×D411yescharacteristic
453C22×C7C2×C4×D411yescharacteristic
454C22×C7C2×C4×D411yescharacteristic
455C22×C7C4×#4111yescharacteristic
456C22×C7#51911yescharacteristic
457C22×C7#52011yescharacteristic
458C22×C7C2×#12111yescharacteristic
459C22×C7C2×#12111yescharacteristic
460C22×C7C2×#12311yescharacteristic
461C22×C7#52511yescharacteristic
462C22×C7C2×#12411yescharacteristic
463C22×C7C2×#12611yescharacteristic
464C22×C7#52911yescharacteristic
465C22×C7#53211yescharacteristic
466C22×C7#53611yescharacteristic
467C22×C7#53711yescharacteristic
468C22×C7#54111yescharacteristic
469C22×C7#54211yescharacteristic
470C22×C7D4211yescharacteristic
471C22×C7#54711yescharacteristic
472C22×C7#54711yescharacteristic
473C22×C7#54711yescharacteristic
474C22×C7#54711yescharacteristic
475C22×C7#54811yescharacteristic
476C22×C7#54811yescharacteristic
477C22×C7#55211yescharacteristic
478C22×C7#55211yescharacteristic
479C22×C7#55211yescharacteristic
480C22×C7#55211yescharacteristic
481C22×C7#55211yescharacteristic
482C22×C7#55311yescharacteristic
483C22×C7#55511yescharacteristic
484C22×C7#55511yescharacteristic
485C22×C7#55611yescharacteristic
486C4×C7—24no—
487C4×C7—42no—
488C4×C7—42no—
489C4×C7—42no—
490C4×C7—42no—
491C4×C7#38818yescomplemented
492Dic7—44no—
493Dic7—44no—
494Dic7—44no—
495Dic7—82no—
496C24—21no—
497C24—21no—
498C24—21no—
499C24—21no—
500C24—21no—
501C24—21no—
502C24—21no—
503C24—21no—
504C24—21no—
505C24—21no—
506C24—21no—
507C24—21no—
508C24C2×C4×D712yes—
509C24C2×D2812yes—
510C24#115712yes—
511C24C23×D711yescharacteristic
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—21no—
539C22×C4—21no—
540C22×C4—28no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—74no—
548C22×C4—74no—
549C22×C4—74no—
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×C4—142no—
574C22×C4—142no—
575C22×C4C2×C4×D712yes—
576C22×C4C2×C4×D712yes—
577C22×C4C2×D2812yes—
578C22×C4C2×D2812yes—
579C22×C4#115712yes—
580C22×C4#115712yes—
581C22×C4#115712yes—
582C22×C4D4×D712yes—
583C22×C4#115912yes—
584C22×C4#115912yes—
585C22×C4#115912yes—
586C22×C4C2×C22⋊D712yes—
587C22×C4C2×C22⋊D712yes—
588C22×C4C2×C22⋊D712yes—
589C4⋊C4—148no—
590C4⋊C4—148no—
591C4⋊C4—148no—
592C4⋊C4—288no—
593C4⋊C4—284no—
594C22⋊C4—28no—
595C22⋊C4—28no—
596C22⋊C4—1416no—
597C22⋊C4—288no—
598C42—28no—
599C42—44no—
600C42—288no—
601C2×C7—44no—
602C2×C7C2×#38811yescharacteristic
603C2×C7C4×#12111yescharacteristic
604C2×C7#232311yescharacteristic
605C2×C7#234411yescharacteristic
606C2×C7#234611yescharacteristic
607C2×C7#236111yescharacteristic
608C2×C7#236211yescharacteristic
609C2×C7#248511yescharacteristic
610C2×C7#248611yescharacteristic
611C2×C7#248911yescharacteristic
612C2×C7#249111yescharacteristic
613C2×C7#249511yescharacteristic
614C2×C7#249611yescharacteristic
615C2×C7#253611yescharacteristic
616C2×C7#253711yescharacteristic
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—22no—
634C23—22no—
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—
649C23—41no—
650C23—41no—
651C23C4×D2814yes—
652C23C22×C4×D711yescharacteristic
653C23C22×D2811yescharacteristic
654C23C2×#115711yescharacteristic
655C23C2×#115711yescharacteristic
656C23C2×#115711yescharacteristic
657C23C2×#115711yescharacteristic
658C23C2×D4×D711yescharacteristic
659C23C2×#115911yescharacteristic
660C23C2×#115911yescharacteristic
661C23C2×#115911yescharacteristic
662C23#655311yescharacteristic
663C23#655411yescharacteristic
664C23#655411yescharacteristic
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—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—22no—
684C2×C4—22no—
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—41no—
700C2×C4—41no—
701C2×C4—416no—
702C2×C4—144no—
703C2×C4—144no—
704C2×C4—144no—
705C2×C4—144no—
706C2×C4—144no—
707C2×C4—144no—
708C2×C4—144no—
709C2×C4—144no—
710C2×C4—144no—
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—282no—
729C2×C4—282no—
730C2×C4#644014yes—
731C2×C4#644214yes—
732C2×C4(C22⋊D7)⋊C414yes—
733C2×C4#644814yes—
734C2×C4C4×C22⋊D714yes—
735C2×C4#649314yes—
736C2×C4#649814yes—
737C2×C4#650114yes—
738C7#1399411yescharacteristic, complemented, Sylow
739C22—24no—
740C22—24no—
741C22—24no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22C2×C4×D2811yescharacteristic
755C22C4×#115711yescharacteristic
756C22#9016811yescharacteristic
757C22#9017011yescharacteristic
758C22C2×#644011yescharacteristic
759C22C2×#644211yescharacteristic
760C22C2×(C22⋊D7)⋊C411yescharacteristic
761C22C2×#644811yescharacteristic
762C22#9020711yescharacteristic
763C22#9020911yescharacteristic
764C22#9021411yescharacteristic
765C22#9022511yescharacteristic
766C22#9023211yescharacteristic
767C22#9023211yescharacteristic
768C22#9023211yescharacteristic
769C22#9023211yescharacteristic
770C22#9023211yescharacteristic
771C22#9023311yescharacteristic
772C22D4×D2811yescharacteristic
773C22#9024211yescharacteristic
774C22#9024311yescharacteristic
775C22#9024311yescharacteristic
776C22#9024611yescharacteristic
777C22#9024611yescharacteristic
778C22#9024611yescharacteristic
779C22#9025411yescharacteristic
780C22#9025411yescharacteristic
781C22#9025611yescharacteristic
782C22C2×C4×C22⋊D711yescharacteristic
783C22C2×#649311yescharacteristic
784C22#9048211yescharacteristic
785C22C2×#649811yescharacteristic
786C22C2×#650111yescharacteristic
787C22#9051611yescharacteristic
788C22#9052411yescharacteristic
789C4—24no—
790C4—42no—
791C4—42no—
792C4—42no—
793C4—42no—
794C4—284no—
795C4—284no—
796C4—284no—
797C4—562no—
798C4#8971618yescomplemented
799C2—44no—
800C2#1173090111yescharacteristic
801C2#1173090411yescharacteristic
802C2#1173091211yescharacteristic
803C2#1173091311yescharacteristic
804C2#1173095011yescharacteristic
805C2#1173095211yescharacteristic
806C2#1173095611yescharacteristic
807C2#1173095711yescharacteristic
808C2C4×#649311yescharacteristic
809C2C2×#8971611yescharacteristic
810C2#1173968011yescharacteristic
811C2#1173981711yescharacteristic
812C2#1173981811yescharacteristic
813C2#1173982011yescharacteristic
814C2#1173986211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C4×C7×C22⋊C4C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×C4×C22⋊C4D7
hypocenterC7#13994
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
5. C2×#89700C2semidirect
6. C2×C4×C4⋊Dic7C2semidirect
8. #11729289C2semidirect
9. #11729289C2semidirect
10. #11727167C2semidirect
11. #11727156C2semidirect
29. #89984C4semidirect
491. C4×C7#388semidirect
738. C7#13994semidirect
798. C4#89716semidirect

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×#897162
C2×#897002
C2×C4×C4⋊Dic72
#117293032
#117292892
#117271672
#117271562
#139947