Finite Group Databasebeta

← #13276926

Subgroups — #13276926

Order 1792.

2106 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6487C211yesmaximal, characteristic
2C2×C7×#380C211yesmaximal, characteristic
3C2×C4×C22⋊Dic7C211yesmaximal, characteristic
4C2×#89746C211yesmaximal, characteristic, complemented
5C2×#89746C211yesmaximal, characteristic, complemented
6C2×#89745C211yesmaximal, characteristic, complemented
7C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
8#11729301C212yesmaximal
9#11729299C212yesmaximal
10#11727175C212yesmaximal, complemented
11Dic7⋊#95C212yesmaximal, complemented
12C24×C4×C7C2211yescharacteristic
13C23×Dic14C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C22⋊C4C2212yes—
17C22×C22⋊Dic7C2211yescharacteristic
18C22×C22⋊Dic7C2212yes—
19C22×C22⋊Dic7C2211yescharacteristic
20C22×C4⋊Dic7C2211yescharacteristic
21C2×#6487—24no—
22C2×#6487—24no—
23C2×#6487C418yescomplemented
24C22×Dic7⋊C4C2212yes—
25C22×Dic7⋊C4C2212yes—
26C22×C4×Dic7C2211yescharacteristic
27C22×C4×Dic7C2212yes—
28C22×C4×Dic7C2211yescharacteristic
29C7×#380—24no—
30C2×C7×#95C2212yes—
31C4×C22⋊Dic7—24no—
32C2×C7⋊#95C2211yescharacteristic
33C2×C7⋊#95C2211yescharacteristic
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2212yes—
40C4⋊C4×Dic7—24no—
41#89746—24no—
42#89746—24no—
43#89745—24no—
44#13997—71nomaximal, Sylow
45C25×C7C2311yescharacteristic
46C23×C4×C7—22no—
47C23×C4×C7—22no—
48C23×C4×C7—22no—
49C23×C4×C7—22no—
50C23×C4×C7—22no—
51C23×C4×C7—22no—
52C23×C4×C7C2×C414yes—
53C23×C4×C7C2312yes—
54C23×C4×C7C2311yescharacteristic
55C23×C4×C7C2312yes—
56C23×C4×C7C2311yescharacteristic
57C23×Dic7C2312yes—
58C23×Dic7C2311yescharacteristic
59C23×Dic7C2311yescharacteristic
60C23×Dic7C2311yescharacteristic
61C23×Dic7C2312yes—
62C23×Dic7C2311yescharacteristic
63C22×Dic14—22no—
64C22×Dic14—22no—
65C22×Dic14—22no—
66C22×Dic14—22no—
67C22×Dic14—22no—
68C22×Dic14—22no—
69C22×Dic14C2×C414yes—
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4—22no—
75C2×C7×C4⋊C4D414yes—
76C2×C7×C22⋊C4—24no—
77C2×C7×C22⋊C4—24no—
78C2×C7×C22⋊C4—42no—
79C2×C22⋊Dic7—22no—
80C2×C22⋊Dic7—24no—
81C2×C22⋊Dic7—24no—
82C2×C22⋊Dic7—22no—
83C2×C22⋊Dic7—22no—
84C2×C22⋊Dic7—22no—
85C2×C22⋊Dic7—22no—
86C2×C22⋊Dic7C2×C418yes—
87C2×C22⋊Dic7Q814yescomplemented
88C2×C4⋊Dic7C2×C414yes—
89C2×C4⋊Dic7D414yes—
90C2×C4⋊Dic7D414yes—
91#6487—232no—
92C2×Dic7⋊C4—24no—
93C2×Dic7⋊C4—24no—
94C2×Dic7⋊C4—24no—
95C2×Dic7⋊C4—24no—
96C2×Dic7⋊C4—42no—
97C2×Dic7⋊C4C2×C418yes—
98C2×C4×Dic7—22no—
99C2×C4×Dic7—22no—
100C2×C4×Dic7—22no—
101C2×C4×Dic7—22no—
102C2×C4×Dic7—22no—
103C2×C4×Dic7—24no—
104C2×C4×Dic7—24no—
105C2×C4×Dic7—42no—
106C2×C4×Dic7D414yes—
107C7×#95—24no—
108C7⋊#95—24no—
109C7⋊#95—24no—
110C7⋊#95—22no—
111C7⋊#95—22no—
112C7⋊#95—24no—
113C7⋊#95—24no—
114C7⋊#95—24no—
115C7⋊#95—24no—
116C22×C22⋊Q8—71no—
117C2×#391—71no—
118C2×#391—71no—
119C2×#389—71no—
120C2×#380D711yescharacteristic
121C2×C4×C4⋊C4—71no—
122C2×C4×C22⋊C4—71no—
123#1445—72no—
124#1439—72no—
125#1437—72no—
126C4⋊#95—72no—
127C24×C7—21no—
128C24×C7—21no—
129C24×C7—21no—
130C24×C7—21no—
131C24×C7—21no—
132C24×C7—21no—
133C24×C7—21no—
134C24×C7—21no—
135C24×C7—21no—
136C24×C7—21no—
137C24×C7—21no—
138C24×C7—21no—
139C24×C7C22×C412yes—
140C24×C7C2×Q812yes—
141C24×C7#4112yes—
142C24×C7C2411yescharacteristic
143C22×C4×C7—21no—
144C22×C4×C7—22no—
145C22×C4×C7—21no—
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—21no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
155C22×C4×C7—28no—
156C22×C4×C7—28no—
157C22×C4×C7—28no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—22no—
164C22×C4×C7—22no—
165C22×C4×C7—44no—
166C22×C4×C7—44no—
167C22×C4×C7—44no—
168C22×C4×C7—44no—
169C22×C4×C7C22×C412yes—
170C22×C4×C7C22×C412yes—
171C22×C4×C7C2×D414yes—
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×Dic7—21no—
179C22×Dic7—22no—
180C22×Dic7—21no—
181C22×Dic7—22no—
182C22×Dic7—21no—
183C22×Dic7—22no—
184C22×Dic7—22no—
185C22×Dic7—21no—
186C22×Dic7—21no—
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—21no—
198C22×Dic7—21no—
199C22×Dic7—21no—
200C22×Dic7—21no—
201C22×Dic7—21no—
202C22×Dic7—22no—
203C22×Dic7—22no—
204C22×Dic7—21no—
205C22×Dic7—21no—
206C22×Dic7—21no—
207C22×Dic7—21no—
208C22×Dic7—21no—
209C22×Dic7—21no—
210C22×Dic7C22×C414yes—
211C22×Dic7C22×C414yes—
212C22×Dic7C2×D412yes—
213C22×Dic7C2×D414yes—
214C22×Dic7C2×D414yes—
215C22×Dic7C2×D412yes—
216C22×Dic7C2×Q812yes—
217C22×Dic7C2×Q812yes—
218C22×Dic7#4112yes—
219C22×Dic7#4112yes—
220C2×Dic14—28no—
221C2×Dic14—28no—
222C2×Dic14—28no—
223C2×Dic14—44no—
224C2×Dic14—44no—
225C2×Dic14—44no—
226C2×Dic14—44no—
227C7×C4⋊C4—28no—
228C7×C4⋊C4—44no—
229C7×C22⋊C4—48no—
230C22⋊Dic7—28no—
231C22⋊Dic7—216no—
232C22⋊Dic7—28no—
233C4⋊Dic7C22⋊C4116yescomplemented
234Dic7⋊C4—216no—
235Dic7⋊C4—48no—
236C4×Dic7—28no—
237C4×Dic7—48no—
238C4×Dic7—44no—
239C23×Q8—71no—
240C24×C4C2×D711yescharacteristic
241C2×C22⋊Q8—78no—
242C2×C22⋊Q8—144no—
243C2×C22⋊Q8—144no—
244C22×C4⋊C4—71no—
245C22×C4⋊C4—72no—
246C22×C4⋊C4—72no—
247C22×C4⋊C4C2×D711yescharacteristic
248C22×C4⋊C4C2×D711yescharacteristic
249C22×C22⋊C4—72no—
250C22×C22⋊C4—71no—
251C22×C22⋊C4—71no—
252C22×C22⋊C4C2×D712yes—
253C22×C42—71no—
254C22×C42—71no—
255C22×C42—72no—
256#391—144no—
257#391—144no—
258#389—144no—
259#380—24no—
260C4×C4⋊C4—144no—
261C4×C22⋊C4—144no—
262C2×#95—71no—
263C2×#95—72no—
264C2×#95—72no—
265C2×#95—72no—
266C2×#95—72no—
267C2×#95—72no—
268C2×#95—72no—
269C2×#95—71no—
270C2×#95C2×D712yes—
271C23×C7—22no—
272C23×C7—22no—
273C23×C7—22no—
274C23×C7—22no—
275C23×C7—22no—
276C23×C7—22no—
277C23×C7—22no—
278C23×C7—22no—
279C23×C7—22no—
280C23×C7—22no—
281C23×C7—22no—
282C23×C7—22no—
283C23×C7—22no—
284C23×C7—22no—
285C23×C7—22no—
286C23×C7—22no—
287C23×C7—22no—
288C23×C7—22no—
289C23×C7—41no—
290C23×C7—41no—
291C23×C7—41no—
292C23×C7—41no—
293C23×C7—41no—
294C23×C7—41no—
295C23×C7—41no—
296C23×C7—41no—
297C23×C7—41no—
298C23×C7—41no—
299C23×C7—41no—
300C23×C7—41no—
301C23×C7—41no—
302C23×C7—41no—
303C23×C7—41no—
304C23×C7—41no—
305C23×C7C4×Q814yes—
306C23×C7C23×C411yescharacteristic
307C23×C7C22×D411yescharacteristic
308C23×C7C22×D411yescharacteristic
309C23×C7C22×D411yescharacteristic
310C23×C7C22×D411yescharacteristic
311C23×C7C22×Q811yescharacteristic
312C23×C7C2×#4111yescharacteristic
313C23×C7C2×#4111yescharacteristic
314C23×C7C2×#4111yescharacteristic
315C23×C7C2×#4111yescharacteristic
316C23×C7C2×#4111yescharacteristic
317C23×C7H(5,𝔽2)11yescharacteristic
318C23×C72−1+411yescharacteristic
319C23×C72−1+411yescharacteristic
320C23×C72−1+411yescharacteristic
321C2×C4×C7—22no—
322C2×C4×C7—22no—
323C2×C4×C7—22no—
324C2×C4×C7—24no—
325C2×C4×C7—24no—
326C2×C4×C7—24no—
327C2×C4×C7—41no—
328C2×C4×C7—41no—
329C2×C4×C7—41no—
330C2×C4×C7—42no—
331C2×C4×C7—41no—
332C2×C4×C7—42no—
333C2×C4×C7—42no—
334C2×C4×C7—42no—
335C2×C4×C7—416no—
336C2×C4×C7—42no—
337C2×C4×C7—42no—
338C2×C4×C7—42no—
339C2×C4×C7—42no—
340C2×C4×C7—42no—
341C2×C4×C7—42no—
342C2×C4×C7—42no—
343C2×C4×C7C2×C22⋊C414yes—
344C2×C4×C7C4×D414yes—
345C2×C4×C7C4×D414yes—
346C2×C4×C7#12114yes—
347C2×C4×C7#12114yes—
348C2×C4×C7#12414yes—
349C2×C4×C7#12714yes—
350C2×Dic7—24no—
351C2×Dic7—24no—
352C2×Dic7—22no—
353C2×Dic7—22no—
354C2×Dic7—22no—
355C2×Dic7—24no—
356C2×Dic7—24no—
357C2×Dic7—24no—
358C2×Dic7—24no—
359C2×Dic7—22no—
360C2×Dic7—22no—
361C2×Dic7—22no—
362C2×Dic7—24no—
363C2×Dic7—24no—
364C2×Dic7—24no—
365C2×Dic7—22no—
366C2×Dic7—22no—
367C2×Dic7—22no—
368C2×Dic7—22no—
369C2×Dic7—22no—
370C2×Dic7—22no—
371C2×Dic7—22no—
372C2×Dic7—22no—
373C2×Dic7—22no—
374C2×Dic7—42no—
375C2×Dic7—42no—
376C2×Dic7—42no—
377C2×Dic7—41no—
378C2×Dic7—41no—
379C2×Dic7—42no—
380C2×Dic7—41no—
381C2×Dic7—41no—
382C2×Dic7—41no—
383C2×Dic7—41no—
384C2×Dic7—41no—
385C2×Dic7—41no—
386C2×Dic7—41no—
387C2×Dic7—41no—
388C2×Dic7—41no—
389C2×Dic7—41no—
390C2×Dic7C2×C22⋊C418yes—
391C2×Dic7C22⋊Q814yescomplemented
392Dic14—416no—
393C25C22×D711yescharacteristic
394C22×Q8—74no—
395C22×Q8—142no—
396C22×Q8—142no—
397C22×Q8—142no—
398C22×Q8—142no—
399C22×Q8—142no—
400C22×Q8—142no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—72no—
408C23×C4—71no—
409C23×C4—71no—
410C23×C4—72no—
411C23×C4—71no—
412C23×C4—71no—
413C23×C4C4×D714yes—
414C23×C4C22×D712yes—
415C23×C4C22×D711yescharacteristic
416C23×C4C22×D712yes—
417C23×C4C22×D711yescharacteristic
418C22⋊Q8—1432no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—74no—
425C2×C4⋊C4—74no—
426C2×C4⋊C4—74no—
427C2×C4⋊C4—78no—
428C2×C4⋊C4—144no—
429C2×C4⋊C4—144no—
430C2×C4⋊C4—144no—
431C2×C4⋊C4—144no—
432C2×C4⋊C4—282no—
433C2×C4⋊C4C22⋊D714yes—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—42no—
437C2×C22⋊C4—78no—
438C2×C22⋊C4—74no—
439C2×C22⋊C4—144no—
440C2×C22⋊C4—144no—
441C2×C22⋊C4—142no—
442C2×C22⋊C4—142no—
443C2×C22⋊C4—142no—
444C2×C22⋊C4—142no—
445C2×C22⋊C4—142no—
446C2×C42—74no—
447C2×C42—142no—
448C2×C42—142no—
449C2×C42—144no—
450C2×C42—144no—
451C2×C42—142no—
452C2×C42—142no—
453C2×C42—142no—
454C2×C42—282no—
455#95—24no—
456#95—142no—
457#95—142no—
458#95—144no—
459#95—144no—
460#95—144no—
461#95—144no—
462#95—144no—
463#95—144no—
464C22×C7—24no—
465C22×C7—24no—
466C22×C7—24no—
467C22×C7—42no—
468C22×C7—42no—
469C22×C7—42no—
470C22×C7—42no—
471C22×C7—42no—
472C22×C7—42no—
473C22×C7—42no—
474C22×C7—42no—
475C22×C7—42no—
476C22×C7—42no—
477C22×C7—42no—
478C22×C7—42no—
479C22×C7C22×C22⋊C411yescharacteristic
480C22×C7C2×C4×D411yescharacteristic
481C22×C7C2×C4×D411yescharacteristic
482C22×C7C2×C4×Q811yescharacteristic
483C22×C7C4×#4111yescharacteristic
484C22×C7#51911yescharacteristic
485C22×C7#52011yescharacteristic
486C22×C7C2×#12111yescharacteristic
487C22×C7C2×#12111yescharacteristic
488C22×C7C2×C22⋊Q811yescharacteristic
489C22×C7#52511yescharacteristic
490C22×C7C2×#12411yescharacteristic
491C22×C7#52911yescharacteristic
492C22×C7C2×#12711yescharacteristic
493C22×C7#53311yescharacteristic
494C22×C7#53611yescharacteristic
495C22×C7#53711yescharacteristic
496C22×C7#54111yescharacteristic
497C22×C7#54211yescharacteristic
498C22×C7#54611yescharacteristic
499C22×C7#54611yescharacteristic
500C22×C7#54611yescharacteristic
501C22×C7#54711yescharacteristic
502C22×C7#54711yescharacteristic
503C22×C7#54711yescharacteristic
504C22×C7#54811yescharacteristic
505C22×C7#54811yescharacteristic
506C22×C7#54811yescharacteristic
507C22×C7D4×Q811yescharacteristic
508C22×C7D4×Q811yescharacteristic
509C22×C7D4×Q811yescharacteristic
510C22×C7#55211yescharacteristic
511C22×C7#55211yescharacteristic
512C22×C7#55411yescharacteristic
513C22×C7#55611yescharacteristic
514C4×C7—44no—
515C4×C7—42no—
516C4×C7—82no—
517C4×C7#39018yes—
518Dic7—28no—
519Dic7—24no—
520Dic7—42no—
521Dic7—42no—
522Dic7—42no—
523Dic7—44no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24—21no—
534C24—21no—
535C24—21no—
536C24C2×C4×D712yes—
537C24#115912yes—
538C24Q8×D712yes—
539C24C23×D711yescharacteristic
540C2×Q8—148no—
541C2×Q8—148no—
542C2×Q8—148no—
543C2×Q8—284no—
544C2×Q8—284no—
545C2×Q8—284no—
546C2×Q8—284no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—28no—
560C22×C4—28no—
561C22×C4—28no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—74no—
574C22×C4—72no—
575C22×C4—74no—
576C22×C4—74no—
577C22×C4—72no—
578C22×C4—72no—
579C22×C4—74no—
580C22×C4—72no—
581C22×C4—72no—
582C22×C4—72no—
583C22×C4—141no—
584C22×C4—141no—
585C22×C4—141no—
586C22×C4—142no—
587C22×C4—142no—
588C22×C4—142no—
589C22×C4—142no—
590C22×C4—141no—
591C22×C4—141no—
592C22×C4—142no—
593C22×C4—141no—
594C22×C4—141no—
595C22×C4—142no—
596C22×C4—141no—
597C22×C4—141no—
598C22×C4—141no—
599C22×C4—142no—
600C22×C4—142no—
601C22×C4—141no—
602C22×C4—141no—
603C22×C4—142no—
604C22×C4—141no—
605C22×C4—141no—
606C22×C4—141no—
607C22×C4—141no—
608C22×C4—141no—
609C22×C4—141no—
610C22×C4—141no—
611C22×C4—141no—
612C22×C4—141no—
613C22×C4—141no—
614C22×C4—142no—
615C22×C4C2×C4×D712yes—
616C22×C4C2×C4×D712yes—
617C22×C4#115712yes—
618C22×C4D4×D712yes—
619C22×C4D4×D712yes—
620C22×C4D4×D712yes—
621C22×C4#115912yes—
622C22×C4C2×C22⋊D714yes—
623C22×C4C2×C22⋊D712yes—
624C4⋊C4—28no—
625C4⋊C4—44no—
626C4⋊C4—716no—
627C4⋊C4—1416no—
628C4⋊C4—288no—
629C22⋊C4—48no—
630C22⋊C4—148no—
631C22⋊C4—1416no—
632C22⋊C4—148no—
633C42—148no—
634C42—288no—
635C42—284no—
636C2×C7—44no—
637C2×C7C2×#39011yescharacteristic
638C2×C7C4×C22⋊Q811yescharacteristic
639C2×C7#232311yescharacteristic
640C2×C7#233911yescharacteristic
641C2×C7Q8×C22⋊C411yescharacteristic
642C2×C7#236011yescharacteristic
643C2×C7#236211yescharacteristic
644C2×C7#241511yescharacteristic
645C2×C7#241711yescharacteristic
646C2×C7#242711yescharacteristic
647C2×C7#242911yescharacteristic
648C2×C7#248911yescharacteristic
649C2×C7#249211yescharacteristic
650C2×C7#254011yescharacteristic
651C2×C7#254211yescharacteristic
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23#645014yes—
687C23C22×C4×D711yescharacteristic
688C23C2×#115711yescharacteristic
689C23C2×D4×D711yescharacteristic
690C23C2×D4×D711yescharacteristic
691C23C2×D4×D711yescharacteristic
692C23C2×#115911yescharacteristic
693C23C2×#115911yescharacteristic
694C23#654811yescharacteristic
695C23C2×Q8×D711yescharacteristic
696C23#655111yescharacteristic
697C23D7×#4111yescharacteristic
698C23D7×#4111yescharacteristic
699C23#655411yescharacteristic
700C23#655411yescharacteristic
701C23C22×C22⋊D711yescharacteristic
702Q8—2816no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—416no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—78no—
726C2×C4—74no—
727C2×C4—142no—
728C2×C4—144no—
729C2×C4—142no—
730C2×C4—144no—
731C2×C4—142no—
732C2×C4—142no—
733C2×C4—142no—
734C2×C4—144no—
735C2×C4—144no—
736C2×C4—144no—
737C2×C4—144no—
738C2×C4—142no—
739C2×C4—144no—
740C2×C4—144no—
741C2×C4—142no—
742C2×C4—144no—
743C2×C4—142no—
744C2×C4—142no—
745C2×C4—142no—
746C2×C4—142no—
747C2×C4—142no—
748C2×C4—142no—
749C2×C4—142no—
750C2×C4—142no—
751C2×C4—282no—
752C2×C4—282no—
753C2×C4—281no—
754C2×C4—281no—
755C2×C4—282no—
756C2×C4—281no—
757C2×C4—281no—
758C2×C4—282no—
759C2×C4—281no—
760C2×C4—281no—
761C2×C4—281no—
762C2×C4—281no—
763C2×C4—281no—
764C2×C4—281no—
765C2×C4—281no—
766C2×C4—281no—
767C2×C4D7×C22⋊C414yes—
768C2×C4(C22⋊D7)⋊C414yes—
769C2×C4#644714yes—
770C2×C4#644814yes—
771C2×C4C4×C22⋊D714yes—
772C2×C4#650214yes—
773C2×C4#650314yes—
774C7#1399711yescharacteristic, complemented, Sylow
775C22—24no—
776C22—24no—
777C22—24no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22C2×D7×C22⋊C411yescharacteristic
791C22C2×(C22⋊D7)⋊C411yescharacteristic
792C22C2×#644711yescharacteristic
793C22C2×#644811yescharacteristic
794C22C2×#645011yescharacteristic
795C22#9019511yescharacteristic
796C22#9020211yescharacteristic
797C22#9020411yescharacteristic
798C22#9020711yescharacteristic
799C22#9021311yescharacteristic
800C22#9022011yescharacteristic
801C22#9022411yescharacteristic
802C22#9028911yescharacteristic
803C22#9028911yescharacteristic
804C22#9029111yescharacteristic
805C22#9029411yescharacteristic
806C22#9029711yescharacteristic
807C22#9029911yescharacteristic
808C22#9030311yescharacteristic
809C22#9030311yescharacteristic
810C22#9031311yescharacteristic
811C22#9031611yescharacteristic
812C22D7×C22⋊Q811yescharacteristic
813C22#9031911yescharacteristic
814C22#9032211yescharacteristic
815C22#9032211yescharacteristic
816C22#9032311yescharacteristic
817C22#9032311yescharacteristic
818C22C2×C4×C22⋊D711yescharacteristic
819C22C2×#650211yescharacteristic
820C22C2×#650311yescharacteristic
821C22#9049711yescharacteristic
822C22Q8×C22⋊D711yescharacteristic
823C22#9051511yescharacteristic
824C22#9052211yescharacteristic
825C4—42no—
826C4—44no—
827C4—82no—
828C4—144no—
829C4—148no—
830C4—282no—
831C4—282no—
832C4—284no—
833C4—282no—
834C4#8972918yes—
835C2—44no—
836C2#1173131111yescharacteristic
837C2#1173131611yescharacteristic
838C2#1173132111yescharacteristic
839C2#1173133311yescharacteristic
840C2#1173135811yescharacteristic
841C2#1173136111yescharacteristic
842C2#1173145311yescharacteristic
843C2#1173146511yescharacteristic
844C2C2×#8972911yescharacteristic
845C2#1173960711yescharacteristic
846C2#1173968811yescharacteristic
847C2#1174009211yescharacteristic
848C2#1174011311yescharacteristic
849C2#1174020311yescharacteristic
850C2#1174022511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#380C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#380D7
hypocenterC7#13997
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
4. C2×#89746C2semidirect
5. C2×#89746C2semidirect
6. C2×#89745C2semidirect
7. C2×C4⋊C4×Dic7C2semidirect
10. #11727175C2semidirect
11. Dic7⋊#95C2semidirect
23. C2×#6487C4semidirect
87. C2×C22⋊Dic7Q8semidirect
233. C4⋊Dic7C22⋊C4semidirect
391. C2×Dic7C22⋊Q8semidirect
774. C7#13997semidirect

Maximal subgroups

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

subgroupindex
C22×#64872
C2×C7×#3802
C2×C4×C22⋊Dic72
C2×#897462
C2×#897452
C2×C4⋊C4×Dic72
#117293012
#117292992
#117271752
Dic7⋊#952
#139977