Finite Group Databasebeta

← #13285211

Subgroups — #13285211

Order 1792.

2494 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6509C211yesmaximal, characteristic
2C22×D7×C4⋊C4C211yesmaximal, characteristic
3C2×C7×#395C211yesmaximal, characteristic, complemented
4C2×#90001C211yesmaximal, characteristic, complemented
5C2×#89761C212yesmaximal
6#11729322C212yesmaximal, complemented
7#11729319C211yesmaximal, characteristic, complemented
8(C2×D7)⋊#95C212yesmaximal
9(C2×D7)⋊#95C211yesmaximal, characteristic
10#11727174C212yesmaximal, complemented
11#11727164C211yesmaximal, characteristic, complemented
12C23×C7×Q8C2211yescharacteristic
13C23×C4×D7C2211yescharacteristic
14C23×C4×D7C2211yescharacteristic
15C23×C4×D7C2211yescharacteristic
16C22×C7×C4⋊C4C2212yes—
17C22×C7×C4⋊C4C2211yescharacteristic
18C2×#6509—24no—
19C2×#6509—28no—
20C22×(C2×D7)⋊C4C2212yes—
21C22×(C2×D7)⋊C4C2212yes—
22C22×C4⋊Dic7C2211yescharacteristic
23C22×C4⋊Dic7C2211yescharacteristic
24C22×Dic7⋊C4C2211yescharacteristic
25C22×Dic7⋊C4C2212yes—
26C22×Dic7⋊C4C2212yes—
27C22×Dic7⋊C4C2211yescharacteristic
28C2×D7×C4⋊C4—24no—
29C2×D7×C4⋊C4—24no—
30C2×D7×C4⋊C4—24no—
31C7×#395—24no—
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2212yes—
34#90001—24no—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2211yescharacteristic
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2212yes—
40C2×C7⋊#95C2212yes—
41C2×C7⋊#95C2212yes—
42#89761—28no—
43#14720—71nomaximal, Sylow
44C24×D7C2311yescharacteristic
45C22×C7×Q8—24no—
46C22×C7×Q8—22no—
47C22×C7×Q8—22no—
48C22×C7×Q8—22no—
49C22×C7×Q8—42no—
50C23×C4×C7C2312yes—
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2312yes—
53C23×C4×C7C2311yescharacteristic
54C23×C4×C7C2311yescharacteristic
55C23×Dic7C2311yescharacteristic
56C23×Dic7C2311yescharacteristic
57C23×Dic7C2312yes—
58C23×Dic7C2312yes—
59C23×Dic7C2311yescharacteristic
60C22×C4×D7—22no—
61C22×C4×D7—22no—
62C22×C4×D7—22no—
63C22×C4×D7—22no—
64C22×C4×D7—22no—
65C22×C4×D7—22no—
66C22×C4×D7—22no—
67C22×C4×D7—24no—
68C22×C4×D7—22no—
69C22×C4×D7—22no—
70C22×C4×D7—22no—
71C22×C4×D7—22no—
72C22×C4×D7—24no—
73C22×C4×D7—42no—
74C22×C4×D7—42no—
75C22×C4×D7D414yes—
76C22×C4×D7Q814yescomplemented
77C2×C7×C4⋊C4—22no—
78C2×C7×C4⋊C4—22no—
79C2×C7×C4⋊C4—24no—
80C2×C7×C4⋊C4—24no—
81C2×C7×C4⋊C4—42no—
82C2×C7×C4⋊C4D414yes—
83#6509—232no—
84C2×(C2×D7)⋊C4—24no—
85C2×(C2×D7)⋊C4—24no—
86C2×(C2×D7)⋊C4—24no—
87C2×(C2×D7)⋊C4—24no—
88C2×(C2×D7)⋊C4D418yes—
89C2×(C2×D7)⋊C4Q818yescomplemented
90C2×C4⋊Dic7—22no—
91C2×C4⋊Dic7—22no—
92C2×C4⋊Dic7—22no—
93C2×C4⋊Dic7—22no—
94C2×C4⋊Dic7—24no—
95C2×Dic7⋊C4—22no—
96C2×Dic7⋊C4—22no—
97C2×Dic7⋊C4—22no—
98C2×Dic7⋊C4—24no—
99C2×Dic7⋊C4—22no—
100C2×Dic7⋊C4—22no—
101C2×Dic7⋊C4—24no—
102C2×Dic7⋊C4—24no—
103C2×Dic7⋊C4—24no—
104C2×Dic7⋊C4—24no—
105C2×Dic7⋊C4—42no—
106C2×Dic7⋊C4D414yes—
107D7×C4⋊C4—232no—
108C7×#95—22no—
109C7×#95—24no—
110C7⋊#95—22no—
111C7⋊#95—24no—
112C7⋊#95—24no—
113C7⋊#95—24no—
114C7⋊#95—24no—
115C7⋊#95—24no—
116C7⋊#95—42no—
117C22×C22⋊Q8—71no—
118C23×C4⋊C4—71no—
119C2×#395—71no—
120C2×#395D711yescharacteristic, complemented
121C2×#385—72no—
122#1444—72no—
123#1444—72no—
124#1441—71no—
125#1441—71no—
126C22⋊#95—72no—
127C22⋊#95—71no—
128C24×C7C2411yescharacteristic
129C23×D7—21no—
130C23×D7—21no—
131C23×D7—21no—
132C23×D7—21no—
133C23×D7—22no—
134C23×D7—22no—
135C23×D7C2×D414yes—
136C23×D7C2×D412yes—
137C23×D7C2×Q814yes—
138C23×D7C2×Q812yes—
139C23×D7#4112yes—
140C2×C7×Q8—28no—
141C2×C7×Q8—48no—
142C2×C7×Q8—48no—
143C2×C7×Q8—44no—
144C2×C7×Q8—44no—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
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—22no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—22no—
164C22×C4×C7—22no—
165C22×C4×C7—22no—
166C22×C4×C7—22no—
167C22×C4×C7C2×D414yes—
168C22×C4×C7C2×D412yes—
169C22×C4×C7C2×D412yes—
170C22×C4×C7C2×D412yes—
171C22×C4×C7C2×D412yes—
172C22×C4×C7C2×D412yes—
173C22×C4×C7C2×Q814yes—
174C22×C4×C7C2×Q812yes—
175C22×C4×C7#4112yes—
176C22×Dic7—21no—
177C22×Dic7—21no—
178C22×Dic7—21no—
179C22×Dic7—21no—
180C22×Dic7—22no—
181C22×Dic7—22no—
182C22×Dic7—22no—
183C22×Dic7—22no—
184C22×Dic7—22no—
185C22×Dic7—22no—
186C22×Dic7—21no—
187C22×Dic7—21no—
188C22×Dic7—21no—
189C22×Dic7—21no—
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×Dic7C2×D414yes—
201C22×Dic7C2×D412yes—
202C22×Dic7C2×D412yes—
203C22×Dic7C2×D412yes—
204C22×Dic7C2×Q814yes—
205C22×Dic7C2×Q812yes—
206C22×Dic7#4112yes—
207C2×C4×D7—28no—
208C2×C4×D7—28no—
209C2×C4×D7—28no—
210C2×C4×D7—28no—
211C2×C4×D7—28no—
212C2×C4×D7—28no—
213C2×C4×D7—28no—
214C2×C4×D7—28no—
215C2×C4×D7—28no—
216C2×C4×D7—28no—
217C2×C4×D7—44no—
218C2×C4×D7—48no—
219C2×C4×D7—48no—
220C2×C4×D7—48no—
221C2×C4×D7—48no—
222C2×C4×D7—44no—
223C2×C4×D7—44no—
224C7×C4⋊C4—28no—
225C7×C4⋊C4—48no—
226(C2×D7)⋊C4—216no—
227(C2×D7)⋊C4—216no—
228C4⋊Dic7—28no—
229C4⋊Dic7—28no—
230Dic7⋊C4—28no—
231Dic7⋊C4—216no—
232Dic7⋊C4—28no—
233Dic7⋊C4—48no—
234C23×Q8C2×D711yescharacteristic
235C24×C4—71no—
236C24×C4—71no—
237C24×C4—71no—
238C2×C22⋊Q8—148no—
239C2×C22⋊Q8—144no—
240C22×C4⋊C4—71no—
241C22×C4⋊C4—71no—
242C22×C4⋊C4—71no—
243C22×C4⋊C4—72no—
244C22×C4⋊C4—71no—
245C22×C4⋊C4—72no—
246C22×C4⋊C4—144no—
247C22×C4⋊C4—144no—
248C22×C4⋊C4—144no—
249C22×C4⋊C4C2×D712yes—
250C22×C4⋊C4C2×D711yescharacteristic
251C22×C22⋊C4—72no—
252C22×C22⋊C4—72no—
253#395—24no—
254#395—144no—
255#385—148no—
256C2×#95—71no—
257C2×#95—72no—
258C2×#95—72no—
259C2×#95—72no—
260C2×#95—72no—
261C2×#95—72no—
262C2×#95—72no—
263C2×#95C2×D711yescharacteristic
264C2×#95C2×D712yes—
265C23×C7C22×D411yescharacteristic
266C23×C7C22×D411yescharacteristic
267C23×C7C22×D412yes—
268C23×C7C22×D411yescharacteristic
269C23×C7C22×Q811yescharacteristic
270C23×C7C22×Q812yes—
271C23×C7C2×#4111yescharacteristic
272C23×C7C2×#4111yescharacteristic
273C23×C7C2×#4111yescharacteristic
274C23×C7H(5,𝔽2)12yes—
275C23×C72−1+412yes—
276C22×D7—22no—
277C22×D7—22no—
278C22×D7—22no—
279C22×D7—22no—
280C22×D7—22no—
281C22×D7—22no—
282C22×D7—22no—
283C22×D7—22no—
284C22×D7—24no—
285C22×D7—24no—
286C22×D7—24no—
287C22×D7—24no—
288C22×D7—24no—
289C22×D7—24no—
290C22×D7—24no—
291C22×D7—24no—
292C22×D7—24no—
293C22×D7—24no—
294C22×D7#12014yes—
295C22×D7C22⋊Q818yes—
296C22×D7C22⋊Q814yes—
297C22×D7C4⋊Q814yes—
298C22×D7C4⋊Q818yes—
299C7×Q8—416no—
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—24no—
309C2×C4×C7—24no—
310C2×C4×C7—24no—
311C2×C4×C7—22no—
312C2×C4×C7—24no—
313C2×C4×C7—24no—
314C2×C4×C7—24no—
315C2×C4×C7—24no—
316C2×C4×C7—24no—
317C2×C4×C7—24no—
318C2×C4×C7—41no—
319C2×C4×C7—42no—
320C2×C4×C7—42no—
321C2×C4×C7—41no—
322C2×C4×C7—42no—
323C2×C4×C7—42no—
324C2×C4×C7—42no—
325C2×C4×C7—42no—
326C2×C4×C7—42no—
327C2×C4×C7—42no—
328C2×C4×C7—42no—
329C2×C4×C7#12014yes—
330C2×C4×C7C22⋊Q814yescomplemented
331C2×Dic7—22no—
332C2×Dic7—22no—
333C2×Dic7—22no—
334C2×Dic7—22no—
335C2×Dic7—22no—
336C2×Dic7—22no—
337C2×Dic7—22no—
338C2×Dic7—24no—
339C2×Dic7—22no—
340C2×Dic7—22no—
341C2×Dic7—24no—
342C2×Dic7—22no—
343C2×Dic7—24no—
344C2×Dic7—24no—
345C2×Dic7—24no—
346C2×Dic7—24no—
347C2×Dic7—24no—
348C2×Dic7—41no—
349C2×Dic7—42no—
350C2×Dic7—42no—
351C2×Dic7—41no—
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×Dic7C22⋊Q814yescomplemented
362C4×D7—232no—
363C4×D7—416no—
364C4×D7—416no—
365C25—71no—
366C22×Q8—24no—
367C22×Q8—22no—
368C22×Q8—22no—
369C22×Q8—22no—
370C22×Q8—42no—
371C23×C4—71no—
372C23×C4—72no—
373C23×C4—72no—
374C23×C4—71no—
375C23×C4—71no—
376C23×C4—74no—
377C23×C4—74no—
378C23×C4—142no—
379C23×C4—142no—
380C23×C4—142no—
381C23×C4—142no—
382C23×C4—142no—
383C23×C4—142no—
384C23×C4—144no—
385C23×C4—144no—
386C23×C4—142no—
387C23×C4—142no—
388C23×C4—142no—
389C23×C4—142no—
390C23×C4—142no—
391C23×C4—282no—
392C23×C4—282no—
393C23×C4C22×D712yes—
394C23×C4C22×D712yes—
395C23×C4C22×D711yescharacteristic
396C23×C4C22×D711yescharacteristic
397C23×C4C22×D711yescharacteristic
398C22⋊Q8—1432no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4—74no—
405C2×C4⋊C4—1432no—
406C2×C4⋊C4—142no—
407C2×C4⋊C4—142no—
408C2×C4⋊C4—142no—
409C2×C4⋊C4—142no—
410C2×C4⋊C4—144no—
411C2×C4⋊C4—144no—
412C2×C4⋊C4—144no—
413C2×C4⋊C4—142no—
414C2×C4⋊C4—144no—
415C2×C4⋊C4—142no—
416C2×C4⋊C4—142no—
417C2×C4⋊C4—142no—
418C2×C4⋊C4—142no—
419C2×C4⋊C4—144no—
420C2×C4⋊C4—144no—
421C2×C4⋊C4—282no—
422C2×C4⋊C4C22⋊D714yes—
423C2×C22⋊C4—78no—
424C2×C22⋊C4—78no—
425C2×C22⋊C4—144no—
426C2×C22⋊C4—144no—
427C2×C22⋊C4—144no—
428C2×C22⋊C4—144no—
429#95—22no—
430#95—24no—
431#95—144no—
432#95—144no—
433#95—144no—
434#95—144no—
435#95—142no—
436#95—144no—
437#95—282no—
438C22×C7C2×#12011yescharacteristic
439C22×C7C2×#12011yescharacteristic
440C22×C7C2×C22⋊Q811yescharacteristic
441C22×C7C2×C22⋊Q811yescharacteristic
442C22×C7C2×C22⋊Q811yescharacteristic
443C22×C7C2×C22⋊Q812yes—
444C22×C7#52511yescharacteristic
445C22×C7#52511yescharacteristic
446C22×C7#52511yescharacteristic
447C22×C7C2×C4⋊Q811yescharacteristic
448C22×C7C2×C4⋊Q812yes—
449C22×C7#53411yescharacteristic
450C22×C7#53611yescharacteristic
451C22×C7#53912yes—
452C22×C7#54412yes—
453C22×C7D4212yes—
454C22×C7D4212yes—
455C22×C7#54712yes—
456C22×C7#54712yes—
457C22×C7D4×Q812yes—
458C22×C7D4×Q812yes—
459C22×C7#55412yes—
460C22×C7#55412yes—
461C2×D7—24no—
462C2×D7—24no—
463C2×D7—24no—
464C2×D7—24no—
465C2×D7—24no—
466C2×D7—24no—
467C2×D7—28no—
468C2×D7—28no—
469C2×D7—28no—
470C2×D7—28no—
471C2×D7#39518yescomplemented
472C4×C7—24no—
473C4×C7—24no—
474C4×C7—42no—
475C4×C7—44no—
476C4×C7—44no—
477Dic7—24no—
478Dic7—42no—
479Dic7—42no—
480Dic7—44no—
481Dic7—44no—
482C24—74no—
483C24—72no—
484C24—74no—
485C24—72no—
486C24—72no—
487C24—141no—
488C24—142no—
489C24—141no—
490C24—142no—
491C24—141no—
492C24—141no—
493C24C23×D711yescharacteristic
494C2×Q8—28no—
495C2×Q8—48no—
496C2×Q8—48no—
497C2×Q8—44no—
498C2×Q8—44no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—72no—
522C22×C4—72no—
523C22×C4—72no—
524C22×C4—74no—
525C22×C4—72no—
526C22×C4—72no—
527C22×C4—74no—
528C22×C4—148no—
529C22×C4—148no—
530C22×C4—148no—
531C22×C4—148no—
532C22×C4—148no—
533C22×C4—148no—
534C22×C4—148no—
535C22×C4—148no—
536C22×C4—141no—
537C22×C4—141no—
538C22×C4—141no—
539C22×C4—141no—
540C22×C4—148no—
541C22×C4—142no—
542C22×C4—142no—
543C22×C4—142no—
544C22×C4—142no—
545C22×C4—142no—
546C22×C4—141no—
547C22×C4—141no—
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—141no—
560C22×C4—141no—
561C22×C4—148no—
562C22×C4—284no—
563C22×C4—288no—
564C22×C4—288no—
565C22×C4—288no—
566C22×C4—288no—
567C22×C4—284no—
568C22×C4—284no—
569C22×C4D4×D714yes—
570C22×C4D4×D712yes—
571C22×C4D4×D712yes—
572C22×C4Q8×D714yes—
573C22×C4Q8×D712yes—
574C22×C4#116112yes—
575C22×C4C2×C22⋊D712yes—
576C22×C4C2×C22⋊D712yes—
577C22×C4C2×C22⋊D712yes—
578C4⋊C4—28no—
579C4⋊C4—48no—
580C4⋊C4—148no—
581C4⋊C4—1416no—
582C4⋊C4—148no—
583C4⋊C4—148no—
584C4⋊C4—148no—
585C4⋊C4—288no—
586C22⋊C4—1416no—
587C22⋊C4—1416no—
588C2×C7C2×#39511yescharacteristic
589C2×C7#240311yescharacteristic
590C2×C7#240611yescharacteristic
591C2×C7#243411yescharacteristic
592C2×C7#244012yes—
593C2×C7#244012yes—
594C2×C7#244912yes—
595C2×C7#244912yes—
596C2×C7#258311yescharacteristic
597C2×C7#262711yescharacteristic
598C2×C7#284811yescharacteristic
599D7—28no—
600C23—74no—
601C23—78no—
602C23—74no—
603C23—78no—
604C23—74no—
605C23—142no—
606C23—144no—
607C23—144no—
608C23—144no—
609C23—144no—
610C23—142no—
611C23—144no—
612C23—142no—
613C23—144no—
614C23—142no—
615C23—142no—
616C23—144no—
617C23—142no—
618C23—142no—
619C23—142no—
620C23—144no—
621C23—144no—
622C23—144no—
623C23C2×D4×D711yescharacteristic
624C23C2×D4×D712yes—
625C23C2×D4×D711yescharacteristic
626C23#654812yes—
627C23C2×Q8×D712yes—
628C23C2×Q8×D711yescharacteristic
629C23C2×#116111yescharacteristic
630C23#655112yes—
631C23D7×#4111yescharacteristic
632C23D7×#4111yescharacteristic
633C23C22×C22⋊D711yescharacteristic
634Q8—416no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—24no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—74no—
665C2×C4—1432no—
666C2×C4—142no—
667C2×C4—142no—
668C2×C4—142no—
669C2×C4—142no—
670C2×C4—142no—
671C2×C4—142no—
672C2×C4—144no—
673C2×C4—144no—
674C2×C4—144no—
675C2×C4—142no—
676C2×C4—142no—
677C2×C4—144no—
678C2×C4—142no—
679C2×C4—142no—
680C2×C4—144no—
681C2×C4—144no—
682C2×C4—144no—
683C2×C4—2816no—
684C2×C4—2816no—
685C2×C4—282no—
686C2×C4—282no—
687C2×C4—282no—
688C2×C4—282no—
689C2×C4—282no—
690C2×C4—281no—
691C2×C4—281no—
692C2×C4—282no—
693C2×C4—282no—
694C2×C4—282no—
695C2×C4—282no—
696C2×C4—282no—
697C2×C4—282no—
698C2×C4#650014yes—
699C2×C4#650914yescomplemented
700C7#1472011yescharacteristic, complemented, Sylow
701C22—78no—
702C22—144no—
703C22—148no—
704C22—148no—
705C22—148no—
706C22—144no—
707C22—144no—
708C22—144no—
709C22—148no—
710C22—144no—
711C22—144no—
712C22D7×#12011yescharacteristic
713C22#9028011yescharacteristic
714C22#9028112yes—
715C22D7×C22⋊Q811yescharacteristic
716C22D7×C22⋊Q812yes—
717C22D7×C22⋊Q811yescharacteristic
718C22#9031811yescharacteristic
719C22#9031811yescharacteristic
720C22#9032212yes—
721C22#9032712yes—
722C22#9032912yes—
723C22D7×C4⋊Q811yescharacteristic
724C22D7×C4⋊Q812yes—
725C22#9041511yescharacteristic
726C22#9041712yes—
727C22#9041812yes—
728C22#9042012yes—
729C22#9042112yes—
730C22C2×#650011yescharacteristic
731C22D4×C22⋊D712yes—
732C22C2×#650911yescharacteristic
733C22Q8×C22⋊D712yes—
734C22#9051911yescharacteristic
735C4—24no—
736C4—24no—
737C4—44no—
738C4—42no—
739C4—44no—
740C4—144no—
741C4—282no—
742C4—282no—
743C4—284no—
744C4—284no—
745C2—148no—
746C2#1173461912yes—
747C2D7×#39511yescharacteristic
748C2#1173469411yescharacteristic
749C2#1173469712yes—
750C2#1173470011yescharacteristic
751C2#1173470211yescharacteristic
752C2#1174004911yescharacteristic
753C2#1174026212yes—
754C2#1174027911yescharacteristic
755C2#1174067711yescharacteristic
756C2#1174067812yes—
subgroupG/H
center, FrattiniC24C23×D7
commutator, socle, cosocleC24×C7C24
FittingC2×C7×#395C2
prime radicalC24×D7C23
hypercenterC2×#395D7
hypocenterC7#14720
LCSG ▷ C24×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
3. C2×C7×#395C2semidirect
4. C2×#90001C2semidirect
6. #11729322C2semidirect
7. #11729319C2semidirect
10. #11727174C2semidirect
11. #11727164C2semidirect
76. C22×C4×D7Q8semidirect
89. C2×(C2×D7)⋊C4Q8semidirect
120. C2×#395D7semidirect
330. C2×C4×C7C22⋊Q8semidirect
361. C2×Dic7C22⋊Q8semidirect
471. C2×D7#395semidirect
699. C2×C4#6509semidirect
700. C7#14720semidirect

Maximal subgroups

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

subgroupindex
C22×#65092
C22×D7×C4⋊C42
C2×C7×#3952
C2×#900012
C2×#897612
#117293222
#117293192
(C2×D7)⋊#952
#117271742
#117271642
#147207