Finite Group Databasebeta

← #13277161

Subgroups — #13277161

Order 1792.

2950 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic7C211yesmaximal, characteristic
2C23×C4⋊Dic7C211yesmaximal, characteristic, complemented
3C2×C7×#386C211yesmaximal, characteristic
4C2×#89992C211yesmaximal, characteristic
5C2×#89722C211yesmaximal, characteristic, complemented
6C2×#89722C212yesmaximal, complemented
7#11729881C211yesmaximal, characteristic, complemented
8#11729300C212yesmaximal, complemented
9#11729298C211yesmaximal, characteristic, complemented
10#11727173C212yesmaximal, complemented
11#11727161C212yesmaximal, complemented
12C23×C7×D4C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C24×Dic7C2211yescharacteristic
15C24×Dic7C2211yescharacteristic
16C24×Dic7C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2212yes—
19C22×C22⋊Dic7C2211yescharacteristic
20C22×C22⋊Dic7C2211yescharacteristic
21C22×C22⋊Dic7C2212yes—
22C22×C22⋊Dic7C2211yescharacteristic
23C2×D4×Dic7—24no—
24C2×D4×Dic7—24no—
25C2×D4×Dic7—24no—
26C22×C4⋊Dic7—24no—
27C22×C4⋊Dic7—28no—
28C22×C4⋊Dic7C2212yes—
29C22×C4⋊Dic7C2211yescharacteristic
30C22×C4⋊Dic7C2212yes—
31C22×C4⋊Dic7C2212yes—
32C22×C4×Dic7C2211yescharacteristic
33C7×#386C418yescomplemented
34C2×C7×#95C2212yes—
35#89992—24no—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2212yes—
40C2×C7⋊#95C2212yes—
41C2×C7⋊#95C2212yes—
42#89722—24no—
43#89722—28no—
44#14015—71nomaximal, Sylow
45C25×C7C2311yescharacteristic
46C25×C7C2311yescharacteristic
47C22×C7×D4—22no—
48C22×C7×D4—22no—
49C22×C7×D4—22no—
50C22×C7×D4—22no—
51C22×C7×D4C2×C414yes—
52C22×C7×D4D414yes—
53C22×C7×D4Q814yes—
54C23×C4×C7—22no—
55C23×C4×C7—22no—
56C23×C4×C7—24no—
57C23×C4×C7—24no—
58C23×C4×C7C2×C414yescomplemented
59C23×C4×C7C2312yes—
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2312yes—
62C23×Dic7—22no—
63C23×Dic7—22no—
64C23×Dic7—22no—
65C23×Dic7—22no—
66C23×Dic7—24no—
67C23×Dic7—24no—
68C23×Dic7—22no—
69C23×Dic7—22no—
70C23×Dic7—22no—
71C23×Dic7—22no—
72C23×Dic7—24no—
73C23×Dic7—42no—
74C23×Dic7—42no—
75C23×Dic7—42no—
76C23×Dic7D414yes—
77C23×Dic7C2312yes—
78C23×Dic7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2312yes—
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—22no—
85C2×C7×C22⋊C4—24no—
86C2×C7×C22⋊C4—24no—
87C2×C7×C22⋊C4C2×C414yescomplemented
88C2×C7×C22⋊C4C2×C418yescomplemented
89C2×C22⋊Dic7—22no—
90C2×C22⋊Dic7—22no—
91C2×C22⋊Dic7—22no—
92C2×C22⋊Dic7—22no—
93C2×C22⋊Dic7—22no—
94C2×C22⋊Dic7—24no—
95C2×C22⋊Dic7—22no—
96C2×C22⋊Dic7—22no—
97C2×C22⋊Dic7—22no—
98C2×C22⋊Dic7—24no—
99C2×C22⋊Dic7—42no—
100C2×C22⋊Dic7D414yes—
101D4×Dic7—232no—
102C2×C4⋊Dic7—232no—
103C2×C4⋊Dic7—24no—
104C2×C4⋊Dic7—22no—
105C2×C4⋊Dic7—24no—
106C2×C4⋊Dic7—24no—
107C2×C4⋊Dic7—24no—
108C2×C4⋊Dic7—24no—
109C2×C4⋊Dic7—22no—
110C2×C4⋊Dic7—22no—
111C2×C4⋊Dic7—24no—
112C2×C4⋊Dic7—24no—
113C2×C4⋊Dic7—42no—
114C2×C4⋊Dic7D418yescomplemented
115C2×C4×Dic7—22no—
116C2×C4×Dic7—22no—
117C2×C4×Dic7—22no—
118C7×#95C2×C418yescomplemented
119C7⋊#95—24no—
120C7⋊#95—24no—
121C7⋊#95—24no—
122C7⋊#95—24no—
123C7⋊#95—24no—
124C7⋊#95—42no—
125C22×C4×D4—71no—
126C23×C4⋊C4—71no—
127C2×#386—71no—
128C2×#386D711yescharacteristic
129C2×#385—71no—
130C2×#385—72no—
131#1444—72no—
132#1439—72no—
133#1436—72no—
134C22⋊#95—71no—
135C22⋊#95—71no—
136C24×C7—22no—
137C24×C7—22no—
138C24×C7—22no—
139C24×C7—22no—
140C24×C7—22no—
141C24×C7—21no—
142C24×C7—21no—
143C24×C7—22no—
144C24×C7—21no—
145C24×C7—21no—
146C24×C7—22no—
147C24×C7—22no—
148C24×C7C22×C412yes—
149C24×C7C22×C412yes—
150C24×C7C2×D412yes—
151C24×C7C2×D412yes—
152C24×C7C2×D412yes—
153C24×C7C2×D412yes—
154C24×C7C2×Q812yes—
155C24×C7C2×Q812yes—
156C24×C7#4112yes—
157C24×C7#4112yes—
158C24×C7C2411yescharacteristic
159C2×C7×D4—28no—
160C2×C7×D4—28no—
161C2×C7×D4—28no—
162C2×C7×D4—28no—
163C2×C7×D4—28no—
164C2×C7×D4—28no—
165C2×C7×D4C4⋊C4116yescomplemented
166C22×C4×C7—28no—
167C22×C4×C7—216no—
168C22×C4×C7—28no—
169C22×C4×C7—28no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—22no—
173C22×C4×C7—22no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—216no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—22no—
185C22×C4×C7C22×C414yes—
186C22×C4×C7C22×C412yes—
187C22×C4×C7C22×C414yes—
188C22×C4×C7C2×D412yes—
189C22×C4×C7C2×D414yes—
190C22×C4×C7C2×Q812yes—
191C22×C4×C7#4114yes—
192C22×Dic7—21no—
193C22×Dic7—21no—
194C22×Dic7—22no—
195C22×Dic7—28no—
196C22×Dic7—28no—
197C22×Dic7—28no—
198C22×Dic7—22no—
199C22×Dic7—22no—
200C22×Dic7—22no—
201C22×Dic7—21no—
202C22×Dic7—21no—
203C22×Dic7—22no—
204C22×Dic7—22no—
205C22×Dic7—22no—
206C22×Dic7—21no—
207C22×Dic7—21no—
208C22×Dic7—21no—
209C22×Dic7—21no—
210C22×Dic7—22no—
211C22×Dic7—22no—
212C22×Dic7—22no—
213C22×Dic7—22no—
214C22×Dic7—22no—
215C22×Dic7—22no—
216C22×Dic7—28no—
217C22×Dic7—22no—
218C22×Dic7—22no—
219C22×Dic7—22no—
220C22×Dic7—22no—
221C22×Dic7—22no—
222C22×Dic7—22no—
223C22×Dic7—22no—
224C22×Dic7—44no—
225C22×Dic7—48no—
226C22×Dic7—48no—
227C22×Dic7—48no—
228C22×Dic7—48no—
229C22×Dic7—48no—
230C22×Dic7—48no—
231C22×Dic7—44no—
232C22×Dic7—44no—
233C22×Dic7—44no—
234C22×Dic7—44no—
235C22×Dic7C2×D412yes—
236C22×Dic7C2×D412yes—
237C22×Dic7C2×D412yes—
238C22×Dic7C2×D414yes—
239C22×Dic7C2×D414yes—
240C22×Dic7C2×D412yes—
241C7×C22⋊C4—28no—
242C7×C22⋊C4—216no—
243C22⋊Dic7—28no—
244C22⋊Dic7—28no—
245C22⋊Dic7—48no—
246C22⋊Dic7—44no—
247C4⋊Dic7—216no—
248C4⋊Dic7—28no—
249C4⋊Dic7—216no—
250C4⋊Dic7—48no—
251C4×Dic7—28no—
252C23×D4C2×D711yescharacteristic
253C24×C4—71no—
254C24×C4—71no—
255C24×C4—71no—
256C24×C4C2×D711yescharacteristic
257C2×C4×D4—144no—
258C2×C4×D4—144no—
259C2×C4×D4—144no—
260C22×C4⋊C4—72no—
261C22×C4⋊C4—72no—
262C22×C4⋊C4—71no—
263C22×C4⋊C4—72no—
264C22×C4⋊C4—148no—
265C22×C4⋊C4—144no—
266C22×C22⋊C4—71no—
267C22×C22⋊C4—71no—
268C22×C22⋊C4—71no—
269C22×C22⋊C4—72no—
270C22×C22⋊C4C2×D711yescharacteristic
271C22×C22⋊C4C2×D712yes—
272C22×C42—71no—
273#386—144no—
274#386Dic718yescomplemented
275#385—144no—
276#385—148no—
277C2×#95—72no—
278C2×#95—72no—
279C2×#95—72no—
280C2×#95—72no—
281C2×#95—72no—
282C2×#95—72no—
283C2×#95C2×D712yes—
284C23×C7—24no—
285C23×C7—24no—
286C23×C7—22no—
287C23×C7—22no—
288C23×C7—24no—
289C23×C7—22no—
290C23×C7—22no—
291C23×C7—24no—
292C23×C7—24no—
293C23×C7—24no—
294C23×C7—24no—
295C23×C7—24no—
296C23×C7—24no—
297C23×C7—24no—
298C23×C7—24no—
299C23×C7—24no—
300C23×C7—24no—
301C23×C7—22no—
302C23×C7—22no—
303C23×C7—24no—
304C23×C7—22no—
305C23×C7—22no—
306C23×C7—22no—
307C23×C7—22no—
308C23×C7—24no—
309C23×C7—24no—
310C23×C7—24no—
311C23×C7—24no—
312C23×C7—41no—
313C23×C7—41no—
314C23×C7—42no—
315C23×C7—41no—
316C23×C7—41no—
317C23×C7—42no—
318C23×C7—42no—
319C23×C7—42no—
320C23×C7—42no—
321C23×C7—42no—
322C23×C7C2×C4⋊C414yes—
323C23×C7C2×C4⋊C414yescomplemented
324C23×C7C4×D414yes—
325C23×C7C4×D414yes—
326C23×C7#12014yes—
327C23×C7C22⋊Q814yes—
328C23×C7C22⋊Q814yes—
329C23×C7#12314yes—
330C23×C7C23×C411yescharacteristic
331C23×C7C22×D411yescharacteristic
332C23×C7C22×D411yescharacteristic
333C23×C7C22×D411yescharacteristic
334C23×C7C22×D412yes—
335C23×C7C22×Q811yescharacteristic
336C23×C7C2×#4111yescharacteristic
337C23×C7C2×#4111yescharacteristic
338C23×C7C2×#4112yes—
339C23×C7H(5,𝔽2)12yes—
340C23×C72−1+412yes—
341C7×D4—232no—
342C2×C4×C7—232no—
343C2×C4×C7—24no—
344C2×C4×C7—24no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—22no—
348C2×C4×C7—24no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—24no—
353C2×C4×C7—24no—
354C2×C4×C7—24no—
355C2×C4×C7—24no—
356C2×C4×C7—24no—
357C2×C4×C7—24no—
358C2×C4×C7—42no—
359C2×C4×C7—42no—
360C2×C4×C7—42no—
361C2×C4×C7—42no—
362C2×C4×C7C2×C4⋊C414yescomplemented
363C2×C4×C7C4×D418yescomplemented
364C2×Dic7—22no—
365C2×Dic7—22no—
366C2×Dic7—24no—
367C2×Dic7—24no—
368C2×Dic7—22no—
369C2×Dic7—22no—
370C2×Dic7—24no—
371C2×Dic7—22no—
372C2×Dic7—22no—
373C2×Dic7—22no—
374C2×Dic7—24no—
375C2×Dic7—24no—
376C2×Dic7—24no—
377C2×Dic7—24no—
378C2×Dic7—416no—
379C2×Dic7—416no—
380C2×Dic7—416no—
381C2×Dic7—42no—
382C2×Dic7—41no—
383C2×Dic7—41no—
384C2×Dic7—42no—
385C2×Dic7—41no—
386C2×Dic7—41no—
387C2×Dic7—42no—
388C2×Dic7—42no—
389C2×Dic7—42no—
390C2×Dic7—42no—
391C2×Dic7—42no—
392C2×Dic7—42no—
393C2×Dic7—42no—
394C2×Dic7—42no—
395C2×Dic7—42no—
396C2×Dic7—42no—
397C2×Dic7—42no—
398C2×Dic7—42no—
399C2×Dic7—42no—
400C2×Dic7#12014yes—
401C25C22×D711yescharacteristic
402C25C22×D711yescharacteristic
403C22×D4—22no—
404C22×D4—22no—
405C22×D4—22no—
406C22×D4—22no—
407C22×D4Dic1414yes—
408C22×D4D2814yes—
409C22×D4C2×Dic714yes—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—24no—
413C23×C4—24no—
414C23×C4—71no—
415C23×C4—71no—
416C23×C4—71no—
417C23×C4—72no—
418C23×C4—71no—
419C23×C4—74no—
420C23×C4—72no—
421C23×C4—144no—
422C23×C4—144no—
423C23×C4—142no—
424C23×C4—142no—
425C23×C4—144no—
426C23×C4—142no—
427C23×C4—142no—
428C23×C4—142no—
429C23×C4—142no—
430C23×C4—142no—
431C23×C4—142no—
432C23×C4—282no—
433C23×C4—282no—
434C23×C4—282no—
435C23×C4C2×Dic714yescomplemented
436C23×C4C22×D712yes—
437C23×C4C22×D711yescharacteristic
438C23×C4C22×D712yes—
439C4×D4—1432no—
440C2×C4⋊C4—78no—
441C2×C4⋊C4—144no—
442C2×C4⋊C4—144no—
443C2×C4⋊C4—144no—
444C2×C4⋊C4—144no—
445C2×C4⋊C4—142no—
446C2×C4⋊C4—142no—
447C2×C4⋊C4—1432no—
448C2×C4⋊C4—142no—
449C2×C4⋊C4—144no—
450C2×C4⋊C4—144no—
451C2×C4⋊C4—144no—
452C2×C4⋊C4—282no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—74no—
458C2×C22⋊C4—142no—
459C2×C22⋊C4—142no—
460C2×C22⋊C4—142no—
461C2×C22⋊C4—142no—
462C2×C22⋊C4—142no—
463C2×C22⋊C4—144no—
464C2×C22⋊C4—144no—
465C2×C22⋊C4—142no—
466C2×C22⋊C4—142no—
467C2×C22⋊C4—142no—
468C2×C22⋊C4—282no—
469C2×C22⋊C4C2×Dic714yescomplemented
470C2×C22⋊C4C2×Dic718yescomplemented
471C2×C42—142no—
472C2×C42—142no—
473C2×C42—142no—
474#95—144no—
475#95—144no—
476#95—144no—
477#95—144no—
478#95—144no—
479#95—282no—
480#95C2×Dic718yescomplemented
481C22×C7—24no—
482C22×C7—24no—
483C22×C7—28no—
484C22×C7—28no—
485C22×C7—24no—
486C22×C7—24no—
487C22×C7—24no—
488C22×C7—28no—
489C22×C7—28no—
490C22×C7—24no—
491C22×C7—28no—
492C22×C7—24no—
493C22×C7—42no—
494C22×C7—42no—
495C22×C7—44no—
496C22×C7—42no—
497C22×C7—42no—
498C22×C7—42no—
499C22×C7—44no—
500C22×C7—44no—
501C22×C7—42no—
502C22×C7#38518yescomplemented
503C22×C7C22×C4⋊C411yescharacteristic
504C22×C7C2×C4×D411yescharacteristic
505C22×C7C2×C4×D412yes—
506C22×C7C2×C4×D411yescharacteristic
507C22×C7#52012yes—
508C22×C7C2×#12011yescharacteristic
509C22×C7C2×#12011yescharacteristic
510C22×C7C2×C22⋊Q811yescharacteristic
511C22×C7C2×C22⋊Q811yescharacteristic
512C22×C7C2×#12311yescharacteristic
513C22×C7#52511yescharacteristic
514C22×C7#52512yes—
515C22×C7#53411yescharacteristic
516C22×C7#53611yescharacteristic
517C22×C7#53912yes—
518C22×C7D4212yes—
519C22×C7D4212yes—
520C22×C7#54712yes—
521C22×C7#54712yes—
522C22×C7#54812yes—
523C22×C7D4×Q812yes—
524C22×C7#55312yes—
525C22×C7#55412yes—
526C4×C7—24no—
527C4×C7—28no—
528C4×C7—44no—
529Dic7—24no—
530Dic7—42no—
531Dic7—44no—
532Dic7—42no—
533Dic7—42no—
534Dic7—82no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—21no—
541C24—21no—
542C24—22no—
543C24—21no—
544C24—21no—
545C24—22no—
546C24—22no—
547C24C2×Dic1412yes—
548C24C2×Dic1412yes—
549C24C2×D2812yes—
550C24C2×D2812yes—
551C24D4×D712yes—
552C24D4×D712yes—
553C24#115912yes—
554C24#115912yes—
555C24C22×Dic712yes—
556C24C22×Dic712yes—
557C24C23×D711yescharacteristic
558C2×D4—28no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—28no—
562C2×D4—28no—
563C2×D4—28no—
564C2×D4C4⋊Dic7116yescomplemented
565C22×C4—28no—
566C22×C4—216no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—216no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—74no—
585C22×C4—72no—
586C22×C4—72no—
587C22×C4—72no—
588C22×C4—74no—
589C22×C4—72no—
590C22×C4—148no—
591C22×C4—141no—
592C22×C4—141no—
593C22×C4—142no—
594C22×C4—148no—
595C22×C4—148no—
596C22×C4—148no—
597C22×C4—142no—
598C22×C4—141no—
599C22×C4—141no—
600C22×C4—141no—
601C22×C4—142no—
602C22×C4—142no—
603C22×C4—141no—
604C22×C4—141no—
605C22×C4—141no—
606C22×C4—142no—
607C22×C4—142no—
608C22×C4—142no—
609C22×C4—142no—
610C22×C4—142no—
611C22×C4—142no—
612C22×C4—142no—
613C22×C4—142no—
614C22×C4—142no—
615C22×C4—142no—
616C22×C4—142no—
617C22×C4—142no—
618C22×C4—142no—
619C22×C4—142no—
620C22×C4—142no—
621C22×C4—142no—
622C22×C4—284no—
623C22×C4—284no—
624C22×C4—288no—
625C22×C4—288no—
626C22×C4—288no—
627C22×C4—288no—
628C22×C4—288no—
629C22×C4—288no—
630C22×C4—284no—
631C22×C4—284no—
632C22×C4—284no—
633C22×C4C2×Dic1412yes—
634C22×C4C2×D2812yes—
635C22×C4D4×D714yes—
636C22×C4#115914yes—
637C22×C4C22×Dic714yes—
638C22×C4C22×Dic712yes—
639C22×C4C22×Dic714yes—
640C4⋊C4—1416no—
641C4⋊C4—1416no—
642C4⋊C4—148no—
643C4⋊C4—288no—
644C22⋊C4—28no—
645C22⋊C4—216no—
646C22⋊C4—148no—
647C22⋊C4—148no—
648C22⋊C4—288no—
649C22⋊C4—284no—
650C42—148no—
651C2×C7—28no—
652C2×C7—44no—
653C2×C7C2×#38511yescharacteristic
654C2×C7C4×#12011yescharacteristic
655C2×C7#232211yescharacteristic
656C2×C7D4×C4⋊C412yes—
657C2×C7#236112yes—
658C2×C7#240311yescharacteristic
659C2×C7#240611yescharacteristic
660C2×C7#240911yescharacteristic
661C2×C7#244312yes—
662C2×C7#244912yes—
663C2×C7#257911yescharacteristic
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—22no—
671C23—24no—
672C23—22no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—22no—
678C23—22no—
679C23—24no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—24no—
685C23—24no—
686C23—22no—
687C23—22no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—41no—
693C23—42no—
694C23—41no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—41no—
700C23—41no—
701C23—42no—
702C23#644114yes—
703C23#644114yes—
704C23#644514yes—
705C23#644914yes—
706C23C2×C4⋊Dic714yes—
707C23C2×C4⋊Dic714yescomplemented
708C23D4×Dic714yes—
709C23D4×Dic714yes—
710C23C22×Dic1411yescharacteristic
711C23C22×D2811yescharacteristic
712C23C2×D4×D711yescharacteristic
713C23C2×D4×D711yescharacteristic
714C23C2×D4×D712yes—
715C23C2×#115911yescharacteristic
716C23C2×#115911yescharacteristic
717C23C2×#115912yes—
718C23#655312yes—
719C23#655412yes—
720C23C23×Dic711yescharacteristic
721D4—232no—
722C2×C4—232no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—74no—
743C2×C4—142no—
744C2×C4—144no—
745C2×C4—144no—
746C2×C4—142no—
747C2×C4—142no—
748C2×C4—142no—
749C2×C4—142no—
750C2×C4—144no—
751C2×C4—144no—
752C2×C4—142no—
753C2×C4—144no—
754C2×C4—144no—
755C2×C4—144no—
756C2×C4—142no—
757C2×C4—2816no—
758C2×C4—2816no—
759C2×C4—2816no—
760C2×C4—282no—
761C2×C4—282no—
762C2×C4—282no—
763C2×C4—282no—
764C2×C4—282no—
765C2×C4—281no—
766C2×C4—281no—
767C2×C4—282no—
768C2×C4—282no—
769C2×C4—281no—
770C2×C4—281no—
771C2×C4—282no—
772C2×C4—282no—
773C2×C4—282no—
774C2×C4—282no—
775C2×C4—282no—
776C2×C4—282no—
777C2×C4—282no—
778C2×C4—282no—
779C2×C4C2×C4⋊Dic714yescomplemented
780C2×C4D4×Dic718yescomplemented
781C7#1401511yescharacteristic, complemented, Sylow
782C22—24no—
783C22—24no—
784C22—24no—
785C22—28no—
786C22—24no—
787C22—24no—
788C22—28no—
789C22—28no—
790C22—28no—
791C22—24no—
792C22—28no—
793C22—24no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—42no—
803C22#8972218yescomplemented
804C22C2×#644111yescharacteristic
805C22C2×#644111yescharacteristic
806C22C2×#644511yescharacteristic
807C22C2×#644911yescharacteristic
808C22D4×Dic1412yes—
809C22#9023412yes—
810C22D4×D2812yes—
811C22#9024612yes—
812C22#9027711yescharacteristic
813C22#9027712yes—
814C22D7×#12011yescharacteristic
815C22#9028912yes—
816C22#9030012yes—
817C22#9030212yes—
818C22#9030912yes—
819C22#9033911yescharacteristic
820C22#9034411yescharacteristic
821C22#9035612yes—
822C22C22×C4⋊Dic711yescharacteristic
823C22C2×D4×Dic711yescharacteristic
824C22C2×D4×Dic712yes—
825C22C2×D4×Dic711yescharacteristic
826C22#9051812yes—
827C4—28no—
828C4—24no—
829C4—44no—
830C4—144no—
831C4—282no—
832C4—282no—
833C4—284no—
834C4—282no—
835C4—562no—
836C2—28no—
837C2—44no—
838C2#1173213211yescharacteristic
839C2#1173213411yescharacteristic
840C2#1173214812yes—
841C2#1173215512yes—
842C2#1173221411yescharacteristic
843C2#1173232911yescharacteristic
844C2C2×#8972211yescharacteristic
845C2D4×C4⋊Dic712yes—
846C2Dic7×#12011yescharacteristic
847C2#1174008112yes—
848C2#1174028111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#386C2
socle, cosocleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC2×#386D7
hypocenterC7#14015
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C23×C4⋊Dic7C2semidirect
5. C2×#89722C2semidirect
6. C2×#89722C2semidirect
7. #11729881C2semidirect
8. #11729300C2semidirect
9. #11729298C2semidirect
10. #11727173C2semidirect
11. #11727161C2semidirect
33. C7×#386C4semidirect
58. C23×C4×C7C2×C4semidirect
87. C2×C7×C22⋊C4C2×C4semidirect
88. C2×C7×C22⋊C4C2×C4semidirect
114. C2×C4⋊Dic7D4semidirect
118. C7×#95C2×C4semidirect
165. C2×C7×D4C4⋊C4semidirect
274. #386Dic7semidirect
323. C23×C7C2×C4⋊C4semidirect
362. C2×C4×C7C2×C4⋊C4semidirect
363. C2×C4×C7C4×D4semidirect
435. C23×C4C2×Dic7semidirect
469. C2×C22⋊C4C2×Dic7semidirect
470. C2×C22⋊C4C2×Dic7semidirect
480. #95C2×Dic7semidirect
502. C22×C7#385semidirect
564. C2×D4C4⋊Dic7semidirect
707. C23C2×C4⋊Dic7semidirect
779. C2×C4C2×C4⋊Dic7semidirect
780. C2×C4D4×Dic7semidirect
781. C7#14015semidirect
803. C22#89722semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic72
C23×C4⋊Dic72
C2×C7×#3862
C2×#899922
C2×#897222
#117298812
#117293002
#117292982
#117271732
#117271612
#140157