Finite Group Databasebeta

← #13276584

Subgroups — #13276584

Order 1792.

2266 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C7×Q8C211yesmaximal, characteristic, complemented
2C22×#6509C211yesmaximal, characteristic
3C2×#90002C211yesmaximal, characteristic, complemented
4C2×#89759C211yesmaximal, characteristic
5C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic
6#11729324C212yesmaximal
7#11729320C212yesmaximal, complemented
8#11729317C211yesmaximal, characteristic, complemented
9#11729291C212yesmaximal
10#11729290C212yesmaximal, complemented
11#11729289C211yesmaximal, characteristic, complemented
12C23×C7×Q8C2211yescharacteristic
13C23×C4×D7C2211yescharacteristic
14C2×C4×C7×Q8—24no—
15C2×C4×C7×Q8—24no—
16C2×C4×C7×Q8—24no—
17C22×C7×C4⋊C4C2212yes—
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C42×C7C2212yes—
20C22×C42×C7C2211yescharacteristic
21C2×#6509—24no—
22C2×#6509—24no—
23C2×#6509C418yescomplemented
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2212yes—
26C22×(C2×D7)⋊C4C2212yes—
27C22×(C2×D7)⋊C4C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×Dic7⋊C4C2212yes—
31C22×C4×Dic7C2211yescharacteristic
32#90002—24no—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2211yescharacteristic
36C2×C7⋊#95C2211yescharacteristic
37C2×C7⋊#95C2212yes—
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2212yes—
40C2×C7⋊#95C2212yes—
41C2×C7⋊#95C2212yes—
42#89759—24no—
43C4×(C2×D7)⋊C4—24no—
44#13969—71nomaximal, Sylow
45C24×D7C2311yescharacteristic
46C22×C7×Q8—22no—
47C22×C7×Q8—22no—
48C22×C7×Q8—22no—
49C22×C7×Q8—22no—
50C22×C7×Q8C2×C414yes—
51C22×C7×Q8D414yes—
52C22×C7×Q8D414yes—
53C23×C4×C7C2312yes—
54C23×C4×C7C2311yescharacteristic
55C23×C4×C7C2312yes—
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×Dic7C2312yes—
59C23×Dic7C2311yescharacteristic
60C23×Dic7C2312yes—
61C23×Dic7C2311yescharacteristic
62C23×Dic7C2311yescharacteristic
63C22×C4×D7—22no—
64C22×C4×D7—22no—
65C22×C4×D7—22no—
66C22×C4×D7—22no—
67C22×C4×D7—22no—
68C22×C4×D7—22no—
69C22×C4×D7C2×C414yes—
70C4×C7×Q8—232no—
71C2×C7×C4⋊C4—24no—
72C2×C7×C4⋊C4—24no—
73C2×C7×C4⋊C4—24no—
74C2×C7×C4⋊C4—22no—
75C2×C7×C4⋊C4—22no—
76C2×C7×C4⋊C4D414yes—
77C2×C42×C7—24no—
78C2×C42×C7—24no—
79C2×C42×C7—24no—
80C2×C42×C7—22no—
81C2×C42×C7—22no—
82C2×C42×C7D414yes—
83#6509—232no—
84C2×(C2×D7)⋊C4—22no—
85C2×(C2×D7)⋊C4—22no—
86C2×(C2×D7)⋊C4—22no—
87C2×(C2×D7)⋊C4—24no—
88C2×(C2×D7)⋊C4—24no—
89C2×(C2×D7)⋊C4—22no—
90C2×(C2×D7)⋊C4—22no—
91C2×(C2×D7)⋊C4—24no—
92C2×(C2×D7)⋊C4—24no—
93C2×(C2×D7)⋊C4—42no—
94C2×(C2×D7)⋊C4C2×C418yes—
95C2×(C2×D7)⋊C4Q814yescomplemented
96C2×C4⋊Dic7—22no—
97C2×C4⋊Dic7—22no—
98C2×C4⋊Dic7—22no—
99C2×C4⋊Dic7—22no—
100C2×C4⋊Dic7—22no—
101C2×C4⋊Dic7C2×C414yes—
102C2×Dic7⋊C4—24no—
103C2×Dic7⋊C4—24no—
104C2×Dic7⋊C4C2×C418yes—
105C2×C4×Dic7—22no—
106C2×C4×Dic7—22no—
107C2×C4×Dic7—22no—
108C7⋊#95—22no—
109C7⋊#95—22no—
110C7⋊#95—24no—
111C7⋊#95—24no—
112C7⋊#95—24no—
113C7⋊#95—24no—
114C7⋊#95—24no—
115C7⋊#95—42no—
116C7⋊#95—42no—
117C22×C22⋊Q8—71no—
118C22×C4×Q8D711yescharacteristic, complemented
119C2×#391—71no—
120C2×#380—71no—
121C2×C4×C22⋊C4—71no—
122#1441—72no—
123#1439—72no—
124#1437—72no—
125#1436—72no—
126C4⋊#95—71no—
127C4⋊#95—71no—
128C24×C7C2411yescharacteristic
129C23×D7—21no—
130C23×D7—21no—
131C23×D7—21no—
132C23×D7—21no—
133C23×D7—21no—
134C23×D7—21no—
135C23×D7—21no—
136C23×D7—21no—
137C23×D7—21no—
138C23×D7—21no—
139C23×D7—21no—
140C23×D7—21no—
141C23×D7C22×C412yes—
142C23×D7C2×Q812yes—
143C23×D7#4112yes—
144C2×C7×Q8—28no—
145C2×C7×Q8—28no—
146C2×C7×Q8—28no—
147C2×C7×Q8—28no—
148C2×C7×Q8—28no—
149C2×C7×Q8—28no—
150C2×C7×Q8C22⋊C4116yescomplemented
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7—22no—
160C22×C4×C7—21no—
161C22×C4×C7—22no—
162C22×C4×C7—21no—
163C22×C4×C7—22no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—22no—
167C22×C4×C7—21no—
168C22×C4×C7—22no—
169C22×C4×C7—21no—
170C22×C4×C7—22no—
171C22×C4×C7C22×C414yes—
172C22×C4×C7C22×C412yes—
173C22×C4×C7C2×D414yes—
174C22×C4×C7C2×D412yes—
175C22×C4×C7C2×D414yes—
176C22×C4×C7C2×D414yes—
177C22×C4×C7C2×D412yes—
178C22×C4×C7C2×D412yes—
179C22×C4×C7C2×D412yes—
180C22×C4×C7C2×D412yes—
181C22×C4×C7C2×D412yes—
182C22×C4×C7C2×Q812yes—
183C22×C4×C7#4112yes—
184C22×C4×C7#4112yes—
185C22×C4×C7#4112yes—
186C22×Dic7—21no—
187C22×Dic7—21no—
188C22×Dic7—21no—
189C22×Dic7—21no—
190C22×Dic7—21no—
191C22×Dic7—21no—
192C22×Dic7—21no—
193C22×Dic7—21no—
194C22×Dic7—22no—
195C22×Dic7—22no—
196C22×Dic7—22no—
197C22×Dic7—22no—
198C22×Dic7—21no—
199C22×Dic7—21no—
200C22×Dic7—21no—
201C22×Dic7—21no—
202C22×Dic7—21no—
203C22×Dic7—21no—
204C22×Dic7—22no—
205C22×Dic7—21no—
206C22×Dic7—22no—
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—22no—
217C22×Dic7C22×C412yes—
218C22×Dic7C22×C414yes—
219C22×Dic7C2×Q812yes—
220C22×Dic7#4112yes—
221C2×C4×D7—28no—
222C2×C4×D7—28no—
223C2×C4×D7—28no—
224C2×C4×D7—44no—
225C2×C4×D7—44no—
226C2×C4×D7—44no—
227C2×C4×D7—44no—
228C7×C4⋊C4—216no—
229C7×C4⋊C4—28no—
230C42×C7—216no—
231C42×C7—28no—
232(C2×D7)⋊C4—28no—
233(C2×D7)⋊C4—216no—
234(C2×D7)⋊C4—28no—
235(C2×D7)⋊C4—48no—
236C4⋊Dic7—28no—
237C4⋊Dic7—44no—
238Dic7⋊C4—216no—
239C4×Dic7—44no—
240C23×Q8C2×D711yescharacteristic
241C24×C4—71no—
242C2×C22⋊Q8—78no—
243C2×C22⋊Q8—144no—
244C2×C22⋊Q8—144no—
245C2×C4×Q8—24no—
246C2×C4×Q8—24no—
247C2×C4×Q8—24no—
248C22×C4⋊C4—72no—
249C22×C4⋊C4—71no—
250C22×C4⋊C4—71no—
251C22×C4⋊C4C2×D712yes—
252C22×C4⋊C4C2×D711yescharacteristic
253C22×C22⋊C4—72no—
254C22×C22⋊C4—71no—
255C22×C22⋊C4—71no—
256C22×C22⋊C4—72no—
257C22×C42—71no—
258C22×C42C2×D712yes—
259C22×C42C2×D711yescharacteristic
260#391—144no—
261#380—144no—
262C4×C22⋊C4—144no—
263C2×#95—72no—
264C2×#95—72no—
265C2×#95—71no—
266C2×#95—72no—
267C2×#95—72no—
268C2×#95—72no—
269C2×#95—71no—
270C2×#95—72no—
271C2×#95—72no—
272C23×C7C23×C411yescharacteristic
273C23×C7C22×D411yescharacteristic
274C23×C7C22×D411yescharacteristic
275C23×C7C22×D411yescharacteristic
276C23×C7C22×D411yescharacteristic
277C23×C7C22×Q811yescharacteristic
278C23×C7C2×#4111yescharacteristic
279C23×C7C2×#4111yescharacteristic
280C23×C7C2×#4111yescharacteristic
281C23×C7C2×#4111yescharacteristic
282C23×C7C2×#4111yescharacteristic
283C23×C7H(5,𝔽2)11yescharacteristic
284C23×C72−1+411yescharacteristic
285C23×C72−1+411yescharacteristic
286C23×C72−1+411yescharacteristic
287C22×D7—22no—
288C22×D7—22no—
289C22×D7—22no—
290C22×D7—22no—
291C22×D7—22no—
292C22×D7—22no—
293C22×D7—22no—
294C22×D7—22no—
295C22×D7—22no—
296C22×D7—22no—
297C22×D7—22no—
298C22×D7—22no—
299C22×D7—22no—
300C22×D7—22no—
301C22×D7—22no—
302C22×D7—22no—
303C22×D7—22no—
304C22×D7—22no—
305C22×D7—41no—
306C22×D7—41no—
307C22×D7—41no—
308C22×D7—41no—
309C22×D7—41no—
310C22×D7—41no—
311C22×D7—41no—
312C22×D7—41no—
313C22×D7—41no—
314C22×D7—41no—
315C22×D7—41no—
316C22×D7—41no—
317C22×D7—41no—
318C22×D7—41no—
319C22×D7—41no—
320C22×D7—41no—
321C22×D7C4×Q814yescomplemented
322C7×Q8—232no—
323C2×C4×C7—24no—
324C2×C4×C7—24no—
325C2×C4×C7—22no—
326C2×C4×C7—24no—
327C2×C4×C7—24no—
328C2×C4×C7—24no—
329C2×C4×C7—24no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—24no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—24no—
340C2×C4×C7—24no—
341C2×C4×C7—42no—
342C2×C4×C7—42no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—42no—
347C2×C4×C7—42no—
348C2×C4×C7—41no—
349C2×C4×C7C2×C22⋊C418yes—
350C2×C4×C7C2×C22⋊C414yes—
351C2×C4×C7C4×D414yes—
352C2×C4×C7C4×D414yes—
353C2×C4×C7#12014yes—
354C2×C4×C7#12114yes—
355C2×C4×C7#12114yes—
356C2×C4×C7C22⋊Q814yescomplemented
357C2×C4×C7#12314yes—
358C2×Dic7—22no—
359C2×Dic7—24no—
360C2×Dic7—22no—
361C2×Dic7—22no—
362C2×Dic7—24no—
363C2×Dic7—24no—
364C2×Dic7—22no—
365C2×Dic7—22no—
366C2×Dic7—22no—
367C2×Dic7—22no—
368C2×Dic7—22no—
369C2×Dic7—22no—
370C2×Dic7—41no—
371C2×Dic7—41no—
372C2×Dic7—41no—
373C2×Dic7—41no—
374C2×Dic7—41no—
375C2×Dic7—41no—
376C2×Dic7—41no—
377C2×Dic7—41no—
378C2×Dic7—42no—
379C2×Dic7—42no—
380C2×Dic7—41no—
381C2×Dic7—42no—
382C2×Dic7—41no—
383C2×Dic7—42no—
384C2×Dic7—41no—
385C2×Dic7—41no—
386C2×Dic7—42no—
387C2×Dic7—42no—
388C2×Dic7—42no—
389C2×Dic7—42no—
390C2×Dic7—42no—
391C2×Dic7—42no—
392C2×Dic7—42no—
393C4×D7—416no—
394C25—71no—
395C22×Q8—22no—
396C22×Q8—22no—
397C22×Q8—22no—
398C22×Q8—22no—
399C22×Q8C4×D714yes—
400C22×Q8D2814yes—
401C22×Q8C22⋊D714yes—
402C23×C4—72no—
403C23×C4—71no—
404C23×C4—71no—
405C23×C4—71no—
406C23×C4—74no—
407C23×C4—72no—
408C23×C4—142no—
409C23×C4—142no—
410C23×C4—142no—
411C23×C4—142no—
412C23×C4—142no—
413C23×C4—142no—
414C23×C4C22×D712yes—
415C23×C4C22×D711yescharacteristic
416C23×C4C22×D712yes—
417C23×C4C22×D711yescharacteristic
418C23×C4C22×D711yescharacteristic
419C22⋊Q8—1432no—
420C4×Q8—232no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—78no—
427C2×C4⋊C4—74no—
428C2×C4⋊C4—144no—
429C2×C4⋊C4—142no—
430C2×C4⋊C4—144no—
431C2×C4⋊C4—142no—
432C2×C4⋊C4—142no—
433C2×C4⋊C4—142no—
434C2×C4⋊C4—142no—
435C2×C4⋊C4C22⋊D714yes—
436C2×C22⋊C4—78no—
437C2×C22⋊C4—74no—
438C2×C22⋊C4—142no—
439C2×C22⋊C4—142no—
440C2×C22⋊C4—144no—
441C2×C22⋊C4—142no—
442C2×C22⋊C4—144no—
443C2×C22⋊C4—142no—
444C2×C22⋊C4—142no—
445C2×C22⋊C4—144no—
446C2×C22⋊C4—144no—
447C2×C22⋊C4—282no—
448C2×C42—24no—
449C2×C42—24no—
450C2×C42—24no—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—142no—
454C2×C42—142no—
455C2×C42—142no—
456C2×C42C22⋊D714yes—
457#95—144no—
458#95—144no—
459#95—144no—
460#95—144no—
461#95—142no—
462#95—142no—
463#95—144no—
464#95—282no—
465#95—282no—
466C22×C7C22×C22⋊C411yescharacteristic
467C22×C7C2×C4×D411yescharacteristic
468C22×C7C2×C4×D411yescharacteristic
469C22×C7C2×C4×Q811yescharacteristic
470C22×C7C4×#4111yescharacteristic
471C22×C7#51911yescharacteristic
472C22×C7#52011yescharacteristic
473C22×C7C2×#12011yescharacteristic
474C22×C7C2×#12111yescharacteristic
475C22×C7C2×#12111yescharacteristic
476C22×C7C2×C22⋊Q811yescharacteristic
477C22×C7C2×#12311yescharacteristic
478C22×C7#52511yescharacteristic
479C22×C7#52911yescharacteristic
480C22×C7#53311yescharacteristic
481C22×C7#53611yescharacteristic
482C22×C7#53711yescharacteristic
483C22×C7#54111yescharacteristic
484C22×C7#54211yescharacteristic
485C22×C7#54611yescharacteristic
486C22×C7#54711yescharacteristic
487C22×C7#54811yescharacteristic
488C22×C7#54811yescharacteristic
489C22×C7#54811yescharacteristic
490C22×C7#54811yescharacteristic
491C22×C7#54811yescharacteristic
492C22×C7D4×Q811yescharacteristic
493C22×C7D4×Q811yescharacteristic
494C22×C7D4×Q811yescharacteristic
495C22×C7#55011yescharacteristic
496C22×C7#55011yescharacteristic
497C22×C7#55211yescharacteristic
498C22×C7#55211yescharacteristic
499C22×C7#55411yescharacteristic
500C22×C7#55611yescharacteristic
501C2×D7—24no—
502C2×D7—24no—
503C2×D7—24no—
504C2×D7—42no—
505C2×D7—42no—
506C2×D7—42no—
507C2×D7—42no—
508C2×D7—42no—
509C2×D7—42no—
510C2×D7—42no—
511C2×D7—42no—
512C2×D7—42no—
513C2×D7—42no—
514C2×D7—42no—
515C2×D7—42no—
516C4×C7—24no—
517C4×C7—28no—
518C4×C7—42no—
519C4×C7—44no—
520C4×C7#38618yes—
521Dic7—44no—
522Dic7—42no—
523Dic7—42no—
524Dic7—42no—
525Dic7—82no—
526C24—72no—
527C24—72no—
528C24—72no—
529C24—141no—
530C24—141no—
531C24—141no—
532C24—141no—
533C24—141no—
534C24—141no—
535C24—141no—
536C24—141no—
537C24—141no—
538C24—141no—
539C24—141no—
540C24—141no—
541C24C23×D711yescharacteristic
542C2×Q8—28no—
543C2×Q8—28no—
544C2×Q8—28no—
545C2×Q8—28no—
546C2×Q8—28no—
547C2×Q8—28no—
548C2×Q8(C2×D7)⋊C4116yescomplemented
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—74no—
570C22×C4—72no—
571C22×C4—72no—
572C22×C4—72no—
573C22×C4—141no—
574C22×C4—141no—
575C22×C4—142no—
576C22×C4—141no—
577C22×C4—141no—
578C22×C4—141no—
579C22×C4—141no—
580C22×C4—141no—
581C22×C4—142no—
582C22×C4—141no—
583C22×C4—142no—
584C22×C4—141no—
585C22×C4—141no—
586C22×C4—142no—
587C22×C4—141no—
588C22×C4—142no—
589C22×C4—141no—
590C22×C4—141no—
591C22×C4—141no—
592C22×C4—141no—
593C22×C4—141no—
594C22×C4—141no—
595C22×C4—142no—
596C22×C4—141no—
597C22×C4—148no—
598C22×C4—148no—
599C22×C4—148no—
600C22×C4—142no—
601C22×C4—142no—
602C22×C4—142no—
603C22×C4—142no—
604C22×C4—142no—
605C22×C4—142no—
606C22×C4—142no—
607C22×C4—284no—
608C22×C4—284no—
609C22×C4—284no—
610C22×C4—284no—
611C22×C4C2×C4×D714yes—
612C22×C4C2×C4×D712yes—
613C22×C4C2×D2814yes—
614C22×C4C2×D2812yes—
615C22×C4#115712yes—
616C22×C4#115712yes—
617C22×C4Q8×D712yes—
618C22×C4#116112yes—
619C22×C4C2×C22⋊D714yes—
620C22×C4C2×C22⋊D712yes—
621C22×C4C2×C22⋊D714yes—
622C22×C4C2×C22⋊D712yes—
623C22×C4C2×C22⋊D712yes—
624C22×C4C2×C22⋊D712yes—
625C22×C4C2×C22⋊D712yes—
626C4⋊C4—216no—
627C4⋊C4—28no—
628C4⋊C4—1416no—
629C4⋊C4—148no—
630C4⋊C4—284no—
631C22⋊C4—148no—
632C22⋊C4—1416no—
633C22⋊C4—148no—
634C22⋊C4—288no—
635C42—216no—
636C42—28no—
637C42—284no—
638C2×C7C2×#38611yescharacteristic
639C2×C7C4×C22⋊Q811yescharacteristic
640C2×C7#232311yescharacteristic
641C2×C7Q8×C22⋊C411yescharacteristic
642C2×C7#234111yescharacteristic
643C2×C7#236011yescharacteristic
644C2×C7#236211yescharacteristic
645C2×C7#240711yescharacteristic
646C2×C7#240911yescharacteristic
647C2×C7#242111yescharacteristic
648C2×C7#242311yescharacteristic
649C2×C7#242611yescharacteristic
650C2×C7#242911yescharacteristic
651C2×C7#253611yescharacteristic
652C2×C7#253811yescharacteristic
653D7—44no—
654C23—74no—
655C23—142no—
656C23—142no—
657C23—142no—
658C23—142no—
659C23—142no—
660C23—142no—
661C23—142no—
662C23—142no—
663C23—142no—
664C23—142no—
665C23—142no—
666C23—142no—
667C23—142no—
668C23—142no—
669C23—142no—
670C23—142no—
671C23—142no—
672C23—142no—
673C23—281no—
674C23—281no—
675C23—281no—
676C23—281no—
677C23—281no—
678C23—281no—
679C23—281no—
680C23—281no—
681C23—281no—
682C23—281no—
683C23—281no—
684C23—281no—
685C23—281no—
686C23—281no—
687C23—281no—
688C23—281no—
689C23C22×C4×D711yescharacteristic
690C23C22×D2811yescharacteristic
691C23C2×#115711yescharacteristic
692C23C2×#115711yescharacteristic
693C23C2×Q8×D711yescharacteristic
694C23C2×#116111yescharacteristic
695C23#655111yescharacteristic
696C23#655111yescharacteristic
697C23D7×#4111yescharacteristic
698C23D7×#4111yescharacteristic
699C23#655311yescharacteristic
700C23#655411yescharacteristic
701C23C22×C22⋊D711yescharacteristic
702C23C22×C22⋊D711yescharacteristic
703C23C22×C22⋊D711yescharacteristic
704Q8—232no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—144no—
732C2×C4—142no—
733C2×C4—142no—
734C2×C4—142no—
735C2×C4—142no—
736C2×C4—142no—
737C2×C4—144no—
738C2×C4—144no—
739C2×C4—142no—
740C2×C4—142no—
741C2×C4—142no—
742C2×C4—142no—
743C2×C4—281no—
744C2×C4—281no—
745C2×C4—281no—
746C2×C4—281no—
747C2×C4—281no—
748C2×C4—281no—
749C2×C4—282no—
750C2×C4—281no—
751C2×C4—282no—
752C2×C4—281no—
753C2×C4—282no—
754C2×C4—281no—
755C2×C4—282no—
756C2×C4—281no—
757C2×C4—281no—
758C2×C4—281no—
759C2×C4—2816no—
760C2×C4—282no—
761C2×C4—282no—
762C2×C4—282no—
763C2×C4—282no—
764C2×C4—282no—
765C2×C4—282no—
766C2×C4—282no—
767C2×C4C2×(C2×D7)⋊C418yes—
768C2×C4C2×(C2×D7)⋊C414yes—
769C2×C4C4×C22⋊D714yes—
770C2×C4C4×C22⋊D714yes—
771C2×C4#649214yes—
772C2×C4#649314yes—
773C2×C4#649314yes—
774C2×C4#650914yescomplemented
775C2×C4#651614yes—
776C7#1396911yescharacteristic, complemented, Sylow
777C22—144no—
778C22—144no—
779C22—144no—
780C22—282no—
781C22—282no—
782C22—282no—
783C22—282no—
784C22—282no—
785C22—282no—
786C22—282no—
787C22—282no—
788C22—282no—
789C22—282no—
790C22—282no—
791C22—282no—
792C22C4×Q8×D711yescharacteristic
793C22#9026311yescharacteristic
794C22C4×#116111yescharacteristic
795C22#9026511yescharacteristic
796C22Q8×D2811yescharacteristic
797C22#9026711yescharacteristic
798C22#9026711yescharacteristic
799C22#9026811yescharacteristic
800C22#9026911yescharacteristic
801C22#9027011yescharacteristic
802C22#9027111yescharacteristic
803C22#9027211yescharacteristic
804C22#9027211yescharacteristic
805C22#9027311yescharacteristic
806C22#9027411yescharacteristic
807C22#9027511yescharacteristic
808C22C22×(C2×D7)⋊C411yescharacteristic
809C22C2×C4×C22⋊D711yescharacteristic
810C22C2×C4×C22⋊D711yescharacteristic
811C22C2×#649211yescharacteristic
812C22C2×#649311yescharacteristic
813C22C2×#649311yescharacteristic
814C22C2×#650911yescharacteristic
815C22Q8×C22⋊D711yescharacteristic
816C22Q8×C22⋊D711yescharacteristic
817C22#9050711yescharacteristic
818C22#9050811yescharacteristic
819C22#9050811yescharacteristic
820C22#9051511yescharacteristic
821C22#9051911yescharacteristic
822C22#9052011yescharacteristic
823C22#9052211yescharacteristic
824C22#9052411yescharacteristic
825C22#9052511yescharacteristic
826C22C2×#651611yescharacteristic
827C4—28no—
828C4—24no—
829C4—44no—
830C4—42no—
831C4—282no—
832C4—282no—
833C4—282no—
834C4—284no—
835C4—562no—
836C4#8998518yes—
837C2—284no—
838C2#1173990211yescharacteristic
839C2#1173990911yescharacteristic
840C2C4×#650911yescharacteristic
841C2#1173993311yescharacteristic
842C2Q8×(C2×D7)⋊C411yescharacteristic
843C2#1173993511yescharacteristic
844C2#1173993811yescharacteristic
845C2#1173993911yescharacteristic
846C2#1173994011yescharacteristic
847C2#1173994111yescharacteristic
848C2#1173994411yescharacteristic
849C2#1173994511yescharacteristic
850C2C2×#8998511yescharacteristic
851C2#1174151311yescharacteristic
852C2#1174154211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC22×C4×C7×Q8C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC22×C4×Q8D7
hypocenterC7#13969
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C4×C7×Q8C2semidirect
3. C2×#90002C2semidirect
7. #11729320C2semidirect
8. #11729317C2semidirect
10. #11729290C2semidirect
11. #11729289C2semidirect
23. C2×#6509C4semidirect
95. C2×(C2×D7)⋊C4Q8semidirect
118. C22×C4×Q8D7semidirect
150. C2×C7×Q8C22⋊C4semidirect
321. C22×D7C4×Q8semidirect
356. C2×C4×C7C22⋊Q8semidirect
548. C2×Q8(C2×D7)⋊C4semidirect
774. C2×C4#6509semidirect
776. C7#13969semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C7×Q82
C22×#65092
C2×#900022
C2×#897592
C2×C4×(C2×D7)⋊C42
#117293242
#117293202
#117293172
#117292912
#117292902
#117292892
#139697