Finite Group Databasebeta

← #13276601

Subgroups — #13276601

Order 1792.

3058 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6493C211yesmaximal, characteristic
2C22×C4×D28C211yesmaximal, characteristic, complemented
3C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
4C2×#89984C211yesmaximal, characteristic, complemented
5C2×#89728C212yesmaximal, complemented
6C2×#89711C211yesmaximal, characteristic, complemented
7#11729304C212yesmaximal, complemented
8#11729289C211yesmaximal, characteristic, complemented
9#11729289C211yesmaximal, characteristic, complemented
10#11727183C212yesmaximal, complemented
11(C2×D7)⋊#95C212yesmaximal, complemented
12C24×C4×C7C2211yescharacteristic
13C23×C22⋊D7C2212yes—
14C23×D28C2211yescharacteristic
15C23×C4×D7C2212yes—
16C22×C7×C22⋊C4C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C42×C7C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C22×C22⋊Dic7C2212yes—
21C2×#6493—24no—
22C2×#6493—24no—
23C2×#6493C418yescomplemented
24C22×(C2×D7)⋊C4C2212yes—
25C22×(C2×D7)⋊C4C2212yes—
26C22×(C2×D7)⋊C4C2212yes—
27C22×(C2×D7)⋊C4C2212yes—
28C22×C4⋊Dic7C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×C4⋊Dic7C2211yescharacteristic
31C2×C4×D28—24no—
32C2×C4×D28—24no—
33C2×C4×D28—24no—
34C4×C7×C22⋊C4—24no—
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2211yescharacteristic
37#89984—24no—
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2212yes—
40C2×C7⋊#95C2212yes—
41C2×C7⋊#95C2212yes—
42C2×C7⋊#95C2212yes—
43#89728—28no—
44#89711—24no—
45#13970—71nomaximal, Sylow
46C25×C7C2311yescharacteristic
47C24×D7C2312yes—
48C23×C4×C7—22no—
49C23×C4×C7—22no—
50C23×C4×C7—22no—
51C23×C4×C7—22no—
52C23×C4×C7—22no—
53C23×C4×C7—22no—
54C23×C4×C7C2×C414yescomplemented
55C23×C4×C7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C22×C22⋊D7—24no—
62C22×C22⋊D7—24no—
63C22×C22⋊D7—24no—
64C22×C22⋊D7—24no—
65C22×C22⋊D7—42no—
66C22×C22⋊D7—42no—
67C22×C22⋊D7C2×C418yescomplemented
68C23×Dic7C2312yes—
69C23×Dic7C2312yes—
70C23×Dic7C2312yes—
71C22×D28—22no—
72C22×D28—22no—
73C22×D28—22no—
74C22×D28—22no—
75C22×D28C2×C414yes—
76C22×D28D414yes—
77C22×D28D414yes—
78C22×C4×D7—24no—
79C22×C4×D7—24no—
80C22×C4×D7—24no—
81C22×C4×D7—24no—
82C22×C4×D7—24no—
83C22×C4×D7—42no—
84C22×C4×D7—42no—
85C2×C7×C22⋊C4—22no—
86C2×C7×C22⋊C4—22no—
87C2×C7×C22⋊C4—22no—
88C2×C7×C22⋊C4—22no—
89C2×C7×C22⋊C4—22no—
90C2×C7×C22⋊C4D414yescomplemented
91C2×C42×C7—22no—
92C2×C42×C7—22no—
93C2×C42×C7—22no—
94C2×C42×C7—22no—
95C2×C42×C7—22no—
96C2×C42×C7D414yescomplemented
97C2×C22⋊Dic7—24no—
98C2×C22⋊Dic7—24no—
99C2×C22⋊Dic7—42no—
100#6493—232no—
101C2×(C2×D7)⋊C4—24no—
102C2×(C2×D7)⋊C4—24no—
103C2×(C2×D7)⋊C4—24no—
104C2×(C2×D7)⋊C4—24no—
105C2×(C2×D7)⋊C4—24no—
106C2×(C2×D7)⋊C4—24no—
107C2×(C2×D7)⋊C4—24no—
108C2×(C2×D7)⋊C4—24no—
109C2×(C2×D7)⋊C4—24no—
110C2×(C2×D7)⋊C4—42no—
111C2×(C2×D7)⋊C4—42no—
112C2×(C2×D7)⋊C4C2×C418yescomplemented
113C2×C4⋊Dic7—22no—
114C2×C4⋊Dic7—22no—
115C2×C4⋊Dic7—22no—
116C2×C4⋊Dic7—22no—
117C2×C4⋊Dic7—22no—
118C2×C4⋊Dic7—22no—
119C2×C4⋊Dic7—22no—
120C2×C4⋊Dic7C2×C414yescomplemented
121C2×C4⋊Dic7D414yescomplemented
122C4×D28—232no—
123C7×#95—22no—
124C7×#95—22no—
125C7⋊#95—24no—
126C7⋊#95—24no—
127C7⋊#95—24no—
128C7⋊#95—42no—
129C7⋊#95—42no—
130C22×#121—71no—
131C22×C4×D4—71no—
132C2×#390—71no—
133C2×#386—72no—
134C2×#380—71no—
135C2×C4×C22⋊C4D711yescharacteristic, complemented
136#1440—72no—
137#1438—72no—
138C4⋊#95—71no—
139C4⋊#95—71no—
140C22⋊#95—72no—
141C24×C7—21no—
142C24×C7—21no—
143C24×C7—21no—
144C24×C7—21no—
145C24×C7—21no—
146C24×C7—21no—
147C24×C7—21no—
148C24×C7—21no—
149C24×C7—21no—
150C24×C7—21no—
151C24×C7—21no—
152C24×C7—21no—
153C24×C7C22×C412yes—
154C24×C7C2×D412yes—
155C24×C7#4112yes—
156C24×C7C2411yescharacteristic
157C23×D7—22no—
158C23×D7—22no—
159C23×D7—22no—
160C23×D7—22no—
161C23×D7—22no—
162C23×D7—22no—
163C23×D7—22no—
164C23×D7—22no—
165C23×D7—22no—
166C23×D7—22no—
167C23×D7—22no—
168C23×D7—22no—
169C23×D7C22×C414yes—
170C23×D7C2×D414yes—
171C23×D7C2×D414yes—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—28no—
201C22×C4×C7—28no—
202C22×C4×C7—28no—
203C22×C4×C7—44no—
204C22×C4×C7—44no—
205C22×C4×C7—44no—
206C22×C4×C7—44no—
207C22×C4×C7C22×C412yes—
208C22×C4×C7C22×C412yes—
209C22×C4×C7C2×D412yes—
210C22×C4×C7C2×D412yes—
211C22×C4×C7C2×D412yes—
212C22×C4×C7C2×D412yes—
213C22×C4×C7C2×D412yes—
214C22×C4×C7C2×D412yes—
215C22×C4×C7C2×D412yes—
216C22×C4×C7C2×D412yes—
217C22×C4×C7#4112yes—
218C22×C4×C7#4112yes—
219C22×C4×C7#4112yes—
220C22×C4×C7#4112yes—
221C2×C22⋊D7—216no—
222C2×C22⋊D7—216no—
223C2×C22⋊D7—48no—
224C2×C22⋊D7—48no—
225C2×C22⋊D7—48no—
226C2×C22⋊D7—48no—
227C2×C22⋊D7—48no—
228C22×Dic7—22no—
229C22×Dic7—22no—
230C22×Dic7—22no—
231C22×Dic7—22no—
232C22×Dic7—22no—
233C22×Dic7—22no—
234C22×Dic7—22no—
235C22×Dic7—22no—
236C22×Dic7—22no—
237C22×Dic7—22no—
238C22×Dic7—22no—
239C22×Dic7—22no—
240C22×Dic7—22no—
241C22×Dic7—22no—
242C22×Dic7—22no—
243C22×Dic7—22no—
244C22×Dic7—22no—
245C22×Dic7—22no—
246C22×Dic7—22no—
247C22×Dic7C22×C414yes—
248C22×Dic7C2×D414yes—
249C2×D28—28no—
250C2×D28—28no—
251C2×D28—28no—
252C2×D28—28no—
253C2×D28—28no—
254C2×D28—28no—
255C2×D28C22⋊C4116yescomplemented
256C2×C4×D7—216no—
257C2×C4×D7—48no—
258C2×C4×D7—48no—
259C2×C4×D7—48no—
260C2×C4×D7—48no—
261C2×C4×D7—48no—
262C2×C4×D7—48no—
263C7×C22⋊C4—28no—
264C7×C22⋊C4—28no—
265C42×C7—28no—
266C42×C7—44no—
267C22⋊Dic7—48no—
268(C2×D7)⋊C4—216no—
269(C2×D7)⋊C4—216no—
270(C2×D7)⋊C4—48no—
271(C2×D7)⋊C4—48no—
272C4⋊Dic7—28no—
273C4⋊Dic7—28no—
274C4⋊Dic7—44no—
275C23×D4—72no—
276C23×D4—71no—
277C24×C4—72no—
278C24×C4C2×D711yescharacteristic
279C2×#121—78no—
280C2×#121—144no—
281C2×#121—144no—
282C2×C4×D4—144no—
283C2×C4×D4—144no—
284C2×C4×D4—144no—
285C22×C4⋊C4—71no—
286C22×C4⋊C4—71no—
287C22×C4⋊C4—71no—
288C22×C22⋊C4—72no—
289C22×C22⋊C4—72no—
290C22×C22⋊C4—72no—
291C22×C22⋊C4—72no—
292C22×C22⋊C4—72no—
293C22×C22⋊C4C2×D711yescharacteristic
294C22×C22⋊C4C2×D711yescharacteristic
295C22×C42C2×D711yescharacteristic
296C22×C42C2×D711yescharacteristic
297#390—144no—
298#386—148no—
299#380—144no—
300C4×C22⋊C4—24no—
301C2×#95—72no—
302C2×#95—72no—
303C2×#95—72no—
304C2×#95—72no—
305C2×#95—72no—
306C2×#95C2×D711yescharacteristic
307C2×#95C2×D711yescharacteristic
308C23×C7—22no—
309C23×C7—22no—
310C23×C7—22no—
311C23×C7—22no—
312C23×C7—22no—
313C23×C7—22no—
314C23×C7—22no—
315C23×C7—22no—
316C23×C7—22no—
317C23×C7—22no—
318C23×C7—22no—
319C23×C7—22no—
320C23×C7—22no—
321C23×C7—22no—
322C23×C7—22no—
323C23×C7—22no—
324C23×C7—22no—
325C23×C7—22no—
326C23×C7—41no—
327C23×C7—41no—
328C23×C7—41no—
329C23×C7—41no—
330C23×C7—41no—
331C23×C7—41no—
332C23×C7—41no—
333C23×C7—41no—
334C23×C7—41no—
335C23×C7—41no—
336C23×C7—41no—
337C23×C7—41no—
338C23×C7—41no—
339C23×C7—41no—
340C23×C7—41no—
341C23×C7—41no—
342C23×C7C4×D414yescomplemented
343C23×C7C23×C411yescharacteristic
344C23×C7C22×D411yescharacteristic
345C23×C7C22×D411yescharacteristic
346C23×C7C22×D411yescharacteristic
347C23×C7C22×D411yescharacteristic
348C23×C7C22×D411yescharacteristic
349C23×C7C2×#4111yescharacteristic
350C23×C7C2×#4111yescharacteristic
351C23×C7C2×#4111yescharacteristic
352C23×C7C2×#4111yescharacteristic
353C23×C7C2×#4111yescharacteristic
354C23×C7H(5,𝔽2)11yescharacteristic
355C23×C7H(5,𝔽2)11yescharacteristic
356C23×C7H(5,𝔽2)11yescharacteristic
357C23×C72−1+411yescharacteristic
358C22×D7—24no—
359C22×D7—24no—
360C22×D7—24no—
361C22×D7—24no—
362C22×D7—24no—
363C22×D7—24no—
364C22×D7—24no—
365C22×D7—24no—
366C22×D7—24no—
367C22×D7—24no—
368C22×D7—24no—
369C22×D7—24no—
370C22×D7—24no—
371C22×D7—24no—
372C22×D7—24no—
373C22×D7—24no—
374C22×D7—24no—
375C22×D7—24no—
376C22×D7—42no—
377C22×D7—42no—
378C22×D7—42no—
379C22×D7—42no—
380C22×D7—42no—
381C22×D7—42no—
382C22×D7—42no—
383C22×D7—42no—
384C22×D7—42no—
385C22×D7—42no—
386C22×D7—42no—
387C22×D7—42no—
388C22×D7—42no—
389C22×D7—42no—
390C22×D7—42no—
391C22×D7—42no—
392C22×D7C2×C22⋊C418yes—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—41no—
412C2×C4×C7—41no—
413C2×C4×C7—41no—
414C2×C4×C7—41no—
415C2×C4×C7—41no—
416C2×C4×C7—41no—
417C2×C4×C7—41no—
418C2×C4×C7—41no—
419C2×C4×C7—41no—
420C2×C4×C7—41no—
421C2×C4×C7—41no—
422C2×C4×C7—41no—
423C2×C4×C7—41no—
424C2×C4×C7—41no—
425C2×C4×C7—41no—
426C2×C4×C7—41no—
427C2×C4×C7—416no—
428C2×C4×C7C2×C22⋊C414yes—
429C2×C4×C7C4×D414yes—
430C2×C4×C7C4×D414yes—
431C2×C4×C7#12014yes—
432C2×C4×C7#12114yes—
433C2×C4×C7#12114yes—
434C2×C4×C7#12114yescomplemented
435C2×C4×C7#12314yes—
436C22⋊D7—432no—
437C2×Dic7—24no—
438C2×Dic7—24no—
439C2×Dic7—24no—
440C2×Dic7—24no—
441C2×Dic7—24no—
442C2×Dic7—24no—
443C2×Dic7—42no—
444C2×Dic7—42no—
445C2×Dic7—42no—
446C2×Dic7—42no—
447C2×Dic7—42no—
448C2×Dic7—42no—
449C2×Dic7—42no—
450C2×Dic7—42no—
451C2×Dic7—42no—
452C2×Dic7—42no—
453C2×Dic7—42no—
454C2×Dic7—42no—
455C2×Dic7—42no—
456C2×Dic7—42no—
457C2×Dic7—42no—
458D28—232no—
459C4×D7—432no—
460C25—72no—
461C25C22×D711yescharacteristic
462C22×D4—78no—
463C22×D4—74no—
464C22×D4—74no—
465C22×D4—74no—
466C22×D4—144no—
467C22×D4—144no—
468C22×D4—144no—
469C22×D4—144no—
470C22×D4—142no—
471C22×D4—142no—
472C22×D4—142no—
473C22×D4—142no—
474C22×D4—282no—
475C22×D4—282no—
476C23×C4—22no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—22no—
481C23×C4—22no—
482C23×C4—72no—
483C23×C4—72no—
484C23×C4—72no—
485C23×C4—144no—
486C23×C4—144no—
487C23×C4—144no—
488C23×C4—144no—
489C23×C4—144no—
490C23×C4—282no—
491C23×C4—282no—
492C23×C4C4×D714yescomplemented
493C23×C4C22×D711yescharacteristic
494C23×C4C22×D711yescharacteristic
495C23×C4C22×D711yescharacteristic
496C23×C4C22×D711yescharacteristic
497C23×C4C22×D711yescharacteristic
498C23×C4C22×D711yescharacteristic
499#121—1432no—
500C4×D4—1432no—
501C2×C4⋊C4—74no—
502C2×C4⋊C4—74no—
503C2×C4⋊C4—142no—
504C2×C4⋊C4—142no—
505C2×C4⋊C4—142no—
506C2×C4⋊C4—142no—
507C2×C4⋊C4—142no—
508C2×C4⋊C4—142no—
509C2×C4⋊C4—142no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—78no—
516C2×C22⋊C4—144no—
517C2×C22⋊C4—144no—
518C2×C22⋊C4—144no—
519C2×C22⋊C4—144no—
520C2×C22⋊C4—144no—
521C2×C22⋊C4—144no—
522C2×C22⋊C4—144no—
523C2×C22⋊C4—144no—
524C2×C22⋊C4—144no—
525C2×C22⋊C4—144no—
526C2×C22⋊C4—144no—
527C2×C22⋊C4—282no—
528C2×C22⋊C4—282no—
529C2×C22⋊C4—282no—
530C2×C22⋊C4D2814yescomplemented
531C2×C42—22no—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42C22⋊D714yescomplemented
537#95—22no—
538#95—22no—
539#95—144no—
540#95—144no—
541#95—144no—
542#95—282no—
543#95—282no—
544C22×C7—24no—
545C22×C7—24no—
546C22×C7—24no—
547C22×C7—42no—
548C22×C7—42no—
549C22×C7—42no—
550C22×C7—42no—
551C22×C7—42no—
552C22×C7—42no—
553C22×C7—42no—
554C22×C7—42no—
555C22×C7—42no—
556C22×C7—42no—
557C22×C7—42no—
558C22×C7—42no—
559C22×C7C22×C22⋊C411yescharacteristic
560C22×C7C2×C4×D411yescharacteristic
561C22×C7C2×C4×D411yescharacteristic
562C22×C7C2×C4×D411yescharacteristic
563C22×C7C4×#4111yescharacteristic
564C22×C7#51811yescharacteristic
565C22×C7#52011yescharacteristic
566C22×C7C2×#12011yescharacteristic
567C22×C7C2×#12111yescharacteristic
568C22×C7C2×#12111yescharacteristic
569C22×C7C2×#12111yescharacteristic
570C22×C7C2×#12311yescharacteristic
571C22×C7#52511yescharacteristic
572C22×C7#52911yescharacteristic
573C22×C7#53211yescharacteristic
574C22×C7#53511yescharacteristic
575C22×C7#53711yescharacteristic
576C22×C7#54011yescharacteristic
577C22×C7#54211yescharacteristic
578C22×C7D4211yescharacteristic
579C22×C7D4211yescharacteristic
580C22×C7D4211yescharacteristic
581C22×C7#54611yescharacteristic
582C22×C7#54611yescharacteristic
583C22×C7#54611yescharacteristic
584C22×C7#54611yescharacteristic
585C22×C7#54611yescharacteristic
586C22×C7#54711yescharacteristic
587C22×C7#54711yescharacteristic
588C22×C7#54711yescharacteristic
589C22×C7#54811yescharacteristic
590C22×C7#55011yescharacteristic
591C22×C7#55311yescharacteristic
592C22×C7#55311yescharacteristic
593C22×C7#55511yescharacteristic
594C2×D7—28no—
595C2×D7—28no—
596C2×D7—28no—
597C2×D7—44no—
598C2×D7—44no—
599C2×D7—44no—
600C2×D7—44no—
601C2×D7—44no—
602C2×D7—44no—
603C2×D7—44no—
604C2×D7—44no—
605C2×D7—44no—
606C2×D7—44no—
607C2×D7—44no—
608C2×D7—44no—
609C4×C7—24no—
610C4×C7—42no—
611C4×C7—42no—
612C4×C7—42no—
613C4×C7—42no—
614C4×C7#38618yescomplemented
615Dic7—44no—
616Dic7—44no—
617Dic7—82no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—74no—
631C24—74no—
632C24—74no—
633C24—142no—
634C24—142no—
635C24—142no—
636C24—142no—
637C24—142no—
638C24—142no—
639C24—142no—
640C24—142no—
641C24—142no—
642C24—142no—
643C24—142no—
644C24—142no—
645C24C2×C4×D712yes—
646C24C2×D2812yes—
647C24#115712yes—
648C24C23×D711yescharacteristic
649C2×D4—716no—
650C2×D4—1416no—
651C2×D4—1416no—
652C2×D4—148no—
653C2×D4—148no—
654C2×D4—148no—
655C2×D4—148no—
656C2×D4—148no—
657C2×D4—148no—
658C2×D4—288no—
659C2×D4—288no—
660C2×D4—288no—
661C2×D4—288no—
662C2×D4—288no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—28no—
692C22×C4—28no—
693C22×C4—28no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—74no—
699C22×C4—74no—
700C22×C4—1416no—
701C22×C4—142no—
702C22×C4—142no—
703C22×C4—142no—
704C22×C4—142no—
705C22×C4—142no—
706C22×C4—142no—
707C22×C4—142no—
708C22×C4—142no—
709C22×C4—142no—
710C22×C4—142no—
711C22×C4—142no—
712C22×C4—142no—
713C22×C4—142no—
714C22×C4—142no—
715C22×C4—142no—
716C22×C4—142no—
717C22×C4—142no—
718C22×C4—142no—
719C22×C4—142no—
720C22×C4—288no—
721C22×C4—288no—
722C22×C4—288no—
723C22×C4—288no—
724C22×C4—288no—
725C22×C4—288no—
726C22×C4C2×C4×D712yes—
727C22×C4C2×C4×D712yes—
728C22×C4C2×D2812yes—
729C22×C4C2×D2812yes—
730C22×C4#115712yes—
731C22×C4#115712yes—
732C22×C4#115712yes—
733C22×C4D4×D712yes—
734C22×C4D4×D712yes—
735C22×C4D4×D712yes—
736C22×C4#115912yes—
737C22×C4C2×C22⋊D712yes—
738C22×C4C2×C22⋊D712yes—
739C22×C4C2×C22⋊D712yes—
740C4⋊C4—148no—
741C4⋊C4—148no—
742C4⋊C4—284no—
743C22⋊C4—28no—
744C22⋊C4—28no—
745C22⋊C4—1416no—
746C22⋊C4—1416no—
747C22⋊C4—288no—
748C22⋊C4—288no—
749C22⋊C4—288no—
750C42—28no—
751C42—44no—
752C2×C7—44no—
753C2×C7C2×#38611yescharacteristic
754C2×C7C4×#12111yescharacteristic
755C2×C7#232411yescharacteristic
756C2×C7D4×C22⋊C411yescharacteristic
757C2×C7#233911yescharacteristic
758C2×C7#236111yescharacteristic
759C2×C7#236311yescharacteristic
760C2×C7#240711yescharacteristic
761C2×C7#240811yescharacteristic
762C2×C7#242011yescharacteristic
763C2×C7#242211yescharacteristic
764C2×C7#242711yescharacteristic
765C2×C7#242811yescharacteristic
766C2×C7#253511yescharacteristic
767C2×C7#253711yescharacteristic
768D7—48no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—78no—
804C23—144no—
805C23—144no—
806C23—144no—
807C23—144no—
808C23—144no—
809C23—144no—
810C23—144no—
811C23—144no—
812C23—144no—
813C23—144no—
814C23—144no—
815C23—144no—
816C23—144no—
817C23—144no—
818C23—144no—
819C23—144no—
820C23—144no—
821C23—144no—
822C23—282no—
823C23—282no—
824C23—282no—
825C23—282no—
826C23—282no—
827C23—282no—
828C23—282no—
829C23—282no—
830C23—282no—
831C23—282no—
832C23—282no—
833C23—282no—
834C23—282no—
835C23—282no—
836C23—282no—
837C23—282no—
838C23C4×D2814yescomplemented
839C23C22×C4×D711yescharacteristic
840C23C22×D2811yescharacteristic
841C23C2×#115711yescharacteristic
842C23C2×#115711yescharacteristic
843C23C2×#115711yescharacteristic
844C23C2×#115711yescharacteristic
845C23C2×D4×D711yescharacteristic
846C23C2×D4×D711yescharacteristic
847C23C2×D4×D711yescharacteristic
848C23C2×#115911yescharacteristic
849C23#655311yescharacteristic
850C23#655311yescharacteristic
851C23#655311yescharacteristic
852C23#655411yescharacteristic
853C23C22×C22⋊D711yescharacteristic
854D4—1432no—
855D4—2832no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—416no—
891C2×C4—144no—
892C2×C4—144no—
893C2×C4—144no—
894C2×C4—144no—
895C2×C4—144no—
896C2×C4—144no—
897C2×C4—2832no—
898C2×C4—282no—
899C2×C4—282no—
900C2×C4—282no—
901C2×C4—282no—
902C2×C4—282no—
903C2×C4—282no—
904C2×C4—282no—
905C2×C4—282no—
906C2×C4—282no—
907C2×C4—282no—
908C2×C4—282no—
909C2×C4—282no—
910C2×C4—282no—
911C2×C4—282no—
912C2×C4—282no—
913C2×C4D7×C22⋊C414yes—
914C2×C4(C22⋊D7)⋊C414yes—
915C2×C4#644614yes—
916C2×C4#644714yes—
917C2×C4C4×C22⋊D714yes—
918C2×C4#649314yescomplemented
919C2×C4#650014yes—
920C2×C4#650114yes—
921C7#1397011yescharacteristic, complemented, Sylow
922C22—24no—
923C22—24no—
924C22—24no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—148no—
938C22—148no—
939C22—148no—
940C22—284no—
941C22—284no—
942C22—284no—
943C22—284no—
944C22—284no—
945C22—284no—
946C22—284no—
947C22—284no—
948C22—284no—
949C22—284no—
950C22—284no—
951C22—284no—
952C22C2×C4×D2811yescharacteristic
953C22C4×#115711yescharacteristic
954C22#9016811yescharacteristic
955C22#9017011yescharacteristic
956C22C2×D7×C22⋊C411yescharacteristic
957C22C2×(C22⋊D7)⋊C411yescharacteristic
958C22C2×#644611yescharacteristic
959C22C2×#644711yescharacteristic
960C22#9021211yescharacteristic
961C22#9021411yescharacteristic
962C22#9022511yescharacteristic
963C22#9022611yescharacteristic
964C22D4×D2811yescharacteristic
965C22D4×D2811yescharacteristic
966C22D4×D2811yescharacteristic
967C22#9024111yescharacteristic
968C22#9024111yescharacteristic
969C22#9024111yescharacteristic
970C22#9024111yescharacteristic
971C22#9024111yescharacteristic
972C22#9024211yescharacteristic
973C22#9024211yescharacteristic
974C22#9024311yescharacteristic
975C22#9024411yescharacteristic
976C22#9024611yescharacteristic
977C22#9025411yescharacteristic
978C22#9025611yescharacteristic
979C22#9025611yescharacteristic
980C22C2×C4×C22⋊D711yescharacteristic
981C22C2×#649311yescharacteristic
982C22#9048211yescharacteristic
983C22C2×#650011yescharacteristic
984C22C2×#650111yescharacteristic
985C22#9052111yescharacteristic
986C22#9052411yescharacteristic
987C4—24no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—42no—
992C4—284no—
993C4—284no—
994C4—562no—
995C4#8972818yescomplemented
996C2—44no—
997C2—288no—
998C2#1173091211yescharacteristic
999C2#1173091411yescharacteristic
1000C2#1173093111yescharacteristic
1001C2#1173093211yescharacteristic
1002C2C22⋊C4×D2811yescharacteristic
1003C2#1173101811yescharacteristic
1004C2#1173102911yescharacteristic
1005C2#1173103011yescharacteristic
1006C2C4×#649311yescharacteristic
1007C2C2×#8972811yescharacteristic
1008C2#1173968111yescharacteristic
1009C2#1173984711yescharacteristic
1010C2#1173984811yescharacteristic
1011C2#1173986011yescharacteristic
1012C2#1173986211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C4×C7×C22⋊C4C2
socle, cosocleC24×C7C24
prime radicalC22×#6493C2
hypercenterC2×C4×C22⋊C4D7
hypocenterC7#13970
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×D28C2semidirect
3. C2×C4×C7×C22⋊C4C2semidirect
4. C2×#89984C2semidirect
5. C2×#89728C2semidirect
6. C2×#89711C2semidirect
7. #11729304C2semidirect
8. #11729289C2semidirect
9. #11729289C2semidirect
10. #11727183C2semidirect
11. (C2×D7)⋊#95C2semidirect
23. C2×#6493C4semidirect
54. C23×C4×C7C2×C4semidirect
67. C22×C22⋊D7C2×C4semidirect
90. C2×C7×C22⋊C4D4semidirect
96. C2×C42×C7D4semidirect
112. C2×(C2×D7)⋊C4C2×C4semidirect
120. C2×C4⋊Dic7C2×C4semidirect
121. C2×C4⋊Dic7D4semidirect
135. C2×C4×C22⋊C4D7semidirect
255. C2×D28C22⋊C4semidirect
342. C23×C7C4×D4semidirect
434. C2×C4×C7#121semidirect
492. C23×C4C4×D7semidirect
530. C2×C22⋊C4D28semidirect
536. C2×C42C22⋊D7semidirect
614. C4×C7#386semidirect
838. C23C4×D28semidirect
918. C2×C4#6493semidirect
921. C7#13970semidirect
995. C4#89728semidirect

Maximal subgroups

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

subgroupindex
C22×#64932
C22×C4×D282
C2×C4×C7×C22⋊C42
C2×#899842
C2×#897282
C2×#897112
#117293042
#117292892
#117271832
(C2×D7)⋊#952
#139707