Finite Group Databasebeta

← #13276597

Subgroups — #13276597

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×#6456C211yesmaximal, characteristic, complemented
3C2×C7×#380C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic7C211yesmaximal, characteristic, complemented
5C2×#89760C211yesmaximal, characteristic, complemented
6C2×#89728C212yesmaximal, complemented
7#11729317C211yesmaximal, characteristic, complemented
8#11729317C211yesmaximal, characteristic, complemented
9#11729304C212yesmaximal, complemented
10#11727183C212yesmaximal, complemented
11(C2×D7)⋊#95C212yesmaximal, complemented
12C24×C4×C7C2211yescharacteristic
13C23×C22⋊D7C2212yes—
14C23×D28C2211yescharacteristic
15C23×C4×D7C2212yes—
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2212yes—
19C22×C22⋊Dic7C2211yescharacteristic
20C22×C22⋊Dic7C2211yescharacteristic
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×#6456—24no—
32C2×#6456—24no—
33C2×#6456—24no—
34C7×#380—24no—
35C2×C7×#95C2212yes—
36C4×C22⋊Dic7—24no—
37C2×C7⋊#95C2211yescharacteristic
38C2×C7⋊#95C2211yescharacteristic
39C2×C7⋊#95C2212yes—
40C2×C7⋊#95C2212yes—
41C2×C7⋊#95C2212yes—
42C2×C7⋊#95C2212yes—
43#89760—24no—
44#89728—28no—
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×C7C2312yes—
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2312yes—
58C23×C4×C7C2311yescharacteristic
59C22×C22⋊D7—24no—
60C22×C22⋊D7—24no—
61C22×C22⋊D7—24no—
62C22×C22⋊D7—24no—
63C22×C22⋊D7—42no—
64C22×C22⋊D7—42no—
65C22×C22⋊D7C2×C418yescomplemented
66C23×Dic7C2312yes—
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
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×C4⋊C4—22no—
86C2×C7×C4⋊C4—22no—
87C2×C7×C4⋊C4—22no—
88C2×C7×C4⋊C4—22no—
89C2×C7×C4⋊C4—22no—
90C2×C7×C4⋊C4D414yescomplemented
91C2×C7×C22⋊C4—24no—
92C2×C7×C22⋊C4—24no—
93C2×C7×C22⋊C4—42no—
94C2×C22⋊Dic7—22no—
95C2×C22⋊Dic7—22no—
96C2×C22⋊Dic7—22no—
97C2×C22⋊Dic7—22no—
98C2×C22⋊Dic7—22no—
99C2×C22⋊Dic7D414yescomplemented
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⋊Dic7C2×C414yescomplemented
116C2×C4×Dic7—22no—
117C2×C4×Dic7—22no—
118C2×C4×Dic7—22no—
119C2×C4×Dic7—22no—
120C2×C4×Dic7—22no—
121C2×C4×Dic7D414yescomplemented
122#6456—232no—
123C7×#95—24no—
124C7⋊#95—22no—
125C7⋊#95—22no—
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×#380D711yescharacteristic, complemented
135C2×C4×C22⋊C4—71no—
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—22no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—28no—
185C22×C4×C7—28no—
186C22×C4×C7—28no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—44no—
195C22×C4×C7—44no—
196C22×C4×C7—44no—
197C22×C4×C7—44no—
198C22×C4×C7C22×C412yes—
199C22×C4×C7C22×C412yes—
200C22×C4×C7C2×D414yes—
201C22×C4×C7C2×D412yes—
202C22×C4×C7C2×D412yes—
203C22×C4×C7C2×D412yes—
204C22×C4×C7C2×D412yes—
205C22×C4×C7#4112yes—
206C22×C4×C7#4112yes—
207C2×C22⋊D7—216no—
208C2×C22⋊D7—216no—
209C2×C22⋊D7—48no—
210C2×C22⋊D7—48no—
211C2×C22⋊D7—48no—
212C2×C22⋊D7—48no—
213C2×C22⋊D7—48no—
214C22×Dic7—21no—
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—22no—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—22no—
226C22×Dic7—22no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—22no—
234C22×Dic7—21no—
235C22×Dic7—21no—
236C22×Dic7—22no—
237C22×Dic7—22no—
238C22×Dic7—21no—
239C22×Dic7—21no—
240C22×Dic7—21no—
241C22×Dic7—21no—
242C22×Dic7C22×C414yes—
243C22×Dic7C2×D412yes—
244C22×Dic7C2×D412yes—
245C22×Dic7C2×D412yes—
246C22×Dic7C2×D412yes—
247C22×Dic7#4112yes—
248C22×Dic7#4112yes—
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×C4⋊C4—28no—
264C7×C4⋊C4—44no—
265C7×C22⋊C4—48no—
266C22⋊Dic7—28no—
267C22⋊Dic7—28no—
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⋊C4C2×D711yescharacteristic
287C22×C4⋊C4C2×D711yescharacteristic
288C22×C22⋊C4—71no—
289C22×C22⋊C4—72no—
290C22×C22⋊C4—71no—
291C22×C22⋊C4—72no—
292C22×C22⋊C4—72no—
293C22×C22⋊C4—72no—
294C22×C22⋊C4C2×D712yes—
295C22×C42—71no—
296C22×C42—71no—
297#390—144no—
298#386—148no—
299#380—24no—
300C4×C22⋊C4—144no—
301C2×#95—71no—
302C2×#95—72no—
303C2×#95—72no—
304C2×#95—71no—
305C2×#95—72no—
306C2×#95—72no—
307C2×#95C2×D712yes—
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—24no—
397C2×C4×C7—24no—
398C2×C4×C7—24no—
399C2×C4×C7—41no—
400C2×C4×C7—42no—
401C2×C4×C7—41no—
402C2×C4×C7—41no—
403C2×C4×C7—41no—
404C2×C4×C7—42no—
405C2×C4×C7—42no—
406C2×C4×C7—42no—
407C2×C4×C7—416no—
408C2×C4×C7—42no—
409C2×C4×C7—42no—
410C2×C4×C7—42no—
411C2×C4×C7—42no—
412C2×C4×C7—42no—
413C2×C4×C7—42no—
414C2×C4×C7—42no—
415C2×C4×C7C2×C22⋊C414yes—
416C2×C4×C7C4×D414yes—
417C2×C4×C7C4×D414yes—
418C2×C4×C7#12014yes—
419C2×C4×C7#12114yes—
420C2×C4×C7#12114yes—
421C2×C4×C7#12314yes—
422C22⋊D7—432no—
423C2×Dic7—22no—
424C2×Dic7—22no—
425C2×Dic7—22no—
426C2×Dic7—22no—
427C2×Dic7—22no—
428C2×Dic7—22no—
429C2×Dic7—24no—
430C2×Dic7—24no—
431C2×Dic7—24no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—22no—
441C2×Dic7—41no—
442C2×Dic7—41no—
443C2×Dic7—41no—
444C2×Dic7—41no—
445C2×Dic7—42no—
446C2×Dic7—42no—
447C2×Dic7—41no—
448C2×Dic7—41no—
449C2×Dic7—42no—
450C2×Dic7—42no—
451C2×Dic7—41no—
452C2×Dic7—41no—
453C2×Dic7—41no—
454C2×Dic7—41no—
455C2×Dic7—41no—
456C2×Dic7—41no—
457C2×Dic7#12114yescomplemented
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—71no—
483C23×C4—71no—
484C23×C4—71no—
485C23×C4—71no—
486C23×C4—72no—
487C23×C4—144no—
488C23×C4—144no—
489C23×C4—144no—
490C23×C4—144no—
491C23×C4—144no—
492C23×C4—282no—
493C23×C4—282no—
494C23×C4C4×D714yescomplemented
495C23×C4C22×D712yes—
496C23×C4C22×D711yescharacteristic
497C23×C4C22×D712yes—
498C23×C4C22×D711yescharacteristic
499#121—1432no—
500C4×D4—1432no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—74no—
507C2×C4⋊C4—142no—
508C2×C4⋊C4—142no—
509C2×C4⋊C4C22⋊D714yescomplemented
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—74no—
514C2×C22⋊C4—78no—
515C2×C22⋊C4—144no—
516C2×C22⋊C4—144no—
517C2×C22⋊C4—144no—
518C2×C22⋊C4—144no—
519C2×C22⋊C4—142no—
520C2×C22⋊C4—142no—
521C2×C22⋊C4—142no—
522C2×C22⋊C4—142no—
523C2×C22⋊C4—142no—
524C2×C22⋊C4—144no—
525C2×C22⋊C4—144no—
526C2×C22⋊C4—144no—
527C2×C22⋊C4—144no—
528C2×C22⋊C4—144no—
529C2×C22⋊C4—282no—
530C2×C22⋊C4—282no—
531C2×C42—74no—
532C2×C42—142no—
533C2×C42—142no—
534C2×C42—142no—
535C2×C42—142no—
536C2×C42—142no—
537#95—24no—
538#95—142no—
539#95—142no—
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—44no—
610C4×C7—42no—
611C4×C7—82no—
612C4×C7#38618yescomplemented
613Dic7—24no—
614Dic7—44no—
615Dic7—42no—
616Dic7—42no—
617Dic7—42no—
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—
646C24D4×D712yes—
647C24#116112yes—
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—22no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—21no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—21no—
675C22×C4—28no—
676C22×C4—28no—
677C22×C4—28no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—44no—
689C22×C4—72no—
690C22×C4—72no—
691C22×C4—72no—
692C22×C4—74no—
693C22×C4—72no—
694C22×C4—72no—
695C22×C4—72no—
696C22×C4—1416no—
697C22×C4—141no—
698C22×C4—141no—
699C22×C4—141no—
700C22×C4—141no—
701C22×C4—141no—
702C22×C4—141no—
703C22×C4—142no—
704C22×C4—141no—
705C22×C4—141no—
706C22×C4—141no—
707C22×C4—141no—
708C22×C4—141no—
709C22×C4—142no—
710C22×C4—142no—
711C22×C4—141no—
712C22×C4—141no—
713C22×C4—141no—
714C22×C4—142no—
715C22×C4—141no—
716C22×C4—141no—
717C22×C4—141no—
718C22×C4—141no—
719C22×C4—141no—
720C22×C4—141no—
721C22×C4—142no—
722C22×C4—142no—
723C22×C4—141no—
724C22×C4—141no—
725C22×C4—288no—
726C22×C4—288no—
727C22×C4—288no—
728C22×C4—288no—
729C22×C4—288no—
730C22×C4—288no—
731C22×C4C2×C4×D712yes—
732C22×C4C2×C4×D712yes—
733C22×C4#115712yes—
734C22×C4D4×D712yes—
735C22×C4D4×D712yes—
736C22×C4D4×D712yes—
737C22×C4#115912yes—
738C22×C4C2×C22⋊D714yes—
739C22×C4C2×C22⋊D712yes—
740C4⋊C4—28no—
741C4⋊C4—44no—
742C4⋊C4—148no—
743C22⋊C4—48no—
744C22⋊C4—1416no—
745C22⋊C4—1416no—
746C22⋊C4—148no—
747C22⋊C4—148no—
748C22⋊C4—288no—
749C22⋊C4—288no—
750C42—148no—
751C42—284no—
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—
838C23#645614yescomplemented
839C23C22×C4×D711yescharacteristic
840C23C2×#115711yescharacteristic
841C23C2×D4×D711yescharacteristic
842C23C2×D4×D711yescharacteristic
843C23C2×D4×D711yescharacteristic
844C23C2×D4×D711yescharacteristic
845C23C2×#115911yescharacteristic
846C23#654811yescharacteristic
847C23C2×#116111yescharacteristic
848C23#655111yescharacteristic
849C23D7×#4111yescharacteristic
850C23D7×#4111yescharacteristic
851C23#655311yescharacteristic
852C23#655311yescharacteristic
853C23C22×C22⋊D711yescharacteristic
854D4—1432no—
855D4—2832no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—416no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—74no—
879C2×C4—142no—
880C2×C4—142no—
881C2×C4—142no—
882C2×C4—142no—
883C2×C4—142no—
884C2×C4—142no—
885C2×C4—144no—
886C2×C4—144no—
887C2×C4—142no—
888C2×C4—144no—
889C2×C4—142no—
890C2×C4—142no—
891C2×C4—142no—
892C2×C4—142no—
893C2×C4—142no—
894C2×C4—142no—
895C2×C4—142no—
896C2×C4—142no—
897C2×C4—2832no—
898C2×C4—281no—
899C2×C4—281no—
900C2×C4—281no—
901C2×C4—281no—
902C2×C4—281no—
903C2×C4—281no—
904C2×C4—281no—
905C2×C4—282no—
906C2×C4—282no—
907C2×C4—281no—
908C2×C4—281no—
909C2×C4—281no—
910C2×C4—282no—
911C2×C4—282no—
912C2×C4—281no—
913C2×C4—281no—
914C2×C4D7×C22⋊C414yes—
915C2×C4(C22⋊D7)⋊C414yes—
916C2×C4#644614yes—
917C2×C4#644714yes—
918C2×C4C4×C22⋊D714yes—
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×D7×C22⋊C411yescharacteristic
953C22C2×(C22⋊D7)⋊C411yescharacteristic
954C22C2×#644611yescharacteristic
955C22C2×#644711yescharacteristic
956C22C2×#645611yescharacteristic
957C22#9019511yescharacteristic
958C22#9019811yescharacteristic
959C22#9020511yescharacteristic
960C22#9021211yescharacteristic
961C22#9021311yescharacteristic
962C22#9022111yescharacteristic
963C22#9022311yescharacteristic
964C22#9028711yescharacteristic
965C22D7×#12111yescharacteristic
966C22#9029811yescharacteristic
967C22#9030011yescharacteristic
968C22#9030011yescharacteristic
969C22#9030311yescharacteristic
970C22#9030311yescharacteristic
971C22#9031011yescharacteristic
972C22#9031511yescharacteristic
973C22#9031811yescharacteristic
974C22#9032011yescharacteristic
975C22#9032111yescharacteristic
976C22#9032111yescharacteristic
977C22#9032211yescharacteristic
978C22#9032211yescharacteristic
979C22#9033411yescharacteristic
980C22C2×C4×C22⋊D711yescharacteristic
981C22C2×#650011yescharacteristic
982C22C2×#650111yescharacteristic
983C22D4×C22⋊D711yescharacteristic
984C22#9050811yescharacteristic
985C22#9052011yescharacteristic
986C22#9052511yescharacteristic
987C4—42no—
988C4—44no—
989C4—82no—
990C4—144no—
991C4—282no—
992C4—282no—
993C4—282no—
994C4—284no—
995C4#8972818yescomplemented
996C2—44no—
997C2—288no—
998C2#1173131011yescharacteristic
999C2#1173131711yescharacteristic
1000C2#1173133611yescharacteristic
1001C2#1173133811yescharacteristic
1002C2#1173137811yescharacteristic
1003C2#1173138011yescharacteristic
1004C2#1173145211yescharacteristic
1005C2#1173145311yescharacteristic
1006C2C2×#8972811yescharacteristic
1007C2#1173960811yescharacteristic
1008C2#1173968911yescharacteristic
1009C2#1174008511yescharacteristic
1010C2#1174009311yescharacteristic
1011C2#1174020111yescharacteristic
1012C2#1174025711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#380C2
socle, cosocleC24×C7C24
prime radicalC22×#6493C2
hypercenterC2×#380D7
hypocenterC7#13970
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C22×#6456C2semidirect
3. C2×C7×#380C2semidirect
4. C2×C4×C22⋊Dic7C2semidirect
5. C2×#89760C2semidirect
6. C2×#89728C2semidirect
7. #11729317C2semidirect
8. #11729317C2semidirect
9. #11729304C2semidirect
10. #11727183C2semidirect
11. (C2×D7)⋊#95C2semidirect
23. C2×#6493C4semidirect
54. C23×C4×C7C2×C4semidirect
65. C22×C22⋊D7C2×C4semidirect
90. C2×C7×C4⋊C4D4semidirect
99. C2×C22⋊Dic7D4semidirect
112. C2×(C2×D7)⋊C4C2×C4semidirect
115. C2×C4⋊Dic7C2×C4semidirect
121. C2×C4×Dic7D4semidirect
134. C2×#380D7semidirect
255. C2×D28C22⋊C4semidirect
342. C23×C7C4×D4semidirect
457. C2×Dic7#121semidirect
494. C23×C4C4×D7semidirect
509. C2×C4⋊C4C22⋊D7semidirect
612. C4×C7#386semidirect
838. C23#6456semidirect
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×#64562
C2×C7×#3802
C2×C4×C22⋊Dic72
C2×#897602
C2×#897282
#117293172
#117293042
#117271832
(C2×D7)⋊#952
#139707