Finite Group Databasebeta

← #13320958

Subgroups — #13320958

Order 1792.

1574 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90482C211yesmaximal, characteristic
2C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×#89979C211yesmaximal, characteristic, complemented
4#11727199C212yesmaximal, complemented
5#11727198C212yesmaximal, complemented
6#11727197C214yesmaximal, complemented
7#11727152C214yesmaximal, complemented
8C24×C4×C7C2211yescharacteristic
9C22×#1157C411yescharacteristic, complemented
10C22×C7×C22⋊C4—21no—
11C22×C42×C7—21no—
12C2×#6516—21no—
13#90482—21no—
14#90482—21no—
15#90482—21no—
16#90482—21no—
17#90482C412yescomplemented
18#90482C412yescomplemented
19#90482C2212yes—
20#90482C2212yes—
21C2×#6493C411yescharacteristic, complemented
22C2×#6493C2211yescharacteristic
23C2×#6492—21no—
24C2×C4×C22⋊D7—21no—
25C2×C4×C22⋊D7—21no—
26C2×#6489C411yescharacteristic, complemented
27C2×#6487C411yescharacteristic, complemented
28C2×#6487C2211yescharacteristic
29C22×#1136—21no—
30C4×C7×C22⋊C4—21no—
31C4×C7×C22⋊C4—21no—
32C4×C7×C22⋊C4C2212yes—
33C4×C7×C22⋊C4C2212yescomplemented
34C2×C7×#95C2212yescomplemented
35#89979—21no—
36#89979—21no—
37#89979C2212yes—
38#89979C2212yescomplemented
39C2×C22⋊(C7⋊C8)—21no—
40C2×C22⋊(C7⋊C8)C2212yescomplemented
41#89247C2218yescomplemented
42#89246C2218yescomplemented
43#17542—71nomaximal, Sylow
44C25×C7D411yescharacteristic
45C23×C4×C7—22no—
46C23×C4×C7—44no—
47C23×C4×C7C2×C411yescharacteristic
48C23×C4×C7C2×C411yescharacteristic
49C23×C4×C7C2×C411yescharacteristic
50C23×C4×C7C2×C411yescharacteristic
51C23×C4×C7D411yescharacteristic
52C23×C4×C7D411yescharacteristic
53C23×C4×C7D411yescharacteristic
54C23×C4×C7D411yescharacteristic
55C23×C4×C7D411yescharacteristic
56C23×C4×C7D411yescharacteristic
57C23×C4×C7D411yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C22×C22⋊D7—21no—
62C22×C22⋊D7—21no—
63C22×C22⋊D7—21no—
64C2×#1157—21no—
65C2×#1157—21no—
66C2×#1157—44no—
67C2×#1157C2×C412yes—
68C2×#1157C2×C412yescomplemented
69C22×D28C2×C411yescharacteristic, complemented
70C22×C4×D7—21no—
71C22×Dic14C2×C411yescharacteristic, complemented
72C2×C7×C22⋊C4—28no—
73C2×C7×C22⋊C4—22no—
74C2×C7×C22⋊C4—22no—
75C2×C42×C7—22no—
76C2×C42×C7—22no—
77C2×C42×C7—44no—
78#6516—22no—
79#6516—22no—
80#6516—22no—
81#6516—22no—
82C2×C22⋊Dic7—21no—
83C2×C22⋊Dic7—21no—
84C2×C22⋊Dic7—21no—
85#6493—21no—
86#6493—21no—
87#6493—21no—
88#6493—21no—
89#6493C2×C412yes—
90#6493C2×C412yescomplemented
91#6493C2×C412yescomplemented
92#6493C2312yes—
93#6492—22no—
94#6492—22no—
95#6492—22no—
96#6492—22no—
97C4×C22⋊D7—22no—
98C4×C22⋊D7—22no—
99C4×C22⋊D7—22no—
100C4×C22⋊D7—22no—
101C4×C22⋊D7—22no—
102C4×C22⋊D7—22no—
103C4×C22⋊D7—22no—
104C4×C22⋊D7—22no—
105C2×(C2×D7)⋊C4—21no—
106C2×(C2×D7)⋊C4—21no—
107#6489—21no—
108#6489—21no—
109#6489C2×C412yes—
110#6489C2×C412yescomplemented
111C2×C4⋊Dic7C2×C411yescharacteristic, complemented
112C2×C4⋊Dic7C2×C411yescharacteristic, complemented
113#6487—21no—
114#6487—21no—
115#6487—21no—
116#6487—21no—
117#6487C2×C412yes—
118#6487C2×C412yescomplemented
119#6487C2×C412yescomplemented
120#6487C2312yes—
121C2×Dic7⋊C4—21no—
122C2×Dic7⋊C4—21no—
123C2×C4×Dic7—21no—
124C2×#1136—22no—
125C2×#1136—22no—
126C2×#1136—44no—
127C22×C7⋊C8—22no—
128C7×#95—22no—
129C7×#95C2314yes—
130C22⋊(C7⋊C8)—22no—
131C22⋊(C7⋊C8)—22no—
132C22⋊(C7⋊C8)—22no—
133C22⋊(C7⋊C8)C2314yes—
134C2×#525—71no—
135C2×#407—71no—
136C2×C4×C22⋊C4D711yescharacteristic, complemented
137#1508—72no—
138#1507—72no—
139#1504—74no—
140#1501—74no—
141C24×C7—24no—
142C24×C7—42no—
143C24×C7—42no—
144C24×C7C22⋊C411yescharacteristic
145C24×C7C22⋊C411yescharacteristic
146C24×C7C22⋊C411yescharacteristic
147C24×C7C22⋊C411yescharacteristic
148C24×C7C2×D411yescharacteristic
149C24×C7C2×D411yescharacteristic
150C24×C7C2×D411yescharacteristic
151C23×D7—21no—
152C22×C4×C7—24no—
153C22×C4×C7—24no—
154C22×C4×C7—24no—
155C22×C4×C7—28no—
156C22×C4×C7—24no—
157C22×C4×C7—42no—
158C22×C4×C7—42no—
159C22×C4×C7—42no—
160C22×C4×C7—42no—
161C22×C4×C7—42no—
162C22×C4×C7—42no—
163C22×C4×C7—42no—
164C22×C4×C7—42no—
165C22×C4×C7—42no—
166C22×C4×C7—42no—
167C22×C4×C7—42no—
168C22×C4×C7—44no—
169C22×C4×C7—44no—
170C22×C4×C7C22⋊C411yescharacteristic
171C22×C4×C7C22⋊C411yescharacteristic
172C22×C4×C7C22⋊C411yescharacteristic
173C22×C4×C7C22⋊C411yescharacteristic
174C22×C4×C7C22⋊C411yescharacteristic
175C22×C4×C7C22⋊C411yescharacteristic
176C22×C4×C7C22⋊C411yescharacteristic
177C22×C4×C7C22⋊C411yescharacteristic
178C22×C4×C7C22⋊C411yescharacteristic
179C22×C4×C7C22⋊C411yescharacteristic
180C22×C4×C7C22⋊C411yescharacteristic
181C22×C4×C7C22⋊C411yescharacteristic
182C22×C4×C7C22×C411yescharacteristic
183C22×C4×C7C22×C411yescharacteristic
184C22×C4×C7C22×C411yescharacteristic
185C22×C4×C7C22×C411yescharacteristic
186C22×C4×C7C22×C411yescharacteristic
187C22×C4×C7C22×C411yescharacteristic
188C22×C4×C7C2×D411yescharacteristic
189C22×C4×C7C2×D411yescharacteristic
190C22×C4×C7C2×D411yescharacteristic
191C22×C4×C7C2×D411yescharacteristic
192C22×C4×C7C2×D411yescharacteristic
193C22×C4×C7C2×D411yescharacteristic
194C22×C4×C7C2×D411yescharacteristic
195C22×C4×C7C2×D411yescharacteristic
196C22×C4×C7C2×D411yescharacteristic
197C22×C4×C7C2411yescharacteristic
198C2×C22⋊D7—22no—
199C2×C22⋊D7—22no—
200C2×C22⋊D7—22no—
201C2×C22⋊D7—22no—
202C2×C22⋊D7—22no—
203C2×C22⋊D7—22no—
204C2×C22⋊D7—44no—
205C2×C22⋊D7—44no—
206C2×C22⋊D7—44no—
207C22×Dic7—21no—
208C22×Dic7—21no—
209C22×Dic7—21no—
210#1157—44no—
211#1157—44no—
212#1157—44no—
213#1157—44no—
214C2×D28—21no—
215C2×D28—42no—
216C2×D28C22×C412yes—
217C2×C4×D7—22no—
218C2×C4×D7—22no—
219C2×C4×D7—44no—
220C2×Dic14—21no—
221C2×Dic14—42no—
222C2×Dic14C22×C412yes—
223C7×C22⋊C4—28no—
224C7×C22⋊C4—28no—
225C42×C7—44no—
226C42×C7—44no—
227C22⋊Dic7—22no—
228C22⋊Dic7—22no—
229C22⋊Dic7—22no—
230C22⋊Dic7—22no—
231C22⋊Dic7—22no—
232C22⋊Dic7—22no—
233(C2×D7)⋊C4—22no—
234(C2×D7)⋊C4—22no—
235(C2×D7)⋊C4—22no—
236(C2×D7)⋊C4—22no—
237C4⋊Dic7—21no—
238C4⋊Dic7—21no—
239C4⋊Dic7C22×C412yes—
240C4⋊Dic7C22×C412yes—
241Dic7⋊C4—22no—
242Dic7⋊C4—22no—
243Dic7⋊C4—22no—
244Dic7⋊C4—22no—
245C4×Dic7—22no—
246C4×Dic7—22no—
247#1136—44no—
248#1136—44no—
249C2×C7⋊C8—24no—
250C2×C7⋊C8—44no—
251C22×#41—71no—
252C24×C4C2×D711yescharacteristic
253C22×M16—141no—
254#525—72no—
255#525—72no—
256#525—72no—
257#525—72no—
258#525—141no—
259#525—141no—
260#525—141no—
261#525—141no—
262C2×#123—141no—
263C2×C22⋊Q8—71no—
264C2×C22⋊Q8—71no—
265C2×#121—71no—
266C2×#121—71no—
267C2×#120—141no—
268C2×C4×D4—141no—
269C2×C4×D4—141no—
270C2×#117—71no—
271C22×C22⋊C4—21no—
272C22×C42—21no—
273#407—72no—
274#407—72no—
275#407—141no—
276#407—141no—
277C2×C22⋊C8—72no—
278C2×C22⋊C8—141no—
279C4×C22⋊C4—21no—
280C4×C22⋊C4—21no—
281C4×C22⋊C4C2×D712yes—
282C4×C22⋊C4C2×D712yescomplemented
283C2×#95C2×D712yescomplemented
284#328—78no—
285#327—78no—
286C23×C7—22no—
287C23×C7—22no—
288C23×C7—22no—
289C23×C7—22no—
290C23×C7—22no—
291C23×C7—22no—
292C23×C7—22no—
293C23×C7—22no—
294C23×C7—22no—
295C23×C7—22no—
296C23×C7—22no—
297C23×C7—22no—
298C23×C7—41no—
299C23×C7—41no—
300C23×C7—41no—
301C23×C7—41no—
302C23×C7—41no—
303C23×C7—41no—
304C23×C7—41no—
305C23×C7—41no—
306C23×C7—416no—
307C23×C7#10414yes—
308C23×C7C2×C22⋊C411yescharacteristic
309C23×C7C2×C22⋊C411yescharacteristic
310C23×C7C2×C22⋊C411yescharacteristic
311C23×C7C2×C22⋊C411yescharacteristic
312C23×C7C2×C22⋊C411yescharacteristic
313C23×C7C2×C22⋊C411yescharacteristic
314C23×C7C22×D411yescharacteristic
315C22×D7—22no—
316C22×D7—42no—
317C22×D7—42no—
318C22×D7—42no—
319C2×C4×C7—22no—
320C2×C4×C7—22no—
321C2×C4×C7—22no—
322C2×C4×C7—22no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—22no—
328C2×C4×C7—22no—
329C2×C4×C7—22no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—28no—
335C2×C4×C7—41no—
336C2×C4×C7—41no—
337C2×C4×C7—41no—
338C2×C4×C7—41no—
339C2×C4×C7—41no—
340C2×C4×C7—41no—
341C2×C4×C7—41no—
342C2×C4×C7—41no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7—44no—
348C2×C4×C7—416no—
349C2×C4×C7—44no—
350C2×C4×C7#9914yes—
351C2×C4×C7C2×C22⋊C411yescharacteristic
352C2×C4×C7C2×C22⋊C411yescharacteristic
353C2×C4×C7C2×C22⋊C411yescharacteristic
354C2×C4×C7C2×C22⋊C411yescharacteristic
355C2×C4×C7C2×C22⋊C411yescharacteristic
356C2×C4×C7C2×C22⋊C411yescharacteristic
357C2×C4×C7C23×C411yescharacteristic
358C2×C4×C7C22×D411yescharacteristic
359C22⋊D7—44no—
360C22⋊D7—44no—
361C22⋊D7—44no—
362C22⋊D7—44no—
363C22⋊D7—44no—
364C22⋊D7—44no—
365C2×Dic7—22no—
366C2×Dic7—22no—
367C2×Dic7—22no—
368C2×Dic7—42no—
369C2×Dic7—42no—
370C2×Dic7—42no—
371D28—42no—
372D28—42no—
373C4×D7—44no—
374C4×D7—44no—
375Dic14—42no—
376Dic14—42no—
377C7⋊C8—44no—
378C25C22⋊D711yescharacteristic
379C2×#41—72no—
380C2×#41—72no—
381C2×#41—141no—
382C2×#41—141no—
383C2×#41—284no—
384C22×Q8—71no—
385C22×D4—71no—
386C22×D4—141no—
387C22×D4—141no—
388C22×D4—141no—
389C23×C4—22no—
390C23×C4—44no—
391C23×C4—141no—
392C23×C4C4×D711yescharacteristic
393C23×C4C4×D711yescharacteristic
394C23×C4C4×D711yescharacteristic
395C23×C4C4×D711yescharacteristic
396C23×C4D2811yescharacteristic
397C23×C4D2811yescharacteristic
398C23×C4D2811yescharacteristic
399C23×C4D2811yescharacteristic
400C23×C4C22⋊D711yescharacteristic
401C23×C4C22⋊D711yescharacteristic
402C23×C4C22⋊D711yescharacteristic
403C23×C4C22×D711yescharacteristic
404C23×C4C22×D711yescharacteristic
405C23×C4C22×D711yescharacteristic
406C2×M16—142no—
407C2×M16—142no—
408C2×M16—284no—
409C22×C8—142no—
410#123—142no—
411#123—142no—
412#123—142no—
413#123—142no—
414C22⋊Q8—72no—
415C22⋊Q8—72no—
416C22⋊Q8—72no—
417C22⋊Q8—72no—
418C22⋊Q8—141no—
419C22⋊Q8—141no—
420C22⋊Q8—141no—
421C22⋊Q8—141no—
422#121—72no—
423#121—72no—
424#121—72no—
425#121—72no—
426#121—141no—
427#121—141no—
428#121—141no—
429#121—141no—
430#120—142no—
431#120—142no—
432#120—142no—
433#120—142no—
434C4×D4—142no—
435C4×D4—142no—
436C4×D4—142no—
437C4×D4—142no—
438C4×D4—142no—
439C4×D4—142no—
440C4×D4—142no—
441C4×D4—142no—
442#117—72no—
443#117—72no—
444#117—141no—
445#117—141no—
446C2×C4⋊C4—71no—
447C2×C4⋊C4—71no—
448C2×C4⋊C4—141no—
449C2×C4⋊C4—141no—
450C2×C22⋊C4—28no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—141no—
454C2×C22⋊C4—141no—
455C2×C22⋊C4—141no—
456C2×C22⋊C4—141no—
457C2×C22⋊C4—141no—
458C2×C42—22no—
459C2×C42—22no—
460C2×C42—44no—
461C2×C42—141no—
462C22⋊C8—74no—
463C22⋊C8—142no—
464C22⋊C8—142no—
465C22⋊C8—142no—
466#95—22no—
467#95C22×D714yes—
468C22×C7—28no—
469C22×C7—21no—
470C22×C7—21no—
471C22×C7—21no—
472C22×C7—21no—
473C22×C7—21no—
474C22×C7—21no—
475C22×C7—21no—
476C22×C7—21no—
477C22×C7—21no—
478C22×C7—21no—
479C22×C7—21no—
480C22×C7—21no—
481C22×C7—21no—
482C22×C7—21no—
483C22×C7—21no—
484C22×C7—21no—
485C22×C7—44no—
486C22×C7—44no—
487C22×C7—44no—
488C22×C7—44no—
489C22×C7—44no—
490C22×C7—44no—
491C22×C7C2×#9912yes—
492C22×C7C2×#10412yes—
493C22×C7C2×#10412yes—
494C22×C7C2×#10412yes—
495C22×C7C22×C22⋊C411yescharacteristic
496C22×C7#57512yes—
497C2×D7—42no—
498C2×D7—42no—
499C2×D7—42no—
500C2×D7—84no—
501C4×C7—21no—
502C4×C7—21no—
503C4×C7—21no—
504C4×C7—21no—
505C4×C7—21no—
506C4×C7—21no—
507C4×C7—48no—
508C4×C7C2×#9912yes—
509C4×C7C2×#9912yes—
510Dic7—42no—
511Dic7—42no—
512Dic7—42no—
513C24—24no—
514C24—42no—
515C24—42no—
516C24—141no—
517C24(C2×D7)⋊C411yescharacteristic
518C24(C2×D7)⋊C411yescharacteristic
519C24(C2×D7)⋊C411yescharacteristic
520C24(C2×D7)⋊C411yescharacteristic
521C24C2×C22⋊D711yescharacteristic
522C24C2×C22⋊D711yescharacteristic
523C24C2×C22⋊D711yescharacteristic
524#41—284no—
525#41—284no—
526#41—284no—
527#41—284no—
528C2×Q8—72no—
529C2×Q8—141no—
530C2×Q8—282no—
531C2×D4—72no—
532C2×D4—142no—
533C2×D4—142no—
534C2×D4—142no—
535C2×D4—142no—
536C2×D4—142no—
537C2×D4—142no—
538C2×D4—141no—
539C2×D4—282no—
540C2×D4—284no—
541C2×D4—284no—
542C2×D4—284no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—28no—
547C22×C4—24no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—141no—
562C22×C4—141no—
563C22×C4—141no—
564C22×C4—142no—
565C22×C4—142no—
566C22×C4—284no—
567C22×C4(C2×D7)⋊C411yescharacteristic
568C22×C4(C2×D7)⋊C411yescharacteristic
569C22×C4(C2×D7)⋊C411yescharacteristic
570C22×C4(C2×D7)⋊C411yescharacteristic
571C22×C4(C2×D7)⋊C411yescharacteristic
572C22×C4(C2×D7)⋊C411yescharacteristic
573C22×C4(C2×D7)⋊C411yescharacteristic
574C22×C4(C2×D7)⋊C411yescharacteristic
575C22×C4(C2×D7)⋊C411yescharacteristic
576C22×C4(C2×D7)⋊C411yescharacteristic
577C22×C4(C2×D7)⋊C411yescharacteristic
578C22×C4(C2×D7)⋊C411yescharacteristic
579C22×C4C2×C4×D711yescharacteristic
580C22×C4C2×C4×D711yescharacteristic
581C22×C4C2×C4×D711yescharacteristic
582C22×C4C2×C4×D711yescharacteristic
583C22×C4C2×C4×D711yescharacteristic
584C22×C4C2×C4×D711yescharacteristic
585C22×C4C2×D2811yescharacteristic
586C22×C4C2×D2811yescharacteristic
587C22×C4C2×D2811yescharacteristic
588C22×C4C2×D2811yescharacteristic
589C22×C4C2×D2811yescharacteristic
590C22×C4C2×D2811yescharacteristic
591C22×C4C2×C22⋊D711yescharacteristic
592C22×C4C2×C22⋊D711yescharacteristic
593C22×C4C2×C22⋊D711yescharacteristic
594C22×C4C23×D711yescharacteristic
595M16—284no—
596M16—284no—
597C2×C8—144no—
598C2×C8—284no—
599C4⋊C4—72no—
600C4⋊C4—72no—
601C4⋊C4—142no—
602C4⋊C4—142no—
603C4⋊C4—142no—
604C4⋊C4—141no—
605C4⋊C4—141no—
606C4⋊C4—142no—
607C22⋊C4—28no—
608C22⋊C4—28no—
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—
619C42—44no—
620C42—44no—
621C42—142no—
622C42—142no—
623C2×C7—22no—
624C2×C7—22no—
625C2×C7—22no—
626C2×C7—22no—
627C2×C7—22no—
628C2×C7—41no—
629C2×C7—41no—
630C2×C7C22×#9911yescharacteristic
631C2×C7#289611yescharacteristic
632C2×C7C22×#10411yescharacteristic
633D7—82no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—416no—
655C23—142no—
656C23—282no—
657C23—282no—
658C23—282no—
659C23#637914yes—
660C23C2×(C2×D7)⋊C411yescharacteristic
661C23C2×(C2×D7)⋊C411yescharacteristic
662C23C2×(C2×D7)⋊C411yescharacteristic
663C23C2×(C2×D7)⋊C411yescharacteristic
664C23C2×(C2×D7)⋊C411yescharacteristic
665C23C2×(C2×D7)⋊C411yescharacteristic
666C23C22×C22⋊D711yescharacteristic
667Q8—282no—
668Q8—282no—
669D4—282no—
670D4—284no—
671D4—284no—
672D4—284no—
673D4—284no—
674D4—284no—
675D4—284no—
676D4—282no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—28no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—44no—
706C2×C4—416no—
707C2×C4—44no—
708C2×C4—142no—
709C2×C4—142no—
710C2×C4—142no—
711C2×C4—284no—
712C2×C4—282no—
713C2×C4—282no—
714C2×C4—282no—
715C2×C4—284no—
716C2×C4#638014yes—
717C2×C4C2×(C2×D7)⋊C411yescharacteristic
718C2×C4C2×(C2×D7)⋊C411yescharacteristic
719C2×C4C2×(C2×D7)⋊C411yescharacteristic
720C2×C4C2×(C2×D7)⋊C411yescharacteristic
721C2×C4C2×(C2×D7)⋊C411yescharacteristic
722C2×C4C2×(C2×D7)⋊C411yescharacteristic
723C2×C4C22×C4×D711yescharacteristic
724C2×C4C22×D2811yescharacteristic
725C8—284no—
726C7#1754211yescharacteristic, complemented, Sylow
727C22—28no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—282no—
751C22—282no—
752C22—282no—
753C22—564no—
754C22C2×#637912yes—
755C22C2×#637912yes—
756C22C2×#637912yes—
757C22C2×#638012yes—
758C22C22×(C2×D7)⋊C411yescharacteristic
759C22#9051312yes—
760C4—21no—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—48no—
767C4—282no—
768C4—282no—
769C4—282no—
770C4C2×#638012yes—
771C4C2×#638012yes—
772C2—22no—
773C2—22no—
774C2—22no—
775C2—22no—
776C2—22no—
777C2—41no—
778C2—41no—
779C2—562no—
780C2C22×#637911yescharacteristic
781C2C22×#638011yescharacteristic
782C2#1173965811yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D7)⋊C4
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C4×C7×C22⋊C4C2
socleC22×C7C22×C22⋊C4
prime radicalC2×#90482C2
cosocleC22×C4×C7C24
hypercenterC2×C4×C22⋊C4D7
hypocenterC7#17542
LCSG ▷ C2×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C7×C22⋊C4C2semidirect
3. C2×#89979C2semidirect
4. #11727199C2semidirect
5. #11727198C2semidirect
6. #11727197C2semidirect
7. #11727152C2semidirect
9. C22×#1157C4semidirect
17. #90482C4semidirect
18. #90482C4semidirect
21. C2×#6493C4semidirect
26. C2×#6489C4semidirect
27. C2×#6487C4semidirect
33. C4×C7×C22⋊C4C22semidirect
34. C2×C7×#95C22semidirect
38. #89979C22semidirect
40. C2×C22⋊(C7⋊C8)C22semidirect
41. #89247C22semidirect
42. #89246C22semidirect
68. C2×#1157C2×C4semidirect
69. C22×D28C2×C4semidirect
71. C22×Dic14C2×C4semidirect
90. #6493C2×C4semidirect
91. #6493C2×C4semidirect
110. #6489C2×C4semidirect
111. C2×C4⋊Dic7C2×C4semidirect
112. C2×C4⋊Dic7C2×C4semidirect
118. #6487C2×C4semidirect
119. #6487C2×C4semidirect
136. C2×C4×C22⋊C4D7semidirect
282. C4×C22⋊C4C2×D7semidirect
283. C2×#95C2×D7semidirect
726. C7#17542semidirect

Maximal subgroups

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

subgroupindex
C2×#904822
C2×C4×C7×C22⋊C42
C2×#899792
#117271992
#117271982
#117271972
#117271522
#175427