Finite Group Databasebeta

← C2×#11740985 #14230649

Subgroups — C2×#11740985 #14230649

Order 1792.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#548C211yesmaximal, characteristic, complemented
2C2×#90256C211yesmaximal, characteristic, complemented
3C2×#90010C211yesmaximal, characteristic, complemented
4C2×#90004C211yesmaximal, characteristic, complemented
5C2×#89999C211yesmaximal, characteristic, complemented
6C2×#89997C211yesmaximal, characteristic, complemented
7#11740985C2116yesmaximal, direct product factor
8C2×#89829C211yesmaximal, characteristic, complemented
9C2×#89828C211yesmaximal, characteristic, complemented
10C2×#89821C211yesmaximal, characteristic, complemented
11C2×#89815C211yesmaximal, characteristic, complemented
12C2×#89811C211yesmaximal, characteristic, complemented
13C2×#89807C211yesmaximal, characteristic, complemented
14C2×#89794C211yesmaximal, characteristic, complemented
15C2×C4×#1143C211yesmaximal, characteristic, complemented
16C2×#89784C211yesmaximal, characteristic, complemented
17C22×C7×#41C2211yescharacteristic
18C23×C7×Q8C2211yescharacteristic
19C7×#548—24no—
20C7×#548C2218yescomplemented
21C2×C7×#124—21no—
22C2×C7×#124C2211yescharacteristic
23C2×C7×C22⋊Q8—21no—
24C2×C7×C22⋊Q8C2211yescharacteristic
25C2×C7×#121—21no—
26C2×C7×#121C2211yescharacteristic
27C2×C4×C7×Q8C2211yescharacteristic
28C2×C4×C7×D4—21no—
29C2×C4×C7×D4C2211yescharacteristic
30C22×#1143C2211yescharacteristic
31C22×#1143C2211yescharacteristic
32C2×#6502—21no—
33C22×#1141C2211yescharacteristic
34C2×#6493C2211yescharacteristic
35C2×#6493C2211yescharacteristic
36C2×#6489C2211yescharacteristic
37C22×C4⋊Dic7C2211yescharacteristic
38C22×#1136C2211yescharacteristic
39C22×#1136C2211yescharacteristic
40#90256—24no—
41#90256C2218yescomplemented
42C2×#6461—21no—
43C2×#6446—21no—
44C2×(C22⋊D7)⋊C4—21no—
45C2×C4×D28C2211yescharacteristic
46C2×#6433C2211yescharacteristic
47#90010C2218yescomplemented
48#90004C2218yescomplemented
49#89999C2218yescomplemented
50#89997C2218yescomplemented
51C2×#6409C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×#6409C2211yescharacteristic
54C2×#6409C2211yescharacteristic
55C2×#6409C2211yescharacteristic
56C2×#6409C2211yescharacteristic
57C2×#6406C2211yescharacteristic
58C2×#6406C2211yescharacteristic
59C2×#6406C2211yescharacteristic
60C2×C22⋊(C7⋊C8)C2211yescharacteristic
61C2×C22⋊(C7⋊C8)C2211yescharacteristic
62#89829C2218yescomplemented
63#89828C2218yescomplemented
64#89821C2218yescomplemented
65#89815C2218yescomplemented
66#89811C2218yescomplemented
67#89807C2218yescomplemented
68C4×#1143C2218yescomplemented
69#89794C2218yescomplemented
70#89784C2218yescomplemented
71C2×#6383C2211yescharacteristic
72C2×#6382C2211yescharacteristic
73C2×#6382C2211yescharacteristic
74C2×#6381C2211yescharacteristic
75C2×C4⋊(C7⋊C8)C2211yescharacteristic
76C2×C4×C7⋊C8C2211yescharacteristic
77C2×#3326—71nomaximal, Sylow
78C2×C7×#41—22no—
79C2×C7×#41—24no—
80C2×C7×#41—42no—
81C2×C7×#41C2314yes—
82C22×C7×Q8—21no—
83C22×C7×Q8—22no—
84C22×C7×Q8—24no—
85C22×C7×Q8—42no—
86C22×C7×Q8C2311yescharacteristic
87C22×C7×Q8C2314yes—
88C22×C7×Q8C2311yescharacteristic
89C22×C7×D4—21no—
90C22×C7×D4—21no—
91C22×C7×D4D411yescharacteristic
92C22×C7×D4C2311yescharacteristic
93C23×C4×C7—21no—
94C23×C4×C7—21no—
95C23×C4×C7C2311yescharacteristic
96C23×C4×C7C2311yescharacteristic
97C22×C22⋊D7—21no—
98C22×C22⋊D7—21no—
99C23×Dic7—21no—
100C22×D28C2311yescharacteristic
101C22×C4×D7—21no—
102C7×#124—28no—
103C7×#124—22no—
104C7×#124C2314yes—
105C7×C22⋊Q8—22no—
106C7×C22⋊Q8—28no—
107C7×C22⋊Q8C2314yes—
108C7×#121—28no—
109C7×#121—22no—
110C7×#121C2314yes—
111C4×C7×Q8—22no—
112C4×C7×Q8C2314yes—
113C4×C7×D4—28no—
114C4×C7×D4D414yes—
115C4×C7×D4C2314yes—
116C2×C7×C4⋊C4—21no—
117C2×C7×C4⋊C4—21no—
118C2×C7×C4⋊C4D411yescharacteristic
119C2×C7×C4⋊C4C2311yescharacteristic
120C2×C7×C22⋊C4—21no—
121C2×C7×C22⋊C4—21no—
122C2×C7×C22⋊C4—21no—
123C2×C7×C22⋊C4—21no—
124C2×C7×C22⋊C4D411yescharacteristic
125C2×C7×C22⋊C4D411yescharacteristic
126C2×C42×C7—21no—
127C2×C42×C7C2311yescharacteristic
128C2×C22⋊Dic7—21no—
129C2×#1143—24no—
130C2×#1143—42no—
131C2×#1143C2314yes—
132C2×#1143C2314yes—
133#6502—28no—
134C2×#1141—42no—
135C2×#1141C2314yes—
136#6493—22no—
137#6493—22no—
138#6493C2314yes—
139#6493C2314yes—
140C2×(C2×D7)⋊C4—21no—
141C2×(C2×D7)⋊C4—21no—
142C2×(C2×D7)⋊C4—21no—
143#6489—22no—
144#6489C2314yes—
145C2×C4⋊Dic7—21no—
146C2×C4⋊Dic7—22no—
147C2×C4⋊Dic7C2311yescharacteristic
148C2×C4⋊Dic7C2311yescharacteristic
149C2×C4⋊Dic7C2311yescharacteristic
150C2×C4⋊Dic7C2314yes—
151C2×Dic7⋊C4—21no—
152C2×Dic7⋊C4—21no—
153C2×C4×Dic7—21no—
154C2×#1136—42no—
155C2×#1136—42no—
156C2×#1136C2314yes—
157C2×#1136C2314yes—
158C22×C7⋊C8C2311yescharacteristic
159C22×C7⋊C8C2311yescharacteristic
160C22×C7⋊C8C2311yescharacteristic
161C22×C7⋊C8C2311yescharacteristic
162#6461—28no—
163#6446—28no—
164(C22⋊D7)⋊C4—28no—
165C4×D28—22no—
166C4×D28C2314yes—
167#6433—22no—
168#6433C2314yes—
169#6409C2314yes—
170#6409C2314yes—
171#6409C2314yes—
172#6409C2314yes—
173#6409C2314yes—
174#6409C2314yes—
175#6406C2314yes—
176#6406C2314yes—
177#6406C2314yes—
178C22⋊(C7⋊C8)C2314yes—
179C22⋊(C7⋊C8)C2314yes—
180#6383C2314yes—
181#6382C2314yes—
182#6382C2314yes—
183#6381C2314yes—
184C4⋊(C7⋊C8)C2314yes—
185C4×C7⋊C8C2314yes—
186C2×#553—71no—
187C2×#548D711yescharacteristic, complemented
188#3326—716no—
189C2×#488—71no—
190C2×#482—71no—
191C2×#483—71no—
192C2×#479—71no—
193C2×#469—71no—
194C2×#468—71no—
195C2×#463—71no—
196C2×#449—71no—
197C2×#448—71no—
198C2×C4×SD16—71no—
199C2×#436—71no—
200C2×#417—71no—
201C2×#419—71no—
202C24×C7—21no—
203C24×C7C2×D411yescharacteristic
204C24×C7C2×D411yescharacteristic
205C23×D7—21no—
206C7×#41—28no—
207C7×#41—44no—
208C7×#41—48no—
209C2×C7×Q8—21no—
210C2×C7×Q8—24no—
211C2×C7×Q8—21no—
212C2×C7×Q8—22no—
213C2×C7×Q8—28no—
214C2×C7×Q8—22no—
215C2×C7×Q8—22no—
216C2×C7×Q8—44no—
217C2×C7×Q8—44no—
218C2×C7×Q8—48no—
219C2×C7×Q8#4114yes—
220C2×C7×Q8C2412yes—
221C2×C7×Q8C2412yes—
222C2×C7×D4—24no—
223C2×C7×D4—24no—
224C2×C7×D4—21no—
225C2×C7×D4—22no—
226C2×C7×D4—22no—
227C2×C7×D4—42no—
228C2×C7×D4—44no—
229C2×C7×D4—44no—
230C2×C7×D4C2×D414yes—
231C2×C7×D4C2412yes—
232C22×C4×C7—21no—
233C22×C4×C7—22no—
234C22×C4×C7—22no—
235C22×C4×C7—22no—
236C22×C4×C7—22no—
237C22×C4×C7—21no—
238C22×C4×C7—21no—
239C22×C4×C7—24no—
240C22×C4×C7—24no—
241C22×C4×C7—44no—
242C22×C4×C7—44no—
243C22×C4×C7C2×D411yescharacteristic
244C22×C4×C7C2×D411yescharacteristic
245C22×C4×C7C2×D411yescharacteristic
246C22×C4×C7C2×D411yescharacteristic
247C22×C4×C7C2×D412yes—
248C22×C4×C7C2×D412yes—
249C22×C4×C7C2412yes—
250C22×C4×C7C2412yes—
251C22×C4×C7C2411yescharacteristic
252C2×C22⋊D7—24no—
253C2×C22⋊D7—24no—
254C2×C22⋊D7—44no—
255C2×C22⋊D7—82no—
256C22×Dic7—21no—
257C22×Dic7—21no—
258C22×Dic7—21no—
259C22×Dic7—24no—
260C22×Dic7—82no—
261C2×D28—22no—
262C2×D28—22no—
263C2×D28—21no—
264C2×D28C2412yes—
265C2×C4×D7—24no—
266C2×C4×D7—82no—
267C7×C4⋊C4—24no—
268C7×C4⋊C4—24no—
269C7×C4⋊C4—21no—
270C7×C4⋊C4C2×D414yes—
271C7×C4⋊C4C2412yes—
272C7×C22⋊C4—24no—
273C7×C22⋊C4—24no—
274C7×C22⋊C4—24no—
275C7×C22⋊C4—24no—
276C7×C22⋊C4C2×D414yes—
277C7×C22⋊C4C2×D414yes—
278C42×C7—24no—
279C42×C7C2×D412yes—
280C42×C7C2412yes—
281C22⋊Dic7—24no—
282#1143—28no—
283#1143—44no—
284#1141—44no—
285(C2×D7)⋊C4—24no—
286(C2×D7)⋊C4—24no—
287(C2×D7)⋊C4—24no—
288C4⋊Dic7—21no—
289C4⋊Dic7—21no—
290C4⋊Dic7—21no—
291C4⋊Dic7—24no—
292C4⋊Dic7C2412yes—
293C4⋊Dic7C2412yes—
294C4⋊Dic7C2412yes—
295Dic7⋊C4—24no—
296Dic7⋊C4—24no—
297C4×Dic7—24no—
298#1136—44no—
299#1136—44no—
300C2×C7⋊C8—22no—
301C2×C7⋊C8—22no—
302C2×C7⋊C8—22no—
303C2×C7⋊C8—22no—
304C2×C7⋊C8C2412yes—
305C2×C7⋊C8C2412yes—
306C2×C7⋊C8C2412yes—
307C2×C7⋊C8C2412yes—
308C22×#41C2×D711yescharacteristic
309C23×Q8C2×D711yescharacteristic
310C22×SD16—71no—
311C22×SD16—71no—
312C22×D8—71no—
313C22×M16—71no—
314C22×M16—71no—
315#553—78no—
316#553—144no—
317#548—24no—
318#548C2×D718yescomplemented
319C2×#126—141no—
320C2×#125—71no—
321C2×#124—21no—
322C2×#124C2×D711yescharacteristic
323C2×#123—141no—
324C2×C22⋊Q8—21no—
325C2×C22⋊Q8C2×D711yescharacteristic
326C2×#121—21no—
327C2×#121—71no—
328C2×#121—71no—
329C2×#121—141no—
330C2×#121C2×D711yescharacteristic
331C2×C4×Q8C2×D711yescharacteristic
332C2×C4×D4—21no—
333C2×C4×D4—71no—
334C2×C4×D4—141no—
335C2×C4×D4C2×D711yescharacteristic
336C2×#117—71no—
337C22×C4⋊C4—71no—
338#488—78no—
339#483—78no—
340#482—78no—
341#479—78no—
342#469—78no—
343#468—78no—
344#463—78no—
345#449—78no—
346#448—78no—
347C4×SD16—78no—
348#436—78no—
349C2×#107—71no—
350C2×#106—71no—
351C2×#106—71no—
352C2×C4⋊C8—71no—
353#419—78no—
354#417—78no—
355C2×#103—71no—
356C2×#103—71no—
357C2×#103—71no—
358C2×#103—71no—
359C2×#103—71no—
360C2×#103—71no—
361C2×#102—71no—
362C2×#102—71no—
363C2×#102—71no—
364C2×#102—71no—
365C2×C22⋊C8—71no—
366C2×C22⋊C8—71no—
367C2×C4×C8—71no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—22no—
375C23×C7—42no—
376C23×C7—42no—
377C23×C7—42no—
378C23×C7C22×D412yes—
379C23×C7C22×D412yes—
380C23×C7C22×D411yescharacteristic
381C22×D7—22no—
382C22×D7—42no—
383C22×D7—42no—
384C22×D7—42no—
385C7×Q8—24no—
386C7×Q8—22no—
387C7×Q8—22no—
388C7×Q8—22no—
389C7×Q8—48no—
390C7×Q8—42no—
391C7×Q8C2×#4114yes—
392C7×D4—22no—
393C7×D4—22no—
394C7×D4—44no—
395C7×D4—48no—
396C7×D4—48no—
397C7×D4—42no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—24no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—24no—
405C2×C4×C7—24no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—48no—
413C2×C4×C7—48no—
414C2×C4×C7—42no—
415C2×C4×C7—42no—
416C2×C4×C7C22×D412yes—
417C2×C4×C7C22×D412yes—
418C2×C4×C7C22×D412yes—
419C2×C4×C7C22×D412yes—
420C2×C4×C7C22×D411yescharacteristic
421C2×C4×C7C2×#4112yes—
422C2×C4×C7H(5,𝔽2)12yes—
423C2×C4×C7C2511yescharacteristic
424C22⋊D7—48no—
425C22⋊D7—84no—
426C2×Dic7—22no—
427C2×Dic7—22no—
428C2×Dic7—22no—
429C2×Dic7—42no—
430C2×Dic7—42no—
431C2×Dic7—42no—
432C2×Dic7—84no—
433D28—22no—
434D28—22no—
435D28—42no—
436C4×D7—84no—
437C7⋊C8—22no—
438C7⋊C8—22no—
439C7⋊C8—22no—
440C7⋊C8—22no—
441C2×#41—22no—
442C2×#41—24no—
443C2×#41—42no—
444C2×#41C22×D714yes—
445C22×Q8—21no—
446C22×Q8—22no—
447C22×Q8—24no—
448C22×Q8—42no—
449C22×Q8C22×D711yescharacteristic
450C22×Q8C22×D714yes—
451C22×Q8C22×D711yescharacteristic
452C22×D4—21no—
453C22×D4—21no—
454C22×D4—71no—
455C22×D4—141no—
456C22×D4—141no—
457C22×D4C22⋊D711yescharacteristic
458C22×D4C22×D711yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—141no—
462C23×C4—141no—
463C23×C4C22×D711yescharacteristic
464C23×C4C22×D711yescharacteristic
465C2×SD16—74no—
466C2×SD16—74no—
467C2×SD16—144no—
468C2×SD16—282no—
469C2×D8—74no—
470C2×D8—282no—
471C2×M16—74no—
472C2×M16—74no—
473C2×M16—282no—
474C2×M16—282no—
475C22×C8—71no—
476C22×C8—71no—
477C22×C8—71no—
478C22×C8—71no—
479#126—148no—
480#125—74no—
481#125—142no—
482#124—28no—
483#124—22no—
484#124C22×D714yes—
485#123—148no—
486C22⋊Q8—22no—
487C22⋊Q8—28no—
488C22⋊Q8C22×D714yes—
489#121—28no—
490#121—22no—
491#121—74no—
492#121—74no—
493#121—148no—
494#121—142no—
495#121—142no—
496#121C22×D714yes—
497C4×Q8—22no—
498C4×Q8C22×D714yes—
499C4×D4—28no—
500C4×D4—74no—
501C4×D4—148no—
502C4×D4—142no—
503C4×D4C22⋊D714yes—
504C4×D4C22×D714yes—
505#117—74no—
506#117—142no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—71no—
510C2×C4⋊C4—71no—
511C2×C4⋊C4—74no—
512C2×C4⋊C4—71no—
513C2×C4⋊C4—141no—
514C2×C4⋊C4—142no—
515C2×C4⋊C4—141no—
516C2×C4⋊C4—141no—
517C2×C4⋊C4C22⋊D711yescharacteristic
518C2×C4⋊C4C22×D711yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—141no—
524C2×C22⋊C4—141no—
525C2×C22⋊C4—141no—
526C2×C22⋊C4—141no—
527C2×C22⋊C4C22⋊D711yescharacteristic
528C2×C22⋊C4C22⋊D711yescharacteristic
529C2×C42—21no—
530C2×C42—141no—
531C2×C42C22×D711yescharacteristic
532#107—74no—
533#106—74no—
534#106—74no—
535C4⋊C8—74no—
536#103—74no—
537#103—74no—
538#103—74no—
539#103—74no—
540#103—74no—
541#103—74no—
542#102—74no—
543#102—74no—
544#102—74no—
545#102—74no—
546C22⋊C8—74no—
547C22⋊C8—74no—
548C4×C8—74no—
549C22×C7—22no—
550C22×C7—22no—
551C22×C7—22no—
552C22×C7—22no—
553C22×C7—22no—
554C22×C7—22no—
555C22×C7—44no—
556C22×C7—44no—
557C22×C7—42no—
558C22×C7—42no—
559C22×C7—42no—
560C22×C7—84no—
561C22×C7#54612yes—
562C22×C7#57512yes—
563C22×C7#57712yes—
564C22×C7C23×D411yescharacteristic
565C2×D7—42no—
566C2×D7—42no—
567C2×D7—42no—
568C2×D7—84no—
569C4×C7—22no—
570C4×C7—22no—
571C4×C7—24no—
572C4×C7—22no—
573C4×C7—22no—
574C4×C7—42no—
575C4×C7—42no—
576C4×C7#54612yes—
577C4×C7C22×#4111yescharacteristic
578C4×C7C2×H(5,𝔽2)11yescharacteristic
579Dic7—42no—
580Dic7—42no—
581Dic7—42no—
582C24—21no—
583C24—141no—
584C24C2×C22⋊D711yescharacteristic
585C24C2×C22⋊D711yescharacteristic
586#41—28no—
587#41—44no—
588#41—48no—
589C2×Q8—22no—
590C2×Q8—21no—
591C2×Q8—24no—
592C2×Q8—21no—
593C2×Q8—28no—
594C2×Q8—22no—
595C2×Q8—22no—
596C2×Q8—44no—
597C2×Q8—44no—
598C2×Q8—48no—
599C2×Q8#115914yes—
600C2×Q8C23×D712yes—
601C2×Q8C23×D712yes—
602C2×D4—24no—
603C2×D4—24no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—21no—
607C2×D4—42no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—72no—
611C2×D4—144no—
612C2×D4—144no—
613C2×D4—142no—
614C2×D4—142no—
615C2×D4—141no—
616C2×D4—284no—
617C2×D4—562no—
618C2×D4C2×C22⋊D714yes—
619C2×D4C23×D712yes—
620C22×C4—21no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—24no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—24no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4—141no—
632C22×C4—141no—
633C22×C4—141no—
634C22×C4—144no—
635C22×C4—144no—
636C22×C4—562no—
637C22×C4—562no—
638C22×C4C2×C22⋊D712yes—
639C22×C4C2×C22⋊D712yes—
640C22×C4C2×C22⋊D711yescharacteristic
641C22×C4C2×C22⋊D711yescharacteristic
642C22×C4C2×C22⋊D711yescharacteristic
643C22×C4C2×C22⋊D711yescharacteristic
644C22×C4C23×D712yes—
645C22×C4C23×D712yes—
646C22×C4C23×D711yescharacteristic
647SD16—148no—
648SD16—284no—
649D8—284no—
650M16—284no—
651M16—284no—
652C2×C8—72no—
653C2×C8—72no—
654C2×C8—72no—
655C2×C8—72no—
656C2×C8—142no—
657C2×C8—142no—
658C2×C8—142no—
659C2×C8—142no—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—72no—
664C4⋊C4—72no—
665C4⋊C4—72no—
666C4⋊C4—144no—
667C4⋊C4—144no—
668C4⋊C4—141no—
669C4⋊C4—141no—
670C4⋊C4—144no—
671C4⋊C4—141no—
672C4⋊C4C2×C22⋊D714yes—
673C4⋊C4C23×D712yes—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—144no—
679C22⋊C4—144no—
680C22⋊C4—144no—
681C22⋊C4—144no—
682C22⋊C4C2×C22⋊D714yes—
683C22⋊C4C2×C22⋊D714yes—
684C42—24no—
685C42—144no—
686C42C2×C22⋊D712yes—
687C42C23×D712yes—
688C2×C7—42no—
689C2×C7—42no—
690C2×C7—82no—
691C2×C7#332614yescomplemented
692C2×C7C2×#54611yescharacteristic
693C2×C7C2×#57511yescharacteristic
694C2×C7C2×#57711yescharacteristic
695D7—82no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—142no—
707C23—282no—
708C23—282no—
709C23—282no—
710C23C22×C22⋊D712yes—
711C23C22×C22⋊D712yes—
712C23C22×C22⋊D711yescharacteristic
713Q8—24no—
714Q8—22no—
715Q8—22no—
716Q8—22no—
717Q8—48no—
718Q8—42no—
719Q8C2×#115914yes—
720D4—22no—
721D4—22no—
722D4—44no—
723D4—48no—
724D4—48no—
725D4—42no—
726D4—142no—
727D4—142no—
728D4—288no—
729D4—282no—
730D4—564no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—48no—
746C2×C4—48no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—142no—
750C2×C4—142no—
751C2×C4—142no—
752C2×C4—282no—
753C2×C4—282no—
754C2×C4—282no—
755C2×C4—564no—
756C2×C4—564no—
757C2×C4C2×#115912yes—
758C2×C4#654812yes—
759C2×C4C22×C22⋊D712yes—
760C2×C4C22×C22⋊D712yes—
761C2×C4C22×C22⋊D712yes—
762C2×C4C22×C22⋊D712yes—
763C2×C4C22×C22⋊D711yescharacteristic
764C2×C4C24×D711yescharacteristic
765C8—142no—
766C8—142no—
767C8—142no—
768C8—142no—
769C7C2×#332611yescharacteristic, complemented, Sylow
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—84no—
782C22—282no—
783C22—282no—
784C22—282no—
785C22—564no—
786C22#9049712yes—
787C22#9051312yes—
788C22#9052812yes—
789C22C23×C22⋊D711yescharacteristic
790C4—22no—
791C4—22no—
792C4—24no—
793C4—22no—
794C4—22no—
795C4—42no—
796C4—42no—
797C4—282no—
798C4—282no—
799C4—282no—
800C4#9049712yes—
801C4C22×#115911yescharacteristic
802C4C2×#654811yescharacteristic
803C2—42no—
804C2—42no—
805C2—82no—
806C2—562no—
807C2#1174098514yesdirect product factor
808C2C2×#9049711yescharacteristic
809C2C2×#9051311yescharacteristic
810C2C2×#9052811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#548C2
socleC23×C7C22×D4
hypercenterC2×#548D7
hypocenterC7C2×#3326
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×C7×#548C2semidirect
2. C2×#90256C2semidirect
3. C2×#90010C2semidirect
4. C2×#90004C2semidirect
5. C2×#89999C2semidirect
6. C2×#89997C2semidirect
7. #11740985C2direct (N × H)
8. C2×#89829C2semidirect
9. C2×#89828C2semidirect
10. C2×#89821C2semidirect
11. C2×#89815C2semidirect
12. C2×#89811C2semidirect
13. C2×#89807C2semidirect
14. C2×#89794C2semidirect
15. C2×C4×#1143C2semidirect
16. C2×#89784C2semidirect
20. C7×#548C22semidirect
41. #90256C22semidirect
47. #90010C22semidirect
48. #90004C22semidirect
49. #89999C22semidirect
50. #89997C22semidirect
62. #89829C22semidirect
63. #89828C22semidirect
64. #89821C22semidirect
65. #89815C22semidirect
66. #89811C22semidirect
67. #89807C22semidirect
68. C4×#1143C22semidirect
69. #89794C22semidirect
70. #89784C22semidirect
187. C2×#548D7semidirect
318. #548C2×D7semidirect
691. C2×C7#3326semidirect
769. C7C2×#3326semidirect
807. C2#11740985direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5482
C2×#902562
C2×#900102
C2×#900042
C2×#899992
C2×#899972
#117409852
C2×#898292
C2×#898282
C2×#898212
C2×#898152
C2×#898112
C2×#898072
C2×#897942
C2×C4×#11432
C2×#897842
C2×#33267